Finite Group Databasebeta

← C3×C25⋊#64418 #36347741

Subgroups — C3×C25⋊#64418 #36347741

Order 22050.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C25×#3862C211yesmaximal, characteristic, complemented, Hall
2C3×C7×D175—31nomaximal
3C25⋊#64418C311yesmaximal, characteristic, direct product factor
4C3×C5⋊#64418—51nomaximal
5C25×#3862—21no—
6C25×#3862C2×C311yescharacteristic, complemented
7C3×C72×C25D311yescharacteristic, complemented
8C7×D175—31noHall
9C3×C5×#3862D511yescharacteristic
10C3×ΓL(1,𝔽8)×C25—141no—
11C3×C7×D35—151no—
12C5⋊#64418—51no—
13C72×C25C3×D311yescharacteristic, complemented, Hall
14C3×D175—31no—
15C3×C7×D25—211no—
16C3×#64418—251noHall
17C3×C5×C72D1511yescharacteristic
18C5×#3862—21no—
19C5×#3862C3×D511yescharacteristic
20C3×C7×C25—21no—
21C3×C7×C25—31no—
22C3×C7×C25—61no—
23ΓL(1,𝔽8)×C25—142no—
24ΓL(1,𝔽8)×C25—141no—
25C7×D35—151no—
26C3×D75—491nomaximal, Hall
27C3×#3862D2511yescharacteristic, complemented, Hall
28D175—31no—
29C7×D25—211no—
30C3×C5×ΓL(1,𝔽8)—141no—
31C3×C7×D7—751no—
32#64418—251no—
33C5×C72C3×D1511yescharacteristic
34C32×C25—491noHall
35C3×D35—151no—
36C3×C7×D5—1051no—
37C7×C25—21no—
38C7×C25—61no—
39C7×C25—61no—
40D75—491no—
41C3×D25—211no—
42C3×C72D7511yescharacteristic, complemented
43#3862—21no—
44#3862C3×D2511yescharacteristic, complemented
45C3×C5×C7—21no—
46C3×C5×C7—31no—
47C3×C5×C7—61no—
48C5×ΓL(1,𝔽8)—142no—
49C5×ΓL(1,𝔽8)—141no—
50C7×D7—751noHall
51C3×D15—2451no—
52C3×C25—981no—
53C3×C25—981no—
54C3×C25#6441811yescharacteristic, complemented
55D35—151no—
56C7×D5—1051no—
57C3×ΓL(1,𝔽8)—141no—
58D25—211noHall
59C72C3×D7511yescharacteristic, complemented, Sylow
60C32×C5—981no—
61C2×C3×C7—5251no—
62C3×D7—751no—
63C5×C7—21no—
64C5×C7—31no—
65C5×C7—61no—
66D15—2451no—
67C3×D5—1051no—
68C25C3×#6441811yescharacteristic, complemented, Sylow
69C3×C7—21no—
70C3×C7—31no—
71C3×C7—61no—
72ΓL(1,𝔽8)—142no—
73ΓL(1,𝔽8)—141no—
74C3×D3—12251noHall
75C3×C5—981no—
76C3×C5—981no—
77C3×C5C5⋊#6441811yescharacteristic
78C2×C7—5251no—
79D7—751no—
80D5—1051no—
81C32—491noSylow
82C7—21no—
83C7—31no—
84C7—61no—
85C2×C3—5251no—
86D3—12251no—
87C5C3×C5⋊#6441811yescharacteristic
88C3—981no—
89C3—981no—
90C3C25⋊#6441811yescharacteristic, direct product factor
91C2—5251noSylow
subgroupG/H
center, hypercenterC3C25⋊#64418
commutator, cosocle, hypocenterC25×#3862C2×C3
FrattiniC5C3×C5⋊#64418
FittingC3×C72×C25D3
socleC3×C5×C72D15
LCSG ▷ C25×#3862
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C25×#3862C2semidirect
3. C25⋊#64418C3direct (N × H)
6. C25×#3862C2×C3semidirect
7. C3×C72×C25D3semidirect
13. C72×C25C3×D3semidirect
27. C3×#3862D25semidirect
42. C3×C72D75semidirect
44. #3862C3×D25semidirect
54. C3×C25#64418semidirect
59. C72C3×D75semidirect
68. C25C3×#64418semidirect
90. C3C25⋊#64418direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C25×#38622
C3×C7×D1753
C25⋊#644183
C3×C5⋊#644185
C3×D7549