Finite Group Databasebeta

← C59×#63103 #28475212

Subgroups — C59×#63103 #28475212

Order 15104.

59452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×2−1+6C2128yesmaximal, complemented
2C59×H(7,𝔽2)C2136yesmaximal, complemented
3C2×C59×#585C2163yesmaximal, complemented
4C59×#585C221336yescomplemented
5C59×#585C2211008yescomplemented
6C2×2−1+4×C59C221378yescomplemented
7C2×H(5,𝔽2)×C59C221630yescomplemented
8C22×#41×C59C221315yescomplemented
92−1+4×C59C2312016yescomplemented
10H(5,𝔽2)×C59C2313360yescomplemented
11C2×#41×C59C2311260yescomplemented
12C2×#41×C59C2313780yescomplemented
13C22×Q8×C59C231315yescomplemented
14C22×D4×C59C231945yescomplemented
15C23×C4×C59C231135yescomplemented
16C24×C59C241135yes—
17#41×C59C241336yes—
18#41×C59C2415040yes—
19C2×Q8×C59C2411260yes—
20C2×D4×C59C2413780yes—
21C22×C4×C59C241315yes—
22C22×C4×C59C241945yes—
23C23×C59—8135no—
24C23×C59C251315yes—
25Q8×C59C251336yes—
26D4×C59C2511008yes—
27C2×C4×C59C251945yes—
28C2×C4×C59C25163yes—
29#63103C5911yesmaximal, characteristic, direct product factor, Sylow
30C22×C59—4315no—
31C22×C59C26163yes—
32C4×C59C26163yes—
33C4×C59C2611yescharacteristic
342−1+6C2×C59128yescomplemented
35H(7,𝔽2)C2×C59136yescomplemented
36C2×#585C2×C59163yescomplemented
37C2×C59—263no—
38C2×C59C2711yescharacteristic
39#585C22×C591336yescomplemented
40#585C22×C5911008yescomplemented
41C2×2−1+4C22×C591378yescomplemented
42C2×H(5,𝔽2)C22×C591630yescomplemented
43C22×#41C22×C591315yescomplemented
44C59#6310311yescharacteristic, direct product factor, Sylow
452−1+4C23×C5912016yescomplemented
46H(5,𝔽2)C23×C5913360yescomplemented
47C2×#41C23×C5911260yescomplemented
48C2×#41C23×C5913780yescomplemented
49C22×Q8C23×C591315yescomplemented
50C22×D4C23×C591945yescomplemented
51C23×C4C23×C591135yescomplemented
52C24C24×C591135yes—
53#41C24×C591336yes—
54#41C24×C5915040yes—
55C2×Q8C24×C5911260yes—
56C2×D4C24×C5913780yes—
57C22×C4C24×C591315yes—
58C22×C4C24×C591945yes—
59C23—8135no—
60C23C25×C591315yes—
61Q8C25×C591336yes—
62D4C25×C5911008yes—
63C2×C4C25×C59163yes—
64C2×C4C25×C591945yes—
65C22—4315no—
66C22C26×C59163yes—
67C4C26×C5911yescharacteristic
68C4C26×C59163yes—
69C2—263no—
70C2C27×C5911yescharacteristic
subgroupG/H
centerC4×C59C26
commutator, Frattini, cosocleC2C27×C59
socleC2×C59C27
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×2−1+6C2semidirect
2. C59×H(7,𝔽2)C2semidirect
3. C2×C59×#585C2semidirect
4. C59×#585C22semidirect
5. C59×#585C22semidirect
6. C2×2−1+4×C59C22semidirect
7. C2×H(5,𝔽2)×C59C22semidirect
8. C22×#41×C59C22semidirect
9. 2−1+4×C59C23semidirect
10. H(5,𝔽2)×C59C23semidirect
11. C2×#41×C59C23semidirect
12. C2×#41×C59C23semidirect
13. C22×Q8×C59C23semidirect
14. C22×D4×C59C23semidirect
15. C23×C4×C59C23semidirect
29. #63103C59direct (N × H)
34. 2−1+6C2×C59semidirect
35. H(7,𝔽2)C2×C59semidirect
36. C2×#585C2×C59semidirect
39. #585C22×C59semidirect
40. #585C22×C59semidirect
41. C2×2−1+4C22×C59semidirect
42. C2×H(5,𝔽2)C22×C59semidirect
43. C22×#41C22×C59semidirect
44. C59#63103direct (N × H)
45. 2−1+4C23×C59semidirect
46. H(5,𝔽2)C23×C59semidirect
47. C2×#41C23×C59semidirect
48. C2×#41C23×C59semidirect
49. C22×Q8C23×C59semidirect
50. C22×D4C23×C59semidirect
51. C23×C4C23×C59semidirect

Maximal subgroups

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

subgroupindex
C59×2−1+62
C59×H(7,𝔽2)2
C2×C59×#5852
#6310359