Finite Group Databasebeta

← C3×D25×D93 #42124428

Subgroups — C3×D25×D93 #42124428

Order 27900.

132 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 42 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×C25×D93C211yesmaximal, characteristic, complemented
3C32×C31×D25C211yesmaximal, characteristic, complemented
4D25×D93C311yesmaximal, characteristic, direct product factor
5C3×D25×D31—31nomaximal
6C32×C25×C31C2211yescharacteristic, complemented, Hall
7C3×D5×D93—51nomaximal
8D2325C2×C311yescharacteristic, complemented
9C25×D93C2×C311yescharacteristic, complemented
10C3×D775—31no—
11C3×C31×D25—21no—
12C3×C31×D25D311yescharacteristic, complemented
13C3×C31×D25C2×C311yescharacteristic, complemented
14C3×C25×D31—31no—
15D25×D31—31noHall
16C3×D465—51no—
17C3×C5×D93D511yescharacteristic
18C32×D5×C31—51no—
19C3×C25×C31—21no—
20C3×C25×C31C2×D311yescharacteristic, complemented
21C3×C25×C31C22×C311yescharacteristic, complemented
22D5×D93—51no—
23C3×D5×D31—151no—
24D775—31no—
25C25×D31—31no—
26C31×D25C3×D311yescharacteristic, complemented
27C32×C5×C31C2×D511yescharacteristic
28C2×C3×D93—251noHall
29D465—51no—
30C5×D93C3×D511yescharacteristic
31C3×D155—151no—
32C3×D5×C31—51no—
33C3×D5×C31—51no—
34C3×D5×C31—101no—
35C3×C5×D31—31no—
36C3×D3×D25—311nomaximal, Hall
37C25×C31C2×C3×D311yescharacteristic, complemented, Hall
38D5×D31—151no—
39C2×C32×C31—251no—
40C3×D93—251no—
41C3×D93D2511yescharacteristic, direct product factor
42C3×C5×C31—21no—
43C3×C5×C31D3×D511yescharacteristic
44C3×C5×C31C2×C3×D511yescharacteristic
45C3×D75—311no—
46C3×D3×C25—311no—
47C32×D25D3111yescharacteristic, complemented
48C2×D93—251no—
49C2×C3×D31—751no—
50D155—151no—
51C5×D31—31no—
52D5×C31—51no—
53C2×C3×D25—931no—
54D3×D25—311no—
55C32×C31C2×D2511yescharacteristic, complemented, Hall
56C32×C25C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—251no—
58C2×C3×C31—251no—
59C2×C3×C31—501no—
60D93—251no—
61D93C3×D2511yescharacteristic, direct product factor
62C3×D31—31no—
63C3×D31—751no—
64C3×D3×D5—1551no—
65C5×C31C3×D3×D511yescharacteristic
66C2×C3×C25—931no—
67D75—311no—
68C3×D25—21no—
69C3×D25—931no—
70C3×D25C3×D3111yescharacteristic, complemented
71C3×D25D9311yescharacteristic, direct product factor
72D3×C25—311no—
73C2×D31—751noHall
74C2×D25—931noHall
75C3×C31—21no—
76C3×C31D3×D2511yescharacteristic, complemented
77C3×C31C2×C3×D2511yescharacteristic, complemented
78C3×D15—1551no—
79C3×C5×D3—311no—
80C32×D5—51no—
81C3×C25—21no—
82C3×C25C2×C3×D3111yescharacteristic, complemented
83C3×C25C2×D9311yescharacteristic, complemented
84C2×C31—251no—
85D31—31no—
86D31—751no—
87C2×C3×D5—4651no—
88D3×D5—1551no—
89C2×C25—931no—
90D25—931no—
91D25C3×D9311yescharacteristic, direct product factor
92C32×C5D5×D3111yescharacteristic
93C2×C3×D3—7751noHall
94C31C3×D3×D2511yescharacteristic, complemented, Sylow
95C2×C3×C5—931no—
96D15—1551no—
97C3×D5—51no—
98C3×D5—51no—
99C3×D5—101no—
100C3×D5—4651no—
101C5×D3—311no—
102C25C2×C3×D9311yescharacteristic, complemented, Sylow
103C2×D5—4651no—
104C2×C32—251no—
105C3×D3—7751no—
106C3×D3—311no—
107C3×C5—21no—
108C3×C5C3×D5×D3111yescharacteristic
109C3×C5D5×D9311yescharacteristic
110C22×C3—23251no—
111C2×D3—7751no—
112C2×C5—931no—
113D5—51no—
114D5—4651no—
115C32D25×D3111yescharacteristic, complemented, Sylow
116C2×C3—23251no—
117C2×C3—251no—
118C2×C3—251no—
119C2×C3—501no—
120C2×C3—931no—
121D3—7751no—
122D3—311no—
123C5C3×D5×D9311yescharacteristic
124C22—23251noSylow
125C3—21no—
126C3C3×D25×D3111yescharacteristic, complemented
127C3D25×D9311yescharacteristic, direct product factor
128C2—23251no—
129C2—251no—
130C2—931no—
subgroupG/H
center, hypercenterC3D25×D93
commutator, cosocle, hypocenterC3×C25×C31C22×C3
FrattiniC5C3×D5×D93
FittingC32×C25×C31C22
socleC32×C5×C31C2×D5
LCSG ▷ C3×C25×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D2325C2semidirect
2. C3×C25×D93C2semidirect
3. C32×C31×D25C2semidirect
4. D25×D93C3direct (N × H)
6. C32×C25×C31C22semidirect
8. D2325C2×C3semidirect
9. C25×D93C2×C3semidirect
12. C3×C31×D25D3semidirect
13. C3×C31×D25C2×C3semidirect
20. C3×C25×C31C2×D3semidirect
21. C3×C25×C31C22×C3semidirect
26. C31×D25C3×D3semidirect
37. C25×C31C2×C3×D3semidirect
41. C3×D93D25direct (N × H)
47. C32×D25D31semidirect
55. C32×C31C2×D25semidirect
56. C32×C25C2×D31semidirect
61. D93C3×D25direct (N × H)
70. C3×D25C3×D31semidirect
71. C3×D25D93direct (N × H)
76. C3×C31D3×D25semidirect
77. C3×C31C2×C3×D25semidirect
82. C3×C25C2×C3×D31semidirect
83. C3×C25C2×D93semidirect
91. D25C3×D93direct (N × H)
94. C31C3×D3×D25semidirect
102. C25C2×C3×D93semidirect
115. C32D25×D31semidirect
126. C3C3×D25×D31semidirect
127. C3D25×D93direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D23252
C3×C25×D932
C32×C31×D252
D25×D933
C3×D25×D313
C3×D5×D935
C3×D3×D2531