Finite Group Databasebeta

← D5×#5059 #14438844

Subgroups — D5×#5059 #14438844

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#124C211yesmaximal, characteristic, complemented
2C2×D5×#216C211yesmaximal, characteristic, complemented
3C2×D5×#215C211yesmaximal, characteristic, complemented
4C2×D5×#214C211yesmaximal, characteristic, complemented
5C2×D5×#213C211yesmaximal, characteristic
6D5×#875C211yesmaximal, characteristic, complemented
7#11751160C211yesmaximal, characteristic, complemented
8C5×#5059C211yesmaximal, characteristic, complemented
9#11749316C211yesmaximal, characteristic, complemented
10#11749313C211yesmaximal, characteristic, complemented
11#11749070C211yesmaximal, characteristic, complemented
12#11749067C211yesmaximal, characteristic, complemented
13#11747072C211yesmaximal, characteristic, complemented
14#11747040C211yesmaximal, characteristic, complemented
15C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
16D5×#495—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×D5×D12C2211yescharacteristic
20C2×D5×Dic6C2211yescharacteristic
21C3×C5×#124C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic, complemented
24C2×#6716C2211yescharacteristic, complemented
25C2×#6715C2211yescharacteristic
26#91764C2211yescharacteristic, complemented
27C2×C5×#216C2211yescharacteristic, complemented
28C2×C5×#215C2211yescharacteristic, complemented
29C2×C5×#214C2211yescharacteristic, complemented
30C2×C5×#213C2211yescharacteristic
31C5×#875C2211yescharacteristic, complemented
32C3×#4093C2211yescharacteristic, complemented
33C3×#4082C2211yescharacteristic, complemented
34C3×#4031—22no—
35C3×D5×C22⋊C4—22no—
36C3×#4021C2211yescharacteristic, complemented
37C3×C42×D5C2211yescharacteristic
38D5×#216—24no—
39D5×#215—24no—
40D5×#214—24no—
41D5×#213—24no—
42D5×(C2×D3)⋊C4—22no—
43#91375C2211yescharacteristic, complemented
44#91373C2211yescharacteristic, complemented
45#91350—22no—
46C2×#6662C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6658C2211yescharacteristic, complemented
49C2×#6657C2211yescharacteristic, complemented
50C2×#6656C2211yescharacteristic, complemented
51C2×#6655C2211yescharacteristic, complemented
52C2×#6653C2211yescharacteristic
53C2×#6652C2211yescharacteristic
54C2×D5×C3⋊C8C2211yescharacteristic
55C2×D5×C3⋊C8C2211yescharacteristic
56C4×C3⋊#168C2211yescharacteristic, complemented
57C4×C5×C3⋊C8C2211yescharacteristic, complemented
58Dic5×C3⋊C8C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60C2×#5059—51nomaximal, Hall
61C2×D5×Q16—31no—
62C2×D5×SD16—31no—
63C2×D5×SD16—31no—
64C2×D5×D8—31no—
65D5×#124—31no—
66D5×#124D311yescharacteristic, complemented
67C5×#495—31no—
68#65480—31no—
69#65457—31no—
70#65457—31no—
71#65444—31no—
72#65348—31no—
73#65348—31no—
74#64985—31no—
75C4×C8×D5—31no—
76C23×C3×D5—21no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×D60C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C5×Dic6C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C3×Q8×D5—22no—
86C3×Q8×D5—22no—
87C3×D4×D5—22no—
88C3×D4×D5—22no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5D412yes—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10—21no—
94C2×C3×Dic10C2311yescharacteristic
95C2×#1204—21no—
96C2×#1203—21no—
97C2×D5×Dic3—21no—
98D5×D12—22no—
99D5×D12—22no—
100D5×Dic6—22no—
101D5×Dic6—22no—
102C3×C5×C22⋊C4—22no—
103C3×C42×C5C2311yescharacteristic
104#6718—22no—
105#6717—22no—
106#6716—22no—
107#6715—22no—
108#6714—22no—
109C2×C3⋊#168C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111C5×#216—22no—
112C5×#215—22no—
113C5×#214—22no—
114C5×#213—22no—
115C5×(C2×D3)⋊C4—22no—
116C2×C5×C3⋊C8C2311yescharacteristic
117C2×C5×C3⋊C8C2311yescharacteristic
118C3×C22⋊Dic5—22no—
119C3×#685—22no—
120C3×#685—22no—
121C3×C4×Dic5D412yes—
122C3×C4×Dic5C2311yescharacteristic
123#6667—22no—
124(C2×D3)⋊Dic5—22no—
125#6662—22no—
126#6661—22no—
127#6658—22no—
128#6657—22no—
129#6656—22no—
130#6655—22no—
131#6653—22no—
132#6652—22no—
133D5×C3⋊C8D414yes—
134D5×C3⋊C8D414yes—
135C2×C3×#124—51no—
136C22×#216—51no—
137C22×#215—51no—
138C22×#214—51no—
139C22×#213—51no—
140C2×#875—51no—
141#5059—51no—
142#5059—51no—
143#5059—51no—
144#5059—51no—
145#5059—51no—
146#5059—51no—
147#5059—51no—
148#5059D511yescharacteristic, direct product factor
149C2×C4×C3⋊C8—51no—
150C2×Q8×D5—31no—
151C2×Q8×D5C2×D311yescharacteristic
152C2×D4×D5—31no—
153C2×D4×D5C2×D311yescharacteristic
154C2×C5×Q16—31no—
155C2×C5×SD16—31no—
156C2×C5×SD16—31no—
157C2×C5×D8—31no—
158C5×#124—31no—
159C5×#124C2×D311yescharacteristic, complemented
160#4093—31no—
161#4093C2×D311yescharacteristic, complemented
162C2×#689—31no—
163C2×#689—31no—
164C2×#688—31no—
165C2×#688—31no—
166#4082—31no—
167#4082C2×D311yescharacteristic, complemented
168C2×#687—31no—
169C2×#687—31no—
170C2×#686—31no—
171C2×#686—31no—
172D5×Q16—64no—
173D5×SD16—64no—
174D5×SD16—64no—
175D5×D8—64no—
176C2×Dic20—31no—
177C2×D40—31no—
178C2×#677—31no—
179C2×#677—31no—
180C2×C8×D5—31no—
181C2×C8×D5—31no—
182#4031—22no—
183#4031—62no—
184D5×C22⋊C4—22no—
185D5×C22⋊C4—62no—
186#4021—31no—
187#4021C2×D311yescharacteristic, complemented
188C42×D5C2×D311yescharacteristic
189C4×C5×C8—31no—
190C8×Dic5—31no—
191C8×Dic5—31no—
192C4×#168—31no—
193C2×#495—151noSylow
194C23×C3×C5—21no—
195C22×D15—21no—
196C22×C5×D3—21no—
197C22×C3×D5—21no—
198C22×C3×D5—42no—
199C22×C3×D5—44no—
200C22×C3×D5C2×D411yescharacteristic
201C2×D3×D5—42no—
202C2×D3×D5—44no—
203C3×C5×Q8—21no—
204C3×C5×Q8—21no—
205C3×C5×D4—21no—
206C3×C5×D4—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D412yes—
209C2×C3×C4×C5C2411yescharacteristic
210C2×Dic15—21no—
211D60—21no—
212D60—21no—
213Dic30—21no—
214Dic30—21no—
215C2×C5×Dic3—21no—
216C5×D12—21no—
217C5×D12—21no—
218C5×Dic6—21no—
219C5×Dic6—21no—
220C3×C22⋊D5—42no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5C2×D412yes—
223C2×C3×Dic5C2×D411yescharacteristic
224C3×D20—21no—
225C3×D20—21no—
226C3×C4×D5—24no—
227C3×C4×D5—42no—
228C3×C4×D5C2×D412yes—
229C3×C4×D5C2×D412yes—
230C3×Dic10—21no—
231C3×Dic10—21no—
232C3×Dic10—42no—
233#1204—42no—
234#1203—42no—
235D5×Dic3—42no—
236C3⋊#168C2×D412yes—
237C3⋊#168C2×D412yes—
238C5×C3⋊C8C2×D412yes—
239C5×C3⋊C8C2×D412yes—
240C22×C3×Q8—51no—
241C22×C3×D4—51no—
242C22×D12—51no—
243C22×Dic6—51no—
244C3×#124—51no—
245C3×#124—51no—
246C3×#124—51no—
247C3×#124—102no—
248C3×#124C2×D511yescharacteristic, complemented
249C2×C3×C22⋊C4—102no—
250C2×C3×C42—51no—
251C2×#216—51no—
252C2×#216—51no—
253C2×#216—51no—
254C2×#216—104no—
255C2×#216C2×D511yescharacteristic, complemented
256C2×#215—51no—
257C2×#215—51no—
258C2×#215—51no—
259C2×#215—104no—
260C2×#215C2×D511yescharacteristic, complemented
261C2×#214—51no—
262C2×#214—51no—
263C2×#214—51no—
264C2×#214—104no—
265C2×#214C2×D511yescharacteristic, complemented
266C2×#213—51no—
267C2×#213—51no—
268C2×#213—51no—
269C2×#213—104no—
270C2×#213C2×D511yescharacteristic
271C2×(C2×D3)⋊C4—102no—
272C22×C3⋊C8—51no—
273C22×C3⋊C8—51no—
274#875—51no—
275#875—51no—
276#875—51no—
277#875—102no—
278#875C2×D511yescharacteristic, complemented
279C4×C3⋊C8—51no—
280C4×C3⋊C8—51no—
281C4×C3⋊C8—51no—
282C4×C3⋊C8C2×D511yescharacteristic, complemented
283C23×D5—21no—
284C23×D5—61no—
285C2×C5×Q8—31no—
286C2×C5×Q8C22×D311yescharacteristic
287C2×C5×D4—31no—
288C2×C5×D4C22×D311yescharacteristic
289C2×C22⋊D5—21no—
290C2×C22⋊D5—61no—
291Q8×D5—22no—
292Q8×D5—22no—
293Q8×D5—62no—
294Q8×D5—62no—
295D4×D5—22no—
296D4×D5—22no—
297D4×D5—62no—
298D4×D5—62no—
299C2×D20—31no—
300C2×D20C22×D311yescharacteristic
301C2×C4×D5—21no—
302C2×C4×D5—61no—
303C2×C4×D5#6712yes—
304C2×C4×D5C22×D311yescharacteristic
305C2×Dic10—21no—
306C2×Dic10—31no—
307C2×Dic10—61no—
308C2×Dic10C22×D311yescharacteristic
309C5×Q16—62no—
310C5×SD16—62no—
311C5×SD16—62no—
312C5×D8—62no—
313C2×C5×C8—31no—
314C2×C5×C8—31no—
315C5×C22⋊C4—22no—
316C5×C22⋊C4—62no—
317C42×C5C22×D311yescharacteristic
318C22⋊Dic5—22no—
319C22⋊Dic5—62no—
320#689—62no—
321#689—62no—
322#688—62no—
323#688—62no—
324#687—62no—
325#687—62no—
326#686—62no—
327#686—62no—
328#685—22no—
329#685—22no—
330#685—62no—
331#685—62no—
332C4×Dic5#6712yes—
333C4×Dic5C22×D311yescharacteristic
334C2×#168—31no—
335C2×#168—31no—
336Dic20—62no—
337D40—62no—
338#677—62no—
339#677—62no—
340C8×D5—34no—
341C8×D5—34no—
342C22×Q16—151no—
343C22×SD16—151no—
344C22×SD16—151no—
345C22×D8—151no—
346C2×#124—51no—
347C2×#124—151no—
348#495—31no—
349#495—151no—
350#495—151no—
351#495—151no—
352#495—151no—
353#495—151no—
354#495—151no—
355#495—151no—
356C2×C4×C8—151no—
357C22×C3×C5—41no—
358C22×C3×C5—42no—
359C22×C3×C5C22×D411yescharacteristic
360C2×D15—41no—
361C2×D15—42no—
362C2×C5×D3—41no—
363C2×C5×D3—42no—
364C2×C3×D5—41no—
365C2×C3×D5—42no—
366C2×C3×D5—84no—
367C2×C3×D5#12712yes—
368C2×C3×D5#13514yes—
369D3×D5—84no—
370C3×C4×C5—22no—
371C3×C4×C5—41no—
372C3×C4×C5C22×D411yescharacteristic
373C3×C4×C5C22×D411yescharacteristic
374Dic15—41no—
375C3×Dic5—22no—
376C3×Dic5—41no—
377C3×Dic5#12712yes—
378C5×Dic3—41no—
379C24×C3—101no—
380C23×D3—101no—
381C2×C3×Q8—51no—
382C2×C3×Q8—101no—
383C2×C3×Q8—102no—
384C2×C3×Q8—102no—
385C2×C3×Q8C22×D511yescharacteristic
386C2×C3×D4—51no—
387C2×C3×D4—102no—
388C2×C3×D4—102no—
389C2×C3×D4—101no—
390C2×C3×D4C22×D511yescharacteristic
391C22×C3×C4—51no—
392C22×C3×C4—52no—
393C22×C3×C4—101no—
394C22×Dic3—101no—
395C2×D12—51no—
396C2×D12—102no—
397C2×D12—102no—
398C2×D12—101no—
399C2×D12C22×D511yescharacteristic
400C2×Dic6—51no—
401C2×Dic6—102no—
402C2×Dic6—102no—
403C2×Dic6—101no—
404C2×Dic6C22×D511yescharacteristic
405C3×C22⋊C4—22no—
406C3×C22⋊C4—102no—
407C3×C22⋊C4—102no—
408C3×C22⋊C4—102no—
409C3×C42—52no—
410C3×C42—51no—
411C3×C42C22×D511yescharacteristic
412#216—22no—
413#216—102no—
414#216—102no—
415#216—102no—
416#215—22no—
417#215—102no—
418#215—102no—
419#215—102no—
420#214—22no—
421#214—102no—
422#214—102no—
423#214—102no—
424#213—22no—
425#213—102no—
426#213—102no—
427#213—102no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—102no—
430(C2×D3)⋊C4—102no—
431(C2×D3)⋊C4—102no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—51no—
434C2×C3⋊C8—54no—
435C2×C3⋊C8—54no—
436C2×C3⋊C8C22×D511yescharacteristic
437C2×C3⋊C8C22×D511yescharacteristic
438C23×C5—21no—
439C23×C5—61no—
440C22×D5—21no—
441C22×D5—42no—
442C22×D5—44no—
443C22×D5—61no—
444C22×D5—122no—
445C22×D5—124no—
446C22×D5C2×#6711yescharacteristic
447C5×Q8—21no—
448C5×Q8—21no—
449C5×Q8—61no—
450C5×Q8—61no—
451C5×D4—21no—
452C5×D4—21no—
453C5×D4—61no—
454C5×D4—61no—
455C2×C4×C5—21no—
456C2×C4×C5—61no—
457C2×C4×C5C2×#6712yes—
458C2×C4×C5C23×D311yescharacteristic
459C22⋊D5—42no—
460C22⋊D5—122no—
461C2×Dic5—21no—
462C2×Dic5—61no—
463C2×Dic5C2×#6712yes—
464C2×Dic5C2×#6711yescharacteristic
465D20—21no—
466D20—21no—
467D20—61no—
468D20—61no—
469C4×D5—24no—
470C4×D5—42no—
471C4×D5—122no—
472C4×D5D3×D412yes—
473C4×D5D3×D412yes—
474Dic10—21no—
475Dic10—21no—
476Dic10—42no—
477Dic10—61no—
478Dic10—61no—
479Dic10—122no—
480C5×C8—32no—
481C5×C8—32no—
482#168—32no—
483#168—32no—
484C22×Q8—51no—
485C22×Q8—151no—
486C22×D4—51no—
487C22×D4—151no—
488C2×Q16—31no—
489C2×Q16—151no—
490C2×Q16—151no—
491C2×Q16—151no—
492C2×Q16—304no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—151no—
496C2×SD16—151no—
497C2×SD16—151no—
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16—151no—
501C2×SD16—304no—
502C2×SD16—304no—
503C2×D8—31no—
504C2×D8—151no—
505C2×D8—151no—
506C2×D8—151no—
507C2×D8—304no—
508C22×C8—151no—
509C22×C8—151no—
510#124—31no—
511#124—51no—
512#124—51no—
513#124—51no—
514#124—102no—
515#124—151no—
516#124—151no—
517#124—151no—
518#124—302no—
519#124D3×D511yescharacteristic, complemented
520C2×C22⋊C4—102no—
521C2×C22⋊C4—302no—
522C2×C42—51no—
523C4×C8—31no—
524C4×C8—151no—
525C4×C8—151no—
526C4×C8—151no—
527C2×C3×C5—81no—
528C2×C3×C5C2×#12711yescharacteristic
529C2×C3×C5C2×#13512yes—
530D15—81no—
531C3×D5—81no—
532C3×D5#49514yescomplemented
533C5×D3—81no—
534C23×C3—21no—
535C23×C3—51no—
536C23×C3—101no—
537C23×C3—202no—
538C23×C3—204no—
539C22×D3—21no—
540C22×D3—101no—
541C22×D3—202no—
542C22×D3—204no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—101no—
546C3×Q8—101no—
547C3×Q8—202no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—101no—
551C3×D4—101no—
552C3×D4—202no—
553C2×C3×C4—21no—
554C2×C3×C4—51no—
555C2×C3×C4—52no—
556C2×C3×C4—52no—
557C2×C3×C4—52no—
558C2×C3×C4—104no—
559C2×C3×C4—101no—
560C2×C3×C4—202no—
561C2×C3×C4D4×D512yes—
562C2×C3×C4C23×D511yescharacteristic
563C2×Dic3—21no—
564C2×Dic3—101no—
565C2×Dic3—202no—
566D12—21no—
567D12—21no—
568D12—101no—
569D12—101no—
570D12—202no—
571Dic6—21no—
572Dic6—21no—
573Dic6—101no—
574Dic6—101no—
575Dic6—202no—
576C3⋊C8—52no—
577C3⋊C8—52no—
578C3⋊C8D4×D512yes—
579C3⋊C8D4×D512yes—
580C22×C5—41no—
581C22×C5—42no—
582C22×C5—121no—
583C22×C5—122no—
584C22×C5C22×#6711yescharacteristic
585C2×D5—41no—
586C2×D5—42no—
587C2×D5—84no—
588C2×D5—121no—
589C2×D5—122no—
590C2×D5—244no—
591C2×D5#94012yes—
592C2×D5#95014yes—
593C4×C5—22no—
594C4×C5—41no—
595C4×C5—121no—
596C4×C5C2×D3×D411yescharacteristic
597C4×C5C2×D3×D411yescharacteristic
598Dic5—22no—
599Dic5—41no—
600Dic5—121no—
601Dic5#94012yes—
602C24—101no—
603C24—301no—
604C2×Q8—31no—
605C2×Q8—51no—
606C2×Q8—101no—
607C2×Q8—102no—
608C2×Q8—102no—
609C2×Q8—151no—
610C2×Q8—301no—
611C2×Q8—302no—
612C2×Q8—302no—
613C2×Q8C2×D3×D511yescharacteristic
614C2×D4—31no—
615C2×D4—51no—
616C2×D4—102no—
617C2×D4—102no—
618C2×D4—101no—
619C2×D4—151no—
620C2×D4—302no—
621C2×D4—302no—
622C2×D4—301no—
623C2×D4C2×D3×D511yescharacteristic
624C22×C4—51no—
625C22×C4—52no—
626C22×C4—101no—
627C22×C4—301no—
628Q16—62no—
629Q16—302no—
630Q16—302no—
631Q16—302no—
632SD16—62no—
633SD16—62no—
634SD16—302no—
635SD16—302no—
636SD16—302no—
637SD16—302no—
638SD16—302no—
639SD16—302no—
640D8—62no—
641D8—302no—
642D8—302no—
643D8—302no—
644C2×C8—31no—
645C2×C8—31no—
646C2×C8—154no—
647C2×C8—154no—
648C2×C8—151no—
649C2×C8—151no—
650C22⋊C4—22no—
651C22⋊C4—62no—
652C22⋊C4—102no—
653C22⋊C4—102no—
654C22⋊C4—102no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C42—52no—
659C42—51no—
660C42C2×D3×D511yescharacteristic
661C3×C5C2×#49511yescharacteristic, complemented, Hall
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—52no—
665C22×C3—54no—
666C22×C3—201no—
667C22×C3—202no—
668C22×C3—404no—
669C22×C3C2×D4×D511yescharacteristic
670C2×D3—41no—
671C2×D3—42no—
672C2×D3—201no—
673C2×D3—202no—
674C2×D3—404no—
675C3×C4—22no—
676C3×C4—41no—
677C3×C4—52no—
678C3×C4—102no—
679C3×C4—201no—
680C3×C4C2×D4×D511yescharacteristic
681C3×C4C2×D4×D511yescharacteristic
682Dic3—41no—
683Dic3—201no—
684C2×C5—81no—
685C2×C5—241no—
686C2×C5C2×#94011yescharacteristic
687C2×C5C2×#95012yes—
688D5—81no—
689D5—241no—
690D5#505914yesdirect product factor
691C23—21no—
692C23—51no—
693C23—61no—
694C23—101no—
695C23—202no—
696C23—204no—
697C23—301no—
698C23—602no—
699C23—604no—
700Q8—21no—
701Q8—21no—
702Q8—61no—
703Q8—61no—
704Q8—101no—
705Q8—101no—
706Q8—202no—
707Q8—301no—
708Q8—301no—
709Q8—602no—
710D4—21no—
711D4—21no—
712D4—61no—
713D4—61no—
714D4—101no—
715D4—101no—
716D4—202no—
717D4—301no—
718D4—301no—
719D4—602no—
720C2×C4—21no—
721C2×C4—51no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—61no—
726C2×C4—104no—
727C2×C4—101no—
728C2×C4—202no—
729C2×C4—301no—
730C2×C4—602no—
731C2×C4D5×#6712yes—
732C2×C4C22×D3×D511yescharacteristic
733C8—32no—
734C8—32no—
735C8—152no—
736C8—152no—
737C2×C3—54no—
738C2×C3—81no—
739C2×C3—401no—
740C2×C3D5×#12711yescharacteristic
741C2×C3D5×#13512yes—
742D3—81no—
743D3—401no—
744C5C2×#505911yescharacteristic, complemented, Sylow
745C22—41no—
746C22—42no—
747C22—52no—
748C22—54no—
749C22—121no—
750C22—122no—
751C22—201no—
752C22—202no—
753C22—404no—
754C22—601no—
755C22—602no—
756C22—1204no—
757C22C2×D5×#6711yescharacteristic
758C4—22no—
759C4—41no—
760C4—52no—
761C4—102no—
762C4—121no—
763C4—201no—
764C4—601no—
765C4D3×D4×D511yescharacteristic
766C4D3×D4×D511yescharacteristic
767C3D5×#49511yescharacteristic, complemented, Sylow
768C2—54no—
769C2—81no—
770C2—241no—
771C2—401no—
772C2—1201no—
773C2D5×#94011yescharacteristic
774C2D5×#95012yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#213C2
hypercenter#124D3×D5
hypocenterC3×C5C2×#495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×D5×#124C2semidirect
2. C2×D5×#216C2semidirect
3. C2×D5×#215C2semidirect
4. C2×D5×#214C2semidirect
6. D5×#875C2semidirect
7. #11751160C2semidirect
8. C5×#5059C2semidirect
9. #11749316C2semidirect
10. #11749313C2semidirect
11. #11749070C2semidirect
12. #11749067C2semidirect
13. #11747072C2semidirect
14. #11747040C2semidirect
15. C4×D5×C3⋊C8C2semidirect
21. C3×C5×#124C22semidirect
22. C2×#6718C22semidirect
23. C2×#6717C22semidirect
24. C2×#6716C22semidirect
26. #91764C22semidirect
27. C2×C5×#216C22semidirect
28. C2×C5×#215C22semidirect
29. C2×C5×#214C22semidirect
31. C5×#875C22semidirect
32. C3×#4093C22semidirect
33. C3×#4082C22semidirect
36. C3×#4021C22semidirect
43. #91375C22semidirect
44. #91373C22semidirect
46. C2×#6662C22semidirect
47. C2×#6661C22semidirect
48. C2×#6658C22semidirect
49. C2×#6657C22semidirect
50. C2×#6656C22semidirect
51. C2×#6655C22semidirect
56. C4×C3⋊#168C22semidirect
57. C4×C5×C3⋊C8C22semidirect
58. Dic5×C3⋊C8C22semidirect
59. Dic5×C3⋊C8C22semidirect
66. D5×#124D3semidirect
148. #5059D5direct (N × H)
159. C5×#124C2×D3semidirect
161. #4093C2×D3semidirect
167. #4082C2×D3semidirect
187. #4021C2×D3semidirect
248. C3×#124C2×D5semidirect
255. C2×#216C2×D5semidirect
260. C2×#215C2×D5semidirect
265. C2×#214C2×D5semidirect
278. #875C2×D5semidirect
282. C4×C3⋊C8C2×D5semidirect
519. #124D3×D5semidirect
532. C3×D5#495semidirect
661. C3×C5C2×#495semidirect
690. D5#5059direct (N × H)
744. C5C2×#5059semidirect
767. C3D5×#495semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
C2×D5×#2162
C2×D5×#2152
C2×D5×#2142
C2×D5×#2132
D5×#8752
#117511602
C5×#50592
#117493162
#117493132
#117490702
#117490672
#117470722
#117470402
C4×D5×C3⋊C82
D5×#4953
C2×#50595