Finite Group Databasebeta

← D15×#468 #14427887

Subgroups — D15×#468 #14427887

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D15C211yesmaximal, characteristic, complemented
2C2×M16×D15C211yesmaximal, characteristic, complemented
3D15×C22⋊Q8C211yesmaximal, characteristic, complemented
4D15×#121C211yesmaximal, characteristic
5C3×C5×#468C211yesmaximal, characteristic, complemented
6#11751275C211yesmaximal, characteristic, complemented
7#11751235C211yesmaximal, characteristic, complemented
8#11751150C211yesmaximal, characteristic, complemented
9#11751143C211yesmaximal, characteristic, complemented
10#11750987C211yesmaximal, characteristic, complemented
11D15×#107C211yesmaximal, characteristic, complemented
12#11750913C211yesmaximal, characteristic, complemented
13D15×#103C211yesmaximal, characteristic, complemented
14#11750881C211yesmaximal, characteristic, complemented
15D15×#102C211yesmaximal, characteristic, complemented
16D5×#468—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×D4×D15—21no—
19C2×D4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic, complemented
22C2×C3×C5×M16C2211yescharacteristic, complemented
23C3×C5×C22⋊Q8C2211yescharacteristic, complemented
24C3×C5×#121C2211yescharacteristic
25#91835C2211yescharacteristic, complemented
26C2×#6717C2211yescharacteristic, complemented
27#91828—21no—
28#91827C2211yescharacteristic
29C2×#6716C2211yescharacteristic, complemented
30#91819C2211yescharacteristic
31#91813C2211yescharacteristic, complemented
32C2×#6710C2211yescharacteristic, complemented
33SD16×D15—24no—
34M16×D15—24no—
35C2×#6706C2211yescharacteristic, complemented
36C2×#6705C2211yescharacteristic, complemented
37C2×#6705C2211yescharacteristic, complemented
38C2×C8×D15C2211yescharacteristic
39C2×C8×D15C2211yescharacteristic
40#91786C2211yescharacteristic, complemented
41#91785—21no—
42#91784C2211yescharacteristic
43C4⋊C4×D15—21no—
44C4⋊C4×D15C2211yescharacteristic
45C4⋊C4×D15C2211yescharacteristic
46#91773—21no—
47C22⋊C4×D15—21no—
48C22⋊C4×D15—21no—
49#91767—21no—
50C3×C5×#107C2211yescharacteristic, complemented
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53#91119C2211yescharacteristic, complemented
54#91116C2211yescharacteristic, complemented
55#91105C2211yescharacteristic, complemented
56#91102C2211yescharacteristic, complemented
57#91100C2211yescharacteristic, complemented
58#91094C2211yescharacteristic, complemented
59#91093C2211yescharacteristic, complemented
60#91091C2211yescharacteristic, complemented
61#91091C2211yescharacteristic, complemented
62D3×#468—51nomaximal, Hall
63C2×D5×SD16—31no—
64C2×D5×M16—31no—
65D5×C22⋊Q8—31no—
66D5×#121—31no—
67C5×#468D311yescharacteristic, complemented
68#65463—31no—
69#65423—31no—
70#65338—31no—
71#65331—31no—
72#65175—31no—
73D5×#107—31no—
74#65101—31no—
75D5×#103—31no—
76#65069—31no—
77D5×#102—31no—
78C23×D15—21no—
79C23×D15D411yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—21no—
85C2×#1220—21no—
86C2×#1220—21no—
87C22×Dic15D411yescharacteristic
88Q8×D15—22no—
89Q8×D15—22no—
90D4×D15—22no—
91D4×D15—22no—
92D4×D15—44no—
93C2×D60—21no—
94C2×D60C2311yescharacteristic
95C2×C4×D15—22no—
96C2×C4×D15—22no—
97C2×C4×D15—21no—
98C2×C4×D15—21no—
99C2×C4×D15—21no—
100C2×C4×D15D411yescharacteristic
101C2×C4×D15D411yescharacteristic
102C2×C4×D15C2311yescharacteristic
103C2×C4×D15C2311yescharacteristic
104C2×Dic30—21no—
105C2×Dic30C2311yescharacteristic
106C3×C5×SD16—22no—
107C3×C5×M16—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C4⋊C4C2311yescharacteristic
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115#6719—21no—
116#6719—21no—
117#6717—22no—
118#6716—22no—
119#6714—21no—
120#6714—21no—
121#6714—21no—
122#6714—21no—
123C4⋊Dic15—21no—
124C4⋊Dic15C2311yescharacteristic
125C4⋊Dic15C2311yescharacteristic
126#6712—21no—
127#6712—21no—
128#6712—21no—
129#6712—21no—
130#6710—22no—
131C2×C3⋊#168C2311yescharacteristic
132C2×C3⋊#168C2311yescharacteristic
133#6706—22no—
134#6705—22no—
135#6705—22no—
136C8×D15—22no—
137C8×D15D414yescomplemented
138C2×D3×SD16—51no—
139C2×D3×M16—51no—
140D3×C22⋊Q8—51no—
141D3×#121—51no—
142C3×#468D511yescharacteristic, complemented
143#5174—51no—
144#5134—51no—
145#5049—51no—
146#5042—51no—
147#4886—51no—
148D3×#107—51no—
149#4812—51no—
150D3×#103—51no—
151#4780—51no—
152D3×#102—51no—
153C2×Q8×D5—31no—
154C2×D4×D5—31no—
155C2×D4×D5—61no—
156C22×C4×D5—31no—
157C2×C5×SD16C2×D311yescharacteristic, complemented
158C2×C5×M16C2×D311yescharacteristic, complemented
159C5×C22⋊Q8C2×D311yescharacteristic, complemented
160C5×#121C2×D311yescharacteristic
161#4092—31no—
162C2×#688—31no—
163#4085—61no—
164#4084—31no—
165C2×#687—31no—
166#4076—31no—
167#4070—31no—
168C2×#681—31no—
169D5×SD16—64no—
170D5×M16—64no—
171C2×#677—31no—
172C2×#676—31no—
173C2×#676—31no—
174C2×C8×D5—31no—
175C2×C8×D5—31no—
176#4043—31no—
177#4042—61no—
178#4041—31no—
179D5×C4⋊C4—31no—
180D5×C4⋊C4—31no—
181D5×C4⋊C4—61no—
182#4030—61no—
183D5×C22⋊C4—61no—
184D5×C22⋊C4—61no—
185#4024—61no—
186C5×#107C2×D311yescharacteristic, complemented
187C5×#103C2×D311yescharacteristic, complemented
188C5×#102C2×D311yescharacteristic, complemented
189#3967—31no—
190#3964—31no—
191#3953—31no—
192#3950—31no—
193#3948—31no—
194#3942—31no—
195#3941—31no—
196#3939—31no—
197#3939—31no—
198C2×#468—151noSylow
199C23×C3×C5—21no—
200C23×C3×C5C2×D411yescharacteristic
201C22×D15—22no—
202C22×D15—22no—
203C22×D15—22no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—42no—
208C22×D15C2×D411yescharacteristic
209C22×D15C2×D411yescharacteristic
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—42no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222#1220—42no—
223#1220—42no—
224#1220—42no—
225C2×Dic15—22no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15C2×D411yescharacteristic
230C2×Dic15C2×D411yescharacteristic
231D60—21no—
232D60—21no—
233D60—42no—
234C4×D15—22no—
235C4×D15—21no—
236C4×D15—21no—
237C4×D15—22no—
238C4×D15—42no—
239C4×D15—42no—
240C4×D15—42no—
241C4×D15C2×D412yes—
242C4×D15#4112yes—
243Dic30—21no—
244Dic30—21no—
245Dic30—42no—
246C3×C5×C8—21no—
247C3×C5×C8C2×D412yescomplemented
248C3⋊#168—21no—
249C3⋊#168C2×D412yescomplemented
250C2×D3×Q8—51no—
251C2×D3×D4—51no—
252C2×D3×D4—101no—
253C22×C4×D3—51no—
254C2×C3×SD16C2×D511yescharacteristic, complemented
255C2×C3×M16C2×D511yescharacteristic, complemented
256C3×C22⋊Q8C2×D511yescharacteristic, complemented
257C3×#121C2×D511yescharacteristic
258#946—51no—
259C2×#215—51no—
260#939—101no—
261#938—51no—
262C2×#214—51no—
263#930—51no—
264#924—51no—
265C2×#208—51no—
266D3×SD16—104no—
267D3×M16—104no—
268C2×#204—51no—
269C2×ΓL(1,𝔽25)—51no—
270C2×ΓL(1,𝔽25)—51no—
271C2×D3×C8—51no—
272C2×D3×C8—51no—
273#897—51no—
274#896—101no—
275#895—51no—
276D3×C4⋊C4—51no—
277D3×C4⋊C4—51no—
278D3×C4⋊C4—101no—
279#884—101no—
280D3×C22⋊C4—101no—
281D3×C22⋊C4—101no—
282#878—101no—
283C3×#107C2×D511yescharacteristic, complemented
284C3×#103C2×D511yescharacteristic, complemented
285C3×#102C2×D511yescharacteristic, complemented
286#835—51no—
287#832—51no—
288#821—51no—
289#818—51no—
290#816—51no—
291#810—51no—
292#809—51no—
293#807—51no—
294#807—51no—
295C23×D5—31no—
296C23×D5—61no—
297C2×C5×Q8C22×D311yescharacteristic
298C2×C5×D4—21no—
299C2×C5×D4C22×D311yescharacteristic
300C22×C4×C5C22×D311yescharacteristic
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303C2×C22⋊D5—61no—
304C22×Dic5—31no—
305Q8×D5—62no—
306Q8×D5—62no—
307D4×D5—62no—
308D4×D5—62no—
309D4×D5—124no—
310C2×D20—31no—
311C2×D20—61no—
312C2×C4×D5—31no—
313C2×C4×D5—31no—
314C2×C4×D5—31no—
315C2×C4×D5—31no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×C4×D5—61no—
321C2×Dic10—31no—
322C2×Dic10—61no—
323C5×SD16—22no—
324C5×M16—22no—
325C2×C5×C8C22×D311yescharacteristic
326C2×C5×C8C22×D311yescharacteristic
327C5×C4⋊C4—21no—
328C5×C4⋊C4C22×D311yescharacteristic
329C5×C4⋊C4C22×D311yescharacteristic
330C5×C22⋊C4—21no—
331C5×C22⋊C4—21no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#688—62no—
335#687—62no—
336#685—61no—
337#685—61no—
338#685—61no—
339#685—61no—
340C4⋊Dic5—31no—
341C4⋊Dic5—31no—
342C4⋊Dic5—61no—
343#683—61no—
344#683—61no—
345#683—61no—
346#683—61no—
347#681—62no—
348C2×#168—31no—
349C2×#168—31no—
350#677—62no—
351#676—62no—
352#676—62no—
353C8×D5—34no—
354C8×D5—62no—
355C22×SD16—151no—
356C22×M16—151no—
357C2×C22⋊Q8—151no—
358C2×#121—151no—
359#468—151no—
360#468—151no—
361#468—151no—
362#468—151no—
363#468—151no—
364#468—151no—
365#468—151no—
366#468D1511yescharacteristic, direct product factor
367C2×#107—151no—
368C2×#103—151no—
369C2×#102—151no—
370C22×C3×C5—21no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5C22×D411yescharacteristic
377C2×D15—21no—
378C2×D15—21no—
379C2×D15—21no—
380C2×D15—44no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—84no—
385C2×D15#12112yes—
386C2×D15AGL(1,ℤ/8)12yes—
387C2×D15#13712yes—
388C3×C4×C5—21no—
389C3×C4×C5—41no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5C2×#4111yescharacteristic
394Dic15—21no—
395Dic15—41no—
396Dic15—41no—
397Dic15—41no—
398Dic15#12112yes—
399C23×D3—51no—
400C23×D3—101no—
401C2×C3×Q8C22×D511yescharacteristic
402C2×C3×D4—21no—
403C2×C3×D4C22×D511yescharacteristic
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—101no—
406C2×#67—101no—
407C2×#67—101no—
408C22×Dic3—51no—
409D3×Q8—102no—
410D3×Q8—102no—
411D3×D4—102no—
412D3×D4—102no—
413D3×D4—204no—
414C2×D12—51no—
415C2×D12—101no—
416C2×C4×D3—51no—
417C2×C4×D3—51no—
418C2×C4×D3—51no—
419C2×C4×D3—51no—
420C2×C4×D3—102no—
421C2×C4×D3—102no—
422C2×C4×D3—101no—
423C2×C4×D3—101no—
424C2×C4×D3—101no—
425C2×Dic6—51no—
426C2×Dic6—101no—
427C3×SD16—22no—
428C3×M16—22no—
429C2×C3×C8C22×D511yescharacteristic
430C2×C3×C8C22×D511yescharacteristic
431C3×C4⋊C4—21no—
432C3×C4⋊C4C22×D511yescharacteristic
433C3×C4⋊C4C22×D511yescharacteristic
434C3×C22⋊C4—21no—
435C3×C22⋊C4—21no—
436#217—101no—
437#217—101no—
438#215—102no—
439#214—102no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444C4⋊Dic3—51no—
445C4⋊Dic3—51no—
446C4⋊Dic3—101no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451#208—102no—
452C2×C3⋊C8—51no—
453C2×C3⋊C8—51no—
454#204—102no—
455ΓL(1,𝔽25)—102no—
456ΓL(1,𝔽25)—102no—
457D3×C8—54no—
458D3×C8—102no—
459C23×C5—21no—
460C23×C5D3×D411yescharacteristic
461C22×D5—31no—
462C22×D5—31no—
463C22×D5—62no—
464C22×D5—62no—
465C22×D5—62no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—122no—
470C5×Q8—21no—
471C5×Q8—21no—
472C5×D4—21no—
473C5×D4—21no—
474C5×D4—42no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5D3×D411yescharacteristic
481C2×C4×C5C23×D311yescharacteristic
482C22⋊D5—122no—
483C22⋊D5—122no—
484C22⋊D5—122no—
485C2×Dic5—31no—
486C2×Dic5—31no—
487C2×Dic5—62no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491D20—61no—
492D20—61no—
493D20—122no—
494C4×D5—32no—
495C4×D5—32no—
496C4×D5—62no—
497C4×D5—62no—
498C4×D5—61no—
499C4×D5—61no—
500C4×D5—122no—
501C4×D5—122no—
502C4×D5—122no—
503Dic10—61no—
504Dic10—61no—
505Dic10—122no—
506C5×C8—21no—
507C5×C8D3×D412yescomplemented
508#168—32no—
509#168—61no—
510C22×Q8—151no—
511C22×D4—151no—
512C22×D4—301no—
513C23×C4—151no—
514C2×SD16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—304no—
518C2×SD16C2×D1511yescharacteristic, complemented
519C2×M16—151no—
520C2×M16—151no—
521C2×M16—151no—
522C2×M16—304no—
523C2×M16C2×D1511yescharacteristic, complemented
524C22×C8—151no—
525C22×C8—151no—
526C22⋊Q8—151no—
527C22⋊Q8—151no—
528C22⋊Q8—151no—
529C22⋊Q8—301no—
530C22⋊Q8—301no—
531C22⋊Q8C2×D1511yescharacteristic, complemented
532#121—151no—
533#121—151no—
534#121—151no—
535#121—301no—
536#121—301no—
537#121C2×D1511yescharacteristic
538C2×C4⋊C4—151no—
539C2×C4⋊C4—151no—
540C2×C4⋊C4—301no—
541C2×C22⋊C4—301no—
542C2×C22⋊C4—301no—
543#107—151no—
544#107—151no—
545#107—151no—
546#107C2×D1511yescharacteristic, complemented
547#103—151no—
548#103—151no—
549#103—151no—
550#103C2×D1511yescharacteristic, complemented
551#102—151no—
552#102—151no—
553#102—151no—
554#102C2×D1511yescharacteristic, complemented
555C2×C3×C5—41no—
556C2×C3×C5—81no—
557C2×C3×C5C2×#12111yescharacteristic
558C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
559C2×C3×C5C2×#13711yescharacteristic
560D15—41no—
561D15—81no—
562D15#46814yesdirect product factor
563C23×C3—21no—
564C23×C3D4×D511yescharacteristic
565C22×D3—51no—
566C22×D3—51no—
567C22×D3—102no—
568C22×D3—102no—
569C22×D3—102no—
570C22×D3—101no—
571C22×D3—202no—
572C22×D3—202no—
573C22×D3—202no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—42no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4D4×D511yescharacteristic
585C2×C3×C4C23×D511yescharacteristic
586#67—202no—
587#67—202no—
588#67—202no—
589C2×Dic3—51no—
590C2×Dic3—51no—
591C2×Dic3—102no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595D12—101no—
596D12—101no—
597D12—202no—
598C4×D3—52no—
599C4×D3—52no—
600C4×D3—102no—
601C4×D3—102no—
602C4×D3—101no—
603C4×D3—101no—
604C4×D3—202no—
605C4×D3—202no—
606C4×D3—202no—
607Dic6—101no—
608Dic6—101no—
609Dic6—202no—
610C3×C8—21no—
611C3×C8D4×D512yescomplemented
612C3⋊C8—52no—
613C3⋊C8—101no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—21no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5C2×D3×D411yescharacteristic
621C2×D5—32no—
622C2×D5—32no—
623C2×D5—32no—
624C2×D5—61no—
625C2×D5—61no—
626C2×D5—61no—
627C2×D5—124no—
628C2×D5—121no—
629C2×D5—121no—
630C2×D5—121no—
631C2×D5—244no—
632C4×C5—21no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5C2×D3×D411yescharacteristic
637C4×C5D3×#4111yescharacteristic
638Dic5—32no—
639Dic5—61no—
640Dic5—121no—
641Dic5—121no—
642Dic5—121no—
643C24—151no—
644C24—301no—
645C2×Q8—151no—
646C2×Q8—301no—
647C2×Q8—302no—
648C2×Q8—302no—
649C2×Q8C22×D1511yescharacteristic
650C2×D4—21no—
651C2×D4—151no—
652C2×D4—301no—
653C2×D4—302no—
654C2×D4—302no—
655C2×D4—301no—
656C2×D4—301no—
657C2×D4—301no—
658C2×D4—604no—
659C2×D4C22×D1511yescharacteristic
660C22×C4—151no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—302no—
666C22×C4—302no—
667C22×C4—301no—
668C22×C4—301no—
669C22×C4—301no—
670C22×C4C22×D1511yescharacteristic
671SD16—22no—
672SD16—302no—
673SD16—302no—
674SD16—302no—
675M16—22no—
676M16—302no—
677M16—302no—
678M16—302no—
679C2×C8—151no—
680C2×C8—154no—
681C2×C8—151no—
682C2×C8—302no—
683C2×C8C22×D1511yescharacteristic
684C2×C8C22×D1511yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—151no—
687C4⋊C4—151no—
688C4⋊C4—301no—
689C4⋊C4—301no—
690C4⋊C4—301no—
691C4⋊C4—301no—
692C4⋊C4—301no—
693C4⋊C4C22×D1511yescharacteristic
694C4⋊C4C22×D1511yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—301no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C22⋊C4—301no—
703C3×C5C2×#46811yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3C2×D4×D511yescharacteristic
711C2×D3—52no—
712C2×D3—52no—
713C2×D3—52no—
714C2×D3—101no—
715C2×D3—101no—
716C2×D3—101no—
717C2×D3—204no—
718C2×D3—201no—
719C2×D3—201no—
720C2×D3—201no—
721C2×D3—404no—
722C3×C4—21no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4C2×D4×D511yescharacteristic
727C3×C4D5×#4111yescharacteristic
728Dic3—52no—
729Dic3—101no—
730Dic3—201no—
731Dic3—201no—
732Dic3—201no—
733C2×C5—41no—
734C2×C5—81no—
735C2×C5D3×#12111yescharacteristic
736C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
737C2×C5D3×#13711yescharacteristic
738D5—34no—
739D5—121no—
740D5—241no—
741C23—21no—
742C23—151no—
743C23—151no—
744C23—302no—
745C23—302no—
746C23—302no—
747C23—301no—
748C23—602no—
749C23—602no—
750C23—602no—
751C23D4×D1511yescharacteristic
752Q8—21no—
753Q8—21no—
754Q8—301no—
755Q8—301no—
756Q8—602no—
757D4—21no—
758D4—21no—
759D4—42no—
760D4—301no—
761D4—301no—
762D4—602no—
763D4—602no—
764D4—602no—
765D4—602no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—151no—
772C2×C4—152no—
773C2×C4—152no—
774C2×C4—151no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—302no—
778C2×C4—301no—
779C2×C4—301no—
780C2×C4—301no—
781C2×C4—301no—
782C2×C4—301no—
783C2×C4—602no—
784C2×C4—602no—
785C2×C4—602no—
786C2×C4D4×D1511yescharacteristic
787C2×C4C23×D1511yescharacteristic
788C8—21no—
789C8—152no—
790C8—301no—
791C8D4×D1512yescomplemented
792C2×C3—41no—
793C2×C3—81no—
794C2×C3D5×#12111yescharacteristic
795C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
796C2×C3D5×#13711yescharacteristic
797D3—54no—
798D3—201no—
799D3—401no—
800C5D3×#46811yescharacteristic, complemented, Sylow
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—152no—
808C22—152no—
809C22—152no—
810C22—301no—
811C22—301no—
812C22—301no—
813C22—604no—
814C22—601no—
815C22—601no—
816C22—601no—
817C22—1204no—
818C22C2×D4×D1511yescharacteristic
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—152no—
824C4—301no—
825C4—601no—
826C4—601no—
827C4—601no—
828C4C2×D4×D1511yescharacteristic
829C4#41×D1511yescharacteristic
830C3D5×#46811yescharacteristic, complemented, Sylow
831C2—41no—
832C2—81no—
833C2—154no—
834C2—601no—
835C2—1201no—
836C2D15×#12111yescharacteristic
837C2D15×AGL(1,ℤ/8)11yescharacteristic
838C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#468C2
socleC22×C3×C5C22×D4
prime radicalD15×#121C2
hypercenter#468D15
hypocenterC3×C5C2×#468
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D15C2semidirect
2. C2×M16×D15C2semidirect
3. D15×C22⋊Q8C2semidirect
5. C3×C5×#468C2semidirect
6. #11751275C2semidirect
7. #11751235C2semidirect
8. #11751150C2semidirect
9. #11751143C2semidirect
10. #11750987C2semidirect
11. D15×#107C2semidirect
12. #11750913C2semidirect
13. D15×#103C2semidirect
14. #11750881C2semidirect
15. D15×#102C2semidirect
21. C2×C3×C5×SD16C22semidirect
22. C2×C3×C5×M16C22semidirect
23. C3×C5×C22⋊Q8C22semidirect
25. #91835C22semidirect
26. C2×#6717C22semidirect
29. C2×#6716C22semidirect
31. #91813C22semidirect
32. C2×#6710C22semidirect
35. C2×#6706C22semidirect
36. C2×#6705C22semidirect
37. C2×#6705C22semidirect
40. #91786C22semidirect
50. C3×C5×#107C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#102C22semidirect
53. #91119C22semidirect
54. #91116C22semidirect
55. #91105C22semidirect
56. #91102C22semidirect
57. #91100C22semidirect
58. #91094C22semidirect
59. #91093C22semidirect
60. #91091C22semidirect
61. #91091C22semidirect
67. C5×#468D3semidirect
137. C8×D15D4semidirect
142. C3×#468D5semidirect
157. C2×C5×SD16C2×D3semidirect
158. C2×C5×M16C2×D3semidirect
159. C5×C22⋊Q8C2×D3semidirect
186. C5×#107C2×D3semidirect
187. C5×#103C2×D3semidirect
188. C5×#102C2×D3semidirect
247. C3×C5×C8C2×D4semidirect
249. C3⋊#168C2×D4semidirect
254. C2×C3×SD16C2×D5semidirect
255. C2×C3×M16C2×D5semidirect
256. C3×C22⋊Q8C2×D5semidirect
283. C3×#107C2×D5semidirect
284. C3×#103C2×D5semidirect
285. C3×#102C2×D5semidirect
366. #468D15direct (N × H)
507. C5×C8D3×D4semidirect
518. C2×SD16C2×D15semidirect
523. C2×M16C2×D15semidirect
531. C22⋊Q8C2×D15semidirect
546. #107C2×D15semidirect
550. #103C2×D15semidirect
554. #102C2×D15semidirect
562. D15#468direct (N × H)
611. C3×C8D4×D5semidirect
703. C3×C5C2×#468semidirect
791. C8D4×D15semidirect
800. C5D3×#468semidirect
830. C3D5×#468semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D152
C2×M16×D152
D15×C22⋊Q82
D15×#1212
C3×C5×#4682
#117512752
#117512352
#117511502
#117511432
#117509872
D15×#1072
#117509132
D15×#1032
#117508812
D15×#1022
D5×#4683
D3×#4685