Finite Group Databasebeta

← #14297595

Subgroups — #14297595

Order 1920.

544 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 137 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×#91776C211yesmaximal, characteristic
2C2×#91108C212yesmaximal
3#11751219C212yesmaximal
4C3×C5×#343C211yesmaximal, characteristic
5#11746351C211yesmaximal, characteristic
6#10599790—31nomaximal, Hall
7C22×Dic30C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6712C412yes—
11C2×C4×Dic15C412yes—
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2212yes—
14#91776—22no—
15#91776—22no—
16#91108—24no—
17#91098—22no—
18#91098—22no—
19#68997—51nomaximal, Hall
20C2×#4033—31no—
21C2×#3956—32no—
22#65407—32no—
23C5×#343D311yescharacteristic
24#64750—31no—
25C22×C3×C4×C5C2×C412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15C2×C411yescharacteristic
28C22×Dic15C2×C412yes—
29C22×Dic15C2×C411yescharacteristic
30C2×Dic30—22no—
31C2×Dic30—22no—
32C2×Dic30D412yes—
33C2×Dic30Q812yes—
34C3×C5×M16—22no—
35C3×C5×M16—22no—
36C2×C3×C5×C8—22no—
37C3×C5×C4⋊C4—22no—
38#6712—24no—
39C4×Dic15—22no—
40C4×Dic15—22no—
41C4×Dic15D412yes—
42C4×Dic15D412yes—
43#6710—22no—
44#6710—22no—
45C2×C3⋊#168—22no—
46C2×#887—51no—
47C2×#824—52no—
48#5118—52no—
49C3×#343D511yescharacteristic
50#4530—51no—
51C22×Dic10—31no—
52C2×C5×M16C2×D312yes—
53C2×C5×C4⋊C4C2×D311yescharacteristic
54C2×#683—32no—
55C2×C4×Dic5—31no—
56C2×C4×Dic5—32no—
57C2×#681—32no—
58#4033—62no—
59#4033—62no—
60#3956—64no—
61#3946—62no—
62#3946—62no—
63#1801—151noSylow
64C23×C3×C5C22×C411yescharacteristic
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69C2×C3×C4×C5C2×Q811yescharacteristic
70C2×C3×C4×C5#4112yes—
71C2×Dic15—22no—
72C2×Dic15—22no—
73C2×Dic15—22no—
74C2×Dic15—41no—
75C2×Dic15C22⋊C411yescharacteristic
76C2×Dic15C22⋊C412yes—
77C2×Dic15C22⋊C411yescharacteristic
78C2×Dic15C4⋊C414yes—
79Dic30—24no—
80Dic30—24no—
81C3×C5×C8—42no—
82C3⋊#168—42no—
83C22×Dic6—51no—
84C2×C3×M16C2×D512yes—
85C2×C3×C4⋊C4C2×D511yescharacteristic
86C2×Dic3⋊C4—52no—
87C2×C4×Dic3—51no—
88C2×C4×Dic3—52no—
89C2×#208—52no—
90#887—102no—
91#887—102no—
92#824—104no—
93Dic3⋊C8—102no—
94Dic3⋊C8—102no—
95C22×C4×C5C4×D312yes—
96C22×C4×C5C22×D311yescharacteristic
97C22×Dic5—32no—
98C22×Dic5—31no—
99C22×Dic5—31no—
100C2×Dic10—32no—
101C2×Dic10—32no—
102C2×Dic10—62no—
103C2×Dic10—62no—
104C5×M16—22no—
105C5×M16—22no—
106C2×C5×C8—22no—
107C5×C4⋊C4—22no—
108#683—64no—
109C4×Dic5—32no—
110C4×Dic5—32no—
111C4×Dic5—62no—
112C4×Dic5—62no—
113#681—62no—
114#681—62no—
115C2×#168—62no—
116C2×C4×Q8—151no—
117#423—152no—
118C2×#101—152no—
119#343—151no—
120#343D1511yescharacteristic
121C22×C3×C5—21no—
122C22×C3×C5—21no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C22×C3×C5C2×C4⋊C411yescharacteristic
125C22×C3×C5#11711yescharacteristic
126C3×C4×C5—42no—
127C3×C4×C5#12112yes—
128C3×C4×C5C22⋊Q812yes—
129Dic15—24no—
130Dic15—21no—
131Dic15—22no—
132Dic15#10112yescomplemented
133C22×C3×C4C4×D512yes—
134C22×C3×C4C22×D511yescharacteristic
135C22×Dic3—51no—
136C22×Dic3—52no—
137C22×Dic3—51no—
138C2×Dic6—52no—
139C2×Dic6—52no—
140C2×Dic6—102no—
141C2×Dic6—102no—
142C3×M16—22no—
143C3×M16—22no—
144C2×C3×C8—22no—
145C3×C4⋊C4—22no—
146Dic3⋊C4—104no—
147C4×Dic3—52no—
148C4×Dic3—52no—
149C4×Dic3—102no—
150C4×Dic3—102no—
151#208—102no—
152#208—102no—
153C2×C3⋊C8—102no—
154C23×C5C2×C4×D311yescharacteristic
155C2×C4×C5—22no—
156C2×C4×C5—42no—
157C2×C4×C5#23512yes—
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5D3×D412yes—
160C2×C4×C5D3×Q811yescharacteristic
161C2×Dic5—31no—
162C2×Dic5—31no—
163C2×Dic5—32no—
164C2×Dic5—34no—
165C2×Dic5—62no—
166C2×Dic5—62no—
167C2×Dic5—62no—
168C2×Dic5—121no—
169Dic10—64no—
170Dic10—64no—
171C5×C8—42no—
172#168—122no—
173C22×Q8—151no—
174C2×M16—152no—
175C2×M16C2×D1512yes—
176C4×Q8—302no—
177C4×Q8—302no—
178C2×C4⋊C4—152no—
179C2×C4⋊C4C2×D1511yescharacteristic
180C2×C42—151no—
181C2×C42—152no—
182C4⋊C8—302no—
183C4⋊C8—302no—
184#101—304no—
185C2×C3×C5—21no—
186C2×C3×C5—21no—
187C2×C3×C5#38011yescharacteristic
188C2×C3×C5C2×#10111yescharacteristic
189C2×C3×C5#41311yescharacteristic
190C23×C3C2×C4×D511yescharacteristic
191C2×C3×C4—22no—
192C2×C3×C4—42no—
193C2×C3×C4#70912yes—
194C2×C3×C4D4×D511yescharacteristic
195C2×C3×C4D4×D512yes—
196C2×C3×C4Q8×D511yescharacteristic
197C2×Dic3—51no—
198C2×Dic3—51no—
199C2×Dic3—52no—
200C2×Dic3—54no—
201C2×Dic3—102no—
202C2×Dic3—102no—
203C2×Dic3—102no—
204C2×Dic3—201no—
205Dic6—104no—
206Dic6—104no—
207C3×C8—42no—
208C3⋊C8—202no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5#87211yescharacteristic
212C22×C5D3×C22⋊C411yescharacteristic
213C22×C5D3×C4⋊C411yescharacteristic
214C4×C5—42no—
215C4×C5#88412yes—
216C4×C5#89612yes—
217Dic5—32no—
218Dic5—64no—
219Dic5—62no—
220Dic5—61no—
221C2×Q8—152no—
222C2×Q8—152no—
223C2×Q8—302no—
224C2×Q8—302no—
225C22×C4—151no—
226C22×C4—152no—
227C22×C4—151no—
228C22×C4C4×D1512yes—
229C22×C4C22×D1511yescharacteristic
230M16—22no—
231M16—22no—
232M16—302no—
233M16—302no—
234C2×C8—22no—
235C2×C8—302no—
236C4⋊C4—22no—
237C4⋊C4—304no—
238C42—152no—
239C42—152no—
240C42—302no—
241C42—302no—
242C3×C5#180111yescharacteristic, complemented, Hall
243C22×C3—21no—
244C22×C3—21no—
245C22×C3#401811yescharacteristic
246C22×C3D5×C22⋊C411yescharacteristic
247C22×C3D5×C4⋊C411yescharacteristic
248C3×C4—42no—
249C3×C4#403012yes—
250C3×C4#404212yes—
251Dic3—52no—
252Dic3—102no—
253Dic3—101no—
254Dic3—104no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5#466711yescharacteristic
258C2×C5#474511yescharacteristic
259C2×C5D3×#10111yescharacteristic
260C23C2×C4×D1511yescharacteristic
261Q8—304no—
262Q8—304no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—151no—
266C2×C4—151no—
267C2×C4—152no—
268C2×C4—154no—
269C2×C4—302no—
270C2×C4—302no—
271C2×C4—302no—
272C2×C4—601no—
273C2×C4#681712yes—
274C2×C4D4×D1511yescharacteristic
275C2×C4D4×D1512yes—
276C2×C4Q8×D1511yescharacteristic
277C8—42no—
278C8—602no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#6495611yescharacteristic
282C2×C3#6503411yescharacteristic
283C2×C3D5×#10111yescharacteristic
284C5#6899711yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22#9176111yescharacteristic
288C22C22⋊C4×D1511yescharacteristic
289C22C4⋊C4×D1511yescharacteristic
290C4—42no—
291C4—152no—
292C4—304no—
293C4—302no—
294C4—301no—
295C4#9177312yes—
296C4#9178512yes—
297C3#1059979011yescharacteristic, complemented, Sylow
298C2—21no—
299C2—21no—
300C2#1175076811yescharacteristic
301C2#1175084611yescharacteristic
302C2D15×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#343D15
hypocenterC3×C5#1801
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
132. Dic15#101semidirect
242. C3×C5#1801semidirect
284. C5#68997semidirect
297. C3#10599790semidirect

Maximal subgroups

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

subgroupindex
C2×#917762
C2×#911082
#117512192
C3×C5×#3432
#117463512
#105997903
#689975