Subgroups — C₃×C₈×Dic₅ #91015

Order 480.

88 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	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×Dic₅	C₄	1	2	yes	—
7	C₃×C₅×C₈	C₄	1	2	yes	complemented
8	C₃×#168	C₄	1	2	yes	complemented
9	C₃×C₄×C₈	—	5	1	no	maximal, Hall
10	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
11	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
12	C₂×#168	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₃×Dic₅	C₈	1	4	yes	direct product factor
17	C₂×C₃×C₈	—	5	1	no	—
18	C₂×C₃×C₈	D₅	1	1	yes	characteristic
19	C₃×C₄²	—	5	1	no	—
20	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
21	C₂×Dic₅	C₃×C₄	1	2	yes	—
22	C₅×C₈	C₃×C₄	1	2	yes	complemented
23	#168	C₃×C₄	1	2	yes	complemented
24	C₄×C₈	—	5	1	no	Sylow
25	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂×C₈	1	2	yes	—
27	C₂×C₃×C₄	—	5	2	no	—
28	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
29	C₃×C₈	—	5	2	no	—
30	C₃×C₈	Dic₅	1	2	yes	direct product factor
31	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
32	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
33	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
34	Dic₅	C₃×C₈	1	4	yes	direct product factor
35	C₂×C₈	—	5	1	no	—
36	C₂×C₈	C₃×D₅	1	1	yes	characteristic
37	C₄²	—	5	1	no	—
38	C₃×C₅	C₄×C₈	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
40	C₃×C₄	—	5	4	no	—
41	C₃×C₄	C₄×D₅	1	1	yes	characteristic
42	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
43	C₂×C₅	C₃×C₄²	1	1	yes	characteristic
44	C₂×C₅	C₂×C₃×C₈	1	2	yes	—
45	C₂×C₄	—	5	2	no	—
46	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
47	C₈	—	5	2	no	—
48	C₈	C₃×Dic₅	1	2	yes	direct product factor
49	C₂×C₃	C₈×D₅	1	2	yes	—
50	C₂×C₃	C₄×Dic₅	1	1	yes	characteristic
51	C₅	C₃×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
52	C₂²	C₃×C₄×D₅	1	1	yes	characteristic
53	C₄	—	5	4	no	—
54	C₄	C₃×C₄×D₅	1	1	yes	characteristic
55	C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
56	C₃	C₈×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	C₃×C₈×D₅	1	2	yes	—
58	C₂	C₃×C₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₅
commutator, hypocenter	C₅	C₃×C₄×C₈
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. C₈×Dic₅	C₃	direct (N × H)
7. C₃×C₅×C₈	C₄	semidirect
8. C₃×#168	C₄	semidirect
16. C₃×Dic₅	C₈	direct (N × H)
22. C₅×C₈	C₃×C₄	semidirect
23. #168	C₃×C₄	semidirect
30. C₃×C₈	Dic₅	direct (N × H)
34. Dic₅	C₃×C₈	direct (N × H)
38. C₃×C₅	C₄×C₈	semidirect
48. C₈	C₃×Dic₅	direct (N × H)
51. C₅	C₃×C₄×C₈	semidirect
56. C₃	C₈×Dic₅	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×C₃×C₅×C₈	2
C₃×C₄×Dic₅	2
C₂×C₃×#168	2
C₈×Dic₅	3
C₃×C₄×C₈	5

Subgroups — C3×C8×Dic5 #91015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×Dic₅ #91015