Finite Group Databasebeta

← C5×#20258902 #44478022

Subgroups — C5×#20258902 #44478022

Order 30420.

192 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C3⋊#11759818C212yesmaximal, complemented
2C3×C5×#11759816C211yesmaximal, characteristic, complemented
3C5×D39⋊D13C311yesmaximal, characteristic, complemented
4C5×#11759818⋊C2—31nomaximal
5C3×C5×#92789C2211yescharacteristic, complemented, Hall
6#20258902C511yesmaximal, characteristic, direct product factor, Hall
7C5×C13×D39C2×C312yescomplemented
8C3×C5×C13⋊D13C2×C311yescharacteristic, complemented
9C5×#11759818—32no—
10C5×#11759816—21no—
11C5×#11759816D311yescharacteristic, complemented
12C5×D132—31noHall
13C3⋊#11759818C2×C512yescomplemented
14C3×#11759816C2×C511yescharacteristic, complemented
15C5×#92789—21no—
16C5×#92789C2×D311yescharacteristic, complemented
17C3×C5×C132C22×C311yescharacteristic, complemented
18C5×D3×D13⋊C3—132nomaximal
19D39⋊D13C3×C511yescharacteristic, complemented
20#11759818⋊C2—31no—
21C5×C13⋊D13C3×D311yescharacteristic, complemented
22C5×C13×D13—32no—
23C3×#92789C22×C511yescharacteristic, complemented, Hall
24C5×C3⋊(D13⋊C3)—132no—
25C5×D3×C13⋊C3—132no—
26C3×C5×D13⋊C3—132no—
27C13×D39C2×C3×C512yescomplemented
28C3×C13⋊D13C2×C3×C511yescharacteristic, complemented
29#11759818—32no—
30#11759816—21no—
31#11759816C5×D311yescharacteristic, complemented
32C5×C132C2×C3×D311yescharacteristic, complemented, Hall
33C5×D3×D13—132no—
34C2×C5×D13⋊C3—392no—
35D132—31noHall
36C3×C5×C13⋊C3—132no—
37C3×C132C22×C3×C511yescharacteristic, complemented
38#92789—21no—
39#92789C2×C5×D311yescharacteristic, complemented
40D3×D13⋊C3—132no—
41C5×D39D13⋊C312yescomplemented
42C5×D3×C13—132no—
43C3×C5×D13—132no—
44C3×C5×D13—782no—
45C2×C5×C13⋊C3—392no—
46C5×D13⋊C3—132no—
47C5×D13⋊C3—262no—
48C5×D13⋊C3—392no—
49C13⋊D13C3×C5×D311yescharacteristic, complemented
50C13×D13—32no—
51C2×C5×D13—392no—
52C3⋊(D13⋊C3)—132no—
53D3×C13⋊C3—132no—
54C3×D13⋊C3—132no—
55C3×C5×C13—62no—
56C3×C5×C13C2×D13⋊C312yescomplemented
57C5×C13⋊C3—132no—
58C5×C13⋊C3—262no—
59C2×C3×C5×D3—1691noHall
60C132C2×C3×C5×D311yescharacteristic, complemented, Sylow
61D3×D13—132no—
62C2×D13⋊C3—392no—
63C2×C5×C13—392no—
64C5×D13—32no—
65C5×D13—132no—
66C5×D13—782no—
67C3×C13⋊C3—132no—
68C2×C32×C5—1691no—
69C3×C5×D3—1692no—
70D39C5×D13⋊C312yescomplemented
71C3×D13—132no—
72C3×D13—782no—
73D3×C13—132no—
74C2×C13⋊C3—392no—
75D13⋊C3—132no—
76D13⋊C3—262no—
77D13⋊C3—392no—
78C5×C13—62no—
79C5×C13D3×D13⋊C312yescomplemented
80C22×C3×C5—5071no—
81C2×C5×D3—1691no—
82C2×D13—392no—
83C32×C5—1691noHall
84C3×C13—62no—
85C3×C13C2×C5×D13⋊C312yescomplemented
86C13⋊C3—132no—
87C13⋊C3—262no—
88C2×C3×D3—1691noHall
89C2×C3×C5—3381no—
90C2×C3×C5—1691no—
91C2×C3×C5—1691no—
92C2×C3×C5—5072no—
93C5×D3—132no—
94C2×C13—392no—
95D13—32no—
96D13—132no—
97D13—782no—
98C22×C5—5071noHall
99C2×C32—1691no—
100C3×D3—1692no—
101C3×C5—3381no—
102C3×C5—1691no—
103C3×C5#11759818⋊C211yescharacteristic, complemented
104C13—62no—
105C13C5×D3×D13⋊C312yescomplemented
106C22×C3—5071no—
107C2×D3—1691no—
108C2×C5—392no—
109C2×C5—1691no—
110C32—1691noSylow
111C2×C3—3381no—
112C2×C3—1691no—
113C2×C3—1691no—
114C2×C3—5072no—
115D3—132no—
116C5#2025890211yescharacteristic, direct product factor, Sylow
117C22—5071noSylow
118C3—3381no—
119C3—1691no—
120C3C5×#11759818⋊C211yescharacteristic, complemented
121C2—392no—
122C2—1691no—
subgroupG/H
center, hypercenterC5#20258902
commutator, cosocle, hypocenterC3×C132C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C132C22×C3
LCSG ▷ C3×C132
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊#11759818C2semidirect
2. C3×C5×#11759816C2semidirect
3. C5×D39⋊D13C3semidirect
5. C3×C5×#92789C22semidirect
6. #20258902C5direct (N × H)
7. C5×C13×D39C2×C3semidirect
8. C3×C5×C13⋊D13C2×C3semidirect
11. C5×#11759816D3semidirect
13. C3⋊#11759818C2×C5semidirect
14. C3×#11759816C2×C5semidirect
16. C5×#92789C2×D3semidirect
17. C3×C5×C132C22×C3semidirect
19. D39⋊D13C3×C5semidirect
21. C5×C13⋊D13C3×D3semidirect
23. C3×#92789C22×C5semidirect
27. C13×D39C2×C3×C5semidirect
28. C3×C13⋊D13C2×C3×C5semidirect
31. #11759816C5×D3semidirect
32. C5×C132C2×C3×D3semidirect
37. C3×C132C22×C3×C5semidirect
39. #92789C2×C5×D3semidirect
41. C5×D39D13⋊C3semidirect
49. C13⋊D13C3×C5×D3semidirect
56. C3×C5×C13C2×D13⋊C3semidirect
60. C132C2×C3×C5×D3semidirect
70. D39C5×D13⋊C3semidirect
79. C5×C13D3×D13⋊C3semidirect
85. C3×C13C2×C5×D13⋊C3semidirect
103. C3×C5#11759818⋊C2semidirect
105. C13C5×D3×D13⋊C3semidirect
116. C5#20258902direct (N × H)
120. C3C5×#11759818⋊C2semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊#117598182
C3×C5×#117598162
C5×D39⋊D133
C5×#11759818⋊C23
#202589025
C5×D3×D13⋊C313