Finite Group Databasebeta

← C2×#10613249 #12967136

Subgroups — C2×#10613249 #12967136

Order 1280.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65962C211yesmaximal, characteristic
2C2×#65857C211yesmaximal, characteristic
3C2×C5×#485C211yesmaximal, characteristic, complemented
4C2×#65333C211yesmaximal, characteristic, complemented
5C2×#65285C211yesmaximal, characteristic, complemented
6#10613249C2116yesmaximal, direct product factor
7C2×#65173C211yesmaximal, characteristic, complemented
8C2×#65170C211yesmaximal, characteristic, complemented
9C2×#65149C211yesmaximal, characteristic, complemented
10C2×#65156C211yesmaximal, characteristic, complemented
11C2×#65104C211yesmaximal, characteristic, complemented
12C2×#65094C211yesmaximal, characteristic, complemented
13C2×#65091C211yesmaximal, characteristic, complemented
14C2×D5×#103C211yesmaximal, characteristic, complemented
15C2×#65016C211yesmaximal, characteristic
16C2×#65010C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C2×#4070C2211yescharacteristic
24C22×#676C2211yescharacteristic
25C22×C8×D5C2211yescharacteristic
26#65962—24no—
27#65962C2218yes—
28#65857—24no—
29#65857C2218yes—
30C2×#4043C2211yescharacteristic
31C2×#4040—21no—
32C2×#4038C2211yescharacteristic
33C2×#4038C2211yescharacteristic
34C2×#4038C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4034—21no—
38C2×#4031—21no—
39C2×#4029—21no—
40C2×#4027—21no—
41C2×#4027—21no—
42C2×C4×D20—21no—
43C2×C4×Dic10—21no—
44C5×#485C2218yescomplemented
45C2×C5×#107C2211yescharacteristic
46C2×C5×#106C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×C22⋊#168C2211yescharacteristic
53C2×#3952C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56C2×#3949C2211yescharacteristic
57C2×#3948C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59#65333C2218yescomplemented
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65173C2218yescomplemented
68#65170C2218yescomplemented
69#65156C2218yescomplemented
70#65149C2218yescomplemented
71#65104C2218yescomplemented
72#65094C2218yescomplemented
73#65091C2218yescomplemented
74D5×#103C2218yescomplemented
75#65016C2218yes—
76#65010C2218yescomplemented
77C2×#3097—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5D411yescharacteristic
81C22×C22⋊D5D411yescharacteristic
82C23×Dic5—21no—
83C2×Q8×D5—22no—
84C2×Q8×D5—24no—
85C2×Q8×D5—24no—
86C2×Q8×D5C2314yes—
87C2×#709—24no—
88C2×#709—24no—
89C2×#709D414yes—
90C2×#709C2314yes—
91C22×D20D411yescharacteristic
92C22×C4×D5—21no—
93C22×C4×D5—21no—
94C22×C4×D5—21no—
95C22×C4×D5C2311yescharacteristic
96C22×C4×D5C2311yescharacteristic
97C22×Dic10—21no—
98C22×Dic10D411yescharacteristic
99C22×Dic10C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C22×C5×C8C2311yescharacteristic
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8C2314yes—
104C5×#117—22no—
105C5×#117C2314yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C42×C5—21no—
113C2×C22⋊Dic5—21no—
114#4092—22no—
115#4092C2314yes—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119C2×#685—21no—
120C2×#685—21no—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—22no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5C2311yescharacteristic
125C2×C4⋊Dic5C2311yescharacteristic
126C2×C4⋊Dic5C2311yescharacteristic
127C2×C4⋊Dic5C2314yes—
128#4070—22no—
129#4070C2314yes—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5—21no—
137C22×#168C2311yescharacteristic
138C22×#168C2311yescharacteristic
139C2×#676—24no—
140C2×#676C2314yes—
141C2×C8×D5—24no—
142C2×C8×D5C2314yes—
143#4043—22no—
144#4043C2314yes—
145#4040—28no—
146#4038—22no—
147#4038—22no—
148#4038—22no—
149#4038C2314yes—
150#4038C2314yes—
151#4038C2314yes—
152D5×C4⋊C4—22no—
153D5×C4⋊C4—22no—
154D5×C4⋊C4C2314yes—
155D5×C4⋊C4C2314yes—
156#4034—28no—
157#4031—28no—
158#4029—28no—
159#4027—28no—
160#4027—28no—
161C4×D20—28no—
162C4×Dic10—28no—
163C5×#107C2314yes—
164C5×#106C2314yes—
165C5×#103C2314yes—
166C5×#103C2314yes—
167C5×C22⋊C8C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170C22⋊#168C2314yes—
171#3952C2314yes—
172#3952C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3942C2314yes—
178#3942C2314yes—
179#3940C2314yes—
180#3939C2314yes—
181#3939C2314yes—
182#3939C2314yes—
183C2×#536—51no—
184C2×#520—51no—
185#3097—516no—
186C2×#484—51no—
187C2×#484—51no—
188C2×#485—51no—
189C2×#485—51no—
190C2×#485—51no—
191C2×#485D511yescharacteristic, complemented
192C2×#483—51no—
193C2×#483—51no—
194C2×#428—51no—
195C2×#427—51no—
196C2×#419—51no—
197C22×#103—51no—
198C2×#408—51no—
199C24×C5C2×D411yescharacteristic
200C23×D5C2×D411yescharacteristic
201C23×D5C2×D411yescharacteristic
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8C2412yes—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2411yescharacteristic
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5C2×D414yes—
219C2×C22⋊D5C2×D414yes—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—24no—
225C22×Dic5—82no—
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228Q8×D5—28no—
229Q8×D5—28no—
230Q8×D5—48no—
231#709—216no—
232#709—28no—
233#709—28no—
234C2×D20—24no—
235C2×D20C2×D414yes—
236C2×C4×D5—22no—
237C2×C4×D5—22no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—44no—
242C2×C4×D5—82no—
243C2×C4×D5—82no—
244C2×C4×D5C2×D412yes—
245C2×C4×D5C2×D412yes—
246C2×C4×D5#4114yes—
247C2×C4×D5#4114yes—
248C2×C4×D5C2412yes—
249C2×C4×D5C2412yes—
250C2×Dic10—24no—
251C2×Dic10—22no—
252C2×Dic10—22no—
253C2×Dic10—21no—
254C2×Dic10—24no—
255C2×Dic10—44no—
256C2×Dic10C2×D414yes—
257C2×Dic10C2412yes—
258C2×C5×C8—22no—
259C2×C5×C8—22no—
260C2×C5×C8C2412yes—
261C2×C5×C8C2412yes—
262C5×C4⋊C4—24no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4C2412yes—
267C5×C4⋊C4C2412yes—
268C5×C4⋊C4C2412yes—
269C5×C22⋊C4—24no—
270C5×C22⋊C4—24no—
271C42×C5—24no—
272C22⋊Dic5—24no—
273#685—24no—
274#685—24no—
275#685—24no—
276#685—24no—
277#685—24no—
278C4⋊Dic5—24no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—21no—
282C4⋊Dic5—24no—
283C4⋊Dic5C2412yes—
284C4⋊Dic5C2412yes—
285C4⋊Dic5C2412yes—
286#683—24no—
287#683—24no—
288#683—24no—
289#683—24no—
290C4×Dic5—24no—
291C4×Dic5—24no—
292C4×Dic5—24no—
293C2×#168—22no—
294C2×#168—22no—
295C2×#168C2412yes—
296C2×#168C2412yes—
297#676—28no—
298C8×D5—28no—
299C22×#41—51no—
300C23×Q8—51no—
301C22×M16—51no—
302C23×C8—51no—
303#536—58no—
304#536—104no—
305C2×C4⋊Q8—101no—
306C2×#124—101no—
307C2×#123—101no—
308C2×#123—101no—
309C2×C22⋊Q8—51no—
310C2×C22⋊Q8—51no—
311C2×C22⋊Q8—51no—
312C2×C22⋊Q8C2×D511yescharacteristic
313#520—58no—
314#520—104no—
315C2×C4×Q8—101no—
316C2×C4×D4—101no—
317C2×C4×D4—101no—
318C2×C4×D4—101no—
319C2×#117—51no—
320C2×#117—51no—
321C2×#117—51no—
322C2×#117C2×D511yescharacteristic
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4—51no—
326#485—58no—
327#485—58no—
328#485—58no—
329#485C2×D518yescomplemented
330#484—58no—
331#484—58no—
332#483—58no—
333#483—58no—
334#428—58no—
335#427—58no—
336C2×#107—51no—
337C2×#107—51no—
338C2×#107—51no—
339C2×#107C2×D511yescharacteristic
340C2×#106—51no—
341C2×#106—51no—
342C2×#106—51no—
343C2×#106C2×D511yescharacteristic
344#419—58no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#103—51no—
350C2×#103—51no—
351C2×#103—58no—
352C2×#103C2×D511yescharacteristic
353C2×#103C2×D511yescharacteristic
354#408—58no—
355C2×C22⋊C8—51no—
356C2×C22⋊C8—51no—
357C2×C22⋊C8—51no—
358C2×C22⋊C8C2×D511yescharacteristic
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5C22×D412yes—
363C23×C5C22×D411yescharacteristic
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5#12314yes—
370C22×D5C22×D412yes—
371C22×D5C22×D412yes—
372C5×Q8—22no—
373C5×Q8—22no—
374C5×Q8—42no—
375C2×C4×C5—22no—
376C2×C4×C5—24no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2×#4112yes—
391C2×C4×C5C2511yescharacteristic
392C22⋊D5—28no—
393C22⋊D5—28no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—84no—
404C2×Dic5#12314yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407D20—28no—
408C4×D5—24no—
409C4×D5—22no—
410C4×D5—22no—
411C4×D5—48no—
412C4×D5—84no—
413C4×D5—84no—
414C4×D5#12318yes—
415C4×D5C2×#4114yes—
416C4×D5C2×#4114yes—
417Dic10—28no—
418Dic10—22no—
419Dic10—22no—
420Dic10—42no—
421Dic10—48no—
422C5×C8—22no—
423C5×C8—22no—
424#168—22no—
425#168—22no—
426C2×#41—54no—
427C2×#41—54no—
428C2×#41—104no—
429C2×#41—104no—
430C22×Q8—51no—
431C22×Q8—54no—
432C22×Q8—51no—
433C22×Q8—101no—
434C22×Q8—102no—
435C22×Q8—104no—
436C22×Q8—104no—
437C22×Q8C22×D511yescharacteristic
438C22×D4—51no—
439C22×D4—51no—
440C22×D4—51no—
441C23×C4—51no—
442C23×C4—51no—
443C23×C4—101no—
444C23×C4—101no—
445C23×C4—101no—
446C23×C4—101no—
447C23×C4C22×D511yescharacteristic
448C2×M16—54no—
449C2×M16—104no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—54no—
453C22×C8—104no—
454C22×C8C22×D511yescharacteristic
455C22×C8C22×D511yescharacteristic
456C4⋊Q8—108no—
457#124—108no—
458#123—108no—
459#123—108no—
460C22⋊Q8—22no—
461C22⋊Q8—54no—
462C22⋊Q8—54no—
463C22⋊Q8—54no—
464C22⋊Q8—102no—
465C22⋊Q8—102no—
466C22⋊Q8—102no—
467C22⋊Q8C22×D514yes—
468C4×Q8—108no—
469C4×D4—108no—
470C4×D4—108no—
471C4×D4—108no—
472#117—22no—
473#117—54no—
474#117—54no—
475#117—54no—
476#117—102no—
477#117—102no—
478#117—102no—
479#117C22×D514yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—102no—
488C2×C4⋊C4—102no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4—101no—
494C2×C4⋊C4—102no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4C22×D511yescharacteristic
497C2×C4⋊C4C22×D511yescharacteristic
498C2×C4⋊C4C22×D511yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C22⋊C4—101no—
504C2×C22⋊C4—101no—
505C2×C22⋊C4—101no—
506C2×C22⋊C4—101no—
507C2×C42—21no—
508C2×C42—101no—
509C2×C42—101no—
510C2×C42—101no—
511#107—54no—
512#107—54no—
513#107—54no—
514#107C22×D514yes—
515#106—54no—
516#106—54no—
517#106—54no—
518#106C22×D514yes—
519#103—54no—
520#103—54no—
521#103—54no—
522#103—54no—
523#103—54no—
524#103—54no—
525#103C22×D514yes—
526#103C22×D514yes—
527C22⋊C8—54no—
528C22⋊C8—54no—
529C22⋊C8—54no—
530C22⋊C8C22×D514yes—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—44no—
535C22×C5C2×#12312yes—
536C22×C5#57712yes—
537C22×C5#57812yes—
538C22×C5C23×D411yescharacteristic
539C2×D5—28no—
540C2×D5—22no—
541C2×D5—22no—
542C2×D5—22no—
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—44no—
546C2×D5C2×#12314yes—
547C4×C5—22no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5—42no—
552C4×C5C2×#12312yes—
553C4×C5C22×#4111yescharacteristic
554C4×C5C22×#4111yescharacteristic
555Dic5—22no—
556Dic5—42no—
557Dic5—42no—
558Dic5—42no—
559Dic5—42no—
560Dic5C2×#12314yes—
561C24—51no—
562C24—51no—
563C24D4×D511yescharacteristic
564#41—1016no—
565#41—108no—
566#41—108no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—54no—
571C2×Q8—52no—
572C2×Q8—104no—
573C2×Q8—104no—
574C2×Q8—108no—
575C2×Q8—108no—
576C2×Q8—101no—
577C2×Q8—102no—
578C2×Q8—102no—
579C2×Q8—204no—
580C2×Q8—208no—
581C2×Q8C23×D512yes—
582C2×D4—54no—
583C2×D4—54no—
584C2×D4—54no—
585C2×D4—104no—
586C2×D4—104no—
587C2×D4—104no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—51no—
595C22×C4—52no—
596C22×C4—54no—
597C22×C4—54no—
598C22×C4—52no—
599C22×C4—51no—
600C22×C4—52no—
601C22×C4—52no—
602C22×C4—104no—
603C22×C4—104no—
604C22×C4—104no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—104no—
612C22×C4—204no—
613C22×C4—402no—
614C22×C4—402no—
615C22×C4—402no—
616C22×C4D4×D512yes—
617C22×C4D4×D511yescharacteristic
618C22×C4C23×D512yes—
619C22×C4C23×D511yescharacteristic
620M16—108no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—52no—
624C2×C8—52no—
625C2×C8—108no—
626C2×C8—102no—
627C2×C8—102no—
628C2×C8C23×D512yes—
629C2×C8C23×D512yes—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—52no—
635C4⋊C4—52no—
636C4⋊C4—52no—
637C4⋊C4—104no—
638C4⋊C4—104no—
639C4⋊C4—104no—
640C4⋊C4—104no—
641C4⋊C4—101no—
642C4⋊C4—101no—
643C4⋊C4—104no—
644C4⋊C4—101no—
645C4⋊C4—104no—
646C4⋊C4C23×D512yes—
647C4⋊C4C23×D512yes—
648C4⋊C4C23×D512yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4—104no—
656C22⋊C4—104no—
657C42—24no—
658C42—104no—
659C42—104no—
660C42—104no—
661C2×C5—42no—
662C2×C5#309714yescomplemented
663C2×C5C22×#12311yescharacteristic
664C2×C5C2×#57711yescharacteristic
665C2×C5C2×#57811yescharacteristic
666D5—24no—
667D5—42no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—54no—
672C23—52no—
673C23—52no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23C2×D4×D512yes—
680C23C2×D4×D511yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—42no—
684Q8—108no—
685Q8—102no—
686Q8—102no—
687Q8—208no—
688Q8—202no—
689D4—108no—
690D4—108no—
691D4—108no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—54no—
705C2×C4—52no—
706C2×C4—58no—
707C2×C4—54no—
708C2×C4—54no—
709C2×C4—52no—
710C2×C4—102no—
711C2×C4—104no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—208no—
719C2×C4—202no—
720C2×C4—202no—
721C2×C4—202no—
722C2×C4—202no—
723C2×C4—404no—
724C2×C4—404no—
725C2×C4—404no—
726C2×C4C2×D4×D512yes—
727C2×C4C2×D4×D511yescharacteristic
728C2×C4D5×#4112yes—
729C2×C4D5×#4112yes—
730C2×C4C24×D511yescharacteristic
731C8—22no—
732C8—22no—
733C8—102no—
734C8—102no—
735C5C2×#309711yescharacteristic, complemented, Sylow
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—54no—
741C22—108no—
742C22—102no—
743C22—102no—
744C22—102no—
745C22—102no—
746C22—102no—
747C22—204no—
748C22D5×#12312yes—
749C22#6610412yes—
750C22#6611312yes—
751C22C22×D4×D511yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—54no—
758C4—102no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4D5×#12312yes—
764C4C2×D5×#4111yescharacteristic
765C4C2×D5×#4111yescharacteristic
766C2—42no—
767C2—104no—
768C2—202no—
769C2#1061324914yesdirect product factor
770C2C2×D5×#12311yescharacteristic
771C2C2×#6610411yescharacteristic
772C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#485C2
socleC23×C5C22×D4
prime radicalC22×#709C22
hypercenterC2×#485D5
hypocenterC5C2×#3097
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. C2×C5×#485C2semidirect
4. C2×#65333C2semidirect
5. C2×#65285C2semidirect
6. #10613249C2direct (N × H)
7. C2×#65173C2semidirect
8. C2×#65170C2semidirect
9. C2×#65149C2semidirect
10. C2×#65156C2semidirect
11. C2×#65104C2semidirect
12. C2×#65094C2semidirect
13. C2×#65091C2semidirect
14. C2×D5×#103C2semidirect
16. C2×#65010C2semidirect
44. C5×#485C22semidirect
59. #65333C22semidirect
60. #65285C22semidirect
67. #65173C22semidirect
68. #65170C22semidirect
69. #65156C22semidirect
70. #65149C22semidirect
71. #65104C22semidirect
72. #65094C22semidirect
73. #65091C22semidirect
74. D5×#103C22semidirect
76. #65010C22semidirect
191. C2×#485D5semidirect
329. #485C2×D5semidirect
662. C2×C5#3097semidirect
735. C5C2×#3097semidirect
769. C2#10613249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659622
C2×#658572
C2×C5×#4852
C2×#653332
C2×#652852
#106132492
C2×#651732
C2×#651702
C2×#651492
C2×#651562
C2×#651042
C2×#650942
C2×#650912
C2×D5×#1032
C2×#650162
C2×#650102
C2×#30975