Finite Group Databasebeta

← #14430735

Subgroups — #14430735

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×#65856C211yesmaximal, characteristic
2C2×#91388C211yesmaximal, characteristic, complemented
3#11751096C211yesmaximal, characteristic, complemented
4C5×#4995C211yesmaximal, characteristic, complemented
5#11748431C211yesmaximal, characteristic, complemented
6#11748369C211yesmaximal, characteristic
7#11748368C211yesmaximal, characteristic
8#11747392C212yesmaximal, complemented
9#11747391C212yesmaximal, complemented
10#11747390C212yesmaximal, complemented
11#11747389C212yesmaximal, complemented
12#10610972—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×#4039C2211yescharacteristic
21C3×#4039C2211yescharacteristic
22C3×#4033C2211yescharacteristic
23C3×#4033C2211yescharacteristic
24C3×#4027—21no—
25C3×#4027—21no—
26C3×#4018—21no—
27C3×C42×D5—21no—
28C2×Dic3⋊Dic5—21no—
29C2×#6669—21no—
30#91388—21no—
31#91388—21no—
32#91388C2212yes—
33#91388C2212yes—
34#91092C2212yes—
35#91091C2212yes—
36C5×#808C2212yes—
37C5×#807C2212yes—
38#90982C2212yes—
39#90982C2212yes—
40#90971C2212yes—
41#90970C2212yes—
42#90965C2212yes—
43#90964C2212yes—
44#82509—51nomaximal, Hall
45#65856D311yescharacteristic
46C2×#4036—31no—
47C5×#428—31no—
48#65422—31no—
49#65407—31no—
50#65284—31no—
51#65255—31no—
52#65180—32no—
53#65166—32no—
54#65160—32no—
55#65146—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C22×C5×Dic3—21no—
59C2×C3×C22⋊D5—21no—
60C22×C3×Dic5D411yescharacteristic
61C22×C3×Dic5D411yescharacteristic
62C3×#709—22no—
63C3×#709Q814yes—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5—21no—
68C2×C3×Dic10C2311yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75#6710—22no—
76C2×C3⋊#168C2312yes—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C5×#208—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—21no—
82C3×#685—21no—
83C3×#683—21no—
84C3×#683—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#5232—51no—
99#5022—52no—
100#5022—52no—
101#5009—52no—
102#5009—52no—
103#4995—51no—
104#4995D511yescharacteristic, complemented
105#4924—51no—
106C2×#709C2×D311yescharacteristic
107C2×C5×M16—31no—
108C5×#117C2×D311yescharacteristic
109C2×C5×C4⋊C4—31no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—61no—
112C2×#683—61no—
113C2×C4×Dic5C2×D311yescharacteristic
114C2×#681—31no—
115#4039C2×D311yescharacteristic
116#4039C2×D311yescharacteristic
117#4036—32no—
118#4036—32no—
119#4036—61no—
120#4036—61no—
121#4033C2×D311yescharacteristic
122#4033C2×D311yescharacteristic
123#4027—21no—
124#4027—21no—
125#4018—21no—
126C42×D5—21no—
127C5×#107—32no—
128C5×#106—32no—
129#3953—32no—
130#3948—32no—
131#3946—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3939—32no—
137#3080—151noSylow
138C23×C3×C5C2×D411yescharacteristic
139C22×C3×D5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×Q812yes—
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15—42no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—42no—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—41no—
153C2×C3×Dic5—41no—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C3×D20—21no—
159C3×D20C2×Q812yes—
160C3×C4×D5—24no—
161C3×C4×D5—42no—
162C3×C4×D5—42no—
163C3×Dic10—21no—
164C3×Dic10C2×Q812yes—
165C3⋊#168—22no—
166C5×C3⋊C8—22no—
167C2×C3×#41—51no—
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—101no—
175C3×#117C2×D511yescharacteristic
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#835—52no—
190#832—52no—
191#832—52no—
192#808—52no—
193#808C2×D512yes—
194#807—52no—
195#807C2×D512yes—
196C4⋊(C3⋊C8)—52no—
197C4⋊(C3⋊C8)—52no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201C22×Dic5—61no—
202C22×Dic5#6711yescharacteristic
203C22×Dic5#6711yescharacteristic
204#709—22no—
205#709Dic614yes—
206C2×D20C22×D311yescharacteristic
207C2×C4×D5—21no—
208C2×C4×D5—21no—
209C2×C4×D5—21no—
210C2×Dic10C22×D311yescharacteristic
211C5×M16—62no—
212C2×C5×C8—32no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C42×C5—21no—
219#685—21no—
220#685—21no—
221C4⋊Dic5—32no—
222C4⋊Dic5—61no—
223C4⋊Dic5—62no—
224C4⋊Dic5—62no—
225#683—21no—
226#683—21no—
227#683—62no—
228#683—62no—
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—31no—
244#428—151no—
245#423—151no—
246#417—151no—
247#417—151no—
248C22×C3×C5—21no—
249C22×C3×C5—21no—
250C22×C3×C5C22⋊Q812yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×C3×D5—22no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C3×C4×C5—41no—
256C3×C4×C5—41no—
257C3×C4×C5C22⋊Q812yes—
258C3×C4×C5C22×Q811yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—42no—
261C3×Dic5—22no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—21no—
265C3×Dic5—21no—
266C5×Dic3—42no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C22×Dic3—21no—
279C22×Dic3—101no—
280C3×C4⋊C4—101no—
281C3×C4⋊C4—101no—
282C3×C4⋊C4C22×D511yescharacteristic
283C3×C4⋊C4C22×D511yescharacteristic
284C3×C22⋊C4—21no—
285C3×C22⋊C4—101no—
286C3×C22⋊C4—101no—
287C3×C42—21no—
288C3×C42—51no—
289C3×C42—51no—
290C3×C42—51no—
291C3×C42—51no—
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×C5C2×#6711yescharacteristic
307C22×D5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—62no—
311C2×C4×C5—122no—
312C2×C4×C5C2×Dic612yes—
313C2×C4×C5#23512yes—
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—24no—
317C2×Dic5—21no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—62no—
321C2×Dic5—122no—
322C2×Dic5C2×#6711yescharacteristic
323C2×Dic5C2×#6711yescharacteristic
324C2×Dic5C2×#6711yescharacteristic
325C2×Dic5C2×#6711yescharacteristic
326D20—21no—
327D20C2×Dic612yes—
328C4×D5—24no—
329C4×D5—42no—
330C4×D5—42no—
331Dic10—21no—
332Dic10C2×Dic612yes—
333C5×C8—62no—
334#168—62no—
335C2×#41—51no—
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—101no—
349#117D3×D511yescharacteristic
350C2×C4⋊C4—31no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—301no—
353C2×C4⋊C4—301no—
354C2×C42—51no—
355C2×C42—101no—
356#107—32no—
357#107—152no—
358#106—32no—
359#106—152no—
360C4⋊C8—152no—
361C4⋊C8—152no—
362#103—152no—
363#103—152no—
364#102—152no—
365#102—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C22⋊Q811yescharacteristic
368C2×C3×C5#57511yescharacteristic
369C2×C3×C5#57511yescharacteristic
370C3×D5—42no—
371C23×C3—101no—
372C23×C3D4×D511yescharacteristic
373C3×Q8—52no—
374C3×Q8—101no—
375C3×D4—52no—
376C3×D4—104no—
377C3×D4—101no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—51no—
381C2×C3×C4—51no—
382C2×C3×C4—51no—
383C2×C3×C4—51no—
384C2×C3×C4—101no—
385C2×C3×C4—104no—
386C2×C3×C4—202no—
387C2×C3×C4—202no—
388C2×C3×C4—201no—
389C2×C3×C4—201no—
390C2×C3×C4#70912yes—
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4Q8×D512yes—
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#92412yes—
403C22×C5C22×#6711yescharacteristic
404C2×D5—22no—
405C2×D5—41no—
406C2×D5—41no—
407C4×C5—41no—
408C4×C5—41no—
409C4×C5—122no—
410C4×C5#92412yes—
411C4×C5C22×Dic611yescharacteristic
412C4×C5C2×#23511yescharacteristic
413Dic5—22no—
414Dic5—21no—
415Dic5—21no—
416Dic5—21no—
417Dic5—21no—
418Dic5—122no—
419#41—54no—
420#41—102no—
421C2×Q8—51no—
422C2×D4—51no—
423C2×D4—101no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—61no—
427C22×C4—101no—
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—61no—
438C4⋊C4—101no—
439C4⋊C4—101no—
440C4⋊C4—152no—
441C4⋊C4—302no—
442C4⋊C4—302no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D511yescharacteristic
447C4⋊C4C2×D3×D511yescharacteristic
448C22⋊C4—21no—
449C22⋊C4—101no—
450C22⋊C4—101no—
451C42—21no—
452C42—51no—
453C42—51no—
454C42—51no—
455C42—51no—
456C42—101no—
457C42—101no—
458C3×C5#308011yescharacteristic, complemented, Hall
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—102no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3#404212yes—
465C22×C3C2×D4×D511yescharacteristic
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—102no—
469C3×C4—101no—
470C3×C4—101no—
471C3×C4—101no—
472C3×C4—101no—
473C3×C4#404212yes—
474C3×C4C2×#70911yescharacteristic
475C3×C4C2×Q8×D511yescharacteristic
476Dic3—42no—
477Dic3—202no—
478C2×C5—22no—
479C2×C5C2×#92411yescharacteristic
480C2×C5#582211yescharacteristic
481C2×C5#582211yescharacteristic
482D5—42no—
483C23—101no—
484C23D5×#6711yescharacteristic
485Q8—52no—
486Q8—101no—
487D4—52no—
488D4—104no—
489D4—101no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—51no—
495C2×C4—51no—
496C2×C4—62no—
497C2×C4—101no—
498C2×C4—104no—
499C2×C4—122no—
500C2×C4—202no—
501C2×C4—202no—
502C2×C4—201no—
503C2×C4—201no—
504C2×C4—302no—
505C2×C4—602no—
506C2×C4D5×Dic612yes—
507C2×C4#677112yes—
508C2×C4D5×#6711yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—302no—
512C2×C3—22no—
513C2×C3—202no—
514C2×C3C2×#404211yescharacteristic
515C2×C3#6610711yescharacteristic
516C2×C3#6611111yescharacteristic
517C5#8250911yescharacteristic, complemented, Sylow
518C22—21no—
519C22—21no—
520C22—102no—
521C22—201no—
522C22—201no—
523C22#9134912yes—
524C22C2×D5×#6711yescharacteristic
525C4—41no—
526C4—41no—
527C4—101no—
528C4—101no—
529C4—101no—
530C4—101no—
531C4—102no—
532C4—122no—
533C4—602no—
534C4#9134912yes—
535C4C2×D5×Dic611yescharacteristic
536C4C2×#677111yescharacteristic
537C3#1061097211yescharacteristic, complemented, Sylow
538C2—22no—
539C2—202no—
540C2C2×#9134911yescharacteristic
541C2#1175534311yescharacteristic
542C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#91388C2semidirect
3. #11751096C2semidirect
4. C5×#4995C2semidirect
5. #11748431C2semidirect
8. #11747392C2semidirect
9. #11747391C2semidirect
10. #11747390C2semidirect
11. #11747389C2semidirect
104. #4995D5semidirect
458. C3×C5#3080semidirect
517. C5#82509semidirect
537. C3#10610972semidirect

Maximal subgroups

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

subgroupindex
C3×#658562
C2×#913882
#117510962
C5×#49952
#117484312
#117483692
#117483682
#117473922
#117473912
#117473902
#117473892
#106109723
#825095