Subgroups — #91185

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#3969	—	3	1	no	maximal, Hall
3	C₅×SL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
4	C₃⋊#168	—	4	1	no	maximal
5	GU(2,𝔽₃)	—	5	1	no	maximal, Hall
6	C₅×#41	D₃	1	1	yes	characteristic
7	C₄×Dic₅	—	3	1	no	—
8	#681	—	3	1	no	—
9	C₃×C₄×C₅	—	4	1	no	—
10	#41⋊C₃	D₅	1	1	yes	characteristic
11	C₅×Q₈	Dic₃	1	1	yes	characteristic
12	C₅×D₄	—	3	1	no	—
13	C₂×C₄×C₅	—	3	1	no	—
14	C₂×Dic₅	—	6	1	no	—
15	#168	—	6	1	no	—
16	#104	—	15	1	no	Sylow
17	C₂×C₃×C₅	—	4	1	no	—
18	SL(2,𝔽₃)	Dic₅	1	1	yes	characteristic, complemented
19	C₃⋊C₈	—	20	1	no	—
20	C₂²×C₅	—	3	1	no	—
21	C₄×C₅	—	3	1	no	—
22	C₄×C₅	S₄	1	1	yes	characteristic
23	Dic₅	—	6	2	no	—
24	#41	D₁₅	1	1	yes	characteristic
25	M₁₆	—	15	1	no	—
26	C₄²	—	15	1	no	—
27	C₃×C₅	—	4	1	no	Hall
28	C₃×C₄	—	4	1	no	—
29	C₂×C₅	—	6	1	no	—
30	C₂×C₅	SL(2,ℤ/4)	1	1	yes	characteristic
31	Q₈	Dic₁₅	1	1	yes	characteristic
32	D₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	—	30	1	no	—
35	C₈	—	30	1	no	—
36	C₂×C₃	—	4	1	no	—
37	C₅	GU(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	3	1	no	—
39	C₄	—	3	1	no	—
40	C₄	—	30	2	no	—
41	C₄	C₅⋊S₄	1	1	yes	characteristic
42	C₃	—	4	1	no	Sylow
43	C₂	—	6	1	no	—
44	C₂	A₄⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₅⋊S₄
commutator, hypocenter	C₅×SL(2,𝔽₃)	C₄
Fitting	C₅×#41	D₃
socle	C₂×C₅	SL(2,ℤ/4)
prime radical, cosocle	C₅×#41⋊C₃	C₂
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₄

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

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