Finite Group Databasebeta

← C2×#10612224 #12975913

Subgroups — C2×#10612224 #12975913

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×#66061C211yesmaximal, characteristic
2C2×#65915C211yesmaximal, characteristic
3C2×C5×#462C211yesmaximal, characteristic, complemented
4C2×#65478C211yesmaximal, characteristic, complemented
5C2×#65477C211yesmaximal, characteristic, complemented
6C2×#65475C211yesmaximal, characteristic, complemented
7C2×#65475C211yesmaximal, characteristic, complemented
8C2×#65371C211yesmaximal, characteristic, complemented
9C2×#65319C211yesmaximal, characteristic, complemented
10#10612224C2116yesmaximal, direct product factor
11C2×#65118C211yesmaximal, characteristic, complemented
12C2×#65125C211yesmaximal, characteristic
13C2×#65094C211yesmaximal, characteristic, complemented
14C2×#65091C211yesmaximal, characteristic, complemented
15C2×D5×#103C211yesmaximal, characteristic, complemented
16C2×#65103C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×C5×Q16C2211yescharacteristic
20C22×C5×Q16C2211yescharacteristic
21C2×C5×C4⋊Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×#4092C2211yescharacteristic
24C2×#4092C2211yescharacteristic
25C2×#4092C2211yescharacteristic
26C2×#4092C2211yescharacteristic
27C22×#689C2211yescharacteristic
28C22×#676C2211yescharacteristic
29C22×C8×D5C2211yescharacteristic
30#66061—24no—
31#66061C2218yes—
32#65915—24no—
33#65915C2218yes—
34C2×#4042—21no—
35C2×#4042—21no—
36C2×#4040—21no—
37C2×#4039—21no—
38C2×#4038C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×#4035—21no—
41C2×#4034—21no—
42C2×#4022—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4018—21no—
45C2×#4016C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#462C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56#65478C2218yescomplemented
57#65477C2218yescomplemented
58#65475C2218yescomplemented
59#65475C2218yescomplemented
60C2×#3952C2211yescharacteristic
61C2×#3952C2211yescharacteristic
62C2×#3950C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66#65371C2218yescomplemented
67#65319C2218yescomplemented
68C2×#3942C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3935C2211yescharacteristic
71#65125C2218yes—
72#65118C2218yescomplemented
73#65103C2218yescomplemented
74#65094C2218yescomplemented
75#65091C2218yescomplemented
76D5×#103C2218yescomplemented
77C2×#3312—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×Q8C2311yescharacteristic
81C2×Q8×D5—22no—
82C2×Q8×D5—22no—
83C2×Q8×D5—24no—
84C2×Q8×D5—24no—
85C2×Q8×D5—42no—
86C2×Q8×D5—42no—
87C2×Q8×D5C2314yes—
88C2×Q8×D5C2314yes—
89C22×D20D411yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×C4×D5C2311yescharacteristic
95C22×Dic10—21no—
96C22×Dic10—21no—
97C22×Dic10C2311yescharacteristic
98C2×C5×Q16—42no—
99C2×C5×Q16—42no—
100C2×C5×Q16C2314yes—
101C2×C5×Q16C2314yes—
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C5×C4⋊Q8—22no—
105C5×C4⋊Q8C2314yes—
106C4×C5×Q8—22no—
107C4×C5×Q8C2314yes—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C42×C5—21no—
113C2×C42×C5C2311yescharacteristic
114#4092—22no—
115#4092—22no—
116#4092—22no—
117#4092—22no—
118#4092C2314yes—
119#4092C2314yes—
120#4092C2314yes—
121#4092C2314yes—
122C2×#689—24no—
123C2×#689C2314yes—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685—21no—
129C2×#685D411yescharacteristic
130C2×#685D411yescharacteristic
131C2×C4⋊Dic5D411yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5—21no—
145C22×#168C2311yescharacteristic
146C22×#168C2311yescharacteristic
147C2×#676—42no—
148C2×#676C2314yes—
149C2×C8×D5—42no—
150C2×C8×D5C2314yes—
151#4042—28no—
152#4042—28no—
153#4040—28no—
154#4039—28no—
155#4038—22no—
156#4038C2314yes—
157D5×C4⋊C4—22no—
158D5×C4⋊C4C2314yes—
159#4035—28no—
160#4034—28no—
161#4022—28no—
162C4×D20D414yes—
163C4×D20C2314yes—
164#4018—28no—
165#4016—22no—
166#4016C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yes—
169C5×C4⋊C8C2314yes—
170C5×#103C2314yes—
171C5×#103C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176#3967C2314yes—
177#3952C2314yes—
178#3952C2314yes—
179#3950C2314yes—
180#3949C2314yes—
181#3948C2314yes—
182#3948C2314yes—
183#3942C2314yes—
184#3940C2314yes—
185#3935C2314yes—
186C2×#552—51no—
187C2×D4×Q8—51no—
188#3312—516no—
189C2×#491—51no—
190C2×#485—51no—
191C2×#483—51no—
192C2×#479—51no—
193C2×#470—51no—
194C2×#467—51no—
195C2×#462D511yescharacteristic, complemented
196C2×#451—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#419—51no—
201C22×#103—51no—
202C23×D5C2×D411yescharacteristic
203C23×D5C2×D411yescharacteristic
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×Q8—22no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8C2412yes—
214C2×C5×Q8C2412yes—
215C2×C5×Q8C2412yes—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2411yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229Q8×D5—28no—
230Q8×D5—28no—
231Q8×D5—44no—
232Q8×D5—44no—
233Q8×D5—48no—
234Q8×D5—48no—
235C2×D20—24no—
236C2×D20C2×D414yes—
237C2×C4×D5—22no—
238C2×C4×D5—22no—
239C2×C4×D5—22no—
240C2×C4×D5—22no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—24no—
244C2×C4×D5—44no—
245C2×C4×D5—44no—
246C2×C4×D5—44no—
247C2×C4×D5C2×D412yes—
248C2×C4×D5C2×D412yes—
249C2×C4×D5C2412yes—
250C2×C4×D5C2412yes—
251C2×Dic10—21no—
252C2×Dic10—22no—
253C2×Dic10—24no—
254C2×Dic10—24no—
255C2×Dic10—44no—
256C2×Dic10—44no—
257C2×Dic10#4114yes—
258C2×Dic10C2412yes—
259C5×Q16—44no—
260C5×Q16—44no—
261C2×C5×C8—22no—
262C2×C5×C8—22no—
263C2×C5×C8C2412yes—
264C2×C5×C8C2412yes—
265C5×C4⋊C4—24no—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4C2412yes—
270C42×C5—24no—
271C42×C5C2×D412yes—
272C42×C5C2412yes—
273#689—28no—
274#685—24no—
275#685—24no—
276#685—24no—
277#685—24no—
278#685—24no—
279#685C2×D414yes—
280#685C2×D414yes—
281C4⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5C2×D414yes—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292#683—24no—
293#683—24no—
294#683—24no—
295#683—24no—
296C4×Dic5—24no—
297C4×Dic5—24no—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168C2412yes—
301C2×#168C2412yes—
302#676—44no—
303C8×D5—44no—
304C23×Q8—51no—
305C23×Q8—51no—
306C22×Q16—51no—
307C22×Q16C2×D511yescharacteristic
308C22×Q16C2×D511yescharacteristic
309C22×M16—51no—
310C23×C8—51no—
311#552—58no—
312#552—104no—
313D4×Q8—58no—
314D4×Q8—104no—
315C2×C4⋊Q8—101no—
316C2×C4⋊Q8C2×D511yescharacteristic
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—51no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C4×Q8—51no—
328C2×C4×Q8C2×D511yescharacteristic
329C2×C4×D4—51no—
330C2×C4×D4—101no—
331C2×#117—51no—
332C2×#117—101no—
333C22×C4⋊C4—51no—
334#491—58no—
335#485—58no—
336#483—58no—
337#479—58no—
338#470—58no—
339#467—58no—
340#462C2×D518yescomplemented
341#451—58no—
342#451—58no—
343#441—58no—
344#435—58no—
345C2×#107—51no—
346C2×#106—51no—
347C2×#106—51no—
348C2×C4⋊C8C2×D511yescharacteristic
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—51no—
358C2×#103—58no—
359C2×#103C2×D511yescharacteristic
360C2×#103C2×D511yescharacteristic
361C2×C22⋊C8—51no—
362C2×C22⋊C8—51no—
363C2×#97—51no—
364C23×C5C22×D411yescharacteristic
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5#13714yes—
371C22×D5C22×D412yes—
372C22×D5C22×D412yes—
373C5×Q8—22no—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—22no—
377C5×Q8—22no—
378C5×Q8—22no—
379C5×Q8—42no—
380C5×Q8—42no—
381C5×Q8—42no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5C22×D412yes—
393C2×C4×C5C22×D412yes—
394C2×C4×C5C22×D411yescharacteristic
395C2×C4×C5C2×#4112yes—
396C2×C4×C5H(5,𝔽2)12yes—
397C2×C4×C5C2511yescharacteristic
398C2×Dic5—24no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—42no—
408C2×Dic5C22×D412yes—
409C2×Dic5C22×D412yes—
410D20—28no—
411C4×D5—24no—
412C4×D5—24no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—22no—
416C4×D5—22no—
417C4×D5—48no—
418C4×D5—48no—
419C4×D5—48no—
420Dic10—24no—
421Dic10—22no—
422Dic10—48no—
423Dic10—48no—
424Dic10C2×#4114yes—
425C5×C8—22no—
426C5×C8—22no—
427#168—22no—
428#168—22no—
429C22×Q8—54no—
430C22×Q8—54no—
431C22×Q8—51no—
432C22×Q8—101no—
433C22×Q8—101no—
434C22×Q8—102no—
435C22×Q8—102no—
436C22×Q8—104no—
437C22×Q8—104no—
438C22×Q8—202no—
439C22×Q8—202no—
440C22×Q8C22×D511yescharacteristic
441C22×Q8C22×D511yescharacteristic
442C22×Q8C22×D511yescharacteristic
443C22×D4—51no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—101no—
447C23×C4—101no—
448C23×C4—101no—
449C2×Q16—42no—
450C2×Q16—42no—
451C2×Q16—54no—
452C2×Q16—104no—
453C2×Q16C22×D514yes—
454C2×Q16C22×D514yes—
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—22no—
464C4⋊Q8—108no—
465C4⋊Q8C22×D514yes—
466#126—108no—
467#125—54no—
468#125—108no—
469#125—102no—
470#123—108no—
471C22⋊Q8—54no—
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⋊Q8—102no—
481C4×Q8—22no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8C22×D514yes—
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—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—51no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—54no—
499C2×C4⋊C4—102no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
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⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—51no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C42—21no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42C22×D511yescharacteristic
520#107—54no—
521#106—54no—
522#106—54no—
523C4⋊C8C22×D514yes—
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⋊C8—54no—
536#97—54no—
537C22×C5#54612yes—
538C22×C5C2×#13712yes—
539C22×C5#57812yes—
540C22×C5C23×D411yescharacteristic
541C2×D5—22no—
542C2×D5—28no—
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—22no—
546C2×D5—22no—
547C2×D5—44no—
548C2×D5C2×#13714yes—
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5—42no—
555C4×C5#54612yes—
556C4×C5C22×#4111yescharacteristic
557C4×C5C2×H(5,𝔽2)11yescharacteristic
558Dic5—24no—
559Dic5—22no—
560Dic5—22no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24—51no—
565C24—51no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—54no—
576C2×Q8—52no—
577C2×Q8—104no—
578C2×Q8—104no—
579C2×Q8—101no—
580C2×Q8—102no—
581C2×Q8—108no—
582C2×Q8—108no—
583C2×Q8—204no—
584C2×Q8—204no—
585C2×Q8—204no—
586C2×Q8—204no—
587C2×Q8—208no—
588C2×Q8—208no—
589C2×Q8C23×D512yes—
590C2×Q8C23×D512yes—
591C2×Q8C23×D512yes—
592C2×D4—54no—
593C2×D4—104no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—52no—
601C22×C4—52no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—104no—
605C22×C4—104no—
606C22×C4—104no—
607C22×C4—101no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4—204no—
618C22×C4D4×D511yescharacteristic
619C22×C4D4×D511yescharacteristic
620C22×C4C23×D511yescharacteristic
621Q16—44no—
622Q16—44no—
623Q16—108no—
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—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—54no—
639C4⋊C4—52no—
640C4⋊C4—52no—
641C4⋊C4—52no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—104no—
646C4⋊C4—104no—
647C4⋊C4—101no—
648C4⋊C4—101no—
649C4⋊C4—101no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4C23×D512yes—
654C22⋊C4—54no—
655C22⋊C4—54no—
656C22⋊C4—104no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C42—24no—
662C42—104no—
663C42—104no—
664C42D4×D512yes—
665C42C23×D512yes—
666C2×C5#331214yescomplemented
667C2×C5C2×#54611yescharacteristic
668C2×C5C22×#13711yescharacteristic
669C2×C5C2×#57811yescharacteristic
670D5—24no—
671D5—42no—
672C23—54no—
673C23—52no—
674C23—52no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23C2×D4×D511yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—54no—
691Q8—104no—
692Q8—102no—
693Q8—208no—
694Q8—208no—
695D4—108no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—52no—
707C2×C4—52no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—104no—
711C2×C4—102no—
712C2×C4—104no—
713C2×C4—104no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—208no—
722C2×C4—208no—
723C2×C4—208no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4C2×D4×D512yes—
728C2×C4C2×D4×D512yes—
729C2×C4C2×D4×D511yescharacteristic
730C2×C4#414412yes—
731C2×C4D5×#4112yes—
732C2×C4C24×D511yescharacteristic
733C8—22no—
734C8—22no—
735C8—102no—
736C8—102no—
737C5C2×#331211yescharacteristic, complemented, Sylow
738C22—54no—
739C22—108no—
740C22—102no—
741C22—102no—
742C22—102no—
743C22—102no—
744C22—102no—
745C22—204no—
746C22#6594612yes—
747C22#6610012yes—
748C22D5×#13712yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—102no—
757C4—102no—
758C4—104no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4#6594612yes—
763C4C2×#414411yescharacteristic
764C4C2×D5×#4111yescharacteristic
765C2—104no—
766C2—202no—
767C2#1061222414yesdirect product factor
768C2C2×#6594611yescharacteristic
769C2C2×#6610011yescharacteristic
770C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#462C2
socleC23×C5C22×D4
prime radicalC22×D20D4
hypercenterC2×#462D5
hypocenterC5C2×#3312
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. C2×C5×#462C2semidirect
4. C2×#65478C2semidirect
5. C2×#65477C2semidirect
6. C2×#65475C2semidirect
7. C2×#65475C2semidirect
8. C2×#65371C2semidirect
9. C2×#65319C2semidirect
10. #10612224C2direct (N × H)
11. C2×#65118C2semidirect
13. C2×#65094C2semidirect
14. C2×#65091C2semidirect
15. C2×D5×#103C2semidirect
16. C2×#65103C2semidirect
47. C5×#462C22semidirect
56. #65478C22semidirect
57. #65477C22semidirect
58. #65475C22semidirect
59. #65475C22semidirect
66. #65371C22semidirect
67. #65319C22semidirect
72. #65118C22semidirect
73. #65103C22semidirect
74. #65094C22semidirect
75. #65091C22semidirect
76. D5×#103C22semidirect
195. C2×#462D5semidirect
340. #462C2×D5semidirect
666. C2×C5#3312semidirect
737. C5C2×#3312semidirect
767. C2#10612224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660612
C2×#659152
C2×C5×#4622
C2×#654782
C2×#654772
C2×#654752
C2×#653712
C2×#653192
#106122242
C2×#651182
C2×#651252
C2×#650942
C2×#650912
C2×D5×#1032
C2×#651032
C2×#33125