Subgroups — #11764706

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587950	C₂	1	2	yes	maximal, complemented
2	C₈×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587841	C₂	1	2	yes	maximal, complemented
6	C₂×D₅×D₇	—	2	2	no	—
7	C₄×D₃₅	C₂²	1	1	yes	characteristic
8	C₇×D₂₀	C₂²	1	2	yes	complemented
9	C₅×D₂₈	C₂²	1	2	yes	complemented
10	#63305	—	2	2	no	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
12	C₇⋊#168	C₂²	1	1	yes	characteristic, complemented
13	D₇×D₈	—	5	1	no	maximal, Hall
14	D₅×D₈	—	7	1	no	maximal, Hall
15	C₂×D₃₅	D₄	1	1	yes	characteristic
16	C₂×C₇×D₅	—	2	2	no	—
17	C₂×C₅×D₇	—	2	2	no	—
18	D₅×D₇	—	4	4	no	—
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	Dic₃₅	D₄	1	1	yes	characteristic
21	D₄×D₇	—	5	2	no	—
22	C₇×D₈	—	5	1	no	—
23	#1141	—	5	2	no	—
24	D₅₆	D₅	1	1	yes	characteristic, complemented
25	C₈×D₇	—	5	1	no	—
26	D₄×D₅	—	7	2	no	—
27	C₅×D₈	—	7	1	no	—
28	#686	—	7	2	no	—
29	D₄₀	D₇	1	1	yes	characteristic, complemented
30	C₈×D₅	—	7	1	no	—
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	D₃₅	D₈	1	2	yes	complemented
33	C₅×D₇	—	4	2	no	—
34	C₇×D₅	—	4	2	no	—
35	C₂²×D₇	—	10	2	no	—
36	C₇×D₄	—	5	2	no	—
37	C₂²⋊D₇	—	10	2	no	—
38	D₂₈	C₂×D₅	1	2	yes	complemented
39	C₄×D₇	—	5	1	no	—
40	C₇×C₈	C₂×D₅	1	1	yes	characteristic, complemented
41	C₇⋊C₈	—	5	1	no	—
42	C₂²×D₅	—	14	2	no	—
43	C₅×D₄	—	7	2	no	—
44	C₂²⋊D₅	—	14	2	no	—
45	D₂₀	C₂×D₇	1	2	yes	complemented
46	C₄×D₅	—	7	1	no	—
47	C₅×C₈	C₂×D₇	1	1	yes	characteristic, complemented
48	#168	—	7	1	no	—
49	C₅×C₇	C₂×D₈	1	1	yes	characteristic, complemented, Hall
50	C₂×D₈	—	35	1	no	Sylow
51	C₂²×C₇	—	10	2	no	—
52	C₂×D₇	—	2	2	no	—
53	C₂×D₇	—	5	1	no	—
54	C₂×D₇	—	20	4	no	—
55	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
56	Dic₇	—	5	1	no	—
57	C₂²×C₅	—	14	2	no	—
58	C₂×D₅	—	2	2	no	—
59	C₂×D₅	—	7	1	no	—
60	C₂×D₅	—	28	4	no	—
61	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
62	Dic₅	—	7	1	no	—
63	C₂×D₄	—	35	2	no	—
64	D₈	—	5	1	no	—
65	D₈	—	7	1	no	—
66	D₈	—	35	2	no	—
67	C₂×C₈	—	35	1	no	—
68	C₂×C₇	—	20	2	no	—
69	C₂×C₇	D₄×D₅	1	1	yes	characteristic
70	D₇	—	4	2	no	—
71	D₇	—	5	2	no	—
72	C₂×C₅	—	28	2	no	—
73	C₂×C₅	D₄×D₇	1	1	yes	characteristic
74	D₅	—	4	2	no	—
75	D₅	—	7	2	no	—
76	C₂³	—	70	2	no	—
77	D₄	—	5	2	no	—
78	D₄	—	7	2	no	—
79	D₄	—	70	2	no	—
80	C₂×C₄	—	35	1	no	—
81	C₈	—	35	1	no	—
82	C₈	D₅×D₇	1	1	yes	characteristic, complemented
83	C₇	D₅×D₈	1	1	yes	characteristic, complemented, Sylow
84	C₅	D₇×D₈	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	10	2	no	—
86	C₂²	—	14	2	no	—
87	C₂²	—	35	1	no	—
88	C₂²	—	140	4	no	—
89	C₄	—	35	1	no	—
90	C₄	C₂×D₅×D₇	1	1	yes	characteristic
91	C₂	—	20	2	no	—
92	C₂	—	28	2	no	—
93	C₂	—	35	2	no	—
94	C₂	#10587950	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10587950
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂×D₅×D₇
Fitting	C₅×C₇×C₈	C₂²
socle	C₂×C₅×C₇	C₂×D₄
hypercenter	C₈	D₅×D₇
hypocenter	C₅×C₇	C₂×D₈
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. #10587950	C₂	semidirect
2. C₈×D₃₅	C₂	semidirect
3. C₇×D₄₀	C₂	semidirect
4. C₅×D₅₆	C₂	semidirect
5. #10587841	C₂	semidirect
8. C₇×D₂₀	C₂²	semidirect
9. C₅×D₂₈	C₂²	semidirect
11. C₅×C₇×C₈	C₂²	semidirect
12. C₇⋊#168	C₂²	semidirect
24. D₅₆	D₅	semidirect
29. D₄₀	D₇	semidirect
32. D₃₅	D₈	semidirect
38. D₂₈	C₂×D₅	semidirect
40. C₇×C₈	C₂×D₅	semidirect
45. D₂₀	C₂×D₇	semidirect
47. C₅×C₈	C₂×D₇	semidirect
49. C₅×C₇	C₂×D₈	semidirect
82. C₈	D₅×D₇	semidirect
83. C₇	D₅×D₈	semidirect
84. C₅	D₇×D₈	semidirect

Maximal subgroups

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

subgroup	index
#10587950	2
C₈×D₃₅	2
C₇×D₄₀	2
C₅×D₅₆	2
#10587841	2
D₇×D₈	5
D₅×D₈	7