Finite Group Databasebeta

← C2×#10613021 #12976100

Subgroups — C2×#10613021 #12976100

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×#65946C211yesmaximal, characteristic, complemented
2C2×#65848C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C2×#65328C211yesmaximal, characteristic, complemented
5C2×#65255C211yesmaximal, characteristic, complemented
6#10613021C2116yesmaximal, direct product factor
7C2×#65180C211yesmaximal, characteristic, complemented
8C2×#65177C211yesmaximal, characteristic, complemented
9C2×#65175C211yesmaximal, characteristic, complemented
10C2×#65161C211yesmaximal, characteristic, complemented
11C2×#65076C211yesmaximal, characteristic, complemented
12C2×#65062C211yesmaximal, characteristic, complemented
13C2×#65059C211yesmaximal, characteristic, complemented
14C2×#65057C211yesmaximal, characteristic, complemented
15C2×#65023C211yesmaximal, characteristic, complemented
16C2×#65018C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic, complemented
21C2×#4084—21no—
22C2×#4083—21no—
23C2×#4082C2211yescharacteristic
24C22×#686C2211yescharacteristic
25C2×#4076—21no—
26C2×#4076C2211yescharacteristic, complemented
27C2×C4×C22⋊D5—21no—
28C2×C4×C22⋊D5C2211yescharacteristic
29C22×#681C2211yescharacteristic, complemented
30C22×D40C2211yescharacteristic
31C22×#677C2211yescharacteristic, complemented
32C22×#676C2211yescharacteristic
33#65946—24no—
34#65946C2218yescomplemented
35#65848—24no—
36#65848C2218yescomplemented
37C2×#4044—21no—
38C2×#4043C2211yescharacteristic
39C2×#4041C2211yescharacteristic
40C2×#4040—21no—
41C2×#4039C2211yescharacteristic
42C2×#4039C2211yescharacteristic, complemented
43C2×#4038C2211yescharacteristic
44C2×#4036C2211yescharacteristic, complemented
45C2×#4029—21no—
46C2×D5×C22⋊C4—21no—
47C5×#480C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#107C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×C5×C22⋊C8C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3952C2211yescharacteristic
56C2×#3948C2211yescharacteristic, complemented
57C2×#3946C2211yescharacteristic, complemented
58C2×C8×Dic5C2211yescharacteristic, complemented
59#65328C2218yescomplemented
60C2×#3942C2211yescharacteristic, complemented
61C2×#3942C2211yescharacteristic, complemented
62#65255C2218yescomplemented
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic, complemented
66C2×#3940C2211yescharacteristic, complemented
67#65180C2218yescomplemented
68#65177C2218yescomplemented
69#65175C2218yescomplemented
70#65161C2218yescomplemented
71#65076C2218yescomplemented
72#65062C2218yescomplemented
73#65059C2218yescomplemented
74#65057C2218yescomplemented
75#65023C2218yescomplemented
76#65018C2218yescomplemented
77C2×#3322—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5D411yescharacteristic
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×D20—21no—
96C22×D20C2311yescharacteristic
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×C4×D5C2311yescharacteristic
102C22×Dic10C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C5×#121—22no—
106C5×#121C2314yes—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—22no—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2314yescomplemented
113C2×C5×C22⋊C4—21no—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5D411yescharacteristic
117#4084—28no—
118#4083—28no—
119#4082—22no—
120#4082C2314yes—
121C2×#686—42no—
122C2×#686C2314yes—
123#4076—22no—
124#4076—28no—
125#4076C2314yescomplemented
126C4×C22⋊D5—28no—
127C4×C22⋊D5D414yes—
128C4×C22⋊D5C2314yes—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685D411yescharacteristic
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5C2311yescharacteristic
139C2×#683—21no—
140C2×#683D411yescharacteristic
141C2×C4×Dic5—21no—
142C2×C4×Dic5C2311yescharacteristic
143C2×#681—42no—
144C2×#681C2314yescomplemented
145C22×#168C2311yescharacteristic
146C22×#168C2311yescharacteristic
147C2×D40—24no—
148C2×D40C2314yes—
149C2×#677—42no—
150C2×#677C2314yescomplemented
151C2×#676—42no—
152C2×#676C2314yes—
153#4044—28no—
154#4043—22no—
155#4043C2314yes—
156#4041—22no—
157#4041C2314yes—
158#4040—28no—
159#4039—22no—
160#4039—22no—
161#4039C2314yes—
162#4039C2314yescomplemented
163#4038—22no—
164#4038C2314yes—
165#4036—22no—
166#4036C2314yescomplemented
167#4029—28no—
168D5×C22⋊C4—28no—
169C5×#107C2314yescomplemented
170C5×#107C2314yescomplemented
171C5×#102C2314yes—
172C5×#102C2314yes—
173C5×C22⋊C8C2314yescomplemented
174#3964C2314yes—
175#3953C2314yes—
176#3952C2314yes—
177#3948C2314yescomplemented
178#3946C2314yescomplemented
179C8×Dic5C2314yescomplemented
180#3942C2314yescomplemented
181#3942C2314yescomplemented
182#3941C2314yes—
183#3941C2314yes—
184#3941C2314yescomplemented
185#3940C2314yescomplemented
186C2×#553—51no—
187C2×#546—51no—
188#3322—516no—
189C2×#488—51no—
190C2×#485—51no—
191C2×#480D511yescharacteristic, complemented
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×#417—51no—
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
211C2×C5×D4—24no—
212C2×C5×D4—21no—
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4—82no—
216C2×C5×D4C2412yes—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—24no—
223C22×C4×C5—82no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2411yescharacteristic
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—24no—
231C2×C22⋊D5—42no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5C2×D414yes—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5C2×D411yescharacteristic
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241D4×D5—28no—
242D4×D5—44no—
243D4×D5—48no—
244#709—28no—
245#709—44no—
246#709—48no—
247C2×D20—21no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—22no—
251C2×D20—21no—
252C2×D20—24no—
253C2×D20—82no—
254C2×D20#4114yes—
255C2×D20C2412yes—
256C2×D20C2412yes—
257C2×C4×D5—22no—
258C2×C4×D5—22no—
259C2×C4×D5—24no—
260C2×C4×D5—24no—
261C2×C4×D5—24no—
262C2×C4×D5—44no—
263C2×C4×D5—82no—
264C2×C4×D5—82no—
265C2×C4×D5C2×D412yes—
266C2×C4×D5C2412yes—
267C2×Dic10—22no—
268C2×Dic10—22no—
269C2×Dic10—21no—
270C2×Dic10C2412yes—
271C2×C5×C8—22no—
272C2×C5×C8—22no—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—24no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4C2412yes—
280C5×C4⋊C4C2412yes—
281C5×C4⋊C4C2412yes—
282C5×C22⋊C4—24no—
283C22⋊Dic5—24no—
284C22⋊Dic5—24no—
285C22⋊Dic5C2×D414yes—
286#686—44no—
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—24no—
296C4⋊Dic5—24no—
297C4⋊Dic5C2412yes—
298#683—24no—
299#683C2×D414yes—
300C4×Dic5—24no—
301C4×Dic5C2×D412yes—
302C4×Dic5C2412yes—
303#681—44no—
304C2×#168—22no—
305C2×#168—22no—
306C2×#168C2412yes—
307C2×#168C2412yes—
308D40—28no—
309#677—44no—
310#676—44no—
311C22×#41—51no—
312C23×D4—51no—
313C22×SD16—51no—
314C22×D8—51no—
315C22×D8—51no—
316C22×M16—51no—
317C22×M16—51no—
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—101no—
331C2×#121—101no—
332C2×#121C2×D511yescharacteristic
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#480C2×D518yescomplemented
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×#107C2×D511yescharacteristic, complemented
353C2×#107C2×D511yescharacteristic, complemented
354C2×#106—51no—
355C2×C4⋊C8—51no—
356#418—58no—
357#417—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
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⋊C8C2×D511yescharacteristic, complemented
370C2×C4×C8—51no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5C22×D412yes—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—24no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—48no—
387C22×D5—48no—
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×D4—22no—
397C5×D4—22no—
398C5×D4—42no—
399C5×D4—84no—
400C2×C4×C5—22no—
401C2×C4×C5—24no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—42no—
408C2×C4×C5—42no—
409C2×C4×C5—42no—
410C2×C4×C5—84no—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D411yescharacteristic
413C2×C4×C5C2×#4112yes—
414C2×C4×C5H(5,𝔽2)12yes—
415C2×C4×C5C2511yescharacteristic
416C22⋊D5—44no—
417C22⋊D5—48no—
418C22⋊D5—48no—
419C22⋊D5—48no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—42no—
426C2×Dic5—42no—
427C2×Dic5C22×D412yes—
428C2×Dic5C22×D412yes—
429C2×Dic5C22×D412yes—
430D20—24no—
431D20—22no—
432D20—22no—
433D20—22no—
434D20—42no—
435D20—84no—
436D20C2×#4114yes—
437C4×D5—24no—
438C4×D5—22no—
439C4×D5—22no—
440C4×D5—48no—
441C4×D5—84no—
442C4×D5—84no—
443Dic10—22no—
444Dic10—22no—
445Dic10—42no—
446C5×C8—22no—
447C5×C8—22no—
448#168—22no—
449#168—22no—
450C25—101no—
451C2×#41—54no—
452C2×#41—104no—
453C2×#41—102no—
454C2×#41—202no—
455C22×Q8—51no—
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—51no—
471C23×C4—101no—
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—54no—
482C2×M16—54no—
483C2×M16—202no—
484C2×M16—202no—
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—22no—
499#121—54no—
500#121—54no—
501#121—108no—
502#121—102no—
503#121—108no—
504#121—102no—
505#121C22×D514yes—
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—101no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4C22×D511yescharacteristic
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C4⋊C4C22×D511yescharacteristic
526C2×C4⋊C4C22×D514yescomplemented
527C2×C22⋊C4—21no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4—51no—
530C2×C22⋊C4—108no—
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#107C22×D514yescomplemented
542#107C22×D514yescomplemented
543#106—54no—
544C4⋊C8—54no—
545#103—54no—
546#103—54no—
547#103—54no—
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⋊C8C22×D514yescomplemented
557C4×C8—54no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—44no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—84no—
566C22×C5#54612yes—
567C22×C5#57512yes—
568C22×C5#57612yes—
569C22×C5C23×D411yescharacteristic
570C2×D5—22no—
571C2×D5—24no—
572C2×D5—22no—
573C2×D5—22no—
574C2×D5—44no—
575C2×D5—48no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—816no—
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—108no—
605#41—204no—
606#41—208no—
607C2×Q8—52no—
608C2×Q8—101no—
609C2×Q8—102no—
610C2×Q8—102no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—54no—
616C2×D4—54no—
617C2×D4—52no—
618C2×D4—52no—
619C2×D4—82no—
620C2×D4—104no—
621C2×D4—104no—
622C2×D4—108no—
623C2×D4—104no—
624C2×D4—104no—
625C2×D4—101no—
626C2×D4—101no—
627C2×D4—102no—
628C2×D4—102no—
629C2×D4—102no—
630C2×D4—204no—
631C2×D4—208no—
632C2×D4—202no—
633C2×D4—204no—
634C2×D4—204no—
635C2×D4—204no—
636C2×D4—402no—
637C2×D4C23×D512yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—51no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—82no—
650C22×C4—104no—
651C22×C4—104no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—104no—
657C22×C4—204no—
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—204no—
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—21no—
681C4⋊C4—54no—
682C4⋊C4—52no—
683C4⋊C4—104no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—101no—
687C4⋊C4C23×D512yes—
688C4⋊C4C23×D512yes—
689C4⋊C4C23×D512yes—
690C22⋊C4—24no—
691C22⋊C4—54no—
692C22⋊C4—54no—
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—42no—
705C2×C5—82no—
706C2×C5#332214yescomplemented
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#57511yescharacteristic
709C2×C5C2×#57611yescharacteristic
710D5—42no—
711D5—44no—
712D5—82no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—52no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—104no—
725C23—102no—
726C23—102no—
727C23—208no—
728C23—208no—
729C23—202no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23—202no—
734C23—404no—
735C23—4016no—
736C23C2×D4×D512yes—
737C23C2×D4×D511yescharacteristic
738Q8—102no—
739Q8—102no—
740Q8—202no—
741D4—22no—
742D4—22no—
743D4—42no—
744D4—54no—
745D4—84no—
746D4—104no—
747D4—102no—
748D4—102no—
749D4—102no—
750D4—204no—
751D4—208no—
752D4—208no—
753D4—208no—
754D4—202no—
755D4—404no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—84no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—104no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—208no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—404no—
782C2×C4—404no—
783C2×C4C2×D4×D512yes—
784C2×C4C2×D4×D511yescharacteristic
785C2×C4D5×#4112yes—
786C2×C4#414912yes—
787C2×C4C24×D511yescharacteristic
788C8—22no—
789C8—22no—
790C8—102no—
791C8—102no—
792C5C2×#332211yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—102no—
802C22—104no—
803C22—102no—
804C22—102no—
805C22—204no—
806C22—208no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22—202no—
811C22—202no—
812C22—4016no—
813C22—404no—
814C22#6598812yes—
815C22#6609112yes—
816C22#6611112yes—
817C22C22×D4×D511yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—102no—
823C4—102no—
824C4—102no—
825C4—202no—
826C4—202no—
827C4#6598812yes—
828C4C2×D5×#4111yescharacteristic
829C4C2×#414911yescharacteristic
830C2—42no—
831C2—82no—
832C2—202no—
833C2—204no—
834C2—402no—
835C2#1061302114yesdirect product factor
836C2C2×#6598811yescharacteristic
837C2C2×#6609111yescharacteristic
838C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#480C2
socleC23×C5C22×D4
hypercenterC2×#480D5
hypocenterC5C2×#3322
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#65946C2semidirect
2. C2×#65848C2semidirect
3. C2×C5×#480C2semidirect
4. C2×#65328C2semidirect
5. C2×#65255C2semidirect
6. #10613021C2direct (N × H)
7. C2×#65180C2semidirect
8. C2×#65177C2semidirect
9. C2×#65175C2semidirect
10. C2×#65161C2semidirect
11. C2×#65076C2semidirect
12. C2×#65062C2semidirect
13. C2×#65059C2semidirect
14. C2×#65057C2semidirect
15. C2×#65023C2semidirect
16. C2×#65018C2semidirect
20. C22×C5×C4⋊C4C22semidirect
26. C2×#4076C22semidirect
29. C22×#681C22semidirect
31. C22×#677C22semidirect
34. #65946C22semidirect
36. #65848C22semidirect
42. C2×#4039C22semidirect
44. C2×#4036C22semidirect
47. C5×#480C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#107C22semidirect
52. C2×C5×C22⋊C8C22semidirect
56. C2×#3948C22semidirect
57. C2×#3946C22semidirect
58. C2×C8×Dic5C22semidirect
59. #65328C22semidirect
60. C2×#3942C22semidirect
61. C2×#3942C22semidirect
62. #65255C22semidirect
65. C2×#3941C22semidirect
66. C2×#3940C22semidirect
67. #65180C22semidirect
68. #65177C22semidirect
69. #65175C22semidirect
70. #65161C22semidirect
71. #65076C22semidirect
72. #65062C22semidirect
73. #65059C22semidirect
74. #65057C22semidirect
75. #65023C22semidirect
76. #65018C22semidirect
112. C2×C5×C4⋊C4C23semidirect
125. #4076C23semidirect
144. C2×#681C23semidirect
150. C2×#677C23semidirect
162. #4039C23semidirect
166. #4036C23semidirect
169. C5×#107C23semidirect
170. C5×#107C23semidirect
173. C5×C22⋊C8C23semidirect
177. #3948C23semidirect
178. #3946C23semidirect
179. C8×Dic5C23semidirect
180. #3942C23semidirect
181. #3942C23semidirect
184. #3941C23semidirect
185. #3940C23semidirect
191. C2×#480D5semidirect
339. C22×C4⋊C4C2×D5semidirect
343. #480C2×D5semidirect
352. C2×#107C2×D5semidirect
353. C2×#107C2×D5semidirect
369. C2×C22⋊C8C2×D5semidirect
526. C2×C4⋊C4C22×D5semidirect
541. #107C22×D5semidirect
542. #107C22×D5semidirect
556. C22⋊C8C22×D5semidirect
706. C2×C5#3322semidirect
792. C5C2×#3322semidirect
835. C2#10613021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659462
C2×#658482
C2×C5×#4802
C2×#653282
C2×#652552
#106130212
C2×#651802
C2×#651772
C2×#651752
C2×#651612
C2×#650762
C2×#650622
C2×#650592
C2×#650572
C2×#650232
C2×#650182
C2×#33225