Finite Group Databasebeta

← C2×#10615272 #12976169

Subgroups — C2×#10615272 #12976169

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×C5×#548C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic, complemented
3C2×#65528C211yesmaximal, characteristic, complemented
4C2×#65521C211yesmaximal, characteristic, complemented
5C2×#65517C211yesmaximal, characteristic, complemented
6C2×#65514C211yesmaximal, characteristic, complemented
7#10615272C2116yesmaximal, direct product factor
8C2×#65343C211yesmaximal, characteristic, complemented
9C2×#65345C211yesmaximal, characteristic, complemented
10C2×#65341C211yesmaximal, characteristic, complemented
11C2×#65333C211yesmaximal, characteristic, complemented
12C2×#65331C211yesmaximal, characteristic, complemented
13C2×#65324C211yesmaximal, characteristic, complemented
14C2×#65311C211yesmaximal, characteristic, complemented
15C2×C4×#689C211yesmaximal, characteristic, complemented
16C2×#65301C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C5×#548—24no—
20C5×#548C2218yes—
21C2×C5×#124—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C2×#4081—21no—
33C22×#687C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C2×#4070C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C22×#681C2211yescharacteristic
40#65875—24no—
41#65875C2218yescomplemented
42C2×#4035—21no—
43C2×#4025—21no—
44C2×#4023—21no—
45C2×#4016C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47#65528C2218yescomplemented
48#65521C2218yescomplemented
49#65517C2218yescomplemented
50#65514C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56C2×#3967C2211yescharacteristic
57C2×#3964C2211yescharacteristic
58C2×#3964C2211yescharacteristic
59C2×#3964C2211yescharacteristic
60C2×C22⋊#168C2211yescharacteristic
61C2×C22⋊#168C2211yescharacteristic
62#65345C2218yescomplemented
63#65343C2218yescomplemented
64#65341C2218yescomplemented
65#65333C2218yescomplemented
66#65331C2218yescomplemented
67#65324C2218yescomplemented
68C4×#689C2218yescomplemented
69#65311C2218yescomplemented
70#65301C2218yescomplemented
71C2×#3942C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3327—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—24no—
80C2×C5×#41—42no—
81C2×C5×#41C2314yes—
82C22×C5×Q8—21no—
83C22×C5×Q8—22no—
84C22×C5×Q8—24no—
85C22×C5×Q8—42no—
86C22×C5×Q8C2311yescharacteristic
87C22×C5×Q8C2314yes—
88C22×C5×Q8C2311yescharacteristic
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4D411yescharacteristic
92C22×C5×D4C2311yescharacteristic
93C23×C4×C5—21no—
94C23×C4×C5—21no—
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C23×Dic5—21no—
98C22×Dic10C2311yescharacteristic
99C5×#124—28no—
100C5×#124—22no—
101C5×#124C2314yes—
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8—28no—
104C5×C22⋊Q8C2314yes—
105C5×#121—28no—
106C5×#121—22no—
107C5×#121C2314yes—
108C4×C5×Q8—22no—
109C4×C5×Q8C2314yes—
110C4×C5×D4—28no—
111C4×C5×D4D414yes—
112C4×C5×D4C2314yes—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4D411yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C5×C22⋊C4D411yescharacteristic
123C2×C42×C5—21no—
124C2×C42×C5C2311yescharacteristic
125C2×C22⋊Dic5—21no—
126C2×C22⋊Dic5—21no—
127C2×C22⋊Dic5—21no—
128C2×#689—24no—
129C2×#689—42no—
130C2×#689C2314yes—
131C2×#689C2314yes—
132#4081—28no—
133C2×#687—42no—
134C2×#687C2314yes—
135#4072—22no—
136#4072C2314yes—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—22no—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2314yes—
143#4070—22no—
144#4070—22no—
145#4070C2314yes—
146#4070C2314yes—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683—21no—
151C2×#683—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×#681—42no—
155C2×#681—42no—
156C2×#681C2314yes—
157C2×#681C2314yes—
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2311yescharacteristic
162#4035—28no—
163#4025—28no—
164#4023—28no—
165#4016—22no—
166#4016C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3967C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177#3964C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3942C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185C4×#168C2314yes—
186C2×#552—51no—
187C2×#548D511yescharacteristic
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×#452—51no—
197C2×#451—51no—
198C2×C4×Q16—51no—
199C2×#436—51no—
200C2×#417—51no—
201C2×#419—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C24×C5C2×D411yescharacteristic
205C5×#41—28no—
206C5×#41—44no—
207C5×#41—48no—
208C2×C5×Q8—21no—
209C2×C5×Q8—24no—
210C2×C5×Q8—21no—
211C2×C5×Q8—22no—
212C2×C5×Q8—28no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—44no—
216C2×C5×Q8—44no—
217C2×C5×Q8—48no—
218C2×C5×Q8#4114yes—
219C2×C5×Q8C2412yes—
220C2×C5×Q8C2412yes—
221C2×C5×D4—24no—
222C2×C5×D4—24no—
223C2×C5×D4—21no—
224C2×C5×D4—22no—
225C2×C5×D4—22no—
226C2×C5×D4—42no—
227C2×C5×D4—44no—
228C2×C5×D4—44no—
229C2×C5×D4C2×D414yes—
230C2×C5×D4C2412yes—
231C22×C4×C5—21no—
232C22×C4×C5—22no—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—22no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—24no—
239C22×C4×C5—24no—
240C22×C4×C5—44no—
241C22×C4×C5—44no—
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D412yes—
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2412yes—
249C22×C4×C5C2412yes—
250C22×C4×C5C2411yescharacteristic
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—24no—
256C22×Dic5—44no—
257C2×Dic10—22no—
258C2×Dic10—22no—
259C2×Dic10—21no—
260C2×Dic10C2412yes—
261C5×C4⋊C4—24no—
262C5×C4⋊C4—24no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4C2×D414yes—
265C5×C4⋊C4C2412yes—
266C5×C22⋊C4—24no—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4C2×D414yes—
271C5×C22⋊C4C2×D414yes—
272C42×C5—24no—
273C42×C5C2×D412yes—
274C42×C5C2412yes—
275C22⋊Dic5—24no—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278#689—28no—
279#689—44no—
280#687—44no—
281C4⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—24no—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292#683—24no—
293C4×Dic5—24no—
294C4×Dic5—24no—
295#681—44no—
296#681—44no—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C2×#168C2412yes—
304C2×#168C2412yes—
305C22×#41C2×D511yescharacteristic
306C23×Q8C2×D511yescharacteristic
307C22×Q16—51no—
308C22×Q16—51no—
309C22×SD16—51no—
310C22×M16—51no—
311C22×M16—51no—
312#552—58no—
313#552—104no—
314#548—24no—
315#548C2×D518yes—
316C2×#126—101no—
317C2×#125—51no—
318C2×#125—101no—
319C2×#124—21no—
320C2×#124C2×D511yescharacteristic
321C2×#123—101no—
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×#121—21no—
327C2×#121C2×D511yescharacteristic
328C2×C4×Q8—51no—
329C2×C4×Q8C2×D511yescharacteristic
330C2×C4×D4—21no—
331C2×C4×D4C2×D511yescharacteristic
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#452—58no—
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×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×C22⋊C8—51no—
363C2×C22⋊C8—51no—
364C2×C4×C8—51no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—42no—
373C23×C5—42no—
374C23×C5—42no—
375C23×C5C22×D412yes—
376C23×C5C22×D412yes—
377C23×C5C22×D411yescharacteristic
378C5×Q8—24no—
379C5×Q8—22no—
380C5×Q8—22no—
381C5×Q8—22no—
382C5×Q8—48no—
383C5×Q8—42no—
384C5×Q8C2×#4114yes—
385C5×D4—22no—
386C5×D4—22no—
387C5×D4—44no—
388C5×D4—48no—
389C5×D4—48no—
390C5×D4—42no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—24no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—24no—
398C2×C4×C5—24no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—48no—
406C2×C4×C5—48no—
407C2×C4×C5—42no—
408C2×C4×C5—42no—
409C2×C4×C5C22×D412yes—
410C2×C4×C5C22×D412yes—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D411yescharacteristic
414C2×C4×C5C2×#4112yes—
415C2×C4×C5H(5,𝔽2)12yes—
416C2×C4×C5C2511yescharacteristic
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—48no—
422C2×Dic5—42no—
423C2×Dic5—42no—
424C2×Dic5—42no—
425C2×Dic5—42no—
426Dic10—22no—
427Dic10—22no—
428Dic10—42no—
429#168—22no—
430#168—22no—
431#168—22no—
432#168—22no—
433C2×#41—22no—
434C2×#41—24no—
435C2×#41—42no—
436C2×#41C22×D514yes—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—24no—
440C22×Q8—42no—
441C22×Q8—51no—
442C22×Q8C22×D511yescharacteristic
443C22×Q8C22×D514yes—
444C22×Q8C22×D511yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22⋊D511yescharacteristic
448C22×D4C22×D511yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—101no—
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454C2×Q16—54no—
455C2×Q16—54no—
456C2×Q16—104no—
457C2×Q16—202no—
458C2×SD16—54no—
459C2×SD16—202no—
460C2×M16—54no—
461C2×M16—54no—
462C2×M16—202no—
463C2×M16—202no—
464C22×C8—51no—
465C22×C8—51no—
466C22×C8—51no—
467C22×C8—51no—
468#126—108no—
469#125—54no—
470#125—108no—
471#125—102no—
472#124—28no—
473#124—22no—
474#124C22×D514yes—
475#123—108no—
476C22⋊Q8—22no—
477C22⋊Q8—28no—
478C22⋊Q8—54no—
479C22⋊Q8—54no—
480C22⋊Q8—102no—
481C22⋊Q8—102no—
482C22⋊Q8C22×D514yes—
483#121—28no—
484#121—22no—
485#121C22×D514yes—
486C4×Q8—22no—
487C4×Q8—54no—
488C4×Q8—102no—
489C4×Q8C22×D514yes—
490C4×D4—28no—
491C4×D4C22⋊D514yes—
492C4×D4C22×D514yes—
493#117—54no—
494#117—102no—
495#117—108no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—102no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—101no—
509C2×C4⋊C4C22⋊D511yescharacteristic
510C2×C4⋊C4C22×D511yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4C22⋊D511yescharacteristic
519C2×C22⋊C4C22⋊D511yescharacteristic
520C2×C42—21no—
521C2×C42—101no—
522C2×C42—101no—
523C2×C42C22×D511yescharacteristic
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#103—54no—
535#102—54no—
536#102—54no—
537#102—54no—
538C22⋊C8—54no—
539C22⋊C8—54no—
540C4×C8—54no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5—22no—
545C22×C5—22no—
546C22×C5—22no—
547C22×C5—44no—
548C22×C5—44no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—84no—
553C22×C5#54612yes—
554C22×C5#57512yes—
555C22×C5#57812yes—
556C22×C5C23×D411yescharacteristic
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—24no—
560C4×C5—22no—
561C4×C5—22no—
562C4×C5—42no—
563C4×C5—42no—
564C4×C5#54612yes—
565C4×C5C22×#4111yescharacteristic
566C4×C5C2×H(5,𝔽2)11yescharacteristic
567Dic5—42no—
568Dic5—42no—
569Dic5—42no—
570Dic5—42no—
571C24—21no—
572C24C2×C22⋊D511yescharacteristic
573C24C2×C22⋊D511yescharacteristic
574#41—28no—
575#41—44no—
576#41—48no—
577C2×Q8—22no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—28no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—48no—
587C2×Q8—52no—
588C2×Q8—101no—
589C2×Q8—102no—
590C2×Q8—102no—
591C2×Q8#71114yes—
592C2×Q8C23×D512yes—
593C2×Q8C23×D512yes—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—42no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4C2×C22⋊D514yes—
603C2×D4C23×D512yes—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—104no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—204no—
621C22×C4C2×C22⋊D512yes—
622C22×C4C2×C22⋊D512yes—
623C22×C4C2×C22⋊D511yescharacteristic
624C22×C4C2×C22⋊D511yescharacteristic
625C22×C4C2×C22⋊D511yescharacteristic
626C22×C4C2×C22⋊D511yescharacteristic
627C22×C4C23×D512yes—
628C22×C4C23×D512yes—
629C22×C4C23×D511yescharacteristic
630Q16—108no—
631Q16—204no—
632SD16—204no—
633M16—204no—
634M16—204no—
635C2×C8—52no—
636C2×C8—52no—
637C2×C8—52no—
638C2×C8—52no—
639C2×C8—102no—
640C2×C8—102no—
641C2×C8—102no—
642C2×C8—102no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—52no—
647C4⋊C4—52no—
648C4⋊C4—52no—
649C4⋊C4—101no—
650C4⋊C4—101no—
651C4⋊C4—104no—
652C4⋊C4—101no—
653C4⋊C4—104no—
654C4⋊C4—104no—
655C4⋊C4—104no—
656C4⋊C4—104no—
657C4⋊C4—104no—
658C4⋊C4C2×C22⋊D514yes—
659C4⋊C4C23×D512yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—104no—
665C22⋊C4—104no—
666C22⋊C4—104no—
667C22⋊C4C2×C22⋊D514yes—
668C22⋊C4C2×C22⋊D514yes—
669C42—24no—
670C42—104no—
671C42—104no—
672C42C2×C22⋊D512yes—
673C42C23×D512yes—
674C2×C5—42no—
675C2×C5—42no—
676C2×C5—82no—
677C2×C5#332714yescomplemented
678C2×C5C2×#54611yescharacteristic
679C2×C5C2×#57511yescharacteristic
680C2×C5C2×#57811yescharacteristic
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C22×C22⋊D512yes—
692C23C22×C22⋊D512yes—
693C23C22×C22⋊D511yescharacteristic
694Q8—24no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—48no—
699Q8—42no—
700Q8—102no—
701Q8—102no—
702Q8—202no—
703Q8C2×#71114yes—
704D4—22no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—48no—
709D4—42no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—208no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4C2×#71112yes—
738C2×C4#414412yes—
739C2×C4C22×C22⋊D512yes—
740C2×C4C22×C22⋊D512yes—
741C2×C4C22×C22⋊D512yes—
742C2×C4C22×C22⋊D512yes—
743C2×C4C22×C22⋊D511yescharacteristic
744C2×C4C24×D511yescharacteristic
745C8—102no—
746C8—102no—
747C8—102no—
748C8—102no—
749C5C2×#332711yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22#6614012yes—
763C22#6615612yes—
764C22#6617212yes—
765C22C23×C22⋊D511yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—24no—
771C4—42no—
772C4—42no—
773C4—202no—
774C4—202no—
775C4—202no—
776C4—202no—
777C4#6614012yes—
778C4C22×#71111yescharacteristic
779C4C2×#414411yescharacteristic
780C2—42no—
781C2—42no—
782C2—82no—
783C2#1061527214yesdirect product factor
784C2C2×#6614011yescharacteristic
785C2C2×#6615611yescharacteristic
786C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#548C2
socleC23×C5C22×D4
hypercenterC2×#548D5
hypocenterC5C2×#3327
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C2×#65875C2semidirect
3. C2×#65528C2semidirect
4. C2×#65521C2semidirect
5. C2×#65517C2semidirect
6. C2×#65514C2semidirect
7. #10615272C2direct (N × H)
8. C2×#65343C2semidirect
9. C2×#65345C2semidirect
10. C2×#65341C2semidirect
11. C2×#65333C2semidirect
12. C2×#65331C2semidirect
13. C2×#65324C2semidirect
14. C2×#65311C2semidirect
15. C2×C4×#689C2semidirect
16. C2×#65301C2semidirect
41. #65875C22semidirect
47. #65528C22semidirect
48. #65521C22semidirect
49. #65517C22semidirect
50. #65514C22semidirect
62. #65345C22semidirect
63. #65343C22semidirect
64. #65341C22semidirect
65. #65333C22semidirect
66. #65331C22semidirect
67. #65324C22semidirect
68. C4×#689C22semidirect
69. #65311C22semidirect
70. #65301C22semidirect
677. C2×C5#3327semidirect
749. C5C2×#3327semidirect
783. C2#10615272direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5482
C2×#658752
C2×#655282
C2×#655212
C2×#655172
C2×#655142
#106152722
C2×#653432
C2×#653452
C2×#653412
C2×#653332
C2×#653312
C2×#653242
C2×#653112
C2×C4×#6892
C2×#653012
C2×#33275