Finite Group Databasebeta

← C2×#10605506 #12258934

Subgroups — C2×#10605506 #12258934

Order 1280.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic
2C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#65278C211yesmaximal, characteristic
4C2×#65267C211yesmaximal, characteristic, complemented
5C2×#65270C211yesmaximal, characteristic, complemented
6C2×#65218C211yesmaximal, characteristic, complemented
7C2×#65222C211yesmaximal, characteristic, complemented
8C2×#65222C211yesmaximal, characteristic, complemented
9C2×C4×#685C211yesmaximal, characteristic
10C2×C4×#685C211yesmaximal, characteristic
11C2×C4×#685C211yesmaximal, characteristic
12#10605506C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic
14C2×D5×#95C211yesmaximal, characteristic
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C4×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4042C4116yescomplemented
39C2×#4042C2218yes—
40C4×C5×C4⋊C4C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65278C2218yes—
56#65270C2218yescomplemented
57#65267C2218yescomplemented
58C4×#685C2218yes—
59C4×#685C2218yes—
60C4×#685C2218yes—
61#65222C2218yescomplemented
62#65222C2218yescomplemented
63#65218C2218yescomplemented
64#64957C2218yes—
65D5×#95C2218yes—
66#64938C2218yescomplemented
67#64935C2218yescomplemented
68C2×#2368—51nomaximal, Sylow
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C22×C4×D5—24no—
85C22×C4×D5—24no—
86C22×C4×D5—24no—
87C22×C4×D5—24no—
88C22×C4×D5—42no—
89C22×C4×D5—42no—
90C22×C4×D5—42no—
91C22×C4×D5—42no—
92C22×C4×D5C2×C418yes—
93C22×C4×D5C2314yes—
94C22×C4×D5C2314yes—
95C22×C4×D5C2314yes—
96C22×Dic10—42no—
97C22×Dic10—42no—
98C22×Dic10C2×C418yescomplemented
99C22×Dic10C2314yes—
100C2×C5×C4⋊C4—24no—
101C2×C5×C4⋊C4C2×C418yescomplemented
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C4⋊C4C2314yes—
104C2×C42×C5—24no—
105C2×C42×C5—42no—
106C2×C42×C5—42no—
107C2×C42×C5C2314yes—
108C2×C42×C5C2314yes—
109C2×C42×C5C2314yes—
110C2×#685—24no—
111C2×#685C2×C418yes—
112C2×#685C2×C418yes—
113C2×#685Q818yescomplemented
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×C4⋊Dic5—42no—
119C2×C4⋊Dic5C2314yes—
120C2×#683—24no—
121C2×#683—42no—
122C2×#683C2×C418yescomplemented
123C2×#683C2×C418yescomplemented
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×C4×Dic5—24no—
129C2×C4×Dic5—42no—
130C2×C4×Dic5—42no—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
133C2×C4×Dic5C2314yes—
134#4042C2×C4164yescomplemented
135C5×#95C2314yes—
136C5×#95C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149C22×C22⋊Q8—51no—
150#2368—516no—
151C2×#391—51no—
152C2×#391—51no—
153C2×#387—51no—
154C2×#387—51no—
155C2×#387—51no—
156C2×#387—51no—
157C2×#385—51no—
158C2×#385—51no—
159C2×C4×C4⋊C4—51no—
160C2×C4×C4⋊C4D511yescharacteristic, complemented
161C2×C4×C22⋊C4—51no—
162C2×C4×C22⋊C4—51no—
163C2×C4×C22⋊C4—51no—
164C22×#95—51no—
165C24×C5C2411yescharacteristic
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5C22×C414yes—
171C23×D5C2×Q814yes—
172C23×D5#4114yes—
173C23×D5C2412yes—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5C22×C414yes—
190C22×C4×C5C22×C414yes—
191C22×C4×C5C22×C414yes—
192C22×C4×C5C2×Q814yes—
193C22×C4×C5#4114yes—
194C22×C4×C5#4114yes—
195C22×C4×C5C2412yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5C22×C414yes—
220C22×Dic5C22×C414yes—
221C22×Dic5C22×C414yes—
222C22×Dic5C2×Q814yes—
223C22×Dic5C2412yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C2×C4×D5—28no—
231C2×C4×D5—28no—
232C2×C4×D5—28no—
233C2×C4×D5—28no—
234C2×C4×D5—416no—
235C2×C4×D5—44no—
236C2×C4×D5—44no—
237C2×C4×D5—44no—
238C2×C4×D5—44no—
239C2×C4×D5—416no—
240C2×C4×D5—416no—
241C2×C4×D5C22×C4116yes—
242C2×Dic10—416no—
243C2×Dic10—44no—
244C2×Dic10—44no—
245C2×Dic10C22×C4116yescomplemented
246C5×C4⋊C4—28no—
247C5×C4⋊C4C22×C4116yescomplemented
248C42×C5—28no—
249C42×C5—44no—
250C42×C5—44no—
251#685—28no—
252#685C22×C4116yes—
253#685C22×C4116yes—
254#685C2×Q8116yescomplemented
255C4⋊Dic5—44no—
256#683—28no—
257#683—44no—
258#683C22×C4116yescomplemented
259#683C22×C4116yescomplemented
260C4×Dic5—28no—
261C4×Dic5—44no—
262C4×Dic5—44no—
263C23×Q8—51no—
264C24×C4—51no—
265C24×C4—51no—
266C24×C4—51no—
267C2×C22⋊Q8—516no—
268C2×C22⋊Q8—58no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4—51no—
271C22×C4⋊C4—51no—
272C22×C4⋊C4—51no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4C2×D511yescharacteristic
275C22×C4⋊C4C2×D511yescharacteristic
276C22×C22⋊C4—51no—
277C22×C22⋊C4—51no—
278C22×C22⋊C4—51no—
279C22×C22⋊C4—51no—
280C22×C42—51no—
281C22×C42—51no—
282C22×C42—51no—
283C22×C42C2×D511yescharacteristic
284C22×C42C2×D511yescharacteristic
285C22×C42C2×D511yescharacteristic
286#391—58no—
287#391—58no—
288#387—58no—
289#387—58no—
290#387—58no—
291#387—58no—
292#385—58no—
293#385—58no—
294C4×C4⋊C4—58no—
295C4×C4⋊C4C2×D518yescomplemented
296C4×C22⋊C4—58no—
297C4×C22⋊C4—58no—
298C4×C22⋊C4—58no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—58no—
312C2×#95C2×D511yescharacteristic
313C2×#95C2×D511yescharacteristic
314C23×C5C23×C412yes—
315C23×C5C22×Q812yes—
316C23×C5C2×#4112yes—
317C23×C5C2×#4112yes—
318C23×C5C2×#4112yes—
319C23×C5H(5,𝔽2)12yes—
320C23×C5H(5,𝔽2)12yes—
321C23×C5C2511yescharacteristic
322C22×D5—28no—
323C22×D5—28no—
324C22×D5—28no—
325C22×D5—28no—
326C22×D5—28no—
327C22×D5—28no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5C4×Q8116yes—
333C22×D5C23×C414yes—
334C22×D5C22×Q814yes—
335C22×D5C2×#4114yes—
336C2×C4×C5—28no—
337C2×C4×C5—28no—
338C2×C4×C5—28no—
339C2×C4×C5—28no—
340C2×C4×C5—28no—
341C2×C4×C5—28no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—44no—
358C2×C4×C5C23×C414yes—
359C2×C4×C5C23×C414yes—
360C2×C4×C5C23×C414yes—
361C2×C4×C5C22×Q814yes—
362C2×C4×C5C2×#4114yes—
363C2×C4×C5C2×#4114yes—
364C2×Dic5—28no—
365C2×Dic5—28no—
366C2×Dic5—28no—
367C2×Dic5—28no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—44no—
386C2×Dic5—44no—
387C2×Dic5—44no—
388C2×Dic5C23×C414yes—
389C2×Dic5C23×C414yes—
390C2×Dic5C23×C414yes—
391C2×Dic5C22×Q814yes—
392C4×D5—416no—
393C4×D5—416no—
394C4×D5—416no—
395Dic10—416no—
396C25—51no—
397C22×Q8—58no—
398C22×Q8—54no—
399C22×Q8—202no—
400C22×Q8—202no—
401C23×C4—51no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—58no—
406C23×C4—54no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—54no—
411C23×C4—54no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—104no—
416C23×C4—202no—
417C23×C4—202no—
418C23×C4—202no—
419C23×C4—202no—
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C22⋊Q8—564no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—58no—
430C2×C4⋊C4—58no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—54no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—104no—
437C2×C4⋊C4—202no—
438C2×C4⋊C4—202no—
439C2×C4⋊C4C4×D518yescomplemented
440C2×C4⋊C4C22×D514yes—
441C2×C4⋊C4C22×D514yes—
442C2×C22⋊C4—58no—
443C2×C22⋊C4—58no—
444C2×C22⋊C4—58no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—104no—
450C2×C42—24no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42—54no—
454C2×C42—54no—
455C2×C42—54no—
456C2×C42—104no—
457C2×C42—202no—
458C2×C42—202no—
459C2×C42C22×D514yes—
460C2×C42C22×D514yes—
461C2×C42C22×D514yes—
462#95—54no—
463#95—54no—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
473#95—54no—
474#95C22×D514yes—
475#95C22×D514yes—
476C22×C5C2×C4×Q814yes—
477C22×C5C4×#4114yes—
478C22×C5#51814yes—
479C22×C5#55114yes—
480C22×C5#55114yes—
481C22×C5#55414yes—
482C22×C5#55414yes—
483C22×C5C24×C411yescharacteristic
484C22×C5C23×Q811yescharacteristic
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C2×H(5,𝔽2)11yescharacteristic
489C22×C5C2×H(5,𝔽2)11yescharacteristic
490C2×D5—232no—
491C2×D5—24no—
492C2×D5—24no—
493C2×D5—24no—
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—24no—
497C2×D5C2×C4×Q818yes—
498C4×C5—24no—
499C4×C5—24no—
500C4×C5—24no—
501C4×C5—24no—
502C4×C5—24no—
503C4×C5—24no—
504C4×C5—42no—
505Dic5—24no—
506Dic5—24no—
507Dic5—24no—
508Dic5—24no—
509Dic5—42no—
510Dic5—42no—
511Dic5—42no—
512C24—54no—
513C24—54no—
514C24—54no—
515C24—52no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24C23×D511yescharacteristic
521C2×Q8—516no—
522C2×Q8—2016no—
523C2×Q8—204no—
524C2×Q8—204no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—54no—
541C22×C4—54no—
542C22×C4—54no—
543C22×C4—54no—
544C22×C4—52no—
545C22×C4—52no—
546C22×C4—52no—
547C22×C4—52no—
548C22×C4—516no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—108no—
553C22×C4—108no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—108no—
572C22×C4—108no—
573C22×C4—2016no—
574C22×C4—204no—
575C22×C4—204no—
576C22×C4—204no—
577C22×C4—204no—
578C22×C4—2016no—
579C22×C4—2016no—
580C22×C4C2×C4×D514yes—
581C22×C4C2×C4×D514yes—
582C22×C4C2×C4×D514yes—
583C22×C4#70914yes—
584C22×C4#70914yes—
585C22×C4Q8×D514yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D512yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C4⋊C4—28no—
594C4⋊C4—516no—
595C4⋊C4—516no—
596C4⋊C4—108no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C4⋊C4C2×C4×D5116yescomplemented
600C22⋊C4—516no—
601C22⋊C4—516no—
602C22⋊C4—516no—
603C22⋊C4—108no—
604C42—28no—
605C42—44no—
606C42—44no—
607C42—108no—
608C42—204no—
609C42—204no—
610C2×C5#236818yescomplemented
611C2×C5C22×C4×Q811yescharacteristic
612C2×C5C2×C4×#4111yescharacteristic
613C2×C5C2×#51811yescharacteristic
614C2×C5C2×#55111yescharacteristic
615C2×C5C2×#55111yescharacteristic
616C2×C5C2×#55411yescharacteristic
617C2×C5C2×#55411yescharacteristic
618D5—28no—
619C23—516no—
620C23—54no—
621C23—54no—
622C23—54no—
623C23—108no—
624C23—108no—
625C23—108no—
626C23—108no—
627C23—108no—
628C23—108no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23C22×C4×D512yes—
634C23C2×#70912yes—
635C23C2×#70912yes—
636C23#414412yes—
637C23C2×Q8×D512yes—
638C23D5×#4112yes—
639C23#414912yes—
640C23C24×D511yescharacteristic
641Q8—2016no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—54no—
665C2×C4—54no—
666C2×C4—54no—
667C2×C4—54no—
668C2×C4—108no—
669C2×C4—108no—
670C2×C4—108no—
671C2×C4—108no—
672C2×C4—102no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—2016no—
690C2×C4—2016no—
691C2×C4—2016no—
692C2×C4—204no—
693C2×C4—204no—
694C2×C4—204no—
695C2×C4C22×C4×D514yes—
696C2×C4C22×C4×D514yes—
697C2×C4C22×C4×D514yes—
698C2×C4C2×#70914yes—
699C2×C4C2×#70914yes—
700C2×C4C2×Q8×D514yes—
701C5C2×#236811yescharacteristic, complemented, Sylow
702C22—58no—
703C22—104no—
704C22—104no—
705C22—104no—
706C22—104no—
707C22—104no—
708C22—1032no—
709C22—104no—
710C22C4×#70914yes—
711C22#6584514yes—
712C22#6586114yes—
713C22#6587914yes—
714C22#6589014yes—
715C22C4×Q8×D514yes—
716C22#6591314yes—
717C22C23×C4×D511yescharacteristic
718C22C22×#70911yescharacteristic
719C22C22×#70911yescharacteristic
720C22C2×#414411yescharacteristic
721C22C22×Q8×D511yescharacteristic
722C22C2×D5×#4111yescharacteristic
723C22C2×#414911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—24no—
730C4—42no—
731C4—104no—
732C4—104no—
733C4—104no—
734C4—104no—
735C4—202no—
736C4—202no—
737C4—202no—
738C2—108no—
739C2#1060550618yesdirect product factor
740C2C2×C4×#70911yescharacteristic
741C2C2×#6584511yescharacteristic
742C2C2×#6586111yescharacteristic
743C2C2×#6587911yescharacteristic
744C2C2×#6589011yescharacteristic
745C2C2×C4×Q8×D511yescharacteristic
746C2C2×#6591311yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC24×D5C23
cosocleC23×C5C25
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×#2368
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C4⋊C4C2semidirect
4. C2×#65267C2semidirect
5. C2×#65270C2semidirect
6. C2×#65218C2semidirect
7. C2×#65222C2semidirect
8. C2×#65222C2semidirect
12. #10605506C2direct (N × H)
15. C2×#64935C2semidirect
16. C2×#64938C2semidirect
38. C2×#4042C4semidirect
40. C4×C5×C4⋊C4C22semidirect
56. #65270C22semidirect
57. #65267C22semidirect
61. #65222C22semidirect
62. #65222C22semidirect
63. #65218C22semidirect
66. #64938C22semidirect
67. #64935C22semidirect
98. C22×Dic10C2×C4semidirect
101. C2×C5×C4⋊C4C2×C4semidirect
113. C2×#685Q8semidirect
122. C2×#683C2×C4semidirect
123. C2×#683C2×C4semidirect
134. #4042C2×C4semidirect
160. C2×C4×C4⋊C4D5semidirect
245. C2×Dic10C22×C4semidirect
247. C5×C4⋊C4C22×C4semidirect
254. #685C2×Q8semidirect
258. #683C22×C4semidirect
259. #683C22×C4semidirect
295. C4×C4⋊C4C2×D5semidirect
439. C2×C4⋊C4C4×D5semidirect
599. C4⋊C4C2×C4×D5semidirect
610. C2×C5#2368semidirect
701. C5C2×#2368semidirect
739. C2#10605506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C2×C4×C5×C4⋊C42
C2×#652782
C2×#652672
C2×#652702
C2×#652182
C2×#652222
C2×C4×#6852
#106055062
C2×#649572
C2×D5×#952
C2×#649352
C2×#649382
C2×#23685