Finite Group Databasebeta

← D15×#577 #14510017

Subgroups — D15×#577 #14510017

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×2−1+4C211yesmaximal, characteristic, complemented
2D15×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C3×C5×#577C211yesmaximal, characteristic, complemented
4#11756596C211yesmaximal, characteristic, complemented
5#11756595C211yesmaximal, characteristic, complemented
6#11756537C213yesmaximal, complemented
7D15×#137C213yesmaximal, complemented
8#11756534C213yesmaximal, complemented
9D15×AGL(1,ℤ/8)C213yesmaximal, complemented
10#11756529C213yesmaximal, complemented
11D15×#135C213yesmaximal, complemented
12#11756521C213yesmaximal, complemented
13C2×SD16×D15C213yesmaximal, complemented
14#11756510C211yesmaximal, characteristic, complemented
15D15×#131C211yesmaximal, characteristic, complemented
16D5×#577—31nomaximal, Hall
17C3×C5×2−1+4C2211yescharacteristic, complemented
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19#92101—23no—
20#92101C2213yescomplemented
21#92101C2211yescharacteristic, complemented
22#92100—21no—
23#92100C2213yescomplemented
24#92100C2211yescharacteristic, complemented
25#41×D15—21no—
26#41×D15—23no—
27#41×D15C2213yes—
28#41×D15C2211yescharacteristic
29#41×D15C2213yescomplemented
30#92098—21no—
31#92098C2213yescomplemented
32C2×Q8×D15—21no—
33C2×Q8×D15C2213yescomplemented
34#92095—23no—
35#92095C2213yescomplemented
36C2×D4×D15—23no—
37C2×D4×D15C2213yes—
38C3×C5×#137C2213yescomplemented
39C3×C5×AGL(1,ℤ/8)C2213yescomplemented
40C3×C5×#135C2213yescomplemented
41C2×C3×C5×SD16C2213yescomplemented
42C3×C5×#131C2211yescharacteristic, complemented
43#91840C2213yescomplemented
44#91839C2213yescomplemented
45#91839C2213yescomplemented
46#91838C2213yescomplemented
47#91837C2211yescharacteristic, complemented
48#91831C2213yescomplemented
49C2×#6717C2213yescomplemented
50C2×#6716C2213yescomplemented
51#91821C2213yescomplemented
52#91808C2213yescomplemented
53#91807C2216yescomplemented
54Q16×D15C2213yescomplemented
55#91805C2213yescomplemented
56#91805C2213yescomplemented
57#91804C2216yescomplemented
58#91803C2216yescomplemented
59SD16×D15C2213yescomplemented
60SD16×D15C2216yescomplemented
61SD16×D15C2211yescharacteristic, complemented
62SD16×D15C2216yescomplemented
63SD16×D15C2216yescomplemented
64#91801C2213yescomplemented
65#91800C2216yescomplemented
66D8×D15C2213yescomplemented
67#91798C2213yescomplemented
68#91797C2213yescomplemented
69#91796C2213yescomplemented
70M16×D15C2213yescomplemented
71#91793C2213yescomplemented
72C2×#6706C2213yescomplemented
73#91790C2213yescomplemented
74C2×C8×D15C2213yescomplemented
75D3×#577—51nomaximal, Hall
76D5×2−1+4—31no—
77D5×H(5,𝔽2)—31no—
78C5×#577D311yescharacteristic, complemented
79#66171—31no—
80#66170—31no—
81#66112—33no—
82D5×#137—33no—
83#66109—33no—
84D5×AGL(1,ℤ/8)—33no—
85#66104—33no—
86D5×#135—33no—
87#66096—33no—
88C2×D5×SD16—33no—
89#66085—31no—
90D5×#131—31no—
91C23×D15—23no—
92C3×C5×#41—21no—
93C3×C5×#41—23no—
94C3×C5×#41C2313yes—
95C3×C5×#41C2311yescharacteristic
96C3×C5×#41C2313yescomplemented
97C2×C3×C5×Q8—21no—
98C2×C3×C5×Q8C2313yescomplemented
99C2×C3×C5×D4—23no—
100C2×C3×C5×D4C2313yes—
101C2×#1220—26no—
102C2×#1220—23no—
103#6821—21no—
104#6821—23no—
105#6821D411yescharacteristic
106#6821C2313yes—
107#6821C2313yescomplemented
108Q8×D15—21no—
109Q8×D15—23no—
110Q8×D15—23no—
111Q8×D15—23no—
112Q8×D15D411yescharacteristic
113Q8×D15C2313yes—
114Q8×D15C2311yescharacteristic
115Q8×D15C2316yescomplemented
116#6819—23no—
117#6819—26no—
118#6819—23no—
119#6819—23no—
120#6819—23no—
121#6819D413yes—
122#6819C2313yes—
123#6819C2313yescomplemented
124D4×D15—23no—
125D4×D15—23no—
126D4×D15—23no—
127D4×D15—26no—
128D4×D15—23no—
129D4×D15—23no—
130D4×D15—23no—
131D4×D15D413yes—
132D4×D15C2311yescharacteristic
133D4×D15C2313yes—
134D4×D15C2316yes—
135#6817—26no—
136#6817—23no—
137#6817—23no—
138#6817—23no—
139#6817—23no—
140#6817C2313yes—
141#6817C2313yes—
142#6817C2313yescomplemented
143C2×D60—23no—
144C2×D60C2313yes—
145C2×C4×D15—23no—
146C2×C4×D15—23no—
147C2×C4×D15—23no—
148C2×C4×D15C2313yes—
149C2×Dic30—23no—
150C2×Dic30—23no—
151C2×Dic30C2313yescomplemented
152C3×C5×Q16C2313yescomplemented
153C3×C5×SD16C2313yescomplemented
154C3×C5×SD16C2316yescomplemented
155C3×C5×SD16C2311yescharacteristic, complemented
156C3×C5×D8C2313yescomplemented
157C3×C5×M16C2313yescomplemented
158C2×C3×C5×C8C2313yescomplemented
159#6718C2313yescomplemented
160#6718C2313yescomplemented
161#6717C2313yescomplemented
162#6717C2316yescomplemented
163#6717C2311yescharacteristic, complemented
164#6716C2316yescomplemented
165#6716C2311yescharacteristic, complemented
166#6716C2313yescomplemented
167#6715C2313yescomplemented
168#6715C2313yescomplemented
169#6710C2313yescomplemented
170C2×C3⋊#168C2313yescomplemented
171Dic60C2313yescomplemented
172D120C2313yescomplemented
173#6706C2313yescomplemented
174#6706C2316yescomplemented
175#6706C2311yescharacteristic, complemented
176#6705C2316yescomplemented
177C8×D15C2311yescharacteristic
178C8×D15C2313yes—
179C8×D15C2313yescomplemented
180C8×D15C2313yescomplemented
181D3×2−1+4—51no—
182D3×H(5,𝔽2)—51no—
183C3×#577D511yescharacteristic, complemented
184#5837—51no—
185#5836—51no—
186#5778—53no—
187D3×#137—53no—
188#5775—53no—
189D3×AGL(1,ℤ/8)—53no—
190#5770—53no—
191D3×#135—53no—
192#5762—53no—
193C2×D3×SD16—53no—
194#5751—51no—
195D3×#131—51no—
196C5×2−1+4C2×D311yescharacteristic, complemented
197C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
198#4150—31no—
199#4150—33no—
200#4150—63no—
201#4149—31no—
202#4149—33no—
203#4149—61no—
204D5×#41—31no—
205D5×#41—33no—
206D5×#41—33no—
207D5×#41—63no—
208D5×#41—61no—
209#4147—33no—
210#4147—61no—
211C2×Q8×D5—33no—
212C2×Q8×D5—61no—
213#4144—33no—
214#4144—63no—
215C2×D4×D5—33no—
216C2×D4×D5—63no—
217C5×#137C2×D313yescomplemented
218C5×AGL(1,ℤ/8)C2×D313yescomplemented
219C5×#135C2×D313yescomplemented
220C2×C5×SD16C2×D313yescomplemented
221C5×#131C2×D311yescharacteristic, complemented
222#4097—33no—
223#4096—33no—
224#4096—33no—
225#4095—33no—
226#4094—31no—
227#4088—33no—
228C2×#688—33no—
229C2×#687—33no—
230#4078—33no—
231#4065—33no—
232#4064—36no—
233D5×Q16—33no—
234#4062—33no—
235#4062—33no—
236#4061—36no—
237#4060—36no—
238D5×SD16—33no—
239D5×SD16—36no—
240D5×SD16—36no—
241D5×SD16—36no—
242D5×SD16—31no—
243#4058—33no—
244#4057—36no—
245D5×D8—33no—
246#4055—33no—
247#4054—33no—
248#4053—33no—
249D5×M16—33no—
250#4050—33no—
251C2×#677—33no—
252#4047—33no—
253C2×C8×D5—33no—
254C2×#577—151noSylow
255C23×C3×C5—23no—
256C22×D15—23no—
257C22×D15—21no—
258C22×D15—23no—
259C22×D15—26no—
260C22×D15—86no—
261C22×D15C2×D413yes—
262C3×C5×Q8—23no—
263C3×C5×Q8C2×D411yescharacteristic
264C3×C5×Q8C2413yes—
265C3×C5×Q8C2411yescharacteristic
266C3×C5×D4—23no—
267C3×C5×D4—23no—
268C3×C5×D4—23no—
269C3×C5×D4C2×D413yes—
270C3×C5×D4C2411yescharacteristic
271C3×C5×D4C2413yes—
272C2×C3×C4×C5—23no—
273C2×C3×C4×C5—23no—
274C2×C3×C4×C5—23no—
275C2×C3×C4×C5C2413yes—
276#1220—23no—
277#1220—23no—
278#1220—23no—
279#1220—23no—
280#1220—21no—
281#1220—23no—
282#1220—26no—
283#1220C2×D416yes—
284C2×Dic15—23no—
285C2×Dic15—23no—
286C2×Dic15—23no—
287C2×Dic15C2×D413yes—
288D60—23no—
289D60—23no—
290D60—23no—
291D60C2×D413yes—
292D60C2413yes—
293D60C2411yescharacteristic
294C4×D15—21no—
295C4×D15—23no—
296C4×D15—26no—
297C4×D15—23no—
298C4×D15—23no—
299C4×D15—23no—
300C4×D15—23no—
301C4×D15C2×D413yes—
302C4×D15C2×D413yes—
303C4×D15C2411yescharacteristic
304C4×D15C2413yes—
305Dic30—23no—
306Dic30—23no—
307Dic30—26no—
308Dic30—21no—
309Dic30C2×D413yes—
310Dic30C2413yes—
311Dic30C2411yescharacteristic
312C3×C5×C8C2411yescharacteristic
313C3×C5×C8C2413yes—
314C3⋊#168C2411yescharacteristic
315C3⋊#168C2413yes—
316C3×2−1+4C2×D511yescharacteristic, complemented
317C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
318#1010—51no—
319#1010—53no—
320#1010—103no—
321#1009—51no—
322#1009—53no—
323#1009—101no—
324D3×#41—51no—
325D3×#41—53no—
326D3×#41—53no—
327D3×#41—103no—
328D3×#41—101no—
329#1007—53no—
330#1007—101no—
331C2×D3×Q8—53no—
332C2×D3×Q8—101no—
333#1004—53no—
334#1004—103no—
335C2×D3×D4—53no—
336C2×D3×D4—103no—
337C3×#137C2×D513yescomplemented
338C3×AGL(1,ℤ/8)C2×D513yescomplemented
339C3×#135C2×D513yescomplemented
340C2×C3×SD16C2×D513yescomplemented
341C3×#131C2×D511yescharacteristic, complemented
342#951—53no—
343#950—53no—
344#950—53no—
345#949—53no—
346#948—51no—
347#942—53no—
348C2×#215—53no—
349C2×#214—53no—
350#932—53no—
351#919—53no—
352#918—56no—
353D3×Q16—53no—
354#916—53no—
355#916—53no—
356#915—56no—
357#914—56no—
358D3×SD16—53no—
359D3×SD16—56no—
360D3×SD16—56no—
361D3×SD16—56no—
362D3×SD16—51no—
363#912—53no—
364#911—56no—
365D3×D8—53no—
366#909—53no—
367#908—53no—
368#907—53no—
369D3×M16—53no—
370#904—53no—
371C2×#204—53no—
372#901—53no—
373C2×D3×C8—53no—
374C23×D5—63no—
375C5×#41—21no—
376C5×#41—23no—
377C5×#41C22×D313yes—
378C5×#41C22×D311yescharacteristic
379C5×#41C22×D313yescomplemented
380C2×C5×Q8—21no—
381C2×C5×Q8C22×D313yescomplemented
382C2×C5×D4—23no—
383C2×C5×D4C22×D313yes—
384C2×C22⋊D5—63no—
385C2×C22⋊D5—66no—
386#713—31no—
387#713—33no—
388#713—33no—
389#713—63no—
390#713—61no—
391Q8×D5—31no—
392Q8×D5—33no—
393Q8×D5—36no—
394Q8×D5—31no—
395Q8×D5—63no—
396Q8×D5—63no—
397Q8×D5—63no—
398Q8×D5—61no—
399#711—33no—
400#711—33no—
401#711—33no—
402#711—63no—
403#711—63no—
404#711—63no—
405#711—66no—
406#711—63no—
407D4×D5—33no—
408D4×D5—33no—
409D4×D5—36no—
410D4×D5—31no—
411D4×D5—63no—
412D4×D5—63no—
413D4×D5—63no—
414D4×D5—66no—
415D4×D5—63no—
416D4×D5—63no—
417D4×D5—63no—
418#709—33no—
419#709—33no—
420#709—33no—
421#709—63no—
422#709—63no—
423#709—63no—
424#709—63no—
425#709—66no—
426C2×D20—33no—
427C2×D20—63no—
428C2×C4×D5—33no—
429C2×C4×D5—63no—
430C2×C4×D5—63no—
431C2×C4×D5—63no—
432C2×Dic10—33no—
433C2×Dic10—63no—
434C2×Dic10—63no—
435C5×Q16C22×D313yescomplemented
436C5×SD16C22×D313yescomplemented
437C5×SD16C22×D316yescomplemented
438C5×SD16C22×D311yescharacteristic, complemented
439C5×D8C22×D313yescomplemented
440C5×M16C22×D313yescomplemented
441C2×C5×C8C22×D313yescomplemented
442#689—33no—
443#689—33no—
444#688—31no—
445#688—33no—
446#688—36no—
447#687—31no—
448#687—33no—
449#687—36no—
450#686—33no—
451#686—33no—
452#681—33no—
453C2×#168—33no—
454Dic20—33no—
455D40—33no—
456#677—33no—
457#677—36no—
458#677—31no—
459#676—36no—
460C8×D5—31no—
461C8×D5—33no—
462C8×D5—33no—
463C8×D5—33no—
464C2×2−1+4—151no—
465C2×H(5,𝔽2)—151no—
466#577—151no—
467#577—151no—
468#577—153no—
469#577—153no—
470#577—153no—
471#577—153no—
472#577—151no—
473#577D1511yescharacteristic, direct product factor
474C2×#137—153no—
475C2×AGL(1,ℤ/8)—153no—
476C2×#135—153no—
477C22×SD16—153no—
478C2×#131—151no—
479C22×C3×C5—21no—
480C22×C3×C5—23no—
481C22×C3×C5—83no—
482C22×C3×C5C22×D413yes—
483C2×D15—26no—
484C2×D15—21no—
485C2×D15—23no—
486C2×D15—42no—
487C2×D15—46no—
488C2×D15—86no—
489C2×D15—83no—
490C2×D15C22×D413yes—
491C2×D15C22×D411yescharacteristic
492C3×C4×C5—23no—
493C3×C4×C5—21no—
494C3×C4×C5C22×D413yes—
495C3×C4×C5C2511yescharacteristic
496Dic15—23no—
497Dic15—21no—
498Dic15C22×D411yescharacteristic
499Dic15C22×D413yes—
500C23×D3—103no—
501C3×#41—21no—
502C3×#41—23no—
503C3×#41C22×D513yes—
504C3×#41C22×D511yescharacteristic
505C3×#41C22×D513yescomplemented
506C2×C3×Q8—21no—
507C2×C3×Q8C22×D513yescomplemented
508C2×C3×D4—23no—
509C2×C3×D4C22×D513yes—
510C2×#67—103no—
511C2×#67—106no—
512#239—51no—
513#239—53no—
514#239—53no—
515#239—103no—
516#239—101no—
517D3×Q8—51no—
518D3×Q8—53no—
519D3×Q8—56no—
520D3×Q8—51no—
521D3×Q8—103no—
522D3×Q8—103no—
523D3×Q8—103no—
524D3×Q8—101no—
525#237—53no—
526#237—53no—
527#237—53no—
528#237—103no—
529#237—103no—
530#237—103no—
531#237—106no—
532#237—103no—
533D3×D4—53no—
534D3×D4—51no—
535D3×D4—53no—
536D3×D4—56no—
537D3×D4—103no—
538D3×D4—103no—
539D3×D4—103no—
540D3×D4—106no—
541D3×D4—103no—
542D3×D4—103no—
543D3×D4—103no—
544#235—53no—
545#235—53no—
546#235—53no—
547#235—103no—
548#235—103no—
549#235—103no—
550#235—103no—
551#235—106no—
552C2×D12—53no—
553C2×D12—103no—
554C2×C4×D3—53no—
555C2×C4×D3—103no—
556C2×C4×D3—103no—
557C2×C4×D3—103no—
558C2×Dic6—53no—
559C2×Dic6—103no—
560C2×Dic6—103no—
561C3×Q16C22×D513yescomplemented
562C3×SD16C22×D513yescomplemented
563C3×SD16C22×D516yescomplemented
564C3×SD16C22×D511yescharacteristic, complemented
565C3×D8C22×D513yescomplemented
566C3×M16C22×D513yescomplemented
567C2×C3×C8C22×D513yescomplemented
568#216—53no—
569#216—53no—
570#215—53no—
571#215—56no—
572#215—51no—
573#214—56no—
574#214—51no—
575#214—53no—
576#213—53no—
577#213—53no—
578#208—53no—
579C2×C3⋊C8—53no—
580Dic12—53no—
581D24—53no—
582#204—53no—
583#204—56no—
584#204—51no—
585ΓL(1,𝔽25)—56no—
586D3×C8—51no—
587D3×C8—53no—
588D3×C8—53no—
589D3×C8—53no—
590C23×C5—23no—
591C22×D5—33no—
592C22×D5—61no—
593C22×D5—63no—
594C22×D5—66no—
595C22×D5—63no—
596C22×D5—246no—
597C5×Q8—23no—
598C5×Q8D3×D411yescharacteristic
599C5×Q8C23×D313yes—
600C5×Q8C23×D311yescharacteristic
601C5×D4—23no—
602C5×D4—23no—
603C5×D4—23no—
604C5×D4D3×D413yes—
605C5×D4C23×D311yescharacteristic
606C5×D4C23×D313yes—
607C2×C4×C5—23no—
608C2×C4×C5—23no—
609C2×C4×C5—23no—
610C2×C4×C5C23×D313yes—
611C22⋊D5—36no—
612C22⋊D5—61no—
613C22⋊D5—66no—
614C22⋊D5—63no—
615C22⋊D5—63no—
616C22⋊D5—63no—
617C22⋊D5—63no—
618C22⋊D5—63no—
619C2×Dic5—33no—
620C2×Dic5—63no—
621C2×Dic5—63no—
622C2×Dic5—63no—
623D20—33no—
624D20—33no—
625D20—31no—
626D20—63no—
627D20—63no—
628D20—63no—
629C4×D5—33no—
630C4×D5—33no—
631C4×D5—31no—
632C4×D5—33no—
633C4×D5—63no—
634C4×D5—63no—
635C4×D5—61no—
636C4×D5—63no—
637C4×D5—66no—
638C4×D5—63no—
639C4×D5—63no—
640Dic10—33no—
641Dic10—33no—
642Dic10—31no—
643Dic10—66no—
644Dic10—63no—
645Dic10—61no—
646Dic10—63no—
647C5×C8C23×D311yescharacteristic
648C5×C8C23×D313yes—
649#168—31no—
650#168—33no—
6512−1+4—151no—
6522−1+4—153no—
6532−1+4—153no—
6542−1+4—301no—
6552−1+4—303no—
6562−1+4C2×D1511yescharacteristic, complemented
657H(5,𝔽2)—153no—
658H(5,𝔽2)—151no—
659H(5,𝔽2)—153no—
660H(5,𝔽2)—303no—
661H(5,𝔽2)—301no—
662H(5,𝔽2)C2×D1511yescharacteristic, complemented
663C2×#41—151no—
664C2×#41—153no—
665C2×#41—153no—
666C2×#41—303no—
667C2×#41—301no—
668C22×Q8—153no—
669C22×Q8—301no—
670C22×D4—153no—
671C22×D4—303no—
672#137—153no—
673#137—153no—
674#137—156no—
675#137—156no—
676#137—153no—
677#137C2×D1513yescomplemented
678AGL(1,ℤ/8)—153no—
679AGL(1,ℤ/8)—153no—
680AGL(1,ℤ/8)—156no—
681AGL(1,ℤ/8)—156no—
682AGL(1,ℤ/8)—153no—
683AGL(1,ℤ/8)C2×D1513yescomplemented
684#135—153no—
685#135—153no—
686#135—153no—
687#135—153no—
688#135—153no—
689#135—153no—
690#135—153no—
691#135C2×D1513yescomplemented
692C2×Q16—153no—
693C2×SD16—153no—
694C2×SD16—153no—
695C2×SD16—153no—
696C2×SD16—156no—
697C2×SD16—156no—
698C2×SD16—156no—
699C2×SD16—151no—
700C2×SD16—153no—
701C2×SD16C2×D1513yescomplemented
702C2×D8—153no—
703#131—151no—
704#131—153no—
705#131—153no—
706#131C2×D1511yescharacteristic, complemented
707C2×M16—153no—
708C22×C8—153no—
709C2×C3×C5—23no—
710C2×C3×C5—43no—
711C2×C3×C5—41no—
712C2×C3×C5C23×D411yescharacteristic
713D15—23no—
714D15—41no—
715D15—43no—
716D15#57712yesdirect product factor
717C23×C3—23no—
718C22×D3—53no—
719C22×D3—101no—
720C22×D3—103no—
721C22×D3—106no—
722C22×D3—103no—
723C22×D3—406no—
724C3×Q8—23no—
725C3×Q8D4×D511yescharacteristic
726C3×Q8C23×D513yes—
727C3×Q8C23×D511yescharacteristic
728C3×D4—23no—
729C3×D4—23no—
730C3×D4—23no—
731C3×D4D4×D513yes—
732C3×D4C23×D511yescharacteristic
733C3×D4C23×D513yes—
734C2×C3×C4—23no—
735C2×C3×C4—23no—
736C2×C3×C4—23no—
737C2×C3×C4C23×D513yes—
738#67—56no—
739#67—101no—
740#67—106no—
741#67—103no—
742#67—103no—
743#67—103no—
744#67—103no—
745#67—103no—
746C2×Dic3—53no—
747C2×Dic3—103no—
748C2×Dic3—103no—
749C2×Dic3—103no—
750D12—53no—
751D12—53no—
752D12—51no—
753D12—103no—
754D12—103no—
755D12—103no—
756C4×D3—53no—
757C4×D3—53no—
758C4×D3—51no—
759C4×D3—53no—
760C4×D3—103no—
761C4×D3—103no—
762C4×D3—101no—
763C4×D3—103no—
764C4×D3—106no—
765C4×D3—103no—
766C4×D3—103no—
767Dic6—53no—
768Dic6—53no—
769Dic6—51no—
770Dic6—106no—
771Dic6—103no—
772Dic6—101no—
773Dic6—103no—
774C3×C8C23×D511yescharacteristic
775C3×C8C23×D513yes—
776C3⋊C8—51no—
777C3⋊C8—53no—
778C22×C5—21no—
779C22×C5—23no—
780C22×C5—83no—
781C22×C5C2×D3×D413yes—
782C2×D5—31no—
783C2×D5—33no—
784C2×D5—66no—
785C2×D5—61no—
786C2×D5—63no—
787C2×D5—122no—
788C2×D5—126no—
789C2×D5—246no—
790C2×D5—243no—
791C4×C5—23no—
792C4×C5—21no—
793C4×C5C2×D3×D413yes—
794C4×C5C24×D311yescharacteristic
795Dic5—33no—
796Dic5—31no—
797Dic5—63no—
798Dic5—61no—
799C24—303no—
800#41—21no—
801#41—23no—
802#41—151no—
803#41—153no—
804#41—153no—
805#41—153no—
806#41—153no—
807#41—153no—
808#41—153no—
809#41—153no—
810#41—153no—
811#41—303no—
812#41—303no—
813#41—306no—
814#41—303no—
815#41—303no—
816#41—303no—
817#41—303no—
818#41—306no—
819#41—303no—
820#41—303no—
821#41—301no—
822#41—303no—
823#41C22×D1513yes—
824#41C22×D1511yescharacteristic
825#41C22×D1513yescomplemented
826C2×Q8—21no—
827C2×Q8—151no—
828C2×Q8—153no—
829C2×Q8—156no—
830C2×Q8—151no—
831C2×Q8—153no—
832C2×Q8—303no—
833C2×Q8—303no—
834C2×Q8—303no—
835C2×Q8—303no—
836C2×Q8—303no—
837C2×Q8—301no—
838C2×Q8C22×D1513yescomplemented
839C2×D4—23no—
840C2×D4—153no—
841C2×D4—151no—
842C2×D4—153no—
843C2×D4—156no—
844C2×D4—153no—
845C2×D4—303no—
846C2×D4—303no—
847C2×D4—303no—
848C2×D4—303no—
849C2×D4—306no—
850C2×D4—303no—
851C2×D4—303no—
852C2×D4—303no—
853C2×D4—306no—
854C2×D4—303no—
855C2×D4C22×D1513yes—
856C22×C4—153no—
857C22×C4—303no—
858C22×C4—303no—
859C22×C4—303no—
860Q16—153no—
861Q16—153no—
862Q16—153no—
863Q16C22×D1513yescomplemented
864SD16—153no—
865SD16—156no—
866SD16—151no—
867SD16—153no—
868SD16—156no—
869SD16—151no—
870SD16—153no—
871SD16—156no—
872SD16—151no—
873SD16C22×D1513yescomplemented
874SD16C22×D1516yescomplemented
875SD16C22×D1511yescharacteristic, complemented
876D8—153no—
877D8—153no—
878D8—153no—
879D8C22×D1513yescomplemented
880M16—153no—
881M16—156no—
882M16C22×D1513yescomplemented
883C2×C8—153no—
884C2×C8—151no—
885C2×C8—153no—
886C2×C8—153no—
887C2×C8—153no—
888C2×C8C22×D1513yescomplemented
889C3×C5C2×#57711yescharacteristic, complemented, Hall
890C22×C3—21no—
891C22×C3—23no—
892C22×C3—83no—
893C22×C3C2×D4×D513yes—
894C2×D3—51no—
895C2×D3—53no—
896C2×D3—106no—
897C2×D3—101no—
898C2×D3—103no—
899C2×D3—202no—
900C2×D3—206no—
901C2×D3—406no—
902C2×D3—403no—
903C3×C4—23no—
904C3×C4—21no—
905C3×C4C2×D4×D513yes—
906C3×C4C24×D511yescharacteristic
907Dic3—53no—
908Dic3—51no—
909Dic3—103no—
910Dic3—101no—
911C2×C5—23no—
912C2×C5—43no—
913C2×C5—41no—
914C2×C5C22×D3×D411yescharacteristic
915D5—32no—
916D5—63no—
917D5—123no—
918D5—121no—
919C23—23no—
920C23—153no—
921C23—301no—
922C23—303no—
923C23—306no—
924C23—303no—
925C23—1206no—
926Q8—23no—
927Q8—153no—
928Q8—153no—
929Q8—151no—
930Q8—303no—
931Q8—306no—
932Q8—301no—
933Q8—303no—
934Q8D4×D1511yescharacteristic
935Q8C23×D1513yes—
936Q8C23×D1511yescharacteristic
937D4—23no—
938D4—23no—
939D4—23no—
940D4—156no—
941D4—153no—
942D4—151no—
943D4—153no—
944D4—303no—
945D4—303no—
946D4—303no—
947D4—306no—
948D4—301no—
949D4—303no—
950D4—303no—
951D4—303no—
952D4—303no—
953D4—303no—
954D4D4×D1513yes—
955D4C23×D1511yescharacteristic
956D4C23×D1513yes—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—23no—
960C2×C4—153no—
961C2×C4—153no—
962C2×C4—153no—
963C2×C4—151no—
964C2×C4—153no—
965C2×C4—303no—
966C2×C4—303no—
967C2×C4—301no—
968C2×C4—303no—
969C2×C4—306no—
970C2×C4—303no—
971C2×C4—303no—
972C2×C4—303no—
973C2×C4—303no—
974C2×C4—303no—
975C2×C4C23×D1513yes—
976C8—151no—
977C8—153no—
978C8C23×D1511yescharacteristic
979C8C23×D1513yes—
980C2×C3—23no—
981C2×C3—43no—
982C2×C3—41no—
983C2×C3C22×D4×D511yescharacteristic
984D3—52no—
985D3—103no—
986D3—203no—
987D3—201no—
988C5D3×#57711yescharacteristic, complemented, Sylow
989C22—21no—
990C22—23no—
991C22—83no—
992C22—151no—
993C22—153no—
994C22—306no—
995C22—301no—
996C22—303no—
997C22—606no—
998C22—602no—
999C22—1203no—
1000C22—1206no—
1001C22C2×D4×D1513yes—
1002C4—21no—
1003C4—23no—
1004C4—151no—
1005C4—153no—
1006C4—301no—
1007C4—303no—
1008C4C2×D4×D1513yes—
1009C4C24×D1511yescharacteristic
1010C3D5×#57711yescharacteristic, complemented, Sylow
1011C2—23no—
1012C2—43no—
1013C2—41no—
1014C2—152no—
1015C2—303no—
1016C2—603no—
1017C2—601no—
1018C2C22×D4×D1511yescharacteristic
subgroupG/H
centerC2C22×D4×D15
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC3×C5×#577C2
socleC2×C3×C5C23×D4
hypercenter#577D15
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41 ◁ #577

Complements

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

NH ≅ G/Ntype
1. D15×2−1+4C2semidirect
2. D15×H(5,𝔽2)C2semidirect
3. C3×C5×#577C2semidirect
4. #11756596C2semidirect
5. #11756595C2semidirect
6. #11756537C2semidirect
7. D15×#137C2semidirect
8. #11756534C2semidirect
9. D15×AGL(1,ℤ/8)C2semidirect
10. #11756529C2semidirect
11. D15×#135C2semidirect
12. #11756521C2semidirect
13. C2×SD16×D15C2semidirect
14. #11756510C2semidirect
15. D15×#131C2semidirect
17. C3×C5×2−1+4C22semidirect
18. C3×C5×H(5,𝔽2)C22semidirect
20. #92101C22semidirect
21. #92101C22semidirect
23. #92100C22semidirect
24. #92100C22semidirect
29. #41×D15C22semidirect
31. #92098C22semidirect
33. C2×Q8×D15C22semidirect
35. #92095C22semidirect
38. C3×C5×#137C22semidirect
39. C3×C5×AGL(1,ℤ/8)C22semidirect
40. C3×C5×#135C22semidirect
41. C2×C3×C5×SD16C22semidirect
42. C3×C5×#131C22semidirect
43. #91840C22semidirect
44. #91839C22semidirect
45. #91839C22semidirect
46. #91838C22semidirect
47. #91837C22semidirect
48. #91831C22semidirect
49. C2×#6717C22semidirect
50. C2×#6716C22semidirect
51. #91821C22semidirect
52. #91808C22semidirect
53. #91807C22semidirect
54. Q16×D15C22semidirect
55. #91805C22semidirect
56. #91805C22semidirect
57. #91804C22semidirect
58. #91803C22semidirect
59. SD16×D15C22semidirect
60. SD16×D15C22semidirect
61. SD16×D15C22semidirect
62. SD16×D15C22semidirect
63. SD16×D15C22semidirect
64. #91801C22semidirect
65. #91800C22semidirect
66. D8×D15C22semidirect
67. #91798C22semidirect
68. #91797C22semidirect
69. #91796C22semidirect
70. M16×D15C22semidirect
71. #91793C22semidirect
72. C2×#6706C22semidirect
73. #91790C22semidirect
74. C2×C8×D15C22semidirect
78. C5×#577D3semidirect
96. C3×C5×#41C23semidirect
98. C2×C3×C5×Q8C23semidirect
107. #6821C23semidirect
115. Q8×D15C23semidirect
123. #6819C23semidirect
142. #6817C23semidirect
151. C2×Dic30C23semidirect
152. C3×C5×Q16C23semidirect
153. C3×C5×SD16C23semidirect
154. C3×C5×SD16C23semidirect
155. C3×C5×SD16C23semidirect
156. C3×C5×D8C23semidirect
157. C3×C5×M16C23semidirect
158. C2×C3×C5×C8C23semidirect
159. #6718C23semidirect
160. #6718C23semidirect
161. #6717C23semidirect
162. #6717C23semidirect
163. #6717C23semidirect
164. #6716C23semidirect
165. #6716C23semidirect
166. #6716C23semidirect
167. #6715C23semidirect
168. #6715C23semidirect
169. #6710C23semidirect
170. C2×C3⋊#168C23semidirect
171. Dic60C23semidirect
172. D120C23semidirect
173. #6706C23semidirect
174. #6706C23semidirect
175. #6706C23semidirect
176. #6705C23semidirect
179. C8×D15C23semidirect
180. C8×D15C23semidirect
183. C3×#577D5semidirect
196. C5×2−1+4C2×D3semidirect
197. C5×H(5,𝔽2)C2×D3semidirect
217. C5×#137C2×D3semidirect
218. C5×AGL(1,ℤ/8)C2×D3semidirect
219. C5×#135C2×D3semidirect
220. C2×C5×SD16C2×D3semidirect
221. C5×#131C2×D3semidirect
316. C3×2−1+4C2×D5semidirect
317. C3×H(5,𝔽2)C2×D5semidirect
337. C3×#137C2×D5semidirect
338. C3×AGL(1,ℤ/8)C2×D5semidirect
339. C3×#135C2×D5semidirect
340. C2×C3×SD16C2×D5semidirect
341. C3×#131C2×D5semidirect
379. C5×#41C22×D3semidirect
381. C2×C5×Q8C22×D3semidirect
435. C5×Q16C22×D3semidirect
436. C5×SD16C22×D3semidirect
437. C5×SD16C22×D3semidirect
438. C5×SD16C22×D3semidirect
439. C5×D8C22×D3semidirect
440. C5×M16C22×D3semidirect
441. C2×C5×C8C22×D3semidirect
473. #577D15direct (N × H)
505. C3×#41C22×D5semidirect
507. C2×C3×Q8C22×D5semidirect
561. C3×Q16C22×D5semidirect
562. C3×SD16C22×D5semidirect
563. C3×SD16C22×D5semidirect
564. C3×SD16C22×D5semidirect
565. C3×D8C22×D5semidirect
566. C3×M16C22×D5semidirect
567. C2×C3×C8C22×D5semidirect
656. 2−1+4C2×D15semidirect
662. H(5,𝔽2)C2×D15semidirect
677. #137C2×D15semidirect
683. AGL(1,ℤ/8)C2×D15semidirect
691. #135C2×D15semidirect
701. C2×SD16C2×D15semidirect
706. #131C2×D15semidirect
716. D15#577direct (N × H)
825. #41C22×D15semidirect
838. C2×Q8C22×D15semidirect
863. Q16C22×D15semidirect
873. SD16C22×D15semidirect
874. SD16C22×D15semidirect
875. SD16C22×D15semidirect
879. D8C22×D15semidirect
882. M16C22×D15semidirect
888. C2×C8C22×D15semidirect
889. C3×C5C2×#577semidirect
988. C5D3×#577semidirect
1010. C3D5×#577semidirect

Maximal subgroups

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

subgroupindex
D15×2−1+42
D15×H(5,𝔽2)2
C3×C5×#5772
#117565962
#117565952
#117565372
D15×#1372
#117565342
D15×AGL(1,ℤ/8)2
#117565292
D15×#1352
#117565212
C2×SD16×D152
#117565102
D15×#1312
D5×#5773
D3×#5775