Subgroups — C₅×C₃⋊D₃×C₂₅₇ #37528913

Order 23130.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₂₅₇	—	3	4	no	maximal
3	C₃⋊D₃×C₂₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₂₅₇	D₃	1	4	yes	complemented
5	C₂×C₅×C₂₅₇	—	9	1	no	Hall
6	C₃²×C₂₅₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₂₅₇	—	3	4	no	—
8	C₅×C₂₅₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₂₅₇	C₅×D₃	1	4	yes	complemented
10	C₂×C₂₅₇	—	9	1	no	Hall
11	C₂₅₇	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₅×C₃⋊D₃	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅	C₂×C₂₅₇	1	1	yes	characteristic, complemented, Hall
14	C₅×D₃	—	3	4	no	—
15	C₃⋊D₃	C₅×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅	D₃×C₂₅₇	1	4	yes	complemented
17	C₂×C₅	—	9	1	no	Hall
18	C₃²	C₂×C₅×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	3	4	no	—
20	C₅	C₃⋊D₃×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₅×D₃×C₂₅₇	1	4	yes	complemented
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₅₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₂₅₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₂₅₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₂₅₇

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.