Finite Group Databasebeta

← #14301459

Subgroups — #14301459

Order 1920.

720 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 160 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
1#11756557C211yesmaximal, characteristic
2C2×C3×#4082C211yesmaximal, characteristic
3C2×C5×#833C211yesmaximal, characteristic
4#11748400C212yesmaximal, complemented
5#11745978C212yesmaximal, complemented
6#10600862—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C3×Dic10C2211yescharacteristic
9C2×#6719—22no—
10D4×Dic15—24no—
11#91815C2212yes—
12C2×C5×#208C2212yes—
13C2×C3×C22⋊Dic5—22no—
14C3×#4082—22no—
15C3×#4082C414yescomplemented
16C2×C3×C4×Dic5C2211yescharacteristic
17C5×#833—22no—
18#90971—24no—
19#71723—51nomaximal, Hall
20#66132—31no—
21C2×#4082D311yescharacteristic
22C2×C5×#100—31no—
23#65409—32no—
24#64775—32no—
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—24no—
32C22×C3×Dic5—21no—
33C22×C3×Dic5—21no—
34C2×C3×Dic10—22no—
35C2×C3×Dic10—22no—
36C2×C3×Dic10—21no—
37C2×C3×Dic10C2×C412yescomplemented
38#6719—24no—
39#6719—22no—
40C4⋊Dic15D414yes—
41C4×Dic15—22no—
42C5×#208—22no—
43C5×#208—22no—
44C2×C5×C3⋊C8—22no—
45C3×C22⋊Dic5—28no—
46C3×C4×Dic5—21no—
47C3×C4×Dic5C2×C412yescomplemented
48C2×C3×#124—51no—
49#5798—51no—
50#5225—52no—
51C2×#833D511yescharacteristic
52#4523—52no—
53C22×C5×D4C2×D311yescharacteristic
54C22×Dic10C2×D311yescharacteristic
55C2×C5×M16—32no—
56C2×C22⋊Dic5—22no—
57C2×C22⋊Dic5—62no—
58#4082—22no—
59#4082Dic314yescomplemented
60D4×Dic5—64no—
61#4072—32no—
62C2×C4×Dic5C2×D311yescharacteristic
63C5×#100—62no—
64#3948—64no—
65#1885—151noSylow
66C23×C3×C5—22no—
67C23×C3×C5—22no—
68C23×C3×C5—44no—
69C23×C3×C5C22⋊C414yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×D4—24no—
72C3×C5×D4—24no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×Dic15—24no—
78C2×Dic15—84no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C2×C3×Dic5—42no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—41no—
84C3×Dic10—24no—
85C3×Dic10—42no—
86C5×C3⋊C8—42no—
87C22×C3×Q8—51no—
88C22×C3×D4C2×D511yescharacteristic
89C3×#124—54no—
90C3×#124—102no—
91C2×C3×C22⋊C4—102no—
92C2×C3×C42—51no—
93C2×#217—102no—
94D4×Dic3—104no—
95#926—52no—
96C2×#208C2×D512yes—
97#835—104no—
98#833—22no—
99C24×C5#6712yes—
100C2×C5×D4—22no—
101C2×C5×D4—22no—
102C2×C5×D4C2×Dic312yes—
103C2×C5×D4#6712yes—
104C22×C4×C5C22×D311yescharacteristic
105C22×Dic5—21no—
106C22×Dic5—21no—
107C22×Dic5—64no—
108C2×Dic10—22no—
109C2×Dic10—22no—
110C2×Dic10—21no—
111C2×Dic10C2×Dic312yescomplemented
112C5×M16—62no—
113C5×M16—62no—
114C2×C5×C8—62no—
115C22⋊Dic5—28no—
116C22⋊Dic5—64no—
117C22⋊Dic5—62no—
118C4⋊Dic5—34no—
119C4×Dic5—21no—
120C4×Dic5—62no—
121C4×Dic5C2×Dic312yescomplemented
122C2×#124—51no—
123#518—151no—
124#419—152no—
125C2×#100—31no—
126#339—152no—
127C22×C3×C5—22no—
128C22×C3×C5—24no—
129C22×C3×C5—44no—
130C22×C3×C5—44no—
131C22×C3×C5—82no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5#12311yescharacteristic
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137Dic15—44no—
138C3×Dic5—42no—
139C3×Dic5—42no—
140C24×C3D2012yes—
141C2×C3×Q8—52no—
142C2×C3×Q8—101no—
143C2×C3×Q8—102no—
144C2×C3×Q8—102no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4C4×D512yes—
148C2×C3×D4C22⋊D512yes—
149C22×C3×C4—101no—
150C22×C3×C4—101no—
151C22×C3×C4C22×D511yescharacteristic
152C22×Dic3—104no—
153C3×C22⋊C4—108no—
154C3×C42—52no—
155C3×C42—101no—
156#217—104no—
157#217—102no—
158C4⋊Dic3—54no—
159C4×Dic3—102no—
160#208—22no—
161#208—22no—
162C2×C3⋊C8—22no—
163C23×C5—22no—
164C23×C5—22no—
165C23×C5—44no—
166C23×C5#21714yes—
167C23×C5C2×#6711yescharacteristic
168C5×D4—24no—
169C5×D4—24no—
170C2×C4×C5D3×D412yes—
171C2×C4×C5#23712yes—
172C2×C4×C5C22×Dic311yescharacteristic
173C2×C4×C5C2×#6711yescharacteristic
174C2×Dic5—22no—
175C2×Dic5—22no—
176C2×Dic5—42no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—64no—
180C2×Dic5—244no—
181Dic10—24no—
182Dic10—42no—
183C5×C8—122no—
184C22×Q8—51no—
185C22×D4D3×D511yescharacteristic
186C2×M16—32no—
187#124—54no—
188#124—102no—
189C4×D4—304no—
190#117—152no—
191C2×C22⋊C4—102no—
192C2×C22⋊C4—302no—
193C2×C42—51no—
194#103—304no—
195#100—62no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—44no—
199C2×C3×C5#38611yescharacteristic
200C2×C3×C5#45512yes—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—44no—
204C23×C3#68514yes—
205C23×C3C2×D2011yescharacteristic
206C3×Q8—104no—
207C3×Q8—202no—
208C3×D4—24no—
209C3×D4—24no—
210C2×C3×C4—102no—
211C2×C3×C4—102no—
212C2×C3×C4—202no—
213C2×C3×C4—201no—
214C2×C3×C4—201no—
215C2×C3×C4C2×C4×D511yescharacteristic
216C2×C3×C4D4×D512yes—
217C2×C3×C4#71112yes—
218C2×C3×C4C2×C22⋊D511yescharacteristic
219C2×Dic3—104no—
220C2×Dic3—404no—
221C3⋊C8—42no—
222C22×C5—22no—
223C22×C5—24no—
224C22×C5—44no—
225C22×C5—44no—
226C22×C5—82no—
227C22×C5#93511yescharacteristic
228C22×C5#93711yescharacteristic
229C22×C5C2×#21711yescharacteristic
230C4×C5D4×Dic312yes—
231C4×C5#93912yes—
232Dic5—42no—
233Dic5—42no—
234Dic5—124no—
235C24#120212yes—
236C2×Q8—52no—
237C2×Q8—101no—
238C2×Q8—102no—
239C2×Q8—102no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4D5×Dic312yes—
243C2×D4#120112yes—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4—304no—
247C22×C4C2×D3×D511yescharacteristic
248M16—62no—
249M16—62no—
250C2×C8—62no—
251C4⋊C4—154no—
252C22⋊C4—108no—
253C22⋊C4—304no—
254C22⋊C4—302no—
255C42—52no—
256C42—101no—
257C42—302no—
258C3×C5#188511yescharacteristic, complemented, Hall
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—82no—
264C22×C3#402811yescharacteristic
265C22×C3#403211yescharacteristic
266C22×C3C2×#68511yescharacteristic
267C3×C4—202no—
268C3×C4—202no—
269C3×C4#402712yes—
270C3×C4#408512yes—
271Dic3—204no—
272C2×C5—21no—
273C2×C5—21no—
274C2×C5—44no—
275C2×C5#506112yes—
276C2×C5#522011yescharacteristic
277C23—22no—
278C23—22no—
279C23—44no—
280C23#666514yes—
281C23C2×#120211yescharacteristic
282Q8—104no—
283Q8—202no—
284D4—24no—
285D4—24no—
286C2×C4—102no—
287C2×C4—102no—
288C2×C4—202no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4—304no—
292C2×C4—1204no—
293C2×C4C2×D5×Dic311yescharacteristic
294C2×C4#678012yes—
295C2×C4C2×#120111yescharacteristic
296C2×C4#679012yes—
297C8—122no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—44no—
301C2×C3#6503512yes—
302C2×C3#6524711yescharacteristic
303C5#7172311yescharacteristic, complemented, Sylow
304C22—22no—
305C22—24no—
306C22—44no—
307C22—44no—
308C22—82no—
309C22C2×#666511yescharacteristic
310C22#9153711yescharacteristic
311C22#9157211yescharacteristic
312C4—202no—
313C4—202no—
314C4—604no—
315C4#9155912yes—
316C4#9157112yes—
317C3#1060086211yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2—44no—
321C2#1174914912yes—
322C2#1174950011yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748400C2semidirect
5. #11745978C2semidirect
15. C3×#4082C4semidirect
37. C2×C3×Dic10C2×C4semidirect
47. C3×C4×Dic5C2×C4semidirect
59. #4082Dic3semidirect
111. C2×Dic10C2×Dic3semidirect
121. C4×Dic5C2×Dic3semidirect
258. C3×C5#1885semidirect
303. C5#71723semidirect
317. C3#10600862semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×C3×#40822
C2×C5×#8332
#117484002
#117459782
#106008623
#717235