Subgroups — C₇×D₅×Q₁₆ #11765161

Order 1120.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×D₅	C₂	1	2	yes	maximal
2	C₅×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#689	C₂	1	2	yes	maximal, complemented
4	C₇×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×C₈×D₅	C₂	1	1	yes	maximal, characteristic
6	C₅×C₇×Q₈	C₂²	1	2	yes	—
7	C₄×C₇×D₅	—	2	2	no	—
8	C₄×C₇×D₅	C₂²	1	1	yes	characteristic
9	C₇×Dic₁₀	—	2	2	no	—
10	C₇×Dic₁₀	C₂²	1	2	yes	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇×#168	C₂²	1	1	yes	characteristic
13	C₂×C₇×Q₁₆	—	5	1	no	maximal, Hall
14	D₅×Q₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₇×D₅	D₄	1	1	yes	characteristic
16	C₄×C₅×C₇	—	2	2	no	—
17	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
18	C₇×Dic₅	—	2	2	no	—
19	C₇×Dic₅	D₄	1	1	yes	characteristic
20	C₂×C₇×Q₈	—	5	2	no	—
21	C₇×Q₁₆	—	5	2	no	—
22	C₇×Q₁₆	—	5	1	no	—
23	C₇×Q₁₆	D₅	1	1	yes	characteristic, direct product factor
24	C₂×C₇×C₈	—	5	1	no	—
25	Q₈×D₅	C₂×C₇	1	2	yes	—
26	C₅×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
27	#689	C₂×C₇	1	2	yes	complemented
28	Dic₂₀	C₂×C₇	1	1	yes	characteristic, complemented
29	C₈×D₅	C₂×C₇	1	1	yes	characteristic
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	C₇×D₅	Q₁₆	1	2	yes	direct product factor
32	C₇×Q₈	—	5	2	no	—
33	C₇×Q₈	—	10	2	no	—
34	C₇×Q₈	C₂×D₅	1	2	yes	—
35	C₂×C₄×C₇	—	5	1	no	—
36	C₂×C₄×C₇	—	10	2	no	—
37	C₇×C₈	—	5	1	no	—
38	C₇×C₈	C₂×D₅	1	1	yes	characteristic
39	C₅×Q₈	C₂²×C₇	1	2	yes	—
40	C₄×D₅	—	2	2	no	—
41	C₄×D₅	C₂²×C₇	1	1	yes	characteristic
42	Dic₁₀	—	2	2	no	—
43	Dic₁₀	C₂²×C₇	1	2	yes	—
44	C₅×C₈	C₂²×C₇	1	1	yes	characteristic
45	#168	C₂²×C₇	1	1	yes	characteristic
46	C₅×C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×Q₁₆	—	5	1	no	Sylow
48	C₂²×C₇	—	5	1	no	—
49	C₄×C₇	—	2	2	no	—
50	C₄×C₇	—	5	1	no	—
51	C₄×C₇	—	10	2	no	—
52	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
53	C₂×D₅	C₇×D₄	1	1	yes	characteristic
54	C₄×C₅	—	2	2	no	—
55	C₄×C₅	C₂³×C₇	1	1	yes	characteristic
56	Dic₅	—	2	2	no	—
57	Dic₅	C₇×D₄	1	1	yes	characteristic
58	C₂×Q₈	—	5	2	no	—
59	Q₁₆	—	5	2	no	—
60	Q₁₆	—	5	1	no	—
61	Q₁₆	C₇×D₅	1	1	yes	characteristic, direct product factor
62	C₂×C₈	—	5	1	no	—
63	C₂×C₇	—	5	2	no	—
64	C₂×C₇	D₄×D₅	1	1	yes	characteristic
65	C₂×C₅	C₂×C₇×D₄	1	1	yes	characteristic
66	D₅	C₇×Q₁₆	1	2	yes	direct product factor
67	Q₈	—	5	2	no	—
68	Q₈	—	10	2	no	—
69	Q₈	C₂×C₇×D₅	1	2	yes	—
70	C₂×C₄	—	5	1	no	—
71	C₂×C₄	—	10	2	no	—
72	C₈	—	5	1	no	—
73	C₈	C₂×C₇×D₅	1	1	yes	characteristic
74	C₇	D₅×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
75	C₅	C₂×C₇×Q₁₆	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	5	1	no	—
77	C₄	—	2	2	no	—
78	C₄	—	5	1	no	—
79	C₄	—	10	2	no	—
80	C₄	C₂²×C₇×D₅	1	1	yes	characteristic
81	C₂	—	5	2	no	—
82	C₂	C₇×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₇
Frattini	C₄	C₂²×C₇×D₅
Fitting	C₅×C₇×Q₁₆	C₂
socle	C₂×C₅×C₇	C₂×D₄
prime radical	C₂×C₇×D₅	D₄
hypercenter	C₇×Q₁₆	D₅
hypocenter	C₅	C₂×C₇×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇ ◁ C₇×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×Q₁₆	C₂	semidirect
3. C₇×#689	C₂	semidirect
4. C₇×Dic₂₀	C₂	semidirect
14. D₅×Q₁₆	C₇	direct (N × H)
23. C₇×Q₁₆	D₅	direct (N × H)
26. C₅×Q₁₆	C₂×C₇	semidirect
27. #689	C₂×C₇	semidirect
28. Dic₂₀	C₂×C₇	semidirect
31. C₇×D₅	Q₁₆	direct (N × H)
46. C₅×C₇	C₂×Q₁₆	semidirect
61. Q₁₆	C₇×D₅	direct (N × H)
66. D₅	C₇×Q₁₆	direct (N × H)
74. C₇	D₅×Q₁₆	direct (N × H)
75. C₅	C₂×C₇×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₇×Q₈×D₅	2
C₅×C₇×Q₁₆	2
C₇×#689	2
C₇×Dic₂₀	2
C₇×C₈×D₅	2
C₂×C₇×Q₁₆	5
D₅×Q₁₆	7

Subgroups — C7×D5×Q16 #11765161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×Q₁₆ #11765161