Finite Group Databasebeta

← C59×2−1+6 #21421913

Subgroups — C59×2−1+6 #21421913

Order 7552.

5796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#585C2136yesmaximal, complemented
2C2×2−1+4×C59C2127yesmaximal, complemented
32−1+4×C59C221216yescomplemented
4H(5,𝔽2)×C59C221120yescomplemented
5C2×#41×C59C221270yescomplemented
6C22×Q8×C59C22145yescomplemented
7#41×C59C231720yes—
8C2×Q8×C59C231270yes—
9C2×D4×C59C231270yes—
10C22×C4×C59C231135yes—
11C23×C59C24145yes—
12Q8×C59C241120yes—
13D4×C59C241216yes—
14C2×C4×C59C241270yes—
15C22×C59—445no—
16C22×C59C25127yes—
17C4×C59C25136yes—
182−1+6C5911yesmaximal, characteristic, direct product factor, Sylow
19C2×C59—227no—
20C2×C59C2611yescharacteristic
21#585C2×C59136yescomplemented
22C2×2−1+4C2×C59127yescomplemented
23C592−1+611yescharacteristic, direct product factor, Sylow
242−1+4C22×C591216yescomplemented
25H(5,𝔽2)C22×C591120yescomplemented
26C2×#41C22×C591270yescomplemented
27C22×Q8C22×C59145yescomplemented
28#41C23×C591720yes—
29C2×Q8C23×C591270yes—
30C2×D4C23×C591270yes—
31C22×C4C23×C591135yes—
32C23C24×C59145yes—
33Q8C24×C591120yes—
34D4C24×C591216yes—
35C2×C4C24×C591270yes—
36C22—445no—
37C22C25×C59127yes—
38C4C25×C59136yes—
39C2—227no—
40C2C26×C5911yescharacteristic
subgroupG/H
center, socleC2×C59C26
commutator, Frattini, cosocleC2C26×C59
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#585C2semidirect
2. C2×2−1+4×C59C2semidirect
3. 2−1+4×C59C22semidirect
4. H(5,𝔽2)×C59C22semidirect
5. C2×#41×C59C22semidirect
6. C22×Q8×C59C22semidirect
18. 2−1+6C59direct (N × H)
21. #585C2×C59semidirect
22. C2×2−1+4C2×C59semidirect
23. C592−1+6direct (N × H)
24. 2−1+4C22×C59semidirect
25. H(5,𝔽2)C22×C59semidirect
26. C2×#41C22×C59semidirect
27. C22×Q8C22×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#5852
C2×2−1+4×C592
2−1+659