Finite Group Databasebeta

← C2×#10608848 #12266747

Subgroups — C2×#10608848 #12266747

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4084C211yesmaximal, characteristic
2C22×#4081C211yesmaximal, characteristic, complemented
3C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×C5×#394C211yesmaximal, characteristic, complemented
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic, complemented
10C2×#65238C211yesmaximal, characteristic, complemented
11C2×#65241C211yesmaximal, characteristic, complemented
12C2×#65240C211yesmaximal, characteristic, complemented
13C2×#65239C211yesmaximal, characteristic, complemented
14#10608848C2116yesmaximal, direct product factor
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64944C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C2×#4084—28no—
35C2×#4084C2218yes—
36C2×#4081—28no—
37C2×#4081C2218yescomplemented
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×D5×C4⋊C4—28no—
49C2×D5×C4⋊C4C2218yescomplemented
50C2×#4027—28no—
51C2×#4027C2218yescomplemented
52C5×#394C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65273C2218yescomplemented
62#65245C2218yescomplemented
63#65245C2218yescomplemented
64#65245C2218yescomplemented
65#65241C2218yescomplemented
66#65240C2218yescomplemented
67#65239C2218yescomplemented
68#65238C2218yescomplemented
69#64957C2218yescomplemented
70#64944C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5D418yes—
90C22×C22⋊D5C2314yes—
91C22×C22⋊D5C2314yes—
92C23×Dic5—24no—
93C23×Dic5—24no—
94C23×Dic5—42no—
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2314yes—
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—24no—
110C22×C4×D5—42no—
111C22×C4×D5—42no—
112C22×C4×D5C2314yes—
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4—42no—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C5×C22⋊C4C2314yes—
124C2×C5×C22⋊C4C2314yes—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—24no—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134C2×C22⋊Dic5C2314yes—
135#4084—232no—
136#4081—232no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×C4⋊Dic5—24no—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5—42no—
144C2×C4⋊Dic5C2314yes—
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yes—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683D418yescomplemented
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157D5×C4⋊C4—232no—
158#4027—232no—
159C5×#95C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394D511yescharacteristic, complemented
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5—22no—
196C24×C5C2×D414yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5C2×D414yes—
205C23×D5#4114yes—
206C23×D5#4114yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—44no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5C2×D414yes—
226C22×C4×C5#4114yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—232no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—416no—
239C2×C22⋊D5C2×D4116yes—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—28no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—28no—
260C22×Dic5—44no—
261C22×Dic5—416no—
262C22×Dic5C2×D414yes—
263C22×Dic5C2×D414yes—
264C22×Dic5C2×D414yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×C4×D5—232no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—28no—
279C2×C4×D5—28no—
280C2×C4×D5—44no—
281C2×C4×D5—44no—
282C2×C4×D5—416no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4—28no—
288C5×C22⋊C4—44no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292C22⋊Dic5—28no—
293C22⋊Dic5—28no—
294#685—28no—
295#685—28no—
296C4⋊Dic5—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5—44no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683C2×D4116yescomplemented
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4—51no—
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—58no—
325C22×C4⋊C4—108no—
326C22×C4⋊C4C2×D511yescharacteristic
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#399—58no—
340#398—58no—
341#397—58no—
342#394C2×D518yescomplemented
343#388—58no—
344#387—58no—
345#386—58no—
346#386—58no—
347#386—58no—
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95C2×D511yescharacteristic
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—44no—
384C23×C5—44no—
385C23×C5C22×D414yes—
386C23×C5C22×D412yes—
387C23×C5C22×D412yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C52−1+412yes—
393C23×C5C2511yescharacteristic
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—28no—
398C22×D5—28no—
399C22×D5—28no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—22no—
404C22×D5#123116yescomplemented
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C22×D5C2×#4114yes—
408C5×D4—416no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C2×#4114yes—
429C22⋊D5—232no—
430C22⋊D5—416no—
431C2×Dic5—28no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—416no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5C22×D414yes—
458C2×Dic5C22×D414yes—
459C2×Dic5C22×D414yes—
460C4×D5—232no—
461C4×D5—416no—
462C4×D5—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—58no—
470C22×D4—54no—
471C22×D4—54no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4C22×D514yes—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—54no—
486C23×C4—54no—
487C23×C4—54no—
488C23×C4—54no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—202no—
499C23×C4—202no—
500C23×C4—202no—
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—58no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—1032no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—104no—
522C2×C4⋊C4—104no—
523C2×C4⋊C4—104no—
524C2×C4⋊C4—202no—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95—54no—
557#95C22×D514yes—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—416no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—88no—
574C22×C5C2×#12314yes—
575C22×C5#52514yes—
576C22×C5#53914yes—
577C22×C5D4214yes—
578C22×C5#54714yes—
579C22×C5#54814yes—
580C22×C5#55314yes—
581C22×C5C23×D411yescharacteristic
582C22×C5C23×D411yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C22×C5C2×H(5,𝔽2)11yescharacteristic
587C22×C5C2×2−1+411yescharacteristic
588C2×D5—24no—
589C2×D5—24no—
590C2×D5—24no—
591C2×D5—24no—
592C2×D5—24no—
593C2×D5—232no—
594C2×D5—24no—
595C2×D5C2×#12318yescomplemented
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—54no—
622C24—54no—
623C24—54no—
624C24—52no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24D4×D514yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—516no—
638C2×D4—1032no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—108no—
644C2×D4—2016no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—54no—
659C22×C4—54no—
660C22×C4—54no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—108no—
669C22×C4—108no—
670C22×C4—108no—
671C22×C4—1032no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—108no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—108no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—108no—
696C22×C4—204no—
697C22×C4—204no—
698C22×C4—2016no—
699C22×C4—2016no—
700C22×C4—204no—
701C22×C4—2016no—
702C22×C4D4×D514yes—
703C22×C4#71114yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—516no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—204no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—44no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—108no—
728C42—108no—
729C2×C5—44no—
730C2×C5—82no—
731C2×C5#244318yescomplemented
732C2×C5C22×#12311yescharacteristic
733C2×C5C2×#52511yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×D4211yescharacteristic
736C2×C5C2×#54711yescharacteristic
737C2×C5C2×#54811yescharacteristic
738C2×C5C2×#55311yescharacteristic
739D5—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—516no—
768C23—54no—
769C23—54no—
770C23—54no—
771C23—108no—
772C23—108no—
773C23—108no—
774C23—108no—
775C23—108no—
776C23—108no—
777C23—102no—
778C23—102no—
779C23—102no—
780C23—102no—
781C23C2×D4×D514yes—
782C23C2×D4×D512yes—
783C23C2×D4×D512yes—
784C23C2×#71112yes—
785C23#414412yes—
786C23D5×#4112yes—
787C23D5×#4112yes—
788C23#415012yes—
789C23C24×D511yescharacteristic
790D4—416no—
791D4—1032no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—1032no—
815C2×C4—108no—
816C2×C4—108no—
817C2×C4—108no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—2016no—
837C2×C4—2016no—
838C2×C4—2016no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C2×#71114yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—58no—
862C22—88no—
863C22—104no—
864C22—104no—
865C22—1032no—
866C22—104no—
867C22—104no—
868C22—104no—
869C22—104no—
870C22#6592414yes—
871C22#6594014yes—
872C22#6594514yes—
873C22#6594814yes—
874C22D5×#12314yes—
875C22#6599414yes—
876C22#6601114yes—
877C22C22×D4×D511yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C22×#71111yescharacteristic
880C22C2×#414411yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×#415011yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—82no—
898C2—108no—
899C2#1060884818yesdirect product factor
900C2C2×#6592411yescharacteristic
901C2C2×#6594011yescharacteristic
902C2C2×#6594511yescharacteristic
903C2C2×#6594811yescharacteristic
904C2C2×D5×#12311yescharacteristic
905C2C2×#6599411yescharacteristic
906C2C2×#6601111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4084C2
hypercenterC2×#394D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#4081C2semidirect
3. C22×D5×C4⋊C4C2semidirect
4. C22×#4027C2semidirect
5. C2×C5×#394C2semidirect
6. C2×#65273C2semidirect
7. C2×#65245C2semidirect
8. C2×#65245C2semidirect
9. C2×#65245C2semidirect
10. C2×#65238C2semidirect
11. C2×#65241C2semidirect
12. C2×#65240C2semidirect
13. C2×#65239C2semidirect
14. #10608848C2direct (N × H)
15. C2×#64957C2semidirect
16. C2×#64944C2semidirect
37. C2×#4081C22semidirect
49. C2×D5×C4⋊C4C22semidirect
51. C2×#4027C22semidirect
52. C5×#394C22semidirect
61. #65273C22semidirect
62. #65245C22semidirect
63. #65245C22semidirect
64. #65245C22semidirect
65. #65241C22semidirect
66. #65240C22semidirect
67. #65239C22semidirect
68. #65238C22semidirect
69. #64957C22semidirect
70. #64944C22semidirect
150. C2×#683D4semidirect
175. C2×#394D5semidirect
302. #683C2×D4semidirect
342. #394C2×D5semidirect
404. C22×D5#123semidirect
595. C2×D5C2×#123semidirect
731. C2×C5#2443semidirect
845. C5C2×#2443semidirect
899. C2#10608848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40842
C22×#40812
C22×D5×C4⋊C42
C22×#40272
C2×C5×#3942
C2×#652732
C2×#652452
C2×#652382
C2×#652412
C2×#652402
C2×#652392
#106088482
C2×#649572
C2×#649442
C2×#24435