Finite Group Databasebeta

← #14309045

Subgroups — #14309045

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
2C2×C5×#805C211yesmaximal, characteristic
3#11748625C211yesmaximal, characteristic
4#11748424C211yesmaximal, characteristic
5C3×#64743C211yesmaximal, characteristic, complemented
6#11745991C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10601161—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12#91815C2211yescharacteristic
13#91813—22no—
14#91759—21no—
15#91758—21no—
16C4×Dic30—22no—
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C5×#805—21no—
21C5×#805—21no—
22#90996—22no—
23#90978—22no—
24#68779—51nomaximal, Hall
25#65804—31no—
26C2×C5×#104—31no—
27#65529—31no—
28#65525—31no—
29#64779—31no—
30#64777—31no—
31#64743D311yescharacteristic, complemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×Dic30—22no—
35C2×C5×#67—21no—
36C5×#235—21no—
37C5×#235—21no—
38C5×#235—21no—
39C5×#235—21no—
40C2×C5×D12Q811yescharacteristic, complemented
41C2×C4×C5×D3—21no—
42C2×C5×Dic6Q811yescharacteristic, complemented
43C3×C42×C5—21no—
44C3×C42×C5D411yescharacteristic
45C3×C42×C5D411yescharacteristic
46#6719—21no—
47#6719D412yes—
48C4⋊Dic15—22no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51#6712—24no—
52C4×Dic15—21no—
53C4×Dic15D412yes—
54C5×#208—21no—
55C5×#208—21no—
56C2×C5×C3⋊C8—21no—
57C3×C22⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4×Dic5—21no—
60C3×#681—21no—
61C3×#681—21no—
62C2×C3×#168—21no—
63#5470—51no—
64#5139—51no—
65#5006—51no—
66C2×#805D511yescharacteristic
67C3×#339—51no—
68#4556—51no—
69#4531—51no—
70C2×C5×#41—31no—
71C2×C5×M16—31no—
72C2×C42×C5C2×D311yescharacteristic
73#4072—31no—
74#4072—31no—
75#4072C2×D311yescharacteristic
76#4070—62no—
77C2×#681C2×D311yescharacteristic
78#4016—61no—
79#4015—61no—
80C4×Dic10—62no—
81C5×#104—61no—
82C5×#104—61no—
83#3969—62no—
84#3966—62no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C5×D3—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×Q811yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—22no—
98C2×Dic15—22no—
99Dic30—44no—
100C5×#67—41no—
101C5×#67—41no—
102C2×C5×Dic3—21no—
103C5×D12—21no—
104C5×D12—21no—
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C5×Dic6—21no—
108C5×Dic6—21no—
109C2×C3×Dic5—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×#235C2×D511yescharacteristic
113C2×C3×M16—51no—
114C3×#117—51no—
115C2×C3×C42C2×D511yescharacteristic
116#926—51no—
117#926—51no—
118#924—102no—
119C2×#208C2×D511yescharacteristic
120#870—101no—
121#869—101no—
122C4×Dic6—102no—
123#825—102no—
124#806—102no—
125#805—21no—
126#805—21no—
127C5×#41—61no—
128C5×#41—61no—
129C5×#41—61no—
130C5×#41—61no—
131C2×C5×Q8—31no—
132C2×C5×D4—31no—
133C2×C5×D4—61no—
134C22×C4×C5—21no—
135C22×C4×C5—61no—
136C22×C4×C5C22×D311yescharacteristic
137C2×Dic10—62no—
138C5×M16—61no—
139C5×M16—61no—
140C2×C5×C8—61no—
141C42×C5—21no—
142C42×C5D1211yescharacteristic
143C42×C5D1211yescharacteristic
144C22⋊Dic5—21no—
145C22⋊Dic5—32no—
146C22⋊Dic5—61no—
147C4⋊Dic5—21no—
148C4⋊Dic5—62no—
149C4⋊Dic5—61no—
150C4⋊Dic5—61no—
151#683—64no—
152C4×Dic5—21no—
153C4×Dic5—32no—
154C4×Dic5—61no—
155#681—21no—
156#681—21no—
157C2×#168—21no—
158#533—151no—
159#421—151no—
160C2×#104—31no—
161#410—151no—
162#344—151no—
163#339—51no—
164H(3,ℤ/4)—151no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×C5×D3—41no—
170C2×C5×D3—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5C22⋊Q811yescharacteristic
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5#12411yescharacteristic
176C3×C4×C5#12411yescharacteristic
177Dic15—42no—
178Dic15—42no—
179C3×Dic5—81no—
180C5×Dic3—41no—
181C22×C3×C4—21no—
182C22×C3×C4C22×D511yescharacteristic
183C2×#67—21no—
184#235—21no—
185#235—21no—
186#235—21no—
187#235—21no—
188C2×D12Dic1011yescharacteristic, complemented
189C2×C4×D3—21no—
190C2×Dic6—102no—
191C2×Dic6Dic1011yescharacteristic, complemented
192C3×M16—101no—
193C3×M16—101no—
194C2×C3×C8—101no—
195C3×C4⋊C4—101no—
196C3×C22⋊C4—101no—
197C3×C42—21no—
198C3×C42—101no—
199C3×C42C22⋊D511yescharacteristic
200C3×C42C22⋊D511yescharacteristic
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—21no—
210#208—21no—
211C2×C3⋊C8—21no—
212C23×C5—61no—
213C23×C5D3×D411yescharacteristic
214C5×Q8—61no—
215C5×Q8—61no—
216C5×D4—61no—
217C5×D4—61no—
218C5×D4—121no—
219C5×D4—121no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—42no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5—121no—
226C2×C4×C5C2×D1211yescharacteristic
227C2×C4×C5#23511yescharacteristic
228C2×C4×C5#23511yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×C4×C5#23711yescharacteristic
231C2×C4×C5D3×Q811yescharacteristic
232C2×Dic5—41no—
233C2×Dic5—62no—
234C2×Dic5—62no—
235Dic10—124no—
236C5×C8—121no—
237#168—41no—
238C2×#41—31no—
239C2×M16—31no—
240C2×M16—51no—
241C4⋊Q8—301no—
242#125—301no—
243C22⋊Q8—302no—
244C4×Q8—302no—
245#117—51no—
246#117—151no—
247#117—151no—
248C2×C42D3×D511yescharacteristic
249#104—61no—
250#104—61no—
251#104—302no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257C5×D3—81no—
258C23×C3D4×D511yescharacteristic
259C22×D3—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—201no—
264C2×C3×C4C2×Dic1011yescharacteristic
265C2×C3×C4#70911yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4#71111yescharacteristic
268C2×C3×C4#71111yescharacteristic
269C2×C3×C4C2×C22⋊D511yescharacteristic
270#67—41no—
271#67—41no—
272C2×Dic3—21no—
273C2×Dic3—102no—
274C2×Dic3—102no—
275D12—21no—
276D12—21no—
277C4×D3—41no—
278C4×D3—41no—
279Dic6—21no—
280Dic6—21no—
281Dic6—204no—
282C3×C8—201no—
283C3⋊C8—41no—
284C22×C5—41no—
285C22×C5—121no—
286C22×C5—241no—
287C22×C5#88211yescharacteristic
288C22×C5#88511yescharacteristic
289C22×C5#89611yescharacteristic
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—121no—
293C4×C5#87511yescharacteristic
294C4×C5#88511yescharacteristic
295C4×C5#89611yescharacteristic
296C4×C5#89711yescharacteristic
297Dic5—81no—
298Dic5—122no—
299Dic5—122no—
300#41—61no—
301#41—61no—
302#41—61no—
303#41—61no—
304C2×Q8—31no—
305C2×Q8—302no—
306C2×D4—31no—
307C2×D4—61no—
308C22×C4—21no—
309C22×C4—61no—
310C22×C4C2×D3×D511yescharacteristic
311M16—61no—
312M16—61no—
313M16—101no—
314M16—101no—
315C2×C8—61no—
316C2×C8—101no—
317C4⋊C4—101no—
318C4⋊C4—304no—
319C4⋊C4—302no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C22⋊C4—101no—
323C22⋊C4—152no—
324C22⋊C4—301no—
325C42—21no—
326C42—101no—
327C42—152no—
328C42—301no—
329C42#120311yescharacteristic
330C42#120311yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3#402411yescharacteristic
334C22×C3#403111yescharacteristic
335C22×C3#408311yescharacteristic
336C2×D3—41no—
337C2×D3—81no—
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—401no—
341C3×C4#402411yescharacteristic
342C3×C4#403111yescharacteristic
343C3×C4#407011yescharacteristic
344C3×C4#408211yescharacteristic
345Dic3—41no—
346Dic3—202no—
347Dic3—202no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—241no—
352C2×C5#467311yescharacteristic
353C23—61no—
354C23#679011yescharacteristic
355Q8—61no—
356Q8—61no—
357Q8—604no—
358D4—61no—
359D4—61no—
360D4—121no—
361D4—121no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—61no—
366C2×C4—121no—
367C2×C4—121no—
368C2×C4—201no—
369C2×C4—302no—
370C2×C4—302no—
371C2×C4#676511yescharacteristic
372C2×C4D3×Dic1011yescharacteristic
373C2×C4#677211yescharacteristic
374C2×C4#677211yescharacteristic
375C2×C4C2×#120311yescharacteristic
376C2×C4#679011yescharacteristic
377C8—121no—
378C8—201no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6523611yescharacteristic
383D3—81no—
384C5#6877911yescharacteristic, complemented, Sylow
385C22—41no—
386C22—121no—
387C22—241no—
388C22#9143211yescharacteristic
389C22#9146211yescharacteristic
390C22#9157311yescharacteristic
391C4—22no—
392C4—41no—
393C4—121no—
394C4—401no—
395C4—602no—
396C4—602no—
397C4#9136511yescharacteristic
398C4#9137311yescharacteristic
399C4#9143211yescharacteristic
400C4#9146211yescharacteristic
401C3#1060116111yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—241no—
406C2#1174879511yescharacteristic
subgroupG/H
centerC4#91462
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#393
prime radicalC2×C5×#235C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #11756229C2semidirect
5. C3×#64743C2semidirect
6. #11745991C2semidirect
7. #11745970C2semidirect
31. #64743D3semidirect
40. C2×C5×D12Q8semidirect
42. C2×C5×Dic6Q8semidirect
188. C2×D12Dic10semidirect
191. C2×Dic6Dic10semidirect
331. C3×C5#2031semidirect
384. C5#68779semidirect
401. C3#10601161semidirect

Maximal subgroups

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

subgroupindex
#117562292
C2×C5×#8052
#117486252
#117484242
C3×#647432
#117459912
#117459702
#106011613
#687795