Subgroups — C₂×#10587858 #11764988

Order 1120.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic
4	#10587858	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₅	C₄	1	4	yes	complemented
7	C₂×Dic₃₅	C₂²	1	2	yes	—
8	C₂×C₇×Dic₅	—	2	2	no	—
9	C₂×C₇×Dic₅	C₂²	1	2	yes	—
10	C₂×C₅×Dic₇	—	2	2	no	—
11	C₂×C₅×Dic₇	C₂²	1	2	yes	—
12	C₂×Dic₇⋊C₄	—	5	1	no	maximal, Hall
13	C₂×#683	—	7	1	no	maximal, Hall
14	C₂²×C₅×C₇	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₇	D₄	1	2	yes	—
16	C₂²×C₅×C₇	Q₈	1	2	yes	—
17	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
18	Dic₃₅	C₂×C₄	1	4	yes	complemented
19	C₅×Dic₇	—	2	2	no	—
20	C₇×Dic₅	—	2	2	no	—
21	C₂²×C₄×C₇	—	5	1	no	—
22	C₂²×Dic₇	—	5	1	no	—
23	C₂²×Dic₇	D₅	1	1	yes	characteristic
24	Dic₇⋊C₄	—	5	4	no	—
25	C₂²×C₄×C₅	—	7	1	no	—
26	C₂²×Dic₅	—	7	1	no	—
27	C₂²×Dic₅	D₇	1	1	yes	characteristic
28	#683	—	7	4	no	—
29	C₂×C₅×C₇	C₄⋊C₄	1	4	yes	complemented
30	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
33	C₂³×C₇	C₂×D₅	1	1	yes	characteristic
34	C₂×C₄×C₇	—	5	2	no	—
35	C₂×C₄×C₇	—	10	2	no	—
36	C₂×Dic₇	—	2	2	no	—
37	C₂×Dic₇	—	5	4	no	—
38	C₂×Dic₇	—	5	2	no	—
39	C₂×Dic₇	C₂×D₅	1	2	yes	—
40	C₂³×C₅	C₂×D₇	1	1	yes	characteristic
41	C₂×C₄×C₅	—	7	2	no	—
42	C₂×C₄×C₅	—	14	2	no	—
43	C₂×Dic₅	—	2	2	no	—
44	C₂×Dic₅	—	7	4	no	—
45	C₂×Dic₅	—	7	2	no	—
46	C₂×Dic₅	C₂×D₇	1	2	yes	—
47	C₅×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂×C₄⋊C₄	—	35	1	no	Sylow
49	C₂²×C₇	Dic₁₀	1	2	yes	—
50	C₂²×C₇	C₄×D₅	1	2	yes	—
51	C₂²×C₇	C₂²⋊D₅	1	2	yes	—
52	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
53	C₄×C₇	—	10	2	no	—
54	Dic₇	—	2	2	no	—
55	Dic₇	—	5	4	no	—
56	C₂²×C₅	Dic₁₄	1	2	yes	—
57	C₂²×C₅	C₄×D₇	1	2	yes	—
58	C₂²×C₅	C₂²⋊D₇	1	2	yes	—
59	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
60	C₄×C₅	—	14	2	no	—
61	Dic₅	—	2	2	no	—
62	Dic₅	—	7	4	no	—
63	C₂²×C₄	—	5	1	no	—
64	C₂²×C₄	—	7	1	no	—
65	C₂²×C₄	—	35	1	no	—
66	C₄⋊C₄	—	35	4	no	—
67	C₂×C₇	#683	1	4	yes	complemented
68	C₂×C₇	C₂×Dic₁₀	1	1	yes	characteristic
69	C₂×C₇	C₂×C₄×D₅	1	1	yes	characteristic
70	C₂×C₇	C₂×C₂²⋊D₅	1	1	yes	characteristic
71	C₂×C₅	Dic₇⋊C₄	1	4	yes	complemented
72	C₂×C₅	C₂×Dic₁₄	1	1	yes	characteristic
73	C₂×C₅	C₂×C₄×D₇	1	1	yes	characteristic
74	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
75	C₂³	D₅×D₇	1	1	yes	characteristic
76	C₂×C₄	—	5	2	no	—
77	C₂×C₄	—	7	2	no	—
78	C₂×C₄	—	10	2	no	—
79	C₂×C₄	—	14	2	no	—
80	C₂×C₄	—	35	4	no	—
81	C₂×C₄	—	35	2	no	—
82	C₇	C₂×#683	1	1	yes	characteristic, complemented, Sylow
83	C₅	C₂×Dic₇⋊C₄	1	1	yes	characteristic, complemented, Sylow
84	C₂²	#63304	1	2	yes	—
85	C₂²	#63305	1	2	yes	—
86	C₂²	#63308	1	2	yes	—
87	C₂²	C₂×D₅×D₇	1	1	yes	characteristic
88	C₄	—	10	2	no	—
89	C₄	—	14	2	no	—
90	C₄	—	35	4	no	—
91	C₂	#10587858	1	4	yes	direct product factor
92	C₂	C₂×#63304	1	1	yes	characteristic
93	C₂	C₂×#63305	1	1	yes	characteristic
94	C₂	C₂×#63308	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #10587858	C₂	direct (N × H)
6. C₂×Dic₃₅	C₄	semidirect
18. Dic₃₅	C₂×C₄	semidirect
29. C₂×C₅×C₇	C₄⋊C₄	semidirect
47. C₅×C₇	C₂×C₄⋊C₄	semidirect
67. C₂×C₇	#683	semidirect
71. C₂×C₅	Dic₇⋊C₄	semidirect
82. C₇	C₂×#683	semidirect
83. C₅	C₂×Dic₇⋊C₄	semidirect
91. C₂	#10587858	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₃₅	2
C₂²×C₇×Dic₅	2
C₂²×C₅×Dic₇	2
#10587858	2
C₂×Dic₇⋊C₄	5
C₂×#683	7

Subgroups — C2×#10587858 #11764988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10587858 #11764988