Subgroups — 5₋¹⁺²×C₁₉₃ #37563227

Order 24125.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₉₃	C₅	1	1	yes	maximal, characteristic
2	C₂₅×C₁₉₃	C₅	1	5	yes	maximal, complemented
3	C₅×C₁₉₃	—	5	1	no	—
4	C₅×C₁₉₃	C₅²	1	1	yes	characteristic
5	C₁₉₃	5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
6	5₋¹⁺²	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₅²	C₅×C₁₉₃	1	1	yes	characteristic
8	C₂₅	C₅×C₁₉₃	1	5	yes	complemented
9	C₅	—	5	1	no	—
10	C₅	C₅²×C₁₉₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₅×C₁₉₃	C₅²
commutator, Frattini, cosocle	C₅	C₅²×C₁₉₃
prime radical	C₅²×C₁₉₃	C₅
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅×C₁₉₃ ◁ G

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.