Subgroups — C₇×#4018 #11765116

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#685	C₂	1	2	yes	maximal
4	C₇×#683	C₂	1	2	yes	maximal, complemented
5	C₄×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
9	C₂×C₇×Dic₅	C₂²	1	2	yes	—
10	C₂×C₇×Dic₅	C₂²	1	1	yes	characteristic
11	C₄×C₇×D₅	C₄	1	4	yes	complemented
12	C₇×#117	—	5	1	no	maximal, Hall
13	#4018	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
15	C₂×C₇×D₅	—	2	2	no	—
16	C₂×C₇×D₅	C₂×C₄	1	2	yes	—
17	C₄×C₅×C₇	—	2	2	no	—
18	C₄×C₅×C₇	C₂×C₄	1	2	yes	—
19	C₇×Dic₅	—	2	2	no	—
20	C₇×Dic₅	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₇	—	5	1	no	—
22	C₇×C₄⋊C₄	—	5	2	no	—
23	C₇×C₂²⋊C₄	—	5	2	no	—
24	C₄²×C₇	—	5	1	no	—
25	C₄²×C₇	D₅	1	1	yes	characteristic, complemented
26	C₂×C₄×D₅	C₂×C₇	1	1	yes	characteristic
27	C₄²×C₅	C₂×C₇	1	1	yes	characteristic, complemented
28	#685	C₂×C₇	1	2	yes	—
29	#683	C₂×C₇	1	2	yes	complemented
30	C₄×Dic₅	C₂×C₇	1	1	yes	characteristic, complemented
31	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₅×C₇	#41	1	2	yes	—
33	C₇×D₅	—	2	2	no	—
34	C₂³×C₇	—	5	1	no	—
35	C₂×C₄×C₇	—	5	1	no	—
36	C₂×C₄×C₇	—	5	4	no	—
37	C₂×C₄×C₇	—	5	2	no	—
38	C₂×C₄×C₇	C₂×D₅	1	2	yes	—
39	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
40	C₂²×D₅	C₂²×C₇	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂²×C₇	1	2	yes	—
42	C₂×C₄×C₅	C₂²×C₇	1	1	yes	characteristic
43	C₂×Dic₅	C₂²×C₇	1	2	yes	—
44	C₂×Dic₅	C₂²×C₇	1	1	yes	characteristic
45	C₄×D₅	C₄×C₇	1	4	yes	complemented
46	C₅×C₇	#117	1	1	yes	characteristic, complemented, Hall
47	#117	—	5	1	no	Sylow
48	C₂²×C₇	—	5	2	no	—
49	C₂²×C₇	—	10	2	no	—
50	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
51	C₄×C₇	—	2	2	no	—
52	C₄×C₇	—	5	2	no	—
53	C₄×C₇	—	10	2	no	—
54	C₄×C₇	C₄×D₅	1	2	yes	—
55	C₂²×C₅	C₂³×C₇	1	1	yes	characteristic
56	C₂×D₅	—	2	2	no	—
57	C₂×D₅	C₂×C₄×C₇	1	2	yes	—
58	C₄×C₅	—	2	2	no	—
59	C₄×C₅	C₂×C₄×C₇	1	2	yes	—
60	Dic₅	—	2	2	no	—
61	Dic₅	C₂×C₄×C₇	1	2	yes	—
62	C₂²×C₄	—	5	1	no	—
63	C₄⋊C₄	—	5	2	no	—
64	C₂²⋊C₄	—	5	2	no	—
65	C₄²	—	5	1	no	—
66	C₄²	C₇×D₅	1	1	yes	characteristic, complemented
67	C₂×C₇	—	10	2	no	—
68	C₂×C₇	C₂×C₄×D₅	1	1	yes	characteristic
69	C₂×C₇	#709	1	2	yes	—
70	C₂×C₅	C₂²×C₄×C₇	1	1	yes	characteristic
71	C₂×C₅	C₇×#41	1	2	yes	—
72	D₅	—	2	2	no	—
73	C₂³	—	5	1	no	—
74	C₂×C₄	—	5	1	no	—
75	C₂×C₄	—	5	4	no	—
76	C₂×C₄	—	5	2	no	—
77	C₂×C₄	C₂×C₇×D₅	1	2	yes	—
78	C₂×C₄	C₂×C₇×D₅	1	1	yes	characteristic
79	C₇	#4018	1	1	yes	characteristic, direct product factor, Sylow
80	C₅	C₇×#117	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	5	2	no	—
82	C₂²	—	10	2	no	—
83	C₂²	C₂²×C₇×D₅	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	5	2	no	—
86	C₄	—	10	2	no	—
87	C₄	C₄×C₇×D₅	1	2	yes	—
88	C₂	—	10	2	no	—
89	C₂	C₂×C₄×C₇×D₅	1	1	yes	characteristic
90	C₂	C₇×#709	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂×D₅
commutator	C₂×C₅	C₂²×C₄×C₇
Frattini	C₂²	C₂²×C₇×D₅
Fitting	C₄²×C₅×C₇	C₂
socle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×C₇×D₅	C₂²
cosocle	C₂²×C₅	C₂³×C₇
hypercenter	C₄²×C₇	D₅
hypocenter	C₅	C₇×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄²×C₇

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₇	C₂	semidirect
4. C₇×#683	C₂	semidirect
5. C₄×C₇×Dic₅	C₂	semidirect
11. C₄×C₇×D₅	C₄	semidirect
13. #4018	C₇	direct (N × H)
25. C₄²×C₇	D₅	semidirect
27. C₄²×C₅	C₂×C₇	semidirect
29. #683	C₂×C₇	semidirect
30. C₄×Dic₅	C₂×C₇	semidirect
45. C₄×D₅	C₄×C₇	semidirect
46. C₅×C₇	#117	semidirect
66. C₄²	C₇×D₅	semidirect
79. C₇	#4018	direct (N × H)
80. C₅	C₇×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×D₅	2
C₄²×C₅×C₇	2
C₇×#685	2
C₇×#683	2
C₄×C₇×Dic₅	2
C₇×#117	5
#4018	7

Subgroups — C7×#4018 #11765116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4018 #11765116