Finite Group Databasebeta

← C2×#10607953 #12267952

Subgroups — C2×#10607953 #12267952

Order 1280.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic
2C22×#4018C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×#65278C211yesmaximal, characteristic
5C2×#65278C211yesmaximal, characteristic
6C2×#65276C211yesmaximal, characteristic
7C2×#65271C211yesmaximal, characteristic, complemented
8C2×#65272C211yesmaximal, characteristic, complemented
9C2×#65269C211yesmaximal, characteristic, complemented
10C2×#65268C211yesmaximal, characteristic, complemented
11C2×#65222C211yesmaximal, characteristic, complemented
12#10607953C2116yesmaximal, direct product factor
13C2×#64953C211yesmaximal, characteristic
14C2×D5×#95C211yesmaximal, characteristic
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64943C211yesmaximal, characteristic, complemented
17C23×C4×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4042—28no—
39C2×#4042C2218yes—
40C2×#4018—28no—
41C2×#4018C2218yes—
42C5×#389C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65278C2218yes—
58#65278C2218yes—
59#65276C2218yes—
60#65272C2218yescomplemented
61#65271C2218yescomplemented
62#65269C2218yescomplemented
63#65268C2218yescomplemented
64#65222C2218yescomplemented
65#64953C2218yes—
66D5×#95C2218yes—
67#64943C2218yescomplemented
68#64935C2218yescomplemented
69C2×#2438—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×C4×D5—24no—
86C22×C4×D5—24no—
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—42no—
92C22×C4×D5—42no—
93C22×C4×D5Q818yescomplemented
94C22×C4×D5C2314yes—
95C22×C4×D5C2314yes—
96C22×C4×D5C2314yes—
97C22×Dic10—24no—
98C22×Dic10—24no—
99C22×Dic10—42no—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—42no—
104C2×C5×C4⋊C4—42no—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C42×C5—24no—
110C2×C42×C5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685D418yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—24no—
125C2×#683—24no—
126C2×#683—42no—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×C4×Dic5—24no—
134C2×C4×Dic5C2314yes—
135#4042—232no—
136#4018—232no—
137C5×#95C2314yes—
138C5×#95C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×C22⋊Q8—51no—
152C22×#117—51no—
153#2438—516no—
154C2×#400—51no—
155C2×#398—51no—
156C2×#398—51no—
157C2×#395—51no—
158C2×#391—51no—
159C2×#389D511yescharacteristic, complemented
160C2×#387—51no—
161C2×#387—51no—
162C2×#385—51no—
163C2×#385—51no—
164C2×#381—51no—
165C2×#380—51no—
166C22×#95—51no—
167C24×C5C2411yescharacteristic
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5C2×D414yes—
173C23×D5C2×Q814yes—
174C23×D5#4114yes—
175C23×D5C2412yes—
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×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5C2×D414yes—
195C22×C4×C5C2×Q814yes—
196C22×C4×C5#4114yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
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×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5C2×D414yes—
223C22×Dic5C2×Q814yes—
224C22×Dic5#4114yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C2×C4×D5—232no—
233C2×C4×D5—28no—
234C2×C4×D5—28no—
235C2×C4×D5—28no—
236C2×C4×D5—28no—
237C2×C4×D5—28no—
238C2×C4×D5—28no—
239C2×C4×D5—44no—
240C2×C4×D5—44no—
241C2×C4×D5—416no—
242C2×C4×D5—416no—
243C2×C4×D5C2×Q8116yescomplemented
244C2×Dic10—28no—
245C2×Dic10—28no—
246C2×Dic10—44no—
247C2×Dic10—416no—
248C5×C4⋊C4—28no—
249C5×C4⋊C4—28no—
250C5×C4⋊C4—44no—
251C5×C4⋊C4—44no—
252C42×C5—28no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685C2×D4116yes—
257C4⋊Dic5—28no—
258#683—28no—
259#683—28no—
260#683—28no—
261#683—28no—
262#683—28no—
263#683—44no—
264C4×Dic5—28no—
265C23×Q8—51no—
266C24×C4—51no—
267C24×C4—51no—
268C24×C4—51no—
269C2×C22⋊Q8—58no—
270C2×C22⋊Q8—108no—
271C2×#117—58no—
272C2×#117—108no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4C2×D511yescharacteristic
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C42—51no—
289C22×C42C2×D511yescharacteristic
290#400—58no—
291#398—58no—
292#398—58no—
293#395—58no—
294#391—58no—
295#389C2×D518yescomplemented
296#387—58no—
297#387—58no—
298#385—58no—
299#385—58no—
300#381—58no—
301#380—58no—
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—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95—58no—
315C2×#95C2×D511yescharacteristic
316C2×#95C2×D511yescharacteristic
317C23×C5C22×D412yes—
318C23×C5C22×Q812yes—
319C23×C5C2×#4112yes—
320C23×C5C2×#4112yes—
321C23×C5C2×#4112yes—
322C23×C5H(5,𝔽2)12yes—
323C23×C52−1+412yes—
324C23×C5C2511yescharacteristic
325C22×D5—28no—
326C22×D5—28no—
327C22×D5—28no—
328C22×D5—28no—
329C22×D5—28no—
330C22×D5—28no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5C22⋊Q8116yes—
336C22×D5C22×D414yes—
337C22×D5C22×Q814yes—
338C22×D5C2×#4114yes—
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—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—44no—
361C2×C4×C5—44no—
362C2×C4×C5—44no—
363C2×C4×C5—44no—
364C2×C4×C5C22×D414yes—
365C2×C4×C5C22×Q814yes—
366C2×C4×C5C2×#4114yes—
367C2×Dic5—28no—
368C2×Dic5—28no—
369C2×Dic5—28no—
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—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—44no—
389C2×Dic5—44no—
390C2×Dic5—44no—
391C2×Dic5—44no—
392C2×Dic5C22×D414yes—
393C2×Dic5C22×Q814yes—
394C2×Dic5C2×#4114yes—
395C4×D5—232no—
396C4×D5—416no—
397C4×D5—416no—
398Dic10—416no—
399C25—51no—
400C22×Q8—54no—
401C22×Q8—104no—
402C22×Q8—104no—
403C22×Q8—202no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—58no—
408C23×C4—54no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—54no—
414C23×C4—54no—
415C23×C4—104no—
416C23×C4—104no—
417C23×C4—104no—
418C23×C4—104no—
419C23×C4—104no—
420C23×C4—104no—
421C23×C4—202no—
422C23×C4—202no—
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C22⋊Q8—1032no—
431#117—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—104no—
444C2×C4⋊C4—104no—
445C2×C4⋊C4—104no—
446C2×C4⋊C4—104no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—202no—
450C2×C4⋊C4C22×D514yes—
451C2×C4⋊C4C22×D514yes—
452C2×C4⋊C4C22×D514yes—
453C2×C4⋊C4C22×D514yes—
454C2×C22⋊C4—58no—
455C2×C22⋊C4—54no—
456C2×C22⋊C4—54no—
457C2×C22⋊C4—54no—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—104no—
460C2×C22⋊C4—104no—
461C2×C22⋊C4—104no—
462C2×C42—24no—
463C2×C42—54no—
464C2×C42—104no—
465C2×C42C22×D514yes—
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#95—54no—
475#95—54no—
476#95—54no—
477#95—54no—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5C2×C22⋊Q814yes—
481C22×C5#53314yes—
482C22×C5#54414yes—
483C22×C5#54614yes—
484C22×C5#54714yes—
485C22×C5#55114yes—
486C22×C5#55214yes—
487C22×C5C23×D411yescharacteristic
488C22×C5C23×Q811yescharacteristic
489C22×C5C22×#4111yescharacteristic
490C22×C5C22×#4111yescharacteristic
491C22×C5C22×#4111yescharacteristic
492C22×C5C2×H(5,𝔽2)11yescharacteristic
493C22×C5C2×2−1+411yescharacteristic
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—232no—
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—24no—
500C2×D5—24no—
501C2×D5C2×C22⋊Q818yes—
502C4×C5—24no—
503C4×C5—24no—
504C4×C5—24no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—42no—
509Dic5—24no—
510Dic5—24no—
511Dic5—24no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516C24—54no—
517C24—54no—
518C24—54no—
519C24—52no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24C23×D511yescharacteristic
525C2×Q8—108no—
526C2×Q8—108no—
527C2×Q8—204no—
528C2×Q8—2016no—
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—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—54no—
548C22×C4—54no—
549C22×C4—54no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—516no—
554C22×C4—52no—
555C22×C4—52no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—108no—
559C22×C4—108no—
560C22×C4—1032no—
561C22×C4—108no—
562C22×C4—108no—
563C22×C4—108no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—108no—
583C22×C4—204no—
584C22×C4—204no—
585C22×C4—2016no—
586C22×C4—2016no—
587C22×C4#70914yes—
588C22×C4D4×D514yes—
589C22×C4Q8×D514yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C22×C4C23×D512yes—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—108no—
602C4⋊C4—108no—
603C4⋊C4—108no—
604C4⋊C4—108no—
605C4⋊C4—108no—
606C4⋊C4—108no—
607C4⋊C4—204no—
608C22⋊C4—516no—
609C22⋊C4—108no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C42—28no—
613C42—108no—
614C2×C5#243818yescomplemented
615C2×C5C22×C22⋊Q811yescharacteristic
616C2×C5C2×#53311yescharacteristic
617C2×C5C2×#54411yescharacteristic
618C2×C5C2×#54611yescharacteristic
619C2×C5C2×#54711yescharacteristic
620C2×C5C2×#55111yescharacteristic
621C2×C5C2×#55211yescharacteristic
622D5—28no—
623C23—516no—
624C23—54no—
625C23—54no—
626C23—54no—
627C23—108no—
628C23—108no—
629C23—108no—
630C23—108no—
631C23—108no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—108no—
637C23C2×#70912yes—
638C23C2×D4×D512yes—
639C23#414412yes—
640C23C2×Q8×D512yes—
641C23#414712yes—
642C23D5×#4112yes—
643C23D5×#4112yes—
644C23C24×D511yescharacteristic
645Q8—2016no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
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—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—54no—
672C2×C4—54no—
673C2×C4—54no—
674C2×C4—1032no—
675C2×C4—108no—
676C2×C4—108no—
677C2×C4—108no—
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—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—2016no—
697C2×C4—2016no—
698C2×C4—204no—
699C2×C4—204no—
700C2×C4—204no—
701C2×C4—204no—
702C2×C4C2×#70914yes—
703C2×C4C2×D4×D514yes—
704C2×C4C2×Q8×D514yes—
705C5C2×#243811yescharacteristic, complemented, Sylow
706C22—58no—
707C22—104no—
708C22—1032no—
709C22—104no—
710C22—104no—
711C22—104no—
712C22—104no—
713C22—104no—
714C22#6584114yes—
715C22#6589014yes—
716C22#6591214yes—
717C22#6594614yes—
718C22D5×C22⋊Q814yes—
719C22#6602714yes—
720C22#6606314yes—
721C22C22×#70911yescharacteristic
722C22C22×D4×D511yescharacteristic
723C22C2×#414411yescharacteristic
724C22C22×Q8×D511yescharacteristic
725C22C2×#414711yescharacteristic
726C22C2×D5×#4111yescharacteristic
727C22C2×D5×#4111yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—104no—
736C4—104no—
737C4—104no—
738C4—202no—
739C4—202no—
740C4—202no—
741C4—202no—
742C2—108no—
743C2#1060795318yesdirect product factor
744C2C2×#6584111yescharacteristic
745C2C2×#6589011yescharacteristic
746C2C2×#6591211yescharacteristic
747C2C2×#6594611yescharacteristic
748C2C2×D5×C22⋊Q811yescharacteristic
749C2C2×#6602711yescharacteristic
750C2C2×#6606311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#389D5
hypocenterC5C2×#2438
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×C5×#389C2semidirect
7. C2×#65271C2semidirect
8. C2×#65272C2semidirect
9. C2×#65269C2semidirect
10. C2×#65268C2semidirect
11. C2×#65222C2semidirect
12. #10607953C2direct (N × H)
15. C2×#64935C2semidirect
16. C2×#64943C2semidirect
42. C5×#389C22semidirect
60. #65272C22semidirect
61. #65271C22semidirect
62. #65269C22semidirect
63. #65268C22semidirect
64. #65222C22semidirect
67. #64943C22semidirect
68. #64935C22semidirect
93. C22×C4×D5Q8semidirect
159. C2×#389D5semidirect
243. C2×C4×D5C2×Q8semidirect
295. #389C2×D5semidirect
614. C2×C5#2438semidirect
705. C5C2×#2438semidirect
743. C2#10607953direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×#40182
C2×C5×#3892
C2×#652782
C2×#652762
C2×#652712
C2×#652722
C2×#652692
C2×#652682
C2×#652222
#106079532
C2×#649532
C2×D5×#952
C2×#649352
C2×#649432
C2×#24385