Finite Group Databasebeta

← C22×C55 #72190850

Subgroups — C22×C55 #72190850

Order 12500.

210880 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C54C51781yesmaximal, direct product factor
2C2×C55C213yesmaximal, direct product factor
3C55C2211yescharacteristic, direct product factor, Sylow
4C2×C54C2×C512343yesdirect product factor
5C54C22×C51781yesdirect product factor
6C22×C53C52120306yesdirect product factor
7C2×C53C2×C52160918yesdirect product factor
8C53C22×C52120306yesdirect product factor
9C22×C52C53120306yesdirect product factor
10C2×C52C2×C53160918yesdirect product factor
11C52C22×C53120306yesdirect product factor
12C22×C5C541781yesdirect product factor
13C2×C5C2×C5412343yesdirect product factor
14C5C22×C541781yesdirect product factor
15C22C5511yescharacteristic, direct product factor, Sylow
16C2C2×C5513yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C54C5direct (N × H)
2. C2×C55C2direct (N × H)
3. C55C22direct (N × H)
4. C2×C54C2×C5direct (N × H)
5. C54C22×C5direct (N × H)
6. C22×C53C52direct (N × H)
7. C2×C53C2×C52direct (N × H)
8. C53C22×C52direct (N × H)
9. C22×C52C53direct (N × H)
10. C2×C52C2×C53direct (N × H)
11. C52C22×C53direct (N × H)
12. C22×C5C54direct (N × H)
13. C2×C5C2×C54direct (N × H)
14. C5C22×C54direct (N × H)
15. C22C55direct (N × H)
16. C2C2×C55direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C545
C2×C552