Finite Group Databasebeta

← #14457665

Subgroups — #14457665

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#577C211yesmaximal, characteristic, complemented
2#11756596C211yesmaximal, characteristic, complemented
3#11756594C211yesmaximal, characteristic, complemented
4#11756528C211yesmaximal, characteristic, complemented
5#11751346C211yesmaximal, characteristic, complemented
6#11751342C211yesmaximal, characteristic, complemented
7#11751304C211yesmaximal, characteristic, complemented
8#11751303C211yesmaximal, characteristic, complemented
9#11751300C211yesmaximal, characteristic, complemented
10#11751299C211yesmaximal, characteristic, complemented
11#11751298C211yesmaximal, characteristic, complemented
12#11751278C211yesmaximal, characteristic, complemented
13#11751277C211yesmaximal, characteristic, complemented
14#11751246C211yesmaximal, characteristic, complemented
15#11751243C211yesmaximal, characteristic, complemented
16#10615746—31nomaximal, Hall
17C3×C5×2−1+4C2211yescharacteristic, complemented
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19#92100C2211yescharacteristic
20#92100C2211yescharacteristic, complemented
21C3×C5×#137—21no—
22C3×C5×#137C2211yescharacteristic, complemented
23C3×C5×AGL(1,ℤ/8)—21no—
24C3×C5×AGL(1,ℤ/8)C2211yescharacteristic, complemented
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×SD16—21no—
28C2×C3×C5×SD16C2211yescharacteristic, complemented
29C3×C5×#131C2211yescharacteristic, complemented
30#91839—21no—
31#91839—21no—
32#91839C2211yescharacteristic
33#91838—21no—
34#91838—21no—
35#91838C2211yescharacteristic
36#91838C2211yescharacteristic, complemented
37#91838C2211yescharacteristic, complemented
38#91838C2211yescharacteristic, complemented
39#91837C2211yescharacteristic, complemented
40#91837C2211yescharacteristic, complemented
41#91836C2211yescharacteristic, complemented
42#91831—21no—
43#91831C2211yescharacteristic, complemented
44C2×#6717—21no—
45C2×#6717C2211yescharacteristic, complemented
46#91829C2211yescharacteristic, complemented
47#91821—21no—
48#91821C2211yescharacteristic
49C2×#6715—21no—
50C2×#6715C2211yescharacteristic, complemented
51#91808—21no—
52#91803—21no—
53#91803—21no—
54D8×D15—21no—
55C2×D120C2211yescharacteristic, complemented
56#91790C2211yescharacteristic, complemented
57#91121C2211yescharacteristic, complemented
58#91121C2211yescharacteristic, complemented
59#91121C2211yescharacteristic, complemented
60#91120C2211yescharacteristic, complemented
61#91117C2211yescharacteristic, complemented
62#91109C2211yescharacteristic, complemented
63#91107C2211yescharacteristic, complemented
64#91107C2211yescharacteristic, complemented
65#91106C2211yescharacteristic, complemented
66#91103C2211yescharacteristic, complemented
67#91099C2211yescharacteristic, complemented
68#84015—51nomaximal, Hall
69C5×#577D311yescharacteristic, complemented
70#66171—31no—
71#66169—31no—
72#66103—31no—
73#65534—31no—
74#65530—31no—
75#65492—31no—
76#65491—31no—
77#65488—31no—
78#65487—31no—
79#65486—31no—
80#65466—31no—
81#65465—31no—
82#65434—31no—
83#65431—31no—
84C3×C5×#41—21no—
85C3×C5×#41—21no—
86C3×C5×#41—21no—
87C3×C5×#41—21no—
88C3×C5×#41—41no—
89C3×C5×#41C2311yescharacteristic
90C3×C5×#41C2311yescharacteristic
91C3×C5×#41C2311yescharacteristic
92C2×C3×C5×Q8—21no—
93C2×C3×C5×Q8—21no—
94C2×C3×C5×Q8C2311yescharacteristic
95C2×C3×C5×D4—21no—
96C2×C3×C5×D4—21no—
97C2×C3×C5×D4—41no—
98C2×C3×C5×D4C2311yescharacteristic
99C2×#1220—41no—
100#6821—21no—
101#6821—21no—
102D4×D15—21no—
103D4×D15—21no—
104D4×D15—41no—
105D4×D15—41no—
106#6817—21no—
107#6817—21no—
108#6817C2311yescharacteristic
109C2×D60—21no—
110C2×D60—21no—
111C2×D60C2311yescharacteristic
112C2×D60C2311yescharacteristic
113C3×C5×Q16—21no—
114C3×C5×Q16D411yescharacteristic, complemented
115C3×C5×SD16—21no—
116C3×C5×SD16—21no—
117C3×C5×SD16—21no—
118C3×C5×SD16—21no—
119C3×C5×SD16D411yescharacteristic, complemented
120C3×C5×SD16D411yescharacteristic, complemented
121C3×C5×D8—21no—
122C3×C5×D8D411yescharacteristic, complemented
123C3×C5×M16—21no—
124C3×C5×M16C2311yescharacteristic
125C2×C3×C5×C8—21no—
126C2×C3×C5×C8C2311yescharacteristic
127#6718—21no—
128#6718D411yescharacteristic, complemented
129#6717—21no—
130#6717—21no—
131#6717—21no—
132#6717—21no—
133#6717—21no—
134#6717—21no—
135#6717—21no—
136#6717D411yescharacteristic, complemented
137#6716—21no—
138#6716D411yescharacteristic, complemented
139#6715—21no—
140#6715—21no—
141#6715—21no—
142#6715—21no—
143#6715—21no—
144#6715—21no—
145#6715—21no—
146#6715D411yescharacteristic, complemented
147#6714—41no—
148C4×Dic15C2311yescharacteristic
149#6710—21no—
150#6710—21no—
151#6710C2311yescharacteristic
152#6710C2311yescharacteristic
153#6710C2311yescharacteristic
154C2×C3⋊#168—21no—
155C2×C3⋊#168—21no—
156C2×C3⋊#168C2311yescharacteristic
157D120—21no—
158D120—21no—
159#6705—21no—
160C8×D15—21no—
161C3×#577D511yescharacteristic, complemented
162#5837—51no—
163#5835—51no—
164#5769—51no—
165#5245—51no—
166#5241—51no—
167#5203—51no—
168#5202—51no—
169#5199—51no—
170#5198—51no—
171#5197—51no—
172#5177—51no—
173#5176—51no—
174#5145—51no—
175#5142—51no—
176C5×2−1+4C2×D311yescharacteristic, complemented
177C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
178#4149—31no—
179#4149—31no—
180C5×#137—21no—
181C5×#137C2×D311yescharacteristic, complemented
182C5×AGL(1,ℤ/8)—21no—
183C5×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
184C5×#135—21no—
185C5×#135C2×D311yescharacteristic
186C2×C5×SD16—21no—
187C2×C5×SD16C2×D311yescharacteristic, complemented
188C5×#131C2×D311yescharacteristic, complemented
189#4096—31no—
190#4096—61no—
191#4096—61no—
192#4095—31no—
193#4095—31no—
194#4095—31no—
195#4095—31no—
196#4095—61no—
197#4095—61no—
198#4094—31no—
199#4094—31no—
200#4093—31no—
201#4088—31no—
202#4088—61no—
203C2×#688—31no—
204C2×#688—61no—
205#4086—31no—
206#4078—31no—
207#4078—61no—
208C2×#686—31no—
209C2×#686—61no—
210#4065—61no—
211#4060—61no—
212#4060—61no—
213D5×D8—61no—
214C2×D40—31no—
215#4047—31no—
216#3969—31no—
217#3969—31no—
218#3969—31no—
219#3968—31no—
220#3965—31no—
221#3957—31no—
222#3955—31no—
223#3955—31no—
224#3954—31no—
225#3951—31no—
226#3947—31no—
227#3288—151noSylow
228C23×C3×C5—21no—
229C23×C3×C5—41no—
230C22×D15—21no—
231C22×D15—21no—
232C22×D15—41no—
233C22×D15—41no—
234C3×C5×Q8—21no—
235C3×C5×Q8—21no—
236C3×C5×Q8—41no—
237C3×C5×Q8C2×D411yescharacteristic
238C3×C5×Q8C2×D411yescharacteristic
239C3×C5×Q8C2×D411yescharacteristic
240C3×C5×D4—21no—
241C3×C5×D4—21no—
242C3×C5×D4—21no—
243C3×C5×D4—21no—
244C3×C5×D4—21no—
245C3×C5×D4—41no—
246C3×C5×D4—41no—
247C3×C5×D4—41no—
248C3×C5×D4C2×D411yescharacteristic
249C3×C5×D4C2×D411yescharacteristic
250C3×C5×D4C2×D411yescharacteristic
251C2×C3×C4×C5—21no—
252C2×C3×C4×C5—21no—
253C2×C3×C4×C5—21no—
254C2×C3×C4×C5—21no—
255C2×C3×C4×C5—41no—
256C2×C3×C4×C5—41no—
257C2×C3×C4×C5—41no—
258C2×C3×C4×C5C2411yescharacteristic
259#1220—21no—
260#1220—41no—
261#1220—41no—
262#1220—82no—
263C2×Dic15—21no—
264D60—21no—
265D60—21no—
266D60—21no—
267D60—21no—
268D60—41no—
269D60—41no—
270D60C2×D411yescharacteristic
271C4×D15—21no—
272C4×D15—41no—
273C4×D15—41no—
274Dic30C2×D411yescharacteristic
275C3×C5×C8—21no—
276C3×C5×C8C2×D411yescharacteristic
277C3×C5×C8C2×D411yescharacteristic
278C3⋊#168—21no—
279C3⋊#168—21no—
280C3⋊#168—21no—
281C3⋊#168C2×D411yescharacteristic
282C3⋊#168C2×D411yescharacteristic
283C3×2−1+4C2×D511yescharacteristic, complemented
284C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
285#1009—51no—
286#1009—51no—
287C3×#137—21no—
288C3×#137C2×D511yescharacteristic, complemented
289C3×AGL(1,ℤ/8)—21no—
290C3×AGL(1,ℤ/8)C2×D511yescharacteristic, complemented
291C3×#135—21no—
292C3×#135C2×D511yescharacteristic
293C2×C3×SD16—21no—
294C2×C3×SD16C2×D511yescharacteristic, complemented
295C3×#131C2×D511yescharacteristic, complemented
296#950—51no—
297#950—101no—
298#950—101no—
299#949—51no—
300#949—51no—
301#949—51no—
302#949—51no—
303#949—101no—
304#949—101no—
305#948—51no—
306#948—51no—
307#947—51no—
308#942—51no—
309#942—101no—
310C2×#215—51no—
311C2×#215—101no—
312#940—51no—
313#932—51no—
314#932—101no—
315C2×#213—51no—
316C2×#213—101no—
317#919—101no—
318#914—101no—
319#914—101no—
320D3×D8—101no—
321C2×D24—51no—
322#901—51no—
323#837—51no—
324#837—51no—
325#837—51no—
326#836—51no—
327#833—51no—
328#825—51no—
329#823—51no—
330#823—51no—
331#822—51no—
332#819—51no—
333#815—51no—
334C5×#41—21no—
335C5×#41—21no—
336C5×#41—21no—
337C5×#41—21no—
338C5×#41—41no—
339C5×#41C22×D311yescharacteristic
340C5×#41C22×D311yescharacteristic
341C5×#41C22×D311yescharacteristic
342C2×C5×Q8—21no—
343C2×C5×Q8—21no—
344C2×C5×Q8C22×D311yescharacteristic
345C2×C5×D4—21no—
346C2×C5×D4—21no—
347C2×C5×D4—41no—
348C2×C5×D4C22×D311yescharacteristic
349C2×C22⋊D5—121no—
350#713—61no—
351#713—61no—
352D4×D5—61no—
353D4×D5—61no—
354D4×D5—121no—
355D4×D5—121no—
356#709—31no—
357#709—61no—
358#709—61no—
359C2×D20—31no—
360C2×D20—31no—
361C2×D20—61no—
362C2×D20—61no—
363C5×Q16—21no—
364C5×Q16#6711yescharacteristic, complemented
365C5×SD16—21no—
366C5×SD16—21no—
367C5×SD16—21no—
368C5×SD16—21no—
369C5×SD16#6711yescharacteristic, complemented
370C5×SD16#6711yescharacteristic, complemented
371C5×D8—21no—
372C5×D8#6711yescharacteristic, complemented
373C5×M16—21no—
374C5×M16C22×D311yescharacteristic
375C2×C5×C8—21no—
376C2×C5×C8C22×D311yescharacteristic
377#689—31no—
378#689—61no—
379#688—31no—
380#688—61no—
381#688—61no—
382#688—61no—
383#688—61no—
384#688—61no—
385#688—61no—
386#688—61no—
387#687—31no—
388#687—61no—
389#686—31no—
390#686—61no—
391#686—61no—
392#686—61no—
393#686—61no—
394#686—61no—
395#686—61no—
396#686—61no—
397#685—121no—
398C4×Dic5—31no—
399#681—31no—
400#681—31no—
401#681—31no—
402#681—61no—
403#681—61no—
404C2×#168—31no—
405C2×#168—61no—
406C2×#168—61no—
407D40—61no—
408D40—61no—
409#676—61no—
410C8×D5—61no—
411#577—151no—
412#577D1511yescharacteristic, complemented
413#576—151no—
414#576—151no—
415#496—151no—
416#472—151no—
417#472—151no—
418#471—151no—
419#471—151no—
420#455—151no—
421#454—151no—
422#453—151no—
423#453—151no—
424#444—151no—
425#444—151no—
426C22×C3×C5—21no—
427C22×C3×C5—21no—
428C22×C3×C5—21no—
429C22×C3×C5—41no—
430C22×C3×C5—81no—
431C22×C3×C5—161no—
432C22×C3×C5H(5,𝔽2)11yescharacteristic
433C2×D15—21no—
434C2×D15—41no—
435C2×D15—41no—
436C2×D15—81no—
437C2×D15—81no—
438C2×D15—161no—
439C2×D15—161no—
440C3×C4×C5—21no—
441C3×C4×C5—21no—
442C3×C4×C5—21no—
443C3×C4×C5—41no—
444C3×C4×C5C22×D411yescharacteristic
445C3×C4×C5C22×D411yescharacteristic
446Dic15—21no—
447Dic15—41no—
448C3×#41—21no—
449C3×#41—21no—
450C3×#41—21no—
451C3×#41—21no—
452C3×#41—41no—
453C3×#41C22×D511yescharacteristic
454C3×#41C22×D511yescharacteristic
455C3×#41C22×D511yescharacteristic
456C2×C3×Q8—21no—
457C2×C3×Q8—21no—
458C2×C3×Q8C22×D511yescharacteristic
459C2×C3×D4—21no—
460C2×C3×D4—21no—
461C2×C3×D4—41no—
462C2×C3×D4C22×D511yescharacteristic
463C2×#67—201no—
464#239—101no—
465#239—101no—
466D3×D4—101no—
467D3×D4—101no—
468D3×D4—201no—
469D3×D4—201no—
470#235—51no—
471#235—101no—
472#235—101no—
473C2×D12—51no—
474C2×D12—51no—
475C2×D12—101no—
476C2×D12—101no—
477C3×Q16—21no—
478C3×Q16C22⋊D511yescharacteristic, complemented
479C3×SD16—21no—
480C3×SD16—21no—
481C3×SD16—21no—
482C3×SD16—21no—
483C3×SD16C22⋊D511yescharacteristic, complemented
484C3×SD16C22⋊D511yescharacteristic, complemented
485C3×D8—21no—
486C3×D8C22⋊D511yescharacteristic, complemented
487C3×M16—21no—
488C3×M16C22×D511yescharacteristic
489C2×C3×C8—21no—
490C2×C3×C8C22×D511yescharacteristic
491#216—51no—
492#216—101no—
493#215—51no—
494#215—101no—
495#215—101no—
496#215—101no—
497#215—101no—
498#215—101no—
499#215—101no—
500#215—101no—
501#214—51no—
502#214—101no—
503#213—51no—
504#213—101no—
505#213—101no—
506#213—101no—
507#213—101no—
508#213—101no—
509#213—101no—
510#213—101no—
511(C2×D3)⋊C4—201no—
512C4×Dic3—51no—
513#208—51no—
514#208—51no—
515#208—51no—
516#208—101no—
517#208—101no—
518C2×C3⋊C8—51no—
519C2×C3⋊C8—101no—
520C2×C3⋊C8—101no—
521D24—101no—
522D24—101no—
523ΓL(1,𝔽25)—101no—
524D3×C8—101no—
525C23×C5—21no—
526C23×C5—41no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—121no—
530C22×D5—121no—
531C5×Q8—21no—
532C5×Q8—21no—
533C5×Q8—41no—
534C5×Q8D3×D411yescharacteristic
535C5×Q8C2×#6711yescharacteristic
536C5×Q8C2×#6711yescharacteristic
537C5×D4—21no—
538C5×D4—21no—
539C5×D4—21no—
540C5×D4—21no—
541C5×D4—21no—
542C5×D4—41no—
543C5×D4—41no—
544C5×D4—41no—
545C5×D4D3×D411yescharacteristic
546C5×D4C2×#6711yescharacteristic
547C5×D4C2×#6711yescharacteristic
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5C23×D311yescharacteristic
556C22⋊D5—61no—
557C22⋊D5—121no—
558C22⋊D5—121no—
559C22⋊D5—242no—
560C2×Dic5—61no—
561D20—31no—
562D20—61no—
563D20—61no—
564D20—61no—
565D20—61no—
566D20—121no—
567D20—121no—
568C4×D5—61no—
569C4×D5—121no—
570C4×D5—121no—
571Dic10—31no—
572C5×C8—21no—
573C5×C8C2×#6711yescharacteristic
574C5×C8C2×#6711yescharacteristic
575#168—31no—
576#168—31no—
577#168—61no—
578#168—61no—
579#168—61no—
5802−1+4C2×D1511yescharacteristic, complemented
581H(5,𝔽2)—151no—
582H(5,𝔽2)—151no—
583H(5,𝔽2)C2×D1511yescharacteristic, complemented
584#137—21no—
585#137—151no—
586#137—301no—
587#137C2×D1511yescharacteristic, complemented
588AGL(1,ℤ/8)—21no—
589AGL(1,ℤ/8)—151no—
590AGL(1,ℤ/8)—151no—
591AGL(1,ℤ/8)—151no—
592AGL(1,ℤ/8)—151no—
593AGL(1,ℤ/8)—151no—
594AGL(1,ℤ/8)—301no—
595AGL(1,ℤ/8)—301no—
596AGL(1,ℤ/8)—301no—
597AGL(1,ℤ/8)—301no—
598AGL(1,ℤ/8)—301no—
599AGL(1,ℤ/8)C2×D1511yescharacteristic, complemented
600#135—21no—
601#135—151no—
602#135—301no—
603#135—301no—
604#135—301no—
605#135C2×D1511yescharacteristic
606C2×SD16—21no—
607C2×SD16—151no—
608C2×SD16—301no—
609C2×SD16C2×D1511yescharacteristic, complemented
610C2×D8—151no—
611C2×D8—151no—
612C2×D8—301no—
613C2×D8—301no—
614#131—151no—
615#131—151no—
616#131—151no—
617#131C2×D1511yescharacteristic, complemented
618#127—151no—
619#124—151no—
620#108—151no—
621#108—151no—
622#104—151no—
623#104—151no—
624#104—151no—
625#104—151no—
626#101—151no—
627#100—151no—
628#100—151no—
629#100—151no—
630#97—151no—
631C2×C3×C5—21no—
632C2×C3×C5—41no—
633C2×C3×C5—41no—
634C2×C3×C5—41no—
635C2×C3×C5—81no—
636C2×C3×C5D4211yescharacteristic
637D15—41no—
638D15—81no—
639D15—81no—
640C23×C3—21no—
641C23×C3—41no—
642C22×D3—101no—
643C22×D3—101no—
644C22×D3—201no—
645C22×D3—201no—
646C3×Q8—21no—
647C3×Q8—21no—
648C3×Q8—41no—
649C3×Q8D4×D511yescharacteristic
650C3×Q8C2×C22⋊D511yescharacteristic
651C3×Q8C2×C22⋊D511yescharacteristic
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—41no—
658C3×D4—41no—
659C3×D4—41no—
660C3×D4D4×D511yescharacteristic
661C3×D4C2×C22⋊D511yescharacteristic
662C3×D4C2×C22⋊D511yescharacteristic
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4C23×D511yescharacteristic
671#67—101no—
672#67—201no—
673#67—201no—
674#67—402no—
675C2×Dic3—101no—
676D12—51no—
677D12—101no—
678D12—101no—
679D12—101no—
680D12—101no—
681D12—201no—
682D12—201no—
683C4×D3—101no—
684C4×D3—201no—
685C4×D3—201no—
686Dic6—51no—
687C3×C8—21no—
688C3×C8C2×C22⋊D511yescharacteristic
689C3×C8C2×C22⋊D511yescharacteristic
690C3⋊C8—51no—
691C3⋊C8—51no—
692C3⋊C8—101no—
693C3⋊C8—101no—
694C3⋊C8—101no—
695C22×C5—21no—
696C22×C5—21no—
697C22×C5—21no—
698C22×C5—41no—
699C22×C5—81no—
700C22×C5—161no—
701C22×C5#100411yescharacteristic
702C2×D5—61no—
703C2×D5—121no—
704C2×D5—121no—
705C2×D5—241no—
706C2×D5—241no—
707C2×D5—481no—
708C2×D5—481no—
709C4×C5—21no—
710C4×C5—21no—
711C4×C5—21no—
712C4×C5—41no—
713C4×C5C2×D3×D411yescharacteristic
714C4×C5C22×#6711yescharacteristic
715Dic5—61no—
716Dic5—121no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—41no—
722#41—151no—
723#41—301no—
724#41—301no—
725#41—301no—
726#41—301no—
727#41C22×D1511yescharacteristic
728#41C22×D1511yescharacteristic
729#41C22×D1511yescharacteristic
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8C22×D1511yescharacteristic
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—151no—
737C2×D4—151no—
738C2×D4—301no—
739C2×D4—301no—
740C2×D4—301no—
741C2×D4—301no—
742C2×D4—601no—
743C2×D4—601no—
744C2×D4—601no—
745C2×D4C22×D1511yescharacteristic
746Q16—21no—
747Q16—151no—
748Q16—301no—
749Q16#122011yescharacteristic, complemented
750SD16—21no—
751SD16—21no—
752SD16—21no—
753SD16—21no—
754SD16—151no—
755SD16—151no—
756SD16—301no—
757SD16—301no—
758SD16—301no—
759SD16—301no—
760SD16—301no—
761SD16—301no—
762SD16—301no—
763SD16—301no—
764SD16#122011yescharacteristic, complemented
765SD16#122011yescharacteristic, complemented
766D8—21no—
767D8—151no—
768D8—301no—
769D8—301no—
770D8—301no—
771D8—301no—
772D8—301no—
773D8—301no—
774D8—301no—
775D8—301no—
776D8—301no—
777D8#122011yescharacteristic, complemented
778M16—21no—
779M16—151no—
780M16—151no—
781M16—151no—
782M16—301no—
783M16—301no—
784M16—301no—
785M16C22×D1511yescharacteristic
786C2×C8—21no—
787C2×C8—151no—
788C2×C8—301no—
789C2×C8—301no—
790C2×C8—301no—
791C2×C8C22×D1511yescharacteristic
792C22⋊C4—601no—
793C42—151no—
794C3×C5#328811yescharacteristic, complemented, Hall
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—41no—
799C22×C3—81no—
800C22×C3—161no—
801C22×C3#414411yescharacteristic
802C2×D3—101no—
803C2×D3—201no—
804C2×D3—201no—
805C2×D3—401no—
806C2×D3—401no—
807C2×D3—801no—
808C2×D3—801no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—41no—
813C3×C4C2×D4×D511yescharacteristic
814C3×C4C22×C22⋊D511yescharacteristic
815Dic3—101no—
816Dic3—201no—
817C2×C5—21no—
818C2×C5—41no—
819C2×C5—41no—
820C2×C5—41no—
821C2×C5—81no—
822C2×C5D4×#6711yescharacteristic
823D5—121no—
824D5—241no—
825D5—241no—
826C23—21no—
827C23—41no—
828C23—301no—
829C23—301no—
830C23—601no—
831C23—601no—
832Q8—21no—
833Q8—21no—
834Q8—41no—
835Q8—151no—
836Q8D4×D1511yescharacteristic
837Q8C2×#122011yescharacteristic
838Q8C2×#122011yescharacteristic
839D4—21no—
840D4—21no—
841D4—21no—
842D4—21no—
843D4—21no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—151no—
848D4—301no—
849D4—301no—
850D4—301no—
851D4—301no—
852D4—301no—
853D4—601no—
854D4—601no—
855D4—601no—
856D4—601no—
857D4—1202no—
858D4D4×D1511yescharacteristic
859D4C2×#122011yescharacteristic
860D4C2×#122011yescharacteristic
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—301no—
869C2×C4—301no—
870C2×C4—601no—
871C2×C4—601no—
872C2×C4C23×D1511yescharacteristic
873C8—21no—
874C8—151no—
875C8—151no—
876C8—301no—
877C8—301no—
878C8—301no—
879C8C2×#122011yescharacteristic
880C8C2×#122011yescharacteristic
881C2×C3—21no—
882C2×C3—41no—
883C2×C3—41no—
884C2×C3—41no—
885C2×C3—81no—
886C2×C3D4×C22⋊D511yescharacteristic
887D3—201no—
888D3—401no—
889D3—401no—
890C5#8401511yescharacteristic, complemented, Sylow
891C22—21no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—81no—
896C22—161no—
897C22—301no—
898C22—601no—
899C22—601no—
900C22—1201no—
901C22—1201no—
902C22—2401no—
903C22—2401no—
904C22#9209511yescharacteristic
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—301no—
910C4—601no—
911C4C2×D4×D1511yescharacteristic
912C4C22×#122011yescharacteristic
913C3#1061574611yescharacteristic, complemented, Sylow
914C2—21no—
915C2—41no—
916C2—41no—
917C2—41no—
918C2—81no—
919C2—601no—
920C2—1201no—
921C2—1201no—
922C2D4×#122011yescharacteristic
subgroupG/H
centerC2D4×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#577C2
socleC2×C3×C5D42
hypercenter#577D15
hypocenterC3×C5#3288
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. C3×C5×#577C2semidirect
2. #11756596C2semidirect
3. #11756594C2semidirect
4. #11756528C2semidirect
5. #11751346C2semidirect
6. #11751342C2semidirect
7. #11751304C2semidirect
8. #11751303C2semidirect
9. #11751300C2semidirect
10. #11751299C2semidirect
11. #11751298C2semidirect
12. #11751278C2semidirect
13. #11751277C2semidirect
14. #11751246C2semidirect
15. #11751243C2semidirect
17. C3×C5×2−1+4C22semidirect
18. C3×C5×H(5,𝔽2)C22semidirect
20. #92100C22semidirect
22. C3×C5×#137C22semidirect
24. C3×C5×AGL(1,ℤ/8)C22semidirect
28. C2×C3×C5×SD16C22semidirect
29. C3×C5×#131C22semidirect
36. #91838C22semidirect
37. #91838C22semidirect
38. #91838C22semidirect
39. #91837C22semidirect
40. #91837C22semidirect
41. #91836C22semidirect
43. #91831C22semidirect
45. C2×#6717C22semidirect
46. #91829C22semidirect
50. C2×#6715C22semidirect
55. C2×D120C22semidirect
56. #91790C22semidirect
57. #91121C22semidirect
58. #91121C22semidirect
59. #91121C22semidirect
60. #91120C22semidirect
61. #91117C22semidirect
62. #91109C22semidirect
63. #91107C22semidirect
64. #91107C22semidirect
65. #91106C22semidirect
66. #91103C22semidirect
67. #91099C22semidirect
69. C5×#577D3semidirect
114. C3×C5×Q16D4semidirect
119. C3×C5×SD16D4semidirect
120. C3×C5×SD16D4semidirect
122. C3×C5×D8D4semidirect
128. #6718D4semidirect
136. #6717D4semidirect
138. #6716D4semidirect
146. #6715D4semidirect
161. C3×#577D5semidirect
176. C5×2−1+4C2×D3semidirect
177. C5×H(5,𝔽2)C2×D3semidirect
181. C5×#137C2×D3semidirect
183. C5×AGL(1,ℤ/8)C2×D3semidirect
187. C2×C5×SD16C2×D3semidirect
188. C5×#131C2×D3semidirect
283. C3×2−1+4C2×D5semidirect
284. C3×H(5,𝔽2)C2×D5semidirect
288. C3×#137C2×D5semidirect
290. C3×AGL(1,ℤ/8)C2×D5semidirect
294. C2×C3×SD16C2×D5semidirect
295. C3×#131C2×D5semidirect
364. C5×Q16#67semidirect
369. C5×SD16#67semidirect
370. C5×SD16#67semidirect
372. C5×D8#67semidirect
412. #577D15semidirect
478. C3×Q16C22⋊D5semidirect
483. C3×SD16C22⋊D5semidirect
484. C3×SD16C22⋊D5semidirect
486. C3×D8C22⋊D5semidirect
580. 2−1+4C2×D15semidirect
583. H(5,𝔽2)C2×D15semidirect
587. #137C2×D15semidirect
599. AGL(1,ℤ/8)C2×D15semidirect
609. C2×SD16C2×D15semidirect
617. #131C2×D15semidirect
749. Q16#1220semidirect
764. SD16#1220semidirect
765. SD16#1220semidirect
777. D8#1220semidirect
794. C3×C5#3288semidirect
890. C5#84015semidirect
913. C3#10615746semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5772
#117565962
#117565942
#117565282
#117513462
#117513422
#117513042
#117513032
#117513002
#117512992
#117512982
#117512782
#117512772
#117512462
#117512432
#106157463
#840155