Finite Group Databasebeta

← C₂×C₄×C₂₅ #6022

Subgroups — C₂×C₄×C₂₅ #6022

Order 200.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂₅	C₄	1	2	yes	direct product factor
4	C₂×C₂₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅	C₅	1	1	yes	maximal, characteristic
6	C₂₅	C₂×C₄	1	1	yes	characteristic, direct product factor, Sylow
7	C₂²×C₅	C₂×C₅	1	1	yes	characteristic
8	C₄×C₅	C₂×C₅	1	2	yes	—
9	C₂×C₅	C₄×C₅	1	2	yes	—
10	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
11	C₂×C₄	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₅	C₂×C₄×C₅	1	1	yes	characteristic
13	C₂²	C₂×C₂₅	1	1	yes	characteristic
14	C₄	C₂×C₂₅	1	2	yes	direct product factor
15	C₂	C₄×C₂₅	1	2	yes	direct product factor
16	C₂	C₂²×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂²×C₅
socle, prime radical	C₂²×C₅	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₅	C₂	direct (N × H)
3. C₂×C₂₅	C₄	direct (N × H)
6. C₂₅	C₂×C₄	direct (N × H)
11. C₂×C₄	C₂₅	direct (N × H)
14. C₄	C₂×C₂₅	direct (N × H)
15. C₂	C₄×C₂₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₅	2
C₄×C₂₅	2
C₂×C₄×C₅	5