Finite Group Databasebeta

← #72260139

Subgroups — #72260139

Order 2880.

788 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13089363C211yesmaximal, characteristic
2C42×C3⋊D15C211yesmaximal, characteristic, complemented
3#13087356C211yesmaximal, characteristic, complemented
4C3×#91089C211yesmaximal, characteristic, complemented
5C3×C5×#805C211yesmaximal, characteristic, complemented
6#13084855C211yesmaximal, characteristic, complemented
7#13084852C211yesmaximal, characteristic, complemented
8D15×#104—31nomaximal
9#11747112—31nomaximal
10C2×C4×C3⋊D15—21no—
11C2×C4×C3⋊D15C2211yescharacteristic
12C3×#6817C2211yescharacteristic
13C3×C5×#235C2211yescharacteristic
14#10624218—21no—
15#10624208—21no—
16#10624205C411yescharacteristic, complemented
17C4×D3×D15—21no—
18#10624199—21no—
19#10624198C411yescharacteristic, complemented
20#10624196C411yescharacteristic, complemented
21#10624194C411yescharacteristic, complemented
22C32×C42×C5C2211yescharacteristic, complemented
23C4×C3⋊Dic15—21no—
24C4×C3⋊Dic15C2211yescharacteristic, complemented
25C3×#6710C2211yescharacteristic, complemented
26C3×C5×#208C2211yescharacteristic, complemented
27#10623797—21no—
28#10623794—21no—
29#10590393—51nomaximal, Hall
30#41×D15—31no—
31#92016—31no—
32M16×D15—31no—
33C42×D15—31no—
34C42×D15—31no—
35C42×D15—61no—
36#91292—31no—
37C3×C5×#104—31no—
38#91121—31no—
39#91109—31no—
40#91089D311yescharacteristic, complemented
41C5×#805D311yescharacteristic, complemented
42C3×#3937—31no—
43#90978—31no—
44#90976—31no—
45C22×C3⋊D15D411yescharacteristic
46C2×D3×D15—21no—
47C2×C32×C4×C5—21no—
48C2×C32×C4×C5C2311yescharacteristic
49C2×C3⋊Dic15—21no—
50C2×C3⋊Dic15D411yescharacteristic
51C4×C3⋊D15—24no—
52C4×C3⋊D15C2×C411yescharacteristic
53C4×C3⋊D15C2×C411yescharacteristic
54C4×C3⋊D15D411yescharacteristic
55C4×C3⋊D15D411yescharacteristic
56C3×#1220—21no—
57C3×D60C2×C411yescharacteristic, complemented
58C3×C4×D15—21no—
59C3×Dic30C2×C411yescharacteristic, complemented
60C3×C5×#67—21no—
61C3×C5×D12C2×C411yescharacteristic, complemented
62C3×C4×C5×D3—21no—
63C3×C5×Dic6C2×C411yescharacteristic, complemented
64#67153—21no—
65#67152—21no—
66#67151—21no—
67#67150—21no—
68#67149—21no—
69D3×Dic15—21no—
70Dic3×D15—21no—
71C3×C3⋊#168—21no—
72C3×C5×C3⋊C8—21no—
73D5×#104—91noHall
74#64306—51no—
75C42×C3⋊D3—51no—
76#63818—51no—
77C3×#805—51no—
78C3×#805D511yescharacteristic, complemented
79#63568—51no—
80#63568—51no—
81C3×C5×#41—31no—
82#6821—31no—
83Q8×D15—31no—
84#6819—31no—
85#6819—61no—
86D4×D15—31no—
87D4×D15—61no—
88#6817—61no—
89#6817C2×D311yescharacteristic
90C2×C4×D15—31no—
91C2×C4×D15—31no—
92C2×C4×D15—61no—
93C2×C4×D15—61no—
94C2×C4×D15—61no—
95C2×C4×D15—61no—
96C2×C4×D15—62no—
97C5×#235C2×D311yescharacteristic
98C3×#709—31no—
99#6790—61no—
100#6780—61no—
101#6777—31no—
102C4×D3×D5—61no—
103#6771—61no—
104D15⋊Q8—31no—
105#6768—31no—
106#6766—31no—
107C3×C5×M16—31no—
108C3×C42×C5—21no—
109C3×C42×C5C2×D311yescharacteristic, complemented
110C3×C42×C5C2×D311yescharacteristic, complemented
111C4×Dic15—31no—
112C4×Dic15—31no—
113C4×Dic15—61no—
114C4×Dic15—61no—
115C4×Dic15—61no—
116C4×Dic15—62no—
117#6710C2×D311yescharacteristic, complemented
118#6705—61no—
119C8×D15—61no—
120C5×#208C2×D311yescharacteristic, complemented
121C3×#681—31no—
122#6651—61no—
123#6648—61no—
124D3×#104—151no—
125D3×#104—151no—
126C22×C32×C5C2×D411yescharacteristic
127C2×C3⋊D15—22no—
128C2×C3⋊D15C22⋊C411yescharacteristic
129C2×C3⋊D15C22⋊C411yescharacteristic
130C2×C3×D15—21no—
131C2×C3×C5×D3—21no—
132D3×D15—42no—
133C32×C4×C5—22no—
134C32×C4×C5C22×C411yescharacteristic
135C32×C4×C5C2×D411yescharacteristic
136C3⋊Dic15—22no—
137C3⋊Dic15C22⋊C411yescharacteristic
138C3⋊Dic15C22⋊C411yescharacteristic
139C3×Dic15—21no—
140C3×C5×Dic3—21no—
141D5×#41—91no—
142D5×M16—91no—
143C42×D5—91no—
144C5×#104—31no—
145#3969—91no—
146#3957—91no—
147#3937—31no—
148C2×C4×C3⋊D3—51no—
149C2×C4×C3⋊D3—101no—
150C3×#235—51no—
151C3×#235C2×D511yescharacteristic
152#3811—101no—
153#3805—101no—
154#3802—51no—
155C4×D32—101no—
156#3798—101no—
157#3797—51no—
158#3796—51no—
159#3796—51no—
160C32×C42C2×D511yescharacteristic, complemented
161C4×C3⋊Dic3—51no—
162C4×C3⋊Dic3—101no—
163C3×#208—51no—
164C3×#208C2×D511yescharacteristic, complemented
165#3712—101no—
166#3710—101no—
167C22×D15—31no—
168C22×D15—31no—
169C22×D15—61no—
170C22×D15—61no—
171C2×D3×D5—61no—
172C3×C5×Q8—31no—
173C3×C5×D4—31no—
174C3×C5×D4—61no—
175C2×C3×C4×C5—22no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—61no—
180C2×C3×C4×C5C22×D311yescharacteristic
181C2×C3×C4×C5C22×D311yescharacteristic
182#1220—21no—
183#1220—61no—
184#1220—61no—
185C2×Dic15—31no—
186C2×Dic15—31no—
187C2×Dic15—61no—
188C2×Dic15—61no—
189C2×Dic15—62no—
190C2×Dic15—61no—
191C2×Dic15—61no—
192D60—61no—
193D60C4×D311yescharacteristic, complemented
194C4×D15—21no—
195C4×D15—31no—
196C4×D15—31no—
197C4×D15—31no—
198C4×D15—31no—
199C4×D15—31no—
200C4×D15—31no—
201C4×D15—31no—
202C4×D15—31no—
203C4×D15—61no—
204C4×D15—61no—
205C4×D15—61no—
206C4×D15—61no—
207C4×D15—61no—
208C4×D15—61no—
209C4×D15—64no—
210C4×D15—64no—
211C4×D15—68no—
212Dic30—61no—
213Dic30C4×D311yescharacteristic, complemented
214C5×#67—21no—
215C5×D12C4×D311yescharacteristic, complemented
216C4×C5×D3—21no—
217C5×Dic6C4×D311yescharacteristic, complemented
218C3×C22⋊D5—61no—
219C3×D20—31no—
220C3×C4×D5—61no—
221C3×Dic10—31no—
222#1204—61no—
223#1203—61no—
224#1202—61no—
225#1201—61no—
226#1200—61no—
227D3×Dic5—61no—
228D5×Dic3—61no—
229C3×C5×C8—61no—
230C3⋊#168—21no—
231C3×#168—61no—
232C5×C3⋊C8—21no—
233D3×#41—151no—
234D3×#41—151no—
235D3×M16—151no—
236D3×M16—151no—
237C42×D3—151no—
238C42×D3—151no—
239C42×D3—301no—
240C3×#104—31no—
241C3×#104—151no—
242#837—151no—
243#837—151no—
244#825—151no—
245#825—151no—
246#805—51no—
247#805D1511yescharacteristic, complemented
248C2×C32×C5—21no—
249C2×C32×C5C2×C22⋊C411yescharacteristic
250C3⋊D15—21no—
251C3⋊D15#10412yescomplemented
252C3×D15—41no—
253C3×C5×D3—41no—
254C5×#41—31no—
255#713—91no—
256Q8×D5—91no—
257#711—91no—
258#711—181no—
259D4×D5—91no—
260D4×D5—181no—
261#709—31no—
262#709—181no—
263C2×C4×D5—91no—
264C2×C4×D5—181no—
265C2×C4×D5—181no—
266C5×M16—31no—
267C42×C5D3211yescharacteristic, complemented
268C4×Dic5—91no—
269C4×Dic5—181no—
270#681—31no—
271#676—181no—
272C8×D5—181no—
273C22×C3⋊D3—51no—
274C2×D32—101no—
275C2×C32×C4—21no—
276C2×C32×C4C22×D511yescharacteristic
277C2×C3⋊Dic3—51no—
278C2×C3⋊Dic3—101no—
279C4×C3⋊D3—51no—
280C4×C3⋊D3—51no—
281C4×C3⋊D3—51no—
282C4×C3⋊D3—51no—
283C4×C3⋊D3—104no—
284C3×#67—21no—
285C3×#67—101no—
286C3×D12—51no—
287C3×D12C4×D511yescharacteristic, complemented
288C3×C4×D3—21no—
289C3×C4×D3—101no—
290C3×Dic6—51no—
291C3×Dic6C4×D511yescharacteristic, complemented
292#627—101no—
293#626—101no—
294#626—101no—
295#625—101no—
296#624—101no—
297D3×Dic3—101no—
298D3×Dic3—101no—
299C3×C3⋊C8—21no—
300C3×C3⋊C8—101no—
301C2×#104—451noSylow
302C22×C3×C5—21no—
303C22×C3×C5—61no—
304C22×C3×C5D3×D411yescharacteristic
305C22×C3×C5D3×D411yescharacteristic
306C2×D15—21no—
307C2×D15—31no—
308C2×D15—31no—
309C2×D15—31no—
310C2×D15—31no—
311C2×D15—61no—
312C2×D15—61no—
313C2×D15—62no—
314C2×D15—62no—
315C2×D15—64no—
316C2×D15—122no—
317C2×C5×D3—21no—
318C2×C3×D5—61no—
319D3×D5—122no—
320C3×C4×C5—24no—
321C3×C4×C5—22no—
322C3×C4×C5—22no—
323C3×C4×C5—21no—
324C3×C4×C5—21no—
325C3×C4×C5—61no—
326C3×C4×C5C2×C4×D311yescharacteristic
327C3×C4×C5C2×C4×D311yescharacteristic
328C3×C4×C5D3×D411yescharacteristic
329C3×C4×C5D3×D411yescharacteristic
330Dic15—21no—
331Dic15—31no—
332Dic15—31no—
333Dic15—31no—
334Dic15—31no—
335Dic15—61no—
336Dic15—61no—
337Dic15—64no—
338Dic15—62no—
339Dic15—62no—
340C3×Dic5—61no—
341C5×Dic3—21no—
342C3×#41—31no—
343C3×#41—151no—
344#239—151no—
345#239—151no—
346D3×Q8—151no—
347D3×Q8—151no—
348#237—151no—
349#237—151no—
350#237—301no—
351#237—301no—
352D3×D4—151no—
353D3×D4—151no—
354D3×D4—301no—
355D3×D4—301no—
356#235—51no—
357#235—301no—
358#235—301no—
359#235C2×D1511yescharacteristic
360C2×C4×D3—151no—
361C2×C4×D3—151no—
362C2×C4×D3—301no—
363C2×C4×D3—301no—
364C2×C4×D3—301no—
365C2×C4×D3—301no—
366C2×C4×D3—301no—
367C2×C4×D3—302no—
368C3×M16—31no—
369C3×M16—151no—
370C3×C42—21no—
371C3×C42D3×D511yescharacteristic, complemented
372C3×C42C2×D1511yescharacteristic, complemented
373C4×Dic3—151no—
374C4×Dic3—151no—
375C4×Dic3—301no—
376C4×Dic3—301no—
377C4×Dic3—301no—
378C4×Dic3—302no—
379#208—51no—
380#208C2×D1511yescharacteristic, complemented
381ΓL(1,𝔽25)—301no—
382ΓL(1,𝔽25)—301no—
383D3×C8—301no—
384D3×C8—301no—
385C32×C5C2×#10411yescharacteristic, complemented, Hall
386C22×D5—91no—
387C22×D5—181no—
388C5×Q8—31no—
389C5×D4—31no—
390C5×D4—61no—
391C2×C4×C5—21no—
392C2×C4×C5—61no—
393C2×C4×C5C2×D3211yescharacteristic
394C22⋊D5—61no—
395C22⋊D5—181no—
396C22⋊D5—181no—
397C2×Dic5—91no—
398C2×Dic5—181no—
399C2×Dic5—181no—
400D20—31no—
401D20—181no—
402C4×D5—61no—
403C4×D5—91no—
404C4×D5—91no—
405C4×D5—91no—
406C4×D5—91no—
407C4×D5—181no—
408C4×D5—181no—
409C4×D5—184no—
410Dic10—31no—
411Dic10—181no—
412C5×C8—61no—
413#168—61no—
414C22×C32D4×D511yescharacteristic
415C2×C3⋊D3—51no—
416C2×C3⋊D3—51no—
417C2×C3⋊D3—102no—
418C2×C3×D3—21no—
419C2×C3×D3—101no—
420D32—202no—
421C32×C4—22no—
422C32×C4C2×C4×D511yescharacteristic
423C32×C4D4×D511yescharacteristic
424C3⋊Dic3—51no—
425C3⋊Dic3—51no—
426C3⋊Dic3—102no—
427C3×Dic3—21no—
428C3×Dic3—101no—
429C2×#41—451no—
430C2×M16—451no—
431C2×C42—451no—
432#104—31no—
433#104—151no—
434#104—451no—
435#104—451no—
436C2×C3×C5—22no—
437C2×C3×C5—21no—
438C2×C3×C5—21no—
439C2×C3×C5—21no—
440C2×C3×C5—121no—
441C2×C3×C5D3×C22⋊C411yescharacteristic
442C2×C3×C5D3×C22⋊C411yescharacteristic
443D15—32no—
444D15—32no—
445D15—41no—
446D15—62no—
447D15—62no—
448D15—61no—
449D15—61no—
450C3×D5—121no—
451C5×D3—41no—
452C22×D3—151no—
453C22×D3—151no—
454C22×D3—301no—
455C22×D3—301no—
456C22×D3—301no—
457C3×Q8—31no—
458C3×Q8—151no—
459C3×D4—31no—
460C3×D4—61no—
461C3×D4—151no—
462C3×D4—301no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—61no—
468C2×C3×C4—301no—
469C2×C3×C4C2×D3×D511yescharacteristic
470C2×C3×C4C22×D1511yescharacteristic
471#67—21no—
472#67—101no—
473#67—301no—
474#67—301no—
475#67—301no—
476#67—301no—
477C2×Dic3—151no—
478C2×Dic3—151no—
479C2×Dic3—301no—
480C2×Dic3—301no—
481C2×Dic3—301no—
482C2×Dic3—302no—
483C2×Dic3—301no—
484C2×Dic3—301no—
485D12—51no—
486D12—301no—
487D12—301no—
488D12C4×D1511yescharacteristic, complemented
489C4×D3—21no—
490C4×D3—101no—
491C4×D3—151no—
492C4×D3—151no—
493C4×D3—151no—
494C4×D3—151no—
495C4×D3—151no—
496C4×D3—151no—
497C4×D3—151no—
498C4×D3—151no—
499C4×D3—301no—
500C4×D3—301no—
501C4×D3—301no—
502C4×D3—301no—
503C4×D3—301no—
504C4×D3—301no—
505C4×D3—301no—
506C4×D3—301no—
507C4×D3—304no—
508C4×D3—304no—
509C4×D3—308no—
510Dic6—51no—
511Dic6—301no—
512Dic6—301no—
513Dic6C4×D1511yescharacteristic, complemented
514C3×C8—61no—
515C3×C8—301no—
516C3⋊C8—21no—
517C3⋊C8—101no—
518C22×C5—61no—
519C22×C5#381111yescharacteristic
520C2×D5—61no—
521C2×D5—91no—
522C2×D5—91no—
523C2×D5—182no—
524C2×D5—362no—
525C4×C5—22no—
526C4×C5—61no—
527C4×C5C4×D3211yescharacteristic
528C4×C5#380211yescharacteristic
529Dic5—61no—
530Dic5—91no—
531Dic5—91no—
532Dic5—182no—
533C2×C32—21no—
534C2×C32D5×C22⋊C411yescharacteristic
535C3⋊D3—52no—
536C3⋊D3—101no—
537C3×D3—41no—
538C3×D3—201no—
539#41—31no—
540#41—151no—
541#41—451no—
542#41—451no—
543#41—901no—
544#41—901no—
545C2×Q8—451no—
546C2×D4—451no—
547C2×D4—901no—
548C22×C4—451no—
549C22×C4—901no—
550C22×C4—901no—
551M16—31no—
552M16—151no—
553M16—901no—
554C2×C8—901no—
555C42—451no—
556C42—901no—
557C42D3×D1511yescharacteristic, complemented
558C3×C5—21no—
559C3×C5D3×#10411yescharacteristic, complemented
560C3×C5D3×#10411yescharacteristic, complemented
561C22×C3—21no—
562C22×C3—61no—
563C22×C3—301no—
564C22×C3#679011yescharacteristic
565C22×C3D4×D1511yescharacteristic
566C2×D3—21no—
567C2×D3—101no—
568C2×D3—151no—
569C2×D3—151no—
570C2×D3—151no—
571C2×D3—151no—
572C2×D3—301no—
573C2×D3—301no—
574C2×D3—302no—
575C2×D3—302no—
576C2×D3—304no—
577C2×D3—602no—
578C2×D3—602no—
579C3×C4—24no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—61no—
585C3×C4—301no—
586C3×C4C4×D3×D511yescharacteristic
587C3×C4#677711yescharacteristic
588C3×C4C2×C4×D1511yescharacteristic
589C3×C4D4×D1511yescharacteristic
590Dic3—21no—
591Dic3—101no—
592Dic3—151no—
593Dic3—151no—
594Dic3—151no—
595Dic3—151no—
596Dic3—301no—
597Dic3—301no—
598Dic3—304no—
599Dic3—302no—
600Dic3—302no—
601C2×C5—21no—
602C2×C5—121no—
603C2×C5#6392111yescharacteristic
604D5—92no—
605D5—121no—
606D5—181no—
607C32D5×#10411yescharacteristic, complemented, Sylow
608C23—451no—
609C23—901no—
610Q8—31no—
611Q8—151no—
612Q8—901no—
613D4—31no—
614D4—61no—
615D4—151no—
616D4—301no—
617D4—901no—
618D4—901no—
619D4—901no—
620C2×C4—21no—
621C2×C4—61no—
622C2×C4—301no—
623C2×C4—451no—
624C2×C4—451no—
625C2×C4—451no—
626C2×C4—451no—
627C2×C4—451no—
628C2×C4—904no—
629C2×C4—901no—
630C2×C4—901no—
631C2×C4—901no—
632C2×C4—901no—
633C2×C4C2×D3×D1511yescharacteristic
634C8—61no—
635C8—301no—
636C2×C3—22no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—121no—
641C2×C3—601no—
642C2×C3#9147311yescharacteristic
643C2×C3C22⋊C4×D1511yescharacteristic
644D3—41no—
645D3—152no—
646D3—152no—
647D3—201no—
648D3—302no—
649D3—302no—
650D3—301no—
651D3—301no—
652C5#1059039311yescharacteristic, complemented, Sylow
653C22—61no—
654C22—301no—
655C22—451no—
656C22—451no—
657C22—902no—
658C22—1802no—
659C22#1062421811yescharacteristic
660C4—22no—
661C4—61no—
662C4—301no—
663C4—451no—
664C4—451no—
665C4—902no—
666C4C4×D3×D1511yescharacteristic
667C4#1062420511yescharacteristic
668C3—21no—
669C3#1174711211yescharacteristic, complemented
670C3D15×#10411yescharacteristic, complemented
671C2—21no—
672C2—121no—
673C2—452no—
674C2—601no—
675C2—901no—
676C2#1308748611yescharacteristic
subgroupG/H
centerC4#10624205
commutatorC32×C4×C5C22×C4
FrattiniC2×C4C2×D3×D15
FittingC32×C42×C5C22
socleC2×C32×C5C2×C22⋊C4
prime radical#13089363C2
cosocleC2×C32×C4×C5C23
hypercenterC42D3×D15
hypocenterC32×C5C2×#104
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C42×C3⋊D15C2semidirect
3. #13087356C2semidirect
4. C3×#91089C2semidirect
5. C3×C5×#805C2semidirect
6. #13084855C2semidirect
7. #13084852C2semidirect
16. #10624205C4semidirect
19. #10624198C4semidirect
20. #10624196C4semidirect
21. #10624194C4semidirect
22. C32×C42×C5C22semidirect
24. C4×C3⋊Dic15C22semidirect
25. C3×#6710C22semidirect
26. C3×C5×#208C22semidirect
40. #91089D3semidirect
41. C5×#805D3semidirect
57. C3×D60C2×C4semidirect
59. C3×Dic30C2×C4semidirect
61. C3×C5×D12C2×C4semidirect
63. C3×C5×Dic6C2×C4semidirect
78. C3×#805D5semidirect
109. C3×C42×C5C2×D3semidirect
110. C3×C42×C5C2×D3semidirect
117. #6710C2×D3semidirect
120. C5×#208C2×D3semidirect
160. C32×C42C2×D5semidirect
164. C3×#208C2×D5semidirect
193. D60C4×D3semidirect
213. Dic30C4×D3semidirect
215. C5×D12C4×D3semidirect
217. C5×Dic6C4×D3semidirect
247. #805D15semidirect
251. C3⋊D15#104semidirect
267. C42×C5D32semidirect
287. C3×D12C4×D5semidirect
291. C3×Dic6C4×D5semidirect
371. C3×C42D3×D5semidirect
372. C3×C42C2×D15semidirect
380. #208C2×D15semidirect
385. C32×C5C2×#104semidirect
488. D12C4×D15semidirect
513. Dic6C4×D15semidirect
557. C42D3×D15semidirect
559. C3×C5D3×#104semidirect
560. C3×C5D3×#104semidirect
607. C32D5×#104semidirect
652. C5#10590393semidirect
669. C3#11747112semidirect
670. C3D15×#104semidirect

Maximal subgroups

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

subgroupindex
#130893632
C42×C3⋊D152
#130873562
C3×#910892
C3×C5×#8052
#130848552
#130848522
D15×#1043
#117471123
#105903935