Subgroups — C₅²×D₃₃⋊D₁₁ #49137744

Order 36300.

480 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×C₁₁×D₃₃	C₂	1	2	yes	maximal, complemented
3	C₅²×D₁₁²	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×D₃₃⋊D₁₁	C₅	1	6	yes	maximal, direct product factor
6	C₅²×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic, complemented
7	C₅²×C₁₁×D₁₁	—	3	2	no	—
8	C₅×C₁₁×D₃₃	C₂×C₅	1	12	yes	complemented
9	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	6	yes	complemented
10	C₅²×D₃×D₁₁	—	11	2	no	maximal
11	C₅²×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₅×D₁₁²	—	3	6	no	—
13	C₃×C₅×C₁₁²	C₂²×C₅	1	6	yes	complemented
14	C₅²×D₃₃	D₁₁	1	2	yes	complemented
15	C₅²×D₃×C₁₁	—	11	2	no	—
16	C₃×C₅²×D₁₁	—	11	2	no	—
17	C₃×C₅²×D₁₁	—	22	5	no	—
18	D₃₃⋊D₁₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₁⋊D₁₁	C₅×D₃	1	6	yes	complemented
20	C₅×C₁₁×D₁₁	—	3	12	no	—
21	C₂×C₅²×D₁₁	—	33	2	no	—
22	C₃×C₅²×C₁₁	—	2	5	no	—
23	C₃×C₅²×C₁₁	C₂×D₁₁	1	2	yes	complemented
24	C₁₁×D₃₃	C₂×C₅²	1	2	yes	complemented
25	C₃×C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic, complemented
26	C₅×D₃×D₁₁	—	11	12	no	—
27	C₅×C₁₁²	C₂×C₅×D₃	1	6	yes	complemented
28	C₂×C₅²×C₁₁	—	33	2	no	—
29	C₅²×D₁₁	—	3	2	no	—
30	C₅²×D₁₁	—	11	2	no	—
31	C₅²×D₁₁	—	22	5	no	—
32	D₁₁²	—	3	1	no	Hall
33	C₃×C₁₁²	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
34	C₅×D₃₃	C₅×D₁₁	1	12	yes	complemented
35	C₅×D₃×C₁₁	—	11	12	no	—
36	C₃×C₅×D₁₁	—	11	12	no	—
37	C₃×C₅×D₁₁	—	22	30	no	—
38	C₂×C₅²×D₃	—	121	1	no	Hall
39	C₅²×C₁₁	—	2	5	no	—
40	C₅²×C₁₁	D₃×D₁₁	1	2	yes	complemented
41	C₁₁⋊D₁₁	C₅²×D₃	1	1	yes	characteristic, complemented
42	C₁₁×D₁₁	—	3	2	no	—
43	C₂×C₅×D₁₁	—	33	12	no	—
44	C₃×C₅×C₁₁	—	2	30	no	—
45	C₃×C₅×C₁₁	C₂×C₅×D₁₁	1	12	yes	complemented
46	C₂×C₃×C₅²	—	121	1	no	—
47	C₅²×D₃	—	11	2	no	—
48	D₃×D₁₁	—	11	2	no	—
49	C₁₁²	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅×C₁₁	—	33	12	no	—
51	C₅×D₁₁	—	3	12	no	—
52	C₅×D₁₁	—	11	12	no	—
53	C₅×D₁₁	—	22	30	no	—
54	C₂²×C₅²	—	363	1	no	Hall
55	C₃×C₅²	D₁₁²	1	1	yes	characteristic, complemented, Hall
56	D₃₃	C₅²×D₁₁	1	2	yes	complemented
57	C₃×D₁₁	—	11	2	no	—
58	C₃×D₁₁	—	22	5	no	—
59	D₃×C₁₁	—	11	2	no	—
60	C₂×C₅×D₃	—	121	6	no	—
61	C₅×C₁₁	—	2	30	no	—
62	C₅×C₁₁	C₅×D₃×D₁₁	1	12	yes	complemented
63	C₂×C₅²	—	33	2	no	—
64	C₂×C₅²	—	121	1	no	—
65	C₂×D₁₁	—	33	2	no	—
66	C₃×C₁₁	—	2	5	no	—
67	C₃×C₁₁	C₂×C₅²×D₁₁	1	2	yes	complemented
68	C₂×C₃×C₅	—	121	6	no	—
69	C₅×D₃	—	11	12	no	—
70	C₅²	D₃₃⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₁₁	—	33	2	no	—
72	D₁₁	—	3	2	no	—
73	D₁₁	—	11	2	no	—
74	D₁₁	—	22	5	no	—
75	C₂²×C₅	—	363	6	no	—
76	C₃×C₅	C₅×D₁₁²	1	6	yes	complemented
77	C₂×D₃	—	121	1	no	Hall
78	C₁₁	—	2	5	no	—
79	C₁₁	C₅²×D₃×D₁₁	1	2	yes	complemented
80	C₂×C₅	—	33	12	no	—
81	C₂×C₅	—	121	6	no	—
82	C₂×C₃	—	121	1	no	—
83	D₃	—	11	2	no	—
84	C₅	C₅×D₃₃⋊D₁₁	1	6	yes	direct product factor
85	C₂²	—	363	1	no	Sylow
86	C₃	C₅²×D₁₁²	1	1	yes	characteristic, complemented, Sylow
87	C₂	—	33	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₅²	D₃₃⋊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×C₁₁×D₃₃	C₂	semidirect
4. C₃×C₅²×C₁₁²	C₂²	semidirect
5. C₅×D₃₃⋊D₁₁	C₅	direct (N × H)
6. C₅²×C₁₁⋊D₁₁	D₃	semidirect
8. C₅×C₁₁×D₃₃	C₂×C₅	semidirect
9. C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	semidirect
11. C₅²×C₁₁²	C₂×D₃	semidirect
13. C₃×C₅×C₁₁²	C₂²×C₅	semidirect
14. C₅²×D₃₃	D₁₁	semidirect
18. D₃₃⋊D₁₁	C₅²	direct (N × H)
19. C₅×C₁₁⋊D₁₁	C₅×D₃	semidirect
23. C₃×C₅²×C₁₁	C₂×D₁₁	semidirect
24. C₁₁×D₃₃	C₂×C₅²	semidirect
25. C₃×C₁₁⋊D₁₁	C₂×C₅²	semidirect
27. C₅×C₁₁²	C₂×C₅×D₃	semidirect
33. C₃×C₁₁²	C₂²×C₅²	semidirect
34. C₅×D₃₃	C₅×D₁₁	semidirect
40. C₅²×C₁₁	D₃×D₁₁	semidirect
41. C₁₁⋊D₁₁	C₅²×D₃	semidirect
45. C₃×C₅×C₁₁	C₂×C₅×D₁₁	semidirect
49. C₁₁²	C₂×C₅²×D₃	semidirect
55. C₃×C₅²	D₁₁²	semidirect
56. D₃₃	C₅²×D₁₁	semidirect
62. C₅×C₁₁	C₅×D₃×D₁₁	semidirect
67. C₃×C₁₁	C₂×C₅²×D₁₁	semidirect
70. C₅²	D₃₃⋊D₁₁	direct (N × H)
76. C₃×C₅	C₅×D₁₁²	semidirect
79. C₁₁	C₅²×D₃×D₁₁	semidirect
84. C₅	C₅×D₃₃⋊D₁₁	direct (N × H)
86. C₃	C₅²×D₁₁²	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×C₁₁×D₃₃	2
C₅²×D₁₁²	3
C₅×D₃₃⋊D₁₁	5
C₅²×D₃×D₁₁	11

Subgroups — C52×D33⋊D11 #49137744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃₃⋊D₁₁ #49137744