Finite Group Databasebeta

← C2×#10615250 #12977863

Subgroups — C2×#10615250 #12977863

Order 1280.

2158 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×C5×#547C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic, complemented
3#10615250C2116yesmaximal, direct product factor
4C2×#65373C211yesmaximal, characteristic, complemented
5C2×#65369C211yesmaximal, characteristic, complemented
6C2×#65328C211yesmaximal, characteristic, complemented
7C2×#65327C211yesmaximal, characteristic, complemented
8C2×#65323C211yesmaximal, characteristic, complemented
9C2×#65324C211yesmaximal, characteristic, complemented
10C2×#65300C211yesmaximal, characteristic, complemented
11C2×#65298C211yesmaximal, characteristic, complemented
12C2×#65303C211yesmaximal, characteristic, complemented
13C2×#65257C211yesmaximal, characteristic, complemented
14C2×#65256C211yesmaximal, characteristic, complemented
15C2×#65253C211yesmaximal, characteristic, complemented
16C22×#3940C211yesmaximal, characteristic, complemented
17C22×C5×#41—21no—
18C5×#547—24no—
19C5×#547C2218yescomplemented
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8—21no—
24C2×C5×#121C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C2×#4085—21no—
31C22×#686C2211yescharacteristic
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65899—24no—
39#65899C2218yescomplemented
40C2×#4044—21no—
41C2×#4029—21no—
42C2×#4027—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4016C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65373C2218yescomplemented
51#65369C2218yescomplemented
52#65328C2218yescomplemented
53#65327C2218yescomplemented
54#65324C2218yescomplemented
55#65323C2218yescomplemented
56#65303C2218yescomplemented
57#65300C2218yescomplemented
58#65298C2218yescomplemented
59#65257C2218yescomplemented
60#65256C2218yescomplemented
61C2×#3941C2211yescharacteristic
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64#65253C2218yescomplemented
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3940C2218yescomplemented
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3345—51nomaximal, Sylow
78C2×C5×#41—28no—
79C2×C5×#41—48no—
80C22×C5×Q8—21no—
81C22×C5×D4—21no—
82C22×C5×D4—21no—
83C22×C5×D4D411yescharacteristic
84C22×C5×D4C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C23×Dic5—21no—
93C22×D20C2311yescharacteristic
94C22×C4×D5—21no—
95C5×C4⋊Q8—22no—
96C5×C4⋊Q8C2314yes—
97C5×#123—28no—
98C5×#123—28no—
99C5×C22⋊Q8—28no—
100C5×#121—22no—
101C5×#121—22no—
102C5×#121C2314yes—
103C5×#121C2314yes—
104C4×C5×D4—22no—
105C4×C5×D4D414yes—
106C4×C5×D4C2314yes—
107C4×C5×D4C2314yes—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—22no—
111C2×C5×C4⋊C4—22no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4D411yescharacteristic
123C2×C5×C22⋊C4D411yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C2×C22⋊Dic5—21no—
126#4085—28no—
127C2×#686—24no—
128C2×#686C2314yes—
129#4076—22no—
130#4076—22no—
131#4076C2314yes—
132#4076C2314yes—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136#4072—22no—
137#4072C2314yes—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—22no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4044—28no—
156#4029—28no—
157#4027—28no—
158C4×D20—22no—
159C4×D20C2314yes—
160#4016—22no—
161#4016C2314yes—
162#3964C2314yes—
163#3964C2314yes—
164#3964C2314yes—
165C22⋊#168C2314yes—
166C22⋊#168C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3941C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3940C2314yes—
175#3940C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179C4⋊#168C2314yes—
180#3935C2314yes—
181C2×#553—51no—
182C2×#547D511yescharacteristic, complemented
183#3345—516no—
184C2×#501—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466—51no—
193C2×#442—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#106—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C5×#41—432no—
202C2×C5×Q8—24no—
203C2×C5×Q8—44no—
204C2×C5×D4—24no—
205C2×C5×D4—24no—
206C2×C5×D4—24no—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4—44no—
211C2×C5×D4—44no—
212C2×C5×D4C2×D414yes—
213C2×C5×D4C2412yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—24no—
222C22×C4×C5—24no—
223C22×C4×C5—24no—
224C22×C4×C5—44no—
225C22×C4×C5—44no—
226C22×C4×C5—44no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D412yes—
232C22×C4×C5C2×D412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2411yescharacteristic
236C2×C22⋊D5—24no—
237C2×C22⋊D5—24no—
238C2×C22⋊D5—44no—
239C2×C22⋊D5—82no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—24no—
244C22×Dic5—82no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—21no—
248C2×D20C2412yes—
249C2×C4×D5—24no—
250C2×C4×D5—82no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—24no—
257C5×C4⋊C4C2×D414yes—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4C2×D414yes—
265C5×C22⋊C4C2×D414yes—
266C42×C5C2×D412yes—
267C42×C5C2412yes—
268C22⋊Dic5—24no—
269#686—28no—
270#685—24no—
271#685—24no—
272#685—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280#683—24no—
281#683—24no—
282C4×Dic5—24no—
283#681—28no—
284C2×#168—22no—
285C2×#168—22no—
286C2×#168—22no—
287C2×#168—28no—
288C2×#168#4114yescomplemented
289C2×#168C2412yes—
290C2×#168C2412yes—
291C2×#168C2412yes—
292C2×#168C2412yes—
293C22×#41—21no—
294C22×D8—51no—
295C22×M16—51no—
296C23×C8—51no—
297#553—58no—
298#553—104no—
299#547—24no—
300#547C2×D518yescomplemented
301C2×C4⋊Q8C2×D511yescharacteristic
302C2×#126—101no—
303C2×#125—51no—
304C2×#123—21no—
305C2×#123—21no—
306C2×#123—101no—
307C2×C22⋊Q8—21no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—101no—
311C2×#121C2×D511yescharacteristic
312C2×#121C2×D511yescharacteristic
313C2×C4×D4—51no—
314C2×C4×D4—101no—
315C2×C4×D4C2×D511yescharacteristic
316C2×C4×D4C2×D511yescharacteristic
317C2×#117—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4C2×D511yescharacteristic
320C22×C4⋊C4C2×D511yescharacteristic
321#501—58no—
322#482—58no—
323#481—58no—
324#481—58no—
325#480—58no—
326#478—58no—
327#476—58no—
328#469—58no—
329#466—58no—
330#442—58no—
331#435—58no—
332#428—58no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—58no—
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×C22⋊C8—51no—
351C2×C22⋊C8—51no—
352C2×#97—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5—42no—
362C23×C5AGL(1,ℤ/8)14yes—
363C23×C5C22×D412yes—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C5×Q8—48no—
371C5×D4—28no—
372C5×D4—22no—
373C5×D4—22no—
374C5×D4—48no—
375C5×D4—48no—
376C5×D4—42no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—24no—
382C2×C4×C5—24no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—48no—
391C2×C4×C5—48no—
392C2×C4×C5—42no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5—48no—
396C2×C4×C5C22×D412yes—
397C2×C4×C5C22×D412yes—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D411yescharacteristic
401C2×C4×C5C2×#4112yes—
402C2×C4×C52−1+412yes—
403C2×C4×C5C2511yescharacteristic
404C22⋊D5—48no—
405C22⋊D5—84no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411C2×Dic5—42no—
412C2×Dic5—84no—
413D20—22no—
414D20—22no—
415D20—42no—
416C4×D5—84no—
417#168—22no—
418#168—22no—
419#168—22no—
420#168C2×#4114yescomplemented
421C2×#41—28no—
422C2×#41—48no—
423C22×Q8—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4C22⋊D511yescharacteristic
430C22×D4C22×D511yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—54no—
441C2×M16—104no—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8—54no—
445C22×C8—51no—
446C22×C8—51no—
447C22×C8—104no—
448C4⋊Q8—22no—
449C4⋊Q8C22×D514yes—
450#126—108no—
451#125—54no—
452#125—102no—
453#123—28no—
454#123—28no—
455#123—108no—
456C22⋊Q8—28no—
457#121—22no—
458#121—22no—
459#121—54no—
460#121—54no—
461#121—108no—
462#121—102no—
463#121—102no—
464#121C22×D514yes—
465#121C22×D514yes—
466C4×D4—22no—
467C4×D4—54no—
468C4×D4—108no—
469C4×D4—102no—
470C4×D4C22⋊D514yes—
471C4×D4C22×D514yes—
472C4×D4C22×D514yes—
473#117—54no—
474#117—102no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—102no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22⋊D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4C22⋊D511yescharacteristic
502C2×C22⋊C4C22⋊D511yescharacteristic
503C2×C42—101no—
504C2×C42C22×D511yescharacteristic
505#107—54no—
506#107—54no—
507#107—54no—
508#106—54no—
509#106—54no—
510#106—54no—
511#106—54no—
512#106—54no—
513#106—54no—
514C4⋊C8—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102—54no—
520#102—54no—
521C22⋊C8—54no—
522C22⋊C8—54no—
523#97—54no—
524C22×C5—28no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—22no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—44no—
531C22×C5—42no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—84no—
535C22×C5#54712yes—
536C22×C5C2×AGL(1,ℤ/8)14yes—
537C22×C5C2×AGL(1,ℤ/8)12yes—
538C22×C5#57712yes—
539C22×C5C23×D411yescharacteristic
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5#54712yes—
552C4×C5C22×#4111yescharacteristic
553C4×C5C2×2−1+411yescharacteristic
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557C24—21no—
558C24—101no—
559C24C2×C22⋊D511yescharacteristic
560C24C2×C22⋊D511yescharacteristic
561#41—432no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—52no—
573C2×D4—104no—
574C2×D4—104no—
575C2×D4—102no—
576C2×D4—102no—
577C2×D4—101no—
578C2×D4—204no—
579C2×D4—402no—
580C2×D4C2×C22⋊D514yes—
581C2×D4C23×D512yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—402no—
601C22×C4—402no—
602C22×C4C2×C22⋊D512yes—
603C22×C4C2×C22⋊D512yes—
604C22×C4C2×C22⋊D511yescharacteristic
605C22×C4C2×C22⋊D511yescharacteristic
606C22×C4C2×C22⋊D511yescharacteristic
607C22×C4C2×C22⋊D511yescharacteristic
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C22×C4C23×D511yescharacteristic
611D8—108no—
612M16—108no—
613C2×C8—54no—
614C2×C8—52no—
615C2×C8—52no—
616C2×C8—52no—
617C2×C8—52no—
618C2×C8—108no—
619C2×C8—102no—
620C2×C8—102no—
621C2×C8—102no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—52no—
629C4⋊C4—52no—
630C4⋊C4—52no—
631C4⋊C4—101no—
632C4⋊C4—101no—
633C4⋊C4—104no—
634C4⋊C4—101no—
635C4⋊C4—104no—
636C4⋊C4—104no—
637C4⋊C4C2×C22⋊D514yes—
638C4⋊C4C23×D512yes—
639C4⋊C4C23×D512yes—
640C4⋊C4C23×D512yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4C2×C22⋊D514yes—
649C22⋊C4C2×C22⋊D514yes—
650C42—104no—
651C42C2×C22⋊D512yes—
652C42C23×D512yes—
653C2×C5—24no—
654C2×C5—42no—
655C2×C5—82no—
656C2×C5#334514yescomplemented
657C2×C5C2×#54711yescharacteristic
658C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C5C2×#57711yescharacteristic
660D5—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—102no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23#407814yes—
675C23C22×C22⋊D512yes—
676C23C22×C22⋊D512yes—
677C23C22×C22⋊D511yescharacteristic
678Q8—48no—
679D4—28no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—48no—
684D4—42no—
685D4—102no—
686D4—102no—
687D4—208no—
688D4—202no—
689D4—404no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—404no—
716C2×C4—404no—
717C2×C4D5×#4112yes—
718C2×C4#415012yes—
719C2×C4C22×C22⋊D512yes—
720C2×C4C22×C22⋊D512yes—
721C2×C4C22×C22⋊D512yes—
722C2×C4C22×C22⋊D512yes—
723C2×C4C22×C22⋊D511yescharacteristic
724C2×C4C24×D511yescharacteristic
725C8—54no—
726C8—102no—
727C8—102no—
728C8—102no—
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—202no—
742C22—202no—
743C22—202no—
744C22—404no—
745C22C2×#407814yes—
746C22C2×#407812yes—
747C22#6615812yes—
748C22#6617112yes—
749C22C23×C22⋊D511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4#6615812yes—
761C4C2×D5×#4111yescharacteristic
762C4C2×#415011yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—402no—
767C2#1061525014yesdirect product factor
768C2C22×#407811yescharacteristic
769C2C2×#6615811yescharacteristic
770C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#547C2
socleC23×C5C22×D4
hypercenterC2×#547D5
hypocenterC5C2×#3345
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C5×#547C2semidirect
2. C2×#65899C2semidirect
3. #10615250C2direct (N × H)
4. C2×#65373C2semidirect
5. C2×#65369C2semidirect
6. C2×#65328C2semidirect
7. C2×#65327C2semidirect
8. C2×#65323C2semidirect
9. C2×#65324C2semidirect
10. C2×#65300C2semidirect
11. C2×#65298C2semidirect
12. C2×#65303C2semidirect
13. C2×#65257C2semidirect
14. C2×#65256C2semidirect
15. C2×#65253C2semidirect
16. C22×#3940C2semidirect
19. C5×#547C22semidirect
39. #65899C22semidirect
50. #65373C22semidirect
51. #65369C22semidirect
52. #65328C22semidirect
53. #65327C22semidirect
54. #65324C22semidirect
55. #65323C22semidirect
56. #65303C22semidirect
57. #65300C22semidirect
58. #65298C22semidirect
59. #65257C22semidirect
60. #65256C22semidirect
64. #65253C22semidirect
71. C2×#3940C22semidirect
182. C2×#547D5semidirect
288. C2×#168#41semidirect
300. #547C2×D5semidirect
420. #168C2×#41semidirect
656. C2×C5#3345semidirect
729. C5C2×#3345semidirect
767. C2#10615250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5472
C2×#658992
#106152502
C2×#653732
C2×#653692
C2×#653282
C2×#653272
C2×#653232
C2×#653242
C2×#653002
C2×#652982
C2×#653032
C2×#652572
C2×#652562
C2×#652532
C22×#39402
C2×#33455