Finite Group Databasebeta

← C3×#91385 #13086474

Subgroups — C3×#91385 #13086474

Order 1440.

310 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×C3×C5×Dic6C211yesmaximal, characteristic
2C2×C32×Dic10C211yesmaximal, characteristic
3C3×C4×Dic15C211yesmaximal, characteristic
4C3×#6669C214yesmaximal
5C3×#4090—31nomaximal
6#91385C311yesmaximal, characteristic, direct product factor
7C2×C32×C4×C5C2211yescharacteristic
8C2×C3×Dic15C2212yes—
9C2×C3×C5×Dic3C2212yes—
10C3×C5×Dic6—22no—
11C2×C32×Dic5C2212yes—
12C32×Dic10—22no—
13C3×#944—51nomaximal, Hall
14C2×C3×C5×Q8—31no—
15C2×C5×Dic6C2×C311yescharacteristic
16C2×C3×Dic10—21no—
17C2×C3×Dic10D311yescharacteristic
18C2×C3×Dic10C2×C311yescharacteristic
19C4×Dic15C2×C311yescharacteristic
20C3×#683—34no—
21C3×C4×Dic5—31no—
22#6669C2×C314yes—
23C22×C32×C5C2311yescharacteristic
24C32×C4×C5D412yes—
25C3×Dic15Q814yescomplemented
26C3×C5×Dic3—22no—
27C32×Dic5—22no—
28#4090—31noHall
29C2×C32×Q8—51no—
30C2×C3×Dic6D511yescharacteristic
31C3×Dic3⋊C4—54no—
32C3×C4×Dic3—51no—
33C3×C5×Q8—62no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5—32no—
36C2×C3×C4×C5C2×D311yescharacteristic
37C2×C3×C4×C5C22×C311yescharacteristic
38C2×Dic15C22×C312yes—
39C2×C5×Dic3C22×C312yes—
40C5×Dic6—22no—
41C2×C3×Dic5—22no—
42C2×C3×Dic5—32no—
43C2×C3×Dic5C2×D312yes—
44C2×C3×Dic5C22×C312yes—
45C3×Dic10—24no—
46C3×Dic10—22no—
47C3×Dic10—22no—
48C3×C4⋊Q8—151no—
49#944—51no—
50C2×C32×C5C2×D411yescharacteristic
51C2×C32×C5C2×Q812yes—
52C2×C5×Q8—31no—
53C2×Dic10C3×D311yescharacteristic
54#683—34no—
55C4×Dic5—31no—
56C32×Q8—102no—
57C2×C32×C4—52no—
58C2×C32×C4C2×D511yescharacteristic
59C2×C3×Dic3—52no—
60C2×C3×Dic3C2×D512yes—
61C3×Dic6—22no—
62C22×C3×C5—21no—
63C22×C3×C5C22×D311yescharacteristic
64C22×C3×C5C23×C311yescharacteristic
65C3×C4×C5—22no—
66C3×C4×C5—62no—
67C3×C4×C5#6712yes—
68C3×C4×C5C3×D412yes—
69Dic15C3×Q814yescomplemented
70C3×Dic5—24no—
71C3×Dic5—22no—
72C3×Dic5—22no—
73C3×Dic5—34no—
74C5×Dic3—22no—
75C2×C3×Q8—31no—
76C2×C3×Q8—51no—
77C2×C3×Q8—51no—
78C2×C3×Q8—101no—
79C2×Dic6C3×D511yescharacteristic
80C3×C4⋊C4—154no—
81C3×C42—151no—
82Dic3⋊C4—54no—
83C4×Dic3—51no—
84C32×C5C4⋊Q811yescharacteristic, complemented, Hall
85C5×Q8—62no—
86C2×C4×C5—32no—
87C2×C4×C5C2×C3×D311yescharacteristic
88C2×Dic5—32no—
89C2×Dic5C2×C3×D312yes—
90Dic10—22no—
91C22×C32C22×D511yescharacteristic
92C32×C4—102no—
93C32×C4C22⋊D512yes—
94C3×Dic3—22no—
95C3×Dic3—54no—
96C4⋊Q8—151noSylow
97C2×C3×C5—22no—
98C2×C3×C5—21no—
99C2×C3×C5D3×Q812yes—
100C2×C3×C5C2×#6711yescharacteristic
101C2×C3×C5C2×C3×D411yescharacteristic
102C2×C3×C5C2×C3×Q812yes—
103C3×Q8—62no—
104C3×Q8—104no—
105C3×Q8—102no—
106C3×Q8—102no—
107C2×C3×C4—21no—
108C2×C3×C4—32no—
109C2×C3×C4—52no—
110C2×C3×C4—52no—
111C2×C3×C4—102no—
112C2×C3×C4—152no—
113C2×C3×C4D3×D511yescharacteristic
114C2×C3×C4C2×C3×D511yescharacteristic
115C2×Dic3—52no—
116C2×Dic3C2×C3×D512yes—
117Dic6—22no—
118C22×C5C22×C3×D311yescharacteristic
119C4×C5—62no—
120C4×C5C3×#6712yes—
121Dic5—22no—
122Dic5—34no—
123C2×C32Q8×D512yes—
124C2×C32C2×C22⋊D511yescharacteristic
125C2×Q8—31no—
126C2×Q8—51no—
127C4⋊C4—154no—
128C42—151no—
129C3×C5—21no—
130C3×C5#94411yescharacteristic, complemented
131C3×C5C3×C4⋊Q811yescharacteristic, complemented
132C22×C3—21no—
133C22×C3C2×D3×D511yescharacteristic
134C22×C3C22×C3×D511yescharacteristic
135C3×C4—22no—
136C3×C4—62no—
137C3×C4—104no—
138C3×C4—102no—
139C3×C4—102no—
140C3×C4—154no—
141C3×C4#120112yes—
142C3×C4C3×C22⋊D512yes—
143Dic3—22no—
144Dic3—54no—
145C2×C5C3×D3×Q812yes—
146C2×C5C2×C3×#6711yescharacteristic
147C32#409011yescharacteristic, complemented, Sylow
148Q8—62no—
149Q8—102no—
150C2×C4—32no—
151C2×C4—52no—
152C2×C4—152no—
153C2×C4C3×D3×D511yescharacteristic
154C2×C3—22no—
155C2×C3—21no—
156C2×C3D15⋊Q812yes—
157C2×C3C2×#120111yescharacteristic
158C2×C3C3×Q8×D512yes—
159C2×C3C2×C3×C22⋊D511yescharacteristic
160C5C3×#94411yescharacteristic, complemented, Sylow
161C22C2×C3×D3×D511yescharacteristic
162C4—62no—
163C4—102no—
164C4—154no—
165C4C3×#120112yes—
166C3—21no—
167C3#9138511yescharacteristic, direct product factor
168C3C3×#409011yescharacteristic, complemented
169C2C3×D15⋊Q812yes—
170C2C2×C3×#120111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D5
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C2×C3×D3×D5
FittingC2×C32×C4×C5C22
socle, prime radicalC22×C32×C5C23
hypercenterC2×C3×C4D3×D5
hypocenterC3×C5C3×C4⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
6. #91385C3direct (N × H)
25. C3×Dic15Q8semidirect
69. Dic15C3×Q8semidirect
84. C32×C5C4⋊Q8semidirect
130. C3×C5#944semidirect
131. C3×C5C3×C4⋊Q8semidirect
147. C32#4090semidirect
160. C5C3×#944semidirect
167. C3#91385direct (N × H)
168. C3C3×#4090semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×Dic62
C2×C32×Dic102
C3×C4×Dic152
C3×#66692
C3×#40903
#913853
C3×#9445