Finite Group Databasebeta

← #14426273

Subgroups — #14426273

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic, complemented
2C2×#91492C212yesmaximal, complemented
3#11752674C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic, complemented
5C5×#5019C211yesmaximal, characteristic, complemented
6#11749068C212yesmaximal, complemented
7#11747501C212yesmaximal, complemented
8#11747372C212yesmaximal, complemented
9#11747094C211yesmaximal, characteristic, complemented
10#11747064C211yesmaximal, characteristic, complemented
11D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10612158—31nomaximal, Hall
13C2×C3×#711C2211yescharacteristic
14C2×#6773C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16C2×#6715C2212yes—
17#91763C2211yescharacteristic
18C2×C5×#214C2212yes—
19C5×#869C2211yescharacteristic
20C3×D4×Dic5C2211yescharacteristic
21C3×C4×C22⋊D5—21no—
22C2×C3×C4×Dic5—21no—
23C3×#4038C2211yescharacteristic
24C3×#4033C2211yescharacteristic
25C3×#4027—21no—
26C3×#4023—21no—
27C3×C42×D5C2211yescharacteristic
28C3×C4×Dic10C2211yescharacteristic
29#91492—28no—
30#91450—21no—
31#91450—21no—
32#91418—21no—
33#91418—21no—
34#91375C2212yes—
35C2×#6661C2212yes—
36C2×#6658C2212yes—
37C2×D5×C3⋊C8C2212yes—
38#91093C2212yes—
39C4⋊(C3⋊#168)C2211yescharacteristic
40C5×#810C2212yes—
41C5×C4⋊(C3⋊C8)C2211yescharacteristic
42#90982C2212yes—
43#90972C2212yes—
44#90968C2212yes—
45#82525—51nomaximal, Hall
46C2×#4062—32no—
47#66059—31no—
48C4×#711D311yescharacteristic, complemented
49C5×#461—31no—
50#65454—32no—
51#65379—31no—
52#65304—31no—
53#65137—31no—
54D5×C4⋊C8—31no—
55#65093—32no—
56#65087—32no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—21no—
59C2×D60—21no—
60C2×D60—21no—
61C2×D60C2312yes—
62C2×C5×Dic6C2312yes—
63C2×C3×C22⋊D5—21no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5—21no—
66C3×#711—22no—
67C3×#711D414yescomplemented
68C2×C3×C4×D5D411yescharacteristic
69C2×C3×C4×D5D411yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×Dic10C2311yescharacteristic
72C2×#1202—22no—
73C2×#1200—22no—
74#6773—24no—
75#6773—24no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79#6715—24no—
80C2×C3⋊#168C2312yes—
81C5×#214—24no—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3—21no—
84C2×C5×C3⋊C8C2312yes—
85C3×C22⋊Dic5—21no—
86C3×#685—21no—
87C3×C4⋊Dic5C2311yescharacteristic
88C3×#683—21no—
89C3×#683—21no—
90C3×C4×Dic5—21no—
91C3×C4×Dic5—21no—
92C3×C4×Dic5—21no—
93C3×C4×Dic5D411yescharacteristic
94C3×C4×Dic5D411yescharacteristic
95C3×C4×Dic5C2311yescharacteristic
96#6667—22no—
97#6667—22no—
98#6661—24no—
99#6658—24no—
100D5×C3⋊C8—24no—
101C3×C4×#41—51no—
102C2×#950—52no—
103#5477—51no—
104#5031—51no—
105#5028—52no—
106#5027—51no—
107#5019D511yescharacteristic, complemented
108#5016—52no—
109#5015—51no—
110#5002—52no—
111C2×C4⋊(C3⋊C8)—51no—
112C2×#713—32no—
113C2×#711C2×D311yescharacteristic
114C2×C5×SD16—32no—
115C5×C4⋊Q8—31no—
116C4×C5×D4C2×D311yescharacteristic
117#4093—32no—
118C2×#689—32no—
119D4×Dic5C2×D311yescharacteristic
120C2×#686—32no—
121C4×C22⋊D5—21no—
122C2×C4×Dic5—21no—
123#4062—68no—
124C2×#677—32no—
125C2×C8×D5—32no—
126#4041—61no—
127#4041—61no—
128#4039—61no—
129#4039—61no—
130#4038C2×D311yescharacteristic
131#4033C2×D311yescharacteristic
132#4027—21no—
133#4023—21no—
134#4020—31no—
135C42×D5C2×D311yescharacteristic
136C4×Dic10C2×D311yescharacteristic
137C5×C4⋊C8—31no—
138C5×#103—32no—
139#3967—32no—
140#3953—32no—
141#3946—32no—
142#3941—32no—
143C4⋊#168—31no—
144#3035—151noSylow
145C23×C3×C5—21no—
146C22×D15—22no—
147C22×C3×D5C2×D411yescharacteristic
148C3×C5×D4—21no—
149C3×C5×D4C2×D412yes—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155D60—22no—
156D60—22no—
157D60—42no—
158D60—42no—
159C2×C5×Dic3—22no—
160C5×Dic6—22no—
161C5×Dic6—22no—
162C3×C22⋊D5—24no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—24no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—42no—
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C3×C4×D5—22no—
171C3×C4×D5—41no—
172C3×C4×D5C2×D412yes—
173C3×C4×D5#4112yes—
174C3×Dic10—21no—
175C3×Dic10C2×D412yes—
176#1202—44no—
177#1200—44no—
178C3⋊#168—22no—
179C5×C3⋊C8—22no—
180C2×C3×#41—51no—
181C2×#235—52no—
182C3×C4×Q8—51no—
183C3×C4×Q8—51no—
184C3×C4×D4—51no—
185C3×C4×D4—101no—
186C3×C4×D4—101no—
187C3×C4×D4C2×D511yescharacteristic
188C3×#117—51no—
189C3×#117—101no—
190C2×C3×C42—51no—
191C2×C3×C42—101no—
192#950—108no—
193C2×#216—52no—
194C2×#215—52no—
195C2×#214C2×D512yes—
196C2×#213—52no—
197#930—101no—
198#930—101no—
199C22×C3⋊C8—52no—
200#875—52no—
201#874—51no—
202C4×D12—101no—
203C4×D12—101no—
204#869C2×D511yescharacteristic
205#810—52no—
206#810C2×D512yes—
207#809—52no—
208#809—52no—
209C4⋊(C3⋊C8)—51no—
210C4⋊(C3⋊C8)—52no—
211C4⋊(C3⋊C8)C2×D511yescharacteristic
212C2×C5×Q8—32no—
213C2×C5×D4C22×D311yescharacteristic
214C22×C4×C5—21no—
215C2×C22⋊D5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218#713—64no—
219#713—64no—
220#711—22no—
221#711D1214yescomplemented
222C2×D20—32no—
223C2×D20—62no—
224C2×D20—61no—
225C2×D20—61no—
226C2×C4×D5—62no—
227C2×C4×D5#6711yescharacteristic
228C2×C4×D5#6711yescharacteristic
229C2×C4×D5C22×D311yescharacteristic
230C2×Dic10C22×D311yescharacteristic
231C5×SD16—64no—
232C2×C5×C8—32no—
233C5×C4⋊C4—61no—
234C5×C4⋊C4—61no—
235C5×C4⋊C4C22×D311yescharacteristic
236C5×C22⋊C4—21no—
237C42×C5C22×D311yescharacteristic
238C22⋊Dic5—21no—
239#689—64no—
240#686—64no—
241#685—21no—
242#685—62no—
243#685—62no—
244C4⋊Dic5C22×D311yescharacteristic
245#683—21no—
246#683—21no—
247C4×Dic5—21no—
248C4×Dic5—21no—
249C4×Dic5—21no—
250C4×Dic5#6711yescharacteristic
251C4×Dic5#6711yescharacteristic
252C4×Dic5C22×D311yescharacteristic
253C2×#168—32no—
254#677—64no—
255C8×D5—64no—
256C2×#135—152no—
257#532—151no—
258C4×#41—51no—
259#464—152no—
260#463—152no—
261#462—151no—
262#461—31no—
263#460—151no—
264#459—151no—
265C2×C4⋊C8—151no—
266#416—152no—
267C22×C3×C5—22no—
268C22×C3×C5—41no—
269C22×C3×C5—41no—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—42no—
272C2×D15—42no—
273C2×D15—42no—
274C2×C3×D5—21no—
275C2×C3×D5—21no—
276C2×C3×D5#12112yes—
277C3×C4×C5—21no—
278C3×C4×C5—41no—
279C3×C4×C5#13512yescomplemented
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282C3×Dic5—22no—
283C3×Dic5—21no—
284C3×Dic5—21no—
285C3×Dic5—41no—
286C3×Dic5#12112yes—
287C5×Dic3—42no—
288C3×#41—54no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×D4—101no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—101no—
298C22×C3×C4—101no—
299C2×#67—102no—
300#235—104no—
301#235—104no—
302C2×D12—52no—
303C2×D12—101no—
304C2×D12—101no—
305C2×C4×D3—102no—
306C2×Dic6C22×D512yes—
307C3×C4⋊C4—51no—
308C3×C4⋊C4—101no—
309C3×C4⋊C4—101no—
310C3×C4⋊C4C22×D511yescharacteristic
311C3×C22⋊C4—21no—
312C3×C22⋊C4—101no—
313C3×C22⋊C4—101no—
314C3×C42—51no—
315C3×C42—51no—
316C3×C42—51no—
317C3×C42—101no—
318C3×C42—101no—
319C3×C42—101no—
320C3×C42C22×D511yescharacteristic
321#216—104no—
322#215—104no—
323#214—24no—
324#213—104no—
325(C2×D3)⋊C4—102no—
326(C2×D3)⋊C4—102no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C2×C3⋊C8—52no—
330C2×C3⋊C8—104no—
331C2×C3⋊C8C22×D512yes—
332C23×C5—21no—
333C22×D5—62no—
334C22×D5C2×#6711yescharacteristic
335C5×Q8—62no—
336C5×Q8—62no—
337C5×D4—21no—
338C5×D4C2×D1212yes—
339C2×C4×C5—21no—
340C2×C4×C5—42no—
341C2×C4×C5—62no—
342C2×C4×C5C2×#6711yescharacteristic
343C2×C4×C5C2×#6711yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—24no—
346C2×Dic5—21no—
347C2×Dic5—24no—
348C2×Dic5—21no—
349C2×Dic5—42no—
350C2×Dic5C2×#6711yescharacteristic
351C2×Dic5C2×#6711yescharacteristic
352C2×Dic5C2×#6711yescharacteristic
353D20—62no—
354D20—62no—
355D20—122no—
356D20—124no—
357D20—122no—
358C4×D5—22no—
359C4×D5—41no—
360C4×D5—124no—
361C4×D5C2×D1212yes—
362C4×D5#23512yes—
363Dic10—21no—
364Dic10C2×D1212yes—
365C5×C8—62no—
366#168—62no—
367C2×#41—51no—
368C2×#41—152no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—32no—
372C2×SD16—152no—
373C2×D8—152no—
374C22×C8—152no—
375C4⋊Q8—31no—
376#127—151no—
377#124—152no—
378#121—301no—
379#121—301no—
380C4×Q8—51no—
381C4×Q8—51no—
382C4×D4—51no—
383C4×D4—101no—
384C4×D4—101no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4D3×D511yescharacteristic
388#117—51no—
389#117—101no—
390C2×C42—51no—
391C2×C42—101no—
392C4⋊C8—31no—
393C4⋊C8—152no—
394C4⋊C8—151no—
395#103—32no—
396#103—152no—
397#102—152no—
398#102—152no—
399C2×C3×C5—42no—
400C2×C3×C5C2×#12111yescharacteristic
401C2×C3×C5C2×#13511yescharacteristic
402C2×C3×C5#57511yescharacteristic
403D15—82no—
404C3×D5—22no—
405C23×C3—21no—
406C23×C3—51no—
407C22×D3—102no—
408C3×Q8—52no—
409C3×Q8—101no—
410C3×D4—21no—
411C3×D4—104no—
412C3×D4D4×D512yes—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—51no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—51no—
419C2×C3×C4—51no—
420C2×C3×C4—104no—
421C2×C3×C4—101no—
422C2×C3×C4—102no—
423C2×C3×C4—101no—
424C2×C3×C4—201no—
425C2×C3×C4—202no—
426C2×C3×C4D4×D511yescharacteristic
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4C23×D511yescharacteristic
429#67—204no—
430C2×Dic3—22no—
431D12—102no—
432D12—102no—
433D12—202no—
434D12—202no—
435C4×D3—204no—
436Dic6—22no—
437Dic6—22no—
438C3⋊C8—22no—
439C3⋊C8—102no—
440C22×C5—22no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5C22×#6711yescharacteristic
444C2×D5—21no—
445C2×D5—21no—
446C2×D5—122no—
447C2×D5—122no—
448C2×D5—122no—
449C2×D5#93012yes—
450C4×C5—21no—
451C4×C5—41no—
452C4×C5—122no—
453C4×C5#95012yescomplemented
454C4×C5C22×D1211yescharacteristic
455C4×C5C2×#23511yescharacteristic
456Dic5—22no—
457Dic5—21no—
458Dic5—21no—
459Dic5—41no—
460Dic5#93012yes—
461#41—54no—
462#41—102no—
463#41—304no—
464#41—304no—
465C2×Q8—32no—
466C2×Q8—51no—
467C2×D4—101no—
468C2×D4—152no—
469C2×D4—302no—
470C2×D4—301no—
471C2×D4—301no—
472C2×D4C2×D3×D511yescharacteristic
473C22×C4—21no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—302no—
480Q16—304no—
481SD16—64no—
482SD16—304no—
483D8—304no—
484C2×C8—32no—
485C2×C8—152no—
486C2×C8—304no—
487C4⋊C4—51no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4C2×D3×D511yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—101no—
495C22⋊C4—101no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—51no—
499C42—51no—
500C42—51no—
501C42—101no—
502C42—101no—
503C42—101no—
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—22no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—52no—
510C22×C3—101no—
511C22×C3—101no—
512C22×C3C2×D4×D511yescharacteristic
513C2×D3—202no—
514C2×D3—202no—
515C2×D3—202no—
516C3×C4—21no—
517C3×C4—41no—
518C3×C4—52no—
519C3×C4—101no—
520C3×C4—101no—
521C3×C4—102no—
522C3×C4—201no—
523C3×C4#406212yescomplemented
524C3×C4C2×D4×D511yescharacteristic
525C3×C4D5×#4111yescharacteristic
526Dic3—42no—
527C2×C5—42no—
528C2×C5C2×#93011yescharacteristic
529C2×C5C2×#95011yescharacteristic
530C2×C5#582211yescharacteristic
531D5—22no—
532D5—242no—
533C23—21no—
534C23—51no—
535C23—302no—
536Q8—52no—
537Q8—62no—
538Q8—62no—
539Q8—101no—
540D4—21no—
541D4—104no—
542D4—302no—
543D4—302no—
544D4—602no—
545D4—604no—
546D4—602no—
547D4D5×D1212yes—
548C2×C4—21no—
549C2×C4—42no—
550C2×C4—51no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—62no—
556C2×C4—104no—
557C2×C4—101no—
558C2×C4—102no—
559C2×C4—101no—
560C2×C4—201no—
561C2×C4—202no—
562C2×C4—604no—
563C2×C4D5×#6711yescharacteristic
564C2×C4D5×#6711yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—62no—
567C8—302no—
568C2×C3—42no—
569C2×C3—102no—
570C2×C3D5×#12111yescharacteristic
571C2×C3C2×#406211yescharacteristic
572C2×C3#6611111yescharacteristic
573D3—402no—
574C5#8252511yescharacteristic, complemented, Sylow
575C22—22no—
576C22—41no—
577C22—41no—
578C22—52no—
579C22—101no—
580C22—101no—
581C22—602no—
582C22—602no—
583C22—602no—
584C22C2×D5×#6711yescharacteristic
585C4—21no—
586C4—41no—
587C4—52no—
588C4—101no—
589C4—102no—
590C4—101no—
591C4—122no—
592C4—201no—
593C4#9149212yescomplemented
594C4C2×D5×D1211yescharacteristic
595C4D5×#23511yescharacteristic
596C3#1061215811yescharacteristic, complemented, Sylow
597C2—42no—
598C2—102no—
599C2—1202no—
600C2D5×#93011yescharacteristic
601C2C2×#9149211yescharacteristic
602C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×#711C2semidirect
2. C2×#91492C2semidirect
3. #11752674C2semidirect
4. #11751116C2semidirect
5. C5×#5019C2semidirect
6. #11749068C2semidirect
7. #11747501C2semidirect
8. #11747372C2semidirect
9. #11747094C2semidirect
10. #11747064C2semidirect
11. D5×C4⋊(C3⋊C8)C2semidirect
48. C4×#711D3semidirect
67. C3×#711D4semidirect
107. #5019D5semidirect
221. #711D12semidirect
279. C3×C4×C5#135semidirect
453. C4×C5#950semidirect
505. C3×C5#3035semidirect
523. C3×C4#4062semidirect
574. C5#82525semidirect
593. C4#91492semidirect
596. C3#10612158semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7112
C2×#914922
#117526742
#117511162
C5×#50192
#117490682
#117475012
#117473722
#117470942
#117470642
D5×C4⋊(C3⋊C8)2
#106121583
#825255