Finite Group Databasebeta

← C2×#10610542 #12975886

Subgroups — C2×#10610542 #12975886

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66151C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic, complemented
3C22×C5×#103C211yesmaximal, characteristic, complemented
4C2×#65517C211yesmaximal, characteristic, complemented
5C2×#65403C211yesmaximal, characteristic, complemented
6C2×#65400C211yesmaximal, characteristic, complemented
7C2×#65257C211yesmaximal, characteristic, complemented
8C2×#65087C211yesmaximal, characteristic, complemented
9#10610542C2116yesmaximal, direct product factor
10C2×#65094C211yesmaximal, characteristic, complemented
11C2×#65105C211yesmaximal, characteristic, complemented
12C2×#65099C211yesmaximal, characteristic, complemented
13C2×#65092C211yesmaximal, characteristic, complemented
14C2×#65084C211yesmaximal, characteristic, complemented
15C2×#65080C211yesmaximal, characteristic, complemented
16C2×#65078C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C22×#713C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21#66151—24no—
22#66151C2218yes—
23C2×#4093—21no—
24C2×#4093C2211yescharacteristic
25C2×#4092—21no—
26C2×#4092C2211yescharacteristic
27C2×Q8×Dic5C2211yescharacteristic
28C22×#689C2211yescharacteristic
29C22×#689C2211yescharacteristic
30C2×#4076—21no—
31C2×#4076C2211yescharacteristic
32C2×C4×C22⋊D5—21no—
33C2×C4×C22⋊D5—21no—
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4070—21no—
36C2×#4070C2211yescharacteristic
37C22×#677C2211yescharacteristic
38C22×#676C2211yescharacteristic
39#65845—24no—
40#65845C2218yescomplemented
41C2×#4043C2211yescharacteristic
42C2×#4042—21no—
43C2×D5×C4⋊C4C2211yescharacteristic
44C2×#4035—21no—
45C2×#4034C2211yescharacteristic
46C2×#4033C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#103C2218yescomplemented
52#65517C2218yescomplemented
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56#65403C2218yescomplemented
57C2×#3953C2211yescharacteristic
58#65400C2218yescomplemented
59C2×#3952C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×#3946C2211yescharacteristic
64#65257C2218yescomplemented
65C2×#3941C2211yescharacteristic
66C2×#3941C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69#65105C2218yescomplemented
70#65099C2218yescomplemented
71#65094C2218yescomplemented
72#65092C2218yescomplemented
73#65087C2218yescomplemented
74#65084C2218yescomplemented
75#65080C2218yescomplemented
76#65078C2218yescomplemented
77C2×#3316—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8—22no—
80C22×C5×Q8—24no—
81C22×C5×Q8—42no—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2314yes—
84C22×C5×Q8C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—21no—
89C22×C22⋊D5D411yescharacteristic
90C2×#713—22no—
91C2×#713—24no—
92C2×#713—42no—
93C2×#713C2314yes—
94C22×D20—21no—
95C22×D20C2311yescharacteristic
96C22×C4×D5—21no—
97C22×C4×D5—21no—
98C22×C4×D5C2311yescharacteristic
99C22×Dic10—21no—
100C22×Dic10C2311yescharacteristic
101C22×C5×C8—42no—
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2314yes—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2314yes—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5D411yescharacteristic
112#4093—28no—
113#4093—22no—
114#4093C2314yes—
115#4092—22no—
116#4092—28no—
117#4092C2314yes—
118Q8×Dic5—22no—
119Q8×Dic5C2314yes—
120C2×#689—24no—
121C2×#689—42no—
122C2×#689C2314yes—
123C2×#689C2314yes—
124#4076—22no—
125#4076—28no—
126#4076C2314yes—
127C4×C22⋊D5—28no—
128C4×C22⋊D5—28no—
129C4×C22⋊D5D414yes—
130C4×C22⋊D5C2314yes—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685D411yescharacteristic
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141#4070—22no—
142#4070—28no—
143#4070C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683D411yescharacteristic
150C2×C4×Dic5—21no—
151C2×C4×Dic5—21no—
152C2×C4×Dic5C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C2×#677—42no—
156C2×#677C2314yes—
157C2×#676—42no—
158C2×#676C2314yes—
159#4043—22no—
160#4043C2314yes—
161#4042—28no—
162D5×C4⋊C4—22no—
163D5×C4⋊C4C2314yes—
164#4035—28no—
165#4034—22no—
166#4034C2314yes—
167#4033—22no—
168#4033C2314yes—
169C5×#103C2314yes—
170C5×#103C2314yes—
171C5×#103C2314yes—
172C5×#103C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175C22⋊#168C2314yes—
176#3953C2314yes—
177#3952C2314yes—
178#3949C2314yes—
179#3948C2314yes—
180#3947C2314yes—
181#3946C2314yes—
182#3941C2314yes—
183#3941C2314yes—
184#3940C2314yes—
185#3940C2314yes—
186C2×#554—51no—
187C2×#548—51no—
188#3316—516no—
189C2×#489—51no—
190C2×#481—51no—
191C2×#483—51no—
192C2×#475—51no—
193C2×#470—51no—
194C2×#465—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#417—51no—
201C22×#103D511yescharacteristic, complemented
202C24×C5C2×D411yescharacteristic
203C23×D5—21no—
204C23×D5C2×D411yescharacteristic
205C2×C5×Q8—21no—
206C2×C5×Q8—24no—
207C2×C5×Q8—21no—
208C2×C5×Q8—22no—
209C2×C5×Q8—28no—
210C2×C5×Q8—22no—
211C2×C5×Q8—22no—
212C2×C5×Q8—44no—
213C2×C5×Q8—44no—
214C2×C5×Q8—48no—
215C2×C5×Q8#4114yes—
216C2×C5×Q8C2412yes—
217C2×C5×Q8C2412yes—
218C22×C4×C5—21no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—24no—
225C22×C4×C5—24no—
226C22×C4×C5—44no—
227C22×C4×C5—82no—
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2411yescharacteristic
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5C2×D414yes—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242#713—28no—
243#713—44no—
244#713—48no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—24no—
248C2×D20—21no—
249C2×D20—44no—
250C2×D20C2412yes—
251C2×C4×D5—22no—
252C2×C4×D5—22no—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—44no—
256C2×C4×D5—82no—
257C2×C4×D5C2×D412yes—
258C2×C4×D5C2412yes—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10—24no—
263C2×Dic10—82no—
264C2×Dic10C2412yes—
265C2×C5×C8—22no—
266C2×C5×C8—22no—
267C2×C5×C8—44no—
268C2×C5×C8C2412yes—
269C2×C5×C8C2412yes—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—24no—
273C5×C4⋊C4C2412yes—
274C5×C4⋊C4C2412yes—
275C22⋊Dic5—24no—
276C22⋊Dic5C2×D414yes—
277#689—28no—
278#689—44no—
279#685—24no—
280#685—24no—
281#685—24no—
282#685—24no—
283#685—24no—
284#685C2×D414yes—
285C4⋊Dic5—21no—
286C4⋊Dic5—21no—
287C4⋊Dic5—24no—
288C4⋊Dic5—24no—
289C4⋊Dic5C2412yes—
290C4⋊Dic5C2412yes—
291#683—24no—
292#683—24no—
293#683—24no—
294#683—24no—
295#683—24no—
296#683C2×D414yes—
297C4×Dic5—24no—
298C4×Dic5—24no—
299C4×Dic5C2×D412yes—
300C4×Dic5C2412yes—
301C2×#168—22no—
302C2×#168—22no—
303C2×#168C2412yes—
304C2×#168C2412yes—
305#677—44no—
306#676—44no—
307C22×#41—51no—
308C23×Q8C2×D511yescharacteristic
309C22×Q16—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×M16—51no—
313C23×C8C2×D511yescharacteristic
314#554—58no—
315#554—104no—
316#548—58no—
317#548—104no—
318C2×C4⋊Q8—51no—
319C2×#125—101no—
320C2×#124—51no—
321C2×#124—101no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C22⋊Q8—101no—
328C2×#121—51no—
329C2×#121—101no—
330C2×C4×Q8—51no—
331C2×C4×Q8—51no—
332C2×C4×D4—51no—
333C2×C4×D4—101no—
334C2×C4×D4—101no—
335C22×C4⋊C4—51no—
336C22×C4⋊C4C2×D511yescharacteristic
337#489—58no—
338#483—58no—
339#481—58no—
340#475—58no—
341#470—58no—
342#465—58no—
343#464—58no—
344#452—58no—
345#451—58no—
346#441—58no—
347#435—58no—
348C2×#106—51no—
349C2×#106—51no—
350C2×#106—51no—
351C2×C4⋊C8—51no—
352#417—58no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103C2×D511yescharacteristic
357C2×#103C2×D511yescharacteristic
358C2×#103C2×D511yescharacteristic
359C2×#103C2×D511yescharacteristic
360C2×#103C2×D518yescomplemented
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×C22⋊C8—51no—
365C2×C22⋊C8—51no—
366C2×#97—51no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5#13714yes—
370C23×C5C22×D412yes—
371C23×C5C22×D411yescharacteristic
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—42no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5C22×D412yes—
380C5×Q8—24no—
381C5×Q8—22no—
382C5×Q8—22no—
383C5×Q8—22no—
384C5×Q8—48no—
385C5×Q8—42no—
386C5×Q8C2×#4114yes—
387C2×C4×C5—24no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—24no—
391C2×C4×C5—22no—
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×C5—42no—
400C2×C4×C5—84no—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D411yescharacteristic
403C2×C4×C5C2×#4112yes—
404C2×C4×C5H(5,𝔽2)12yes—
405C2×C4×C5C2511yescharacteristic
406C22⋊D5—28no—
407C22⋊D5—48no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5C22×D412yes—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420D20—22no—
421D20—22no—
422D20—48no—
423D20—42no—
424C4×D5—24no—
425C4×D5—22no—
426C4×D5—22no—
427C4×D5—48no—
428C4×D5—84no—
429Dic10—22no—
430Dic10—22no—
431Dic10—42no—
432Dic10—84no—
433C5×C8—22no—
434C5×C8—22no—
435#168—22no—
436#168—22no—
437C2×#41—54no—
438C2×#41—102no—
439C2×#41—104no—
440C2×#41—202no—
441C22×Q8—21no—
442C22×Q8—22no—
443C22×Q8—24no—
444C22×Q8—42no—
445C22×Q8—51no—
446C22×Q8—101no—
447C22×Q8C22×D511yescharacteristic
448C22×Q8C22×D514yes—
449C22×Q8C22×D511yescharacteristic
450C22×D4—51no—
451C22×D4—51no—
452C22×D4—101no—
453C22×D4—101no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—51no—
457C23×C4—101no—
458C23×C4—101no—
459C23×C4C22×D511yescharacteristic
460C2×Q16—54no—
461C2×Q16—54no—
462C2×Q16—104no—
463C2×Q16—202no—
464C2×SD16—54no—
465C2×SD16—202no—
466C2×M16—54no—
467C2×M16—202no—
468C22×C8—42no—
469C22×C8—51no—
470C22×C8—51no—
471C22×C8C22×D511yescharacteristic
472C22×C8C22×D511yescharacteristic
473C22×C8C22×D514yes—
474C4⋊Q8—54no—
475C4⋊Q8—102no—
476#125—108no—
477#124—54no—
478#124—102no—
479#124—108no—
480C22⋊Q8—54no—
481C22⋊Q8—54no—
482C22⋊Q8—54no—
483C22⋊Q8—108no—
484C22⋊Q8—108no—
485C22⋊Q8—102no—
486C22⋊Q8—108no—
487C22⋊Q8—102no—
488C22⋊Q8—102no—
489#121—54no—
490#121—108no—
491#121—102no—
492C4×Q8—54no—
493C4×Q8—54no—
494C4×Q8—102no—
495C4×Q8—102no—
496C4×D4—54no—
497C4×D4—54no—
498C4×D4—108no—
499C4×D4—108no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—51no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—102no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—101no—
509C2×C4⋊C4—101no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4C22×D511yescharacteristic
515C2×C4⋊C4C22×D511yescharacteristic
516C2×C4⋊C4C22×D514yes—
517C2×C22⋊C4—51no—
518C2×C22⋊C4—51no—
519C2×C22⋊C4—101no—
520C2×C22⋊C4—101no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C42—51no—
526C2×C42—101no—
527C2×C42—101no—
528#106—54no—
529#106—54no—
530#106—54no—
531C4⋊C8—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#103C22×D514yes—
536#103C22×D514yes—
537#103C22×D514yes—
538#103C22×D514yes—
539#102—54no—
540#102—54no—
541#102—54no—
542C22⋊C8—54no—
543C22⋊C8—54no—
544#97—54no—
545C22×C5—22no—
546C22×C5—28no—
547C22×C5—22no—
548C22×C5#54612yes—
549C22×C5C2×#13714yes—
550C22×C5C2×#13712yes—
551C22×C5#57712yes—
552C22×C5C23×D411yescharacteristic
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5—44no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—84no—
561C4×C5—24no—
562C4×C5—22no—
563C4×C5—42no—
564C4×C5—42no—
565C4×C5—42no—
566C4×C5#54612yes—
567C4×C5C22×#4111yescharacteristic
568C4×C5C2×H(5,𝔽2)11yescharacteristic
569Dic5—22no—
570Dic5—22no—
571Dic5—22no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575C24—51no—
576C24—101no—
577C24D4×D511yescharacteristic
578#41—108no—
579#41—204no—
580#41—208no—
581C2×Q8—21no—
582C2×Q8—24no—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—28no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—48no—
591C2×Q8—52no—
592C2×Q8—104no—
593C2×Q8—101no—
594C2×Q8—102no—
595C2×Q8—102no—
596C2×Q8—402no—
597C2×Q8#70914yes—
598C2×Q8C23×D512yes—
599C2×Q8C23×D512yes—
600C2×D4—54no—
601C2×D4—52no—
602C2×D4—104no—
603C2×D4—104no—
604C2×D4—104no—
605C2×D4—102no—
606C2×D4—101no—
607C2×D4—102no—
608C2×D4—204no—
609C2×D4—204no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—44no—
619C22×C4—51no—
620C22×C4—51no—
621C22×C4—51no—
622C22×C4—52no—
623C22×C4—52no—
624C22×C4—82no—
625C22×C4—104no—
626C22×C4—104no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—204no—
633C22×C4—402no—
634C22×C4D4×D512yes—
635C22×C4D4×D511yescharacteristic
636C22×C4C23×D512yes—
637C22×C4C23×D511yescharacteristic
638Q16—108no—
639Q16—204no—
640SD16—204no—
641M16—204no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—52no—
646C2×C8—52no—
647C2×C8—102no—
648C2×C8—102no—
649C2×C8C23×D512yes—
650C2×C8C23×D512yes—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—54no—
655C4⋊C4—52no—
656C4⋊C4—52no—
657C4⋊C4—104no—
658C4⋊C4—104no—
659C4⋊C4—104no—
660C4⋊C4—104no—
661C4⋊C4—104no—
662C4⋊C4—104no—
663C4⋊C4—101no—
664C4⋊C4—101no—
665C4⋊C4—104no—
666C4⋊C4C23×D512yes—
667C4⋊C4C23×D512yes—
668C22⋊C4—54no—
669C22⋊C4—54no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4—104no—
675C22⋊C4—104no—
676C42—52no—
677C42—52no—
678C42—104no—
679C42—104no—
680C2×C5—24no—
681C2×C5#331614yescomplemented
682C2×C5C2×#54611yescharacteristic
683C2×C5C22×#13711yescharacteristic
684C2×C5C2×#57711yescharacteristic
685D5—42no—
686D5—82no—
687C23—22no—
688C23—22no—
689C23—52no—
690C23—102no—
691C23—102no—
692C23—102no—
693C23—102no—
694C23—202no—
695C23—202no—
696C23—202no—
697C23#406414yes—
698C23C2×D4×D512yes—
699C23C2×D4×D511yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—42no—
706Q8—102no—
707Q8—102no—
708Q8—202no—
709Q8—404no—
710Q8C2×#70914yes—
711D4—108no—
712D4—102no—
713D4—102no—
714D4—208no—
715D4—208no—
716D4—202no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—52no—
731C2×C4—52no—
732C2×C4—52no—
733C2×C4—84no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—104no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—208no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—404no—
748C2×C4C2×#70912yes—
749C2×C4C2×D4×D512yes—
750C2×C4C2×D4×D511yescharacteristic
751C2×C4#414412yes—
752C2×C4C24×D511yescharacteristic
753C8—22no—
754C8—22no—
755C8—102no—
756C8—102no—
757C5C2×#331611yescharacteristic, complemented, Sylow
758C22—28no—
759C22—22no—
760C22—22no—
761C22—102no—
762C22—102no—
763C22—102no—
764C22—204no—
765C22—202no—
766C22—202no—
767C22—202no—
768C22—404no—
769C22#6582412yes—
770C22#6609612yes—
771C22C2×#406414yes—
772C22C2×#406412yes—
773C22C22×D4×D511yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—102no—
780C4—102no—
781C4—102no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4#6582412yes—
786C4C22×#70911yescharacteristic
787C4C2×#414411yescharacteristic
788C2—24no—
789C2—202no—
790C2—402no—
791C2#1061054214yesdirect product factor
792C2C2×#6582411yescharacteristic
793C2C2×#6609611yescharacteristic
794C2C22×#406411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#103C2
socleC23×C5C22×D4
prime radicalC2×#66151C2
hypercenterC22×#103D5
hypocenterC5C2×#3316
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#65845C2semidirect
3. C22×C5×#103C2semidirect
4. C2×#65517C2semidirect
5. C2×#65403C2semidirect
6. C2×#65400C2semidirect
7. C2×#65257C2semidirect
8. C2×#65087C2semidirect
9. #10610542C2direct (N × H)
10. C2×#65094C2semidirect
11. C2×#65105C2semidirect
12. C2×#65099C2semidirect
13. C2×#65092C2semidirect
14. C2×#65084C2semidirect
15. C2×#65080C2semidirect
16. C2×#65078C2semidirect
40. #65845C22semidirect
51. C2×C5×#103C22semidirect
52. #65517C22semidirect
56. #65403C22semidirect
58. #65400C22semidirect
64. #65257C22semidirect
69. #65105C22semidirect
70. #65099C22semidirect
71. #65094C22semidirect
72. #65092C22semidirect
73. #65087C22semidirect
74. #65084C22semidirect
75. #65080C22semidirect
76. #65078C22semidirect
201. C22×#103D5semidirect
360. C2×#103C2×D5semidirect
681. C2×C5#3316semidirect
757. C5C2×#3316semidirect
791. C2#10610542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661512
C2×#658452
C22×C5×#1032
C2×#655172
C2×#654032
C2×#654002
C2×#652572
C2×#650872
#106105422
C2×#650942
C2×#651052
C2×#650992
C2×#650922
C2×#650842
C2×#650802
C2×#650782
C2×#33165