Finite Group Databasebeta

← #14283003

Subgroups — #14283003

Order 1920.

668 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#11756386C211yesmaximal, characteristic
2#11748888C211yesmaximal, characteristic, complemented
3#11748509C211yesmaximal, characteristic, complemented
4C5×#4538C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic, complemented
8#10599127—31nomaximal, Hall
9C2×#6821C411yescharacteristic, complemented
10C22×C4×D15C2211yescharacteristic
11C22×#1200—21no—
12C3×C5×C22⋊Q8C2211yescharacteristic
13#91835C411yescharacteristic, complemented
14#91819C2211yescharacteristic
15#91784C411yescharacteristic, complemented
16#91783—21no—
17#91782—21no—
18#91781C411yescharacteristic, complemented
19#91771—21no—
20#91770—21no—
21C2×#6651—21no—
22C5×C3⋊#95C2211yescharacteristic
23C5×#830C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90994—21no—
27#90957—21no—
28#68334—51nomaximal, Hall
29#65961—31no—
30#65015—31no—
31D5×#95—31no—
32C5×#328—31no—
33#64758D311yescharacteristic, complemented
34#64690—31no—
35#64671—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15D411yescharacteristic
41#6821—42no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60C2×C411yescharacteristic, complemented
45C2×C4×D15—21no—
46C2×C4×D15—42no—
47C2×C4×D15C2×C411yescharacteristic
48C2×C4×D15C2×C411yescharacteristic
49C2×C4×D15D411yescharacteristic
50C2×C4×D15D411yescharacteristic
51C22×C5×Dic3—21no—
52C22×C3×Dic5—21no—
53C2×#1200—24no—
54C2×#1200—42no—
55C2×#1200—42no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
58C3×C5×C22⋊C4—21no—
59#6714—21no—
60#6714—21no—
61#6714—21no—
62#6714—21no—
63C4⋊Dic15C2×C411yescharacteristic, complemented
64#6712—21no—
65C4×Dic15—21no—
66C2×C5×C3⋊C8—21no—
67C2×C3×#168—21no—
68#6651—42no—
69#5627—51no—
70#4726—51no—
71D3×#95—51no—
72C3×#328—51no—
73#4538D511yescharacteristic, complemented
74#4470—51no—
75#4451—51no—
76C2×#713—31no—
77C22×C4×D5—31no—
78C22×C4×D5—61no—
79C5×C22⋊Q8C2×D311yescharacteristic
80#4092—31no—
81#4076—31no—
82C2×#676—61no—
83#4041—31no—
84#4040—61no—
85#4039—61no—
86#4038—31no—
87#4028—61no—
88#4027—61no—
89C5×C22⋊C8—31no—
90C5×#95—31no—
91#3963—61no—
92#3963C2×D311yescharacteristic
93C22⋊#168C2×D311yescharacteristic
94#3952—61no—
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—22no—
100C22×D15—22no—
101C22×D15—21no—
102C22×D15C22⋊C411yescharacteristic
103C22×D15C22⋊C411yescharacteristic
104C3×C5×Q8—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110#1220—41no—
111#1220—41no—
112C2×Dic15—21no—
113C2×Dic15—41no—
114C2×Dic15C22⋊C411yescharacteristic
115C2×Dic15C22⋊C411yescharacteristic
116D60—41no—
117D60—42no—
118D60—42no—
119C4×D15—22no—
120C4×D15—22no—
121C4×D15—41no—
122C4×D15—41no—
123C4×D15—42no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130#1200—48no—
131C3×#168—41no—
132C5×C3⋊C8—41no—
133C2×#239—51no—
134C22×C4×D3—51no—
135C22×C4×D3—101no—
136C3×C22⋊Q8C2×D511yescharacteristic
137#946—51no—
138#930—51no—
139C2×ΓL(1,𝔽25)—101no—
140#895—51no—
141#894—101no—
142#893—101no—
143#892—51no—
144#882—101no—
145#67⋊C4—101no—
146C3×C22⋊C8—51no—
147C3×#95—51no—
148C3⋊#95—101no—
149C3⋊#95C2×D511yescharacteristic
150#830C2×D511yescharacteristic
151(C2×D3)⋊C8—101no—
152C23×D5—31no—
153C2×C5×Q8C4×D311yescharacteristic, complemented
154C22×C4×C5—61no—
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—61no—
157C22×Dic5—21no—
158C22×Dic5—31no—
159#713—122no—
160C2×D20—31no—
161C2×D20—61no—
162C2×D20—61no—
163C2×C4×D5—31no—
164C2×C4×D5—31no—
165C2×C4×D5—31no—
166C2×C4×D5—31no—
167C2×C4×D5—64no—
168C2×C4×D5—61no—
169C2×C4×D5—122no—
170C2×C4×D5—122no—
171C2×C4×D5—122no—
172C2×C5×C8—61no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4C4×D311yescharacteristic, complemented
175C5×C22⋊C4—21no—
176#685—61no—
177#685—61no—
178#685—61no—
179#685—61no—
180C4⋊Dic5—31no—
181#683—61no—
182C4×Dic5—61no—
183C2×#168—21no—
184#676—122no—
185#525—151no—
186#407—151no—
187C2×#95—151no—
188#328—31no—
189#328—51no—
190#327—151no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×D15—24no—
198C2×D15—24no—
199C2×D15—21no—
200C2×D15—21no—
201C2×D15—21no—
202C2×D15—21no—
203C2×D15—41no—
204C2×D15—41no—
205C2×D15—41no—
206C2×D15#9912yes—
207C2×D15#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212Dic15—21no—
213Dic15—21no—
214Dic15—41no—
215C3×Dic5—42no—
216C5×Dic3—42no—
217C23×D3—51no—
218C2×C3×Q8C4×D511yescharacteristic, complemented
219C22×C3×C4—101no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—101no—
222C22×Dic3—21no—
223C22×Dic3—51no—
224#239—202no—
225C2×D12—51no—
226C2×D12—101no—
227C2×D12—101no—
228C2×C4×D3—51no—
229C2×C4×D3—51no—
230C2×C4×D3—51no—
231C2×C4×D3—51no—
232C2×C4×D3—104no—
233C2×C4×D3—101no—
234C2×C4×D3—202no—
235C2×C4×D3—202no—
236C2×C4×D3—202no—
237C2×C3×C8—101no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C4×D511yescharacteristic, complemented
240C3×C22⋊C4—21no—
241(C2×D3)⋊C4—101no—
242(C2×D3)⋊C4—101no—
243(C2×D3)⋊C4—101no—
244(C2×D3)⋊C4—101no—
245C4⋊Dic3—51no—
246Dic3⋊C4—101no—
247C4×Dic3—101no—
248C2×C3⋊C8—21no—
249ΓL(1,𝔽25)—202no—
250C23×C5D3×D411yescharacteristic
251C22×D5—31no—
252C22×D5—31no—
253C22×D5—62no—
254C22×D5—62no—
255C22×D5—61no—
256C22×D5—61no—
257C22×D5—61no—
258C5×Q8—41no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—41no—
262C2×C4×C5—62no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5C2×C4×D311yescharacteristic
266C2×C4×C5D3×D411yescharacteristic
267C22⋊D5—121no—
268C22⋊D5—121no—
269C2×Dic5—22no—
270C2×Dic5—31no—
271C2×Dic5—31no—
272C2×Dic5—41no—
273C2×Dic5—41no—
274C2×Dic5—61no—
275C2×Dic5—121no—
276D20—121no—
277D20—122no—
278D20—122no—
279C4×D5—62no—
280C4×D5—62no—
281C4×D5—128no—
282C4×D5—121no—
283C4×D5—121no—
284C4×D5—122no—
285C5×C8—121no—
286#168—41no—
287C2×#41—151no—
288C23×C4—151no—
289C23×C4—301no—
290C2×M16—301no—
291#123—301no—
292C22⋊Q8—151no—
293C22⋊Q8D3×D511yescharacteristic
294#121—151no—
295#121—151no—
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—31no—
301C22⋊C8—51no—
302C22⋊C8—301no—
303#95—31no—
304#95—51no—
305#95—301no—
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311D15—22no—
312D15—22no—
313D15—81no—
314C23×C3D4×D511yescharacteristic
315C22×D3—51no—
316C22×D3—51no—
317C22×D3—102no—
318C22×D3—102no—
319C22×D3—101no—
320C22×D3—101no—
321C22×D3—101no—
322C3×Q8—41no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—102no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331#67—201no—
332#67—201no—
333C2×Dic3—22no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—51no—
337C2×Dic3—51no—
338C2×Dic3—101no—
339C2×Dic3—201no—
340D12—201no—
341D12—202no—
342D12—202no—
343C4×D3—102no—
344C4×D3—102no—
345C4×D3—208no—
346C4×D3—201no—
347C4×D3—201no—
348C4×D3—202no—
349C3×C8—201no—
350C3⋊C8—41no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5D3×C22⋊C411yescharacteristic
354C22×C5#91411yescharacteristic
355C22×C5#91811yescharacteristic
356C2×D5—32no—
357C2×D5—32no—
358C2×D5—64no—
359C2×D5—64no—
360C2×D5—61no—
361C2×D5—61no—
362C2×D5—61no—
363C2×D5—61no—
364C2×D5—121no—
365C2×D5—121no—
366C2×D5—121no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—41no—
370C4×C5—41no—
371C4×C5—122no—
372Dic5—42no—
373Dic5—61no—
374Dic5—61no—
375Dic5—121no—
376C24—151no—
377#41—602no—
378C2×Q8#120011yescharacteristic, complemented
379C2×D4—151no—
380C2×D4—301no—
381C2×D4—301no—
382C2×D4—301no—
383C22×C4—61no—
384C22×C4—101no—
385C22×C4—151no—
386C22×C4—151no—
387C22×C4—151no—
388C22×C4—151no—
389C22×C4—151no—
390C22×C4—301no—
391C22×C4—304no—
392C22×C4—602no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—61no—
398C2×C8—101no—
399C4⋊C4—21no—
400C4⋊C4—151no—
401C4⋊C4—301no—
402C4⋊C4#120011yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—301no—
405C22⋊C4—301no—
406C22⋊C4—301no—
407C22⋊C4—301no—
408C42—301no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3D5×C22⋊C411yescharacteristic
413C22×C3#406011yescharacteristic
414C22×C3#406411yescharacteristic
415C2×D3—52no—
416C2×D3—52no—
417C2×D3—104no—
418C2×D3—104no—
419C2×D3—101no—
420C2×D3—101no—
421C2×D3—101no—
422C2×D3—101no—
423C2×D3—201no—
424C2×D3—201no—
425C2×D3—201no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—202no—
431Dic3—42no—
432Dic3—101no—
433Dic3—101no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5D3×#9911yescharacteristic
438C2×C5#480311yescharacteristic
439C2×C5D3×#10411yescharacteristic
440D5—62no—
441D5—62no—
442D5—241no—
443C23—151no—
444C23—151no—
445C23—302no—
446C23—302no—
447C23—301no—
448C23—301no—
449C23—301no—
450C23#679011yescharacteristic
451Q8—41no—
452D4—601no—
453D4—602no—
454D4—602no—
455D4—601no—
456D4—601no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—102no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—151no—
465C2×C4—151no—
466C2×C4—201no—
467C2×C4—201no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—301no—
471C2×C4—601no—
472C2×C4—601no—
473C2×C4—602no—
474C2×C4—608no—
475C2×C4—601no—
476C2×C4C2×#120011yescharacteristic
477C2×C4#679011yescharacteristic
478C8—121no—
479C8—201no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3D5×#9911yescharacteristic
483C2×C3#6509211yescharacteristic
484C2×C3D5×#10411yescharacteristic
485D3—102no—
486D3—102no—
487D3—401no—
488C5#6833411yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—152no—
492C22—152no—
493C22—304no—
494C22—304no—
495C22—301no—
496C22—301no—
497C22—301no—
498C22—301no—
499C22—601no—
500C22—601no—
501C22—601no—
502C22#9150611yescharacteristic
503C22#9151211yescharacteristic
504C22#9156111yescharacteristic
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—122no—
510C4—202no—
511C4—301no—
512C4—301no—
513C4—601no—
514C3#1059912711yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—302no—
518C2—302no—
519C2—1201no—
520C2#1174917111yescharacteristic
521C2#1174920511yescharacteristic
522C2#1174943011yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756386C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11748888C2semidirect
3. #11748509C2semidirect
4. C5×#4538C2semidirect
5. C3×#64758C2semidirect
6. #11745959C2semidirect
7. #11745958C2semidirect
9. C2×#6821C4semidirect
13. #91835C4semidirect
15. #91784C4semidirect
18. #91781C4semidirect
33. #64758D3semidirect
37. C2×C3×C5×Q8C2×C4semidirect
44. C2×D60C2×C4semidirect
57. C3×C5×C4⋊C4C2×C4semidirect
63. C4⋊Dic15C2×C4semidirect
73. #4538D5semidirect
153. C2×C5×Q8C4×D3semidirect
174. C5×C4⋊C4C4×D3semidirect
218. C2×C3×Q8C4×D5semidirect
239. C3×C4⋊C4C4×D5semidirect
378. C2×Q8#1200semidirect
402. C4⋊C4#1200semidirect
409. C3×C5#1504semidirect
488. C5#68334semidirect
514. C3#10599127semidirect

Maximal subgroups

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

subgroupindex
#117563862
#117488882
#117485092
C5×#45382
C3×#647582
#117459592
#117459582
#105991273
#683345