Subgroups — C₃²×C₁₁×D₅₅ #24926210

Order 10890.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₁×D₅₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₁×D₁₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁²	C₂×C₃	1	4	yes	complemented
5	C₁₁×D₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₁²	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₅₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor
8	C₃²×D₅×C₁₁	—	11	1	no	maximal
9	C₃×C₁₁×D₁₁	—	5	4	no	—
10	C₅×C₁₁²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₁₁	—	2	5	no	—
12	C₃²×C₅×C₁₁	D₁₁	1	1	yes	characteristic, complemented
13	C₃²×C₅×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₃×C₁₁²	C₃×D₅	1	4	yes	complemented
15	C₃×D₅₅	C₃×C₁₁	1	4	yes	direct product factor
16	C₃×D₅×C₁₁	—	11	4	no	—
17	C₁₁×D₁₁	—	5	1	no	Hall
18	C₂×C₃²×C₁₁	—	55	1	no	—
19	C₃²×D₁₁	—	5	1	no	—
20	C₃×C₅×C₁₁	—	2	20	no	—
21	C₃×C₅×C₁₁	C₃×D₁₁	1	4	yes	complemented
22	C₃×C₅×C₁₁	C₂×C₃×C₁₁	1	4	yes	complemented
23	C₁₁²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
24	D₅₅	C₃²×C₁₁	1	1	yes	characteristic, direct product factor
25	D₅×C₁₁	—	11	1	no	—
26	C₃²×C₁₁	—	2	5	no	—
27	C₃²×C₁₁	D₅×C₁₁	1	1	yes	characteristic, complemented
28	C₃²×C₁₁	D₅₅	1	1	yes	characteristic, direct product factor
29	C₃²×D₅	—	11	1	no	Hall
30	C₂×C₃×C₁₁	—	55	4	no	—
31	C₃×D₁₁	—	5	4	no	—
32	C₅×C₁₁	—	2	5	no	—
33	C₅×C₁₁	C₃²×D₁₁	1	1	yes	characteristic, complemented
34	C₅×C₁₁	C₂×C₃²×C₁₁	1	1	yes	characteristic, complemented
35	C₃²×C₅	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
36	C₃×C₁₁	—	2	20	no	—
37	C₃×C₁₁	C₃×D₅×C₁₁	1	4	yes	complemented
38	C₃×C₁₁	C₃×D₅₅	1	4	yes	direct product factor
39	C₃×D₅	—	11	4	no	—
40	C₂×C₁₁	—	55	1	no	—
41	D₁₁	—	5	1	no	—
42	C₂×C₃²	—	55	1	no	Hall
43	C₃×C₅	C₃×C₁₁×D₁₁	1	4	yes	complemented
44	C₁₁	—	2	5	no	—
45	C₁₁	C₃²×D₅×C₁₁	1	1	yes	characteristic, complemented
46	C₁₁	C₃²×D₅₅	1	1	yes	characteristic, direct product factor
47	D₅	—	11	1	no	Hall
48	C₃²	C₁₁×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃	—	55	4	no	—
50	C₅	C₃²×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
51	C₃	C₃×C₁₁×D₅₅	1	4	yes	direct product factor
52	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁²	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁²	C₂	semidirect
2. C₃×C₁₁×D₅₅	C₃	direct (N × H)
4. C₃×C₅×C₁₁²	C₂×C₃	semidirect
5. C₁₁×D₅₅	C₃²	direct (N × H)
6. C₃²×C₁₁²	D₅	semidirect
7. C₃²×D₅₅	C₁₁	direct (N × H)
10. C₅×C₁₁²	C₂×C₃²	semidirect
12. C₃²×C₅×C₁₁	D₁₁	semidirect
13. C₃²×C₅×C₁₁	C₂×C₁₁	semidirect
14. C₃×C₁₁²	C₃×D₅	semidirect
15. C₃×D₅₅	C₃×C₁₁	direct (N × H)
21. C₃×C₅×C₁₁	C₃×D₁₁	semidirect
22. C₃×C₅×C₁₁	C₂×C₃×C₁₁	semidirect
23. C₁₁²	C₃²×D₅	semidirect
24. D₅₅	C₃²×C₁₁	direct (N × H)
27. C₃²×C₁₁	D₅×C₁₁	semidirect
28. C₃²×C₁₁	D₅₅	direct (N × H)
33. C₅×C₁₁	C₃²×D₁₁	semidirect
34. C₅×C₁₁	C₂×C₃²×C₁₁	semidirect
35. C₃²×C₅	C₁₁×D₁₁	semidirect
37. C₃×C₁₁	C₃×D₅×C₁₁	semidirect
38. C₃×C₁₁	C₃×D₅₅	direct (N × H)
43. C₃×C₅	C₃×C₁₁×D₁₁	semidirect
45. C₁₁	C₃²×D₅×C₁₁	semidirect
46. C₁₁	C₃²×D₅₅	direct (N × H)
48. C₃²	C₁₁×D₅₅	direct (N × H)
50. C₅	C₃²×C₁₁×D₁₁	semidirect
51. C₃	C₃×C₁₁×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×C₁₁²	2
C₃×C₁₁×D₅₅	3
C₃²×C₁₁×D₁₁	5
C₃²×D₅₅	11
C₃²×D₅×C₁₁	11

Subgroups — C32×C11×D55 #24926210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₁×D₅₅ #24926210