Subgroups — #11764747

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₇	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇⋊Dic₅	C₂	1	2	yes	maximal, complemented
5	(C₂×D₇)⋊Dic₅	C₂	1	2	yes	maximal
6	C₂²×C₅×D₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₅	C₂²	1	2	yes	—
9	C₂×C₇×Dic₅	C₂²	1	2	yes	—
10	C₂×C₅×Dic₇	C₂²	1	1	yes	characteristic
11	C₄×C₅×D₇	C₄	1	4	yes	complemented
12	#6435	—	5	1	no	maximal, Hall
13	#4072	—	7	1	no	maximal, Hall
14	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
15	C₂×C₅×D₇	—	2	2	no	—
16	C₂×C₅×D₇	C₂×C₄	1	2	yes	—
17	C₄×C₅×C₇	C₂×C₄	1	2	yes	—
18	Dic₃₅	—	2	2	no	—
19	C₅×Dic₇	C₂×C₄	1	2	yes	—
20	C₇×Dic₅	—	2	2	no	—
21	C₂×C₄×D₇	D₅	1	1	yes	characteristic
22	C₄²×C₇	—	5	1	no	—
23	(C₂×D₇)⋊C₄	—	5	2	no	—
24	Dic₇⋊C₄	—	5	2	no	—
25	C₄×Dic₇	—	5	1	no	—
26	C₂²×C₄×C₅	—	7	1	no	—
27	C₂²⋊Dic₅	—	7	2	no	—
28	C₄⋊Dic₅	—	7	2	no	—
29	C₄×Dic₅	—	7	1	no	—
30	C₄×Dic₅	D₇	1	1	yes	characteristic, complemented
31	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₅×C₇	#41	1	2	yes	—
33	C₅×D₇	—	2	2	no	—
34	C₂²×D₇	C₂×D₅	1	1	yes	characteristic
35	C₂×C₄×C₇	—	5	2	no	—
36	C₂×C₄×C₇	C₂×D₅	1	1	yes	characteristic
37	C₂×Dic₇	—	5	2	no	—
38	C₂×Dic₇	C₂×D₅	1	1	yes	characteristic
39	C₄×D₇	Dic₅	1	4	yes	complemented
40	C₂³×C₅	—	7	1	no	—
41	C₂×C₄×C₅	—	7	1	no	—
42	C₂×C₄×C₅	—	7	4	no	—
43	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
44	C₂×Dic₅	—	7	2	no	—
45	C₂×Dic₅	C₂×D₇	1	2	yes	—
46	C₅×C₇	#117	1	1	yes	characteristic, complemented, Hall
47	#117	—	35	1	no	Sylow
48	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
49	C₂×D₇	—	2	2	no	—
50	C₂×D₇	C₂×Dic₅	1	2	yes	—
51	C₄×C₇	—	10	2	no	—
52	C₄×C₇	C₂×Dic₅	1	2	yes	—
53	Dic₇	—	10	2	no	—
54	Dic₇	C₂×Dic₅	1	2	yes	—
55	C₂²×C₅	—	7	2	no	—
56	C₂²×C₅	—	14	2	no	—
57	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
58	C₄×C₅	—	7	2	no	—
59	C₄×C₅	C₄×D₇	1	2	yes	—
60	Dic₅	—	2	2	no	—
61	Dic₅	—	14	2	no	—
62	C₂²×C₄	—	7	1	no	—
63	C₄⋊C₄	—	35	2	no	—
64	C₂²⋊C₄	—	35	2	no	—
65	C₄²	—	5	1	no	—
66	C₄²	—	35	1	no	—
67	C₂×C₇	#709	1	2	yes	—
68	C₂×C₇	C₂²×Dic₅	1	1	yes	characteristic
69	D₇	—	2	2	no	—
70	C₂×C₅	—	14	2	no	—
71	C₂×C₅	C₂×C₄×D₇	1	1	yes	characteristic
72	C₂×C₅	#1157	1	2	yes	—
73	C₂³	—	7	1	no	—
74	C₂×C₄	—	5	2	no	—
75	C₂×C₄	—	7	1	no	—
76	C₂×C₄	—	7	4	no	—
77	C₂×C₄	—	35	2	no	—
78	C₂×C₄	D₅×D₇	1	1	yes	characteristic
79	C₇	#4072	1	1	yes	characteristic, complemented, Sylow
80	C₅	#6435	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	7	2	no	—
82	C₂²	—	14	2	no	—
83	C₂²	C₂×D₅×D₇	1	1	yes	characteristic
84	C₄	—	7	2	no	—
85	C₄	—	10	2	no	—
86	C₄	—	70	2	no	—
87	C₄	D₇×Dic₅	1	2	yes	—
88	C₂	—	14	2	no	—
89	C₂	#10587944	1	2	yes	—
90	C₂	C₂×D₇×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×D₇
commutator	C₂×C₅×C₇	C₂²×C₄
Frattini	C₂²	C₂×D₅×D₇
Fitting	C₂×C₄×C₅×C₇	C₂²
socle, cosocle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×C₅×D₇	C₂²
hypocenter	C₅×C₇	#117
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×Dic₃₅	C₂	semidirect
3. C₄×C₇×Dic₅	C₂	semidirect
4. Dic₇⋊Dic₅	C₂	semidirect
11. C₄×C₅×D₇	C₄	semidirect
30. C₄×Dic₅	D₇	semidirect
39. C₄×D₇	Dic₅	semidirect
46. C₅×C₇	#117	semidirect
79. C₇	#4072	semidirect
80. C₅	#6435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₇	2
C₄×Dic₃₅	2
C₄×C₇×Dic₅	2
Dic₇⋊Dic₅	2
(C₂×D₇)⋊Dic₅	2
#6435	5
#4072	7