Subgroups — #37556891

Order 23660.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₄₅₅	C₂	1	2	yes	maximal, complemented
3	C₅×C₇×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₉₁⋊D₁₃	—	5	1	no	maximal, Hall
5	D₆₅⋊D₁₃	—	7	1	no	maximal, Hall
6	C₁₃×D₉₁	—	5	2	no	—
7	C₇×C₁₃⋊D₁₃	D₅	1	1	yes	characteristic, complemented
8	D₁₃×D₃₅	—	13	2	no	maximal
9	C₁₃×D₆₅	—	7	2	no	—
10	C₅×C₁₃⋊D₁₃	D₇	1	1	yes	characteristic, complemented
11	C₇×C₁₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	D₄₅₅	D₁₃	1	2	yes	complemented
13	C₁₃×D₃₅	—	13	2	no	—
14	C₅×C₇×D₁₃	—	13	2	no	—
15	C₅×C₇×D₁₃	—	26	6	no	—
16	C₅×C₁₃²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	D₁₃²	—	35	1	no	Hall
18	C₅×C₇×C₁₃	—	2	6	no	—
19	C₅×C₇×C₁₃	C₂×D₁₃	1	2	yes	complemented
20	D₇×D₁₃	—	65	2	no	—
21	C₁₃⋊D₁₃	D₃₅	1	1	yes	characteristic, complemented
22	C₁₃×D₁₃	—	35	2	no	—
23	D₅×D₁₃	—	91	2	no	—
24	D₉₁	—	5	2	no	—
25	C₇×D₁₃	—	13	2	no	—
26	C₇×D₁₃	—	26	6	no	—
27	C₁₃×D₇	—	65	2	no	—
28	C₁₃²	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₃₅	—	169	1	no	Hall
30	D₆₅	—	7	2	no	—
31	C₅×D₁₃	—	13	2	no	—
32	C₅×D₁₃	—	26	6	no	—
33	D₅×C₁₃	—	91	2	no	—
34	C₇×C₁₃	—	2	6	no	—
35	C₇×C₁₃	D₅×D₁₃	1	2	yes	complemented
36	C₂×C₅×C₇	—	169	1	no	—
37	D₃₅	—	13	2	no	—
38	C₅×C₁₃	—	2	6	no	—
39	C₅×C₁₃	D₇×D₁₃	1	2	yes	complemented
40	C₂×D₁₃	—	455	2	no	—
41	C₅×C₇	D₁₃²	1	1	yes	characteristic, complemented, Hall
42	C₂×D₇	—	845	1	no	Hall
43	C₂×C₁₃	—	455	2	no	—
44	D₁₃	—	13	2	no	—
45	D₁₃	—	26	6	no	—
46	D₁₃	—	35	2	no	—
47	C₂×D₅	—	1183	1	no	Hall
48	C₂×C₇	—	169	1	no	—
49	D₇	—	65	2	no	—
50	C₁₃	—	2	6	no	—
51	C₁₃	D₁₃×D₃₅	1	2	yes	complemented
52	C₂×C₅	—	169	1	no	—
53	D₅	—	91	2	no	—
54	C₇	D₆₅⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
55	C₅	D₉₁⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	5915	1	no	Sylow
57	C₂	—	169	1	no	—
58	C₂	—	455	2	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×C₇×C₁₃⋊D₁₃	C₂	semidirect
2. C₁₃×D₄₅₅	C₂	semidirect
3. C₅×C₇×C₁₃²	C₂²	semidirect
7. C₇×C₁₃⋊D₁₃	D₅	semidirect
10. C₅×C₁₃⋊D₁₃	D₇	semidirect
11. C₇×C₁₃²	C₂×D₅	semidirect
12. D₄₅₅	D₁₃	semidirect
16. C₅×C₁₃²	C₂×D₇	semidirect
19. C₅×C₇×C₁₃	C₂×D₁₃	semidirect
21. C₁₃⋊D₁₃	D₃₅	semidirect
28. C₁₃²	C₂×D₃₅	semidirect
35. C₇×C₁₃	D₅×D₁₃	semidirect
39. C₅×C₁₃	D₇×D₁₃	semidirect
41. C₅×C₇	D₁₃²	semidirect
51. C₁₃	D₁₃×D₃₅	semidirect
54. C₇	D₆₅⋊D₁₃	semidirect
55. C₅	D₉₁⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃⋊D₁₃	2
C₁₃×D₄₅₅	2
D₉₁⋊D₁₃	5
D₆₅⋊D₁₃	7
D₁₃×D₃₅	13