Finite Group Databasebeta

← C2×#10609180 #12305457

Subgroups — C2×#10609180 #12305457

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×#4042C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65272C211yesmaximal, characteristic, complemented
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65273C211yesmaximal, characteristic, complemented
9C2×#65248C211yesmaximal, characteristic
10C2×#65241C211yesmaximal, characteristic, complemented
11C2×#65237C211yesmaximal, characteristic, complemented
12C2×#65250C211yesmaximal, characteristic
13C2×#65236C211yesmaximal, characteristic, complemented
14#10609180C2116yesmaximal, direct product factor
15C2×#64964C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C2×#4042—28no—
43C2×#4042C2218yescomplemented
44C2×#4029—28no—
45C2×#4029C2218yes—
46C5×#396C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65282C2218yescomplemented
58#65276C2218yescomplemented
59#65273C2218yescomplemented
60#65273C2218yescomplemented
61#65272C2218yescomplemented
62#65250C2218yes—
63#65248C2218yes—
64#65241C2218yescomplemented
65#65237C2218yescomplemented
66#65236C2218yescomplemented
67#64964C2218yescomplemented
68#64945C2218yescomplemented
69C2×#2814—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—42no—
80C22×C22⋊D5—42no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
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—42no—
99C2×C5×C4⋊C4—42no—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4—42no—
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—42no—
111C2×C22⋊Dic5—42no—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—42no—
119C2×#685—42no—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5—42no—
127C2×C4⋊Dic5—42no—
128C2×C4⋊Dic5C2314yes—
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#4029—232no—
143C5×#95C2314yes—
144#3963C2314yes—
145#3963C2314yes—
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×#398—51no—
159C2×#397—51no—
160C2×#397—51no—
161C2×#397—51no—
162C2×#396—51no—
163C2×#396D511yescharacteristic, complemented
164C2×#395—51no—
165C2×#394—51no—
166C2×#394—51no—
167C2×#393—51no—
168C2×#380—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×D5C2×D414yes—
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—44no—
212C2×C22⋊D5—44no—
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×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5C2×D414yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
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—44no—
252C5×C4⋊C4—44no—
253C5×C22⋊C4—28no—
254C5×C22⋊C4—44no—
255C5×C22⋊C4—44no—
256C22⋊Dic5—28no—
257C22⋊Dic5—44no—
258C22⋊Dic5—44no—
259#685—28no—
260#685—28no—
261#685—28no—
262#685—44no—
263#685—44no—
264C4⋊Dic5—28no—
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⋊C4—51no—
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⋊C4C2×D511yescharacteristic
299C22×C22⋊C4C2×D511yescharacteristic
300C22×C22⋊C4C2×D511yescharacteristic
301#398—58no—
302#398—58no—
303#398—58no—
304#397—58no—
305#397—58no—
306#397—58no—
307#396—58no—
308#396C2×D518yescomplemented
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×#95—51no—
322C2×#95—51no—
323C2×#95C2×D511yescharacteristic
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5C22×D412yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C52−1+412yes—
343C23×C52−1+412yes—
344C23×C52−1+412yes—
345C23×C5C2511yescharacteristic
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
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—44no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5C22×D414yes—
384C22⋊D5—416no—
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—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×Dic5—44no—
412C2×Dic5C22×D414yes—
413C4×D5—416no—
414Dic10—416no—
415C25—51no—
416C25C22×D511yescharacteristic
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—51no—
434C23×C4—202no—
435C23×C4—202no—
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—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—54no—
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—104no—
459C2×C4⋊C4—202no—
460C2×C4⋊C4—202no—
461C2×C4⋊C4—202no—
462C2×C4⋊C4—202no—
463C2×C4⋊C4C22×D514yes—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
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—202no—
482C2×C22⋊C4—202no—
483C2×C22⋊C4—202no—
484C2×C22⋊C4—202no—
485C2×C22⋊C4C22×D514yes—
486C2×C22⋊C4C22×D514yes—
487C2×C22⋊C4C22×D514yes—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95—54no—
496#95—54no—
497#95C22×D514yes—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—88no—
506C22×C5#53414yes—
507C22×C5#53614yes—
508C22×C5#53714yes—
509C22×C5#56214yes—
510C22×C5#56214yes—
511C22×C5#56314yes—
512C22×C5#56314yes—
513C22×C5C23×D411yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×H(5,𝔽2)11yescharacteristic
516C22×C5C2×H(5,𝔽2)11yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C22×C5C2×2−1+411yescharacteristic
519C22×C5C2×2−1+411yescharacteristic
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—416no—
528C4×C5—24no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534Dic5—24no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—54no—
549C24—52no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24C23×D512yes—
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—54no—
584C22×C4—52no—
585C22×C4—516no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
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×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—102no—
612C22×C4—2016no—
613C22×C4—204no—
614C22×C4—204no—
615C22×C4D4×D514yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—28no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C4⋊C4—204no—
630C4⋊C4—204no—
631C4⋊C4—204no—
632C4⋊C4—204no—
633C22⋊C4—28no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—108no—
640C22⋊C4—204no—
641C22⋊C4—204no—
642C22⋊C4—204no—
643C22⋊C4—204no—
644C2×C5—82no—
645C2×C5#281418yescomplemented
646C2×C5C2×#53411yescharacteristic
647C2×C5C2×#53611yescharacteristic
648C2×C5C2×#53711yescharacteristic
649C2×C5C2×#56211yescharacteristic
650C2×C5C2×#56211yescharacteristic
651C2×C5C2×#56311yescharacteristic
652C2×C5C2×#56311yescharacteristic
653D5—44no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—54no—
669C23—108no—
670C23—108no—
671C23—108no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×D4×D512yes—
683C23#414412yes—
684C23#414412yes—
685C23#414712yes—
686C23#414912yes—
687C23#415012yes—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—54no—
716C2×C4—108no—
717C2×C4—102no—
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—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—2016no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4C2×D4×D514yes—
745C5C2×#281411yescharacteristic, complemented, Sylow
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—202no—
758C22—2016no—
759C22—202no—
760C22—202no—
761C22—202no—
762C22#6593914yes—
763C22#6594214yes—
764C22#6595514yes—
765C22#6596214yes—
766C22#6598014yes—
767C22#6598114yes—
768C22#6604614yes—
769C22C22×D4×D511yescharacteristic
770C22C2×#414411yescharacteristic
771C22C2×#414411yescharacteristic
772C22C2×#414711yescharacteristic
773C22C2×#414911yescharacteristic
774C22C2×#415011yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—104no—
783C4—202no—
784C4—202no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—82no—
790C2—204no—
791C2#1060918018yesdirect product factor
792C2C2×#6593911yescharacteristic
793C2C2×#6594211yescharacteristic
794C2C2×#6595511yescharacteristic
795C2C2×#6598011yescharacteristic
796C2C2×#6596211yescharacteristic
797C2C2×#6598111yescharacteristic
798C2C2×#6604611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2814
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
3. C2×C5×#396C2semidirect
4. C2×#65282C2semidirect
5. C2×#65276C2semidirect
6. C2×#65272C2semidirect
7. C2×#65273C2semidirect
8. C2×#65273C2semidirect
10. C2×#65241C2semidirect
11. C2×#65237C2semidirect
13. C2×#65236C2semidirect
14. #10609180C2direct (N × H)
15. C2×#64964C2semidirect
16. C2×#64945C2semidirect
43. C2×#4042C22semidirect
46. C5×#396C22semidirect
57. #65282C22semidirect
58. #65276C22semidirect
59. #65273C22semidirect
60. #65273C22semidirect
61. #65272C22semidirect
64. #65241C22semidirect
65. #65237C22semidirect
66. #65236C22semidirect
67. #64964C22semidirect
68. #64945C22semidirect
163. C2×#396D5semidirect
308. #396C2×D5semidirect
645. C2×C5#2814semidirect
745. C5C2×#2814semidirect
791. C2#10609180direct (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×#40292
C2×C5×#3962
C2×#652822
C2×#652762
C2×#652722
C2×#652732
C2×#652482
C2×#652412
C2×#652372
C2×#652502
C2×#652362
#106091802
C2×#649642
C2×#649452
C2×#28145