Finite Group Databasebeta

← C2×#10609149 #12266724

Subgroups — C2×#10609149 #12266724

Order 1280.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×#4043C211yesmaximal, characteristic, complemented
3C22×D5×C22⋊C4C211yesmaximal, characteristic
4C22×D5×C22⋊C4C211yesmaximal, characteristic
5C2×C5×#396C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65278C211yesmaximal, characteristic, complemented
9C2×#65276C211yesmaximal, characteristic, complemented
10C2×#65244C211yesmaximal, characteristic
11C2×#65238C211yesmaximal, characteristic, complemented
12C2×#65237C211yesmaximal, characteristic, complemented
13C2×#65236C211yesmaximal, characteristic, complemented
14#10609149C2116yesmaximal, direct product factor
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64956C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic, complemented
23C22×C5×C4⋊C4C2211yescharacteristic, complemented
24C22×C5×C4⋊C4C2211yescharacteristic, complemented
25C22×C5×C4⋊C4C2211yescharacteristic, complemented
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic, complemented
41C22×C4⋊Dic5C2211yescharacteristic, complemented
42C22×#683C2211yescharacteristic, complemented
43C22×#683C2211yescharacteristic, complemented
44C22×#683C2211yescharacteristic, complemented
45C22×#683C2211yescharacteristic, complemented
46C2×#4043—28no—
47C2×#4043C2218yescomplemented
48C2×#4042—28no—
49C2×#4042C2218yescomplemented
50C2×D5×C22⋊C4—28no—
51C2×D5×C22⋊C4—28no—
52C2×D5×C22⋊C4C2218yes—
53C2×D5×C22⋊C4C2218yes—
54C5×#396C2218yescomplemented
55C2×C5×#95C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57C2×#3963C2211yescharacteristic, complemented
58C2×#3963C2211yescharacteristic, complemented
59C2×#3963C2211yescharacteristic, complemented
60C2×#3963C2211yescharacteristic, complemented
61#65278C2218yescomplemented
62#65278C2218yescomplemented
63#65278C2218yescomplemented
64#65276C2218yescomplemented
65#65244C2218yes—
66#65238C2218yescomplemented
67#65237C2218yescomplemented
68#65236C2218yescomplemented
69#64957C2218yescomplemented
70#64956C2218yescomplemented
71C2×#2437—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5—24no—
74C24×D5—24no—
75C24×D5—24no—
76C24×D5—24no—
77C24×D5—42no—
78C24×D5—42no—
79C24×D5Q818yescomplemented
80C24×D5C2314yes—
81C24×D5C2311yescharacteristic
82C24×D5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5—42no—
105C22×C4×D5—42no—
106C22×C4×D5—42no—
107C22×C4×D5C2314yes—
108C22×C4×D5C2314yes—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C22×Dic10—24no—
112C22×Dic10—24no—
113C22×Dic10—42no—
114C22×Dic10C2314yescomplemented
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—42no—
118C2×C5×C4⋊C4C2314yescomplemented
119C2×C5×C4⋊C4C2314yescomplemented
120C2×C5×C4⋊C4C2314yescomplemented
121C2×C5×C22⋊C4—24no—
122C2×C5×C22⋊C4—24no—
123C2×C5×C22⋊C4—42no—
124C2×C5×C22⋊C4C2314yes—
125C2×C5×C22⋊C4C2314yes—
126C2×C5×C22⋊C4C2314yes—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—42no—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685D418yes—
140C2×#685D418yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×#685C2314yes—
146C2×#685C2314yes—
147C2×#685C2314yes—
148C2×#685C2314yes—
149C2×C4⋊Dic5—24no—
150C2×C4⋊Dic5—24no—
151C2×C4⋊Dic5C2314yescomplemented
152C2×C4⋊Dic5C2314yescomplemented
153C2×#683—24no—
154C2×#683—24no—
155C2×#683—42no—
156C2×#683—42no—
157C2×#683C2314yescomplemented
158C2×#683C2314yescomplemented
159C2×#683C2314yescomplemented
160C2×#683C2314yescomplemented
161#4043—232no—
162#4042—232no—
163D5×C22⋊C4—232no—
164D5×C22⋊C4—232no—
165C5×#95C2314yescomplemented
166#3963C2314yescomplemented
167#3963C2314yescomplemented
168#3963C2314yescomplemented
169#3963C2314yescomplemented
170#3963C2314yescomplemented
171C22×C22⋊Q8—51no—
172C22×C22⋊Q8—51no—
173C23×C22⋊C4—51no—
174C23×C22⋊C4—51no—
175#2437—516no—
176C2×#399—51no—
177C2×#396—51no—
178C2×#396D511yescharacteristic, complemented
179C2×#393—51no—
180C2×#385—51no—
181C2×#385—51no—
182C2×#385—51no—
183C2×#385—51no—
184C2×#380—51no—
185C2×#380—51no—
186C2×#379—51no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5C2×Q814yes—
194C24×C5C2412yes—
195C24×C5C2411yescharacteristic
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—232no—
205C23×D5—232no—
206C23×D5—28no—
207C23×D5—28no—
208C23×D5—28no—
209C23×D5—28no—
210C23×D5—416no—
211C23×D5—44no—
212C23×D5—44no—
213C23×D5—416no—
214C23×D5—416no—
215C23×D5—416no—
216C23×D5—416no—
217C23×D5C2×D414yes—
218C23×D5C2×D414yes—
219C23×D5C2×Q814yes—
220C23×D5C2×Q814yes—
221C23×D5C2×Q8116yescomplemented
222C23×D5#4114yes—
223C23×D5#4114yes—
224C23×D5C2412yes—
225C23×D5C2412yes—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—22no—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—22no—
236C22×C4×C5—22no—
237C22×C4×C5—22no—
238C22×C4×C5—22no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5C2×D414yes—
243C22×C4×C5C2×D414yes—
244C22×C4×C5C2412yes—
245C22×C4×C5C2412yes—
246C22×C4×C5C2412yes—
247C22×C4×C5C2412yes—
248C22×C4×C5C2412yes—
249C22×C4×C5C2412yes—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5C2×D414yes—
267C22×Dic5C2×D414yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—28no—
279C2×C4×D5—28no—
280C2×C4×D5—28no—
281C2×C4×D5—28no—
282C2×C4×D5—44no—
283C2×C4×D5—44no—
284C2×C4×D5—44no—
285C2×C4×D5—44no—
286C2×C4×D5—416no—
287C2×C4×D5—416no—
288C2×C4×D5—416no—
289C2×C4×D5—416no—
290C2×Dic10—28no—
291C2×Dic10—28no—
292C2×Dic10—44no—
293C2×Dic10—416no—
294C5×C4⋊C4—28no—
295C5×C4⋊C4—28no—
296C5×C4⋊C4—44no—
297C5×C22⋊C4—28no—
298C5×C22⋊C4—28no—
299C5×C22⋊C4—44no—
300C22⋊Dic5—28no—
301C22⋊Dic5—28no—
302C22⋊Dic5—44no—
303#685—28no—
304#685—28no—
305#685—28no—
306#685—28no—
307#685—28no—
308#685—28no—
309#685C2×D4116yes—
310#685C2×D4116yes—
311C4⋊Dic5—28no—
312C4⋊Dic5—28no—
313#683—28no—
314#683—28no—
315#683—44no—
316#683—44no—
317C26—51no—
318C23×Q8—51no—
319C24×C4—51no—
320C24×C4—51no—
321C24×C4—51no—
322C24×C4—51no—
323C2×C22⋊Q8—58no—
324C2×C22⋊Q8—58no—
325C2×C22⋊Q8—108no—
326C2×C22⋊Q8—108no—
327C22×C4⋊C4—51no—
328C22×C4⋊C4—51no—
329C22×C4⋊C4—51no—
330C22×C4⋊C4—51no—
331C22×C4⋊C4—51no—
332C22×C4⋊C4—51no—
333C22×C4⋊C4C2×D511yescharacteristic, complemented
334C22×C4⋊C4C2×D511yescharacteristic, complemented
335C22×C4⋊C4C2×D511yescharacteristic, complemented
336C22×C22⋊C4—51no—
337C22×C22⋊C4—51no—
338C22×C22⋊C4—51no—
339C22×C22⋊C4—51no—
340C22×C22⋊C4—51no—
341C22×C22⋊C4—51no—
342C22×C22⋊C4—51no—
343C22×C22⋊C4—51no—
344C22×C22⋊C4—51no—
345C22×C22⋊C4—51no—
346C22×C22⋊C4—51no—
347C22×C22⋊C4—58no—
348C22×C22⋊C4—58no—
349C22×C22⋊C4—108no—
350C22×C22⋊C4—108no—
351C22×C22⋊C4C2×D511yescharacteristic
352C22×C22⋊C4C2×D511yescharacteristic
353C22×C22⋊C4C2×D511yescharacteristic
354#399—58no—
355#396—58no—
356#396C2×D518yescomplemented
357#393—58no—
358#385—58no—
359#385—58no—
360#385—58no—
361#385—58no—
362#380—58no—
363#380—58no—
364#379—58no—
365C2×#95—51no—
366C2×#95—51no—
367C2×#95—51no—
368C2×#95—51no—
369C2×#95—51no—
370C2×#95C2×D511yescharacteristic, complemented
371C23×C5—28no—
372C23×C5—28no—
373C23×C5—28no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—44no—
384C23×C5C22×D412yes—
385C23×C5C22×D412yes—
386C23×C5C22×Q814yes—
387C23×C5C22×Q812yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5H(5,𝔽2)12yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C5C2511yescharacteristic
393C22×D5—28no—
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—28no—
398C22×D5—28no—
399C22×D5—28no—
400C22×D5—28no—
401C22×D5—28no—
402C22×D5—28no—
403C22×D5—28no—
404C22×D5—28no—
405C22×D5—22no—
406C22×D5—22no—
407C22×D5—22no—
408C22×D5—22no—
409C22×D5—22no—
410C22×D5—22no—
411C22×D5—22no—
412C22×D5—22no—
413C22×D5—232no—
414C22×D5—232no—
415C22×D5—416no—
416C22×D5—4128no—
417C22×D5—416no—
418C22×D5—416no—
419C22×D5—416no—
420C22×D5—416no—
421C22×D5C22⋊Q8116yescomplemented
422C22×D5C22⋊Q8116yescomplemented
423C22×D5C22×D414yes—
424C22×D5C22×D414yes—
425C22×D5C22×Q814yes—
426C22×D5C22×Q814yes—
427C22×D5C2×#4114yes—
428C22×D5C2×#4114yes—
429C2×C4×C5—28no—
430C2×C4×C5—28no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—44no—
448C2×C4×C5—44no—
449C2×C4×C5—44no—
450C2×C4×C5—44no—
451C2×C4×C5C22×D414yes—
452C2×C4×C5C22×D414yes—
453C2×Dic5—28no—
454C2×Dic5—28no—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
461C2×Dic5—22no—
462C2×Dic5—22no—
463C2×Dic5—22no—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—22no—
467C2×Dic5—22no—
468C2×Dic5—22no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—44no—
472C2×Dic5—44no—
473C2×Dic5—44no—
474C2×Dic5—44no—
475C2×Dic5C22×D414yes—
476C2×Dic5C22×D414yes—
477C4×D5—416no—
478C4×D5—416no—
479C4×D5—416no—
480C4×D5—416no—
481Dic10—416no—
482C25—51no—
483C25—51no—
484C25—58no—
485C25—54no—
486C25—104no—
487C25—104no—
488C25—104no—
489C25—104no—
490C25—202no—
491C25—202no—
492C25C22×D511yescharacteristic
493C22×Q8—54no—
494C22×Q8—104no—
495C22×Q8—104no—
496C22×Q8—202no—
497C23×C4—51no—
498C23×C4—51no—
499C23×C4—51no—
500C23×C4—51no—
501C23×C4—51no—
502C23×C4—51no—
503C23×C4—54no—
504C23×C4—54no—
505C23×C4—54no—
506C23×C4—54no—
507C23×C4—104no—
508C23×C4—104no—
509C23×C4—104no—
510C23×C4—104no—
511C23×C4—104no—
512C23×C4—104no—
513C23×C4—104no—
514C23×C4—104no—
515C23×C4—202no—
516C23×C4—202no—
517C23×C4—202no—
518C23×C4—202no—
519C23×C4C22×D511yescharacteristic
520C23×C4C22×D511yescharacteristic
521C23×C4C22×D511yescharacteristic
522C23×C4C22×D511yescharacteristic
523C23×C4C22×D511yescharacteristic
524C23×C4C22×D511yescharacteristic
525C22⋊Q8—1032no—
526C22⋊Q8—1032no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—54no—
531C2×C4⋊C4—54no—
532C2×C4⋊C4—54no—
533C2×C4⋊C4—54no—
534C2×C4⋊C4—54no—
535C2×C4⋊C4—54no—
536C2×C4⋊C4—104no—
537C2×C4⋊C4—104no—
538C2×C4⋊C4—104no—
539C2×C4⋊C4—104no—
540C2×C4⋊C4—202no—
541C2×C4⋊C4—202no—
542C2×C4⋊C4C22×D514yescomplemented
543C2×C4⋊C4C22×D514yescomplemented
544C2×C4⋊C4C22×D514yescomplemented
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—58no—
549C2×C22⋊C4—58no—
550C2×C22⋊C4—54no—
551C2×C22⋊C4—54no—
552C2×C22⋊C4—54no—
553C2×C22⋊C4—54no—
554C2×C22⋊C4—54no—
555C2×C22⋊C4—54no—
556C2×C22⋊C4—54no—
557C2×C22⋊C4—54no—
558C2×C22⋊C4—54no—
559C2×C22⋊C4—54no—
560C2×C22⋊C4—54no—
561C2×C22⋊C4—1032no—
562C2×C22⋊C4—1032no—
563C2×C22⋊C4—104no—
564C2×C22⋊C4—104no—
565C2×C22⋊C4—104no—
566C2×C22⋊C4—104no—
567C2×C22⋊C4—104no—
568C2×C22⋊C4—104no—
569C2×C22⋊C4—104no—
570C2×C22⋊C4—104no—
571C2×C22⋊C4—202no—
572C2×C22⋊C4C22×D514yes—
573C2×C22⋊C4C22×D514yes—
574C2×C22⋊C4C22×D514yes—
575#95—54no—
576#95—54no—
577#95—54no—
578#95—54no—
579#95—54no—
580#95C22×D514yescomplemented
581C22×C5—24no—
582C22×C5—24no—
583C22×C5—24no—
584C22×C5—416no—
585C22×C5—42no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5C2×C22⋊Q814yes—
590C22×C5C2×C22⋊Q814yes—
591C22×C5#54314yes—
592C22×C5D4214yes—
593C22×C5#54614yes—
594C22×C5#54614yes—
595C22×C5#55114yes—
596C22×C5C23×D411yescharacteristic
597C22×C5C23×D411yescharacteristic
598C22×C5C23×Q811yescharacteristic
599C22×C5C22×#4111yescharacteristic
600C22×C5C22×#4111yescharacteristic
601C22×C5C2×H(5,𝔽2)11yescharacteristic
602C22×C5C2×H(5,𝔽2)11yescharacteristic
603C2×D5—24no—
604C2×D5—24no—
605C2×D5—24no—
606C2×D5—24no—
607C2×D5—232no—
608C2×D5—232no—
609C2×D5—24no—
610C2×D5—24no—
611C2×D5—24no—
612C2×D5—24no—
613C2×D5—24no—
614C2×D5—24no—
615C2×D5—24no—
616C2×D5—24no—
617C2×D5—464no—
618C2×D5C2×C22⋊Q818yescomplemented
619C2×D5C2×C22⋊Q818yescomplemented
620C4×C5—24no—
621C4×C5—24no—
622C4×C5—42no—
623C4×C5—42no—
624C4×C5—42no—
625C4×C5—42no—
626Dic5—24no—
627Dic5—24no—
628Dic5—42no—
629Dic5—42no—
630Dic5—42no—
631Dic5—42no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—54no—
639C24—54no—
640C24—54no—
641C24—54no—
642C24—54no—
643C24—54no—
644C24—52no—
645C24—52no—
646C24—516no—
647C24—108no—
648C24—108no—
649C24—1032no—
650C24—1032no—
651C24—108no—
652C24—108no—
653C24—102no—
654C24—102no—
655C24—102no—
656C24—102no—
657C24—102no—
658C24—102no—
659C24—102no—
660C24—102no—
661C24—2016no—
662C24—204no—
663C24—204no—
664C24—2016no—
665C24—2016no—
666C24—2016no—
667C24—2016no—
668C24Q8×D514yes—
669C24C23×D512yes—
670C24C23×D511yescharacteristic
671C2×Q8—108no—
672C2×Q8—108no—
673C2×Q8—204no—
674C2×Q8—2016no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—54no—
692C22×C4—54no—
693C22×C4—52no—
694C22×C4—52no—
695C22×C4—52no—
696C22×C4—52no—
697C22×C4—52no—
698C22×C4—52no—
699C22×C4—108no—
700C22×C4—108no—
701C22×C4—108no—
702C22×C4—108no—
703C22×C4—108no—
704C22×C4—108no—
705C22×C4—102no—
706C22×C4—102no—
707C22×C4—102no—
708C22×C4—102no—
709C22×C4—102no—
710C22×C4—102no—
711C22×C4—102no—
712C22×C4—102no—
713C22×C4—102no—
714C22×C4—102no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—102no—
721C22×C4—108no—
722C22×C4—108no—
723C22×C4—204no—
724C22×C4—204no—
725C22×C4—204no—
726C22×C4—204no—
727C22×C4—2016no—
728C22×C4—2016no—
729C22×C4—2016no—
730C22×C4—2016no—
731C22×C4D4×D514yes—
732C22×C4D4×D514yes—
733C22×C4C23×D512yes—
734C22×C4C23×D512yes—
735C22×C4C23×D512yes—
736C22×C4C23×D512yes—
737C22×C4C23×D512yes—
738C22×C4C23×D512yes—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—44no—
742C4⋊C4—108no—
743C4⋊C4—108no—
744C4⋊C4—108no—
745C4⋊C4—108no—
746C4⋊C4—204no—
747C4⋊C4—204no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—44no—
751C22⋊C4—516no—
752C22⋊C4—516no—
753C22⋊C4—108no—
754C22⋊C4—108no—
755C22⋊C4—108no—
756C22⋊C4—108no—
757C22⋊C4—108no—
758C22⋊C4—108no—
759C22⋊C4—108no—
760C22⋊C4—108no—
761C22⋊C4—204no—
762C2×C5—44no—
763C2×C5#243718yescomplemented
764C2×C5C22×C22⋊Q811yescharacteristic
765C2×C5C22×C22⋊Q811yescharacteristic
766C2×C5C2×#54311yescharacteristic
767C2×C5C2×D4211yescharacteristic
768C2×C5C2×#54611yescharacteristic
769C2×C5C2×#54611yescharacteristic
770C2×C5C2×#55111yescharacteristic
771D5—28no—
772D5—28no—
773C23—28no—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—516no—
787C23—516no—
788C23—54no—
789C23—54no—
790C23—54no—
791C23—54no—
792C23—54no—
793C23—54no—
794C23—1032no—
795C23—1032no—
796C23—108no—
797C23—108no—
798C23—108no—
799C23—108no—
800C23—108no—
801C23—108no—
802C23—108no—
803C23—108no—
804C23—108no—
805C23—108no—
806C23—102no—
807C23—102no—
808C23—102no—
809C23—102no—
810C23—102no—
811C23—102no—
812C23—102no—
813C23—102no—
814C23—108no—
815C23—108no—
816C23—2016no—
817C23—2016no—
818C23—2016no—
819C23—2016no—
820C23—2016no—
821C23—20128no—
822C23C2×D4×D512yes—
823C23C2×D4×D512yes—
824C23#414412yes—
825C23C2×Q8×D514yes—
826C23C2×Q8×D512yes—
827C23D5×#4112yes—
828C23D5×#4112yes—
829C23#414912yes—
830C23C24×D511yescharacteristic
831Q8—2016no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—54no—
855C2×C4—54no—
856C2×C4—108no—
857C2×C4—108no—
858C2×C4—102no—
859C2×C4—102no—
860C2×C4—102no—
861C2×C4—102no—
862C2×C4—102no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—102no—
872C2×C4—102no—
873C2×C4—102no—
874C2×C4—2016no—
875C2×C4—2016no—
876C2×C4—2016no—
877C2×C4—2016no—
878C2×C4—204no—
879C2×C4—204no—
880C2×C4—204no—
881C2×C4—204no—
882C2×C4C2×D4×D514yes—
883C2×C4C2×D4×D514yes—
884C5C2×#243711yescharacteristic, complemented, Sylow
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—416no—
893C22—58no—
894C22—58no—
895C22—104no—
896C22—104no—
897C22—104no—
898C22—104no—
899C22—104no—
900C22—104no—
901C22—104no—
902C22—104no—
903C22—104no—
904C22—104no—
905C22—104no—
906C22—104no—
907C22—1032no—
908C22—1032no—
909C22—2064no—
910C22#6594314yes—
911C22#6594414yes—
912C22#6594614yes—
913C22D5×C22⋊Q814yes—
914C22D5×C22⋊Q814yes—
915C22#6596814yes—
916C22#6603914yes—
917C22C22×D4×D511yescharacteristic
918C22C22×D4×D511yescharacteristic
919C22C2×#414411yescharacteristic
920C22C22×Q8×D511yescharacteristic
921C22C2×D5×#4111yescharacteristic
922C22C2×D5×#4111yescharacteristic
923C22C2×#414911yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—104no—
931C4—104no—
932C4—202no—
933C4—202no—
934C4—202no—
935C4—202no—
936C2—44no—
937C2—108no—
938C2—108no—
939C2#1060914918yesdirect product factor
940C2C2×#6594311yescharacteristic
941C2C2×#6594411yescharacteristic
942C2C2×#6594611yescharacteristic
943C2C2×D5×C22⋊Q811yescharacteristic
944C2C2×D5×C22⋊Q811yescharacteristic
945C2C2×#6596811yescharacteristic
946C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2437
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
2. C22×#4043C2semidirect
5. C2×C5×#396C2semidirect
6. C2×#65278C2semidirect
7. C2×#65278C2semidirect
8. C2×#65278C2semidirect
9. C2×#65276C2semidirect
11. C2×#65238C2semidirect
12. C2×#65237C2semidirect
13. C2×#65236C2semidirect
14. #10609149C2direct (N × H)
15. C2×#64957C2semidirect
16. C2×#64956C2semidirect
22. C23×Dic10C22semidirect
23. C22×C5×C4⋊C4C22semidirect
24. C22×C5×C4⋊C4C22semidirect
25. C22×C5×C4⋊C4C22semidirect
40. C22×C4⋊Dic5C22semidirect
41. C22×C4⋊Dic5C22semidirect
42. C22×#683C22semidirect
43. C22×#683C22semidirect
44. C22×#683C22semidirect
45. C22×#683C22semidirect
47. C2×#4043C22semidirect
49. C2×#4042C22semidirect
54. C5×#396C22semidirect
55. C2×C5×#95C22semidirect
56. C2×#3963C22semidirect
57. C2×#3963C22semidirect
58. C2×#3963C22semidirect
59. C2×#3963C22semidirect
60. C2×#3963C22semidirect
61. #65278C22semidirect
62. #65278C22semidirect
63. #65278C22semidirect
64. #65276C22semidirect
66. #65238C22semidirect
67. #65237C22semidirect
68. #65236C22semidirect
69. #64957C22semidirect
70. #64956C22semidirect
79. C24×D5Q8semidirect
114. C22×Dic10C23semidirect
118. C2×C5×C4⋊C4C23semidirect
119. C2×C5×C4⋊C4C23semidirect
120. C2×C5×C4⋊C4C23semidirect
151. C2×C4⋊Dic5C23semidirect
152. C2×C4⋊Dic5C23semidirect
157. C2×#683C23semidirect
158. C2×#683C23semidirect
159. C2×#683C23semidirect
160. C2×#683C23semidirect
165. C5×#95C23semidirect
166. #3963C23semidirect
167. #3963C23semidirect
168. #3963C23semidirect
169. #3963C23semidirect
170. #3963C23semidirect
178. C2×#396D5semidirect
221. C23×D5C2×Q8semidirect
333. C22×C4⋊C4C2×D5semidirect
334. C22×C4⋊C4C2×D5semidirect
335. C22×C4⋊C4C2×D5semidirect
356. #396C2×D5semidirect
370. C2×#95C2×D5semidirect
421. C22×D5C22⋊Q8semidirect
422. C22×D5C22⋊Q8semidirect
542. C2×C4⋊C4C22×D5semidirect
543. C2×C4⋊C4C22×D5semidirect
544. C2×C4⋊C4C22×D5semidirect
580. #95C22×D5semidirect
618. C2×D5C2×C22⋊Q8semidirect
619. C2×D5C2×C22⋊Q8semidirect
763. C2×C5#2437semidirect
884. C5C2×#2437semidirect
939. C2#10609149direct (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×#40432
C22×D5×C22⋊C42
C2×C5×#3962
C2×#652782
C2×#652762
C2×#652442
C2×#652382
C2×#652372
C2×#652362
#106091492
C2×#649572
C2×#649562
C2×#24375