Subgroups — C₃²×C₃₁×D₅₅ #44501872

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃₁×D₅₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₁₁×C₃₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	4	yes	complemented
5	C₃₁×D₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₅×C₃₁	—	11	1	no	maximal, Hall
8	C₃×D₁₁×C₃₁	—	5	4	no	—
9	C₅×C₁₁×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅×C₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₃×D₅	1	4	yes	complemented
12	C₃²×D₅₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×C₃₁	—	11	4	no	—
14	D₁₁×C₃₁	—	5	1	no	Hall
15	C₂×C₃²×C₃₁	—	55	1	no	Hall
16	C₃²×C₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	C₃×D₁₁	1	4	yes	complemented
18	C₁₁×C₃₁	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
19	C₃×D₅₅	C₃×C₃₁	1	4	yes	direct product factor
20	D₅×C₃₁	—	11	1	no	Hall
21	C₃²×C₃₁	D₅₅	1	1	yes	characteristic, direct product factor, Hall
22	C₃²×D₁₁	—	5	1	no	Hall
23	C₂×C₃×C₃₁	—	55	4	no	—
24	C₃×C₅×C₁₁	C₂×C₃×C₃₁	1	4	yes	complemented
25	C₅×C₃₁	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
26	D₅₅	C₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₃²×C₁₁	D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₃×D₅₅	1	4	yes	direct product factor
29	C₃²×D₅	—	11	1	no	Hall
30	C₃×D₁₁	—	5	4	no	—
31	C₂×C₃₁	—	55	1	no	Hall
32	C₅×C₁₁	C₂×C₃²×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₃²×C₅	D₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₃×D₅×C₃₁	1	4	yes	complemented
35	C₃₁	C₃²×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×D₅	—	11	4	no	—
37	D₁₁	—	5	1	no	Hall
38	C₂×C₃²	—	55	1	no	Hall
39	C₃×C₅	C₃×D₁₁×C₃₁	1	4	yes	complemented
40	C₁₁	C₃²×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	11	1	no	Hall
42	C₃²	C₃₁×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	55	4	no	—
44	C₅	C₃²×D₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₃₁×D₅₅	1	4	yes	direct product factor
46	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₃₁	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃²×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₃₁	C₂	semidirect
2. C₃×C₃₁×D₅₅	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
5. C₃₁×D₅₅	C₃²	direct (N × H)
6. C₃²×C₁₁×C₃₁	D₅	semidirect
9. C₅×C₁₁×C₃₁	C₂×C₃²	semidirect
10. C₃²×C₅×C₃₁	D₁₁	semidirect
11. C₃×C₁₁×C₃₁	C₃×D₅	semidirect
12. C₃²×D₅₅	C₃₁	direct (N × H)
16. C₃²×C₅×C₁₁	C₂×C₃₁	semidirect
17. C₃×C₅×C₃₁	C₃×D₁₁	semidirect
18. C₁₁×C₃₁	C₃²×D₅	semidirect
19. C₃×D₅₅	C₃×C₃₁	direct (N × H)
21. C₃²×C₃₁	D₅₅	direct (N × H)
24. C₃×C₅×C₁₁	C₂×C₃×C₃₁	semidirect
25. C₅×C₃₁	C₃²×D₁₁	semidirect
26. D₅₅	C₃²×C₃₁	direct (N × H)
27. C₃²×C₁₁	D₅×C₃₁	semidirect
28. C₃×C₃₁	C₃×D₅₅	direct (N × H)
32. C₅×C₁₁	C₂×C₃²×C₃₁	semidirect
33. C₃²×C₅	D₁₁×C₃₁	semidirect
34. C₃×C₁₁	C₃×D₅×C₃₁	semidirect
35. C₃₁	C₃²×D₅₅	direct (N × H)
39. C₃×C₅	C₃×D₁₁×C₃₁	semidirect
40. C₁₁	C₃²×D₅×C₃₁	semidirect
42. C₃²	C₃₁×D₅₅	direct (N × H)
44. C₅	C₃²×D₁₁×C₃₁	semidirect
45. C₃	C₃×C₃₁×D₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₁×C₃₁	2
C₃×C₃₁×D₅₅	3
C₃²×D₁₁×C₃₁	5
C₃²×D₅×C₃₁	11
C₃²×D₅₅	31

Subgroups — C32×C31×D55 #44501872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃₁×D₅₅ #44501872