Subgroups — C₇×C₅⋊((C₁₃⋊C₃)⋊D₇) #34062126

Order 19110.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×(C₁₃⋊C₃)⋊D₇	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊((C₁₃⋊C₃)⋊D₇)	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₅⋊(D₁₃⋊C₃)	—	7	1	no	maximal
7	C₇²×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₃₅	—	13	1	no	maximal, Hall
9	C₅×C₇×C₁₃⋊C₃	—	2	3	no	—
10	C₅×C₇×C₁₃⋊C₃	D₇	1	1	yes	characteristic, complemented
11	C₅×C₇×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₉₁	—	5	1	no	Hall
13	D₄₅₅	C₃×C₇	1	1	yes	characteristic, complemented
14	C₇×D₆₅	—	7	1	no	—
15	C₃×C₅×C₇²	—	13	1	no	Hall
16	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
17	(C₁₃⋊C₃)⋊D₇	—	5	1	no	—
18	C₇×D₁₃⋊C₃	—	35	1	no	—
19	C₇×D₃₅	—	39	1	no	Hall
20	C₅×C₇×C₁₃	—	2	3	no	—
21	C₅×C₇×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₅⋊(D₁₃⋊C₃)	—	7	1	no	Hall
24	C₃×C₇×D₇	—	65	1	no	Hall
25	C₇×C₁₃⋊C₃	—	2	3	no	—
26	C₇×C₁₃⋊C₃	C₇×D₅	1	1	yes	characteristic, complemented
27	C₇×C₁₃⋊C₃	D₃₅	1	1	yes	characteristic, complemented
28	C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃₅	—	13	1	no	—
30	C₃×C₇×D₅	—	91	1	no	—
31	C₅×C₁₃⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
32	D₉₁	—	5	1	no	—
33	C₇×D₁₃	—	35	1	no	—
34	C₃×C₇²	—	13	1	no	Hall
35	D₆₅	—	7	1	no	Hall
36	C₃×C₅×C₇	—	13	1	no	—
37	C₃×C₅×C₇	—	13	1	no	—
38	C₃×C₅×C₇	—	26	3	no	—
39	C₇×D₇	—	195	1	no	Hall
40	C₇×C₁₃	—	2	3	no	—
41	C₇×C₁₃	C₃×C₇×D₅	1	1	yes	characteristic, complemented
42	C₇×C₁₃	C₃×D₃₅	1	1	yes	characteristic, complemented
43	D₁₃⋊C₃	—	35	1	no	Hall
44	D₃₅	—	39	1	no	—
45	C₇×D₅	—	273	1	no	—
46	C₅×C₁₃	C₃×C₇×D₇	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₇	—	455	1	no	—
49	C₃×D₇	—	65	1	no	—
50	C₁₃⋊C₃	C₇×D₃₅	1	1	yes	characteristic, complemented, Hall
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
53	C₅×C₇	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
54	C₃×D₅	—	91	1	no	Hall
55	D₁₃	—	35	1	no	Hall
56	C₃×C₇	—	13	1	no	—
57	C₃×C₇	—	13	1	no	—
58	C₃×C₇	—	26	3	no	—
59	C₃×C₅	—	13	1	no	Hall
60	C₂×C₇	—	1365	1	no	—
61	D₇	—	195	1	no	—
62	C₁₃	C₃×C₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	273	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	C₇×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
66	C₇	C₅⋊((C₁₃⋊C₃)⋊D₇)	1	1	yes	characteristic, direct product factor
67	C₂×C₃	—	455	1	no	Hall
68	C₅	C₇×(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	13	1	no	Sylow
70	C₂	—	1365	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₅⋊((C₁₃⋊C₃)⋊D₇)
commutator, cosocle, hypocenter	C₅×C₇×C₁₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇²×C₁₃⋊C₃	C₂	semidirect
2. C₇×D₄₅₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
5. C₅⋊((C₁₃⋊C₃)⋊D₇)	C₇	direct (N × H)
7. C₇²×C₁₃⋊C₃	D₅	semidirect
10. C₅×C₇×C₁₃⋊C₃	D₇	semidirect
11. C₅×C₇×C₁₃⋊C₃	C₂×C₇	semidirect
13. D₄₅₅	C₃×C₇	semidirect
16. C₇²×C₁₃	C₃×D₅	semidirect
21. C₅×C₇×C₁₃	C₃×D₇	semidirect
22. C₅×C₇×C₁₃	C₂×C₃×C₇	semidirect
26. C₇×C₁₃⋊C₃	C₇×D₅	semidirect
27. C₇×C₁₃⋊C₃	D₃₅	semidirect
28. C₅×C₇²	D₁₃⋊C₃	semidirect
31. C₅×C₁₃⋊C₃	C₇×D₇	semidirect
41. C₇×C₁₃	C₃×C₇×D₅	semidirect
42. C₇×C₁₃	C₃×D₃₅	semidirect
46. C₅×C₁₃	C₃×C₇×D₇	semidirect
47. C₇²	C₅⋊(D₁₃⋊C₃)	semidirect
50. C₁₃⋊C₃	C₇×D₃₅	semidirect
52. C₅×C₇	C₇×D₁₃⋊C₃	semidirect
53. C₅×C₇	(C₁₃⋊C₃)⋊D₇	semidirect
62. C₁₃	C₃×C₇×D₃₅	semidirect
65. C₇	C₇×C₅⋊(D₁₃⋊C₃)	semidirect
66. C₇	C₅⋊((C₁₃⋊C₃)⋊D₇)	direct (N × H)
68. C₅	C₇×(C₁₃⋊C₃)⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇²×C₁₃⋊C₃	2
C₇×D₄₅₅	3
C₇×(C₁₃⋊C₃)⋊D₇	5
C₅⋊((C₁₃⋊C₃)⋊D₇)	7
C₇×C₅⋊(D₁₃⋊C₃)	7
C₃×C₇×D₃₅	13

Subgroups — C7×C5⋊((C13⋊C3)⋊D7) #34062126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₅⋊((C₁₃⋊C₃)⋊D₇) #34062126