Finite Group Databasebeta

← D15×#440 #14416310

Subgroups — D15×#440 #14416310

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D15C211yesmaximal, characteristic
2C4×Q8×D15C211yesmaximal, characteristic, complemented
3C4×D4×D15C211yesmaximal, characteristic
4C3×C5×#440C211yesmaximal, characteristic, complemented
5#11751265C211yesmaximal, characteristic, complemented
6#11751127C211yesmaximal, characteristic, complemented
7#11751119C211yesmaximal, characteristic, complemented
8#11750990C211yesmaximal, characteristic, complemented
9D15×#107C211yesmaximal, characteristic, complemented
10#11750918C211yesmaximal, characteristic, complemented
11D15×#103C211yesmaximal, characteristic, complemented
12D15×#102C211yesmaximal, characteristic
13#11750858C211yesmaximal, characteristic, complemented
14#11750811C211yesmaximal, characteristic, complemented
15D15×#97C211yesmaximal, characteristic, complemented
16D5×#440—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×D4×D15C2211yescharacteristic
19C22×C4×D15—21no—
20C2×C3×C5×SD16C2211yescharacteristic
21C3×C4×C5×Q8C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23Q8×Dic15C2211yescharacteristic, complemented
24C2×#6717C2211yescharacteristic
25D4×Dic15C2211yescharacteristic
26C2×#6716C2211yescharacteristic
27C4×#1220—21no—
28SD16×D15C418yescomplemented
29C2×#6706C2211yescharacteristic
30C2×C8×D15C2211yescharacteristic
31C2×C8×D15C2211yescharacteristic
32#91782C2211yescharacteristic
33C4⋊C4×D15—21no—
34C4⋊C4×D15C2211yescharacteristic
35C4⋊C4×D15C2211yescharacteristic
36#91776—21no—
37#91776C2211yescharacteristic, complemented
38#91770—21no—
39C22⋊C4×D15—21no—
40C4×D60C2211yescharacteristic
41C42×D15—21no—
42C42×D15C2211yescharacteristic
43C4×Dic30—21no—
44C4×Dic30C2211yescharacteristic, complemented
45C3×C5×#107C2211yescharacteristic, complemented
46C3×C5×#103C2211yescharacteristic, complemented
47C3×C5×#102C2211yescharacteristic
48C3×C5×#97C2211yescharacteristic, complemented
49#91119C2211yescharacteristic, complemented
50#91116C2211yescharacteristic
51#91105C2211yescharacteristic
52#91102C2211yescharacteristic, complemented
53#91100C2211yescharacteristic, complemented
54#91099C2211yescharacteristic, complemented
55#91099C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91093C2211yescharacteristic
58#91091C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60#91087C2211yescharacteristic, complemented
61D3×#440—51nomaximal, Hall
62C2×D5×SD16—31no—
63C4×Q8×D5—31no—
64C4×D4×D5—31no—
65C5×#440D311yescharacteristic, complemented
66#65453—31no—
67#65315—31no—
68#65307—31no—
69#65178—31no—
70D5×#107—31no—
71#65106—31no—
72D5×#103—31no—
73D5×#102—31no—
74#65046—31no—
75#64999—31no—
76D5×#97—31no—
77C23×D15—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×#1220—21no—
82C22×Dic15—21no—
83Q8×D15—22no—
84Q8×D15C2×C414yescomplemented
85D4×D15—22no—
86D4×D15C2×C414yes—
87C2×D60C2311yescharacteristic
88C2×C4×D15—21no—
89C2×C4×D15—21no—
90C2×C4×D15—21no—
91C2×C4×D15—21no—
92C2×C4×D15—21no—
93C2×C4×D15—44no—
94C2×C4×D15D411yescharacteristic
95C2×C4×D15D411yescharacteristic
96C2×C4×D15C2311yescharacteristic
97C2×Dic30—21no—
98C2×Dic30C2311yescharacteristic
99C3×C5×SD16C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C3×C5×C4⋊C4—21no—
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106C3×C42×C5—21no—
107C3×C42×C5C2311yescharacteristic
108#6719—21no—
109#6717C2×C414yescomplemented
110#6716C2×C414yescomplemented
111#6714—21no—
112#6714—21no—
113C4⋊Dic15—21no—
114C4⋊Dic15C2311yescharacteristic
115C4⋊Dic15C2311yescharacteristic
116#6712—21no—
117#6712—21no—
118#6712—21no—
119#6712—21no—
120C4×Dic15—21no—
121C4×Dic15—21no—
122C4×Dic15—21no—
123C4×Dic15D411yescharacteristic
124C4×Dic15D411yescharacteristic
125C4×Dic15C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128#6706C2×C414yescomplemented
129C8×D15—22no—
130C8×D15C2×C414yescomplemented
131C2×D3×SD16—51no—
132C4×D3×Q8—51no—
133C4×D3×D4—51no—
134C3×#440D511yescharacteristic, complemented
135#5164—51no—
136#5026—51no—
137#5018—51no—
138#4889—51no—
139D3×#107—51no—
140#4817—51no—
141D3×#103—51no—
142D3×#102—51no—
143#4757—51no—
144#4710—51no—
145D3×#97—51no—
146C2×Q8×D5—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16C2×D311yescharacteristic
150C4×C5×Q8C2×D311yescharacteristic, complemented
151C4×C5×D4C2×D311yescharacteristic
152Q8×Dic5—31no—
153C2×#688—31no—
154D4×Dic5—31no—
155C2×#687—31no—
156C4×C22⋊D5—61no—
157D5×SD16—38no—
158C2×#677—31no—
159C2×C8×D5—31no—
160C2×C8×D5—31no—
161#4039—31no—
162D5×C4⋊C4—31no—
163D5×C4⋊C4—31no—
164D5×C4⋊C4—61no—
165#4033—31no—
166#4033—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C42×D5—31no—
171C42×D5—61no—
172C4×Dic10—31no—
173C4×Dic10—61no—
174C5×#107C2×D311yescharacteristic, complemented
175C5×#103C2×D311yescharacteristic, complemented
176C5×#102C2×D311yescharacteristic
177C5×#97C2×D311yescharacteristic, complemented
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3950—31no—
182#3948—31no—
183#3947—31no—
184#3947—31no—
185#3942—31no—
186#3941—31no—
187#3939—31no—
188#3939—31no—
189#3935—31no—
190C2×#440—151noSylow
191C23×C3×C5—21no—
192C22×D15—21no—
193C22×D15—24no—
194C22×D15—42no—
195C22×D15—42no—
196C22×D15C2×D411yescharacteristic
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yescomplemented
199C3×C5×D4—21no—
200C3×C5×D4C22×C412yes—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—42no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208#1220—24no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—42no—
213C2×Dic15C2×D411yescharacteristic
214C2×Dic15C2×D411yescharacteristic
215C2×Dic15C2×D411yescharacteristic
216D60—21no—
217D60C22×C412yes—
218C4×D15—24no—
219C4×D15—22no—
220C4×D15—22no—
221C4×D15—42no—
222C4×D15—42no—
223C4×D15—42no—
224C4×D15—42no—
225C4×D15C22×C412yes—
226C4×D15#4112yes—
227Dic30—21no—
228Dic30—24no—
229Dic30C22×C412yescomplemented
230C3×C5×C8—21no—
231C3×C5×C8C22×C412yescomplemented
232C3⋊#168—21no—
233C3⋊#168C22×C412yescomplemented
234C2×D3×Q8—51no—
235C2×D3×D4—51no—
236C22×C4×D3—101no—
237C2×C3×SD16C2×D511yescharacteristic
238C3×C4×Q8C2×D511yescharacteristic, complemented
239C3×C4×D4C2×D511yescharacteristic
240Q8×Dic3—51no—
241C2×#215—51no—
242D4×Dic3—51no—
243C2×#214—51no—
244C4×#67—101no—
245D3×SD16—58no—
246C2×#204—51no—
247C2×D3×C8—51no—
248C2×D3×C8—51no—
249#893—51no—
250D3×C4⋊C4—51no—
251D3×C4⋊C4—51no—
252D3×C4⋊C4—101no—
253#887—51no—
254#887—101no—
255#67⋊C4—101no—
256D3×C22⋊C4—101no—
257C4×D12—51no—
258C42×D3—51no—
259C42×D3—101no—
260C4×Dic6—51no—
261C4×Dic6—101no—
262C3×#107C2×D511yescharacteristic, complemented
263C3×#103C2×D511yescharacteristic, complemented
264C3×#102C2×D511yescharacteristic
265C3×#97C2×D511yescharacteristic, complemented
266#835—51no—
267#832—51no—
268#821—51no—
269#818—51no—
270#816—51no—
271#815—51no—
272#815—51no—
273#810—51no—
274#809—51no—
275#807—51no—
276#807—51no—
277#803—51no—
278C23×D5—61no—
279C2×C5×Q8C22×D311yescharacteristic
280C2×C5×D4C22×D311yescharacteristic
281C22×C4×C5—21no—
282C2×C22⋊D5—61no—
283C22×Dic5—61no—
284Q8×D5—34no—
285Q8×D5—62no—
286D4×D5—34no—
287D4×D5—62no—
288C2×D20—31no—
289C2×C4×D5—31no—
290C2×C4×D5—31no—
291C2×C4×D5—31no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—124no—
298C2×Dic10—31no—
299C2×Dic10—61no—
300C5×SD16C4×D314yescomplemented
301C2×C5×C8C22×D311yescharacteristic
302C2×C5×C8C22×D311yescharacteristic
303C5×C4⋊C4—21no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C4⋊C4C22×D311yescharacteristic
306C5×C22⋊C4—21no—
307C42×C5—21no—
308C42×C5C22×D311yescharacteristic
309C22⋊Dic5—61no—
310#688—34no—
311#687—34no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317#683—61no—
318#683—61no—
319#683—61no—
320#683—61no—
321C4×Dic5—31no—
322C4×Dic5—31no—
323C4×Dic5—31no—
324C4×Dic5—61no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C2×#168—31no—
328C2×#168—31no—
329#677—34no—
330C8×D5—34no—
331C8×D5—62no—
332C22×SD16—151no—
333C2×C4×Q8—151no—
334C2×C4×D4—151no—
335#440—151no—
336#440—151no—
337#440—151no—
338#440—151no—
339#440—151no—
340#440—151no—
341#440—151no—
342#440D1511yescharacteristic, direct product factor
343C2×#107—151no—
344C2×#103—151no—
345C2×#102—151no—
346C2×#97—151no—
347C22×C3×C5—22no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—48no—
355C2×D15C4×D412yes—
356C2×D15AGL(1,ℤ/8)12yes—
357C2×D15#13712yes—
358C3×C4×C5—22no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×C4×C5C23×C411yescharacteristic
364C3×C4×C5C2×#4111yescharacteristic
365Dic15—22no—
366Dic15—21no—
367Dic15—21no—
368Dic15—41no—
369Dic15—41no—
370Dic15C4×D412yes—
371C23×D3—101no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4C22×D511yescharacteristic
374C22×C3×C4—21no—
375C2×#67—101no—
376C22×Dic3—101no—
377D3×Q8—54no—
378D3×Q8—102no—
379D3×D4—54no—
380D3×D4—102no—
381C2×D12—51no—
382C2×C4×D3—51no—
383C2×C4×D3—51no—
384C2×C4×D3—51no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C2×C4×D3—204no—
391C2×Dic6—51no—
392C2×Dic6—101no—
393C3×SD16C4×D514yescomplemented
394C2×C3×C8C22×D511yescharacteristic
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4—21no—
397C3×C4⋊C4C22×D511yescharacteristic
398C3×C4⋊C4C22×D511yescharacteristic
399C3×C22⋊C4—21no—
400C3×C42—21no—
401C3×C42C22×D511yescharacteristic
402#217—101no—
403#215—54no—
404#214—54no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407C4⋊Dic3—51no—
408C4⋊Dic3—51no—
409C4⋊Dic3—101no—
410Dic3⋊C4—101no—
411Dic3⋊C4—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—51no—
415C4×Dic3—51no—
416C4×Dic3—51no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C2×C3⋊C8—51no—
421C2×C3⋊C8—51no—
422#204—54no—
423D3×C8—54no—
424D3×C8—102no—
425C23×C5—21no—
426C22×D5—31no—
427C22×D5—64no—
428C22×D5—61no—
429C22×D5—122no—
430C22×D5—122no—
431C5×Q8—21no—
432C5×Q8C2×C4×D312yescomplemented
433C5×D4—21no—
434C5×D4C2×C4×D312yes—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—42no—
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5D3×D411yescharacteristic
441C2×C4×C5C23×D311yescharacteristic
442C22⋊D5—64no—
443C2×Dic5—31no—
444C2×Dic5—31no—
445C2×Dic5—31no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—122no—
450D20—32no—
451D20—61no—
452C4×D5—32no—
453C4×D5—32no—
454C4×D5—62no—
455C4×D5—62no—
456C4×D5—64no—
457C4×D5—122no—
458C4×D5—122no—
459C4×D5—122no—
460C4×D5—122no—
461Dic10—32no—
462Dic10—64no—
463Dic10—61no—
464C5×C8—21no—
465C5×C8C2×C4×D312yescomplemented
466#168—32no—
467#168—61no—
468C22×Q8—151no—
469C22×D4—151no—
470C23×C4—301no—
471C2×SD16—151no—
472C2×SD16—151no—
473C2×SD16—158no—
474C2×SD16—151no—
475C2×SD16C2×D1511yescharacteristic
476C22×C8—151no—
477C22×C8—151no—
478C4×Q8—151no—
479C4×Q8—151no—
480C4×Q8—151no—
481C4×Q8—301no—
482C4×Q8—301no—
483C4×Q8C2×D1511yescharacteristic, complemented
484C4×D4—151no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—301no—
488C4×D4—301no—
489C4×D4C2×D1511yescharacteristic
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—301no—
493C2×C22⋊C4—301no—
494C2×C42—151no—
495C2×C42—301no—
496#107—151no—
497#107—151no—
498#107—151no—
499#107C2×D1511yescharacteristic, complemented
500#103—151no—
501#103—151no—
502#103—151no—
503#103C2×D1511yescharacteristic, complemented
504#102—151no—
505#102—151no—
506#102—151no—
507#102C2×D1511yescharacteristic
508#97—151no—
509#97—151no—
510#97—151no—
511#97C2×D1511yescharacteristic, complemented
512C2×C3×C5—42no—
513C2×C3×C5C2×C4×D411yescharacteristic
514C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
515C2×C3×C5C2×#13711yescharacteristic
516D15—42no—
517D15#44014yesdirect product factor
518C23×C3—21no—
519C22×D3—51no—
520C22×D3—104no—
521C22×D3—101no—
522C22×D3—202no—
523C22×D3—202no—
524C3×Q8—21no—
525C3×Q8C2×C4×D512yescomplemented
526C3×D4—21no—
527C3×D4C2×C4×D512yes—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—42no—
532C2×C3×C4D4×D511yescharacteristic
533C2×C3×C4D4×D511yescharacteristic
534C2×C3×C4C23×D511yescharacteristic
535#67—104no—
536C2×Dic3—51no—
537C2×Dic3—51no—
538C2×Dic3—51no—
539C2×Dic3—101no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—202no—
543D12—52no—
544D12—101no—
545C4×D3—52no—
546C4×D3—52no—
547C4×D3—102no—
548C4×D3—102no—
549C4×D3—104no—
550C4×D3—202no—
551C4×D3—202no—
552C4×D3—202no—
553C4×D3—202no—
554Dic6—52no—
555Dic6—104no—
556Dic6—101no—
557C3×C8—21no—
558C3×C8C2×C4×D512yescomplemented
559C3⋊C8—52no—
560C3⋊C8—101no—
561C22×C5—22no—
562C22×C5—41no—
563C22×C5—41no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—32no—
566C2×D5—32no—
567C2×D5—32no—
568C2×D5—62no—
569C2×D5—128no—
570C2×D5—121no—
571C2×D5—121no—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—22no—
575C4×C5—41no—
576C4×C5—41no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5D3×#4111yescharacteristic
579Dic5—32no—
580Dic5—61no—
581Dic5—61no—
582Dic5—62no—
583Dic5—121no—
584Dic5—121no—
585C24—301no—
586C2×Q8—154no—
587C2×Q8—151no—
588C2×Q8—301no—
589C2×Q8—302no—
590C2×Q8C22×D1511yescharacteristic
591C2×D4—154no—
592C2×D4—151no—
593C2×D4—302no—
594C2×D4—301no—
595C2×D4C22×D1511yescharacteristic
596C22×C4—21no—
597C22×C4—151no—
598C22×C4—151no—
599C22×C4—151no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—604no—
607SD16—154no—
608SD16—154no—
609SD16—154no—
610SD16C4×D1514yescomplemented
611C2×C8—151no—
612C2×C8—154no—
613C2×C8—151no—
614C2×C8—302no—
615C2×C8C22×D1511yescharacteristic
616C2×C8C22×D1511yescharacteristic
617C4⋊C4—21no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4C22×D1511yescharacteristic
626C4⋊C4C22×D1511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C42—21no—
632C42—151no—
633C42—151no—
634C42—151no—
635C42—301no—
636C42—301no—
637C42—301no—
638C42C22×D1511yescharacteristic
639C3×C5C2×#44011yescharacteristic, complemented, Hall
640C22×C3—22no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3C2×D4×D511yescharacteristic
644C2×D3—52no—
645C2×D3—52no—
646C2×D3—52no—
647C2×D3—102no—
648C2×D3—208no—
649C2×D3—201no—
650C2×D3—201no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4D5×#4111yescharacteristic
658Dic3—52no—
659Dic3—101no—
660Dic3—101no—
661Dic3—102no—
662Dic3—201no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5C4×D3×D411yescharacteristic
666C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
667C2×C5D3×#13711yescharacteristic
668D5—34no—
669D5—122no—
670C23—21no—
671C23—151no—
672C23—304no—
673C23—301no—
674C23—602no—
675C23—602no—
676Q8—21no—
677Q8—152no—
678Q8—304no—
679Q8—301no—
680Q8C2×C4×D1512yescomplemented
681D4—21no—
682D4—152no—
683D4—304no—
684D4—301no—
685D4C2×C4×D1512yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—42no—
690C2×C4—151no—
691C2×C4—152no—
692C2×C4—152no—
693C2×C4—151no—
694C2×C4—151no—
695C2×C4—302no—
696C2×C4—302no—
697C2×C4—304no—
698C2×C4—301no—
699C2×C4—301no—
700C2×C4—301no—
701C2×C4—602no—
702C2×C4—602no—
703C2×C4—602no—
704C2×C4—602no—
705C2×C4—602no—
706C2×C4D4×D1511yescharacteristic
707C2×C4D4×D1511yescharacteristic
708C2×C4C23×D1511yescharacteristic
709C8—21no—
710C8—152no—
711C8—301no—
712C8C2×C4×D1512yescomplemented
713C2×C3—42no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
716C2×C3D5×#13711yescharacteristic
717D3—54no—
718D3—202no—
719C5D3×#44011yescharacteristic, complemented, Sylow
720C22—22no—
721C22—41no—
722C22—41no—
723C22—152no—
724C22—152no—
725C22—152no—
726C22—302no—
727C22—608no—
728C22—601no—
729C22—601no—
730C22C2×D4×D1511yescharacteristic
731C4—22no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—152no—
737C4—302no—
738C4—301no—
739C4—301no—
740C4—601no—
741C4—601no—
742C4C22×C4×D1511yescharacteristic
743C4#41×D1511yescharacteristic
744C3D5×#44011yescharacteristic, complemented, Sylow
745C2—42no—
746C2—154no—
747C2—602no—
748C2C4×D4×D1511yescharacteristic
749C2D15×AGL(1,ℤ/8)11yescharacteristic
750C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC2×D4×D15C22
cosocleC2×C3×C4×C5C24
hypercenter#440D15
hypocenterC3×C5C2×#440
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D15C2semidirect
4. C3×C5×#440C2semidirect
5. #11751265C2semidirect
6. #11751127C2semidirect
7. #11751119C2semidirect
8. #11750990C2semidirect
9. D15×#107C2semidirect
10. #11750918C2semidirect
11. D15×#103C2semidirect
13. #11750858C2semidirect
14. #11750811C2semidirect
15. D15×#97C2semidirect
21. C3×C4×C5×Q8C22semidirect
23. Q8×Dic15C22semidirect
28. SD16×D15C4semidirect
37. #91776C22semidirect
44. C4×Dic30C22semidirect
45. C3×C5×#107C22semidirect
46. C3×C5×#103C22semidirect
48. C3×C5×#97C22semidirect
49. #91119C22semidirect
52. #91102C22semidirect
53. #91100C22semidirect
54. #91099C22semidirect
55. #91099C22semidirect
56. #91094C22semidirect
58. #91091C22semidirect
59. #91091C22semidirect
60. #91087C22semidirect
65. C5×#440D3semidirect
84. Q8×D15C2×C4semidirect
99. C3×C5×SD16C2×C4semidirect
109. #6717C2×C4semidirect
110. #6716C2×C4semidirect
128. #6706C2×C4semidirect
130. C8×D15C2×C4semidirect
134. C3×#440D5semidirect
150. C4×C5×Q8C2×D3semidirect
174. C5×#107C2×D3semidirect
175. C5×#103C2×D3semidirect
177. C5×#97C2×D3semidirect
198. C3×C5×Q8C22×C4semidirect
229. Dic30C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
233. C3⋊#168C22×C4semidirect
238. C3×C4×Q8C2×D5semidirect
262. C3×#107C2×D5semidirect
263. C3×#103C2×D5semidirect
265. C3×#97C2×D5semidirect
300. C5×SD16C4×D3semidirect
342. #440D15direct (N × H)
393. C3×SD16C4×D5semidirect
432. C5×Q8C2×C4×D3semidirect
465. C5×C8C2×C4×D3semidirect
483. C4×Q8C2×D15semidirect
499. #107C2×D15semidirect
503. #103C2×D15semidirect
511. #97C2×D15semidirect
517. D15#440direct (N × H)
525. C3×Q8C2×C4×D5semidirect
558. C3×C8C2×C4×D5semidirect
610. SD16C4×D15semidirect
639. C3×C5C2×#440semidirect
680. Q8C2×C4×D15semidirect
712. C8C2×C4×D15semidirect
719. C5D3×#440semidirect
744. C3D5×#440semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D152
C4×Q8×D152
C4×D4×D152
C3×C5×#4402
#117512652
#117511272
#117511192
#117509902
D15×#1072
#117509182
D15×#1032
D15×#1022
#117508582
#117508112
D15×#972
D5×#4403
D3×#4405