Subgroups — D₂₅×C₅₉₃ #44445697

Order 29650.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₅₉₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₅₉₃	—	5	1	no	maximal
3	C₅×C₅₉₃	D₅	1	1	yes	characteristic
4	C₂×C₅₉₃	—	25	1	no	Hall
5	C₅₉₃	D₂₅	1	1	yes	characteristic, direct product factor, Sylow
6	D₂₅	C₅₉₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂₅	C₂×C₅₉₃	1	1	yes	characteristic, complemented, Sylow
8	D₅	—	5	1	no	—
9	C₅	D₅×C₅₉₃	1	1	yes	characteristic
10	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉₃	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₅₉₃
Frattini	C₅	D₅×C₅₉₃
Fitting	C₂₅×C₅₉₃	C₂
socle	C₅×C₅₉₃	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₅₉₃

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.