Finite Group Databasebeta

← C2×#10614628 #12266749

Subgroups — C2×#10614628 #12266749

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#123C211yesmaximal, characteristic, complemented
2C22×#4084C211yesmaximal, characteristic
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7#10614628C2116yesmaximal, direct product factor
8C2×#65278C211yesmaximal, characteristic, complemented
9C2×#65273C211yesmaximal, characteristic, complemented
10C2×#65270C211yesmaximal, characteristic, complemented
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65245C211yesmaximal, characteristic, complemented
13C2×#65245C211yesmaximal, characteristic, complemented
14C2×#65238C211yesmaximal, characteristic, complemented
15C2×#65242C211yesmaximal, characteristic, complemented
16C2×#65234C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C2×C5×#123—28no—
25C2×C5×#123C2218yescomplemented
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C22×C22⋊Dic5C2211yescharacteristic
36C22×C22⋊Dic5C2211yescharacteristic
37C2×#4084—28no—
38C2×#4084C2218yes—
39C2×C4×C22⋊D5—28no—
40C2×C4×C22⋊D5C2218yescomplemented
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C22×C4⋊Dic5C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×D5×C4⋊C4—28no—
51C2×D5×C4⋊C4C2218yescomplemented
52#65511C2218yescomplemented
53#65499C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65278C2218yescomplemented
63#65273C2218yescomplemented
64#65270C2218yescomplemented
65#65245C2218yescomplemented
66#65245C2218yescomplemented
67#65245C2218yescomplemented
68#65242C2218yescomplemented
69#65238C2218yescomplemented
70#65234C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5D418yes—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—24no—
110C22×C4×D5—42no—
111C22×C4×D5—42no—
112C22×C4×D5C2314yes—
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C5×#123—232no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4D418yescomplemented
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2314yes—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4—24no—
122C2×C5×C22⋊C4—24no—
123C2×C5×C22⋊C4C2314yes—
124C2×C5×C22⋊C4C2314yes—
125C2×C5×C22⋊C4C2314yes—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—24no—
130C2×C22⋊Dic5—24no—
131C2×C22⋊Dic5—42no—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134C2×C22⋊Dic5C2314yes—
135C2×C22⋊Dic5C2314yes—
136C2×C22⋊Dic5C2314yes—
137C2×C22⋊Dic5C2314yes—
138#4084—232no—
139C4×C22⋊D5—232no—
140C2×#685—24no—
141C2×#685—24no—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×C4⋊Dic5—24no—
145C2×C4⋊Dic5—24no—
146C2×C4⋊Dic5C2314yes—
147C2×C4⋊Dic5C2314yes—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—24no—
151C2×#683—42no—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158D5×C4⋊C4—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123D511yescharacteristic, complemented
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5—22no—
196C24×C5C2×D414yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5C2×D414yes—
205C23×D5#4114yes—
206C23×D5#4114yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—44no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—28no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—28no—
226C22×C4×C5—44no—
227C22×C4×C5—416no—
228C22×C4×C5C2×D414yes—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
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×Dic5C2×D414yes—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×C4×D5—232no—
273C2×C4×D5—28no—
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—44no—
281C2×C4×D5—44no—
282C2×C4×D5—416no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4C2×D4116yescomplemented
286C5×C22⋊C4—28no—
287C5×C22⋊C4—28no—
288C5×C22⋊C4—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292C22⋊Dic5—28no—
293C22⋊Dic5—28no—
294C22⋊Dic5—44no—
295#685—28no—
296#685—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5—28no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683—44no—
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#123—28no—
312C2×#123C2×D518yescomplemented
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—58no—
324C22×C4⋊C4—108no—
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C4⋊C4C2×D511yescharacteristic
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#399—58no—
340#398—58no—
341#397—58no—
342#394—58no—
343#388—58no—
344#387—58no—
345#386—58no—
346#386—58no—
347#386—58no—
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95—51no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—44no—
384C23×C5—44no—
385C23×C5C22×D414yes—
386C23×C5C22×D412yes—
387C23×C5C22×D412yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C52−1+412yes—
393C23×C5C2511yescharacteristic
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—28no—
398C22×D5—28no—
399C22×D5—28no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—22no—
404C22×D5#123116yescomplemented
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C22×D5C2×#4114yes—
408C5×D4—416no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—416no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C22⋊D5—232no—
431C22⋊D5—416no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5C22×D414yes—
459C2×Dic5C2×#4114yes—
460C4×D5—232no—
461C4×D5—416no—
462C4×D5—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—58no—
470C22×D4—54no—
471C22×D4—54no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4C22×D514yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—54no—
489C23×C4—54no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—202no—
499C23×C4—202no—
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D514yes—
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—232no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—1032no—
522C2×C4⋊C4—202no—
523C2×C4⋊C4C22⋊D518yescomplemented
524C2×C4⋊C4C22×D514yes—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4—202no—
545C2×C22⋊C4C22×D514yes—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95—54no—
557#95—54no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—416no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—88no—
574C22×C5C2×#12314yes—
575C22×C5#52514yes—
576C22×C5#53914yes—
577C22×C5D4214yes—
578C22×C5#54714yes—
579C22×C5#54814yes—
580C22×C5#55314yes—
581C22×C5C23×D411yescharacteristic
582C22×C5C23×D411yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C22×C5C2×H(5,𝔽2)11yescharacteristic
587C22×C5C2×2−1+411yescharacteristic
588C2×D5—24no—
589C2×D5—24no—
590C2×D5—24no—
591C2×D5—24no—
592C2×D5—24no—
593C2×D5—232no—
594C2×D5—24no—
595C2×D5C2×#12318yescomplemented
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—54no—
622C24—54no—
623C24—54no—
624C24—52no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24D4×D514yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—516no—
638C2×D4—1032no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—108no—
644C2×D4—2016no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—28no—
659C22×C4—44no—
660C22×C4—416no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—108no—
671C22×C4—108no—
672C22×C4—1032no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—108no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—108no—
696C22×C4—108no—
697C22×C4—204no—
698C22×C4—204no—
699C22×C4—2016no—
700C22×C4—2016no—
701C22×C4C2×C22⋊D514yes—
702C22×C4C2×C22⋊D514yes—
703C22×C4C2×C22⋊D514yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—108no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—204no—
716C4⋊C4C2×C22⋊D5116yescomplemented
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—204no—
728C42—108no—
729C2×C5—44no—
730C2×C5—82no—
731C2×C5#244318yescomplemented
732C2×C5C22×#12311yescharacteristic
733C2×C5C2×#52511yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×D4211yescharacteristic
736C2×C5C2×#54711yescharacteristic
737C2×C5C2×#54811yescharacteristic
738C2×C5C2×#55311yescharacteristic
739D5—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—516no—
768C23—54no—
769C23—54no—
770C23—54no—
771C23—108no—
772C23—108no—
773C23—108no—
774C23—108no—
775C23—108no—
776C23—108no—
777C23—102no—
778C23—102no—
779C23—102no—
780C23—102no—
781C23C2×D4×D514yes—
782C23C2×D4×D512yes—
783C23#414412yes—
784C23D5×#4112yes—
785C23D5×#4112yes—
786C23D5×#4112yes—
787C23#415012yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790D4—416no—
791D4—1032no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—1032no—
814C2×C4—108no—
815C2×C4—108no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—2016no—
836C2×C4—2016no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4C22×C22⋊D514yes—
843C2×C4C22×C22⋊D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—58no—
862C22—88no—
863C22—104no—
864C22—104no—
865C22—104no—
866C22—104no—
867C22—104no—
868C22—104no—
869C22—1032no—
870C22D5×#12314yes—
871C22#6598914yes—
872C22#6599414yes—
873C22#6599514yes—
874C22D4×C22⋊D514yes—
875C22#6616214yes—
876C22#6616514yes—
877C22C22×D4×D511yescharacteristic
878C22C2×#414411yescharacteristic
879C22C2×D5×#4111yescharacteristic
880C22C2×D5×#4111yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×#415011yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—202no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—82no—
898C2—108no—
899C2#1061462818yesdirect product factor
900C2C2×#6599511yescharacteristic
901C2C2×D5×#12311yescharacteristic
902C2C2×#6599411yescharacteristic
903C2C2×#6598911yescharacteristic
904C2C2×D4×C22⋊D511yescharacteristic
905C2C2×#6616211yescharacteristic
906C2C2×#6616511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC22×#4084C2
hypercenterC22×#123D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×D5×C4⋊C4C2semidirect
5. C2×#65511C2semidirect
6. C2×#65499C2semidirect
7. #10614628C2direct (N × H)
8. C2×#65278C2semidirect
9. C2×#65273C2semidirect
10. C2×#65270C2semidirect
11. C2×#65245C2semidirect
12. C2×#65245C2semidirect
13. C2×#65245C2semidirect
14. C2×#65238C2semidirect
15. C2×#65242C2semidirect
16. C2×#65234C2semidirect
25. C2×C5×#123C22semidirect
40. C2×C4×C22⋊D5C22semidirect
51. C2×D5×C4⋊C4C22semidirect
52. #65511C22semidirect
53. #65499C22semidirect
62. #65278C22semidirect
63. #65273C22semidirect
64. #65270C22semidirect
65. #65245C22semidirect
66. #65245C22semidirect
67. #65245C22semidirect
68. #65242C22semidirect
69. #65238C22semidirect
70. #65234C22semidirect
117. C2×C5×C4⋊C4D4semidirect
167. C22×#123D5semidirect
285. C5×C4⋊C4C2×D4semidirect
312. C2×#123C2×D5semidirect
404. C22×D5#123semidirect
523. C2×C4⋊C4C22⋊D5semidirect
595. C2×D5C2×#123semidirect
716. C4⋊C4C2×C22⋊D5semidirect
731. C2×C5#2443semidirect
845. C5C2×#2443semidirect
899. C2#10614628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×#40842
C22×C4×C22⋊D52
C22×D5×C4⋊C42
C2×#655112
C2×#654992
#106146282
C2×#652782
C2×#652732
C2×#652702
C2×#652452
C2×#652382
C2×#652422
C2×#652342
C2×#24435