Finite Group Databasebeta

← #12020767

Subgroups — #12020767

Order 1280.

3562 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C22×#4027C212yesmaximal
3C22×#3963C211yesmaximal, characteristic, complemented
4C2×D5×#95C211yesmaximal, characteristic, complemented
5C5×C22⋊#95C211yesmaximal, characteristic, complemented
6#10602337C212yesmaximal, complemented
7#10600218C211yesmaximal, characteristic, complemented
8#10600218C212yesmaximal, complemented
9#10600197C211yesmaximal, characteristic, complemented
10#10600197C212yesmaximal, complemented
11Dic5×#95C211yesmaximal, characteristic, complemented
12C24×C4×C5C2211yescharacteristic
13C23×C22⋊D5C2211yescharacteristic
14C24×Dic5C2212yes—
15C23×C4×D5C2212yes—
16C23×C4×D5C2211yescharacteristic
17C22×C5×C22⋊C4C2212yes—
18C22×C22⋊Dic5C2211yescharacteristic
19C2×C4×C22⋊D5—28no—
20C2×C4×C22⋊D5C418yescomplemented
21C22×#685C2212yes—
22C22×#685C2211yescharacteristic
23C22×#683C2212yes—
24C22×#683C2211yescharacteristic
25C22×C4×Dic5C2212yes—
26C22×C4×Dic5C2211yescharacteristic
27C2×#4027—28no—
28C2×#4027—28no—
29C2×#4027C4116yescomplemented
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2212yes—
33C2×#3963—24no—
34C2×#3963C2212yes—
35C2×#3963C2211yescharacteristic
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C2×#3963C2211yescharacteristic
41D5×#95—24no—
42D4×#95—51nomaximal, Sylow
43C25×C5C2311yescharacteristic
44C24×D5C2311yescharacteristic
45C23×C4×C5—24no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—42no—
49C23×C4×C5C2×C414yescomplemented
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2312yes—
53C23×C4×C5C2311yescharacteristic
54C22×C22⋊D5C2×C418yes—
55C22×C22⋊D5C2×C414yes—
56C22×C22⋊D5D414yes—
57C22×C22⋊D5D418yes—
58C22×C22⋊D5Q814yes—
59C23×Dic5—24no—
60C23×Dic5—24no—
61C23×Dic5—24no—
62C23×Dic5—24no—
63C23×Dic5—42no—
64C23×Dic5—42no—
65C23×Dic5C2×C418yescomplemented
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2312yes—
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2312yes—
70C23×Dic5C2311yescharacteristic
71C22×C4×D5—24no—
72C22×C4×D5—24no—
73C22×C4×D5—24no—
74C22×C4×D5—22no—
75C22×C4×D5—22no—
76C22×C4×D5—24no—
77C22×C4×D5—24no—
78C22×C4×D5—42no—
79C22×C4×D5—42no—
80C22×C4×D5—42no—
81C22×C4×D5C2×C418yescomplemented
82C22×C4×D5C2×C414yescomplemented
83C2×C5×C22⋊C4—24no—
84C2×C5×C22⋊C4—24no—
85C2×C5×C22⋊C4C2×C418yescomplemented
86C2×C22⋊Dic5—24no—
87C2×C22⋊Dic5C2×C414yescomplemented
88C4×C22⋊D5—232no—
89C2×#685—24no—
90C2×#685—24no—
91C2×#685—24no—
92C2×#685C2×C418yescomplemented
93C2×#685C2×C414yescomplemented
94C2×#683—24no—
95C2×#683—24no—
96C2×#683—24no—
97C2×#683C2×C418yescomplemented
98C2×#683C2×C414yescomplemented
99C2×C4×Dic5—24no—
100C2×C4×Dic5—24no—
101C2×C4×Dic5—24no—
102C2×C4×Dic5C2×C418yescomplemented
103C2×C4×Dic5C2×C414yescomplemented
104#4027—264no—
105C5×#95—22no—
106C5×#95—22no—
107C5×#95—42no—
108#3963—22no—
109#3963—24no—
110#3963—24no—
111#3963—24no—
112#3963—42no—
113#3963—42no—
114#3963D414yescomplemented
115C22×C4×D4—51no—
116C22×C4×D4—52no—
117C22×#95—51no—
118C22×#95—51no—
119C4⋊#95—52no—
120C4⋊#95—51no—
121C22⋊#95—52no—
122C22⋊#95—51no—
123C22⋊#95—52no—
124C22⋊#95D511yescharacteristic, complemented
125C4×#95—51no—
126C24×C5—21no—
127C24×C5—22no—
128C24×C5—21no—
129C24×C5—21no—
130C24×C5—22no—
131C24×C5—21no—
132C24×C5C22×C412yes—
133C24×C5C22×C414yes—
134C24×C5C2×D414yes—
135C24×C5C2×D412yes—
136C24×C5C2×Q812yes—
137C24×C5C2411yescharacteristic
138C23×D5—21no—
139C23×D5—21no—
140C23×D5—22no—
141C23×D5—22no—
142C23×D5—21no—
143C23×D5—21no—
144C23×D5C22×C414yes—
145C23×D5C22×C412yes—
146C23×D5C2×D412yes—
147C23×D5C2×D414yes—
148C23×D5C2×Q812yes—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—28no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—28no—
169C22×C4×C5—44no—
170C22×C4×C5—48no—
171C22×C4×C5—48no—
172C22×C4×C5C22×C414yes—
173C22×C4×C5C22×C414yes—
174C22×C4×C5C22×C412yes—
175C22×C4×C5C22×C412yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5#4112yes—
178C2×C22⋊D5C42116yes—
179C2×C22⋊D5C22⋊C4132yes—
180C2×C22⋊D5C22⋊C4116yes—
181C2×C22⋊D5C4⋊C4132yes—
182C2×C22⋊D5C4⋊C4116yes—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—216no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—21no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—21no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—216no—
203C22×Dic5—48no—
204C22×Dic5—48no—
205C22×Dic5—48no—
206C22×Dic5—48no—
207C22×Dic5—48no—
208C22×Dic5C22×C412yes—
209C22×Dic5C22×C412yes—
210C22×Dic5C22×C414yes—
211C22×Dic5C22×C414yes—
212C22×Dic5C22×C414yes—
213C22×Dic5C22×C412yes—
214C22×Dic5C2×D414yes—
215C22×Dic5C2×D412yes—
216C22×Dic5C2×D414yes—
217C22×Dic5C2×Q812yes—
218C22×Dic5#4114yes—
219C2×C4×D5—216no—
220C2×C4×D5—28no—
221C2×C4×D5—28no—
222C2×C4×D5—216no—
223C2×C4×D5—48no—
224C2×C4×D5—44no—
225C2×C4×D5—48no—
226C2×C4×D5—48no—
227C2×C4×D5—48no—
228C2×C4×D5—48no—
229C2×C4×D5—48no—
230C2×C4×D5—48no—
231C5×C22⋊C4—216no—
232C22⋊Dic5—28no—
233#685—216no—
234#685—28no—
235#683—216no—
236#683—28no—
237C4×Dic5—216no—
238C4×Dic5—28no—
239C23×D4—51no—
240C24×C4—52no—
241C24×C4—52no—
242C24×C4—51no—
243C24×C4C2×D511yescharacteristic
244C2×C4×D4—58no—
245C2×C4×D4—516no—
246C2×C4×D4—108no—
247C2×C4×D4—108no—
248C2×C4×D4—108no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—52no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—51no—
253C22×C22⋊C4—52no—
254C22×C22⋊C4C2×D512yes—
255C22×C42—52no—
256C22×C42—51no—
257C2×#95—51no—
258C2×#95—52no—
259C2×#95—52no—
260C2×#95—52no—
261C2×#95—51no—
262C2×#95—52no—
263C2×#95—52no—
264C2×#95—104no—
265C2×#95—104no—
266C2×#95C2×D511yescharacteristic
267C2×#95C2×D511yescharacteristic
268C2×#95C2×D512yes—
269C23×C5—24no—
270C23×C5—22no—
271C23×C5—22no—
272C23×C5—24no—
273C23×C5—24no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—24no—
277C23×C5—22no—
278C23×C5—24no—
279C23×C5—24no—
280C23×C5—24no—
281C23×C5—24no—
282C23×C5—22no—
283C23×C5—24no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—24no—
287C23×C5C2×C4214yes—
288C23×C5C2×C22⋊C414yes—
289C23×C5C2×C22⋊C418yes—
290C23×C5C2×C4⋊C414yes—
291C23×C5C2×C4⋊C418yes—
292C23×C5C23×C411yescharacteristic
293C23×C5C23×C412yes—
294C23×C5C22×D412yes—
295C23×C5C22×D411yescharacteristic
296C23×C5C22×D411yescharacteristic
297C23×C5C22×Q811yescharacteristic
298C23×C5C2×#4111yescharacteristic
299C23×C5C2×#4112yes—
300C23×C5H(5,𝔽2)12yes—
301C23×C5H(5,𝔽2)11yescharacteristic
302C23×C52−1+411yescharacteristic
303C22×D5—22no—
304C22×D5—24no—
305C22×D5—22no—
306C22×D5—24no—
307C22×D5—22no—
308C22×D5—24no—
309C22×D5—22no—
310C22×D5—24no—
311C22×D5—24no—
312C22×D5—22no—
313C22×D5—24no—
314C22×D5—24no—
315C22×D5—24no—
316C22×D5—22no—
317C22×D5—24no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—24no—
321C22×D5C2×C4214yes—
322C22×D5C2×C22⋊C418yes—
323C22×D5C2×C22⋊C414yes—
324C22×D5C2×C4⋊C418yes—
325C22×D5C2×C4⋊C414yes—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—24no—
329C2×C4×C5—24no—
330C2×C4×C5—24no—
331C2×C4×C5—22no—
332C2×C4×C5—24no—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—24no—
336C2×C4×C5—24no—
337C2×C4×C5—22no—
338C2×C4×C5—24no—
339C2×C4×C5—416no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—42no—
347C2×C4×C5—42no—
348C2×C4×C5—42no—
349C2×C4×C5—42no—
350C2×C4×C5C4×D414yescomplemented
351C22⋊D5#95164yescomplemented
352C2×Dic5—24no—
353C2×Dic5—24no—
354C2×Dic5—24no—
355C2×Dic5—24no—
356C2×Dic5—24no—
357C2×Dic5—24no—
358C2×Dic5—22no—
359C2×Dic5—24no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—24no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—432no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5C2×C4214yes—
377C2×Dic5C2×C22⋊C418yes—
378C2×Dic5C2×C22⋊C414yes—
379C2×Dic5C2×C4⋊C418yes—
380C2×Dic5C2×C4⋊C414yes—
381C2×Dic5C4×D418yescomplemented
382C4×D5—432no—
383C4×D5—416no—
384C25—51no—
385C25C22×D511yescharacteristic
386C22×D4—54no—
387C22×D4—58no—
388C22×D4—54no—
389C22×D4—58no—
390C22×D4—54no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—42no—
395C23×C4—51no—
396C23×C4—52no—
397C23×C4—51no—
398C23×C4—51no—
399C23×C4—52no—
400C23×C4—58no—
401C23×C4—58no—
402C23×C4—54no—
403C23×C4—104no—
404C23×C4—104no—
405C23×C4—104no—
406C23×C4—104no—
407C23×C4—104no—
408C23×C4—104no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4—102no—
413C23×C4—102no—
414C23×C4—202no—
415C23×C4—202no—
416C23×C4—202no—
417C23×C4—202no—
418C23×C4—202no—
419C23×C4C4×D514yescomplemented
420C23×C4C22×D512yes—
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D512yes—
423C23×C4C22×D511yescharacteristic
424C4×D4—1064no—
425C4×D4—1032no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—58no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—54no—
434C2×C22⋊C4—54no—
435C2×C22⋊C4—58no—
436C2×C22⋊C4—104no—
437C2×C22⋊C4—104no—
438C2×C22⋊C4—104no—
439C2×C22⋊C4—104no—
440C2×C22⋊C4C4×D518yescomplemented
441C2×C42—58no—
442C2×C42—54no—
443C2×C42—104no—
444C2×C42—104no—
445C2×C42—104no—
446#95—22no—
447#95—22no—
448#95—42no—
449#95—54no—
450#95—104no—
451#95—104no—
452#95—104no—
453#95—102no—
454#95—202no—
455#95—202no—
456C22×C5—28no—
457C22×C5—24no—
458C22×C5—24no—
459C22×C5—28no—
460C22×C5—28no—
461C22×C5—24no—
462C22×C5—28no—
463C22×C5—24no—
464C22×C5—24no—
465C22×C5—24no—
466C22×C5C2×#9518yescomplemented
467C22×C5C22×C4211yescharacteristic
468C22×C5C22×C22⋊C411yescharacteristic
469C22×C5C22×C22⋊C412yes—
470C22×C5C22×C4⋊C412yes—
471C22×C5C22×C4⋊C411yescharacteristic
472C22×C5C2×C4×D411yescharacteristic
473C22×C5C2×C4×D412yes—
474C22×C5C4×#4111yescharacteristic
475C22×C5C4×#4112yes—
476C22×C5#51811yescharacteristic
477C22×C5#51812yes—
478C22×C5#52011yescharacteristic
479C22×C5#52012yes—
480C22×C5D4212yes—
481C22×C5D4211yescharacteristic
482C22×C5#54612yes—
483C22×C5#54612yes—
484C22×C5#54612yes—
485C22×C5#54711yescharacteristic
486C22×C5#54712yes—
487C22×C5D4×Q811yescharacteristic
488C22×C5#55411yescharacteristic
489C22×C5#55412yes—
490C2×D5—24no—
491C2×D5—28no—
492C2×D5—24no—
493C2×D5—28no—
494C2×D5—28no—
495C2×D5—24no—
496C2×D5—28no—
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—24no—
500C2×D5C2×#9518yescomplemented
501C4×C5—24no—
502C4×C5—44no—
503C4×C5—42no—
504C4×C5—44no—
505Dic5—28no—
506Dic5—42no—
507Dic5—44no—
508Dic5—42no—
509Dic5C2×#9518yescomplemented
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—21no—
516C24—52no—
517C24—54no—
518C24—54no—
519C24—52no—
520C24—52no—
521C24—101no—
522C24—101no—
523C24—102no—
524C24—102no—
525C24—101no—
526C24—101no—
527C24C2×C4×D512yes—
528C24C2×C4×D514yes—
529C24D4×D512yes—
530C24D4×D514yes—
531C24Q8×D512yes—
532C24C23×D511yescharacteristic
533C2×D4—516no—
534C2×D4—532no—
535C2×D4—516no—
536C2×D4—532no—
537C2×D4—516no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—52no—
562C22×C4—54no—
563C22×C4—54no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—54no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—54no—
572C22×C4—1016no—
573C22×C4—108no—
574C22×C4—1016no—
575C22×C4—1016no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—101no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—101no—
592C22×C4—102no—
593C22×C4—101no—
594C22×C4—1016no—
595C22×C4—108no—
596C22×C4—204no—
597C22×C4—208no—
598C22×C4—208no—
599C22×C4—208no—
600C22×C4—208no—
601C22×C4—208no—
602C22×C4—208no—
603C22×C4—208no—
604C22×C4—208no—
605C22×C4—208no—
606C22×C4—208no—
607C22×C4—208no—
608C22×C4—208no—
609C22×C4C2×C4×D514yes—
610C22×C4C2×C4×D512yes—
611C22×C4C2×C4×D514yes—
612C22×C4C2×C4×D512yes—
613C22×C4D4×D512yes—
614C22×C4#71112yes—
615C4⋊C4—1016no—
616C4⋊C4—108no—
617C22⋊C4—216no—
618C22⋊C4—1016no—
619C22⋊C4—108no—
620C22⋊C4—108no—
621C42—108no—
622C42—1016no—
623C2×C5—28no—
624C2×C5C22×#9511yescharacteristic
625C2×C5C42×D411yescharacteristic
626C2×C5#227511yescharacteristic
627C2×C5D4×C22⋊C411yescharacteristic
628C2×C5D4×C22⋊C412yes—
629C2×C5#233911yescharacteristic
630C2×C5#233912yes—
631C2×C5D4×C4⋊C412yes—
632C2×C5D4×C4⋊C411yescharacteristic
633C2×C5#234912yes—
634C2×C5#234911yescharacteristic
635D5—28no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—54no—
655C23—54no—
656C23—58no—
657C23—58no—
658C23—54no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—104no—
664C23—104no—
665C23—104no—
666C23—104no—
667C23—104no—
668C23—104no—
669C23—102no—
670C23—104no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—104no—
675C23—104no—
676C23—104no—
677C23C42×D514yes—
678C23D5×C22⋊C418yes—
679C23D5×C22⋊C414yes—
680C23D5×C4⋊C418yes—
681C23D5×C4⋊C414yes—
682C23C22×C4×D511yescharacteristic
683C23C22×C4×D512yes—
684C23C2×D4×D512yes—
685C23C2×D4×D511yescharacteristic
686C23C2×D4×D511yescharacteristic
687C23C2×#71111yescharacteristic
688C23#414412yes—
689C23C2×Q8×D511yescharacteristic
690C23D5×#4112yes—
691C23#414911yescharacteristic
692C23#415011yescharacteristic
693D4—564no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—416no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—58no—
721C2×C4—58no—
722C2×C4—54no—
723C2×C4—58no—
724C2×C4—104no—
725C2×C4—104no—
726C2×C4—104no—
727C2×C4—104no—
728C2×C4—104no—
729C2×C4—104no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—104no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—104no—
738C2×C4—104no—
739C2×C4—2016no—
740C2×C4—2032no—
741C2×C4—2032no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—202no—
748C2×C4—202no—
749C2×C4—202no—
750C2×C4#402714yescomplemented
751C5D4×#9511yescharacteristic, complemented, Sylow
752C22—24no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—28no—
757C22—28no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—58no—
763C22—104no—
764C22—108no—
765C22—104no—
766C22—108no—
767C22—108no—
768C22—108no—
769C22—104no—
770C22—104no—
771C22—104no—
772C22—104no—
773C22D5×#9518yescomplemented
774C22C2×C42×D511yescharacteristic
775C22C2×D5×C22⋊C411yescharacteristic
776C22C2×D5×C22⋊C412yes—
777C22C2×#402711yescharacteristic
778C22#6582011yescharacteristic
779C22C2×D5×C4⋊C412yes—
780C22C2×D5×C4⋊C411yescharacteristic
781C22#6585611yescharacteristic
782C22#6585711yescharacteristic
783C22C4×#71112yes—
784C22C4×D4×D512yes—
785C22#6587912yes—
786C22#6588012yes—
787C22#6592412yes—
788C22#6592512yes—
789C22#6594311yescharacteristic
790C22#6594412yes—
791C22#6594511yescharacteristic
792C22#6596611yescharacteristic
793C22#6596911yescharacteristic
794C22#6597012yes—
795C22#6598812yes—
796C22#6598912yes—
797C4—24no—
798C4—42no—
799C4—44no—
800C4—44no—
801C4—58no—
802C4—108no—
803C4—202no—
804C4—204no—
805C4—202no—
806C2—28no—
807C2—108no—
808C2C2×D5×#9511yescharacteristic
809C2C4×#402711yescharacteristic
810C2#1060516711yescharacteristic
811C2#1060558111yescharacteristic
812C2#1060574111yescharacteristic
813C2#1060574211yescharacteristic
814C2#1060585211yescharacteristic
815C2#1060612412yes—
816C2#1060612512yes—
817C2#1060640312yes—
818C2#1060660912yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22⋊#95D5
hypocenterC5D4×#95
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C22×#3963C2semidirect
4. C2×D5×#95C2semidirect
5. C5×C22⋊#95C2semidirect
6. #10602337C2semidirect
7. #10600218C2semidirect
8. #10600218C2semidirect
9. #10600197C2semidirect
10. #10600197C2semidirect
11. Dic5×#95C2semidirect
20. C2×C4×C22⋊D5C4semidirect
29. C2×#4027C4semidirect
49. C23×C4×C5C2×C4semidirect
65. C23×Dic5C2×C4semidirect
81. C22×C4×D5C2×C4semidirect
82. C22×C4×D5C2×C4semidirect
85. C2×C5×C22⋊C4C2×C4semidirect
87. C2×C22⋊Dic5C2×C4semidirect
92. C2×#685C2×C4semidirect
93. C2×#685C2×C4semidirect
97. C2×#683C2×C4semidirect
98. C2×#683C2×C4semidirect
102. C2×C4×Dic5C2×C4semidirect
103. C2×C4×Dic5C2×C4semidirect
114. #3963D4semidirect
124. C22⋊#95D5semidirect
350. C2×C4×C5C4×D4semidirect
351. C22⋊D5#95semidirect
381. C2×Dic5C4×D4semidirect
419. C23×C4C4×D5semidirect
440. C2×C22⋊C4C4×D5semidirect
466. C22×C5C2×#95semidirect
500. C2×D5C2×#95semidirect
509. Dic5C2×#95semidirect
750. C2×C4#4027semidirect
751. C5D4×#95semidirect
773. C22D5×#95semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40272
C22×#39632
C2×D5×#952
C5×C22⋊#952
#106023372
#106002182
#106001972
Dic5×#952
D4×#955