Finite Group Databasebeta

← C2×#10605068 #12258799

Subgroups — C2×#10605068 #12258799

Order 1280.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4075C211yesmaximal, characteristic
2C22×C4×C22⋊D5C211yesmaximal, characteristic
3C22×#4072C211yesmaximal, characteristic, complemented
4C22×C5×#95C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#64957C211yesmaximal, characteristic, complemented
9#10605068C2116yesmaximal, direct product factor
10C2×#64936C211yesmaximal, characteristic, complemented
11C2×#64959C211yesmaximal, characteristic, complemented
12C2×#64958C211yesmaximal, characteristic, complemented
13C2×#64944C211yesmaximal, characteristic, complemented
14C2×#64941C211yesmaximal, characteristic, complemented
15C2×#64938C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C2×#4075C4116yescomplemented
26C2×#4075C2218yes—
27C2×C4×C22⋊D5—28no—
28C2×C4×C22⋊D5C2218yes—
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C2×#4072—28no—
35C2×#4072C2218yescomplemented
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2218yescomplemented
53#65502C2218yes—
54#65499C2218yescomplemented
55C4×C22⋊Dic5C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#64959C2218yescomplemented
63#64958C2218yescomplemented
64#64957C2218yescomplemented
65#64955C2218yescomplemented
66#64944C2218yescomplemented
67#64941C2218yescomplemented
68#64938C2218yescomplemented
69#64936C2218yescomplemented
70C2×#2359—51nomaximal, Sylow
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5—42no—
81C23×C4×C5C2×C418yescomplemented
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2314yes—
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5C2×C418yes—
94C22×C22⋊D5C2314yes—
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—42no—
105C22×C4×D5C2314yes—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5C2×C418yescomplemented
108C2×C22⋊Dic5D418yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×C22⋊Dic5C2314yes—
112#4075C2×C4164yescomplemented
113C4×C22⋊D5—232no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—42no—
117C2×#685C2×C418yescomplemented
118C2×#685C2×C418yescomplemented
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124#4072—232no—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5—24no—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—42no—
132C2×#683C2×C418yescomplemented
133C2×#683C2×C418yescomplemented
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×#683C2314yes—
139C2×C4×Dic5—24no—
140C2×C4×Dic5—24no—
141C2×C4×Dic5—24no—
142C2×C4×Dic5—24no—
143C2×C4×Dic5—42no—
144C2×C4×Dic5C2314yes—
145C2×C4×Dic5C2314yes—
146C2×C4×Dic5C2314yes—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C5×#95C2314yes—
150C5×#95C2314yes—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×C4×D4—51no—
161C22×#117—51no—
162#2359—516no—
163C2×#389—51no—
164C2×#388—51no—
165C2×#388—51no—
166C2×#387—51no—
167C2×#387—51no—
168C2×#386—51no—
169C2×#385—51no—
170C2×#385—51no—
171C2×C4×C4⋊C4—51no—
172C2×C4×C22⋊C4—51no—
173C2×C4×C22⋊C4—51no—
174C22×#95D511yescharacteristic, complemented
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5C22×C414yes—
180C24×C5C2×D414yes—
181C24×C5#4114yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5C22×C414yes—
191C23×D5C2412yes—
192C22×C4×C5—232no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—28no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—28no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—28no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—28no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—28no—
212C22×C4×C5—28no—
213C22×C4×C5—44no—
214C22×C4×C5—44no—
215C22×C4×C5—416no—
216C22×C4×C5—416no—
217C22×C4×C5C22×C414yes—
218C22×C4×C5C22×C414yes—
219C22×C4×C5C22×C4116yescomplemented
220C22×C4×C5#4114yes—
221C22×C4×C5#4114yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—232no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5C22×C4116yes—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5C22×C414yes—
249C22×Dic5C22×C414yes—
250C22×Dic5C22×C414yes—
251C22×Dic5C2×D414yes—
252C22×Dic5C2×D414yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—44no—
263C2×C4×D5—416no—
264C22⋊Dic5—28no—
265C22⋊Dic5C22×C4116yescomplemented
266C22⋊Dic5C2×D4116yes—
267#685—28no—
268#685—28no—
269#685—44no—
270#685C22×C4116yescomplemented
271#685C22×C4116yescomplemented
272C4⋊Dic5—28no—
273C4⋊Dic5—28no—
274#683—28no—
275#683—28no—
276#683—44no—
277#683C22×C4116yescomplemented
278#683C22×C4116yescomplemented
279C4×Dic5—28no—
280C4×Dic5—28no—
281C4×Dic5—28no—
282C4×Dic5—28no—
283C4×Dic5—44no—
284C23×D4—51no—
285C24×C4—51no—
286C24×C4C2×D511yescharacteristic
287C24×C4C2×D511yescharacteristic
288C24×C4C2×D511yescharacteristic
289C2×#123—516no—
290C2×#123—58no—
291C2×C4×D4—58no—
292C2×C4×D4—108no—
293C2×#117—58no—
294C2×#117—108no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C22⋊C4—51no—
303C22×C22⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C42—51no—
311C22×C42—51no—
312C22×C42—51no—
313C22×C42—51no—
314C22×C42—51no—
315#389—58no—
316#388—58no—
317#388—58no—
318#387—58no—
319#387—58no—
320#386—58no—
321#385—58no—
322#385—58no—
323C4×C4⋊C4—58no—
324C4×C22⋊C4—58no—
325C4×C22⋊C4—58no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95C2×D511yescharacteristic
333C2×#95C2×D511yescharacteristic
334C2×#95C2×D511yescharacteristic
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D518yescomplemented
337C23×C5—28no—
338C23×C5—28no—
339C23×C5—28no—
340C23×C5—28no—
341C23×C5—28no—
342C23×C5—28no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5C4×D4116yes—
348C23×C5C23×C414yes—
349C23×C5C23×C412yes—
350C23×C5C22×D414yes—
351C23×C5C22×D412yes—
352C23×C5C2×#4112yes—
353C23×C5C2×#4112yes—
354C23×C5C2×#4114yes—
355C23×C5C2×#4112yes—
356C23×C5H(5,𝔽2)12yes—
357C23×C52−1+412yes—
358C23×C5C2511yescharacteristic
359C22×D5—28no—
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—44no—
369C22×D5—44no—
370C22×D5—44no—
371C22×D5—44no—
372C22×D5C23×C414yes—
373C2×C4×C5—28no—
374C2×C4×C5—28no—
375C2×C4×C5—232no—
376C2×C4×C5—28no—
377C2×C4×C5—28no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—416no—
393C2×C4×C5—416no—
394C2×C4×C5—44no—
395C2×C4×C5—44no—
396C2×C4×C5C23×C414yes—
397C2×C4×C5C23×C414yes—
398C2×C4×C5C2×#4114yes—
399C2×C4×C5C2×#4114yes—
400C22⋊D5—232no—
401C2×Dic5—28no—
402C2×Dic5—28no—
403C2×Dic5—28no—
404C2×Dic5—28no—
405C2×Dic5—28no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—44no—
423C2×Dic5—44no—
424C2×Dic5C23×C414yes—
425C2×Dic5C23×C414yes—
426C2×Dic5C23×C414yes—
427C2×Dic5C22×D414yes—
428C2×Dic5C22×D414yes—
429C4×D5—416no—
430C25—51no—
431C25C22×D511yescharacteristic
432C22×D4—58no—
433C22×D4—54no—
434C22×D4—104no—
435C22×D4—104no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—24no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—51no—
447C23×C4—51no—
448C23×C4—51no—
449C23×C4—51no—
450C23×C4—51no—
451C23×C4—54no—
452C23×C4—104no—
453C23×C4—104no—
454C23×C4—202no—
455C23×C4C4×D518yescomplemented
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D511yescharacteristic
458C23×C4C22×D514yes—
459C23×C4C22×D514yes—
460C23×C4C22×D511yescharacteristic
461C23×C4C22×D511yescharacteristic
462C23×C4C22×D514yes—
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465#123—564no—
466C4×D4—1032no—
467#117—1032no—
468C2×C4⋊C4—58no—
469C2×C4⋊C4—58no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—104no—
478C2×C4⋊C4—104no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—202no—
482C2×C22⋊C4—58no—
483C2×C22⋊C4—58no—
484C2×C22⋊C4—54no—
485C2×C22⋊C4—54no—
486C2×C22⋊C4—58no—
487C2×C22⋊C4—58no—
488C2×C22⋊C4—54no—
489C2×C22⋊C4—54no—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—54no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—104no—
495C2×C22⋊C4—104no—
496C2×C22⋊C4—104no—
497C2×C22⋊C4—202no—
498C2×C42—54no—
499C2×C42—54no—
500C2×C42—54no—
501C2×C42—54no—
502C2×C42—54no—
503C2×C42—104no—
504C2×C42—104no—
505C2×C42—104no—
506C2×C42—104no—
507C2×C42—202no—
508#95—54no—
509#95—54no—
510#95—54no—
511#95—54no—
512#95—54no—
513#95—54no—
514#95C22×D514yes—
515#95C22×D514yes—
516#95C22×D514yes—
517#95C22×D514yes—
518C22×C5—232no—
519C22×C5—24no—
520C22×C5—24no—
521C22×C5—24no—
522C22×C5—24no—
523C22×C5—24no—
524C22×C5—24no—
525C22×C5C2×C4×D418yes—
526C22×C5C2×C4×D414yes—
527C22×C5C4×#4114yes—
528C22×C5#52014yes—
529C22×C5#54614yes—
530C22×C5#54714yes—
531C22×C5#55114yes—
532C22×C5#55214yes—
533C22×C5C24×C411yescharacteristic
534C22×C5C23×D411yescharacteristic
535C22×C5C22×#4111yescharacteristic
536C22×C5C22×#4111yescharacteristic
537C22×C5C22×#4111yescharacteristic
538C22×C5C2×H(5,𝔽2)11yescharacteristic
539C22×C5C2×2−1+411yescharacteristic
540C2×D5—24no—
541C2×D5—24no—
542C2×D5—24no—
543C2×D5—416no—
544C2×D5—42no—
545C2×D5—42no—
546C2×D5—42no—
547C2×D5—42no—
548C4×C5—24no—
549C4×C5—24no—
550C4×C5—24no—
551C4×C5—24no—
552C4×C5—42no—
553C4×C5—42no—
554Dic5—24no—
555Dic5—24no—
556Dic5—24no—
557Dic5—24no—
558Dic5—24no—
559Dic5—42no—
560Dic5—42no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—54no—
566C24—52no—
567C24—102no—
568C24—102no—
569C24—102no—
570C24—102no—
571C24—102no—
572C24—102no—
573C24C2×C4×D514yes—
574C24D4×D514yes—
575C24#71114yes—
576C24C23×D512yes—
577C24C23×D511yescharacteristic
578C2×D4—516no—
579C2×D4—108no—
580C2×D4—108no—
581C2×D4—1032no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—232no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—416no—
606C22×C4—416no—
607C22×C4—54no—
608C22×C4—54no—
609C22×C4—54no—
610C22×C4—54no—
611C22×C4—54no—
612C22×C4—52no—
613C22×C4—52no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—52no—
617C22×C4—52no—
618C22×C4—52no—
619C22×C4—108no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—102no—
630C22×C4—102no—
631C22×C4—102no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—102no—
636C22×C4—108no—
637C22×C4—204no—
638C22×C4—2016no—
639C22×C4C2×C4×D514yes—
640C22×C4C2×C4×D514yes—
641C22×C4C2×C4×D5116yescomplemented
642C22×C4#70914yes—
643C22×C4#70914yes—
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D512yes—
647C22×C4C23×D512yes—
648C22×C4C23×D512yes—
649C22×C4C23×D512yes—
650C4⋊C4—516no—
651C4⋊C4—516no—
652C4⋊C4—108no—
653C4⋊C4—108no—
654C4⋊C4—108no—
655C4⋊C4—108no—
656C4⋊C4—204no—
657C22⋊C4—516no—
658C22⋊C4—516no—
659C22⋊C4—516no—
660C22⋊C4—516no—
661C22⋊C4—108no—
662C22⋊C4—108no—
663C22⋊C4—108no—
664C22⋊C4—204no—
665C42—108no—
666C42—108no—
667C42—108no—
668C42—108no—
669C42—204no—
670C2×C5—28no—
671C2×C5#235918yescomplemented
672C2×C5C22×C4×D411yescharacteristic
673C2×C5C2×C4×#4111yescharacteristic
674C2×C5C2×#52011yescharacteristic
675C2×C5C2×#54611yescharacteristic
676C2×C5C2×#54711yescharacteristic
677C2×C5C2×#55111yescharacteristic
678C2×C5C2×#55211yescharacteristic
679D5—44no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—54no—
691C23—108no—
692C23—108no—
693C23—108no—
694C23—102no—
695C23—102no—
696C23—102no—
697C23—102no—
698C23—102no—
699C23—102no—
700C23—204no—
701C23—204no—
702C23—204no—
703C23—204no—
704C23#4027116yes—
705C23C22×C4×D514yes—
706C23C22×C4×D512yes—
707C23C2×#70912yes—
708C23C2×#70912yes—
709C23C2×D4×D514yes—
710C23C2×D4×D512yes—
711C23C2×#71114yes—
712C23C2×#71112yes—
713C23#414412yes—
714C23#414712yes—
715C23C24×D511yescharacteristic
716D4—1032no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—232no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—54no—
741C2×C4—54no—
742C2×C4—54no—
743C2×C4—54no—
744C2×C4—54no—
745C2×C4—108no—
746C2×C4—108no—
747C2×C4—108no—
748C2×C4—108no—
749C2×C4—108no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—2016no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4C22×C4×D514yes—
770C2×C4C22×C4×D514yes—
771C2×C4C2×#70914yes—
772C2×C4C2×#70914yes—
773C5C2×#235911yescharacteristic, complemented, Sylow
774C22—24no—
775C22—24no—
776C22—232no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—104no—
782C22—104no—
783C22—104no—
784C22—202no—
785C22—2016no—
786C22—202no—
787C22—202no—
788C22—202no—
789C22C4×#70914yes—
790C22C2×#402718yes—
791C22C2×#402714yes—
792C22#6582414yes—
793C22#6582914yes—
794C22#6583814yes—
795C22#6584114yes—
796C22#6584714yes—
797C22C23×C4×D511yescharacteristic
798C22C22×#70911yescharacteristic
799C22C22×#70911yescharacteristic
800C22C22×D4×D511yescharacteristic
801C22C22×#71111yescharacteristic
802C22C2×#414411yescharacteristic
803C22C2×#414711yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—104no—
811C4—104no—
812C4—104no—
813C4—104no—
814C4—104no—
815C4—202no—
816C4—202no—
817C2—28no—
818C2—204no—
819C2#1060506818yesdirect product factor
820C2C2×C4×#70911yescharacteristic
821C2C22×#402711yescharacteristic
822C2C2×#6582911yescharacteristic
823C2C2×#6582411yescharacteristic
824C2C2×#6584711yescharacteristic
825C2C2×#6583811yescharacteristic
826C2C2×#6584111yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC22×C5×#95C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
cosocleC23×C5C25
hypercenterC22×#95D5
hypocenterC5C2×#2359
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C22×#4072C2semidirect
4. C22×C5×#95C2semidirect
6. C2×#65499C2semidirect
7. C2×C4×C22⋊Dic5C2semidirect
8. C2×#64957C2semidirect
9. #10605068C2direct (N × H)
10. C2×#64936C2semidirect
11. C2×#64959C2semidirect
12. C2×#64958C2semidirect
13. C2×#64944C2semidirect
14. C2×#64941C2semidirect
15. C2×#64938C2semidirect
16. C2×#64955C2semidirect
25. C2×#4075C4semidirect
35. C2×#4072C22semidirect
52. C2×C5×#95C22semidirect
54. #65499C22semidirect
55. C4×C22⋊Dic5C22semidirect
62. #64959C22semidirect
63. #64958C22semidirect
64. #64957C22semidirect
65. #64955C22semidirect
66. #64944C22semidirect
67. #64941C22semidirect
68. #64938C22semidirect
69. #64936C22semidirect
81. C23×C4×C5C2×C4semidirect
107. C2×C22⋊Dic5C2×C4semidirect
112. #4075C2×C4semidirect
117. C2×#685C2×C4semidirect
118. C2×#685C2×C4semidirect
132. C2×#683C2×C4semidirect
133. C2×#683C2×C4semidirect
174. C22×#95D5semidirect
219. C22×C4×C5C22×C4semidirect
265. C22⋊Dic5C22×C4semidirect
270. #685C22×C4semidirect
271. #685C22×C4semidirect
277. #683C22×C4semidirect
278. #683C22×C4semidirect
336. C2×#95C2×D5semidirect
455. C23×C4C4×D5semidirect
641. C22×C4C2×C4×D5semidirect
671. C2×C5#2359semidirect
773. C5C2×#2359semidirect
819. C2#10605068direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40752
C22×C4×C22⋊D52
C22×#40722
C22×C5×#952
C2×#655022
C2×#654992
C2×C4×C22⋊Dic52
C2×#649572
#106050682
C2×#649362
C2×#649592
C2×#649582
C2×#649442
C2×#649412
C2×#649382
C2×#649552
C2×#23595