Subgroups — C₂×#10587848 #11764815

Order 1120.

136 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, complemented
2	C₂×C₇×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587848	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×D₅	—	2	1	no	—
6	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₅	—	2	1	no	—
8	Dic₇₀	—	2	1	no	—
9	Dic₇₀	C₂²	1	2	yes	complemented
10	C₇×D₂₀	—	2	1	no	—
11	C₇×D₂₀	C₂²	1	2	yes	—
12	C₅×C₇⋊C₈	C₂²	1	2	yes	complemented
13	C₂×#1142	—	5	1	no	maximal, Hall
14	C₂×#677	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
16	C₂×C₇×D₅	—	2	2	no	—
17	C₂×C₇×D₅	—	4	2	no	—
18	C₄×C₅×C₇	D₄	1	1	yes	characteristic
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	Dic₃₅	—	2	2	no	—
21	C₂×C₇×D₄	—	5	1	no	—
22	C₂×Dic₁₄	—	5	1	no	—
23	#1142	—	5	4	no	—
24	C₂×C₇⋊C₈	D₅	1	1	yes	characteristic, complemented
25	C₂×D₂₀	D₇	1	1	yes	characteristic
26	C₂×Dic₁₀	—	7	1	no	—
27	C₂×C₅×C₈	—	7	1	no	—
28	#677	—	7	4	no	—
29	C₂×C₅×C₇	SD₁₆	1	2	yes	complemented
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	C₇×D₅	—	4	2	no	—
32	C₂³×C₇	—	10	1	no	—
33	C₇×D₄	—	5	2	no	—
34	C₇×D₄	—	10	1	no	—
35	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
36	C₂×Dic₇	—	10	1	no	—
37	Dic₁₄	—	5	2	no	—
38	Dic₁₄	—	10	1	no	—
39	C₇⋊C₈	C₂×D₅	1	2	yes	complemented
40	C₂²×D₅	—	2	1	no	—
41	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
42	C₂×Dic₅	—	14	1	no	—
43	D₂₀	—	2	1	no	—
44	D₂₀	C₂×D₇	1	2	yes	—
45	Dic₁₀	—	7	2	no	—
46	Dic₁₀	—	14	1	no	—
47	C₅×C₈	—	7	2	no	—
48	C₅×C₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
49	C₂×SD₁₆	—	35	1	no	Sylow
50	C₂²×C₇	—	10	2	no	—
51	C₂²×C₇	—	20	2	no	—
52	C₂²×C₇	D₂₀	1	1	yes	characteristic
53	C₄×C₇	D₂₀	1	1	yes	characteristic
54	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
55	Dic₇	—	10	2	no	—
56	C₂²×C₅	C₂²⋊D₇	1	1	yes	characteristic
57	C₂×D₅	—	2	2	no	—
58	C₂×D₅	—	4	2	no	—
59	C₄×C₅	C₂²⋊D₇	1	1	yes	characteristic
60	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
61	Dic₅	—	14	2	no	—
62	C₂×Q₈	—	35	1	no	—
63	C₂×D₄	—	5	1	no	—
64	SD₁₆	—	35	4	no	—
65	C₂×C₈	—	7	1	no	—
66	C₂×C₇	—	20	2	no	—
67	C₂×C₇	#677	1	2	yes	complemented
68	C₂×C₇	C₂×D₂₀	1	1	yes	characteristic
69	C₂×C₅	#1142	1	2	yes	complemented
70	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
71	D₅	—	4	2	no	—
72	C₂³	—	10	1	no	—
73	Q₈	—	35	2	no	—
74	Q₈	—	70	1	no	—
75	D₄	—	5	2	no	—
76	D₄	—	10	1	no	—
77	C₂×C₄	—	70	1	no	—
78	C₂×C₄	D₅×D₇	1	1	yes	characteristic
79	C₈	—	7	2	no	—
80	C₇	C₂×#677	1	1	yes	characteristic, complemented, Sylow
81	C₅	C₂×#1142	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	10	2	no	—
83	C₂²	—	20	2	no	—
84	C₂²	#63307	1	1	yes	characteristic
85	C₄	—	70	2	no	—
86	C₄	#63307	1	1	yes	characteristic
87	C₄	C₂×D₅×D₇	1	1	yes	characteristic
88	C₂	—	20	2	no	—
89	C₂	#10587848	1	2	yes	direct product factor
90	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	C₂²×C₅×C₇	D₄
prime radical	C₂×C₇×D₂₀	C₂
hypercenter	C₂×C₄	D₅×D₇
hypocenter	C₅×C₇	C₂×SD₁₆
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
1. C₂×Dic₇₀	C₂	semidirect
3. C₂×C₅×C₇⋊C₈	C₂	semidirect
4. #10587848	C₂	direct (N × H)
9. Dic₇₀	C₂²	semidirect
12. C₅×C₇⋊C₈	C₂²	semidirect
24. C₂×C₇⋊C₈	D₅	semidirect
29. C₂×C₅×C₇	SD₁₆	semidirect
39. C₇⋊C₈	C₂×D₅	semidirect
48. C₅×C₇	C₂×SD₁₆	semidirect
67. C₂×C₇	#677	semidirect
69. C₂×C₅	#1142	semidirect
80. C₇	C₂×#677	semidirect
81. C₅	C₂×#1142	semidirect
89. C₂	#10587848	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×D₂₀	2
C₂×C₅×C₇⋊C₈	2
#10587848	2
C₂×#1142	5
C₂×#677	7

Subgroups — C2×#10587848 #11764815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587848 #11764815