Finite Group Databasebeta

← C2×#10612423 #12975896

Subgroups — C2×#10612423 #12975896

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×#65969C211yesmaximal, characteristic, complemented
2C2×#65932C211yesmaximal, characteristic
3C2×C5×#465C211yesmaximal, characteristic, complemented
4C2×#65462C211yesmaximal, characteristic, complemented
5C2×#65455C211yesmaximal, characteristic, complemented
6C22×#3948C211yesmaximal, characteristic, complemented
7C2×#65400C211yesmaximal, characteristic, complemented
8C2×#65339C211yesmaximal, characteristic, complemented
9C2×#65323C211yesmaximal, characteristic, complemented
10#10612423C2116yesmaximal, direct product factor
11C2×#65143C211yesmaximal, characteristic, complemented
12C2×#65151C211yesmaximal, characteristic, complemented
13C2×#65105C211yesmaximal, characteristic, complemented
14C2×#65078C211yesmaximal, characteristic, complemented
15C2×#65060C211yesmaximal, characteristic, complemented
16C2×#65054C211yesmaximal, characteristic, complemented
17C22×#711C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic
23C2×#4092C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C22×#689C2211yescharacteristic
26C22×#689C2211yescharacteristic
27C2×#4085—21no—
28C2×#4082C2211yescharacteristic
29C2×D4×Dic5—21no—
30C2×C4×C22⋊D5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×#676C2211yescharacteristic
33#65969—24no—
34#65969C2218yescomplemented
35#65932—24no—
36#65932C2218yes—
37C2×#4043—21no—
38C2×#4043C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×#4035—21no—
41C2×#4034C2211yescharacteristic
42C2×#4033C2211yescharacteristic
43C2×#4031—21no—
44C2×#4027—21no—
45C2×#4024—21no—
46C2×#4024—21no—
47C5×#465C2218yescomplemented
48C2×C5×#106C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×#102C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic
54#65462C2218yescomplemented
55#65455C2218yescomplemented
56#65400C2218yescomplemented
57C2×#3952C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3948C2218yescomplemented
63C2×#3947C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65#65339C2218yescomplemented
66#65323C2218yescomplemented
67C2×#3942C2211yescharacteristic
68C2×#3942C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71#65151C2218yescomplemented
72#65143C2218yescomplemented
73#65105C2218yescomplemented
74#65078C2218yescomplemented
75#65060C2218yescomplemented
76#65054C2218yescomplemented
77C2×#3316—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#711—22no—
88C2×#711—24no—
89C2×#711—42no—
90C2×#711C2314yes—
91C22×C4×D5—21no—
92C22×C4×D5C2311yescharacteristic
93C22×Dic10—24no—
94C22×Dic10—21no—
95C22×Dic10—22no—
96C22×Dic10—21no—
97C22×Dic10—42no—
98C22×Dic10C2311yescharacteristic
99C22×Dic10C2314yes—
100C22×Dic10C2311yescharacteristic
101C2×C5×SD16—42no—
102C2×C5×SD16C2314yes—
103C22×C5×C8—42no—
104C22×C5×C8C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2314yes—
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8C2314yes—
109C5×#121—22no—
110C5×#121C2314yes—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5D411yescharacteristic
119#4092—22no—
120#4092C2314yes—
121Q8×Dic5—22no—
122Q8×Dic5C2314yes—
123C2×#689—24no—
124C2×#689—42no—
125C2×#689C2314yes—
126C2×#689C2314yes—
127#4085—28no—
128#4082—22no—
129#4082C2314yes—
130D4×Dic5—28no—
131C4×C22⋊D5D414yes—
132C4×C22⋊D5C2314yes—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685D411yescharacteristic
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—22no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2314yes—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683D411yescharacteristic
148C2×C4×Dic5—21no—
149C2×C4×Dic5—21no—
150C2×C4×Dic5C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C2×#676—42no—
154C2×#676C2314yes—
155#4043—22no—
156#4043—28no—
157#4043C2314yes—
158D5×C4⋊C4—22no—
159D5×C4⋊C4C2314yes—
160#4035—28no—
161#4034—22no—
162#4034C2314yes—
163#4033—22no—
164#4033C2314yes—
165#4031—28no—
166#4027—28no—
167#4024—28no—
168#4024—28no—
169C5×#106C2314yes—
170C5×#103C2314yes—
171C5×#102C2314yes—
172#3964C2314yes—
173#3964C2314yes—
174C22⋊#168C2314yes—
175#3952C2314yes—
176#3948C2314yes—
177#3948C2314yes—
178#3948C2314yes—
179#3948C2314yes—
180#3947C2314yes—
181#3946C2314yes—
182#3942C2314yes—
183#3942C2314yes—
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×#465D511yescharacteristic, complemented
195C2×#464—51no—
196C2×#452—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#417—51no—
201C22×#103—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5C2×D411yescharacteristic
205C2×C5×Q8—21no—
206C2×C5×Q8—22no—
207C2×C5×Q8—22no—
208C2×C5×Q8C2412yes—
209C2×C5×D4—24no—
210C2×C5×D4—21no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—44no—
214C2×C5×D4C2412yes—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2411yescharacteristic
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5C2×D414yes—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—24no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—24no—
234C22×Dic5—24no—
235C22×Dic5—44no—
236C22×Dic5—44no—
237C22×Dic5—82no—
238C22×Dic5C2×D411yescharacteristic
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241#711—28no—
242#711—44no—
243#711—48no—
244C2×C4×D5—22no—
245C2×C4×D5—22no—
246C2×C4×D5—24no—
247C2×C4×D5—82no—
248C2×C4×D5C2×D412yes—
249C2×C4×D5C2412yes—
250C2×Dic10—21no—
251C2×Dic10—22no—
252C2×Dic10—22no—
253C2×Dic10—22no—
254C2×Dic10—28no—
255C2×Dic10—24no—
256C2×Dic10—21no—
257C2×Dic10—24no—
258C2×Dic10—44no—
259C2×Dic10—48no—
260C2×Dic10—44no—
261C2×Dic10—82no—
262C2×Dic10#4114yes—
263C2×Dic10C2412yes—
264C2×Dic10C2412yes—
265C5×SD16—44no—
266C2×C5×C8—22no—
267C2×C5×C8—22no—
268C2×C5×C8—44no—
269C2×C5×C8C2412yes—
270C2×C5×C8C2412yes—
271C5×C4⋊C4—24no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4C2412yes—
275C5×C4⋊C4C2412yes—
276C5×C22⋊C4—24no—
277C5×C22⋊C4—24no—
278C22⋊Dic5—24no—
279C22⋊Dic5—24no—
280C22⋊Dic5C2×D414yes—
281#689—28no—
282#689—44no—
283#685—24no—
284#685—24no—
285#685C2×D414yes—
286C4⋊Dic5—21no—
287C4⋊Dic5—24no—
288C4⋊Dic5—21no—
289C4⋊Dic5—24no—
290C4⋊Dic5—24no—
291C4⋊Dic5C2412yes—
292C4⋊Dic5C2412yes—
293#683—24no—
294#683—24no—
295#683—24no—
296#683—24no—
297#683C2×D414yes—
298C4×Dic5—24no—
299C4×Dic5—24no—
300C4×Dic5C2×D412yes—
301C4×Dic5C2412yes—
302C2×#168—22no—
303C2×#168—22no—
304C2×#168C2412yes—
305C2×#168C2412yes—
306#676—44no—
307C22×#41—51no—
308C23×Q8—51no—
309C22×Q16—51no—
310C22×Q16—51no—
311C22×SD16C2×D511yescharacteristic
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—101no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C22⋊Q8C2×D511yescharacteristic
328C2×#121—101no—
329C2×#121C2×D511yescharacteristic
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⋊C4—51no—
337#489—58no—
338#483—58no—
339#481—58no—
340#475—58no—
341#470—58no—
342#465C2×D518yescomplemented
343#464—58no—
344#452—58no—
345#451—58no—
346#441—58no—
347#435—58no—
348C2×#106—51no—
349C2×#106—51no—
350C2×#106C2×D511yescharacteristic
351C2×C4⋊C8—51no—
352#417—58no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103C2×D511yescharacteristic
361C2×#102—51no—
362C2×#102—51no—
363C2×#102C2×D511yescharacteristic
364C2×C22⋊C8—51no—
365C2×C22⋊C8—51no—
366C2×#97—51no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—42no—
371C23×C5—42no—
372C23×C5—42no—
373C23×C5#13714yes—
374C23×C5C22×D412yes—
375C23×C5C22×D411yescharacteristic
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5C22×D412yes—
380C5×Q8—22no—
381C5×Q8—22no—
382C5×Q8—42no—
383C5×D4—22no—
384C5×D4—22no—
385C5×D4—48no—
386C5×D4—42no—
387C2×C4×C5—22no—
388C2×C4×C5—24no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5—42no—
397C2×C4×C5C22×D412yes—
398C2×C4×C5C22×D411yescharacteristic
399C2×C4×C5C2×#4112yes—
400C2×C4×C5H(5,𝔽2)12yes—
401C2×C4×C5C2511yescharacteristic
402C22⋊D5—28no—
403C22⋊D5—48no—
404C2×Dic5—24no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—48no—
413C2×Dic5—48no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5—84no—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420C2×Dic5C22×D412yes—
421C4×D5—24no—
422C4×D5—22no—
423C4×D5—22no—
424C4×D5—84no—
425Dic10—24no—
426Dic10—22no—
427Dic10—22no—
428Dic10—22no—
429Dic10—48no—
430Dic10—42no—
431Dic10—84no—
432Dic10C2×#4114yes—
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—51no—
442C22×Q8—51no—
443C22×Q8—54no—
444C22×Q8—101no—
445C22×Q8—104no—
446C22×Q8—101no—
447C22×Q8—102no—
448C22×Q8—202no—
449C22×Q8C22×D511yescharacteristic
450C22×D4—21no—
451C22×D4—51no—
452C22×D4—101no—
453C22×D4C22×D511yescharacteristic
454C23×C4—51no—
455C23×C4—101no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4—101no—
459C23×C4C22×D511yescharacteristic
460C2×Q16—54no—
461C2×Q16—54no—
462C2×Q16—104no—
463C2×Q16—202no—
464C2×SD16—42no—
465C2×SD16C22×D514yes—
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—22no—
481C22⋊Q8—54no—
482C22⋊Q8—54no—
483C22⋊Q8—108no—
484C22⋊Q8—108no—
485C22⋊Q8—108no—
486C22⋊Q8—102no—
487C22⋊Q8—102no—
488C22⋊Q8C22×D514yes—
489#121—22no—
490#121—108no—
491#121C22×D514yes—
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—51no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—54no—
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⋊C4—102no—
515C2×C4⋊C4C22×D511yescharacteristic
516C2×C4⋊C4C22×D511yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—51no—
520C2×C22⋊C4—51no—
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#106C22×D514yes—
531C4⋊C8—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#103—54no—
536#103—54no—
537#103—54no—
538#103C22×D514yes—
539#102—54no—
540#102—54no—
541#102C22×D514yes—
542C22⋊C8—54no—
543C22⋊C8—54no—
544#97—54no—
545C22×C5—22no—
546C22×C5—28no—
547C22×C5—22no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—84no—
552C22×C5#54612yes—
553C22×C5C2×#13714yes—
554C22×C5C2×#13712yes—
555C22×C5#57712yes—
556C22×C5C23×D411yescharacteristic
557C2×D5—22no—
558C2×D5—22no—
559C2×D5—22no—
560C2×D5—44no—
561C4×C5—22no—
562C4×C5—42no—
563C4×C5—42no—
564C4×C5—42no—
565C4×C5#54612yes—
566C4×C5C22×#4111yescharacteristic
567C4×C5C2×H(5,𝔽2)11yescharacteristic
568Dic5—24no—
569Dic5—22no—
570Dic5—22no—
571Dic5—22no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575C24—21no—
576C24—51no—
577C24D4×D511yescharacteristic
578#41—108no—
579#41—204no—
580#41—208no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—54no—
585C2×Q8—52no—
586C2×Q8—52no—
587C2×Q8—104no—
588C2×Q8—108no—
589C2×Q8—101no—
590C2×Q8—104no—
591C2×Q8—101no—
592C2×Q8—102no—
593C2×Q8—102no—
594C2×Q8—102no—
595C2×Q8—204no—
596C2×Q8—204no—
597C2×Q8—208no—
598C2×Q8—402no—
599C2×Q8C23×D512yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—44no—
605C2×D4—54no—
606C2×D4—104no—
607C2×D4—104no—
608C2×D4—204no—
609C2×D4C23×D512yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—51no—
616C22×C4—51no—
617C22×C4—51no—
618C22×C4—52no—
619C22×C4—52no—
620C22×C4—104no—
621C22×C4—104no—
622C22×C4—101no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—104no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—104no—
630C22×C4—204no—
631C22×C4—204no—
632C22×C4—402no—
633C22×C4—402no—
634C22×C4D4×D512yes—
635C22×C4D4×D511yescharacteristic
636C22×C4C23×D512yes—
637C22×C4C23×D511yescharacteristic
638Q16—108no—
639Q16—204no—
640SD16—44no—
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—24no—
652C4⋊C4—21no—
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—104no—
665C4⋊C4—101no—
666C4⋊C4C23×D512yes—
667C4⋊C4C23×D512yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—54no—
671C22⋊C4—54no—
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—82no—
682C2×C5#331614yescomplemented
683C2×C5C2×#54611yescharacteristic
684C2×C5C22×#13711yescharacteristic
685C2×C5C2×#57711yescharacteristic
686D5—42no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—52no—
694C23—102no—
695C23—102no—
696C23—102no—
697C23#406114yes—
698C23C2×D4×D512yes—
699C23C2×D4×D511yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—42no—
703Q8—54no—
704Q8—104no—
705Q8—102no—
706Q8—102no—
707Q8—102no—
708Q8—208no—
709Q8—202no—
710Q8—404no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—42no—
715D4—108no—
716D4—208no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—52no—
728C2×C4—52no—
729C2×C4—52no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—104no—
734C2×C4—102no—
735C2×C4—104no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—208no—
742C2×C4—208no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—404no—
747C2×C4—404no—
748C2×C4C2×D4×D512yes—
749C2×C4C2×D4×D511yescharacteristic
750C2×C4#414412yes—
751C2×C4D5×#4112yes—
752C2×C4C24×D511yescharacteristic
753C8—22no—
754C8—22no—
755C8—102no—
756C8—102no—
757C5C2×#331611yescharacteristic, complemented, Sylow
758C22—28no—
759C22—22no—
760C22—22no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—84no—
765C22—102no—
766C22—102no—
767C22—102no—
768C22—204no—
769C22#6594412yes—
770C22C2×#406114yes—
771C22C2×#406112yes—
772C22#6610412yes—
773C22C22×D4×D511yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—102no—
779C4—102no—
780C4—102no—
781C4—104no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4#6594412yes—
786C4C2×#414411yescharacteristic
787C4C2×D5×#4111yescharacteristic
788C2—24no—
789C2—82no—
790C2—202no—
791C2#1061242314yesdirect product factor
792C2C2×#6594411yescharacteristic
793C2C22×#406111yescharacteristic
794C2C2×#6610411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#465C2
socleC23×C5C22×D4
prime radicalC2×#65932C2
hypercenterC2×#465D5
hypocenterC5C2×#3316
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#65969C2semidirect
3. C2×C5×#465C2semidirect
4. C2×#65462C2semidirect
5. C2×#65455C2semidirect
6. C22×#3948C2semidirect
7. C2×#65400C2semidirect
8. C2×#65339C2semidirect
9. C2×#65323C2semidirect
10. #10612423C2direct (N × H)
11. C2×#65143C2semidirect
12. C2×#65151C2semidirect
13. C2×#65105C2semidirect
14. C2×#65078C2semidirect
15. C2×#65060C2semidirect
16. C2×#65054C2semidirect
34. #65969C22semidirect
47. C5×#465C22semidirect
54. #65462C22semidirect
55. #65455C22semidirect
56. #65400C22semidirect
62. C2×#3948C22semidirect
65. #65339C22semidirect
66. #65323C22semidirect
71. #65151C22semidirect
72. #65143C22semidirect
73. #65105C22semidirect
74. #65078C22semidirect
75. #65060C22semidirect
76. #65054C22semidirect
194. C2×#465D5semidirect
342. #465C2×D5semidirect
682. C2×C5#3316semidirect
757. C5C2×#3316semidirect
791. C2#10612423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659692
C2×#659322
C2×C5×#4652
C2×#654622
C2×#654552
C22×#39482
C2×#654002
C2×#653392
C2×#653232
#106124232
C2×#651432
C2×#651512
C2×#651052
C2×#650782
C2×#650602
C2×#650542
C2×#33165