Finite Group Databasebeta

← D15×#449 #14423402

Subgroups — D15×#449 #14423402

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic, complemented
2C2×SD16×D15C211yesmaximal, characteristic, complemented
3C2×D8×D15C211yesmaximal, characteristic, complemented
4D15×#121C211yesmaximal, characteristic, complemented
5C3×C5×#449C211yesmaximal, characteristic, complemented
6#11751339C211yesmaximal, characteristic, complemented
7#11751273C211yesmaximal, characteristic, complemented
8#11751259C211yesmaximal, characteristic, complemented
9#11751138C211yesmaximal, characteristic, complemented
10#11750911C211yesmaximal, characteristic, complemented
11D15×#103C211yesmaximal, characteristic, complemented
12#11750882C211yesmaximal, characteristic, complemented
13D15×#102C211yesmaximal, characteristic, complemented
14#11750835C211yesmaximal, characteristic, complemented
15D15×C22⋊C8C211yesmaximal, characteristic, complemented
16D5×#449—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18#41×D15—24no—
19#41×D15—24no—
20C2×#6821C2211yescharacteristic, complemented
21C2×Q8×D15C2211yescharacteristic
22C2×#6819—21no—
23C2×#6819C2211yescharacteristic, complemented
24C2×D4×D15—21no—
25C2×D4×D15—21no—
26C2×D4×D15C2211yescharacteristic
27C2×D4×D15C2211yescharacteristic
28C2×#6817—21no—
29C2×#6817C2211yescharacteristic, complemented
30C22×C4×D15—21no—
31C22×C4×D15C2211yescharacteristic
32C2×C3×C5×SD16C2211yescharacteristic, complemented
33C2×C3×C5×D8C2211yescharacteristic, complemented
34C3×C5×#121C2211yescharacteristic, complemented
35C2×#6717C2211yescharacteristic, complemented
36#91828—21no—
37#91827C2211yescharacteristic, complemented
38C2×#6716C2211yescharacteristic, complemented
39C2×#6715C2211yescharacteristic, complemented
40C2×#6715C2211yescharacteristic, complemented
41#91819C2211yescharacteristic, complemented
42SD16×D15—24no—
43D8×D15—24no—
44C2×D120C2211yescharacteristic, complemented
45C2×#6706C2211yescharacteristic, complemented
46C2×C8×D15C2211yescharacteristic
47C2×C8×D15C2211yescharacteristic
48#91784C2211yescharacteristic, complemented
49C4⋊C4×D15C2211yescharacteristic
50#91773—21no—
51C22⋊C4×D15—21no—
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×C22⋊C8C2211yescharacteristic, complemented
55#91119C2211yescharacteristic, complemented
56#91116C2211yescharacteristic, complemented
57#91114C2211yescharacteristic, complemented
58#91105C2211yescharacteristic, complemented
59#91104C2211yescharacteristic, complemented
60#91104C2211yescharacteristic, complemented
61#91100C2211yescharacteristic, complemented
62#91094C2211yescharacteristic, complemented
63#91093C2211yescharacteristic, complemented
64D3×#449—51nomaximal, Hall
65C2×D5×#41—31no—
66C2×D5×SD16—31no—
67C2×D5×D8—31no—
68D5×#121—31no—
69C5×#449D311yescharacteristic, complemented
70#65527—31no—
71#65461—31no—
72#65447—31no—
73#65326—31no—
74#65100—31no—
75D5×#103—31no—
76#65070—31no—
77D5×#102—31no—
78#65023—31no—
79D5×C22⋊C8—31no—
80C23×D15—21no—
81C23×D15—21no—
82C23×D15D411yescharacteristic
83C3×C5×#41—22no—
84C3×C5×#41—22no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—21no—
93C2×#1220—21no—
94C2×#1220—21no—
95C2×#1220—21no—
96C2×#1220—21no—
97C2×#1220—21no—
98C22×Dic15—21no—
99C22×Dic15D411yescharacteristic
100#6821—22no—
101#6821—22no—
102Q8×D15—22no—
103Q8×D15D414yescomplemented
104#6819—28no—
105#6819—22no—
106#6819—22no—
107D4×D15—28no—
108D4×D15—22no—
109D4×D15—22no—
110D4×D15—22no—
111D4×D15—44no—
112D4×D15D414yescomplemented
113#6817—28no—
114#6817—22no—
115#6817—22no—
116C2×D60—21no—
117C2×D60—21no—
118C2×D60C2311yescharacteristic
119C2×D60C2311yescharacteristic
120C2×C4×D15—28no—
121C2×C4×D15—21no—
122C2×C4×D15—21no—
123C2×C4×D15—21no—
124C2×C4×D15—22no—
125C2×C4×D15—22no—
126C2×C4×D15—21no—
127C2×C4×D15D411yescharacteristic
128C2×C4×D15D411yescharacteristic
129C2×C4×D15C2311yescharacteristic
130C2×C4×D15C2311yescharacteristic
131C2×Dic30—21no—
132C2×Dic30C2311yescharacteristic
133C3×C5×SD16—22no—
134C3×C5×D8—22no—
135C2×C3×C5×C8C2311yescharacteristic
136C2×C3×C5×C8C2311yescharacteristic
137C3×C5×C4⋊C4C2311yescharacteristic
138C3×C5×C22⋊C4—21no—
139#6719—21no—
140#6717—22no—
141#6716—22no—
142#6715—22no—
143#6715—22no—
144#6714—21no—
145#6714—21no—
146C4⋊Dic15C2311yescharacteristic
147#6712—21no—
148C2×C3⋊#168C2311yescharacteristic
149C2×C3⋊#168C2311yescharacteristic
150D120—22no—
151#6706—22no—
152C8×D15—22no—
153C8×D15—22no—
154C2×D3×#41—51no—
155C2×D3×SD16—51no—
156C2×D3×D8—51no—
157D3×#121—51no—
158C3×#449D511yescharacteristic, complemented
159#5238—51no—
160#5172—51no—
161#5158—51no—
162#5037—51no—
163#4810—51no—
164D3×#103—51no—
165#4781—51no—
166D3×#102—51no—
167#4734—51no—
168D3×C22⋊C8—51no—
169C2×C5×#41C2×D311yescharacteristic, complemented
170D5×#41—64no—
171D5×#41—64no—
172C2×#713—31no—
173C2×Q8×D5—31no—
174C2×#711—31no—
175C2×#711—61no—
176C2×D4×D5—31no—
177C2×D4×D5—31no—
178C2×D4×D5—61no—
179C2×D4×D5—61no—
180C2×#709—31no—
181C2×#709—61no—
182C22×C4×D5—31no—
183C22×C4×D5—61no—
184C2×C5×SD16C2×D311yescharacteristic, complemented
185C2×C5×D8C2×D311yescharacteristic, complemented
186C5×#121C2×D311yescharacteristic, complemented
187C2×#688—31no—
188#4085—61no—
189#4084—31no—
190C2×#687—31no—
191C2×#686—31no—
192C2×#686—31no—
193#4076—31no—
194D5×SD16—64no—
195D5×D8—64no—
196C2×D40—31no—
197C2×#677—31no—
198C2×C8×D5—31no—
199C2×C8×D5—31no—
200#4041—31no—
201D5×C4⋊C4—31no—
202#4030—61no—
203D5×C22⋊C4—61no—
204C5×#103C2×D311yescharacteristic, complemented
205C5×#102C2×D311yescharacteristic, complemented
206C5×C22⋊C8C2×D311yescharacteristic, complemented
207#3967—31no—
208#3964—31no—
209C22⋊#168—31no—
210#3953—31no—
211#3952—31no—
212#3952—31no—
213#3948—31no—
214#3942—31no—
215#3941—31no—
216C2×#449—151noSylow
217C23×C3×C5—21no—
218C23×C3×C5—21no—
219C23×C3×C5C2×D411yescharacteristic
220C22×D15—21no—
221C22×D15—22no—
222C22×D15—24no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—21no—
226C22×D15—42no—
227C22×D15—42no—
228C22×D15—42no—
229C22×D15—42no—
230C22×D15—42no—
231C22×D15C2×D411yescharacteristic
232C22×D15C2×D411yescharacteristic
233C3×C5×Q8—21no—
234C3×C5×Q8C2×D412yescomplemented
235C3×C5×D4—24no—
236C3×C5×D4—21no—
237C3×C5×D4—21no—
238C3×C5×D4—21no—
239C3×C5×D4—42no—
240C3×C5×D4C2×D412yescomplemented
241C2×C3×C4×C5—24no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—21no—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5—21no—
246C2×C3×C4×C5C2×D411yescharacteristic
247C2×C3×C4×C5C2411yescharacteristic
248#1220—24no—
249#1220—24no—
250#1220—24no—
251#1220—42no—
252#1220—42no—
253#1220—42no—
254C2×Dic15—24no—
255C2×Dic15—21no—
256C2×Dic15—22no—
257C2×Dic15—21no—
258C2×Dic15C2×D411yescharacteristic
259C2×Dic15C2×D411yescharacteristic
260D60—24no—
261D60—21no—
262D60—21no—
263D60—21no—
264D60—42no—
265D60C2×D412yescomplemented
266C4×D15—24no—
267C4×D15—24no—
268C4×D15—22no—
269C4×D15—24no—
270C4×D15—21no—
271C4×D15—21no—
272C4×D15—22no—
273C4×D15—42no—
274C4×D15C2×D412yes—
275C4×D15C2×D412yes—
276Dic30—21no—
277Dic30—24no—
278Dic30C2×D412yescomplemented
279C3×C5×C8—21no—
280C3×C5×C8—21no—
281C3⋊#168—21no—
282C3⋊#168—21no—
283C2×C3×#41C2×D511yescharacteristic, complemented
284D3×#41—104no—
285D3×#41—104no—
286C2×#239—51no—
287C2×D3×Q8—51no—
288C2×#237—51no—
289C2×#237—101no—
290C2×D3×D4—51no—
291C2×D3×D4—51no—
292C2×D3×D4—101no—
293C2×D3×D4—101no—
294C2×#235—51no—
295C2×#235—101no—
296C22×C4×D3—51no—
297C22×C4×D3—101no—
298C2×C3×SD16C2×D511yescharacteristic, complemented
299C2×C3×D8C2×D511yescharacteristic, complemented
300C3×#121C2×D511yescharacteristic, complemented
301C2×#215—51no—
302#939—101no—
303#938—51no—
304C2×#214—51no—
305C2×#213—51no—
306C2×#213—51no—
307#930—51no—
308D3×SD16—104no—
309D3×D8—104no—
310C2×D24—51no—
311C2×#204—51no—
312C2×D3×C8—51no—
313C2×D3×C8—51no—
314#895—51no—
315D3×C4⋊C4—51no—
316#884—101no—
317D3×C22⋊C4—101no—
318C3×#103C2×D511yescharacteristic, complemented
319C3×#102C2×D511yescharacteristic, complemented
320C3×C22⋊C8C2×D511yescharacteristic, complemented
321#835—51no—
322#832—51no—
323#830—51no—
324#821—51no—
325(C2×D3)⋊C8—51no—
326(C2×D3)⋊C8—51no—
327#816—51no—
328#810—51no—
329#809—51no—
330C23×D5—31no—
331C23×D5—61no—
332C23×D5—61no—
333C5×#41—22no—
334C5×#41—22no—
335C2×C5×Q8C22×D311yescharacteristic
336C2×C5×D4—21no—
337C2×C5×D4—21no—
338C2×C5×D4C22×D311yescharacteristic
339C2×C5×D4C22×D311yescharacteristic
340C22×C4×C5—21no—
341C22×C4×C5C22×D311yescharacteristic
342C2×C22⋊D5—61no—
343C2×C22⋊D5—61no—
344C2×C22⋊D5—61no—
345C2×C22⋊D5—61no—
346C2×C22⋊D5—61no—
347C2×C22⋊D5—61no—
348C22×Dic5—31no—
349C22×Dic5—61no—
350#713—62no—
351#713—62no—
352Q8×D5—34no—
353Q8×D5—62no—
354#711—62no—
355#711—68no—
356#711—62no—
357D4×D5—34no—
358D4×D5—62no—
359D4×D5—62no—
360D4×D5—62no—
361D4×D5—68no—
362D4×D5—124no—
363#709—62no—
364#709—62no—
365#709—68no—
366C2×D20—31no—
367C2×D20—31no—
368C2×D20—61no—
369C2×D20—61no—
370C2×C4×D5—31no—
371C2×C4×D5—31no—
372C2×C4×D5—31no—
373C2×C4×D5—31no—
374C2×C4×D5—62no—
375C2×C4×D5—62no—
376C2×C4×D5—61no—
377C2×C4×D5—61no—
378C2×C4×D5—68no—
379C2×C4×D5—61no—
380C2×C4×D5—61no—
381C2×Dic10—31no—
382C2×Dic10—61no—
383C5×SD16—22no—
384C5×D8—22no—
385C2×C5×C8C22×D311yescharacteristic
386C2×C5×C8C22×D311yescharacteristic
387C5×C4⋊C4C22×D311yescharacteristic
388C5×C22⋊C4—21no—
389C22⋊Dic5—61no—
390#688—62no—
391#687—62no—
392#686—62no—
393#686—62no—
394#685—61no—
395#685—61no—
396C4⋊Dic5—31no—
397#683—61no—
398C2×#168—31no—
399C2×#168—31no—
400D40—62no—
401#677—62no—
402C8×D5—62no—
403C8×D5—62no—
404C22×#41—151no—
405C22×SD16—151no—
406C22×D8—151no—
407C2×#121—151no—
408#449—151no—
409#449—151no—
410#449—151no—
411#449—151no—
412#449—151no—
413#449—151no—
414#449—151no—
415#449D1511yescharacteristic, direct product factor
416C2×#103—151no—
417C2×#102—151no—
418C2×C22⋊C8—151no—
419C22×C3×C5—21no—
420C22×C3×C5—22no—
421C22×C3×C5—21no—
422C22×C3×C5—21no—
423C22×C3×C5—41no—
424C22×C3×C5—41no—
425C22×C3×C5—41no—
426C22×C3×C5—41no—
427C22×C3×C5—41no—
428C22×C3×C5C22×D411yescharacteristic
429C2×D15—21no—
430C2×D15—22no—
431C2×D15—21no—
432C2×D15—21no—
433C2×D15—41no—
434C2×D15—41no—
435C2×D15—44no—
436C2×D15—48no—
437C2×D15—41no—
438C2×D15—41no—
439C2×D15—41no—
440C2×D15—84no—
441C2×D15#12012yes—
442C2×D15#13512yes—
443C2×D15AGL(1,ℤ/8)12yes—
444C3×C4×C5—22no—
445C3×C4×C5—21no—
446C3×C4×C5—41no—
447C3×C4×C5C22×D411yescharacteristic
448C3×C4×C5C22×D411yescharacteristic
449Dic15—22no—
450Dic15—21no—
451Dic15—41no—
452Dic15#12012yes—
453C23×D3—51no—
454C23×D3—101no—
455C23×D3—101no—
456C3×#41—22no—
457C3×#41—22no—
458C2×C3×Q8C22×D511yescharacteristic
459C2×C3×D4—21no—
460C2×C3×D4—21no—
461C2×C3×D4C22×D511yescharacteristic
462C2×C3×D4C22×D511yescharacteristic
463C22×C3×C4—21no—
464C22×C3×C4C22×D511yescharacteristic
465C2×#67—101no—
466C2×#67—101no—
467C2×#67—101no—
468C2×#67—101no—
469C2×#67—101no—
470C2×#67—101no—
471C22×Dic3—51no—
472C22×Dic3—101no—
473#239—102no—
474#239—102no—
475D3×Q8—54no—
476D3×Q8—102no—
477#237—102no—
478#237—108no—
479#237—102no—
480D3×D4—54no—
481D3×D4—102no—
482D3×D4—102no—
483D3×D4—102no—
484D3×D4—108no—
485D3×D4—204no—
486#235—102no—
487#235—102no—
488#235—108no—
489C2×D12—51no—
490C2×D12—51no—
491C2×D12—101no—
492C2×D12—101no—
493C2×C4×D3—51no—
494C2×C4×D3—51no—
495C2×C4×D3—51no—
496C2×C4×D3—51no—
497C2×C4×D3—102no—
498C2×C4×D3—102no—
499C2×C4×D3—101no—
500C2×C4×D3—101no—
501C2×C4×D3—108no—
502C2×C4×D3—101no—
503C2×C4×D3—101no—
504C2×Dic6—51no—
505C2×Dic6—101no—
506C3×SD16—22no—
507C3×D8—22no—
508C2×C3×C8C22×D511yescharacteristic
509C2×C3×C8C22×D511yescharacteristic
510C3×C4⋊C4C22×D511yescharacteristic
511C3×C22⋊C4—21no—
512#217—101no—
513#215—102no—
514#214—102no—
515#213—102no—
516#213—102no—
517(C2×D3)⋊C4—101no—
518(C2×D3)⋊C4—101no—
519C4⋊Dic3—51no—
520Dic3⋊C4—101no—
521C2×C3⋊C8—51no—
522C2×C3⋊C8—51no—
523D24—102no—
524#204—102no—
525D3×C8—102no—
526D3×C8—102no—
527C23×C5—21no—
528C23×C5—21no—
529C23×C5D3×D411yescharacteristic
530C22×D5—31no—
531C22×D5—31no—
532C22×D5—64no—
533C22×D5—62no—
534C22×D5—62no—
535C22×D5—62no—
536C22×D5—61no—
537C22×D5—61no—
538C22×D5—122no—
539C22×D5—122no—
540C22×D5—122no—
541C22×D5—122no—
542C22×D5—122no—
543C5×Q8—21no—
544C5×Q8D3×D412yescomplemented
545C5×D4—24no—
546C5×D4—21no—
547C5×D4—21no—
548C5×D4—21no—
549C5×D4—42no—
550C5×D4D3×D412yescomplemented
551C2×C4×C5—24no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—21no—
555C2×C4×C5—21no—
556C2×C4×C5D3×D411yescharacteristic
557C2×C4×C5C23×D311yescharacteristic
558C22⋊D5—64no—
559C22⋊D5—64no—
560C22⋊D5—64no—
561C22⋊D5—122no—
562C22⋊D5—122no—
563C22⋊D5—122no—
564C2×Dic5—31no—
565C2×Dic5—31no—
566C2×Dic5—62no—
567C2×Dic5—64no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570D20—32no—
571D20—64no—
572D20—61no—
573D20—61no—
574D20—61no—
575D20—122no—
576C4×D5—32no—
577C4×D5—32no—
578C4×D5—62no—
579C4×D5—62no—
580C4×D5—64no—
581C4×D5—64no—
582C4×D5—64no—
583C4×D5—61no—
584C4×D5—61no—
585C4×D5—122no—
586Dic10—32no—
587Dic10—64no—
588Dic10—61no—
589C5×C8—21no—
590C5×C8—21no—
591#168—61no—
592#168—61no—
593C2×#41—151no—
594C2×#41—151no—
595C2×#41—151no—
596C2×#41—301no—
597C2×#41—301no—
598C2×#41—304no—
599C2×#41—304no—
600C2×#41C2×D1511yescharacteristic, complemented
601C22×Q8—151no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—301no—
605C22×D4—301no—
606C23×C4—151no—
607C23×C4—301no—
608C2×SD16—151no—
609C2×SD16—151no—
610C2×SD16—151no—
611C2×SD16—304no—
612C2×SD16C2×D1511yescharacteristic, complemented
613C2×D8—151no—
614C2×D8—151no—
615C2×D8—151no—
616C2×D8—304no—
617C2×D8C2×D1511yescharacteristic, complemented
618C22×C8—151no—
619C22×C8—151no—
620#121—151no—
621#121—151no—
622#121—151no—
623#121—301no—
624#121—301no—
625#121C2×D1511yescharacteristic, complemented
626C2×C4⋊C4—151no—
627C2×C22⋊C4—301no—
628#103—151no—
629#103—151no—
630#103—151no—
631#103C2×D1511yescharacteristic, complemented
632#102—151no—
633#102—151no—
634#102—151no—
635#102C2×D1511yescharacteristic, complemented
636C22⋊C8—151no—
637C22⋊C8—151no—
638C22⋊C8—151no—
639C22⋊C8C2×D1511yescharacteristic, complemented
640C2×C3×C5—41no—
641C2×C3×C5—42no—
642C2×C3×C5—81no—
643C2×C3×C5C2×#12011yescharacteristic
644C2×C3×C5C2×#13511yescharacteristic
645C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
646D15—41no—
647D15—42no—
648D15—81no—
649D15#44914yesdirect product factor
650C23×C3—21no—
651C23×C3—21no—
652C23×C3D4×D511yescharacteristic
653C22×D3—51no—
654C22×D3—51no—
655C22×D3—104no—
656C22×D3—102no—
657C22×D3—102no—
658C22×D3—102no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—202no—
662C22×D3—202no—
663C22×D3—202no—
664C22×D3—202no—
665C22×D3—202no—
666C3×Q8—21no—
667C3×Q8D4×D512yescomplemented
668C3×D4—24no—
669C3×D4—21no—
670C3×D4—21no—
671C3×D4—21no—
672C3×D4—42no—
673C3×D4D4×D512yescomplemented
674C2×C3×C4—24no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4D4×D511yescharacteristic
680C2×C3×C4C23×D511yescharacteristic
681#67—104no—
682#67—104no—
683#67—104no—
684#67—202no—
685#67—202no—
686#67—202no—
687C2×Dic3—51no—
688C2×Dic3—51no—
689C2×Dic3—102no—
690C2×Dic3—104no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693D12—52no—
694D12—104no—
695D12—101no—
696D12—101no—
697D12—101no—
698D12—202no—
699C4×D3—52no—
700C4×D3—52no—
701C4×D3—102no—
702C4×D3—102no—
703C4×D3—104no—
704C4×D3—104no—
705C4×D3—104no—
706C4×D3—101no—
707C4×D3—101no—
708C4×D3—202no—
709Dic6—52no—
710Dic6—104no—
711Dic6—101no—
712C3×C8—21no—
713C3×C8—21no—
714C3⋊C8—101no—
715C3⋊C8—101no—
716C22×C5—21no—
717C22×C5—21no—
718C22×C5—21no—
719C22×C5—22no—
720C22×C5—41no—
721C22×C5—41no—
722C22×C5—41no—
723C22×C5—41no—
724C22×C5—41no—
725C22×C5C2×D3×D411yescharacteristic
726C2×D5—32no—
727C2×D5—32no—
728C2×D5—32no—
729C2×D5—61no—
730C2×D5—61no—
731C2×D5—62no—
732C2×D5—61no—
733C2×D5—124no—
734C2×D5—128no—
735C2×D5—121no—
736C2×D5—121no—
737C2×D5—121no—
738C2×D5—121no—
739C2×D5—121no—
740C2×D5—244no—
741C4×C5—22no—
742C4×C5—21no—
743C4×C5—41no—
744C4×C5C2×D3×D411yescharacteristic
745C4×C5C2×D3×D411yescharacteristic
746Dic5—32no—
747Dic5—62no—
748Dic5—61no—
749Dic5—121no—
750C24—151no—
751C24—301no—
752C24—301no—
753#41—22no—
754#41—22no—
755#41—302no—
756#41—302no—
757#41—308no—
758#41—302no—
759#41—308no—
760#41—302no—
761#41—302no—
762#41—302no—
763C2×Q8—154no—
764C2×Q8—151no—
765C2×Q8—301no—
766C2×Q8—302no—
767C2×Q8C22×D1511yescharacteristic
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—154no—
771C2×D4—151no—
772C2×D4—151no—
773C2×D4—301no—
774C2×D4—301no—
775C2×D4—302no—
776C2×D4—302no—
777C2×D4—302no—
778C2×D4—301no—
779C2×D4—301no—
780C2×D4—308no—
781C2×D4—301no—
782C2×D4—301no—
783C2×D4—301no—
784C2×D4—301no—
785C2×D4—604no—
786C2×D4C22×D1511yescharacteristic
787C2×D4C22×D1511yescharacteristic
788C22×C4—21no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—301no—
797C22×C4—301no—
798C22×C4—308no—
799C22×C4—301no—
800C22×C4—301no—
801C22×C4—301no—
802C22×C4C22×D1511yescharacteristic
803SD16—22no—
804SD16—302no—
805SD16—302no—
806SD16—302no—
807D8—22no—
808D8—302no—
809D8—302no—
810D8—302no—
811C2×C8—151no—
812C2×C8—151no—
813C2×C8—302no—
814C2×C8—302no—
815C2×C8C22×D1511yescharacteristic
816C2×C8C22×D1511yescharacteristic
817C4⋊C4—151no—
818C4⋊C4—301no—
819C4⋊C4C22×D1511yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—301no—
822C22⋊C4—301no—
823C22⋊C4—301no—
824C3×C5C2×#44911yescharacteristic, complemented, Hall
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—22no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3C2×D4×D511yescharacteristic
835C2×D3—52no—
836C2×D3—52no—
837C2×D3—52no—
838C2×D3—101no—
839C2×D3—101no—
840C2×D3—102no—
841C2×D3—101no—
842C2×D3—204no—
843C2×D3—208no—
844C2×D3—201no—
845C2×D3—201no—
846C2×D3—201no—
847C2×D3—201no—
848C2×D3—201no—
849C2×D3—404no—
850C3×C4—22no—
851C3×C4—21no—
852C3×C4—41no—
853C3×C4C2×D4×D511yescharacteristic
854C3×C4C2×D4×D511yescharacteristic
855Dic3—52no—
856Dic3—102no—
857Dic3—101no—
858Dic3—201no—
859C2×C5—41no—
860C2×C5—42no—
861C2×C5—81no—
862C2×C5D3×#12011yescharacteristic
863C2×C5D3×#13511yescharacteristic
864C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
865D5—34no—
866D5—121no—
867D5—122no—
868D5—241no—
869C23—21no—
870C23—21no—
871C23—151no—
872C23—151no—
873C23—304no—
874C23—302no—
875C23—302no—
876C23—302no—
877C23—301no—
878C23—301no—
879C23—602no—
880C23—602no—
881C23—602no—
882C23—602no—
883C23—602no—
884C23D4×D1511yescharacteristic
885Q8—21no—
886Q8—152no—
887Q8—304no—
888Q8—301no—
889Q8D4×D1512yescomplemented
890D4—24no—
891D4—21no—
892D4—21no—
893D4—21no—
894D4—42no—
895D4—152no—
896D4—304no—
897D4—304no—
898D4—304no—
899D4—304no—
900D4—301no—
901D4—301no—
902D4—301no—
903D4—602no—
904D4—602no—
905D4—602no—
906D4—602no—
907D4D4×D1512yescomplemented
908C2×C4—24no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—151no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—151no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—304no—
920C2×C4—304no—
921C2×C4—304no—
922C2×C4—302no—
923C2×C4—304no—
924C2×C4—301no—
925C2×C4—301no—
926C2×C4—301no—
927C2×C4—301no—
928C2×C4—602no—
929C2×C4D4×D1511yescharacteristic
930C2×C4C23×D1511yescharacteristic
931C8—21no—
932C8—21no—
933C8—301no—
934C8—301no—
935C2×C3—41no—
936C2×C3—42no—
937C2×C3—81no—
938C2×C3D5×#12011yescharacteristic
939C2×C3D5×#13511yescharacteristic
940C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
941D3—54no—
942D3—201no—
943D3—202no—
944D3—401no—
945C5D3×#44911yescharacteristic, complemented, Sylow
946C22—21no—
947C22—22no—
948C22—21no—
949C22—21no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—152no—
956C22—152no—
957C22—152no—
958C22—302no—
959C22—301no—
960C22—301no—
961C22—301no—
962C22—604no—
963C22—608no—
964C22—601no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22—1204no—
970C22C2×D4×D1511yescharacteristic
971C4—21no—
972C4—22no—
973C4—41no—
974C4—152no—
975C4—301no—
976C4—302no—
977C4—601no—
978C4C2×D4×D1511yescharacteristic
979C4C2×D4×D1511yescharacteristic
980C3D5×#44911yescharacteristic, complemented, Sylow
981C2—41no—
982C2—42no—
983C2—81no—
984C2—154no—
985C2—601no—
986C2—602no—
987C2—1201no—
988C2D15×#12011yescharacteristic
989C2D15×#13511yescharacteristic
990C2D15×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenter#449D15
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C2×SD16×D15C2semidirect
3. C2×D8×D15C2semidirect
4. D15×#121C2semidirect
5. C3×C5×#449C2semidirect
6. #11751339C2semidirect
7. #11751273C2semidirect
8. #11751259C2semidirect
9. #11751138C2semidirect
10. #11750911C2semidirect
11. D15×#103C2semidirect
12. #11750882C2semidirect
13. D15×#102C2semidirect
14. #11750835C2semidirect
15. D15×C22⋊C8C2semidirect
17. C2×C3×C5×#41C22semidirect
20. C2×#6821C22semidirect
23. C2×#6819C22semidirect
29. C2×#6817C22semidirect
32. C2×C3×C5×SD16C22semidirect
33. C2×C3×C5×D8C22semidirect
34. C3×C5×#121C22semidirect
35. C2×#6717C22semidirect
37. #91827C22semidirect
38. C2×#6716C22semidirect
39. C2×#6715C22semidirect
40. C2×#6715C22semidirect
41. #91819C22semidirect
44. C2×D120C22semidirect
45. C2×#6706C22semidirect
48. #91784C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×C22⋊C8C22semidirect
55. #91119C22semidirect
56. #91116C22semidirect
57. #91114C22semidirect
58. #91105C22semidirect
59. #91104C22semidirect
60. #91104C22semidirect
61. #91100C22semidirect
62. #91094C22semidirect
63. #91093C22semidirect
69. C5×#449D3semidirect
103. Q8×D15D4semidirect
112. D4×D15D4semidirect
158. C3×#449D5semidirect
169. C2×C5×#41C2×D3semidirect
184. C2×C5×SD16C2×D3semidirect
185. C2×C5×D8C2×D3semidirect
186. C5×#121C2×D3semidirect
204. C5×#103C2×D3semidirect
205. C5×#102C2×D3semidirect
206. C5×C22⋊C8C2×D3semidirect
234. C3×C5×Q8C2×D4semidirect
240. C3×C5×D4C2×D4semidirect
265. D60C2×D4semidirect
278. Dic30C2×D4semidirect
283. C2×C3×#41C2×D5semidirect
298. C2×C3×SD16C2×D5semidirect
299. C2×C3×D8C2×D5semidirect
300. C3×#121C2×D5semidirect
318. C3×#103C2×D5semidirect
319. C3×#102C2×D5semidirect
320. C3×C22⋊C8C2×D5semidirect
415. #449D15direct (N × H)
544. C5×Q8D3×D4semidirect
550. C5×D4D3×D4semidirect
600. C2×#41C2×D15semidirect
612. C2×SD16C2×D15semidirect
617. C2×D8C2×D15semidirect
625. #121C2×D15semidirect
631. #103C2×D15semidirect
635. #102C2×D15semidirect
639. C22⋊C8C2×D15semidirect
649. D15#449direct (N × H)
667. C3×Q8D4×D5semidirect
673. C3×D4D4×D5semidirect
824. C3×C5C2×#449semidirect
889. Q8D4×D15semidirect
907. D4D4×D15semidirect
945. C5D3×#449semidirect
980. C3D5×#449semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C2×SD16×D152
C2×D8×D152
D15×#1212
C3×C5×#4492
#117513392
#117512732
#117512592
#117511382
#117509112
D15×#1032
#117508822
D15×#1022
#117508352
D15×C22⋊C82
D5×#4493
D3×#4495