Finite Group Databasebeta

← #12101201

Subgroups — #12101201

Order 1280.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2#10619161C211yesmaximal, characteristic, complemented
3C2×#65529C211yesmaximal, characteristic, complemented
4C2×#65525C211yesmaximal, characteristic, complemented
5#10615803C211yesmaximal, characteristic, complemented
6#10602894C214yesmaximal, complemented
7#10602882C214yesmaximal, complemented
8C2×#64776C211yesmaximal, characteristic, complemented
9C2×#64777C211yesmaximal, characteristic, complemented
10C22×C5×#41C2211yescharacteristic
11C22×C5×#41C2211yescharacteristic
12C5×#575—22no—
13C5×#575—22no—
14C5×#575—22no—
15C5×#575—22no—
16C2×C5×#137C412yescomplemented
17C2×C5×#137C2212yes—
18C2×C5×AGL(1,ℤ/8)C412yescomplemented
19C2×C5×AGL(1,ℤ/8)C2212yes—
20C2×C5×#135C414yescomplemented
21C22×C5×M16C2211yescharacteristic
22#66161—22no—
23#66161—22no—
24#41×Dic5—22no—
25#41×Dic5—22no—
26#66146C2212yescomplemented
27#66132—22no—
28#66132C2212yescomplemented
29C2×#4072—22no—
30C2×#4072C2211yescharacteristic
31C2×#4072C2211yescharacteristic
32C2×#4072C2211yescharacteristic
33C22×#681C2211yescharacteristic
34#65529—22no—
35#65529C2214yes—
36#65525—22no—
37#65525C2214yes—
38C2×#3969—22no—
39#65522—22no—
40#65521—22no—
41#65514C2212yescomplemented
42C2×#3966—22no—
43#65504C2212yescomplemented
44#64777C2214yescomplemented
45#64776C2214yescomplemented
46#20998—51nomaximal, Sylow
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41—21no—
51C2×C5×#41—21no—
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41—21no—
55C2×C5×#41—21no—
56C2×C5×#41—21no—
57C2×C5×#41—21no—
58C2×C5×#41—21no—
59C2×C5×#41—21no—
60C2×C5×#41—21no—
61C2×C5×#41—21no—
62C2×C5×#41—21no—
63C2×C5×#41C2×C412yes—
64C2×C5×#41C2×C412yes—
65C2×C5×#41C2×C412yescomplemented
66C2×C5×#41D412yes—
67C2×C5×#41D412yes—
68C2×C5×#41D412yes—
69C2×C5×#41D412yes—
70C2×C5×#41C2312yes—
71C22×C5×Q8C2×C411yescharacteristic, complemented
72C22×C5×Q8C2311yescharacteristic
73C22×C5×D4—21no—
74C22×C5×D4—21no—
75C22×C5×D4C2×C411yescharacteristic, complemented
76C22×C5×D4C2311yescharacteristic
77C23×C4×C5—21no—
78C23×C4×C5—21no—
79C23×C4×C5C2311yescharacteristic
80C5×#137—24no—
81C5×#137—24no—
82C5×#137—24no—
83C5×#137—24no—
84C5×AGL(1,ℤ/8)—24no—
85C5×AGL(1,ℤ/8)—24no—
86C5×AGL(1,ℤ/8)—24no—
87C5×AGL(1,ℤ/8)—24no—
88C5×#135—28no—
89C5×#135—28no—
90C2×C5×Q16C2×C414yescomplemented
91C2×C5×SD16C2×C414yescomplemented
92C2×C5×SD16C2×C414yescomplemented
93C2×C5×D8C2×C414yescomplemented
94C2×C5×M16—21no—
95C2×C5×M16—21no—
96C2×C5×M16—21no—
97C2×C5×M16—21no—
98C2×C5×M16C2×C412yescomplemented
99C2×C5×M16C2312yes—
100C22×C5×C8C2×C412yescomplemented
101C2×C22⋊Dic5—21no—
102C2×C22⋊Dic5—24no—
103C2×C22⋊Dic5—21no—
104C2×C22⋊Dic5D412yes—
105Q8×Dic5—24no—
106Q8×Dic5—24no—
107D4×Dic5—28no—
108D4×Dic5—28no—
109D4×Dic5—24no—
110D4×Dic5—24no—
111#4072—24no—
112#4072—24no—
113#4072—21no—
114#4072—21no—
115#4072—21no—
116#4072—21no—
117#4072—24no—
118#4072—21no—
119#4072—21no—
120#4072—21no—
121#4072D412yes—
122#4072D412yes—
123#4072C2312yes—
124#4072C2312yes—
125#4072C2312yes—
126C2×C4⋊Dic5—24no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4×Dic5—24no—
131C2×C4×Dic5—21no—
132C2×C4×Dic5—21no—
133C2×C4×Dic5D412yes—
134C2×#681—21no—
135C2×#681—21no—
136C2×#681—21no—
137C2×#681—21no—
138C2×#681—21no—
139C2×#681C2312yes—
140C22×#168—21no—
141#3969—28no—
142#3967—24no—
143#3966—28no—
144#3964—24no—
145C2×#575D511yescharacteristic
146#3428—51no—
147C2×#421—51no—
148#2896—51no—
149C2×#410—51no—
150#1905—54no—
151#1904—54no—
152C2×#344—51no—
153C2×H(3,ℤ/4)—51no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5C2×D411yescharacteristic
157C5×#41—22no—
158C5×#41—22no—
159C5×#41—22no—
160C5×#41—22no—
161C5×#41—22no—
162C5×#41—22no—
163C5×#41—22no—
164C5×#41—22no—
165C5×#41—22no—
166C5×#41—22no—
167C5×#41—22no—
168C5×#41—22no—
169C5×#41—22no—
170C5×#41—22no—
171C5×#41—22no—
172C5×#41—22no—
173C5×#41—22no—
174C5×#41—22no—
175C5×#41—22no—
176C5×#41—22no—
177C5×#41—41no—
178C5×#41—41no—
179C5×#41—41no—
180C5×#41—41no—
181C5×#41—41no—
182C5×#41—41no—
183C5×#41—41no—
184C5×#41—41no—
185C5×#41C22⋊C414yes—
186C5×#41C22⋊C414yes—
187C5×#41C22⋊C414yes—
188C5×#41C22⋊C414yes—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—21no—
192C2×C5×Q8—21no—
193C2×C5×Q8—21no—
194C2×C5×Q8—21no—
195C2×C5×Q8—21no—
196C2×C5×Q8—21no—
197C2×C5×Q8C22×C412yes—
198C2×C5×Q8C22×C412yes—
199C2×C5×Q8C2×D412yes—
200C2×C5×Q8C2×D412yes—
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—22no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4—21no—
214C2×C5×D4—21no—
215C2×C5×D4—21no—
216C2×C5×D4—21no—
217C2×C5×D4—41no—
218C2×C5×D4—41no—
219C2×C5×D4—41no—
220C2×C5×D4—41no—
221C2×C5×D4C22×C412yes—
222C2×C5×D4C22×C412yes—
223C2×C5×D4C2×D412yes—
224C2×C5×D4C2×D412yes—
225C22×C4×C5—21no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—21no—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—41no—
236C22×C4×C5—41no—
237C22×C4×C5—41no—
238C22×C4×C5—41no—
239C22×C4×C5C22×C411yescharacteristic
240C22×C4×C5C22×C411yescharacteristic
241C22×C4×C5C2×D411yescharacteristic
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D411yescharacteristic
248C22×C4×C5#4111yescharacteristic
249C22×C4×C5#4111yescharacteristic
250C22×C4×C5#4111yescharacteristic
251C22×C4×C5#4111yescharacteristic
252C22×C4×C5C2411yescharacteristic
253C22×Dic5—28no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—41no—
257C5×Q16—28no—
258C5×SD16—28no—
259C5×SD16—28no—
260C5×D8—28no—
261C5×M16—22no—
262C5×M16—22no—
263C5×M16—22no—
264C5×M16—22no—
265C2×C5×C8—22no—
266C2×C5×C8—22no—
267C2×C5×C8C22×C414yes—
268C22⋊Dic5—28no—
269C22⋊Dic5—22no—
270C22⋊Dic5—22no—
271C22⋊Dic5—22no—
272C22⋊Dic5—22no—
273C22⋊Dic5—41no—
274C22⋊Dic5C2×D414yes—
275C4⋊Dic5—28no—
276C4⋊Dic5—22no—
277C4⋊Dic5—22no—
278C4⋊Dic5—22no—
279C4⋊Dic5—22no—
280C4⋊Dic5—22no—
281C4⋊Dic5—41no—
282C4×Dic5—28no—
283C4×Dic5—22no—
284C4×Dic5—22no—
285C4×Dic5—22no—
286C4×Dic5—22no—
287C4×Dic5—41no—
288C4×Dic5C2×D414yes—
289#681—22no—
290#681—22no—
291#681—41no—
292#681—41no—
293C2×#168—22no—
294C2×#168—41no—
295C2×#168—41no—
296C22×#41C2×D511yescharacteristic
297C22×#41C2×D511yescharacteristic
298#575—22no—
299#575—22no—
300#575—22no—
301#575—22no—
302C2×#137Dic512yescomplemented
303C2×#137C2×D512yes—
304C2×AGL(1,ℤ/8)Dic512yescomplemented
305C2×AGL(1,ℤ/8)C2×D512yes—
306C2×#135Dic514yescomplemented
307C22×M16—51no—
308C22×M16C2×D511yescharacteristic
309#520—102no—
310#520—102no—
311#519—52no—
312#518—52no—
313#518—102no—
314C4×#41—102no—
315C4×#41—102no—
316C2×#117—51no—
317C2×#117—51no—
318C2×#117—51no—
319C2×#117—102no—
320#421—54no—
321#421—102no—
322C2×#104—102no—
323#419—52no—
324#418—52no—
325#417—102no—
326#416—102no—
327#410—54no—
328#410—102no—
329C2×#99—102no—
330#344—54no—
331H(3,ℤ/4)—54no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—81no—
339C23×C5—82no—
340C23×C5—82no—
341C23×C5C4×D411yescharacteristic
342C23×C5C4×D411yescharacteristic
343C23×C5#12011yescharacteristic
344C23×C5#12011yescharacteristic
345C23×C5#12111yescharacteristic
346C23×C5#12111yescharacteristic
347C23×C5C22×D411yescharacteristic
348C5×Q8—22no—
349C5×Q8—22no—
350C5×Q8—22no—
351C5×Q8—22no—
352C5×Q8—22no—
353C5×Q8—41no—
354C5×Q8—41no—
355C5×Q8C2×C22⋊C414yes—
356C5×D4—24no—
357C5×D4—24no—
358C5×D4—24no—
359C5×D4—24no—
360C5×D4—22no—
361C5×D4—22no—
362C5×D4—22no—
363C5×D4—22no—
364C5×D4—22no—
365C5×D4—42no—
366C5×D4—42no—
367C5×D4—42no—
368C5×D4—42no—
369C5×D4—41no—
370C5×D4—41no—
371C5×D4C2×C22⋊C414yes—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—24no—
377C2×C4×C5—24no—
378C2×C4×C5—24no—
379C2×C4×C5—22no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5C2×C22⋊C411yescharacteristic
387C2×C4×C5C2×C22⋊C411yescharacteristic
388C2×C4×C5C2×C22⋊C411yescharacteristic
389C2×C4×C5C2×C22⋊C411yescharacteristic
390C2×C4×C5C4×D411yescharacteristic
391C2×C4×C5C4×D411yescharacteristic
392C2×C4×C5C4×D411yescharacteristic
393C2×C4×C5C4×D411yescharacteristic
394C2×C4×C5C4×D411yescharacteristic
395C2×C4×C5C4×D411yescharacteristic
396C2×C4×C5#12011yescharacteristic
397C2×C4×C5#12011yescharacteristic
398C2×C4×C5#12111yescharacteristic
399C2×C4×C5#12111yescharacteristic
400C2×C4×C5#12111yescharacteristic
401C2×C4×C5#12111yescharacteristic
402C2×C4×C5#12111yescharacteristic
403C2×C4×C5#12111yescharacteristic
404C2×C4×C5#12311yescharacteristic
405C2×C4×C5#12311yescharacteristic
406C2×C4×C5#12311yescharacteristic
407C2×C4×C5#12311yescharacteristic
408C2×C4×C5C23×C411yescharacteristic
409C2×C4×C5C22×D411yescharacteristic
410C2×C4×C5C22×D411yescharacteristic
411C2×C4×C5C22×D411yescharacteristic
412C2×C4×C5C2×#4111yescharacteristic
413C2×C4×C5C2×#4111yescharacteristic
414C2×Dic5—24no—
415C2×Dic5—24no—
416C2×Dic5—42no—
417C2×Dic5—82no—
418C2×Dic5—82no—
419C2×Dic5—88no—
420C2×Dic5—82no—
421C5×C8—24no—
422#168—42no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41C2×Dic512yes—
440C2×#41C2×Dic512yes—
441C2×#41C2×Dic512yescomplemented
442C2×#41C22⋊D512yes—
443C2×#41C22⋊D512yes—
444C2×#41C22⋊D512yes—
445C2×#41C22⋊D512yes—
446C2×#41C22×D512yes—
447C22×Q8C2×Dic511yescharacteristic, complemented
448C22×Q8C22×D511yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C2×Dic511yescharacteristic, complemented
452C22×D4C22×D511yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C22×D511yescharacteristic
456#137—24no—
457#137—24no—
458#137—24no—
459#137—24no—
460AGL(1,ℤ/8)—24no—
461AGL(1,ℤ/8)—24no—
462AGL(1,ℤ/8)—24no—
463AGL(1,ℤ/8)—24no—
464#135—28no—
465#135—28no—
466C2×Q16C2×Dic514yescomplemented
467C2×SD16C2×Dic514yescomplemented
468C2×SD16C2×Dic514yescomplemented
469C2×D8C2×Dic514yescomplemented
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—52no—
475C2×M16—101no—
476C2×M16—101no—
477C2×M16—101no—
478C2×M16—101no—
479C2×M16—101no—
480C2×M16C2×Dic512yescomplemented
481C2×M16C22×D512yes—
482C22×C8—101no—
483C22×C8C2×Dic512yescomplemented
484C4×Q8—104no—
485C4×Q8—104no—
486C4×D4—104no—
487C4×D4—108no—
488C4×D4—108no—
489C4×D4—104no—
490#117—52no—
491#117—52no—
492#117—52no—
493#117—52no—
494#117—52no—
495#117—104no—
496#117—104no—
497#117—104no—
498#117—101no—
499#117—101no—
500#117—101no—
501#117—101no—
502#117—101no—
503#117—101no—
504#117—101no—
505C2×C4⋊C4—104no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—101no—
509C2×C22⋊C4—52no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C42—52no—
514C2×C42—104no—
515C2×C42—101no—
516C2×C42—101no—
517#104—108no—
518#103—104no—
519#102—104no—
520#99—108no—
521C22×C5—24no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—44no—
530C22×C5—42no—
531C22×C5—82no—
532C22×C5—82no—
533C22×C5—82no—
534C22×C5—82no—
535C22×C5—82no—
536C22×C5#38611yescharacteristic
537C22×C5#38611yescharacteristic
538C22×C5#38611yescharacteristic
539C22×C5#38611yescharacteristic
540C22×C5C2×C4×D411yescharacteristic
541C22×C5C2×#12011yescharacteristic
542C22×C5C2×#12111yescharacteristic
543C4×C5—24no—
544C4×C5—42no—
545C4×C5#38611yescharacteristic
546C4×C5#38611yescharacteristic
547C4×C5#38611yescharacteristic
548C4×C5#38611yescharacteristic
549C4×C5C22×C22⋊C411yescharacteristic
550C4×C5C2×C4×D411yescharacteristic
551C4×C5C2×#12111yescharacteristic
552C4×C5C2×#12311yescharacteristic
553Dic5—44no—
554Dic5—44no—
555Dic5—82no—
556C24—21no—
557C24—21no—
558C24D4×D511yescharacteristic
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41C22⋊Dic514yes—
588#41C22⋊Dic514yes—
589#41C22⋊Dic514yes—
590#41C22⋊Dic514yes—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8C22×Dic512yes—
600C2×Q8C22×Dic512yes—
601C2×Q8C2×C22⋊D512yes—
602C2×Q8C2×C22⋊D512yes—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4C22×Dic512yes—
624C2×D4C22×Dic512yes—
625C2×D4C2×C22⋊D512yes—
626C2×D4C2×C22⋊D512yes—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—108no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—201no—
645C22×C4D4×D511yescharacteristic
646C22×C4D4×D511yescharacteristic
647C22×C4D4×D511yescharacteristic
648C22×C4#71111yescharacteristic
649C22×C4#71111yescharacteristic
650C22×C4#71111yescharacteristic
651C22×C4#71111yescharacteristic
652C22×C4C22×Dic511yescharacteristic
653C22×C4C22×Dic511yescharacteristic
654C22×C4C2×C22⋊D511yescharacteristic
655C22×C4C2×C22⋊D511yescharacteristic
656C22×C4C2×C22⋊D511yescharacteristic
657C22×C4C2×C22⋊D511yescharacteristic
658C22×C4C23×D511yescharacteristic
659Q16—28no—
660SD16—28no—
661SD16—28no—
662D8—28no—
663M16—22no—
664M16—22no—
665M16—22no—
666M16—22no—
667M16—102no—
668M16—102no—
669M16—201no—
670M16—201no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—102no—
674C2×C8—201no—
675C2×C8—201no—
676C2×C8C22×Dic514yes—
677C4⋊C4—108no—
678C4⋊C4—102no—
679C4⋊C4—102no—
680C4⋊C4—102no—
681C4⋊C4—102no—
682C4⋊C4—102no—
683C4⋊C4—201no—
684C22⋊C4—54no—
685C22⋊C4—108no—
686C22⋊C4—102no—
687C22⋊C4—102no—
688C22⋊C4—102no—
689C22⋊C4—102no—
690C22⋊C4—201no—
691C42—54no—
692C42—108no—
693C42—102no—
694C42—102no—
695C42—102no—
696C42—102no—
697C42—201no—
698C2×C5—21no—
699C2×C5—21no—
700C2×C5—21no—
701C2×C5—21no—
702C2×C5—21no—
703C2×C5—21no—
704C2×C5—21no—
705C2×C5—44no—
706C2×C5—82no—
707C2×C5C2×#38611yescharacteristic
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—41no—
713C23—41no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23D4×Dic511yescharacteristic
718C23D4×Dic511yescharacteristic
719C23#408311yescharacteristic
720C23#408311yescharacteristic
721C23#408511yescharacteristic
722C23#408511yescharacteristic
723C23C2×D4×D511yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—41no—
730Q8—41no—
731Q8C2×C22⋊Dic514yes—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—42no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4C2×C22⋊Dic514yes—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—104no—
763C2×C4—104no—
764C2×C4—202no—
765C2×C4—402no—
766C2×C4—402no—
767C2×C4—408no—
768C2×C4—402no—
769C2×C4D4×Dic511yescharacteristic
770C2×C4D4×Dic511yescharacteristic
771C2×C4D4×Dic511yescharacteristic
772C2×C4D4×Dic511yescharacteristic
773C2×C4D4×Dic511yescharacteristic
774C2×C4D4×Dic511yescharacteristic
775C2×C4#408111yescharacteristic
776C2×C4#408111yescharacteristic
777C2×C4#408111yescharacteristic
778C2×C4#408111yescharacteristic
779C2×C4#408311yescharacteristic
780C2×C4#408311yescharacteristic
781C2×C4#408511yescharacteristic
782C2×C4#408511yescharacteristic
783C2×C4#408511yescharacteristic
784C2×C4#408511yescharacteristic
785C2×C4#408511yescharacteristic
786C2×C4#408511yescharacteristic
787C2×C4C2×C22⋊Dic511yescharacteristic
788C2×C4C2×C22⋊Dic511yescharacteristic
789C2×C4C2×C22⋊Dic511yescharacteristic
790C2×C4C2×C22⋊Dic511yescharacteristic
791C2×C4C2×D4×D511yescharacteristic
792C2×C4C2×#71111yescharacteristic
793C2×C4C2×#71111yescharacteristic
794C2×C4C23×Dic511yescharacteristic
795C2×C4C22×C22⋊D511yescharacteristic
796C2×C4C22×C22⋊D511yescharacteristic
797C8—24no—
798C8—202no—
799C5#2099811yescharacteristic, complemented, Sylow
800C22—24no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22#6550911yescharacteristic
816C22#6550911yescharacteristic
817C22#6550911yescharacteristic
818C22#6550911yescharacteristic
819C22C2×D4×Dic511yescharacteristic
820C22C2×#408311yescharacteristic
821C22C2×#408511yescharacteristic
822C4—24no—
823C4—42no—
824C4—204no—
825C4—204no—
826C4—402no—
827C4#6550911yescharacteristic
828C4#6550911yescharacteristic
829C4#6550911yescharacteristic
830C4#6550911yescharacteristic
831C4C2×D4×Dic511yescharacteristic
832C4C2×#408111yescharacteristic
833C4C2×#408511yescharacteristic
834C4C22×C22⋊Dic511yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—44no—
843C2—82no—
844C2C2×#6550911yescharacteristic
subgroupG/H
centerC4#65509
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
Fitting, prime radicalC2×C5×#575C2
socleC2×C5C2×#386
cosocleC22×C4×C5C24
hypercenterC2×#575D5
hypocenterC5#20998
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. #10619161C2semidirect
3. C2×#65529C2semidirect
4. C2×#65525C2semidirect
5. #10615803C2semidirect
6. #10602894C2semidirect
7. #10602882C2semidirect
8. C2×#64776C2semidirect
9. C2×#64777C2semidirect
16. C2×C5×#137C4semidirect
18. C2×C5×AGL(1,ℤ/8)C4semidirect
20. C2×C5×#135C4semidirect
26. #66146C22semidirect
28. #66132C22semidirect
41. #65514C22semidirect
43. #65504C22semidirect
44. #64777C22semidirect
45. #64776C22semidirect
65. C2×C5×#41C2×C4semidirect
71. C22×C5×Q8C2×C4semidirect
75. C22×C5×D4C2×C4semidirect
90. C2×C5×Q16C2×C4semidirect
91. C2×C5×SD16C2×C4semidirect
92. C2×C5×SD16C2×C4semidirect
93. C2×C5×D8C2×C4semidirect
98. C2×C5×M16C2×C4semidirect
100. C22×C5×C8C2×C4semidirect
302. C2×#137Dic5semidirect
304. C2×AGL(1,ℤ/8)Dic5semidirect
306. C2×#135Dic5semidirect
441. C2×#41C2×Dic5semidirect
447. C22×Q8C2×Dic5semidirect
451. C22×D4C2×Dic5semidirect
466. C2×Q16C2×Dic5semidirect
467. C2×SD16C2×Dic5semidirect
468. C2×SD16C2×Dic5semidirect
469. C2×D8C2×Dic5semidirect
480. C2×M16C2×Dic5semidirect
483. C22×C8C2×Dic5semidirect
799. C5#20998semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5752
#106191612
C2×#655292
C2×#655252
#106158032
#106028942
#106028822
C2×#647762
C2×#647772
#209985