Finite Group Databasebeta

← #14430212

Subgroups — #14430212

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756487C211yesmaximal, characteristic, complemented
2C4×#6821C211yesmaximal, characteristic
3C3×C5×#475C211yesmaximal, characteristic, complemented
4#11751188C211yesmaximal, characteristic, complemented
5#11751122C211yesmaximal, characteristic, complemented
6#11750972C212yesmaximal, complemented
7#11750961C212yesmaximal, complemented
8#11750943C211yesmaximal, characteristic, complemented
9D15×C4⋊C8C211yesmaximal, characteristic, complemented
10#11750905C212yesmaximal
11#11750900C212yesmaximal, complemented
12#10612741—31nomaximal, Hall
13C2×#6821C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×Q8C2211yescharacteristic
16#91835—21no—
17Q8×Dic15—21no—
18Q8×Dic15C2211yescharacteristic
19C2×C8×D15C2212yes—
20#91786—21no—
21#91782—21no—
22#91782C2211yescharacteristic
23#91781—21no—
24#91781C2211yescharacteristic
25#91781C2212yes—
26#91779C2212yes—
27#91776—21no—
28C4×D60—21no—
29C4×D60C2211yescharacteristic
30C42×D15—21no—
31C42×D15C2211yescharacteristic
32#91758C2211yescharacteristic
33C3×C5×#106C2212yes—
34C3×C5×C4⋊C8C2211yescharacteristic
35C3×C5×#103C2212yes—
36#91119C2212yes—
37#91105C2212yes—
38#91101C2212yes—
39#91098C2212yes—
40#91093C2212yes—
41#91091C2212yes—
42#91091C2212yes—
43C4⋊(C3⋊#168)C2211yescharacteristic
44#81010—51nomaximal, Hall
45#66062—31no—
46C4×#713—31no—
47C5×#475D311yescharacteristic, complemented
48#65376—31no—
49#65310—31no—
50#65160—32no—
51#65149—32no—
52#65131—31no—
53D5×C4⋊C8—31no—
54#65093—32no—
55#65088—32no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8C2311yescharacteristic
58#6821—22no—
59#6821Q814yescomplemented
60C2×D60—21no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×C4×D15—21no—
64C2×C4×D15—21no—
65C2×C4×D15D411yescharacteristic
66C2×C4×D15D411yescharacteristic
67C2×C4×D15C2311yescharacteristic
68C2×Dic30—21no—
69C2×C3×C5×C8C2312yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C42×C5—21no—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—22no—
78#6714—21no—
79#6714—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15—22no—
83C4⋊Dic15C2312yes—
84C4⋊Dic15C2311yescharacteristic
85#6712—22no—
86C4×Dic15—21no—
87C4×Dic15—21no—
88C4×Dic15—22no—
89C4×Dic15D411yescharacteristic
90C4×Dic15D411yescharacteristic
91C4×Dic15C2311yescharacteristic
92C2×C3⋊#168C2312yes—
93C8×D15—24no—
94#5728—51no—
95C4×#239—51no—
96C3×#475D511yescharacteristic, complemented
97#5087—51no—
98#5021—51no—
99#4871—52no—
100#4860—52no—
101#4842—51no—
102D3×C4⋊C8—51no—
103#4804—52no—
104#4799—52no—
105C2×#713—31no—
106C5×C4⋊Q8C2×D311yescharacteristic
107C4×C5×Q8C2×D311yescharacteristic
108#4092—61no—
109Q8×Dic5—31no—
110Q8×Dic5—61no—
111C2×C8×D5—32no—
112#4043—61no—
113#4039—31no—
114#4039—61no—
115#4038—32no—
116#4038—31no—
117#4038—61no—
118#4036—32no—
119#4033—61no—
120C4×D20—31no—
121C4×D20—61no—
122C42×D5—31no—
123C42×D5—61no—
124#4015—31no—
125C5×#106C2×D312yes—
126C5×C4⋊C8C2×D311yescharacteristic
127C5×#103C2×D312yes—
128#3967—32no—
129#3953—32no—
130#3949—32no—
131#3946—32no—
132#3941—32no—
133#3939—32no—
134#3939—32no—
135C4⋊#168—31no—
136#3076—151noSylow
137C22×D15—21no—
138C22×D15C2×D411yescharacteristic
139C3×C5×Q8—21no—
140C3×C5×Q8—42no—
141C3×C5×Q8C2×Q812yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15—22no—
150C2×Dic15C2×D411yescharacteristic
151C2×Dic15C2×D411yescharacteristic
152C2×Dic15C2×D411yescharacteristic
153D60—24no—
154D60—21no—
155D60C2×Q812yes—
156C4×D15—22no—
157C4×D15—24no—
158C4×D15—41no—
159C4×D15—42no—
160C4×D15—42no—
161C4×D15C2×Q812yes—
162C4×D15#4112yes—
163Dic30—42no—
164C3×C5×C8—22no—
165C3⋊#168—22no—
166C2×#239—51no—
167C3×C4⋊Q8C2×D511yescharacteristic
168C3×C4×Q8C2×D511yescharacteristic
169#946—101no—
170Q8×Dic3—51no—
171Q8×Dic3—101no—
172C2×D3×C8—52no—
173#897—101no—
174#893—51no—
175#893—101no—
176#892—52no—
177#892—51no—
178#892—101no—
179#890—52no—
180#887—101no—
181C4×D12—51no—
182C4×D12—101no—
183C42×D3—51no—
184C42×D3—101no—
185#869—51no—
186C3×#106C2×D512yes—
187C3×C4⋊C8C2×D511yescharacteristic
188C3×#103C2×D512yes—
189#835—52no—
190#821—52no—
191#817—52no—
192Dic3⋊C8—52no—
193#809—52no—
194#807—52no—
195#807—52no—
196C4⋊(C3⋊C8)—51no—
197C2×C5×Q8—21no—
198C2×C5×Q8C22×D311yescharacteristic
199#713—34no—
200#713—62no—
201C2×D20—31no—
202C2×D20—61no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×Dic10—61no—
210C2×C5×C8C22×D312yes—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C4⋊C4C22×D312yes—
215C42×C5—21no—
216C42×C5C22×D311yescharacteristic
217#685—61no—
218#685—61no—
219#685—62no—
220#685—61no—
221C4⋊Dic5—31no—
222C4⋊Dic5—32no—
223C4⋊Dic5—61no—
224C4⋊Dic5—62no—
225C4⋊Dic5—61no—
226#683—62no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—31no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C4×Dic5—62no—
233C2×#168—32no—
234C8×D5—64no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475D1511yescharacteristic, complemented
242#474—151no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—21no—
248C2×D15—21no—
249C2×D15—22no—
250C2×D15—41no—
251C2×D15—41no—
252C2×D15C22⋊Q812yes—
253C3×C4×C5—22no—
254C3×C4×C5—21no—
255C3×C4×C5—42no—
256C3×C4×C5—41no—
257C3×C4×C5#13512yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—21no—
261Dic15—21no—
262Dic15—41no—
263Dic15—42no—
264Dic15C22⋊Q812yes—
265C2×C3×Q8—21no—
266C2×C3×Q8C22×D511yescharacteristic
267#239—54no—
268#239—102no—
269C2×D12—51no—
270C2×D12—101no—
271C2×C4×D3—51no—
272C2×C4×D3—51no—
273C2×C4×D3—51no—
274C2×C4×D3—101no—
275C2×C4×D3—101no—
276C2×C4×D3—101no—
277C2×Dic6—101no—
278C2×C3×C8C22×D512yes—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C4⋊C4C22×D512yes—
283C3×C42—21no—
284C3×C42C22×D511yescharacteristic
285(C2×D3)⋊C4—101no—
286(C2×D3)⋊C4—101no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—101no—
289C4⋊Dic3—51no—
290C4⋊Dic3—52no—
291C4⋊Dic3—101no—
292C4⋊Dic3—102no—
293C4⋊Dic3—101no—
294Dic3⋊C4—102no—
295C4×Dic3—51no—
296C4×Dic3—51no—
297C4×Dic3—51no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C4×Dic3—102no—
301C2×C3⋊C8—52no—
302D3×C8—104no—
303C22×D5—31no—
304C22×D5—61no—
305C5×Q8—21no—
306C5×Q8—42no—
307C5×Q8D3×Q812yes—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C2×Dic5—31no—
315C2×Dic5—31no—
316C2×Dic5—31no—
317C2×Dic5—61no—
318C2×Dic5—62no—
319D20—32no—
320D20—64no—
321D20—61no—
322C4×D5—32no—
323C4×D5—32no—
324C4×D5—64no—
325C4×D5—62no—
326C4×D5—121no—
327C4×D5—122no—
328C4×D5—122no—
329Dic10—122no—
330C5×C8—22no—
331#168—62no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—151no—
335C4⋊Q8C2×D1511yescharacteristic
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—151no—
340C4×Q8—301no—
341C4×Q8—301no—
342C4×Q8C2×D1511yescharacteristic
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—151no—
348#117—152no—
349#117—301no—
350C2×C42—151no—
351C2×C42—301no—
352#107—152no—
353#107—152no—
354#106—152no—
355#106C2×D1512yes—
356C4⋊C8—152no—
357C4⋊C8—151no—
358C4⋊C8C2×D1511yescharacteristic
359#103—152no—
360#103C2×D1512yes—
361#102—152no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366D15—22no—
367D15—42no—
368C22×D3—51no—
369C22×D3—101no—
370C3×Q8—21no—
371C3×Q8—42no—
372C3×Q8Q8×D512yes—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—51no—
380C2×Dic3—51no—
381C2×Dic3—51no—
382C2×Dic3—101no—
383C2×Dic3—102no—
384D12—52no—
385D12—104no—
386D12—101no—
387C4×D3—52no—
388C4×D3—52no—
389C4×D3—104no—
390C4×D3—102no—
391C4×D3—201no—
392C4×D3—202no—
393C4×D3—202no—
394Dic6—202no—
395C3×C8—22no—
396C3⋊C8—102no—
397C22×C5C2×D3×D411yescharacteristic
398C2×D5—32no—
399C2×D5—61no—
400C2×D5—61no—
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C4×C5—21no—
405C4×C5—22no—
406C4×C5—42no—
407C4×C5—41no—
408C4×C5#91612yes—
409C4×C5C2×D3×Q811yescharacteristic
410C4×C5D3×#4111yescharacteristic
411Dic5—32no—
412Dic5—61no—
413Dic5—61no—
414Dic5—121no—
415Dic5—122no—
416#41—154no—
417#41—302no—
418C2×Q8—21no—
419C2×Q8—301no—
420C2×Q8C22×D1511yescharacteristic
421C2×D4—151no—
422C2×D4—301no—
423C22×C4—151no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—301no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—152no—
430C2×C8—304no—
431C2×C8C22×D1512yes—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—152no—
435C4⋊C4—151no—
436C4⋊C4—301no—
437C4⋊C4—302no—
438C4⋊C4—302no—
439C4⋊C4—301no—
440C4⋊C4C22×D1512yes—
441C4⋊C4C22×D1511yescharacteristic
442C22⋊C4—301no—
443C22⋊C4—301no—
444C22⋊C4—302no—
445C22⋊C4—301no—
446C42—21no—
447C42—151no—
448C42—151no—
449C42—151no—
450C42—301no—
451C42—301no—
452C42—302no—
453C42C22×D1511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—52no—
457C2×D3—101no—
458C2×D3—101no—
459C2×D3—102no—
460C2×D3—201no—
461C2×D3—201no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—42no—
465C3×C4—41no—
466C3×C4#406212yes—
467C3×C4C2×Q8×D511yescharacteristic
468C3×C4D5×#4111yescharacteristic
469Dic3—52no—
470Dic3—101no—
471Dic3—101no—
472Dic3—201no—
473Dic3—202no—
474C2×C5D3×C22⋊Q811yescharacteristic
475C2×C5C2×#91611yescharacteristic
476C2×C5#577711yescharacteristic
477D5—62no—
478D5—122no—
479C23—151no—
480C23—301no—
481Q8—21no—
482Q8—42no—
483Q8—602no—
484Q8Q8×D1512yes—
485D4—152no—
486D4—304no—
487D4—301no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—151no—
492C2×C4—152no—
493C2×C4—152no—
494C2×C4—151no—
495C2×C4—151no—
496C2×C4—304no—
497C2×C4—302no—
498C2×C4—301no—
499C2×C4—302no—
500C2×C4—601no—
501C2×C4—602no—
502C2×C4—602no—
503C2×C4D4×D1511yescharacteristic
504C2×C4D4×D1511yescharacteristic
505C2×C4C23×D1511yescharacteristic
506C8—22no—
507C8—302no—
508C2×C3D5×C22⋊Q811yescharacteristic
509C2×C3C2×#406211yescharacteristic
510C2×C3#6611111yescharacteristic
511D3—102no—
512D3—202no—
513C5#8101011yescharacteristic, complemented, Sylow
514C22—152no—
515C22—301no—
516C22—301no—
517C22—302no—
518C22—601no—
519C22—601no—
520C22C2×D4×D1511yescharacteristic
521C4—22no—
522C4—21no—
523C4—42no—
524C4—41no—
525C4—152no—
526C4—301no—
527C4—301no—
528C4—601no—
529C4—602no—
530C4#9180512yes—
531C4C2×Q8×D1511yescharacteristic
532C4#41×D1511yescharacteristic
533C3#1061274111yescharacteristic, complemented, Sylow
534C2—302no—
535C2—602no—
536C2D15×C22⋊Q811yescharacteristic
537C2C2×#9180511yescharacteristic
538C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#475C2
socleC22×C3×C5C22×D4
prime radicalC2×#6821C22
hypercenter#475D15
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #11756487C2semidirect
3. C3×C5×#475C2semidirect
4. #11751188C2semidirect
5. #11751122C2semidirect
6. #11750972C2semidirect
7. #11750961C2semidirect
8. #11750943C2semidirect
9. D15×C4⋊C8C2semidirect
11. #11750900C2semidirect
47. C5×#475D3semidirect
59. #6821Q8semidirect
96. C3×#475D5semidirect
241. #475D15semidirect
454. C3×C5#3076semidirect
513. C5#81010semidirect
533. C3#10612741semidirect

Maximal subgroups

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

subgroupindex
#117564872
C4×#68212
C3×C5×#4752
#117511882
#117511222
#117509722
#117509612
#117509432
D15×C4⋊C82
#117509052
#117509002
#106127413
#810105