Finite Group Databasebeta

← #12020599

Subgroups — #12020599

Order 1280.

2686 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4027C211yesmaximal, characteristic
2C2×#65502C211yesmaximal, characteristic
3C22×#3963C211yesmaximal, characteristic, complemented
4C2×#65247C211yesmaximal, characteristic
5C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
6C5×C22⋊#95C211yesmaximal, characteristic, complemented
7#10602337C211yesmaximal, characteristic, complemented
8#10600218C212yesmaximal, complemented
9#10600201C212yesmaximal, complemented
10#10600199C212yesmaximal, complemented
11#10600196C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C23×C22⋊D5C2211yescharacteristic
14C24×Dic5C2211yescharacteristic
15C24×Dic5C2211yescharacteristic
16C23×C4×D5C2211yescharacteristic
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic5C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×#683C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2212yes—
26C2×#4027—24no—
27C2×#4027—24no—
28C2×#4027C418yescomplemented
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31#65502C418yescomplemented
32C2×#3963—24no—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40#65247C418yescomplemented
41C22⋊C4×Dic5—24no—
42#13784—51nomaximal, Sylow
43C25×C5C2311yescharacteristic
44C24×D5C2311yescharacteristic
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—42no—
48C23×C4×C5—42no—
49C23×C4×C5C2×C414yescomplemented
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2312yes—
54C22×C22⋊D5—22no—
55C22×C22⋊D5—22no—
56C22×C22⋊D5—22no—
57C22×C22⋊D5—22no—
58C22×C22⋊D5C2×C414yes—
59C22×C22⋊D5C2×C414yes—
60C22×C22⋊D5C2×C414yes—
61C23×Dic5—22no—
62C23×Dic5—22no—
63C23×Dic5—42no—
64C23×Dic5—42no—
65C23×Dic5—42no—
66C23×Dic5—42no—
67C23×Dic5C2×C414yes—
68C23×Dic5C2×C414yescomplemented
69C23×Dic5D414yes—
70C23×Dic5D414yes—
71C23×Dic5C2312yes—
72C23×Dic5C2312yes—
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C22×C4×D5—22no—
77C22×C4×D5—22no—
78C22×C4×D5—42no—
79C22×C4×D5—42no—
80C22×C4×D5C2×C414yescomplemented
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4C2×C414yes—
86C2×C5×C22⋊C4C2×C414yescomplemented
87C2×C22⋊Dic5—22no—
88C2×C22⋊Dic5—22no—
89C2×C22⋊Dic5C2×C414yescomplemented
90C2×#685—22no—
91C2×#685—22no—
92C2×#685—42no—
93C2×#685—42no—
94C2×#685—42no—
95C2×#685—42no—
96C2×#685C2×C414yescomplemented
97C2×#685C2×C418yescomplemented
98C2×#685C2×C418yescomplemented
99C2×#683—22no—
100C2×#683—22no—
101C2×#683C2×C414yescomplemented
102C2×C4×Dic5—22no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—24no—
105C2×C4×Dic5—42no—
106C2×C4×Dic5—42no—
107C2×C4×Dic5C2×C414yescomplemented
108#4027—232no—
109C5×#95—42no—
110C5×#95—42no—
111#3963—24no—
112#3963—24no—
113#3963—24no—
114#3963—42no—
115#3963—42no—
116#3963C2×C418yescomplemented
117#3963C2×C418yescomplemented
118C22×C4×D4—51no—
119C2×#386—51no—
120C2×#386—51no—
121C2×C4×C22⋊C4—51no—
122C22×#95—51no—
123#1437—52no—
124#1436—52no—
125#1434—52no—
126C22⋊#95—52no—
127C22⋊#95—51no—
128C22⋊#95D511yescharacteristic, complemented
129C24×C5—22no—
130C24×C5—22no—
131C24×C5—22no—
132C24×C5—22no—
133C24×C5C22×C412yes—
134C24×C5C22×C412yes—
135C24×C5C22×C412yes—
136C24×C5C2×D412yes—
137C24×C5C2×D412yes—
138C24×C5#4112yes—
139C24×C5#4112yes—
140C24×C5C2411yescharacteristic
141C23×D5—21no—
142C23×D5—21no—
143C23×D5—21no—
144C23×D5—21no—
145C23×D5—22no—
146C23×D5—22no—
147C23×D5—22no—
148C23×D5—22no—
149C23×D5C22×C412yes—
150C23×D5C22×C412yes—
151C23×D5C22×C412yes—
152C22×C4×C5—28no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
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—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—48no—
174C22×C4×C5—44no—
175C22×C4×C5—44no—
176C22×C4×C5—48no—
177C22×C4×C5C22×C412yes—
178C22×C4×C5C22×C412yes—
179C22×C4×C5C22×C414yes—
180C22×C4×C5C22×C414yes—
181C2×C22⋊D5—28no—
182C2×C22⋊D5—28no—
183C2×C22⋊D5—28no—
184C2×C22⋊D5—28no—
185C2×C22⋊D5—28no—
186C2×C22⋊D5—28no—
187C2×C22⋊D5C42116yescomplemented
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—28no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—48no—
210C22×Dic5—48no—
211C22×Dic5—48no—
212C22×Dic5—44no—
213C22×Dic5—44no—
214C22×Dic5—44no—
215C22×Dic5—44no—
216C22×Dic5—48no—
217C22×Dic5C22⋊C4116yescomplemented
218C22×Dic5C22×C414yes—
219C22×Dic5C22×C414yes—
220C22×Dic5C22×C412yes—
221C22×Dic5C22×C412yes—
222C22×Dic5C22×C412yes—
223C22×Dic5C22×C412yes—
224C22×Dic5C22×C412yes—
225C22×Dic5C2×D412yes—
226C22×Dic5C2×D412yes—
227C22×Dic5C2×D412yes—
228C22×Dic5C2×D412yes—
229C2×C4×D5—28no—
230C2×C4×D5—48no—
231C2×C4×D5—44no—
232C2×C4×D5—48no—
233C2×C4×D5—44no—
234C5×C22⋊C4—28no—
235C5×C22⋊C4—28no—
236C22⋊Dic5—28no—
237#685—28no—
238#685—48no—
239#685—48no—
240#683—28no—
241C4×Dic5—28no—
242C4×Dic5—48no—
243C23×D4—51no—
244C24×C4—51no—
245C24×C4—51no—
246C24×C4—51no—
247C24×C4C2×D511yescharacteristic
248C2×C4×D4—58no—
249C2×C4×D4—104no—
250C2×C4×D4—104no—
251C22×C4⋊C4—51no—
252C22×C22⋊C4—51no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—52no—
255C22×C22⋊C4—52no—
256C22×C22⋊C4C2×D511yescharacteristic
257C22×C22⋊C4C2×D511yescharacteristic
258C22×C42—51no—
259C22×C42—52no—
260#386—58no—
261#386—58no—
262C4×C22⋊C4—104no—
263C2×#95—52no—
264C2×#95—52no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95—52no—
268C2×#95—52no—
269C2×#95—52no—
270C2×#95—104no—
271C2×#95C2×D512yes—
272C2×#95C2×D512yes—
273C23×C5—24no—
274C23×C5—24no—
275C23×C5—24no—
276C23×C5—24no—
277C23×C5—24no—
278C23×C5—24no—
279C23×C5—22no—
280C23×C5—22no—
281C23×C5—24no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5—24no—
285C23×C5—24no—
286C23×C5—24no—
287C23×C5—24no—
288C23×C5—24no—
289C23×C5C2×C4214yes—
290C23×C5C2×C22⋊C414yes—
291C23×C5#11714yes—
292C23×C5C4×D414yes—
293C23×C5C4×D414yes—
294C23×C5C4×D414yes—
295C23×C5C4×D414yes—
296C23×C5C23×C411yescharacteristic
297C23×C5C23×C411yescharacteristic
298C23×C5C23×C411yescharacteristic
299C23×C5C22×D411yescharacteristic
300C23×C5C22×D411yescharacteristic
301C23×C5C2×#4111yescharacteristic
302C23×C5C2×#4111yescharacteristic
303C23×C5H(5,𝔽2)12yes—
304C23×C5H(5,𝔽2)12yes—
305C23×C5H(5,𝔽2)12yes—
306C23×C52−1+412yes—
307C22×D5—22no—
308C22×D5—22no—
309C22×D5—22no—
310C22×D5—22no—
311C22×D5—22no—
312C22×D5—22no—
313C22×D5—24no—
314C22×D5—24no—
315C22×D5—24no—
316C22×D5—24no—
317C22×D5—24no—
318C22×D5—24no—
319C22×D5—41no—
320C22×D5—42no—
321C22×D5—41no—
322C22×D5—41no—
323C22×D5—41no—
324C22×D5—42no—
325C22×D5—42no—
326C22×D5—42no—
327C22×D5—42no—
328C22×D5—42no—
329C22×D5C2×C4214yes—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—24no—
333C2×C4×C5—24no—
334C2×C4×C5—24no—
335C2×C4×C5—24no—
336C2×C4×C5—24no—
337C2×C4×C5—24no—
338C2×C4×C5—24no—
339C2×C4×C5—24no—
340C2×C4×C5—416no—
341C2×C4×C5—42no—
342C2×C4×C5—41no—
343C2×C4×C5—42no—
344C2×C4×C5—41no—
345C2×C4×C5—42no—
346C2×C4×C5—41no—
347C2×C4×C5—42no—
348C2×C4×C5—41no—
349C2×C4×C5—42no—
350C2×C4×C5—42no—
351C2×C4×C5—42no—
352C2×C4×C5—42no—
353C2×C4×C5—42no—
354C2×C4×C5—42no—
355C22⋊D5—232no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—24no—
363C2×Dic5—24no—
364C2×Dic5—24no—
365C2×Dic5—22no—
366C2×Dic5—24no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—24no—
371C2×Dic5—24no—
372C2×Dic5—24no—
373C2×Dic5—24no—
374C2×Dic5—24no—
375C2×Dic5—24no—
376C2×Dic5—416no—
377C2×Dic5—416no—
378C2×Dic5—42no—
379C2×Dic5—42no—
380C2×Dic5—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5C2×C4214yes—
387C2×Dic5C2×C22⋊C414yes—
388C2×Dic5C2×C22⋊C414yes—
389C4×D5—416no—
390C25—51no—
391C25C22×D511yescharacteristic
392C22×D4—54no—
393C22×D4—54no—
394C22×D4—54no—
395C22×D4—102no—
396C22×D4—102no—
397C22×D4—102no—
398C22×D4—102no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—54no—
407C23×C4—54no—
408C23×C4—54no—
409C23×C4—52no—
410C23×C4—52no—
411C23×C4—54no—
412C23×C4—54no—
413C23×C4—102no—
414C23×C4—102no—
415C23×C4—102no—
416C23×C4—102no—
417C23×C4—202no—
418C23×C4—202no—
419C23×C4—202no—
420C23×C4—202no—
421C23×C4—202no—
422C23×C4—202no—
423C23×C4C4×D514yescomplemented
424C23×C4C22×D512yes—
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D512yes—
427C23×C4C22×D511yescharacteristic
428C4×D4—1032no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—102no—
431C2×C4⋊C4—102no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—54no—
437C2×C22⋊C4—54no—
438C2×C22⋊C4—58no—
439C2×C22⋊C4—58no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—102no—
442C2×C22⋊C4—102no—
443C2×C22⋊C4—102no—
444C2×C22⋊C4—202no—
445C2×C22⋊C4—202no—
446C2×C22⋊C4—202no—
447C2×C22⋊C4—202no—
448C2×C22⋊C4C4×D514yes—
449C2×C22⋊C4C4×D514yescomplemented
450C2×C42—54no—
451C2×C42—102no—
452C2×C42—102no—
453C2×C42—104no—
454C2×C42—202no—
455C2×C42—202no—
456#95—42no—
457#95—42no—
458#95—58no—
459#95—58no—
460#95—104no—
461#95—104no—
462#95—104no—
463#95—202no—
464#95—202no—
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—28no—
468C22×C5—24no—
469C22×C5—24no—
470C22×C5—24no—
471C22×C5—24no—
472C22×C5—28no—
473C22×C5—28no—
474C22×C5—28no—
475C22×C5C4×C22⋊C418yes—
476C22×C5C22×C4211yescharacteristic
477C22×C5C22×C22⋊C411yescharacteristic
478C22×C5C2×#11711yescharacteristic
479C22×C5C2×C4×D411yescharacteristic
480C22×C5C2×C4×D411yescharacteristic
481C22×C5C2×C4×D411yescharacteristic
482C22×C5C2×C4×D411yescharacteristic
483C22×C5#51812yes—
484C22×C5#51812yes—
485C22×C5#51812yes—
486C22×C5#52012yes—
487C22×C5#52012yes—
488C22×C5#52012yes—
489C22×C5#53411yescharacteristic
490C22×C5#53412yes—
491C22×C5#53411yescharacteristic
492C22×C5#53511yescharacteristic
493C22×C5#53611yescharacteristic
494C22×C5#53712yes—
495C22×C5#53812yes—
496C22×C5#53812yes—
497C22×C5#53912yes—
498C22×C5#53912yes—
499C2×D5—24no—
500C2×D5—28no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—44no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C2×D5—44no—
509C2×D5—44no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—44no—
513C4×C5—44no—
514Dic5—24no—
515Dic5—24no—
516Dic5—24no—
517Dic5—44no—
518Dic5—44no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—52no—
524C24—52no—
525C24—52no—
526C24—101no—
527C24—101no—
528C24—101no—
529C24—102no—
530C24—102no—
531C24—101no—
532C24—102no—
533C24—102no—
534C24C2×C4×D512yes—
535C24C2×C4×D512yes—
536C24C2×C4×D512yes—
537C24D4×D512yes—
538C24D4×D512yes—
539C24#71112yes—
540C24#71312yes—
541C24C23×D511yescharacteristic
542C2×D4—516no—
543C2×D4—108no—
544C2×D4—108no—
545C2×D4—108no—
546C2×D4—108no—
547C2×D4—108no—
548C2×D4—108no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—516no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—108no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—101no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—108no—
608C22×C4—208no—
609C22×C4—204no—
610C22×C4—208no—
611C22×C4—204no—
612C22×C4—208no—
613C22×C4—204no—
614C22×C4—208no—
615C22×C4—204no—
616C22×C4—208no—
617C22×C4—204no—
618C22×C4—208no—
619C22×C4—204no—
620C22×C4C2×C4×D514yes—
621C22×C4C2×C4×D514yes—
622C22×C4C2×C4×D512yes—
623C22×C4C2×C4×D512yes—
624C4⋊C4—108no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—208no—
630C22⋊C4—208no—
631C42—108no—
632C42—208no—
633C2×C5—28no—
634C2×C5C2×C4×C22⋊C411yescharacteristic
635C2×C5#227512yes—
636C2×C5#230811yescharacteristic
637C2×C5#231111yescharacteristic
638C2×C5#231812yes—
639C2×C5#232111yescharacteristic
640C2×C5#232111yescharacteristic
641C2×C5#232211yescharacteristic
642C2×C5#232211yescharacteristic
643C2×C5#232512yes—
644C2×C5#232512yes—
645D5—44no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—54no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—104no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—104no—
671C23—104no—
672C23—104no—
673C23—104no—
674C23—104no—
675C23—201no—
676C23—201no—
677C23—202no—
678C23—202no—
679C23—202no—
680C23—202no—
681C23—202no—
682C23—201no—
683C23—201no—
684C23—202no—
685C23C42×D514yes—
686C23D5×C22⋊C414yes—
687C23#402714yes—
688C23#402714yes—
689C23#403814yes—
690C23#403914yes—
691C23#403914yes—
692C23C22×C4×D511yescharacteristic
693C23C22×C4×D511yescharacteristic
694C23C22×C4×D511yescharacteristic
695C23C2×D4×D511yescharacteristic
696C23C2×D4×D511yescharacteristic
697C23C2×#71111yescharacteristic
698C23#414412yes—
699C23#414412yes—
700C23C2×#71311yescharacteristic
701C23#414912yes—
702C23#415012yes—
703D4—1032no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—54no—
730C2×C4—54no—
731C2×C4—54no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—104no—
743C2×C4—104no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—104no—
747C2×C4—104no—
748C2×C4—104no—
749C2×C4—104no—
750C2×C4—104no—
751C2×C4—104no—
752C2×C4—2016no—
753C2×C4—2016no—
754C2×C4—2016no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C5#1378411yescharacteristic, complemented, Sylow
764C22—24no—
765C22—28no—
766C22—24no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—108no—
775C22—104no—
776C22—202no—
777C22—204no—
778C22—202no—
779C22—204no—
780C22—202no—
781C22—204no—
782C22—202no—
783C22—202no—
784C22—202no—
785C22#6495518yes—
786C22C2×C42×D511yescharacteristic
787C22C2×D5×C22⋊C411yescharacteristic
788C22C2×#402711yescharacteristic
789C22C2×#402711yescharacteristic
790C22#6582012yes—
791C22C2×#403811yescharacteristic
792C22C2×#403911yescharacteristic
793C22C2×#403911yescharacteristic
794C22#6585712yes—
795C22#6587912yes—
796C22#6587912yes—
797C22#6588012yes—
798C22#6588012yes—
799C22#6592311yescharacteristic
800C22#6592611yescharacteristic
801C22#6592712yes—
802C22#6593112yes—
803C22#6593912yes—
804C22#6597812yes—
805C22#6597912yes—
806C22#6598211yescharacteristic
807C22#6598711yescharacteristic
808C22#6599912yes—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—44no—
813C4—104no—
814C4—104no—
815C4—104no—
816C4—204no—
817C4—204no—
818C2—28no—
819C2—204no—
820C2C2×#6495511yescharacteristic
821C2#1060516712yes—
822C2#1060555211yescharacteristic
823C2#1060560412yes—
824C2#1060578711yescharacteristic
825C2#1060611412yes—
826C2#1060611511yescharacteristic
827C2#1060632311yescharacteristic
828C2#1060639311yescharacteristic
829C2#1060639712yes—
830C2#1060660511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22⋊#95D5
hypocenterC5#13784
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
5. C2×C22⋊C4×Dic5C2semidirect
6. C5×C22⋊#95C2semidirect
7. #10602337C2semidirect
8. #10600218C2semidirect
9. #10600201C2semidirect
10. #10600199C2semidirect
11. #10600196C2semidirect
28. C2×#4027C4semidirect
31. #65502C4semidirect
40. #65247C4semidirect
49. C23×C4×C5C2×C4semidirect
68. C23×Dic5C2×C4semidirect
80. C22×C4×D5C2×C4semidirect
86. C2×C5×C22⋊C4C2×C4semidirect
89. C2×C22⋊Dic5C2×C4semidirect
96. C2×#685C2×C4semidirect
97. C2×#685C2×C4semidirect
98. C2×#685C2×C4semidirect
101. C2×#683C2×C4semidirect
107. C2×C4×Dic5C2×C4semidirect
116. #3963C2×C4semidirect
117. #3963C2×C4semidirect
128. C22⋊#95D5semidirect
187. C2×C22⋊D5C42semidirect
217. C22×Dic5C22⋊C4semidirect
423. C23×C4C4×D5semidirect
449. C2×C22⋊C4C4×D5semidirect
763. C5#13784semidirect

Maximal subgroups

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

subgroupindex
C22×#40272
C2×#655022
C22×#39632
C2×#652472
C2×C22⋊C4×Dic52
C5×C22⋊#952
#106023372
#106002182
#106002012
#106001992
#106001962
#137845