Subgroups — C₅×#95⋊C₃ #90998

Order 480.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#95	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×A₄	—	4	1	no	maximal
3	#95⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₄×C₅	—	3	1	no	—
5	C₅×A₄	—	4	1	no	—
6	C₂³×C₅	A₄	1	1	yes	characteristic
7	C₂×C₄×C₅	—	3	2	no	—
8	C₂×C₄×C₅	—	6	2	no	—
9	#95	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃×C₅	—	16	1	no	—
11	C₂×A₄	—	4	1	no	—
12	C₂²×C₅	—	3	1	no	—
13	C₂²×C₅	—	3	1	no	—
14	C₂²×C₅	SL(2,𝔽₃)	1	1	yes	characteristic
15	C₄×C₅	—	6	2	no	—
16	C₂²×C₄	—	3	1	no	—
17	C₃×C₅	—	16	1	no	Hall
18	A₄	—	4	1	no	—
19	C₂×C₅	—	3	1	no	—
20	C₂×C₅	—	3	1	no	—
21	C₂×C₅	C₄²⋊C₃	1	1	yes	characteristic
22	C₂³	C₅×A₄	1	1	yes	characteristic
23	C₂×C₄	—	3	2	no	—
24	C₂×C₄	—	6	2	no	—
25	C₂×C₃	—	16	1	no	—
26	C₅	#95⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	3	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	C₅×SL(2,𝔽₃)	1	1	yes	characteristic
30	C₄	—	6	2	no	—
31	C₃	—	16	1	no	Sylow
32	C₂	—	3	1	no	—
33	C₂	—	3	1	no	—
34	C₂	C₅×C₄²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃×C₅
Frattini	C₂³	C₅×A₄
Fitting	C₅×#95	C₃
socle	C₂³×C₅	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₅

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.