Subgroups — C₂⁸×C₅×C₁₉ #72201628

Order 24320.

1668796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₅×C₁₉	C₂	1	255	yes	maximal, direct product factor
2	C₂⁶×C₅×C₁₉	C₂²	1	10795	yes	direct product factor
3	C₂⁵×C₅×C₁₉	C₂³	1	97155	yes	direct product factor
4	C₂⁸×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁷×C₁₉	C₂×C₅	1	255	yes	direct product factor
6	C₂⁴×C₅×C₁₉	C₂⁴	1	200787	yes	direct product factor
7	C₂⁸×C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁶×C₁₉	C₂²×C₅	1	10795	yes	direct product factor
9	C₂³×C₅×C₁₉	C₂⁵	1	97155	yes	direct product factor
10	C₂⁷×C₅	C₂×C₁₉	1	255	yes	direct product factor
11	C₂⁵×C₁₉	C₂³×C₅	1	97155	yes	direct product factor
12	C₂²×C₅×C₁₉	C₂⁶	1	10795	yes	direct product factor
13	C₂⁶×C₅	C₂²×C₁₉	1	10795	yes	direct product factor
14	C₂⁴×C₁₉	C₂⁴×C₅	1	200787	yes	direct product factor
15	C₂⁸	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₅×C₁₉	C₂⁷	1	255	yes	direct product factor
17	C₂⁵×C₅	C₂³×C₁₉	1	97155	yes	direct product factor
18	C₂³×C₁₉	C₂⁵×C₅	1	97155	yes	direct product factor
19	C₂⁷	C₂×C₅×C₁₉	1	255	yes	direct product factor
20	C₅×C₁₉	C₂⁸	1	1	yes	characteristic, direct product factor, Hall
21	C₂⁴×C₅	C₂⁴×C₁₉	1	200787	yes	direct product factor
22	C₂²×C₁₉	C₂⁶×C₅	1	10795	yes	direct product factor
23	C₂⁶	C₂²×C₅×C₁₉	1	10795	yes	direct product factor
24	C₂³×C₅	C₂⁵×C₁₉	1	97155	yes	direct product factor
25	C₂×C₁₉	C₂⁷×C₅	1	255	yes	direct product factor
26	C₂⁵	C₂³×C₅×C₁₉	1	97155	yes	direct product factor
27	C₂²×C₅	C₂⁶×C₁₉	1	10795	yes	direct product factor
28	C₁₉	C₂⁸×C₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂⁴	C₂⁴×C₅×C₁₉	1	200787	yes	direct product factor
30	C₂×C₅	C₂⁷×C₁₉	1	255	yes	direct product factor
31	C₂³	C₂⁵×C₅×C₁₉	1	97155	yes	direct product factor
32	C₅	C₂⁸×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	C₂⁶×C₅×C₁₉	1	10795	yes	direct product factor
34	C₂	C₂⁷×C₅×C₁₉	1	255	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁷×C₅×C₁₉	C₂	direct (N × H)
2. C₂⁶×C₅×C₁₉	C₂²	direct (N × H)
3. C₂⁵×C₅×C₁₉	C₂³	direct (N × H)
4. C₂⁸×C₁₉	C₅	direct (N × H)
5. C₂⁷×C₁₉	C₂×C₅	direct (N × H)
6. C₂⁴×C₅×C₁₉	C₂⁴	direct (N × H)
7. C₂⁸×C₅	C₁₉	direct (N × H)
8. C₂⁶×C₁₉	C₂²×C₅	direct (N × H)
9. C₂³×C₅×C₁₉	C₂⁵	direct (N × H)
10. C₂⁷×C₅	C₂×C₁₉	direct (N × H)
11. C₂⁵×C₁₉	C₂³×C₅	direct (N × H)
12. C₂²×C₅×C₁₉	C₂⁶	direct (N × H)
13. C₂⁶×C₅	C₂²×C₁₉	direct (N × H)
14. C₂⁴×C₁₉	C₂⁴×C₅	direct (N × H)
15. C₂⁸	C₅×C₁₉	direct (N × H)
16. C₂×C₅×C₁₉	C₂⁷	direct (N × H)
17. C₂⁵×C₅	C₂³×C₁₉	direct (N × H)
18. C₂³×C₁₉	C₂⁵×C₅	direct (N × H)
19. C₂⁷	C₂×C₅×C₁₉	direct (N × H)
20. C₅×C₁₉	C₂⁸	direct (N × H)
21. C₂⁴×C₅	C₂⁴×C₁₉	direct (N × H)
22. C₂²×C₁₉	C₂⁶×C₅	direct (N × H)
23. C₂⁶	C₂²×C₅×C₁₉	direct (N × H)
24. C₂³×C₅	C₂⁵×C₁₉	direct (N × H)
25. C₂×C₁₉	C₂⁷×C₅	direct (N × H)
26. C₂⁵	C₂³×C₅×C₁₉	direct (N × H)
27. C₂²×C₅	C₂⁶×C₁₉	direct (N × H)
28. C₁₉	C₂⁸×C₅	direct (N × H)
29. C₂⁴	C₂⁴×C₅×C₁₉	direct (N × H)
30. C₂×C₅	C₂⁷×C₁₉	direct (N × H)
31. C₂³	C₂⁵×C₅×C₁₉	direct (N × H)
32. C₅	C₂⁸×C₁₉	direct (N × H)
33. C₂²	C₂⁶×C₅×C₁₉	direct (N × H)
34. C₂	C₂⁷×C₅×C₁₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁷×C₅×C₁₉	2
C₂⁸×C₁₉	5
C₂⁸×C₅	19

Subgroups — C28×C5×C19 #72201628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁸×C₅×C₁₉ #72201628