Finite Group Databasebeta

← C2×#10606149 #12266752

Subgroups — C2×#10606149 #12266752

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×#4076C211yesmaximal, characteristic
2C23×#683C211yesmaximal, characteristic, complemented
3C22×#4040C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×C5×#385C211yesmaximal, characteristic, complemented
6C2×#65281C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65273C211yesmaximal, characteristic, complemented
9C2×#65247C211yesmaximal, characteristic, complemented
10C2×#65247C211yesmaximal, characteristic, complemented
11C2×#65247C211yesmaximal, characteristic, complemented
12#10606149C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64961C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64944C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×D20C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C2×#4076—28no—
29C2×#4076C2218yes—
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683—28no—
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2218yescomplemented
47C22×C4×Dic5C2211yescharacteristic
48C2×#4040—28no—
49C2×#4040C2218yescomplemented
50C2×#4027—28no—
51C2×#4027C2218yescomplemented
52C5×#385C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65281C2218yescomplemented
62#65278C2218yescomplemented
63#65273C2218yescomplemented
64#65247C2218yescomplemented
65#65247C2218yescomplemented
66#65247C2218yescomplemented
67#64964C2218yescomplemented
68#64961C2218yescomplemented
69#64958C2218yescomplemented
70#64944C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—42no—
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5D418yes—
91C22×C22⋊D5C2314yes—
92C22×C22⋊D5C2314yes—
93C23×Dic5—24no—
94C23×Dic5—24no—
95C23×Dic5—24no—
96C23×Dic5—24no—
97C23×Dic5—24no—
98C23×Dic5—42no—
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2314yes—
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2314yes—
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×D20—24no—
108C22×D20—24no—
109C22×D20—42no—
110C22×D20C2314yes—
111C22×C4×D5—24no—
112C22×C4×D5—24no—
113C22×C4×D5—42no—
114C22×C4×D5C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4—42no—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123#4076—232no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—42no—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5C2314yes—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—232no—
149C2×#683D418yescomplemented
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157#4040—232no—
158#4027—232no—
159C5×#95C2314yes—
160C5×#95C2314yes—
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×#394—51no—
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385D511yescharacteristic, complemented
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×D414yes—
188C24×C5#4114yes—
189C24×C5#4114yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5C2×D414yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—28no—
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×C5—22no—
226C22×C4×C5—28no—
227C22×C4×C5—44no—
228C22×C4×C5—416no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
244C22×Dic5—232no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—28no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—28no—
255C22×Dic5—28no—
256C22×Dic5—28no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—28no—
264C22×Dic5—44no—
265C22×Dic5—416no—
266C22×Dic5C2×D414yes—
267C22×Dic5C2×D414yes—
268C22×Dic5C2×D414yes—
269C22×Dic5#4114yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×D20—28no—
277C2×D20—28no—
278C2×D20—44no—
279C2×D20—416no—
280C2×C4×D5—28no—
281C2×C4×D5—28no—
282C2×C4×D5—44no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—44no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—44no—
297C4⋊Dic5—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683C2×D4116yescomplemented
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
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—58no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—108no—
325C22×C4⋊C4C2×D511yescharacteristic
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#385C2×D518yescomplemented
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95C2×D511yescharacteristic
357C2×#95C2×D511yescharacteristic
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#123116yescomplemented
369C23×C5C22×D414yes—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4114yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4114yes—
375C23×C5C2×#4112yes—
376C23×C5C2×#4112yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C52−1+412yes—
379C23×C5C2511yescharacteristic
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5C22×D414yes—
408C2×C4×C5—28no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
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—22no—
425C2×C4×C5—22no—
426C2×C4×C5—416no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5—44no—
432C2×C4×C5C22×D414yes—
433C22⋊D5—232no—
434C22⋊D5—416no—
435C2×Dic5—232no—
436C2×Dic5—28no—
437C2×Dic5—28no—
438C2×Dic5—28no—
439C2×Dic5—28no—
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—22no—
454C2×Dic5—416no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5C22×D414yes—
458C2×Dic5C22×D414yes—
459C2×Dic5C22×D414yes—
460C2×Dic5C2×#4114yes—
461D20—416no—
462C4×D5—416no—
463C25—51no—
464C25—51no—
465C25C22×D511yescharacteristic
466C22×D4—58no—
467C22×D4—54no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—202no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—54no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—54no—
489C23×C4—54no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D514yes—
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—58no—
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⋊C4C22×D514yes—
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#95C22×D514yes—
557#95C22×D514yes—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—232no—
564C22×C5—24no—
565C22×C5C2×#12314yes—
566C22×C5C2×#12318yescomplemented
567C22×C5#52514yes—
568C22×C5#53914yes—
569C22×C5D4214yes—
570C22×C5#54714yes—
571C22×C5#54814yes—
572C22×C5#55314yes—
573C22×C5C23×D411yescharacteristic
574C22×C5C23×D411yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C22×#4111yescharacteristic
577C22×C5C22×#4111yescharacteristic
578C22×C5C2×H(5,𝔽2)11yescharacteristic
579C22×C5C2×2−1+411yescharacteristic
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—416no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—88no—
596C4×C5—24no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602Dic5—24no—
603Dic5—24no—
604Dic5—24no—
605Dic5—24no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—52no—
614C24—52no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#70914yes—
629C24D4×D514yes—
630C24#71314yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—516no—
634C2×D4—108no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—1032no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—204no—
643C2×D4—2016no—
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—28no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—54no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—108no—
677C22×C4—108no—
678C22×C4—108no—
679C22×C4—108no—
680C22×C4—108no—
681C22×C4—1032no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—108no—
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—108no—
696C22×C4—102no—
697C22×C4—102no—
698C22×C4—204no—
699C22×C4—2016no—
700C22×C4—204no—
701C22×C4—2016no—
702C22×C4D4×D514yes—
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—44no—
711C4⋊C4—516no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—108no—
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#244318yescomplemented
731C2×C5C22×#12311yescharacteristic
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#53911yescharacteristic
734C2×C5C2×D4211yescharacteristic
735C2×C5C2×#54711yescharacteristic
736C2×C5C2×#54811yescharacteristic
737C2×C5C2×#55311yescharacteristic
738D5—44no—
739D5—82no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—54no—
751C23—108no—
752C23—108no—
753C23—108no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23#4040116yescomplemented
779C23C2×#70914yes—
780C23C2×#70912yes—
781C23C2×D4×D514yes—
782C23C2×D4×D512yes—
783C23C2×D4×D512yes—
784C23#414412yes—
785C23C2×#71314yes—
786C23C2×#71312yes—
787C23D5×#4112yes—
788C23#415012yes—
789C23C24×D511yescharacteristic
790D4—1032no—
791D4—2016no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—22no—
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—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—416no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—54no—
818C2×C4—54no—
819C2×C4—54no—
820C2×C4—54no—
821C2×C4—1032no—
822C2×C4—108no—
823C2×C4—108no—
824C2×C4—108no—
825C2×C4—108no—
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—102no—
837C2×C4—102no—
838C2×C4—102no—
839C2×C4—102no—
840C2×C4—2016no—
841C2×C4—2016no—
842C2×C4—204no—
843C2×C4—204no—
844C2×C4C2×D4×D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—232no—
852C22—24no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—2016no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—408no—
869C22C2×#404014yes—
870C22C2×#404018yescomplemented
871C22#6587414yes—
872C22#6588614yes—
873C22#6592414yes—
874C22#6596114yes—
875C22#6597914yes—
876C22#6598914yes—
877C22C22×#70911yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C2×#414411yescharacteristic
881C22C22×#71311yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×#415011yescharacteristic
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—104no—
891C4—104no—
892C4—104no—
893C4—104no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—204no—
898C2—402no—
899C2#1060614918yesdirect product factor
900C2C22×#404011yescharacteristic
901C2C2×#6588611yescharacteristic
902C2C2×#6587411yescharacteristic
903C2C2×#6592411yescharacteristic
904C2C2×#6596111yescharacteristic
905C2C2×#6597911yescharacteristic
906C2C2×#6598911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC22×#4076C2
hypercenterC2×#385D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C23×#683C2semidirect
3. C22×#4040C2semidirect
4. C22×#4027C2semidirect
5. C2×C5×#385C2semidirect
6. C2×#65281C2semidirect
7. C2×#65278C2semidirect
8. C2×#65273C2semidirect
9. C2×#65247C2semidirect
10. C2×#65247C2semidirect
11. C2×#65247C2semidirect
12. #10606149C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64961C2semidirect
15. C2×#64958C2semidirect
16. C2×#64944C2semidirect
46. C22×#683C22semidirect
49. C2×#4040C22semidirect
51. C2×#4027C22semidirect
52. C5×#385C22semidirect
61. #65281C22semidirect
62. #65278C22semidirect
63. #65273C22semidirect
64. #65247C22semidirect
65. #65247C22semidirect
66. #65247C22semidirect
67. #64964C22semidirect
68. #64961C22semidirect
69. #64958C22semidirect
70. #64944C22semidirect
149. C2×#683D4semidirect
182. C2×#385D5semidirect
302. #683C2×D4semidirect
349. #385C2×D5semidirect
368. C23×C5#123semidirect
566. C22×C5C2×#123semidirect
730. C2×C5#2443semidirect
778. C23#4040semidirect
845. C5C2×#2443semidirect
870. C22C2×#4040semidirect
899. C2#10606149direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40762
C23×#6832
C22×#40402
C22×#40272
C2×C5×#3852
C2×#652812
C2×#652782
C2×#652732
C2×#652472
#106061492
C2×#649642
C2×#649612
C2×#649582
C2×#649442
C2×#24435