Finite Group Databasebeta

← C2×C3×C25×D93 #42124464

Subgroups — C2×C3×C25×D93 #42124464

Order 27900.

132 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3×C25×D93C212yesmaximal, direct product factor
2C2×C32×C25×C31C211yesmaximal, characteristic, complemented
3C2×C25×D93C311yesmaximal, characteristic, direct product factor
4C2×C3×C25×D31—31nomaximal
5C32×C25×C31C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D93C511yesmaximal, characteristic
7C25×D93C2×C312yesdirect product factor
8C3×C25×D31—32no—
9C2×C3×C25×C31—21no—
10C2×C3×C25×C31D311yescharacteristic, complemented
11C2×C3×C25×C31C2×C311yescharacteristic, complemented
12C2×C25×D31—31noHall
13C3×C5×D93C2×C512yes—
14C2×C32×C5×C31C2×C511yescharacteristic
15C3×C25×C31—21no—
16C3×C25×C31C2×D311yescharacteristic, complemented
17C3×C25×C31C22×C311yescharacteristic, complemented
18C2×C5×D93C3×C511yescharacteristic
19C2×C3×C5×D31—31no—
20C2×C25×C31C3×D311yescharacteristic, complemented
21C25×D31—32no—
22C32×C5×C31C22×C511yescharacteristic
23C2×C3×D93C2511yescharacteristic, direct product factor, Hall
24C2×C3×C5×C31—21no—
25C2×C3×C5×C31C5×D311yescharacteristic
26C2×C3×C5×C31C2×C3×C511yescharacteristic
27C5×D93C2×C3×C512yes—
28C3×C5×D31—32no—
29C2×C3×D3×C25—311nomaximal, Hall
30C25×C31C2×C3×D311yescharacteristic, complemented, Hall
31C2×C5×D31—31no—
32C2×C32×C31C2×C2511yescharacteristic, complemented
33C3×D93C2×C2512yesdirect product factor
34C3×C5×C31—21no—
35C3×C5×C31C2×C5×D311yescharacteristic
36C3×C5×C31C22×C3×C511yescharacteristic
37C2×C32×C25D3111yescharacteristic, complemented
38C3×D3×C25—312no—
39C2×D93C3×C2511yescharacteristic, direct product factor
40C2×C3×D31—31no—
41C2×C5×C31C3×C5×D311yescharacteristic
42C5×D31—32no—
43C22×C3×C25—931no—
44C2×D3×C25—311no—
45C32×C31C22×C2511yescharacteristic, complemented, Hall
46C32×C25C2×D3111yescharacteristic, complemented, Hall
47C2×C3×C31—21no—
48C2×C3×C31D3×C2511yescharacteristic, complemented
49C2×C3×C31C2×C3×C2511yescharacteristic, complemented
50D93C2×C3×C2512yesdirect product factor
51C3×D31—32no—
52C2×C3×C5×D3—311no—
53C5×C31C2×C3×C5×D311yescharacteristic
54C2×C3×C25—21no—
55C2×C3×C25—932no—
56C2×C3×C25C3×D3111yescharacteristic, complemented
57C2×C3×C25D9311yescharacteristic, direct product factor
58D3×C25—312no—
59C2×D31—31noHall
60C22×C25—931noHall
61C3×C31—21no—
62C3×C31C2×D3×C2511yescharacteristic, complemented
63C3×C31C22×C3×C2511yescharacteristic, complemented
64C2×C32×C5C5×D3111yescharacteristic
65C3×C5×D3—312no—
66C3×C25—21no—
67C3×C25C2×C3×D3111yescharacteristic, complemented
68C3×C25C2×D9311yescharacteristic, direct product factor
69C2×C31C3×D3×C2511yescharacteristic, complemented
70D31—32no—
71C22×C3×C5—931no—
72C2×C5×D3—311no—
73C2×C25—932no—
74C2×C25C3×D9311yescharacteristic, direct product factor
75C32×C5C2×C5×D3111yescharacteristic
76C2×C3×D3—311noHall
77C31C2×C3×D3×C2511yescharacteristic, complemented, Sylow
78C2×C3×C5—21no—
79C2×C3×C5—932no—
80C2×C3×C5C3×C5×D3111yescharacteristic
81C2×C3×C5C5×D9311yescharacteristic
82C5×D3—312no—
83C25C2×C3×D9311yescharacteristic, direct product factor, Sylow
84C22×C5—931no—
85C2×C32C25×D3111yescharacteristic, complemented
86C3×D3—312no—
87C3×C5—21no—
88C3×C5C2×C3×C5×D3111yescharacteristic
89C3×C5C2×C5×D9311yescharacteristic
90C22×C3—931no—
91C2×D3—311no—
92C2×C5—932no—
93C2×C5C3×C5×D9311yescharacteristic
94C32C2×C25×D3111yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—932no—
97C2×C3C3×C25×D3111yescharacteristic, complemented
98C2×C3C25×D9311yescharacteristic, direct product factor
99D3—312no—
100C5C2×C3×C5×D9311yescharacteristic
101C22—931noSylow
102C3—21no—
103C3C2×C3×C25×D3111yescharacteristic, complemented
104C3C2×C25×D9311yescharacteristic, direct product factor
105C2—932no—
106C2C3×C25×D9311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C25D93
commutator, hypocenterC3×C31C22×C3×C25
FrattiniC5C2×C3×C5×D93
FittingC2×C32×C25×C31C2
socleC2×C32×C5×C31C2×C5
prime radicalC2×C3×C5×D93C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C2×C3×C25

Complements

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

NH ≅ G/Ntype
1. C3×C25×D93C2direct (N × H)
2. C2×C32×C25×C31C2semidirect
3. C2×C25×D93C3direct (N × H)
5. C32×C25×C31C22semidirect
7. C25×D93C2×C3direct (N × H)
10. C2×C3×C25×C31D3semidirect
11. C2×C3×C25×C31C2×C3semidirect
16. C3×C25×C31C2×D3semidirect
17. C3×C25×C31C22×C3semidirect
20. C2×C25×C31C3×D3semidirect
23. C2×C3×D93C25direct (N × H)
30. C25×C31C2×C3×D3semidirect
32. C2×C32×C31C2×C25semidirect
33. C3×D93C2×C25direct (N × H)
37. C2×C32×C25D31semidirect
39. C2×D93C3×C25direct (N × H)
45. C32×C31C22×C25semidirect
46. C32×C25C2×D31semidirect
48. C2×C3×C31D3×C25semidirect
49. C2×C3×C31C2×C3×C25semidirect
50. D93C2×C3×C25direct (N × H)
56. C2×C3×C25C3×D31semidirect
57. C2×C3×C25D93direct (N × H)
62. C3×C31C2×D3×C25semidirect
63. C3×C31C22×C3×C25semidirect
67. C3×C25C2×C3×D31semidirect
68. C3×C25C2×D93direct (N × H)
69. C2×C31C3×D3×C25semidirect
74. C2×C25C3×D93direct (N × H)
77. C31C2×C3×D3×C25semidirect
83. C25C2×C3×D93direct (N × H)
85. C2×C32C25×D31semidirect
94. C32C2×C25×D31semidirect
97. C2×C3C3×C25×D31semidirect
98. C2×C3C25×D93direct (N × H)
103. C3C2×C3×C25×D31semidirect
104. C3C2×C25×D93direct (N × H)
106. C2C3×C25×D93direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C25×D932
C2×C32×C25×C312
C2×C25×D933
C2×C3×C25×D313
C2×C3×C5×D935
C2×C3×D3×C2531