Finite Group Databasebeta

← #14430990

Subgroups — #14430990

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755144C211yesmaximal, characteristic
2#11753650C211yesmaximal, characteristic
3#11750892C211yesmaximal, characteristic, complemented
4C5×#4802C211yesmaximal, characteristic
5C3×#65083C211yesmaximal, characteristic, complemented
6#11749337C211yesmaximal, characteristic, complemented
7#11749329C211yesmaximal, characteristic, complemented
8D3×#3967C211yesmaximal, characteristic
9#11747887C211yesmaximal, characteristic, complemented
10#11747860C211yesmaximal, characteristic, complemented
11#11747661C211yesmaximal, characteristic
12#11747630C211yesmaximal, characteristic
13#11747435C211yesmaximal, characteristic
14#11747300C211yesmaximal, characteristic, complemented
15#11747282C211yesmaximal, characteristic, complemented
16#10610681—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18Q8×Dic15C2211yescharacteristic
19#91777C2211yescharacteristic
20C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
21C5×#892C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×#4034C2211yescharacteristic
24#91432—21no—
25D3×C4⋊Dic5C2211yescharacteristic
26#91410—21no—
27#91389—21no—
28#91388C2211yescharacteristic
29#91384C2211yescharacteristic
30#91379—21no—
31#91371—21no—
32#91371C2211yescharacteristic
33#91344—21no—
34#91344C2211yescharacteristic
35#91338—21no—
36#91338C2211yescharacteristic
37Dic5×Dic6—21no—
38Dic5×Dic6C2211yescharacteristic
39C2×D3×#168C2211yescharacteristic
40C3×C5×#103C2211yescharacteristic
41#91119C2211yescharacteristic
42#91101C2211yescharacteristic
43#91098C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#816C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3946C2211yescharacteristic
51C3×#3939C2211yescharacteristic
52#90990C2211yescharacteristic
53#90988C2211yescharacteristic
54#90987C2211yescharacteristic
55#90986C2211yescharacteristic
56#90983C2211yescharacteristic
57#90982C2211yescharacteristic
58#90973C2211yescharacteristic
59#90972C2211yescharacteristic
60#81110—51nomaximal, Hall
61#66146—31no—
62#65853—31no—
63C5×#419—31no—
64C2×#3967—31no—
65#65410—31no—
66#65408—31no—
67#65287—31no—
68#65088—31no—
69#65088—31no—
70#65085—31no—
71#65085—31no—
72#65083—31no—
73#65083D311yescharacteristic, complemented
74#65080—31no—
75#65080—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30—21no—
78C5×D3×Q8—22no—
79C5×D3×Q8Q814yescomplemented
80C2×C4×C5×D3—21no—
81C2×C4×C5×D3C2311yescharacteristic
82C2×C5×Dic6—21no—
83C2×C5×Dic6C2311yescharacteristic
84C2×C3×Dic10—21no—
85C2×D3×Dic5—21no—
86C2×C3×C5×C8C2311yescharacteristic
87C3×C5×C4⋊C4C2311yescharacteristic
88C4⋊Dic15—21no—
89C4⋊Dic15C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91#6712—21no—
92C4×Dic15—21no—
93C4×Dic15C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×(C2×D3)⋊C4—21no—
96C5×C4⋊Dic3C2311yescharacteristic
97C4×C5×Dic3—21no—
98C2×C5×C3⋊C8C2311yescharacteristic
99C5×ΓL(1,𝔽25)—22no—
100C3×C4⋊Dic5—21no—
101C3×C4⋊Dic5C2311yescharacteristic
102C3×C4⋊Dic5C2311yescharacteristic
103C3×#683—21no—
104C3×C4×Dic5—21no—
105C3×C4×Dic5C2311yescharacteristic
106C2×C3×#168C2311yescharacteristic
107Dic3⋊Dic5—21no—
108Dic3⋊Dic5—21no—
109Dic3⋊Dic5—21no—
110Dic3⋊Dic5—21no—
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5D411yescharacteristic
113Dic3⋊Dic5D411yescharacteristic
114#6669—21no—
115#6668—21no—
116(C2×D3)⋊Dic5—21no—
117(C2×D3)⋊Dic5D411yescharacteristic
118(C2×D3)⋊Dic5D411yescharacteristic
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122D3×#168—22no—
123#5729—51no—
124#5572—51no—
125C3×#477—51no—
126#5094—51no—
127#5022—51no—
128#4881—51no—
129#4880—51no—
130#4877—51no—
131#4875—51no—
132#4839—51no—
133#4829—51no—
134#4802D511yescharacteristic
135D3×#103—51no—
136#4796—51no—
137#4791—51no—
138C22×C5×Q8—31no—
139C2×C5×M16—31no—
140C5×#117—31no—
141Q8×Dic5—31no—
142Q8×Dic5—31no—
143Q8×Dic5—31no—
144Q8×Dic5—61no—
145Q8×Dic5—61no—
146Q8×Dic5C2×D311yescharacteristic
147#4072—31no—
148#4072—31no—
149#4072—61no—
150#4072—61no—
151C2×C4⋊Dic5—31no—
152C22×#168—31no—
153#4036—31no—
154#4036—31no—
155#4034—31no—
156#4034C2×D311yescharacteristic
157#4024—61no—
158#4024—61no—
159#4016—61no—
160#4015—61no—
161C5×#103—31no—
162C5×#103—31no—
163C5×#103—31no—
164C5×#103C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3967—31no—
168#3967C2×D311yescharacteristic
169#3950—31no—
170#3950C2×D311yescharacteristic
171#3949—31no—
172#3949—31no—
173#3946—31no—
174#3946—31no—
175#3946—31no—
176#3946C2×D311yescharacteristic
177#3940—31no—
178#3940—31no—
179#3939—31no—
180#3939C2×D311yescharacteristic
181#3082—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C3×C5×Q8—21no—
184C3×C5×Q8C2×Q812yes—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15C2×D411yescharacteristic
191C2×Dic15C2×D411yescharacteristic
192Dic30—81no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3C2×D411yescharacteristic
196C4×C5×D3—24no—
197C4×C5×D3C2×Q812yes—
198C4×C5×D3#4112yes—
199C5×Dic6—21no—
200C5×Dic6—24no—
201C5×Dic6C2×Q812yes—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C3×Dic10—81no—
207D3×Dic5—81no—
208C3×C5×C8—21no—
209C3⋊#168—21no—
210C3×#168—21no—
211C5×C3⋊C8—21no—
212C2×D3×Q8C2×D511yescharacteristic
213C3×C4⋊Q8—51no—
214C3×C4×Q8—51no—
215#946—101no—
216Q8×Dic3—51no—
217#944—101no—
218C2×ΓL(1,𝔽25)C2×D511yescharacteristic
219C2×D3×C8—51no—
220#896—101no—
221#892—51no—
222#892—101no—
223#892C2×D511yescharacteristic
224D3×C4⋊C4—51no—
225#890—51no—
226#889—101no—
227#888—51no—
228#887—51no—
229#887—101no—
230#872—51no—
231#872—101no—
232#870—51no—
233C4×Dic6—51no—
234C4×Dic6—101no—
235C3×#107—51no—
236C3×#107—51no—
237C3×C4⋊C8—51no—
238C3×#103—51no—
239C3×#103C2×D511yescharacteristic
240#835—51no—
241#835C2×D511yescharacteristic
242#818—51no—
243#817—51no—
244#816—51no—
245#816C2×D511yescharacteristic
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248#810—51no—
249#810C2×D511yescharacteristic
250#808—51no—
251#808—51no—
252#808—51no—
253#807—51no—
254C4⋊(C3⋊C8)—51no—
255C2×C5×Q8—34no—
256C2×C5×Q8—31no—
257C2×C5×Q8—61no—
258C2×C5×Q8—62no—
259C2×C5×Q8C22×D311yescharacteristic
260C22×C4×C5—31no—
261C22×C4×C5—61no—
262C22×Dic5—61no—
263C2×Dic10—21no—
264C2×Dic10—61no—
265C5×M16—62no—
266C2×C5×C8—31no—
267C2×C5×C8C22×D311yescharacteristic
268C5×C4⋊C4—31no—
269C5×C4⋊C4C22×D311yescharacteristic
270C5×C22⋊C4—61no—
271C42×C5—61no—
272C22⋊Dic5—31no—
273C22⋊Dic5—31no—
274C22⋊Dic5—61no—
275C4⋊Dic5—21no—
276C4⋊Dic5—31no—
277C4⋊Dic5—31no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280C4⋊Dic5—61no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5—61no—
285C4⋊Dic5—61no—
286C4⋊Dic5C22×D311yescharacteristic
287C4⋊Dic5C22×D311yescharacteristic
288#683—21no—
289#683—61no—
290#683—61no—
291#683—61no—
292C4×Dic5—21no—
293C4×Dic5—31no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C4×Dic5C22×D311yescharacteristic
299C2×#168—31no—
300C2×#168—62no—
301C2×#168C22×D311yescharacteristic
302#544—151no—
303#519—151no—
304#479—151no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—51no—
309#477—151no—
310#475—151no—
311#475—151no—
312#428—151no—
313#427—151no—
314#424—151no—
315#419—31no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C5×D3—21no—
319C2×C5×D3—21no—
320C2×C5×D3C22⋊Q812yes—
321C3×C4×C5—22no—
322C3×C4×C5—41no—
323C3×C4×C5C22×Q811yescharacteristic
324C3×C4×C5C2×#4111yescharacteristic
325Dic15—21no—
326Dic15—21no—
327Dic15—41no—
328Dic15—41no—
329C3×Dic5—21no—
330C3×Dic5—21no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C5×Dic3—22no—
334C5×Dic3—41no—
335C5×Dic3C22⋊Q812yes—
336C2×C3×Q8—101no—
337C2×C3×Q8C22×D511yescharacteristic
338D3×Q8—22no—
339D3×Q8Dic1014yescomplemented
340C2×C4×D3—21no—
341C2×C4×D3—101no—
342C2×C4×D3C22×D511yescharacteristic
343C2×Dic6—21no—
344C2×Dic6—101no—
345C2×Dic6C22×D511yescharacteristic
346C2×C3×C8—51no—
347C2×C3×C8C22×D511yescharacteristic
348C3×C4⋊C4—51no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—101no—
351C3×C4⋊C4—101no—
352C3×C4⋊C4C22×D511yescharacteristic
353C3×C42—51no—
354C3×C42—101no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—51no—
357(C2×D3)⋊C4—51no—
358(C2×D3)⋊C4—101no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3—101no—
363C4⋊Dic3C22×D511yescharacteristic
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373C4×Dic3—21no—
374C4×Dic3—51no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3—101no—
379C2×C3⋊C8—51no—
380C2×C3⋊C8C22×D511yescharacteristic
381ΓL(1,𝔽25)—22no—
382D3×C8—102no—
383C23×C5—31no—
384C5×Q8—21no—
385C5×Q8—32no—
386C5×Q8—64no—
387C5×Q8—61no—
388C5×Q8D3×Q812yes—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—31no—
392C2×C4×C5—32no—
393C2×C4×C5—32no—
394C2×C4×C5—64no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5C23×D311yescharacteristic
398C2×Dic5—21no—
399C2×Dic5—21no—
400C2×Dic5—31no—
401C2×Dic5—31no—
402C2×Dic5—61no—
403C2×Dic5—61no—
404C2×Dic5—241no—
405C2×Dic5D3×D411yescharacteristic
406C2×Dic5D3×D411yescharacteristic
407Dic10—81no—
408Dic10—241no—
409C5×C8—21no—
410C5×C8—61no—
411#168—21no—
412#168—61no—
413C22×Q8—31no—
414C2×M16—31no—
415C22×C8—151no—
416C4⋊Q8—51no—
417C4⋊Q8—151no—
418C4⋊Q8—301no—
419#125—151no—
420#125—151no—
421#125—301no—
422C22⋊Q8—301no—
423C22⋊Q8—301no—
424C4×Q8—51no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—31no—
431#117—151no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—151no—
436#107—51no—
437#107—51no—
438#107—151no—
439#107—151no—
440#106—151no—
441#106—151no—
442#106—151no—
443#106—151no—
444C4⋊C8—51no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—31no—
449#103—31no—
450#103—31no—
451#103—51no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103D3×D511yescharacteristic
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C5×D3—22no—
460C22×D3D4×D511yescharacteristic
461C3×Q8—21no—
462C3×Q8—401no—
463C3×Q8C2×Dic1012yes—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4—101no—
469C2×C3×C4—101no—
470C2×C3×C4C23×D511yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—51no—
474C2×Dic3—51no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3D4×D511yescharacteristic
478C4×D3—24no—
479C4×D3—401no—
480C4×D3C2×Dic1012yes—
481C4×D3#71112yes—
482Dic6—21no—
483Dic6—24no—
484Dic6—401no—
485Dic6C2×Dic1012yes—
486C3×C8—21no—
487C3×C8—101no—
488C3⋊C8—21no—
489C3⋊C8—101no—
490C22×C5—32no—
491C22×C5—61no—
492C22×C5—61no—
493C22×C5C2×D3×D411yescharacteristic
494C4×C5—22no—
495C4×C5—32no—
496C4×C5—41no—
497C4×C5—62no—
498C4×C5—121no—
499C4×C5C2×D3×Q811yescharacteristic
500C4×C5D3×#4111yescharacteristic
501Dic5—21no—
502Dic5—21no—
503Dic5—41no—
504Dic5—41no—
505Dic5—61no—
506Dic5—61no—
507Dic5—121no—
508Dic5—121no—
509C2×Q8—34no—
510C2×Q8—31no—
511C2×Q8—61no—
512C2×Q8—62no—
513C2×Q8—101no—
514C2×Q8—301no—
515C2×Q8C2×D3×D511yescharacteristic
516C22×C4—31no—
517C22×C4—61no—
518C22×C4—301no—
519M16—62no—
520C2×C8—31no—
521C2×C8—51no—
522C2×C8—151no—
523C2×C8—302no—
524C2×C8C2×D3×D511yescharacteristic
525C4⋊C4—31no—
526C4⋊C4—51no—
527C4⋊C4—51no—
528C4⋊C4—101no—
529C4⋊C4—101no—
530C4⋊C4—151no—
531C4⋊C4—151no—
532C4⋊C4—151no—
533C4⋊C4—151no—
534C4⋊C4—301no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4—301no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4—301no—
543C4⋊C4C2×D3×D511yescharacteristic
544C22⋊C4—61no—
545C22⋊C4—151no—
546C22⋊C4—151no—
547C22⋊C4—301no—
548C42—51no—
549C42—61no—
550C42—101no—
551C42—151no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42—301no—
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3C2×D4×D511yescharacteristic
558C2×D3—21no—
559C2×D3—21no—
560C2×D3#402412yes—
561C3×C4—22no—
562C3×C4—41no—
563C3×C4—101no—
564C3×C4—101no—
565C3×C4—201no—
566C3×C4—201no—
567C3×C4C22×Dic1011yescharacteristic
568C3×C4C2×#71111yescharacteristic
569Dic3—22no—
570Dic3—41no—
571Dic3—101no—
572Dic3—101no—
573Dic3—201no—
574Dic3—201no—
575Dic3#402412yes—
576C2×C5—62no—
577C2×C5D3×C22⋊Q811yescharacteristic
578C2×C5#576611yescharacteristic
579C2×C5#577511yescharacteristic
580C23—31no—
581Q8—21no—
582Q8—32no—
583Q8—64no—
584Q8—61no—
585Q8—401no—
586Q8—1201no—
587Q8D3×Dic1012yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—31no—
591C2×C4—32no—
592C2×C4—32no—
593C2×C4—51no—
594C2×C4—51no—
595C2×C4—64no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—101no—
599C2×C4—101no—
600C2×C4—151no—
601C2×C4—151no—
602C2×C4—301no—
603C2×C4—301no—
604C2×C4—1201no—
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—61no—
608C8—101no—
609C8—301no—
610C2×C3C2×#402411yescharacteristic
611C2×C3#6611211yescharacteristic
612C2×C3#6611311yescharacteristic
613D3—22no—
614C5#8111011yescharacteristic, complemented, Sylow
615C22—32no—
616C22—61no—
617C22—61no—
618C22D3×D4×D511yescharacteristic
619C4—22no—
620C4—32no—
621C4—41no—
622C4—62no—
623C4—101no—
624C4—101no—
625C4—121no—
626C4—201no—
627C4—201no—
628C4—301no—
629C4—301no—
630C4—601no—
631C4—601no—
632C4C2×D3×Dic1011yescharacteristic
633C4D3×#71111yescharacteristic
634C3#1061068111yescharacteristic, complemented, Sylow
635C2—62no—
636C2D3×#402411yescharacteristic
637C2#1175408811yescharacteristic
638C2#1175410711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenter#103D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #11750892C2semidirect
5. C3×#65083C2semidirect
6. #11749337C2semidirect
7. #11749329C2semidirect
9. #11747887C2semidirect
10. #11747860C2semidirect
14. #11747300C2semidirect
15. #11747282C2semidirect
73. #65083D3semidirect
79. C5×D3×Q8Q8semidirect
339. D3×Q8Dic10semidirect
556. C3×C5#3082semidirect
614. C5#81110semidirect
634. C3#10610681semidirect

Maximal subgroups

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

subgroupindex
#117551442
#117536502
#117508922
C5×#48022
C3×#650832
#117493372
#117493292
D3×#39672
#117478872
#117478602
#117476612
#117476302
#117474352
#117473002
#117472822
#106106813
#811105