Subgroups — C₇×#4036 #11765135

Order 1120.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊Dic₅	C₂	1	2	yes	maximal
3	C₇×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₇×#683	C₂	1	2	yes	maximal
5	C₄×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×C₇×Dic₅	C₂²	1	1	yes	characteristic
9	C₂×C₇×Dic₅	C₂²	1	1	yes	characteristic
10	C₂×C₇×Dic₅	C₂²	1	2	yes	—
11	C₇×#125	—	5	1	no	maximal, Hall
12	#4036	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₅×C₇	—	2	2	no	—
15	C₄×C₅×C₇	Q₈	1	2	yes	—
16	C₇×Dic₅	—	2	1	no	—
17	C₇×Dic₅	—	2	1	no	—
18	C₇×Dic₅	—	2	2	no	—
19	C₇×C₄⋊C₄	—	5	2	no	—
20	C₇×C₄⋊C₄	—	5	2	no	—
21	C₇×C₄⋊C₄	—	5	1	no	—
22	C₇×C₄⋊C₄	D₅	1	1	yes	characteristic
23	C₄²×C₇	—	5	1	no	—
24	C₅×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
25	C₄⋊Dic₅	C₂×C₇	1	2	yes	—
26	C₄⋊Dic₅	C₂×C₇	1	1	yes	characteristic
27	#683	C₂×C₇	1	2	yes	—
28	C₄×Dic₅	C₂×C₇	1	1	yes	characteristic
29	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₅×C₇	#41	1	1	yes	characteristic
31	C₂×C₅×C₇	#41	1	1	yes	characteristic
32	C₂×C₄×C₇	—	5	1	no	—
33	C₂×C₄×C₇	—	5	1	no	—
34	C₂×C₄×C₇	—	5	2	no	—
35	C₂×C₄×C₇	C₂×D₅	1	2	yes	—
36	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂²×C₇	1	2	yes	—
38	C₂×C₄×C₅	C₂²×C₇	1	1	yes	characteristic
39	C₂×Dic₅	C₂²×C₇	1	1	yes	characteristic
40	C₂×Dic₅	C₂²×C₇	1	1	yes	characteristic
41	C₂×Dic₅	C₂²×C₇	1	2	yes	—
42	C₅×C₇	#125	1	1	yes	characteristic, complemented, Hall
43	#125	—	5	1	no	Sylow
44	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
45	C₄×C₇	—	2	2	no	—
46	C₄×C₇	—	10	1	no	—
47	C₄×C₇	—	10	1	no	—
48	C₄×C₇	—	10	2	no	—
49	C₄×C₇	Dic₁₀	1	2	yes	—
50	C₂²×C₅	C₂³×C₇	1	1	yes	characteristic
51	C₄×C₅	—	2	2	no	—
52	C₄×C₅	C₇×Q₈	1	2	yes	—
53	Dic₅	—	2	1	no	—
54	Dic₅	—	2	1	no	—
55	Dic₅	—	2	2	no	—
56	C₄⋊C₄	—	5	2	no	—
57	C₄⋊C₄	—	5	2	no	—
58	C₄⋊C₄	—	5	1	no	—
59	C₄⋊C₄	C₇×D₅	1	1	yes	characteristic
60	C₄²	—	5	1	no	—
61	C₂×C₇	C₂×Dic₁₀	1	1	yes	characteristic
62	C₂×C₇	#711	1	1	yes	characteristic
63	C₂×C₇	#713	1	1	yes	characteristic
64	C₂×C₅	C₂×C₇×Q₈	1	1	yes	characteristic
65	C₂×C₅	C₇×#41	1	1	yes	characteristic
66	C₂×C₅	C₇×#41	1	1	yes	characteristic
67	C₂×C₄	—	5	1	no	—
68	C₂×C₄	—	5	1	no	—
69	C₂×C₄	—	5	2	no	—
70	C₂×C₄	C₂×C₇×D₅	1	2	yes	—
71	C₂×C₄	C₂×C₇×D₅	1	1	yes	characteristic
72	C₇	#4036	1	1	yes	characteristic, direct product factor, Sylow
73	C₅	C₇×#125	1	1	yes	characteristic, complemented, Sylow
74	C₂²	C₂²×C₇×D₅	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	10	1	no	—
77	C₄	—	10	1	no	—
78	C₄	—	10	2	no	—
79	C₄	C₇×Dic₁₀	1	2	yes	—
80	C₂	C₂×C₇×Dic₁₀	1	1	yes	characteristic
81	C₂	C₇×#711	1	1	yes	characteristic
82	C₂	C₇×#713	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₇
Frattini	C₂²	C₂²×C₇×D₅
Fitting	C₅×C₇×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₅×C₇	C₂³
hypercenter	C₇×C₄⋊C₄	D₅
hypocenter	C₅	C₇×#125
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
12. #4036	C₇	direct (N × H)
42. C₅×C₇	#125	semidirect
72. C₇	#4036	direct (N × H)
73. C₅	C₇×#125	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₄⋊C₄	2
C₇×C₄⋊Dic₅	2
C₇×#683	2
C₄×C₇×Dic₅	2
C₇×#125	5
#4036	7

Subgroups — C7×#4036 #11765135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4036 #11765135