Subgroups — #11765242

Order 1120.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587989	C₂	1	2	yes	maximal, complemented
2	C₅×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587904	C₂	1	2	yes	maximal, complemented
4	Dic₁₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×C₇×D₄	C₂²	1	2	yes	—
7	C₂²⋊D₃₅	—	2	2	no	—
8	C₂×Dic₃₅	—	2	2	no	—
9	C₄×D₃₅	C₂²	1	1	yes	characteristic
10	Dic₇₀	C₂²	1	2	yes	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇⋊#168	C₂²	1	1	yes	characteristic
13	#6475	—	5	1	no	maximal, Hall
14	#4058	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	—	2	2	no	—
16	C₂×D₃₅	D₄	1	1	yes	characteristic
17	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
18	Dic₃₅	—	2	2	no	—
19	Dic₃₅	D₄	1	1	yes	characteristic
20	#1159	—	5	2	no	—
21	C₇×D₈	D₅	1	1	yes	characteristic, complemented
22	#1142	—	5	2	no	—
23	Dic₂₈	—	5	1	no	—
24	C₈×D₇	—	5	1	no	—
25	#711	—	7	2	no	—
26	C₅×D₈	D₇	1	1	yes	characteristic, complemented
27	#687	—	7	2	no	—
28	Dic₂₀	—	7	1	no	—
29	C₈×D₅	—	7	1	no	—
30	C₂×C₅×C₇	—	4	2	no	—
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	D₃₅	—	2	1	no	—
33	C₇×D₄	C₂×D₅	1	2	yes	—
34	C₂²⋊D₇	—	10	2	no	—
35	C₂×Dic₇	—	10	2	no	—
36	C₄×D₇	—	5	1	no	—
37	Dic₁₄	—	5	2	no	—
38	C₇×C₈	C₂×D₅	1	1	yes	characteristic
39	C₇⋊C₈	—	5	1	no	—
40	C₅×D₄	C₂×D₇	1	2	yes	—
41	C₂²⋊D₅	—	14	2	no	—
42	C₂×Dic₅	—	14	2	no	—
43	C₄×D₅	—	7	1	no	—
44	Dic₁₀	—	7	2	no	—
45	C₅×C₈	C₂×D₇	1	1	yes	characteristic
46	#168	—	7	1	no	—
47	C₅×C₇	#135	1	1	yes	characteristic, complemented, Hall
48	#135	—	35	1	no	Sylow
49	C₂²×C₇	—	2	2	no	—
50	C₂×D₇	—	5	1	no	—
51	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
52	Dic₇	—	5	1	no	—
53	Dic₇	—	10	2	no	—
54	C₂²×C₅	—	2	2	no	—
55	C₂×D₅	—	7	1	no	—
56	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
57	Dic₅	—	7	1	no	—
58	Dic₅	—	14	2	no	—
59	#41	—	35	2	no	—
60	Q₁₆	—	35	1	no	—
61	SD₁₆	—	35	2	no	—
62	D₈	D₃₅	1	1	yes	characteristic, complemented
63	C₂×C₈	—	35	1	no	—
64	C₂×C₇	—	4	2	no	—
65	C₂×C₇	D₄×D₅	1	1	yes	characteristic
66	D₇	—	10	1	no	—
67	C₂×C₅	—	4	2	no	—
68	C₂×C₅	D₄×D₇	1	1	yes	characteristic
69	D₅	—	14	1	no	—
70	Q₈	—	35	2	no	—
71	D₄	—	70	2	no	—
72	D₄	C₂×D₃₅	1	2	yes	—
73	C₂×C₄	—	35	1	no	—
74	C₂×C₄	—	70	2	no	—
75	C₈	—	35	1	no	—
76	C₈	C₂×D₃₅	1	1	yes	characteristic
77	C₇	#4058	1	1	yes	characteristic, complemented, Sylow
78	C₅	#6475	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	2	2	no	—
80	C₂²	—	35	1	no	—
81	C₄	—	35	1	no	—
82	C₄	—	70	2	no	—
83	C₄	C₂²×D₃₅	1	1	yes	characteristic
84	C₂	—	4	2	no	—
85	C₂	—	70	1	no	—
86	C₂	D₄×D₃₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₅
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂²×D₃₅
Fitting	C₅×C₇×D₈	C₂
socle	C₂×C₅×C₇	C₂×D₄
hypercenter	D₈	D₃₅
hypocenter	C₅×C₇	#135
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #10587989	C₂	semidirect
2. C₅×C₇×D₈	C₂	semidirect
3. #10587904	C₂	semidirect
4. Dic₁₄₀	C₂	semidirect
5. C₈×D₃₅	C₂	semidirect
21. C₇×D₈	D₅	semidirect
26. C₅×D₈	D₇	semidirect
47. C₅×C₇	#135	semidirect
62. D₈	D₃₅	semidirect
77. C₇	#4058	semidirect
78. C₅	#6475	semidirect

Maximal subgroups

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

subgroup	index
#10587989	2
C₅×C₇×D₈	2
#10587904	2
Dic₁₄₀	2
C₈×D₃₅	2
#6475	5
#4058	7