Subgroups — C₅×C₁₇×5₋¹⁺² #24922290

Order 10625.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₁₇	C₅	1	1	yes	maximal, characteristic
2	C₁₇×5₋¹⁺²	C₅	1	25	yes	maximal, direct product factor
3	C₅×C₁₇×C₂₅	C₅	1	5	yes	maximal, complemented
4	C₅×5₋¹⁺²	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₅²×C₁₇	—	5	5	no	—
6	C₅²×C₁₇	C₅²	1	5	yes	—
7	C₅²×C₁₇	C₅²	1	1	yes	characteristic
8	C₁₇×C₂₅	C₅²	1	25	yes	complemented
9	C₅³	C₅×C₁₇	1	1	yes	characteristic
10	5₋¹⁺²	C₅×C₁₇	1	25	yes	direct product factor
11	C₅×C₂₅	C₅×C₁₇	1	5	yes	complemented
12	C₅×C₁₇	—	5	5	no	—
13	C₅×C₁₇	5₋¹⁺²	1	5	yes	direct product factor
14	C₅×C₁₇	C₅³	1	1	yes	characteristic
15	C₅²	—	5	5	no	—
16	C₅²	C₅²×C₁₇	1	5	yes	—
17	C₅²	C₅²×C₁₇	1	1	yes	characteristic
18	C₂₅	C₅²×C₁₇	1	25	yes	complemented
19	C₁₇	C₅×5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	—	5	5	no	—
21	C₅	C₁₇×5₋¹⁺²	1	5	yes	direct product factor
22	C₅	C₅³×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₅²×C₁₇	C₅²
commutator, Frattini, cosocle	C₅	C₅³×C₁₇
prime radical	C₅³×C₁₇	C₅
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅²×C₁₇ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.