Subgroups — C₇×#4294⋊Dic₅ #37560905

Order 23940.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×Dic₉₅	C₃	1	1	yes	maximal, characteristic
3	C₅×C₇×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×#4294⋊C₄	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
6	#4294⋊Dic₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×Dic₉₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×#4294	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
10	C₂×C₅×#4294	C₂×C₇	1	1	yes	characteristic
11	C₃×C₇×Dic₁₉	—	5	1	no	—
12	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic
13	C₇×C₉×Dic₅	—	19	1	no	maximal, Hall
14	C₇×#4294	Dic₅	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₉₅	C₃×C₇	1	1	yes	characteristic
16	C₅×#4294	C₄×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic
18	#4294⋊C₄	—	5	1	no	Hall
19	C₅×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇×C₉	—	19	1	no	—
21	C₂×C₃×C₅×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic
22	C₇×Dic₁₉	—	5	1	no	Hall
23	C₃×C₇×Dic₅	—	57	1	no	—
24	C₃×C₇×C₁₉	C₃×Dic₅	1	1	yes	characteristic
25	Dic₉₅	C₇×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×#4294	C₇×D₅	1	1	yes	characteristic
27	C₅×C₇×C₉	—	19	1	no	Hall
28	C₃×C₅×C₁₉	C₃×C₄×C₇	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	D₁₉⋊C₃	1	1	yes	characteristic
33	C₂×C₅×C₁₉	C₂×C₇×C₉	1	1	yes	characteristic
34	C₉×Dic₅	—	19	1	no	Hall
35	#4294	C₇×Dic₅	1	1	yes	characteristic, complemented, Hall
36	C₇×Dic₅	—	57	1	no	Hall
37	C₇×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇×C₉	—	19	1	no	—
39	C₂×C₃×C₁₉	C₃×C₇×D₅	1	1	yes	characteristic
40	C₃×C₅×C₇	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic
41	C₅×C₁₉	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Hall
42	C₂×C₅×C₉	—	19	1	no	—
43	C₃×C₄×C₇	—	95	1	no	—
44	Dic₁₉	—	5	1	no	Hall
45	C₂×C₅×C₇	#4294⋊C₂	1	1	yes	characteristic
46	C₇×C₉	—	19	1	no	Hall
47	C₃×Dic₅	—	57	1	no	—
48	C₃×C₁₉	C₃×C₇×Dic₅	1	1	yes	characteristic
49	C₅×C₉	—	19	1	no	Hall
50	C₂×C₃×C₇	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic
51	C₂×C₁₉	C₇×C₉×D₅	1	1	yes	characteristic
52	C₄×C₉	—	95	1	no	Hall
53	C₅×C₇	#4294⋊C₄	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	C₇×D₁₉⋊C₃	1	1	yes	characteristic
55	C₄×C₇	—	95	1	no	Hall
56	C₃×C₇	(C₁₉⋊C₃)⋊Dic₅	1	1	yes	characteristic
57	Dic₅	—	57	1	no	Hall
58	C₁₉	C₇×C₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₉	—	19	1	no	—
60	C₃×C₅	C₇×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic
61	C₂×C₇	C₅⋊(#4294⋊C₂)	1	1	yes	characteristic
62	C₃×C₄	—	95	1	no	—
63	C₂×C₅	C₇×#4294⋊C₂	1	1	yes	characteristic
64	C₉	—	19	1	no	Sylow
65	C₇	#4294⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	C₇×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic
67	C₅	C₇×#4294⋊C₄	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	95	1	no	Sylow
69	C₃	C₇×(C₁₉⋊C₃)⋊Dic₅	1	1	yes	characteristic
70	C₂	C₇×C₅⋊(#4294⋊C₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	C₅⋊(D₁₉⋊C₃)
commutator, hypocenter	C₅×C₁₉	C₄×C₇×C₉
Frattini	C₂×C₃	C₇×C₅⋊(D₁₉⋊C₃)
Fitting, socle, prime radical	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₅×C₁₉	C₂×C₃×C₇
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×#4294	C₄	semidirect
6. #4294⋊Dic₅	C₇	direct (N × H)
7. C₇×Dic₉₅	C₉	semidirect
14. C₇×#4294	Dic₅	semidirect
16. C₅×#4294	C₄×C₇	semidirect
19. C₅×C₇×C₁₉	C₄×C₉	semidirect
25. Dic₉₅	C₇×C₉	semidirect
35. #4294	C₇×Dic₅	semidirect
37. C₇×C₁₉	C₉×Dic₅	semidirect
41. C₅×C₁₉	C₄×C₇×C₉	semidirect
53. C₅×C₇	#4294⋊C₄	semidirect
58. C₁₉	C₇×C₉×Dic₅	semidirect
65. C₇	#4294⋊Dic₅	direct (N × H)
67. C₅	C₇×#4294⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×#4294	2
C₃×C₇×Dic₉₅	3
C₇×#4294⋊C₄	5
#4294⋊Dic₅	7
C₇×C₉×Dic₅	19

Subgroups — C7×#4294⋊Dic5 #37560905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4294⋊Dic₅ #37560905