Subgroups — C₅×#822 #91065

Order 480.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#108	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×C₈	—	2	1	no	—
7	C₅×C₃⋊C₈	—	2	1	no	—
8	C₅×C₃⋊C₈	C₄	1	2	yes	—
9	#822	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×M₁₆	—	3	1	no	—
11	C₅×M₁₆	D₃	1	1	yes	characteristic
12	C₂×C₅×C₈	—	3	1	no	—
13	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
14	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
17	#208	C₂×C₅	1	1	yes	characteristic
18	C₂×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
19	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
20	C₅×C₈	—	2	1	no	—
21	C₅×C₈	—	3	2	no	—
22	C₅×C₈	—	6	1	no	—
23	#108	—	3	1	no	Sylow
24	C₂×C₃×C₅	—	2	1	no	—
25	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
27	C₃×C₈	—	2	1	no	—
28	C₃⋊C₈	—	2	1	no	—
29	C₃⋊C₈	C₄×C₅	1	2	yes	—
30	C₂²×C₅	Dic₆	1	1	yes	characteristic
31	C₄×C₅	C₄×D₃	1	1	yes	characteristic
32	C₄×C₅	#67	1	1	yes	characteristic
33	M₁₆	—	3	1	no	—
34	M₁₆	C₅×D₃	1	1	yes	characteristic
35	C₂×C₈	—	3	1	no	—
36	C₃×C₅	#108	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃	C₅×Q₈	1	1	yes	characteristic
38	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
39	C₃×C₄	C₅×D₄	1	1	yes	characteristic
40	C₂×C₅	—	2	1	no	—
41	C₂×C₅	Dic₃⋊C₄	1	1	yes	characteristic
42	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	3	2	no	—
45	C₈	—	6	1	no	—
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
48	C₅	#822	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	C₅×Dic₆	1	1	yes	characteristic
50	C₄	C₄×C₅×D₃	1	1	yes	characteristic
51	C₄	C₅×#67	1	1	yes	characteristic
52	C₃	C₅×#108	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	2	1	no	—
54	C₂	C₅×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#67
commutator	C₃×C₄	C₂×C₄×C₅
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₃×C₅×M₁₆	C₂
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂²×C₃×C₅	Q₈
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₅×M₁₆	D₃
hypocenter	C₃	C₅×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₅×M₁₆

Complements

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

N	H ≅ G/N	type
9. #822	C₅	direct (N × H)
36. C₃×C₅	#108	semidirect
48. C₅	#822	direct (N × H)
52. C₃	C₅×#108	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×M₁₆	2
C₅×#208	2
C₂×C₅×C₃⋊C₈	2
C₅×#108	3
#822	5

Subgroups — C5×#822 #91065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#822 #91065