Finite Group Databasebeta

← #12004820

Subgroups — #12004820

Order 1280.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65838C211yesmaximal, characteristic
2C2×#65255C211yesmaximal, characteristic
3C22×#3937C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#64750C211yesmaximal, characteristic, complemented
6#10602351C211yesmaximal, characteristic, complemented
7C2×#64743C211yesmaximal, characteristic, complemented
8C22×#709C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C42×C5C2211yescharacteristic
12C2×C4×C22⋊D5—22no—
13C2×#4072C2211yescharacteristic
14C22×#681C2211yescharacteristic
15C22×#681C2211yescharacteristic
16#65838—22no—
17#65838—22no—
18#65838—22no—
19#65838C414yescomplemented
20C2×#4039—21no—
21C2×#4038—21no—
22C2×D5×C4⋊C4—21no—
23C2×#4033—21no—
24C2×C5×#95—22no—
25C2×#3942—21no—
26#65255—22no—
27#65255C414yescomplemented
28C2×#3941—21no—
29C2×#3937—22no—
30C2×#3937—22no—
31C2×#3937C414yescomplemented
32#64750—22no—
33#64749—21no—
34#64749—21no—
35#64743—22no—
36#10781—51nomaximal, Sylow
37C23×C4×C5—21no—
38C23×C4×C5—21no—
39C23×C4×C5D412yes—
40C23×C4×C5C2311yescharacteristic
41C22×C22⋊D5—21no—
42C2×#709—21no—
43C2×#709—21no—
44C2×#709—21no—
45C2×#709—21no—
46C2×#709—21no—
47C2×#709—21no—
48C2×#709C2×C412yes—
49C2×#709C2×C412yes—
50C2×#709C2×C412yes—
51C2×#709D412yes—
52C2×#709D412yes—
53C2×#709Q812yes—
54C22×D20D411yescharacteristic
55C22×C4×D5—21no—
56C22×C4×D5—22no—
57C22×Dic10D411yescharacteristic
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4—21no—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4—21no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4C2×C412yes—
68C2×C5×C4⋊C4C2×C412yescomplemented
69C2×C5×C4⋊C4D412yes—
70C2×C42×C5—21no—
71C2×C42×C5—21no—
72C2×C42×C5—21no—
73C2×C42×C5—21no—
74C2×C42×C5—21no—
75C2×C42×C5C2×C412yescomplemented
76C2×C22⋊Dic5—21no—
77C4×C22⋊D5—28no—
78C4×C22⋊D5—28no—
79C2×#685—22no—
80#4072—21no—
81#4072—21no—
82#4072C2×C412yes—
83#4072D412yes—
84C2×C4⋊Dic5D411yescharacteristic
85C2×C4⋊Dic5D411yescharacteristic
86C2×#683—22no—
87C2×C4×Dic5—22no—
88C2×C4×Dic5—21no—
89C2×#681—21no—
90C2×#681—21no—
91C2×#681—21no—
92C2×#681—21no—
93C2×#681—21no—
94C2×#681—21no—
95C2×#681—21no—
96C2×#681—21no—
97C2×#681—21no—
98C2×#681—21no—
99C2×#681C2×C412yescomplemented
100C2×#681C2×C412yescomplemented
101C22×#168—21no—
102C22×#168—21no—
103#4039—24no—
104#4039—24no—
105#4038—24no—
106#4038—24no—
107D5×C4⋊C4—24no—
108D5×C4⋊C4—24no—
109#4033—24no—
110#4033—24no—
111C5×#95—44no—
112#3942—24no—
113#3941—24no—
114#3937—28no—
115C2×#520—51no—
116C22×#104—51no—
117C2×#417—51no—
118C2×#343—51no—
119#1736—51no—
120C2×#339—51no—
121C4⋊#95D511yescharacteristic, complemented
122C24×C5C2×D411yescharacteristic
123C23×D5—21no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—41no—
131C22×C4×C5—41no—
132C22×C4×C5—41no—
133C22×C4×C5—41no—
134C22×C4×C5—42no—
135C22×C4×C5—42no—
136C22×C4×C5—42no—
137C22×C4×C5—42no—
138C22×C4×C5—41no—
139C22×C4×C5—41no—
140C22×C4×C5C22⋊C414yes—
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C22×C411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×Q811yescharacteristic
151C22×C4×C5#4111yescharacteristic
152C22×C4×C5#4111yescharacteristic
153C22×C4×C5#4111yescharacteristic
154C22×C4×C5#4111yescharacteristic
155C2×C22⋊D5—22no—
156C2×C22⋊D5—22no—
157C2×C22⋊D5—22no—
158C2×C22⋊D5—22no—
159C2×C22⋊D5—22no—
160C2×C22⋊D5—22no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164#709—22no—
165#709—22no—
166#709—22no—
167#709—22no—
168#709—22no—
169#709—22no—
170#709—22no—
171#709—22no—
172#709—22no—
173#709—22no—
174#709—22no—
175#709—22no—
176#709C4214yes—
177#709C22⋊C414yes—
178#709C4⋊C414yes—
179#709C4⋊C414yes—
180C2×D20—21no—
181C2×D20—21no—
182C2×D20—21no—
183C2×D20C22⋊C412yes—
184C2×D20C22⋊C412yes—
185C2×D20C4⋊C412yes—
186C2×C4×D5—22no—
187C2×C4×D5—22no—
188C2×C4×D5—22no—
189C2×C4×D5—22no—
190C2×C4×D5—22no—
191C2×C4×D5—22no—
192C2×C4×D5—28no—
193C2×C4×D5—82no—
194C2×C4×D5—82no—
195C2×Dic10—21no—
196C2×Dic10—21no—
197C2×Dic10—21no—
198C2×Dic10C22⋊C412yes—
199C2×Dic10C22⋊C412yes—
200C2×Dic10C4⋊C412yes—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—41no—
208C5×C4⋊C4—41no—
209C42×C5—22no—
210C42×C5—22no—
211C42×C5—41no—
212C42×C5—41no—
213C22⋊Dic5—22no—
214C22⋊Dic5—22no—
215#685—28no—
216C4⋊Dic5—21no—
217C4⋊Dic5—21no—
218C4⋊Dic5C22⋊C412yes—
219C4⋊Dic5C22⋊C412yes—
220#683—28no—
221C4×Dic5—28no—
222C4×Dic5—22no—
223C4×Dic5—22no—
224#681—22no—
225#681—22no—
226#681—22no—
227#681—22no—
228#681—41no—
229#681—41no—
230#681—41no—
231#681—41no—
232C2×#168—22no—
233C2×#168—22no—
234C2×#168—41no—
235C2×#168—41no—
236C2×#168—41no—
237C2×#168—41no—
238C22×#41—51no—
239C22×M16—51no—
240C22×M16—51no—
241#520—54no—
242#520—102no—
243#520—102no—
244#520—102no—
245C2×C4×Q8—101no—
246C2×C4×D4—101no—
247C2×C4×D4—102no—
248C2×#117—51no—
249C2×#117—101no—
250C22×C4⋊C4—101no—
251C22×C4⋊C4C2×D511yescharacteristic
252C22×C4⋊C4C2×D511yescharacteristic
253C22×C42C2×D511yescharacteristic
254C2×#104—54no—
255C2×#104—102no—
256C2×#104—102no—
257#417—54no—
258#417—102no—
259C2×#103—101no—
260C2×#102—101no—
261C2×#95—22no—
262#343—102no—
263#340—101no—
264#340—101no—
265#339—102no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—21no—
270C23×C5C2×C22⋊C411yescharacteristic
271C23×C5C4×D411yescharacteristic
272C23×C5C4×D411yescharacteristic
273C23×C5#12011yescharacteristic
274C23×C5#12011yescharacteristic
275C23×C5#12111yescharacteristic
276C23×C5C22⋊Q811yescharacteristic
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—41no—
281C22×D5—41no—
282C22×D5—41no—
283C22×D5—41no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—42no—
289C2×C4×C5—42no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—44no—
295C2×C4×C5—44no—
296C2×C4×C5—42no—
297C2×C4×C5—82no—
298C2×C4×C5—82no—
299C2×C4×C5—81no—
300C2×C4×C5—81no—
301C2×C4×C5C2×C4211yescharacteristic
302C2×C4×C5C2×C22⋊C411yescharacteristic
303C2×C4×C5C2×C22⋊C411yescharacteristic
304C2×C4×C5C2×C22⋊C411yescharacteristic
305C2×C4×C5C2×C22⋊C411yescharacteristic
306C2×C4×C5C2×C4⋊C411yescharacteristic
307C2×C4×C5C2×C4⋊C411yescharacteristic
308C2×C4×C5C2×C4⋊C411yescharacteristic
309C2×C4×C5#11711yescharacteristic
310C2×C4×C5#11711yescharacteristic
311C2×C4×C5C4×D411yescharacteristic
312C2×C4×C5C4×D411yescharacteristic
313C2×C4×C5C4×D411yescharacteristic
314C2×C4×C5C4×D411yescharacteristic
315C2×C4×C5C4×D411yescharacteristic
316C2×C4×C5C4×D411yescharacteristic
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12111yescharacteristic
320C2×C4×C5#12111yescharacteristic
321C2×C4×C5#12111yescharacteristic
322C2×C4×C5C22⋊Q811yescharacteristic
323C2×C4×C5C22⋊Q811yescharacteristic
324C2×C4×C5C22⋊Q811yescharacteristic
325C2×C4×C5#12311yescharacteristic
326C2×C4×C5#12311yescharacteristic
327C2×C4×C5#12311yescharacteristic
328C2×C4×C5#12311yescharacteristic
329C22⋊D5—24no—
330C22⋊D5—24no—
331C22⋊D5—24no—
332C22⋊D5—24no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—41no—
339C2×Dic5—41no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342D20—22no—
343D20—22no—
344D20—22no—
345D20#9514yescomplemented
346C4×D5—24no—
347C4×D5—24no—
348C4×D5—24no—
349C4×D5—24no—
350C4×D5—88no—
351Dic10—22no—
352Dic10—22no—
353Dic10—22no—
354Dic10#9514yescomplemented
355#168—42no—
356#168—42no—
357C2×#41—52no—
358C2×#41—52no—
359C2×#41—52no—
360C2×#41—52no—
361C2×#41—52no—
362C2×#41—52no—
363C2×#41—101no—
364C2×#41—101no—
365C2×#41—101no—
366C2×#41—101no—
367C2×#41—101no—
368C2×#41—101no—
369C22×Q8—51no—
370C22×D4—51no—
371C22×D4—101no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—102no—
375C23×C4—101no—
376C23×C4C22⋊D512yes—
377C23×C4C22×D511yescharacteristic
378C2×M16—52no—
379C2×M16—52no—
380C2×M16—101no—
381C2×M16—101no—
382C2×M16—101no—
383C2×M16—101no—
384C2×M16—101no—
385C2×M16—101no—
386C2×M16—101no—
387C2×M16—101no—
388C2×M16—101no—
389C2×M16—101no—
390C22×C8—101no—
391C22×C8—101no—
392C4×Q8—104no—
393C4×Q8—104no—
394C4×D4—104no—
395C4×D4—104no—
396C4×D4—108no—
397C4×D4—108no—
398#117—52no—
399#117—52no—
400#117—104no—
401#117—104no—
402#117—101no—
403#117—101no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—51no—
414C2×C4⋊C4—51no—
415C2×C4⋊C4—104no—
416C2×C4⋊C4—104no—
417C2×C4⋊C4—102no—
418C2×C4⋊C4C4×D512yes—
419C2×C4⋊C4C4×D512yescomplemented
420C2×C4⋊C4D2012yes—
421C2×C22⋊C4—102no—
422C2×C22⋊C4—101no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—102no—
429C2×C42—101no—
430C2×C42C4×D512yescomplemented
431#104—108no—
432#103—104no—
433#102—104no—
434#95—44no—
435C22×C5—21no—
436C22×C5—21no—
437C22×C5—21no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—21no—
443C22×C5—21no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—21no—
447C22×C5C4×C22⋊C411yescharacteristic
448C22×C5#37911yescharacteristic
449C22×C5#38011yescharacteristic
450C22×C5#38511yescharacteristic
451C22×C5#38511yescharacteristic
452C22×C5#38611yescharacteristic
453C22×C5#38611yescharacteristic
454C22×C5#45311yescharacteristic
455C22×C5#45411yescharacteristic
456C22×C5#45511yescharacteristic
457C22×C5#45611yescharacteristic
458C2×D5—24no—
459C2×D5—42no—
460C2×D5—42no—
461C2×D5—42no—
462C2×D5—42no—
463C2×D5—42no—
464C2×D5—42no—
465C4×C5—44no—
466C4×C5—44no—
467C4×C5—82no—
468C4×C5C2×#9511yescharacteristic
469C4×C5C4×C22⋊C411yescharacteristic
470C4×C5#38011yescharacteristic
471C4×C5#38111yescharacteristic
472C4×C5#38511yescharacteristic
473C4×C5#38511yescharacteristic
474C4×C5#38611yescharacteristic
475C4×C5#38611yescharacteristic
476Dic5—24no—
477Dic5—42no—
478Dic5—42no—
479C24—101no—
480C24C2×C22⋊D511yescharacteristic
481#41—54no—
482#41—54no—
483#41—54no—
484#41—54no—
485#41—102no—
486#41—102no—
487#41—102no—
488#41—102no—
489#41—102no—
490#41—102no—
491#41—102no—
492#41—102no—
493#41—102no—
494#41—102no—
495#41—102no—
496#41—102no—
497C2×Q8—52no—
498C2×Q8—52no—
499C2×Q8—52no—
500C2×Q8—101no—
501C2×Q8—101no—
502C2×Q8—101no—
503C2×D4—52no—
504C2×D4—52no—
505C2×D4—52no—
506C2×D4—102no—
507C2×D4—102no—
508C2×D4—102no—
509C2×D4—102no—
510C2×D4—102no—
511C2×D4—102no—
512C2×D4—101no—
513C2×D4—101no—
514C2×D4—101no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—108no—
532C22×C4—101no—
533C22×C4—102no—
534C22×C4—102no—
535C22×C4—102no—
536C22×C4—102no—
537C22×C4—102no—
538C22×C4—102no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—402no—
542C22×C4—402no—
543C22×C4#68514yes—
544C22×C4C2×C4×D511yescharacteristic
545C22×C4C2×C4×D511yescharacteristic
546C22×C4C2×C4×D511yescharacteristic
547C22×C4C2×D2011yescharacteristic
548C22×C4#70911yescharacteristic
549C22×C4#70911yescharacteristic
550C22×C4D4×D511yescharacteristic
551C22×C4D4×D511yescharacteristic
552C22×C4D4×D511yescharacteristic
553C22×C4D4×D511yescharacteristic
554C22×C4D4×D511yescharacteristic
555C22×C4#71111yescharacteristic
556C22×C4Q8×D511yescharacteristic
557C22×C4#71311yescharacteristic
558M16—102no—
559M16—102no—
560M16—102no—
561M16—102no—
562M16—201no—
563M16—201no—
564M16—201no—
565M16—201no—
566C2×C8—102no—
567C2×C8—102no—
568C2×C8—201no—
569C2×C8—201no—
570C2×C8—201no—
571C2×C8—201no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—52no—
581C4⋊C4—52no—
582C4⋊C4—108no—
583C4⋊C4—101no—
584C4⋊C4—101no—
585C22⋊C4—108no—
586C22⋊C4—102no—
587C22⋊C4—102no—
588C42—22no—
589C42—22no—
590C42—41no—
591C42—41no—
592C42—108no—
593C42—102no—
594C42—102no—
595C2×C5—21no—
596C2×C5—21no—
597C2×C5—21no—
598C2×C5—21no—
599C2×C5C22⋊#9511yescharacteristic
600C2×C5#179211yescharacteristic
601C2×C5#179311yescharacteristic
602C2×C5#185911yescharacteristic
603C2×C5#186011yescharacteristic
604C2×C5#188211yescharacteristic
605C2×C5#188311yescharacteristic
606D5—44no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—102no—
612C23—102no—
613C23—102no—
614C23—201no—
615C23—201no—
616C23—201no—
617C23—201no—
618C23C2×#68511yescharacteristic
619C23C4×C22⋊D511yescharacteristic
620C23C4×C22⋊D511yescharacteristic
621C23#408311yescharacteristic
622C23#408311yescharacteristic
623C23#408411yescharacteristic
624C23#409211yescharacteristic
625Q8—54no—
626Q8—102no—
627Q8—102no—
628Q8—102no—
629D4—54no—
630D4—104no—
631D4—104no—
632D4—104no—
633D4—104no—
634D4—102no—
635D4—102no—
636D4—102no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—104no—
658C2×C4—104no—
659C2×C4—104no—
660C2×C4—104no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—201no—
664C2×C4—201no—
665C2×C4—201no—
666C2×C4—201no—
667C2×C4—408no—
668C2×C4C42×D511yescharacteristic
669C2×C4#401811yescharacteristic
670C2×C4C4×D2011yescharacteristic
671C2×C4C4×D2011yescharacteristic
672C2×C4D5×C22⋊C411yescharacteristic
673C2×C4D5×C22⋊C411yescharacteristic
674C2×C4D5×C22⋊C411yescharacteristic
675C2×C4D5×C22⋊C411yescharacteristic
676C2×C4#402711yescharacteristic
677C2×C4#402711yescharacteristic
678C2×C4#402811yescharacteristic
679C2×C4#402811yescharacteristic
680C2×C4#402911yescharacteristic
681C2×C4#402911yescharacteristic
682C2×C4#403011yescharacteristic
683C2×C4#403011yescharacteristic
684C2×C4D5×C4⋊C411yescharacteristic
685C2×C4D5×C4⋊C411yescharacteristic
686C2×C4D5×C4⋊C411yescharacteristic
687C2×C4#403811yescharacteristic
688C2×C4#403911yescharacteristic
689C2×C4#403911yescharacteristic
690C2×C4#404011yescharacteristic
691C2×C4#404011yescharacteristic
692C2×C4#404111yescharacteristic
693C2×C4#404211yescharacteristic
694C2×C4#404211yescharacteristic
695C2×C4#404311yescharacteristic
696C8—202no—
697C8—202no—
698C5#1078111yescharacteristic, complemented, Sylow
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—104no—
712C22—202no—
713C22—202no—
714C22—202no—
715C22—202no—
716C22—202no—
717C22—202no—
718C22C4×#68511yescharacteristic
719C22#6524411yescharacteristic
720C22#6524511yescharacteristic
721C22#6524511yescharacteristic
722C22#6527611yescharacteristic
723C22#6527811yescharacteristic
724C22#6527811yescharacteristic
725C22#6535011yescharacteristic
726C22#6535111yescharacteristic
727C22#6536611yescharacteristic
728C22#6538411yescharacteristic
729C4—44no—
730C4—44no—
731C4—82no—
732C4—104no—
733C4—202no—
734C4—202no—
735C4D5×#9511yescharacteristic
736C4#6495311yescharacteristic
737C4#6495411yescharacteristic
738C4#6495411yescharacteristic
739C4#6495511yescharacteristic
740C4#6495611yescharacteristic
741C4#6495711yescharacteristic
742C4#6495711yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—204no—
748C2#1060021811yescharacteristic
749C2#1060035511yescharacteristic
750C2#1060038511yescharacteristic
751C2#1060045511yescharacteristic
752C2#1060045611yescharacteristic
753C2#1060048511yescharacteristic
754C2#1060048611yescharacteristic
subgroupG/H
centerC23#4083
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC5×C4⋊#95C2
socleC23×C5#120
prime radicalC22×#709C22
cosocleC23×C4×C5C23
hypercenterC4⋊#95D5
hypocenterC5#10781
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C5×C4⋊#95C2semidirect
5. C2×#64750C2semidirect
6. #10602351C2semidirect
7. C2×#64743C2semidirect
19. #65838C4semidirect
27. #65255C4semidirect
31. C2×#3937C4semidirect
68. C2×C5×C4⋊C4C2×C4semidirect
75. C2×C42×C5C2×C4semidirect
99. C2×#681C2×C4semidirect
100. C2×#681C2×C4semidirect
121. C4⋊#95D5semidirect
345. D20#95semidirect
354. Dic10#95semidirect
419. C2×C4⋊C4C4×D5semidirect
430. C2×C42C4×D5semidirect
698. C5#10781semidirect

Maximal subgroups

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

subgroupindex
C2×#658382
C2×#652552
C22×#39372
C5×C4⋊#952
C2×#647502
#106023512
C2×#647432
#107815