Finite Group Databasebeta

← D3×C25×D93 #42124440

Subgroups — D3×C25×D93 #42124440

Order 27900.

132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C25×C3⋊D93C211yesmaximal, characteristic, complemented
2C3×C25×D93C211yesmaximal, characteristic, complemented
3C3×D3×C25×C31C211yesmaximal, characteristic, complemented
4C2×C25×D93—31nomaximal
5D3×C25×D31—31nomaximal
6C32×C25×C31C2211yescharacteristic, complemented, Hall
7C5×D3×D93C511yesmaximal, characteristic
8C25×D93—31no—
9C25×D93—31no—
10C25×D93—61no—
11C25×D93D311yescharacteristic, direct product factor
12D3×C25×C31D311yescharacteristic, complemented
13C3×C25×D31—31no—
14C2×C3×C25×C31—31no—
15C2×C25×D31—91noHall
16C5×C3⋊D93C2×C511yescharacteristic
17C3×C5×D93C2×C511yescharacteristic
18C3×C5×D3×C31C2×C511yescharacteristic
19C3×C25×C31—21no—
20C3×C25×C31C2×D311yescharacteristic, complemented
21C3×C25×C31C2×D311yescharacteristic, complemented
22C2×C5×D93—31no—
23C5×D3×D31—31no—
24C2×C25×C31—31no—
25C25×D31—31no—
26C25×D31—91no—
27C32×C5×C31C22×C511yescharacteristic
28D3×D93C2511yescharacteristic, direct product factor, Hall
29C2×C3×C5×C31—31no—
30C5×D93—31no—
31C5×D93—31no—
32C5×D93—61no—
33C5×D93C5×D311yescharacteristic
34C5×D3×C31C5×D311yescharacteristic
35C3×C5×D31—31no—
36D32×C25—311nomaximal, Hall
37C25×C31D3211yescharacteristic, complemented, Hall
38C2×C5×D31—91no—
39C3⋊D93C2×C2511yescharacteristic, complemented
40C3×D93C2×C2511yescharacteristic, complemented
41C3×D3×C31C2×C2511yescharacteristic, complemented
42C3×C5×C31—21no—
43C3×C5×C31C2×C5×D311yescharacteristic
44C3×C5×C31C2×C5×D311yescharacteristic
45C3⋊D3×C25—311no—
46C3×D3×C25—311no—
47C3×D3×C25D3111yescharacteristic, complemented
48C2×D93—31no—
49D3×D31—31no—
50C2×C5×C31—31no—
51C5×D31—31no—
52C5×D31—91no—
53C2×D3×C25—931no—
54C2×D3×C25—931no—
55C32×C31C22×C2511yescharacteristic, complemented, Hall
56C32×C25C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—31no—
58D93—31no—
59D93—31no—
60D93—61no—
61D93D3×C2511yescharacteristic, direct product factor
62C3×D31—31no—
63D3×C31D3×C2511yescharacteristic, complemented
64C5×D32—311no—
65C5×C31C5×D3211yescharacteristic
66C2×C3×C25—31no—
67C2×C3×C25—931no—
68D3×C25—311no—
69D3×C25—931no—
70D3×C25—931no—
71D3×C25—1861no—
72D3×C25D9311yescharacteristic, direct product factor
73C2×D31—91noHall
74C22×C25—2791noHall
75C3×C31—21no—
76C3×C31C2×D3×C2511yescharacteristic, complemented
77C3×C31C2×D3×C2511yescharacteristic, complemented
78C5×C3⋊D3—311no—
79C3×C5×D3—311no—
80C3×C5×D3C5×D3111yescharacteristic
81C3×C25—21no—
82C3×C25D3×D3111yescharacteristic, complemented
83C3×C25C2×D9311yescharacteristic, complemented
84C2×C31—31no—
85D31—31no—
86D31—91no—
87C2×C5×D3—931no—
88C2×C5×D3—931no—
89C2×C25—31no—
90C2×C25—2791no—
91C2×C25—931no—
92C32×C5C2×C5×D3111yescharacteristic
93D32—311noHall
94C31D32×C2511yescharacteristic, complemented, Sylow
95C2×C3×C5—31no—
96C2×C3×C5—931no—
97C5×D3—311no—
98C5×D3—931no—
99C5×D3—931no—
100C5×D3—1861no—
101C5×D3C5×D9311yescharacteristic
102C25D3×D9311yescharacteristic, direct product factor, Sylow
103C22×C5—2791no—
104C3⋊D3—311no—
105C3×D3—311no—
106C3×D3C25×D3111yescharacteristic, complemented
107C3×C5—21no—
108C3×C5C5×D3×D3111yescharacteristic
109C3×C5C2×C5×D9311yescharacteristic
110C2×D3—931no—
111C2×D3—931no—
112C2×C5—31no—
113C2×C5—2791no—
114C2×C5—931no—
115C32C2×C25×D3111yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—931no—
118D3—311no—
119D3—931no—
120D3—931no—
121D3—1861no—
122D3C25×D9311yescharacteristic, direct product factor
123C5C5×D3×D9311yescharacteristic
124C22—2791noSylow
125C3—21no—
126C3D3×C25×D3111yescharacteristic, complemented
127C3C2×C25×D9311yescharacteristic, complemented
128C2—31no—
129C2—2791no—
130C2—931no—
subgroupG/H
center, hypercenterC25D3×D93
commutator, hypocenterC32×C31C22×C25
FrattiniC5C5×D3×D93
FittingC32×C25×C31C22
socle, cosocleC32×C5×C31C22×C5
prime radicalC5×D3×D93C5
LCSG ▷ C32×C31
UCSC1 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D93C2semidirect
2. C3×C25×D93C2semidirect
3. C3×D3×C25×C31C2semidirect
6. C32×C25×C31C22semidirect
11. C25×D93D3direct (N × H)
12. D3×C25×C31D3semidirect
20. C3×C25×C31C2×D3semidirect
21. C3×C25×C31C2×D3semidirect
28. D3×D93C25direct (N × H)
37. C25×C31D32semidirect
39. C3⋊D93C2×C25semidirect
40. C3×D93C2×C25semidirect
41. C3×D3×C31C2×C25semidirect
47. C3×D3×C25D31semidirect
55. C32×C31C22×C25semidirect
56. C32×C25C2×D31semidirect
61. D93D3×C25direct (N × H)
63. D3×C31D3×C25semidirect
72. D3×C25D93direct (N × H)
76. C3×C31C2×D3×C25semidirect
77. C3×C31C2×D3×C25semidirect
82. C3×C25D3×D31semidirect
83. C3×C25C2×D93semidirect
94. C31D32×C25semidirect
102. C25D3×D93direct (N × H)
106. C3×D3C25×D31semidirect
115. C32C2×C25×D31semidirect
122. D3C25×D93direct (N × H)
126. C3D3×C25×D31semidirect
127. C3C2×C25×D93semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D932
C3×C25×D932
C3×D3×C25×C312
C2×C25×D933
D3×C25×D313
C5×D3×D935
D32×C2531