Subgroups — C₇×C₁₁×Dic₃×C₂₅ #37528201

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	C₄×C₇×C₁₁×C₂₅	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₁×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₇×C₁₁×Dic₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₇×C₁₁×C₂₅	D₃	1	1	yes	characteristic
6	C₁₁×Dic₃×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₇×Dic₃×C₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₂₅	Dic₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic
11	C₄×C₅×C₇×C₁₁	—	3	1	no	—
12	C₃×C₅×C₇×C₁₁	C₄×C₅	1	1	yes	characteristic
13	C₄×C₁₁×C₂₅	—	3	1	no	Hall
14	C₂×C₃×C₇×C₂₅	C₂×C₁₁	1	1	yes	characteristic
15	C₇×C₁₁×Dic₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁×C₂₅	C₄×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₇×C₁₁	C₅×D₃	1	1	yes	characteristic
18	C₄×C₇×C₂₅	—	3	1	no	Hall
19	C₅×C₁₁×Dic₃	C₅×C₇	1	1	yes	characteristic
20	C₂×C₁₁×C₂₅	D₃×C₇	1	1	yes	characteristic
21	C₃×C₇×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic
23	C₅×C₇×Dic₃	C₅×C₁₁	1	1	yes	characteristic
24	C₅×C₇×C₁₁	C₅×Dic₃	1	1	yes	characteristic
25	C₂×C₇×C₂₅	D₃×C₁₁	1	1	yes	characteristic
26	C₂×C₃×C₅×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
27	C₄×C₇×C₁₁	—	3	1	no	Hall
28	Dic₃×C₂₅	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₁₁×C₂₅	C₇×Dic₃	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₇×C₁₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
31	C₄×C₅×C₁₁	—	3	1	no	—
32	C₂×C₃×C₅×C₇	C₂×C₅×C₁₁	1	1	yes	characteristic
33	C₇×C₂₅	C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₅×C₁₁	C₄×C₅×C₇	1	1	yes	characteristic
35	C₂×C₇×C₁₁	D₃×C₂₅	1	1	yes	characteristic
36	C₂×C₃×C₂₅	C₂×C₇×C₁₁	1	1	yes	characteristic
37	C₄×C₅×C₇	—	3	1	no	—
38	C₁₁×Dic₃	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₅×C₁₁	C₅×D₃×C₇	1	1	yes	characteristic
40	C₃×C₅×C₇	C₄×C₅×C₁₁	1	1	yes	characteristic
41	C₄×C₂₅	—	3	1	no	Hall
42	C₇×Dic₃	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
43	C₇×C₁₁	Dic₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₂₅	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×C₇	C₅×D₃×C₁₁	1	1	yes	characteristic
46	C₂×C₃×C₁₁	C₂×C₇×C₂₅	1	1	yes	characteristic
47	C₅×Dic₃	C₅×C₇×C₁₁	1	1	yes	characteristic
48	C₅×C₁₁	C₅×C₇×Dic₃	1	1	yes	characteristic
49	C₂×C₂₅	D₃×C₇×C₁₁	1	1	yes	characteristic
50	C₄×C₁₁	—	3	1	no	Hall
51	C₂×C₃×C₇	C₂×C₁₁×C₂₅	1	1	yes	characteristic
52	C₅×C₇	C₅×C₁₁×Dic₃	1	1	yes	characteristic
53	C₃×C₁₁	C₄×C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic
55	C₄×C₇	—	3	1	no	Hall
56	C₂₅	C₇×C₁₁×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₁₁	D₃×C₇×C₂₅	1	1	yes	characteristic
58	C₃×C₇	C₄×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Hall
59	C₄×C₅	—	3	1	no	—
60	C₃×C₅	C₄×C₅×C₇×C₁₁	1	1	yes	characteristic
61	C₂×C₇	D₃×C₁₁×C₂₅	1	1	yes	characteristic
62	Dic₃	C₇×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
63	C₁₁	C₇×Dic₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	C₅×D₃×C₇×C₁₁	1	1	yes	characteristic
65	C₇	C₁₁×Dic₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	C₂×C₇×C₁₁×C₂₅	1	1	yes	characteristic
67	C₅	C₅×C₇×C₁₁×Dic₃	1	1	yes	characteristic
68	C₄	—	3	1	no	Sylow
69	C₃	C₄×C₇×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	D₃×C₇×C₁₁×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁×C₂₅	D₃
commutator, hypocenter	C₃	C₄×C₇×C₁₁×C₂₅
Frattini	C₂×C₅	C₅×D₃×C₇×C₁₁
Fitting	C₂×C₃×C₇×C₁₁×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅
cosocle	C₂×C₃×C₅	C₂×C₅×C₇×C₁₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇×C₁₁×C₂₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₁×C₂₅	C₄	semidirect
6. C₁₁×Dic₃×C₂₅	C₇	direct (N × H)
8. C₇×Dic₃×C₂₅	C₁₁	direct (N × H)
9. C₇×C₁₁×C₂₅	Dic₃	direct (N × H)
15. C₇×C₁₁×Dic₃	C₂₅	direct (N × H)
16. C₃×C₁₁×C₂₅	C₄×C₇	semidirect
21. C₃×C₇×C₂₅	C₄×C₁₁	semidirect
28. Dic₃×C₂₅	C₇×C₁₁	direct (N × H)
29. C₁₁×C₂₅	C₇×Dic₃	direct (N × H)
30. C₃×C₇×C₁₁	C₄×C₂₅	semidirect
33. C₇×C₂₅	C₁₁×Dic₃	direct (N × H)
38. C₁₁×Dic₃	C₇×C₂₅	direct (N × H)
42. C₇×Dic₃	C₁₁×C₂₅	direct (N × H)
43. C₇×C₁₁	Dic₃×C₂₅	direct (N × H)
44. C₃×C₂₅	C₄×C₇×C₁₁	semidirect
53. C₃×C₁₁	C₄×C₇×C₂₅	semidirect
56. C₂₅	C₇×C₁₁×Dic₃	direct (N × H)
58. C₃×C₇	C₄×C₁₁×C₂₅	semidirect
62. Dic₃	C₇×C₁₁×C₂₅	direct (N × H)
63. C₁₁	C₇×Dic₃×C₂₅	direct (N × H)
65. C₇	C₁₁×Dic₃×C₂₅	direct (N × H)
69. C₃	C₄×C₇×C₁₁×C₂₅	semidirect

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
C₄×C₇×C₁₁×C₂₅	3
C₅×C₇×C₁₁×Dic₃	5
C₁₁×Dic₃×C₂₅	7
C₇×Dic₃×C₂₅	11

Subgroups — C7×C11×Dic3×C25 #37528201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×Dic₃×C₂₅ #37528201