Finite Group Databasebeta

← C2×#10612554 #12975821

Subgroups — C2×#10612554 #12975821

Order 1280.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65969C211yesmaximal, characteristic, complemented
2C2×#65946C211yesmaximal, characteristic
3C2×C5×#468C211yesmaximal, characteristic, complemented
4C2×#65458C211yesmaximal, characteristic, complemented
5C2×#65455C211yesmaximal, characteristic, complemented
6C2×#65422C211yesmaximal, characteristic, complemented
7C2×#65416C211yesmaximal, characteristic, complemented
8C2×#65336C211yesmaximal, characteristic, complemented
9C2×#65322C211yesmaximal, characteristic, complemented
10#10612554C2116yesmaximal, direct product factor
11C2×#65179C211yesmaximal, characteristic, complemented
12C2×#65173C211yesmaximal, characteristic, complemented
13C2×#65102C211yesmaximal, characteristic, complemented
14C2×#65106C211yesmaximal, characteristic, complemented
15C2×D5×#102C211yesmaximal, characteristic, complemented
16C2×#65054C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic, complemented
21C2×C5×C22⋊Q8C2211yescharacteristic, complemented
22C2×C5×#121C2211yescharacteristic
23C2×#4092C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic, complemented
25C22×#689C2211yescharacteristic, complemented
26C22×#688C2211yescharacteristic
27C2×#4084—21no—
28C2×#4083—21no—
29C2×#4082C2211yescharacteristic
30C2×C4×C22⋊D5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic, complemented
32C22×C8×D5C2211yescharacteristic
33#65969—24no—
34#65969C2218yescomplemented
35#65946—24no—
36#65946C2218yes—
37C2×#4043—21no—
38C2×#4043C2211yescharacteristic
39C2×#4039C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4035—21no—
42C2×#4034C2211yescharacteristic, complemented
43C2×#4029—21no—
44C2×#4027—21no—
45C2×D5×C22⋊C4—21no—
46C2×#4024—21no—
47C5×#468C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#103C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic, complemented
54#65458C2218yescomplemented
55#65455C2218yescomplemented
56#65422C2218yescomplemented
57#65416C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3952C2211yescharacteristic
61C2×#3948C2211yescharacteristic, complemented
62C2×#3948C2211yescharacteristic, complemented
63C2×#3947C2211yescharacteristic, complemented
64C2×#3946C2211yescharacteristic, complemented
65#65336C2218yescomplemented
66#65322C2218yescomplemented
67C2×#3942C2211yescharacteristic, complemented
68C2×#3941C2211yescharacteristic
69C2×#3939C2211yescharacteristic, complemented
70C2×#3939C2211yescharacteristic, complemented
71#65179C2218yescomplemented
72#65173C2218yescomplemented
73#65106C2218yescomplemented
74#65102C2218yescomplemented
75D5×#102C2218yescomplemented
76#65054C2218yescomplemented
77C2×#3314—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5D411yescharacteristic
86C23×Dic5—21no—
87C2×D4×D5—24no—
88C2×D4×D5—22no—
89C2×D4×D5—42no—
90C2×D4×D5C2314yes—
91C2×#709—22no—
92C2×#709—24no—
93C2×#709—42no—
94C2×#709C2314yes—
95C22×D20C2311yescharacteristic
96C22×C4×D5—21no—
97C22×C4×D5—21no—
98C22×C4×D5—21no—
99C22×C4×D5C2311yescharacteristic
100C22×Dic10—21no—
101C22×Dic10C2311yescharacteristic
102C2×C5×SD16—42no—
103C2×C5×SD16C2314yes—
104C2×C5×M16—42no—
105C2×C5×M16C2314yescomplemented
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C5×C22⋊Q8—22no—
109C5×C22⋊Q8C2314yescomplemented
110C5×#121—22no—
111C5×#121C2314yes—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5D411yescharacteristic
120#4092—22no—
121#4092C2314yes—
122Q8×Dic5—22no—
123Q8×Dic5C2314yescomplemented
124C2×#689—42no—
125C2×#689C2314yescomplemented
126C2×#688—24no—
127C2×#688C2314yes—
128#4084—28no—
129#4083—28no—
130#4082—22no—
131#4082C2314yes—
132C4×C22⋊D5D414yes—
133C4×C22⋊D5C2314yes—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685D411yescharacteristic
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—22no—
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5—21no—
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2314yescomplemented
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683D411yescharacteristic
149C2×C4×Dic5—21no—
150C2×C4×Dic5C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C2×C8×D5—42no—
154C2×C8×D5C2314yes—
155#4043—22no—
156#4043—28no—
157#4043C2314yes—
158#4039—22no—
159#4039C2314yes—
160D5×C4⋊C4—22no—
161D5×C4⋊C4C2314yes—
162#4035—28no—
163#4034—22no—
164#4034C2314yescomplemented
165#4029—28no—
166#4027—28no—
167D5×C22⋊C4—28no—
168#4024—28no—
169C5×#107C2314yescomplemented
170C5×#103C2314yescomplemented
171C5×#102C2314yes—
172#3964C2314yes—
173#3964C2314yes—
174C22⋊#168C2314yescomplemented
175#3953C2314yes—
176#3953C2314yes—
177#3952C2314yes—
178#3948C2314yescomplemented
179#3948C2314yescomplemented
180#3947C2314yescomplemented
181#3946C2314yescomplemented
182#3942C2314yescomplemented
183#3941C2314yes—
184#3939C2314yescomplemented
185#3939C2314yescomplemented
186C2×#554—51no—
187C2×#546—51no—
188#3314—516no—
189C2×#489—51no—
190C2×#484—51no—
191C2×#480—51no—
192C2×#474—51no—
193C2×#468D511yescharacteristic, complemented
194C2×#467—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#450—51no—
198C2×#440—51no—
199C2×#435—51no—
200C2×#417—51no—
201C22×#102—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—24no—
206C23×D5—44no—
207C23×D5—44no—
208C23×D5—82no—
209C23×D5C2×D411yescharacteristic
210C2×C5×Q8—21no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8C2412yes—
214C2×C5×D4—24no—
215C2×C5×D4—21no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4—82no—
219C2×C5×D4C2412yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C2×C22⋊D5—24no—
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5C2×D414yes—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—24no—
239C22×Dic5—82no—
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243D4×D5—28no—
244D4×D5—44no—
245D4×D5—48no—
246#709—28no—
247#709—44no—
248#709—48no—
249C2×D20—21no—
250C2×D20—22no—
251C2×D20#4114yes—
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—82no—
260C2×C4×D5—82no—
261C2×C4×D5C2×D412yes—
262C2×C4×D5C2412yes—
263C2×Dic10—22no—
264C2×Dic10—22no—
265C2×Dic10—21no—
266C2×Dic10—24no—
267C2×Dic10—82no—
268C2×Dic10C2412yes—
269C5×SD16—44no—
270C5×M16—44no—
271C2×C5×C8—22no—
272C2×C5×C8—22no—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C5×C4⋊C4—24no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4C2412yes—
279C5×C4⋊C4C2412yes—
280C5×C22⋊C4—24no—
281C5×C22⋊C4—24no—
282C22⋊Dic5—24no—
283C22⋊Dic5—24no—
284C22⋊Dic5C2×D414yes—
285#689—44no—
286#688—28no—
287#685—24no—
288#685—24no—
289#685—24no—
290#685C2×D414yes—
291C4⋊Dic5—21no—
292C4⋊Dic5—24no—
293C4⋊Dic5—21no—
294C4⋊Dic5—24no—
295C4⋊Dic5—24no—
296C4⋊Dic5C2412yes—
297C4⋊Dic5C2412yes—
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—
309C8×D5—44no—
310C22×#41—51no—
311C23×D4—51no—
312C22×Q16—51no—
313C22×SD16—51no—
314C22×SD16C2×D511yescharacteristic
315C22×M16C2×D511yescharacteristic, complemented
316C23×C8—51no—
317#554—58no—
318#554—104no—
319#546—58no—
320#546—104no—
321C2×C4⋊Q8—51no—
322C2×#125—101no—
323C2×#124—51no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×C22⋊Q8—101no—
328C2×C22⋊Q8—101no—
329C2×C22⋊Q8C2×D511yescharacteristic, complemented
330C2×#121—101no—
331C2×#121C2×D511yescharacteristic
332C2×#120—101no—
333C2×C4×Q8—51no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—101no—
337C22×C4⋊C4—51no—
338C22×C4⋊C4—51no—
339C22×C22⋊C4—101no—
340#489—58no—
341#484—58no—
342#480—58no—
343#474—58no—
344#468C2×D518yescomplemented
345#467—58no—
346#464—58no—
347#452—58no—
348#450—58no—
349#440—58no—
350#435—58no—
351C2×#107—51no—
352C2×#107—51no—
353C2×#107C2×D511yescharacteristic, complemented
354C2×C4⋊C8—51no—
355#417—58no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103C2×D511yescharacteristic, complemented
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—58no—
366C2×#102C2×D511yescharacteristic
367C2×C22⋊C8—51no—
368C2×C22⋊C8—51no—
369C2×#97—51no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—42no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5C22×D412yes—
378C23×C5C22×D411yescharacteristic
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—24no—
382C22×D5—22no—
383C22×D5—48no—
384C22×D5—42no—
385C22×D5—42no—
386C22×D5—48no—
387C22×D5—84no—
388C22×D5—816no—
389C22×D5#13714yes—
390C22×D5C22×D412yes—
391C5×Q8—22no—
392C5×Q8—22no—
393C5×Q8—42no—
394C5×D4—22no—
395C5×D4—22no—
396C5×D4—42no—
397C5×D4—84no—
398C2×C4×C5—22no—
399C2×C4×C5—24no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—42no—
406C2×C4×C5—42no—
407C2×C4×C5—42no—
408C2×C4×C5C22×D412yes—
409C2×C4×C5C22×D411yescharacteristic
410C2×C4×C5C2×#4112yes—
411C2×C4×C5H(5,𝔽2)12yes—
412C2×C4×C5C2511yescharacteristic
413C22⋊D5—28no—
414C22⋊D5—48no—
415C22⋊D5—48no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—42no—
423C2×Dic5—42no—
424C2×Dic5—42no—
425C2×Dic5—84no—
426C2×Dic5C22×D412yes—
427C2×Dic5C22×D412yes—
428C2×Dic5C22×D412yes—
429D20—24no—
430D20—22no—
431D20C2×#4114yes—
432C4×D5—24no—
433C4×D5—22no—
434C4×D5—22no—
435C4×D5—48no—
436C4×D5—84no—
437C4×D5—84no—
438Dic10—22no—
439Dic10—22no—
440Dic10—42no—
441Dic10—84no—
442C5×C8—22no—
443C5×C8—22no—
444#168—22no—
445#168—22no—
446C25—101no—
447C2×#41—54no—
448C2×#41—104no—
449C2×#41—102no—
450C2×#41—202no—
451C22×Q8—51no—
452C22×Q8—101no—
453C22×Q8C22×D511yescharacteristic
454C22×D4—21no—
455C22×D4—51no—
456C22×D4—54no—
457C22×D4—51no—
458C22×D4—102no—
459C22×D4—101no—
460C22×D4—104no—
461C22×D4—101no—
462C22×D4—202no—
463C22×D4C22×D511yescharacteristic
464C23×C4—51no—
465C23×C4—101no—
466C23×C4—101no—
467C23×C4—101no—
468C23×C4—101no—
469C23×C4C22×D511yescharacteristic
470C2×Q16—54no—
471C2×Q16—202no—
472C2×SD16—42no—
473C2×SD16—54no—
474C2×SD16—104no—
475C2×SD16C22×D514yes—
476C2×M16—42no—
477C2×M16C22×D514yescomplemented
478C22×C8—51no—
479C22×C8—51no—
480C22×C8—54no—
481C22×C8—202no—
482C22×C8C22×D511yescharacteristic
483C22×C8C22×D511yescharacteristic
484C4⋊Q8—54no—
485C4⋊Q8—102no—
486#125—108no—
487#124—54no—
488#124—102no—
489#123—108no—
490C22⋊Q8—22no—
491C22⋊Q8—54no—
492C22⋊Q8—54no—
493C22⋊Q8—108no—
494C22⋊Q8—108no—
495C22⋊Q8—102no—
496C22⋊Q8—102no—
497C22⋊Q8C22×D514yescomplemented
498#121—22no—
499#121—108no—
500#121C22×D514yes—
501#120—108no—
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—51no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4—54no—
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—102no—
523C2×C4⋊C4C22×D511yescharacteristic
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—51no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4—108no—
530C2×C22⋊C4—101no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C42—51no—
536C2×C42—101no—
537#107—54no—
538#107—54no—
539#107C22×D514yescomplemented
540C4⋊C8—54no—
541#103—54no—
542#103—54no—
543#103—54no—
544#103C22×D514yescomplemented
545#102—54no—
546#102—54no—
547#102—54no—
548#102—54no—
549#102—54no—
550#102C22×D514yes—
551C22⋊C8—54no—
552C22⋊C8—54no—
553#97—54no—
554C22×C5—22no—
555C22×C5—22no—
556C22×C5—22no—
557C22×C5—44no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—84no—
562C22×C5#54612yes—
563C22×C5C2×#13712yes—
564C22×C5#57612yes—
565C22×C5C23×D411yescharacteristic
566C2×D5—22no—
567C2×D5—28no—
568C2×D5—22no—
569C2×D5—24no—
570C2×D5—48no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—816no—
574C2×D5C2×#13714yes—
575C4×C5—22no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579C4×C5#54612yes—
580C4×C5C22×#4111yescharacteristic
581C4×C5C2×H(5,𝔽2)11yescharacteristic
582Dic5—22no—
583Dic5—22no—
584Dic5—22no—
585Dic5—42no—
586Dic5—42no—
587Dic5—42no—
588C24—21no—
589C24—51no—
590C24—104no—
591C24—101no—
592C24—204no—
593C24—204no—
594C24—402no—
595C24D4×D511yescharacteristic
596#41—108no—
597#41—204no—
598#41—208no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—52no—
603C2×Q8—104no—
604C2×Q8—101no—
605C2×Q8—102no—
606C2×Q8—102no—
607C2×Q8—402no—
608C2×Q8C23×D512yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—54no—
614C2×D4—54no—
615C2×D4—52no—
616C2×D4—82no—
617C2×D4—104no—
618C2×D4—108no—
619C2×D4—104no—
620C2×D4—104no—
621C2×D4—101no—
622C2×D4—102no—
623C2×D4—204no—
624C2×D4—208no—
625C2×D4—204no—
626C2×D4—204no—
627C2×D4C23×D512yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—51no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—104no—
639C22×C4—104no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—101no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—104no—
646C22×C4—104no—
647C22×C4—204no—
648C22×C4—402no—
649C22×C4—402no—
650C22×C4—402no—
651C22×C4D4×D512yes—
652C22×C4D4×D511yescharacteristic
653C22×C4C23×D512yes—
654C22×C4C23×D511yescharacteristic
655Q16—204no—
656SD16—44no—
657SD16—108no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—52no—
662C2×C8—52no—
663C2×C8—102no—
664C2×C8—102no—
665C2×C8—204no—
666C2×C8C23×D512yes—
667C2×C8C23×D512yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—54no—
672C4⋊C4—52no—
673C4⋊C4—52no—
674C4⋊C4—104no—
675C4⋊C4—104no—
676C4⋊C4—104no—
677C4⋊C4—104no—
678C4⋊C4—104no—
679C4⋊C4—101no—
680C4⋊C4—104no—
681C4⋊C4—101no—
682C4⋊C4C23×D512yes—
683C4⋊C4C23×D512yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—54no—
687C22⋊C4—54no—
688C22⋊C4—104no—
689C22⋊C4—104no—
690C22⋊C4—104no—
691C22⋊C4—104no—
692C22⋊C4—104no—
693C42—52no—
694C42—52no—
695C42—104no—
696C2×C5—42no—
697C2×C5—82no—
698C2×C5#331414yescomplemented
699C2×C5C2×#54611yescharacteristic
700C2×C5C22×#13711yescharacteristic
701C2×C5C2×#57611yescharacteristic
702D5—24no—
703D5—44no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—54no—
712C23—52no—
713C23—102no—
714C23—102no—
715C23—104no—
716C23—102no—
717C23—208no—
718C23—208no—
719C23—202no—
720C23—202no—
721C23—404no—
722C23—4016no—
723C23C2×D4×D512yes—
724C23C2×D4×D511yescharacteristic
725Q8—22no—
726Q8—22no—
727Q8—42no—
728Q8—102no—
729Q8—102no—
730Q8—202no—
731Q8—404no—
732D4—22no—
733D4—22no—
734D4—42no—
735D4—54no—
736D4—84no—
737D4—108no—
738D4—104no—
739D4—102no—
740D4—208no—
741D4—208no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—52no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—104no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—208no—
765C2×C4—202no—
766C2×C4—202no—
767C2×C4—202no—
768C2×C4—404no—
769C2×C4—404no—
770C2×C4—404no—
771C2×C4C2×D4×D512yes—
772C2×C4C2×D4×D511yescharacteristic
773C2×C4#414412yes—
774C2×C4D5×#4112yes—
775C2×C4C24×D511yescharacteristic
776C8—22no—
777C8—22no—
778C8—102no—
779C8—102no—
780C5C2×#331411yescharacteristic, complemented, Sylow
781C22—22no—
782C22—22no—
783C22—22no—
784C22—44no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—54no—
789C22—84no—
790C22—108no—
791C22—102no—
792C22—102no—
793C22—104no—
794C22—208no—
795C22—202no—
796C22—202no—
797C22—4016no—
798C22#6594412yes—
799C22#6610812yes—
800C22D5×#13712yes—
801C22C22×D4×D511yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—102no—
807C4—102no—
808C4—102no—
809C4—202no—
810C4—202no—
811C4—202no—
812C4#6594412yes—
813C4C2×#414411yescharacteristic
814C4C2×D5×#4111yescharacteristic
815C2—42no—
816C2—82no—
817C2—104no—
818C2—204no—
819C2#1061255414yesdirect product factor
820C2C2×#6594411yescharacteristic
821C2C2×#6610811yescharacteristic
822C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#468C2
socleC23×C5C22×D4
prime radicalC2×#65946C2
hypercenterC2×#468D5
hypocenterC5C2×#3314
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#65969C2semidirect
3. C2×C5×#468C2semidirect
4. C2×#65458C2semidirect
5. C2×#65455C2semidirect
6. C2×#65422C2semidirect
7. C2×#65416C2semidirect
8. C2×#65336C2semidirect
9. C2×#65322C2semidirect
10. #10612554C2direct (N × H)
11. C2×#65179C2semidirect
12. C2×#65173C2semidirect
13. C2×#65102C2semidirect
14. C2×#65106C2semidirect
15. C2×D5×#102C2semidirect
16. C2×#65054C2semidirect
20. C22×C5×M16C22semidirect
21. C2×C5×C22⋊Q8C22semidirect
24. C2×Q8×Dic5C22semidirect
25. C22×#689C22semidirect
31. C22×C4⋊Dic5C22semidirect
34. #65969C22semidirect
42. C2×#4034C22semidirect
47. C5×#468C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#103C22semidirect
53. C2×C22⋊#168C22semidirect
54. #65458C22semidirect
55. #65455C22semidirect
56. #65422C22semidirect
57. #65416C22semidirect
61. C2×#3948C22semidirect
62. C2×#3948C22semidirect
63. C2×#3947C22semidirect
64. C2×#3946C22semidirect
65. #65336C22semidirect
66. #65322C22semidirect
67. C2×#3942C22semidirect
69. C2×#3939C22semidirect
70. C2×#3939C22semidirect
71. #65179C22semidirect
72. #65173C22semidirect
73. #65106C22semidirect
74. #65102C22semidirect
75. D5×#102C22semidirect
76. #65054C22semidirect
105. C2×C5×M16C23semidirect
109. C5×C22⋊Q8C23semidirect
123. Q8×Dic5C23semidirect
125. C2×#689C23semidirect
144. C2×C4⋊Dic5C23semidirect
164. #4034C23semidirect
169. C5×#107C23semidirect
170. C5×#103C23semidirect
174. C22⋊#168C23semidirect
178. #3948C23semidirect
179. #3948C23semidirect
180. #3947C23semidirect
181. #3946C23semidirect
182. #3942C23semidirect
184. #3939C23semidirect
185. #3939C23semidirect
193. C2×#468D5semidirect
315. C22×M16C2×D5semidirect
329. C2×C22⋊Q8C2×D5semidirect
344. #468C2×D5semidirect
353. C2×#107C2×D5semidirect
359. C2×#103C2×D5semidirect
477. C2×M16C22×D5semidirect
497. C22⋊Q8C22×D5semidirect
539. #107C22×D5semidirect
544. #103C22×D5semidirect
698. C2×C5#3314semidirect
780. C5C2×#3314semidirect
819. C2#10612554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659692
C2×#659462
C2×C5×#4682
C2×#654582
C2×#654552
C2×#654222
C2×#654162
C2×#653362
C2×#653222
#106125542
C2×#651792
C2×#651732
C2×#651022
C2×#651062
C2×D5×#1022
C2×#650542
C2×#33145