Subgroups — #91161

Order 480.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6758	C₂	1	1	yes	maximal, characteristic
2	C₃×#700	C₂	1	1	yes	maximal, characteristic
3	D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#3995	—	3	1	no	maximal, Hall
5	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₃⋊#170	—	2	1	no	—
7	C₃×#170	—	2	1	no	—
8	C₃⋊#168	C₄	1	1	yes	characteristic
9	C₅×C₃⋊C₈	C₄	1	1	yes	characteristic
10	#822	—	5	1	no	maximal, Hall
11	#700	—	3	1	no	—
12	#700	D₃	1	1	yes	characteristic
13	C₈×D₅	—	3	1	no	—
14	C₂×C₃×D₅	Q₈	1	1	yes	characteristic
15	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₃×Dic₅	D₄	1	1	yes	characteristic
17	C₃×M₁₆	—	5	1	no	—
18	#208	—	5	1	no	—
19	C₂×C₃⋊C₈	—	5	1	no	—
20	C₄×D₅	C₂×D₃	1	1	yes	characteristic
21	#170	—	2	1	no	—
22	#170	—	6	1	no	—
23	C₅×C₈	—	3	1	no	—
24	#168	—	3	1	no	—
25	#108	—	15	1	no	Sylow
26	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
27	C₃×D₅	—	2	1	no	—
28	C₂×C₃×C₄	—	5	1	no	—
29	C₃×C₈	—	10	1	no	—
30	C₃⋊C₈	—	5	1	no	—
31	C₃⋊C₈	—	10	1	no	—
32	C₃⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₂×D₅	Dic₆	1	1	yes	characteristic
34	C₄×C₅	C₄×D₃	1	1	yes	characteristic
35	Dic₅	#67	1	1	yes	characteristic
36	M₁₆	—	5	1	no	—
37	M₁₆	—	15	1	no	—
38	C₂×C₈	—	15	1	no	—
39	C₃×C₅	#108	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₃	—	5	1	no	—
41	C₃×C₄	—	5	1	no	—
42	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₂×C₅	Dic₃⋊C₄	1	1	yes	characteristic
44	D₅	—	2	1	no	—
45	C₂×C₄	—	5	1	no	—
46	C₈	—	3	1	no	—
47	C₈	—	10	1	no	—
48	C₈	—	15	1	no	—
49	C₈	—	30	1	no	—
50	C₂×C₃	—	10	1	no	—
51	C₂×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₅	#822	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	5	1	no	—
54	C₄	—	5	1	no	—
55	C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
56	C₃	#3995	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	10	1	no	—
58	C₂	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	Dic₃⋊AGL(1,𝔽₅)
commutator, Fitting	C₃×C₄×C₅	C₂×C₄
Frattini, hypercenter	C₄	D₃×AGL(1,𝔽₅)
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂×C₃×D₅	Q₈
cosocle	C₃×C₄×D₅	C₂²
hypocenter	C₃×C₅	#108
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
39. C₃×C₅	#108	semidirect
52. C₅	#822	semidirect
56. C₃	#3995	semidirect

Maximal subgroups

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

subgroup	index
#6758	2
C₃×#700	2
D₅×C₃⋊C₈	2
#3995	3
#822	5