Subgroups — C₅×Dic₃⋊C₈ #91057

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×C₄⋊C₈	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₅×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₅×Dic₃	C₄	1	1	yes	characteristic
8	C₃×C₅×C₈	—	2	1	no	—
9	C₅×C₃⋊C₈	—	2	1	no	—
10	Dic₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₈	—	3	1	no	—
12	C₂×C₅×C₈	D₃	1	1	yes	characteristic
13	C₄²×C₅	—	3	1	no	—
14	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
17	C₅×Dic₃	—	2	1	no	—
18	C₅×Dic₃	C₈	1	2	yes	complemented
19	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic
20	C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
21	C₂×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
22	C₂×C₄×C₅	—	3	1	no	—
23	C₂×C₄×C₅	—	3	1	no	—
24	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
25	C₅×C₈	—	2	1	no	—
26	C₅×C₈	—	6	1	no	—
27	C₄⋊C₈	—	3	1	no	Sylow
28	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
30	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
32	C₂×Dic₃	C₄×C₅	1	1	yes	characteristic
33	C₂×Dic₃	C₄×C₅	1	1	yes	characteristic
34	C₃×C₈	—	2	1	no	—
35	C₃⋊C₈	—	2	1	no	—
36	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
37	C₄×C₅	—	3	2	no	—
38	C₄×C₅	—	6	1	no	—
39	C₄×C₅	Dic₆	1	1	yes	characteristic
40	C₄×C₅	#67	1	1	yes	characteristic
41	C₂×C₈	—	3	1	no	—
42	C₂×C₈	C₅×D₃	1	1	yes	characteristic
43	C₄²	—	3	1	no	—
44	C₃×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
46	C₃×C₄	C₅×D₄	1	1	yes	characteristic
47	C₃×C₄	C₅×Q₈	1	1	yes	characteristic
48	Dic₃	—	2	1	no	—
49	Dic₃	C₅×C₈	1	2	yes	complemented
50	C₂×C₅	D₃×C₈	1	1	yes	characteristic
51	C₂×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
52	C₂×C₅	Dic₃⋊C₄	1	1	yes	characteristic
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	3	1	no	—
55	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	6	1	no	—
58	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₃	C₂×C₅×C₈	1	1	yes	characteristic
60	C₂×C₃	C₅×M₁₆	1	1	yes	characteristic
61	C₅	Dic₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
62	C₂²	C₄×C₅×D₃	1	1	yes	characteristic
63	C₄	—	3	2	no	—
64	C₄	—	6	1	no	—
65	C₄	C₅×Dic₆	1	1	yes	characteristic
66	C₄	C₅×#67	1	1	yes	characteristic
67	C₃	C₅×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
68	C₂	C₅×D₃×C₈	1	1	yes	characteristic
69	C₂	C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
70	C₂	C₅×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₂×C₅×C₈
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₂×C₅×C₈	D₃
hypocenter	C₃	C₅×C₄⋊C₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
10. Dic₃⋊C₈	C₅	direct (N × H)
18. C₅×Dic₃	C₈	semidirect
44. C₃×C₅	C₄⋊C₈	semidirect
49. Dic₃	C₅×C₈	semidirect
61. C₅	Dic₃⋊C₈	direct (N × H)
67. C₃	C₅×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₈	2
C₄×C₅×Dic₃	2
C₂×C₅×C₃⋊C₈	2
C₅×C₄⋊C₈	3
Dic₃⋊C₈	5

Subgroups — C5×Dic3⋊C8 #91057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃⋊C₈ #91057