Finite Group Databasebeta

← C2×#10611927 #12975899

Subgroups — C2×#10611927 #12975899

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×Q8×C22⋊D5C211yesmaximal, characteristic
2C2×#65973C211yesmaximal, characteristic
3C2×C5×#451C211yesmaximal, characteristic, complemented
4C2×#65514C211yesmaximal, characteristic, complemented
5C2×#65477C211yesmaximal, characteristic, complemented
6C2×#65475C211yesmaximal, characteristic, complemented
7C2×#65471C211yesmaximal, characteristic, complemented
8C2×#65473C211yesmaximal, characteristic, complemented
9C2×#65341C211yesmaximal, characteristic, complemented
10#10611927C2116yesmaximal, direct product factor
11C2×#65094C211yesmaximal, characteristic, complemented
12C2×D5×#103C211yesmaximal, characteristic, complemented
13C2×#65086C211yesmaximal, characteristic, complemented
14C2×#65085C211yesmaximal, characteristic, complemented
15C2×#65017C211yesmaximal, characteristic
16C2×#65012C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×C5×Q16C2211yescharacteristic
20C22×C5×Q16C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22Q8×C22⋊D5—24no—
23Q8×C22⋊D5C2218yes—
24C2×#4092—21no—
25C2×#4092C2211yescharacteristic
26C2×#4092C2211yescharacteristic
27C2×Q8×Dic5C2211yescharacteristic
28C2×Q8×Dic5C2211yescharacteristic
29C2×#4090—21no—
30C2×#4090C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C2×C4×C22⋊D5—21no—
33C2×C4×C22⋊D5C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C2×#4070—21no—
36C2×#4070C2211yescharacteristic
37C22×#681C2211yescharacteristic
38C22×C8×D5C2211yescharacteristic
39#65973—24no—
40#65973C2218yes—
41C2×#4038—21no—
42C2×D5×C4⋊C4C2211yescharacteristic
43C2×#4036C2211yescharacteristic
44C2×#4035—21no—
45C2×#4029—21no—
46C2×#4025—21no—
47C5×#451C2218yescomplemented
48C2×C5×#103C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51#65514C2218yescomplemented
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56C2×#3967C2211yescharacteristic
57#65477C2218yescomplemented
58#65475C2218yescomplemented
59#65473C2218yescomplemented
60#65471C2218yescomplemented
61C2×#3952C2211yescharacteristic
62C2×#3950C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3947C2211yescharacteristic
67C2×#3946C2211yescharacteristic
68#65341C2218yescomplemented
69C2×#3942C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71#65094C2218yescomplemented
72D5×#103C2218yescomplemented
73#65086C2218yescomplemented
74#65085C2218yescomplemented
75#65017C2218yes—
76#65012C2218yescomplemented
77C2×#3312—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8—22no—
80C22×C5×Q8—24no—
81C22×C5×Q8—42no—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×Q8C2314yes—
85C22×C5×Q8C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5D411yescharacteristic
89C2×Q8×D5—22no—
90C2×Q8×D5—24no—
91C2×Q8×D5—42no—
92C2×Q8×D5C2314yes—
93C22×C4×D5—21no—
94C22×C4×D5—21no—
95C22×C4×D5C2311yescharacteristic
96C22×Dic10—21no—
97C22×Dic10C2311yescharacteristic
98C2×C5×Q16—24no—
99C2×C5×Q16—42no—
100C2×C5×Q16C2314yes—
101C2×C5×Q16C2314yes—
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8C2314yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C22⋊C4—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5D411yescharacteristic
112#4092—22no—
113#4092—22no—
114#4092—28no—
115#4092C2314yes—
116#4092C2314yes—
117Q8×Dic5—22no—
118Q8×Dic5—22no—
119Q8×Dic5C2314yes—
120Q8×Dic5C2314yes—
121#4090—28no—
122#4090—22no—
123#4090C2314yes—
124C2×#689—42no—
125C2×#689C2314yes—
126C4×C22⋊D5—28no—
127C4×C22⋊D5D414yes—
128C4×C22⋊D5C2314yes—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685D411yescharacteristic
132#4072—22no—
133#4072C2314yes—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5—21no—
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5C2311yescharacteristic
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2311yescharacteristic
140#4070—22no—
141#4070—28no—
142#4070C2314yes—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683D411yescharacteristic
151C2×C4×Dic5—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×C4×Dic5C2311yescharacteristic
155C2×#681—42no—
156C2×#681C2314yes—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C2×C8×D5—42no—
160C2×C8×D5C2314yes—
161#4038—28no—
162D5×C4⋊C4—22no—
163D5×C4⋊C4C2314yes—
164#4036—22no—
165#4036C2314yes—
166#4035—28no—
167#4029—28no—
168#4025—28no—
169C5×#103C2314yes—
170C5×#103C2314yes—
171C5×C22⋊C8C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176#3967C2314yes—
177#3952C2314yes—
178#3950C2314yes—
179#3949C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3947C2314yes—
183#3946C2314yes—
184#3942C2314yes—
185#3940C2314yes—
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×#451D511yescharacteristic, complemented
198C2×#441—51no—
199C2×#435—51no—
200C2×#419—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C23×D5C2×D411yescharacteristic
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—24no—
207C2×C5×Q8—21no—
208C2×C5×Q8—22no—
209C2×C5×Q8—28no—
210C2×C5×Q8—22no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8—22no—
214C2×C5×Q8—44no—
215C2×C5×Q8—44no—
216C2×C5×Q8—48no—
217C2×C5×Q8#4114yes—
218C2×C5×Q8C2412yes—
219C2×C5×Q8C2412yes—
220C2×C5×Q8C2412yes—
221C22×C4×C5—21no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2411yescharacteristic
233C2×C22⋊D5—24no—
234C2×C22⋊D5C2×D414yes—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242Q8×D5—28no—
243Q8×D5—44no—
244Q8×D5—48no—
245C2×C4×D5—22no—
246C2×C4×D5—22no—
247C2×C4×D5—24no—
248C2×C4×D5—24no—
249C2×C4×D5—44no—
250C2×C4×D5—44no—
251C2×C4×D5C2×D412yes—
252C2×C4×D5C2412yes—
253C2×Dic10—22no—
254C2×Dic10—22no—
255C2×Dic10—21no—
256C2×Dic10—24no—
257C2×Dic10—44no—
258C2×Dic10C2412yes—
259C5×Q16—28no—
260C5×Q16—44no—
261C2×C5×C8—22no—
262C2×C5×C8—22no—
263C2×C5×C8C2412yes—
264C2×C5×C8C2412yes—
265C5×C4⋊C4—24no—
266C5×C4⋊C4—21no—
267C5×C4⋊C4C2412yes—
268C5×C22⋊C4—24no—
269C22⋊Dic5—24no—
270C22⋊Dic5—24no—
271C22⋊Dic5C2×D414yes—
272#689—44no—
273#685—24no—
274#685—24no—
275#685C2×D414yes—
276C4⋊Dic5—21no—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5—24no—
280C4⋊Dic5—24no—
281C4⋊Dic5—24no—
282C4⋊Dic5C2412yes—
283C4⋊Dic5C2412yes—
284C4⋊Dic5C2412yes—
285#683—24no—
286#683—24no—
287#683—24no—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292#683C2×D414yes—
293C4×Dic5—24no—
294C4×Dic5—24no—
295C4×Dic5—24no—
296C4×Dic5C2×D412yes—
297C4×Dic5C2412yes—
298#681—44no—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C8×D5—44no—
304C23×Q8—51no—
305C23×Q8C2×D511yescharacteristic
306C22×Q16—51no—
307C22×Q16C2×D511yescharacteristic
308C22×Q16C2×D511yescharacteristic
309C22×M16—51no—
310C23×C8—51no—
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—101no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8C2×D511yescharacteristic
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×D4—51no—
330C2×C4×D4—101no—
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#451C2×D518yescomplemented
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—58no—
359C2×#103C2×D511yescharacteristic
360C2×#103C2×D511yescharacteristic
361C2×C22⋊C8—51no—
362C2×C22⋊C8C2×D511yescharacteristic
363C2×#97—51no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5C22×D412yes—
368C23×C5C22×D411yescharacteristic
369C22×D5—22no—
370C22×D5—22no—
371C22×D5#13714yes—
372C22×D5C22×D412yes—
373C5×Q8—24no—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—22no—
377C5×Q8—22no—
378C5×Q8—22no—
379C5×Q8—48no—
380C5×Q8—42no—
381C5×Q8—42no—
382C5×Q8C2×#4114yes—
383C2×C4×C5—24no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—24no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—48no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5C22×D412yes—
397C2×C4×C5C22×D411yescharacteristic
398C2×C4×C5C2×#4112yes—
399C2×C4×C5H(5,𝔽2)12yes—
400C2×C4×C5C2511yescharacteristic
401C22⋊D5—28no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411C2×Dic5—42no—
412C2×Dic5—42no—
413C2×Dic5C22×D412yes—
414C2×Dic5C22×D412yes—
415C2×Dic5C22×D412yes—
416C4×D5—24no—
417C4×D5—22no—
418C4×D5—22no—
419C4×D5—48no—
420C4×D5—48no—
421Dic10—22no—
422Dic10—22no—
423Dic10—48no—
424Dic10—42no—
425C5×C8—22no—
426C5×C8—22no—
427#168—22no—
428#168—22no—
429C22×Q8—21no—
430C22×Q8—22no—
431C22×Q8—24no—
432C22×Q8—42no—
433C22×Q8—54no—
434C22×Q8—51no—
435C22×Q8—101no—
436C22×Q8—102no—
437C22×Q8—104no—
438C22×Q8—202no—
439C22×Q8C22×D511yescharacteristic
440C22×Q8C22×D511yescharacteristic
441C22×Q8C22×D514yes—
442C22×Q8C22×D511yescharacteristic
443C22×D4—51no—
444C23×C4—21no—
445C23×C4—51no—
446C23×C4—101no—
447C23×C4—101no—
448C23×C4C22×D511yescharacteristic
449C2×Q16—24no—
450C2×Q16—42no—
451C2×Q16—54no—
452C2×Q16—202no—
453C2×Q16C22×D514yes—
454C2×Q16C22×D514yes—
455C2×M16—54no—
456C2×M16—202no—
457C22×C8—51no—
458C22×C8—51no—
459C22×C8—54no—
460C22×C8—202no—
461C22×C8C22×D511yescharacteristic
462C22×C8C22×D511yescharacteristic
463C4⋊Q8—54no—
464C4⋊Q8—102no—
465C4⋊Q8—108no—
466#126—108no—
467#125—54no—
468#125—102no—
469#125—108no—
470#123—108no—
471C22⋊Q8—22no—
472C22⋊Q8—54no—
473C22⋊Q8—54no—
474C22⋊Q8—54no—
475C22⋊Q8—108no—
476C22⋊Q8—108no—
477C22⋊Q8—102no—
478C22⋊Q8—102no—
479C22⋊Q8—102no—
480C22⋊Q8C22×D514yes—
481C4×Q8—54no—
482C4×Q8—54no—
483C4×Q8—102no—
484C4×Q8—102no—
485C4×D4—54no—
486C4×D4—54no—
487C4×D4—108no—
488#117—54no—
489#117—108no—
490#117—102no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—54no—
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⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C42—51no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42—101no—
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#103C22×D514yes—
533#103C22×D514yes—
534C22⋊C8—54no—
535C22⋊C8C22×D514yes—
536#97—54no—
537C22×C5—22no—
538C22×C5—22no—
539C22×C5—22no—
540C22×C5—44no—
541C22×C5#54612yes—
542C22×C5C2×#13712yes—
543C22×C5#57812yes—
544C22×C5C23×D411yescharacteristic
545C2×D5—22no—
546C2×D5—28no—
547C2×D5—22no—
548C2×D5C2×#13714yes—
549C4×C5—24no—
550C4×C5—22no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5#54612yes—
555C4×C5C22×#4111yescharacteristic
556C4×C5C2×H(5,𝔽2)11yescharacteristic
557Dic5—22no—
558Dic5—22no—
559Dic5—22no—
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24—51no—
565C24D4×D511yescharacteristic
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—24no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—28no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—48no—
579C2×Q8—52no—
580C2×Q8—104no—
581C2×Q8—101no—
582C2×Q8—108no—
583C2×Q8—102no—
584C2×Q8—102no—
585C2×Q8—204no—
586C2×Q8—204no—
587C2×Q8—208no—
588C2×Q8#71114yes—
589C2×Q8C23×D512yes—
590C2×Q8C23×D512yes—
591C2×Q8C23×D512yes—
592C2×D4—54no—
593C2×D4—104no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—44no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—52no—
606C22×C4—52no—
607C22×C4—104no—
608C22×C4—104no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4D4×D512yes—
618C22×C4D4×D511yescharacteristic
619C22×C4C23×D512yes—
620C22×C4C23×D511yescharacteristic
621Q16—28no—
622Q16—44no—
623Q16—204no—
624M16—204no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—52no—
628C2×C8—52no—
629C2×C8—102no—
630C2×C8—102no—
631C2×C8—204no—
632C2×C8C23×D512yes—
633C2×C8C23×D512yes—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—54no—
637C4⋊C4—52no—
638C4⋊C4—52no—
639C4⋊C4—52no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—104no—
646C4⋊C4—104no—
647C4⋊C4—104no—
648C4⋊C4—104no—
649C4⋊C4—101no—
650C4⋊C4—101no—
651C4⋊C4—101no—
652C4⋊C4—104no—
653C4⋊C4C23×D512yes—
654C22⋊C4—24no—
655C22⋊C4—54no—
656C22⋊C4—54no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C42—52no—
662C42—52no—
663C42—104no—
664C42—104no—
665C42—104no—
666C2×C5—42no—
667C2×C5#331214yescomplemented
668C2×C5C2×#54611yescharacteristic
669C2×C5C22×#13711yescharacteristic
670C2×C5C2×#57811yescharacteristic
671D5—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—54no—
676C23—52no—
677C23—102no—
678C23—102no—
679C23C2×D4×D512yes—
680C23C2×D4×D511yescharacteristic
681Q8—24no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—42no—
689Q8—42no—
690Q8—102no—
691Q8—102no—
692Q8—208no—
693Q8—202no—
694Q8C2×#71114yes—
695D4—108no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—52no—
710C2×C4—52no—
711C2×C4—52no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—104no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—208no—
723C2×C4—208no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4C2×D4×D512yes—
729C2×C4C2×D4×D511yescharacteristic
730C2×C4C2×#71112yes—
731C2×C4#414412yes—
732C2×C4C24×D511yescharacteristic
733C8—22no—
734C8—22no—
735C8—102no—
736C8—102no—
737C5C2×#331211yescharacteristic, complemented, Sylow
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—54no—
743C22—102no—
744C22—108no—
745C22—102no—
746C22#6592512yes—
747C22#6610012yes—
748C22D5×#13712yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—102no—
756C4—102no—
757C4—102no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4#6592512yes—
763C4C22×#71111yescharacteristic
764C4C2×#414411yescharacteristic
765C2—42no—
766C2—104no—
767C2#1061192714yesdirect product factor
768C2C2×#6592511yescharacteristic
769C2C2×#6610011yescharacteristic
770C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#451C2
socleC23×C5C22×D4
prime radicalC22×C22⋊D5D4
hypercenterC2×#451D5
hypocenterC5C2×#3312
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. C2×C5×#451C2semidirect
4. C2×#65514C2semidirect
5. C2×#65477C2semidirect
6. C2×#65475C2semidirect
7. C2×#65471C2semidirect
8. C2×#65473C2semidirect
9. C2×#65341C2semidirect
10. #10611927C2direct (N × H)
11. C2×#65094C2semidirect
12. C2×D5×#103C2semidirect
13. C2×#65086C2semidirect
14. C2×#65085C2semidirect
16. C2×#65012C2semidirect
47. C5×#451C22semidirect
51. #65514C22semidirect
57. #65477C22semidirect
58. #65475C22semidirect
59. #65473C22semidirect
60. #65471C22semidirect
68. #65341C22semidirect
71. #65094C22semidirect
72. D5×#103C22semidirect
73. #65086C22semidirect
74. #65085C22semidirect
76. #65012C22semidirect
197. C2×#451D5semidirect
342. #451C2×D5semidirect
667. C2×C5#3312semidirect
737. C5C2×#3312semidirect
767. C2#10611927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D52
C2×#659732
C2×C5×#4512
C2×#655142
C2×#654772
C2×#654752
C2×#654712
C2×#654732
C2×#653412
#106119272
C2×#650942
C2×D5×#1032
C2×#650862
C2×#650852
C2×#650172
C2×#650122
C2×#33125