Subgroups — C₅⋊PSU(3,𝔽₂) #67206

Order 360.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4379	C₂	1	2	yes	maximal
2	C₅×#157	C₂	1	1	yes	maximal, characteristic
3	C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
4	PSU(3,𝔽₂)	—	5	1	no	maximal, Hall
5	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
6	Dic₁₀	—	9	1	no	maximal, Hall
7	#157	—	5	2	no	—
8	#157	D₅	1	1	yes	characteristic
9	C₅×D₃	—	12	1	no	—
10	C₄×C₅	—	9	1	no	—
11	Dic₅	—	9	2	no	—
12	C₃⋊D₃	C₂×D₅	1	1	yes	characteristic
13	C₃×C₅	—	4	1	no	—
14	C₂×C₅	—	9	1	no	—
15	C₃²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
16	Q₈	—	45	1	no	Sylow
17	D₃	—	12	1	no	—
18	C₅	PSU(3,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
19	C₄	—	9	1	no	—
20	C₄	—	45	2	no	—
21	C₃	—	4	1	no	—
22	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, prime radical, cosocle	C₅×C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃²×C₅	Q₈
LCS	G ▷ C₅×C₃⋊D₃ ▷ C₃²×C₅
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.