Finite Group Databasebeta

← C2×#10615283 #12975906

Subgroups — C2×#10615283 #12975906

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×C5×D4×Q8C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic
3C2×#65517C211yesmaximal, characteristic, complemented
4C2×#65517C211yesmaximal, characteristic, complemented
5C2×#65514C211yesmaximal, characteristic, complemented
6C22×#3967C211yesmaximal, characteristic, complemented
7#10615283C2116yesmaximal, direct product factor
8C2×#65379C211yesmaximal, characteristic, complemented
9C2×#65371C211yesmaximal, characteristic, complemented
10C2×#65341C211yesmaximal, characteristic, complemented
11C2×#65340C211yesmaximal, characteristic, complemented
12C2×#65334C211yesmaximal, characteristic, complemented
13C2×#65332C211yesmaximal, characteristic, complemented
14C2×#65311C211yesmaximal, characteristic, complemented
15C2×#65319C211yesmaximal, characteristic, complemented
16C2×#65300C211yesmaximal, characteristic
17C23×C5×Q8C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C5×D4×Q8—24no—
20C5×D4×Q8C2218yes—
21C2×C5×C4⋊Q8—21no—
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C22×#689C2211yescharacteristic
33C2×#4081—21no—
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C2×#4070C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65875—24no—
41#65875C2218yes—
42C2×#4035—21no—
43C2×#4025—21no—
44C2×#4023—21no—
45C2×#4016C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47#65517C2218yescomplemented
48#65517C2218yescomplemented
49#65514C2218yescomplemented
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56C2×#3967C2211yescharacteristic
57C2×#3967C2211yescharacteristic
58C2×#3967C2211yescharacteristic
59C2×#3967C2218yescomplemented
60C2×C22⋊#168C2211yescharacteristic
61C2×C22⋊#168C2211yescharacteristic
62#65379C2218yescomplemented
63#65371C2218yescomplemented
64#65341C2218yescomplemented
65#65340C2218yescomplemented
66#65334C2218yescomplemented
67#65332C2218yescomplemented
68#65319C2218yescomplemented
69#65311C2218yescomplemented
70#65300C2218yes—
71C2×#3942C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3312—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8—21no—
80C22×C5×Q8—22no—
81C22×C5×Q8—22no—
82C22×C5×Q8—24no—
83C22×C5×Q8—24no—
84C22×C5×Q8—42no—
85C22×C5×Q8—42no—
86C22×C5×Q8C2311yescharacteristic
87C22×C5×Q8C2311yescharacteristic
88C22×C5×Q8C2314yes—
89C22×C5×Q8C2314yes—
90C22×C5×Q8C2311yescharacteristic
91C22×C5×D4D411yescharacteristic
92C23×C4×C5—21no—
93C23×C4×C5—21no—
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×Dic5—21no—
97C22×Dic10C2311yescharacteristic
98C5×C4⋊Q8—28no—
99C5×C4⋊Q8—22no—
100C5×C4⋊Q8C2314yes—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8—28no—
104C5×C22⋊Q8—28no—
105C5×C22⋊Q8C2314yes—
106C5×C22⋊Q8C2314yes—
107C4×C5×Q8—22no—
108C4×C5×Q8C2314yes—
109C4×C5×D4—28no—
110C4×C5×D4D414yes—
111C4×C5×D4C2314yes—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
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×#689—42no—
130C2×#689—42no—
131C2×#689C2314yes—
132C2×#689C2314yes—
133C2×#689C2314yes—
134#4081—28no—
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#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176#3967C2314yes—
177#3967C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3942C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185#3935C2314yes—
186C2×#552—51no—
187C2×D4×Q8D511yescharacteristic
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×#435—51no—
200C2×#419—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C2×C5×Q8—21no—
205C2×C5×Q8—24no—
206C2×C5×Q8—24no—
207C2×C5×Q8—21no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8—28no—
211C2×C5×Q8—28no—
212C2×C5×Q8—22no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8—44no—
217C2×C5×Q8—44no—
218C2×C5×Q8—44no—
219C2×C5×Q8—44no—
220C2×C5×Q8—48no—
221C2×C5×Q8—48no—
222C2×C5×Q8#4114yes—
223C2×C5×Q8C2412yes—
224C2×C5×Q8C2412yes—
225C2×C5×Q8C2412yes—
226C2×C5×D4—24no—
227C2×C5×D4C2×D414yes—
228C22×C4×C5—21no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—22no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—24no—
237C22×C4×C5—24no—
238C22×C4×C5—44no—
239C22×C4×C5—44no—
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2×D411yescharacteristic
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D412yes—
245C22×C4×C5C2×D412yes—
246C22×C4×C5C2412yes—
247C22×C4×C5C2412yes—
248C22×C4×C5C2411yescharacteristic
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—24no—
254C22×Dic5—44no—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10—21no—
258C2×Dic10C2412yes—
259C5×C4⋊C4—24no—
260C5×C4⋊C4—24no—
261C5×C4⋊C4—24no—
262C5×C4⋊C4—24no—
263C5×C4⋊C4—24no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4C2×D414yes—
266C5×C4⋊C4C2412yes—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4C2×D414yes—
270C5×C22⋊C4C2×D414yes—
271C42×C5—24no—
272C42×C5C2×D412yes—
273C42×C5C2412yes—
274C22⋊Dic5—24no—
275C22⋊Dic5—24no—
276C22⋊Dic5—24no—
277#689—28no—
278#689—44no—
279#689—44no—
280C4⋊Dic5—21no—
281C4⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5—24no—
284C4⋊Dic5C2412yes—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287#683—24no—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292C4×Dic5—24no—
293C4×Dic5—24no—
294#681—44no—
295C2×#168—22no—
296C2×#168—22no—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168—44no—
300C2×#168C2412yes—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C2×#168C2412yes—
304C23×Q8C2×D511yescharacteristic
305C23×Q8C2×D511yescharacteristic
306C22×Q16—51no—
307C22×Q16—51no—
308C22×Q16—51no—
309C22×M16—51no—
310C23×C8—51no—
311#552—58no—
312#552—104no—
313D4×Q8—24no—
314D4×Q8C2×D518yes—
315C2×C4⋊Q8—21no—
316C2×C4⋊Q8C2×D511yescharacteristic
317C2×#126—101no—
318C2×#125—51no—
319C2×#125—101no—
320C2×#123—101no—
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×C22⋊Q8C2×D511yescharacteristic
327C2×C4×Q8—51no—
328C2×C4×Q8C2×D511yescharacteristic
329C2×C4×D4—21no—
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#435—58no—
345C2×#107—51no—
346C2×#106—51no—
347C2×#106—51no—
348C2×C4⋊C8—51no—
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⋊C8—51no—
362C2×C22⋊C8—51no—
363C2×#97—51no—
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×Q8—24no—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—22no—
377C5×Q8—22no—
378C5×Q8—22no—
379C5×Q8—48no—
380C5×Q8—48no—
381C5×Q8—42no—
382C5×Q8—42no—
383C5×Q8C2×#4114yes—
384C5×D4—28no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—24no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—24no—
392C2×C4×C5—24no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—48no—
401C2×C4×C5—48no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5—42no—
405C2×C4×C5C22×D412yes—
406C2×C4×C5C22×D412yes—
407C2×C4×C5C22×D412yes—
408C2×C4×C5C22×D412yes—
409C2×C4×C5C22×D411yescharacteristic
410C2×C4×C5C2×#4112yes—
411C2×C4×C5H(5,𝔽2)12yes—
412C2×C4×C5C2511yescharacteristic
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—42no—
418C2×Dic5—48no—
419C2×Dic5—42no—
420C2×Dic5—42no—
421C2×Dic5—42no—
422Dic10—22no—
423Dic10—22no—
424Dic10—42no—
425#168—22no—
426#168—22no—
427#168—22no—
428#168—22no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8—42no—
436C22×Q8—42no—
437C22×Q8—51no—
438C22×Q8C22×D511yescharacteristic
439C22×Q8C22×D511yescharacteristic
440C22×Q8C22×D514yes—
441C22×Q8C22×D514yes—
442C22×Q8C22×D511yescharacteristic
443C22×D4C22⋊D511yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
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—54no—
456C2×M16—202no—
457C22×C8—51no—
458C22×C8—51no—
459C22×C8—51no—
460C22×C8—51no—
461C22×C8—54no—
462C22×C8—202no—
463C4⋊Q8—28no—
464C4⋊Q8—22no—
465C4⋊Q8C22×D514yes—
466#126—108no—
467#125—54no—
468#125—108no—
469#125—102no—
470#123—108no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—54no—
476C22⋊Q8—54no—
477C22⋊Q8—102no—
478C22⋊Q8—102no—
479C22⋊Q8C22×D514yes—
480C22⋊Q8C22×D514yes—
481C4×Q8—22no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8C22×D514yes—
485C4×D4—28no—
486C4×D4C22⋊D514yes—
487C4×D4C22×D514yes—
488#117—54no—
489#117—102no—
490#117—108no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—51no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—54no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—102no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4C22⋊D511yescharacteristic
508C2×C4⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4C22⋊D511yescharacteristic
515C2×C22⋊C4C22⋊D511yescharacteristic
516C2×C42—21no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42C22×D511yescharacteristic
520#107—54no—
521#106—54no—
522#106—54no—
523C4⋊C8—54no—
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⋊C8—54no—
535C22⋊C8—54no—
536#97—54no—
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—24no—
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—42no—
555C4×C5—42no—
556C4×C5—42no—
557C4×C5#54612yes—
558C4×C5C22×#4111yescharacteristic
559C4×C5C2×H(5,𝔽2)11yescharacteristic
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24C2×C22⋊D511yescharacteristic
565C24C2×C22⋊D511yescharacteristic
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—24no—
569C2×Q8—24no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—28no—
573C2×Q8—28no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—48no—
584C2×Q8—52no—
585C2×Q8—101no—
586C2×Q8—102no—
587C2×Q8—102no—
588C2×Q8#71114yes—
589C2×Q8C23×D512yes—
590C2×Q8C23×D512yes—
591C2×Q8C23×D512yes—
592C2×D4—24no—
593C2×D4C2×C22⋊D514yes—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—104no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—204no—
612C22×C4C2×C22⋊D512yes—
613C22×C4C2×C22⋊D512yes—
614C22×C4C2×C22⋊D511yescharacteristic
615C22×C4C2×C22⋊D511yescharacteristic
616C22×C4C2×C22⋊D511yescharacteristic
617C22×C4C2×C22⋊D511yescharacteristic
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D511yescharacteristic
621Q16—108no—
622Q16—204no—
623Q16—204no—
624M16—204no—
625C2×C8—52no—
626C2×C8—52no—
627C2×C8—52no—
628C2×C8—52no—
629C2×C8—102no—
630C2×C8—102no—
631C2×C8—102no—
632C2×C8—102no—
633C2×C8—204no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—52no—
641C4⋊C4—52no—
642C4⋊C4—52no—
643C4⋊C4—101no—
644C4⋊C4—101no—
645C4⋊C4—104no—
646C4⋊C4—101no—
647C4⋊C4—104no—
648C4⋊C4—104no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4C2×C22⋊D514yes—
653C4⋊C4C23×D512yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—104no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4C2×C22⋊D514yes—
660C22⋊C4C2×C22⋊D514yes—
661C42—24no—
662C42—104no—
663C42—104no—
664C42C2×C22⋊D512yes—
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#408814yes—
678C23C22×C22⋊D512yes—
679C23C22×C22⋊D512yes—
680C23C22×C22⋊D511yescharacteristic
681Q8—24no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—102no—
692Q8—102no—
693Q8—202no—
694Q8C2×#71114yes—
695D4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—202no—
721C2×C4—208no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4C2×#71112yes—
726C2×C4#414412yes—
727C2×C4C22×C22⋊D512yes—
728C2×C4C22×C22⋊D512yes—
729C2×C4C22×C22⋊D512yes—
730C2×C4C22×C22⋊D512yes—
731C2×C4C22×C22⋊D511yescharacteristic
732C2×C4C24×D511yescharacteristic
733C8—102no—
734C8—102no—
735C8—102no—
736C8—102no—
737C5C2×#331211yescharacteristic, complemented, Sylow
738C22—22no—
739C22—28no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#6614012yes—
746C22C2×#408814yes—
747C22C2×#408812yes—
748C22#6617212yes—
749C22C23×C22⋊D511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4#6614012yes—
763C4C22×#71111yescharacteristic
764C4C2×#414411yescharacteristic
765C2—24no—
766C2—42no—
767C2#1061528314yesdirect product factor
768C2C2×#6614011yescharacteristic
769C2C22×#408811yescharacteristic
770C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×D4×Q8C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
hypercenterC2×D4×Q8D5
hypocenterC5C2×#3312
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#65517C2semidirect
4. C2×#65517C2semidirect
5. C2×#65514C2semidirect
6. C22×#3967C2semidirect
7. #10615283C2direct (N × H)
8. C2×#65379C2semidirect
9. C2×#65371C2semidirect
10. C2×#65341C2semidirect
11. C2×#65340C2semidirect
12. C2×#65334C2semidirect
13. C2×#65332C2semidirect
14. C2×#65311C2semidirect
15. C2×#65319C2semidirect
47. #65517C22semidirect
48. #65517C22semidirect
49. #65514C22semidirect
59. C2×#3967C22semidirect
62. #65379C22semidirect
63. #65371C22semidirect
64. #65341C22semidirect
65. #65340C22semidirect
66. #65334C22semidirect
67. #65332C22semidirect
68. #65319C22semidirect
69. #65311C22semidirect
668. C2×C5#3312semidirect
737. C5C2×#3312semidirect
767. C2#10615283direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×D4×Q82
C2×#658752
C2×#655172
C2×#655142
C22×#39672
#106152832
C2×#653792
C2×#653712
C2×#653412
C2×#653402
C2×#653342
C2×#653322
C2×#653112
C2×#653192
C2×#653002
C2×#33125