Subgroups — C₅×C₁₁⋊C₅×D₆₃ #46831473

Order 34650.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₂₁×C₁₁⋊C₅	—	3	1	no	maximal
3	C₁₁⋊C₅×D₆₃	C₅	1	5	yes	maximal, direct product factor
4	C₅×C₁₁×D₆₃	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×C₇×C₁₁⋊C₅	D₃	1	1	yes	characteristic
6	C₅×D₉×C₁₁⋊C₅	—	7	1	no	maximal, Hall
7	C₅×D₇×C₁₁⋊C₅	—	9	1	no	Hall
8	C₇×C₉×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
9	C₅×C₇×C₉×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅²×D₆₃	—	11	1	no	maximal, Hall
11	C₅×C₉×C₁₁⋊C₅	D₇	1	1	yes	characteristic, complemented, Hall
12	D₂₁×C₁₁⋊C₅	—	3	5	no	—
13	C₅×C₁₁×D₂₁	—	3	1	no	—
14	C₅×C₇×C₁₁⋊C₅	D₉	1	1	yes	characteristic, complemented, Hall
15	C₅×D₃×C₁₁⋊C₅	—	21	1	no	—
16	C₅²×C₇×C₉	—	11	1	no	Hall
17	C₁₁×D₆₃	C₅²	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₇×C₁₁	C₅×D₃	1	1	yes	characteristic
19	C₃×C₇×C₁₁⋊C₅	C₅×D₃	1	5	yes	—
20	C₅²×D₂₁	—	33	1	no	—
21	C₅×C₁₁×D₉	—	7	1	no	—
22	D₉×C₁₁⋊C₅	—	7	5	no	—
23	C₃×C₅×C₁₁⋊C₅	D₂₁	1	1	yes	characteristic
24	C₅×C₁₁×D₇	—	9	1	no	—
25	D₇×C₁₁⋊C₅	—	9	5	no	—
26	C₇×C₉×C₁₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
27	C₅×D₆₃	—	11	5	no	—
28	C₅×D₆₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
29	C₂×C₅×C₁₁⋊C₅	—	63	1	no	Hall
30	C₃×C₅²×C₇	—	11	1	no	—
31	C₅×C₉×C₁₁	C₅×D₇	1	1	yes	characteristic, complemented
32	C₉×C₁₁⋊C₅	C₅×D₇	1	5	yes	complemented
33	C₁₁×D₂₁	—	3	1	no	—
34	C₅²×D₉	—	77	1	no	Hall
35	C₅×C₇×C₁₁	C₅×D₉	1	1	yes	characteristic, complemented
36	C₇×C₁₁⋊C₅	C₅×D₉	1	5	yes	complemented
37	C₅²×D₇	—	99	1	no	Hall
38	C₅×D₃×C₁₁	—	21	1	no	—
39	D₃×C₁₁⋊C₅	—	21	5	no	—
40	C₅×C₇×C₉	—	11	5	no	—
41	C₅×C₇×C₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
42	C₅×C₁₁⋊C₅	D₆₃	1	1	yes	characteristic, direct product factor, Hall
43	C₃×C₇×C₁₁	C₅²×D₃	1	1	yes	characteristic
44	C₅²×C₉	—	11	1	no	Hall
45	C₅×D₂₁	—	3	1	no	—
46	C₅×D₂₁	—	33	5	no	—
47	C₁₁×D₉	—	7	1	no	Hall
48	C₅²×C₇	—	11	1	no	Hall
49	C₃×C₅×C₁₁	C₅×D₂₁	1	1	yes	characteristic
50	C₃×C₁₁⋊C₅	C₅×D₂₁	1	5	yes	—
51	C₁₁×D₇	—	9	1	no	Hall
52	C₅²×D₃	—	231	1	no	—
53	D₆₃	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₅×C₁₁	—	63	1	no	—
55	C₂×C₁₁⋊C₅	—	63	5	no	—
56	C₃×C₅×C₇	—	11	5	no	—
57	C₃×C₅×C₇	D₃×C₁₁⋊C₅	1	1	yes	characteristic
58	C₉×C₁₁	C₅²×D₇	1	1	yes	characteristic, complemented, Hall
59	C₅×D₉	—	7	1	no	—
60	C₅×D₉	—	77	5	no	—
61	C₇×C₁₁	C₅²×D₉	1	1	yes	characteristic, complemented, Hall
62	C₃×C₅²	—	11	1	no	—
63	C₅×D₇	—	9	1	no	—
64	C₅×D₇	—	99	5	no	—
65	D₃×C₁₁	—	21	1	no	—
66	C₇×C₉	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
67	C₅×C₁₁	C₅×D₆₃	1	1	yes	characteristic, complemented
68	C₁₁⋊C₅	C₅×D₆₃	1	5	yes	direct product factor
69	C₂×C₅²	—	693	1	no	Hall
70	C₅×C₉	—	11	5	no	—
71	C₅×C₉	D₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented
72	D₂₁	—	3	1	no	—
73	C₅×C₇	—	11	5	no	—
74	C₅×C₇	D₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented
75	C₃×C₁₁	C₅²×D₂₁	1	1	yes	characteristic
76	C₅×D₃	—	21	1	no	—
77	C₅×D₃	—	231	5	no	—
78	C₅²	—	11	1	no	Sylow
79	C₂×C₁₁	—	63	1	no	Hall
80	C₃×C₇	C₅×D₃×C₁₁⋊C₅	1	1	yes	characteristic
81	D₉	—	7	1	no	Hall
82	C₃×C₅	—	11	5	no	—
83	C₃×C₅	D₂₁×C₁₁⋊C₅	1	1	yes	characteristic
84	D₇	—	9	1	no	Hall
85	C₁₁	C₅²×D₆₃	1	1	yes	characteristic, complemented, Sylow
86	C₂×C₅	—	63	1	no	—
87	C₂×C₅	—	693	5	no	—
88	C₉	C₅×D₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
89	C₇	C₅×D₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
90	D₃	—	21	1	no	—
91	C₅	—	11	5	no	—
92	C₅	C₁₁⋊C₅×D₆₃	1	1	yes	characteristic, direct product factor
93	C₃	C₅×D₂₁×C₁₁⋊C₅	1	1	yes	characteristic
94	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊C₅×D₆₃
commutator, cosocle, hypocenter	C₇×C₉×C₁₁	C₂×C₅²
Frattini	C₃	C₅×D₂₁×C₁₁⋊C₅
Fitting	C₅×C₇×C₉×C₁₁	C₂×C₅
socle	C₃×C₅×C₇×C₁₁	C₅×D₃
LCS	G ▷ C₇×C₉×C₁₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₁₁⋊C₅	C₂	semidirect
3. C₁₁⋊C₅×D₆₃	C₅	direct (N × H)
4. C₅×C₁₁×D₆₃	C₅	semidirect
8. C₇×C₉×C₁₁⋊C₅	C₂×C₅	semidirect
9. C₅×C₇×C₉×C₁₁	C₂×C₅	semidirect
11. C₅×C₉×C₁₁⋊C₅	D₇	semidirect
14. C₅×C₇×C₁₁⋊C₅	D₉	semidirect
17. C₁₁×D₆₃	C₅²	semidirect
26. C₇×C₉×C₁₁	C₂×C₅²	semidirect
28. C₅×D₆₃	C₁₁⋊C₅	direct (N × H)
31. C₅×C₉×C₁₁	C₅×D₇	semidirect
32. C₉×C₁₁⋊C₅	C₅×D₇	semidirect
35. C₅×C₇×C₁₁	C₅×D₉	semidirect
36. C₇×C₁₁⋊C₅	C₅×D₉	semidirect
41. C₅×C₇×C₉	C₂×C₁₁⋊C₅	semidirect
42. C₅×C₁₁⋊C₅	D₆₃	direct (N × H)
53. D₆₃	C₅×C₁₁⋊C₅	direct (N × H)
58. C₉×C₁₁	C₅²×D₇	semidirect
61. C₇×C₁₁	C₅²×D₉	semidirect
66. C₇×C₉	C₂×C₅×C₁₁⋊C₅	semidirect
67. C₅×C₁₁	C₅×D₆₃	semidirect
68. C₁₁⋊C₅	C₅×D₆₃	direct (N × H)
71. C₅×C₉	D₇×C₁₁⋊C₅	semidirect
74. C₅×C₇	D₉×C₁₁⋊C₅	semidirect
85. C₁₁	C₅²×D₆₃	semidirect
88. C₉	C₅×D₇×C₁₁⋊C₅	semidirect
89. C₇	C₅×D₉×C₁₁⋊C₅	semidirect
92. C₅	C₁₁⋊C₅×D₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₉×C₁₁⋊C₅	2
C₅×D₂₁×C₁₁⋊C₅	3
C₁₁⋊C₅×D₆₃	5
C₅×C₁₁×D₆₃	5
C₅×D₉×C₁₁⋊C₅	7
C₅²×D₆₃	11

Subgroups — C5×C11⋊C5×D63 #46831473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊C₅×D₆₃ #46831473