Subgroups — C₅²×D₃×C₁₁⋊D₁₁ #49137745

Order 36300.

1120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₃⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×C₁₁⋊D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₁₁⋊D₁₁	C₅	1	6	yes	maximal, direct product factor
7	C₅²×C₁₁⋊D₁₁	—	3	1	no	—
8	C₅²×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅²×C₁₁²	—	3	1	no	—
10	C₅×C₃⋊(C₁₁⋊D₁₁)	C₂×C₅	1	6	yes	complemented
11	C₅×D₃×C₁₁²	C₂×C₅	1	6	yes	complemented
12	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	6	yes	complemented
13	C₅²×D₃×D₁₁	—	11	12	no	maximal
14	C₅²×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₁⋊D₁₁	—	3	6	no	—
16	C₃×C₅×C₁₁²	C₂²×C₅	1	6	yes	complemented
17	C₅²×D₃₃	—	11	12	no	—
18	C₅²×D₃×C₁₁	D₁₁	1	12	yes	complemented
19	C₃×C₅²×D₁₁	—	11	12	no	—
20	D₃×C₁₁⋊D₁₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₁₁²	—	3	6	no	—
22	C₅×C₁₁⋊D₁₁	—	3	6	no	—
23	C₅×C₁₁⋊D₁₁	C₅×D₃	1	6	yes	direct product factor
24	C₂×C₅²×D₁₁	—	33	12	no	—
25	C₃×C₅²×C₁₁	C₂×D₁₁	1	12	yes	complemented
26	C₃⋊(C₁₁⋊D₁₁)	C₂×C₅²	1	1	yes	characteristic, complemented
27	D₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented
28	C₃×C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic, complemented
29	C₅×D₃×D₁₁	—	11	72	no	—
30	C₅×C₁₁²	C₂×C₅×D₃	1	6	yes	complemented
31	C₂×C₅²×C₁₁	—	3	12	no	—
32	C₅²×D₁₁	—	11	12	no	—
33	C₅²×D₁₁	—	33	12	no	—
34	C₂×C₁₁⋊D₁₁	—	3	1	no	Hall
35	C₃×C₁₁²	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
36	C₅×D₃₃	—	11	72	no	—
37	C₅×D₃×C₁₁	C₅×D₁₁	1	72	yes	complemented
38	C₃×C₅×D₁₁	—	11	72	no	—
39	C₂×C₅²×D₃	—	121	1	no	Hall
40	C₅²×C₁₁	D₃×D₁₁	1	12	yes	complemented
41	C₂×C₁₁²	—	3	1	no	—
42	C₁₁⋊D₁₁	—	3	1	no	—
43	C₁₁⋊D₁₁	C₅²×D₃	1	1	yes	characteristic, direct product factor
44	C₂×C₅×D₁₁	—	33	72	no	—
45	C₃×C₅×C₁₁	C₂×C₅×D₁₁	1	72	yes	complemented
46	C₂×C₃×C₅²	—	121	1	no	—
47	C₅²×D₃	—	121	1	no	—
48	C₅²×D₃	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
49	D₃×D₁₁	—	11	12	no	—
50	C₁₁²	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅×C₁₁	—	3	72	no	—
52	C₅×D₁₁	—	11	72	no	—
53	C₅×D₁₁	—	33	72	no	—
54	C₂²×C₅²	—	363	1	no	Hall
55	C₃×C₅²	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
56	D₃₃	—	11	12	no	—
57	C₃×D₁₁	—	11	12	no	—
58	D₃×C₁₁	C₅²×D₁₁	1	12	yes	complemented
59	C₂×C₅×D₃	—	121	6	no	—
60	C₅×C₁₁	C₅×D₃×D₁₁	1	72	yes	complemented
61	C₂×C₅²	—	3	1	no	—
62	C₂×C₅²	—	363	1	no	—
63	C₂×C₅²	—	121	1	no	—
64	C₂×D₁₁	—	33	12	no	—
65	C₃×C₁₁	C₂×C₅²×D₁₁	1	12	yes	complemented
66	C₂×C₃×C₅	—	121	6	no	—
67	C₅×D₃	—	121	6	no	—
68	C₅×D₃	C₅×C₁₁⋊D₁₁	1	6	yes	direct product factor
69	C₅²	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₁₁	—	3	12	no	—
71	D₁₁	—	11	12	no	—
72	D₁₁	—	33	12	no	—
73	C₂²×C₅	—	363	6	no	—
74	C₃×C₅	C₂×C₅×C₁₁⋊D₁₁	1	6	yes	complemented
75	C₂×D₃	—	121	1	no	Hall
76	C₁₁	C₅²×D₃×D₁₁	1	12	yes	complemented
77	C₂×C₅	—	3	6	no	—
78	C₂×C₅	—	363	6	no	—
79	C₂×C₅	—	121	6	no	—
80	C₂×C₃	—	121	1	no	—
81	D₃	—	121	1	no	—
82	D₃	C₅²×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
83	C₅	C₅×D₃×C₁₁⋊D₁₁	1	6	yes	direct product factor
84	C₂²	—	363	1	no	Sylow
85	C₃	C₂×C₅²×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
86	C₂	—	3	1	no	—
87	C₂	—	363	1	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	D₃×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₂²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁⋊D₁₁	C₂	semidirect
2. C₅²×D₃×C₁₁²	C₂	semidirect
3. C₅²×C₃⋊(C₁₁⋊D₁₁)	C₂	semidirect
5. C₃×C₅²×C₁₁²	C₂²	semidirect
6. C₅×D₃×C₁₁⋊D₁₁	C₅	direct (N × H)
8. C₅²×C₁₁⋊D₁₁	D₃	direct (N × H)
10. C₅×C₃⋊(C₁₁⋊D₁₁)	C₂×C₅	semidirect
11. C₅×D₃×C₁₁²	C₂×C₅	semidirect
12. C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	semidirect
14. C₅²×C₁₁²	C₂×D₃	semidirect
16. C₃×C₅×C₁₁²	C₂²×C₅	semidirect
18. C₅²×D₃×C₁₁	D₁₁	semidirect
20. D₃×C₁₁⋊D₁₁	C₅²	direct (N × H)
23. C₅×C₁₁⋊D₁₁	C₅×D₃	direct (N × H)
25. C₃×C₅²×C₁₁	C₂×D₁₁	semidirect
26. C₃⋊(C₁₁⋊D₁₁)	C₂×C₅²	semidirect
27. D₃×C₁₁²	C₂×C₅²	semidirect
28. C₃×C₁₁⋊D₁₁	C₂×C₅²	semidirect
30. C₅×C₁₁²	C₂×C₅×D₃	semidirect
35. C₃×C₁₁²	C₂²×C₅²	semidirect
37. C₅×D₃×C₁₁	C₅×D₁₁	semidirect
40. C₅²×C₁₁	D₃×D₁₁	semidirect
43. C₁₁⋊D₁₁	C₅²×D₃	direct (N × H)
45. C₃×C₅×C₁₁	C₂×C₅×D₁₁	semidirect
48. C₅²×D₃	C₁₁⋊D₁₁	direct (N × H)
50. C₁₁²	C₂×C₅²×D₃	semidirect
55. C₃×C₅²	C₂×C₁₁⋊D₁₁	semidirect
58. D₃×C₁₁	C₅²×D₁₁	semidirect
60. C₅×C₁₁	C₅×D₃×D₁₁	semidirect
65. C₃×C₁₁	C₂×C₅²×D₁₁	semidirect
68. C₅×D₃	C₅×C₁₁⋊D₁₁	direct (N × H)
69. C₅²	D₃×C₁₁⋊D₁₁	direct (N × H)
74. C₃×C₅	C₂×C₅×C₁₁⋊D₁₁	semidirect
76. C₁₁	C₅²×D₃×D₁₁	semidirect
82. D₃	C₅²×C₁₁⋊D₁₁	direct (N × H)
83. C₅	C₅×D₃×C₁₁⋊D₁₁	direct (N × H)
85. C₃	C₂×C₅²×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁⋊D₁₁	2
C₅²×D₃×C₁₁²	2
C₅²×C₃⋊(C₁₁⋊D₁₁)	2
C₂×C₅²×C₁₁⋊D₁₁	3
C₅×D₃×C₁₁⋊D₁₁	5
C₅²×D₃×D₁₁	11

Subgroups — C52×D3×C11⋊D11 #49137745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×C₁₁⋊D₁₁ #49137745