Finite Group Databasebeta

← #14309004

Subgroups — #14309004

Order 1920.

580 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 117 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#11756242C211yesmaximal, characteristic
2#11751044C211yesmaximal, characteristic
3#11751044C212yesmaximal
4C3×C5×#342C211yesmaximal, characteristic
5#11746348C212yesmaximal
6#10599749—31nomaximal, Hall
7C23×Dic15C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2212yes—
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×#6719C2211yescharacteristic
11C2×#6719C2212yes—
12#91813—22no—
13#91767—24no—
14#91115—22no—
15#91115—24no—
16#68956—51nomaximal, Hall
17#65817—31no—
18#65232—32no—
19#65232—31no—
20C5×#342D311yescharacteristic
21#64747—32no—
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5—22no—
24C22×C3×C4×C5D412yes—
25C22×Dic15—21no—
26C22×Dic15—22no—
27C22×Dic15—22no—
28C22×Dic15—21no—
29C22×Dic15—21no—
30C22×Dic15D414yes—
31C22×Dic15Q812yescomplemented
32C2×Dic30—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36#6719—22no—
37#6719—22no—
38#6719—22no—
39C4⋊Dic15—22no—
40#6712—24no—
41#5483—51no—
42#4943—52no—
43#4943—51no—
44C3×#342D511yescharacteristic
45#4527—52no—
46C23×Dic5—31no—
47C2×C5×C22⋊C4C2×D312yes—
48C2×C5×C22⋊C4C2×D311yescharacteristic
49C2×C22⋊Dic5—32no—
50C2×C22⋊Dic5—31no—
51#4070—62no—
52#4024—64no—
53#3963—64no—
54#3963—62no—
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×C3×C4×C5—44no—
65C2×C3×C4×C5—42no—
66C2×Dic15—24no—
67C2×Dic15—24no—
68C2×Dic15—22no—
69C2×Dic15—41no—
70C2×Dic15—41no—
71C2×Dic15—42no—
72C2×Dic15—44no—
73C2×Dic15—42no—
74C2×Dic15—41no—
75Dic30—82no—
76C23×Dic3—51no—
77C2×C3×C22⋊C4C2×D512yes—
78C2×C3×C22⋊C4C2×D511yescharacteristic
79C2×#217—52no—
80C2×#217—51no—
81#924—102no—
82#878—104no—
83C3⋊#95—104no—
84C3⋊#95—102no—
85C24×C5C22×D311yescharacteristic
86C22×C4×C5—22no—
87C22×C4×C5D1212yes—
88C22×Dic5—32no—
89C22×Dic5—34no—
90C22×Dic5—61no—
91C22×Dic5—62no—
92C22×Dic5—62no—
93C22×Dic5—61no—
94C22×Dic5—61no—
95C2×Dic10—62no—
96C5×C22⋊C4—22no—
97C5×C22⋊C4—22no—
98C5×C22⋊C4—22no—
99C22⋊Dic5—62no—
100C22⋊Dic5—62no—
101C22⋊Dic5—62no—
102C4⋊Dic5—62no—
103#683—64no—
104#543—151no—
105#381—152no—
106#381—151no—
107#342—152no—
108#342D1511yescharacteristic
109C22×C3×C5—22no—
110C22×C3×C5—24no—
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—
120C3×C4×C5—82no—
121Dic15—42no—
122Dic15—44no—
123Dic15—81no—
124C24×C3C22×D511yescharacteristic
125C22×C3×C4—22no—
126C22×C3×C4D2012yes—
127C22×Dic3—52no—
128C22×Dic3—54no—
129C22×Dic3—101no—
130C22×Dic3—102no—
131C22×Dic3—102no—
132C22×Dic3—101no—
133C22×Dic3—101no—
134C2×Dic6—102no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138#217—102no—
139#217—102no—
140#217—102no—
141C4⋊Dic3—102no—
142Dic3⋊C4—104no—
143C23×C5—42no—
144C23×C5C2×D1211yescharacteristic
145C23×C5#23512yes—
146C23×C5D3×D412yes—
147C23×C5#23711yescharacteristic
148C23×C5D3×Q811yescharacteristic
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5—44no—
152C2×C4×C5—42no—
153C2×Dic5—64no—
154C2×Dic5—64no—
155C2×Dic5—62no—
156C2×Dic5—121no—
157C2×Dic5—121no—
158C2×Dic5—122no—
159C2×Dic5—124no—
160C2×Dic5—122no—
161C2×Dic5—121no—
162Dic10—242no—
163C23×C4—151no—
164C22⋊Q8—304no—
165C22⋊Q8—302no—
166C2×C22⋊C4—152no—
167C2×C22⋊C4—151no—
168C2×C22⋊C4C2×D1512yes—
169C2×C22⋊C4C2×D1511yescharacteristic
170#95—304no—
171#95—302no—
172C2×C3×C5—21no—
173C2×C3×C5—22no—
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
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—44no—
187C2×C3×C4—42no—
188C2×Dic3—104no—
189C2×Dic3—104no—
190C2×Dic3—102no—
191C2×Dic3—201no—
192C2×Dic3—201no—
193C2×Dic3—202no—
194C2×Dic3—204no—
195C2×Dic3—202no—
196C2×Dic3—201no—
197Dic6—402no—
198C22×C5—22no—
199C22×C5—24no—
200C22×C5—42no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5#87511yescharacteristic
204C22×C5#88211yescharacteristic
205C22×C5#88512yes—
206C22×C5#89612yes—
207C22×C5#89711yescharacteristic
208C4×C5—42no—
209C4×C5—82no—
210Dic5—122no—
211Dic5—124no—
212Dic5—241no—
213C24C22×D1511yescharacteristic
214C2×Q8—302no—
215C22×C4—22no—
216C22×C4—152no—
217C22×C4—154no—
218C22×C4—301no—
219C22×C4—302no—
220C22×C4—302no—
221C22×C4—301no—
222C22×C4—301no—
223C22×C4D6012yes—
224C4⋊C4—304no—
225C4⋊C4—302no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—22no—
229C22⋊C4—302no—
230C22⋊C4—302no—
231C22⋊C4—302no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—22no—
234C22×C3—24no—
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—82no—
245Dic3—204no—
246Dic3—202no—
247Dic3—401no—
248C2×C5—21no—
249C2×C5—22no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5#467311yescharacteristic
253C2×C5#474212yes—
254C23—42no—
255C23C2×D6011yescharacteristic
256C23#681712yes—
257C23D4×D1512yes—
258C23#681911yescharacteristic
259C23Q8×D1511yescharacteristic
260Q8—1202no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—304no—
266C2×C4—304no—
267C2×C4—302no—
268C2×C4—601no—
269C2×C4—601no—
270C2×C4—602no—
271C2×C4—604no—
272C2×C4—602no—
273C2×C4—601no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3#6496211yescharacteristic
279C2×C3#6503112yes—
280C5#6895611yescharacteristic, complemented, Sylow
281C22—22no—
282C22—24no—
283C22—42no—
284C22—41no—
285C22—41no—
286C22#9176411yescharacteristic
287C22#9177111yescharacteristic
288C22#9177412yes—
289C22#9178512yes—
290C22#9178611yescharacteristic
291C4—42no—
292C4—82no—
293C4—602no—
294C4—604no—
295C4—1201no—
296C3#1059974911yescharacteristic, complemented, Sylow
297C2—22no—
298C2—21no—
299C2—22no—
300C2—21no—
301C2#1175077411yescharacteristic
302C2#1175084312yes—
subgroupG/H
centerC22#91771
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC22×C3×C5#120
hypercenter#342D15
hypocenterC3×C5#2030
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
31. C22×Dic15Q8semidirect
232. C3×C5#2030semidirect
280. C5#68956semidirect
296. C3#10599749semidirect

Maximal subgroups

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

subgroupindex
#117562422
#117510442
C3×C5×#3422
#117463482
#105997493
#689565