Subgroups — D₇×C₅⋊(C₁₃⋊D₁₃) #37556902

Order 23660.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₅⋊(C₁₃⋊D₁₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(C₇⋊(C₁₃⋊D₁₃))	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×C₁₃⋊D₁₃	—	5	1	no	maximal, Hall
6	C₂×C₅⋊(C₁₃⋊D₁₃)	—	7	1	no	maximal, Hall
7	C₇⋊(C₁₃⋊D₁₃)	—	5	1	no	—
8	C₁₃²×D₇	D₅	1	1	yes	characteristic, complemented
9	C₇×C₁₃⋊D₁₃	—	5	1	no	—
10	D₇×D₆₅	—	13	14	no	maximal
11	C₂×C₅×C₁₃²	—	7	1	no	—
12	C₅⋊(C₁₃⋊D₁₃)	—	7	1	no	—
13	C₅⋊(C₁₃⋊D₁₃)	D₇	1	1	yes	characteristic, direct product factor
14	C₇×C₁₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	D₄₅₅	—	13	14	no	—
16	C₇×D₆₅	—	13	14	no	—
17	C₅×C₁₃×D₇	D₁₃	1	14	yes	complemented
18	C₅×C₁₃²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₃⋊D₁₃	—	35	1	no	Hall
20	C₅×C₇×C₁₃	C₂×D₁₃	1	14	yes	complemented
21	D₇×D₁₃	—	65	14	no	—
22	C₂×C₁₃²	—	7	1	no	—
23	C₁₃⋊D₁₃	—	5	1	no	—
24	C₁₃⋊D₁₃	—	35	1	no	—
25	C₂×D₆₅	—	91	14	no	—
26	D₉₁	—	65	14	no	—
27	C₇×D₁₃	—	65	14	no	—
28	C₁₃×D₇	D₆₅	1	14	yes	complemented
29	C₁₃²	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
30	D₅×D₇	—	169	1	no	Hall
31	C₂×C₅×C₁₃	—	7	14	no	—
32	D₆₅	—	13	14	no	—
33	D₆₅	—	91	14	no	—
34	C₇×C₁₃	C₂×D₆₅	1	14	yes	complemented
35	D₃₅	—	169	1	no	—
36	C₅×D₇	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
37	C₇×D₅	—	169	1	no	—
38	C₅×C₁₃	D₇×D₁₃	1	14	yes	complemented
39	C₂×D₁₃	—	455	14	no	—
40	C₅×C₇	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×D₇	—	845	1	no	Hall
42	C₂×C₁₃	—	7	14	no	—
43	D₁₃	—	65	14	no	—
44	D₁₃	—	455	14	no	—
45	C₂×D₅	—	1183	1	no	Hall
46	C₂×C₇	—	845	1	no	—
47	D₇	—	845	1	no	—
48	D₇	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor
49	C₁₃	D₇×D₆₅	1	14	yes	complemented
50	C₂×C₅	—	7	1	no	—
51	D₅	—	1183	1	no	—
52	D₅	—	169	1	no	—
53	C₇	C₂×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, complemented, Sylow
54	C₅	D₇×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	5915	1	no	Sylow
56	C₂	—	7	1	no	—
57	C₂	—	5915	1	no	—
58	C₂	—	845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₃²	C₂²
LCS	G ▷ C₅×C₇×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃²×D₇	C₂	semidirect
2. C₇×C₅⋊(C₁₃⋊D₁₃)	C₂	semidirect
3. C₅⋊(C₇⋊(C₁₃⋊D₁₃))	C₂	semidirect
4. C₅×C₇×C₁₃²	C₂²	semidirect
8. C₁₃²×D₇	D₅	semidirect
13. C₅⋊(C₁₃⋊D₁₃)	D₇	direct (N × H)
14. C₇×C₁₃²	C₂×D₅	semidirect
17. C₅×C₁₃×D₇	D₁₃	semidirect
18. C₅×C₁₃²	C₂×D₇	semidirect
20. C₅×C₇×C₁₃	C₂×D₁₃	semidirect
28. C₁₃×D₇	D₆₅	semidirect
29. C₁₃²	D₅×D₇	semidirect
34. C₇×C₁₃	C₂×D₆₅	semidirect
36. C₅×D₇	C₁₃⋊D₁₃	semidirect
38. C₅×C₁₃	D₇×D₁₃	semidirect
40. C₅×C₇	C₂×C₁₃⋊D₁₃	semidirect
48. D₇	C₅⋊(C₁₃⋊D₁₃)	direct (N × H)
49. C₁₃	D₇×D₆₅	semidirect
53. C₇	C₂×C₅⋊(C₁₃⋊D₁₃)	semidirect
54. C₅	D₇×C₁₃⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃²×D₇	2
C₇×C₅⋊(C₁₃⋊D₁₃)	2
C₅⋊(C₇⋊(C₁₃⋊D₁₃))	2
D₇×C₁₃⋊D₁₃	5
C₂×C₅⋊(C₁₃⋊D₁₃)	7
D₇×D₆₅	13

Subgroups — D7×C5⋊(C13⋊D13) #37556902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₅⋊(C₁₃⋊D₁₃) #37556902