Finite Group Databasebeta

← D15×#464 #14426120

Subgroups — D15×#464 #14426120

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D15C211yesmaximal, characteristic, complemented
2C2×SD16×D15C211yesmaximal, characteristic
3D15×#124C211yesmaximal, characteristic
4C4×Q8×D15C211yesmaximal, characteristic, complemented
5C3×C5×#464C211yesmaximal, characteristic, complemented
6#11751286C211yesmaximal, characteristic, complemented
7#11751267C211yesmaximal, characteristic, complemented
8#11751155C211yesmaximal, characteristic, complemented
9#11751129C211yesmaximal, characteristic, complemented
10#11750946C211yesmaximal, characteristic, complemented
11D15×C4⋊C8C211yesmaximal, characteristic, complemented
12D15×#103C211yesmaximal, characteristic, complemented
13#11750899C211yesmaximal, characteristic, complemented
14D15×#102C211yesmaximal, characteristic
15#11750868C211yesmaximal, characteristic, complemented
16D5×#464—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×Q8×D15C2211yescharacteristic
19C2×D4×D15C2211yescharacteristic
20C2×C3×C5×Q16C2211yescharacteristic, complemented
21C2×C3×C5×SD16C2211yescharacteristic
22C3×C5×#124C2211yescharacteristic
23C3×C4×C5×Q8C2211yescharacteristic, complemented
24#91836C2211yescharacteristic
25Q8×Dic15C2211yescharacteristic, complemented
26C2×#6718C2211yescharacteristic, complemented
27C2×#6718C2211yescharacteristic, complemented
28C2×#6717C2211yescharacteristic
29#91825C2211yescharacteristic
30C2×#6716C2211yescharacteristic
31Q16×D15—24no—
32SD16×D15—24no—
33C2×Dic60C2211yescharacteristic, complemented
34C2×#6706C2211yescharacteristic
35C2×C8×D15C2211yescharacteristic
36C2×C8×D15C2211yescharacteristic
37C4⋊C4×D15—21no—
38C4⋊C4×D15C2211yescharacteristic
39#91776—21no—
40#91776C2211yescharacteristic, complemented
41#91774—21no—
42#91774—21no—
43C22⋊C4×D15—21no—
44C22⋊C4×D15—21no—
45#91764C2211yescharacteristic
46C42×D15—21no—
47C42×D15C2211yescharacteristic
48C4×Dic30—21no—
49C4×Dic30C2211yescharacteristic, complemented
50C3×C5×C4⋊C8C2211yescharacteristic, complemented
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic
53#91119C2211yescharacteristic, complemented
54#91116C2211yescharacteristic
55#91105C2211yescharacteristic
56#91100C2211yescharacteristic, complemented
57#91098C2211yescharacteristic, complemented
58#91098C2211yescharacteristic, complemented
59#91094C2211yescharacteristic, complemented
60#91093C2211yescharacteristic
61C4⋊(C3⋊#168)C2211yescharacteristic, complemented
62D3×#464—51nomaximal, Hall
63C2×D5×Q16—31no—
64C2×D5×SD16—31no—
65D5×#124—31no—
66C4×Q8×D5—31no—
67C5×#464D311yescharacteristic, complemented
68#65474—31no—
69#65455—31no—
70#65343—31no—
71#65317—31no—
72#65134—31no—
73D5×C4⋊C8—31no—
74D5×#103—31no—
75#65087—31no—
76D5×#102—31no—
77#65056—31no—
78C23×D15—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C2×#1220—21no—
83Q8×D15—22no—
84Q8×D15—22no—
85Q8×D15—22no—
86Q8×D15D414yes—
87D4×D15—22no—
88D4×D15—22no—
89C2×D60C2311yescharacteristic
90C2×C4×D15—21no—
91C2×C4×D15—21no—
92C2×C4×D15—21no—
93C2×C4×D15D411yescharacteristic
94C2×C4×D15D411yescharacteristic
95C2×C4×D15C2311yescharacteristic
96C2×Dic30—21no—
97C2×Dic30—21no—
98C2×Dic30C2311yescharacteristic
99C2×Dic30C2311yescharacteristic
100C3×C5×Q16—22no—
101C3×C5×SD16—22no—
102C2×C3×C5×C8C2311yescharacteristic
103C2×C3×C5×C8C2311yescharacteristic
104C3×C5×C4⋊C4—21no—
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C22⋊C4—21no—
107C3×C5×C22⋊C4—21no—
108C3×C42×C5—21no—
109C3×C42×C5C2311yescharacteristic
110#6719—21no—
111#6719—21no—
112#6718—22no—
113#6718—22no—
114#6717—22no—
115#6716—22no—
116#6714—21no—
117#6714—21no—
118#6714—21no—
119#6714—21no—
120C4⋊Dic15—21no—
121C4⋊Dic15C2311yescharacteristic
122#6712—21no—
123#6712—21no—
124#6712—21no—
125C4×Dic15—21no—
126C4×Dic15—21no—
127C4×Dic15—21no—
128C4×Dic15D411yescharacteristic
129C4×Dic15D411yescharacteristic
130C4×Dic15C2311yescharacteristic
131C2×C3⋊#168C2311yescharacteristic
132C2×C3⋊#168C2311yescharacteristic
133Dic60—22no—
134#6706—22no—
135C8×D15—22no—
136C8×D15—22no—
137C2×D3×Q16—51no—
138C2×D3×SD16—51no—
139D3×#124—51no—
140C4×D3×Q8—51no—
141C3×#464D511yescharacteristic, complemented
142#5185—51no—
143#5166—51no—
144#5054—51no—
145#5028—51no—
146#4845—51no—
147D3×C4⋊C8—51no—
148D3×#103—51no—
149#4798—51no—
150D3×#102—51no—
151#4767—51no—
152C2×Q8×D5—31no—
153C2×Q8×D5—31no—
154C2×D4×D5—31no—
155C2×C5×Q16C2×D311yescharacteristic, complemented
156C2×C5×SD16C2×D311yescharacteristic
157C5×#124C2×D311yescharacteristic
158C4×C5×Q8C2×D311yescharacteristic, complemented
159#4093—31no—
160Q8×Dic5—31no—
161C2×#689—31no—
162C2×#689—31no—
163C2×#688—31no—
164#4082—31no—
165C2×#687—31no—
166D5×Q16—64no—
167D5×SD16—64no—
168C2×Dic20—31no—
169C2×#677—31no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172D5×C4⋊C4—31no—
173D5×C4⋊C4—61no—
174#4033—31no—
175#4033—61no—
176#4031—61no—
177#4031—61no—
178D5×C22⋊C4—61no—
179D5×C22⋊C4—61no—
180#4021—31no—
181C42×D5—31no—
182C42×D5—61no—
183C4×Dic10—31no—
184C4×Dic10—61no—
185C5×C4⋊C8C2×D311yescharacteristic, complemented
186C5×#103C2×D311yescharacteristic, complemented
187C5×#102C2×D311yescharacteristic
188#3967—31no—
189#3964—31no—
190#3953—31no—
191#3948—31no—
192#3946—31no—
193#3946—31no—
194#3942—31no—
195#3941—31no—
196C4⋊#168—31no—
197C2×#464—151noSylow
198C23×C3×C5—21no—
199C22×D15—21no—
200C22×D15—42no—
201C22×D15—42no—
202C22×D15—42no—
203C22×D15C2×D411yescharacteristic
204C3×C5×Q8—21no—
205C3×C5×Q8—21no—
206C3×C5×Q8—21no—
207C3×C5×Q8C2×D412yes—
208C3×C5×D4—21no—
209C3×C5×D4—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216#1220—42no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15C2×D411yescharacteristic
221C2×Dic15C2×D411yescharacteristic
222C2×Dic15C2×D411yescharacteristic
223D60—21no—
224D60—21no—
225C4×D15—24no—
226C4×D15—22no—
227C4×D15—22no—
228C4×D15—42no—
229C4×D15—42no—
230C4×D15C2×D412yes—
231C4×D15#4112yes—
232Dic30—21no—
233Dic30—24no—
234Dic30—21no—
235Dic30—21no—
236Dic30—42no—
237Dic30C2×D412yes—
238C3×C5×C8—21no—
239C3×C5×C8—21no—
240C3⋊#168—21no—
241C3⋊#168—21no—
242C2×D3×Q8—51no—
243C2×D3×Q8—51no—
244C2×D3×D4—51no—
245C2×C3×Q16C2×D511yescharacteristic, complemented
246C2×C3×SD16C2×D511yescharacteristic
247C3×#124C2×D511yescharacteristic
248C3×C4×Q8C2×D511yescharacteristic, complemented
249#947—51no—
250Q8×Dic3—51no—
251C2×#216—51no—
252C2×#216—51no—
253C2×#215—51no—
254#936—51no—
255C2×#214—51no—
256D3×Q16—104no—
257D3×SD16—104no—
258C2×Dic12—51no—
259C2×#204—51no—
260C2×D3×C8—51no—
261C2×D3×C8—51no—
262D3×C4⋊C4—51no—
263D3×C4⋊C4—101no—
264#887—51no—
265#887—101no—
266#885—101no—
267#885—101no—
268D3×C22⋊C4—101no—
269D3×C22⋊C4—101no—
270#875—51no—
271C42×D3—51no—
272C42×D3—101no—
273C4×Dic6—51no—
274C4×Dic6—101no—
275C3×C4⋊C8C2×D511yescharacteristic, complemented
276C3×#103C2×D511yescharacteristic, complemented
277C3×#102C2×D511yescharacteristic
278#835—51no—
279#832—51no—
280#821—51no—
281#816—51no—
282Dic3⋊C8—51no—
283Dic3⋊C8—51no—
284#810—51no—
285#809—51no—
286C4⋊(C3⋊C8)—51no—
287C23×D5—61no—
288C2×C5×Q8C22×D311yescharacteristic
289C2×C5×Q8C22×D311yescharacteristic
290C2×C5×D4C22×D311yescharacteristic
291C2×C22⋊D5—61no—
292Q8×D5—34no—
293Q8×D5—62no—
294Q8×D5—62no—
295Q8×D5—62no—
296D4×D5—62no—
297D4×D5—62no—
298C2×D20—31no—
299C2×C4×D5—31no—
300C2×C4×D5—31no—
301C2×C4×D5—31no—
302C2×C4×D5—61no—
303C2×C4×D5—61no—
304C2×C4×D5—61no—
305C2×Dic10—31no—
306C2×Dic10—31no—
307C2×Dic10—61no—
308C2×Dic10—61no—
309C5×Q16—22no—
310C5×SD16—22no—
311C2×C5×C8C22×D311yescharacteristic
312C2×C5×C8C22×D311yescharacteristic
313C5×C4⋊C4—21no—
314C5×C4⋊C4C22×D311yescharacteristic
315C5×C22⋊C4—21no—
316C5×C22⋊C4—21no—
317C42×C5—21no—
318C42×C5C22×D311yescharacteristic
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321#689—62no—
322#689—62no—
323#688—62no—
324#687—62no—
325#685—61no—
326#685—61no—
327#685—61no—
328#685—61no—
329C4⋊Dic5—31no—
330C4⋊Dic5—61no—
331#683—61no—
332#683—61no—
333#683—61no—
334C4×Dic5—31no—
335C4×Dic5—31no—
336C4×Dic5—31no—
337C4×Dic5—61no—
338C4×Dic5—61no—
339C4×Dic5—61no—
340C2×#168—31no—
341C2×#168—31no—
342Dic20—62no—
343#677—62no—
344C8×D5—62no—
345C8×D5—62no—
346C22×Q16—151no—
347C22×SD16—151no—
348C2×#124—151no—
349C2×C4×Q8—151no—
350#464—151no—
351#464—151no—
352#464—151no—
353#464—151no—
354#464—151no—
355#464—151no—
356#464—151no—
357#464D1511yescharacteristic, direct product factor
358C2×C4⋊C8—151no—
359C2×#103—151no—
360C2×#102—151no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5C22×D411yescharacteristic
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C2×D15—84no—
369C2×D15#12112yes—
370C2×D15#13512yes—
371C2×D15#13712yes—
372C3×C4×C5—22no—
373C3×C4×C5—21no—
374C3×C4×C5—21no—
375C3×C4×C5—41no—
376C3×C4×C5—41no—
377C3×C4×C5C22×D411yescharacteristic
378C3×C4×C5C2×#4111yescharacteristic
379Dic15—22no—
380Dic15—21no—
381Dic15—21no—
382Dic15—41no—
383Dic15—41no—
384Dic15#12112yes—
385C23×D3—101no—
386C2×C3×Q8C22×D511yescharacteristic
387C2×C3×Q8C22×D511yescharacteristic
388C2×C3×D4C22×D511yescharacteristic
389C2×#67—101no—
390D3×Q8—54no—
391D3×Q8—102no—
392D3×Q8—102no—
393D3×Q8—102no—
394D3×D4—102no—
395D3×D4—102no—
396C2×D12—51no—
397C2×C4×D3—51no—
398C2×C4×D3—51no—
399C2×C4×D3—51no—
400C2×C4×D3—101no—
401C2×C4×D3—101no—
402C2×C4×D3—101no—
403C2×Dic6—51no—
404C2×Dic6—51no—
405C2×Dic6—101no—
406C2×Dic6—101no—
407C3×Q16—22no—
408C3×SD16—22no—
409C2×C3×C8C22×D511yescharacteristic
410C2×C3×C8C22×D511yescharacteristic
411C3×C4⋊C4—21no—
412C3×C4⋊C4C22×D511yescharacteristic
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C42—21no—
416C3×C42C22×D511yescharacteristic
417#217—101no—
418#217—101no—
419#216—102no—
420#216—102no—
421#215—102no—
422#214—102no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4—101no—
426(C2×D3)⋊C4—101no—
427C4⋊Dic3—51no—
428C4⋊Dic3—101no—
429Dic3⋊C4—101no—
430Dic3⋊C4—101no—
431Dic3⋊C4—101no—
432C4×Dic3—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3—101no—
436C4×Dic3—101no—
437C4×Dic3—101no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440Dic12—102no—
441#204—102no—
442D3×C8—102no—
443D3×C8—102no—
444C23×C5—21no—
445C22×D5—31no—
446C22×D5—61no—
447C22×D5—122no—
448C22×D5—122no—
449C22×D5—122no—
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—21no—
453C5×Q8D3×D412yes—
454C5×D4—21no—
455C5×D4—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5D3×D411yescharacteristic
460C2×C4×C5D3×D411yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—122no—
463C2×Dic5—31no—
464C2×Dic5—31no—
465C2×Dic5—31no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469D20—61no—
470D20—61no—
471C4×D5—32no—
472C4×D5—32no—
473C4×D5—62no—
474C4×D5—62no—
475C4×D5—64no—
476C4×D5—122no—
477C4×D5—122no—
478Dic10—32no—
479Dic10—64no—
480Dic10—61no—
481Dic10—61no—
482Dic10—61no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—61no—
487#168—61no—
488C22×Q8—151no—
489C22×Q8—151no—
490C22×D4—151no—
491C2×Q16—151no—
492C2×Q16—151no—
493C2×Q16—151no—
494C2×Q16—304no—
495C2×Q16C2×D1511yescharacteristic, complemented
496C2×SD16—151no—
497C2×SD16—151no—
498C2×SD16—151no—
499C2×SD16—304no—
500C2×SD16C2×D1511yescharacteristic
501C22×C8—151no—
502C22×C8—151no—
503#124—151no—
504#124—151no—
505#124—151no—
506#124—301no—
507#124—301no—
508#124C2×D1511yescharacteristic
509C4×Q8—151no—
510C4×Q8—151no—
511C4×Q8—151no—
512C4×Q8—301no—
513C4×Q8—301no—
514C4×Q8C2×D1511yescharacteristic, complemented
515C2×C4⋊C4—151no—
516C2×C4⋊C4—301no—
517C2×C22⋊C4—301no—
518C2×C22⋊C4—301no—
519C2×C42—151no—
520C2×C42—301no—
521C4⋊C8—151no—
522C4⋊C8—151no—
523C4⋊C8—151no—
524C4⋊C8C2×D1511yescharacteristic, complemented
525#103—151no—
526#103—151no—
527#103—151no—
528#103C2×D1511yescharacteristic, complemented
529#102—151no—
530#102—151no—
531#102—151no—
532#102C2×D1511yescharacteristic
533C2×C3×C5—81no—
534C2×C3×C5C2×#12111yescharacteristic
535C2×C3×C5C2×#13511yescharacteristic
536C2×C3×C5C2×#13711yescharacteristic
537D15—81no—
538D15#46414yesdirect product factor
539C23×C3—21no—
540C22×D3—51no—
541C22×D3—101no—
542C22×D3—202no—
543C22×D3—202no—
544C22×D3—202no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8D4×D512yes—
549C3×D4—21no—
550C3×D4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4D4×D511yescharacteristic
555C2×C3×C4D4×D511yescharacteristic
556C2×C3×C4C23×D511yescharacteristic
557#67—202no—
558C2×Dic3—51no—
559C2×Dic3—51no—
560C2×Dic3—51no—
561C2×Dic3—101no—
562C2×Dic3—101no—
563C2×Dic3—101no—
564D12—101no—
565D12—101no—
566C4×D3—52no—
567C4×D3—52no—
568C4×D3—102no—
569C4×D3—102no—
570C4×D3—104no—
571C4×D3—202no—
572C4×D3—202no—
573Dic6—52no—
574Dic6—104no—
575Dic6—101no—
576Dic6—101no—
577Dic6—101no—
578Dic6—202no—
579C3×C8—21no—
580C3×C8—21no—
581C3⋊C8—101no—
582C3⋊C8—101no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5C2×D3×D411yescharacteristic
587C2×D5—32no—
588C2×D5—32no—
589C2×D5—32no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—121no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—21no—
596C4×C5—22no—
597C4×C5—41no—
598C4×C5—41no—
599C4×C5C2×D3×D411yescharacteristic
600C4×C5D3×#4111yescharacteristic
601Dic5—32no—
602Dic5—61no—
603Dic5—61no—
604Dic5—62no—
605Dic5—121no—
606Dic5—121no—
607C24—301no—
608C2×Q8—154no—
609C2×Q8—151no—
610C2×Q8—151no—
611C2×Q8—301no—
612C2×Q8—301no—
613C2×Q8—302no—
614C2×Q8—302no—
615C2×Q8—302no—
616C2×Q8C22×D1511yescharacteristic
617C2×Q8C22×D1511yescharacteristic
618C2×D4—151no—
619C2×D4—302no—
620C2×D4—302no—
621C2×D4—301no—
622C2×D4C22×D1511yescharacteristic
623C22×C4—151no—
624C22×C4—151no—
625C22×C4—151no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4—301no—
629Q16—22no—
630Q16—302no—
631Q16—302no—
632Q16—302no—
633SD16—22no—
634SD16—302no—
635SD16—302no—
636SD16—302no—
637C2×C8—151no—
638C2×C8—151no—
639C2×C8—302no—
640C2×C8—302no—
641C2×C8C22×D1511yescharacteristic
642C2×C8C22×D1511yescharacteristic
643C4⋊C4—21no—
644C4⋊C4—151no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C4⋊C4C22×D1511yescharacteristic
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—301no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C22⋊C4—301no—
657C22⋊C4—301no—
658C42—21no—
659C42—151no—
660C42—151no—
661C42—151no—
662C42—301no—
663C42—301no—
664C42—301no—
665C42C22×D1511yescharacteristic
666C3×C5C2×#46411yescharacteristic, complemented, Hall
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3C2×D4×D511yescharacteristic
671C2×D3—52no—
672C2×D3—52no—
673C2×D3—52no—
674C2×D3—201no—
675C2×D3—201no—
676C2×D3—201no—
677C2×D3—404no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—22no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4C2×D4×D511yescharacteristic
684C3×C4D5×#4111yescharacteristic
685Dic3—52no—
686Dic3—101no—
687Dic3—101no—
688Dic3—102no—
689Dic3—201no—
690Dic3—201no—
691C2×C5—81no—
692C2×C5D3×#12111yescharacteristic
693C2×C5D3×#13511yescharacteristic
694C2×C5D3×#13711yescharacteristic
695D5—34no—
696D5—241no—
697C23—21no—
698C23—151no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23—602no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—152no—
707Q8—304no—
708Q8—301no—
709Q8—301no—
710Q8—301no—
711Q8—602no—
712Q8D4×D1512yes—
713D4—21no—
714D4—21no—
715D4—301no—
716D4—301no—
717D4—602no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—151no—
722C2×C4—152no—
723C2×C4—152no—
724C2×C4—151no—
725C2×C4—151no—
726C2×C4—302no—
727C2×C4—302no—
728C2×C4—304no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—602no—
733C2×C4—602no—
734C2×C4D4×D1511yescharacteristic
735C2×C4D4×D1511yescharacteristic
736C2×C4C23×D1511yescharacteristic
737C8—21no—
738C8—21no—
739C8—301no—
740C8—301no—
741C2×C3—81no—
742C2×C3D5×#12111yescharacteristic
743C2×C3D5×#13511yescharacteristic
744C2×C3D5×#13711yescharacteristic
745D3—54no—
746D3—401no—
747C5D3×#46411yescharacteristic, complemented, Sylow
748C22—41no—
749C22—41no—
750C22—41no—
751C22—152no—
752C22—152no—
753C22—152no—
754C22—601no—
755C22—601no—
756C22—601no—
757C22—1204no—
758C22C2×D4×D1511yescharacteristic
759C4—22no—
760C4—21no—
761C4—21no—
762C4—41no—
763C4—41no—
764C4—152no—
765C4—302no—
766C4—301no—
767C4—301no—
768C4—601no—
769C4—601no—
770C4C2×D4×D1511yescharacteristic
771C4#41×D1511yescharacteristic
772C3D5×#46411yescharacteristic, complemented, Sylow
773C2—81no—
774C2—154no—
775C2—1201no—
776C2D15×#12111yescharacteristic
777C2D15×#13511yescharacteristic
778C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#464C2
socleC22×C3×C5C22×D4
prime radicalC2×D4×D15C22
hypercenter#464D15
hypocenterC3×C5C2×#464
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D15C2semidirect
4. C4×Q8×D15C2semidirect
5. C3×C5×#464C2semidirect
6. #11751286C2semidirect
7. #11751267C2semidirect
8. #11751155C2semidirect
9. #11751129C2semidirect
10. #11750946C2semidirect
11. D15×C4⋊C8C2semidirect
12. D15×#103C2semidirect
13. #11750899C2semidirect
15. #11750868C2semidirect
20. C2×C3×C5×Q16C22semidirect
23. C3×C4×C5×Q8C22semidirect
25. Q8×Dic15C22semidirect
26. C2×#6718C22semidirect
27. C2×#6718C22semidirect
33. C2×Dic60C22semidirect
40. #91776C22semidirect
49. C4×Dic30C22semidirect
50. C3×C5×C4⋊C8C22semidirect
51. C3×C5×#103C22semidirect
53. #91119C22semidirect
56. #91100C22semidirect
57. #91098C22semidirect
58. #91098C22semidirect
59. #91094C22semidirect
61. C4⋊(C3⋊#168)C22semidirect
67. C5×#464D3semidirect
141. C3×#464D5semidirect
155. C2×C5×Q16C2×D3semidirect
158. C4×C5×Q8C2×D3semidirect
185. C5×C4⋊C8C2×D3semidirect
186. C5×#103C2×D3semidirect
245. C2×C3×Q16C2×D5semidirect
248. C3×C4×Q8C2×D5semidirect
275. C3×C4⋊C8C2×D5semidirect
276. C3×#103C2×D5semidirect
357. #464D15direct (N × H)
495. C2×Q16C2×D15semidirect
514. C4×Q8C2×D15semidirect
524. C4⋊C8C2×D15semidirect
528. #103C2×D15semidirect
538. D15#464direct (N × H)
666. C3×C5C2×#464semidirect
747. C5D3×#464semidirect
772. C3D5×#464semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D152
C2×SD16×D152
D15×#1242
C4×Q8×D152
C3×C5×#4642
#117512862
#117512672
#117511552
#117511292
#117509462
D15×C4⋊C82
D15×#1032
#117508992
D15×#1022
#117508682
D5×#4643
D3×#4645