Finite Group Databasebeta

← C2×#10611990 #12976162

Subgroups — C2×#10611990 #12976162

Order 1280.

2114 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×#66165C211yesmaximal, characteristic
2C2×#65976C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic, complemented
4C2×#65521C211yesmaximal, characteristic, complemented
5C2×#65475C211yesmaximal, characteristic, complemented
6C2×Q16×Dic5C211yesmaximal, characteristic, complemented
7C2×#65463C211yesmaximal, characteristic, complemented
8C2×#65455C211yesmaximal, characteristic, complemented
9C2×#65341C211yesmaximal, characteristic, complemented
10#10611990C2116yesmaximal, direct product factor
11C2×#65091C211yesmaximal, characteristic, complemented
12C2×#65085C211yesmaximal, characteristic, complemented
13C2×#65073C211yesmaximal, characteristic, complemented
14C2×#65057C211yesmaximal, characteristic, complemented
15C2×#65018C211yesmaximal, characteristic, complemented
16C2×#65011C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×C5×Q16C2211yescharacteristic
20C22×C5×SD16C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22#66165—24no—
23#66165C2218yes—
24C2×#4092C2211yescharacteristic
25C2×Q8×Dic5C2211yescharacteristic
26C2×Q8×Dic5C2211yescharacteristic
27C22×#689C2211yescharacteristic
28C2×#4084—21no—
29C2×#4084C2211yescharacteristic
30C2×#4082—21no—
31C2×#4082C2211yescharacteristic
32C2×C4×C22⋊D5—21no—
33C2×C4×C22⋊D5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C2×#4070—21no—
36C2×#4070C2211yescharacteristic
37C22×#681C2211yescharacteristic
38C22×#676C2211yescharacteristic
39#65976—24no—
40#65976C2218yescomplemented
41C2×#4044—21no—
42C2×#4038C2211yescharacteristic
43C2×#4036—21no—
44C2×#4036C2211yescharacteristic
45C2×#4032—21no—
46C2×#4023—21no—
47C5×#452C2218yescomplemented
48C2×C5×#103C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51#65521C2218yescomplemented
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3964C2211yescharacteristic
56C2×#3964C2211yescharacteristic
57#65475C2218yescomplemented
58Q16×Dic5C2218yescomplemented
59#65463C2218yescomplemented
60#65455C2218yescomplemented
61C2×#3952C2211yescharacteristic
62C2×#3950C2211yescharacteristic
63C2×#3950C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3946C2211yescharacteristic
67C2×C8×Dic5C2211yescharacteristic
68#65341C2218yescomplemented
69C2×#3942C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71#65091C2218yescomplemented
72#65085C2218yescomplemented
73#65073C2218yescomplemented
74#65057C2218yescomplemented
75#65018C2218yescomplemented
76#65011C2218yescomplemented
77C2×#3327—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—24no—
80C2×C5×#41—42no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—21no—
89C22×C22⋊D5D411yescharacteristic
90C23×Dic5—21no—
91C2×Q8×D5—22no—
92C2×Q8×D5—24no—
93C2×Q8×D5—42no—
94C2×Q8×D5C2314yes—
95C22×C4×D5—21no—
96C22×C4×D5C2311yescharacteristic
97C22×Dic10—21no—
98C22×Dic10C2311yescharacteristic
99C2×C5×Q16—24no—
100C2×C5×Q16C2314yes—
101C2×C5×SD16—42no—
102C2×C5×SD16C2314yes—
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8C2314yes—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C22⋊C4—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5D411yescharacteristic
115#4092—22no—
116#4092C2314yes—
117Q8×Dic5—22no—
118Q8×Dic5—22no—
119Q8×Dic5C2314yes—
120Q8×Dic5C2314yes—
121C2×#689—42no—
122C2×#689C2314yes—
123#4084—28no—
124#4084—22no—
125#4084C2314yes—
126#4082—28no—
127#4082—22no—
128#4082C2314yes—
129C4×C22⋊D5—28no—
130C4×C22⋊D5D414yes—
131C4×C22⋊D5C2314yes—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685D411yescharacteristic
135C2×C4⋊Dic5—21no—
136C2×C4⋊Dic5—22no—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2314yes—
144#4070—22no—
145#4070—28no—
146#4070C2314yes—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683D411yescharacteristic
151C2×C4×Dic5—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×C4×Dic5C2311yescharacteristic
155C2×#681—42no—
156C2×#681C2314yes—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C2×#676—42no—
160C2×#676C2314yes—
161#4044—28no—
162#4038—22no—
163#4038C2314yes—
164#4036—28no—
165#4036—22no—
166#4036C2314yes—
167#4032—28no—
168#4023—28no—
169C5×#103C2314yes—
170C5×#102C2314yes—
171C5×C22⋊C8C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177#3952C2314yes—
178#3950C2314yes—
179#3950C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3946C2314yes—
183C8×Dic5C2314yes—
184#3942C2314yes—
185#3940C2314yes—
186C2×#552—51no—
187C2×#548—51no—
188#3327—516no—
189C2×#488—51no—
190C2×#484—51no—
191C2×#482—51no—
192C2×#479—51no—
193C2×#470—51no—
194C2×#468—51no—
195C2×#464—51no—
196C2×#452D511yescharacteristic, complemented
197C2×#451—51no—
198C2×C4×Q16—51no—
199C2×#436—51no—
200C2×#417—51no—
201C2×#419—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5C2×D411yescharacteristic
205C5×#41—28no—
206C5×#41—44no—
207C5×#41—48no—
208C2×C5×Q8—21no—
209C2×C5×Q8—21no—
210C2×C5×Q8—22no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8#4114yes—
214C2×C5×Q8C2412yes—
215C2×C5×Q8C2412yes—
216C2×C5×D4—24no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—22no—
220C2×C5×D4—44no—
221C2×C5×D4C2412yes—
222C22×C4×C5—21no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2411yescharacteristic
233C2×C22⋊D5—24no—
234C2×C22⋊D5—42no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5C2×D414yes—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—24no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—44no—
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C22×Dic5C2×D411yescharacteristic
246Q8×D5—28no—
247Q8×D5—44no—
248Q8×D5—48no—
249C2×C4×D5—22no—
250C2×C4×D5—22no—
251C2×C4×D5—24no—
252C2×C4×D5—44no—
253C2×C4×D5C2×D412yes—
254C2×C4×D5C2412yes—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10—21no—
258C2×Dic10—24no—
259C2×Dic10—44no—
260C2×Dic10C2412yes—
261C5×Q16—28no—
262C5×SD16—44no—
263C2×C5×C8—22no—
264C2×C5×C8—22no—
265C2×C5×C8C2412yes—
266C2×C5×C8C2412yes—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4C2412yes—
270C5×C22⋊C4—24no—
271C22⋊Dic5—24no—
272C22⋊Dic5—24no—
273C22⋊Dic5—24no—
274C22⋊Dic5—24no—
275C22⋊Dic5C2×D414yes—
276#689—44no—
277#685—24no—
278#685—24no—
279#685C2×D414yes—
280C4⋊Dic5—24no—
281C4⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—24no—
285C4⋊Dic5—24no—
286C4⋊Dic5—24no—
287C4⋊Dic5C2412yes—
288C4⋊Dic5C2412yes—
289C4⋊Dic5C2412yes—
290#683—24no—
291#683—24no—
292#683—24no—
293#683C2×D414yes—
294C4×Dic5—24no—
295C4×Dic5—24no—
296C4×Dic5—24no—
297C4×Dic5C2×D412yes—
298C4×Dic5C2412yes—
299#681—44no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168C2412yes—
303C2×#168C2412yes—
304#676—44no—
305C22×#41C2×D511yescharacteristic
306C23×Q8—51no—
307C22×Q16—51no—
308C22×Q16C2×D511yescharacteristic
309C22×SD16C2×D511yescharacteristic
310C22×M16—51no—
311C22×M16—51no—
312#552—58no—
313#552—104no—
314#548—58no—
315#548—104no—
316C2×#126—101no—
317C2×#125—51no—
318C2×#125—101no—
319C2×#124—51no—
320C2×#124—101no—
321C2×#123—101no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—101no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×#121—51no—
327C2×#121—101no—
328C2×C4×Q8—51no—
329C2×C4×Q8—51no—
330C2×C4×D4—51no—
331C2×C4×D4—101no—
332C2×#117—51no—
333C2×#117—101no—
334C22×C4⋊C4—51no—
335#488—58no—
336#484—58no—
337#482—58no—
338#479—58no—
339#470—58no—
340#468—58no—
341#464—58no—
342#452C2×D518yescomplemented
343#451—58no—
344C4×Q16—58no—
345#436—58no—
346C2×#107—51no—
347C2×#107—51no—
348C2×#106—51no—
349C2×C4⋊C8—51no—
350#419—58no—
351#417—58no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103C2×D511yescharacteristic
359C2×#102—51no—
360C2×#102—51no—
361C2×#102C2×D511yescharacteristic
362C2×C22⋊C8—51no—
363C2×C22⋊C8C2×D511yescharacteristic
364C2×C4×C8—51no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—42no—
370C23×C5—42no—
371C23×C5—42no—
372C23×C5C22×D412yes—
373C23×C5C22×D411yescharacteristic
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5C22×D412yes—
378C5×Q8—24no—
379C5×Q8—22no—
380C5×Q8—22no—
381C5×Q8—22no—
382C5×Q8—42no—
383C5×Q8C2×#4114yes—
384C5×D4—22no—
385C5×D4—22no—
386C5×D4—48no—
387C5×D4—42no—
388C2×C4×C5—24no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—24no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—48no—
397C2×C4×C5—42no—
398C2×C4×C5—42no—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D411yescharacteristic
401C2×C4×C5C2×#4112yes—
402C2×C4×C5H(5,𝔽2)12yes—
403C2×C4×C5C2511yescharacteristic
404C22⋊D5—44no—
405C22⋊D5—48no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—48no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5—42no—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420C2×Dic5C22×D412yes—
421C4×D5—24no—
422C4×D5—22no—
423C4×D5—22no—
424C4×D5—48no—
425Dic10—22no—
426Dic10—22no—
427Dic10—48no—
428Dic10—42no—
429C5×C8—22no—
430C5×C8—22no—
431#168—22no—
432#168—22no—
433C2×#41—22no—
434C2×#41—24no—
435C2×#41—42no—
436C2×#41C22×D514yes—
437C22×Q8—54no—
438C22×Q8—51no—
439C22×Q8—101no—
440C22×Q8—102no—
441C22×Q8—104no—
442C22×Q8—202no—
443C22×Q8C22×D511yescharacteristic
444C22×Q8C22×D511yescharacteristic
445C22×D4—21no—
446C22×D4—51no—
447C22×D4—101no—
448C22×D4C22×D511yescharacteristic
449C23×C4—21no—
450C23×C4—51no—
451C23×C4—101no—
452C23×C4—101no—
453C23×C4C22×D511yescharacteristic
454C2×Q16—24no—
455C2×Q16—54no—
456C2×Q16—202no—
457C2×Q16C22×D514yes—
458C2×SD16—42no—
459C2×SD16C22×D514yes—
460C2×M16—54no—
461C2×M16—54no—
462C2×M16—202no—
463C2×M16—202no—
464C22×C8—51no—
465C22×C8—51no—
466C22×C8C22×D511yescharacteristic
467C22×C8C22×D511yescharacteristic
468#126—108no—
469#125—54no—
470#125—102no—
471#125—108no—
472#124—54no—
473#124—102no—
474#124—108no—
475#123—108no—
476C22⋊Q8—22no—
477C22⋊Q8—54no—
478C22⋊Q8—54no—
479C22⋊Q8—108no—
480C22⋊Q8—102no—
481C22⋊Q8—102no—
482C22⋊Q8C22×D514yes—
483#121—54no—
484#121—102no—
485#121—108no—
486C4×Q8—54no—
487C4×Q8—54no—
488C4×Q8—102no—
489C4×Q8—102no—
490C4×D4—54no—
491C4×D4—54no—
492C4×D4—108no—
493#117—54no—
494#117—108no—
495#117—102no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—102no—
509C2×C4⋊C4—101no—
510C2×C4⋊C4C22×D511yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4—101no—
519C2×C22⋊C4—101no—
520C2×C42—51no—
521C2×C42—101no—
522C2×C42—101no—
523C2×C42—101no—
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#103C22×D514yes—
535#102—54no—
536#102—54no—
537#102C22×D514yes—
538C22⋊C8—54no—
539C22⋊C8C22×D514yes—
540C4×C8—54no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5—44no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—84no—
549C22×C5#54612yes—
550C22×C5#57512yes—
551C22×C5#57812yes—
552C22×C5C23×D411yescharacteristic
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5—44no—
557C4×C5—24no—
558C4×C5—22no—
559C4×C5—42no—
560C4×C5—42no—
561C4×C5#54612yes—
562C4×C5C22×#4111yescharacteristic
563C4×C5C2×H(5,𝔽2)11yescharacteristic
564Dic5—22no—
565Dic5—22no—
566Dic5—22no—
567Dic5—42no—
568Dic5—42no—
569Dic5—42no—
570Dic5—42no—
571C24—21no—
572C24—51no—
573C24D4×D511yescharacteristic
574#41—28no—
575#41—44no—
576#41—48no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—52no—
583C2×Q8—104no—
584C2×Q8—101no—
585C2×Q8—108no—
586C2×Q8—102no—
587C2×Q8—102no—
588C2×Q8—204no—
589C2×Q8—204no—
590C2×Q8—208no—
591C2×Q8#71114yes—
592C2×Q8C23×D512yes—
593C2×Q8C23×D512yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—44no—
599C2×D4—54no—
600C2×D4—104no—
601C2×D4—202no—
602C2×D4—204no—
603C2×D4C23×D512yes—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—44no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—51no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—104no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—104no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—204no—
625C22×C4—204no—
626C22×C4D4×D512yes—
627C22×C4D4×D511yescharacteristic
628C22×C4C23×D512yes—
629C22×C4C23×D511yescharacteristic
630Q16—28no—
631Q16—204no—
632SD16—44no—
633M16—204no—
634M16—204no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—52no—
638C2×C8—52no—
639C2×C8—102no—
640C2×C8—102no—
641C2×C8C23×D512yes—
642C2×C8C23×D512yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—54no—
646C4⋊C4—52no—
647C4⋊C4—52no—
648C4⋊C4—52no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4—104no—
654C4⋊C4—101no—
655C4⋊C4—101no—
656C4⋊C4—104no—
657C4⋊C4—101no—
658C4⋊C4—104no—
659C4⋊C4C23×D512yes—
660C22⋊C4—24no—
661C22⋊C4—54no—
662C22⋊C4—54no—
663C22⋊C4—104no—
664C22⋊C4—104no—
665C22⋊C4—104no—
666C22⋊C4—104no—
667C22⋊C4—104no—
668C22⋊C4—104no—
669C42—52no—
670C42—52no—
671C42—104no—
672C42—104no—
673C42—104no—
674C2×C5—42no—
675C2×C5—82no—
676C2×C5#332714yescomplemented
677C2×C5C2×#54611yescharacteristic
678C2×C5C2×#57511yescharacteristic
679C2×C5C2×#57811yescharacteristic
680D5—42no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—52no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23C2×D4×D512yes—
693C23C2×D4×D511yescharacteristic
694Q8—24no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—42no—
699Q8—102no—
700Q8—102no—
701Q8—208no—
702Q8—202no—
703Q8C2×#71114yes—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—42no—
708D4—204no—
709D4—208no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—104no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—208no—
735C2×C4—208no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4C2×D4×D512yes—
741C2×C4C2×D4×D511yescharacteristic
742C2×C4C2×#71112yes—
743C2×C4#414412yes—
744C2×C4C24×D511yescharacteristic
745C8—22no—
746C8—22no—
747C8—102no—
748C8—102no—
749C5C2×#332711yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—204no—
762C22#6592512yes—
763C22#6610512yes—
764C22#6611112yes—
765C22C22×D4×D511yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—102no—
771C4—102no—
772C4—102no—
773C4—202no—
774C4—202no—
775C4—202no—
776C4—202no—
777C4#6592512yes—
778C4C22×#71111yescharacteristic
779C4C2×#414411yescharacteristic
780C2—42no—
781C2—82no—
782C2—202no—
783C2#1061199014yesdirect product factor
784C2C2×#6592511yescharacteristic
785C2C2×#6610511yescharacteristic
786C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC2×#66165C2
hypercenterC2×#452D5
hypocenterC5C2×#3327
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#65976C2semidirect
3. C2×C5×#452C2semidirect
4. C2×#65521C2semidirect
5. C2×#65475C2semidirect
6. C2×Q16×Dic5C2semidirect
7. C2×#65463C2semidirect
8. C2×#65455C2semidirect
9. C2×#65341C2semidirect
10. #10611990C2direct (N × H)
11. C2×#65091C2semidirect
12. C2×#65085C2semidirect
13. C2×#65073C2semidirect
14. C2×#65057C2semidirect
15. C2×#65018C2semidirect
16. C2×#65011C2semidirect
40. #65976C22semidirect
47. C5×#452C22semidirect
51. #65521C22semidirect
57. #65475C22semidirect
58. Q16×Dic5C22semidirect
59. #65463C22semidirect
60. #65455C22semidirect
68. #65341C22semidirect
71. #65091C22semidirect
72. #65085C22semidirect
73. #65073C22semidirect
74. #65057C22semidirect
75. #65018C22semidirect
76. #65011C22semidirect
196. C2×#452D5semidirect
342. #452C2×D5semidirect
676. C2×C5#3327semidirect
749. C5C2×#3327semidirect
783. C2#10611990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661652
C2×#659762
C2×C5×#4522
C2×#655212
C2×#654752
C2×Q16×Dic52
C2×#654632
C2×#654552
C2×#653412
#106119902
C2×#650912
C2×#650852
C2×#650732
C2×#650572
C2×#650182
C2×#650112
C2×#33275