Finite Group Databasebeta

← C2×#10609224 #12268432

Subgroups — C2×#10609224 #12268432

Order 1280.

2726 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4044C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#397C211yesmaximal, characteristic, complemented
4C2×#65265C211yesmaximal, characteristic, complemented
5C2×#65237C211yesmaximal, characteristic, complemented
6C2×#65246C211yesmaximal, characteristic
7C2×#65246C211yesmaximal, characteristic
8C2×#65246C211yesmaximal, characteristic
9C2×#65234C211yesmaximal, characteristic, complemented
10#10609224C2116yesmaximal, direct product factor
11C2×#64965C211yesmaximal, characteristic, complemented
12C2×#64963C211yesmaximal, characteristic, complemented
13C2×#64936C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64938C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C2×#4025—28no—
49C2×#4025C2218yescomplemented
50C5×#397C2218yescomplemented
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65265C2218yescomplemented
58#65246C2218yes—
59#65246C2218yes—
60#65246C2218yes—
61#65237C2218yescomplemented
62#65234C2218yescomplemented
63#64965C2218yescomplemented
64#64963C2218yescomplemented
65#64958C2218yescomplemented
66#64938C2218yescomplemented
67#64938C2218yescomplemented
68#64936C2218yescomplemented
69C2×#2512—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C2×C5×C4⋊C4—24no—
90C2×C5×C4⋊C4C2314yes—
91C2×C5×C22⋊C4—24no—
92C2×C5×C22⋊C4—42no—
93C2×C5×C22⋊C4—42no—
94C2×C5×C22⋊C4C2314yes—
95C2×C5×C22⋊C4C2314yes—
96C2×C5×C22⋊C4C2314yes—
97C2×C22⋊Dic5—24no—
98C2×C22⋊Dic5—24no—
99C2×C22⋊Dic5—24no—
100C2×C22⋊Dic5C2314yes—
101C2×C22⋊Dic5C2314yes—
102C2×C22⋊Dic5C2314yes—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×C4⋊Dic5—24no—
116C2×C4⋊Dic5—24no—
117C2×C4⋊Dic5C2314yes—
118C2×C4⋊Dic5C2314yes—
119C2×#683—24no—
120C2×#683—24no—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683D418yescomplemented
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143C2×C4×Dic5C2314yes—
144C2×C4×Dic5C2314yes—
145#4044—232no—
146#4025—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149C5×#95C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#126—51no—
155#2512—516no—
156C2×#397—51no—
157C2×#397D511yescharacteristic, complemented
158C2×#396—51no—
159C2×#396—51no—
160C2×#390—51no—
161C2×#390—51no—
162C2×#390—51no—
163C2×#389—51no—
164C2×#388—51no—
165C2×#388—51no—
166C2×#384—51no—
167C2×C4×C4⋊C4—51no—
168C2×C4×C4⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5C2412yes—
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—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5C2×D414yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5C2×D414yes—
230C22×Dic5C2×D414yes—
231C22×Dic5#4114yes—
232C22×Dic5#4114yes—
233C22×Dic5#4114yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C5×C4⋊C4—28no—
243C5×C22⋊C4—28no—
244C5×C22⋊C4—44no—
245C5×C22⋊C4—44no—
246C22⋊Dic5—28no—
247C22⋊Dic5—28no—
248C22⋊Dic5—28no—
249#685—28no—
250#685—28no—
251#685—28no—
252#685—28no—
253#685—44no—
254#685—44no—
255C4⋊Dic5—28no—
256C4⋊Dic5—28no—
257#683—28no—
258#683—28no—
259#683—28no—
260#683—28no—
261#683—28no—
262#683—44no—
263#683—44no—
264#683C2×D4116yescomplemented
265C4×Dic5—28no—
266C4×Dic5—28no—
267C4×Dic5—28no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C23×D4—51no—
271C2×#126—58no—
272C2×#126—58no—
273C2×#126—108no—
274C2×#126—108no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42—51no—
302C22×C42—51no—
303#397—58no—
304#397C2×D518yescomplemented
305#396—58no—
306#396—58no—
307#390—58no—
308#390—58no—
309#390—58no—
310#389—58no—
311#388—58no—
312#388—58no—
313#384—58no—
314C4×C4⋊C4—58no—
315C4×C4⋊C4—58no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95C2×D511yescharacteristic
320C2×#95C2×D511yescharacteristic
321C2×#95C2×D511yescharacteristic
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—44no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5C22×D412yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C52−1+412yes—
343C23×C5C2511yescharacteristic
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C2×C4×C5—28no—
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—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—44no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5C22×D414yes—
382C22⋊D5—416no—
383C2×Dic5—28no—
384C2×Dic5—28no—
385C2×Dic5—28no—
386C2×Dic5—22no—
387C2×Dic5—22no—
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—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—44no—
402C2×Dic5—44no—
403C2×Dic5—44no—
404C2×Dic5#126116yescomplemented
405C2×Dic5C22×D414yes—
406C2×Dic5C22×D414yes—
407C2×Dic5C2×#4114yes—
408C2×Dic5C2×#4114yes—
409C2×Dic5C2×#4114yes—
410C2×Dic5C2×#4114yes—
411C25—51no—
412C25C22×D511yescharacteristic
413C22×D4—54no—
414C22×D4—104no—
415C22×D4—104no—
416C22×D4—104no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430#126—1032no—
431#126—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—58no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—104no—
445C2×C4⋊C4—104no—
446C2×C4⋊C4—104no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—202no—
452C2×C4⋊C4—202no—
453C2×C4⋊C4C22×D514yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—54no—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—54no—
460C2×C22⋊C4—54no—
461C2×C22⋊C4—54no—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—104no—
467C2×C22⋊C4—104no—
468C2×C22⋊C4—104no—
469C2×C22⋊C4—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—202no—
474C2×C22⋊C4—202no—
475C2×C22⋊C4C22×D514yes—
476C2×C22⋊C4C22×D514yes—
477C2×C22⋊C4C22×D514yes—
478C2×C42—54no—
479C2×C42—54no—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—104no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—104no—
487C2×C42—104no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95C22×D514yes—
492#95C22×D514yes—
493#95C22×D514yes—
494C22×C5—42no—
495C22×C5—42no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—88no—
502C22×C5C2×#12614yes—
503C22×C5#53214yes—
504C22×C5#54214yes—
505C22×C5#54714yes—
506C22×C5#55014yes—
507C22×C5#55314yes—
508C22×C5#55614yes—
509C22×C5C23×D411yescharacteristic
510C22×C5C22×#4111yescharacteristic
511C22×C5C22×#4111yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×2−1+411yescharacteristic
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—88no—
524C4×C5—24no—
525C4×C5—42no—
526C4×C5—42no—
527C4×C5—42no—
528C4×C5—42no—
529C4×C5—42no—
530Dic5—24no—
531Dic5—24no—
532Dic5—24no—
533Dic5—42no—
534Dic5—42no—
535Dic5—42no—
536Dic5C2×#12618yescomplemented
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—52no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24C23×D512yes—
553C24C23×D511yescharacteristic
554C2×D4—108no—
555C2×D4—108no—
556C2×D4—108no—
557C2×D4—2016no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—52no—
579C22×C4—54no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4D4×D514yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C4⋊C4—28no—
611C4⋊C4—516no—
612C4⋊C4—108no—
613C4⋊C4—108no—
614C4⋊C4—108no—
615C4⋊C4—108no—
616C4⋊C4—108no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—204no—
620C4⋊C4—204no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—108no—
625C22⋊C4—108no—
626C22⋊C4—108no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—204no—
632C22⋊C4—204no—
633C42—108no—
634C42—108no—
635C42—108no—
636C42—108no—
637C42—108no—
638C2×C5—82no—
639C2×C5#251218yescomplemented
640C2×C5C22×#12611yescharacteristic
641C2×C5C2×#53211yescharacteristic
642C2×C5C2×#54211yescharacteristic
643C2×C5C2×#54711yescharacteristic
644C2×C5C2×#55011yescharacteristic
645C2×C5C2×#55311yescharacteristic
646C2×C5C2×#55611yescharacteristic
647D5—82no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—204no—
670C23—204no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23C2×D4×D512yes—
677C23#414412yes—
678C23D5×#4112yes—
679C23D5×#4112yes—
680C23D5×#4112yes—
681C23D5×#4112yes—
682C23#415012yes—
683C23C24×D511yescharacteristic
684D4—2016no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—54no—
709C2×C4—54no—
710C2×C4—54no—
711C2×C4—516no—
712C2×C4—54no—
713C2×C4—54no—
714C2×C4—54no—
715C2×C4—108no—
716C2×C4—108no—
717C2×C4—108no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—204no—
734C2×C4—204no—
735C2×C4—204no—
736C2×C4C2×D4×D514yes—
737C5C2×#251211yescharacteristic, complemented, Sylow
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—408no—
754C22#6593314yes—
755C22#6598914yes—
756C22#6599514yes—
757C22#6599614yes—
758C22#6600214yes—
759C22#6603614yes—
760C22D5×#12614yes—
761C22C22×D4×D511yescharacteristic
762C22C2×#414411yescharacteristic
763C22C2×D5×#4111yescharacteristic
764C22C2×D5×#4111yescharacteristic
765C22C2×D5×#4111yescharacteristic
766C22C2×D5×#4111yescharacteristic
767C22C2×#415011yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—58no—
775C4—104no—
776C4—104no—
777C4—104no—
778C4—202no—
779C4—202no—
780C4—202no—
781C2—82no—
782C2—402no—
783C2#1060922418yesdirect product factor
784C2C2×#6593311yescharacteristic
785C2C2×#6599611yescharacteristic
786C2C2×#6599511yescharacteristic
787C2C2×#6598911yescharacteristic
788C2C2×#6600211yescharacteristic
789C2C2×#6603611yescharacteristic
790C2C2×D5×#12611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2512
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#4044C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#397C2semidirect
4. C2×#65265C2semidirect
5. C2×#65237C2semidirect
9. C2×#65234C2semidirect
10. #10609224C2direct (N × H)
11. C2×#64965C2semidirect
12. C2×#64963C2semidirect
13. C2×#64936C2semidirect
14. C2×#64958C2semidirect
15. C2×#64938C2semidirect
16. C2×#64938C2semidirect
47. C2×#4044C22semidirect
49. C2×#4025C22semidirect
50. C5×#397C22semidirect
57. #65265C22semidirect
61. #65237C22semidirect
62. #65234C22semidirect
63. #64965C22semidirect
64. #64963C22semidirect
65. #64958C22semidirect
66. #64938C22semidirect
67. #64938C22semidirect
68. #64936C22semidirect
126. C2×#683D4semidirect
157. C2×#397D5semidirect
264. #683C2×D4semidirect
304. #397C2×D5semidirect
404. C2×Dic5#126semidirect
536. Dic5C2×#126semidirect
639. C2×C5#2512semidirect
737. C5C2×#2512semidirect
783. C2#10609224direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40442
C22×#40252
C2×C5×#3972
C2×#652652
C2×#652372
C2×#652462
C2×#652342
#106092242
C2×#649652
C2×#649632
C2×#649362
C2×#649582
C2×#649382
C2×#25125