Finite Group Databasebeta

← #14309029

Subgroups — #14309029

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756229C211yesmaximal, characteristic, complemented
2#11751240C211yesmaximal, characteristic
3#11751107C211yesmaximal, characteristic
4C2×#91089C211yesmaximal, characteristic
5C3×C5×#339C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7#11746352C211yesmaximal, characteristic, complemented
8#10599572—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91815C2211yescharacteristic
14#91815C2211yescharacteristic
15#91813—22no—
16C2×#6710C2211yescharacteristic
17#91759—21no—
18#91758—21no—
19C4×Dic30—22no—
20#91109—22no—
21#91090—22no—
22#91089—21no—
23#91089—21no—
24#68779—51nomaximal, Hall
25#65804—31no—
26#65428—31no—
27#65295—31no—
28C2×#3937—31no—
29C5×#339D311yescharacteristic, complemented
30#64776—31no—
31#64751—31no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220—21no—
35#6817—21no—
36#6817—21no—
37#6817—21no—
38#6817—21no—
39C2×D60Q811yescharacteristic, complemented
40C2×C4×D15—21no—
41C2×Dic30—22no—
42C2×Dic30Q811yescharacteristic, complemented
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C3×C42×C5D411yescharacteristic
51C3×C42×C5D411yescharacteristic
52#6719—21no—
53#6719D412yes—
54C4⋊Dic15—22no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57#6712—24no—
58C4×Dic15—21no—
59C4×Dic15D412yes—
60#6710—21no—
61#6710—21no—
62C2×C3⋊#168—21no—
63#5470—51no—
64#5139—51no—
65#5006—51no—
66C2×#805—51no—
67C3×#339D511yescharacteristic, complemented
68#4556—51no—
69#4531—51no—
70C2×#709—31no—
71C2×C5×M16C2×D311yescharacteristic
72C5×#117C2×D311yescharacteristic
73C2×C42×C5C2×D311yescharacteristic
74#4072—31no—
75#4072—31no—
76#4070—62no—
77C2×#681—31no—
78#4016—61no—
79#4015—61no—
80C4×Dic10—62no—
81#3957—62no—
82#3938—62no—
83#3937—61no—
84#3937—61no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×D15—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×Q811yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98#1220—41no—
99#1220—41no—
100C2×Dic15—22no—
101C2×Dic15—22no—
102C2×Dic15—21no—
103D60—21no—
104D60—21no—
105C4×D15—41no—
106C4×D15—41no—
107Dic30—21no—
108Dic30—21no—
109Dic30—44no—
110C3×C5×C8—41no—
111C3⋊#168—41no—
112C2×#235—51no—
113C2×C3×M16C2×D511yescharacteristic
114C3×#117C2×D511yescharacteristic
115C2×C3×C42C2×D511yescharacteristic
116#926—51no—
117#926—51no—
118#924—102no—
119C2×#208—51no—
120#870—101no—
121#869—101no—
122C4×Dic6—102no—
123#825—102no—
124#806—102no—
125#805—101no—
126#805—101no—
127C22×C4×C5—21no—
128C22×C4×C5C22×D311yescharacteristic
129C2×C22⋊D5—61no—
130#709—61no—
131#709—61no—
132#709—61no—
133#709—61no—
134C2×D20—31no—
135C2×C4×D5—61no—
136C2×Dic10—31no—
137C2×Dic10—62no—
138C5×M16—21no—
139C5×M16—21no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C22⋊C4—21no—
143C42×C5—21no—
144C42×C5—21no—
145C42×C5D1211yescharacteristic
146C42×C5D1211yescharacteristic
147C22⋊Dic5—32no—
148C22⋊Dic5—61no—
149C4⋊Dic5—62no—
150C4⋊Dic5—61no—
151C4⋊Dic5—61no—
152#683—64no—
153C4×Dic5—32no—
154C4×Dic5—61no—
155#681—61no—
156#681—61no—
157C2×#168—61no—
158#533—151no—
159#421—151no—
160C2×#104—151no—
161#410—151no—
162#344—151no—
163#339D1511yescharacteristic, complemented
164H(3,ℤ/4)—151no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×D15—41no—
170C2×D15—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5—81no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178Dic15—42no—
179Dic15—42no—
180Dic15—41no—
181C22×C3×C4—21no—
182C22×C3×C4C22×D511yescharacteristic
183C2×#67—101no—
184#235—101no—
185#235—101no—
186#235—101no—
187#235—101no—
188C2×D12—51no—
189C2×C4×D3—101no—
190C2×Dic6—51no—
191C2×Dic6—102no—
192C3×M16—21no—
193C3×M16—21no—
194C2×C3×C8—21no—
195C3×C4⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42D2011yescharacteristic
200C3×C42D2011yescharacteristic
201#217—52no—
202#217—101no—
203C4⋊Dic3—102no—
204C4⋊Dic3—101no—
205C4⋊Dic3—101no—
206Dic3⋊C4—104no—
207C4×Dic3—52no—
208C4×Dic3—101no—
209#208—101no—
210#208—101no—
211C2×C3⋊C8—101no—
212C23×C5D3×D411yescharacteristic
213C22×D5—61no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5C2×D1211yescharacteristic
219C2×C4×C5#23511yescharacteristic
220C2×C4×C5#23511yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5#23711yescharacteristic
223C2×C4×C5D3×Q811yescharacteristic
224C22⋊D5—121no—
225C22⋊D5—121no—
226C2×Dic5—62no—
227C2×Dic5—62no—
228C2×Dic5—61no—
229D20—61no—
230D20—61no—
231C4×D5—121no—
232C4×D5—121no—
233Dic10—61no—
234Dic10—61no—
235Dic10—124no—
236C5×C8—41no—
237#168—121no—
238C2×#41—151no—
239C2×M16—151no—
240C2×M16C2×D1511yescharacteristic
241C4⋊Q8—301no—
242#125—301no—
243C22⋊Q8—302no—
244C4×Q8—302no—
245#117—151no—
246#117—151no—
247#117C2×D1511yescharacteristic
248C2×C42C2×D1511yescharacteristic
249#104—302no—
250#104—301no—
251#104—301no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257D15—81no—
258C23×C3D4×D511yescharacteristic
259C22×D3—101no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—41no—
264C2×C3×C4C2×D2011yescharacteristic
265C2×C3×C4#70911yescharacteristic
266C2×C3×C4#70911yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268C2×C3×C4#71111yescharacteristic
269C2×C3×C4Q8×D511yescharacteristic
270#67—201no—
271#67—201no—
272C2×Dic3—102no—
273C2×Dic3—102no—
274C2×Dic3—101no—
275D12—101no—
276D12—101no—
277C4×D3—201no—
278C4×D3—201no—
279Dic6—101no—
280Dic6—101no—
281Dic6—204no—
282C3×C8—41no—
283C3⋊C8—201no—
284C22×C5—41no—
285C22×C5#88211yescharacteristic
286C22×C5#88511yescharacteristic
287C22×C5#89611yescharacteristic
288C2×D5—121no—
289C2×D5—241no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—81no—
293C4×C5#87511yescharacteristic
294C4×C5#88511yescharacteristic
295C4×C5#89611yescharacteristic
296C4×C5#89711yescharacteristic
297Dic5—122no—
298Dic5—122no—
299Dic5—121no—
300#41—301no—
301#41—301no—
302#41—301no—
303#41—301no—
304C2×Q8—151no—
305C2×Q8—302no—
306C2×D4—151no—
307C2×D4—301no—
308C22×C4—21no—
309C22×C4—301no—
310C22×C4C22×D1511yescharacteristic
311M16—21no—
312M16—21no—
313M16—301no—
314M16—301no—
315C2×C8—21no—
316C2×C8—301no—
317C4⋊C4—21no—
318C4⋊C4—304no—
319C4⋊C4—302no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C22⋊C4—21no—
323C22⋊C4—152no—
324C22⋊C4—301no—
325C42—21no—
326C42—21no—
327C42—152no—
328C42—301no—
329C42D6011yescharacteristic
330C42D6011yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3#402811yescharacteristic
334C22×C3#403111yescharacteristic
335C22×C3#404211yescharacteristic
336C2×D3—201no—
337C2×D3—401no—
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—81no—
341C3×C4#402111yescharacteristic
342C3×C4#403111yescharacteristic
343C3×C4#404211yescharacteristic
344C3×C4#404311yescharacteristic
345Dic3—202no—
346Dic3—202no—
347Dic3—201no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#467311yescharacteristic
352D5—241no—
353C23—301no—
354C23D4×D1511yescharacteristic
355Q8—301no—
356Q8—301no—
357Q8—604no—
358D4—301no—
359D4—301no—
360D4—601no—
361D4—601no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—302no—
367C2×C4—302no—
368C2×C4—301no—
369C2×C4—601no—
370C2×C4—601no—
371C2×C4C2×D6011yescharacteristic
372C2×C4#681711yescharacteristic
373C2×C4#681711yescharacteristic
374C2×C4D4×D1511yescharacteristic
375C2×C4#681911yescharacteristic
376C2×C4Q8×D1511yescharacteristic
377C8—41no—
378C8—601no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6496211yescharacteristic
383D3—401no—
384C5#6877911yescharacteristic, complemented, Sylow
385C22—41no—
386C22—601no—
387C22—1201no—
388C22#9177111yescharacteristic
389C22#9177411yescharacteristic
390C22#9178511yescharacteristic
391C4—22no—
392C4—41no—
393C4—81no—
394C4—602no—
395C4—602no—
396C4—601no—
397C4#9176411yescharacteristic
398C4#9177411yescharacteristic
399C4#9178511yescharacteristic
400C4#9178611yescharacteristic
401C3#1059957211yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—1201no—
406C2#1175077411yescharacteristic
subgroupG/H
centerC4#91774
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC2×C3×C5#393
prime radicalC2×#6817C22
hypercenter#339D15
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #11756229C2semidirect
5. C3×C5×#339C2semidirect
6. #11746377C2semidirect
7. #11746352C2semidirect
29. C5×#339D3semidirect
39. C2×D60Q8semidirect
42. C2×Dic30Q8semidirect
67. C3×#339D5semidirect
163. #339D15semidirect
331. C3×C5#2031semidirect
384. C5#68779semidirect
401. C3#10599572semidirect

Maximal subgroups

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

subgroupindex
#117562292
#117512402
#117511072
C2×#910892
C3×C5×#3392
#117463772
#117463522
#105995723
#687795