Subgroups — C₂×C₅⋊D₂₅ #92546

Order 500.

70 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	—	5	5	no	maximal
6	C₂×C₅²	D₅	1	1	yes	characteristic
7	C₅⋊D₅	—	5	2	no	—
8	C₂×C₂₅	D₅	1	5	yes	complemented
9	D₂₅	—	5	10	no	—
10	C₅²	C₂×D₅	1	1	yes	characteristic
11	C₂₅	C₂×D₅	1	5	yes	complemented
12	C₂×D₅	—	25	1	no	—
13	C₂×D₅	—	25	5	no	—
14	C₂×C₅	D₂₅	1	5	yes	complemented
15	C₂×C₅	C₅⋊D₅	1	1	yes	characteristic
16	D₅	—	25	10	no	—
17	D₅	—	25	2	no	—
18	C₅	C₂×D₂₅	1	5	yes	complemented
19	C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
20	C₂²	—	125	1	no	Sylow
21	C₂	—	125	2	no	—
22	C₂	C₅⋊D₂₅	1	1	yes	characteristic, direct product factor

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

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.