Finite Group Databasebeta

← C2×#10611285 #12976115

Subgroups — C2×#10611285 #12976115

Order 1280.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65884C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic, complemented
3C2×C5×#436C211yesmaximal, characteristic, complemented
4C2×#65426C211yesmaximal, characteristic, complemented
5C2×#65423C211yesmaximal, characteristic, complemented
6C2×#65422C211yesmaximal, characteristic, complemented
7C2×#65420C211yesmaximal, characteristic, complemented
8#10611285C2116yesmaximal, direct product factor
9C2×#65134C211yesmaximal, characteristic, complemented
10C2×#65136C211yesmaximal, characteristic, complemented
11C2×#65022C211yesmaximal, characteristic, complemented
12C2×#65020C211yesmaximal, characteristic, complemented
13C2×#65024C211yesmaximal, characteristic, complemented
14C2×#65012C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic, complemented
16C2×#64986C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic, complemented
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4083—21no—
23C2×#4081—21no—
24C2×#4076C2211yescharacteristic
25C2×#4072C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic, complemented
27C2×#4070C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic, complemented
30C22×Dic20C2211yescharacteristic, complemented
31C22×#677C2211yescharacteristic
32C22×#677C2211yescharacteristic
33#65884—24no—
34#65884C2218yes—
35#65875—24no—
36#65875C2218yescomplemented
37C2×#4040—21no—
38C2×#4035—21no—
39C2×#4030—21no—
40C2×D5×C22⋊C4—21no—
41C2×#4025—21no—
42C2×#4023—21no—
43C2×#4021C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×#4016C2211yescharacteristic, complemented
46C2×C4×Dic10C2211yescharacteristic, complemented
47C5×#436C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C5×C8C2211yescharacteristic, complemented
52#65426C2218yescomplemented
53#65423C2218yescomplemented
54#65422C2218yescomplemented
55#65420C2218yescomplemented
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3950C2211yescharacteristic, complemented
63C2×#3949C2211yescharacteristic, complemented
64C2×#3949C2211yescharacteristic, complemented
65C2×#3948C2211yescharacteristic, complemented
66C2×#3948C2211yescharacteristic, complemented
67C2×#3948C2211yescharacteristic, complemented
68C2×#3948C2211yescharacteristic, complemented
69#65136C2218yescomplemented
70#65134C2218yescomplemented
71#65024C2218yescomplemented
72#65022C2218yescomplemented
73#65020C2218yescomplemented
74#65012C2218yescomplemented
75#64986C2218yescomplemented
76C4×#677C2218yescomplemented
77C2×#3323—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4D411yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C23×Dic5—21no—
85C2×#709—22no—
86C2×#709—24no—
87C2×#709—42no—
88C2×#709C2314yes—
89C22×D20—24no—
90C22×D20—21no—
91C22×D20—22no—
92C22×D20—42no—
93C22×D20C2311yescharacteristic
94C22×D20C2314yes—
95C22×D20C2311yescharacteristic
96C22×C4×D5—21no—
97C22×C4×D5—21no—
98C22×Dic10C2311yescharacteristic
99C22×Dic10C2311yescharacteristic
100C2×C5×M16—42no—
101C2×C5×M16—42no—
102C2×C5×M16C2314yes—
103C2×C5×M16C2314yescomplemented
104C22×C5×C8C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C4×C5×D4D414yes—
109C4×C5×D4C2314yes—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118#4083—28no—
119#4081—28no—
120#4076—22no—
121#4076C2314yes—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126#4072—22no—
127#4072C2314yes—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—22no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2314yescomplemented
135#4070—22no—
136#4070—22no—
137#4070—22no—
138#4070C2314yes—
139#4070C2314yes—
140#4070C2314yescomplemented
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C2×Dic20—42no—
150C2×Dic20C2314yescomplemented
151C2×#677—24no—
152C2×#677—42no—
153C2×#677C2314yes—
154C2×#677C2314yes—
155#4040—28no—
156#4035—28no—
157#4030—28no—
158D5×C22⋊C4—28no—
159#4025—28no—
160#4023—28no—
161#4021—22no—
162#4021C2314yes—
163C4×D20—22no—
164C4×D20C2314yes—
165#4016—22no—
166#4016C2314yescomplemented
167C4×Dic10—22no—
168C4×Dic10C2314yescomplemented
169C5×C4⋊C8C2314yescomplemented
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yescomplemented
172C4×C5×C8C2314yescomplemented
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3950C2314yescomplemented
180#3949C2314yescomplemented
181#3949C2314yescomplemented
182#3948C2314yescomplemented
183#3948C2314yescomplemented
184#3948C2314yescomplemented
185#3948C2314yescomplemented
186C2×#552—51no—
187C2×#546—51no—
188#3323—516no—
189C2×#488—51no—
190C2×#481—51no—
191C2×#485—51no—
192C2×#478—51no—
193C2×#470—51no—
194C2×#468—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#450—51no—
198C2×C4×SD16—51no—
199C2×#436D511yescharacteristic, complemented
200C2×#417—51no—
201C2×#418—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5—82no—
210C2×C5×D4—42no—
211C2×C5×D4C2×D414yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2411yescharacteristic
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—82no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—44no—
237#709—28no—
238#709—44no—
239#709—48no—
240C2×D20—21no—
241C2×D20—22no—
242C2×D20—22no—
243C2×D20—22no—
244C2×D20—28no—
245C2×D20—21no—
246C2×D20—24no—
247C2×D20—44no—
248C2×D20—48no—
249C2×D20—44no—
250C2×D20#4114yes—
251C2×D20C2412yes—
252C2×D20C2412yes—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—44no—
256C2×C4×D5—82no—
257C2×Dic10—22no—
258C2×Dic10—22no—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10—21no—
263C2×Dic10C2412yes—
264C2×Dic10C2412yes—
265C5×M16—44no—
266C5×M16—44no—
267C2×C5×C8—22no—
268C2×C5×C8—22no—
269C2×C5×C8—22no—
270C2×C5×C8—22no—
271C2×C5×C8C2412yes—
272C2×C5×C8C2412yes—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C5×C4⋊C4C2×D414yes—
276C5×C22⋊C4C2×D414yes—
277C5×C22⋊C4C2×D414yes—
278C42×C5C2×D412yes—
279C42×C5C2412yes—
280C22⋊Dic5—24no—
281C22⋊Dic5—24no—
282C22⋊Dic5—24no—
283C22⋊Dic5—24no—
284#685—24no—
285#685—24no—
286#685—24no—
287#685—24no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5—21no—
292C4⋊Dic5—24no—
293C4⋊Dic5C2412yes—
294C4⋊Dic5C2412yes—
295C4⋊Dic5C2412yes—
296C4⋊Dic5C2412yes—
297#683—24no—
298#683—24no—
299#683—24no—
300#683—24no—
301#683—24no—
302#683—24no—
303C4×Dic5—24no—
304C4×Dic5—24no—
305Dic20—44no—
306#677—28no—
307#677—44no—
308C22×#41—51no—
309C23×D4—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16C2×D511yescharacteristic
314C22×M16C2×D511yescharacteristic, complemented
315#552—58no—
316#552—104no—
317#546—58no—
318#546—104no—
319C2×#126—101no—
320C2×#125—51no—
321C2×#125—101no—
322C2×#124—51no—
323C2×#123—101no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×C22⋊Q8—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#120—101no—
331C2×C4×Q8—51no—
332C2×C4×D4—51no—
333C2×C4×D4C2×D511yescharacteristic
334C2×#117—51no—
335C2×#117—101no—
336C22×C4⋊C4—51no—
337C22×C22⋊C4—101no—
338#488—58no—
339#485—58no—
340#481—58no—
341#478—58no—
342#470—58no—
343#468—58no—
344#464—58no—
345#452—58no—
346#450—58no—
347C4×SD16—58no—
348#436C2×D518yescomplemented
349C2×#107—51no—
350C2×#106—51no—
351C2×#106—51no—
352C2×C4⋊C8C2×D511yescharacteristic, complemented
353#418—58no—
354#417—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8C2×D511yescharacteristic
366C2×C22⋊C8C2×D511yescharacteristic, complemented
367C2×C4×C8C2×D511yescharacteristic, complemented
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5C22×D412yes—
375C23×C5C22×D412yes—
376C23×C5C22×D411yescharacteristic
377C22×D5—24no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—48no—
381C22×D5—42no—
382C22×D5—42no—
383C22×D5—48no—
384C22×D5—42no—
385C22×D5—42no—
386C22×D5—42no—
387C22×D5—84no—
388C22×D5—816no—
389C5×D4—44no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—24no—
395C2×C4×C5—24no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5C22×D412yes—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D412yes—
404C2×C4×C5C22×D411yescharacteristic
405C2×C4×C5C2×#4112yes—
406C2×C4×C5H(5,𝔽2)12yes—
407C2×C4×C5C2511yescharacteristic
408C22⋊D5—48no—
409C22⋊D5—84no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—48no—
417C2×Dic5—42no—
418C2×Dic5—42no—
419C2×Dic5—42no—
420C2×Dic5—42no—
421C2×Dic5—42no—
422C2×Dic5—42no—
423D20—24no—
424D20—22no—
425D20—22no—
426D20—22no—
427D20—48no—
428D20—42no—
429D20C2×#4114yes—
430C4×D5—48no—
431C4×D5—84no—
432Dic10—22no—
433Dic10—22no—
434Dic10—22no—
435Dic10—22no—
436Dic10—42no—
437Dic10—42no—
438C5×C8—22no—
439C5×C8—22no—
440C5×C8—22no—
441C5×C8—22no—
442C25—101no—
443C2×#41—54no—
444C2×#41—104no—
445C2×#41—102no—
446C2×#41—202no—
447C22×Q8—51no—
448C22×Q8—51no—
449C22×D4—51no—
450C22×D4—51no—
451C22×D4—54no—
452C22×D4—104no—
453C22×D4—101no—
454C22×D4—101no—
455C22×D4—101no—
456C22×D4—102no—
457C22×D4—202no—
458C22×D4D2011yescharacteristic
459C23×C4—101no—
460C23×C4—101no—
461C23×C4—101no—
462C23×C4C22×D511yescharacteristic
463C23×C4C22×D511yescharacteristic
464C2×Q16—54no—
465C2×Q16—202no—
466C2×SD16—54no—
467C2×SD16—54no—
468C2×SD16—104no—
469C2×SD16—202no—
470C2×M16—42no—
471C2×M16—42no—
472C2×M16C22×D514yes—
473C2×M16C22×D514yescomplemented
474C22×C8C22×D511yescharacteristic
475C22×C8C22×D511yescharacteristic
476C22×C8C22×D511yescharacteristic
477C22×C8C22×D511yescharacteristic
478#126—108no—
479#125—54no—
480#125—108no—
481#125—102no—
482#124—54no—
483#124—102no—
484#123—108no—
485#123—108no—
486C22⋊Q8—54no—
487C22⋊Q8—54no—
488C22⋊Q8—54no—
489C22⋊Q8—102no—
490C22⋊Q8—102no—
491C22⋊Q8—102no—
492#121—54no—
493#121—102no—
494#121—108no—
495#120—108no—
496C4×Q8—54no—
497C4×Q8—102no—
498C4×D4—54no—
499C4×D4—102no—
500C4×D4D2014yes—
501C4×D4C22×D514yes—
502#117—54no—
503#117—102no—
504#117—108no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4—51no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4—102no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4—101no—
518C2×C4⋊C4D2011yescharacteristic
519C2×C22⋊C4—101no—
520C2×C22⋊C4—101no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4—108no—
528C2×C22⋊C4D2011yescharacteristic
529C2×C22⋊C4D2011yescharacteristic
530C2×C42—101no—
531C2×C42—101no—
532C2×C42C22×D511yescharacteristic
533#107—54no—
534#106—54no—
535#106—54no—
536C4⋊C8C22×D514yescomplemented
537#103—54no—
538#103—54no—
539#103—54no—
540#103—54no—
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546#102—54no—
547C22⋊C8C22×D514yes—
548C22⋊C8C22×D514yescomplemented
549C4×C8C22×D514yescomplemented
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—22no—
556C22×C5—44no—
557C22×C5—44no—
558C22×C5#54612yes—
559C22×C5#57512yes—
560C22×C5#57712yes—
561C22×C5C23×D411yescharacteristic
562C2×D5—24no—
563C2×D5—48no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—816no—
570C2×D5—84no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—22no—
575C4×C5#54612yes—
576C4×C5C22×#4111yescharacteristic
577C4×C5C2×H(5,𝔽2)11yescharacteristic
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—101no—
585C24—101no—
586C24—104no—
587C24—204no—
588C24—204no—
589C24—402no—
590C24C2×D2011yescharacteristic
591C24C2×D2011yescharacteristic
592#41—108no—
593#41—204no—
594#41—208no—
595C2×Q8—52no—
596C2×Q8—52no—
597C2×Q8—101no—
598C2×Q8—101no—
599C2×Q8—102no—
600C2×Q8—102no—
601C2×Q8—102no—
602C2×Q8—102no—
603C2×D4—42no—
604C2×D4—54no—
605C2×D4—52no—
606C2×D4—52no—
607C2×D4—108no—
608C2×D4—104no—
609C2×D4—104no—
610C2×D4—101no—
611C2×D4—104no—
612C2×D4—101no—
613C2×D4—102no—
614C2×D4—102no—
615C2×D4—102no—
616C2×D4—204no—
617C2×D4—208no—
618C2×D4—204no—
619C2×D4—204no—
620C2×D4—402no—
621C2×D4C2×D2014yes—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—104no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—104no—
634C22×C4—104no—
635C22×C4—204no—
636C22×C4—204no—
637C22×C4—402no—
638C22×C4C2×D2012yes—
639C22×C4C2×D2012yes—
640C22×C4C2×D2011yescharacteristic
641C22×C4C2×D2011yescharacteristic
642C22×C4C2×D2011yescharacteristic
643C22×C4C2×D2011yescharacteristic
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647Q16—204no—
648SD16—108no—
649SD16—204no—
650M16—44no—
651M16—44no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8C23×D512yes—
657C2×C8C23×D512yes—
658C2×C8C23×D512yes—
659C2×C8C23×D512yes—
660C4⋊C4—52no—
661C4⋊C4—52no—
662C4⋊C4—52no—
663C4⋊C4—52no—
664C4⋊C4—101no—
665C4⋊C4—101no—
666C4⋊C4—104no—
667C4⋊C4—101no—
668C4⋊C4—101no—
669C4⋊C4—104no—
670C4⋊C4—104no—
671C4⋊C4—104no—
672C4⋊C4—104no—
673C4⋊C4—104no—
674C4⋊C4—104no—
675C4⋊C4C2×D2014yes—
676C22⋊C4—104no—
677C22⋊C4—104no—
678C22⋊C4—104no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4—104no—
682C22⋊C4—104no—
683C22⋊C4—104no—
684C22⋊C4C2×D2014yes—
685C22⋊C4C2×D2014yes—
686C42—104no—
687C42—104no—
688C42C2×D2012yes—
689C42C23×D512yes—
690C2×C5—42no—
691C2×C5—42no—
692C2×C5#332314yescomplemented
693C2×C5C2×#54611yescharacteristic
694C2×C5C2×#57511yescharacteristic
695C2×C5C2×#57711yescharacteristic
696D5—44no—
697D5—82no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—104no—
705C23—102no—
706C23—102no—
707C23—208no—
708C23—208no—
709C23—202no—
710C23—202no—
711C23—202no—
712C23—202no—
713C23—202no—
714C23—404no—
715C23—4016no—
716C23C22×D2012yes—
717C23C22×D2012yes—
718C23C22×D2011yescharacteristic
719Q8—102no—
720Q8—102no—
721Q8—102no—
722Q8—102no—
723Q8—202no—
724Q8—202no—
725D4—44no—
726D4—54no—
727D4—104no—
728D4—102no—
729D4—102no—
730D4—102no—
731D4—208no—
732D4—208no—
733D4—202no—
734D4—404no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—208no—
752C2×C4—208no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—404no—
760C2×C4C22×D2012yes—
761C2×C4C22×D2012yes—
762C2×C4C22×D2012yes—
763C2×C4C22×D2012yes—
764C2×C4C22×D2011yescharacteristic
765C2×C4#414412yes—
766C2×C4D5×#4112yes—
767C2×C4C24×D511yescharacteristic
768C8—22no—
769C8—22no—
770C8—22no—
771C8—22no—
772C5C2×#332311yescharacteristic, complemented, Sylow
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—104no—
782C22—208no—
783C22—202no—
784C22—202no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—4016no—
789C22—404no—
790C22#6588812yes—
791C22#6608212yes—
792C22#6608512yes—
793C22C23×D2011yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—202no—
799C4—202no—
800C4—202no—
801C4—202no—
802C4—202no—
803C4—202no—
804C4#6588812yes—
805C4C2×#414411yescharacteristic
806C4C2×D5×#4111yescharacteristic
807C2—42no—
808C2—42no—
809C2—204no—
810C2—402no—
811C2#1061128514yesdirect product factor
812C2C2×#6588811yescharacteristic
813C2C2×#6608211yescharacteristic
814C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#436C2
socleC23×C5C22×D4
prime radicalC2×#65884C2
hypercenterC2×#436D5
hypocenterC5C2×#3323
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#65875C2semidirect
3. C2×C5×#436C2semidirect
4. C2×#65426C2semidirect
5. C2×#65423C2semidirect
6. C2×#65422C2semidirect
7. C2×#65420C2semidirect
8. #10611285C2direct (N × H)
9. C2×#65134C2semidirect
10. C2×#65136C2semidirect
11. C2×#65022C2semidirect
12. C2×#65020C2semidirect
13. C2×#65024C2semidirect
14. C2×#65012C2semidirect
15. C2×C4×#677C2semidirect
16. C2×#64986C2semidirect
20. C22×C5×M16C22semidirect
26. C22×C4⋊Dic5C22semidirect
29. C2×#4070C22semidirect
30. C22×Dic20C22semidirect
36. #65875C22semidirect
45. C2×#4016C22semidirect
46. C2×C4×Dic10C22semidirect
47. C5×#436C22semidirect
48. C2×C5×C4⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C4×C5×C8C22semidirect
52. #65426C22semidirect
53. #65423C22semidirect
54. #65422C22semidirect
55. #65420C22semidirect
62. C2×#3950C22semidirect
63. C2×#3949C22semidirect
64. C2×#3949C22semidirect
65. C2×#3948C22semidirect
66. C2×#3948C22semidirect
67. C2×#3948C22semidirect
68. C2×#3948C22semidirect
69. #65136C22semidirect
70. #65134C22semidirect
71. #65024C22semidirect
72. #65022C22semidirect
73. #65020C22semidirect
74. #65012C22semidirect
75. #64986C22semidirect
76. C4×#677C22semidirect
103. C2×C5×M16C23semidirect
134. C2×C4⋊Dic5C23semidirect
140. #4070C23semidirect
150. C2×Dic20C23semidirect
166. #4016C23semidirect
168. C4×Dic10C23semidirect
169. C5×C4⋊C8C23semidirect
171. C5×C22⋊C8C23semidirect
172. C4×C5×C8C23semidirect
179. #3950C23semidirect
180. #3949C23semidirect
181. #3949C23semidirect
182. #3948C23semidirect
183. #3948C23semidirect
184. #3948C23semidirect
185. #3948C23semidirect
199. C2×#436D5semidirect
314. C22×M16C2×D5semidirect
348. #436C2×D5semidirect
352. C2×C4⋊C8C2×D5semidirect
366. C2×C22⋊C8C2×D5semidirect
367. C2×C4×C8C2×D5semidirect
473. C2×M16C22×D5semidirect
536. C4⋊C8C22×D5semidirect
548. C22⋊C8C22×D5semidirect
549. C4×C8C22×D5semidirect
692. C2×C5#3323semidirect
772. C5C2×#3323semidirect
811. C2#10611285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658842
C2×#658752
C2×C5×#4362
C2×#654262
C2×#654232
C2×#654222
C2×#654202
#106112852
C2×#651342
C2×#651362
C2×#650222
C2×#650202
C2×#650242
C2×#650122
C2×C4×#6772
C2×#649862
C2×#33235