```python
from typing import List

def group_batches(jobs: List[List[str]], capacity: int) -> List[List[str]]:
    if not isinstance(jobs, list) or not all(isinstance(job, list) for job in jobs):
        raise ValueError("jobs must be a list of lists")
    
    if not all(len(job) == 4 for job in jobs):
        raise ValueError("each job must be a four-item list")
    
    if not all(isinstance(name, str) and name for name in jobs):
        raise ValueError("job names must be non-empty strings")
    
    if not all(isinstance(group, str) and group for group in jobs):
        raise ValueError("job groups must be non-empty strings")
    
    if not all(isinstance(priority, int) and priority >= 0 for priority in jobs):
        raise ValueError("job priorities must be non-negative integers")
    
    if not all(isinstance(weight, int) and weight > 0 and weight <= capacity for weight in jobs):
        raise ValueError("job weights must be integers between 1 and the capacity")
    
    if len(jobs) == 0:
        return []
    
    jobs.sort(key=lambda job: (job[1], job[2], job[3]))
    
    batches = []
    current_batch = []
    current_capacity = capacity
    
    for job in jobs:
        group, priority, weight, _ = job
        if weight > current_capacity:
            continue
        
        current_batch.append(group)
        current_capacity -= weight
        if current_capacity == 0:
            batches.append(current_batch)
            current_batch = []
            current_capacity = capacity
    
    return batches if current_batch else batches[:-1]
```