Subgroups — C₂×C₅×Dic₂₈ #11765063

Order 1120.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₄	C₂	1	2	yes	maximal
2	C₂×C₅×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₂₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₅×Dic₇	—	2	2	no	—
6	C₅×Dic₁₄	—	2	2	no	—
7	C₅×Dic₁₄	C₂²	1	4	yes	—
8	C₅×C₇×C₈	C₂²	1	2	yes	—
9	C₂×Dic₂₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×Q₁₆	—	7	1	no	maximal, Hall
11	C₂²×C₅×C₇	D₄	1	1	yes	characteristic
12	C₄×C₅×C₇	D₄	1	1	yes	characteristic
13	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₅×Dic₇	—	2	4	no	—
15	C₂×Dic₁₄	C₂×C₅	1	2	yes	—
16	C₂×C₇×C₈	C₂×C₅	1	1	yes	characteristic
17	Dic₂₈	C₂×C₅	1	4	yes	direct product factor
18	C₂×C₅×Q₈	—	7	2	no	—
19	C₅×Q₁₆	—	7	4	no	—
20	C₂×C₅×C₈	D₇	1	1	yes	characteristic
21	C₂×C₅×C₇	Q₁₆	1	2	yes	complemented
22	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
24	C₂×Dic₇	—	2	2	no	—
25	Dic₁₄	—	2	2	no	—
26	Dic₁₄	C₂²×C₅	1	4	yes	—
27	C₇×C₈	C₂²×C₅	1	2	yes	—
28	C₅×Q₈	—	7	4	no	—
29	C₅×Q₈	—	14	2	no	—
30	C₂×C₄×C₅	—	14	2	no	—
31	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
32	C₅×C₈	C₂×D₇	1	2	yes	—
33	C₅×C₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
34	C₂×Q₁₆	—	7	1	no	Sylow
35	C₂²×C₇	C₅×D₄	1	1	yes	characteristic
36	C₄×C₇	C₅×D₄	1	1	yes	characteristic
37	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
38	Dic₇	—	2	4	no	—
39	C₂²×C₅	D₂₈	1	1	yes	characteristic
40	C₄×C₅	—	14	4	no	—
41	C₄×C₅	D₂₈	1	1	yes	characteristic
42	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
43	C₂×Q₈	—	7	2	no	—
44	Q₁₆	—	7	4	no	—
45	C₂×C₈	C₅×D₇	1	1	yes	characteristic
46	C₂×C₇	C₅×Q₁₆	1	2	yes	complemented
47	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
48	C₂×C₅	Dic₂₈	1	2	yes	direct product factor
49	C₂×C₅	C₂×D₂₈	1	1	yes	characteristic
50	Q₈	—	7	4	no	—
51	Q₈	—	14	2	no	—
52	C₂×C₄	—	14	2	no	—
53	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
54	C₈	C₂×C₅×D₇	1	2	yes	—
55	C₇	C₂×C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₅	C₂×Dic₂₈	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	C₅×D₂₈	1	1	yes	characteristic
58	C₄	—	14	4	no	—
59	C₄	C₅×D₂₈	1	1	yes	characteristic
60	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
61	C₂	C₅×Dic₂₈	1	2	yes	direct product factor
62	C₂	C₂×C₅×D₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₂₈
commutator, cosocle	C₄×C₇	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₇
Fitting	C₂×C₅×C₇×C₈	C₂
socle, prime radical	C₂²×C₅×C₇	D₄
hypercenter	C₂×C₅×C₈	D₇
hypocenter	C₇	C₂×C₅×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
3. C₅×Dic₂₈	C₂	direct (N × H)
9. C₂×Dic₂₈	C₅	direct (N × H)
17. Dic₂₈	C₂×C₅	direct (N × H)
21. C₂×C₅×C₇	Q₁₆	semidirect
33. C₅×C₇	C₂×Q₁₆	semidirect
46. C₂×C₇	C₅×Q₁₆	semidirect
48. C₂×C₅	Dic₂₈	direct (N × H)
55. C₇	C₂×C₅×Q₁₆	semidirect
56. C₅	C₂×Dic₂₈	direct (N × H)
61. C₂	C₅×Dic₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₁₄	2
C₂×C₅×C₇×C₈	2
C₅×Dic₂₈	2
C₂×Dic₂₈	5
C₂×C₅×Q₁₆	7

Subgroups — C2×C5×Dic28 #11765063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₂₈ #11765063