Subgroups — C₂×C₇×#683 #11765167

Order 1120.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₇×#683	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₇	—	2	2	no	—
7	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
8	C₂×C₇×Dic₅	—	2	2	no	—
9	C₂×C₇×Dic₅	C₄	1	4	yes	complemented
10	C₂×C₇×Dic₅	C₂²	1	2	yes	—
11	C₂×C₇×Dic₅	C₂²	1	2	yes	—
12	C₂×C₇×C₄⋊C₄	—	5	1	no	maximal, Hall
13	C₂×#683	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	C₄×C₅×C₇	—	2	2	no	—
19	C₇×Dic₅	—	2	2	no	—
20	C₇×Dic₅	C₂×C₄	1	4	yes	complemented
21	C₂²×C₄×C₇	—	5	1	no	—
22	C₂²×C₄×C₇	—	5	1	no	—
23	C₂²×C₄×C₇	D₅	1	1	yes	characteristic
24	C₇×C₄⋊C₄	—	5	4	no	—
25	C₂²×C₄×C₅	C₂×C₇	1	1	yes	characteristic
26	C₂²×Dic₅	C₂×C₇	1	1	yes	characteristic
27	C₂²×Dic₅	C₂×C₇	1	1	yes	characteristic
28	#683	C₂×C₇	1	4	yes	direct product factor
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	—	2	2	no	—
35	C₂×C₄×C₇	—	5	4	no	—
36	C₂×C₄×C₇	—	5	2	no	—
37	C₂×C₄×C₇	—	5	2	no	—
38	C₂×C₄×C₇	—	10	2	no	—
39	C₂×C₄×C₇	C₂×D₅	1	2	yes	—
40	C₂³×C₅	C₂²×C₇	1	1	yes	characteristic
41	C₂×C₄×C₅	—	2	2	no	—
42	C₂×C₄×C₅	C₂²×C₇	1	2	yes	—
43	C₂×Dic₅	—	2	2	no	—
44	C₂×Dic₅	C₄×C₇	1	4	yes	complemented
45	C₂×Dic₅	C₂²×C₇	1	2	yes	—
46	C₂×Dic₅	C₂²×C₇	1	2	yes	—
47	C₅×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂×C₄⋊C₄	—	5	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	—	2	2	no	—
54	C₄×C₇	—	5	4	no	—
55	C₄×C₇	—	10	2	no	—
56	C₂²×C₅	C₂×C₄×C₇	1	2	yes	—
57	C₂²×C₅	C₇×D₄	1	2	yes	—
58	C₂²×C₅	C₇×Q₈	1	2	yes	—
59	C₂²×C₅	C₂³×C₇	1	1	yes	characteristic
60	C₄×C₅	—	2	2	no	—
61	Dic₅	—	2	2	no	—
62	Dic₅	C₂×C₄×C₇	1	4	yes	complemented
63	C₂²×C₄	—	5	1	no	—
64	C₂²×C₄	—	5	1	no	—
65	C₂²×C₄	C₇×D₅	1	1	yes	characteristic
66	C₄⋊C₄	—	5	4	no	—
67	C₂×C₇	#683	1	4	yes	direct product factor
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	C₇×C₄⋊C₄	1	4	yes	complemented
72	C₂×C₅	C₂²×C₄×C₇	1	1	yes	characteristic
73	C₂×C₅	C₂×C₇×D₄	1	1	yes	characteristic
74	C₂×C₅	C₂×C₇×Q₈	1	1	yes	characteristic
75	C₂³	C₂×C₇×D₅	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	5	4	no	—
78	C₂×C₄	—	5	2	no	—
79	C₂×C₄	—	5	2	no	—
80	C₂×C₄	—	10	2	no	—
81	C₂×C₄	C₂×C₇×D₅	1	2	yes	—
82	C₇	C₂×#683	1	1	yes	characteristic, direct product factor, Sylow
83	C₅	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
84	C₂²	C₇×Dic₁₀	1	2	yes	—
85	C₂²	C₄×C₇×D₅	1	2	yes	—
86	C₂²	C₇×C₂²⋊D₅	1	2	yes	—
87	C₂²	C₂²×C₇×D₅	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	5	4	no	—
90	C₄	—	10	2	no	—
91	C₂	C₇×#683	1	4	yes	direct product factor
92	C₂	C₂×C₇×Dic₁₀	1	1	yes	characteristic
93	C₂	C₂×C₄×C₇×D₅	1	1	yes	characteristic
94	C₂	C₂×C₇×C₂²⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₇×#683	C₂	direct (N × H)
9. C₂×C₇×Dic₅	C₄	semidirect
13. C₂×#683	C₇	direct (N × H)
20. C₇×Dic₅	C₂×C₄	semidirect
28. #683	C₂×C₇	direct (N × H)
29. C₂×C₅×C₇	C₄⋊C₄	semidirect
44. C₂×Dic₅	C₄×C₇	semidirect
47. C₅×C₇	C₂×C₄⋊C₄	semidirect
62. Dic₅	C₂×C₄×C₇	semidirect
67. C₂×C₇	#683	direct (N × H)
71. C₂×C₅	C₇×C₄⋊C₄	semidirect
82. C₇	C₂×#683	direct (N × H)
83. C₅	C₂×C₇×C₄⋊C₄	semidirect
91. C₂	C₇×#683	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×C₄×C₅×C₇	2
C₂²×C₇×Dic₅	2
C₇×#683	2
C₂×C₇×C₄⋊C₄	5
C₂×#683	7

Subgroups — C2×C7×#683 #11765167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#683 #11765167