Subgroups — C₅×C₄⋊(C₃⋊C₈) #91047

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₅×C₄⋊C₈	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₅×C₃⋊C₈	—	2	2	no	—
8	C₄⋊(C₃⋊C₈)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₈	—	3	2	no	—
10	C₄²×C₅	D₃	1	1	yes	characteristic
11	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	—	2	1	no	—
13	C₃×C₄×C₅	C₈	1	2	yes	complemented
14	C₃×C₄×C₅	D₄	1	1	yes	characteristic
15	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
16	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
17	C₂×C₃⋊C₈	C₂×C₅	1	2	yes	—
18	C₂×C₄×C₅	Dic₃	1	1	yes	characteristic
19	C₂×C₄×C₅	Dic₃	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	C₅×C₈	—	6	2	no	—
22	C₄⋊C₈	—	3	1	no	Sylow
23	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃×C₅	M₁₆	1	1	yes	characteristic
26	C₂×C₃×C₄	C₄×C₅	1	1	yes	characteristic
27	C₂×C₃×C₄	C₄×C₅	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
29	C₃⋊C₈	—	2	2	no	—
30	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
31	C₄×C₅	—	2	1	no	—
32	C₄×C₅	C₃⋊C₈	1	2	yes	complemented
33	C₄×C₅	Dic₆	1	1	yes	characteristic
34	C₄×C₅	D₁₂	1	1	yes	characteristic
35	C₂×C₈	—	3	2	no	—
36	C₄²	C₅×D₃	1	1	yes	characteristic
37	C₃×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	C₅×C₈	1	2	yes	complemented
41	C₃×C₄	C₅×D₄	1	1	yes	characteristic
42	C₃×C₄	C₅×Q₈	1	1	yes	characteristic
43	C₂×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
44	C₂×C₅	#208	1	1	yes	characteristic
45	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
46	C₂×C₄	C₅×Dic₃	1	1	yes	characteristic
47	C₂×C₄	C₅×Dic₃	1	1	yes	characteristic
48	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
49	C₈	—	6	2	no	—
50	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃	C₂×C₅×C₈	1	1	yes	characteristic
52	C₂×C₃	C₅×M₁₆	1	1	yes	characteristic
53	C₅	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	C₂×C₅×Dic₃	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	C₅×C₃⋊C₈	1	2	yes	complemented
57	C₄	C₅×Dic₆	1	1	yes	characteristic
58	C₄	C₅×D₁₂	1	1	yes	characteristic
59	C₃	C₅×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
60	C₂	C₂×C₅×C₃⋊C₈	1	1	yes	characteristic
61	C₂	C₅×#208	1	1	yes	characteristic
62	C₂	C₅×C₄⋊Dic₃	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	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×C₄⋊C₈
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
8. C₄⋊(C₃⋊C₈)	C₅	direct (N × H)
13. C₃×C₄×C₅	C₈	semidirect
32. C₄×C₅	C₃⋊C₈	semidirect
37. C₃×C₅	C₄⋊C₈	semidirect
40. C₃×C₄	C₅×C₈	semidirect
53. C₅	C₄⋊(C₃⋊C₈)	direct (N × H)
56. C₄	C₅×C₃⋊C₈	semidirect
59. 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
C₃×C₄²×C₅	2
C₂×C₅×C₃⋊C₈	2
C₅×C₄⋊C₈	3
C₄⋊(C₃⋊C₈)	5

Subgroups — C5×C4⋊(C3⋊C8) #91047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊(C₃⋊C₈) #91047