Finite Group Databasebeta

← C2×#10614386 #12266748

Subgroups — C2×#10614386 #12266748

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×C5×#121C211yesmaximal, characteristic
2C22×#4081C211yesmaximal, characteristic, complemented
3C22×D4×Dic5C211yesmaximal, characteristic, complemented
4C23×#683C211yesmaximal, characteristic, complemented
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65509C211yesmaximal, characteristic, complemented
7C2×#65509C211yesmaximal, characteristic, complemented
8C2×#65509C211yesmaximal, characteristic, complemented
9C2×#65499C211yesmaximal, characteristic, complemented
10#10614386C2116yesmaximal, direct product factor
11C2×#65272C211yesmaximal, characteristic, complemented
12C2×#65267C211yesmaximal, characteristic, complemented
13C2×#65238C211yesmaximal, characteristic, complemented
14C2×#65241C211yesmaximal, characteristic, complemented
15C2×#65233C211yesmaximal, characteristic, complemented
16C2×#65235C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C23×C5×D4C2211yescharacteristic
20C24×C4×C5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C24×Dic5C2211yescharacteristic
23C24×Dic5C2211yescharacteristic
24C2×C5×#121—28no—
25C2×C5×#121C2218yes—
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C22×C22⋊Dic5C2211yescharacteristic
36C22×C22⋊Dic5C2211yescharacteristic
37C22×C22⋊Dic5C2211yescharacteristic
38C2×#4081—28no—
39C2×#4081C2218yescomplemented
40C2×D4×Dic5—28no—
41C2×D4×Dic5C2218yescomplemented
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683—28no—
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×#683C2211yescharacteristic
50C22×#683C2218yescomplemented
51C22×C4×Dic5C2211yescharacteristic
52#65511C2218yescomplemented
53#65509C2218yescomplemented
54#65509C2218yescomplemented
55#65509C2218yescomplemented
56#65499C2218yescomplemented
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64C2×#3963C2211yescharacteristic
65#65272C2218yescomplemented
66#65267C2218yescomplemented
67#65241C2218yescomplemented
68#65238C2218yescomplemented
69#65235C2218yescomplemented
70#65233C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C25×C5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4—24no—
79C22×C5×D4—24no—
80C22×C5×D4—24no—
81C22×C5×D4—24no—
82C22×C5×D4—42no—
83C22×C5×D4D418yes—
84C22×C5×D4C2314yes—
85C22×C5×D4C2314yes—
86C22×C5×D4C2314yes—
87C23×C4×C5—24no—
88C23×C4×C5—24no—
89C23×C4×C5—42no—
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2314yes—
93C23×C4×C5C2311yescharacteristic
94C23×C4×C5C2311yescharacteristic
95C23×Dic5—24no—
96C23×Dic5—24no—
97C23×Dic5—24no—
98C23×Dic5—24no—
99C23×Dic5—24no—
100C23×Dic5—24no—
101C23×Dic5—24no—
102C23×Dic5—42no—
103C23×Dic5—42no—
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C23×Dic5C2311yescharacteristic
108C23×Dic5C2311yescharacteristic
109C23×Dic5C2314yes—
110C23×Dic5C2314yes—
111C23×Dic5C2314yes—
112C23×Dic5C2311yescharacteristic
113C23×Dic5C2311yescharacteristic
114C23×Dic5C2311yescharacteristic
115C5×#121—232no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—24no—
130C2×C22⋊Dic5—42no—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134C2×C22⋊Dic5C2314yes—
135C2×C22⋊Dic5C2314yes—
136C2×C22⋊Dic5C2314yes—
137C2×C22⋊Dic5C2314yes—
138C2×C22⋊Dic5C2314yes—
139C2×C22⋊Dic5C2314yes—
140#4081—232no—
141D4×Dic5—232no—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5C2314yes—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—232no—
149C2×#683—42no—
150C2×#683D418yescomplemented
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×#683C2314yes—
157C2×C4×Dic5—24no—
158C2×C4×Dic5C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121D511yescharacteristic
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
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×C5—22no—
197C24×C5—22no—
198C24×C5—22no—
199C24×C5—22no—
200C24×C5C2×D414yes—
201C24×C5C2×D414yes—
202C24×C5#4114yes—
203C24×C5#4114yes—
204C24×C5C2412yes—
205C24×C5C2412yes—
206C24×C5C2412yes—
207C24×C5C2411yescharacteristic
208C2×C5×D4—232no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—28no—
212C2×C5×D4—28no—
213C2×C5×D4—28no—
214C2×C5×D4—28no—
215C2×C5×D4—28no—
216C2×C5×D4—44no—
217C2×C5×D4—416no—
218C2×C5×D4—416no—
219C2×C5×D4C2×D4116yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—28no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—28no—
232C22×C4×C5—44no—
233C22×C4×C5—416no—
234C22×C4×C5C2×D414yes—
235C22×C4×C5C2×D414yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C22×Dic5—232no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—28no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—28no—
249C22×Dic5—28no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—28no—
257C22×Dic5—28no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5—28no—
268C22×Dic5—28no—
269C22×Dic5—44no—
270C22×Dic5—44no—
271C22×Dic5—416no—
272C22×Dic5—416no—
273C22×Dic5C2×D414yes—
274C22×Dic5C2×D414yes—
275C22×Dic5#4114yes—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C22×Dic5C2412yes—
279C22×Dic5C2412yes—
280C22×Dic5C2412yes—
281C22×Dic5C2412yes—
282C22×Dic5C2412yes—
283C22×Dic5C2412yes—
284C5×C4⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292C22⋊Dic5—28no—
293C22⋊Dic5—28no—
294C22⋊Dic5—28no—
295C22⋊Dic5—44no—
296C4⋊Dic5—28no—
297#683—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301#683—44no—
302#683C2×D4116yescomplemented
303C4×Dic5—28no—
304C23×D4C2×D511yescharacteristic
305C23×D4C2×D511yescharacteristic
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—28no—
314C2×#121C2×D518yes—
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—58no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
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⋊C4—51no—
335C22×C22⋊C4—51no—
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#399—58no—
340#398—58no—
341#397—58no—
342#394—58no—
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×#95—51no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—28no—
369C23×C5—28no—
370C23×C5—28no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—44no—
385C23×C5—44no—
386C23×C5—44no—
387C23×C5—44no—
388C23×C5—44no—
389C23×C5—44no—
390C23×C5—44no—
391C23×C5—44no—
392C23×C5—44no—
393C23×C5—44no—
394C23×C5—44no—
395C23×C5#123116yescomplemented
396C23×C5C22×D412yes—
397C23×C5C22×D414yes—
398C23×C5C22×D414yes—
399C23×C5C22×D412yes—
400C23×C5C2×#4114yes—
401C23×C5C2×#4114yes—
402C23×C5C2×#4112yes—
403C23×C5C2×#4112yes—
404C23×C5C2×#4112yes—
405C23×C5H(5,𝔽2)12yes—
406C23×C52−1+412yes—
407C23×C5C2511yescharacteristic
408C5×D4—232no—
409C5×D4—416no—
410C5×D4—416no—
411C2×C4×C5—28no—
412C2×C4×C5—28no—
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—416no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×Dic5—232no—
429C2×Dic5—28no—
430C2×Dic5—28no—
431C2×Dic5—28no—
432C2×Dic5—22no—
433C2×Dic5—22no—
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—22no—
453C2×Dic5—416no—
454C2×Dic5—416no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5—44no—
460C2×Dic5C22×D414yes—
461C2×Dic5C22×D414yes—
462C2×Dic5C2×#4114yes—
463C25C22×D511yescharacteristic
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—42no—
474C22×D4C22⋊D518yes—
475C22×D4C22×D514yes—
476C22×D4C22×D514yes—
477C22×D4C22×D514yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—54no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—54no—
491C23×C4—54no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—104no—
499C23×C4—202no—
500C23×C4—202no—
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D514yes—
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—232no—
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—54no—
529C2×C22⋊C4—54no—
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⋊C4—104no—
545C2×C22⋊C4—202no—
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#95—54no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—232no—
564C22×C5—24no—
565C22×C5—24no—
566C22×C5—24no—
567C22×C5—24no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—416no—
572C22×C5—42no—
573C22×C5—42no—
574C22×C5—42no—
575C22×C5—42no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—88no—
581C22×C5C2×#12314yes—
582C22×C5C2×#12318yescomplemented
583C22×C5#52514yes—
584C22×C5#53914yes—
585C22×C5D4214yes—
586C22×C5#54714yes—
587C22×C5#54814yes—
588C22×C5#55314yes—
589C22×C5C23×D411yescharacteristic
590C22×C5C23×D411yescharacteristic
591C22×C5C22×#4111yescharacteristic
592C22×C5C22×#4111yescharacteristic
593C22×C5C22×#4111yescharacteristic
594C22×C5C2×H(5,𝔽2)11yescharacteristic
595C22×C5C2×2−1+411yescharacteristic
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
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—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24#71114yes—
626C24#71114yes—
627C24C2×C22⋊D514yes—
628C24C2×C22⋊D514yes—
629C24C23×D512yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—232no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—44no—
642C2×D4—416no—
643C2×D4—416no—
644C2×D4C2×C22⋊D5116yes—
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—28no—
656C22×C4—28no—
657C22×C4—44no—
658C22×C4—416no—
659C22×C4—54no—
660C22×C4—54no—
661C22×C4—54no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—108no—
671C22×C4—108no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—1032no—
675C22×C4—102no—
676C22×C4—108no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—102no—
696C22×C4—102no—
697C22×C4—108no—
698C22×C4—108no—
699C22×C4—204no—
700C22×C4—204no—
701C22×C4—2016no—
702C22×C4—2016no—
703C22×C4D4×D514yes—
704C22×C4C2×C22⋊D514yes—
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—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—204no—
728C42—108no—
729C2×C5—28no—
730C2×C5—44no—
731C2×C5—82no—
732C2×C5#244318yescomplemented
733C2×C5C22×#12311yescharacteristic
734C2×C5C2×#52511yescharacteristic
735C2×C5C2×#53911yescharacteristic
736C2×C5C2×D4211yescharacteristic
737C2×C5C2×#54711yescharacteristic
738C2×C5C2×#54811yescharacteristic
739C2×C5C2×#55311yescharacteristic
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23#4081116yescomplemented
778C23C2×D4×D512yes—
779C23C2×#71114yes—
780C23C2×#71114yes—
781C23C2×#71112yes—
782C23C2×#71112yes—
783C23#414412yes—
784C23D5×#4112yes—
785C23#415012yes—
786C23C22×C22⋊D514yes—
787C23C22×C22⋊D514yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790D4—232no—
791D4—416no—
792D4—416no—
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—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—54no—
809C2×C4—54no—
810C2×C4—54no—
811C2×C4—1032no—
812C2×C4—108no—
813C2×C4—108no—
814C2×C4—108no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
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—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—232no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—416no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22#6593214yes—
870C22#6593514yes—
871C22#6593614yes—
872C22#6594014yes—
873C22C2×#408114yes—
874C22C2×#408118yescomplemented
875C22D4×C22⋊D514yes—
876C22#6615814yes—
877C22C22×D4×D511yescharacteristic
878C22C22×#71111yescharacteristic
879C22C22×#71111yescharacteristic
880C22C2×#414411yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×#415011yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—104no—
889C4—104no—
890C4—104no—
891C4—202no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2#1061438618yesdirect product factor
900C2C2×#6594011yescharacteristic
901C2C2×#6593611yescharacteristic
902C2C2×#6593211yescharacteristic
903C2C2×#6593511yescharacteristic
904C2C22×#408111yescharacteristic
905C2C2×D4×C22⋊D511yescharacteristic
906C2C2×#6615811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC22×C5×#121C2
socleC24×C5C24
hypercenterC22×#121D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#4081C2semidirect
3. C22×D4×Dic5C2semidirect
4. C23×#683C2semidirect
5. C2×#65511C2semidirect
6. C2×#65509C2semidirect
7. C2×#65509C2semidirect
8. C2×#65509C2semidirect
9. C2×#65499C2semidirect
10. #10614386C2direct (N × H)
11. C2×#65272C2semidirect
12. C2×#65267C2semidirect
13. C2×#65238C2semidirect
14. C2×#65241C2semidirect
15. C2×#65233C2semidirect
16. C2×#65235C2semidirect
39. C2×#4081C22semidirect
41. C2×D4×Dic5C22semidirect
50. C22×#683C22semidirect
52. #65511C22semidirect
53. #65509C22semidirect
54. #65509C22semidirect
55. #65509C22semidirect
56. #65499C22semidirect
65. #65272C22semidirect
66. #65267C22semidirect
67. #65241C22semidirect
68. #65238C22semidirect
69. #65235C22semidirect
70. #65233C22semidirect
150. C2×#683D4semidirect
302. #683C2×D4semidirect
395. C23×C5#123semidirect
582. C22×C5C2×#123semidirect
732. C2×C5#2443semidirect
777. C23#4081semidirect
845. C5C2×#2443semidirect
874. C22C2×#4081semidirect
899. C2#10614386direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1212
C22×#40812
C22×D4×Dic52
C23×#6832
C2×#655112
C2×#655092
C2×#654992
#106143862
C2×#652722
C2×#652672
C2×#652382
C2×#652412
C2×#652332
C2×#652352
C2×#24435