Subgroups — D₇×D₄₀ #11764696

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×D₂₀	C₂	1	2	yes	maximal, complemented
2	D₂₈₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587843	C₂	1	2	yes	maximal, complemented
6	C₂×D₅×D₇	—	2	2	no	—
7	D₁₄₀	C₂²	1	2	yes	complemented
8	C₇×D₂₀	C₂²	1	2	yes	complemented
9	C₄×C₅×D₇	C₂²	1	1	yes	characteristic
10	#63307	—	2	2	no	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
12	C₅×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
13	D₇×D₈	—	5	1	no	maximal, Hall
14	C₂×D₄₀	—	7	1	no	maximal, Hall
15	C₂×D₃₅	—	2	2	no	—
16	C₂×C₇×D₅	—	2	2	no	—
17	C₂×C₅×D₇	D₄	1	1	yes	characteristic
18	D₅×D₇	—	4	4	no	—
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	C₅×Dic₇	D₄	1	1	yes	characteristic
21	D₄×D₇	—	5	2	no	—
22	C₇×D₈	—	5	1	no	—
23	#1141	—	5	2	no	—
24	D₅₆	—	5	1	no	—
25	C₈×D₇	D₅	1	1	yes	characteristic, complemented
26	C₂×D₂₀	—	7	2	no	—
27	C₂×C₅×C₈	—	7	1	no	—
28	D₄₀	—	7	2	no	—
29	D₄₀	—	7	1	no	—
30	D₄₀	D₇	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	D₃₅	—	4	2	no	—
33	C₅×D₇	D₈	1	2	yes	complemented
34	C₇×D₅	—	4	2	no	—
35	C₂²×D₇	—	10	2	no	—
36	C₇×D₄	—	5	2	no	—
37	C₂²⋊D₇	—	10	2	no	—
38	D₂₈	—	5	2	no	—
39	C₄×D₇	C₂×D₅	1	1	yes	characteristic
40	C₇×C₈	C₂×D₅	1	1	yes	characteristic, complemented
41	C₇⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
42	C₂²×D₅	—	14	2	no	—
43	C₂×C₄×C₅	—	7	1	no	—
44	D₂₀	—	7	2	no	—
45	D₂₀	—	14	2	no	—
46	D₂₀	C₂×D₇	1	2	yes	complemented
47	C₅×C₈	—	7	1	no	—
48	C₅×C₈	C₂×D₇	1	1	yes	characteristic, complemented
49	C₅×C₇	C₂×D₈	1	1	yes	characteristic, complemented, Hall
50	C₂×D₈	—	35	1	no	Sylow
51	C₂²×C₇	—	10	2	no	—
52	C₂×D₇	—	10	2	no	—
53	C₂×D₇	—	20	4	no	—
54	C₂×D₇	D₂₀	1	1	yes	characteristic
55	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
56	Dic₇	D₂₀	1	1	yes	characteristic
57	C₂²×C₅	—	7	1	no	—
58	C₂×D₅	—	2	2	no	—
59	C₂×D₅	—	14	2	no	—
60	C₂×D₅	—	28	4	no	—
61	C₄×C₅	—	7	1	no	—
62	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
63	C₂×D₄	—	35	2	no	—
64	D₈	—	5	1	no	—
65	D₈	—	35	2	no	—
66	D₈	—	35	1	no	—
67	C₂×C₈	—	7	1	no	—
68	C₂×C₇	—	20	2	no	—
69	C₂×C₇	C₂×D₂₀	1	1	yes	characteristic
70	D₇	—	20	2	no	—
71	D₇	D₄₀	1	2	yes	direct product factor
72	C₂×C₅	—	7	2	no	—
73	C₂×C₅	D₄×D₇	1	1	yes	characteristic
74	D₅	—	4	2	no	—
75	D₅	—	28	2	no	—
76	C₂³	—	70	2	no	—
77	D₄	—	5	2	no	—
78	D₄	—	35	2	no	—
79	D₄	—	70	2	no	—
80	C₂×C₄	—	7	1	no	—
81	C₈	—	7	1	no	—
82	C₈	D₅×D₇	1	1	yes	characteristic, complemented
83	C₇	C₂×D₄₀	1	1	yes	characteristic, complemented, Sylow
84	C₅	D₇×D₈	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	7	1	no	—
86	C₂²	—	10	2	no	—
87	C₂²	—	70	2	no	—
88	C₂²	—	140	4	no	—
89	C₄	—	7	1	no	—
90	C₄	C₂×D₅×D₇	1	1	yes	characteristic
91	C₂	—	7	2	no	—
92	C₂	—	20	2	no	—
93	C₂	—	140	2	no	—
94	C₂	D₇×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₇×D₂₀
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂×D₅×D₇
Fitting	C₅×C₇×C₈	C₂²
socle	C₂×C₅×C₇	C₂×D₄
hypercenter	C₈	D₅×D₇
hypocenter	C₅×C₇	C₂×D₈
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₇×D₂₀	C₂	semidirect
2. D₂₈₀	C₂	semidirect
3. C₇×D₄₀	C₂	semidirect
4. C₅×C₈×D₇	C₂	semidirect
5. #10587843	C₂	semidirect
7. D₁₄₀	C₂²	semidirect
8. C₇×D₂₀	C₂²	semidirect
11. C₅×C₇×C₈	C₂²	semidirect
12. C₅×C₇⋊C₈	C₂²	semidirect
25. C₈×D₇	D₅	semidirect
30. D₄₀	D₇	direct (N × H)
33. C₅×D₇	D₈	semidirect
40. C₇×C₈	C₂×D₅	semidirect
41. C₇⋊C₈	C₂×D₅	semidirect
46. D₂₀	C₂×D₇	semidirect
48. C₅×C₈	C₂×D₇	semidirect
49. C₅×C₇	C₂×D₈	semidirect
71. D₇	D₄₀	direct (N × H)
82. C₈	D₅×D₇	semidirect
83. C₇	C₂×D₄₀	semidirect
84. C₅	D₇×D₈	semidirect

Maximal subgroups

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

subgroup	index
D₇×D₂₀	2
D₂₈₀	2
C₇×D₄₀	2
C₅×C₈×D₇	2
#10587843	2
D₇×D₈	5
C₂×D₄₀	7

Subgroups — D7×D40 #11764696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₄₀ #11764696