Finite Group Databasebeta

← C2×#10610536 #12975679

Subgroups — C2×#10610536 #12975679

Order 1280.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic
3C22×C5×#103C211yesmaximal, characteristic, complemented
4C2×#65516C211yesmaximal, characteristic, complemented
5C2×#65403C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×#65260C211yesmaximal, characteristic, complemented
8C2×#65107C211yesmaximal, characteristic, complemented
9#10610536C2116yesmaximal, direct product factor
10C2×#65094C211yesmaximal, characteristic, complemented
11C2×#65096C211yesmaximal, characteristic, complemented
12C2×#65095C211yesmaximal, characteristic, complemented
13C2×D5×#103C211yesmaximal, characteristic, complemented
14C2×#65081C211yesmaximal, characteristic, complemented
15C2×#65080C211yesmaximal, characteristic, complemented
16C2×#65077C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C22×Q8×D5C2211yescharacteristic
19C22×#709—21no—
20C23×C5×C8C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22Q8×C22⋊D5—24no—
23Q8×C22⋊D5C2218yescomplemented
24C2×#4092—21no—
25C2×#4092C2211yescharacteristic
26C2×Q8×Dic5C2211yescharacteristic
27C2×#4090—21no—
28C2×#4090C2211yescharacteristic
29C22×#688C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C2×#4076C2211yescharacteristic
32C2×#4075—21no—
33C2×C4×C22⋊D5—21no—
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4070—21no—
36C2×#4070C2211yescharacteristic
37C22×#677C2211yescharacteristic
38C22×C8×D5C2211yescharacteristic
39C2×#4042—21no—
40#65841—24no—
41#65841C2218yes—
42C2×#4041C2211yescharacteristic
43C2×#4040—21no—
44C2×#4039C2211yescharacteristic
45C2×D5×C4⋊C4C2211yescharacteristic
46C2×#4034C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#103C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#103C2218yescomplemented
52#65516C2218yescomplemented
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56#65403C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C8×C22⋊D5C2218yescomplemented
59C2×#3952C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3946C2211yescharacteristic
63C2×C8×Dic5C2211yescharacteristic
64#65260C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69#65107C2218yescomplemented
70#65096C2218yescomplemented
71#65095C2218yescomplemented
72#65094C2218yescomplemented
73D5×#103C2218yescomplemented
74#65081C2218yescomplemented
75#65080C2218yescomplemented
76#65077C2218yescomplemented
77C2×#3298—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8—22no—
80C22×C5×Q8—24no—
81C22×C5×Q8—42no—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2314yes—
84C22×C5×Q8C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—21no—
89C22×C22⋊D5D411yescharacteristic
90C2×Q8×D5—22no—
91C2×Q8×D5—24no—
92C2×Q8×D5—42no—
93C2×Q8×D5C2314yes—
94C2×#709—28no—
95C2×#709—48no—
96C22×D20—21no—
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×C4×D5C2311yescharacteristic
102C22×Dic10—21no—
103C22×Dic10—21no—
104C22×Dic10C2311yescharacteristic
105C22×C5×C8—42no—
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2314yes—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—22no—
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2314yes—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5D411yescharacteristic
116#4092—22no—
117#4092—28no—
118#4092C2314yes—
119Q8×Dic5—22no—
120Q8×Dic5C2314yes—
121#4090—28no—
122#4090—22no—
123#4090C2314yes—
124C2×#688—24no—
125C2×#688—42no—
126C2×#688C2314yes—
127C2×#688C2314yes—
128#4076—22no—
129#4076C2314yes—
130#4075—28no—
131C4×C22⋊D5—28no—
132C4×C22⋊D5D414yes—
133C4×C22⋊D5C2314yes—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685D411yescharacteristic
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142#4070—22no—
143#4070—28no—
144#4070C2314yes—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683—21no—
149C2×#683—21no—
150C2×#683—21no—
151C2×#683D411yescharacteristic
152C2×C4×Dic5—21no—
153C2×C4×Dic5C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C22×#168C2311yescharacteristic
156C2×#677—42no—
157C2×#677C2314yes—
158C2×C8×D5—42no—
159C2×C8×D5C2314yes—
160#4042—28no—
161#4041—22no—
162#4041C2314yes—
163#4040—28no—
164#4039—22no—
165#4039C2314yes—
166D5×C4⋊C4—22no—
167D5×C4⋊C4C2314yes—
168#4034—22no—
169#4034C2314yes—
170C5×#103C2314yes—
171C5×#103C2314yes—
172C5×#103C2314yes—
173C5×#103C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176C22⋊#168C2314yes—
177#3953C2314yes—
178#3952C2314yes—
179#3949C2314yes—
180#3948C2314yes—
181#3946C2314yes—
182C8×Dic5C2314yes—
183#3942C2314yes—
184#3942C2314yes—
185#3940C2314yes—
186#3940C2314yes—
187C2×D4×Q8—51no—
188C2×#547—51no—
189#3298—516no—
190C2×#487—51no—
191C2×#483—51no—
192C2×#483—51no—
193C2×#475—51no—
194C2×#465—51no—
195C2×#465—51no—
196C2×#461—51no—
197C2×#448—51no—
198C2×#448—51no—
199C2×C4×SD16—51no—
200C2×C8×D4—51no—
201C22×#103—51no—
202C22×#103D511yescharacteristic, complemented
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5C2×D411yescharacteristic
206C2×C5×Q8—21no—
207C2×C5×Q8—24no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8—28no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8—44no—
214C2×C5×Q8—44no—
215C2×C5×Q8—48no—
216C2×C5×Q8#4114yescomplemented
217C2×C5×Q8C2412yes—
218C2×C5×Q8C2412yes—
219C22×C4×C5—21no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—24no—
225C22×C4×C5—21no—
226C22×C4×C5—24no—
227C22×C4×C5—44no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2411yescharacteristic
233C2×C22⋊D5—24no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5SD1618yescomplemented
236C2×C22⋊D5C2×D414yes—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243Q8×D5—28no—
244Q8×D5—44no—
245Q8×D5—48no—
246#709—432no—
247C2×D20—22no—
248C2×D20—22no—
249C2×D20—24no—
250C2×D20—21no—
251C2×D20—44no—
252C2×D20C2412yes—
253C2×C4×D5—22no—
254C2×C4×D5—22no—
255C2×C4×D5—24no—
256C2×C4×D5—24no—
257C2×C4×D5—24no—
258C2×C4×D5—44no—
259C2×C4×D5—44no—
260C2×C4×D5—44no—
261C2×C4×D5C2×D412yes—
262C2×C4×D5C2412yes—
263C2×Dic10—22no—
264C2×Dic10—22no—
265C2×Dic10—21no—
266C2×Dic10—24no—
267C2×Dic10—24no—
268C2×Dic10—44no—
269C2×Dic10—44no—
270C2×Dic10C2412yes—
271C2×C5×C8—22no—
272C2×C5×C8—22no—
273C2×C5×C8—44no—
274C2×C5×C8C2412yes—
275C2×C5×C8C2412yes—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—24no—
279C5×C4⋊C4C2412yes—
280C5×C4⋊C4C2412yes—
281C22⋊Dic5—24no—
282C22⋊Dic5C2×D414yes—
283#688—28no—
284#688—44no—
285#685—24no—
286#685—24no—
287#685—24no—
288#685—24no—
289#685C2×D414yes—
290C4⋊Dic5—21no—
291C4⋊Dic5—21no—
292C4⋊Dic5—24no—
293C4⋊Dic5C2412yes—
294C4⋊Dic5C2412yes—
295#683—24no—
296#683—24no—
297#683—24no—
298#683—24no—
299#683—24no—
300#683—24no—
301#683C2×D414yes—
302C4×Dic5—24no—
303C4×Dic5C2×D412yes—
304C4×Dic5C2412yes—
305C2×#168—22no—
306C2×#168—22no—
307C2×#168C2412yes—
308C2×#168C2412yes—
309#677—44no—
310C8×D5—44no—
311C22×#41—101no—
312C23×Q8—51no—
313C23×Q8C2×D511yescharacteristic
314C22×SD16—51no—
315C22×SD16—51no—
316C22×SD16—51no—
317C23×C8—51no—
318C23×C8C2×D511yescharacteristic
319D4×Q8—58no—
320D4×Q8—104no—
321#547—58no—
322#547—104no—
323C2×C4⋊Q8—51no—
324C2×C4⋊Q8—51no—
325C2×C4⋊Q8—101no—
326C2×#123—101no—
327C2×#123—101no—
328C2×C22⋊Q8—51no—
329C2×C22⋊Q8—51no—
330C2×C22⋊Q8—101no—
331C2×C22⋊Q8—101no—
332C2×C22⋊Q8—101no—
333C2×#121—51no—
334C2×#121—51no—
335C2×C4×Q8—51no—
336C2×C4×D4—51no—
337C2×C4×D4—51no—
338C2×C4×D4—101no—
339C22×C4⋊C4—51no—
340C22×C4⋊C4C2×D511yescharacteristic
341#487—58no—
342#483—58no—
343#483—58no—
344#475—58no—
345#465—58no—
346#465—58no—
347#461—58no—
348#448—58no—
349#448—58no—
350C4×SD16—58no—
351C8×D4—58no—
352C2×#106—51no—
353C2×#106—51no—
354C2×#106—51no—
355C2×C4⋊C8—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
361C2×#103—58no—
362C2×#103C2×D511yescharacteristic
363C2×#103C2×D511yescharacteristic
364C2×#103C2×D511yescharacteristic
365C2×#103C2×D511yescharacteristic
366C2×#103C2×D518yescomplemented
367C2×#102—51no—
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×C4×C8—51no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5C2×SD1614yes—
374C23×C5C22×D412yes—
375C23×C5C22×D411yescharacteristic
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—42no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5C2×SD1614yes—
383C22×D5C22×D412yes—
384C5×Q8—24no—
385C5×Q8—22no—
386C5×Q8—22no—
387C5×Q8—22no—
388C5×Q8—48no—
389C5×Q8—42no—
390C5×Q8C2×#4114yescomplemented
391C2×C4×C5—24no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—24no—
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—42no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5—48no—
405C2×C4×C5C22×D412yes—
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C2×#4112yes—
408C2×C4×C5H(5,𝔽2)12yes—
409C2×C4×C5C2511yescharacteristic
410C22⋊D5—48no—
411C22⋊D5C2×SD16116yescomplemented
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—42no—
418C2×Dic5—42no—
419C2×Dic5—42no—
420C2×Dic5C2×SD1614yes—
421C2×Dic5C22×D412yes—
422C2×Dic5C22×D412yes—
423C2×Dic5C22×D412yes—
424D20—22no—
425D20—22no—
426D20—48no—
427D20—42no—
428C4×D5—24no—
429C4×D5—22no—
430C4×D5—22no—
431C4×D5—48no—
432C4×D5—48no—
433C4×D5—48no—
434Dic10—22no—
435Dic10—22no—
436Dic10—48no—
437Dic10—42no—
438Dic10—48no—
439C5×C8—22no—
440C5×C8—22no—
441#168—22no—
442#168—22no—
443C2×#41—108no—
444C2×#41—208no—
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8—54no—
450C22×Q8—51no—
451C22×Q8—101no—
452C22×Q8—101no—
453C22×Q8—102no—
454C22×Q8—104no—
455C22×Q8—202no—
456C22×Q8C22×D511yescharacteristic
457C22×Q8C22×D514yes—
458C22×Q8C22×D511yescharacteristic
459C22×D4—51no—
460C22×D4—51no—
461C22×D4—101no—
462C22×D4—101no—
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—51no—
466C23×C4—101no—
467C23×C4—101no—
468C23×C4—101no—
469C23×C4C22×D511yescharacteristic
470C2×SD16—54no—
471C2×SD16—54no—
472C2×SD16—54no—
473C2×SD16—104no—
474C2×SD16—202no—
475C2×SD16—202no—
476C22×C8—42no—
477C22×C8—51no—
478C22×C8—51no—
479C22×C8—54no—
480C22×C8—202no—
481C22×C8C22×D511yescharacteristic
482C22×C8C22×D511yescharacteristic
483C22×C8C22×D514yes—
484C4⋊Q8—54no—
485C4⋊Q8—54no—
486C4⋊Q8—102no—
487C4⋊Q8—102no—
488C4⋊Q8—108no—
489#123—108no—
490#123—108no—
491C22⋊Q8—54no—
492C22⋊Q8—54no—
493C22⋊Q8—108no—
494C22⋊Q8—108no—
495C22⋊Q8—108no—
496C22⋊Q8—102no—
497C22⋊Q8—102no—
498#121—54no—
499#121—54no—
500#121—102no—
501#121—102no—
502C4×Q8—54no—
503C4×Q8—102no—
504C4×D4—54no—
505C4×D4—54no—
506C4×D4—54no—
507C4×D4—102no—
508C4×D4—108no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4—51no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—102no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4—101no—
518C2×C4⋊C4—101no—
519C2×C4⋊C4—101no—
520C2×C4⋊C4—101no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4C22×D511yescharacteristic
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—51no—
527C2×C22⋊C4—51no—
528C2×C22⋊C4—101no—
529C2×C22⋊C4—101no—
530C2×C22⋊C4—101no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C42—51no—
534C2×C42—101no—
535#106—54no—
536#106—54no—
537#106—54no—
538C4⋊C8—54no—
539#103—54no—
540#103—54no—
541#103—54no—
542#103—54no—
543#103—54no—
544#103C22×D514yes—
545#103C22×D514yes—
546#103C22×D514yes—
547#103C22×D514yes—
548#102—54no—
549C22⋊C8—54no—
550C22⋊C8—54no—
551C4×C8—54no—
552C22×C5—22no—
553C22×C5—28no—
554C22×C5—22no—
555C22×C5#54612yes—
556C22×C5C22×SD1614yes—
557C22×C5C22×SD1612yes—
558C22×C5#57812yes—
559C22×C5C23×D411yescharacteristic
560C2×D5—22no—
561C2×D5—28no—
562C2×D5—22no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—84no—
567C2×D5C22×SD1614yes—
568C4×C5—24no—
569C4×C5—22no—
570C4×C5—42no—
571C4×C5—42no—
572C4×C5—42no—
573C4×C5#54612yes—
574C4×C5C22×#4111yescharacteristic
575C4×C5C2×H(5,𝔽2)11yescharacteristic
576Dic5—22no—
577Dic5—22no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5C22×SD1614yes—
582C24—51no—
583C24—101no—
584C24D4×D511yescharacteristic
585#41—2032no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—48no—
596C2×Q8—52no—
597C2×Q8—104no—
598C2×Q8—104no—
599C2×Q8—101no—
600C2×Q8—108no—
601C2×Q8—102no—
602C2×Q8—102no—
603C2×Q8—204no—
604C2×Q8—204no—
605C2×Q8—204no—
606C2×Q8—208no—
607C2×Q8#70914yescomplemented
608C2×Q8C23×D512yes—
609C2×Q8C23×D512yes—
610C2×D4—54no—
611C2×D4—58no—
612C2×D4—52no—
613C2×D4—104no—
614C2×D4—104no—
615C2×D4—102no—
616C2×D4—101no—
617C2×D4—102no—
618C2×D4—204no—
619C2×D4—204no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—104no—
636C22×C4—104no—
637C22×C4—104no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—101no—
641C22×C4—101no—
642C22×C4—101no—
643C22×C4—204no—
644C22×C4—204no—
645C22×C4—204no—
646C22×C4D4×D512yes—
647C22×C4D4×D511yescharacteristic
648C22×C4C23×D512yes—
649C22×C4C23×D511yescharacteristic
650SD16—108no—
651SD16—204no—
652SD16—204no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—44no—
656C2×C8—52no—
657C2×C8—52no—
658C2×C8—102no—
659C2×C8—102no—
660C2×C8—204no—
661C2×C8C23×D512yes—
662C2×C8C23×D512yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—24no—
666C4⋊C4—54no—
667C4⋊C4—52no—
668C4⋊C4—52no—
669C4⋊C4—104no—
670C4⋊C4—104no—
671C4⋊C4—104no—
672C4⋊C4—104no—
673C4⋊C4—104no—
674C4⋊C4—104no—
675C4⋊C4—101no—
676C4⋊C4—101no—
677C4⋊C4—104no—
678C4⋊C4C23×D512yes—
679C4⋊C4C23×D512yes—
680C22⋊C4—54no—
681C22⋊C4—54no—
682C22⋊C4—104no—
683C22⋊C4—104no—
684C22⋊C4—104no—
685C22⋊C4—104no—
686C22⋊C4—104no—
687C42—52no—
688C42—52no—
689C42—104no—
690C2×C5—24no—
691C2×C5#329814yescomplemented
692C2×C5C2×#54611yescharacteristic
693C2×C5C23×SD1611yescharacteristic
694C2×C5C2×#57811yescharacteristic
695D5—24no—
696D5—82no—
697C23—22no—
698C23—22no—
699C23—54no—
700C23—52no—
701C23—102no—
702C23—102no—
703C23—102no—
704C23—202no—
705C23—202no—
706C23—202no—
707C23D5×SD1614yes—
708C23C2×D4×D512yes—
709C23C2×D4×D511yescharacteristic
710Q8—24no—
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—48no—
715Q8—42no—
716Q8—102no—
717Q8—102no—
718Q8—208no—
719Q8—208no—
720Q8—202no—
721Q8C2×#70914yescomplemented
722D4—516no—
723D4—102no—
724D4—102no—
725D4—208no—
726D4—208no—
727D4—202no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—48no—
742C2×C4—54no—
743C2×C4—52no—
744C2×C4—52no—
745C2×C4—52no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—104no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—208no—
755C2×C4—208no—
756C2×C4—208no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4C2×#70912yes—
761C2×C4C2×D4×D512yes—
762C2×C4C2×D4×D511yescharacteristic
763C2×C4#414412yes—
764C2×C4C24×D511yescharacteristic
765C8—22no—
766C8—22no—
767C8—102no—
768C8—102no—
769C5C2×#329811yescharacteristic, complemented, Sylow
770C22—28no—
771C22—22no—
772C22—22no—
773C22—54no—
774C22—108no—
775C22—102no—
776C22—102no—
777C22—202no—
778C22—202no—
779C22—202no—
780C22—404no—
781C22#6582412yes—
782C22C2×D5×SD1614yes—
783C22C2×D5×SD1612yes—
784C22#6610012yes—
785C22C22×D4×D511yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—54no—
792C4—102no—
793C4—102no—
794C4—202no—
795C4—202no—
796C4—202no—
797C4#6582412yes—
798C4C22×#70911yescharacteristic
799C4C2×#414411yescharacteristic
800C2—24no—
801C2—104no—
802C2—402no—
803C2#1061053614yesdirect product factor
804C2C2×#6582411yescharacteristic
805C2C22×D5×SD1611yescharacteristic
806C2C2×#6610011yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#103C2
socleC23×C5C22×D4
prime radicalC2×#65841C2
hypercenterC22×#103D5
hypocenterC5C2×#3298
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D5C2semidirect
3. C22×C5×#103C2semidirect
4. C2×#65516C2semidirect
5. C2×#65403C2semidirect
6. C2×C8×C22⋊D5C2semidirect
7. C2×#65260C2semidirect
8. C2×#65107C2semidirect
9. #10610536C2direct (N × H)
10. C2×#65094C2semidirect
11. C2×#65096C2semidirect
12. C2×#65095C2semidirect
13. C2×D5×#103C2semidirect
14. C2×#65081C2semidirect
15. C2×#65080C2semidirect
16. C2×#65077C2semidirect
23. Q8×C22⋊D5C22semidirect
51. C2×C5×#103C22semidirect
52. #65516C22semidirect
56. #65403C22semidirect
58. C8×C22⋊D5C22semidirect
64. #65260C22semidirect
69. #65107C22semidirect
70. #65096C22semidirect
71. #65095C22semidirect
72. #65094C22semidirect
73. D5×#103C22semidirect
74. #65081C22semidirect
75. #65080C22semidirect
76. #65077C22semidirect
202. C22×#103D5semidirect
216. C2×C5×Q8#41semidirect
235. C2×C22⋊D5SD16semidirect
366. C2×#103C2×D5semidirect
390. C5×Q8C2×#41semidirect
411. C22⋊D5C2×SD16semidirect
607. C2×Q8#709semidirect
691. C2×C5#3298semidirect
721. Q8C2×#709semidirect
769. C5C2×#3298semidirect
803. C2#10610536direct (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×#658412
C22×C5×#1032
C2×#655162
C2×#654032
C2×C8×C22⋊D52
C2×#652602
C2×#651072
#106105362
C2×#650942
C2×#650962
C2×#650952
C2×D5×#1032
C2×#650812
C2×#650802
C2×#650772
C2×#32985