Finite Group Databasebeta

← #14430282

Subgroups — #14430282

Order 1920.

776 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
1C5×#5517C211yesmaximal, characteristic, complemented
2Dic3×#709C211yesmaximal, characteristic
3#11751099C211yesmaximal, characteristic, complemented
4C3×#65291C211yesmaximal, characteristic
5#11748458C211yesmaximal, characteristic, complemented
6C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic
8#11747296C211yesmaximal, characteristic, complemented
9#11747295C211yesmaximal, characteristic, complemented
10#11747294C211yesmaximal, characteristic, complemented
11#11747293C211yesmaximal, characteristic, complemented
12#11747251C211yesmaximal, characteristic, complemented
13#11747249C211yesmaximal, characteristic, complemented
14#11747247C211yesmaximal, characteristic, complemented
15#11747245C211yesmaximal, characteristic, complemented
16#10615080—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19#91815C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C5×#926C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C5×#890C2211yescharacteristic
24C5×#890C2211yescharacteristic
25C5×#888C2211yescharacteristic
26C5×#888C2211yescharacteristic
27C5×#878—21no—
28C5×#878—21no—
29C4×C5×Dic6—21no—
30C4×C5×Dic6—21no—
31C22×C3×#168C2211yescharacteristic
32Dic3×C22⋊D5—21no—
33Dic3×C22⋊D5—21no—
34Dic3×D20C2211yescharacteristic
35Dic3×D20C2211yescharacteristic
36C4×D5×Dic3—21no—
37#91357—21no—
38Dic3×Dic10C2211yescharacteristic
39Dic3×Dic10C2211yescharacteristic
40#91092C2211yescharacteristic
41#91092C2211yescharacteristic
42#91091C2211yescharacteristic
43#91091C2211yescharacteristic
44C3×#3942C2211yescharacteristic
45C3×#3942C2211yescharacteristic
46C3×#3941C2211yescharacteristic
47C3×#3941C2211yescharacteristic
48#90988C2211yescharacteristic
49#90988C2211yescharacteristic
50#90985C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56#90970C2211yescharacteristic
57#90970C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#78822—51nomaximal, Hall
61C5×#533—31no—
62C4×#709—31no—
63#65383—31no—
64#65380—31no—
65#65376—31no—
66#65373—31no—
67#65355—31no—
68#65355—31no—
69#65352—31no—
70#65352—31no—
71#65291—31no—
72#65291D311yescharacteristic
73#65287—31no—
74#65287—31no—
75C2×C4⋊#168—31no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C5×Dic3D411yescharacteristic
78C22×C5×Dic3D411yescharacteristic
79C2×C5×Dic6—21no—
80C2×C5×Dic6—21no—
81C2×C3×C22⋊D5—21no—
82C3×#709—22no—
83C3×#709Q814yescomplemented
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×Dic10C2311yescharacteristic
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C22⋊C4—21no—
92C3×C42×C5—21no—
93#6719—21no—
94C4⋊Dic15C2311yescharacteristic
95C4⋊Dic15C2311yescharacteristic
96C4×Dic15—21no—
97C2×C3⋊#168—22no—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C5×#217—21no—
101C5×C4⋊Dic3—21no—
102C5×C4⋊Dic3—21no—
103C5×C4⋊Dic3C2311yescharacteristic
104C5×C4⋊Dic3C2311yescharacteristic
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C4×C5×Dic3—21no—
110C4×C5×Dic3D411yescharacteristic
111C4×C5×Dic3D411yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C4×C5×Dic3C2311yescharacteristic
114C2×C3×#168—22no—
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117#6668—21no—
118#6668—21no—
119#6665—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123Dic3×#41—51no—
124#5517D511yescharacteristic, complemented
125C3×#416—51no—
126#5233—51no—
127#5106—51no—
128C2×Dic3⋊C8—51no—
129#4998—51no—
130#4799—51no—
131#4796—51no—
132#4793—51no—
133#4791—51no—
134#4766—51no—
135#4763—51no—
136#4761—51no—
137#4759—51no—
138C2×#709C2×D311yescharacteristic
139C5×C4⋊Q8—31no—
140C5×C4⋊Q8—31no—
141C5×#125—31no—
142C5×#125—31no—
143C5×C22⋊Q8—61no—
144C5×C22⋊Q8—61no—
145C4×C5×Q8—61no—
146C4×C5×Q8—61no—
147C5×#117—31no—
148C5×#117C2×D311yescharacteristic
149C2×C42×C5—31no—
150C4×C22⋊D5—61no—
151C4×C22⋊D5—61no—
152#4072—31no—
153C22×#168—31no—
154C22×#168C2×D311yescharacteristic
155C4×D20—31no—
156C4×D20—31no—
157#4018—61no—
158C42×D5—61no—
159C4×Dic10—31no—
160C4×Dic10—31no—
161#3942—31no—
162#3942—31no—
163#3942C2×D311yescharacteristic
164#3942C2×D311yescharacteristic
165#3941—31no—
166#3941—31no—
167#3941C2×D311yescharacteristic
168#3941C2×D311yescharacteristic
169#3940—31no—
170#3940—31no—
171#3940—31no—
172#3940—31no—
173#3939—31no—
174#3939—31no—
175#3939—31no—
176#3939—31no—
177C4⋊#168—31no—
178C4⋊#168—31no—
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3076—151noSylow
182C23×C3×C5C2×D411yescharacteristic
183C22×C3×D5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×Q812yes—
188C2×C3×C4×C5#4112yes—
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×C5×Dic3—22no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—41no—
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C5×Dic6—42no—
201C5×Dic6—42no—
202C3×C22⋊D5—24no—
203C2×C3×Dic5—21no—
204C3×D20—21no—
205C3×D20C2×Q812yes—
206C3×C4×D5—24no—
207C3×Dic10—21no—
208C3×Dic10C2×Q812yes—
209D5×Dic3—42no—
210D5×Dic3—42no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C3×#168—21no—
214C3×#168—21no—
215C2×C3×#41—51no—
216C22×C3×C8—51no—
217C3×#117C2×D511yescharacteristic
218Q8×Dic3—51no—
219Q8×Dic3—51no—
220D4×Dic3—51no—
221D4×Dic3—51no—
222D4×Dic3—101no—
223D4×Dic3—101no—
224#926—51no—
225#926—101no—
226#926C2×D511yescharacteristic
227C2×C4×Dic3—101no—
228C2×C4×Dic3C2×D511yescharacteristic
229C22×C3⋊C8—51no—
230#890C2×D511yescharacteristic
231#890C2×D511yescharacteristic
232#888C2×D511yescharacteristic
233#888C2×D511yescharacteristic
234#878—21no—
235#878—21no—
236C4×Dic6—21no—
237C4×Dic6—21no—
238C3×#103—51no—
239C3×#103—51no—
240C3×#102—51no—
241C3×#102—51no—
242#835—51no—
243#835—51no—
244#832—51no—
245#832—51no—
246#818—51no—
247#818—51no—
248#817—51no—
249#817—51no—
250Dic3⋊C8—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254#808—51no—
255#808—51no—
256#807—51no—
257#807—51no—
258C2×C5×Q8—61no—
259C2×C5×Q8—61no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5C22×D311yescharacteristic
263C2×C22⋊D5—21no—
264#709—22no—
265#709Dic614yescomplemented
266C2×D20C22×D311yescharacteristic
267C2×C4×D5—21no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×Dic10C22×D311yescharacteristic
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C4⋊C4C22×D311yescharacteristic
281C5×C22⋊C4—21no—
282C5×C22⋊C4—61no—
283C42×C5—21no—
284C42×C5—31no—
285C42×C5—31no—
286C42×C5—31no—
287C42×C5—31no—
288C42×C5—61no—
289C22⋊Dic5—61no—
290#685—61no—
291#685—61no—
292C4⋊Dic5—31no—
293C4⋊Dic5—31no—
294#683—61no—
295#683—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C2×#168—22no—
300C2×#168—31no—
301C2×#168—31no—
302C2×#168—62no—
303C2×#168C22×D311yescharacteristic
304C2×#168C22×D311yescharacteristic
305#533—31no—
306C4×#41—151no—
307#479—151no—
308#479—151no—
309#478—151no—
310#478—151no—
311#477—151no—
312#476—151no—
313#475—151no—
314#474—151no—
315#427—151no—
316#427—151no—
317C2×C4⋊C8—151no—
318#416—51no—
319#416—151no—
320C22×C3×C5—21no—
321C22×C3×C5—21no—
322C22×C3×C5C22⋊Q812yes—
323C22×C3×C5C22×D411yescharacteristic
324C2×C3×D5—22no—
325C2×C3×D5—41no—
326C2×C3×D5—41no—
327C3×C4×C5—41no—
328C3×C4×C5—41no—
329C3×C4×C5C22⋊Q812yes—
330C3×C4×C5C22×Q811yescharacteristic
331C3×C4×C5C2×#4111yescharacteristic
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—22no—
335C5×Dic3—21no—
336C5×Dic3—21no—
337C5×Dic3—21no—
338C5×Dic3—41no—
339C5×Dic3—41no—
340C5×Dic3#13512yes—
341C3×#41—54no—
342C3×#41—102no—
343C2×C3×Q8—51no—
344C2×C3×D4—51no—
345C2×C3×D4—101no—
346C22×C3×C4—101no—
347C22×C3×C4C22×D511yescharacteristic
348C22×Dic3—101no—
349C22×Dic3—101no—
350C22×Dic3C22⋊D511yescharacteristic
351C22×Dic3C22⋊D511yescharacteristic
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×C3×C8—51no—
355C2×C3×C8—51no—
356C2×C3×C8—102no—
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C4⋊C4C22×D511yescharacteristic
359C3×C22⋊C4—21no—
360C3×C42—21no—
361#217—21no—
362#217—101no—
363#217—101no—
364#217—101no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—51no—
368C4⋊Dic3—51no—
369C4⋊Dic3—101no—
370C4⋊Dic3—101no—
371C4⋊Dic3C22×D511yescharacteristic
372C4⋊Dic3C22×D511yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377C4×Dic3—21no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3C22⋊D511yescharacteristic
382C4×Dic3C22⋊D511yescharacteristic
383C4×Dic3C22×D511yescharacteristic
384C4×Dic3C22×D511yescharacteristic
385C2×C3⋊C8—51no—
386C2×C3⋊C8—51no—
387C2×C3⋊C8—102no—
388C23×C5D3×D411yescharacteristic
389C22×D5—21no—
390C5×Q8—122no—
391C5×Q8—122no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—31no—
395C2×C4×C5—31no—
396C2×C4×C5—31no—
397C2×C4×C5—31no—
398C2×C4×C5—62no—
399C2×C4×C5—61no—
400C2×C4×C5—61no—
401C2×C4×C5—121no—
402C2×C4×C5C2×Dic612yes—
403C2×C4×C5D3×D411yescharacteristic
404C2×C4×C5#23712yes—
405C2×C4×C5C23×D311yescharacteristic
406C22⋊D5—24no—
407C2×Dic5—21no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410D20—21no—
411D20C2×Dic612yes—
412C4×D5—24no—
413C4×D5—122no—
414C4×D5—122no—
415Dic10—21no—
416Dic10C2×Dic612yes—
417#168—21no—
418#168—21no—
419#168—61no—
420#168—61no—
421C2×#41—51no—
422C22×C8—51no—
423C22×C8—151no—
424C4⋊Q8—31no—
425C4⋊Q8—31no—
426#125—31no—
427#125—31no—
428C22⋊Q8—61no—
429C22⋊Q8—61no—
430C4×Q8—61no—
431C4×Q8—61no—
432C4×Q8—151no—
433C4×Q8—151no—
434C4×D4—151no—
435C4×D4—151no—
436C4×D4—301no—
437C4×D4—301no—
438#117—31no—
439#117—151no—
440#117—301no—
441#117D3×D511yescharacteristic
442C2×C42—31no—
443C2×C42—301no—
444#107—151no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—151no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—151no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—51no—
457#103—51no—
458#103—151no—
459#103—151no—
460#102—51no—
461#102—51no—
462#102—151no—
463#102—151no—
464C2×C3×C5—22no—
465C2×C3×C5C2×C22⋊Q811yescharacteristic
466C2×C3×C5C2×#13511yescharacteristic
467C2×C3×C5#57511yescharacteristic
468C3×D5—42no—
469C23×C3—101no—
470C23×C3C2×C22⋊D511yescharacteristic
471C3×Q8—52no—
472C3×Q8—101no—
473C3×D4—52no—
474C3×D4—104no—
475C3×D4—101no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—101no—
479C2×C3×C4—104no—
480C2×C3×C4Q8×D512yes—
481C2×C3×C4#71312yes—
482C2×C3×C4C2×C22⋊D511yescharacteristic
483C2×C3×C4C23×D511yescharacteristic
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—41no—
488C2×Dic3—101no—
489C2×Dic3—101no—
490C2×Dic3—202no—
491C2×Dic3—202no—
492C2×Dic3C2×C22⋊D511yescharacteristic
493C2×Dic3C2×C22⋊D511yescharacteristic
494C2×Dic3C2×C22⋊D511yescharacteristic
495C2×Dic3C2×C22⋊D511yescharacteristic
496Dic6—42no—
497Dic6—42no—
498C3×C8—101no—
499C3×C8—101no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5—21no—
503C22×C5—21no—
504C22×C5#87812yes—
505C22×C5C2×D3×D411yescharacteristic
506C2×D5—22no—
507C2×D5—41no—
508C2×D5—41no—
509C4×C5—32no—
510C4×C5—41no—
511C4×C5—41no—
512C4×C5—61no—
513C4×C5—61no—
514C4×C5—61no—
515C4×C5—121no—
516C4×C5—121no—
517C4×C5#87812yes—
518C4×C5C22×Dic611yescharacteristic
519C4×C5C2×#23711yescharacteristic
520Dic5—22no—
521Dic5—121no—
522Dic5—121no—
523#41—54no—
524#41—102no—
525C2×Q8—51no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×D4—51no—
529C2×D4—101no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—101no—
533C22×C4—301no—
534C22×C4—301no—
535C22×C4C2×D3×D511yescharacteristic
536C2×C8—51no—
537C2×C8—51no—
538C2×C8—102no—
539C2×C8—151no—
540C2×C8—151no—
541C2×C8—302no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—151no—
551C4⋊C4—151no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4C2×D3×D511yescharacteristic
555C4⋊C4C2×D3×D511yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—61no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—21no—
562C42—31no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—301no—
568C42—301no—
569C42—301no—
570C3×C5#307611yescharacteristic, complemented, Hall
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—102no—
574C22×C3—201no—
575C22×C3—201no—
576C22×C3#409212yes—
577C22×C3C22×C22⋊D511yescharacteristic
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—102no—
581C3×C4#409212yes—
582C3×C4C2×Q8×D511yescharacteristic
583C3×C4C2×#71311yescharacteristic
584Dic3—21no—
585Dic3—21no—
586Dic3—21no—
587Dic3—41no—
588Dic3—41no—
589Dic3—201no—
590Dic3—201no—
591Dic3#409612yes—
592C2×C5—22no—
593C2×C5C2×#87811yescharacteristic
594C2×C5D3×#13511yescharacteristic
595C2×C5#576811yescharacteristic
596D5—42no—
597C23—101no—
598C23D3×C22⋊D511yescharacteristic
599Q8—52no—
600Q8—101no—
601Q8—122no—
602Q8—122no—
603D4—52no—
604D4—104no—
605D4—101no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—31no—
611C2×C4—31no—
612C2×C4—62no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—101no—
616C2×C4—104no—
617C2×C4—121no—
618C2×C4—301no—
619C2×C4—301no—
620C2×C4—602no—
621C2×C4—602no—
622C2×C4D5×Dic612yes—
623C2×C4#676612yes—
624C2×C4D3×C22⋊D511yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—101no—
627C8—101no—
628C8—301no—
629C8—301no—
630C2×C3—22no—
631C2×C3—202no—
632C2×C3C2×#409211yescharacteristic
633C2×C3C2×#409611yescharacteristic
634C2×C3#6615611yescharacteristic
635C5#7882211yescharacteristic, complemented, Sylow
636C22—21no—
637C22—21no—
638C22—102no—
639C22—201no—
640C22—201no—
641C22#9142112yes—
642C22C2×D3×C22⋊D511yescharacteristic
643C4—32no—
644C4—41no—
645C4—41no—
646C4—61no—
647C4—61no—
648C4—61no—
649C4—102no—
650C4—121no—
651C4—121no—
652C4—601no—
653C4—601no—
654C4#9142112yes—
655C4C2×D5×Dic611yescharacteristic
656C4C2×#676611yescharacteristic
657C3#1061508011yescharacteristic, complemented, Sylow
658C2—22no—
659C2—202no—
660C2C2×#9142111yescharacteristic
661C2D3×#409611yescharacteristic
662C2#1175532211yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5517C2semidirect
3. #11751099C2semidirect
5. #11748458C2semidirect
6. C2×Dic3⋊#168C2semidirect
8. #11747296C2semidirect
9. #11747295C2semidirect
10. #11747294C2semidirect
11. #11747293C2semidirect
12. #11747251C2semidirect
13. #11747249C2semidirect
14. #11747247C2semidirect
15. #11747245C2semidirect
83. C3×#709Q8semidirect
124. #5517D5semidirect
265. #709Dic6semidirect
570. C3×C5#3076semidirect
635. C5#78822semidirect
657. C3#10615080semidirect

Maximal subgroups

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

subgroupindex
C5×#55172
Dic3×#7092
#117510992
C3×#652912
#117484582
C2×Dic3⋊#1682
#117483642
#117472962
#117472952
#117472942
#117472932
#117472512
#117472492
#117472472
#117472452
#106150803
#788225