Finite Group Databasebeta

← C2×#10609736 #12305459

Subgroups — C2×#10609736 #12305459

Order 1280.

2674 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C211yesmaximal, characteristic
2C22×#4042C211yesmaximal, characteristic, complemented
3C2×C5×#398C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65283C211yesmaximal, characteristic, complemented
6C2×#65280C211yesmaximal, characteristic
7C2×#65276C211yesmaximal, characteristic, complemented
8C2×#65273C211yesmaximal, characteristic, complemented
9C2×#65268C211yesmaximal, characteristic, complemented
10#10609736C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64964C211yesmaximal, characteristic, complemented
13C2×#64962C211yesmaximal, characteristic, complemented
14C2×#64946C211yesmaximal, characteristic, complemented
15C2×#64963C211yesmaximal, characteristic, complemented
16C2×#64961C211yesmaximal, characteristic
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C2×#4042—28no—
43C2×#4042C2218yescomplemented
44C2×#4040—28no—
45C2×#4040C2218yes—
46C5×#398C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65283C2218yescomplemented
59#65280C2218yes—
60#65276C2218yescomplemented
61#65273C2218yescomplemented
62#65268C2218yescomplemented
63#64964C2218yescomplemented
64#64964C2218yescomplemented
65#64963C2218yescomplemented
66#64962C2218yescomplemented
67#64961C2218yes—
68#64946C2218yescomplemented
69C2×#2814—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×D20—24no—
86C22×D20—42no—
87C22×D20—42no—
88C22×D20C2314yes—
89C22×C4×D5—42no—
90C22×C4×D5—42no—
91C22×C4×D5D418yes—
92C22×C4×D5C2314yes—
93C22×Dic10—24no—
94C22×Dic10—42no—
95C22×Dic10—42no—
96C22×Dic10C2314yes—
97C2×C5×C4⋊C4—24no—
98C2×C5×C4⋊C4—24no—
99C2×C5×C4⋊C4—42no—
100C2×C5×C4⋊C4—42no—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C4⋊C4C2314yes—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—42no—
111C2×#685—42no—
112C2×#685—42no—
113C2×#685—42no—
114C2×#685—42no—
115C2×#685—42no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×C4⋊Dic5—42no—
128C2×C4⋊Dic5—42no—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683—24no—
134C2×#683—42no—
135C2×#683—42no—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×#683C2314yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141#4042—232no—
142#4040—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#123—51no—
154C22×C22⋊Q8—51no—
155#2814—516no—
156C2×#398—51no—
157C2×#398—51no—
158C2×#398D511yescharacteristic, complemented
159C2×#397—51no—
160C2×#397—51no—
161C2×#397—51no—
162C2×#396—51no—
163C2×#396—51no—
164C2×#395—51no—
165C2×#394—51no—
166C2×#394—51no—
167C2×#393—51no—
168C2×#380—51no—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5C2×D414yes—
184C23×D5C2412yes—
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×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5C2×D414yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
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×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5C2×D414yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×D20—28no—
239C2×D20—44no—
240C2×D20—44no—
241C2×D20—416no—
242C2×C4×D5—416no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×C4×D5C2×D4116yes—
246C2×Dic10—28no—
247C2×Dic10—44no—
248C2×Dic10—44no—
249C2×Dic10—416no—
250C5×C4⋊C4—28no—
251C5×C4⋊C4—28no—
252C5×C4⋊C4—44no—
253C5×C4⋊C4—44no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—44no—
260#685—44no—
261#685—44no—
262#685—44no—
263#685—44no—
264#685—44no—
265C4⋊Dic5—44no—
266C4⋊Dic5—44no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—44no—
271#683—44no—
272C23×Q8—51no—
273C23×D4—51no—
274C24×C4—51no—
275C2×#123—58no—
276C2×#123—108no—
277C2×C22⋊Q8—58no—
278C2×C22⋊Q8—108no—
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⋊C4—51no—
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
289C22×C4⋊C4C2×D511yescharacteristic
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C22⋊C4—51no—
299C22×C22⋊C4—51no—
300C22×C22⋊C4—51no—
301#398—58no—
302#398—58no—
303#398C2×D518yescomplemented
304#397—58no—
305#397—58no—
306#397—58no—
307#396—58no—
308#396—58no—
309#395—58no—
310#394—58no—
311#394—58no—
312#393—58no—
313#380—58no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C23×C5C22×D412yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)12yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C52−1+412yes—
329C23×C52−1+412yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—44no—
349C22×D5—44no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5C22×D414yes—
360C2×C4×C5—28no—
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—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5—44no—
386C2×C4×C5—44no—
387C2×C4×C5C22×D414yes—
388C2×Dic5—28no—
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—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5C22×D414yes—
412D20—416no—
413C4×D5—416no—
414Dic10—416no—
415C25—51no—
416C25—51no—
417C22×Q8—54no—
418C22×Q8—104no—
419C22×Q8—202no—
420C22×Q8—202no—
421C22×D4—54no—
422C22×D4—104no—
423C22×D4—202no—
424C22×D4—202no—
425C23×C4—51no—
426C23×C4—58no—
427C23×C4—54no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—202no—
434C23×C4—202no—
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#123—1032no—
443C22⋊Q8—1032no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—202no—
459C2×C4⋊C4—202no—
460C2×C4⋊C4—202no—
461C2×C4⋊C4—202no—
462C2×C4⋊C4C22×D514yes—
463C2×C4⋊C4C22×D514yes—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—54no—
476C2×C22⋊C4—54no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—104no—
481C2×C22⋊C4—104no—
482C2×C22⋊C4—202no—
483C2×C22⋊C4—202no—
484C2×C22⋊C4—202no—
485C2×C22⋊C4—202no—
486C2×C22⋊C4—202no—
487C2×C22⋊C4—202no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95C22×D514yes—
496#95C22×D514yes—
497#95C22×D514yes—
498C22×C5#53414yes—
499C22×C5#53614yes—
500C22×C5#53714yes—
501C22×C5#56214yes—
502C22×C5#56214yes—
503C22×C5#56314yes—
504C22×C5#56314yes—
505C22×C5C23×D411yescharacteristic
506C22×C5C2×H(5,𝔽2)11yescharacteristic
507C22×C5C2×H(5,𝔽2)11yescharacteristic
508C22×C5C2×H(5,𝔽2)11yescharacteristic
509C22×C5C2×2−1+411yescharacteristic
510C22×C5C2×2−1+411yescharacteristic
511C22×C5C2×2−1+411yescharacteristic
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—416no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—88no—
528C4×C5—24no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535Dic5—24no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—54no—
542C24—52no—
543C24—52no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24C23×D511yescharacteristic
558C2×Q8—108no—
559C2×Q8—204no—
560C2×Q8—204no—
561C2×Q8—2016no—
562C2×D4—108no—
563C2×D4—204no—
564C2×D4—204no—
565C2×D4—2016no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—54no—
587C22×C4—52no—
588C22×C4—516no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
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×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—2016no—
612C22×C4—204no—
613C22×C4—204no—
614C22×C4D4×D514yes—
615C22×C4C23×D512yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C4⋊C4—204no—
630C4⋊C4—204no—
631C4⋊C4—204no—
632C4⋊C4—204no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—204no—
639C22⋊C4—204no—
640C22⋊C4—204no—
641C22⋊C4—204no—
642C22⋊C4—204no—
643C22⋊C4—204no—
644C2×C5#281418yescomplemented
645C2×C5C2×#53411yescharacteristic
646C2×C5C2×#53611yescharacteristic
647C2×C5C2×#53711yescharacteristic
648C2×C5C2×#56211yescharacteristic
649C2×C5C2×#56211yescharacteristic
650C2×C5C2×#56311yescharacteristic
651C2×C5C2×#56311yescharacteristic
652D5—44no—
653D5—82no—
654C23—54no—
655C23—108no—
656C23—108no—
657C23—108no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×D4×D512yes—
683C23#414412yes—
684C23#414712yes—
685C23#414712yes—
686C23#414912yes—
687C23#414912yes—
688C23#415012yes—
689C23C24×D511yescharacteristic
690Q8—2016no—
691D4—2016no—
692C2×C4—28no—
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—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—54no—
720C2×C4—108no—
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—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—2016no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4C2×D4×D514yes—
745C5C2×#281411yescharacteristic, complemented, Sylow
746C22—104no—
747C22—104no—
748C22—104no—
749C22—202no—
750C22—202no—
751C22—2016no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—408no—
762C22#6593914yes—
763C22#6596214yes—
764C22#6596314yes—
765C22#6600114yes—
766C22#6603314yes—
767C22#6603414yes—
768C22#6606914yes—
769C22C22×D4×D511yescharacteristic
770C22C2×#414411yescharacteristic
771C22C2×#414711yescharacteristic
772C22C2×#414711yescharacteristic
773C22C2×#414911yescharacteristic
774C22C2×#414911yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—104no—
784C4—202no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—204no—
790C2—402no—
791C2#1060973618yesdirect product factor
792C2C2×#6593911yescharacteristic
793C2C2×#6596211yescharacteristic
794C2C2×#6596311yescharacteristic
795C2C2×#6600111yescharacteristic
796C2C2×#6603411yescharacteristic
797C2C2×#6603311yescharacteristic
798C2C2×#6606911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#398D5
hypocenterC5C2×#2814
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#4042C2semidirect
3. C2×C5×#398C2semidirect
4. C2×#65283C2semidirect
5. C2×#65283C2semidirect
7. C2×#65276C2semidirect
8. C2×#65273C2semidirect
9. C2×#65268C2semidirect
10. #10609736C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64964C2semidirect
13. C2×#64962C2semidirect
14. C2×#64946C2semidirect
15. C2×#64963C2semidirect
43. C2×#4042C22semidirect
46. C5×#398C22semidirect
57. #65283C22semidirect
58. #65283C22semidirect
60. #65276C22semidirect
61. #65273C22semidirect
62. #65268C22semidirect
63. #64964C22semidirect
64. #64964C22semidirect
65. #64963C22semidirect
66. #64962C22semidirect
68. #64946C22semidirect
158. C2×#398D5semidirect
303. #398C2×D5semidirect
644. C2×C5#2814semidirect
745. C5C2×#2814semidirect
791. C2#10609736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40402
C22×#40422
C2×C5×#3982
C2×#652832
C2×#652802
C2×#652762
C2×#652732
C2×#652682
#106097362
C2×#649642
C2×#649622
C2×#649462
C2×#649632
C2×#649612
C2×#28145