Finite Group Databasebeta

← C2×#10605513 #12267159

Subgroups — C2×#10605513 #12267159

Order 1280.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C211yesmaximal, characteristic, complemented
2C22×#4042C211yesmaximal, characteristic, complemented
3C22×#4021C211yesmaximal, characteristic, complemented
4C22×C4×D20C211yesmaximal, characteristic, complemented
5C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65280C211yesmaximal, characteristic, complemented
8C2×#65228C211yesmaximal, characteristic, complemented
9C2×#65229C211yesmaximal, characteristic, complemented
10C2×#65229C211yesmaximal, characteristic, complemented
11C2×#65229C211yesmaximal, characteristic, complemented
12#10605513C2116yesmaximal, direct product factor
13C2×#64960C211yesmaximal, characteristic
14C2×#64954C211yesmaximal, characteristic, complemented
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C2×#4042—28no—
47C2×#4042C2218yescomplemented
48C2×#4040—28no—
49C2×#4040C2218yescomplemented
50C2×#4021—28no—
51C2×#4021C2218yescomplemented
52C2×C4×D20—28no—
53C2×C4×D20C2218yescomplemented
54C4×C5×C4⋊C4C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65280C2218yescomplemented
63#65229C2218yescomplemented
64#65229C2218yescomplemented
65#65229C2218yescomplemented
66#65228C2218yescomplemented
67#64960C2218yes—
68#64957C2218yescomplemented
69#64954C2218yescomplemented
70#64945C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×D20—24no—
88C22×D20—24no—
89C22×D20—24no—
90C22×D20—24no—
91C22×D20—24no—
92C22×D20—24no—
93C22×D20—24no—
94C22×D20—42no—
95C22×D20—42no—
96C22×D20C2314yes—
97C22×D20C2314yes—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5—42no—
105C22×C4×D5C2314yes—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4D418yescomplemented
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C4⋊C4C2314yes—
115C2×C42×C5—24no—
116C2×C42×C5—24no—
117C2×C42×C5—24no—
118C2×C42×C5C2314yes—
119C2×C42×C5C2314yes—
120C2×C42×C5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
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—24no—
133C2×#685D418yescomplemented
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×#685C2314yes—
146C2×#685C2314yes—
147C2×C4⋊Dic5—24no—
148C2×C4⋊Dic5—42no—
149C2×C4⋊Dic5C2314yes—
150C2×C4⋊Dic5C2314yes—
151C2×#683—24no—
152C2×#683—24no—
153C2×#683—24no—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×#683C2314yes—
157#4042—232no—
158#4040—232no—
159#4021—232no—
160C4×D20—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123—51no—
169C22×C22⋊Q8—51no—
170C22×C4×D4—51no—
171#2461—516no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×C4×C4⋊C4D511yescharacteristic, complemented
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
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×D5C2×D414yes—
204C23×D5#4114yes—
205C23×D5C2412yes—
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—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×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2×D414yes—
227C22×C4×C5#4114yes—
228C22×C4×C5#4114yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
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×Dic5C2×D414yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—232no—
257C2×D20—28no—
258C2×D20—28no—
259C2×D20—28no—
260C2×D20—28no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—28no—
264C2×D20—44no—
265C2×D20—44no—
266C2×D20—416no—
267C2×D20—416no—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—28no—
272C2×C4×D5—44no—
273C2×C4×D5—44no—
274C2×C4×D5—416no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4C2×D4116yescomplemented
282C42×C5—28no—
283C42×C5—28no—
284C42×C5—28no—
285#685—28no—
286#685—28no—
287#685—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—28no—
297#685C2×D4116yescomplemented
298C4⋊Dic5—28no—
299C4⋊Dic5—44no—
300#683—28no—
301#683—28no—
302#683—28no—
303C23×Q8—51no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—58no—
312C2×#123—108no—
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—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⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
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⋊C4—51no—
337C22×C42C2×D511yescharacteristic
338C22×C42C2×D511yescharacteristic
339C22×C42C2×D511yescharacteristic
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388—58no—
348#386—58no—
349#385—58no—
350C4×C4⋊C4C2×D518yescomplemented
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5C22×D412yes—
358C23×C5C22×D412yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5H(5,𝔽2)12yes—
363C23×C52−1+412yes—
364C23×C5C2511yescharacteristic
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5—44no—
393C22×D5—44no—
394C22×D5—44no—
395C22×D5—44no—
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×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
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—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—44no—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C22×D414yes—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C2×#4114yes—
434C2×C4×C5C2×#4114yes—
435C2×Dic5—28no—
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—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5C22×D414yes—
455D20—232no—
456D20—416no—
457D20—416no—
458C4×D5—416no—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25—51no—
463C25—51no—
464C22×Q8—54no—
465C22×Q8—104no—
466C22×Q8—104no—
467C22×Q8—202no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—54no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4—202no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—54no—
486C23×C4—54no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—202no—
492C23×C4—202no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—1032no—
502C22⋊Q8—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—104no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—202no—
515C2×C4⋊C4D2018yescomplemented
516C2×C4⋊C4C22×D514yes—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—58no—
519C2×C22⋊C4—54no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—104no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
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×C42—24no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42C22×D514yes—
548C2×C42C22×D514yes—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5#52514yes—
557C22×C5#53214yes—
558C22×C5#54214yes—
559C22×C5D4214yes—
560C22×C5#54714yes—
561C22×C5#54814yes—
562C22×C5#55114yes—
563C22×C5C23×D411yescharacteristic
564C22×C5C23×D411yescharacteristic
565C22×C5C22×#4111yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C2×H(5,𝔽2)11yescharacteristic
569C22×C5C2×2−1+411yescharacteristic
570C2×D5—24no—
571C2×D5—24no—
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—24no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—416no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—88no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—24no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606C24—54no—
607C24—54no—
608C24—52no—
609C24—52no—
610C24—52no—
611C24—102no—
612C24—102no—
613C24—102no—
614C24—102no—
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—102no—
629C24—102no—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—1032no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—2016no—
646C2×D4—2016no—
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—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—108no—
669C22×C4—108no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—108no—
685C22×C4—108no—
686C22×C4—204no—
687C22×C4—204no—
688C22×C4—2016no—
689C22×C4—2016no—
690C22×C4C2×D2014yes—
691C22×C4C2×D2014yes—
692C22×C4C2×D2014yes—
693C22×C4#70914yes—
694C22×C4#70914yes—
695C22×C4D4×D514yes—
696C22×C4C23×D512yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—204no—
709C4⋊C4C2×D20116yescomplemented
710C22⋊C4—516no—
711C22⋊C4—108no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C42—28no—
724C42—28no—
725C42—28no—
726C2×C5#246118yescomplemented
727C2×C5C2×#52511yescharacteristic
728C2×C5C2×#53211yescharacteristic
729C2×C5C2×#54211yescharacteristic
730C2×C5C2×D4211yescharacteristic
731C2×C5C2×#54711yescharacteristic
732C2×C5C2×#54811yescharacteristic
733C2×C5C2×#55111yescharacteristic
734D5—44no—
735D5—44no—
736D5—82no—
737C23—54no—
738C23—54no—
739C23—108no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—108no—
744C23—108no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—102no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—204no—
765C23—204no—
766C23—204no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23C22×D2012yes—
780C23C2×#70912yes—
781C23C2×#70912yes—
782C23C2×D4×D512yes—
783C23#414712yes—
784C23D5×#4112yes—
785C23#414912yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—1032no—
789D4—2016no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
812C2×C4—44no—
813C2×C4—54no—
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—2016no—
830C2×C4—2016no—
831C2×C4—204no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4—204no—
835C2×C4C22×D2014yes—
836C2×C4C22×D2014yes—
837C2×C4C22×D2014yes—
838C2×C4C2×#70914yes—
839C2×C4C2×#70914yes—
840C2×C4C2×D4×D514yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—104no—
847C22—104no—
848C22—202no—
849C22—202no—
850C22—202no—
851C22—202no—
852C22—202no—
853C22—202no—
854C22—2016no—
855C22—2016no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6581114yes—
867C22#6584114yes—
868C22#6586114yes—
869C22#6588114yes—
870C22D4×D2014yes—
871C22#6591014yes—
872C22#6591614yes—
873C22C23×D2011yescharacteristic
874C22C22×#70911yescharacteristic
875C22C22×#70911yescharacteristic
876C22C22×D4×D511yescharacteristic
877C22C2×#414711yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×#414911yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—104no—
888C4—202no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—204no—
893C2—204no—
894C2—402no—
895C2#1060551318yesdirect product factor
896C2C2×#6581111yescharacteristic
897C2C2×#6584111yescharacteristic
898C2C2×#6586111yescharacteristic
899C2C2×#6588111yescharacteristic
900C2C2×D4×D2011yescharacteristic
901C2C2×#6591611yescharacteristic
902C2C2×#6591011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC2×#64960C2
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#4040C2semidirect
2. C22×#4042C2semidirect
3. C22×#4021C2semidirect
4. C22×C4×D20C2semidirect
5. C2×C4×C5×C4⋊C4C2semidirect
6. C2×#65283C2semidirect
7. C2×#65280C2semidirect
8. C2×#65228C2semidirect
9. C2×#65229C2semidirect
10. C2×#65229C2semidirect
11. C2×#65229C2semidirect
12. #10605513C2direct (N × H)
14. C2×#64954C2semidirect
15. C2×#64957C2semidirect
16. C2×#64945C2semidirect
47. C2×#4042C22semidirect
49. C2×#4040C22semidirect
51. C2×#4021C22semidirect
53. C2×C4×D20C22semidirect
54. C4×C5×C4⋊C4C22semidirect
61. #65283C22semidirect
62. #65280C22semidirect
63. #65229C22semidirect
64. #65229C22semidirect
65. #65229C22semidirect
66. #65228C22semidirect
68. #64957C22semidirect
69. #64954C22semidirect
70. #64945C22semidirect
112. C2×C5×C4⋊C4D4semidirect
133. C2×#685D4semidirect
182. C2×C4×C4⋊C4D5semidirect
281. C5×C4⋊C4C2×D4semidirect
297. #685C2×D4semidirect
350. C4×C4⋊C4C2×D5semidirect
515. C2×C4⋊C4D20semidirect
709. C4⋊C4C2×D20semidirect
726. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10605513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40402
C22×#40422
C22×#40212
C22×C4×D202
C2×C4×C5×C4⋊C42
C2×#652832
C2×#652802
C2×#652282
C2×#652292
#106055132
C2×#649602
C2×#649542
C2×#649572
C2×#649452
C2×#24615