Subgroups — C₃×D₂₅×C₂₂₇ #46801468

Order 34050.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₅×C₂₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₂₂₇	—	5	1	no	maximal
4	C₂₅×C₂₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₂₂₇	D₅	1	1	yes	characteristic
6	D₅×C₂₂₇	—	5	1	no	—
7	C₂×C₃×C₂₂₇	—	25	1	no	Hall
8	C₅×C₂₂₇	C₃×D₅	1	1	yes	characteristic
9	C₃×C₂₂₇	D₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₂₇	—	25	1	no	Hall
11	C₂₂₇	C₃×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×D₂₅	C₂₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₂₅	C₂×C₂₂₇	1	1	yes	characteristic, complemented, Hall
14	D₂₅	C₃×C₂₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×D₅	—	5	1	no	—
16	C₂₅	C₂×C₃×C₂₂₇	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	D₅×C₂₂₇	1	1	yes	characteristic
18	D₅	—	5	1	no	—
19	C₂×C₃	—	25	1	no	Hall
20	C₅	C₃×D₅×C₂₂₇	1	1	yes	characteristic
21	C₃	D₂₅×C₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₂₇	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃×C₂₂₇
Frattini	C₅	C₃×D₅×C₂₂₇
Fitting	C₃×C₂₅×C₂₂₇	C₂
socle	C₃×C₅×C₂₂₇	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₂₂₇

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.