Finite Group Databasebeta

← C2×#10615333 #12975701

Subgroups — C2×#10615333 #12975701

Order 1280.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic, complemented
2C2×#65886C211yesmaximal, characteristic
3#10615333C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65357C211yesmaximal, characteristic, complemented
6C2×#65339C211yesmaximal, characteristic, complemented
7C2×#65336C211yesmaximal, characteristic, complemented
8C2×#65340C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65317C211yesmaximal, characteristic, complemented
11C2×C4×#689C211yesmaximal, characteristic, complemented
12C2×D4×#168C211yesmaximal, characteristic, complemented
13C2×#65285C211yesmaximal, characteristic, complemented
14C2×#65291C211yesmaximal, characteristic, complemented
15C22×#3942C211yesmaximal, characteristic, complemented
16C2×#65256C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C5×#552—24no—
20C5×#552C2218yescomplemented
21C2×C5×#126—21no—
22C2×C5×#125—21no—
23C2×C5×#125C2211yescharacteristic
24C2×C5×#123—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C2×C5×#117C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C22×#689C2211yescharacteristic
33C22×#689C2211yescharacteristic
34C22×#688C2211yescharacteristic
35C2×#4085—21no—
36C2×#4076C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C23×#168C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65886—24no—
41#65886C2218yes—
42C2×#4042—21no—
43C2×#4031—21no—
44C2×#4027—21no—
45C2×#4021C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65357C2218yescomplemented
51#65352C2218yescomplemented
52#65340C2218yescomplemented
53#65339C2218yescomplemented
54#65337C2218yescomplemented
55#65336C2218yescomplemented
56C4×#689C2218yescomplemented
57#65317C2218yescomplemented
58D4×#168C2218yescomplemented
59#65291C2218yescomplemented
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3942C2218yescomplemented
68#65256C2218yescomplemented
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71C2×#3941C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3300—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C2×#709—22no—
87C2×#709—24no—
88C2×#709—42no—
89C2×#709C2314yes—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×Dic10—24no—
93C22×Dic10—21no—
94C22×Dic10—22no—
95C22×Dic10—42no—
96C22×Dic10C2311yescharacteristic
97C22×Dic10C2314yes—
98C22×Dic10C2311yescharacteristic
99C5×#126—28no—
100C5×#125—28no—
101C5×#125—22no—
102C5×#125C2314yes—
103C5×#123—28no—
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8C2314yes—
107C5×C22⋊Q8C2314yes—
108C4×C5×Q8—22no—
109C4×C5×Q8C2314yes—
110C4×C5×D4D414yes—
111C4×C5×D4C2314yes—
112C5×#117—22no—
113C5×#117—28no—
114C5×#117C2314yes—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—22no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4D411yescharacteristic
123C2×C5×C4⋊C4C2311yescharacteristic
124C2×C5×C4⋊C4C2311yescharacteristic
125C2×C5×C4⋊C4C2314yes—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—21no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4D411yescharacteristic
131C2×C5×C22⋊C4D411yescharacteristic
132C2×C42×C5—21no—
133C2×C42×C5—21no—
134C2×C42×C5C2311yescharacteristic
135C2×C22⋊Dic5—21no—
136C2×#689—24no—
137C2×#689—42no—
138C2×#689C2314yes—
139C2×#689C2314yes—
140C2×#688—42no—
141C2×#688C2314yes—
142#4085—28no—
143#4076—22no—
144#4076C2314yes—
145C2×#685—21no—
146C2×#685—21no—
147C2×#685—21no—
148C2×C4⋊Dic5C2311yescharacteristic
149#4070—22no—
150#4070C2314yes—
151C2×#683—21no—
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C22×#168—42no—
155C22×#168—42no—
156C22×#168C2311yescharacteristic
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2314yes—
161C22×#168C2314yes—
162#4042—28no—
163#4031—28no—
164#4027—28no—
165#4021—22no—
166#4021C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yes—
169#3967C2314yes—
170C22⋊#168C2314yes—
171C22⋊#168C2314yes—
172#3942C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3942C2314yes—
176#3942C2314yes—
177#3942C2314yes—
178#3941C2314yes—
179#3941C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185C4×#168C2314yes—
186C2×#552D511yescharacteristic, complemented
187C2×#548—51no—
188#3300—516no—
189C2×#488—51no—
190C2×#485—51no—
191C2×#480—51no—
192C2×#479—51no—
193C2×#467—51no—
194C2×#465—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#451—51no—
198C2×C4×Q16—51no—
199C2×C8×D4—51no—
200C2×#416—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—22no—
207C2×C5×Q8—22no—
208C2×C5×Q8C2412yes—
209C2×C5×D4—24no—
210C2×C5×D4C2×D414yes—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—24no—
220C22×C4×C5—44no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—24no—
238C22×Dic5—44no—
239#709—28no—
240#709—44no—
241#709—48no—
242C2×D20—22no—
243C2×D20—22no—
244C2×D20—21no—
245C2×D20C2412yes—
246C2×C4×D5—24no—
247C2×C4×D5—44no—
248C2×Dic10—21no—
249C2×Dic10—22no—
250C2×Dic10—22no—
251C2×Dic10—22no—
252C2×Dic10—28no—
253C2×Dic10—21no—
254C2×Dic10—24no—
255C2×Dic10—44no—
256C2×Dic10—48no—
257C2×Dic10—44no—
258C2×Dic10#4114yes—
259C2×Dic10C2412yes—
260C2×Dic10C2412yes—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
263C5×C4⋊C4—24no—
264C5×C4⋊C4—24no—
265C5×C4⋊C4—24no—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—24no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4C2×D414yes—
271C5×C4⋊C4C2412yes—
272C5×C4⋊C4C2412yes—
273C5×C4⋊C4C2412yes—
274C5×C22⋊C4—24no—
275C5×C22⋊C4—24no—
276C5×C22⋊C4—24no—
277C5×C22⋊C4C2×D414yes—
278C5×C22⋊C4C2×D414yes—
279C42×C5—24no—
280C42×C5—24no—
281C42×C5C2×D412yes—
282C42×C5C2412yes—
283C22⋊Dic5—24no—
284#689—28no—
285#689—44no—
286#688—44no—
287#685—24no—
288#685—24no—
289#685—24no—
290C4⋊Dic5—21no—
291C4⋊Dic5C2412yes—
292#683—24no—
293#683—24no—
294C4×Dic5—24no—
295C2×#168—22no—
296C2×#168—22no—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168—44no—
300C2×#168—44no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C2×#168C2412yes—
304C2×#168C2412yes—
305C22×#41—51no—
306C23×Q8—51no—
307C22×Q16—51no—
308C22×Q16—51no—
309C22×SD16—51no—
310C23×C8—51no—
311C23×C8—51no—
312#552—24no—
313#552C2×D518yescomplemented
314#548—58no—
315#548—104no—
316C2×#126—21no—
317C2×#125—21no—
318C2×#125C2×D511yescharacteristic
319C2×#124—51no—
320C2×#124—101no—
321C2×#123—21no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—101no—
324C2×C22⋊Q8C2×D511yescharacteristic
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×#121—51no—
327C2×#121—101no—
328C2×C4×Q8—51no—
329C2×C4×Q8C2×D511yescharacteristic
330C2×C4×D4—101no—
331C2×C4×D4C2×D511yescharacteristic
332C2×#117—21no—
333C2×#117C2×D511yescharacteristic
334C22×C4⋊C4C2×D511yescharacteristic
335#488—58no—
336#485—58no—
337#480—58no—
338#479—58no—
339#467—58no—
340#465—58no—
341#464—58no—
342#452—58no—
343#451—58no—
344C4×Q16—58no—
345C8×D4—58no—
346C2×#107—51no—
347C2×#107—51no—
348C2×#106—51no—
349C2×C4⋊C8—51no—
350#416—58no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—58no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×C22⋊C8—51no—
363C2×C22⋊C8—51no—
364C2×C4×C8—51no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5#13514yes—
371C23×C5C22×D412yes—
372C23×C5C22×D412yes—
373C23×C5C22×D411yescharacteristic
374C22×D5—22no—
375C22×D5—42no—
376C22×D5—42no—
377C22×D5—42no—
378C5×Q8—22no—
379C5×Q8—22no—
380C5×Q8—42no—
381C5×D4—28no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—24no—
387C2×C4×C5—24no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—42no—
397C2×C4×C5—48no—
398C2×C4×C5—42no—
399C2×C4×C5—42no—
400C2×C4×C5—42no—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D412yes—
404C2×C4×C5C22×D412yes—
405C2×C4×C5C22×D411yescharacteristic
406C2×C4×C5C2×#4112yes—
407C2×C4×C5H(5,𝔽2)12yes—
408C2×C4×C5C2511yescharacteristic
409C22⋊D5—48no—
410C22⋊D5—48no—
411C2×Dic5—24no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—48no—
416C2×Dic5—42no—
417C2×Dic5—42no—
418D20—22no—
419D20—22no—
420D20—42no—
421C4×D5—48no—
422Dic10—24no—
423Dic10—22no—
424Dic10—22no—
425Dic10—22no—
426Dic10—48no—
427Dic10—42no—
428Dic10C2×#4114yes—
429#168—22no—
430#168—22no—
431#168—22no—
432#168—22no—
433C2×#41—54no—
434C2×#41—104no—
435C2×#41—102no—
436C2×#41—202no—
437C22×Q8—51no—
438C22×Q8—51no—
439C22×Q8—54no—
440C22×Q8—104no—
441C22×Q8—101no—
442C22×Q8—102no—
443C22×Q8—202no—
444C22×Q8C22×D511yescharacteristic
445C22×D4—51no—
446C22×D4—101no—
447C22×D4—101no—
448C22×D4C22⋊D511yescharacteristic
449C23×C4—21no—
450C23×C4—101no—
451C23×C4—101no—
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454C2×Q16—54no—
455C2×Q16—54no—
456C2×Q16—104no—
457C2×Q16—202no—
458C2×SD16—54no—
459C2×SD16—202no—
460C22×C8—51no—
461C22×C8—51no—
462C22×C8—51no—
463C22×C8—51no—
464C22×C8—54no—
465C22×C8—54no—
466C22×C8—202no—
467C22×C8—202no—
468#126—28no—
469#125—28no—
470#125—22no—
471#125C22×D514yes—
472#124—54no—
473#124—108no—
474#124—102no—
475#123—28no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—54no—
479C22⋊Q8—102no—
480C22⋊Q8—108no—
481C22⋊Q8C22×D514yes—
482C22⋊Q8C22×D514yes—
483#121—54no—
484#121—108no—
485#121—102no—
486C4×Q8—22no—
487C4×Q8—54no—
488C4×Q8—102no—
489C4×Q8C22×D514yes—
490C4×D4—108no—
491C4×D4C22⋊D514yes—
492C4×D4C22×D514yes—
493#117—22no—
494#117—28no—
495#117C22×D514yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4C22⋊D511yescharacteristic
507C2×C4⋊C4C22×D511yescharacteristic
508C2×C4⋊C4C22×D511yescharacteristic
509C2×C4⋊C4C22×D514yes—
510C2×C4⋊C4C22×D511yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4C22⋊D511yescharacteristic
519C2×C22⋊C4C22⋊D511yescharacteristic
520C2×C42—21no—
521C2×C42—21no—
522C2×C42—101no—
523C2×C42C22×D511yescharacteristic
524#107—54no—
525#107—54no—
526#106—54no—
527C4⋊C8—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#103—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#102—54no—
536#102—54no—
537#102—54no—
538C22⋊C8—54no—
539C22⋊C8—54no—
540C4×C8—54no—
541C22×C5—22no—
542C22×C5—28no—
543C22×C5—22no—
544C22×C5—22no—
545C22×C5—22no—
546C22×C5—22no—
547C22×C5—44no—
548C22×C5#54612yes—
549C22×C5C2×#13514yes—
550C22×C5C2×#13512yes—
551C22×C5#57812yes—
552C22×C5C23×D411yescharacteristic
553C2×D5—42no—
554C2×D5—42no—
555C2×D5—42no—
556C2×D5—84no—
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—22no—
560C4×C5—22no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5—42no—
564C4×C5—42no—
565C4×C5#54612yes—
566C4×C5C22×#4111yescharacteristic
567C4×C5C2×H(5,𝔽2)11yescharacteristic
568Dic5—24no—
569Dic5—42no—
570Dic5—42no—
571C24—101no—
572C24C2×C22⋊D511yescharacteristic
573C24C2×C22⋊D511yescharacteristic
574#41—108no—
575#41—204no—
576#41—208no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—54no—
581C2×Q8—52no—
582C2×Q8—52no—
583C2×Q8—108no—
584C2×Q8—102no—
585C2×Q8—101no—
586C2×Q8—104no—
587C2×Q8—101no—
588C2×Q8—102no—
589C2×Q8—102no—
590C2×Q8—204no—
591C2×Q8—204no—
592C2×Q8—208no—
593C2×Q8C23×D512yes—
594C2×D4—24no—
595C2×D4—52no—
596C2×D4—104no—
597C2×D4—104no—
598C2×D4—102no—
599C2×D4—102no—
600C2×D4—101no—
601C2×D4—204no—
602C2×D4—204no—
603C2×D4C2×C22⋊D514yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—44no—
614C22×C4—101no—
615C22×C4—104no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—104no—
619C22×C4—204no—
620C22×C4—204no—
621C22×C4C2×C22⋊D512yes—
622C22×C4C2×C22⋊D512yes—
623C22×C4C2×C22⋊D511yescharacteristic
624C22×C4C2×C22⋊D511yescharacteristic
625C22×C4C2×C22⋊D511yescharacteristic
626C22×C4C2×C22⋊D511yescharacteristic
627C22×C4C23×D512yes—
628C22×C4C23×D512yes—
629C22×C4C23×D511yescharacteristic
630Q16—108no—
631Q16—204no—
632SD16—204no—
633C2×C8—52no—
634C2×C8—52no—
635C2×C8—52no—
636C2×C8—52no—
637C2×C8—102no—
638C2×C8—102no—
639C2×C8—102no—
640C2×C8—102no—
641C2×C8—204no—
642C2×C8—204no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—52no—
653C4⋊C4—101no—
654C4⋊C4—104no—
655C4⋊C4—104no—
656C4⋊C4C2×C22⋊D514yes—
657C4⋊C4C23×D512yes—
658C4⋊C4C23×D512yes—
659C4⋊C4C23×D512yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—104no—
664C22⋊C4—104no—
665C22⋊C4—104no—
666C22⋊C4—104no—
667C22⋊C4C2×C22⋊D514yes—
668C22⋊C4C2×C22⋊D514yes—
669C42—24no—
670C42—24no—
671C42—104no—
672C42C2×C22⋊D512yes—
673C42C23×D512yes—
674C2×C5—24no—
675C2×C5—42no—
676C2×C5#330014yescomplemented
677C2×C5C2×#54611yescharacteristic
678C2×C5C22×#13511yescharacteristic
679C2×C5C2×#57811yescharacteristic
680D5—82no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—102no—
687C23—202no—
688C23—202no—
689C23—202no—
690C23#409614yes—
691C23C22×C22⋊D512yes—
692C23C22×C22⋊D512yes—
693C23C22×C22⋊D511yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—54no—
698Q8—104no—
699Q8—102no—
700Q8—102no—
701Q8—102no—
702Q8—208no—
703Q8—202no—
704D4—28no—
705D4—102no—
706D4—102no—
707D4—208no—
708D4—208no—
709D4—202no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—104no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—208no—
734C2×C4—208no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4D5×#4112yes—
738C2×C4#414912yes—
739C2×C4C22×C22⋊D512yes—
740C2×C4C22×C22⋊D512yes—
741C2×C4C22×C22⋊D512yes—
742C2×C4C22×C22⋊D512yes—
743C2×C4C22×C22⋊D511yescharacteristic
744C2×C4C24×D511yescharacteristic
745C8—102no—
746C8—102no—
747C8—102no—
748C8—102no—
749C5C2×#330011yescharacteristic, complemented, Sylow
750C22—22no—
751C22—28no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—404no—
761C22C2×#409614yes—
762C22C2×#409612yes—
763C22#6616312yes—
764C22#6617212yes—
765C22C23×C22⋊D511yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—104no—
775C4—202no—
776C4—202no—
777C4#6616312yes—
778C4C2×D5×#4111yescharacteristic
779C4C2×#414911yescharacteristic
780C2—24no—
781C2—42no—
782C2—402no—
783C2#1061533314yesdirect product factor
784C2C22×#409611yescharacteristic
785C2C2×#6616311yescharacteristic
786C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC2×#65886C2
hypercenterC2×#552D5
hypocenterC5C2×#3300
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
3. #10615333C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65357C2semidirect
6. C2×#65339C2semidirect
7. C2×#65336C2semidirect
8. C2×#65340C2semidirect
9. C2×#65337C2semidirect
10. C2×#65317C2semidirect
11. C2×C4×#689C2semidirect
12. C2×D4×#168C2semidirect
13. C2×#65285C2semidirect
14. C2×#65291C2semidirect
15. C22×#3942C2semidirect
16. C2×#65256C2semidirect
20. C5×#552C22semidirect
50. #65357C22semidirect
51. #65352C22semidirect
52. #65340C22semidirect
53. #65339C22semidirect
54. #65337C22semidirect
55. #65336C22semidirect
56. C4×#689C22semidirect
57. #65317C22semidirect
58. D4×#168C22semidirect
59. #65291C22semidirect
60. #65285C22semidirect
67. C2×#3942C22semidirect
68. #65256C22semidirect
186. C2×#552D5semidirect
313. #552C2×D5semidirect
676. C2×C5#3300semidirect
749. C5C2×#3300semidirect
783. C2#10615333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×#658862
#106153332
C2×#653522
C2×#653572
C2×#653392
C2×#653362
C2×#653402
C2×#653372
C2×#653172
C2×C4×#6892
C2×D4×#1682
C2×#652852
C2×#652912
C22×#39422
C2×#652562
C2×#33005