Finite Group Databasebeta

← C2×#10607231 #12267314

Subgroups — C2×#10607231 #12267314

Order 1280.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4034C211yesmaximal, characteristic, complemented
2C22×#4024C211yesmaximal, characteristic
3C22×#4024C211yesmaximal, characteristic
4C22×C4×Dic10C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65237C211yesmaximal, characteristic
8C2×#65237C211yesmaximal, characteristic
9C2×#65240C211yesmaximal, characteristic
10C2×C22⋊C4×Dic5C211yesmaximal, characteristic
11C2×#65217C211yesmaximal, characteristic, complemented
12#10607231C2116yesmaximal, direct product factor
13C2×#64950C211yesmaximal, characteristic, complemented
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4034—28no—
45C2×#4034C2218yescomplemented
46C2×#4024—28no—
47C2×#4024—28no—
48C2×#4024C2218yes—
49C2×#4024C2218yes—
50C2×C4×Dic10—28no—
51C2×C4×Dic10C2218yescomplemented
52C5×#388C2218yes—
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65273C2218yescomplemented
62#65240C2218yes—
63#65237C2218yes—
64#65237C2218yes—
65C22⋊C4×Dic5C2218yes—
66#65217C2218yescomplemented
67#64950C2218yescomplemented
68#64936C2218yescomplemented
69#64936C2218yescomplemented
70#64935C2218yescomplemented
71C2×#2429—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5—24no—
80C23×Dic5—24no—
81C23×Dic5—24no—
82C23×Dic5C2314yes—
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×Dic10—24no—
92C22×Dic10—24no—
93C22×Dic10—24no—
94C22×Dic10—24no—
95C22×Dic10—24no—
96C22×Dic10D418yes—
97C22×Dic10C2314yes—
98C22×Dic10C2314yes—
99C2×C5×C4⋊C4—24no—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4Q818yescomplemented
104C2×C5×C22⋊C4C2314yes—
105C2×C5×C22⋊C4C2314yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C42×C5—24no—
108C2×C42×C5C2314yes—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×C4⋊Dic5—24no—
116C2×C4⋊Dic5—24no—
117C2×C4⋊Dic5—24no—
118C2×C4⋊Dic5—24no—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5C2314yes—
121C2×C4⋊Dic5C2314yes—
122C2×C4⋊Dic5C2314yes—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×#683—24no—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683D418yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×#683C2314yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×C4×Dic5—24no—
142C2×C4×Dic5—24no—
143C2×C4×Dic5—24no—
144C2×C4×Dic5C2314yes—
145C2×C4×Dic5C2314yes—
146C2×C4×Dic5C2314yes—
147#4034—232no—
148#4024—232no—
149#4024—232no—
150C4×Dic10—232no—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×C4⋊Q8—51no—
160C22×C22⋊Q8—51no—
161C22×C22⋊Q8—51no—
162C22×C4×Q8—51no—
163#2429—516no—
164C2×#398—51no—
165C2×#398—51no—
166C2×#396—51no—
167C2×#396—51no—
168C2×#391—51no—
169C2×#389—51no—
170C2×#389—51no—
171C2×#389—51no—
172C2×#388—51no—
173C2×#388D511yescharacteristic
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5C2×Q814yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
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×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5C2×D414yes—
199C22×C4×C5C2×D414yes—
200C22×C4×C5C2×Q814yes—
201C22×C4×C5C2×Q814yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
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×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—28no—
227C22×Dic5—28no—
228C22×Dic5—28no—
229C22×Dic5—416no—
230C22×Dic5C2×D414yes—
231C22×Dic5C2×D414yes—
232C22×Dic5C2×D414yes—
233C22×Dic5C2×D414yes—
234C22×Dic5#4114yes—
235C22×Dic5#4114yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C2×Dic10—232no—
245C2×Dic10—28no—
246C2×Dic10—28no—
247C2×Dic10—28no—
248C2×Dic10—28no—
249C2×Dic10—28no—
250C2×Dic10—416no—
251C2×Dic10C2×D4116yes—
252C5×C4⋊C4—28no—
253C5×C22⋊C4—28no—
254C5×C22⋊C4—28no—
255C5×C22⋊C4C2×Q8116yescomplemented
256C42×C5—28no—
257C22⋊Dic5—28no—
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C4⋊Dic5—28no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—28no—
264C4⋊Dic5—28no—
265#683—28no—
266#683—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—28no—
271#683—28no—
272#683C2×D4116yes—
273C4×Dic5—28no—
274C4×Dic5—28no—
275C4×Dic5—28no—
276C23×Q8—51no—
277C23×Q8—51no—
278C24×C4—51no—
279C2×C4⋊Q8—58no—
280C2×C4⋊Q8—108no—
281C2×C22⋊Q8—58no—
282C2×C22⋊Q8—58no—
283C2×C22⋊Q8—108no—
284C2×C22⋊Q8—108no—
285C2×C4×Q8—58no—
286C2×C4×Q8—108no—
287C22×C4⋊C4—51no—
288C22×C4⋊C4—51no—
289C22×C4⋊C4—51no—
290C22×C4⋊C4—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—51no—
293C22×C4⋊C4—51no—
294C22×C4⋊C4—51no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4C2×D511yescharacteristic
301C22×C22⋊C4—51no—
302C22×C22⋊C4—51no—
303C22×C22⋊C4—51no—
304C22×C22⋊C4C2×D511yescharacteristic
305C22×C22⋊C4C2×D511yescharacteristic
306C22×C22⋊C4C2×D511yescharacteristic
307C22×C42—51no—
308C22×C42—51no—
309C22×C42—51no—
310C22×C42C2×D511yescharacteristic
311#398—58no—
312#398—58no—
313#396—58no—
314#396—58no—
315#391—58no—
316#389—58no—
317#389—58no—
318#389—58no—
319#388—58no—
320#388C2×D518yes—
321C4×C22⋊C4—58no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95C2×D511yescharacteristic
329C2×#95C2×D511yescharacteristic
330C23×C5—28no—
331C23×C5—28no—
332C23×C5—28no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—44no—
340C23×C5—44no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5C22×D412yes—
344C23×C5C22×D412yes—
345C23×C5C22×Q814yes—
346C23×C5C22×Q812yes—
347C23×C5C2×#4112yes—
348C23×C5C2×#4112yes—
349C23×C52−1+412yes—
350C23×C52−1+412yes—
351C23×C5C2511yescharacteristic
352C2×C4×C5—28no—
353C2×C4×C5—28no—
354C2×C4×C5—28no—
355C2×C4×C5—28no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×C4×C5C22×D414yes—
373C2×C4×C5C22×D414yes—
374C2×C4×C5C22×Q814yes—
375C2×C4×C5C22×Q814yes—
376C2×Dic5—28no—
377C2×Dic5—28no—
378C2×Dic5—28no—
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—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C2×Dic5—44no—
400C2×Dic5—44no—
401C2×Dic5—416no—
402C2×Dic5#121116yes—
403C2×Dic5C22×D414yes—
404C2×Dic5C22×D414yes—
405C2×Dic5C22×D414yes—
406C2×Dic5C22×D414yes—
407C2×Dic5C2×#4114yes—
408C2×Dic5C2×#4114yes—
409Dic10—232no—
410Dic10—416no—
411C25C22×D511yescharacteristic
412C22×Q8—58no—
413C22×Q8—54no—
414C22×Q8—54no—
415C22×Q8—104no—
416C22×Q8—104no—
417C22×Q8—104no—
418C22×Q8—104no—
419C22×Q8—104no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—54no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—104no—
430C23×C4—104no—
431C23×C4—104no—
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C4⋊Q8—1032no—
439C22⋊Q8—1032no—
440C22⋊Q8—1032no—
441C4×Q8—1032no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—58no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—104no—
464C2×C4⋊C4—104no—
465C2×C4⋊C4—104no—
466C2×C4⋊C4—104no—
467C2×C4⋊C4—104no—
468C2×C4⋊C4—104no—
469C2×C4⋊C4C22×D514yes—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4Dic1018yescomplemented
479C2×C22⋊C4C22×D514yes—
480C2×C22⋊C4C22×D514yes—
481C2×C22⋊C4C22×D514yes—
482C2×C42—24no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—54no—
486C2×C42—104no—
487C2×C42—104no—
488C2×C42—104no—
489C2×C42C22×D514yes—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95—54no—
496#95C22×D514yes—
497#95C22×D514yes—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—24no—
501C22×C5—42no—
502C22×C5—416no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5C2×#12114yes—
507C22×C5#53314yes—
508C22×C5#54114yes—
509C22×C5#54714yes—
510C22×C5#54814yes—
511C22×C5D4×Q814yes—
512C22×C5D4×Q814yes—
513C22×C5C23×D411yescharacteristic
514C22×C5C23×D411yescharacteristic
515C22×C5C23×Q811yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C2×2−1+411yescharacteristic
519C22×C5C2×2−1+411yescharacteristic
520C4×C5—24no—
521C4×C5—24no—
522C4×C5—24no—
523C4×C5—24no—
524C4×C5—42no—
525C4×C5—42no—
526Dic5—24no—
527Dic5—24no—
528Dic5—24no—
529Dic5—42no—
530Dic5—42no—
531Dic5—42no—
532Dic5—42no—
533Dic5C2×#12118yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24C2×Dic1014yes—
541C24C23×D512yes—
542C24C23×D511yescharacteristic
543C2×Q8—516no—
544C2×Q8—108no—
545C2×Q8—1032no—
546C2×Q8—108no—
547C2×Q8—108no—
548C2×Q8—108no—
549C2×Q8—108no—
550C2×Q8—2016no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—54no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—52no—
569C22×C4—54no—
570C22×C4—54no—
571C22×C4—54no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—108no—
580C22×C4—108no—
581C22×C4—108no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—2016no—
601C22×C4C2×Dic1014yes—
602C22×C4C2×Dic1014yes—
603C22×C4D4×D514yes—
604C22×C4D4×D514yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C22×C4C23×D512yes—
611C4⋊C4—28no—
612C4⋊C4—516no—
613C4⋊C4—108no—
614C4⋊C4—108no—
615C4⋊C4—108no—
616C4⋊C4—108no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—108no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4C2×Dic10116yescomplemented
631C42—28no—
632C42—108no—
633C42—108no—
634C42—108no—
635C2×C5—44no—
636C2×C5#242918yescomplemented
637C2×C5C22×#12111yescharacteristic
638C2×C5C2×#53311yescharacteristic
639C2×C5C2×#54111yescharacteristic
640C2×C5C2×#54711yescharacteristic
641C2×C5C2×#54811yescharacteristic
642C2×C5C2×D4×Q811yescharacteristic
643C2×C5C2×D4×Q811yescharacteristic
644C23—28no—
645C23—28no—
646C23—28no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23C22×Dic1014yes—
658C23C22×Dic1012yes—
659C23C2×D4×D512yes—
660C23C2×D4×D512yes—
661C23D5×#4112yes—
662C23D5×#4112yes—
663C23#415012yes—
664C23#415012yes—
665C23C24×D511yescharacteristic
666Q8—1032no—
667Q8—2016no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—516no—
689C2×C4—54no—
690C2×C4—54no—
691C2×C4—54no—
692C2×C4—54no—
693C2×C4—54no—
694C2×C4—54no—
695C2×C4—108no—
696C2×C4—108no—
697C2×C4—108no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—2016no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4—204no—
721C2×C4C22×Dic1014yes—
722C2×C4C22×Dic1014yes—
723C2×C4C2×D4×D514yes—
724C2×C4C2×D4×D514yes—
725C5C2×#242911yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—416no—
732C22—42no—
733C22—42no—
734C22#6585114yes—
735C22D4×Dic1014yes—
736C22D4×Dic1014yes—
737C22D5×#12114yes—
738C22#6598914yes—
739C22#6601114yes—
740C22#6603514yes—
741C22C23×Dic1011yescharacteristic
742C22C22×D4×D511yescharacteristic
743C22C22×D4×D511yescharacteristic
744C22C2×D5×#4111yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×#415011yescharacteristic
747C22C2×#415011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—58no—
755C4—104no—
756C4—104no—
757C4—104no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4—202no—
762C2—44no—
763C2#1060723118yesdirect product factor
764C2C2×#6585111yescharacteristic
765C2C2×D4×Dic1011yescharacteristic
766C2C2×D4×Dic1011yescharacteristic
767C2C2×D5×#12111yescharacteristic
768C2C2×#6598911yescharacteristic
769C2C2×#6601111yescharacteristic
770C2C2×#6603511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5C2×#2429
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. C22×C4×Dic10C2semidirect
6. C2×#65273C2semidirect
11. C2×#65217C2semidirect
12. #10607231C2direct (N × H)
13. C2×#64950C2semidirect
14. C2×#64935C2semidirect
15. C2×#64936C2semidirect
16. C2×#64936C2semidirect
45. C2×#4034C22semidirect
51. C2×C4×Dic10C22semidirect
61. #65273C22semidirect
66. #65217C22semidirect
67. #64950C22semidirect
68. #64936C22semidirect
69. #64936C22semidirect
70. #64935C22semidirect
103. C2×C5×C22⋊C4Q8semidirect
255. C5×C22⋊C4C2×Q8semidirect
478. C2×C22⋊C4Dic10semidirect
630. C22⋊C4C2×Dic10semidirect
636. C2×C5#2429semidirect
725. C5C2×#2429semidirect
763. C2#10607231direct (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
C22×C4×Dic102
C2×C5×#3882
C2×#652732
C2×#652372
C2×#652402
C2×C22⋊C4×Dic52
C2×#652172
#106072312
C2×#649502
C2×#649352
C2×#649362
C2×#24295