Finite Group Databasebeta

← #14430823

Subgroups — #14430823

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756304C211yesmaximal, characteristic
2#11752655C211yesmaximal, characteristic, complemented
3C5×#5007C211yesmaximal, characteristic, complemented
4C3×#65298C211yesmaximal, characteristic, complemented
5#11749116C211yesmaximal, characteristic, complemented
6#11749091C211yesmaximal, characteristic, complemented
7#11748972C211yesmaximal, characteristic
8#11748957C211yesmaximal, characteristic
9#11747456C211yesmaximal, characteristic, complemented
10#11747440C211yesmaximal, characteristic, complemented
11#11747185C211yesmaximal, characteristic, complemented
12#11747180C211yesmaximal, characteristic, complemented
13#11747001C211yesmaximal, characteristic, complemented
14#11746951C211yesmaximal, characteristic, complemented
15#11746885C211yesmaximal, characteristic, complemented
16#10612698—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19D4×Dic15C2211yescharacteristic
20C4×#1220—21no—
21C2×#6714—21no—
22#91782C2211yescharacteristic
23#91781C2211yescharacteristic
24#91770—21no—
25C22⋊C4×D15—21no—
26C4×D60C2211yescharacteristic
27#91761C2211yescharacteristic
28C5×#869C2211yescharacteristic, complemented
29C3×#4016C2211yescharacteristic, complemented
30#91470C2211yescharacteristic, complemented
31#91437C2211yescharacteristic
32#91424—21no—
33#91419—21no—
34#91384C2211yescharacteristic, complemented
35#91347C2211yescharacteristic
36#91336—21no—
37#91329—21no—
38C2×#6651C2211yescharacteristic
39C2×#6648C2211yescharacteristic
40C5×#832C2211yescharacteristic
41C5×#832C2211yescharacteristic
42C5×#807C2211yescharacteristic, complemented
43C5×#807C2211yescharacteristic, complemented
44C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
45C3×#3964C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3940C2211yescharacteristic, complemented
48C3×#3939C2211yescharacteristic, complemented
49C3×C4⋊#168C2211yescharacteristic, complemented
50#90990C2211yescharacteristic, complemented
51#90987C2211yescharacteristic, complemented
52#90985C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90983C2211yescharacteristic, complemented
55#90983C2211yescharacteristic, complemented
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic
58#90968C2211yescharacteristic
59#90968C2211yescharacteristic
60#81168—51nomaximal, Hall
61#66063—31no—
62#65879—31no—
63C5×#474—31no—
64#65373—31no—
65#65298D311yescharacteristic, complemented
66#65180—31no—
67#65179—31no—
68#65170—31no—
69#65169—31no—
70#65136—31no—
71#65128—31no—
72#65059—31no—
73D5×#102—31no—
74#65055—31no—
75#65050—31no—
76C23×D15—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×#1220—21no—
80C22×Dic15—21no—
81D4×D15—22no—
82D4×D15Q814yescomplemented
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C4×D15—21no—
86C2×C4×D15C2311yescharacteristic
87C2×C5×Dic6—21no—
88C2×#1204—21no—
89C2×#1200—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C22⋊C4—21no—
92C3×C42×C5C2311yescharacteristic
93#6719—21no—
94#6714—21no—
95#6714—21no—
96#6714—21no—
97#6714D411yescharacteristic
98#6714D411yescharacteristic
99C4⋊Dic15C2311yescharacteristic
100#6712D411yescharacteristic
101#6712D411yescharacteristic
102C4×Dic15—21no—
103C4×Dic15C2311yescharacteristic
104C5×C4⋊Dic3—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C5×C4⋊Dic3C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C2×C5×C3⋊C8C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×#683—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6669—21no—
118#6668—21no—
119#6667—21no—
120Dic3×Dic5—21no—
121#6651—22no—
122#6648—22no—
123#5689—51no—
124#5545—51no—
125C3×#478—51no—
126#5066—51no—
127#5007D511yescharacteristic, complemented
128#4890—51no—
129#4881—51no—
130#4871—51no—
131#4860—51no—
132#4842—51no—
133#4839—51no—
134#4770—51no—
135D3×#102—51no—
136#4763—51no—
137#4761—51no—
138C2×D4×D5—31no—
139C5×C4⋊Q8—31no—
140C4×C5×D4C2×D311yescharacteristic
141#4092—61no—
142#4090—61no—
143D4×Dic5—31no—
144C4×C22⋊D5—61no—
145C2×#685—61no—
146C2×#676—31no—
147C2×C8×D5—31no—
148#4042—61no—
149#4039—31no—
150#4038—31no—
151#4038—31no—
152D5×C4⋊C4—31no—
153#4036—31no—
154#4035—61no—
155#4034—31no—
156#4027—61no—
157D5×C22⋊C4—61no—
158C4×D20—31no—
159#4018—31no—
160#4016C2×D311yescharacteristic, complemented
161C5×#107—31no—
162C5×#107—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102—31no—
166#3964C2×D311yescharacteristic
167#3964C2×D311yescharacteristic
168#3953—31no—
169#3953—31no—
170#3950—31no—
171#3949—31no—
172#3946—31no—
173#3946—31no—
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3940—31no—
178#3940C2×D311yescharacteristic, complemented
179#3939C2×D311yescharacteristic, complemented
180C4⋊#168C2×D311yescharacteristic, complemented
181#3081—151noSylow
182C23×C3×C5—21no—
183C22×D15—21no—
184C22×D15—24no—
185C22×D15—81no—
186C22×D15—81no—
187C22×D15C2×D411yescharacteristic
188C3×C5×D4—21no—
189C3×C5×D4C2×Q812yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—81no—
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2×D411yescharacteristic
194C2×C3×C4×C5C2411yescharacteristic
195#1220—24no—
196C2×Dic15—21no—
197C2×Dic15—81no—
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200C2×Dic15C2×D411yescharacteristic
201D60—21no—
202D60C2×Q812yes—
203C4×D15—81no—
204C4×D15—81no—
205C4×D15C2×Q812yes—
206C4×D15#4112yes—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C5×Dic6—81no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212#1204—81no—
213#1200—81no—
214C3×#168—21no—
215C3×#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×D3×D4—51no—
219C3×#125—51no—
220C3×C4×D4C2×D511yescharacteristic
221D4×Dic3—51no—
222C4×#67—101no—
223C2×(C2×D3)⋊C4—101no—
224C2×ΓL(1,𝔽25)—51no—
225C2×D3×C8—51no—
226#897—101no—
227#896—101no—
228#893—51no—
229#892—51no—
230#892—51no—
231D3×C4⋊C4—51no—
232#890—51no—
233#889—101no—
234#888—51no—
235#888—101no—
236#67⋊C4—101no—
237D3×C22⋊C4—101no—
238C4×D12—51no—
239#872—51no—
240#869C2×D511yescharacteristic, complemented
241C3×#107—51no—
242C3×#106—51no—
243C3×C4⋊C8—51no—
244C3×#102—51no—
245C3×#102—51no—
246#832C2×D511yescharacteristic
247#832C2×D511yescharacteristic
248#821—51no—
249#821—51no—
250#817—51no—
251#817—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254#809—51no—
255#809—51no—
256#808—51no—
257#807—51no—
258#807C2×D511yescharacteristic, complemented
259#807C2×D511yescharacteristic, complemented
260C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
261C23×D5—61no—
262C2×C5×Q8—61no—
263C2×C5×D4C22×D311yescharacteristic
264C22×C4×C5—21no—
265C2×C22⋊D5—61no—
266C22×Dic5—61no—
267D4×D5—34no—
268D4×D5—62no—
269C2×D20—31no—
270C2×C4×D5—31no—
271C2×C4×D5—61no—
272C2×C4×D5—61no—
273C2×C4×D5—61no—
274C2×Dic10—61no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4C22×D311yescharacteristic
281C5×C22⋊C4—21no—
282C42×C5C22×D311yescharacteristic
283C22⋊Dic5—61no—
284#685—31no—
285#685—31no—
286#685—61no—
287#685—61no—
288#685—61no—
289#685—61no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—21no—
296#683—31no—
297#683—31no—
298#683—61no—
299#683—61no—
300#683—61no—
301C4×Dic5—31no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C2×#168C22×D311yescharacteristic
305C2×#168C22×D311yescharacteristic
306#676—62no—
307C8×D5—62no—
308#544—151no—
309#518—151no—
310#478—51no—
311#478—151no—
312#478—151no—
313#478—151no—
314#476—151no—
315#476—151no—
316#474—31no—
317#474—151no—
318#428—151no—
319#427—151no—
320#424—151no—
321#418—151no—
322C2×#102—151no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5C22×D411yescharacteristic
327C2×D15—21no—
328C2×D15—21no—
329C2×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C2×D15—84no—
333C2×D15C22⋊Q812yes—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—41no—
337C3×C4×C5C22×Q811yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339Dic15—21no—
340Dic15—21no—
341Dic15—41no—
342Dic15C22⋊Q812yes—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C5×Dic3—41no—
346C5×Dic3—41no—
347C23×D3—101no—
348C2×C3×D4C22×D511yescharacteristic
349C22×C3×C4—21no—
350C2×#67—101no—
351C22×Dic3—101no—
352D3×D4—54no—
353D3×D4—102no—
354C2×D12—51no—
355C2×C4×D3—51no—
356C2×C4×D3—101no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×Dic6—21no—
360C2×Dic6—101no—
361C2×C3×C8—51no—
362C2×C3×C8—51no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—51no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C22⋊C4—21no—
369C3×C42C22×D511yescharacteristic
370#217—101no—
371(C2×D3)⋊C4—51no—
372(C2×D3)⋊C4—51no—
373(C2×D3)⋊C4—101no—
374(C2×D3)⋊C4—101no—
375(C2×D3)⋊C4—101no—
376(C2×D3)⋊C4—101no—
377C4⋊Dic3—21no—
378C4⋊Dic3—51no—
379C4⋊Dic3—101no—
380C4⋊Dic3C22×D511yescharacteristic
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—51no—
383Dic3⋊C4—51no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—51no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C2×C3⋊C8C22×D511yescharacteristic
391C2×C3⋊C8C22×D511yescharacteristic
392ΓL(1,𝔽25)—102no—
393D3×C8—102no—
394C23×C5—21no—
395C22×D5—31no—
396C22×D5—64no—
397C22×D5—61no—
398C22×D5—241no—
399C22×D5—241no—
400C5×Q8—241no—
401C5×D4—21no—
402C5×D4D3×Q812yes—
403C2×C4×C5—21no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—81no—
407C2×C4×C5D3×D411yescharacteristic
408C2×C4×C5D3×D411yescharacteristic
409C2×C4×C5C23×D311yescharacteristic
410C22⋊D5—64no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—31no—
414C2×Dic5—31no—
415C2×Dic5—31no—
416C2×Dic5—61no—
417C2×Dic5—241no—
418D20—32no—
419D20—61no—
420C4×D5—32no—
421C4×D5—32no—
422C4×D5—241no—
423C4×D5—241no—
424C4×D5—241no—
425Dic10—241no—
426C5×C8—61no—
427C5×C8—61no—
428#168—21no—
429#168—21no—
430C22×D4—151no—
431C2×M16—151no—
432C22×C8—151no—
433C4⋊Q8—31no—
434C4⋊Q8—151no—
435C4⋊Q8—301no—
436#125—51no—
437#125—151no—
438#125—301no—
439C22⋊Q8—301no—
440C22⋊Q8—301no—
441C4×D4—151no—
442C4×D4—151no—
443C4×D4—151no—
444C4×D4—301no—
445C4×D4—301no—
446C4×D4D3×D511yescharacteristic
447#117—151no—
448#117—151no—
449#117—151no—
450C2×C4⋊C4—151no—
451C2×C22⋊C4—301no—
452C2×C22⋊C4—301no—
453#107—31no—
454#107—31no—
455#107—51no—
456#107—151no—
457#106—51no—
458#106—151no—
459#106—151no—
460#106—151no—
461C4⋊C8—31no—
462C4⋊C8—51no—
463C4⋊C8—151no—
464C4⋊C8—151no—
465#102—31no—
466#102—31no—
467#102—51no—
468#102—51no—
469#102—151no—
470#102—151no—
471#102—151no—
472#102—151no—
473C2×C3×C5—42no—
474C2×C3×C5C2×C22⋊Q811yescharacteristic
475C2×C3×C5#57611yescharacteristic
476C2×C3×C5#57711yescharacteristic
477D15—22no—
478D15—42no—
479C23×C3—21no—
480C22×D3—51no—
481C22×D3—104no—
482C22×D3—101no—
483C22×D3—401no—
484C22×D3—401no—
485C3×D4—21no—
486C3×D4Q8×D512yes—
487C2×C3×C4—21no—
488C2×C3×C4—81no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4D4×D511yescharacteristic
492C2×C3×C4D4×D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494#67—104no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—51no—
498C2×Dic3—51no—
499C2×Dic3—51no—
500C2×Dic3—101no—
501C2×Dic3—401no—
502D12—52no—
503D12—101no—
504C4×D3—52no—
505C4×D3—52no—
506C4×D3—401no—
507C4×D3—401no—
508C4×D3—401no—
509Dic6—81no—
510Dic6—401no—
511C3×C8—101no—
512C3×C8—101no—
513C3⋊C8—21no—
514C3⋊C8—21no—
515C22×C5—22no—
516C22×C5—41no—
517C22×C5—41no—
518C22×C5C2×D3×D411yescharacteristic
519C2×D5—32no—
520C2×D5—61no—
521C2×D5—61no—
522C2×D5—62no—
523C2×D5—121no—
524C2×D5—121no—
525C2×D5—244no—
526C4×C5—21no—
527C4×C5—21no—
528C4×C5—41no—
529C4×C5—121no—
530C4×C5—121no—
531C4×C5C2×D3×Q811yescharacteristic
532C4×C5D3×#4111yescharacteristic
533Dic5—32no—
534Dic5—41no—
535Dic5—41no—
536Dic5—61no—
537Dic5—61no—
538Dic5—121no—
539C24—301no—
540C2×Q8—61no—
541C2×Q8—301no—
542C2×D4—154no—
543C2×D4—151no—
544C2×D4—302no—
545C2×D4—301no—
546C2×D4C2×D3×D511yescharacteristic
547C22×C4—21no—
548C22×C4—151no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—301no—
552C22×C4—301no—
553M16—302no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8—302no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—51no—
562C4⋊C4—51no—
563C4⋊C4—61no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—151no—
567C4⋊C4—151no—
568C4⋊C4—151no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4C2×D3×D511yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—151no—
576C22⋊C4—151no—
577C22⋊C4—301no—
578C22⋊C4—301no—
579C22⋊C4—301no—
580C22⋊C4—301no—
581C22⋊C4—301no—
582C42—151no—
583C42—301no—
584C42—301no—
585C42C2×D3×D511yescharacteristic
586C3×C5#308111yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×D4×D511yescharacteristic
591C2×D3—52no—
592C2×D3—101no—
593C2×D3—101no—
594C2×D3—102no—
595C2×D3—201no—
596C2×D3—201no—
597C2×D3—404no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—41no—
601C3×C4—201no—
602C3×C4—201no—
603C3×C4C2×Q8×D511yescharacteristic
604C3×C4D5×#4111yescharacteristic
605Dic3—41no—
606Dic3—41no—
607Dic3—52no—
608Dic3—101no—
609Dic3—101no—
610Dic3—201no—
611C2×C5—42no—
612C2×C5D3×C22⋊Q811yescharacteristic
613C2×C5#577011yescharacteristic
614C2×C5#577411yescharacteristic
615D5—62no—
616D5—122no—
617C23—21no—
618C23—151no—
619C23—304no—
620C23—301no—
621C23—1201no—
622C23—1201no—
623Q8—241no—
624Q8—1201no—
625D4—21no—
626D4—152no—
627D4—304no—
628D4—301no—
629D4D15⋊Q812yes—
630C2×C4—21no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—81no—
634C2×C4—101no—
635C2×C4—101no—
636C2×C4—151no—
637C2×C4—152no—
638C2×C4—152no—
639C2×C4—151no—
640C2×C4—151no—
641C2×C4—301no—
642C2×C4—1201no—
643C2×C4—1201no—
644C2×C4—1201no—
645C2×C4—1201no—
646C2×C4#679011yescharacteristic
647C2×C4#679011yescharacteristic
648C2×C4C22×D3×D511yescharacteristic
649C8—61no—
650C8—61no—
651C8—101no—
652C8—101no—
653C2×C3—42no—
654C2×C3D5×C22⋊Q811yescharacteristic
655C2×C3#6609111yescharacteristic
656C2×C3#6611211yescharacteristic
657D3—102no—
658D3—202no—
659C5#8116811yescharacteristic, complemented, Sylow
660C22—22no—
661C22—41no—
662C22—41no—
663C22—152no—
664C22—301no—
665C22—301no—
666C22—302no—
667C22—601no—
668C22—601no—
669C22—1204no—
670C22C2×#679011yescharacteristic
671C4—21no—
672C4—21no—
673C4—41no—
674C4—121no—
675C4—121no—
676C4—152no—
677C4—201no—
678C4—201no—
679C4—301no—
680C4—301no—
681C4—601no—
682C4C2×D15⋊Q811yescharacteristic
683C4#9201611yescharacteristic
684C3#1061269811yescharacteristic, complemented, Sylow
685C2—42no—
686C2—302no—
687C2—602no—
688C2#1175438311yescharacteristic
689C2#1175470411yescharacteristic
690C2#1175535111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×D4×D15C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3081
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
2. #11752655C2semidirect
3. C5×#5007C2semidirect
4. C3×#65298C2semidirect
5. #11749116C2semidirect
6. #11749091C2semidirect
9. #11747456C2semidirect
10. #11747440C2semidirect
11. #11747185C2semidirect
12. #11747180C2semidirect
13. #11747001C2semidirect
14. #11746951C2semidirect
15. #11746885C2semidirect
28. C5×#869C22semidirect
29. C3×#4016C22semidirect
30. #91470C22semidirect
34. #91384C22semidirect
42. C5×#807C22semidirect
43. C5×#807C22semidirect
44. C5×C4⋊(C3⋊C8)C22semidirect
47. C3×#3940C22semidirect
48. C3×#3939C22semidirect
49. C3×C4⋊#168C22semidirect
50. #90990C22semidirect
51. #90987C22semidirect
52. #90985C22semidirect
53. #90985C22semidirect
54. #90983C22semidirect
55. #90983C22semidirect
65. #65298D3semidirect
82. D4×D15Q8semidirect
127. #5007D5semidirect
160. #4016C2×D3semidirect
178. #3940C2×D3semidirect
179. #3939C2×D3semidirect
180. C4⋊#168C2×D3semidirect
240. #869C2×D5semidirect
258. #807C2×D5semidirect
259. #807C2×D5semidirect
260. C4⋊(C3⋊C8)C2×D5semidirect
586. C3×C5#3081semidirect
659. C5#81168semidirect
684. C3#10612698semidirect

Maximal subgroups

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

subgroupindex
#117563042
#117526552
C5×#50072
C3×#652982
#117491162
#117490912
#117489722
#117489572
#117474562
#117474402
#117471852
#117471802
#117470012
#117469512
#117468852
#106126983
#811685