Finite Group Databasebeta

← #14471729

Subgroups — #14471729

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5690C211yesmaximal, characteristic, complemented
2#11752464C211yesmaximal, characteristic, complemented
3#11751169C211yesmaximal, characteristic, complemented
4C3×#65352C211yesmaximal, characteristic, complemented
5#11747422C211yesmaximal, characteristic, complemented
6#11747420C211yesmaximal, characteristic, complemented
7#11747379C211yesmaximal, characteristic, complemented
8#11747377C211yesmaximal, characteristic
9#11747290C211yesmaximal, characteristic, complemented
10#11747277C211yesmaximal, characteristic, complemented
11#11747248C211yesmaximal, characteristic, complemented
12#11747230C211yesmaximal, characteristic
13C4×#6656C211yesmaximal, characteristic, complemented
14#11747038C211yesmaximal, characteristic
15#11746857C211yesmaximal, characteristic, complemented
16#10615368—31nomaximal, Hall
17C3×C5×#125C2211yescharacteristic
18#91764C2211yescharacteristic
19C5×#897—21no—
20C5×#896—21no—
21C5×#896—21no—
22C5×#893C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C5×D3×C4⋊C4—21no—
25C5×#890C2211yescharacteristic
26C5×#888C2211yescharacteristic
27C4×C5×D12C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C3×C4×Dic10C2211yescharacteristic
30#91428C2211yescharacteristic
31#91424—21no—
32#91402—21no—
33#91389C2211yescharacteristic
34#91387—21no—
35#91374C2211yescharacteristic
36#91340C2211yescharacteristic
37#91337—21no—
38C2×#6659C2211yescharacteristic
39C2×#6656C2211yescharacteristic
40C2×#6654C2211yescharacteristic
41#91094C2211yescharacteristic
42#91094C2211yescharacteristic
43#91093C2211yescharacteristic
44#91093C2211yescharacteristic
45C4×C3⋊#168C2211yescharacteristic
46C3×#3942C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3940C2211yescharacteristic
49C3×#3939C2211yescharacteristic
50C3×C4⋊#168C2211yescharacteristic
51#90986C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90970C2211yescharacteristic
56#90969C2211yescharacteristic
57#90966C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81215—51nomaximal, Hall
61C5×#554—31no—
62#65918—31no—
63#65382—31no—
64#65373—31no—
65#65357—31no—
66#65357—31no—
67#65352—31no—
68#65352D311yescharacteristic, complemented
69Q8×#168—31no—
70#65308—31no—
71C4×#687—31no—
72C4×#687—31no—
73#65305—31no—
74#65305—31no—
75C4×#686—31no—
76C2×D60C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C2×C5×D12C2311yescharacteristic
79C2×C4×C5×D3—21no—
80C2×C4×C5×D3—21no—
81C2×C4×C5×D3—21no—
82C2×C5×Dic6—21no—
83C2×C5×Dic6D411yescharacteristic
84C2×C3×Dic10C2311yescharacteristic
85C2×#1200—21no—
86C3×C5×C4⋊C4—21no—
87C3×C5×C4⋊C4—21no—
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C42×C5C2311yescharacteristic
91#6714—21no—
92#6714—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×(C2×D3)⋊C4—21no—
96C5×(C2×D3)⋊C4—21no—
97C5×(C2×D3)⋊C4—21no—
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3D411yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4D411yescharacteristic
104C5×Dic3⋊C4D411yescharacteristic
105C4×C5×Dic3C2311yescharacteristic
106C4×C5×Dic3C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×C4×Dic5—21no—
110C2×C3×#168C2311yescharacteristic
111C2×C3×#168C2311yescharacteristic
112Dic3⋊Dic5—21no—
113Dic3⋊Dic5—21no—
114#6669—21no—
115#6667—21no—
116#6667—21no—
117#6667—21no—
118Dic3×Dic5—21no—
119#6659—22no—
120#6656—22no—
121#6654—22no—
122#5690D511yescharacteristic, complemented
123#5568—51no—
124C3×#479—51no—
125#5068—51no—
126C4×#215—51no—
127#4877—51no—
128#4872—51no—
129#4870—51no—
130#4852—51no—
131#4844—51no—
132#4830—51no—
133#4819—51no—
134#4818—51no—
135#4800—51no—
136#4792—51no—
137C5×C4⋊Q8—31no—
138C5×#125—31no—
139C5×#125C2×D311yescharacteristic
140C5×C22⋊Q8—61no—
141C5×C22⋊Q8—61no—
142C5×C22⋊Q8—61no—
143C4×C5×Q8—31no—
144C4×C5×D4—31no—
145C4×C5×D4—31no—
146C4×C5×D4—31no—
147C2×C5×C4⋊C4—61no—
148#4092—61no—
149C2×#687—31no—
150C2×#687—31no—
151C2×#686—31no—
152#4044—61no—
153#4044—61no—
154#4038—61no—
155#4021—31no—
156#4021—31no—
157C4×D20—31no—
158#4015—31no—
159C4×Dic10—31no—
160C4×Dic10C2×D311yescharacteristic
161#3964—31no—
162#3942—31no—
163#3942—31no—
164#3942—31no—
165#3942—31no—
166#3942C2×D311yescharacteristic
167#3942C2×D311yescharacteristic
168#3941—31no—
169#3941—31no—
170#3941—31no—
171#3940—31no—
172#3940C2×D311yescharacteristic
173#3939C2×D311yescharacteristic
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168C2×D311yescharacteristic
177C4×#168—31no—
178C4×#168—31no—
179C4×#168—31no—
180#3360—151noSylow
181C22×D15—21no—
182C22×C5×D3—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189D60—21no—
190D60—21no—
191Dic30—21no—
192Dic30—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3C2×D411yescharacteristic
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C5×D12—21no—
199C5×D12#4112yes—
200C4×C5×D3—42no—
201C4×C5×D3—81no—
202C4×C5×D3—81no—
203C5×Dic6—22no—
204C5×Dic6—81no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C3×Dic10—21no—
208C3×Dic10—21no—
209#1200—42no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C3×#168—21no—
213C3×#168—21no—
214C3×#125C2×D511yescharacteristic
215C3×C4×Q8—51no—
216#947—51no—
217#944—51no—
218C2×#215—51no—
219C2×D24—51no—
220C2×#204—51no—
221#898—101no—
222#897—21no—
223#896—21no—
224#896—21no—
225#896—101no—
226#893—51no—
227#893C2×D511yescharacteristic
228#893C2×D511yescharacteristic
229D3×C4⋊C4—21no—
230#890C2×D511yescharacteristic
231#888C2×D511yescharacteristic
232#887—51no—
233#876—101no—
234#875—51no—
235C4×D12C2×D511yescharacteristic
236#872—101no—
237C4×Dic6C2×D511yescharacteristic
238C3×#107—51no—
239C3×#106—51no—
240C3×C4⋊C8—51no—
241C3×#103—51no—
242C3×#103—51no—
243#835—51no—
244#821—51no—
245#816—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248C8×Dic3—51no—
249C8×Dic3—51no—
250#810—51no—
251#810—51no—
252#809—51no—
253#809—51no—
254#809—51no—
255#808—51no—
256C4×C3⋊C8—51no—
257C2×C5×Q8—31no—
258C2×C5×Q8—61no—
259C2×C5×D4—31no—
260C22×C4×C5—61no—
261C22×C4×C5—61no—
262C22×C4×C5—61no—
263C2×D20—31no—
264C2×C4×D5—61no—
265C2×Dic10—31no—
266C2×Dic10C22×D311yescharacteristic
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—31no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—61no—
279C5×C22⋊C4—61no—
280C5×C22⋊C4—61no—
281C42×C5—31no—
282C42×C5—31no—
283C42×C5C22×D311yescharacteristic
284#687—62no—
285#687—62no—
286#686—62no—
287#685—61no—
288#685—61no—
289#685—61no—
290#685—61no—
291#685—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5—61no—
294C4⋊Dic5C22×D311yescharacteristic
295#683—21no—
296#683—61no—
297C4×Dic5—21no—
298C4×Dic5—61no—
299C2×#168—31no—
300C2×#168—31no—
301C2×#168C22×D311yescharacteristic
302C2×#168C22×D311yescharacteristic
303#556—151no—
304#554—31no—
305#488—151no—
306#488—151no—
307#487—151no—
308#479—51no—
309#479—151no—
310#476—151no—
311#463—151no—
312#463—151no—
313#461—151no—
314C8×Q8—151no—
315C4×SD16—151no—
316C4×SD16—151no—
317C4×D8—151no—
318C22×C3×C5C22×D411yescharacteristic
319C2×D15—41no—
320C2×D15—41no—
321C2×D15—41no—
322C2×C5×D3—22no—
323C2×C5×D3—41no—
324C2×C5×D3—41no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—41no—
328C3×C4×C5—41no—
329C3×C4×C5C2×#4111yescharacteristic
330C3×C4×C52−1+411yescharacteristic
331Dic15—41no—
332C3×Dic5—41no—
333C3×Dic5—41no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3—21no—
337C5×Dic3—41no—
338C5×Dic3#13512yes—
339C2×C3×Q8—51no—
340C2×D12—51no—
341C2×D12C22×D511yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—101no—
346C2×Dic6—21no—
347C2×Dic6—51no—
348C2×Dic6C22⋊D511yescharacteristic
349C2×C3×C8—51no—
350C2×C3×C8—51no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4C22×D511yescharacteristic
356C3×C4⋊C4C22×D511yescharacteristic
357C3×C42—101no—
358C3×C42C22×D511yescharacteristic
359#215—102no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—101no—
364(C2×D3)⋊C4—101no—
365(C2×D3)⋊C4—101no—
366(C2×D3)⋊C4—101no—
367(C2×D3)⋊C4—101no—
368C4⋊Dic3—21no—
369C4⋊Dic3C22⋊D511yescharacteristic
370C4⋊Dic3C22×D511yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376Dic3⋊C4C22⋊D511yescharacteristic
377Dic3⋊C4C22⋊D511yescharacteristic
378C4×Dic3—101no—
379C4×Dic3C22×D511yescharacteristic
380C4×Dic3C22×D511yescharacteristic
381C2×C3⋊C8—51no—
382C2×C3⋊C8—51no—
383D24—102no—
384#204—102no—
385C23×C5—61no—
386C22×D5—61no—
387C5×Q8—62no—
388C5×Q8—241no—
389C5×D4—32no—
390C5×D4—61no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—31no—
394C2×C4×C5—31no—
395C2×C4×C5—31no—
396C2×C4×C5—31no—
397C2×C4×C5—61no—
398C2×C4×C5—122no—
399C2×C4×C5—241no—
400C2×C4×C5—241no—
401C2×C4×C5D3×D411yescharacteristic
402C2×C4×C5D3×D411yescharacteristic
403C2×C4×C5C23×D311yescharacteristic
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—61no—
407D20—61no—
408D20—61no—
409C4×D5—122no—
410Dic10—21no—
411Dic10—21no—
412Dic10—61no—
413Dic10—61no—
414#168—21no—
415#168—21no—
416#168—61no—
417#168—61no—
418C2×SD16—151no—
419C2×SD16—151no—
420C2×D8—151no—
421C4⋊Q8—31no—
422C4⋊Q8—151no—
423#126—301no—
424#126—301no—
425#125—31no—
426#125D3×D511yescharacteristic
427#124—151no—
428#124—151no—
429C22⋊Q8—61no—
430C22⋊Q8—61no—
431C22⋊Q8—61no—
432C22⋊Q8—301no—
433C4×Q8—31no—
434C4×Q8—51no—
435C4×Q8—151no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—151no—
440#117—301no—
441C2×C4⋊C4—61no—
442#107—51no—
443#106—51no—
444#106—151no—
445C4⋊C8—51no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—51no—
449#103—51no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#102—151no—
455#102—151no—
456#102—151no—
457#102—151no—
458C4×C8—151no—
459C4×C8—151no—
460C4×C8—151no—
461C2×C3×C5#54811yescharacteristic
462C2×C3×C5C2×#13511yescharacteristic
463C2×C3×C5#57711yescharacteristic
464D15—81no—
465C5×D3—42no—
466C22×D3—21no—
467C22×D3—101no—
468C3×Q8—101no—
469C3×Q8—101no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—101no—
473C2×C3×C4—101no—
474C2×C3×C4C2×C22⋊D511yescharacteristic
475C2×C3×C4C2×C22⋊D511yescharacteristic
476C2×C3×C4C23×D511yescharacteristic
477C2×Dic3—21no—
478C2×Dic3—101no—
479C2×Dic3C2×C22⋊D511yescharacteristic
480C2×Dic3C2×C22⋊D511yescharacteristic
481C2×Dic3C2×C22⋊D511yescharacteristic
482C2×Dic3C2×C22⋊D511yescharacteristic
483D12—21no—
484D12—101no—
485D12—101no—
486D12#71312yes—
487C4×D3—42no—
488C4×D3—81no—
489C4×D3—81no—
490C4×D3—202no—
491Dic6—22no—
492Dic6—81no—
493Dic6—101no—
494Dic6—101no—
495C3×C8—101no—
496C3×C8—101no—
497C3⋊C8—101no—
498C3⋊C8—101no—
499C22×C5—62no—
500C22×C5—121no—
501C22×C5—121no—
502C22×C5C2×D3×D411yescharacteristic
503C2×D5—121no—
504C2×D5—121no—
505C2×D5—121no—
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—32no—
509C4×C5—41no—
510C4×C5—41no—
511C4×C5—61no—
512C4×C5—61no—
513C4×C5—61no—
514C4×C5—121no—
515C4×C5#100711yescharacteristic
516C4×C5D3×#4111yescharacteristic
517Dic5—41no—
518Dic5—41no—
519Dic5—121no—
520C2×Q8—31no—
521C2×Q8—51no—
522C2×Q8—61no—
523C2×Q8—151no—
524C2×D4—31no—
525C2×D4—151no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—301no—
530SD16—302no—
531SD16—302no—
532D8—302no—
533C2×C8—51no—
534C2×C8—51no—
535C2×C8—151no—
536C2×C8—151no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—51no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4C2×D3×D511yescharacteristic
552C4⋊C4C2×D3×D511yescharacteristic
553C22⋊C4—61no—
554C22⋊C4—61no—
555C22⋊C4—61no—
556C22⋊C4—301no—
557C22⋊C4—301no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—31no—
562C42—31no—
563C42—101no—
564C42—301no—
565C42C2×D3×D511yescharacteristic
566C3×C5#336011yescharacteristic, complemented, Hall
567C22×C3C22×C22⋊D511yescharacteristic
568C2×D3—22no—
569C2×D3—41no—
570C2×D3—41no—
571C2×D3—201no—
572C2×D3—201no—
573C2×D3—201no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—201no—
579C3×C4—201no—
580C3×C4C2×#71311yescharacteristic
581C3×C4#414711yescharacteristic
582Dic3—21no—
583Dic3—21no—
584Dic3—21no—
585Dic3—41no—
586Dic3—201no—
587Dic3#409612yes—
588C2×C5—122no—
589C2×C5#563311yescharacteristic
590C2×C5D3×#13511yescharacteristic
591C2×C5#577811yescharacteristic
592D5—241no—
593C23—61no—
594C23—301no—
595Q8—62no—
596Q8—101no—
597Q8—101no—
598Q8—241no—
599Q8—301no—
600Q8—301no—
601D4—32no—
602D4—61no—
603D4—301no—
604D4—301no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—31no—
611C2×C4—61no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—122no—
615C2×C4—241no—
616C2×C4—241no—
617C2×C4—301no—
618C2×C4—602no—
619C2×C4D3×C22⋊D511yescharacteristic
620C2×C4D3×C22⋊D511yescharacteristic
621C2×C4C22×D3×D511yescharacteristic
622C8—101no—
623C8—101no—
624C8—301no—
625C8—301no—
626C2×C3#6615111yescharacteristic
627C2×C3C2×#409611yescharacteristic
628C2×C3#6617011yescharacteristic
629D3—42no—
630D3—401no—
631C5#8121511yescharacteristic, complemented, Sylow
632C22—62no—
633C22—121no—
634C22—121no—
635C22—601no—
636C22—601no—
637C22—601no—
638C22C2×D3×C22⋊D511yescharacteristic
639C4—21no—
640C4—21no—
641C4—32no—
642C4—41no—
643C4—41no—
644C4—61no—
645C4—61no—
646C4—61no—
647C4—121no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4#9202911yescharacteristic
652C4D3×#71311yescharacteristic
653C3#1061536811yescharacteristic, complemented, Sylow
654C2—122no—
655C2—1201no—
656C2#1175523411yescharacteristic
657C2D3×#409611yescharacteristic
658C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC2×#6654C22
hypercenter#125D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C5×#5690C2semidirect
2. #11752464C2semidirect
3. #11751169C2semidirect
4. C3×#65352C2semidirect
5. #11747422C2semidirect
6. #11747420C2semidirect
7. #11747379C2semidirect
9. #11747290C2semidirect
10. #11747277C2semidirect
11. #11747248C2semidirect
13. C4×#6656C2semidirect
15. #11746857C2semidirect
68. #65352D3semidirect
122. #5690D5semidirect
566. C3×C5#3360semidirect
631. C5#81215semidirect
653. C3#10615368semidirect

Maximal subgroups

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

subgroupindex
C5×#56902
#117524642
#117511692
C3×#653522
#117474222
#117474202
#117473792
#117473772
#117472902
#117472772
#117472482
#117472302
C4×#66562
#117470382
#117468572
#106153683
#812155