Subgroups — C₃²×C₅×D₂₅₇ #37528906

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	C₃×C₅×D₂₅₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₂₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₂₅₇	C₂×C₃	1	4	yes	complemented
5	C₅×D₂₅₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₂₅₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₂₅₇	C₃×C₅	1	4	yes	direct product factor
8	C₅×C₂₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₅₇	C₂×C₃×C₅	1	4	yes	complemented
10	D₂₅₇	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂₅₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃²×C₅	—	257	1	no	maximal, Hall
13	C₃²×C₅	D₂₅₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅	—	257	4	no	—
15	C₂×C₃²	—	257	1	no	Hall
16	C₃×C₅	C₃×D₂₅₇	1	4	yes	direct product factor
17	C₂×C₅	—	257	1	no	Hall
18	C₃²	C₅×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	257	4	no	—
20	C₅	C₃²×D₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₃×C₅×D₂₅₇	1	4	yes	direct product factor
22	C₂	—	257	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅	D₂₅₇
commutator, cosocle, hypocenter	C₂₅₇	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₂₅₇	C₂
LCS	G ▷ C₂₅₇
UCS	C₁ ◁ C₃²×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.