Finite Group Databasebeta

← D3×D2325 #42124443

Subgroups — D3×D2325 #42124443

Order 27900.

132 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 40 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⋊D2325C211yesmaximal, characteristic, complemented
2C3×D2325C211yesmaximal, characteristic, complemented
3C3×D3×C25×C31C211yesmaximal, characteristic, complemented
4C2×D2325—31nomaximal
5D3×D775—31nomaximal
6C32×C25×C31C2211yescharacteristic, complemented, Hall
7D3×D465—51nomaximal
8D2325—31no—
9D2325—31no—
10D2325—61no—
11D2325D311yescharacteristic, direct product factor
12D3×C25×C31D311yescharacteristic, complemented
13C3×D775—31no—
14C2×C3×C25×C31—31no—
15C2×D775—91noHall
16C3⋊D465—51no—
17C3×D465—51no—
18C3×C5×D3×C31D511yescharacteristic
19C3×C25×C31—21no—
20C3×C25×C31C2×D311yescharacteristic, complemented
21C3×C25×C31C2×D311yescharacteristic, complemented
22C2×D465—151no—
23D3×D155—151no—
24C2×C25×C31—31no—
25D775—31no—
26D775—91no—
27C32×C5×C31C2×D511yescharacteristic
28D3×D93—251noHall
29C2×C3×C5×C31—31no—
30D465—51no—
31D465—151no—
32D465—151no—
33D465—301no—
34C5×D3×C31D1511yescharacteristic
35C3×D155—151no—
36D3×D75—311nomaximal, Hall
37C25×C31D3211yescharacteristic, complemented, Hall
38C2×D155—451no—
39C3⋊D93—251no—
40C3×D93—251no—
41C3×D3×C31D2511yescharacteristic, complemented
42C3×C5×C31—21no—
43C3×C5×C31D3×D511yescharacteristic
44C3×C5×C31C2×D1511yescharacteristic
45C3⋊D75—311no—
46C3×D75—311no—
47C3×D3×C25D3111yescharacteristic, complemented
48C2×D93—751no—
49D3×D31—751no—
50C2×C5×C31—31no—
51D155—151no—
52D155—451no—
53C2×D75—931no—
54D3×D25—931no—
55C32×C31C2×D2511yescharacteristic, complemented, Hall
56C32×C25C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—31no—
58D93—251no—
59D93—751no—
60D93—751no—
61D93—1501no—
62C3×D31—751no—
63D3×C31D7511yescharacteristic, complemented
64D3×D15—1551no—
65C5×C31D3×D1511yescharacteristic
66C2×C3×C25—31no—
67D75—311no—
68D75—931no—
69D75—931no—
70D75—1861no—
71C3×D25—931no—
72D3×C25D9311yescharacteristic, complemented
73C2×D31—2251noHall
74C2×D25—2791noHall
75C3×C31—21no—
76C3×C31D3×D2511yescharacteristic, complemented
77C3×C31C2×D7511yescharacteristic, complemented
78C3⋊D15—1551no—
79C3×D15—1551no—
80C3×C5×D3D15511yescharacteristic
81C3×C25—21no—
82C3×C25D3×D3111yescharacteristic, complemented
83C3×C25C2×D9311yescharacteristic, complemented
84C2×C31—31no—
85D31—751no—
86D31—2251no—
87C2×D15—4651no—
88D3×D5—4651no—
89C2×C25—31no—
90D25—2791no—
91D25—931no—
92C32×C5C2×D15511yescharacteristic
93D32—7751noHall
94C31D3×D7511yescharacteristic, complemented, Sylow
95C2×C3×C5—31no—
96D15—1551no—
97D15—9301no—
98D15—4651no—
99D15—4651no—
100C3×D5—4651no—
101C5×D3D46511yescharacteristic
102C25D3×D9311yescharacteristic, complemented, Sylow
103C2×D5—13951no—
104C3⋊D3—7751no—
105C3×D3—7751no—
106C3×D3D77511yescharacteristic, complemented
107C3×C5—21no—
108C3×C5D3×D15511yescharacteristic
109C3×C5C2×D46511yescharacteristic
110C2×D3—23251no—
111C2×D3—23251no—
112C2×C5—31no—
113D5—13951no—
114D5—4651no—
115C32C2×D77511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—23251no—
118D3—7751no—
119D3—23251no—
120D3—23251no—
121D3—46501no—
122D3D232511yescharacteristic, direct product factor
123C5D3×D46511yescharacteristic
124C22—69751noSylow
125C3—21no—
126C3D3×D77511yescharacteristic, complemented
127C3C2×D232511yescharacteristic, complemented
128C2—31no—
129C2—23251no—
130C2—69751no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C25×C31C22
FrattiniC5D3×D465
socleC32×C5×C31C2×D5
LCSG ▷ C32×C25×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊D2325C2semidirect
2. C3×D2325C2semidirect
3. C3×D3×C25×C31C2semidirect
6. C32×C25×C31C22semidirect
11. D2325D3direct (N × H)
12. D3×C25×C31D3semidirect
20. C3×C25×C31C2×D3semidirect
21. C3×C25×C31C2×D3semidirect
37. C25×C31D32semidirect
41. C3×D3×C31D25semidirect
47. C3×D3×C25D31semidirect
55. C32×C31C2×D25semidirect
56. C32×C25C2×D31semidirect
63. D3×C31D75semidirect
72. D3×C25D93semidirect
76. C3×C31D3×D25semidirect
77. C3×C31C2×D75semidirect
82. C3×C25D3×D31semidirect
83. C3×C25C2×D93semidirect
94. C31D3×D75semidirect
102. C25D3×D93semidirect
106. C3×D3D775semidirect
115. C32C2×D775semidirect
122. D3D2325direct (N × H)
126. C3D3×D775semidirect
127. C3C2×D2325semidirect

Maximal subgroups

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

subgroupindex
C3⋊D23252
C3×D23252
C3×D3×C25×C312
C2×D23253
D3×D7753
D3×D4655
D3×D7531