Finite Group Databasebeta

← #14308959

Subgroups — #14308959

Order 1920.

492 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C5×#5500C211yesmaximal, characteristic
2C3×#65263C211yesmaximal, characteristic
3#11748399C212yesmaximal
4#11746351C211yesmaximal, characteristic
5#11745977C212yesmaximal
6#10602698—31nomaximal, Hall
7C22×C3×Dic10C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6710C2212yes—
10C5×#926C2212yes—
11C5×#924—22no—
12C5×#890—22no—
13C5×#888—22no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×#3963—22no—
16#90970—22no—
17#90970—22no—
18#69673—51nomaximal, Hall
19C5×#544—31no—
20#65293—32no—
21#65263D311yescharacteristic
22#64752—32no—
23#64750—31no—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C2×C5×Dic6—22no—
27C22×C3×Dic5—21no—
28C22×C3×Dic5—21no—
29C2×C3×Dic10—22no—
30C2×C3×Dic10—22no—
31C2×C3×Dic10—21no—
32C2×C3×Dic10Q812yescomplemented
33C3×C5×C4⋊C4—22no—
34#6710—22no—
35#6710—22no—
36C2×C3⋊#168—22no—
37C5×#217—22no—
38C5×C4⋊Dic3—22no—
39C5×C4⋊Dic3D412yes—
40C5×C4⋊Dic3D412yes—
41C5×Dic3⋊C4—24no—
42C4×C5×Dic3—22no—
43C3×C4×Dic5—22no—
44#5500D511yescharacteristic
45C3×#391—51no—
46#5225—52no—
47#4530—51no—
48#4523—52no—
49C22×Dic10C2×D311yescharacteristic
50C5×C4⋊Q8—62no—
51C5×#125—62no—
52C5×C22⋊Q8—62no—
53C5×#117—32no—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×C4×Dic5C2×D311yescharacteristic
56C2×#681—32no—
57#3963—22no—
58#3942—62no—
59#3942—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5C2×Q811yescharacteristic
66C2×C3×C4×C5#4112yes—
67C2×C3×C4×C5#4111yescharacteristic
68C2×C5×Dic3—22no—
69C2×C5×Dic3—22no—
70C5×Dic6—82no—
71C2×C3×Dic5—22no—
72C2×C3×Dic5—22no—
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5—41no—
76C2×C3×Dic5—41no—
77C3×Dic10—24no—
78C3×Dic10—42no—
79C3⋊#168—42no—
80C22×C3×Q8—51no—
81C2×C3×C4⋊C4C2×D511yescharacteristic
82C2×C3×C42—51no—
83#926C2×D512yes—
84#924—22no—
85C2×#208—52no—
86#890—22no—
87#888—22no—
88C3×#95—102no—
89#835—102no—
90#835—102no—
91C2×C5×Q8—62no—
92C22×C4×C5#6712yes—
93C22×C4×C5C22×D311yescharacteristic
94C22×Dic5—21no—
95C22×Dic5—21no—
96C2×Dic10—22no—
97C2×Dic10—22no—
98C2×Dic10—21no—
99C2×Dic10Dic612yescomplemented
100C5×C4⋊C4—22no—
101C5×C4⋊C4—32no—
102C5×C4⋊C4—32no—
103C5×C4⋊C4—62no—
104C5×C4⋊C4—64no—
105C5×C22⋊C4—62no—
106C42×C5—62no—
107C4×Dic5—22no—
108#681—62no—
109#681—62no—
110C2×#168—62no—
111#544—31no—
112#419—152no—
113#391—51no—
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×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124C3×Dic5—42no—
125C3×Dic5—42no—
126C5×Dic3—42no—
127C5×Dic3—42no—
128C2×C3×Q8—52no—
129C2×C3×Q8—101no—
130C2×C3×Q8—102no—
131C2×C3×Q8—102no—
132C22×C3×C4—101no—
133C22×C3×C4—101no—
134C22×C3×C4C22⋊D512yes—
135C22×C3×C4C22×D511yescharacteristic
136C2×Dic6—22no—
137C3×C4⋊C4—22no—
138C3×C42—102no—
139#217—22no—
140C4⋊Dic3—22no—
141C4⋊Dic3C22⋊D512yes—
142C4⋊Dic3C22⋊D512yes—
143Dic3⋊C4—24no—
144C4×Dic3—22no—
145#208—102no—
146#208—102no—
147C2×C3⋊C8—102no—
148C23×C5C2×#6711yescharacteristic
149C5×Q8—242no—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5—62no—
153C2×C4×C5—62no—
154C2×C4×C5C2×Dic611yescharacteristic
155C2×C4×C5#23511yescharacteristic
156C2×C4×C5D3×D412yes—
157C2×C4×C5#23712yes—
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164Dic10—24no—
165Dic10—42no—
166#168—122no—
167C22×Q8—51no—
168C2×M16—152no—
169C4⋊Q8—62no—
170#125—62no—
171C22⋊Q8—62no—
172#117—32no—
173C2×C4⋊C4D3×D511yescharacteristic
174C2×C42—51no—
175#103—302no—
176#103—302no—
177#95—102no—
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—104no—
185C3×Q8—202no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4—102no—
189C2×C3×C4—102no—
190C2×C3×C4—201no—
191C2×C3×C4—201no—
192C2×C3×C4—201no—
193C2×C3×C4—201no—
194C2×C3×C4Q8×D511yescharacteristic
195C2×C3×C4#71312yes—
196C2×C3×C4#71311yescharacteristic
197C2×C3×C4C2×C22⋊D512yes—
198C2×Dic3—22no—
199C2×Dic3—22no—
200Dic6—82no—
201C3⋊C8—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#92411yescharacteristic
205C22×C5#93611yescharacteristic
206C22×C5#93711yescharacteristic
207C4×C5—42no—
208C4×C5—122no—
209C4×C5—122no—
210C4×C5#87812yes—
211C4×C5#88512yes—
212Dic5—42no—
213Dic5—42no—
214C2×Q8—52no—
215C2×Q8—62no—
216C2×Q8—101no—
217C2×Q8—102no—
218C2×Q8—102no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4#120112yes—
222C22×C4C2×D3×D511yescharacteristic
223M16—302no—
224M16—302no—
225C2×C8—302no—
226C4⋊C4—22no—
227C4⋊C4—32no—
228C4⋊C4—32no—
229C4⋊C4—62no—
230C4⋊C4—64no—
231C22⋊C4—62no—
232C42—62no—
233C42—102no—
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—202no—
242C3×C4—202no—
243C3×C4#409212yes—
244C3×C4#409312yes—
245Dic3—42no—
246Dic3—42no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#494711yescharacteristic
250C2×C5#506111yescharacteristic
251C2×C5#509511yescharacteristic
252C23C2×#120111yescharacteristic
253Q8—104no—
254Q8—202no—
255Q8—242no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4D5×Dic611yescharacteristic
267C2×C4#676612yes—
268C2×C4#677311yescharacteristic
269C2×C4D3×C22⋊D512yes—
270C8—602no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6552011yescharacteristic
274C2×C3#6553111yescharacteristic
275C2×C3#6553511yescharacteristic
276C5#6967311yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9135911yescharacteristic
280C22#9136811yescharacteristic
281C22#9156811yescharacteristic
282C4—42no—
283C4—122no—
284C4—122no—
285C4—202no—
286C4—202no—
287C4#9142112yes—
288C4#9145512yes—
289C3#1060269811yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1174877311yescharacteristic
293C2#1174914711yescharacteristic
294C2#1174939311yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
32. C2×C3×Dic10Q8semidirect
99. C2×Dic10Dic6semidirect
234. C3×C5#2028semidirect
276. C5#69673semidirect
289. C3#10602698semidirect

Maximal subgroups

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

subgroupindex
C5×#55002
C3×#652632
#117483992
#117463512
#117459772
#106026983
#696735