Subgroups — C₅×#800 #91043

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×SD₃₂	—	3	1	no	maximal, Hall
5	C₅×D₁₂	—	2	1	no	—
6	C₅×Dic₆	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	#800	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₁₆	—	3	1	no	—
10	C₅×D₈	—	3	1	no	—
11	C₅×C₁₆	D₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₃	—	4	1	no	—
13	C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	C₅×Dic₃	—	4	1	no	—
15	Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
16	D₂₄	C₂×C₅	1	1	yes	characteristic
17	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅×Q₈	—	6	1	no	—
19	C₅×D₄	—	6	1	no	—
20	C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	SD₃₂	—	3	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	C₅×D₃	—	8	1	no	—
24	D₁₂	—	2	1	no	—
25	Dic₆	—	2	1	no	—
26	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
27	C₂²×C₅	—	12	1	no	—
28	C₄×C₅	—	12	1	no	—
29	C₄×C₅	D₁₂	1	1	yes	characteristic
30	Q₁₆	—	3	1	no	—
31	D₈	—	3	1	no	—
32	C₁₆	C₅×D₃	1	1	yes	characteristic, complemented
33	C₃×C₅	SD₃₂	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃	—	4	1	no	—
35	C₃×C₄	C₅×D₄	1	1	yes	characteristic
36	Dic₃	—	4	1	no	—
37	C₂×C₅	—	24	1	no	—
38	C₂×C₅	D₂₄	1	1	yes	characteristic
39	Q₈	—	6	1	no	—
40	D₄	—	6	1	no	—
41	C₈	C₂×C₅×D₃	1	1	yes	characteristic
42	C₂×C₃	C₅×D₈	1	1	yes	characteristic
43	D₃	—	8	1	no	—
44	C₅	#800	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	—	12	1	no	—
46	C₄	—	12	1	no	—
47	C₄	C₅×D₁₂	1	1	yes	characteristic
48	C₃	C₅×SD₃₂	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	24	1	no	—
50	C₂	C₅×D₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₂₄
commutator, cosocle	C₃×C₈	C₂²×C₅
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	D₈
prime radical	C₅×D₂₄	C₂
hypercenter	C₅×C₁₆	D₃
hypocenter	C₃	C₅×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₅×Dic₁₂	C₂	semidirect
3. C₃×C₅×C₁₆	C₂	semidirect
8. #800	C₅	direct (N × H)
11. C₅×C₁₆	D₃	semidirect
15. Dic₁₂	C₂×C₅	semidirect
17. C₃×C₁₆	C₂×C₅	semidirect
32. C₁₆	C₅×D₃	semidirect
33. C₃×C₅	SD₃₂	semidirect
44. C₅	#800	direct (N × H)
48. C₃	C₅×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₁₂	2
C₅×D₂₄	2
C₃×C₅×C₁₆	2
C₅×SD₃₂	3
#800	5

Subgroups — C5×#800 #91043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#800 #91043