Finite Group Databasebeta

← C2×#10615304 #12976018

Subgroups — C2×#10615304 #12976018

Order 1280.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#550C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic, complemented
3C2×#65528C211yesmaximal, characteristic, complemented
4C2×#65528C211yesmaximal, characteristic, complemented
5C2×#65521C211yesmaximal, characteristic, complemented
6C2×#65522C211yesmaximal, characteristic, complemented
7#10615304C2116yesmaximal, direct product factor
8C2×#65364C211yesmaximal, characteristic, complemented
9C2×#65360C211yesmaximal, characteristic, complemented
10C2×#65331C211yesmaximal, characteristic, complemented
11C2×#65330C211yesmaximal, characteristic, complemented
12C2×#65323C211yesmaximal, characteristic, complemented
13C2×#65324C211yesmaximal, characteristic, complemented
14C2×#65311C211yesmaximal, characteristic, complemented
15C2×#65319C211yesmaximal, characteristic, complemented
16C2×#65300C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic
19C5×#550—24no—
20C5×#550C2218yes—
21C2×C5×#127—21no—
22C2×C5×#127C2211yescharacteristic
23C2×C5×#121—21no—
24C2×C5×#121—21no—
25C2×C5×#121C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C2×#4081—21no—
32C22×#687C2211yescharacteristic
33C22×#687C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C2×#4070C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65875—24no—
41#65875C2218yescomplemented
42C2×#4035—21no—
43C2×#4025—21no—
44C2×#4023—21no—
45C2×#4016C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47#65528C2218yescomplemented
48#65528C2218yescomplemented
49#65522C2218yescomplemented
50#65521C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×#3964C2211yescharacteristic
56C2×#3964C2211yescharacteristic
57C2×#3964C2211yescharacteristic
58C2×#3964C2211yescharacteristic
59C2×#3964C2211yescharacteristic
60C2×C22⋊#168C2211yescharacteristic
61C2×C22⋊#168C2211yescharacteristic
62#65364C2218yescomplemented
63#65360C2218yescomplemented
64#65331C2218yescomplemented
65#65330C2218yescomplemented
66#65324C2218yescomplemented
67#65323C2218yescomplemented
68#65319C2218yescomplemented
69#65311C2218yescomplemented
70#65300C2218yescomplemented
71C2×#3942C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3317—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—22no—
80C2×C5×#41—24no—
81C2×C5×#41—24no—
82C2×C5×#41—42no—
83C2×C5×#41—42no—
84C2×C5×#41C2314yes—
85C2×C5×#41C2314yes—
86C22×C5×Q8C2311yescharacteristic
87C22×C5×D4—21no—
88C22×C5×D4—21no—
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4—21no—
92C22×C5×D4—21no—
93C22×C5×D4D411yescharacteristic
94C22×C5×D4C2311yescharacteristic
95C22×C5×D4C2311yescharacteristic
96C23×C4×C5—21no—
97C23×C4×C5—21no—
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×Dic5—21no—
101C22×Dic10C2311yescharacteristic
102C5×#127—28no—
103C5×#127—22no—
104C5×#127C2314yes—
105C5×#121—22no—
106C5×#121—22no—
107C5×#121—28no—
108C5×#121—28no—
109C5×#121C2314yes—
110C5×#121C2314yes—
111C4×C5×Q8—22no—
112C4×C5×Q8C2314yes—
113C4×C5×D4—28no—
114C4×C5×D4D414yes—
115C4×C5×D4C2314yes—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4D411yescharacteristic
118C2×C5×C4⋊C4C2311yescharacteristic
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C5×C22⋊C4D411yescharacteristic
123C2×C42×C5—21no—
124C2×C42×C5C2311yescharacteristic
125C2×C22⋊Dic5—21no—
126C2×C22⋊Dic5—21no—
127C2×C22⋊Dic5—21no—
128C2×#689—24no—
129C2×#689C2314yes—
130#4081—28no—
131C2×#687—42no—
132C2×#687—42no—
133C2×#687C2314yes—
134C2×#687C2314yes—
135#4072—22no—
136#4072C2314yes—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—22no—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2314yes—
143#4070—22no—
144#4070—22no—
145#4070C2314yes—
146#4070C2314yes—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683—21no—
151C2×#683—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×#681—42no—
155C2×#681C2314yes—
156C22×#168—42no—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2314yes—
162#4035—28no—
163#4025—28no—
164#4023—28no—
165#4016—22no—
166#4016C2314yes—
167C4×Dic10—22no—
168C4×Dic10C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3967C2314yes—
172#3964C2314yes—
173#3964C2314yes—
174#3964C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177#3964C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3942C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185#3935C2314yes—
186C2×#552—51no—
187C2×#550D511yescharacteristic
188#3317—516no—
189C2×#490—51no—
190C2×#481—51no—
191C2×#482—51no—
192C2×#479—51no—
193C2×#468—51no—
194C2×#465—51no—
195C2×#460—51no—
196C2×#452—51no—
197C2×#452—51no—
198C2×#441—51no—
199C2×#435—51no—
200C2×#417—51no—
201C2×#416—51no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5C2×D411yescharacteristic
205C24×C5C2×D411yescharacteristic
206C5×#41—28no—
207C5×#41—28no—
208C5×#41—44no—
209C5×#41—44no—
210C5×#41—48no—
211C5×#41—48no—
212C2×C5×Q8—21no—
213C2×C5×Q8—22no—
214C2×C5×Q8#4114yes—
215C2×C5×Q8C2412yes—
216C2×C5×D4—24no—
217C2×C5×D4—24no—
218C2×C5×D4—24no—
219C2×C5×D4—24no—
220C2×C5×D4—24no—
221C2×C5×D4—21no—
222C2×C5×D4—21no—
223C2×C5×D4—24no—
224C2×C5×D4—22no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—22no—
228C2×C5×D4—42no—
229C2×C5×D4—44no—
230C2×C5×D4—44no—
231C2×C5×D4—44no—
232C2×C5×D4—82no—
233C2×C5×D4—82no—
234C2×C5×D4—82no—
235C2×C5×D4C2×D414yes—
236C2×C5×D4C2412yes—
237C2×C5×D4C2412yes—
238C22×C4×C5—21no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5—22no—
243C22×C4×C5—21no—
244C22×C4×C5—24no—
245C22×C4×C5—24no—
246C22×C4×C5—44no—
247C22×C4×C5—44no—
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2×D412yes—
253C22×C4×C5C2×D412yes—
254C22×C4×C5C2412yes—
255C22×C4×C5C2412yes—
256C22×C4×C5C2411yescharacteristic
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5—24no—
262C22×Dic5—44no—
263C2×Dic10—22no—
264C2×Dic10—22no—
265C2×Dic10—21no—
266C2×Dic10C2412yes—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4C2×D414yes—
270C5×C4⋊C4C2412yes—
271C5×C22⋊C4—24no—
272C5×C22⋊C4—24no—
273C5×C22⋊C4C2×D414yes—
274C5×C22⋊C4C2×D414yes—
275C42×C5—24no—
276C42×C5C2×D412yes—
277C42×C5C2412yes—
278C22⋊Dic5—24no—
279C22⋊Dic5—24no—
280C22⋊Dic5—24no—
281#689—28no—
282#687—44no—
283#687—44no—
284C4⋊Dic5—21no—
285C4⋊Dic5—21no—
286C4⋊Dic5—21no—
287C4⋊Dic5—24no—
288C4⋊Dic5C2412yes—
289C4⋊Dic5C2412yes—
290C4⋊Dic5C2412yes—
291#683—24no—
292#683—24no—
293#683—24no—
294#683—24no—
295#683—24no—
296C4×Dic5—24no—
297C4×Dic5—24no—
298#681—44no—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168—22no—
303C2×#168—44no—
304C2×#168C2412yes—
305C2×#168C2412yes—
306C2×#168C2412yes—
307C2×#168C2412yes—
308C22×#41C2×D511yescharacteristic
309C22×#41C2×D511yescharacteristic
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16—51no—
314C23×C8—51no—
315#552—58no—
316#552—104no—
317#550—24no—
318#550C2×D518yes—
319C2×#127—21no—
320C2×#127C2×D511yescharacteristic
321C2×#126—101no—
322C2×#125—51no—
323C2×#125—101no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×#121—21no—
328C2×#121—21no—
329C2×#121C2×D511yescharacteristic
330C2×#121C2×D511yescharacteristic
331C2×C4×Q8—51no—
332C2×C4×Q8C2×D511yescharacteristic
333C2×C4×D4—21no—
334C2×C4×D4C2×D511yescharacteristic
335C2×#117—51no—
336C2×#117—101no—
337C22×C4⋊C4—51no—
338#490—58no—
339#482—58no—
340#481—58no—
341#479—58no—
342#468—58no—
343#465—58no—
344#460—58no—
345#452—58no—
346#452—58no—
347#441—58no—
348#435—58no—
349C2×#107—51no—
350C2×#106—51no—
351C2×#106—51no—
352C2×C4⋊C8—51no—
353#417—58no—
354#416—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8—51no—
366C2×C22⋊C8—51no—
367C2×#97—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5C22×D412yes—
383C23×C5C22×D412yes—
384C23×C5C22×D411yescharacteristic
385C5×Q8—24no—
386C5×Q8—22no—
387C5×Q8C2×#4114yes—
388C5×D4—22no—
389C5×D4—22no—
390C5×D4—22no—
391C5×D4—22no—
392C5×D4—44no—
393C5×D4—48no—
394C5×D4—48no—
395C5×D4—48no—
396C5×D4—42no—
397C5×D4—42no—
398C5×D4—84no—
399C5×D4—84no—
400C5×D4—84no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—24no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—24no—
408C2×C4×C5—24no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—48no—
415C2×C4×C5—48no—
416C2×C4×C5—42no—
417C2×C4×C5C22×D412yes—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D412yes—
420C2×C4×C5C22×D412yes—
421C2×C4×C5C22×D411yescharacteristic
422C2×C4×C5C2×#4112yes—
423C2×C4×C5H(5,𝔽2)12yes—
424C2×C4×C5C2511yescharacteristic
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—48no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432C2×Dic5—42no—
433C2×Dic5—42no—
434Dic10—22no—
435Dic10—22no—
436Dic10—42no—
437#168—22no—
438#168—22no—
439#168—22no—
440#168—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—24no—
444C2×#41—24no—
445C2×#41—42no—
446C2×#41—42no—
447C2×#41C22×D514yes—
448C2×#41C22×D514yes—
449C22×Q8—51no—
450C22×Q8C22×D511yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22⋊D511yescharacteristic
458C22×D4C22×D511yescharacteristic
459C22×D4C22×D511yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—101no—
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465C2×Q16—54no—
466C2×Q16—104no—
467C2×SD16—54no—
468C2×SD16—54no—
469C2×SD16—202no—
470C2×SD16—202no—
471C2×M16—54no—
472C2×M16—202no—
473C22×C8—51no—
474C22×C8—51no—
475C22×C8—51no—
476C22×C8—51no—
477C22×C8—54no—
478C22×C8—202no—
479#127—28no—
480#127—22no—
481#127C22×D514yes—
482#126—108no—
483#125—54no—
484#125—108no—
485#125—102no—
486#123—108no—
487C22⋊Q8—54no—
488C22⋊Q8—54no—
489C22⋊Q8—102no—
490C22⋊Q8—102no—
491#121—22no—
492#121—22no—
493#121—28no—
494#121—28no—
495#121C22×D514yes—
496#121C22×D514yes—
497C4×Q8—22no—
498C4×Q8—54no—
499C4×Q8—102no—
500C4×Q8C22×D514yes—
501C4×D4—28no—
502C4×D4C22⋊D514yes—
503C4×D4C22×D514yes—
504#117—54no—
505#117—102no—
506#117—108no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—102no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4—101no—
518C2×C4⋊C4—101no—
519C2×C4⋊C4C22⋊D511yescharacteristic
520C2×C4⋊C4C22×D511yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4C22⋊D511yescharacteristic
527C2×C22⋊C4C22⋊D511yescharacteristic
528C2×C42—21no—
529C2×C42—101no—
530C2×C42—101no—
531C2×C42C22×D511yescharacteristic
532#107—54no—
533#106—54no—
534#106—54no—
535C4⋊C8—54no—
536#103—54no—
537#103—54no—
538#103—54no—
539#103—54no—
540#102—54no—
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546C22⋊C8—54no—
547C22⋊C8—54no—
548#97—54no—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—44no—
556C22×C5—44no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—84no—
564C22×C5—84no—
565C22×C5#54612yes—
566C22×C5#57512yes—
567C22×C5#57712yes—
568C22×C5C23×D411yescharacteristic
569C4×C5—22no—
570C4×C5—22no—
571C4×C5—24no—
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—42no—
575C4×C5#54612yes—
576C4×C5C22×#4111yescharacteristic
577C4×C5C2×H(5,𝔽2)11yescharacteristic
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—21no—
583C24—21no—
584C24C2×C22⋊D511yescharacteristic
585C24C2×C22⋊D511yescharacteristic
586#41—28no—
587#41—28no—
588#41—44no—
589#41—44no—
590#41—48no—
591#41—48no—
592C2×Q8—22no—
593C2×Q8—21no—
594C2×Q8—52no—
595C2×Q8—101no—
596C2×Q8—102no—
597C2×Q8—102no—
598C2×Q8#71114yes—
599C2×Q8C23×D512yes—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4C2×C22⋊D514yes—
620C2×D4C23×D512yes—
621C2×D4C23×D512yes—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—104no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—101no—
637C22×C4—204no—
638C22×C4C2×C22⋊D512yes—
639C22×C4C2×C22⋊D512yes—
640C22×C4C2×C22⋊D511yescharacteristic
641C22×C4C2×C22⋊D511yescharacteristic
642C22×C4C2×C22⋊D511yescharacteristic
643C22×C4C2×C22⋊D511yescharacteristic
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647Q16—108no—
648SD16—204no—
649SD16—204no—
650M16—204no—
651C2×C8—52no—
652C2×C8—52no—
653C2×C8—52no—
654C2×C8—52no—
655C2×C8—102no—
656C2×C8—102no—
657C2×C8—102no—
658C2×C8—102no—
659C2×C8—204no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—52no—
663C4⋊C4—52no—
664C4⋊C4—52no—
665C4⋊C4—101no—
666C4⋊C4—101no—
667C4⋊C4—104no—
668C4⋊C4—101no—
669C4⋊C4—104no—
670C4⋊C4—104no—
671C4⋊C4—104no—
672C4⋊C4—104no—
673C4⋊C4—104no—
674C4⋊C4C2×C22⋊D514yes—
675C4⋊C4C23×D512yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—104no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4C2×C22⋊D514yes—
682C22⋊C4C2×C22⋊D514yes—
683C42—24no—
684C42—104no—
685C42—104no—
686C42C2×C22⋊D512yes—
687C42C23×D512yes—
688C2×C5—42no—
689C2×C5—42no—
690C2×C5—82no—
691C2×C5—82no—
692C2×C5#331714yescomplemented
693C2×C5C2×#54611yescharacteristic
694C2×C5C2×#57511yescharacteristic
695C2×C5C2×#57711yescharacteristic
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23C22×C22⋊D512yes—
711C23C22×C22⋊D512yes—
712C23C22×C22⋊D511yescharacteristic
713Q8—24no—
714Q8—22no—
715Q8—102no—
716Q8—102no—
717Q8—202no—
718Q8C2×#71114yes—
719D4—22no—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—42no—
729D4—84no—
730D4—84no—
731D4—84no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—208no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4C2×#71112yes—
758C2×C4#414412yes—
759C2×C4C22×C22⋊D512yes—
760C2×C4C22×C22⋊D512yes—
761C2×C4C22×C22⋊D512yes—
762C2×C4C22×C22⋊D512yes—
763C2×C4C22×C22⋊D511yescharacteristic
764C2×C4C24×D511yescharacteristic
765C8—102no—
766C8—102no—
767C8—102no—
768C8—102no—
769C5C2×#331711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#6614012yes—
787C22#6615612yes—
788C22#6617012yes—
789C22C23×C22⋊D511yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—42no—
796C4—202no—
797C4—202no—
798C4—202no—
799C4—202no—
800C4#6614012yes—
801C4C22×#71111yescharacteristic
802C4C2×#414411yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#1061530414yesdirect product factor
808C2C2×#6614011yescharacteristic
809C2C2×#6615611yescharacteristic
810C2C2×#6617011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#550C2
socleC23×C5C22×D4
hypercenterC2×#550D5
hypocenterC5C2×#3317
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
2. C2×#65875C2semidirect
3. C2×#65528C2semidirect
4. C2×#65528C2semidirect
5. C2×#65521C2semidirect
6. C2×#65522C2semidirect
7. #10615304C2direct (N × H)
8. C2×#65364C2semidirect
9. C2×#65360C2semidirect
10. C2×#65331C2semidirect
11. C2×#65330C2semidirect
12. C2×#65323C2semidirect
13. C2×#65324C2semidirect
14. C2×#65311C2semidirect
15. C2×#65319C2semidirect
16. C2×#65300C2semidirect
41. #65875C22semidirect
47. #65528C22semidirect
48. #65528C22semidirect
49. #65522C22semidirect
50. #65521C22semidirect
62. #65364C22semidirect
63. #65360C22semidirect
64. #65331C22semidirect
65. #65330C22semidirect
66. #65324C22semidirect
67. #65323C22semidirect
68. #65319C22semidirect
69. #65311C22semidirect
70. #65300C22semidirect
692. C2×C5#3317semidirect
769. C5C2×#3317semidirect
807. C2#10615304direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5502
C2×#658752
C2×#655282
C2×#655212
C2×#655222
#106153042
C2×#653642
C2×#653602
C2×#653312
C2×#653302
C2×#653232
C2×#653242
C2×#653112
C2×#653192
C2×#653002
C2×#33175