Finite Group Databasebeta

← #14309009

Subgroups — #14309009

Order 1920.

580 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 118 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×#65817C211yesmaximal, characteristic
2#11751044C211yesmaximal, characteristic
3#11749473C212yesmaximal
4C5×#4526C211yesmaximal, characteristic
5#11746019C212yesmaximal
6#10599749—31nomaximal, Hall
7C23×Dic15C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2211yescharacteristic
10C2×C5×#217C2212yes—
11C2×C3×C22⋊Dic5C2212yes—
12C3×#4070—22no—
13C3×#4024—24no—
14#91115—22no—
15#90994—24no—
16#71894—51nomaximal, Hall
17#65817D311yescharacteristic
18#65232—31no—
19#65232—32no—
20C5×#342—31no—
21#64747—32no—
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5D412yes—
24C22×Dic15—22no—
25C22×Dic15—21no—
26C22×Dic15—22no—
27C22×Dic15—21no—
28C22×Dic15—21no—
29C22×Dic15Q812yescomplemented
30C22×C5×Dic3—22no—
31C22×C3×Dic5D414yes—
32C2×C3×Dic10—22no—
33C3×C5×C22⋊C4—22no—
34#6719—22no—
35C5×#217—22no—
36C5×#217—22no—
37C3×C22⋊Dic5—22no—
38C3×C22⋊Dic5—22no—
39C3×C4⋊Dic5—22no—
40C3×#683—24no—
41C3×#543—51no—
42#4943—51no—
43#4943—52no—
44#4526—52no—
45#4526D511yescharacteristic
46C23×Dic5—31no—
47C2×C5×C22⋊C4—32no—
48C2×C5×C22⋊C4C2×D311yescharacteristic
49C2×C22⋊Dic5—31no—
50C2×C22⋊Dic5C2×D312yes—
51#4070—22no—
52#4024—24no—
53#3963—62no—
54#3963—64no—
55#2030—151noSylow
56C23×C3×C5—42no—
57C23×C3×C5C2×D411yescharacteristic
58C23×C3×C5C2×D412yes—
59C23×C3×C5C2×Q811yescharacteristic
60C23×C3×C5#4112yes—
61C23×C3×C5#4111yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×Dic15—24no—
65C2×Dic15—22no—
66C2×Dic15—41no—
67C2×Dic15—41no—
68C2×Dic15—42no—
69C2×Dic15—42no—
70C2×Dic15—41no—
71C2×C5×Dic3—44no—
72C2×C5×Dic3—42no—
73C2×C3×Dic5—24no—
74C2×C3×Dic5—44no—
75C3×Dic10—82no—
76C23×Dic3—51no—
77C3×C22⋊Q8—104no—
78C3×C22⋊Q8—102no—
79C2×C3×C22⋊C4—52no—
80C2×C3×C22⋊C4C2×D511yescharacteristic
81C2×#217—51no—
82C2×#217C2×D512yes—
83C3⋊#95—104no—
84C3⋊#95—102no—
85C24×C5C22×D311yescharacteristic
86C22×C4×C5—62no—
87C22×C4×C5#6712yes—
88C22×Dic5—32no—
89C22×Dic5—61no—
90C22×Dic5—62no—
91C22×Dic5—61no—
92C22×Dic5—62no—
93C22×Dic5—61no—
94C22×Dic5#6714yes—
95C2×Dic10—22no—
96C5×C22⋊C4—22no—
97C5×C22⋊C4—62no—
98C5×C22⋊C4—62no—
99C22⋊Dic5—22no—
100C22⋊Dic5—22no—
101C22⋊Dic5—62no—
102C4⋊Dic5—22no—
103#683—24no—
104#543—51no—
105#381—152no—
106#381—151no—
107#342—31no—
108#342—152no—
109C22×C3×C5—24no—
110C22×C3×C5—22no—
111C22×C3×C5—41no—
112C22×C3×C5—42no—
113C22×C3×C5—41no—
114C22×C3×C5#12011yescharacteristic
115C22×C3×C5C22⋊Q812yes—
116C22×C3×C5C22⋊Q811yescharacteristic
117C22×C3×C5#12411yescharacteristic
118C22×C3×C5#12412yes—
119C3×C4×C5—42no—
120Dic15—42no—
121Dic15—81no—
122C3×Dic5—44no—
123C5×Dic3—82no—
124C24×C3C22×D511yescharacteristic
125C2×C3×Q8—102no—
126C22×C3×C4—54no—
127C22×C3×C4D2012yes—
128C22×Dic3—22no—
129C22×Dic3—52no—
130C22×Dic3—101no—
131C22×Dic3—102no—
132C22×Dic3—102no—
133C22×Dic3—101no—
134C22×Dic3—101no—
135C3×C4⋊C4—104no—
136C3×C4⋊C4—102no—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—102no—
139C3×C22⋊C4—102no—
140#217—22no—
141#217—22no—
142#217—102no—
143C23×C5—42no—
144C23×C5D3×Q811yescharacteristic
145C23×C5#23911yescharacteristic
146C23×C5#23912yes—
147C23×C5C2×#6711yescharacteristic
148C23×C5C2×#6712yes—
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5—124no—
152C2×C4×C5—122no—
153C2×Dic5—24no—
154C2×Dic5—44no—
155C2×Dic5—64no—
156C2×Dic5—62no—
157C2×Dic5—122no—
158C2×Dic5—121no—
159C2×Dic5—121no—
160C2×Dic5—122no—
161C2×Dic5—121no—
162Dic10—82no—
163C23×C4—151no—
164C22⋊Q8—104no—
165C22⋊Q8—102no—
166C2×C22⋊C4—32no—
167C2×C22⋊C4—52no—
168C2×C22⋊C4—151no—
169C2×C22⋊C4D3×D511yescharacteristic
170#95—304no—
171#95—302no—
172C2×C3×C5—22no—
173C2×C3×C5—21no—
174C2×C3×C5—22no—
175C2×C3×C5—21no—
176C2×C3×C5#39311yescharacteristic
177C2×C3×C5#45812yes—
178C23×C3—42no—
179C23×C3C2×D2011yescharacteristic
180C23×C3#70912yes—
181C23×C3D4×D512yes—
182C23×C3#71111yescharacteristic
183C23×C3Q8×D511yescharacteristic
184C3×Q8—402no—
185C2×C3×C4—22no—
186C2×C3×C4—42no—
187C2×C3×C4—104no—
188C2×C3×C4—204no—
189C2×Dic3—44no—
190C2×Dic3—42no—
191C2×Dic3—104no—
192C2×Dic3—102no—
193C2×Dic3—201no—
194C2×Dic3—201no—
195C2×Dic3—202no—
196C2×Dic3—202no—
197C2×Dic3—201no—
198C22×C5—24no—
199C22×C5—22no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—42no—
203C22×C5#94612yes—
204C22×C5#94611yescharacteristic
205C22×C5#94712yes—
206C22×C5#94711yescharacteristic
207C22×C5#95311yescharacteristic
208C4×C5—42no—
209C4×C5—242no—
210Dic5—44no—
211Dic5—122no—
212Dic5—241no—
213C24C2×D3×D511yescharacteristic
214C2×Q8—102no—
215C22×C4—54no—
216C22×C4—62no—
217C22×C4—152no—
218C22×C4—301no—
219C22×C4—302no—
220C22×C4—301no—
221C22×C4—302no—
222C22×C4—301no—
223C22×C4#120212yes—
224C4⋊C4—104no—
225C4⋊C4—102no—
226C22⋊C4—22no—
227C22⋊C4—62no—
228C22⋊C4—62no—
229C22⋊C4—102no—
230C22⋊C4—102no—
231C22⋊C4—302no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—24no—
234C22×C3—22no—
235C22×C3—42no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3#402111yescharacteristic
239C22×C3#402811yescharacteristic
240C22×C3#403112yes—
241C22×C3#404212yes—
242C22×C3#404311yescharacteristic
243C3×C4—42no—
244C3×C4—204no—
245Dic3—82no—
246Dic3—202no—
247Dic3—401no—
248C2×C5—21no—
249C2×C5—22no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5#523111yescharacteristic
253C2×C5#524312yes—
254C23—42no—
255C23#676811yescharacteristic
256C23#676912yes—
257C23D15⋊Q811yescharacteristic
258C23C2×#120211yescharacteristic
259C23D5×#6712yes—
260Q8—402no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—104no—
264C2×C4—124no—
265C2×C4—122no—
266C2×C4—204no—
267C2×C4—304no—
268C2×C4—302no—
269C2×C4—601no—
270C2×C4—602no—
271C2×C4—601no—
272C2×C4—602no—
273C2×C4—601no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3#6496211yescharacteristic
279C2×C3#6503112yes—
280C5#7189411yescharacteristic, complemented, Sylow
281C22—22no—
282C22—24no—
283C22—41no—
284C22—42no—
285C22—41no—
286C22#9132612yes—
287C22#9137411yescharacteristic
288C22#9139011yescharacteristic
289C22#9141112yes—
290C22#9156411yescharacteristic
291C4—42no—
292C4—204no—
293C4—242no—
294C4—602no—
295C4—1201no—
296C3#1059974911yescharacteristic, complemented, Sylow
297C2—22no—
298C2—21no—
299C2—22no—
300C2—21no—
301C2#1174875311yescharacteristic
302C2#1174918212yes—
subgroupG/H
centerC22#91564
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2030
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
29. C22×Dic15Q8semidirect
232. C3×C5#2030semidirect
280. C5#71894semidirect
296. C3#10599749semidirect

Maximal subgroups

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

subgroupindex
C3×#658172
#117510442
#117494732
C5×#45262
#117460192
#105997493
#718945