Finite Group Databasebeta

← C2×#10618370 #13007804

Subgroups — C2×#10618370 #13007804

Order 1280.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#540C211yesmaximal, characteristic, complemented
2#10618370C2132yesmaximal, direct product factor
3C2×#66053C211yesmaximal, characteristic, complemented
4C2×#66050C211yesmaximal, characteristic, complemented
5C2×#66031C211yesmaximal, characteristic, complemented
6C2×D5×#125C211yesmaximal, characteristic, complemented
7C2×#65995C214yesmaximal, complemented
8C2×#65984C214yesmaximal, complemented
9C2×#65948C214yesmaximal, complemented
10C2×#65942C212yesmaximal, complemented
11C2×#65935C214yesmaximal, complemented
12C2×#65934C212yesmaximal, complemented
13C2×#65891C212yesmaximal, complemented
14C2×#65880C212yesmaximal, complemented
15C2×#65852C211yesmaximal, characteristic, complemented
16C2×#65856C211yesmaximal, characteristic, complemented
17C22×#711C2212yes—
18C22×#709C2211yescharacteristic
19C5×#540C22116yescomplemented
20C2×C5×#127C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123C2214yes—
23C2×C5×#121C2212yes—
24C2×C5×#121C2214yes—
25C2×C4×C5×D4C2212yes—
26C2×C5×#117C2211yescharacteristic
27C2×#4085C2214yes—
28C2×#4085C2214yes—
29C2×#4084C2214yes—
30C2×#4084C2212yes—
31C2×#4084C2214yes—
32C2×#4082C2212yes—
33C2×#4081C2214yes—
34C2×#4081C2214yes—
35C2×D4×Dic5C2214yes—
36C2×D4×Dic5C2212yes—
37C2×D4×Dic5C2214yes—
38C2×C4×C22⋊D5C2214yes—
39C2×C4×C22⋊D5C2214yes—
40C2×#4072C2214yes—
41C2×#4070C2212yes—
42C22×#683C2214yes—
43C22×C4×Dic5C2211yescharacteristic
44#66053C22116yescomplemented
45#66050C22116yescomplemented
46#66031C22116yescomplemented
47D5×#125C22116yescomplemented
48#65995C22164yescomplemented
49#65984C22164yescomplemented
50#65948C22164yescomplemented
51#65942C22132yescomplemented
52#65935C22164yescomplemented
53#65934C22132yescomplemented
54#65891C22132yescomplemented
55#65880C22132yescomplemented
56#65856C22116yescomplemented
57#65852C22116yescomplemented
58C2×#4044C2214yes—
59C2×#4043C2212yes—
60C2×#4039C2212yes—
61C2×D5×C4⋊C4C2214yes—
62C2×D5×C4⋊C4C2212yes—
63C2×#4036C2214yes—
64C2×#4036C2212yes—
65C2×#4035C2214yes—
66C2×#4035C2214yes—
67C2×#4033C2212yes—
68C2×#4033C2212yes—
69C2×#4030C2214yes—
70C2×#4029C2214yes—
71C2×#4027C2212yes—
72C2×#4027C2212yes—
73C2×#4027C2214yes—
74C2×#4025C2214yes—
75C2×#4025C2214yes—
76C2×#4025C2214yes—
77C2×#4024C2214yes—
78C2×#4023C2214yes—
79C2×#4023C2214yes—
80C2×#4018C2211yescharacteristic
81C2×#4018C2211yescharacteristic
82C2×C42×D5C2211yescharacteristic
83C2×C42×D5C2211yescharacteristic
84C2×#4016C2211yescharacteristic
85C2×#4015C2211yescharacteristic
86C2×C4×Dic10C2212yes—
87C2×#3512—51nomaximal, Sylow
88C22×C5×D4C2312yes—
89C22×C5×D4C2314yes—
90C22×C5×D4C2314yes—
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2314yes—
93C22×C22⋊D5C2311yescharacteristic
94C22×C22⋊D5C2311yescharacteristic
95C22×C22⋊D5C2314yes—
96C22×C22⋊D5C2314yes—
97C23×Dic5C2314yes—
98C23×Dic5C2314yes—
99C23×Dic5C2312yes—
100C2×#711—216no—
101C2×#711C23116yes—
102C2×#709—28no—
103C2×#709C2318yes—
104C22×D20C2311yescharacteristic
105C22×C4×D5C2311yescharacteristic
106C22×C4×D5C2312yes—
107C22×C4×D5C2312yes—
108C22×C4×D5C2314yes—
109C22×C4×D5C2311yescharacteristic
110C22×Dic10C2312yes—
111C22×Dic10C2311yescharacteristic
112C5×#127C2318yes—
113C5×#125C2318yes—
114C5×#123C23132yes—
115C5×#121C23116yes—
116C5×#121C23132yes—
117C4×C5×D4C23116yes—
118C5×#117C2318yes—
119C2×C5×C4⋊C4C2312yes—
120C2×C5×C4⋊C4C2312yes—
121C2×C5×C4⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C5×C22⋊C4C2314yes—
124C2×C5×C22⋊C4C2312yes—
125C2×C42×C5C2311yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132#4085C23132yes—
133#4085C23132yes—
134#4084C23132yes—
135#4084C23116yes—
136#4084C23132yes—
137#4082C23116yes—
138#4081C23132yes—
139#4081C23132yes—
140D4×Dic5C23132yes—
141D4×Dic5C23116yes—
142D4×Dic5C23132yes—
143C4×C22⋊D5C23132yes—
144C4×C22⋊D5C23132yes—
145C2×#685C2312yes—
146C2×#685C2312yes—
147C2×#685C2314yes—
148#4072C23132yes—
149C2×C4⋊Dic5C2312yes—
150C2×C4⋊Dic5C2314yes—
151C2×C4⋊Dic5C2314yes—
152C2×C4⋊Dic5C2314yes—
153#4070C23116yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×#683C2312yes—
157C2×#683C2312yes—
158C2×#683C2314yes—
159C2×#683C2314yes—
160C2×#683C2314yes—
161C2×#683C2314yes—
162C2×#683C23132yes—
163C2×C4×Dic5C2314yes—
164C2×C4×Dic5C2311yescharacteristic
165C2×C4×Dic5C2312yes—
166C2×C4×Dic5C2312yes—
167C2×C4×Dic5C2311yescharacteristic
168C2×C4×Dic5C2312yes—
169C2×C4×Dic5C2314yes—
170C2×C4×Dic5C2318yes—
171#4044C23132yes—
172#4043C23116yes—
173#4039C23116yes—
174D5×C4⋊C4C23116yes—
175D5×C4⋊C4C23132yes—
176#4036C23116yes—
177#4036C23132yes—
178#4035C23132yes—
179#4035C23132yes—
180#4033C23116yes—
181#4033C23116yes—
182#4030C23132yes—
183#4029C23132yes—
184#4027C23116yes—
185#4027C23116yes—
186#4027C23132yes—
187#4025C23132yes—
188#4025C23132yes—
189#4025C23132yes—
190#4024C23132yes—
191#4023C23132yes—
192#4023C23132yes—
193#4018C2318yes—
194#4018C2318yes—
195C42×D5C2318yes—
196C42×D5C2318yes—
197#4016C2318yes—
198#4015C2318yes—
199C4×Dic10C23116yes—
200#3512—532no—
201C2×#553—54no—
202C2×#553—54no—
203C2×#553—54no—
204C2×#552—54no—
205C2×#541—51no—
206C2×#541—51no—
207C2×#540—51no—
208C2×#540D511yescharacteristic, complemented
209C2×#537—52no—
210C2×#532—51no—
211C2×#529—52no—
212C2×#529—52no—
213C22×#125—51no—
214C2×#520—52no—
215C2×C4×#41—51no—
216C24×C5C2414yes—
217C24×C5C2411yescharacteristic
218C23×D5C2411yescharacteristic
219C23×D5C2411yescharacteristic
220C2×C5×D4—28no—
221C2×C5×D4—48no—
222C2×C5×D4—48no—
223C2×C5×D4C2418yes—
224C2×C5×D4C24116yes—
225C2×C5×D4C24116yes—
226C22×C4×C5—24no—
227C22×C4×C5—48no—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C22×C4×C5C2414yes—
232C22×C4×C5C2414yes—
233C22×C4×C5C24116yes—
234C22×C4×C5C2411yescharacteristic
235C2×C22⋊D5—24no—
236C2×C22⋊D5—216no—
237C2×C22⋊D5—24no—
238C2×C22⋊D5—48no—
239C2×C22⋊D5C2414yes—
240C2×C22⋊D5C2414yes—
241C2×C22⋊D5C24116yes—
242C2×C22⋊D5C24116yes—
243C22×Dic5—216no—
244C22×Dic5—44no—
245C22×Dic5—48no—
246C22×Dic5C2411yescharacteristic
247C22×Dic5C2412yes—
248C22×Dic5C2414yes—
249C22×Dic5C2414yes—
250C22×Dic5C2412yes—
251C22×Dic5C24116yes—
252C22×Dic5C24116yes—
253C22×Dic5C2418yes—
254C22×Dic5C2411yescharacteristic
255#711—264no—
256#709—232no—
257C2×D20—24no—
258C2×D20C2414yes—
259C2×C4×D5—24no—
260C2×C4×D5—44no—
261C2×C4×D5—44no—
262C2×C4×D5—48no—
263C2×C4×D5#4118yes—
264C2×C4×D5C2414yes—
265C2×C4×D5C2418yes—
266C2×C4×D5C2418yes—
267C2×C4×D5C24116yes—
268C2×C4×D5C2414yes—
269C2×Dic10—28no—
270C2×Dic10—24no—
271C2×Dic10C2414yes—
272C2×Dic10C2418yes—
273C5×C4⋊C4C2418yes—
274C5×C4⋊C4C2418yes—
275C5×C4⋊C4C24116yes—
276C5×C22⋊C4C2418yes—
277C5×C22⋊C4C24116yes—
278C5×C22⋊C4C24116yes—
279C42×C5C2414yes—
280C42×C5C2414yes—
281C22⋊Dic5C24116yes—
282C22⋊Dic5C24116yes—
283C22⋊Dic5C24116yes—
284C22⋊Dic5C24116yes—
285C22⋊Dic5C24116yes—
286#685C2418yes—
287#685C2418yes—
288#685C24116yes—
289C4⋊Dic5C2418yes—
290C4⋊Dic5C24116yes—
291C4⋊Dic5C24116yes—
292C4⋊Dic5C24116yes—
293#683C24116yes—
294#683C24116yes—
295#683C2418yes—
296#683C2418yes—
297#683C24116yes—
298#683C24116yes—
299#683C24116yes—
300#683C24116yes—
301C4×Dic5C24116yes—
302C4×Dic5C2414yes—
303C4×Dic5C2418yes—
304C4×Dic5C2418yes—
305C4×Dic5C2414yes—
306C4×Dic5C2418yes—
307C4×Dic5C24116yes—
308C22×#41—52no—
309C22×#41—51no—
310#553—564no—
311#553—564no—
312#553—564no—
313#552—564no—
314#541—516no—
315#541—516no—
316#540—516no—
317#540C2×D5116yescomplemented
318#537—532no—
319#532—516no—
320C2×C4⋊Q8—51no—
321C2×#127C2×D511yescharacteristic
322#529—532no—
323#529—532no—
324C2×#126—54no—
325C2×#126—54no—
326C2×#126—54no—
327C2×#126—54no—
328C2×#125—516no—
329C2×#125—54no—
330C2×#125—54no—
331C2×#125—52no—
332C2×#125—54no—
333C2×#125—51no—
334C2×#125C2×D511yescharacteristic
335C2×#124—52no—
336C2×#123—54no—
337C2×#123—54no—
338C2×#123—54no—
339C2×#123C2×D514yes—
340C2×C22⋊Q8—52no—
341C2×C22⋊Q8—52no—
342C2×C22⋊Q8—54no—
343C2×#121—52no—
344C2×#121—54no—
345C2×#121—54no—
346C2×#121—54no—
347C2×#121—54no—
348C2×#121—54no—
349C2×#121C2×D512yes—
350C2×#121C2×D514yes—
351#520—532no—
352C4×#41—516no—
353C2×C4×Q8—52no—
354C2×C4×Q8—52no—
355C2×C4×Q8—52no—
356C2×C4×D4—52no—
357C2×C4×D4—54no—
358C2×C4×D4—54no—
359C2×C4×D4—54no—
360C2×C4×D4—54no—
361C2×C4×D4—52no—
362C2×C4×D4—52no—
363C2×C4×D4—52no—
364C2×C4×D4—54no—
365C2×C4×D4C2×D512yes—
366C2×#117—54no—
367C2×#117—54no—
368C2×#117—54no—
369C2×#117—51no—
370C2×#117—51no—
371C2×#117C2×D511yescharacteristic
372C22×C4⋊C4—54no—
373C22×C4⋊C4—52no—
374C22×C4⋊C4—54no—
375C22×C42—51no—
376C22×C42—51no—
377C22×C42—51no—
378C23×C5—28no—
379C23×C5—22no—
380C23×C5—28no—
381C23×C5—24no—
382C23×C5—28no—
383C23×C5C2518yes—
384C23×C5C2512yes—
385C23×C5C2511yescharacteristic
386C22×D5—24no—
387C22×D5—22no—
388C22×D5—24no—
389C22×D5C2×#4114yes—
390C22×D5C2512yes—
391C22×D5C2512yes—
392C5×D4—216no—
393C5×D4—416no—
394C5×D4—416no—
395C2×C4×C5—22no—
396C2×C4×C5—24no—
397C2×C4×C5—28no—
398C2×C4×C5—24no—
399C2×C4×C5—28no—
400C2×C4×C5—416no—
401C2×C4×C5C2×#4114yes—
402C2×C4×C5C2514yes—
403C2×C4×C5C2512yes—
404C2×C4×C5C2514yes—
405C2×C4×C5C2518yes—
406C2×C4×C5C2512yes—
407C22⋊D5—28no—
408C22⋊D5—232no—
409C22⋊D5—28no—
410C22⋊D5—416no—
411C2×Dic5—22no—
412C2×Dic5—28no—
413C2×Dic5—24no—
414C2×Dic5—28no—
415C2×Dic5—24no—
416C2×Dic5—232no—
417C2×Dic5—48no—
418C2×Dic5—416no—
419C2×Dic5C2×#4114yes—
420C2×Dic5C2514yes—
421C2×Dic5C2514yes—
422C2×Dic5C2518yes—
423C2×Dic5C2512yes—
424C2×Dic5C2518yes—
425C2×Dic5C2512yes—
426D20—28no—
427C4×D5—28no—
428C4×D5—48no—
429C4×D5—48no—
430C4×D5—416no—
431C4×D5C2×#41116yes—
432Dic10—216no—
433Dic10—28no—
434C2×#41—516no—
435C2×#41—58no—
436C2×#41—108no—
437C2×#41—1016no—
438C22×Q8—51no—
439C22×Q8—52no—
440C22×D4—51no—
441C22×D4—54no—
442C22×D4—51no—
443C22×D4—54no—
444C22×D4—51no—
445C22×D4C22×D512yes—
446C22×D4C22×D514yes—
447C22×D4C22×D514yes—
448C23×C4—51no—
449C23×C4—54no—
450C23×C4—54no—
451C23×C4—52no—
452C23×C4—51no—
453C23×C4—54no—
454C23×C4—52no—
455C23×C4—52no—
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D514yes—
458C4⋊Q8—58no—
459#127C22×D518yes—
460#126—532no—
461#126—532no—
462#126—532no—
463#126—532no—
464#125—516no—
465#125—532no—
466#125—532no—
467#125—532no—
468#125—58no—
469#125C22×D518yes—
470#124—516no—
471#123—532no—
472#123—532no—
473#123—532no—
474#123C22×D5132yes—
475C22⋊Q8—516no—
476C22⋊Q8—516no—
477C22⋊Q8—532no—
478#121—516no—
479#121—532no—
480#121—532no—
481#121—532no—
482#121—532no—
483#121—532no—
484#121C22×D5116yes—
485#121C22×D5132yes—
486C4×Q8—516no—
487C4×Q8—516no—
488C4×Q8—516no—
489C4×D4—516no—
490C4×D4—532no—
491C4×D4—532no—
492C4×D4—532no—
493C4×D4—532no—
494C4×D4—516no—
495C4×D4—516no—
496C4×D4—516no—
497C4×D4—532no—
498C4×D4C22×D5116yes—
499#117—532no—
500#117—532no—
501#117—532no—
502#117—58no—
503#117—58no—
504#117C22×D518yes—
505C2×C4⋊C4—52no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—52no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—532no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—52no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—516no—
519C2×C4⋊C4—532no—
520C2×C4⋊C4C22×D512yes—
521C2×C4⋊C4C22×D514yes—
522C2×C4⋊C4C22×D512yes—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—52no—
529C2×C22⋊C4—52no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4C22×D514yes—
532C2×C22⋊C4C22×D514yes—
533C2×C22⋊C4C22×D512yes—
534C2×C42—51no—
535C2×C42—54no—
536C2×C42—54no—
537C2×C42—52no—
538C2×C42—52no—
539C2×C42—52no—
540C2×C42—58no—
541C2×C42—51no—
542C2×C42—58no—
543C2×C42—58no—
544C2×C42C22×D511yescharacteristic
545C2×C42C22×D511yescharacteristic
546C22×C5—28no—
547C22×C5—22no—
548C22×C5—28no—
549C22×C5—24no—
550C22×C5—28no—
551C22×C5—416no—
552C22×C5—44no—
553C22×C5C22×#4112yes—
554C22×C5#58514yes—
555C22×C5C2611yescharacteristic
556C2×D5—24no—
557C2×D5—28no—
558C2×D5—22no—
559C2×D5—24no—
560C2×D5—44no—
561C2×D5C22×#4114yes—
562C4×C5—22no—
563C4×C5—24no—
564C4×C5—28no—
565C4×C5—24no—
566C4×C5C22×#4114yes—
567Dic5—22no—
568Dic5—28no—
569Dic5—24no—
570Dic5—28no—
571Dic5—24no—
572Dic5C22×#4114yes—
573C24—51no—
574C24—51no—
575C24C23×D511yescharacteristic
576C24C23×D514yes—
577#41—1032no—
578#41—1064no—
579C2×Q8—54no—
580C2×Q8—58no—
581C2×Q8—104no—
582C2×Q8—108no—
583C2×D4—28no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—54no—
587C2×D4—516no—
588C2×D4—54no—
589C2×D4—516no—
590C2×D4—54no—
591C2×D4—104no—
592C2×D4—104no—
593C2×D4—104no—
594C2×D4—1016no—
595C2×D4—208no—
596C2×D4C23×D518yes—
597C2×D4C23×D5116yes—
598C2×D4C23×D5116yes—
599C22×C4—24no—
600C22×C4—48no—
601C22×C4—51no—
602C22×C4—58no—
603C22×C4—54no—
604C22×C4—516no—
605C22×C4—52no—
606C22×C4—52no—
607C22×C4—54no—
608C22×C4—51no—
609C22×C4—54no—
610C22×C4—58no—
611C22×C4—516no—
612C22×C4—54no—
613C22×C4—58no—
614C22×C4—58no—
615C22×C4—516no—
616C22×C4—1016no—
617C22×C4—104no—
618C22×C4—204no—
619C22×C4—208no—
620C22×C4—204no—
621C22×C4—204no—
622C22×C4—208no—
623C22×C4C23×D514yes—
624C22×C4C23×D512yes—
625C22×C4C23×D511yescharacteristic
626C22×C4C23×D512yes—
627C22×C4C23×D514yes—
628C22×C4C23×D5116yes—
629C22×C4C23×D511yescharacteristic
630C4⋊C4—58no—
631C4⋊C4—516no—
632C4⋊C4—516no—
633C4⋊C4—516no—
634C4⋊C4—58no—
635C4⋊C4—516no—
636C4⋊C4—516no—
637C4⋊C4—516no—
638C4⋊C4—58no—
639C4⋊C4—516no—
640C4⋊C4—516no—
641C4⋊C4—516no—
642C4⋊C4C23×D518yes—
643C4⋊C4C23×D5116yes—
644C4⋊C4C23×D518yes—
645C22⋊C4—516no—
646C22⋊C4—516no—
647C22⋊C4—516no—
648C22⋊C4—516no—
649C22⋊C4—516no—
650C22⋊C4—58no—
651C22⋊C4—58no—
652C22⋊C4—516no—
653C22⋊C4C23×D5116yes—
654C22⋊C4C23×D5116yes—
655C22⋊C4C23×D518yes—
656C42—54no—
657C42—54no—
658C42—58no—
659C42—58no—
660C42—58no—
661C42—516no—
662C42—516no—
663C42C23×D514yes—
664C42C23×D514yes—
665C2×C5—48no—
666C2×C5—42no—
667C2×C5#351214yescomplemented
668C2×C5C23×#4111yescharacteristic
669C2×C5C2×#58512yes—
670D5—24no—
671D5—42no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—24no—
676C23—28no—
677C23—54no—
678C23—52no—
679C23—52no—
680C23—104no—
681C23—102no—
682C23—104no—
683C23C24×D512yes—
684C23C24×D518yes—
685C23C24×D511yescharacteristic
686Q8—108no—
687Q8—1016no—
688D4—216no—
689D4—416no—
690D4—416no—
691D4—108no—
692D4—108no—
693D4—108no—
694D4—1032no—
695D4—2016no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—416no—
702C2×C4—54no—
703C2×C4—52no—
704C2×C4—516no—
705C2×C4—54no—
706C2×C4—54no—
707C2×C4—52no—
708C2×C4—58no—
709C2×C4—58no—
710C2×C4—1032no—
711C2×C4—108no—
712C2×C4—102no—
713C2×C4—104no—
714C2×C4—104no—
715C2×C4—108no—
716C2×C4—108no—
717C2×C4—208no—
718C2×C4—2016no—
719C2×C4—208no—
720C2×C4—208no—
721C2×C4—2016no—
722C2×C4D5×#4114yes—
723C2×C4C24×D514yes—
724C2×C4C24×D512yes—
725C2×C4C24×D514yes—
726C2×C4C24×D518yes—
727C2×C4C24×D512yes—
728C5C2×#351211yescharacteristic, complemented, Sylow
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—54no—
737C22—108no—
738C22—104no—
739C22—102no—
740C22—104no—
741C22—204no—
742C22C2×D5×#4112yes—
743C22#6628514yes—
744C22C25×D511yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—54no—
750C4—108no—
751C4—102no—
752C4—104no—
753C4—104no—
754C4—108no—
755C4C2×D5×#4114yes—
756C2—42no—
757C2—48no—
758C2—104no—
759C2—202no—
760C2#1061837014yesdirect product factor
761C2C22×D5×#4111yescharacteristic
762C2C2×#6628512yes—
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#540C2
socleC23×C5C25
hypercenterC2×#540D5
hypocenterC5C2×#3512
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C5×#540C2semidirect
2. #10618370C2direct (N × H)
3. C2×#66053C2semidirect
4. C2×#66050C2semidirect
5. C2×#66031C2semidirect
6. C2×D5×#125C2semidirect
7. C2×#65995C2semidirect
8. C2×#65984C2semidirect
9. C2×#65948C2semidirect
10. C2×#65942C2semidirect
11. C2×#65935C2semidirect
12. C2×#65934C2semidirect
13. C2×#65891C2semidirect
14. C2×#65880C2semidirect
15. C2×#65852C2semidirect
16. C2×#65856C2semidirect
19. C5×#540C22semidirect
44. #66053C22semidirect
45. #66050C22semidirect
46. #66031C22semidirect
47. D5×#125C22semidirect
48. #65995C22semidirect
49. #65984C22semidirect
50. #65948C22semidirect
51. #65942C22semidirect
52. #65935C22semidirect
53. #65934C22semidirect
54. #65891C22semidirect
55. #65880C22semidirect
56. #65856C22semidirect
57. #65852C22semidirect
208. C2×#540D5semidirect
317. #540C2×D5semidirect
667. C2×C5#3512semidirect
728. C5C2×#3512semidirect
760. C2#10618370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5402
#106183702
C2×#660532
C2×#660502
C2×#660312
C2×D5×#1252
C2×#659952
C2×#659842
C2×#659482
C2×#659422
C2×#659352
C2×#659342
C2×#658912
C2×#658802
C2×#658522
C2×#658562
C2×#35125