Subgroups — C₂×C₅×D₂₅ #92542

Order 500.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₅×C₂₅	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅×D₅	—	5	1	no	maximal
5	C₂×D₂₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅²	D₅	1	1	yes	characteristic
7	C₅×D₅	—	5	2	no	—
8	C₂×C₂₅	—	2	2	no	—
9	C₂×C₂₅	C₂×C₅	1	1	yes	characteristic, complemented
10	D₂₅	C₂×C₅	1	2	yes	direct product factor
11	C₅²	C₂×D₅	1	1	yes	characteristic
12	C₂₅	—	2	2	no	—
13	C₂₅	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂²×C₅	—	25	1	no	—
15	C₂×D₅	—	5	1	no	—
16	C₂×C₅	—	2	2	no	—
17	C₂×C₅	—	25	2	no	—
18	C₂×C₅	D₂₅	1	1	yes	characteristic, direct product factor
19	C₂×C₅	C₅×D₅	1	1	yes	characteristic
20	D₅	—	5	2	no	—
21	C₅	—	2	2	no	—
22	C₅	C₂×D₂₅	1	1	yes	characteristic, direct product factor
23	C₅	C₂×C₅×D₅	1	1	yes	characteristic
24	C₂²	—	25	1	no	Sylow
25	C₂	—	25	2	no	—
26	C₂	C₅×D₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₅
Frattini	C₅	C₂×C₅×D₅
Fitting	C₂×C₅×C₂₅	C₂
socle	C₂×C₅²	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₅

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.