Finite Group Databasebeta

← C2×#10607581 #12266800

Subgroups — C2×#10607581 #12266800

Order 1280.

3894 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4029C211yesmaximal, characteristic, complemented
2C22×#4032C211yesmaximal, characteristic, complemented
3C22×#4027C211yesmaximal, characteristic, complemented
4C22×C4×D20C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×#65280C211yesmaximal, characteristic, complemented
7C2×#65274C211yesmaximal, characteristic, complemented
8C2×#65249C211yesmaximal, characteristic
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65239C211yesmaximal, characteristic, complemented
11C2×#65217C211yesmaximal, characteristic, complemented
12#10607581C2116yesmaximal, direct product factor
13C2×#64966C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4032—28no—
47C2×#4032C2218yescomplemented
48C2×#4029—28no—
49C2×#4029C2218yescomplemented
50C2×#4027—28no—
51C2×#4027C2218yescomplemented
52C2×C4×D20—28no—
53C2×C4×D20C2218yescomplemented
54C5×#388C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65280C2218yescomplemented
62#65274C2218yescomplemented
63#65250C2218yescomplemented
64#65249C2218yes—
65#65239C2218yescomplemented
66#65217C2218yescomplemented
67#64966C2218yescomplemented
68#64959C2218yescomplemented
69#64957C2218yescomplemented
70#64957C2218yescomplemented
71C2×#2455—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—42no—
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—24no—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5—42no—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4D418yescomplemented
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C42×C5—24no—
120C2×C42×C5C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5C2314yes—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—42no—
130C2×#685D418yescomplemented
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—24no—
141C2×C4⋊Dic5—24no—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5—24no—
144C2×C4⋊Dic5—42no—
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yes—
147C2×C4⋊Dic5C2314yes—
148C2×C4⋊Dic5C2314yes—
149C2×C4⋊Dic5C2314yes—
150C2×C4⋊Dic5C2314yes—
151C2×#683—24no—
152C2×#683—24no—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157#4032—232no—
158#4029—232no—
159#4027—232no—
160C4×D20—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#123—51no—
169C22×C4×D4—51no—
170C22×C4×D4—51no—
171#2455—516no—
172C2×#399—51no—
173C2×#394—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#389—51no—
177C2×#389—51no—
178C2×#388—51no—
179C2×#388D511yescharacteristic, complemented
180C2×#385—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×C5C2×D414yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
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×D5C2×D414yes—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
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—22no—
222C22×C4×C5C2×D414yes—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5#4114yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—232no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—44no—
239C2×C22⋊D5—416no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—28no—
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—28no—
258C22×Dic5—44no—
259C22×Dic5—416no—
260C22×Dic5C2×D414yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—232no—
269C2×D20—28no—
270C2×D20—28no—
271C2×D20—28no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—44no—
277C2×C4×D5—44no—
278C2×C4×D5—416no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4C2×D4116yescomplemented
284C42×C5—28no—
285C22⋊Dic5—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—44no—
293#685C2×D4116yescomplemented
294C4⋊Dic5—28no—
295C4⋊Dic5—28no—
296C4⋊Dic5—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5—28no—
299C4⋊Dic5—44no—
300#683—28no—
301#683—28no—
302C4×Dic5—28no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4—51no—
306C24×C4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#123—58no—
310C2×#123—58no—
311C2×#123—108no—
312C2×#123—108no—
313C2×C4×D4—58no—
314C2×C4×D4—58no—
315C2×C4×D4—108no—
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—51no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C22⋊C4—51no—
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—
339C22×C42C2×D511yescharacteristic
340#399—58no—
341#394—58no—
342#394—58no—
343#392—58no—
344#389—58no—
345#389—58no—
346#388—58no—
347#388C2×D518yescomplemented
348#385—58no—
349#385—58no—
350#385—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D414yes—
371C23×C5C22×D412yes—
372C23×C5C22×D412yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C52−1+412yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—28no—
384C22×D5—28no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—22no—
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—22no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C2×#4114yes—
431C22⋊D5—232no—
432C22⋊D5—416no—
433C2×Dic5—28no—
434C2×Dic5—28no—
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—416no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458D20—232no—
459C4×D5—416no—
460C4×D5—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×D4—54no—
465C22×D4—54no—
466C22×D4—54no—
467C22×D4—104no—
468C22×D4—104no—
469C22×D4—104no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—202no—
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—54no—
483C23×C4—54no—
484C23×C4—54no—
485C23×C4—104no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—202no—
492C23×C4—202no—
493C23×C4—202no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#123—1032no—
501#123—1032no—
502C4×D4—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—202no—
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—58no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—202no—
542C2×C22⋊C4D2018yescomplemented
543C2×C22⋊C4C22×D514yes—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—24no—
547C2×C42—54no—
548C2×C42—104no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—416no—
563C22×C5—42no—
564C22×C5#52514yes—
565C22×C5#52514yes—
566C22×C5#53914yes—
567C22×C5D4214yes—
568C22×C5#54714yes—
569C22×C5#54714yes—
570C22×C5#55914yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C2×H(5,𝔽2)11yescharacteristic
577C22×C5C2×2−1+411yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5—24no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—416no—
591C2×D5—416no—
592C2×D5—42no—
593C2×D5—42no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—54no—
614C24—52no—
615C24—52no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24C2×D2014yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×D4—108no—
632C2×D4—108no—
633C2×D4—1032no—
634C2×D4—108no—
635C2×D4—108no—
636C2×D4—1032no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—204no—
642C2×D4—2016no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—54no—
658C22×C4—54no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—108no—
666C22×C4—108no—
667C22×C4—108no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—108no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—108no—
686C22×C4—108no—
687C22×C4—204no—
688C22×C4—204no—
689C22×C4—2016no—
690C22×C4—2016no—
691C22×C4—204no—
692C22×C4—2016no—
693C22×C4C2×D2014yes—
694C22×C4C2×D2014yes—
695C22×C4D4×D514yes—
696C22×C4#71114yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C4⋊C4—108no—
711C4⋊C4—204no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—516no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—204no—
723C22⋊C4C2×D20116yescomplemented
724C42—28no—
725C42—108no—
726C2×C5—44no—
727C2×C5#245518yescomplemented
728C2×C5C2×#52511yescharacteristic
729C2×C5C2×#52511yescharacteristic
730C2×C5C2×#53911yescharacteristic
731C2×C5C2×D4211yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#54711yescharacteristic
734C2×C5C2×#55911yescharacteristic
735D5—44no—
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—54no—
751C23—54no—
752C23—108no—
753C23—108no—
754C23—108no—
755C23—108no—
756C23—108no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—108no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C22×D2014yes—
779C23C22×D2012yes—
780C23C2×D4×D512yes—
781C23C2×#71112yes—
782C23D5×#4112yes—
783C23D5×#4112yes—
784C23#414912yes—
785C23#415012yes—
786C23C24×D511yescharacteristic
787D4—1032no—
788D4—1032no—
789D4—2016no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
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—44no—
809C2×C4—44no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—108no—
813C2×C4—108no—
814C2×C4—102no—
815C2×C4—102no—
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—2016no—
831C2×C4—2016no—
832C2×C4—2016no—
833C2×C4—204no—
834C2×C4—204no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4C22×D2014yes—
838C2×C4C22×D2014yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×#71114yes—
841C5C2×#245511yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—2016no—
865C22—2016no—
866C22#6585814yes—
867C22D4×D2014yes—
868C22#6588914yes—
869C22#6594014yes—
870C22#6598914yes—
871C22#6601514yes—
872C22#6604114yes—
873C22C23×D2011yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×#71111yescharacteristic
876C22C2×D5×#4111yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×#414911yescharacteristic
879C22C2×#415011yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—104no—
887C4—104no—
888C4—202no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—204no—
894C2—204no—
895C2#1060758118yesdirect product factor
896C2C2×#6585811yescharacteristic
897C2C2×#6588911yescharacteristic
898C2C2×D4×D2011yescharacteristic
899C2C2×#6594011yescharacteristic
900C2C2×#6598911yescharacteristic
901C2C2×#6601511yescharacteristic
902C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#388D5
hypocenterC5C2×#2455
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4029C2semidirect
2. C22×#4032C2semidirect
3. C22×#4027C2semidirect
4. C22×C4×D20C2semidirect
5. C2×C5×#388C2semidirect
6. C2×#65280C2semidirect
7. C2×#65274C2semidirect
9. C2×#65250C2semidirect
10. C2×#65239C2semidirect
11. C2×#65217C2semidirect
12. #10607581C2direct (N × H)
13. C2×#64966C2semidirect
14. C2×#64957C2semidirect
15. C2×#64957C2semidirect
16. C2×#64959C2semidirect
47. C2×#4032C22semidirect
49. C2×#4029C22semidirect
51. C2×#4027C22semidirect
53. C2×C4×D20C22semidirect
54. C5×#388C22semidirect
61. #65280C22semidirect
62. #65274C22semidirect
63. #65250C22semidirect
65. #65239C22semidirect
66. #65217C22semidirect
67. #64966C22semidirect
68. #64959C22semidirect
69. #64957C22semidirect
70. #64957C22semidirect
115. C2×C5×C22⋊C4D4semidirect
130. C2×#685D4semidirect
179. C2×#388D5semidirect
283. C5×C22⋊C4C2×D4semidirect
293. #685C2×D4semidirect
347. #388C2×D5semidirect
542. C2×C22⋊C4D20semidirect
723. C22⋊C4C2×D20semidirect
727. C2×C5#2455semidirect
841. C5C2×#2455semidirect
895. C2#10607581direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40292
C22×#40322
C22×#40272
C22×C4×D202
C2×C5×#3882
C2×#652802
C2×#652742
C2×#652492
C2×#652502
C2×#652392
C2×#652172
#106075812
C2×#649662
C2×#649572
C2×#649592
C2×#24555