Subgroups — C₃×C₅²×D₂₂₇ #46801481

Order 34050.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₂₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×D₂₂₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₂₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₂₂₇	C₂×C₅	1	6	yes	complemented
6	C₅×D₂₂₇	C₃×C₅	1	6	yes	direct product factor
7	C₃×D₂₂₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₂₇	C₂×C₃×C₅	1	6	yes	complemented
9	C₃×C₂₂₇	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	D₂₂₇	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂₂₇	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃×C₅²	—	227	1	no	maximal, Hall
13	C₃×C₅²	D₂₂₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅²	—	227	1	no	Hall
15	C₂×C₃×C₅	—	227	6	no	—
16	C₅²	C₃×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₅×D₂₂₇	1	6	yes	direct product factor
18	C₂×C₅	—	227	6	no	—
19	C₂×C₃	—	227	1	no	Hall
20	C₅	C₃×C₅×D₂₂₇	1	6	yes	direct product factor
21	C₃	C₅²×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	227	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅²	D₂₂₇
commutator, cosocle, hypocenter	C₂₂₇	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₂₇	C₂
LCS	G ▷ C₂₂₇
UCS	C₁ ◁ C₃×C₅²

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.