Finite Group Databasebeta

← C2×#10613182 #12975904

Subgroups — C2×#10613182 #12975904

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65966C211yesmaximal, characteristic
2C2×#65847C211yesmaximal, characteristic
3C2×C5×#483C211yesmaximal, characteristic, complemented
4C2×#65340C211yesmaximal, characteristic, complemented
5C22×#3942C211yesmaximal, characteristic, complemented
6#10613182C2116yesmaximal, direct product factor
7C2×#65146C211yesmaximal, characteristic, complemented
8C2×#65157C211yesmaximal, characteristic, complemented
9C2×#65156C211yesmaximal, characteristic, complemented
10C2×#65142C211yesmaximal, characteristic, complemented
11C2×#65082C211yesmaximal, characteristic, complemented
12C2×#65097C211yesmaximal, characteristic, complemented
13C2×#65091C211yesmaximal, characteristic, complemented
14C2×#65086C211yesmaximal, characteristic, complemented
15C2×#65028C211yesmaximal, characteristic, complemented
16C2×#65019C211yesmaximal, characteristic
17C22×Q8×D5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4090C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C2×#4075—21no—
24C2×C4×C22⋊D5C2211yescharacteristic
25C2×#4072—21no—
26C2×#4070C2211yescharacteristic
27C23×#168C2211yescharacteristic
28C22×Dic20C2211yescharacteristic
29C22×Dic20C2211yescharacteristic
30C22×#676C2211yescharacteristic
31#65966—24no—
32#65966C2218yes—
33#65847—24no—
34#65847C2218yes—
35C2×#4044—21no—
36C2×#4043C2211yescharacteristic
37C2×#4043C2211yescharacteristic
38C2×#4042—21no—
39C2×#4038C2211yescharacteristic
40C2×#4036C2211yescharacteristic
41C2×#4035—21no—
42C2×#4034—21no—
43C2×#4033C2211yescharacteristic
44C2×#4033C2211yescharacteristic
45C2×#4027—21no—
46C2×#4024—21no—
47C5×#483C2218yescomplemented
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#103C2211yescharacteristic
52C2×C5×C22⋊C8C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65340C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3942C2218yescomplemented
66C2×#3939C2211yescharacteristic
67#65157C2218yescomplemented
68#65156C2218yescomplemented
69#65146C2218yescomplemented
70#65142C2218yescomplemented
71#65097C2218yescomplemented
72#65091C2218yescomplemented
73#65086C2218yescomplemented
74#65082C2218yescomplemented
75#65028C2218yescomplemented
76#65019C2218yes—
77C2×#3312—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C23×C4×C5—21no—
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5D411yescharacteristic
82C23×Dic5—21no—
83C2×Q8×D5—22no—
84C2×Q8×D5—24no—
85C2×Q8×D5—42no—
86C2×Q8×D5C2314yes—
87C22×C4×D5—21no—
88C22×C4×D5C2311yescharacteristic
89C22×Dic10—24no—
90C22×Dic10—21no—
91C22×Dic10—22no—
92C22×Dic10—21no—
93C22×Dic10—42no—
94C22×Dic10C2311yescharacteristic
95C22×Dic10C2311yescharacteristic
96C22×Dic10C2314yes—
97C22×Dic10C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8C2314yes—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C22⋊C4—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5D411yescharacteristic
112#4090—22no—
113#4090C2314yes—
114C2×#689—42no—
115C2×#689C2314yes—
116#4075—28no—
117C4×C22⋊D5D414yes—
118C4×C22⋊D5C2314yes—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685D411yescharacteristic
123#4072—28no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5C2311yescharacteristic
128#4070—22no—
129#4070C2314yes—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683D411yescharacteristic
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5—21no—
140C2×C4×Dic5C2311yescharacteristic
141C22×#168—42no—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2314yes—
145C2×Dic20—24no—
146C2×Dic20—42no—
147C2×Dic20C2314yes—
148C2×Dic20C2314yes—
149C2×#676—42no—
150C2×#676C2314yes—
151#4044—28no—
152#4043—22no—
153#4043—22no—
154#4043C2314yes—
155#4043C2314yes—
156#4042—28no—
157#4038—22no—
158#4038C2314yes—
159#4036—22no—
160#4036C2314yes—
161#4035—28no—
162#4034—28no—
163#4033—22no—
164#4033—22no—
165#4033C2314yes—
166#4033C2314yes—
167#4027—28no—
168#4024—28no—
169C5×#106C2314yes—
170C5×#106C2314yes—
171C5×#103C2314yes—
172C5×#103C2314yes—
173C5×C22⋊C8C2314yes—
174#3967C2314yes—
175#3952C2314yes—
176#3948C2314yes—
177#3948C2314yes—
178#3947C2314yes—
179#3946C2314yes—
180#3942C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3942C2314yes—
184#3942C2314yes—
185#3939C2314yes—
186C2×#552—51no—
187C2×D4×Q8—51no—
188#3312—516no—
189C2×#491—51no—
190C2×#485—51no—
191C2×#483D511yescharacteristic, complemented
192C2×#479—51no—
193C2×#470—51no—
194C2×#467—51no—
195C2×#462—51no—
196C2×#451—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#419—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C23×D5C2×D411yescharacteristic
204C2×C5×Q8—21no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—44no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2411yescharacteristic
220C2×C22⋊D5—24no—
221C2×C22⋊D5C2×D414yes—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—24no—
226C22×Dic5—21no—
227C22×Dic5—44no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231Q8×D5—28no—
232Q8×D5—44no—
233Q8×D5—48no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5—24no—
237C2×C4×D5—44no—
238C2×C4×D5C2×D412yes—
239C2×C4×D5C2412yes—
240C2×Dic10—21no—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—22no—
244C2×Dic10—22no—
245C2×Dic10—22no—
246C2×Dic10—28no—
247C2×Dic10—24no—
248C2×Dic10—21no—
249C2×Dic10—21no—
250C2×Dic10—24no—
251C2×Dic10—44no—
252C2×Dic10—48no—
253C2×Dic10—44no—
254C2×Dic10—44no—
255C2×Dic10#4114yes—
256C2×Dic10C2412yes—
257C2×Dic10C2412yes—
258C2×Dic10C2412yes—
259C2×C5×C8—22no—
260C2×C5×C8—22no—
261C2×C5×C8C2412yes—
262C2×C5×C8C2412yes—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—24no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4C2412yes—
269C5×C4⋊C4C2412yes—
270C5×C4⋊C4C2412yes—
271C5×C22⋊C4—24no—
272C22⋊Dic5—24no—
273C22⋊Dic5C2×D414yes—
274#689—44no—
275#685—24no—
276#685—24no—
277#685—24no—
278#685C2×D414yes—
279C4⋊Dic5—21no—
280C4⋊Dic5—24no—
281C4⋊Dic5—24no—
282C4⋊Dic5—24no—
283C4⋊Dic5C2412yes—
284#683—24no—
285#683—24no—
286#683—24no—
287#683—24no—
288#683—24no—
289#683—24no—
290#683C2×D414yes—
291C4×Dic5—24no—
292C4×Dic5—24no—
293C4×Dic5—24no—
294C4×Dic5C2×D412yes—
295C4×Dic5C2412yes—
296C2×#168—22no—
297C2×#168—22no—
298C2×#168—44no—
299C2×#168C2412yes—
300C2×#168C2412yes—
301Dic20—28no—
302Dic20—44no—
303#676—44no—
304C23×Q8—51no—
305C23×Q8—51no—
306C22×Q16—51no—
307C22×Q16—51no—
308C22×Q16—51no—
309C22×M16—51no—
310C23×C8—51no—
311#552—58no—
312#552—104no—
313D4×Q8—58no—
314D4×Q8—104no—
315C2×C4⋊Q8—51no—
316C2×C4⋊Q8—101no—
317C2×#126—101no—
318C2×#125—51no—
319C2×#125—101no—
320C2×#123—101no—
321C2×C22⋊Q8—51no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—101no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8C2×D511yescharacteristic
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×D4—51no—
330C2×C4×D4—101no—
331C2×#117—51no—
332C2×#117—101no—
333C22×C4⋊C4C2×D511yescharacteristic
334#491—58no—
335#485—58no—
336#483C2×D518yescomplemented
337#479—58no—
338#470—58no—
339#467—58no—
340#462—58no—
341#451—58no—
342#451—58no—
343#441—58no—
344#435—58no—
345C2×#107—51no—
346C2×#106C2×D511yescharacteristic
347C2×#106C2×D511yescharacteristic
348C2×C4⋊C8—51no—
349#419—58no—
350C2×#103—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—58no—
358C2×#103—51no—
359C2×#103C2×D511yescharacteristic
360C2×#103C2×D511yescharacteristic
361C2×C22⋊C8—51no—
362C2×C22⋊C8C2×D511yescharacteristic
363C2×#97—51no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5#13714yes—
367C23×C5C22×D412yes—
368C23×C5C22×D411yescharacteristic
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5C22×D412yes—
373C5×Q8—22no—
374C5×Q8—22no—
375C5×Q8—42no—
376C2×C4×C5—22no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—42no—
385C2×C4×C5—48no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4112yes—
392C2×C4×C5H(5,𝔽2)12yes—
393C2×C4×C5C2511yescharacteristic
394C22⋊D5—28no—
395C2×Dic5—24no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—48no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5C22×D412yes—
408C2×Dic5C22×D412yes—
409C2×Dic5C22×D412yes—
410C4×D5—24no—
411C4×D5—22no—
412C4×D5—22no—
413C4×D5—48no—
414Dic10—24no—
415Dic10—22no—
416Dic10—22no—
417Dic10—22no—
418Dic10—22no—
419Dic10—22no—
420Dic10—48no—
421Dic10—48no—
422Dic10—42no—
423Dic10—42no—
424Dic10C2×#4114yes—
425C5×C8—22no—
426C5×C8—22no—
427#168—22no—
428#168—22no—
429C22×Q8—54no—
430C22×Q8—51no—
431C22×Q8—51no—
432C22×Q8—51no—
433C22×Q8—54no—
434C22×Q8—101no—
435C22×Q8—104no—
436C22×Q8—102no—
437C22×Q8—101no—
438C22×Q8—102no—
439C22×Q8—104no—
440C22×Q8—202no—
441C22×Q8—202no—
442C22×Q8C22×D511yescharacteristic
443C22×D4—51no—
444C23×C4—21no—
445C23×C4—51no—
446C23×C4—101no—
447C23×C4—101no—
448C23×C4C22×D511yescharacteristic
449C2×Q16—54no—
450C2×Q16—54no—
451C2×Q16—54no—
452C2×Q16—104no—
453C2×Q16—202no—
454C2×Q16—202no—
455C2×M16—54no—
456C2×M16—202no—
457C22×C8—51no—
458C22×C8—51no—
459C22×C8—54no—
460C22×C8—202no—
461C22×C8C22×D511yescharacteristic
462C22×C8C22×D511yescharacteristic
463C4⋊Q8—54no—
464C4⋊Q8—102no—
465C4⋊Q8—108no—
466#126—108no—
467#125—54no—
468#125—102no—
469#125—108no—
470#123—108no—
471C22⋊Q8—22no—
472C22⋊Q8—54no—
473C22⋊Q8—54no—
474C22⋊Q8—54no—
475C22⋊Q8—108no—
476C22⋊Q8—108no—
477C22⋊Q8—102no—
478C22⋊Q8—102no—
479C22⋊Q8—102no—
480C22⋊Q8C22×D514yes—
481C4×Q8—54no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8—102no—
485C4×D4—54no—
486C4×D4—54no—
487C4×D4—108no—
488#117—54no—
489#117—108no—
490#117—102no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C4⋊C4C22×D511yescharacteristic
507C2×C4⋊C4C22×D514yes—
508C2×C4⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C42—51no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42—101no—
520#107—54no—
521#106C22×D514yes—
522#106C22×D514yes—
523C4⋊C8—54no—
524#103—54no—
525#103—54no—
526#103—54no—
527#103—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#103—54no—
532#103C22×D514yes—
533#103C22×D514yes—
534C22⋊C8—54no—
535C22⋊C8C22×D514yes—
536#97—54no—
537C22×C5—22no—
538C22×C5—28no—
539C22×C5—22no—
540C22×C5#54612yes—
541C22×C5C2×#13714yes—
542C22×C5C2×#13712yes—
543C22×C5#57812yes—
544C22×C5C23×D411yescharacteristic
545C2×D5—22no—
546C2×D5—22no—
547C2×D5—22no—
548C2×D5—44no—
549C4×C5—22no—
550C4×C5—42no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5#54612yes—
555C4×C5C22×#4111yescharacteristic
556C4×C5C2×H(5,𝔽2)11yescharacteristic
557Dic5—24no—
558Dic5—22no—
559Dic5—22no—
560Dic5—22no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24—51no—
565C24D4×D511yescharacteristic
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—54no—
570C2×Q8—52no—
571C2×Q8—52no—
572C2×Q8—52no—
573C2×Q8—104no—
574C2×Q8—108no—
575C2×Q8—101no—
576C2×Q8—101no—
577C2×Q8—104no—
578C2×Q8—101no—
579C2×Q8—102no—
580C2×Q8—108no—
581C2×Q8—102no—
582C2×Q8—102no—
583C2×Q8—102no—
584C2×Q8—102no—
585C2×Q8—204no—
586C2×Q8—204no—
587C2×Q8—208no—
588C2×Q8—204no—
589C2×Q8—204no—
590C2×Q8—208no—
591C2×Q8C23×D512yes—
592C2×D4—54no—
593C2×D4—104no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—44no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—52no—
606C22×C4—52no—
607C22×C4—104no—
608C22×C4—101no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—104no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4D4×D512yes—
618C22×C4D4×D511yescharacteristic
619C22×C4C23×D512yes—
620C22×C4C23×D511yescharacteristic
621Q16—108no—
622Q16—204no—
623Q16—204no—
624M16—204no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—52no—
628C2×C8—52no—
629C2×C8—102no—
630C2×C8—102no—
631C2×C8—204no—
632C2×C8C23×D512yes—
633C2×C8C23×D512yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—54no—
640C4⋊C4—52no—
641C4⋊C4—104no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—104no—
646C4⋊C4—104no—
647C4⋊C4—104no—
648C4⋊C4—104no—
649C4⋊C4—101no—
650C4⋊C4—104no—
651C4⋊C4C23×D512yes—
652C4⋊C4C23×D512yes—
653C4⋊C4C23×D512yes—
654C22⋊C4—24no—
655C22⋊C4—54no—
656C22⋊C4—54no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C42—52no—
662C42—52no—
663C42—104no—
664C42—104no—
665C42—104no—
666C2×C5—24no—
667C2×C5#331214yescomplemented
668C2×C5C2×#54611yescharacteristic
669C2×C5C22×#13711yescharacteristic
670C2×C5C2×#57811yescharacteristic
671D5—42no—
672C23—22no—
673C23—22no—
674C23—52no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23#406114yes—
679C23C2×D4×D512yes—
680C23C2×D4×D511yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—42no—
684Q8—54no—
685Q8—104no—
686Q8—102no—
687Q8—102no—
688Q8—102no—
689Q8—102no—
690Q8—102no—
691Q8—208no—
692Q8—208no—
693Q8—202no—
694Q8—202no—
695D4—108no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—52no—
710C2×C4—52no—
711C2×C4—52no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—104no—
716C2×C4—102no—
717C2×C4—104no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—208no—
724C2×C4—208no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4C2×D4×D512yes—
729C2×C4C2×D4×D511yescharacteristic
730C2×C4D5×#4112yes—
731C2×C4#414912yes—
732C2×C4C24×D511yescharacteristic
733C8—22no—
734C8—22no—
735C8—102no—
736C8—102no—
737C5C2×#331211yescharacteristic, complemented, Sylow
738C22—22no—
739C22—28no—
740C22—22no—
741C22—102no—
742C22—102no—
743C22—102no—
744C22—204no—
745C22#6598812yes—
746C22C2×#406114yes—
747C22C2×#406112yes—
748C22#6611312yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—102no—
756C4—104no—
757C4—102no—
758C4—102no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4#6598812yes—
763C4C2×D5×#4111yescharacteristic
764C4C2×#414911yescharacteristic
765C2—24no—
766C2—202no—
767C2#1061318214yesdirect product factor
768C2C2×#6598811yescharacteristic
769C2C22×#406111yescharacteristic
770C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#483C2
socleC23×C5C22×D4
prime radicalC22×C22⋊D5D4
hypercenterC2×#483D5
hypocenterC5C2×#3312
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. C2×C5×#483C2semidirect
4. C2×#65340C2semidirect
5. C22×#3942C2semidirect
6. #10613182C2direct (N × H)
7. C2×#65146C2semidirect
8. C2×#65157C2semidirect
9. C2×#65156C2semidirect
10. C2×#65142C2semidirect
11. C2×#65082C2semidirect
12. C2×#65097C2semidirect
13. C2×#65091C2semidirect
14. C2×#65086C2semidirect
15. C2×#65028C2semidirect
47. C5×#483C22semidirect
59. #65340C22semidirect
65. C2×#3942C22semidirect
67. #65157C22semidirect
68. #65156C22semidirect
69. #65146C22semidirect
70. #65142C22semidirect
71. #65097C22semidirect
72. #65091C22semidirect
73. #65086C22semidirect
74. #65082C22semidirect
75. #65028C22semidirect
191. C2×#483D5semidirect
336. #483C2×D5semidirect
667. C2×C5#3312semidirect
737. C5C2×#3312semidirect
767. C2#10613182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659662
C2×#658472
C2×C5×#4832
C2×#653402
C22×#39422
#106131822
C2×#651462
C2×#651572
C2×#651562
C2×#651422
C2×#650822
C2×#650972
C2×#650912
C2×#650862
C2×#650282
C2×#650192
C2×#33125