Subgroups — C₅×C₂₉×5₋¹⁺² #31827358

Order 18125.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₂₉	C₅	1	1	yes	maximal, characteristic
2	C₂₉×5₋¹⁺²	C₅	1	25	yes	maximal, direct product factor
3	C₅×C₂₅×C₂₉	C₅	1	5	yes	maximal, complemented
4	C₅²×C₂₉	—	5	5	no	—
5	C₅²×C₂₉	C₅²	1	5	yes	—
6	C₅²×C₂₉	C₅²	1	1	yes	characteristic
7	C₂₅×C₂₉	C₅²	1	25	yes	complemented
8	C₅×5₋¹⁺²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₅×C₂₉	—	5	5	no	—
10	C₅×C₂₉	5₋¹⁺²	1	5	yes	direct product factor
11	C₅×C₂₉	C₅³	1	1	yes	characteristic
12	C₅³	C₅×C₂₉	1	1	yes	characteristic
13	5₋¹⁺²	C₅×C₂₉	1	25	yes	direct product factor
14	C₅×C₂₅	C₅×C₂₉	1	5	yes	complemented
15	C₂₉	C₅×5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
16	C₅²	—	5	5	no	—
17	C₅²	C₅²×C₂₉	1	5	yes	—
18	C₅²	C₅²×C₂₉	1	1	yes	characteristic
19	C₂₅	C₅²×C₂₉	1	25	yes	complemented
20	C₅	—	5	5	no	—
21	C₅	C₂₉×5₋¹⁺²	1	5	yes	direct product factor
22	C₅	C₅³×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₅²×C₂₉	C₅²
commutator, Frattini, cosocle	C₅	C₅³×C₂₉
prime radical	C₅³×C₂₉	C₅
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅²×C₂₉ ◁ 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.