Finite Group Databasebeta

← C3×#10599282 #14285417

Subgroups — C3×#10599282 #14285417

Order 1920.

508 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 134 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×#66059C211yesmaximal, characteristic
2C3×#65126C212yesmaximal, complemented
3C3×C5×#333C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5C3×#64705C212yesmaximal, complemented
6#10599282C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4093C412yes—
10C2×C3×#676—22no—
11C3×#4041—22no—
12C3×#4039—22no—
13C3×#4020C2211yescharacteristic
14C3×C42×D5C2211yescharacteristic
15C3×C5×C4⋊C8C2212yes—
16C3×#3946—22no—
17C3×C4⋊#168C2212yes—
18C3×#1560—51nomaximal, Hall
19#66059C2×C311yescharacteristic
20#65126C2×C312yescomplemented
21C5×#333C2×C311yescharacteristic, complemented
22#64766C2×C311yescharacteristic, complemented
23#64705C2×C312yescomplemented
24C2×C3×C5×Q8C2×C412yes—
25C3×#713—44no—
26C2×C3×D20—22no—
27C2×C3×D20—22no—
28C2×C3×D20C2×C412yes—
29C2×C3×C4×D5—22no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D412yes—
32C2×C3×C5×C8—22no—
33C3×C5×C4⋊C4—22no—
34C3×C42×C5C2311yescharacteristic
35C3×#685—24no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38C2×C3×#168—22no—
39C3×#676—44no—
40C3×#532—51no—
41C3×#423—52no—
42C3×#333—51no—
43C3×#333D511yescharacteristic, complemented
44C3×#331—52no—
45C2×#713C3×C412yes—
46C5×C4⋊Q8C22×C311yescharacteristic
47#4093C3×C412yes—
48C2×#676—22no—
49#4041—22no—
50#4039—22no—
51#4020C22×C311yescharacteristic
52C42×D5C22×C311yescharacteristic
53C5×C4⋊C8C22×C312yes—
54#3946—22no—
55C4⋊#168C22×C312yes—
56#1560—51noSylow
57C22×C3×D5—22no—
58C22×C3×D5C22⋊C411yescharacteristic
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×C3×Dic5C22⋊C412yes—
64C2×C3×Dic5C22⋊C411yescharacteristic
65C3×D20—42no—
66C3×D20—44no—
67C3×D20—42no—
68C3×D20—42no—
69C3×C4×D5—22no—
70C3×C4×D5—22no—
71C3×C4×D5—22no—
72C3×C4×D5—44no—
73C3×C5×C8—42no—
74C3×#168—42no—
75C2×C3×#41—52no—
76C2×C3×M16—102no—
77C3×C4⋊Q8C2×D511yescharacteristic
78C3×#127—51no—
79C3×#124—52no—
80C3×#121—102no—
81C3×C4×D4—102no—
82C2×C3×C42—51no—
83C3×C4⋊C8—52no—
84C3×C4⋊C8—102no—
85C3×C4⋊C8C2×D512yes—
86C2×C5×Q8C2×C3×C412yes—
87#713—44no—
88C2×D20—22no—
89C2×D20—22no—
90C2×D20C2×C3×C412yes—
91C2×C4×D5—22no—
92C2×C4×D5C2×C3×C411yescharacteristic
93C2×C4×D5C3×D412yes—
94C2×C5×C8—22no—
95C5×C4⋊C4—22no—
96C42×C5C23×C311yescharacteristic
97#685—24no—
98C4×Dic5C2×C3×C411yescharacteristic
99C4×Dic5C3×D412yes—
100C2×#168—22no—
101#676—44no—
102#532—51no—
103#423—52no—
104#333—51no—
105#333C3×D511yescharacteristic, complemented
106#331—52no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×C3×D5—21no—
109C2×C3×D5—22no—
110C2×C3×D5—42no—
111C2×C3×D5—44no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5AGL(1,ℤ/8)12yes—
115C3×C4×C5#13712yes—
116C3×Dic5—22no—
117C3×Dic5#10012yes—
118C3×#41—204no—
119C2×C3×Q8C4×D512yes—
120C2×C3×D4—52no—
121C2×C3×D4—102no—
122C2×C3×D4—102no—
123C22×C3×C4—51no—
124C22×C3×C4—52no—
125C22×C3×C4—102no—
126C3×M16—204no—
127C2×C3×C8—22no—
128C2×C3×C8—102no—
129C3×C4⋊C4—22no—
130C3×C22⋊C4—104no—
131C3×C42—51no—
132C3×C42—52no—
133C3×C42C22×D511yescharacteristic
134C22×D5—22no—
135C22×D5C3×C22⋊C411yescharacteristic
136C5×Q8—42no—
137C2×C4×C5—22no—
138C2×C4×C5C22×C3×C411yescharacteristic
139C2×C4×C5C2×C3×D412yes—
140C2×Dic5C3×C22⋊C412yes—
141C2×Dic5C3×C22⋊C411yescharacteristic
142D20—42no—
143D20—44no—
144D20—42no—
145D20—42no—
146C4×D5—22no—
147C4×D5—22no—
148C4×D5—22no—
149C4×D5—44no—
150C5×C8—42no—
151#168—42no—
152C2×#41—52no—
153C2×M16—102no—
154C4⋊Q8C2×C3×D511yescharacteristic
155#127—51no—
156#124—52no—
157#121—102no—
158C4×D4—102no—
159C2×C42—51no—
160C4⋊C8—52no—
161C4⋊C8—102no—
162C4⋊C8C2×C3×D512yes—
163C2×C3×C5C2×#10011yescharacteristic
164C2×C3×C5#41712yes—
165C3×D5—41no—
166C3×D5—82no—
167C23×C3—51no—
168C23×C3—102no—
169C3×Q8—42no—
170C3×D4—202no—
171C3×D4—204no—
172C3×D4—202no—
173C3×D4—202no—
174C2×C3×C4—22no—
175C2×C3×C4—51no—
176C2×C3×C4—52no—
177C2×C3×C4—102no—
178C2×C3×C4—102no—
179C2×C3×C4—102no—
180C2×C3×C4—204no—
181C2×C3×C4C2×C4×D511yescharacteristic
182C2×C3×C4D4×D512yes—
183C3×C8—42no—
184C3×C8—202no—
185C22×C5C2×C3×C22⋊C411yescharacteristic
186C2×D5—21no—
187C2×D5—22no—
188C2×D5—42no—
189C2×D5—44no—
190C4×C5—21no—
191C4×C5—42no—
192C4×C5C3×AGL(1,ℤ/8)12yes—
193C4×C5C3×#13712yes—
194Dic5—22no—
195Dic5C3×#10012yes—
196#41—204no—
197C2×Q8C3×C4×D512yes—
198C2×D4—52no—
199C2×D4—102no—
200C2×D4—102no—
201C22×C4—51no—
202C22×C4—52no—
203C22×C4—102no—
204M16—204no—
205C2×C8—22no—
206C2×C8—102no—
207C4⋊C4—22no—
208C22⋊C4—104no—
209C42—51no—
210C42—52no—
211C42C22×C3×D511yescharacteristic
212C3×C5#156011yescharacteristic, complemented, Hall
213C22×C3—101no—
214C22×C3—102no—
215C22×C3—202no—
216C22×C3—204no—
217C22×C3D5×C22⋊C411yescharacteristic
218C3×C4—21no—
219C3×C4—42no—
220C3×C4—52no—
221C3×C4—102no—
222C3×C4#406012yes—
223C3×C4#406412yes—
224C2×C5C2×C3×#10011yescharacteristic
225C2×C5C3×#41712yes—
226D5—41no—
227D5—82no—
228C23—51no—
229C23—102no—
230Q8—42no—
231D4—202no—
232D4—204no—
233D4—202no—
234D4—202no—
235C2×C4—22no—
236C2×C4—51no—
237C2×C4—52no—
238C2×C4—102no—
239C2×C4—102no—
240C2×C4—102no—
241C2×C4—204no—
242C2×C4C2×C3×C4×D511yescharacteristic
243C2×C4C3×D4×D512yes—
244C8—42no—
245C8—202no—
246C2×C3—201no—
247C2×C3—402no—
248C2×C3D5×#10011yescharacteristic
249C2×C3#6509212yes—
250C5C3×#156011yescharacteristic, complemented, Sylow
251C22—101no—
252C22—102no—
253C22—202no—
254C22—204no—
255C22C3×D5×C22⋊C411yescharacteristic
256C4—21no—
257C4—42no—
258C4—52no—
259C4—102no—
260C4C3×#406012yes—
261C4C3×#406412yes—
262C3#1059928211yescharacteristic, direct product factor, Sylow
263C2—201no—
264C2—402no—
265C2C3×D5×#10011yescharacteristic
266C2C3×#6509212yes—
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC42×C5C23×C3
hypercenterC3×#333D5
hypocenterC5C3×#1560
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
2. C3×#65126C2semidirect
3. C3×C5×#333C2semidirect
4. C3×#64766C2semidirect
5. C3×#64705C2semidirect
6. #10599282C3direct (N × H)
20. #65126C2×C3semidirect
21. C5×#333C2×C3semidirect
22. #64766C2×C3semidirect
23. #64705C2×C3semidirect
43. C3×#333D5semidirect
105. #333C3×D5semidirect
212. C3×C5#1560semidirect
250. C5C3×#1560semidirect
262. C3#10599282direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660592
C3×#651262
C3×C5×#3332
C3×#647662
C3×#647052
#105992823
C3×#15605