Finite Group Databasebeta

← C2×C3×D2325 #42124462

Subgroups — C2×C3×D2325 #42124462

Order 27900.

132 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 54 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×D2325C212yesmaximal, direct product factor
2C2×C32×C25×C31C211yesmaximal, characteristic, complemented
3C2×D2325C311yesmaximal, characteristic, direct product factor
4C2×C3×D775—31nomaximal
5C32×C25×C31C2211yescharacteristic, complemented, Hall
6C2×C3×D465—51nomaximal
7D2325C2×C312yesdirect product factor
8C3×D775—32no—
9C2×C3×C25×C31—21no—
10C2×C3×C25×C31D311yescharacteristic, complemented
11C2×C3×C25×C31C2×C311yescharacteristic, complemented
12C2×D775—31noHall
13C3×D465—52no—
14C2×C32×C5×C31D511yescharacteristic
15C3×C25×C31—21no—
16C3×C25×C31C2×D311yescharacteristic, complemented
17C3×C25×C31C22×C311yescharacteristic, complemented
18C2×D465—51no—
19C2×C3×D155—151no—
20C2×C25×C31C3×D311yescharacteristic, complemented
21D775—32no—
22C32×C5×C31C2×D511yescharacteristic
23C2×C3×D93—251noHall
24C2×C3×C5×C31—21no—
25C2×C3×C5×C31C3×D511yescharacteristic
26C2×C3×C5×C31D1511yescharacteristic
27D465—52no—
28C3×D155—152no—
29C2×C3×D75—311nomaximal, Hall
30C25×C31C2×C3×D311yescharacteristic, complemented, Hall
31C2×D155—151no—
32C2×C32×C31D2511yescharacteristic, complemented
33C3×D93—252no—
34C3×C5×C31—21no—
35C3×C5×C31C2×C3×D511yescharacteristic
36C3×C5×C31C2×D1511yescharacteristic
37C2×C32×C25D3111yescharacteristic, complemented
38C3×D75—312no—
39C2×D93—251no—
40C2×C3×D31—751no—
41C2×C5×C31C3×D1511yescharacteristic
42D155—152no—
43C2×D75—311no—
44C2×C3×D25—931no—
45C32×C31C2×D2511yescharacteristic, complemented, Hall
46C32×C25C2×D3111yescharacteristic, complemented, Hall
47C2×C3×C31—21no—
48C2×C3×C31C3×D2511yescharacteristic, complemented
49C2×C3×C31D7511yescharacteristic, complemented
50D93—252no—
51C3×D31—752no—
52C2×C3×D15—1551no—
53C5×C31C2×C3×D1511yescharacteristic
54C2×C3×C25—21no—
55C2×C3×C25C3×D3111yescharacteristic, complemented
56C2×C3×C25D9311yescharacteristic, complemented
57D75—312no—
58C3×D25—932no—
59C2×D31—751noHall
60C2×D25—931noHall
61C3×C31—21no—
62C3×C31C2×C3×D2511yescharacteristic, complemented
63C3×C31C2×D7511yescharacteristic, complemented
64C2×C32×C5D15511yescharacteristic
65C3×D15—1552no—
66C3×C25—21no—
67C3×C25C2×C3×D3111yescharacteristic, complemented
68C3×C25C2×D9311yescharacteristic, complemented
69C2×C31C3×D7511yescharacteristic, complemented
70D31—752no—
71C2×D15—1551no—
72C2×C3×D5—4651no—
73C2×C25C3×D9311yescharacteristic, complemented
74D25—932no—
75C32×C5C2×D15511yescharacteristic
76C2×C3×D3—7751noHall
77C31C2×C3×D7511yescharacteristic, complemented, Sylow
78C2×C3×C5—21no—
79C2×C3×C5C3×D15511yescharacteristic
80C2×C3×C5D46511yescharacteristic
81D15—1552no—
82C3×D5—4652no—
83C25C2×C3×D9311yescharacteristic, complemented, Sylow
84C2×D5—4651no—
85C2×C32D77511yescharacteristic, complemented
86C3×D3—7752no—
87C3×C5—21no—
88C3×C5C2×C3×D15511yescharacteristic
89C3×C5C2×D46511yescharacteristic
90C22×C3—23251no—
91C2×D3—7751no—
92C2×C5C3×D46511yescharacteristic
93D5—4652no—
94C32C2×D77511yescharacteristic, complemented, Sylow
95C2×C3—21no—
96C2×C3—23252no—
97C2×C3C3×D77511yescharacteristic, complemented
98C2×C3D232511yescharacteristic, direct product factor
99D3—7752no—
100C5C2×C3×D46511yescharacteristic
101C22—23251noSylow
102C3—21no—
103C3C2×C3×D77511yescharacteristic, complemented
104C3C2×D232511yescharacteristic, direct product factor
105C2—23252no—
106C2C3×D232511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D2325
commutator, cosocle, hypocenterC3×C25×C31C22×C3
FrattiniC5C2×C3×D465
FittingC2×C32×C25×C31C2
socleC2×C32×C5×C31D5
LCSG ▷ C3×C25×C31
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×D2325C2direct (N × H)
2. C2×C32×C25×C31C2semidirect
3. C2×D2325C3direct (N × H)
5. C32×C25×C31C22semidirect
7. D2325C2×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
30. C25×C31C2×C3×D3semidirect
32. C2×C32×C31D25semidirect
37. C2×C32×C25D31semidirect
45. C32×C31C2×D25semidirect
46. C32×C25C2×D31semidirect
48. C2×C3×C31C3×D25semidirect
49. C2×C3×C31D75semidirect
55. C2×C3×C25C3×D31semidirect
56. C2×C3×C25D93semidirect
62. C3×C31C2×C3×D25semidirect
63. C3×C31C2×D75semidirect
67. C3×C25C2×C3×D31semidirect
68. C3×C25C2×D93semidirect
69. C2×C31C3×D75semidirect
73. C2×C25C3×D93semidirect
77. C31C2×C3×D75semidirect
83. C25C2×C3×D93semidirect
85. C2×C32D775semidirect
94. C32C2×D775semidirect
97. C2×C3C3×D775semidirect
98. C2×C3D2325direct (N × H)
103. C3C2×C3×D775semidirect
104. C3C2×D2325direct (N × H)
106. C2C3×D2325direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D23252
C2×C32×C25×C312
C2×D23253
C2×C3×D7753
C2×C3×D4655
C2×C3×D7531