Subgroups — C₃×C₇×D₂₅ #11760367

Order 1050.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×D₅	—	5	1	no	maximal
4	C₇×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇	D₅	1	1	yes	characteristic
7	C₃×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₅	—	5	1	no	—
9	D₂₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇	—	25	1	no	Hall
11	C₅×C₇	C₃×D₅	1	1	yes	characteristic
12	C₃×D₅	—	5	1	no	—
13	C₂₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₇	D₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅	C₇×D₅	1	1	yes	characteristic
16	C₂×C₇	—	25	1	no	Hall
17	D₅	—	5	1	no	—
18	C₇	C₃×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	25	1	no	Hall
20	C₅	C₃×C₇×D₅	1	1	yes	characteristic
21	C₃	C₇×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃×C₇
Frattini	C₅	C₃×C₇×D₅
Fitting	C₃×C₇×C₂₅	C₂
socle	C₃×C₅×C₇	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₇

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.