Subgroups — C₅×D₇×D₈ #11765068

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×D₇	C₂	semidirect
2. C₅×C₇×D₈	C₂	semidirect
3. C₅×#1141	C₂	semidirect
4. C₅×D₅₆	C₂	semidirect
5. C₅×C₈×D₇	C₂	semidirect
7. C₅×C₇×D₄	C₂²	semidirect
9. C₅×D₂₈	C₂²	semidirect
11. C₅×C₇×C₈	C₂²	semidirect
12. C₅×C₇⋊C₈	C₂²	semidirect
13. D₇×D₈	C₅	direct (N × H)
21. D₄×D₇	C₂×C₅	semidirect
22. C₇×D₈	C₂×C₅	semidirect
23. #1141	C₂×C₅	semidirect
24. D₅₆	C₂×C₅	semidirect
25. C₈×D₇	C₂×C₅	semidirect
29. C₅×D₈	D₇	direct (N × H)
34. C₅×D₇	D₈	direct (N × H)
36. C₇×D₄	C₂²×C₅	semidirect
38. D₂₈	C₂²×C₅	semidirect
40. C₇×C₈	C₂²×C₅	semidirect
41. C₇⋊C₈	C₂²×C₅	semidirect
45. C₅×D₄	C₂×D₇	semidirect
48. C₅×C₈	C₂×D₇	semidirect
49. C₅×C₇	C₂×D₈	semidirect
66. D₈	C₅×D₇	direct (N × H)
71. D₇	C₅×D₈	direct (N × H)
79. D₄	C₂×C₅×D₇	semidirect
82. C₈	C₂×C₅×D₇	semidirect
83. C₇	C₂×C₅×D₈	semidirect
84. C₅	D₇×D₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₄×D₇	2
C₅×C₇×D₈	2
C₅×#1141	2
C₅×D₅₆	2
C₅×C₈×D₇	2
D₇×D₈	5
C₂×C₅×D₈	7

Subgroups — C5×D7×D8 #11765068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×D₈ #11765068