Subgroups — C₃×C₂₅×Dic₇₇ #37528196

Order 23100.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅×Dic₇₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₁×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×Dic₇₇	C₅	1	1	yes	maximal, characteristic
5	C₂×C₇×C₁₁×C₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₂₅×Dic₁₁	—	7	1	no	maximal, Hall
7	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₂₅×Dic₇	—	11	1	no	maximal, Hall
9	C₇×C₁₁×C₂₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₁×C₂₅	D₇	1	1	yes	characteristic
11	C₅×Dic₇₇	C₃×C₅	1	1	yes	characteristic
12	C₃×C₅×C₇×C₁₁	C₄×C₅	1	1	yes	characteristic
13	C₂₅×Dic₁₁	—	7	1	no	Hall
14	C₂×C₃×C₇×C₂₅	D₁₁	1	1	yes	characteristic
15	C₃×Dic₇₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁×C₂₅	Dic₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₇×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
18	C₂₅×Dic₇	—	11	1	no	Hall
19	C₃×C₅×Dic₁₁	—	7	1	no	—
20	C₂×C₁₁×C₂₅	C₃×D₇	1	1	yes	characteristic
21	C₃×C₇×C₂₅	Dic₁₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic
23	C₃×C₅×Dic₇	—	11	1	no	—
24	C₅×C₇×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic
25	C₂×C₇×C₂₅	C₃×D₁₁	1	1	yes	characteristic
26	C₂×C₃×C₅×C₁₁	C₅×D₇	1	1	yes	characteristic
27	Dic₇₇	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₄×C₂₅	—	77	1	no	Hall
29	C₁₁×C₂₅	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
31	C₅×Dic₁₁	—	7	1	no	—
32	C₂×C₃×C₅×C₇	C₅×D₁₁	1	1	yes	characteristic
33	C₇×C₂₅	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×C₁₁	C₅×Dic₇	1	1	yes	characteristic
35	C₂×C₇×C₁₁	C₂×C₃×C₂₅	1	1	yes	characteristic
36	C₂×C₃×C₂₅	D₇₇	1	1	yes	characteristic
37	C₅×Dic₇	—	11	1	no	—
38	C₃×Dic₁₁	—	7	1	no	Hall
39	C₂×C₅×C₁₁	C₃×C₅×D₇	1	1	yes	characteristic
40	C₃×C₅×C₇	C₅×Dic₁₁	1	1	yes	characteristic
41	C₄×C₂₅	—	77	1	no	Hall
42	C₃×Dic₇	—	11	1	no	Hall
43	C₇×C₁₁	C₃×C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
44	C₃×C₂₅	Dic₇₇	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₅×C₇	C₃×C₅×D₁₁	1	1	yes	characteristic
46	C₂×C₃×C₁₁	D₇×C₂₅	1	1	yes	characteristic
47	C₃×C₄×C₅	—	77	1	no	—
48	C₅×C₁₁	C₃×C₅×Dic₇	1	1	yes	characteristic
49	C₂×C₂₅	C₃×D₇₇	1	1	yes	characteristic
50	Dic₁₁	—	7	1	no	Hall
51	C₂×C₃×C₇	D₁₁×C₂₅	1	1	yes	characteristic
52	C₅×C₇	C₃×C₅×Dic₁₁	1	1	yes	characteristic
53	C₃×C₁₁	C₂₅×Dic₇	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	C₅×D₇₇	1	1	yes	characteristic
55	Dic₇	—	11	1	no	Hall
56	C₂₅	C₃×Dic₇₇	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₁₁	C₃×D₇×C₂₅	1	1	yes	characteristic
58	C₃×C₇	C₂₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
59	C₄×C₅	—	77	1	no	—
60	C₃×C₅	C₅×Dic₇₇	1	1	yes	characteristic
61	C₂×C₇	C₃×D₁₁×C₂₅	1	1	yes	characteristic
62	C₃×C₄	—	77	1	no	Hall
63	C₁₁	C₃×C₂₅×Dic₇	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	C₃×C₅×D₇₇	1	1	yes	characteristic
65	C₇	C₃×C₂₅×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	C₂₅×D₇₇	1	1	yes	characteristic
67	C₅	C₃×C₅×Dic₇₇	1	1	yes	characteristic
68	C₄	—	77	1	no	Sylow
69	C₃	C₂₅×Dic₇₇	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	C₃×C₂₅×D₇₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₅	D₇₇
commutator, hypocenter	C₇×C₁₁	C₃×C₄×C₂₅
Frattini	C₂×C₅	C₃×C₅×D₇₇
Fitting	C₂×C₃×C₇×C₁₁×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅
cosocle	C₂×C₅×C₇×C₁₁	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₃×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₂₅×Dic₇₇	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₂₅	C₄	semidirect
9. C₇×C₁₁×C₂₅	C₃×C₄	semidirect
15. C₃×Dic₇₇	C₂₅	direct (N × H)
16. C₃×C₁₁×C₂₅	Dic₇	semidirect
21. C₃×C₇×C₂₅	Dic₁₁	semidirect
27. Dic₇₇	C₃×C₂₅	direct (N × H)
29. C₁₁×C₂₅	C₃×Dic₇	semidirect
30. C₃×C₇×C₁₁	C₄×C₂₅	semidirect
33. C₇×C₂₅	C₃×Dic₁₁	semidirect
43. C₇×C₁₁	C₃×C₄×C₂₅	semidirect
44. C₃×C₂₅	Dic₇₇	direct (N × H)
53. C₃×C₁₁	C₂₅×Dic₇	semidirect
56. C₂₅	C₃×Dic₇₇	direct (N × H)
58. C₃×C₇	C₂₅×Dic₁₁	semidirect
63. C₁₁	C₃×C₂₅×Dic₇	semidirect
65. C₇	C₃×C₂₅×Dic₁₁	semidirect
69. C₃	C₂₅×Dic₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₁×C₂₅	2
C₂₅×Dic₇₇	3
C₃×C₅×Dic₇₇	5
C₃×C₂₅×Dic₁₁	7
C₃×C₂₅×Dic₇	11

Subgroups — C3×C25×Dic77 #37528196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₅×Dic₇₇ #37528196