Subgroups — C₇⋊C₉×Dic₉₅ #37560906

Order 23940.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×Dic₉₅	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₉×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇⋊C₉×Dic₁₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₉×Dic₉₅	—	7	1	no	maximal, Hall
7	C₇×Dic₉₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₉×C₇⋊C₉	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
10	C₂×C₅×C₉×C₁₉	—	7	1	no	—
11	C₃×C₇×Dic₁₉	—	5	1	no	—
12	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic
13	Dic₅×C₇⋊C₉	—	19	1	no	maximal, Hall
14	C₁₉×C₇⋊C₉	Dic₅	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₉₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₅×C₉×C₁₉	—	7	1	no	Hall
17	C₂×C₃×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic
18	C₉×Dic₁₉	—	35	1	no	Hall
19	C₅×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇⋊C₉	D₁₉	1	1	yes	characteristic
21	C₂×C₃×C₅×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₇×Dic₁₉	—	5	1	no	Hall
23	C₃×C₇×Dic₅	—	19	1	no	—
24	C₃×C₇×C₁₉	C₃×Dic₅	1	1	yes	characteristic
25	Dic₉₅	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₉×C₁₉	—	7	1	no	—
27	C₅×C₇⋊C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₅×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₂×C₇×C₁₉	C₉×D₅	1	1	yes	characteristic
30	C₄×C₇⋊C₉	—	95	1	no	Hall
31	C₃×Dic₁₉	—	5	1	no	—
32	C₂×C₃×C₅×C₇	C₃×D₁₉	1	1	yes	characteristic
33	C₂×C₅×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic
34	C₉×Dic₅	—	133	1	no	Hall
35	C₉×C₁₉	—	7	1	no	Hall
36	C₇×Dic₅	—	19	1	no	Hall
37	C₇×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇⋊C₉	D₉₅	1	1	yes	characteristic
39	C₂×C₃×C₁₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₃×C₅×C₇	C₃×Dic₁₉	1	1	yes	characteristic
41	C₅×C₁₉	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
42	C₂×C₅×C₉	—	7	1	no	—
43	C₃×C₄×C₇	—	95	1	no	—
44	Dic₁₉	—	5	1	no	Hall
45	C₂×C₅×C₇	C₉×D₁₉	1	1	yes	characteristic
46	C₇⋊C₉	Dic₉₅	1	1	yes	characteristic, direct product factor, Hall
47	C₃×Dic₅	—	19	1	no	—
48	C₃×C₁₉	Dic₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₅×C₉	—	7	1	no	Hall
50	C₂×C₃×C₇	C₃×D₉₅	1	1	yes	characteristic
51	C₂×C₁₉	D₅×C₇⋊C₉	1	1	yes	characteristic
52	C₄×C₉	—	665	1	no	Hall
53	C₅×C₇	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic
55	C₄×C₇	—	95	1	no	Hall
56	C₃×C₇	C₃×Dic₉₅	1	1	yes	characteristic
57	Dic₅	—	19	1	no	Hall
58	C₁₉	Dic₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₉	—	7	1	no	—
60	C₃×C₅	ΓL(1,𝔽₈)×Dic₁₉	1	1	yes	characteristic
61	C₂×C₇	C₉×D₉₅	1	1	yes	characteristic
62	C₃×C₄	—	95	1	no	—
63	C₂×C₅	D₁₉×C₇⋊C₉	1	1	yes	characteristic
64	C₉	—	7	1	no	Sylow
65	C₇	C₉×Dic₉₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	ΓL(1,𝔽₈)×D₉₅	1	1	yes	characteristic
67	C₅	C₇⋊C₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	95	1	no	Sylow
69	C₃	ΓL(1,𝔽₈)×Dic₉₅	1	1	yes	characteristic
70	C₂	C₇⋊C₉×D₉₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	ΓL(1,𝔽₈)×D₉₅
commutator, hypocenter	C₅×C₇×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₉×C₇⋊C₉	C₄	semidirect
7. C₇×Dic₉₅	C₉	semidirect
14. C₁₉×C₇⋊C₉	Dic₅	semidirect
19. C₅×C₇×C₁₉	C₄×C₉	semidirect
25. Dic₉₅	C₇⋊C₉	direct (N × H)
27. C₅×C₇⋊C₉	Dic₁₉	semidirect
37. C₇×C₁₉	C₉×Dic₅	semidirect
41. C₅×C₁₉	C₄×C₇⋊C₉	semidirect
46. C₇⋊C₉	Dic₉₅	direct (N × H)
53. C₅×C₇	C₉×Dic₁₉	semidirect
58. C₁₉	Dic₅×C₇⋊C₉	semidirect
65. C₇	C₉×Dic₉₅	semidirect
67. C₅	C₇⋊C₉×Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₉×C₇⋊C₉	2
C₃×C₇×Dic₉₅	3
C₇⋊C₉×Dic₁₉	5
C₉×Dic₉₅	7
Dic₅×C₇⋊C₉	19

Subgroups — C7⋊C9×Dic95 #37560906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊C₉×Dic₉₅ #37560906