Subgroups — C₃²×C₂₅×D₇₇ #46831433

Order 34650.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₅×D₇₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×D₇₇	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇×C₁₁×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×D₁₁×C₂₅	—	7	1	no	maximal, Hall
6	C₂₅×D₇₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₃²×D₇×C₂₅	—	11	1	no	maximal, Hall
9	C₃²×C₁₁×C₂₅	D₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×D₇₇	C₃×C₅	1	4	yes	—
11	C₇×C₁₁×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₁×C₂₅	—	7	4	no	—
13	C₃²×C₇×C₂₅	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃²×D₇₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₇×C₁₁	C₂×C₃×C₅	1	4	yes	—
16	C₃×D₇×C₂₅	—	11	4	no	—
17	C₃²×C₅×D₁₁	—	7	1	no	—
18	C₃×C₁₁×C₂₅	C₃×D₇	1	4	yes	complemented
19	C₅×D₇₇	C₃²×C₅	1	1	yes	characteristic
20	C₃²×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₅×D₇	—	11	1	no	—
22	D₁₁×C₂₅	—	7	1	no	Hall
23	C₃×C₇×C₂₅	C₃×D₁₁	1	4	yes	complemented
24	C₃²×C₅×C₁₁	C₅×D₇	1	1	yes	characteristic
25	C₃×D₇₇	C₃×C₂₅	1	4	yes	direct product factor
26	C₂×C₃²×C₂₅	—	77	1	no	Hall
27	C₅×C₇×C₁₁	C₂×C₃²×C₅	1	1	yes	characteristic
28	D₇×C₂₅	—	11	1	no	Hall
29	C₃×C₅×D₁₁	—	7	4	no	—
30	C₃²×C₅×C₇	C₅×D₁₁	1	1	yes	characteristic
31	C₁₁×C₂₅	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₂×C₃×C₂₅	1	4	yes	complemented
33	C₃²×C₂₅	D₇₇	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₅×D₇	—	11	4	no	—
35	C₃²×D₁₁	—	7	1	no	Hall
36	C₇×C₂₅	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₃×C₅×D₇	1	4	yes	—
38	D₇₇	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃×C₂₅	—	77	4	no	—
40	C₃²×D₇	—	11	1	no	Hall
41	C₅×D₁₁	—	7	1	no	—
42	C₃×C₅×C₇	C₃×C₅×D₁₁	1	4	yes	—
43	C₃²×C₁₁	D₇×C₂₅	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃²×C₅	—	77	1	no	—
45	C₇×C₁₁	C₂×C₃²×C₂₅	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₅	C₃×D₇₇	1	4	yes	direct product factor
47	C₅×D₇	—	11	1	no	—
48	C₃×D₁₁	—	7	4	no	—
49	C₃²×C₇	D₁₁×C₂₅	1	1	yes	characteristic, complemented, Hall
50	C₅×C₁₁	C₃²×C₅×D₇	1	1	yes	characteristic
51	C₂×C₂₅	—	77	1	no	Hall
52	C₃²×C₅	C₅×D₇₇	1	1	yes	characteristic
53	C₃×D₇	—	11	4	no	—
54	C₅×C₇	C₃²×C₅×D₁₁	1	1	yes	characteristic
55	C₃×C₁₁	C₃×D₇×C₂₅	1	4	yes	complemented
56	C₂×C₃×C₅	—	77	4	no	—
57	C₂₅	C₃²×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
58	D₁₁	—	7	1	no	Hall
59	C₃×C₇	C₃×D₁₁×C₂₅	1	4	yes	complemented
60	C₂×C₃²	—	77	1	no	Hall
61	C₃×C₅	C₃×C₅×D₇₇	1	4	yes	—
62	D₇	—	11	1	no	Hall
63	C₁₁	C₃²×D₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	—	77	1	no	—
65	C₃²	C₂₅×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₃²×D₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	—	77	4	no	—
68	C₅	C₃²×C₅×D₇₇	1	1	yes	characteristic
69	C₃	C₃×C₂₅×D₇₇	1	4	yes	direct product factor
70	C₂	—	77	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₂₅	D₇₇
commutator, hypocenter	C₇×C₁₁	C₂×C₃²×C₂₅
Frattini	C₅	C₃²×C₅×D₇₇
Fitting	C₃²×C₇×C₁₁×C₂₅	C₂
socle	C₃²×C₅×C₇×C₁₁	C₂×C₅
prime radical	C₃²×C₅×D₇₇	C₅
cosocle	C₅×C₇×C₁₁	C₂×C₃²×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₃²×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₂₅	C₂	semidirect
2. C₃×C₂₅×D₇₇	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₂₅	C₂×C₃	semidirect
6. C₂₅×D₇₇	C₃²	direct (N × H)
9. C₃²×C₁₁×C₂₅	D₇	semidirect
11. C₇×C₁₁×C₂₅	C₂×C₃²	semidirect
13. C₃²×C₇×C₂₅	D₁₁	semidirect
14. C₃²×D₇₇	C₂₅	direct (N × H)
18. C₃×C₁₁×C₂₅	C₃×D₇	semidirect
20. C₃²×C₇×C₁₁	C₂×C₂₅	semidirect
23. C₃×C₇×C₂₅	C₃×D₁₁	semidirect
25. C₃×D₇₇	C₃×C₂₅	direct (N × H)
31. C₁₁×C₂₅	C₃²×D₇	semidirect
32. C₃×C₇×C₁₁	C₂×C₃×C₂₅	semidirect
33. C₃²×C₂₅	D₇₇	direct (N × H)
36. C₇×C₂₅	C₃²×D₁₁	semidirect
38. D₇₇	C₃²×C₂₅	direct (N × H)
43. C₃²×C₁₁	D₇×C₂₅	semidirect
45. C₇×C₁₁	C₂×C₃²×C₂₅	semidirect
46. C₃×C₂₅	C₃×D₇₇	direct (N × H)
49. C₃²×C₇	D₁₁×C₂₅	semidirect
55. C₃×C₁₁	C₃×D₇×C₂₅	semidirect
57. C₂₅	C₃²×D₇₇	direct (N × H)
59. C₃×C₇	C₃×D₁₁×C₂₅	semidirect
63. C₁₁	C₃²×D₇×C₂₅	semidirect
65. C₃²	C₂₅×D₇₇	direct (N × H)
66. C₇	C₃²×D₁₁×C₂₅	semidirect
69. C₃	C₃×C₂₅×D₇₇	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×C₇×C₁₁×C₂₅	2
C₃×C₂₅×D₇₇	3
C₃²×C₅×D₇₇	5
C₃²×D₁₁×C₂₅	7
C₃²×D₇×C₂₅	11

Subgroups — C32×C25×D77 #46831433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₂₅×D₇₇ #46831433