Subgroups — C₂³×D₂₅ #87760

Order 400.

201 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₅	C₂	1	14	yes	maximal, direct product factor
3	C₂²×C₂₅	C₂²	1	7	yes	complemented
4	C₂×D₂₅	C₂²	1	28	yes	direct product factor
5	C₂³×D₅	—	5	1	no	maximal
6	C₂×C₂₅	C₂³	1	7	yes	complemented
7	D₂₅	C₂³	1	8	yes	direct product factor
8	C₂³×C₅	D₅	1	1	yes	characteristic
9	C₂²×D₅	—	5	14	no	—
10	C₂₅	C₂⁴	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₅	C₂×D₅	1	7	yes	—
12	C₂×D₅	—	5	28	no	—
13	C₂⁴	—	25	1	no	Sylow
14	C₂×C₅	C₂²×D₅	1	7	yes	—
15	D₅	—	5	8	no	—
16	C₂³	—	25	14	no	—
17	C₂³	D₂₅	1	1	yes	characteristic, direct product factor
18	C₅	C₂³×D₅	1	1	yes	characteristic
19	C₂²	—	25	28	no	—
20	C₂²	C₂×D₂₅	1	7	yes	direct product factor
21	C₂	—	25	8	no	—
22	C₂	C₂²×D₂₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂⁴
Frattini	C₅	C₂³×D₅
Fitting	C₂³×C₂₅	C₂
socle	C₂³×C₅	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂³

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.