Finite Group Databasebeta

← C2×#10612521 #12969237

Subgroups — C2×#10612521 #12969237

Order 1280.

2234 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65956C211yesmaximal, characteristic, complemented
2C2×#65930C211yesmaximal, characteristic
3C2×C5×#468C211yesmaximal, characteristic, complemented
4C2×#65464C211yesmaximal, characteristic, complemented
5C2×#65453C211yesmaximal, characteristic, complemented
6C2×#65423C211yesmaximal, characteristic, complemented
7C2×M16×Dic5C211yesmaximal, characteristic, complemented
8C2×#65338C211yesmaximal, characteristic, complemented
9C2×#65331C211yesmaximal, characteristic, complemented
10#10612521C2116yesmaximal, direct product factor
11C2×#65163C211yesmaximal, characteristic, complemented
12C2×#65178C211yesmaximal, characteristic, complemented
13C2×#65081C211yesmaximal, characteristic, complemented
14C2×#65106C211yesmaximal, characteristic, complemented
15C2×#65049C211yesmaximal, characteristic, complemented
16C2×#65046C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×SD16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C2×#4090C2211yescharacteristic
24C22×#688C2211yescharacteristic
25C2×#4086C2211yescharacteristic
26C2×#4085—21no—
27C2×D4×Dic5C2211yescharacteristic
28C22×#687C2211yescharacteristic
29C2×#4076C2211yescharacteristic
30C2×#4070C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×#681C2211yescharacteristic
33C22×#677C2211yescharacteristic
34#65956—24no—
35#65956C2218yescomplemented
36#65930—24no—
37#65930C2218yes—
38C2×#4039C2211yescharacteristic
39C2×#4035—21no—
40C2×#4034C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4033—21no—
43C2×#4033C2211yescharacteristic
44C2×#4031—21no—
45C2×#4027—21no—
46C2×#4024—21no—
47C2×#4023—21no—
48C5×#468C2218yescomplemented
49C2×C5×#107C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65464C2218yescomplemented
55#65453C2218yescomplemented
56#65423C2218yescomplemented
57M16×Dic5C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3947C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×C8×Dic5C2211yescharacteristic
64C2×C8×Dic5C2211yescharacteristic
65#65338C2218yescomplemented
66#65331C2218yescomplemented
67C2×#3942C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65178C2218yescomplemented
72#65163C2218yescomplemented
73#65106C2218yescomplemented
74#65081C2218yescomplemented
75#65049C2218yescomplemented
76#65046C2218yescomplemented
77C2×#3182—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C23×Dic5D411yescharacteristic
87C23×Dic5D411yescharacteristic
88C2×#711—28no—
89C2×#711—48no—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×Dic10—21no—
93C22×Dic10—21no—
94C22×Dic10C2311yescharacteristic
95C2×C5×SD16—24no—
96C2×C5×SD16C2314yes—
97C2×C5×M16—24no—
98C2×C5×M16C2314yes—
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8C2314yes—
103C5×#121—22no—
104C5×#121C2314yes—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112Q8×Dic5—22no—
113Q8×Dic5C2314yes—
114#4090—22no—
115#4090C2314yes—
116C2×#688—24no—
117C2×#688C2314yes—
118#4086—22no—
119#4086C2314yes—
120#4085—28no—
121D4×Dic5—22no—
122D4×Dic5C2314yes—
123C2×#687—24no—
124C2×#687C2314yes—
125#4076—22no—
126#4076C2314yes—
127C2×#685—21no—
128C2×#685—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132#4070—22no—
133#4070C2314yes—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683—21no—
140C2×C4×Dic5—21no—
141C2×C4×Dic5—21no—
142C2×C4×Dic5D411yescharacteristic
143C2×C4×Dic5D411yescharacteristic
144C2×C4×Dic5D414yes—
145C2×C4×Dic5C2311yescharacteristic
146C2×C4×Dic5C2311yescharacteristic
147C2×C4×Dic5C2314yes—
148C2×#681—24no—
149C2×#681C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C2×#677—24no—
153C2×#677C2314yes—
154#4039—22no—
155#4039C2314yes—
156#4035—28no—
157#4034—22no—
158#4034—22no—
159#4034C2314yes—
160#4034C2314yes—
161#4033—28no—
162#4033—22no—
163#4033C2314yes—
164#4031—28no—
165#4027—28no—
166#4024—28no—
167#4023—28no—
168C5×#107C2314yes—
169C5×#103C2314yes—
170C5×#102C2314yes—
171#3967C2314yes—
172#3964C2314yes—
173#3953C2314yes—
174#3950C2314yes—
175#3948C2314yes—
176#3947C2314yes—
177#3947C2314yes—
178C8×Dic5C2314yes—
179C8×Dic5C2314yes—
180#3942C2314yes—
181#3941C2314yes—
182#3939C2314yes—
183#3939C2314yes—
184C2×#533—51no—
185C2×#532—51no—
186#3182—516no—
187C2×#500—51no—
188C2×#492—51no—
189C2×#487—51no—
190C2×#486—51no—
191C2×#468—51no—
192C2×#468—51no—
193C2×#468—51no—
194C2×#468D511yescharacteristic, complemented
195C2×#440—51no—
196C2×#440—51no—
197C2×#440—51no—
198C2×#440—51no—
199C2×C4×M16—51no—
200C24×C5—21no—
201C24×C5C2×D411yescharacteristic
202C23×D5—21no—
203C2×C5×Q8—21no—
204C2×C5×Q8—22no—
205C2×C5×Q8—22no—
206C2×C5×Q8C2412yes—
207C2×C5×D4—24no—
208C2×C5×D4—21no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—44no—
212C2×C5×D4C2412yes—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2411yescharacteristic
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—24no—
225C2×C22⋊D5—44no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—44no—
228C22×Dic5—24no—
229C22×Dic5—24no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—24no—
234C22×Dic5—44no—
235C22×Dic5C2×D411yescharacteristic
236C22×Dic5C2×D411yescharacteristic
237C22×Dic5C2×D414yes—
238C22×Dic5C2×D414yes—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241#711—432no—
242C2×D20—22no—
243C2×D20—22no—
244C2×D20—21no—
245C2×D20C2412yes—
246C2×C4×D5—24no—
247C2×C4×D5—44no—
248C2×Dic10—22no—
249C2×Dic10—22no—
250C2×Dic10—21no—
251C2×Dic10—24no—
252C2×Dic10—24no—
253C2×Dic10—44no—
254C2×Dic10—44no—
255C2×Dic10C2412yes—
256C5×SD16—28no—
257C5×M16—28no—
258C2×C5×C8—22no—
259C2×C5×C8#4114yescomplemented
260C2×C5×C8C2412yes—
261C2×C5×C8C2412yes—
262C5×C4⋊C4—24no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4C2412yes—
266C5×C4⋊C4C2412yes—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C22⋊Dic5—24no—
270C22⋊Dic5—24no—
271#688—28no—
272#687—28no—
273#685—24no—
274#685—24no—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—24no—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280#683—24no—
281#683—24no—
282#683—24no—
283#683—24no—
284#683—24no—
285#683—24no—
286C4×Dic5—24no—
287C4×Dic5—24no—
288C4×Dic5C2×D414yes—
289C4×Dic5C2×D414yes—
290C4×Dic5C2×D412yes—
291C4×Dic5C2×D412yes—
292C4×Dic5C2412yes—
293C4×Dic5C2412yes—
294#681—28no—
295C2×#168—22no—
296C2×#168#4114yescomplemented
297C2×#168C2412yes—
298C2×#168C2412yes—
299#677—28no—
300C22×#41—101no—
301C22×SD16—51no—
302C22×SD16—51no—
303C22×SD16—51no—
304C22×SD16C2×D511yescharacteristic
305C22×M16—51no—
306C22×M16C2×D511yescharacteristic
307#533—58no—
308#533—104no—
309#532—58no—
310#532—104no—
311C2×C4⋊Q8—51no—
312C2×C4⋊Q8—51no—
313C2×C4⋊Q8—51no—
314C2×#127—51no—
315C2×#125—101no—
316C2×#124—101no—
317C2×C22⋊Q8—51no—
318C2×C22⋊Q8—101no—
319C2×C22⋊Q8C2×D511yescharacteristic
320C2×#121—51no—
321C2×#121—101no—
322C2×#121C2×D511yescharacteristic
323C2×C4×Q8—51no—
324C2×C4×Q8—51no—
325C2×C4×Q8—101no—
326C2×C4×D4—51no—
327C2×C4×D4—51no—
328C2×C4×D4—101no—
329C2×#117—101no—
330C22×C42—51no—
331#500—58no—
332#492—58no—
333#487—58no—
334#486—58no—
335#468—58no—
336#468—58no—
337#468—58no—
338#468C2×D518yescomplemented
339#440—58no—
340#440—58no—
341#440—58no—
342#440—58no—
343C2×#107—51no—
344C2×#107—51no—
345C2×#107—51no—
346C2×#107C2×D511yescharacteristic
347C2×#103—51no—
348C2×#103—51no—
349C2×#103—51no—
350C2×#103C2×D511yescharacteristic
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—51no—
354C2×#102C2×D511yescharacteristic
355C4×M16—58no—
356C2×#97—51no—
357C2×#97—51no—
358C2×C4×C8—51no—
359C2×C4×C8—51no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5C22×D412yes—
368C23×C5C22×D411yescharacteristic
369C22×D5—22no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C5×Q8—22no—
374C5×Q8—22no—
375C5×Q8—42no—
376C5×D4—22no—
377C5×D4—22no—
378C5×D4—48no—
379C5×D4—42no—
380C2×C4×C5—22no—
381C2×C4×C5—24no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D411yescharacteristic
392C2×C4×C5C2×#4112yes—
393C2×C4×C5C2×#4112yes—
394C2×C4×C5C2511yescharacteristic
395C22⋊D5—48no—
396C22⋊D5—48no—
397C22⋊D5—48no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—28no—
401C2×Dic5—28no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—48no—
406C2×Dic5—42no—
407C2×Dic5—42no—
408C2×Dic5—42no—
409C2×Dic5AGL(1,ℤ/8)14yes—
410C2×Dic5#13714yes—
411C2×Dic5C22×D412yes—
412C2×Dic5C22×D412yes—
413C2×Dic5C22×D412yes—
414C2×Dic5C22×D412yes—
415D20—22no—
416D20—22no—
417D20—42no—
418C4×D5—48no—
419Dic10—22no—
420Dic10—22no—
421Dic10—42no—
422Dic10—48no—
423Dic10—48no—
424C5×C8—22no—
425C5×C8C2×#4114yescomplemented
426#168—22no—
427#168C2×#4114yescomplemented
428C2×#41—108no—
429C2×#41—208no—
430C22×Q8—51no—
431C22×Q8—101no—
432C22×Q8—101no—
433C22×Q8C22×D511yescharacteristic
434C22×D4—21no—
435C22×D4—51no—
436C22×D4—101no—
437C22×D4—101no—
438C22×D4—101no—
439C22×D4C22×D511yescharacteristic
440C23×C4—51no—
441C23×C4—51no—
442C23×C4—101no—
443C23×C4—101no—
444C23×C4C22×D511yescharacteristic
445C2×SD16—24no—
446C2×SD16—54no—
447C2×SD16—54no—
448C2×SD16—54no—
449C2×SD16—104no—
450C2×SD16—104no—
451C2×SD16—104no—
452C2×SD16C22×D514yes—
453C2×M16—24no—
454C2×M16—54no—
455C2×M16—104no—
456C2×M16C22×D514yes—
457C22×C8—51no—
458C22×C8—51no—
459C22×C8C22×D511yescharacteristic
460C22×C8C22×D511yescharacteristic
461C4⋊Q8—54no—
462C4⋊Q8—54no—
463C4⋊Q8—54no—
464C4⋊Q8—102no—
465C4⋊Q8—102no—
466C4⋊Q8—102no—
467#127—54no—
468#127—102no—
469#125—108no—
470#124—108no—
471C22⋊Q8—22no—
472C22⋊Q8—54no—
473C22⋊Q8—108no—
474C22⋊Q8—102no—
475C22⋊Q8C22×D514yes—
476#121—22no—
477#121—54no—
478#121—108no—
479#121—102no—
480#121C22×D514yes—
481C4×Q8—54no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8—108no—
485C4×Q8—102no—
486C4×D4—54no—
487C4×D4—54no—
488C4×D4—108no—
489C4×D4—102no—
490C4×D4—102no—
491#117—108no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4C22×D511yescharacteristic
503C2×C4⋊C4C22×D511yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C42—51no—
511C2×C42—51no—
512C2×C42—54no—
513C2×C42—51no—
514C2×C42—51no—
515C2×C42—54no—
516C2×C42—101no—
517C2×C42—101no—
518#107—54no—
519#107—54no—
520#107—54no—
521#107C22×D514yes—
522#103—54no—
523#103—54no—
524#103—54no—
525#103C22×D514yes—
526#102—54no—
527#102—54no—
528#102—54no—
529#102C22×D514yes—
530#97—54no—
531#97—54no—
532C4×C8—54no—
533C4×C8—54no—
534C22×C5—22no—
535C22×C5—22no—
536C22×C5—22no—
537C22×C5—44no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—84no—
542C22×C5#53212yes—
543C22×C5C2×AGL(1,ℤ/8)12yes—
544C22×C5C2×#13712yes—
545C22×C5C23×D411yescharacteristic
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—84no—
550C4×C5—22no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5#53212yes—
555C4×C5C22×#4111yescharacteristic
556C4×C5C22×#4111yescharacteristic
557Dic5—22no—
558Dic5—22no—
559Dic5—42no—
560Dic5—42no—
561Dic5—42no—
562Dic5C2×AGL(1,ℤ/8)14yes—
563Dic5C2×#13714yes—
564C24—21no—
565C24—101no—
566C24D4×D511yescharacteristic
567#41—2032no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—52no—
572C2×Q8—104no—
573C2×Q8—104no—
574C2×Q8—101no—
575C2×Q8—102no—
576C2×Q8—102no—
577C2×Q8—204no—
578C2×Q8—204no—
579C2×Q8C23×D512yes—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—52no—
586C2×D4—104no—
587C2×D4—104no—
588C2×D4—104no—
589C2×D4—101no—
590C2×D4—102no—
591C2×D4—102no—
592C2×D4—204no—
593C2×D4—204no—
594C2×D4—204no—
595C2×D4C23×D512yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—51no—
602C22×C4—51no—
603C22×C4—54no—
604C22×C4—54no—
605C22×C4—51no—
606C22×C4—51no—
607C22×C4—104no—
608C22×C4—104no—
609C22×C4—104no—
610C22×C4—104no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—204no—
615C22×C4—204no—
616C22×C4D4×D512yes—
617C22×C4D4×D511yescharacteristic
618C22×C4C23×D512yes—
619C22×C4C23×D511yescharacteristic
620SD16—28no—
621SD16—108no—
622SD16—108no—
623SD16—108no—
624M16—28no—
625M16—108no—
626C2×C8—22no—
627C2×C8—54no—
628C2×C8—52no—
629C2×C8—52no—
630C2×C8—102no—
631C2×C8#71114yescomplemented
632C2×C8C23×D512yes—
633C2×C8C23×D512yes—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—52no—
638C4⋊C4—52no—
639C4⋊C4—104no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—101no—
646C4⋊C4—101no—
647C4⋊C4—104no—
648C4⋊C4C23×D512yes—
649C4⋊C4C23×D512yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4—104no—
656C42—52no—
657C42—54no—
658C42—54no—
659C42—52no—
660C42—52no—
661C42—52no—
662C42—104no—
663C42—104no—
664C2×C5—42no—
665C2×C5—82no—
666C2×C5#318214yescomplemented
667C2×C5C2×#53211yescharacteristic
668C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
669C2×C5C22×#13711yescharacteristic
670D5—82no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—102no—
679C23—202no—
680C23—202no—
681C23—202no—
682C23C2×D4×D512yes—
683C23C2×D4×D511yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—102no—
688Q8—102no—
689Q8—208no—
690Q8—208no—
691Q8—202no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—42no—
696D4—102no—
697D4—102no—
698D4—208no—
699D4—208no—
700D4—208no—
701D4—202no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—54no—
713C2×C4—54no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—52no—
717C2×C4—52no—
718C2×C4—108no—
719C2×C4—108no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—208no—
726C2×C4—208no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4C2×D4×D512yes—
731C2×C4C2×D4×D511yescharacteristic
732C2×C4C2×#71112yes—
733C2×C4D5×#4112yes—
734C2×C4C24×D511yescharacteristic
735C8—22no—
736C8—54no—
737C8—102no—
738C8C2×#71114yescomplemented
739C5C2×#318211yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—404no—
752C22#6593012yes—
753C22D5×AGL(1,ℤ/8)12yes—
754C22D5×#13712yes—
755C22C22×D4×D511yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—54no—
761C4—54no—
762C4—102no—
763C4—102no—
764C4—202no—
765C4—202no—
766C4—202no—
767C4#6593012yes—
768C4C22×#71111yescharacteristic
769C4C2×D5×#4111yescharacteristic
770C2—42no—
771C2—82no—
772C2—402no—
773C2#1061252114yesdirect product factor
774C2C2×#6593011yescharacteristic
775C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
776C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#468C2
socleC23×C5C22×D4
prime radicalC2×#65930C2
hypercenterC2×#468D5
hypocenterC5C2×#3182
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#65956C2semidirect
3. C2×C5×#468C2semidirect
4. C2×#65464C2semidirect
5. C2×#65453C2semidirect
6. C2×#65423C2semidirect
7. C2×M16×Dic5C2semidirect
8. C2×#65338C2semidirect
9. C2×#65331C2semidirect
10. #10612521C2direct (N × H)
11. C2×#65163C2semidirect
12. C2×#65178C2semidirect
13. C2×#65081C2semidirect
14. C2×#65106C2semidirect
15. C2×#65049C2semidirect
16. C2×#65046C2semidirect
35. #65956C22semidirect
48. C5×#468C22semidirect
54. #65464C22semidirect
55. #65453C22semidirect
56. #65423C22semidirect
57. M16×Dic5C22semidirect
65. #65338C22semidirect
66. #65331C22semidirect
71. #65178C22semidirect
72. #65163C22semidirect
73. #65106C22semidirect
74. #65081C22semidirect
75. #65049C22semidirect
76. #65046C22semidirect
194. C2×#468D5semidirect
259. C2×C5×C8#41semidirect
296. C2×#168#41semidirect
338. #468C2×D5semidirect
425. C5×C8C2×#41semidirect
427. #168C2×#41semidirect
631. C2×C8#711semidirect
666. C2×C5#3182semidirect
738. C8C2×#711semidirect
739. C5C2×#3182semidirect
773. C2#10612521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659562
C2×#659302
C2×C5×#4682
C2×#654642
C2×#654532
C2×#654232
C2×M16×Dic52
C2×#653382
C2×#653312
#106125212
C2×#651632
C2×#651782
C2×#650812
C2×#651062
C2×#650492
C2×#650462
C2×#31825