Subgroups — #91117

Order 480.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	#6710	C₂	1	2	yes	maximal, complemented
3	#3965	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₅	C₄	1	2	yes	—
5	C₃×C₅×D₄	—	2	2	no	—
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃⋊#168	—	2	2	no	—
8	#833	—	5	1	no	maximal, Hall
9	C₂×C₅×D₄	D₃	1	1	yes	characteristic
10	#681	—	3	2	no	—
11	C₂²×C₃×C₅	—	2	2	no	—
12	C₂²×C₃×C₅	—	4	2	no	—
13	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₅	D₄	1	2	yes	—
15	C₂×C₃×D₄	D₅	1	1	yes	characteristic
16	#208	—	5	2	no	—
17	C₂³×C₅	Dic₃	1	2	yes	—
18	C₅×D₄	—	2	2	no	—
19	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
20	#168	—	6	2	no	—
21	#100	—	15	1	no	Sylow
22	C₂×C₃×C₅	—	2	1	no	—
23	C₂×C₃×C₅	—	4	2	no	—
24	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	C₂³×C₃	Dic₅	1	2	yes	—
26	C₃×D₄	—	2	2	no	—
27	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
28	C₃⋊C₈	—	10	2	no	—
29	C₂²×C₅	—	2	2	no	—
30	C₂²×C₅	—	4	2	no	—
31	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
32	C₄×C₅	#67	1	2	yes	—
33	C₂×D₄	D₁₅	1	1	yes	characteristic
34	M₁₆	—	15	2	no	—
35	C₃×C₅	#100	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	—	2	2	no	—
37	C₂²×C₃	—	4	2	no	—
38	C₂²×C₃	C₂×Dic₅	1	1	yes	characteristic
39	C₃×C₄	C₂²⋊D₅	1	2	yes	—
40	C₂×C₅	—	2	1	no	—
41	C₂×C₅	—	4	2	no	—
42	C₂×C₅	#217	1	1	yes	characteristic
43	C₂³	Dic₁₅	1	2	yes	—
44	D₄	—	2	2	no	—
45	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
46	C₈	—	30	2	no	—
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	—	4	2	no	—
49	C₂×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
50	C₅	#833	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	2	2	no	—
52	C₂²	—	4	2	no	—
53	C₂²	C₂×Dic₁₅	1	1	yes	characteristic
54	C₄	#1220	1	2	yes	—
55	C₃	#3965	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	4	2	no	—
58	C₂	#6719	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#6719
commutator	C₂²×C₃×C₅	C₂×C₄
Frattini	C₂×C₄	C₂×D₁₅
Fitting, prime radical	C₂×C₃×C₅×D₄	C₂
socle	C₂×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₅	C₂²
hypercenter	C₂×D₄	D₁₅
hypocenter	C₃×C₅	#100
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. #6710	C₂	semidirect
35. C₃×C₅	#100	semidirect
50. C₅	#833	semidirect
55. C₃	#3965	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×D₄	2
#6710	2
#3965	3
#833	5