Finite Group Databasebeta

← C2×#10610633 #12976098

Subgroups — C2×#10610633 #12976098

Order 1280.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66163C211yesmaximal, characteristic, complemented
2C2×#65848C211yesmaximal, characteristic, complemented
3C2×C5×#417C211yesmaximal, characteristic, complemented
4C2×#65527C211yesmaximal, characteristic, complemented
5C2×#65424C211yesmaximal, characteristic, complemented
6C2×#65417C211yesmaximal, characteristic, complemented
7C2×#65256C211yesmaximal, characteristic, complemented
8#10610633C2116yesmaximal, direct product factor
9C2×#65108C211yesmaximal, characteristic, complemented
10C2×#65104C211yesmaximal, characteristic, complemented
11C2×#65101C211yesmaximal, characteristic, complemented
12C2×#65089C211yesmaximal, characteristic, complemented
13C2×#65062C211yesmaximal, characteristic, complemented
14C2×#65059C211yesmaximal, characteristic, complemented
15C2×#65052C211yesmaximal, characteristic, complemented
16C2×#65045C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic, complemented
20C22×C5×C4⋊C4C2211yescharacteristic, complemented
21#66163—24no—
22#66163C2218yescomplemented
23C2×#4093C2211yescharacteristic
24C2×#4092C2211yescharacteristic
25C22×#688C2211yescharacteristic, complemented
26C2×#4085—21no—
27C2×#4083—21no—
28C2×D4×Dic5C2211yescharacteristic
29C22×#686C2211yescharacteristic
30C2×#4076—21no—
31C2×#4076C2211yescharacteristic
32C2×#4076C2211yescharacteristic, complemented
33C2×#4075—21no—
34C2×C4×C22⋊D5—21no—
35C2×C4×C22⋊D5C2211yescharacteristic
36C22×#685—21no—
37C22×D40C2211yescharacteristic
38C22×#676C2211yescharacteristic
39#65848—24no—
40#65848C2218yescomplemented
41C2×#4044—21no—
42C2×#4041C2211yescharacteristic
43C2×#4040—21no—
44C2×#4039C2211yescharacteristic, complemented
45C2×#4038C2211yescharacteristic
46C2×#4036C2211yescharacteristic, complemented
47C5×#417C2218yescomplemented
48C2×C5×#103C2211yescharacteristic, complemented
49C2×C5×#103C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52#65527C2218yescomplemented
53C2×#3967C2211yescharacteristic, complemented
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic, complemented
56#65424C2218yescomplemented
57#65417C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic, complemented
60C2×#3952C2211yescharacteristic
61C2×#3949C2211yescharacteristic, complemented
62C2×#3946C2211yescharacteristic, complemented
63C2×C8×Dic5C2211yescharacteristic, complemented
64#65256C2218yescomplemented
65C2×#3941C2211yescharacteristic
66C2×#3941C2211yescharacteristic
67C2×#3939C2211yescharacteristic, complemented
68C2×#3939C2211yescharacteristic, complemented
69#65108C2218yescomplemented
70#65104C2218yescomplemented
71#65101C2218yescomplemented
72#65089C2218yescomplemented
73#65062C2218yescomplemented
74#65059C2218yescomplemented
75#65052C2218yescomplemented
76#65045C2218yescomplemented
77C2×#3322—51nomaximal, Sylow
78C24×D5—21no—
79C2×C5×#41—22no—
80C2×C5×#41—24no—
81C2×C5×#41—42no—
82C2×C5×#41C2314yes—
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C22×C22⋊D5—21no—
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C22×C22⋊D5D411yescharacteristic
93C23×Dic5—21no—
94C2×D4×D5—24no—
95C2×D4×D5—22no—
96C2×D4×D5—42no—
97C2×D4×D5C2314yes—
98C22×D20—21no—
99C22×D20C2311yescharacteristic
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C22×C4×D5C2311yescharacteristic
103C2×C5×M16—42no—
104C2×C5×M16C2314yescomplemented
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2314yescomplemented
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5D411yescharacteristic
114#4093—22no—
115#4093C2314yes—
116#4092—22no—
117#4092C2314yes—
118C2×#688—42no—
119C2×#688C2314yescomplemented
120#4085—28no—
121#4083—28no—
122D4×Dic5—22no—
123D4×Dic5C2314yes—
124C2×#686—24no—
125C2×#686C2314yes—
126#4076—22no—
127#4076—22no—
128#4076—28no—
129#4076C2314yes—
130#4076C2314yescomplemented
131#4075—28no—
132C4×C22⋊D5—28no—
133C4×C22⋊D5D414yes—
134C4×C22⋊D5C2314yes—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×#685—21no—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143C2×#685—28no—
144C2×#685D411yescharacteristic
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5C2311yescharacteristic
147C2×C4⋊Dic5C2311yescharacteristic
148C2×#683—21no—
149C2×#683—21no—
150C2×#683D411yescharacteristic
151C2×C4×Dic5—21no—
152C2×C4×Dic5C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C2×D40—42no—
156C2×D40C2314yes—
157C2×#676—42no—
158C2×#676C2314yes—
159#4044—28no—
160#4041—22no—
161#4041C2314yes—
162#4040—28no—
163#4039—22no—
164#4039C2314yescomplemented
165#4038—22no—
166#4038C2314yes—
167#4036—22no—
168#4036C2314yescomplemented
169C5×#103C2314yescomplemented
170C5×#103C2314yescomplemented
171C5×#102C2314yes—
172C5×#102C2314yes—
173#3967C2314yescomplemented
174#3964C2314yes—
175C22⋊#168C2314yescomplemented
176#3953C2314yes—
177#3953C2314yescomplemented
178#3952C2314yes—
179#3949C2314yescomplemented
180#3946C2314yescomplemented
181C8×Dic5C2314yescomplemented
182#3941C2314yes—
183#3941C2314yes—
184#3939C2314yescomplemented
185#3939C2314yescomplemented
186C2×#553—51no—
187C2×#546—51no—
188#3322—516no—
189C2×#488—51no—
190C2×#485—51no—
191C2×#480—51no—
192C2×#478—51no—
193C2×#469—51no—
194C2×#468—51no—
195C2×#463—51no—
196C2×#449—51no—
197C2×#447—51no—
198C2×C4×D8—51no—
199C2×#436—51no—
200C2×#417D511yescharacteristic, complemented
201C2×#418—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5—82no—
210C23×D5C2×D411yescharacteristic
211C5×#41—28no—
212C5×#41—44no—
213C5×#41—48no—
214C2×C5×Q8—21no—
215C2×C5×Q8—22no—
216C2×C5×Q8—22no—
217C2×C5×Q8C2412yes—
218C2×C5×D4—24no—
219C2×C5×D4—21no—
220C2×C5×D4—22no—
221C2×C5×D4—44no—
222C2×C5×D4#4114yes—
223C2×C5×D4C2412yes—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—24no—
230C22×C4×C5—24no—
231C22×C4×C5—44no—
232C22×C4×C5—82no—
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2411yescharacteristic
237C2×C22⋊D5—24no—
238C2×C22⋊D5—24no—
239C2×C22⋊D5—24no—
240C2×C22⋊D5—42no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—44no—
243C2×C22⋊D5—82no—
244C2×C22⋊D5C2×D414yes—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—24no—
248C22×Dic5—82no—
249C22×Dic5C2×D411yescharacteristic
250C22×Dic5C2×D411yescharacteristic
251C22×Dic5C2×D411yescharacteristic
252D4×D5—28no—
253D4×D5—44no—
254D4×D5—48no—
255C2×D20—22no—
256C2×D20—22no—
257C2×D20—22no—
258C2×D20—22no—
259C2×D20—21no—
260C2×D20—21no—
261C2×D20—24no—
262C2×D20—82no—
263C2×D20C2412yes—
264C2×D20C2412yes—
265C2×C4×D5—22no—
266C2×C4×D5—22no—
267C2×C4×D5—24no—
268C2×C4×D5—82no—
269C2×C4×D5C2×D412yes—
270C2×C4×D5C2412yes—
271C5×M16—44no—
272C2×C5×C8—22no—
273C2×C5×C8—22no—
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—44no—
284#686—28no—
285#685—24no—
286#685—24no—
287#685—24no—
288#685—24no—
289#685—24no—
290#685—24no—
291#685—24no—
292#685—24no—
293#685C2×D414yes—
294C4⋊Dic5—21no—
295C4⋊Dic5—21no—
296C4⋊Dic5—24no—
297C4⋊Dic5C2412yes—
298C4⋊Dic5C2412yes—
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—
309D40—44no—
310#676—44no—
311C22×#41C2×D511yescharacteristic
312C23×D4—51no—
313C22×SD16—51no—
314C22×D8—51no—
315C22×D8—51no—
316C22×M16—51no—
317C22×M16C2×D511yescharacteristic, complemented
318#553—58no—
319#553—104no—
320#546—58no—
321#546—104no—
322C2×#126—101no—
323C2×#125—51no—
324C2×#124—51no—
325C2×#123—101no—
326C2×#123—101no—
327C2×C22⋊Q8—51no—
328C2×#121—51no—
329C2×#121—51no—
330C2×#121—51no—
331C2×#121—101no—
332C2×#121—101no—
333C2×#120—101no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—51no—
337C2×C4×D4—101no—
338C2×#117—51no—
339C22×C4⋊C4C2×D511yescharacteristic, complemented
340C22×C22⋊C4—101no—
341#488—58no—
342#485—58no—
343#480—58no—
344#478—58no—
345#469—58no—
346#468—58no—
347#463—58no—
348#449—58no—
349#447—58no—
350C4×D8—58no—
351#436—58no—
352C2×#107—51no—
353C2×#107—51no—
354C2×#106—51no—
355C2×C4⋊C8—51no—
356#418—58no—
357#417C2×D518yescomplemented
358C2×#103—51no—
359C2×#103C2×D511yescharacteristic, complemented
360C2×#103C2×D511yescharacteristic, complemented
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102C2×D511yescharacteristic
367C2×#102C2×D511yescharacteristic
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×C4×C8—51no—
371C23×C5—24no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5C22×D412yes—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—48no—
386C22×D5—48no—
387C22×D5—42no—
388C22×D5—42no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—84no—
394C22×D5—816no—
395C22×D5C22×D412yes—
396C5×Q8—22no—
397C5×Q8—22no—
398C5×Q8—42no—
399C5×D4—24no—
400C5×D4—22no—
401C5×D4—48no—
402C5×D4C2×#4114yes—
403C2×C4×C5—22no—
404C2×C4×C5—24no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—48no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—84no—
415C2×C4×C5C22×D412yes—
416C2×C4×C5C22×D411yescharacteristic
417C2×C4×C5C2×#4112yes—
418C2×C4×C5H(5,𝔽2)12yes—
419C2×C4×C5C2511yescharacteristic
420C22⋊D5—44no—
421C22⋊D5—48no—
422C22⋊D5—48no—
423C22⋊D5—84no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5—84no—
432C2×Dic5C22×D412yes—
433C2×Dic5C22×D412yes—
434C2×Dic5C22×D412yes—
435D20—22no—
436D20—22no—
437D20—22no—
438D20—22no—
439D20—42no—
440D20—42no—
441D20—84no—
442C4×D5—24no—
443C4×D5—22no—
444C4×D5—22no—
445C4×D5—84no—
446C5×C8—22no—
447C5×C8—22no—
448#168—22no—
449#168—22no—
450C25—101no—
451C2×#41—22no—
452C2×#41—24no—
453C2×#41—42no—
454C2×#41C22×D514yes—
455C22×Q8C22×D511yescharacteristic
456C22×D4—21no—
457C22×D4—51no—
458C22×D4—54no—
459C22×D4—51no—
460C22×D4—51no—
461C22×D4—101no—
462C22×D4—102no—
463C22×D4—101no—
464C22×D4—104no—
465C22×D4—101no—
466C22×D4—101no—
467C22×D4—202no—
468C22×D4C22×D511yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—51no—
472C23×C4—101no—
473C23×C4—101no—
474C23×C4C22×D511yescharacteristic
475C2×SD16—54no—
476C2×SD16—202no—
477C2×D8—54no—
478C2×D8—54no—
479C2×D8—104no—
480C2×D8—202no—
481C2×M16—42no—
482C2×M16—54no—
483C2×M16—202no—
484C2×M16C22×D514yescomplemented
485C22×C8—51no—
486C22×C8—51no—
487C22×C8C22×D511yescharacteristic
488C22×C8C22×D511yescharacteristic
489#126—108no—
490#125—54no—
491#125—102no—
492#124—54no—
493#124—102no—
494#123—108no—
495#123—108no—
496C22⋊Q8—54no—
497C22⋊Q8—102no—
498#121—54no—
499#121—54no—
500#121—54no—
501#121—108no—
502#121—102no—
503#121—108no—
504#121—102no—
505#121—102no—
506#120—108no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—102no—
512C4×D4—102no—
513C4×D4—108no—
514#117—54no—
515#117—102no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C4⋊C4C22×D511yescharacteristic
526C2×C4⋊C4C22×D514yescomplemented
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×C22⋊C4—101no—
536C2×C22⋊C4—101no—
537C2×C22⋊C4—101no—
538C2×C22⋊C4—101no—
539C2×C42—51no—
540C2×C42—101no—
541#107—54no—
542#107—54no—
543#106—54no—
544C4⋊C8—54no—
545#103—54no—
546#103C22×D514yescomplemented
547#103C22×D514yescomplemented
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102C22×D514yes—
554#102C22×D514yes—
555C22⋊C8—54no—
556C22⋊C8—54no—
557C4×C8—54no—
558C22×C5—24no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—48no—
563C22×C5—44no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5#54612yes—
567C22×C5#57512yes—
568C22×C5#57612yes—
569C22×C5C23×D411yescharacteristic
570C2×D5—22no—
571C2×D5—22no—
572C2×D5—22no—
573C2×D5—44no—
574C2×D5—42no—
575C2×D5—42no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—816no—
581C2×D5—84no—
582C2×D5—84no—
583C4×C5—22no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5#54612yes—
588C4×C5C22×#4111yescharacteristic
589C4×C5C2×H(5,𝔽2)11yescharacteristic
590Dic5—22no—
591Dic5—22no—
592Dic5—22no—
593Dic5—42no—
594Dic5—42no—
595C24—21no—
596C24—51no—
597C24—104no—
598C24—101no—
599C24—101no—
600C24—204no—
601C24—204no—
602C24—402no—
603C24D4×D511yescharacteristic
604#41—28no—
605#41—44no—
606#41—48no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8C23×D512yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—54no—
616C2×D4—52no—
617C2×D4—52no—
618C2×D4—104no—
619C2×D4—104no—
620C2×D4—108no—
621C2×D4—104no—
622C2×D4—104no—
623C2×D4—102no—
624C2×D4—102no—
625C2×D4—101no—
626C2×D4—101no—
627C2×D4—102no—
628C2×D4—102no—
629C2×D4—204no—
630C2×D4—208no—
631C2×D4—202no—
632C2×D4—204no—
633C2×D4—204no—
634C2×D4—402no—
635C2×D4—402no—
636C2×D4#70914yes—
637C2×D4C23×D512yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—44no—
646C22×C4—51no—
647C22×C4—51no—
648C22×C4—51no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—82no—
652C22×C4—104no—
653C22×C4—104no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—402no—
659C22×C4—402no—
660C22×C4D4×D512yes—
661C22×C4D4×D511yescharacteristic
662C22×C4C23×D512yes—
663C22×C4C23×D511yescharacteristic
664SD16—204no—
665D8—108no—
666D8—204no—
667M16—44no—
668M16—204no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—52no—
672C2×C8—52no—
673C2×C8—102no—
674C2×C8—102no—
675C2×C8C23×D512yes—
676C2×C8C23×D512yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—54no—
681C4⋊C4—52no—
682C4⋊C4—52no—
683C4⋊C4—104no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—101no—
687C4⋊C4—101no—
688C4⋊C4C23×D512yes—
689C4⋊C4C23×D512yes—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—104no—
693C22⋊C4—104no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C22⋊C4—104no—
701C42—52no—
702C42—52no—
703C42—104no—
704C2×C5—44no—
705C2×C5—42no—
706C2×C5#332214yescomplemented
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#57511yescharacteristic
709C2×C5C2×#57611yescharacteristic
710D5—42no—
711D5—82no—
712D5—82no—
713C23—22no—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—52no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—208no—
727C23—208no—
728C23—202no—
729C23—202no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23—202no—
734C23—404no—
735C23—4016no—
736C23C2×D4×D512yes—
737C23C2×D4×D511yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741D4—24no—
742D4—22no—
743D4—48no—
744D4—102no—
745D4—102no—
746D4—102no—
747D4—102no—
748D4—204no—
749D4—208no—
750D4—208no—
751D4—202no—
752D4—202no—
753D4—404no—
754D4—404no—
755D4C2×#70914yes—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—84no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—104no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—404no—
782C2×C4—404no—
783C2×C4C2×#70912yes—
784C2×C4C2×D4×D512yes—
785C2×C4C2×D4×D511yescharacteristic
786C2×C4#414412yes—
787C2×C4C24×D511yescharacteristic
788C8—22no—
789C8—22no—
790C8—102no—
791C8—102no—
792C5C2×#332211yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—102no—
802C22—102no—
803C22—102no—
804C22—204no—
805C22—202no—
806C22—202no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22—202no—
811C22—4016no—
812C22—404no—
813C22—404no—
814C22#6582412yes—
815C22#6610812yes—
816C22#6611112yes—
817C22C22×D4×D511yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—102no—
823C4—102no—
824C4—102no—
825C4—202no—
826C4—202no—
827C4#6582412yes—
828C4C22×#70911yescharacteristic
829C4C2×#414411yescharacteristic
830C2—42no—
831C2—44no—
832C2—202no—
833C2—402no—
834C2—402no—
835C2#1061063314yesdirect product factor
836C2C2×#6582411yescharacteristic
837C2C2×#6610811yescharacteristic
838C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#417C2
socleC23×C5C22×D4
hypercenterC2×#417D5
hypocenterC5C2×#3322
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#66163C2semidirect
2. C2×#65848C2semidirect
3. C2×C5×#417C2semidirect
4. C2×#65527C2semidirect
5. C2×#65424C2semidirect
6. C2×#65417C2semidirect
7. C2×#65256C2semidirect
8. #10610633C2direct (N × H)
9. C2×#65108C2semidirect
10. C2×#65104C2semidirect
11. C2×#65101C2semidirect
12. C2×#65089C2semidirect
13. C2×#65062C2semidirect
14. C2×#65059C2semidirect
15. C2×#65052C2semidirect
16. C2×#65045C2semidirect
19. C22×C5×M16C22semidirect
20. C22×C5×C4⋊C4C22semidirect
22. #66163C22semidirect
25. C22×#688C22semidirect
32. C2×#4076C22semidirect
40. #65848C22semidirect
44. C2×#4039C22semidirect
46. C2×#4036C22semidirect
47. C5×#417C22semidirect
48. C2×C5×#103C22semidirect
49. C2×C5×#103C22semidirect
52. #65527C22semidirect
53. C2×#3967C22semidirect
55. C2×C22⋊#168C22semidirect
56. #65424C22semidirect
57. #65417C22semidirect
59. C2×#3953C22semidirect
61. C2×#3949C22semidirect
62. C2×#3946C22semidirect
63. C2×C8×Dic5C22semidirect
64. #65256C22semidirect
67. C2×#3939C22semidirect
68. C2×#3939C22semidirect
69. #65108C22semidirect
70. #65104C22semidirect
71. #65101C22semidirect
72. #65089C22semidirect
73. #65062C22semidirect
74. #65059C22semidirect
75. #65052C22semidirect
76. #65045C22semidirect
104. C2×C5×M16C23semidirect
111. C2×C5×C4⋊C4C23semidirect
119. C2×#688C23semidirect
130. #4076C23semidirect
164. #4039C23semidirect
168. #4036C23semidirect
169. C5×#103C23semidirect
170. C5×#103C23semidirect
173. #3967C23semidirect
175. C22⋊#168C23semidirect
177. #3953C23semidirect
179. #3949C23semidirect
180. #3946C23semidirect
181. C8×Dic5C23semidirect
184. #3939C23semidirect
185. #3939C23semidirect
200. C2×#417D5semidirect
317. C22×M16C2×D5semidirect
339. C22×C4⋊C4C2×D5semidirect
357. #417C2×D5semidirect
359. C2×#103C2×D5semidirect
360. C2×#103C2×D5semidirect
484. C2×M16C22×D5semidirect
526. C2×C4⋊C4C22×D5semidirect
546. #103C22×D5semidirect
547. #103C22×D5semidirect
706. C2×C5#3322semidirect
792. C5C2×#3322semidirect
835. C2#10610633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661632
C2×#658482
C2×C5×#4172
C2×#655272
C2×#654242
C2×#654172
C2×#652562
#106106332
C2×#651082
C2×#651042
C2×#651012
C2×#650892
C2×#650622
C2×#650592
C2×#650522
C2×#650452
C2×#33225