Finite Group Databasebeta

← #14308940

Subgroups — #14308940

Order 1920.

492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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×C5×#544C211yesmaximal, characteristic
2#11751105C212yesmaximal
3#11751074C211yesmaximal, characteristic
4#11746353C212yesmaximal
5#11746351C211yesmaximal, characteristic
6#10602698—31nomaximal, Hall
7C22×Dic30C2211yescharacteristic
8C3×C5×C4⋊Q8—22no—
9C3×C5×#125—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#117C2212yes—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×#6710C2212yes—
15#91115—22no—
16#91094—22no—
17#91094—22no—
18#71905—51nomaximal, Hall
19C5×#544D311yescharacteristic
20#65293—32no—
21#65263—31no—
22#64752—32no—
23#64750—31no—
24C2×C3×C5×Q8—22no—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15—21no—
28C22×Dic15—21no—
29C2×Dic30—22no—
30C2×Dic30—22no—
31C2×Dic30—21no—
32C2×Dic30Q812yescomplemented
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—24no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4D412yes—
37C3×C5×C4⋊C4D412yes—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5—22no—
40C4×Dic15—22no—
41#6710—22no—
42#6710—22no—
43C2×C3⋊#168—22no—
44C3×#544D511yescharacteristic
45#5004—52no—
46#4973—51no—
47#4532—52no—
48#4530—51no—
49C22×Dic10—31no—
50C5×C4⋊Q8—22no—
51C5×#125—22no—
52C5×C22⋊Q8—22no—
53C5×#117C2×D312yes—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×C4×Dic5—31no—
56C2×#681—32no—
57#3963—62no—
58#3942—62no—
59#3942—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C3×C5×Q8—82no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5C2×D412yes—
68C2×C3×C4×C5C2×Q811yescharacteristic
69C2×C3×C4×C5#4112yes—
70C2×C3×C4×C5#4111yescharacteristic
71C2×Dic15—22no—
72C2×Dic15—22no—
73C2×Dic15—41no—
74C2×Dic15—41no—
75C2×Dic15—41no—
76C2×Dic15—41no—
77Dic30—24no—
78Dic30—42no—
79C3⋊#168—42no—
80C22×Dic6—51no—
81C3×C4⋊Q8—22no—
82C3×#125—22no—
83C3×C22⋊Q8—22no—
84C3×#117C2×D512yes—
85C2×C3×C4⋊C4C2×D511yescharacteristic
86C2×C4×Dic3—51no—
87C2×#208—52no—
88C3⋊#95—102no—
89#810—102no—
90#810—102no—
91C2×C5×Q8—22no—
92C22×C4×C5#6712yes—
93C22×C4×C5C22×D311yescharacteristic
94C22×Dic5—61no—
95C22×Dic5—61no—
96C2×Dic10—32no—
97C2×Dic10—62no—
98C2×Dic10—62no—
99C2×Dic10—61no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—24no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4#6712yes—
104C5×C4⋊C4#6712yes—
105C5×C22⋊C4—22no—
106C42×C5—22no—
107C4×Dic5—62no—
108#681—62no—
109#681—62no—
110C2×#168—62no—
111#544D1511yescharacteristic
112#419—152no—
113#391—151no—
114#343—151no—
115#339—152no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5#12011yescharacteristic
119C22×C3×C5C22⋊Q811yescharacteristic
120C22×C3×C5#12411yescharacteristic
121C3×C4×C5—42no—
122C3×C4×C5—42no—
123C3×C4×C5—42no—
124C3×C4×C5C22⋊Q812yes—
125C3×C4×C5#12412yes—
126Dic15—42no—
127Dic15—42no—
128C2×C3×Q8—22no—
129C22×C3×C4C22⋊D512yes—
130C22×C3×C4C22×D511yescharacteristic
131C22×Dic3—101no—
132C22×Dic3—101no—
133C2×Dic6—52no—
134C2×Dic6—102no—
135C2×Dic6—102no—
136C2×Dic6—101no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4C22⋊D512yes—
141C3×C4⋊C4C22⋊D512yes—
142C3×C22⋊C4—22no—
143C3×C42—22no—
144C4×Dic3—102no—
145#208—102no—
146#208—102no—
147C2×C3⋊C8—102no—
148C23×C5C2×#6711yescharacteristic
149C5×Q8—82no—
150C2×C4×C5—22no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—42no—
154C2×C4×C5D3×Q811yescharacteristic
155C2×C4×C5#23912yes—
156C2×C4×C5#23911yescharacteristic
157C2×C4×C5C2×#6712yes—
158C2×Dic5—62no—
159C2×Dic5—62no—
160C2×Dic5—121no—
161C2×Dic5—121no—
162C2×Dic5—121no—
163C2×Dic5—121no—
164Dic10—64no—
165Dic10—122no—
166#168—122no—
167C22×Q8—151no—
168C2×M16—152no—
169C4⋊Q8—22no—
170#125—22no—
171C22⋊Q8—22no—
172#117C2×D1512yes—
173C2×C4⋊C4C2×D1511yescharacteristic
174C2×C42—151no—
175#103—302no—
176#103—302no—
177#95—302no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×C22⋊D511yescharacteristic
184C3×Q8—82no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—42no—
189C2×C3×C4Q8×D511yescharacteristic
190C2×C3×C4#71312yes—
191C2×C3×C4#71311yescharacteristic
192C2×C3×C4C2×C22⋊D512yes—
193C2×Dic3—102no—
194C2×Dic3—102no—
195C2×Dic3—201no—
196C2×Dic3—201no—
197C2×Dic3—201no—
198C2×Dic3—201no—
199Dic6—104no—
200Dic6—202no—
201C3⋊C8—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#94611yescharacteristic
205C22×C5#94711yescharacteristic
206C22×C5#95311yescharacteristic
207C4×C5—42no—
208C4×C5—42no—
209C4×C5—42no—
210C4×C5#94612yes—
211C4×C5#94712yes—
212Dic5—122no—
213Dic5—122no—
214C2×Q8—22no—
215C2×Q8—152no—
216C2×Q8—301no—
217C2×Q8—302no—
218C2×Q8—302no—
219C22×C4—301no—
220C22×C4—301no—
221C22×C4#122012yes—
222C22×C4C22×D1511yescharacteristic
223M16—302no—
224M16—302no—
225C2×C8—302no—
226C4⋊C4—22no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4#122012yes—
230C4⋊C4#122012yes—
231C22⋊C4—22no—
232C42—22no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#409211yescharacteristic
238C22×C3#409311yescharacteristic
239C22×C3#409911yescharacteristic
240C3×C4—42no—
241C3×C4—42no—
242C3×C4—42no—
243C3×C4#409212yes—
244C3×C4#409312yes—
245Dic3—202no—
246Dic3—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#523111yescharacteristic
250C2×C5#524211yescharacteristic
251C2×C5#524611yescharacteristic
252C23C2×#122011yescharacteristic
253Q8—82no—
254Q8—304no—
255Q8—602no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—302no—
261C2×C4—302no—
262C2×C4—601no—
263C2×C4—601no—
264C2×C4—601no—
265C2×C4—601no—
266C2×C4Q8×D1511yescharacteristic
267C2×C4#682112yes—
268C2×C4#682111yescharacteristic
269C2×C4C2×#122012yes—
270C8—602no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6552011yescharacteristic
274C2×C3#6553111yescharacteristic
275C2×C3#6553511yescharacteristic
276C5#7190511yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9183511yescharacteristic
280C22#9183611yescharacteristic
281C22#9184211yescharacteristic
282C4—42no—
283C4—42no—
284C4—42no—
285C4—602no—
286C4—602no—
287C4#9183512yes—
288C4#9183612yes—
289C3#1060269811yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1175133211yescharacteristic
293C2#1175134311yescharacteristic
294C2#1175134711yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#544C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#544D15
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
32. C2×Dic30Q8semidirect
234. C3×C5#2028semidirect
276. C5#71905semidirect
289. C3#10602698semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5442
#117511052
#117510742
#117463532
#117463512
#106026983
#719055