Finite Group Databasebeta

← #14299596

Subgroups — #14299596

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756557C211yesmaximal, characteristic
2C2×C5×#833C211yesmaximal, characteristic
3C3×#65510C211yesmaximal, characteristic
4#11748453C212yesmaximal, complemented
5#11745978C212yesmaximal, complemented
6#10600861—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6719—22no—
9D4×Dic15—22no—
10D4×Dic15—22no—
11#91815C2212yes—
12C2×C5×#208C2212yes—
13C2×C3×C22⋊Dic5—22no—
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C5×#833C414yescomplemented
17#90990—22no—
18#90987—22no—
19#69642—51nomaximal, Hall
20#66132—31no—
21C2×C5×#100—31no—
22#65510D311yescharacteristic
23#65410—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×D4Q812yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—22no—
32C22×Dic15—22no—
33C22×C3×Dic5—21no—
34C22×C3×Dic5—21no—
35#6719—24no—
36#6719—22no—
37C4⋊Dic15D412yes—
38C4⋊Dic15D412yes—
39C4×Dic15—22no—
40C5×#208—22no—
41C5×#208C2×C414yescomplemented
42C2×C5×C3⋊C8—22no—
43C3×C22⋊Dic5—44no—
44C3×C4⋊Dic5—22no—
45C3×C4×Dic5—22no—
46#5798—51no—
47C3×#390—51no—
48C2×#833D511yescharacteristic
49#4964—52no—
50#4523—52no—
51C22×C5×D4C2×D311yescharacteristic
52C2×C5×M16—32no—
53C2×C22⋊Dic5—22no—
54C2×C22⋊Dic5—62no—
55D4×Dic5—62no—
56D4×Dic5—62no—
57#4072—32no—
58C2×C4⋊Dic5C2×D311yescharacteristic
59C2×C4×Dic5C2×D311yescharacteristic
60C5×#100—34no—
61#3950—62no—
62#3949—62no—
63#1856—151noSylow
64C23×C3×C5—22no—
65C23×C3×C5—22no—
66C23×C3×C5—42no—
67C23×C3×C5—42no—
68C23×C3×C5C4⋊C414yes—
69C23×C3×C5C2×D411yescharacteristic
70C3×C5×D4—24no—
71C3×C5×D4—24no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×Q811yescharacteristic
75C2×C3×C4×C5#4112yes—
76C2×Dic15—22no—
77C2×Dic15—22no—
78C2×Dic15—82no—
79C2×Dic15—82no—
80C2×C3×Dic5—22no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—42no—
84C2×C3×Dic5—41no—
85C5×C3⋊C8—24no—
86C22×C3×D4C2×D511yescharacteristic
87C2×C3×C4⋊C4—51no—
88C2×C3×C22⋊C4—102no—
89C2×C3×C42—51no—
90C2×#217—102no—
91D4×Dic3—102no—
92D4×Dic3—102no—
93#926—52no—
94C2×#208C2×D512yes—
95#833Dic514yescomplemented
96#808—102no—
97#807—102no—
98C24×C5#6712yes—
99C2×C5×D4—22no—
100C2×C5×D4—22no—
101C2×C5×D4Dic612yes—
102C2×C5×D4C4×D312yes—
103C22×C4×C5C22×D311yescharacteristic
104C22×Dic5—21no—
105C22×Dic5—21no—
106C22×Dic5—62no—
107C22×Dic5—62no—
108C5×M16—34no—
109C5×M16—62no—
110C2×C5×C8—62no—
111C22⋊Dic5—44no—
112C22⋊Dic5—64no—
113C22⋊Dic5—62no—
114C4⋊Dic5—22no—
115C4⋊Dic5—32no—
116C4⋊Dic5—32no—
117C4×Dic5—22no—
118C4×Dic5—62no—
119#518—151no—
120#428—152no—
121C2×#100—31no—
122#390—51no—
123#339—152no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—24no—
127C22×C3×C5—44no—
128C22×C3×C5—42no—
129C22×C3×C5—42no—
130C22×C3×C5—82no—
131C22×C3×C5C2×C4⋊C411yescharacteristic
132C22×C3×C5#12011yescharacteristic
133C22×C3×C5#12311yescharacteristic
134C3×C4×C5C4×D412yes—
135C3×C4×C5C22⋊Q812yes—
136Dic15—42no—
137Dic15—42no—
138C3×Dic5—42no—
139C3×Dic5—81no—
140C24×C3D2012yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4Dic1012yes—
144C2×C3×D4C2×Dic512yes—
145C22×C3×C4—101no—
146C22×C3×C4—101no—
147C22×C3×C4C22×D511yescharacteristic
148C22×Dic3—102no—
149C22×Dic3—102no—
150C3×C4⋊C4—102no—
151C3×C22⋊C4—204no—
152C3×C42—102no—
153#217—104no—
154#217—102no—
155C4⋊Dic3—52no—
156C4⋊Dic3—52no—
157C4×Dic3—102no—
158#208—22no—
159#208C2×Dic514yescomplemented
160C2×C3⋊C8—22no—
161C23×C5—22no—
162C23×C5—22no—
163C23×C5—42no—
164C23×C5—42no—
165C23×C5Dic3⋊C414yes—
166C23×C5C2×#6711yescharacteristic
167C5×D4—24no—
168C5×D4—24no—
169C2×C4×C5C2×Dic611yescharacteristic
170C2×C4×C5C2×C4×D311yescharacteristic
171C2×C4×C5D3×D412yes—
172C2×C4×C5#23712yes—
173C2×Dic5—22no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—42no—
177C2×Dic5—41no—
178C2×Dic5—62no—
179C2×Dic5—62no—
180C2×Dic5—242no—
181C2×Dic5—242no—
182C5×C8—64no—
183C22×D4D3×D511yescharacteristic
184C2×M16—32no—
185C4×D4—302no—
186C4×D4—302no—
187#117—152no—
188C2×C4⋊C4—51no—
189C2×C22⋊C4—102no—
190C2×C22⋊C4—302no—
191C2×C42—51no—
192#107—302no—
193#106—302no—
194#100—34no—
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—44no—
198C2×C3×C5#38511yescharacteristic
199C2×C3×C5#45311yescharacteristic
200C2×C3×C5#45511yescharacteristic
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—42no—
204C23×C3—42no—
205C23×C3C4⋊Dic514yes—
206C23×C3C2×D2011yescharacteristic
207C3×D4—24no—
208C3×D4—24no—
209C2×C3×C4—102no—
210C2×C3×C4—201no—
211C2×C3×C4—201no—
212C2×C3×C4—202no—
213C2×C3×C4—201no—
214C2×C3×C4C2×Dic1011yescharacteristic
215C2×C3×C4D4×D512yes—
216C2×C3×C4#71112yes—
217C2×C3×C4C22×Dic511yescharacteristic
218C2×Dic3—102no—
219C2×Dic3—102no—
220C2×Dic3—402no—
221C2×Dic3—402no—
222C3⋊C8—24no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5—24no—
226C22×C5—44no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5C2×Dic3⋊C411yescharacteristic
231C22×C5#93511yescharacteristic
232C22×C5#93711yescharacteristic
233C4×C5#87812yes—
234C4×C5#67⋊C412yes—
235Dic5—42no—
236Dic5—81no—
237Dic5—122no—
238Dic5—122no—
239C24#120212yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4D3×Dic512yes—
243C2×D4#120412yes—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4—302no—
247C22×C4—302no—
248C22×C4C2×D3×D511yescharacteristic
249M16—34no—
250M16—62no—
251C2×C8—62no—
252C4⋊C4—102no—
253C4⋊C4—152no—
254C4⋊C4—152no—
255C22⋊C4—204no—
256C22⋊C4—304no—
257C22⋊C4—302no—
258C42—102no—
259C42—302no—
260C3×C5#185611yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—24no—
264C22×C3—44no—
265C22×C3—42no—
266C22×C3—42no—
267C22×C3—82no—
268C22×C3#402811yescharacteristic
269C22×C3#403211yescharacteristic
270C22×C3C2×C4⋊Dic511yescharacteristic
271C3×C4—202no—
272C3×C4—401no—
273C3×C4#402412yes—
274C3×C4D4×Dic512yes—
275Dic3—202no—
276Dic3—202no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—44no—
280C2×C5#494611yescharacteristic
281C2×C5#506111yescharacteristic
282C2×C5#507711yescharacteristic
283C23—22no—
284C23—22no—
285C23—42no—
286C23—42no—
287C23Dic3⋊Dic514yes—
288C23C2×#120211yescharacteristic
289D4—24no—
290D4—24no—
291C2×C4—102no—
292C2×C4—201no—
293C2×C4—201no—
294C2×C4—202no—
295C2×C4—201no—
296C2×C4—302no—
297C2×C4—302no—
298C2×C4—1202no—
299C2×C4—1202no—
300C2×C4#678012yes—
301C2×C4C2×D3×Dic511yescharacteristic
302C2×C4C2×#120411yescharacteristic
303C2×C4#679012yes—
304C8—64no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—44no—
308C2×C3#6503511yescharacteristic
309C2×C3#6503611yescharacteristic
310C2×C3#6523911yescharacteristic
311C5#6964211yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—24no—
315C22—44no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22#9153711yescharacteristic
320C22C2×Dic3⋊Dic511yescharacteristic
321C22#9157211yescharacteristic
322C4—202no—
323C4—401no—
324C4—602no—
325C4—602no—
326C4#67⋊Dic512yes—
327C4#9157612yes—
328C3#1060086111yescharacteristic, complemented, Sylow
329C2—21no—
330C2—21no—
331C2—44no—
332C2#1174914211yescharacteristic
333C2#1174914911yescharacteristic
334C2#1174951711yescharacteristic
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#1856
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. #11748453C2semidirect
5. #11745978C2semidirect
16. C5×#833C4semidirect
41. C5×#208C2×C4semidirect
95. #833Dic5semidirect
159. #208C2×Dic5semidirect
260. C3×C5#1856semidirect
311. C5#69642semidirect
328. C3#10600861semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×C5×#8332
C3×#655102
#117484532
#117459782
#106008613
#696425