Finite Group Databasebeta

← C2×#10607278 #12268518

Subgroups — C2×#10607278 #12268518

Order 1280.

2854 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×#4034C211yesmaximal, characteristic, complemented
2C22×#4024C211yesmaximal, characteristic
3C2×C5×#388C211yesmaximal, characteristic
4C2×#65275C211yesmaximal, characteristic, complemented
5C2×#65236C211yesmaximal, characteristic
6C2×#65236C211yesmaximal, characteristic
7C2×#65240C211yesmaximal, characteristic
8C2×#65231C211yesmaximal, characteristic
9C2×C22⋊C4×Dic5C211yesmaximal, characteristic
10C2×#65218C211yesmaximal, characteristic, complemented
11C2×C4×#683C211yesmaximal, characteristic, complemented
12#10607278C2116yesmaximal, direct product factor
13C2×#64949C211yesmaximal, characteristic, complemented
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64935C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4034—28no—
39C2×#4034C2218yescomplemented
40C2×#4024—28no—
41C2×#4024C2218yes—
42C5×#388C2218yes—
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#65275C2218yescomplemented
58#65240C2218yes—
59#65236C2218yes—
60#65236C2218yes—
61#65231C2218yes—
62C22⋊C4×Dic5C2218yes—
63C4×#683C2218yescomplemented
64#65218C2218yescomplemented
65#64949C2218yescomplemented
66#64935C2218yescomplemented
67#64935C2218yescomplemented
68#64935C2218yescomplemented
69C2×#2492—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5—24no—
78C23×Dic5—24no—
79C23×Dic5—24no—
80C23×Dic5C2314yes—
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×Dic10—24no—
90C22×Dic10—24no—
91C22×Dic10—24no—
92C22×Dic10—24no—
93C22×Dic10—24no—
94C22×Dic10—24no—
95C22×Dic10—24no—
96C22×Dic10—42no—
97C22×Dic10—42no—
98C22×Dic10C2314yes—
99C22×Dic10C2314yes—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4Q818yescomplemented
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C42×C5—42no—
110C2×C42×C5C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—42no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×C4⋊Dic5—24no—
118C2×C4⋊Dic5—24no—
119C2×C4⋊Dic5C2314yes—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683D418yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×C4×Dic5—24no—
130C2×C4×Dic5—24no—
131C2×C4×Dic5—42no—
132C2×C4×Dic5C2314yes—
133C2×C4×Dic5C2314yes—
134C2×C4×Dic5C2314yes—
135#4034—232no—
136#4024—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×C4⋊Q8—51no—
152C22×C22⋊Q8—51no—
153#2492—516no—
154C2×#400—51no—
155C2×#400—51no—
156C2×#393—51no—
157C2×#393—51no—
158C2×#391—51no—
159C2×#391—51no—
160C2×#391—51no—
161C2×#391—51no—
162C2×#388—51no—
163C2×#388D511yescharacteristic
164C2×#380—51no—
165C2×C4×C4⋊C4—51no—
166C2×C4×C22⋊C4—51no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5C2×Q814yes—
174C24×C5C2412yes—
175C24×C5C2411yescharacteristic
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×C5C2×D414yes—
192C22×C4×C5C2×Q814yes—
193C22×C4×C5C2×Q814yes—
194C22×C4×C5C2412yes—
195C22×C4×C5C2412yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×Dic5—22no—
201C22×Dic5—22no—
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×Dic5—28no—
220C22×Dic5—28no—
221C22×Dic5—28no—
222C22×Dic5—416no—
223C22×Dic5C2×D414yes—
224C22×Dic5C2×D414yes—
225C22×Dic5#4114yes—
226C22×Dic5#4114yes—
227C22×Dic5#4114yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C2×Dic10—28no—
237C2×Dic10—28no—
238C2×Dic10—28no—
239C2×Dic10—28no—
240C2×Dic10—28no—
241C2×Dic10—28no—
242C2×Dic10—28no—
243C2×Dic10—44no—
244C2×Dic10—44no—
245C2×Dic10—416no—
246C2×Dic10—416no—
247C2×Dic10—416no—
248C5×C4⋊C4—28no—
249C5×C22⋊C4—28no—
250C5×C22⋊C4—44no—
251C5×C22⋊C4C2×Q8116yescomplemented
252C42×C5—44no—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255C22⋊Dic5—44no—
256C4⋊Dic5—28no—
257C4⋊Dic5—28no—
258#683—28no—
259#683—28no—
260#683—28no—
261#683C2×D4116yes—
262C4×Dic5—28no—
263C4×Dic5—28no—
264C4×Dic5—44no—
265C23×Q8—51no—
266C23×Q8—51no—
267C23×Q8—51no—
268C24×C4—51no—
269C2×C4⋊Q8—58no—
270C2×C4⋊Q8—108no—
271C2×C22⋊Q8—58no—
272C2×C22⋊Q8—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⋊C4C2×D511yescharacteristic
280C22×C22⋊C4—51no—
281C22×C22⋊C4—51no—
282C22×C22⋊C4—51no—
283C22×C22⋊C4C2×D511yescharacteristic
284C22×C22⋊C4C2×D511yescharacteristic
285C22×C22⋊C4C2×D511yescharacteristic
286C22×C42—51no—
287C22×C42—51no—
288C22×C42—51no—
289C22×C42C2×D511yescharacteristic
290#400—58no—
291#400—58no—
292#393—58no—
293#393—58no—
294#391—58no—
295#391—58no—
296#391—58no—
297#391—58no—
298#388—58no—
299#388C2×D518yes—
300#380—58no—
301C4×C4⋊C4—58no—
302C4×C22⋊C4—58no—
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—51no—
315C2×#95C2×D511yescharacteristic
316C2×#95C2×D511yescharacteristic
317C23×C5—28no—
318C23×C5—28no—
319C23×C5—28no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—44no—
327C23×C5—44no—
328C23×C5—44no—
329C23×C5—44no—
330C23×C5C22×D412yes—
331C23×C5C22×Q814yes—
332C23×C5C22×Q812yes—
333C23×C5C2×#4112yes—
334C23×C5C2×#4112yes—
335C23×C5C2×#4112yes—
336C23×C5H(5,𝔽2)12yes—
337C23×C52−1+412yes—
338C23×C5C2511yescharacteristic
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×C5—44no—
359C2×C4×C5—44no—
360C2×C4×C5C22×D414yes—
361C2×C4×C5C22×Q814yes—
362C2×C4×C5C22×Q814yes—
363C2×Dic5—28no—
364C2×Dic5—28no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
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—44no—
385C2×Dic5—44no—
386C2×Dic5—44no—
387C2×Dic5—44no—
388C2×Dic5—44no—
389C2×Dic5—416no—
390C2×Dic5#124116yes—
391C2×Dic5C22×D414yes—
392C2×Dic5C22×D414yes—
393C2×Dic5C2×#4114yes—
394C2×Dic5C2×#4114yes—
395C2×Dic5C2×#4114yes—
396Dic10—416no—
397Dic10—416no—
398Dic10—416no—
399C25C22×D511yescharacteristic
400C22×Q8—54no—
401C22×Q8—54no—
402C22×Q8—54no—
403C22×Q8—104no—
404C22×Q8—104no—
405C22×Q8—104no—
406C22×Q8—104no—
407C22×Q8—104no—
408C22×Q8—104no—
409C22×Q8—104no—
410C22×Q8—202no—
411C22×Q8—202no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—54no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—104no—
422C23×C4—104no—
423C23×C4—104no—
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C4⋊Q8—1032no—
431C22⋊Q8—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—58no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—104no—
441C2×C4⋊C4—104no—
442C2×C4⋊C4—104no—
443C2×C4⋊C4—104no—
444C2×C4⋊C4—104no—
445C2×C4⋊C4C22×D514yes—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4Dic1018yescomplemented
455C2×C22⋊C4C22×D514yes—
456C2×C22⋊C4C22×D514yes—
457C2×C22⋊C4C22×D514yes—
458C2×C42—42no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—54no—
462C2×C42—104no—
463C2×C42—104no—
464C2×C42—202no—
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×C5—24no—
481C22×C5—24no—
482C22×C5—24no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—42no—
487C22×C5—416no—
488C22×C5C2×#12414yes—
489C22×C5#53314yes—
490C22×C5#54214yes—
491C22×C5#54614yes—
492C22×C5D4×Q814yes—
493C22×C5#55414yes—
494C22×C5#55614yes—
495C22×C5C23×D411yescharacteristic
496C22×C5C23×Q811yescharacteristic
497C22×C5C22×#4111yescharacteristic
498C22×C5C22×#4111yescharacteristic
499C22×C5C22×#4111yescharacteristic
500C22×C5C2×H(5,𝔽2)11yescharacteristic
501C22×C5C2×2−1+411yescharacteristic
502C4×C5—24no—
503C4×C5—24no—
504C4×C5—24no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5—42no—
508Dic5—24no—
509Dic5—24no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5C2×#12418yes—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24C2×Dic1014yes—
523C24C23×D512yes—
524C24C23×D511yescharacteristic
525C2×Q8—108no—
526C2×Q8—108no—
527C2×Q8—108no—
528C2×Q8—108no—
529C2×Q8—108no—
530C2×Q8—108no—
531C2×Q8—108no—
532C2×Q8—204no—
533C2×Q8—204no—
534C2×Q8—2016no—
535C2×Q8—2016no—
536C2×Q8—2016no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—54no—
553C22×C4—54no—
554C22×C4—54no—
555C22×C4—52no—
556C22×C4—54no—
557C22×C4—54no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—108no—
566C22×C4—108no—
567C22×C4—108no—
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—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—2016no—
588C22×C4C2×Dic1014yes—
589C22×C4C2×Dic1014yes—
590C22×C4D4×D514yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C22×C4C23×D512yes—
597C4⋊C4—28no—
598C4⋊C4—516no—
599C4⋊C4—108no—
600C4⋊C4—108no—
601C4⋊C4—108no—
602C4⋊C4—108no—
603C4⋊C4—108no—
604C22⋊C4—28no—
605C22⋊C4—44no—
606C22⋊C4—108no—
607C22⋊C4—108no—
608C22⋊C4—204no—
609C22⋊C4C2×Dic10116yescomplemented
610C42—44no—
611C42—108no—
612C42—108no—
613C42—204no—
614C2×C5—44no—
615C2×C5#249218yescomplemented
616C2×C5C22×#12411yescharacteristic
617C2×C5C2×#53311yescharacteristic
618C2×C5C2×#54211yescharacteristic
619C2×C5C2×#54611yescharacteristic
620C2×C5C2×D4×Q811yescharacteristic
621C2×C5C2×#55411yescharacteristic
622C2×C5C2×#55611yescharacteristic
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23C22×Dic1014yes—
637C23C22×Dic1012yes—
638C23C2×D4×D512yes—
639C23#414412yes—
640C23D5×#4112yes—
641C23D5×#4112yes—
642C23D5×#4112yes—
643C23#415012yes—
644C23C24×D511yescharacteristic
645Q8—2016no—
646Q8—2016no—
647Q8—2016no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
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—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—516no—
670C2×C4—54no—
671C2×C4—54no—
672C2×C4—54no—
673C2×C4—54no—
674C2×C4—54no—
675C2×C4—108no—
676C2×C4—108no—
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—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—2016no—
697C2×C4—204no—
698C2×C4—204no—
699C2×C4—204no—
700C2×C4—204no—
701C2×C4—204no—
702C2×C4C22×Dic1014yes—
703C2×C4C22×Dic1014yes—
704C2×C4C2×D4×D514yes—
705C5C2×#249211yescharacteristic, complemented, Sylow
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—416no—
713C22—42no—
714C22#6585114yes—
715C22D4×Dic1014yes—
716C22#6587314yes—
717C22#6594414yes—
718C22#6599614yes—
719C22D5×#12414yes—
720C22#6603614yes—
721C22C23×Dic1011yescharacteristic
722C22C22×D4×D511yescharacteristic
723C22C2×#414411yescharacteristic
724C22C2×D5×#4111yescharacteristic
725C22C2×D5×#4111yescharacteristic
726C22C2×D5×#4111yescharacteristic
727C22C2×#415011yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—58no—
735C4—104no—
736C4—104no—
737C4—202no—
738C4—202no—
739C4—202no—
740C4—202no—
741C4—202no—
742C2—44no—
743C2#1060727818yesdirect product factor
744C2C2×#6585111yescharacteristic
745C2C2×D4×Dic1011yescharacteristic
746C2C2×#6587311yescharacteristic
747C2C2×#6594411yescharacteristic
748C2C2×#6599611yescharacteristic
749C2C2×D5×#12411yescharacteristic
750C2C2×#6603611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5C2×#2492
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4034C2semidirect
4. C2×#65275C2semidirect
10. C2×#65218C2semidirect
11. C2×C4×#683C2semidirect
12. #10607278C2direct (N × H)
13. C2×#64949C2semidirect
14. C2×#64935C2semidirect
15. C2×#64935C2semidirect
16. C2×#64935C2semidirect
39. C2×#4034C22semidirect
57. #65275C22semidirect
63. C4×#683C22semidirect
64. #65218C22semidirect
65. #64949C22semidirect
66. #64935C22semidirect
67. #64935C22semidirect
68. #64935C22semidirect
105. C2×C5×C22⋊C4Q8semidirect
251. C5×C22⋊C4C2×Q8semidirect
454. C2×C22⋊C4Dic10semidirect
609. C22⋊C4C2×Dic10semidirect
615. C2×C5#2492semidirect
705. C5C2×#2492semidirect
743. C2#10607278direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40342
C22×#40242
C2×C5×#3882
C2×#652752
C2×#652362
C2×#652402
C2×#652312
C2×C22⋊C4×Dic52
C2×#652182
C2×C4×#6832
#106072782
C2×#649492
C2×#649352
C2×#24925