Finite Group Databasebeta

← #14430693

Subgroups — #14430693

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#125C211yesmaximal, characteristic, complemented
2C4×#6772C211yesmaximal, characteristic
3#11751164C211yesmaximal, characteristic, complemented
4C5×#5066C211yesmaximal, characteristic, complemented
5#11747498C211yesmaximal, characteristic
6#11747498C211yesmaximal, characteristic
7#11747453C211yesmaximal, characteristic, complemented
8#11747452C211yesmaximal, characteristic, complemented
9#11747288C211yesmaximal, characteristic, complemented
10#11747286C211yesmaximal, characteristic, complemented
11#11747243C211yesmaximal, characteristic, complemented
12#11747241C211yesmaximal, characteristic, complemented
13#11747007C211yesmaximal, characteristic, complemented
14#11746934C211yesmaximal, characteristic, complemented
15#11746902C211yesmaximal, characteristic, complemented
16#10612898—31nomaximal, Hall
17C2×#6772C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C4×C5×D12C2211yescharacteristic
21C3×D5×C4⋊C4—21no—
22C3×D5×C4⋊C4—21no—
23C3×D5×C4⋊C4C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25C3×#4036C2211yescharacteristic
26C3×#4036C2211yescharacteristic
27C3×#4035—21no—
28C3×#4035—21no—
29C3×C42×D5C2211yescharacteristic
30C3×#4016C2211yescharacteristic
31#91440—21no—
32C4×#1201—21no—
33Dic5×D12C2211yescharacteristic
34#91398—21no—
35C4×D3×Dic5—21no—
36#91358C2211yescharacteristic
37#91333C2211yescharacteristic
38C2×#6649C2211yescharacteristic
39C2×#6649C2211yescharacteristic
40#91094C2211yescharacteristic
41#91094C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#809C2211yescharacteristic
46C5×#809C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90989C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90966C2211yescharacteristic
59#90966C2211yescharacteristic
60#83017—51nomaximal, Hall
61D5×#125D311yescharacteristic, complemented
62C4×#711—31no—
63C5×#478—31no—
64#65352—31no—
65#65298—31no—
66#65170—31no—
67#65166—31no—
68#65150—31no—
69#65146—31no—
70#65126—31no—
71#65118—31no—
72#65060—31no—
73#65060—31no—
74#65055—31no—
75#65052—31no—
76C2×Dic30C2311yescharacteristic
77C2×C5×D12C2311yescharacteristic
78C2×C4×C5×D3—21no—
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5D411yescharacteristic
82C2×C3×C4×D5D411yescharacteristic
83C2×C3×C4×D5C2311yescharacteristic
84C2×#1201—21no—
85C2×D3×Dic5—21no—
86C2×D3×Dic5—21no—
87#6772—22no—
88#6772Q814yes—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C42×C5C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15—21no—
97C2×C3⋊#168C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C5×(C2×D3)⋊C4—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C2×C5×C3⋊C8C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683—21no—
112C3×#683—21no—
113C3×C4×Dic5D411yescharacteristic
114C3×C4×Dic5D411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116#6669—21no—
117(C2×D3)⋊Dic5—21no—
118#6665—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6649—22no—
122#6649—22no—
123C2×C3×#125—51no—
124C4×#235—51no—
125#5066—51no—
126#5066—51no—
127#5066—51no—
128#5066D511yescharacteristic, complemented
129#5063—51no—
130#5063—51no—
131#5063—51no—
132#5063—51no—
133#4966—51no—
134#4966—51no—
135#4964—51no—
136#4964—51no—
137#4924—51no—
138C2×#711—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×D4—31no—
141D4×Dic5—31no—
142C4×C22⋊D5—61no—
143C2×C4×Dic5—61no—
144C2×#676—31no—
145C2×#676—31no—
146#4038—31no—
147D5×C4⋊C4—21no—
148D5×C4⋊C4—21no—
149D5×C4⋊C4C2×D311yescharacteristic
150D5×C4⋊C4C2×D311yescharacteristic
151#4036C2×D311yescharacteristic
152#4036C2×D311yescharacteristic
153#4035—21no—
154#4035—21no—
155#4033—31no—
156#4027—61no—
157#4023—61no—
158C42×D5C2×D311yescharacteristic
159#4016C2×D311yescharacteristic
160C4×Dic10—31no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102—31no—
166#3964—31no—
167#3964—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3080—151noSylow
182C22×C5×D3—21no—
183C22×C3×D5C2×D411yescharacteristic
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190C2×Dic15—21no—
191Dic30—21no—
192Dic30C2×Q812yes—
193C2×C5×Dic3—21no—
194C5×D12—21no—
195C5×D12C2×Q812yes—
196C4×C5×D3—42no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C3×C4×D5—41no—
203C3×C4×D5—41no—
204C3×C4×D5—42no—
205C3×C4×D5—42no—
206C3×C4×D5C2×Q812yes—
207C3×C4×D5#4112yes—
208#1201—24no—
209D3×Dic5—24no—
210D3×Dic5—42no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C5×C3⋊C8—21no—
214C5×C3⋊C8—21no—
215C2×#235—51no—
216C3×#125—51no—
217C3×#125—51no—
218C3×#125—51no—
219C3×#125—101no—
220C3×#125—101no—
221C3×#125C2×D511yescharacteristic
222C2×C3×C4⋊C4—51no—
223C2×C3×C4⋊C4—51no—
224C2×C3×C4⋊C4—101no—
225C2×C3×C4⋊C4—101no—
226C2×C3×C42—51no—
227C4×#67—101no—
228C4×#67—101no—
229#926—51no—
230C2×#208—51no—
231C2×#208—51no—
232C4×D12—51no—
233C4×D12C2×D511yescharacteristic
234#872—101no—
235C42×D3—101no—
236C4×Dic6—51no—
237C4×Dic6—51no—
238#810—51no—
239#810—51no—
240#810—51no—
241#810—51no—
242#809—51no—
243#809—51no—
244#809C2×D511yescharacteristic
245#809C2×D511yescharacteristic
246#808—51no—
247#808—51no—
248#808—51no—
249#808C2×D511yescharacteristic
250#807—51no—
251#807—51no—
252#807—51no—
253#807C2×D511yescharacteristic
254C4⋊(C3⋊C8)—51no—
255C4⋊(C3⋊C8)—51no—
256C4⋊(C3⋊C8)—51no—
257C4⋊(C3⋊C8)C2×D511yescharacteristic
258C2×C5×D4—31no—
259C22×C4×C5—61no—
260C2×C22⋊D5—61no—
261C22×Dic5—61no—
262C22×Dic5—61no—
263#711—34no—
264#711—62no—
265C2×C4×D5—21no—
266C2×C4×D5—21no—
267C2×C4×D5#6711yescharacteristic
268C2×C4×D5#6711yescharacteristic
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10—31no—
271C2×C5×C8—31no—
272C2×C5×C8—31no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—61no—
279C42×C5C22×D311yescharacteristic
280C22⋊Dic5—61no—
281#685—61no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—31no—
285C4⋊Dic5C22×D311yescharacteristic
286C4⋊Dic5C22×D311yescharacteristic
287#683—21no—
288#683—21no—
289#683—21no—
290#683—21no—
291#683—21no—
292#683—21no—
293#683—61no—
294#683—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C4×Dic5#6711yescharacteristic
299C4×Dic5#6711yescharacteristic
300C4×Dic5C22×D311yescharacteristic
301C2×#168—31no—
302C2×#168—31no—
303#676—62no—
304#676—62no—
305C2×#125—51no—
306C4×#41—151no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—31no—
312#478—151no—
313#478—151no—
314#478—151no—
315#428—151no—
316#428—151no—
317#423—151no—
318#417—151no—
319#417—151no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C5×D3—22no—
322C2×C5×D3—41no—
323C2×C5×D3—41no—
324C2×C3×D5—21no—
325C2×C3×D5—21no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5—41no—
330C3×C4×C5—41no—
331C3×C4×C5C22×Q811yescharacteristic
332C3×C4×C5C2×#4111yescharacteristic
333Dic15—22no—
334Dic15—41no—
335C3×Dic5—21no—
336C3×Dic5—21no—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C3×Dic5C22⋊Q812yes—
340C5×Dic3—41no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—101no—
345C22×C3×C4—101no—
346C2×#67—101no—
347#235—54no—
348#235—102no—
349C2×D12C22×D511yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—101no—
352C2×C4×D3—101no—
353C2×Dic6—51no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4C22×D511yescharacteristic
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C42—51no—
369C3×C42—51no—
370C3×C42—51no—
371C3×C42C22×D511yescharacteristic
372#217—101no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—101no—
375C4⋊Dic3—51no—
376C4⋊Dic3C22×D511yescharacteristic
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3—101no—
382#208—102no—
383#208—102no—
384C2×C3⋊C8—51no—
385C2×C3⋊C8—51no—
386C2×C3⋊C8C22×D511yescharacteristic
387C2×C3⋊C8C22×D511yescharacteristic
388C23×C5—61no—
389C22×D5C2×#6711yescharacteristic
390C5×D4—32no—
391C5×D4—61no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—61no—
395C2×C4×C5—122no—
396C2×C4×C5C2×#6711yescharacteristic
397C2×C4×C5C2×#6711yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—64no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—61no—
403C2×Dic5—64no—
404C2×Dic5—61no—
405C2×Dic5—122no—
406C2×Dic5C2×#6711yescharacteristic
407C2×Dic5C2×#6711yescharacteristic
408C2×Dic5C2×#6711yescharacteristic
409C4×D5—41no—
410C4×D5—41no—
411C4×D5—42no—
412C4×D5—42no—
413C4×D5D3×Q812yes—
414C4×D5#23912yes—
415Dic10—32no—
416Dic10—61no—
417C5×C8—61no—
418C5×C8—61no—
419#168—61no—
420#168—61no—
421C2×#41—151no—
422C2×M16—151no—
423C2×M16—151no—
424#125—51no—
425#125—51no—
426#125—51no—
427#125—101no—
428#125—101no—
429#125D3×D511yescharacteristic
430C4×Q8—151no—
431C4×Q8—151no—
432C4×D4—31no—
433C4×D4—151no—
434C4×D4—301no—
435C4×D4—301no—
436#117—151no—
437#117—301no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—51no—
440C2×C4⋊C4—101no—
441C2×C4⋊C4—101no—
442C2×C42—51no—
443C2×C42—301no—
444#107—31no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—31no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—31no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460#102—31no—
461#102—31no—
462#102—151no—
463#102—151no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57511yescharacteristic
466C2×C3×C5#57511yescharacteristic
467C3×D5—22no—
468C5×D3—42no—
469C23×C3—51no—
470C22×D3—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—51no—
474C2×C3×C4—52no—
475C2×C3×C4—52no—
476C2×C3×C4—51no—
477C2×C3×C4—51no—
478C2×C3×C4—101no—
479C2×C3×C4—101no—
480C2×C3×C4—201no—
481C2×C3×C4—201no—
482C2×C3×C4—202no—
483C2×C3×C4—202no—
484C2×C3×C4D4×D511yescharacteristic
485C2×C3×C4D4×D511yescharacteristic
486C2×C3×C4C23×D511yescharacteristic
487#67—104no—
488C2×Dic3—21no—
489C2×Dic3—101no—
490C2×Dic3—101no—
491D12—21no—
492D12Q8×D512yes—
493C4×D3—42no—
494C4×D3—104no—
495C4×D3—202no—
496Dic6—52no—
497Dic6—101no—
498C3⋊C8—21no—
499C3⋊C8—21no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5—62no—
503C22×C5—121no—
504C22×C5—121no—
505C22×C5C22×#6711yescharacteristic
506C2×D5—21no—
507C2×D5—21no—
508C2×D5#94612yes—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—41no—
512C4×C5—41no—
513C4×C5—121no—
514C4×C5C2×D3×Q811yescharacteristic
515C4×C5C2×#23911yescharacteristic
516Dic5—21no—
517Dic5—21no—
518Dic5—41no—
519Dic5—41no—
520Dic5—62no—
521Dic5—121no—
522Dic5#94612yes—
523#41—154no—
524#41—302no—
525C2×Q8—151no—
526C2×D4—31no—
527C2×D4—301no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—61no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—301no—
535C22×C4—301no—
536M16—302no—
537M16—302no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—151no—
541C2×C8—151no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—31no—
545C4⋊C4—51no—
546C4⋊C4—51no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—101no—
550C4⋊C4—101no—
551C4⋊C4—101no—
552C4⋊C4—101no—
553C4⋊C4—101no—
554C4⋊C4—101no—
555C4⋊C4—151no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4C2×D3×D511yescharacteristic
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—61no—
561C22⋊C4—301no—
562C22⋊C4—301no—
563C42—51no—
564C42—51no—
565C42—51no—
566C42—301no—
567C42—301no—
568C42—301no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—52no—
572C22×C3—101no—
573C22×C3—101no—
574C22×C3C2×D4×D511yescharacteristic
575C2×D3—22no—
576C2×D3—41no—
577C2×D3—41no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—52no—
583C3×C4—101no—
584C3×C4—101no—
585C3×C4—201no—
586C3×C4—201no—
587C3×C4C2×Q8×D511yescharacteristic
588C3×C4D5×#4111yescharacteristic
589Dic3—41no—
590Dic3—102no—
591Dic3—201no—
592C2×C5—122no—
593C2×C5C2×#94611yescharacteristic
594C2×C5#582211yescharacteristic
595C2×C5#582211yescharacteristic
596D5—22no—
597C23—51no—
598C23—61no—
599Q8—152no—
600Q8—301no—
601D4—32no—
602D4—61no—
603D4—304no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—51no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—51no—
610C2×C4—51no—
611C2×C4—61no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—122no—
615C2×C4—201no—
616C2×C4—201no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—304no—
620C2×C4—301no—
621C2×C4—301no—
622C2×C4—602no—
623C2×C4D5×#6711yescharacteristic
624C2×C4D5×#6711yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—61no—
627C8—61no—
628C8—301no—
629C8—301no—
630C2×C3—102no—
631C2×C3D5×C22⋊Q811yescharacteristic
632C2×C3#6610211yescharacteristic
633C2×C3#6610711yescharacteristic
634D3—42no—
635C5#8301711yescharacteristic, complemented, Sylow
636C22—52no—
637C22—62no—
638C22—101no—
639C22—101no—
640C22—121no—
641C22—121no—
642C22C2×D5×#6711yescharacteristic
643C4—21no—
644C4—21no—
645C4—41no—
646C4—41no—
647C4—52no—
648C4—101no—
649C4—101no—
650C4—121no—
651C4—201no—
652C4—201no—
653C4—302no—
654C4—601no—
655C4D3×Q8×D511yescharacteristic
656C4D5×#23911yescharacteristic
657C3#1061289811yescharacteristic, complemented, Sylow
658C2—102no—
659C2—122no—
660C2D5×#94611yescharacteristic
661C2#1175531511yescharacteristic
662C2#1175534311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC2×#6772C22
hypercenter#125D3×D5
hypocenterC3×C5#3080
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. C3×D5×#125C2semidirect
3. #11751164C2semidirect
4. C5×#5066C2semidirect
7. #11747453C2semidirect
8. #11747452C2semidirect
9. #11747288C2semidirect
10. #11747286C2semidirect
11. #11747243C2semidirect
12. #11747241C2semidirect
13. #11747007C2semidirect
14. #11746934C2semidirect
15. #11746902C2semidirect
61. D5×#125D3semidirect
128. #5066D5semidirect
570. C3×C5#3080semidirect
635. C5#83017semidirect
657. C3#10612898semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
C4×#67722
#117511642
C5×#50662
#117474982
#117474532
#117474522
#117472882
#117472862
#117472432
#117472412
#117470072
#117469342
#117469022
#106128983
#830175