Finite Group Databasebeta

← #14430726

Subgroups — #14430726

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×Dic5C211yesmaximal, characteristic
2C2×#91388C211yesmaximal, characteristic, complemented
3#11751333C211yesmaximal, characteristic
4C5×#5232C211yesmaximal, characteristic
5#11749332C212yesmaximal, complemented
6#11749329C212yesmaximal, complemented
7#11749086C212yesmaximal, complemented
8#11749083C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10#11748455C211yesmaximal, characteristic, complemented
11#11748431C211yesmaximal, characteristic, complemented
12#10610602—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×Q8×Dic5C2211yescharacteristic
19C3×Q8×Dic5C2211yescharacteristic
20C3×D4×Dic5—21no—
21C3×D4×Dic5—21no—
22C3×D4×Dic5C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic
24C3×#4072—21no—
25C3×#4072C2211yescharacteristic
26C2×C3×C4×Dic5—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5—21no—
29C2×#6669—21no—
30#91388—21no—
31#91388—21no—
32#91388C2212yes—
33#91388C2212yes—
34#91119C2212yes—
35#91116C2212yes—
36C5×#835C2212yes—
37C5×#832C2212yes—
38#90990C2212yes—
39#90989C2212yes—
40#90987C2212yes—
41#90986C2212yes—
42#90982C2212yes—
43#90982C2212yes—
44#82509—51nomaximal, Hall
45#41×Dic5D311yescharacteristic
46C2×#4036—31no—
47C5×#417—31no—
48#65521—31no—
49#65410—31no—
50#65407—31no—
51#65253—31no—
52#65088—32no—
53#65085—32no—
54#65055—32no—
55#65052—32no—
56C3×C5×#41—22no—
57C3×C5×#41Q814yes—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C22×C5×Dic3—21no—
65C22×C3×Dic5—21no—
66C22×C3×Dic5—21no—
67C22×C3×Dic5D411yescharacteristic
68C22×C3×Dic5D411yescharacteristic
69C4⋊Dic15—21no—
70C4⋊Dic15C2312yes—
71#6710—22no—
72C2×C3⋊#168C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3C2312yes—
75C5×#208—22no—
76C2×C5×C3⋊C8C2312yes—
77C3×C22⋊Dic5—21no—
78C3×C22⋊Dic5—21no—
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4×Dic5—21no—
85C3×C4×Dic5—21no—
86C3×C4×Dic5—21no—
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90C3×C4×Dic5C2311yescharacteristic
91Dic3⋊Dic5—22no—
92Dic3⋊Dic5—22no—
93#6669—22no—
94#6669—22no—
95C3×C4×#41—51no—
96C2×#870—51no—
97#5232—51no—
98#5232D511yescharacteristic
99#5022—52no—
100#5022—52no—
101#5009—52no—
102#5009—52no—
103#4995—51no—
104#4995—51no—
105#4924—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×C5×M16—31no—
108C2×C5×C4⋊C4—31no—
109Q8×Dic5C2×D311yescharacteristic
110Q8×Dic5C2×D311yescharacteristic
111D4×Dic5—21no—
112D4×Dic5—21no—
113D4×Dic5C2×D311yescharacteristic
114D4×Dic5C2×D311yescharacteristic
115#4072—21no—
116#4072C2×D311yescharacteristic
117C2×C4⋊Dic5—31no—
118C2×C4⋊Dic5—61no—
119C2×#683—61no—
120C2×C4×Dic5—21no—
121C2×C4×Dic5C2×D311yescharacteristic
122C2×#681—31no—
123#4036—32no—
124#4036—32no—
125#4036—61no—
126#4036—61no—
127C5×#103—32no—
128C5×#102—32no—
129#3967—32no—
130#3964—32no—
131#3950—32no—
132#3949—32no—
133#3946—32no—
134#3946—32no—
135#3940—32no—
136#3939—32no—
137#3080—151noSylow
138C23×C3×C5—21no—
139C23×C3×C5C2×D411yescharacteristic
140C3×C5×Q8—21no—
141C3×C5×Q8C2×Q812yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C2×Q812yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×Q812yes—
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—22no—
152C2×Dic15—42no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—42no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—41no—
158C2×C3×Dic5—41no—
159C2×C3×Dic5—42no—
160C2×C3×Dic5—42no—
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163C2×C3×Dic5C2×D411yescharacteristic
164C2×C3×Dic5C2×D411yescharacteristic
165C3⋊#168—22no—
166C5×C3⋊C8—22no—
167C2×C3×#41C2×D511yescharacteristic
168C3×C4×Q8—51no—
169C3×C4×Q8—51no—
170C3×C4×D4—51no—
171C3×C4×D4—51no—
172C3×C4×D4—101no—
173C3×C4×D4—101no—
174C3×#117—51no—
175C3×#117—101no—
176C2×C3×C42—51no—
177C2×C3×C42—101no—
178C2×C4⋊Dic3—51no—
179C2×C4⋊Dic3C2×D511yescharacteristic
180C2×Dic3⋊C4—101no—
181C2×Dic3⋊C4—101no—
182C2×#208—51no—
183C2×#208C2×D511yescharacteristic
184#870—52no—
185#870—52no—
186#870—101no—
187#870—101no—
188#835—52no—
189#835C2×D512yes—
190#832—52no—
191#832C2×D512yes—
192#808—52no—
193#808—52no—
194#807—52no—
195#807—52no—
196C4⋊(C3⋊C8)—52no—
197C4⋊(C3⋊C8)—52no—
198C5×#41—22no—
199C5×#41Dic614yes—
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—61no—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—61no—
209C22×Dic5#6711yescharacteristic
210C22×Dic5#6711yescharacteristic
211C5×M16—62no—
212C2×C5×C8—32no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215C22⋊Dic5—21no—
216C22⋊Dic5—21no—
217C22⋊Dic5—21no—
218C4⋊Dic5—21no—
219C4⋊Dic5—21no—
220C4⋊Dic5—32no—
221C4⋊Dic5—61no—
222C4⋊Dic5—62no—
223C4⋊Dic5—62no—
224C4⋊Dic5C22×D311yescharacteristic
225C4⋊Dic5C22×D311yescharacteristic
226#683—62no—
227#683—62no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5—21no—
231C4×Dic5#6711yescharacteristic
232C4×Dic5#6711yescharacteristic
233C4×Dic5C22×D311yescharacteristic
234C4×Dic5C22×D311yescharacteristic
235#681—62no—
236C2×#168—32no—
237C2×#125—151no—
238C4×#41—51no—
239#479—152no—
240#479—152no—
241#478—152no—
242#478—152no—
243#428—151no—
244#428—151no—
245#423—151no—
246#417—31no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5—22no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5C22⋊Q812yes—
254C22×C3×C5C22×D411yescharacteristic
255C3×C4×C5—22no—
256C3×C4×C5C22⋊Q812yes—
257C3×C4×C5C22×Q811yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—42no—
260C3×Dic5—21no—
261C3×Dic5—21no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—41no—
265C3×Dic5—41no—
266C5×Dic3—42no—
267C3×#41—22no—
268C3×#41Dic1014yes—
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4C22×D511yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4—51no—
274C22×C3×C4—51no—
275C22×C3×C4—101no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C22×Dic3—21no—
279C22×Dic3—101no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4—51no—
282C3×C4⋊C4—101no—
283C3×C4⋊C4—101no—
284C3×C22⋊C4—101no—
285C3×C22⋊C4—101no—
286C3×C22⋊C4—101no—
287C3×C42—51no—
288C3×C42—51no—
289C3×C42—51no—
290C3×C42—51no—
291C3×C42—101no—
292C3×C42—101no—
293C3×C42—101no—
294C4⋊Dic3—21no—
295C4⋊Dic3—52no—
296C4⋊Dic3—101no—
297C4⋊Dic3C22×D512yes—
298Dic3⋊C4—102no—
299Dic3⋊C4—102no—
300Dic3⋊C4—102no—
301Dic3⋊C4—102no—
302#208—22no—
303#208—102no—
304C2×C3⋊C8—52no—
305C2×C3⋊C8C22×D512yes—
306C23×C5—21no—
307C23×C5C2×#6711yescharacteristic
308C5×Q8—21no—
309C5×Q8C2×Dic612yes—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4C2×Dic612yes—
313C2×C4×C5—21no—
314C2×C4×C5—24no—
315C2×C4×C5—62no—
316C2×C4×C5—122no—
317C2×C4×C5C2×Dic612yes—
318C2×C4×C5#23512yes—
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—42no—
326C2×Dic5—42no—
327C2×Dic5—62no—
328C2×Dic5—122no—
329C2×Dic5C2×#6711yescharacteristic
330C2×Dic5C2×#6711yescharacteristic
331C2×Dic5C2×#6711yescharacteristic
332C2×Dic5C2×#6711yescharacteristic
333C5×C8—62no—
334#168—62no—
335C2×#41D3×D511yescharacteristic
336C2×M16—31no—
337C2×M16—151no—
338#125—152no—
339#125—152no—
340#125—301no—
341#125—301no—
342C4×Q8—51no—
343C4×Q8—51no—
344C4×D4—51no—
345C4×D4—51no—
346C4×D4—101no—
347C4×D4—101no—
348#117—51no—
349#117—101no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—51no—
355C2×C42—101no—
356#107—152no—
357#107—152no—
358#106—152no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—32no—
363#103—152no—
364#102—32no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C22⋊Q811yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C2×C3×C5#57511yescharacteristic
371C23×C3—21no—
372C23×C3D4×D511yescharacteristic
373C3×Q8—21no—
374C3×Q8C2×Dic1012yes—
375C3×D4—24no—
376C3×D4—21no—
377C3×D4C2×Dic1012yes—
378C2×C3×C4—21no—
379C2×C3×C4—24no—
380C2×C3×C4—51no—
381C2×C3×C4—51no—
382C2×C3×C4—51no—
383C2×C3×C4—51no—
384C2×C3×C4—101no—
385C2×C3×C4—101no—
386C2×C3×C4—201no—
387C2×C3×C4—201no—
388C2×C3×C4—202no—
389C2×C3×C4—202no—
390C2×C3×C4C2×Dic1012yes—
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4#71112yes—
393C2×C3×C4C23×D511yescharacteristic
394C2×Dic3—22no—
395C2×Dic3—42no—
396C2×Dic3—102no—
397C2×Dic3—202no—
398C3⋊C8—22no—
399C3⋊C8—102no—
400C22×C5—21no—
401C22×C5—21no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5#92412yes—
406C22×C5C22×#6711yescharacteristic
407C4×C5—22no—
408C4×C5—122no—
409C4×C5#92412yes—
410C4×C5C22×Dic611yescharacteristic
411C4×C5C2×#23511yescharacteristic
412Dic5—21no—
413Dic5—21no—
414Dic5—21no—
415Dic5—21no—
416Dic5—41no—
417Dic5—41no—
418Dic5—122no—
419#41—22no—
420#41#120414yes—
421C2×Q8C2×D3×D511yescharacteristic
422C2×D4—21no—
423C2×D4C2×D3×D511yescharacteristic
424C22×C4—21no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—61no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—301no—
431C22×C4C2×D3×D511yescharacteristic
432M16—62no—
433M16—302no—
434C2×C8—32no—
435C2×C8—152no—
436C4⋊C4—32no—
437C4⋊C4—51no—
438C4⋊C4—51no—
439C4⋊C4—61no—
440C4⋊C4—101no—
441C4⋊C4—101no—
442C4⋊C4—152no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C4⋊C4—301no—
448C22⋊C4—101no—
449C22⋊C4—101no—
450C22⋊C4—101no—
451C42—51no—
452C42—51no—
453C42—51no—
454C42—51no—
455C42—101no—
456C42—101no—
457C42—101no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3#402412yes—
465C22×C3C2×D4×D511yescharacteristic
466C3×C4—22no—
467C3×C4—101no—
468C3×C4—101no—
469C3×C4—101no—
470C3×C4—101no—
471C3×C4—201no—
472C3×C4—201no—
473C3×C4#402412yes—
474C3×C4C22×Dic1011yescharacteristic
475C3×C4C2×#71111yescharacteristic
476Dic3—42no—
477Dic3—202no—
478C2×C5—22no—
479C2×C5—42no—
480C2×C5C2×#92411yescharacteristic
481C2×C5#582211yescharacteristic
482C2×C5#582211yescharacteristic
483C23—21no—
484C23D5×#6711yescharacteristic
485Q8—21no—
486Q8C2×#120412yes—
487D4—24no—
488D4—21no—
489D4C2×#120412yes—
490C2×C4—21no—
491C2×C4—24no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—51no—
495C2×C4—51no—
496C2×C4—62no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—122no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—202no—
503C2×C4—202no—
504C2×C4—302no—
505C2×C4—602no—
506C2×C4#678212yes—
507C2×C4C2×#120412yes—
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—302no—
512C2×C3—22no—
513C2×C3—42no—
514C2×C3C2×#402411yescharacteristic
515C2×C3#6610711yescharacteristic
516C2×C3#6611111yescharacteristic
517C5#8250911yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22#9157412yes—
524C22C2×D5×#6711yescharacteristic
525C4—22no—
526C4—101no—
527C4—101no—
528C4—101no—
529C4—101no—
530C4—122no—
531C4—201no—
532C4—201no—
533C4—602no—
534C4#9157412yes—
535C4C2×#678211yescharacteristic
536C4C22×#120411yescharacteristic
537C3#1061060211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—42no—
540C2#1175534311yescharacteristic
541C2#1175534411yescharacteristic
542C2C2×#9157411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91388C2semidirect
5. #11749332C2semidirect
6. #11749329C2semidirect
7. #11749086C2semidirect
8. #11749083C2semidirect
9. #11748472C2semidirect
10. #11748455C2semidirect
11. #11748431C2semidirect
458. C3×C5#3080semidirect
517. C5#82509semidirect
537. C3#10610602semidirect

Maximal subgroups

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

subgroupindex
C3×#41×Dic52
C2×#913882
#117513332
C5×#52322
#117493322
#117493292
#117490862
#117490832
#117484722
#117484552
#117484312
#106106023
#825095