Subgroups — D₅×Dic₂₈ #11764710

Order 1120.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×Dic₁₄	C₂	1	2	yes	maximal
2	Dic₁₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587851	C₂	1	2	yes	maximal, complemented
6	Dic₇₀	C₂²	1	2	yes	—
7	C₄×C₇×D₅	C₂²	1	1	yes	characteristic
8	C₅×Dic₁₄	C₂²	1	2	yes	—
9	#63308	—	2	2	no	—
10	D₅×Dic₇	—	2	2	no	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₇×#168	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₈	—	5	1	no	maximal, Hall
14	D₅×Q₁₆	—	7	1	no	maximal, Hall
15	C₂×C₇×D₅	D₄	1	1	yes	characteristic
16	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
17	Dic₃₅	—	2	2	no	—
18	C₅×Dic₇	—	2	2	no	—
19	C₇×Dic₅	D₄	1	1	yes	characteristic
20	C₂×Dic₁₄	—	5	2	no	—
21	C₂×C₇×C₈	—	5	1	no	—
22	Dic₂₈	—	5	2	no	—
23	Dic₂₈	—	5	1	no	—
24	Dic₂₈	D₅	1	1	yes	characteristic, direct product factor
25	Q₈×D₅	—	7	2	no	—
26	C₅×Q₁₆	—	7	1	no	—
27	#689	—	7	2	no	—
28	Dic₂₀	—	7	1	no	—
29	C₈×D₅	D₇	1	1	yes	characteristic
30	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
31	C₇×D₅	Q₁₆	1	2	yes	complemented
32	C₂×C₄×C₇	—	5	1	no	—
33	C₂×Dic₇	—	10	2	no	—
34	Dic₁₄	—	5	2	no	—
35	Dic₁₄	—	10	2	no	—
36	Dic₁₄	C₂×D₅	1	2	yes	—
37	C₇×C₈	—	5	1	no	—
38	C₇×C₈	C₂×D₅	1	1	yes	characteristic
39	C₅×Q₈	—	7	2	no	—
40	C₄×D₅	—	14	2	no	—
41	C₄×D₅	C₂×D₇	1	1	yes	characteristic
42	Dic₁₀	—	7	2	no	—
43	Dic₁₀	—	14	2	no	—
44	C₅×C₈	C₂×D₇	1	1	yes	characteristic
45	#168	C₂×D₇	1	1	yes	characteristic
46	C₅×C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×Q₁₆	—	35	1	no	Sylow
48	C₂²×C₇	—	5	1	no	—
49	C₄×C₇	—	5	1	no	—
50	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
51	Dic₇	—	2	2	no	—
52	Dic₇	—	10	2	no	—
53	C₂×D₅	D₂₈	1	1	yes	characteristic
54	C₄×C₅	—	14	2	no	—
55	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
56	Dic₅	—	14	2	no	—
57	Dic₅	D₂₈	1	1	yes	characteristic
58	C₂×Q₈	—	35	2	no	—
59	Q₁₆	—	7	1	no	—
60	Q₁₆	—	35	2	no	—
61	Q₁₆	—	35	1	no	—
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×D₂₈	1	1	yes	characteristic
66	D₅	Dic₂₈	1	2	yes	direct product factor
67	Q₈	—	7	2	no	—
68	Q₈	—	35	2	no	—
69	Q₈	—	70	2	no	—
70	C₂×C₄	—	5	1	no	—
71	C₂×C₄	—	70	2	no	—
72	C₈	—	5	1	no	—
73	C₈	D₅×D₇	1	1	yes	characteristic
74	C₇	D₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₅	C₂×Dic₂₈	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	5	1	no	—
77	C₄	—	5	1	no	—
78	C₄	—	14	2	no	—
79	C₄	—	70	2	no	—
80	C₄	C₂×D₅×D₇	1	1	yes	characteristic
81	C₂	—	5	2	no	—
82	C₂	D₅×D₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₅×D₂₈
commutator, cosocle	C₄×C₅×C₇	C₂³
Frattini	C₄	C₂×D₅×D₇
Fitting	C₅×C₇×C₈	C₂²
socle	C₂×C₅×C₇	C₂×D₄
prime radical	C₂×C₇×D₅	D₄
hypercenter	C₈	D₅×D₇
hypocenter	C₅×C₇	C₂×Q₁₆
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
2. Dic₁₄₀	C₂	semidirect
4. C₅×Dic₂₈	C₂	semidirect
5. #10587851	C₂	semidirect
24. Dic₂₈	D₅	direct (N × H)
31. C₇×D₅	Q₁₆	semidirect
46. C₅×C₇	C₂×Q₁₆	semidirect
66. D₅	Dic₂₈	direct (N × H)
74. C₇	D₅×Q₁₆	semidirect
75. C₅	C₂×Dic₂₈	semidirect

Maximal subgroups

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

subgroup	index
D₅×Dic₁₄	2
Dic₁₄₀	2
C₇×C₈×D₅	2
C₅×Dic₂₈	2
#10587851	2
C₂×Dic₂₈	5
D₅×Q₁₆	7

Subgroups — D5×Dic28 #11764710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×Dic₂₈ #11764710