Subgroups — C₂×#10587905 #11765273

Order 1120.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₄₀	C₂	1	1	yes	maximal, characteristic
3	#10587905	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₅	—	2	1	no	—
6	C₅×C₇×Q₈	—	2	1	no	—
7	C₅×C₇×Q₈	C₂²	1	2	yes	complemented
8	C₂×C₄×C₅×C₇	—	2	1	no	—
9	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
10	D₁₄₀	—	2	1	no	—
11	D₁₄₀	C₂²	1	2	yes	—
12	C₇⋊#168	C₂²	1	2	yes	complemented
13	C₂×#1143	—	5	1	no	maximal, Hall
14	C₂×#688	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
16	C₂×D₃₅	—	2	2	no	—
17	C₂×D₃₅	—	4	2	no	—
18	C₄×C₅×C₇	—	2	2	no	—
19	C₄×C₅×C₇	D₄	1	1	yes	characteristic
20	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
21	C₂×C₇×Q₈	D₅	1	1	yes	characteristic, complemented
22	C₂×D₂₈	—	5	1	no	—
23	#1143	—	5	4	no	—
24	C₂×C₇⋊C₈	—	5	1	no	—
25	C₂×C₅×Q₈	D₇	1	1	yes	characteristic, complemented
26	C₂×D₂₀	—	7	1	no	—
27	#688	—	7	4	no	—
28	C₂×#168	—	7	1	no	—
29	C₂×C₅×C₇	SD₁₆	1	2	yes	complemented
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	D₃₅	—	4	2	no	—
32	C₂²×D₇	—	10	1	no	—
33	C₇×Q₈	—	2	1	no	—
34	C₇×Q₈	C₂×D₅	1	2	yes	complemented
35	C₂×C₄×C₇	—	2	1	no	—
36	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
37	D₂₈	—	5	2	no	—
38	D₂₈	—	10	1	no	—
39	C₇⋊C₈	—	5	2	no	—
40	C₂²×D₅	—	14	1	no	—
41	C₅×Q₈	—	2	1	no	—
42	C₅×Q₈	C₂×D₇	1	2	yes	complemented
43	C₂×C₄×C₅	—	2	1	no	—
44	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
45	D₂₀	—	7	2	no	—
46	D₂₀	—	14	1	no	—
47	#168	—	7	2	no	—
48	C₅×C₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
49	C₂×SD₁₆	—	35	1	no	Sylow
50	C₂²×C₇	C₂²⋊D₅	1	1	yes	characteristic
51	C₂×D₇	—	10	2	no	—
52	C₂×D₇	—	20	2	no	—
53	C₄×C₇	—	2	2	no	—
54	C₄×C₇	C₂²⋊D₅	1	1	yes	characteristic
55	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
56	C₂²×C₅	C₂²⋊D₇	1	1	yes	characteristic
57	C₂×D₅	—	14	2	no	—
58	C₂×D₅	—	28	2	no	—
59	C₄×C₅	—	2	2	no	—
60	C₄×C₅	C₂²⋊D₇	1	1	yes	characteristic
61	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
62	C₂×Q₈	D₃₅	1	1	yes	characteristic, complemented
63	C₂×D₄	—	35	1	no	—
64	SD₁₆	—	35	4	no	—
65	C₂×C₈	—	35	1	no	—
66	C₂×C₇	#688	1	2	yes	complemented
67	C₂×C₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
68	D₇	—	20	2	no	—
69	C₂×C₅	#1143	1	2	yes	complemented
70	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
71	D₅	—	28	2	no	—
72	C₂³	—	70	1	no	—
73	Q₈	—	2	1	no	—
74	Q₈	C₂×D₃₅	1	2	yes	complemented
75	D₄	—	35	2	no	—
76	D₄	—	70	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	C₂×D₃₅	1	1	yes	characteristic
79	C₈	—	35	2	no	—
80	C₇	C₂×#688	1	1	yes	characteristic, complemented, Sylow
81	C₅	C₂×#1143	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	70	2	no	—
83	C₂²	—	140	2	no	—
84	C₂²	C₂²⋊D₃₅	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	C₂²⋊D₃₅	1	1	yes	characteristic
87	C₄	C₂²×D₃₅	1	1	yes	characteristic
88	C₂	—	140	2	no	—
89	C₂	#10587905	1	2	yes	direct product factor
90	C₂	C₂×C₂²⋊D₃₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₃₅
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂²×D₃₅
Fitting	C₂×C₅×C₇×Q₈	C₂
socle	C₂²×C₅×C₇	D₄
prime radical	C₂×D₁₄₀	C₂
hypercenter	C₂×Q₈	D₃₅
hypocenter	C₅×C₇	C₂×SD₁₆
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇×Q₈	C₂	semidirect
3. #10587905	C₂	direct (N × H)
4. C₂×C₇⋊#168	C₂	semidirect
7. C₅×C₇×Q₈	C₂²	semidirect
12. C₇⋊#168	C₂²	semidirect
21. C₂×C₇×Q₈	D₅	semidirect
25. C₂×C₅×Q₈	D₇	semidirect
29. C₂×C₅×C₇	SD₁₆	semidirect
34. C₇×Q₈	C₂×D₅	semidirect
42. C₅×Q₈	C₂×D₇	semidirect
48. C₅×C₇	C₂×SD₁₆	semidirect
62. C₂×Q₈	D₃₅	semidirect
66. C₂×C₇	#688	semidirect
69. C₂×C₅	#1143	semidirect
74. Q₈	C₂×D₃₅	semidirect
80. C₇	C₂×#688	semidirect
81. C₅	C₂×#1143	semidirect
89. C₂	#10587905	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×C₅×C₇×Q₈	2
C₂×D₁₄₀	2
#10587905	2
C₂×C₇⋊#168	2
C₂×#1143	5
C₂×#688	7

Subgroups — C2×#10587905 #11765273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587905 #11765273