Finite Group Databasebeta

← C2×#10605197 #12258818

Subgroups — C2×#10605197 #12258818

Order 1280.

3614 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
1C23×#683C211yesmaximal, characteristic
2C22×#4024C211yesmaximal, characteristic
3C22×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C2×#65499C211yesmaximal, characteristic
6C2×#65239C211yesmaximal, characteristic
7C2×C22⋊C4×Dic5C211yesmaximal, characteristic
8C2×C22⋊C4×Dic5C211yesmaximal, characteristic
9C2×#65217C211yesmaximal, characteristic, complemented
10C2×#65222C211yesmaximal, characteristic, complemented
11C2×C4×#683C211yesmaximal, characteristic, complemented
12#10605197C2116yesmaximal, direct product factor
13C2×#64935C211yesmaximal, characteristic, complemented
14C2×#64936C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64943C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×#683—28no—
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2218yes—
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4024C4116yescomplemented
45C2×#4024C2218yes—
46C2×C4×Dic10—28no—
47C2×C4×Dic10C2218yescomplemented
48C4×C5×C22⋊C4C2218yes—
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51#65499C2218yes—
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65239C2218yes—
61C22⋊C4×Dic5C2218yes—
62C22⋊C4×Dic5C2218yes—
63#65222C2218yescomplemented
64C4×#683C2218yescomplemented
65#65217C2218yescomplemented
66#64943C2218yescomplemented
67#64936C2218yescomplemented
68#64936C2218yescomplemented
69#64935C2218yescomplemented
70C2×#2360—51nomaximal, Sylow
71C25×C5C2311yescharacteristic
72C23×C4×C5—24no—
73C23×C4×C5—24no—
74C23×C4×C5—42no—
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2314yes—
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×Dic5—24no—
83C23×Dic5—24no—
84C23×Dic5—24no—
85C23×Dic5—24no—
86C23×Dic5—42no—
87C23×Dic5C2×C418yes—
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2314yes—
92C23×Dic5C2314yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C22×Dic10—24no—
99C22×Dic10—24no—
100C22×Dic10C2×C418yescomplemented
101C22×Dic10C2314yes—
102C2×C5×C22⋊C4C2×C418yes—
103C2×C5×C22⋊C4Q818yescomplemented
104C2×C5×C22⋊C4C2314yes—
105C2×C5×C22⋊C4C2314yes—
106C2×C42×C5—24no—
107C2×C42×C5—42no—
108C2×C42×C5C2314yes—
109C2×C42×C5C2314yes—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5C2×C418yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C4⋊Dic5—24no—
115C2×C4⋊Dic5—42no—
116C2×C4⋊Dic5C2×C418yescomplemented
117C2×C4⋊Dic5C2314yes—
118C2×C4⋊Dic5C2314yes—
119C2×C4⋊Dic5C2314yes—
120C2×#683—24no—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—232no—
125C2×#683—42no—
126C2×#683C2×C418yescomplemented
127C2×#683C2×C418yescomplemented
128C2×#683D418yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5—42no—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143C2×C4×Dic5C2314yes—
144C2×C4×Dic5C2314yes—
145#4024C2×C4164yescomplemented
146C4×Dic10—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157C22×C22⋊Q8—51no—
158C22×C4×Q8—51no—
159C23×C4⋊C4—51no—
160#2360—516no—
161C2×#391—51no—
162C2×#389—51no—
163C2×#389—51no—
164C2×#389—51no—
165C2×#387—51no—
166C2×#387—51no—
167C2×#385—51no—
168C2×#385—51no—
169C2×C4×C4⋊C4—51no—
170C2×C4×C22⋊C4—51no—
171C2×C4×C22⋊C4—51no—
172C2×C4×C22⋊C4D511yescharacteristic
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5C22×C414yes—
178C24×C5C2×Q814yes—
179C24×C5#4114yes—
180C24×C5C2412yes—
181C24×C5C2411yescharacteristic
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—28no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—28no—
197C22×C4×C5—44no—
198C22×C4×C5—416no—
199C22×C4×C5C22×C414yes—
200C22×C4×C5C22×C414yes—
201C22×C4×C5C2×D414yes—
202C22×C4×C5C2×Q814yes—
203C22×C4×C5C2×Q814yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
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—232no—
219C22×Dic5—28no—
220C22×Dic5—28no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—28no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—28no—
232C22×Dic5—44no—
233C22×Dic5—416no—
234C22×Dic5C22×C414yes—
235C22×Dic5C22×C414yes—
236C22×Dic5C22×C4116yes—
237C22×Dic5C22×C414yes—
238C22×Dic5C22×C414yes—
239C22×Dic5C2×D414yes—
240C22×Dic5C2×D414yes—
241C22×Dic5#4114yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C2×Dic10—232no—
251C2×Dic10—28no—
252C2×Dic10—28no—
253C2×Dic10C22×C4116yescomplemented
254C5×C22⋊C4C22×C4116yes—
255C5×C22⋊C4C2×Q8116yescomplemented
256C42×C5—28no—
257C42×C5—44no—
258C22⋊Dic5—28no—
259C22⋊Dic5C22×C4116yes—
260C4⋊Dic5—28no—
261C4⋊Dic5—44no—
262C4⋊Dic5C22×C4116yescomplemented
263#683—28no—
264#683—28no—
265#683—28no—
266#683—28no—
267#683—44no—
268#683C22×C4116yescomplemented
269#683C22×C4116yescomplemented
270#683C2×D4116yes—
271C4×Dic5—28no—
272C4×Dic5—28no—
273C4×Dic5—28no—
274C4×Dic5—44no—
275C23×Q8—51no—
276C24×C4—51no—
277C24×C4—51no—
278C24×C4C2×D511yescharacteristic
279C2×C22⋊Q8—516no—
280C2×C22⋊Q8—58no—
281C2×C4×Q8—58no—
282C2×C4×Q8—108no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊C4—58no—
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—108no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C22⋊C4C2×D511yescharacteristic
299C22×C22⋊C4C2×D511yescharacteristic
300C22×C42—51no—
301C22×C42—51no—
302C22×C42—51no—
303C22×C42—51no—
304C22×C42C2×D511yescharacteristic
305C22×C42C2×D511yescharacteristic
306#391—58no—
307#389—58no—
308#389—58no—
309#389—58no—
310#387—58no—
311#387—58no—
312#385—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C4×C22⋊C4—58no—
316C4×C22⋊C4—58no—
317C4×C22⋊C4C2×D518yes—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95C2×D511yescharacteristic
327C2×#95C2×D511yescharacteristic
328C23×C5—28no—
329C23×C5—28no—
330C23×C5—28no—
331C23×C5—28no—
332C23×C5—28no—
333C23×C5—28no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5C4×Q8116yescomplemented
339C23×C5C23×C414yes—
340C23×C5C23×C412yes—
341C23×C5C22×D412yes—
342C23×C5C22×Q814yes—
343C23×C5C22×Q812yes—
344C23×C5C2×#4114yes—
345C23×C5C2×#4112yes—
346C23×C5C2×#4112yes—
347C23×C5H(5,𝔽2)12yes—
348C23×C52−1+412yes—
349C23×C5C2511yescharacteristic
350C2×C4×C5—28no—
351C2×C4×C5—28no—
352C2×C4×C5—28no—
353C2×C4×C5—28no—
354C2×C4×C5—28no—
355C2×C4×C5—22no—
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—416no—
369C2×C4×C5—44no—
370C2×C4×C5C23×C414yes—
371C2×C4×C5C23×C414yes—
372C2×C4×C5C22×D414yes—
373C2×C4×C5C22×Q814yes—
374C2×C4×C5C22×Q814yes—
375C2×Dic5—28no—
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—232no—
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—416no—
398C2×Dic5—44no—
399C2×Dic5—44no—
400C2×Dic5—44no—
401C2×Dic5C4×D4116yes—
402C2×Dic5C23×C414yes—
403C2×Dic5C23×C414yes—
404C2×Dic5C23×C414yes—
405C2×Dic5C23×C414yes—
406C2×Dic5C22×D414yes—
407C2×Dic5C22×D414yes—
408C2×Dic5C2×#4114yes—
409Dic10—232no—
410C25C22×D511yescharacteristic
411C22×Q8—58no—
412C22×Q8—54no—
413C22×Q8—104no—
414C22×Q8—104no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—42no—
418C23×C4—51no—
419C23×C4—58no—
420C23×C4—54no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—54no—
429C23×C4—104no—
430C23×C4—104no—
431C23×C4—104no—
432C23×C4—104no—
433C23×C4—202no—
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D514yes—
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C22⋊Q8—564no—
442C4×Q8—1032no—
443C2×C4⋊C4—58no—
444C2×C4⋊C4—58no—
445C2×C4⋊C4—58no—
446C2×C4⋊C4—58no—
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—54no—
458C2×C4⋊C4—1032no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—104no—
464C2×C4⋊C4—202no—
465C2×C4⋊C4—202no—
466C2×C22⋊C4—58no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—104no—
470C2×C22⋊C4Dic1018yescomplemented
471C2×C22⋊C4C4×D518yes—
472C2×C22⋊C4C22×D514yes—
473C2×C22⋊C4C22×D514yes—
474C2×C42—24no—
475C2×C42—42no—
476C2×C42—54no—
477C2×C42—54no—
478C2×C42—54no—
479C2×C42—54no—
480C2×C42—104no—
481C2×C42—104no—
482C2×C42—104no—
483C2×C42—202no—
484C2×C42C22×D514yes—
485C2×C42C22×D514yes—
486#95—54no—
487#95—54no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95C22×D514yes—
495#95C22×D514yes—
496C22×C5—232no—
497C22×C5—24no—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5C2×C4×D414yes—
504C22×C5C2×C4×Q814yes—
505C22×C5C2×C4×Q818yescomplemented
506C22×C5#52014yes—
507C22×C5#54614yes—
508C22×C5D4×Q814yes—
509C22×C5#55214yes—
510C22×C5#55414yes—
511C22×C5C24×C411yescharacteristic
512C22×C5C23×D411yescharacteristic
513C22×C5C23×Q811yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C2×H(5,𝔽2)11yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C4×C5—24no—
519C4×C5—24no—
520C4×C5—24no—
521C4×C5—24no—
522C4×C5—24no—
523C4×C5—42no—
524Dic5—24no—
525Dic5—24no—
526Dic5—24no—
527Dic5—24no—
528Dic5—42no—
529Dic5—42no—
530Dic5—42no—
531Dic5C2×C4×D418yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24C2×Dic1014yes—
537C24C2×C4×D514yes—
538C24#70914yes—
539C24C23×D512yes—
540C24C23×D511yescharacteristic
541C2×Q8—516no—
542C2×Q8—108no—
543C2×Q8—1032no—
544C2×Q8—108no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—416no—
562C22×C4—54no—
563C22×C4—54no—
564C22×C4—54no—
565C22×C4—52no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—54no—
569C22×C4—516no—
570C22×C4—54no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—108no—
579C22×C4—1032no—
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—108no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—204no—
601C22×C4—2016no—
602C22×C4C2×Dic1014yes—
603C22×C4C2×Dic1014yes—
604C22×C4C2×C4×D514yes—
605C22×C4C2×C4×D514yes—
606C22×C4D4×D514yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C4⋊C4—516no—
614C4⋊C4—516no—
615C4⋊C4—516no—
616C4⋊C4—516no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C22⋊C4—516no—
625C22⋊C4—108no—
626C22⋊C4C2×Dic10116yescomplemented
627C22⋊C4C2×C4×D5116yes—
628C42—28no—
629C42—44no—
630C42—108no—
631C42—108no—
632C42—108no—
633C42—204no—
634C2×C5—28no—
635C2×C5#236018yescomplemented
636C2×C5C22×C4×D411yescharacteristic
637C2×C5C22×C4×Q811yescharacteristic
638C2×C5C2×#52011yescharacteristic
639C2×C5C2×#54611yescharacteristic
640C2×C5C2×D4×Q811yescharacteristic
641C2×C5C2×#55211yescharacteristic
642C2×C5C2×#55411yescharacteristic
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23C4×Dic10116yescomplemented
654C23C22×Dic1014yes—
655C23C22×Dic1012yes—
656C23C22×C4×D514yes—
657C23C22×C4×D512yes—
658C23C2×#70914yes—
659C23C2×#70912yes—
660C23C2×D4×D512yes—
661C23#414412yes—
662C23D5×#4112yes—
663C23#415012yes—
664C23C24×D511yescharacteristic
665Q8—1032no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—22no—
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—416no—
685C2×C4—44no—
686C2×C4—516no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—54no—
691C2×C4—54no—
692C2×C4—54no—
693C2×C4—54no—
694C2×C4—1032no—
695C2×C4—108no—
696C2×C4—108no—
697C2×C4—108no—
698C2×C4—108no—
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×C4C22×Dic1014yes—
721C2×C4C22×Dic1014yes—
722C2×C4C22×C4×D514yes—
723C2×C4C22×C4×D514yes—
724C2×C4C2×D4×D514yes—
725C5C2×#236011yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22C2×C4×Dic1014yes—
734C22C2×C4×Dic1018yescomplemented
735C22#6582414yes—
736C22#6586514yes—
737C22D4×Dic1014yes—
738C22#6587314yes—
739C22C4×D4×D514yes—
740C22#6588014yes—
741C22C23×Dic1011yescharacteristic
742C22C23×C4×D511yescharacteristic
743C22C22×#70911yescharacteristic
744C22C22×D4×D511yescharacteristic
745C22C2×#414411yescharacteristic
746C22C2×D5×#4111yescharacteristic
747C22C2×#415011yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—58no—
755C4—104no—
756C4—104no—
757C4—104no—
758C4—104no—
759C4—202no—
760C4—202no—
761C4—202no—
762C2—28no—
763C2#1060519718yesdirect product factor
764C2C22×C4×Dic1011yescharacteristic
765C2C2×#6582411yescharacteristic
766C2C2×#6586511yescharacteristic
767C2C2×#6588011yescharacteristic
768C2C2×D4×Dic1011yescharacteristic
769C2C2×#6587311yescharacteristic
770C2C2×C4×D4×D511yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C4×C5×C22⋊C4C2
socleC24×C5C24
prime radicalC25×C5C23
cosocleC23×C5C25
hypercenterC2×C4×C22⋊C4D5
hypocenterC5C2×#2360
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic10C2semidirect
9. C2×#65217C2semidirect
10. C2×#65222C2semidirect
11. C2×C4×#683C2semidirect
12. #10605197C2direct (N × H)
13. C2×#64935C2semidirect
14. C2×#64936C2semidirect
15. C2×#64936C2semidirect
16. C2×#64943C2semidirect
44. C2×#4024C4semidirect
47. C2×C4×Dic10C22semidirect
63. #65222C22semidirect
64. C4×#683C22semidirect
65. #65217C22semidirect
66. #64943C22semidirect
67. #64936C22semidirect
68. #64936C22semidirect
69. #64935C22semidirect
100. C22×Dic10C2×C4semidirect
103. C2×C5×C22⋊C4Q8semidirect
116. C2×C4⋊Dic5C2×C4semidirect
126. C2×#683C2×C4semidirect
127. C2×#683C2×C4semidirect
145. #4024C2×C4semidirect
253. C2×Dic10C22×C4semidirect
255. C5×C22⋊C4C2×Q8semidirect
262. C4⋊Dic5C22×C4semidirect
268. #683C22×C4semidirect
269. #683C22×C4semidirect
338. C23×C5C4×Q8semidirect
470. C2×C22⋊C4Dic10semidirect
505. C22×C5C2×C4×Q8semidirect
626. C22⋊C4C2×Dic10semidirect
635. C2×C5#2360semidirect
653. C23C4×Dic10semidirect
725. C5C2×#2360semidirect
734. C22C2×C4×Dic10semidirect
763. C2#10605197direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6832
C22×#40242
C22×C4×Dic102
C2×C4×C5×C22⋊C42
C2×#654992
C2×#652392
C2×C22⋊C4×Dic52
C2×#652172
C2×#652222
C2×C4×#6832
#106051972
C2×#649352
C2×#649362
C2×#649432
C2×#23605