Finite Group Databasebeta

← C3×#91338 #13086437

Subgroups — C3×#91338 #13086437

Order 1440.

330 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 136 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×C4×C5×D3C211yesmaximal, characteristic
2C3×C4⋊Dic15C211yesmaximal, characteristic, complemented
3C32×C4⋊Dic5C211yesmaximal, characteristic, complemented
4C3×(C2×D3)⋊Dic5C212yesmaximal
5C3×Dic3×Dic5C212yesmaximal, complemented
6C3×#4072—31nomaximal
7#91338C311yesmaximal, characteristic, direct product factor
8C22×C3×C5×D3C2211yescharacteristic
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3×Dic15C2212yes—
11C2×C3×C5×Dic3C2211yescharacteristic
12C3×C4×C5×D3C414yescomplemented
13C2×C32×Dic5C2212yes—
14C3×#892—51nomaximal, Hall
15C22×C3×C4×C5—31no—
16C2×C4×C5×D3C2×C311yescharacteristic
17C4⋊Dic15C2×C311yescharacteristic, complemented
18C3×C22⋊Dic5—32no—
19C3×C4⋊Dic5—21no—
20C3×C4⋊Dic5—31no—
21C3×C4⋊Dic5D311yescharacteristic, complemented
22C3×C4⋊Dic5C2×C311yescharacteristic, complemented
23C3×C4×Dic5—32no—
24(C2×D3)⋊Dic5C2×C312yes—
25Dic3×Dic5C2×C312yescomplemented
26C22×C32×C5C2311yescharacteristic
27C2×C3×C5×D3—21no—
28C2×C3×C5×D3—21no—
29C2×C3×C5×D3C2×C412yes—
30C32×C4×C5C2×C412yes—
31C3×Dic15—22no—
32C3×C5×Dic3C2×C412yes—
33C32×Dic5—22no—
34#4072—31noHall
35C2×C3×C4×D3D511yescharacteristic
36C32×C4⋊C4—51no—
37C3×(C2×D3)⋊C4—52no—
38C3×C4⋊Dic3—51no—
39C3×C4×Dic3—52no—
40C23×C3×C5—31no—
41C22×C5×D3C22×C311yescharacteristic
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—31no—
44C2×C3×C4×C5—34no—
45C2×C3×C4×C5C2×D311yescharacteristic
46C2×C3×C4×C5C22×C311yescharacteristic
47C2×Dic15C22×C312yes—
48C2×C5×Dic3C22×C311yescharacteristic
49C4×C5×D3C3×C414yescomplemented
50C2×C3×Dic5—22no—
51C2×C3×Dic5—32no—
52C2×C3×Dic5C2×D312yes—
53C2×C3×Dic5C22×C312yes—
54C3×#117—151no—
55#892—51no—
56C2×C32×C5C22×C411yescharacteristic
57C2×C32×C5#4111yescharacteristic
58C2×C32×C5#4111yescharacteristic
59C3×C5×D3—22no—
60C22×C4×C5—31no—
61C22⋊Dic5—32no—
62C4⋊Dic5—31no—
63C4⋊Dic5C3×D311yescharacteristic, complemented
64C4×Dic5—32no—
65C22×C3×D3C2×D511yescharacteristic
66C2×C32×C4—52no—
67C2×C32×C4C2×D511yescharacteristic
68C2×C3×Dic3—52no—
69C2×C3×Dic3C2×D511yescharacteristic
70C3×C4×D3Dic514yescomplemented
71C22×C3×C5—21no—
72C22×C3×C5—32no—
73C22×C3×C5—61no—
74C22×C3×C5—61no—
75C22×C3×C5C22×D311yescharacteristic
76C22×C3×C5C23×C311yescharacteristic
77C2×C5×D3—21no—
78C2×C5×D3—21no—
79C2×C5×D3C2×C3×C412yes—
80C3×C4×C5—22no—
81C3×C4×C5—32no—
82C3×C4×C5C4×D312yes—
83C3×C4×C5C2×C3×C412yes—
84Dic15—22no—
85C3×Dic5—22no—
86C3×Dic5—22no—
87C3×Dic5—42no—
88C3×Dic5—62no—
89C5×Dic3C2×C3×C412yes—
90C22×C3×C4—31no—
91C2×C4×D3C3×D511yescharacteristic
92C3×C4⋊C4—51no—
93C3×C4⋊C4—51no—
94C3×C4⋊C4—101no—
95C3×C4⋊C4—151no—
96C3×C22⋊C4—152no—
97C3×C42—152no—
98(C2×D3)⋊C4—52no—
99C4⋊Dic3—51no—
100C4×Dic3—52no—
101C32×C5#11711yescharacteristic, complemented, Hall
102C23×C5—31no—
103C2×C4×C5—31no—
104C2×C4×C5—34no—
105C2×C4×C5C2×C3×D311yescharacteristic
106C2×Dic5—32no—
107C2×Dic5C2×C3×D312yes—
108C22×C32C22×D511yescharacteristic
109C2×C3×D3—21no—
110C2×C3×D3—21no—
111C2×C3×D3C2×Dic512yes—
112C32×C4—102no—
113C32×C4C2×Dic512yes—
114C3×Dic3—102no—
115C3×Dic3C2×Dic512yes—
116#117—151noSylow
117C2×C3×C5—21no—
118C2×C3×C5—21no—
119C2×C3×C5—21no—
120C2×C3×C5—62no—
121C2×C3×C5C2×C4×D311yescharacteristic
122C2×C3×C5#23711yescharacteristic
123C2×C3×C5#23911yescharacteristic
124C2×C3×C5C22×C3×C411yescharacteristic
125C2×C3×C5C3×#4111yescharacteristic
126C2×C3×C5C3×#4111yescharacteristic
127C5×D3—22no—
128C23×C3—31no—
129C22×D3C2×C3×D511yescharacteristic
130C2×C3×C4—21no—
131C2×C3×C4—31no—
132C2×C3×C4—34no—
133C2×C3×C4—52no—
134C2×C3×C4—52no—
135C2×C3×C4—102no—
136C2×C3×C4—152no—
137C2×C3×C4D3×D511yescharacteristic
138C2×C3×C4C2×C3×D511yescharacteristic
139C2×Dic3—52no—
140C2×Dic3C2×C3×D511yescharacteristic
141C4×D3C3×Dic514yescomplemented
142C22×C5—32no—
143C22×C5—61no—
144C22×C5—61no—
145C22×C5C22×C3×D311yescharacteristic
146C4×C5—32no—
147C4×C5C3×C4×D312yes—
148Dic5—22no—
149Dic5—62no—
150C2×C32#70911yescharacteristic
151C2×C32#70911yescharacteristic
152C2×C32C22×Dic511yescharacteristic
153C3×D3—22no—
154C22×C4—31no—
155C4⋊C4—51no—
156C4⋊C4—151no—
157C22⋊C4—152no—
158C42—152no—
159C3×C5—21no—
160C3×C5#89211yescharacteristic, complemented
161C3×C5C3×#11711yescharacteristic, complemented
162C22×C3—21no—
163C22×C3—32no—
164C22×C3—61no—
165C22×C3—61no—
166C22×C3C2×D3×D511yescharacteristic
167C22×C3C22×C3×D511yescharacteristic
168C2×D3—21no—
169C2×D3—21no—
170C2×D3C2×C3×Dic512yes—
171C3×C4—22no—
172C3×C4—32no—
173C3×C4—102no—
174C3×C4—102no—
175C3×C4—202no—
176C3×C4—302no—
177C3×C4D3×Dic512yes—
178C3×C4C2×C3×Dic512yes—
179Dic3—102no—
180Dic3C2×C3×Dic512yes—
181C2×C5—62no—
182C2×C5C2×C3×C4×D311yescharacteristic
183C2×C5C3×#23711yescharacteristic
184C2×C5C3×#23911yescharacteristic
185C32#407211yescharacteristic, complemented, Sylow
186C23—31no—
187C2×C4—31no—
188C2×C4—34no—
189C2×C4—52no—
190C2×C4—152no—
191C2×C4C3×D3×D511yescharacteristic
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—62no—
196C2×C3#676511yescharacteristic
197C2×C3#676911yescharacteristic
198C2×C3C2×D3×Dic511yescharacteristic
199C2×C3C3×#70911yescharacteristic
200C2×C3C3×#70911yescharacteristic
201C2×C3C22×C3×Dic511yescharacteristic
202D3—22no—
203C5C3×#89211yescharacteristic, complemented, Sylow
204C22—32no—
205C22—61no—
206C22—61no—
207C22C2×C3×D3×D511yescharacteristic
208C4—32no—
209C4—102no—
210C4—302no—
211C4C3×D3×Dic512yes—
212C3—21no—
213C3#9133811yescharacteristic, direct product factor
214C3C3×#407211yescharacteristic, complemented
215C2—62no—
216C2C3×#676511yescharacteristic
217C2C3×#676911yescharacteristic
218C2C2×C3×D3×Dic511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D5
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×D5
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C3×C5×D3C22
cosocleC22×C3×C5C23×C3
hypercenterC2×C3×C4D3×D5
hypocenterC3×C5C3×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4⋊Dic15C2semidirect
3. C32×C4⋊Dic5C2semidirect
5. C3×Dic3×Dic5C2semidirect
7. #91338C3direct (N × H)
12. C3×C4×C5×D3C4semidirect
17. C4⋊Dic15C2×C3semidirect
21. C3×C4⋊Dic5D3semidirect
22. C3×C4⋊Dic5C2×C3semidirect
25. Dic3×Dic5C2×C3semidirect
49. C4×C5×D3C3×C4semidirect
63. C4⋊Dic5C3×D3semidirect
70. C3×C4×D3Dic5semidirect
101. C32×C5#117semidirect
141. C4×D3C3×Dic5semidirect
160. C3×C5#892semidirect
161. C3×C5C3×#117semidirect
185. C32#4072semidirect
203. C5C3×#892semidirect
213. C3#91338direct (N × H)
214. C3C3×#4072semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D32
C3×C4⋊Dic152
C32×C4⋊Dic52
C3×(C2×D3)⋊Dic52
C3×Dic3×Dic52
C3×#40723
#913383
C3×#8925