Subgroups — C₂×#10587852 #11764819

Order 1120.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10587852	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₅	—	2	1	no	—
7	Dic₇₀	—	2	1	no	—
8	Dic₇₀	C₂²	1	2	yes	—
9	C₂×C₇×Dic₅	—	2	1	no	—
10	C₇×Dic₁₀	—	2	1	no	—
11	C₇×Dic₁₀	C₂²	1	2	yes	—
12	C₅×C₇⋊C₈	C₂²	1	2	yes	—
13	C₂×#1144	—	5	1	no	maximal, Hall
14	C₂×Dic₂₀	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
16	C₄×C₅×C₇	D₄	1	1	yes	characteristic
17	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
18	Dic₃₅	—	2	2	no	—
19	C₇×Dic₅	—	2	2	no	—
20	C₂×C₇×Q₈	—	5	1	no	—
21	C₂×Dic₁₄	—	5	1	no	—
22	#1144	—	5	4	no	—
23	C₂×C₇⋊C₈	D₅	1	1	yes	characteristic
24	C₂×Dic₁₀	—	7	1	no	—
25	C₂×Dic₁₀	D₇	1	1	yes	characteristic
26	C₂×C₅×C₈	—	7	1	no	—
27	Dic₂₀	—	7	4	no	—
28	C₂×C₅×C₇	Q₁₆	1	2	yes	complemented
29	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
30	C₇×Q₈	—	5	2	no	—
31	C₇×Q₈	—	10	1	no	—
32	C₂×C₄×C₇	—	10	1	no	—
33	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
34	C₂×Dic₇	—	10	1	no	—
35	Dic₁₄	—	5	2	no	—
36	Dic₁₄	—	10	1	no	—
37	C₇⋊C₈	C₂×D₅	1	2	yes	—
38	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
39	C₂×Dic₅	—	2	1	no	—
40	C₂×Dic₅	—	14	1	no	—
41	Dic₁₀	—	2	1	no	—
42	Dic₁₀	—	7	2	no	—
43	Dic₁₀	—	14	1	no	—
44	Dic₁₀	C₂×D₇	1	2	yes	—
45	C₅×C₈	—	7	2	no	—
46	C₅×C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×Q₁₆	—	35	1	no	Sylow
48	C₂²×C₇	D₂₀	1	1	yes	characteristic
49	C₄×C₇	—	10	2	no	—
50	C₄×C₇	D₂₀	1	1	yes	characteristic
51	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
52	Dic₇	—	10	2	no	—
53	C₂²×C₅	C₂²⋊D₇	1	1	yes	characteristic
54	C₄×C₅	C₂²⋊D₇	1	1	yes	characteristic
55	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
56	Dic₅	—	2	2	no	—
57	Dic₅	—	14	2	no	—
58	C₂×Q₈	—	5	1	no	—
59	C₂×Q₈	—	35	1	no	—
60	Q₁₆	—	35	4	no	—
61	C₂×C₈	—	7	1	no	—
62	C₂×C₇	Dic₂₀	1	2	yes	complemented
63	C₂×C₇	C₂×D₂₀	1	1	yes	characteristic
64	C₂×C₅	#1144	1	2	yes	complemented
65	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
66	Q₈	—	5	2	no	—
67	Q₈	—	10	1	no	—
68	Q₈	—	35	2	no	—
69	Q₈	—	70	1	no	—
70	C₂×C₄	—	10	1	no	—
71	C₂×C₄	—	70	1	no	—
72	C₂×C₄	D₅×D₇	1	1	yes	characteristic
73	C₈	—	7	2	no	—
74	C₇	C₂×Dic₂₀	1	1	yes	characteristic, complemented, Sylow
75	C₅	C₂×#1144	1	1	yes	characteristic, complemented, Sylow
76	C₂²	#63307	1	1	yes	characteristic
77	C₄	—	10	2	no	—
78	C₄	—	70	2	no	—
79	C₄	#63307	1	1	yes	characteristic
80	C₄	C₂×D₅×D₇	1	1	yes	characteristic
81	C₂	#10587852	1	2	yes	direct product factor
82	C₂	C₂×#63307	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63307
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂×D₅×D₇
Fitting	C₂×C₄×C₅×C₇	C₂²
socle, prime radical	C₂²×C₅×C₇	D₄
hypercenter	C₂×C₄	D₅×D₇
hypocenter	C₅×C₇	C₂×Q₁₆
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
4. #10587852	C₂	direct (N × H)
28. C₂×C₅×C₇	Q₁₆	semidirect
46. C₅×C₇	C₂×Q₁₆	semidirect
62. C₂×C₇	Dic₂₀	semidirect
64. C₂×C₅	#1144	semidirect
74. C₇	C₂×Dic₂₀	semidirect
75. C₅	C₂×#1144	semidirect
81. C₂	#10587852	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₇₀	2
C₂×C₇×Dic₁₀	2
C₂×C₅×C₇⋊C₈	2
#10587852	2
C₂×#1144	5
C₂×Dic₂₀	7

Subgroups — C2×#10587852 #11764819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587852 #11764819