Finite Group Databasebeta

← C2×#10611993 #12970641

Subgroups — C2×#10611993 #12970641

Order 1280.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66164C211yesmaximal, characteristic
2C2×#65959C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic, complemented
4C2×#65528C211yesmaximal, characteristic, complemented
5C2×#65479C211yesmaximal, characteristic, complemented
6C2×#65474C211yesmaximal, characteristic, complemented
7C2×#65464C211yesmaximal, characteristic, complemented
8C2×#65452C211yesmaximal, characteristic, complemented
9C2×#65335C211yesmaximal, characteristic, complemented
10#10611993C2116yesmaximal, direct product factor
11C2×#65087C211yesmaximal, characteristic, complemented
12C2×#65089C211yesmaximal, characteristic, complemented
13C2×#65051C211yesmaximal, characteristic, complemented
14C2×#65053C211yesmaximal, characteristic, complemented
15C2×#65020C211yesmaximal, characteristic, complemented
16C2×#65009C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C22×C5×Q16C2211yescharacteristic, complemented
20C22×C5×SD16C2211yescharacteristic, complemented
21C2×C5×C22⋊Q8C2211yescharacteristic
22#66164—24no—
23#66164C2218yes—
24C2×#4093C2211yescharacteristic
25C2×#4093C2211yescharacteristic
26C2×Q8×Dic5C2211yescharacteristic, complemented
27C2×#4090C2211yescharacteristic, complemented
28C22×#689C2211yescharacteristic, complemented
29C22×#688C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C2×#4086C2211yescharacteristic
32C2×#4086C2211yescharacteristic
33C2×#4083—21no—
34C2×#4083—21no—
35C22×#687C2211yescharacteristic, complemented
36C2×#4076—21no—
37C2×#4076—21no—
38C2×#4072C2211yescharacteristic
39C2×#4070C2211yescharacteristic
40C22×#677C2211yescharacteristic
41C22×#677C2211yescharacteristic
42#65959—24no—
43#65959C2218yescomplemented
44C2×#4036—21no—
45C2×#4036C2211yescharacteristic, complemented
46C2×#4035—21no—
47C2×#4033C2211yescharacteristic, complemented
48C2×#4025—21no—
49C2×#4025—21no—
50C5×#452C2218yescomplemented
51C2×C5×#103C2211yescharacteristic, complemented
52C2×C5×#102C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic
54#65528C2218yescomplemented
55C2×#3967C2211yescharacteristic, complemented
56C2×#3964C2211yescharacteristic, complemented
57C2×C22⋊#168C2211yescharacteristic
58#65479C2218yescomplemented
59#65474C2218yescomplemented
60#65464C2218yescomplemented
61#65452C2218yescomplemented
62C2×#3953C2211yescharacteristic
63C2×#3953C2211yescharacteristic
64C2×#3947C2211yescharacteristic, complemented
65C2×#3946C2211yescharacteristic, complemented
66C2×#3946C2211yescharacteristic, complemented
67C2×C8×Dic5C2211yescharacteristic, complemented
68#65335C2218yescomplemented
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71#65089C2218yescomplemented
72#65087C2218yescomplemented
73#65053C2218yescomplemented
74#65051C2218yescomplemented
75#65020C2218yescomplemented
76#65009C2218yescomplemented
77C2×#3222—51nomaximal, Sylow
78C24×D5—21no—
79C2×C5×#41—22no—
80C2×C5×#41—42no—
81C2×C5×#41—42no—
82C2×C5×#41C2314yes—
83C22×C5×Q8C2311yescharacteristic
84C22×C5×Q8C2311yescharacteristic
85C22×C5×D4—21no—
86C22×C5×D4C2311yescharacteristic
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C22×C22⋊D5—21no—
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C22×C22⋊D5—21no—
93C22×D20—21no—
94C22×D20—22no—
95C22×D20—42no—
96C22×D20—42no—
97C22×D20C2311yescharacteristic
98C22×D20C2311yescharacteristic
99C22×D20C2314yes—
100C22×Dic10C2311yescharacteristic
101C2×C5×Q16—42no—
102C2×C5×Q16C2314yescomplemented
103C2×C5×SD16—42no—
104C2×C5×SD16C2314yescomplemented
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8C2314yes—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5D411yescharacteristic
114C2×C22⋊Dic5D411yescharacteristic
115#4093—22no—
116#4093—22no—
117#4093C2314yes—
118#4093C2314yes—
119Q8×Dic5—22no—
120Q8×Dic5C2314yescomplemented
121#4090—22no—
122#4090C2314yescomplemented
123C2×#689—42no—
124C2×#689C2314yescomplemented
125C2×#688—42no—
126C2×#688—42no—
127C2×#688C2314yes—
128C2×#688C2314yes—
129#4086—22no—
130#4086—22no—
131#4086C2314yes—
132#4086C2314yes—
133#4083—28no—
134#4083—28no—
135C2×#687—42no—
136C2×#687C2314yescomplemented
137#4076—28no—
138#4076—28no—
139C2×#685—21no—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143#4072D414yes—
144#4072C2314yes—
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5—21no—
147C2×C4⋊Dic5D411yescharacteristic
148C2×C4⋊Dic5D411yescharacteristic
149C2×C4⋊Dic5C2311yescharacteristic
150#4070—22no—
151#4070C2314yes—
152C2×#683—21no—
153C2×#683—21no—
154C2×#683—21no—
155C2×#683—21no—
156C2×#683—21no—
157C2×C4×Dic5—21no—
158C2×C4×Dic5—21no—
159C2×C4×Dic5C2311yescharacteristic
160C2×C4×Dic5C2311yescharacteristic
161C22×#168C2311yescharacteristic
162C22×#168C2311yescharacteristic
163C2×#677—42no—
164C2×#677—42no—
165C2×#677C2314yes—
166C2×#677C2314yes—
167#4036—28no—
168#4036—22no—
169#4036C2314yescomplemented
170#4035—28no—
171#4033—22no—
172#4033C2314yescomplemented
173#4025—28no—
174#4025—28no—
175C5×#103C2314yescomplemented
176C5×#102C2314yescomplemented
177C5×C22⋊C8C2314yes—
178#3967C2314yescomplemented
179#3964C2314yescomplemented
180C22⋊#168C2314yes—
181#3953C2314yes—
182#3953C2314yes—
183#3947C2314yescomplemented
184#3946C2314yescomplemented
185#3946C2314yescomplemented
186C8×Dic5C2314yescomplemented
187#3941C2314yes—
188#3941C2314yes—
189C2×#541—51no—
190C2×#535—51no—
191#3222—516no—
192C2×#497—51no—
193C2×#492—51no—
194C2×#490—51no—
195C2×#488—51no—
196C2×#464—51no—
197C2×#464—51no—
198C2×#460—51no—
199C2×#460—51no—
200C2×#452—51no—
201C2×#452D511yescharacteristic, complemented
202C2×#450—51no—
203C2×#450—51no—
204C2×#433—51no—
205C24×C5—21no—
206C24×C5C2×D411yescharacteristic
207C23×D5—21no—
208C23×D5—21no—
209C23×D5—24no—
210C23×D5—44no—
211C23×D5—82no—
212C23×D5—82no—
213C5×#41—44no—
214C5×#41—44no—
215C5×#41—48no—
216C2×C5×Q8—21no—
217C2×C5×Q8—21no—
218C2×C5×Q8—22no—
219C2×C5×Q8—22no—
220C2×C5×Q8—22no—
221C2×C5×Q8—22no—
222C2×C5×Q8C2412yes—
223C2×C5×Q8C2412yes—
224C2×C5×D4—24no—
225C2×C5×D4—21no—
226C2×C5×D4—22no—
227C2×C5×D4—22no—
228C2×C5×D4—44no—
229C2×C5×D4C2412yes—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—24no—
236C22×C4×C5—44no—
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D412yes—
239C22×C4×C5C2412yes—
240C22×C4×C5C2411yescharacteristic
241C2×C22⋊D5—24no—
242C2×C22⋊D5—24no—
243C2×C22⋊D5—24no—
244C2×C22⋊D5—24no—
245C2×C22⋊D5—82no—
246C2×C22⋊D5—82no—
247C2×C22⋊D5—82no—
248C2×C22⋊D5—82no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5C2×D411yescharacteristic
252C22×Dic5C2×D411yescharacteristic
253C22×Dic5C2×D411yescharacteristic
254C22×Dic5C2×D411yescharacteristic
255C2×D20—22no—
256C2×D20—22no—
257C2×D20—22no—
258C2×D20—22no—
259C2×D20—24no—
260C2×D20—21no—
261C2×D20—21no—
262C2×D20—44no—
263C2×D20—44no—
264C2×D20—44no—
265C2×D20—48no—
266C2×D20C2412yes—
267C2×D20C2412yes—
268C2×Dic10—22no—
269C2×Dic10—22no—
270C2×Dic10—21no—
271C2×Dic10C2412yes—
272C5×Q16—44no—
273C5×SD16—44no—
274C2×C5×C8—22no—
275C2×C5×C8—22no—
276C2×C5×C8C2412yes—
277C2×C5×C8C2412yes—
278C5×C4⋊C4—24no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4C2412yes—
281C5×C22⋊C4—24no—
282C22⋊Dic5—24no—
283C22⋊Dic5C2×D414yes—
284C22⋊Dic5C2×D414yes—
285#689—44no—
286#688—44no—
287#688—44no—
288#687—44no—
289#685—24no—
290#685—24no—
291#685—24no—
292#685—24no—
293C4⋊Dic5—21no—
294C4⋊Dic5—24no—
295C4⋊Dic5—24no—
296C4⋊Dic5C2×D414yes—
297C4⋊Dic5C2×D414yes—
298C4⋊Dic5C2412yes—
299#683—24no—
300#683—24no—
301#683—24no—
302#683—24no—
303#683—24no—
304C4×Dic5—24no—
305C4×Dic5—24no—
306C4×Dic5C2×D412yes—
307C4×Dic5C2×D412yes—
308C4×Dic5C2412yes—
309C4×Dic5C2412yes—
310C2×#168—22no—
311C2×#168—22no—
312C2×#168C2412yes—
313C2×#168C2412yes—
314#677—44no—
315#677—44no—
316C22×#41C2×D511yescharacteristic
317C23×D4—51no—
318C22×Q16—51no—
319C22×Q16C2×D511yescharacteristic, complemented
320C22×SD16—51no—
321C22×SD16—51no—
322C22×SD16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×SD16C2×D511yescharacteristic, complemented
326#541—58no—
327#541—104no—
328#535—58no—
329#535—104no—
330C2×C4⋊Q8—51no—
331C2×#127—51no—
332C2×#127—51no—
333C2×#126—101no—
334C2×#126—101no—
335C2×#125—51no—
336C2×#125—101no—
337C2×#125—101no—
338C2×#124—51no—
339C2×#124—51no—
340C2×C22⋊Q8—51no—
341C2×C22⋊Q8C2×D511yescharacteristic
342C2×#121—101no—
343C2×#121—101no—
344C2×#120—101no—
345C2×#120—101no—
346C2×C4×Q8—51no—
347C2×C4×Q8—51no—
348C2×#117—51no—
349#497—58no—
350#492—58no—
351#490—58no—
352#488—58no—
353#464—58no—
354#464—58no—
355#460—58no—
356#460—58no—
357#452—58no—
358#452C2×D518yescomplemented
359#450—58no—
360#450—58no—
361#433—58no—
362C2×C4⋊C8—51no—
363C2×C4⋊C8—51no—
364C2×#103—51no—
365C2×#103C2×D511yescharacteristic, complemented
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—51no—
370C2×#102—51no—
371C2×#102C2×D511yescharacteristic, complemented
372C2×C22⋊C8—51no—
373C2×C22⋊C8C2×D511yescharacteristic
374C2×#97—51no—
375C2×C4×C8—51no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5—42no—
383C23×C5C22×D412yes—
384C23×C5C22×D411yescharacteristic
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—48no—
388C22×D5—42no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—84no—
395C22×D5—84no—
396C22×D5—816no—
397C5×Q8—22no—
398C5×Q8—22no—
399C5×Q8—22no—
400C5×Q8—22no—
401C5×Q8—42no—
402C5×Q8—42no—
403C5×D4—22no—
404C5×D4—22no—
405C5×D4—48no—
406C5×D4—42no—
407C2×C4×C5—22no—
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—42no—
416C2×C4×C5—42no—
417C2×C4×C5—42no—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5H(5,𝔽2)12yes—
421C2×C4×C5H(5,𝔽2)12yes—
422C2×C4×C5C2511yescharacteristic
423C22⋊D5—84no—
424C22⋊D5—84no—
425C22⋊D5—84no—
426C22⋊D5—84no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—42no—
434C2×Dic5—42no—
435C2×Dic5C22×D412yes—
436C2×Dic5C22×D412yes—
437C2×Dic5C22×D412yes—
438C2×Dic5C22×D412yes—
439D20—22no—
440D20—22no—
441D20—22no—
442D20—22no—
443D20—48no—
444D20—42no—
445D20—42no—
446Dic10—22no—
447Dic10—22no—
448Dic10—42no—
449C5×C8—22no—
450C5×C8—22no—
451#168—22no—
452#168—22no—
453C25—101no—
454C2×#41—22no—
455C2×#41—42no—
456C2×#41—42no—
457C2×#41C22×D514yes—
458C22×Q8—51no—
459C22×Q8C22×D511yescharacteristic
460C22×Q8C22×D511yescharacteristic
461C22×D4—21no—
462C22×D4—51no—
463C22×D4—51no—
464C22×D4—54no—
465C22×D4—101no—
466C22×D4—101no—
467C22×D4—101no—
468C22×D4—101no—
469C22×D4—101no—
470C22×D4—102no—
471C22×D4—202no—
472C22×D4—202no—
473C22×D4C22×D511yescharacteristic
474C23×C4—21no—
475C23×C4C22×D511yescharacteristic
476C2×Q16—42no—
477C2×Q16—54no—
478C2×Q16—202no—
479C2×Q16C22×D514yescomplemented
480C2×SD16—42no—
481C2×SD16—54no—
482C2×SD16—54no—
483C2×SD16—54no—
484C2×SD16—54no—
485C2×SD16—54no—
486C2×SD16—202no—
487C2×SD16—202no—
488C2×SD16—202no—
489C2×SD16—202no—
490C2×SD16—202no—
491C2×SD16C22×D514yescomplemented
492C22×C8—51no—
493C22×C8—51no—
494C22×C8C22×D511yescharacteristic
495C22×C8C22×D511yescharacteristic
496C4⋊Q8—54no—
497C4⋊Q8—102no—
498#127—54no—
499#127—54no—
500#127—102no—
501#127—102no—
502#126—108no—
503#126—108no—
504#125—54no—
505#125—102no—
506#125—108no—
507#125—108no—
508#124—54no—
509#124—54no—
510#124—102no—
511#124—102no—
512C22⋊Q8—22no—
513C22⋊Q8—54no—
514C22⋊Q8—102no—
515C22⋊Q8C22×D514yes—
516#121—108no—
517#121—108no—
518#120—108no—
519#120—108no—
520C4×Q8—54no—
521C4×Q8—54no—
522C4×Q8—102no—
523C4×Q8—102no—
524#117—54no—
525#117—54no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—101no—
531C2×C4⋊C4—101no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4C22×D511yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C42—51no—
547C2×C42—51no—
548C2×C42—101no—
549C2×C42—101no—
550C4⋊C8—54no—
551C4⋊C8—54no—
552#103—54no—
553#103C22×D514yescomplemented
554#102—54no—
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102C22×D514yescomplemented
560C22⋊C8—54no—
561C22⋊C8C22×D514yes—
562#97—54no—
563C4×C8—54no—
564C22×C5—22no—
565C22×C5—22no—
566C22×C5—22no—
567C22×C5—44no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—84no—
572C22×C5#53512yes—
573C22×C5#57712yes—
574C22×C5#57712yes—
575C22×C5C23×D411yescharacteristic
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—816no—
583C2×D5—84no—
584C2×D5—84no—
585C4×C5—22no—
586C4×C5—42no—
587C4×C5—42no—
588C4×C5—42no—
589C4×C5#53512yes—
590C4×C5C2×H(5,𝔽2)11yescharacteristic
591C4×C5C2×H(5,𝔽2)11yescharacteristic
592Dic5—22no—
593Dic5—22no—
594Dic5—22no—
595Dic5—22no—
596Dic5—42no—
597Dic5—42no—
598C24—21no—
599C24—101no—
600C24—101no—
601C24—104no—
602C24—204no—
603C24—402no—
604C24—402no—
605C24D4×D511yescharacteristic
606#41—44no—
607#41—44no—
608#41—48no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—52no—
616C2×Q8—101no—
617C2×Q8—102no—
618C2×Q8—102no—
619C2×Q8C23×D512yes—
620C2×Q8C23×D512yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—52no—
627C2×D4—52no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—104no—
631C2×D4—104no—
632C2×D4—104no—
633C2×D4—101no—
634C2×D4—101no—
635C2×D4—102no—
636C2×D4—102no—
637C2×D4—102no—
638C2×D4—102no—
639C2×D4—204no—
640C2×D4—204no—
641C2×D4—204no—
642C2×D4—208no—
643C2×D4—402no—
644C2×D4—402no—
645C2×D4—402no—
646C2×D4—402no—
647C2×D4C23×D512yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—101no—
660C22×C4—101no—
661C22×C4D4×D512yes—
662C22×C4D4×D511yescharacteristic
663C22×C4C23×D512yes—
664C22×C4C23×D511yescharacteristic
665Q16—44no—
666Q16—204no—
667SD16—44no—
668SD16—204no—
669SD16—204no—
670SD16—204no—
671SD16—204no—
672SD16—204no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—52no—
676C2×C8—52no—
677C2×C8—102no—
678C2×C8—102no—
679C2×C8C23×D512yes—
680C2×C8C23×D512yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—54no—
684C4⋊C4—54no—
685C4⋊C4—52no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—104no—
689C4⋊C4—104no—
690C4⋊C4—104no—
691C4⋊C4—104no—
692C4⋊C4—101no—
693C4⋊C4—104no—
694C4⋊C4C23×D512yes—
695C22⋊C4—24no—
696C22⋊C4—54no—
697C22⋊C4—54no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C22⋊C4—104no—
701C22⋊C4—104no—
702C22⋊C4—104no—
703C42—52no—
704C42—52no—
705C42—52no—
706C42—52no—
707C42—104no—
708C42—104no—
709C2×C5—42no—
710C2×C5—82no—
711C2×C5#322214yescomplemented
712C2×C5C2×#53511yescharacteristic
713C2×C5C2×#57711yescharacteristic
714C2×C5C2×#57711yescharacteristic
715D5—82no—
716D5—82no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—102no—
725C23—102no—
726C23—208no—
727C23—202no—
728C23—202no—
729C23—202no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23—404no—
734C23—404no—
735C23—4016no—
736C23C2×D4×D512yes—
737C23C2×D4×D511yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—42no—
743Q8—42no—
744Q8—102no—
745Q8—102no—
746Q8—202no—
747D4—22no—
748D4—22no—
749D4—48no—
750D4—42no—
751D4—102no—
752D4—102no—
753D4—102no—
754D4—102no—
755D4—208no—
756D4—202no—
757D4—202no—
758D4—404no—
759D4—404no—
760D4—404no—
761D4—404no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—52no—
774C2×C4—52no—
775C2×C4—52no—
776C2×C4—52no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—202no—
784C2×C4—202no—
785C2×C4C2×D4×D512yes—
786C2×C4C2×D4×D511yescharacteristic
787C2×C4#414412yes—
788C2×C4#414412yes—
789C2×C4C24×D511yescharacteristic
790C8—22no—
791C8—22no—
792C8—102no—
793C8—102no—
794C5C2×#322211yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—202no—
804C22—202no—
805C22—202no—
806C22—202no—
807C22—202no—
808C22—202no—
809C22—4016no—
810C22—404no—
811C22—404no—
812C22#6592612yes—
813C22#6610412yes—
814C22#6611212yes—
815C22C22×D4×D511yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—102no—
821C4—102no—
822C4—102no—
823C4—102no—
824C4—202no—
825C4—202no—
826C4#6592612yes—
827C4C2×#414411yescharacteristic
828C4C2×#414411yescharacteristic
829C2—42no—
830C2—82no—
831C2—402no—
832C2—402no—
833C2#1061199314yesdirect product factor
834C2C2×#6592611yescharacteristic
835C2C2×#6610411yescharacteristic
836C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC2×#66164C2
hypercenterC2×#452D5
hypocenterC5C2×#3222
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#65959C2semidirect
3. C2×C5×#452C2semidirect
4. C2×#65528C2semidirect
5. C2×#65479C2semidirect
6. C2×#65474C2semidirect
7. C2×#65464C2semidirect
8. C2×#65452C2semidirect
9. C2×#65335C2semidirect
10. #10611993C2direct (N × H)
11. C2×#65087C2semidirect
12. C2×#65089C2semidirect
13. C2×#65051C2semidirect
14. C2×#65053C2semidirect
15. C2×#65020C2semidirect
16. C2×#65009C2semidirect
19. C22×C5×Q16C22semidirect
20. C22×C5×SD16C22semidirect
26. C2×Q8×Dic5C22semidirect
27. C2×#4090C22semidirect
28. C22×#689C22semidirect
35. C22×#687C22semidirect
43. #65959C22semidirect
45. C2×#4036C22semidirect
47. C2×#4033C22semidirect
50. C5×#452C22semidirect
51. C2×C5×#103C22semidirect
52. C2×C5×#102C22semidirect
54. #65528C22semidirect
55. C2×#3967C22semidirect
56. C2×#3964C22semidirect
58. #65479C22semidirect
59. #65474C22semidirect
60. #65464C22semidirect
61. #65452C22semidirect
64. C2×#3947C22semidirect
65. C2×#3946C22semidirect
66. C2×#3946C22semidirect
67. C2×C8×Dic5C22semidirect
68. #65335C22semidirect
71. #65089C22semidirect
72. #65087C22semidirect
73. #65053C22semidirect
74. #65051C22semidirect
75. #65020C22semidirect
76. #65009C22semidirect
102. C2×C5×Q16C23semidirect
104. C2×C5×SD16C23semidirect
120. Q8×Dic5C23semidirect
122. #4090C23semidirect
124. C2×#689C23semidirect
136. C2×#687C23semidirect
169. #4036C23semidirect
172. #4033C23semidirect
175. C5×#103C23semidirect
176. C5×#102C23semidirect
178. #3967C23semidirect
179. #3964C23semidirect
183. #3947C23semidirect
184. #3946C23semidirect
185. #3946C23semidirect
186. C8×Dic5C23semidirect
201. C2×#452D5semidirect
319. C22×Q16C2×D5semidirect
325. C22×SD16C2×D5semidirect
358. #452C2×D5semidirect
365. C2×#103C2×D5semidirect
371. C2×#102C2×D5semidirect
479. C2×Q16C22×D5semidirect
491. C2×SD16C22×D5semidirect
553. #103C22×D5semidirect
559. #102C22×D5semidirect
711. C2×C5#3222semidirect
794. C5C2×#3222semidirect
833. C2#10611993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661642
C2×#659592
C2×C5×#4522
C2×#655282
C2×#654792
C2×#654742
C2×#654642
C2×#654522
C2×#653352
#106119932
C2×#650872
C2×#650892
C2×#650512
C2×#650532
C2×#650202
C2×#650092
C2×#32225