Subgroups — #4094⋊C₃ #91191

Order 480.

44 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	#4094	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
4	C₃×#168	—	4	1	no	maximal
5	#131⋊C₃	—	5	1	no	maximal, Hall
6	C₅×#41	C₂×C₃	1	1	yes	characteristic
7	#681	—	3	1	no	—
8	C₂×#168	—	3	1	no	—
9	C₃×C₄×C₅	—	4	1	no	—
10	#41⋊C₃	D₅	1	1	yes	characteristic
11	C₅×Q₈	C₃×C₄	1	1	yes	characteristic
12	C₅×D₄	—	3	1	no	—
13	C₂×C₄×C₅	—	3	1	no	—
14	#168	—	3	1	no	—
15	#168	A₄	1	1	yes	characteristic
16	#131	—	5	1	no	Sylow
17	C₂×C₃×C₅	—	4	1	no	—
18	SL(2,𝔽₃)	Dic₅	1	1	yes	characteristic
19	C₃×C₈	—	20	1	no	—
20	C₂²×C₅	—	3	1	no	—
21	C₄×C₅	—	3	1	no	—
22	C₄×C₅	C₂×A₄	1	1	yes	characteristic
23	#41	C₃×D₅	1	1	yes	characteristic
24	M₁₆	—	15	1	no	—
25	C₂×C₈	—	15	1	no	—
26	C₃×C₅	—	4	1	no	Hall
27	C₃×C₄	—	4	1	no	—
28	C₂×C₅	—	6	1	no	—
29	C₂×C₅	C₄×A₄	1	1	yes	characteristic
30	Q₈	C₃×Dic₅	1	1	yes	characteristic
31	D₄	—	3	1	no	—
32	C₂×C₄	—	3	1	no	—
33	C₈	—	5	1	no	—
34	C₈	—	15	1	no	—
35	C₂×C₃	—	4	1	no	—
36	C₅	#131⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	3	1	no	—
38	C₄	—	3	1	no	—
39	C₄	D₅×A₄	1	1	yes	characteristic
40	C₃	—	4	1	no	Sylow
41	C₂	—	6	1	no	—
42	C₂	A₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅×A₄
commutator, hypocenter	C₅×Q₈	C₃×C₄
Fitting, cosocle	C₅×#41	C₂×C₃
socle	C₂×C₅	C₄×A₄
prime radical	C₅×#41⋊C₃	C₂
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₄

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

N	H ≅ G/N	type
2. #4094	C₃	semidirect
36. C₅	#131⋊C₃	semidirect

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