Finite Group Databasebeta

← C22×C5×C72×C25 #72201765

Subgroups — C22×C5×C72×C25 #72201765

Order 24500.

700 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C72×C25C213yesmaximal, direct product factor
2C5×C72×C25C2211yescharacteristic, direct product factor, Hall
3C22×C5×C7×C25C718yesmaximal, direct product factor
4C22×C52×C72C511yesmaximal, characteristic
5C22×C72×C25C515yesmaximal, direct product factor
6C2×C52×C72C2×C513yes—
7C2×C72×C25C2×C5115yesdirect product factor
8C2×C5×C7×C25C2×C7124yesdirect product factor
9C52×C72C22×C511yescharacteristic
10C72×C25C22×C515yesdirect product factor
11C22×C5×C72C2515yesdirect product factor
12C22×C5×C72C5211yescharacteristic
13C5×C7×C25C22×C718yesdirect product factor
14C22×C52×C7C5×C718yes—
15C22×C7×C25C5×C7140yesdirect product factor
16C22×C5×C25C7211yescharacteristic, direct product factor, Hall
17C2×C5×C72C2×C25115yesdirect product factor
18C2×C5×C72C2×C5213yes—
19C2×C52×C7C2×C5×C7124yes—
20C2×C7×C25C2×C5×C71120yesdirect product factor
21C2×C5×C25C2×C7213yesdirect product factor
22C5×C72C22×C2515yesdirect product factor
23C5×C72C22×C5211yescharacteristic
24C22×C72C5×C2511yescharacteristic, direct product factor, Hall
25C52×C7C22×C5×C718yes—
26C7×C25C22×C5×C7140yesdirect product factor
27C22×C5×C7C7×C25140yesdirect product factor
28C22×C5×C7C52×C718yes—
29C5×C25C22×C7211yescharacteristic, direct product factor, Sylow
30C22×C52C5×C7211yescharacteristic
31C22×C25C5×C7215yesdirect product factor
32C2×C72C2×C5×C2513yesdirect product factor
33C2×C5×C7C2×C7×C251120yesdirect product factor
34C2×C5×C7C2×C52×C7124yes—
35C2×C52C2×C5×C7213yes—
36C2×C25C2×C5×C72115yesdirect product factor
37C72C22×C5×C2511yescharacteristic, direct product factor, Sylow
38C5×C7C22×C7×C25140yesdirect product factor
39C5×C7C22×C52×C718yes—
40C22×C7C5×C7×C2518yesdirect product factor
41C52C22×C5×C7211yescharacteristic
42C25C22×C5×C7215yesdirect product factor
43C22×C5C72×C2515yesdirect product factor
44C22×C5C52×C7211yescharacteristic
45C2×C7C2×C5×C7×C25124yesdirect product factor
46C2×C5C2×C72×C25115yesdirect product factor
47C2×C5C2×C52×C7213yes—
48C7C22×C5×C7×C2518yesdirect product factor
49C5C22×C72×C2515yesdirect product factor
50C5C22×C52×C7211yescharacteristic
51C22C5×C72×C2511yescharacteristic, direct product factor, Sylow
52C2C2×C5×C72×C2513yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C22×C52×C72
socle, prime radicalC22×C52×C72C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×C72×C25C2direct (N × H)
2. C5×C72×C25C22direct (N × H)
3. C22×C5×C7×C25C7direct (N × H)
5. C22×C72×C25C5direct (N × H)
7. C2×C72×C25C2×C5direct (N × H)
8. C2×C5×C7×C25C2×C7direct (N × H)
10. C72×C25C22×C5direct (N × H)
11. C22×C5×C72C25direct (N × H)
13. C5×C7×C25C22×C7direct (N × H)
15. C22×C7×C25C5×C7direct (N × H)
16. C22×C5×C25C72direct (N × H)
17. C2×C5×C72C2×C25direct (N × H)
20. C2×C7×C25C2×C5×C7direct (N × H)
21. C2×C5×C25C2×C72direct (N × H)
22. C5×C72C22×C25direct (N × H)
24. C22×C72C5×C25direct (N × H)
26. C7×C25C22×C5×C7direct (N × H)
27. C22×C5×C7C7×C25direct (N × H)
29. C5×C25C22×C72direct (N × H)
31. C22×C25C5×C72direct (N × H)
32. C2×C72C2×C5×C25direct (N × H)
33. C2×C5×C7C2×C7×C25direct (N × H)
36. C2×C25C2×C5×C72direct (N × H)
37. C72C22×C5×C25direct (N × H)
38. C5×C7C22×C7×C25direct (N × H)
40. C22×C7C5×C7×C25direct (N × H)
42. C25C22×C5×C72direct (N × H)
43. C22×C5C72×C25direct (N × H)
45. C2×C7C2×C5×C7×C25direct (N × H)
46. C2×C5C2×C72×C25direct (N × H)
48. C7C22×C5×C7×C25direct (N × H)
49. C5C22×C72×C25direct (N × H)
51. C22C5×C72×C25direct (N × H)
52. C2C2×C5×C72×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C72×C252
C22×C5×C7×C257
C22×C52×C725
C22×C72×C255