Finite Group Databasebeta

← #14471645

Subgroups — #14471645

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×#5539C211yesmaximal, characteristic, complemented
2#11752464C211yesmaximal, characteristic, complemented
3#11751117C211yesmaximal, characteristic
4C3×C4×#687C211yesmaximal, characteristic, complemented
5#11749114C211yesmaximal, characteristic, complemented
6#11749080C211yesmaximal, characteristic
7#11749011C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic
9#11747422C211yesmaximal, characteristic, complemented
10#11747379C211yesmaximal, characteristic, complemented
11#11747291C211yesmaximal, characteristic, complemented
12#11747248C211yesmaximal, characteristic, complemented
13#11746919C211yesmaximal, characteristic, complemented
14#11746913C211yesmaximal, characteristic, complemented
15Dic6×#168C211yesmaximal, characteristic, complemented
16#10615368—31nomaximal, Hall
17C3×C4×C5×D4C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20#91764C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic
23C5×#924—21no—
24C2×C5×Dic3⋊C4—21no—
25C5×#890C2211yescharacteristic
26C5×#888C2211yescharacteristic
27C5×#878—21no—
28C5×#878—21no—
29C5×#870C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic
31C2×C3×#687C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic
33#91428C2211yescharacteristic
34#91424—21no—
35#91402—21no—
36#91389C2211yescharacteristic
37#91387—21no—
38#91374C2211yescharacteristic
39#91340C2211yescharacteristic
40#91337—21no—
41#91094C2211yescharacteristic
42#91093C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C3×#3964C2211yescharacteristic
45C3×#3942C2211yescharacteristic
46C3×#3940C2211yescharacteristic
47C3×C4×#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90986C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90970C2211yescharacteristic
55#90970C2211yescharacteristic
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#79620—51nomaximal, Hall
61C5×#554—31no—
62#65918—31no—
63#65382—31no—
64#65373—31no—
65#65357—31no—
66#65357—31no—
67#65352—31no—
68#65352—31no—
69Q8×#168—31no—
70#65308—31no—
71C4×#687—31no—
72C4×#687D311yescharacteristic, complemented
73#65305—31no—
74#65305—31no—
75C4×#686—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×D60C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C22×C5×Dic3—21no—
81C22×C5×Dic3—21no—
82C2×C5×Dic6—21no—
83C2×C5×Dic6D411yescharacteristic
84C2×C3×Dic10C2311yescharacteristic
85C2×#1200—21no—
86C3×C5×C4⋊C4C2311yescharacteristic
87C3×C5×C22⋊C4—21no—
88C3×C42×C5C2311yescharacteristic
89#6716—22no—
90#6715—22no—
91#6714—21no—
92#6714—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#217—21no—
96C5×#217—21no—
97C5×C4⋊Dic3—21no—
98C5×C4⋊Dic3D411yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4D411yescharacteristic
106C5×Dic3⋊C4D411yescharacteristic
107C4×C5×Dic3C2311yescharacteristic
108C4×C5×Dic3C2311yescharacteristic
109C3×#687—22no—
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×C4×Dic5—21no—
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6667—21no—
119#6667—21no—
120#6667—21no—
121Dic3×Dic5—21no—
122#5568—51no—
123#5539D511yescharacteristic, complemented
124C3×C4×SD16—51no—
125#5165—51no—
126#5162—51no—
127#5022—51no—
128#5016—51no—
129#4870—51no—
130#4857—51no—
131#4800—51no—
132#4792—51no—
133#4758—51no—
134#4756—51no—
135#4697—51no—
136C8×Dic6—51no—
137C5×C4⋊Q8—31no—
138C5×#125—31no—
139C5×#125—31no—
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×D4C2×D311yescharacteristic
147C2×C5×C4⋊C4—61no—
148#4092—61no—
149C2×#687—31no—
150C2×#687C2×D311yescharacteristic
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#3964C2×D311yescharacteristic
162#3942—31no—
163#3942—31no—
164#3942—31no—
165#3942—31no—
166#3942—31no—
167#3942C2×D311yescharacteristic
168#3941—31no—
169#3941—31no—
170#3941—31no—
171#3940—31no—
172#3940C2×D311yescharacteristic
173#3939—31no—
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4×#168—31no—
178C4×#168—31no—
179C4×#168C2×D311yescharacteristic
180#3360—151noSylow
181C23×C3×C5—21no—
182C22×D15—21no—
183C3×C5×D4—21no—
184C3×C5×D4#4112yes—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—81no—
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191D60—21no—
192D60—21no—
193Dic30—21no—
194Dic30—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—42no—
198C2×C5×Dic3—81no—
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
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—
214C2×C3×SD16—51no—
215C3×C4×Q8—51no—
216C3×C4×D4C2×D511yescharacteristic
217#947—51no—
218#944—51no—
219D4×Dic3C2×D511yescharacteristic
220D4×Dic3C2×D511yescharacteristic
221C2×#214—51no—
222C2×#213—51no—
223#924—21no—
224C2×Dic3⋊C4—21no—
225#898—101no—
226#896—101no—
227#893—51no—
228#890C2×D511yescharacteristic
229#888C2×D511yescharacteristic
230#887—51no—
231#878—21no—
232#878—21no—
233#876—101no—
234#875—51no—
235#872—101no—
236#870C2×D511yescharacteristic
237C4×Dic6C2×D511yescharacteristic
238C3×#106—51no—
239C3×#103—51no—
240C3×#102—51no—
241C3×C4×C8—51no—
242#835—51no—
243#835—51no—
244#821—51no—
245#821—51no—
246#816—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250C8×Dic3—51no—
251C8×Dic3—51no—
252#810—51no—
253#809—51no—
254#808—51no—
255#807—51no—
256C4⋊(C3⋊C8)—51no—
257C2×C5×Q8—31no—
258C2×C5×Q8—61no—
259C2×C5×D4C22×D311yescharacteristic
260C22×C4×C5—21no—
261C22×C4×C5—61no—
262C22×C4×C5—61no—
263C2×D20—31no—
264C2×C4×D5—61no—
265C2×Dic10—31no—
266C2×Dic10C22×D311yescharacteristic
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—31no—
271C5×C4⋊C4—31no—
272C5×C4⋊C4—61no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—21no—
279C5×C22⋊C4—61no—
280C5×C22⋊C4—61no—
281C42×C5—31no—
282C42×C5—31no—
283C42×C5C22×D311yescharacteristic
284#687—22no—
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—151no—
309#479—151no—
310#476—151no—
311#463—151no—
312#463—151no—
313#461—151no—
314C8×Q8—151no—
315C4×SD16—51no—
316C4×SD16—151no—
317C4×D8—151no—
318C22×C3×C5—22no—
319C22×C3×C5—41no—
320C22×C3×C5—41no—
321C22×C3×C5C22×D411yescharacteristic
322C2×D15—41no—
323C2×D15—41no—
324C2×D15—41no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—41no—
328C3×C4×C5C2×#4111yescharacteristic
329C3×C4×C52−1+411yescharacteristic
330Dic15—41no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3—41no—
337C5×Dic3—41no—
338C5×Dic3#13512yes—
339C2×C3×Q8—51no—
340C2×C3×D4C22×D511yescharacteristic
341C22×C3×C4—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C2×D12—51no—
345C2×C4×D3—101no—
346C2×Dic6—21no—
347C2×Dic6—51no—
348C2×Dic6C22⋊D511yescharacteristic
349C3×SD16—102no—
350C2×C3×C8—51no—
351C2×C3×C8—51no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4C22×D511yescharacteristic
355C3×C22⋊C4—21no—
356C3×C42—101no—
357C3×C42C22×D511yescharacteristic
358#217—21no—
359#217—21no—
360#214—102no—
361#213—102no—
362(C2×D3)⋊C4—101no—
363(C2×D3)⋊C4—101no—
364(C2×D3)⋊C4—101no—
365(C2×D3)⋊C4—101no—
366(C2×D3)⋊C4—101no—
367C4⋊Dic3—21no—
368C4⋊Dic3C22⋊D511yescharacteristic
369C4⋊Dic3C22×D511yescharacteristic
370C4⋊Dic3C22×D511yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378Dic3⋊C4C22⋊D511yescharacteristic
379Dic3⋊C4C22⋊D511yescharacteristic
380C4×Dic3—101no—
381C4×Dic3C22×D511yescharacteristic
382C4×Dic3C22×D511yescharacteristic
383C2×C3⋊C8—51no—
384C2×C3⋊C8—51no—
385C23×C5—21no—
386C22×D5—61no—
387C5×Q8—62no—
388C5×Q8—241no—
389C5×D4—21no—
390C5×D4#23512yes—
391C2×C4×C5—21no—
392C2×C4×C5—31no—
393C2×C4×C5—31no—
394C2×C4×C5—31no—
395C2×C4×C5—31no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5—81no—
399C2×C4×C5—122no—
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—51no—
419C2×SD16—151no—
420C2×D8—151no—
421C4⋊Q8—31no—
422C4⋊Q8—151no—
423#126—301no—
424#126—301no—
425#125—31no—
426#125—31no—
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—151no—
439C4×D4D3×D511yescharacteristic
440#117—301no—
441C2×C4⋊C4—61no—
442#107—151no—
443#106—51no—
444#106—151no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—51no—
449#103—151no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#102—51no—
455#102—151no—
456#102—151no—
457#102—151no—
458C4×C8—51no—
459C4×C8—151no—
460C4×C8—151no—
461C2×C3×C5—42no—
462C2×C3×C5#54811yescharacteristic
463C2×C3×C5C2×#13511yescharacteristic
464C2×C3×C5#57711yescharacteristic
465D15—81no—
466C23×C3—21no—
467C22×D3—101no—
468C3×Q8—101no—
469C3×Q8—101no—
470C3×D4—21no—
471C3×D4#71312yes—
472C2×C3×C4—21no—
473C2×C3×C4—81no—
474C2×C3×C4—101no—
475C2×C3×C4—101no—
476C2×C3×C4C2×C22⋊D511yescharacteristic
477C2×C3×C4C2×C22⋊D511yescharacteristic
478C2×C3×C4C23×D511yescharacteristic
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—42no—
482C2×Dic3—81no—
483C2×Dic3—101no—
484C2×Dic3C2×C22⋊D511yescharacteristic
485C2×Dic3C2×C22⋊D511yescharacteristic
486C2×Dic3C2×C22⋊D511yescharacteristic
487C2×Dic3C2×C22⋊D511yescharacteristic
488D12—101no—
489D12—101no—
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—22no—
500C22×C5—41no—
501C22×C5—41no—
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—61no—
511C4×C5—61no—
512C4×C5—61no—
513C4×C5—121no—
514C4×C5—121no—
515C4×C5C2×#23511yescharacteristic
516C4×C5#101011yescharacteristic
517Dic5—41no—
518Dic5—41no—
519Dic5—121no—
520C2×Q8—31no—
521C2×Q8—51no—
522C2×Q8—61no—
523C2×Q8—151no—
524C2×D4—151no—
525C2×D4C2×D3×D511yescharacteristic
526C22×C4—21no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—301no—
530SD16—102no—
531SD16—302no—
532D8—302no—
533C2×C8—51no—
534C2×C8—51no—
535C2×C8—151no—
536C2×C8—151no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—51no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—101no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C22⋊C4—21no—
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×C3—22no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3C22×C22⋊D511yescharacteristic
571C2×D3—201no—
572C2×D3—201no—
573C2×D3—201no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—201no—
578C3×C4—201no—
579C3×C4C2×#71311yescharacteristic
580C3×C4#414711yescharacteristic
581Dic3—21no—
582Dic3—21no—
583Dic3—21no—
584Dic3—41no—
585Dic3—41no—
586Dic3—201no—
587Dic3#409612yes—
588C2×C5—42no—
589C2×C5#555211yescharacteristic
590C2×C5#576211yescharacteristic
591C2×C5D3×#13511yescharacteristic
592D5—241no—
593C23—21no—
594C23—301no—
595Q8—62no—
596Q8—101no—
597Q8—101no—
598Q8—241no—
599Q8—301no—
600Q8—301no—
601D4—21no—
602D4—301no—
603D4—301no—
604D4#677312yes—
605C2×C4—21no—
606C2×C4—31no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—81no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—122no—
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—42no—
627C2×C3#6615111yescharacteristic
628C2×C3C2×#409611yescharacteristic
629C2×C3#6617011yescharacteristic
630D3—401no—
631C5#7962011yescharacteristic, complemented, Sylow
632C22—22no—
633C22—41no—
634C22—41no—
635C22—601no—
636C22—601no—
637C22—601no—
638C22C2×D3×C22⋊D511yescharacteristic
639C4—21no—
640C4—21no—
641C4—32no—
642C4—41no—
643C4—61no—
644C4—61no—
645C4—61no—
646C4—121no—
647C4—121no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4#9200011yescharacteristic
652C4C2×#677311yescharacteristic
653C3#1061536811yescharacteristic, complemented, Sylow
654C2—42no—
655C2—1201no—
656C2#1175454411yescharacteristic
657C2#1175471111yescharacteristic
658C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3360
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
1. C5×#5539C2semidirect
2. #11752464C2semidirect
4. C3×C4×#687C2semidirect
5. #11749114C2semidirect
7. #11749011C2semidirect
9. #11747422C2semidirect
10. #11747379C2semidirect
11. #11747291C2semidirect
12. #11747248C2semidirect
13. #11746919C2semidirect
14. #11746913C2semidirect
15. Dic6×#168C2semidirect
72. C4×#687D3semidirect
123. #5539D5semidirect
566. C3×C5#3360semidirect
631. C5#79620semidirect
653. C3#10615368semidirect

Maximal subgroups

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

subgroupindex
C5×#55392
#117524642
#117511172
C3×C4×#6872
#117491142
#117490802
#117490112
#117489862
#117474222
#117473792
#117472912
#117472482
#117469192
#117469132
Dic6×#1682
#106153683
#796205