Finite Group Databasebeta

← C2×#10611242 #12975908

Subgroups — C2×#10611242 #12975908

Order 1280.

2094 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×#65875C211yesmaximal, characteristic
2C2×D4×Dic10C211yesmaximal, characteristic
3C2×C5×#435C211yesmaximal, characteristic
4C2×#65426C211yesmaximal, characteristic, complemented
5C2×#65409C211yesmaximal, characteristic, complemented
6C2×#65405C211yesmaximal, characteristic, complemented
7C22×#3948C211yesmaximal, characteristic, complemented
8#10611242C2116yesmaximal, direct product factor
9C2×#65118C211yesmaximal, characteristic, complemented
10C2×#65138C211yesmaximal, characteristic, complemented
11C2×#65028C211yesmaximal, characteristic, complemented
12C2×#65028C211yesmaximal, characteristic, complemented
13C2×#65012C211yesmaximal, characteristic, complemented
14C2×#65010C211yesmaximal, characteristic, complemented
15C2×#64992C211yesmaximal, characteristic, complemented
16C2×#65005C211yesmaximal, characteristic, complemented
17C23×Dic10C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4081—21no—
23C2×D4×Dic5—21no—
24C2×#4072C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C2×#4070C2211yescharacteristic
27C2×#4070C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic
30C22×Dic20C2211yescharacteristic
31C22×Dic20C2211yescharacteristic
32C22×Dic20C2211yescharacteristic
33#65875—24no—
34#65875C2218yes—
35D4×Dic10—24no—
36D4×Dic10C2218yes—
37C2×#4035—21no—
38C2×#4034—21no—
39C2×#4025—21no—
40C2×#4024—21no—
41C2×#4024—21no—
42C2×#4023—21no—
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#435C2218yes—
48C2×C5×C4⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×C5×#97C2211yescharacteristic
52#65426C2218yescomplemented
53#65409C2218yescomplemented
54#65405C2218yescomplemented
55C2×#3950C2211yescharacteristic
56C2×#3949C2211yescharacteristic
57C2×#3949C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3948C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2218yescomplemented
69#65138C2218yescomplemented
70#65118C2218yescomplemented
71#65028C2218yescomplemented
72#65028C2218yescomplemented
73#65012C2218yescomplemented
74#65010C2218yescomplemented
75#65005C2218yescomplemented
76#64992C2218yescomplemented
77C2×#3312—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×Dic5—21no—
82C23×Dic5—21no—
83C23×Dic5—21no—
84C22×Dic10—24no—
85C22×Dic10—24no—
86C22×Dic10—21no—
87C22×Dic10—21no—
88C22×Dic10—22no—
89C22×Dic10—22no—
90C22×Dic10—42no—
91C22×Dic10—42no—
92C22×Dic10C2311yescharacteristic
93C22×Dic10C2311yescharacteristic
94C22×Dic10C2311yescharacteristic
95C22×Dic10C2314yes—
96C22×Dic10C2314yes—
97C22×Dic10C2311yescharacteristic
98C2×C5×M16—42no—
99C2×C5×M16C2314yes—
100C22×C5×C8—42no—
101C22×C5×C8C2311yescharacteristic
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C22×C5×C8C2314yes—
106C4×C5×D4D414yes—
107C4×C5×D4C2314yes—
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C22⋊C4D411yescharacteristic
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C42×C5C2311yescharacteristic
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117#4081—28no—
118D4×Dic5—28no—
119#4072—22no—
120#4072C2314yes—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5—22no—
125C2×C4⋊Dic5C2311yescharacteristic
126C2×C4⋊Dic5C2311yescharacteristic
127C2×C4⋊Dic5C2311yescharacteristic
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2314yes—
130#4070—22no—
131#4070—22no—
132#4070—22no—
133#4070—22no—
134#4070C2314yes—
135#4070C2314yes—
136#4070C2314yes—
137#4070C2314yes—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C2×Dic20—24no—
150C2×Dic20—42no—
151C2×Dic20—42no—
152C2×Dic20C2314yes—
153C2×Dic20C2314yes—
154C2×Dic20C2314yes—
155#4035—28no—
156#4034—28no—
157#4025—28no—
158#4024—28no—
159#4024—28no—
160#4023—28no—
161#4016—22no—
162#4016C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10—22no—
167C4×Dic10C2314yes—
168C4×Dic10C2314yes—
169C5×C4⋊C8C2314yes—
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yes—
172C5×#97C2314yes—
173#3950C2314yes—
174#3949C2314yes—
175#3949C2314yes—
176#3948C2314yes—
177#3948C2314yes—
178#3948C2314yes—
179#3948C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3948C2314yes—
183#3948C2314yes—
184#3948C2314yes—
185#3948C2314yes—
186C2×#552—51no—
187C2×D4×Q8—51no—
188#3312—516no—
189C2×#491—51no—
190C2×#485—51no—
191C2×#483—51no—
192C2×#479—51no—
193C2×#470—51no—
194C2×#467—51no—
195C2×#462—51no—
196C2×#451—51no—
197C2×#451—51no—
198C2×#441—51no—
199C2×#435D511yescharacteristic
200C2×#419—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C2×C5×D4—24no—
205C2×C5×D4C2×D414yes—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2411yescharacteristic
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—24no—
230C22×Dic5—44no—
231C22×Dic5—44no—
232C22×Dic5—44no—
233C2×Dic10—21no—
234C2×Dic10—22no—
235C2×Dic10—22no—
236C2×Dic10—22no—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—22no—
240C2×Dic10—22no—
241C2×Dic10—28no—
242C2×Dic10—28no—
243C2×Dic10—21no—
244C2×Dic10—21no—
245C2×Dic10—24no—
246C2×Dic10—24no—
247C2×Dic10—21no—
248C2×Dic10—44no—
249C2×Dic10—44no—
250C2×Dic10—48no—
251C2×Dic10—48no—
252C2×Dic10—44no—
253C2×Dic10—44no—
254C2×Dic10#4114yes—
255C2×Dic10C2412yes—
256C2×Dic10C2412yes—
257C2×Dic10C2412yes—
258C2×Dic10C2412yes—
259C5×M16—44no—
260C2×C5×C8—22no—
261C2×C5×C8—22no—
262C2×C5×C8—22no—
263C2×C5×C8—22no—
264C2×C5×C8—44no—
265C2×C5×C8C2412yes—
266C2×C5×C8C2412yes—
267C2×C5×C8C2412yes—
268C2×C5×C8C2412yes—
269C5×C4⋊C4C2×D414yes—
270C5×C22⋊C4C2×D414yes—
271C5×C22⋊C4C2×D414yes—
272C42×C5C2×D412yes—
273C42×C5C2412yes—
274C22⋊Dic5—24no—
275C22⋊Dic5—24no—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278C22⋊Dic5—24no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—24no—
282C4⋊Dic5—24no—
283C4⋊Dic5—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—24no—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288C4⋊Dic5C2412yes—
289C4⋊Dic5C2412yes—
290#683—24no—
291#683—24no—
292#683—24no—
293#683—24no—
294#683—24no—
295#683—24no—
296#683—24no—
297#683—24no—
298C4×Dic5—24no—
299C4×Dic5—24no—
300C4×Dic5—24no—
301Dic20—28no—
302Dic20—44no—
303Dic20—44no—
304C23×Q8—51no—
305C23×Q8—51no—
306C22×Q16—51no—
307C22×Q16—51no—
308C22×Q16—51no—
309C22×M16C2×D511yescharacteristic
310C23×C8C2×D511yescharacteristic
311#552—58no—
312#552—104no—
313D4×Q8—58no—
314D4×Q8—104no—
315C2×C4⋊Q8—51no—
316C2×C4⋊Q8—101no—
317C2×#126—101no—
318C2×#125—51no—
319C2×#125—101no—
320C2×#123—101no—
321C2×C22⋊Q8—51no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×D4—101no—
330C2×C4×D4C2×D511yescharacteristic
331C2×#117—51no—
332C2×#117—101no—
333C22×C4⋊C4—51no—
334#491—58no—
335#485—58no—
336#483—58no—
337#479—58no—
338#470—58no—
339#467—58no—
340#462—58no—
341#451—58no—
342#451—58no—
343#441—58no—
344#435C2×D518yes—
345C2×#107—51no—
346C2×#106—51no—
347C2×#106—51no—
348C2×C4⋊C8C2×D511yescharacteristic
349#419—58no—
350C2×#103—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—58no—
360C2×#103—51no—
361C2×C22⋊C8C2×D511yescharacteristic
362C2×C22⋊C8C2×D511yescharacteristic
363C2×#97C2×D511yescharacteristic
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5#13714yes—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C22×D411yescharacteristic
373C5×D4—28no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—24no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C2×#4112yes—
390C2×C4×C5H(5,𝔽2)12yes—
391C2×C4×C5C2511yescharacteristic
392C2×Dic5—24no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—48no—
402C2×Dic5—48no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406C2×Dic5—48no—
407C2×Dic5—42no—
408C2×Dic5—42no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411Dic10—24no—
412Dic10—22no—
413Dic10—22no—
414Dic10—22no—
415Dic10—22no—
416Dic10—22no—
417Dic10—22no—
418Dic10—22no—
419Dic10—48no—
420Dic10—48no—
421Dic10—42no—
422Dic10—42no—
423Dic10—42no—
424Dic10C2×#4114yes—
425C5×C8—22no—
426C5×C8—22no—
427C5×C8—22no—
428C5×C8—22no—
429C22×Q8—51no—
430C22×Q8—51no—
431C22×Q8—51no—
432C22×Q8—51no—
433C22×Q8—54no—
434C22×Q8—54no—
435C22×Q8—104no—
436C22×Q8—104no—
437C22×Q8—101no—
438C22×Q8—101no—
439C22×Q8—102no—
440C22×Q8—102no—
441C22×Q8—202no—
442C22×Q8—202no—
443C22×D4D2011yescharacteristic
444C23×C4—101no—
445C23×C4—101no—
446C23×C4—101no—
447C23×C4C22×D511yescharacteristic
448C23×C4C22×D511yescharacteristic
449C2×Q16—54no—
450C2×Q16—54no—
451C2×Q16—54no—
452C2×Q16—104no—
453C2×Q16—202no—
454C2×Q16—202no—
455C2×M16—42no—
456C2×M16C22×D514yes—
457C22×C8—42no—
458C22×C8C22×D511yescharacteristic
459C22×C8C22×D511yescharacteristic
460C22×C8C22×D511yescharacteristic
461C22×C8C22×D511yescharacteristic
462C22×C8C22×D514yes—
463C4⋊Q8—54no—
464C4⋊Q8—108no—
465C4⋊Q8—102no—
466#126—108no—
467#125—54no—
468#125—108no—
469#125—102no—
470#123—108no—
471C22⋊Q8—54no—
472C22⋊Q8—54no—
473C22⋊Q8—54no—
474C22⋊Q8—54no—
475C22⋊Q8—102no—
476C22⋊Q8—102no—
477C22⋊Q8—102no—
478C22⋊Q8—102no—
479C22⋊Q8—108no—
480C22⋊Q8—108no—
481C4×Q8—54no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8—102no—
485C4×D4—108no—
486C4×D4D2014yes—
487C4×D4C22×D514yes—
488#117—54no—
489#117—102no—
490#117—108no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—54no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4D2011yescharacteristic
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4D2011yescharacteristic
515C2×C22⋊C4D2011yescharacteristic
516C2×C42—101no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42C22×D511yescharacteristic
520#107—54no—
521#106—54no—
522#106—54no—
523C4⋊C8C22×D514yes—
524#103—54no—
525#103—54no—
526#103—54no—
527#103—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#103—54no—
532#103—54no—
533#103—54no—
534C22⋊C8C22×D514yes—
535C22⋊C8C22×D514yes—
536#97C22×D514yes—
537C22×C5—22no—
538C22×C5—28no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—44no—
544C22×C5#54612yes—
545C22×C5C2×#13714yes—
546C22×C5C2×#13712yes—
547C22×C5#57812yes—
548C22×C5C23×D411yescharacteristic
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—22no—
552C4×C5—22no—
553C4×C5#54612yes—
554C4×C5C22×#4111yescharacteristic
555C4×C5C2×H(5,𝔽2)11yescharacteristic
556Dic5—24no—
557Dic5—42no—
558Dic5—42no—
559Dic5—42no—
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24C2×D2011yescharacteristic
565C24C2×D2011yescharacteristic
566C2×Q8—54no—
567C2×Q8—52no—
568C2×Q8—52no—
569C2×Q8—52no—
570C2×Q8—52no—
571C2×Q8—108no—
572C2×Q8—108no—
573C2×Q8—101no—
574C2×Q8—101no—
575C2×Q8—104no—
576C2×Q8—104no—
577C2×Q8—101no—
578C2×Q8—101no—
579C2×Q8—102no—
580C2×Q8—102no—
581C2×Q8—102no—
582C2×Q8—102no—
583C2×Q8—102no—
584C2×Q8—102no—
585C2×Q8—102no—
586C2×Q8—204no—
587C2×Q8—204no—
588C2×Q8—204no—
589C2×Q8—204no—
590C2×Q8—208no—
591C2×Q8—208no—
592C2×D4—24no—
593C2×D4C2×D2014yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—101no—
599C22×C4—104no—
600C22×C4—104no—
601C22×C4—104no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—204no—
610C22×C4—204no—
611C22×C4—204no—
612C22×C4C2×D2012yes—
613C22×C4C2×D2012yes—
614C22×C4C2×D2011yescharacteristic
615C22×C4C2×D2011yescharacteristic
616C22×C4C2×D2011yescharacteristic
617C22×C4C2×D2011yescharacteristic
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D511yescharacteristic
621Q16—108no—
622Q16—204no—
623Q16—204no—
624M16—44no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—44no—
630C2×C8C23×D512yes—
631C2×C8C23×D512yes—
632C2×C8C23×D512yes—
633C2×C8C23×D512yes—
634C4⋊C4—52no—
635C4⋊C4—52no—
636C4⋊C4—52no—
637C4⋊C4—52no—
638C4⋊C4—101no—
639C4⋊C4—101no—
640C4⋊C4—104no—
641C4⋊C4—101no—
642C4⋊C4—101no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—104no—
646C4⋊C4—104no—
647C4⋊C4—104no—
648C4⋊C4—104no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4C2×D2014yes—
654C22⋊C4—104no—
655C22⋊C4—104no—
656C22⋊C4—104no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4C2×D2014yes—
660C22⋊C4C2×D2014yes—
661C42—104no—
662C42—104no—
663C42—104no—
664C42C2×D2012yes—
665C42C23×D512yes—
666C2×C5—24no—
667C2×C5—42no—
668C2×C5#331214yescomplemented
669C2×C5C2×#54611yescharacteristic
670C2×C5C22×#13711yescharacteristic
671C2×C5C2×#57811yescharacteristic
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23#405514yes—
678C23C22×D2012yes—
679C23C22×D2012yes—
680C23C22×D2011yescharacteristic
681Q8—54no—
682Q8—104no—
683Q8—102no—
684Q8—102no—
685Q8—102no—
686Q8—102no—
687Q8—102no—
688Q8—102no—
689Q8—102no—
690Q8—208no—
691Q8—208no—
692Q8—202no—
693Q8—202no—
694Q8—202no—
695D4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—104no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—208no—
716C2×C4—208no—
717C2×C4—208no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4—202no—
721C2×C4—202no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4C22×D2012yes—
726C2×C4C22×D2012yes—
727C2×C4C22×D2012yes—
728C2×C4C22×D2012yes—
729C2×C4C22×D2011yescharacteristic
730C2×C4#414412yes—
731C2×C4D5×#4112yes—
732C2×C4C24×D511yescharacteristic
733C8—22no—
734C8—22no—
735C8—22no—
736C8—22no—
737C5C2×#331211yescharacteristic, complemented, Sylow
738C22—28no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#6588812yes—
746C22C2×#405514yes—
747C22C2×#405512yes—
748C22#6608712yes—
749C22C23×D2011yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—104no—
755C4—202no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4#6588812yes—
763C4C2×#414411yescharacteristic
764C4C2×D5×#4111yescharacteristic
765C2—24no—
766C2—42no—
767C2#1061124214yesdirect product factor
768C2C2×#6588811yescharacteristic
769C2C22×#405511yescharacteristic
770C2C2×#6608711yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
hypercenterC2×#435D5
hypocenterC5C2×#3312
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
4. C2×#65426C2semidirect
5. C2×#65409C2semidirect
6. C2×#65405C2semidirect
7. C22×#3948C2semidirect
8. #10611242C2direct (N × H)
9. C2×#65118C2semidirect
10. C2×#65138C2semidirect
11. C2×#65028C2semidirect
12. C2×#65028C2semidirect
13. C2×#65012C2semidirect
14. C2×#65010C2semidirect
15. C2×#64992C2semidirect
16. C2×#65005C2semidirect
52. #65426C22semidirect
53. #65409C22semidirect
54. #65405C22semidirect
68. C2×#3948C22semidirect
69. #65138C22semidirect
70. #65118C22semidirect
71. #65028C22semidirect
72. #65028C22semidirect
73. #65012C22semidirect
74. #65010C22semidirect
75. #65005C22semidirect
76. #64992C22semidirect
668. C2×C5#3312semidirect
737. C5C2×#3312semidirect
767. C2#10611242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658752
C2×D4×Dic102
C2×C5×#4352
C2×#654262
C2×#654092
C2×#654052
C22×#39482
#106112422
C2×#651182
C2×#651382
C2×#650282
C2×#650122
C2×#650102
C2×#649922
C2×#650052
C2×#33125