Subgroups — #91087

Order 480.

80 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×C₃⋊#168	C₂	1	2	yes	maximal
3	#3935	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	2	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₃⋊#168	C₄	1	4	yes	complemented
7	#803	—	5	1	no	maximal, Hall
8	C₄²×C₅	D₃	1	1	yes	characteristic
9	C₂×#168	—	3	2	no	—
10	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₅	—	2	2	no	—
12	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
13	C₃×C₄²	D₅	1	1	yes	characteristic
14	C₂×C₃⋊C₈	—	5	2	no	—
15	C₂×C₄×C₅	Dic₃	1	2	yes	—
16	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
17	#168	—	3	4	no	—
18	#97	—	15	1	no	Sylow
19	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
20	C₂×C₃×C₅	M₁₆	1	2	yes	—
21	C₂×C₃×C₄	Dic₅	1	2	yes	—
22	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
23	C₃⋊C₈	—	5	4	no	—
24	C₂²×C₅	C₂×Dic₃	1	1	yes	characteristic
25	C₄×C₅	—	2	2	no	—
26	C₄×C₅	C₄×D₃	1	2	yes	—
27	C₂×C₈	—	15	2	no	—
28	C₄²	D₁₅	1	1	yes	characteristic
29	C₃×C₅	#97	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂×Dic₅	1	1	yes	characteristic
31	C₃×C₄	—	2	2	no	—
32	C₃×C₄	C₄×D₅	1	2	yes	—
33	C₂×C₅	#208	1	2	yes	—
34	C₂×C₅	C₄×Dic₃	1	1	yes	characteristic
35	C₂×C₄	Dic₁₅	1	2	yes	—
36	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
37	C₈	—	15	4	no	—
38	C₂×C₃	#681	1	2	yes	—
39	C₂×C₃	C₄×Dic₅	1	1	yes	characteristic
40	C₅	#803	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₂×Dic₁₅	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	C₄×D₁₅	1	2	yes	—
44	C₃	#3935	1	1	yes	characteristic, complemented, Sylow
45	C₂	#6710	1	2	yes	—
46	C₂	C₄×Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₁₅
commutator	C₂×C₃×C₅	C₄²
Fitting	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²
hypercenter	C₄²	D₁₅
hypocenter	C₃×C₅	#97
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
6. C₃⋊#168	C₄	semidirect
29. C₃×C₅	#97	semidirect
40. C₅	#803	semidirect
44. C₃	#3935	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×C₃⋊#168	2
#3935	3
#803	5