Subgroups — C₅⋊#857 #91182

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#3937	—	3	1	no	maximal, Hall
3	C₅⋊S₄	—	4	1	no	maximal
4	#857	—	5	1	no	maximal, Hall
5	#709	—	3	1	no	—
6	C₄²×C₅	D₃	1	1	yes	characteristic, complemented
7	#681	—	3	1	no	—
8	C₅×A₄	—	4	1	no	—
9	C₄²⋊C₃	D₅	1	1	yes	characteristic, complemented
10	C₂×C₄×C₅	—	3	1	no	—
11	C₂²⋊D₅	—	6	1	no	—
12	D₂₀	—	3	1	no	—
13	C₄×D₅	—	6	1	no	—
14	Dic₁₀	—	3	1	no	—
15	#168	—	6	1	no	—
16	#104	—	15	1	no	Sylow
17	D₁₅	—	16	1	no	—
18	S₄	—	20	1	no	—
19	C₂²×C₅	S₄	1	1	yes	characteristic
20	C₂×D₅	—	6	1	no	—
21	C₄×C₅	—	3	1	no	—
22	C₄×C₅	—	3	1	no	—
23	Dic₅	—	6	1	no	—
24	#41	—	15	1	no	—
25	M₁₆	—	15	1	no	—
26	C₄²	D₁₅	1	1	yes	characteristic, complemented
27	C₃×C₅	—	16	1	no	Hall
28	A₄	—	4	1	no	—
29	C₂×C₅	—	3	1	no	—
30	D₅	—	12	1	no	—
31	Q₈	—	15	1	no	—
32	D₄	—	15	1	no	—
33	D₄	—	30	1	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	30	1	no	—
36	C₈	—	30	1	no	—
37	D₃	—	80	1	no	—
38	C₅	#857	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	30	1	no	—
40	C₂²	C₅⋊S₄	1	1	yes	characteristic
41	C₄	—	3	1	no	—
42	C₄	—	3	1	no	—
43	C₄	—	30	1	no	—
44	C₃	—	16	1	no	Sylow
45	C₂	—	3	1	no	—
46	C₂	—	60	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×C₄²⋊C₃	C₂
Frattini	C₂²	C₅⋊S₄
Fitting	C₄²×C₅	D₃
socle	C₂²×C₅	S₄
LCS	G ▷ C₅×C₄²⋊C₃
UCS	C₁

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.