Subgroups — C₅×D₇×Q₁₆ #11765075

Order 1120.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×D₇	C₂	1	2	yes	maximal
2	C₅×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1144	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×D₇	C₂	1	1	yes	maximal, characteristic
6	C₅×C₇×Q₈	C₂²	1	2	yes	—
7	C₄×C₅×D₇	—	2	2	no	—
8	C₄×C₅×D₇	C₂²	1	1	yes	characteristic
9	C₅×Dic₁₄	—	2	2	no	—
10	C₅×Dic₁₄	C₂²	1	2	yes	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₇⋊C₈	C₂²	1	1	yes	characteristic
13	D₇×Q₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×Q₁₆	—	7	1	no	maximal, Hall
15	C₂×C₅×D₇	D₄	1	1	yes	characteristic
16	C₄×C₅×C₇	—	2	2	no	—
17	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
18	C₅×Dic₇	—	2	2	no	—
19	C₅×Dic₇	D₄	1	1	yes	characteristic
20	Q₈×D₇	C₂×C₅	1	2	yes	—
21	C₇×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
22	#1144	C₂×C₅	1	2	yes	complemented
23	Dic₂₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₈×D₇	C₂×C₅	1	1	yes	characteristic
25	C₂×C₅×Q₈	—	7	2	no	—
26	C₅×Q₁₆	—	7	2	no	—
27	C₅×Q₁₆	—	7	1	no	—
28	C₅×Q₁₆	D₇	1	1	yes	characteristic, direct product factor
29	C₂×C₅×C₈	—	7	1	no	—
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	C₅×D₇	Q₁₆	1	2	yes	direct product factor
32	C₇×Q₈	C₂²×C₅	1	2	yes	—
33	C₄×D₇	—	2	2	no	—
34	C₄×D₇	C₂²×C₅	1	1	yes	characteristic
35	Dic₁₄	—	2	2	no	—
36	Dic₁₄	C₂²×C₅	1	2	yes	—
37	C₇×C₈	C₂²×C₅	1	1	yes	characteristic
38	C₇⋊C₈	C₂²×C₅	1	1	yes	characteristic
39	C₅×Q₈	—	7	2	no	—
40	C₅×Q₈	—	14	2	no	—
41	C₅×Q₈	C₂×D₇	1	2	yes	—
42	C₂×C₄×C₅	—	7	1	no	—
43	C₂×C₄×C₅	—	14	2	no	—
44	C₅×C₈	—	7	1	no	—
45	C₅×C₈	C₂×D₇	1	1	yes	characteristic
46	C₅×C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×Q₁₆	—	7	1	no	Sylow
48	C₂×D₇	C₅×D₄	1	1	yes	characteristic
49	C₄×C₇	—	2	2	no	—
50	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
51	Dic₇	—	2	2	no	—
52	Dic₇	C₅×D₄	1	1	yes	characteristic
53	C₂²×C₅	—	7	1	no	—
54	C₄×C₅	—	2	2	no	—
55	C₄×C₅	—	7	1	no	—
56	C₄×C₅	—	14	2	no	—
57	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
58	C₂×Q₈	—	7	2	no	—
59	Q₁₆	—	7	2	no	—
60	Q₁₆	—	7	1	no	—
61	Q₁₆	C₅×D₇	1	1	yes	characteristic, direct product factor
62	C₂×C₈	—	7	1	no	—
63	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
64	D₇	C₅×Q₁₆	1	2	yes	direct product factor
65	C₂×C₅	—	7	2	no	—
66	C₂×C₅	D₄×D₇	1	1	yes	characteristic
67	Q₈	—	7	2	no	—
68	Q₈	—	14	2	no	—
69	Q₈	C₂×C₅×D₇	1	2	yes	—
70	C₂×C₄	—	7	1	no	—
71	C₂×C₄	—	14	2	no	—
72	C₈	—	7	1	no	—
73	C₈	C₂×C₅×D₇	1	1	yes	characteristic
74	C₇	C₂×C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₅	D₇×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	—	7	1	no	—
77	C₄	—	2	2	no	—
78	C₄	—	7	1	no	—
79	C₄	—	14	2	no	—
80	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
81	C₂	—	7	2	no	—
82	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×Q₁₆	C₂
socle	C₂×C₅×C₇	C₂×D₄
prime radical	C₂×C₅×D₇	D₄
hypercenter	C₅×Q₁₆	D₇
hypocenter	C₇	C₂×C₅×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×Q₁₆	C₂	semidirect
3. C₅×#1144	C₂	semidirect
4. C₅×Dic₂₈	C₂	semidirect
13. D₇×Q₁₆	C₅	direct (N × H)
21. C₇×Q₁₆	C₂×C₅	semidirect
22. #1144	C₂×C₅	semidirect
23. Dic₂₈	C₂×C₅	semidirect
28. C₅×Q₁₆	D₇	direct (N × H)
31. C₅×D₇	Q₁₆	direct (N × H)
46. C₅×C₇	C₂×Q₁₆	semidirect
61. Q₁₆	C₅×D₇	direct (N × H)
64. D₇	C₅×Q₁₆	direct (N × H)
74. C₇	C₂×C₅×Q₁₆	semidirect
75. C₅	D₇×Q₁₆	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×Q₈×D₇	2
C₅×C₇×Q₁₆	2
C₅×#1144	2
C₅×Dic₂₈	2
C₅×C₈×D₇	2
D₇×Q₁₆	5
C₂×C₅×Q₁₆	7

Subgroups — C5×D7×Q16 #11765075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×Q₁₆ #11765075