Finite Group Databasebeta

← #14300280

Subgroups — #14300280

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91286C211yesmaximal, characteristic
2C5×#5002C211yesmaximal, characteristic
3C3×#65288C211yesmaximal, characteristic, complemented
4C2×#90993C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic
6#11746353C211yesmaximal, characteristic, complemented
7#11745968C211yesmaximal, characteristic, complemented
8#10601085—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6650—21no—
17#91286—22no—
18#91286—22no—
19C2×D3×#168—21no—
20C5×#810C411yescharacteristic, complemented
21C5×#810C411yescharacteristic, complemented
22C5×#809C411yescharacteristic, complemented
23C5×#809C411yescharacteristic, complemented
24C3×C4⋊#168—21no—
25C3×C4⋊#168—21no—
26#90993—22no—
27#90978—22no—
28#70545—51nomaximal, Hall
29C2×#4094—31no—
30C5×#416—31no—
31C2×#3969—31no—
32C2×#3951—31no—
33#65288D311yescharacteristic, complemented
34#64770—31no—
35#64752—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235D412yes—
42C5×#235Q812yes—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5—21no—
50C4×Dic15—21no—
51C4×Dic15—21no—
52#6710—21no—
53#6710D412yes—
54C2×C3⋊#168—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8C2×C411yescharacteristic
58C2×C5×C3⋊C8C2×C411yescharacteristic
59C3×#681—21no—
60C3×#681—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168D411yescharacteristic
65C2×C3×#168D411yescharacteristic
66#6650—24no—
67D3×#168—24no—
68C2×#901—51no—
69C3×#424—51no—
70C2×#825—51no—
71C2×#822—51no—
72#5002D511yescharacteristic
73#4550—51no—
74#4532—51no—
75C2×C5×#41—31no—
76C22×C5×C8—31no—
77C5×#117C2×D311yescharacteristic
78#4094—62no—
79#4094—62no—
80C2×C4×Dic5—31no—
81C2×#681—31no—
82C2×#681—61no—
83C2×#681C2×D311yescharacteristic
84C22×#168—61no—
85C22×#168C2×D311yescharacteristic
86C5×#103—31no—
87C5×#103—31no—
88C5×#102—31no—
89C5×#102—31no—
90#3969—62no—
91#3951—62no—
92C4⋊#168—21no—
93C4⋊#168—21no—
94#1866—151noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C5×D3—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×Q811yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×Dic15—22no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C5×#67—22no—
109C5×#67—22no—
110C2×C5×Dic3—21no—
111C5×D12—21no—
112C5×D12C4⋊C412yes—
113C4×C5×D3—22no—
114C4×C5×D3—22no—
115C5×Dic6—21no—
116C5×Dic6C4⋊C412yes—
117C3⋊#168—22no—
118C3×#168—21no—
119C3×#168—21no—
120C3×#168—41no—
121C5×C3⋊C8—21no—
122C5×C3⋊C8—21no—
123C2×#235C2×D511yescharacteristic
124C2×C3×M16—51no—
125C22×C3×C8—51no—
126C3×#117C2×D511yescharacteristic
127C2×C4×Dic3—51no—
128C2×#208—51no—
129C22×C3⋊C8C2×D511yescharacteristic
130#901—102no—
131#901—102no—
132C2×ΓL(1,𝔽25)—101no—
133C2×D3×C8—101no—
134C3×C4⋊C8—101no—
135C3×C4⋊C8—101no—
136#825—102no—
137#822—102no—
138#810Dic511yescharacteristic, complemented
139#810Dic511yescharacteristic, complemented
140#809Dic511yescharacteristic, complemented
141#809Dic511yescharacteristic, complemented
142C5×#41—32no—
143C5×#41—32no—
144C5×#41—61no—
145C5×#41—61no—
146C2×C5×Q8—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C22×C4×C5—61no—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—61no—
152C2×C5×C8—31no—
153C2×C5×C8—31no—
154C2×C5×C8—61no—
155C2×C5×C8—61no—
156C5×C4⋊C4C4×D311yescharacteristic
157C5×C4⋊C4C4×D311yescharacteristic
158C5×C22⋊C4—21no—
159C42×C5—21no—
160C4×Dic5—61no—
161C4×Dic5—61no—
162#681—21no—
163#681—21no—
164#681—32no—
165#681—64no—
166#681—61no—
167C2×#168—21no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—64no—
171C2×#168—61no—
172C2×#168#6711yescharacteristic
173C2×#168#6711yescharacteristic
174C2×#131—151no—
175C2×#108—151no—
176#424—51no—
177C2×#104—151no—
178#416—31no—
179#339—151no—
180#336—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C5×D3—22no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5—41no—
190C3×C4×C5—41no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5#12011yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195Dic15—42no—
196C5×Dic3—22no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—21no—
199C22×Dic3—101no—
200#235—21no—
201#235—21no—
202#235Dic1012yes—
203#235D2012yes—
204C2×D12C2×Dic511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C2×Dic511yescharacteristic
207C3×M16—101no—
208C3×M16—101no—
209C2×C3×C8—51no—
210C2×C3×C8—51no—
211C2×C3×C8—101no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C3×C4⋊C4C2×Dic511yescharacteristic
215C3×C4⋊C4C2×Dic511yescharacteristic
216C3×C22⋊C4—21no—
217C3×C42—21no—
218C4×Dic3—101no—
219C4×Dic3—101no—
220#208—52no—
221#208—101no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8C2×Dic511yescharacteristic
226C2×C3⋊C8C2×Dic511yescharacteristic
227ΓL(1,𝔽25)—104no—
228D3×C8—104no—
229C23×C5—61no—
230C23×C5#23511yescharacteristic
231C5×Q8—32no—
232C5×Q8—61no—
233C5×D4—32no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—61no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—61no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×Q811yescharacteristic
246C2×C4×C5#23911yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C2×Dic5—62no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C5×C8—61no—
252C5×C8—61no—
253#168—21no—
254#168—21no—
255#168—41no—
256#168—62no—
257C2×#41—31no—
258#131—302no—
259#131—302no—
260C2×M16—51no—
261C2×M16—151no—
262C2×M16—301no—
263C22×C8—31no—
264C22×C8—51no—
265C22×C8—301no—
266#117D3×D511yescharacteristic
267C2×C42—151no—
268#108—302no—
269C4⋊C8—101no—
270C4⋊C8—101no—
271#104—302no—
272#103—31no—
273#103—31no—
274#102—31no—
275#102—31no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#44311yescharacteristic
280C2×C3×C5#44411yescharacteristic
281C5×D3—42no—
282C23×C3#71111yescharacteristic
283C22×D3—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4C2×Dic1011yescharacteristic
287C2×C3×C4C2×D2011yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4#71111yescharacteristic
291C2×C3×C4C22×Dic511yescharacteristic
292#67—22no—
293#67—22no—
294C2×Dic3—21no—
295C2×Dic3—102no—
296C2×Dic3—201no—
297C2×Dic3—201no—
298D12—21no—
299D12C4⋊Dic512yes—
300C4×D3—22no—
301C4×D3—22no—
302Dic6—21no—
303Dic6C4⋊Dic512yes—
304C3×C8—101no—
305C3×C8—101no—
306C3×C8—201no—
307C3⋊C8—21no—
308C3⋊C8—21no—
309C3⋊C8—102no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—62no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5#89411yescharacteristic
316C22×C5#89611yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C4×C5—41no—
319C4×C5—41no—
320C4×C5—62no—
321C4×C5D3×C4⋊C411yescharacteristic
322C4×C5#89311yescharacteristic
323C4×C5#93711yescharacteristic
324C4×C5#94611yescharacteristic
325Dic5—122no—
326#41—32no—
327#41—32no—
328#41—61no—
329#41—61no—
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C22×C4—61no—
334C22×C4—301no—
335C22×C4C2×D3×D511yescharacteristic
336M16—101no—
337M16—101no—
338M16—152no—
339M16—304no—
340M16—301no—
341C2×C8—31no—
342C2×C8—31no—
343C2×C8—51no—
344C2×C8—51no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—101no—
348C2×C8—101no—
349C2×C8—101no—
350C2×C8—304no—
351C2×C8—301no—
352C4⋊C4D3×Dic511yescharacteristic
353C4⋊C4D3×Dic511yescharacteristic
354C22⋊C4—21no—
355C42—21no—
356C42—301no—
357C42—301no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3#402411yescharacteristic
362C22×C3#403211yescharacteristic
363C22×C3D4×Dic511yescharacteristic
364C2×D3—22no—
365C2×D3—41no—
366C2×D3—41no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4#402411yescharacteristic
370C3×C4#402811yescharacteristic
371C3×C4C2×C4⋊Dic511yescharacteristic
372C3×C4D4×Dic511yescharacteristic
373Dic3—22no—
374Dic3—202no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5—122no—
378C2×C5#498911yescharacteristic
379C2×C5#514411yescharacteristic
380C2×C5#514511yescharacteristic
381C23—61no—
382C23#678211yescharacteristic
383Q8—32no—
384Q8—61no—
385D4—32no—
386D4—62no—
387D4—62no—
388D4—61no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—61no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—302no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4D3×Dic1011yescharacteristic
398C2×C4#676811yescharacteristic
399C2×C4D3×D2011yescharacteristic
400C2×C4#677711yescharacteristic
401C2×C4C2×D3×Dic511yescharacteristic
402C2×C4D5×#6711yescharacteristic
403C8—61no—
404C8—61no—
405C8—101no—
406C8—101no—
407C8—201no—
408C8—302no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3#6523911yescharacteristic
412C2×C3#6548511yescharacteristic
413C2×C3#6548611yescharacteristic
414D3—42no—
415C5#7054511yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—62no—
419C22—121no—
420C22—121no—
421C22#9142711yescharacteristic
422C22#9143611yescharacteristic
423C22Dic5×#6711yescharacteristic
424C4—41no—
425C4—41no—
426C4—62no—
427C4—602no—
428C4#9141011yescharacteristic
429C4D3×C4⋊Dic511yescharacteristic
430C4#9143511yescharacteristic
431C4#9147411yescharacteristic
432C3#1060108511yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—122no—
436C2#1174889711yescharacteristic
437C2#1174943211yescharacteristic
438C2#1174943311yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1866
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#65288C2semidirect
4. C2×#90993C2semidirect
6. #11746353C2semidirect
7. #11745968C2semidirect
20. C5×#810C4semidirect
21. C5×#810C4semidirect
22. C5×#809C4semidirect
23. C5×#809C4semidirect
33. #65288D3semidirect
138. #810Dic5semidirect
139. #810Dic5semidirect
140. #809Dic5semidirect
141. #809Dic5semidirect
358. C3×C5#1866semidirect
415. C5#70545semidirect
432. C3#10601085semidirect

Maximal subgroups

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

subgroupindex
C2×#912862
C5×#50022
C3×#652882
C2×#909932
C2×#909782
#117463532
#117459682
#106010853
#705455