Finite Group Databasebeta

← C2×#10607028 #12258032

Subgroups — C2×#10607028 #12258032

Order 1280.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C211yesmaximal, characteristic
2C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C4×D20C211yesmaximal, characteristic
4C2×C5×#387C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65274C211yesmaximal, characteristic, complemented
7C2×#65222C211yesmaximal, characteristic, complemented
8#10607028C2116yesmaximal, direct product factor
9C2×#64954C211yesmaximal, characteristic
10C2×#64957C211yesmaximal, characteristic, complemented
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64953C211yesmaximal, characteristic, complemented
13C2×#64936C211yesmaximal, characteristic, complemented
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4040C4116yescomplemented
43C2×#4040C2218yes—
44C2×D5×C4⋊C4—28no—
45C2×D5×C4⋊C4C2218yescomplemented
46C2×C4×D20—28no—
47C2×C4×D20C2218yes—
48C5×#387C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65278C2218yescomplemented
60#65274C2218yescomplemented
61#65222C2218yescomplemented
62#64959C2218yescomplemented
63#64958C2218yescomplemented
64#64957C2218yescomplemented
65#64957C2218yescomplemented
66#64955C2218yescomplemented
67#64954C2218yes—
68#64953C2218yescomplemented
69#64936C2218yescomplemented
70C2×#2322—51nomaximal, Sylow
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C22×D20—24no—
87C22×D20—24no—
88C22×D20C2×C418yes—
89C22×D20C2314yes—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—42no—
95C22×C4×D5—42no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5—42no—
100C22×C4×D5C2×C418yescomplemented
101C22×C4×D5D418yes—
102C22×C4×D5C2314yes—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C22×C4×D5C2314yes—
106C2×C5×C4⋊C4—24no—
107C2×C5×C4⋊C4C2×C418yescomplemented
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C4⋊C4C2314yes—
110C2×C42×C5—24no—
111C2×C42×C5C2314yes—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—42no—
116C2×#685—42no—
117C2×#685C2×C418yescomplemented
118C2×#685C2×C418yescomplemented
119C2×#685C2×C418yescomplemented
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5—24no—
130C2×C4⋊Dic5—42no—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×C4⋊Dic5C2314yes—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—42no—
137C2×#683C2×C418yescomplemented
138C2×#683C2314yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×C4×Dic5—42no—
143C2×C4×Dic5—42no—
144C2×C4×Dic5C2314yes—
145C2×C4×Dic5C2314yes—
146#4040C2×C4164yescomplemented
147D5×C4⋊C4—232no—
148C4×D20—232no—
149C5×#95C2314yes—
150C5×#95C2314yes—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×C4×D4—51no—
161C23×C4⋊C4—51no—
162#2322—516no—
163C2×#389—51no—
164C2×#389—51no—
165C2×#388—51no—
166C2×#388—51no—
167C2×#387—51no—
168C2×#387D511yescharacteristic, complemented
169C2×#386—51no—
170C2×#385—51no—
171C2×#385—51no—
172C2×#385—51no—
173C2×#381—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5C2411yescharacteristic
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5—22no—
186C23×D5C22×C414yes—
187C23×D5C22×C414yes—
188C23×D5C2×D414yes—
189C23×D5#4114yes—
190C23×D5C2412yes—
191C23×D5C2412yes—
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×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5C22×C414yes—
210C22×C4×C5C22×C414yes—
211C22×C4×C5C22×C414yes—
212C22×C4×C5C2×D414yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
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×Dic5—22no—
235C22×Dic5C22×C414yes—
236C22×Dic5C22×C414yes—
237C22×Dic5C2×D414yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C2×D20—232no—
245C2×D20—28no—
246C2×D20—28no—
247C2×D20C22×C4116yes—
248C2×C4×D5—232no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—28no—
252C2×C4×D5—28no—
253C2×C4×D5—416no—
254C2×C4×D5—44no—
255C2×C4×D5—44no—
256C2×C4×D5—44no—
257C2×C4×D5—44no—
258C2×C4×D5—44no—
259C2×C4×D5—44no—
260C2×C4×D5—416no—
261C2×C4×D5—416no—
262C2×C4×D5C22×C4116yescomplemented
263C2×C4×D5C2×D4116yes—
264C5×C4⋊C4—28no—
265C5×C4⋊C4C22×C4116yescomplemented
266C42×C5—28no—
267#685—28no—
268#685—28no—
269#685—28no—
270#685—44no—
271#685—44no—
272#685C22×C4116yescomplemented
273#685C22×C4116yescomplemented
274#685C22×C4116yescomplemented
275C4⋊Dic5—28no—
276C4⋊Dic5—28no—
277C4⋊Dic5—44no—
278#683—28no—
279#683—28no—
280#683—44no—
281#683C22×C4116yescomplemented
282C4×Dic5—44no—
283C4×Dic5—44no—
284C23×D4—51no—
285C24×C4—51no—
286C24×C4—51no—
287C24×C4—51no—
288C24×C4—51no—
289C2×#123—516no—
290C2×#123—58no—
291C2×C4×D4—58no—
292C2×C4×D4—108no—
293C22×C4⋊C4—51no—
294C22×C4⋊C4—51no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—58no—
301C22×C4⋊C4—108no—
302C22×C4⋊C4C2×D511yescharacteristic
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C42—51no—
313C22×C42—51no—
314C22×C42C2×D511yescharacteristic
315#389—58no—
316#389—58no—
317#388—58no—
318#388—58no—
319#387—58no—
320#387C2×D518yescomplemented
321#386—58no—
322#385—58no—
323#385—58no—
324#385—58no—
325#381—58no—
326C4×C22⋊C4—58no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95C2×D511yescharacteristic
334C2×#95C2×D511yescharacteristic
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D511yescharacteristic
337C23×C5C23×C412yes—
338C23×C5C22×D412yes—
339C23×C5C2×#4112yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C52−1+412yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—28no—
356C22×D5—28no—
357C22×D5—28no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—44no—
365C22×D5—44no—
366C22×D5—44no—
367C22×D5—44no—
368C22×D5C4×D4116yes—
369C22×D5C23×C414yes—
370C22×D5C23×C414yes—
371C22×D5C22×D414yes—
372C22×D5C2×#4114yes—
373C2×C4×C5—28no—
374C2×C4×C5—28no—
375C2×C4×C5—28no—
376C2×C4×C5—28no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—44no—
395C2×C4×C5—44no—
396C2×C4×C5—44no—
397C2×C4×C5C23×C414yes—
398C2×C4×C5C23×C414yes—
399C2×C4×C5C23×C414yes—
400C2×C4×C5C22×D414yes—
401C2×Dic5—28no—
402C2×Dic5—28no—
403C2×Dic5—28no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—44no—
420C2×Dic5—44no—
421C2×Dic5—44no—
422C2×Dic5C23×C414yes—
423C2×Dic5C23×C414yes—
424C2×Dic5C22×D414yes—
425D20—232no—
426C4×D5—232no—
427C4×D5—416no—
428C4×D5—416no—
429C4×D5—416no—
430C25—51no—
431C25—51no—
432C22×D4—58no—
433C22×D4—54no—
434C22×D4—104no—
435C22×D4—104no—
436C23×C4—51no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4—58no—
440C23×C4—54no—
441C23×C4—58no—
442C23×C4—54no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—54no—
447C23×C4—54no—
448C23×C4—104no—
449C23×C4—104no—
450C23×C4—104no—
451C23×C4—104no—
452C23×C4—202no—
453C23×C4—202no—
454C23×C4—202no—
455C23×C4—202no—
456C23×C4—202no—
457C23×C4—202no—
458C23×C4C22×D511yescharacteristic
459C23×C4C22×D511yescharacteristic
460C23×C4C22×D511yescharacteristic
461C23×C4C22×D511yescharacteristic
462C23×C4C22×D511yescharacteristic
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465#123—564no—
466C4×D4—1032no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—58no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—1032no—
477C2×C4⋊C4—104no—
478C2×C4⋊C4—104no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—202no—
482C2×C4⋊C4—202no—
483C2×C4⋊C4C4×D518yescomplemented
484C2×C4⋊C4C22×D514yes—
485C2×C4⋊C4C22×D514yes—
486C2×C22⋊C4—58no—
487C2×C22⋊C4—58no—
488C2×C22⋊C4—58no—
489C2×C22⋊C4—54no—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—54no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—104no—
498C2×C22⋊C4—104no—
499C2×C22⋊C4—104no—
500C2×C22⋊C4—202no—
501C2×C22⋊C4—202no—
502C2×C42—24no—
503C2×C42—54no—
504C2×C42—54no—
505C2×C42—202no—
506C2×C42—202no—
507C2×C42C22×D514yes—
508#95—54no—
509#95—54no—
510#95—54no—
511#95—54no—
512#95—54no—
513#95—54no—
514#95C22×D514yes—
515#95C22×D514yes—
516#95C22×D514yes—
517#95C22×D514yes—
518C22×C5C2×C4×D414yes—
519C22×C5#52014yes—
520C22×C5#52014yes—
521C22×C5#53414yes—
522C22×C5#53614yes—
523C22×C5#53914yes—
524C22×C5#53914yes—
525C22×C5C24×C411yescharacteristic
526C22×C5C23×D411yescharacteristic
527C22×C5C22×#4111yescharacteristic
528C22×C5C2×H(5,𝔽2)11yescharacteristic
529C22×C5C2×H(5,𝔽2)11yescharacteristic
530C22×C5C2×2−1+411yescharacteristic
531C22×C5C2×2−1+411yescharacteristic
532C2×D5—232no—
533C2×D5—24no—
534C2×D5—24no—
535C2×D5—24no—
536C2×D5—24no—
537C2×D5—24no—
538C2×D5—24no—
539C2×D5—24no—
540C2×D5—24no—
541C2×D5—24no—
542C2×D5—416no—
543C2×D5—42no—
544C2×D5—42no—
545C2×D5—42no—
546C2×D5—42no—
547C2×D5C2×C4×D418yes—
548C4×C5—24no—
549C4×C5—24no—
550C4×C5—24no—
551C4×C5—24no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5—42no—
555Dic5—24no—
556Dic5—24no—
557Dic5—24no—
558Dic5—42no—
559Dic5—42no—
560Dic5—42no—
561C24—54no—
562C24—54no—
563C24—54no—
564C24—52no—
565C24—54no—
566C24—52no—
567C24—102no—
568C24—102no—
569C24—102no—
570C24—102no—
571C24—102no—
572C24—102no—
573C24—102no—
574C24—102no—
575C24—102no—
576C24—102no—
577C24C23×D511yescharacteristic
578C2×D4—516no—
579C2×D4—108no—
580C2×D4—1032no—
581C2×D4—108no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—54no—
600C22×C4—54no—
601C22×C4—54no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—516no—
606C22×C4—516no—
607C22×C4—52no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—108no—
611C22×C4—1032no—
612C22×C4—108no—
613C22×C4—108no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—108no—
630C22×C4—2016no—
631C22×C4—204no—
632C22×C4—204no—
633C22×C4—204no—
634C22×C4—204no—
635C22×C4—204no—
636C22×C4—204no—
637C22×C4—2016no—
638C22×C4—2016no—
639C22×C4C2×C4×D514yes—
640C22×C4C2×C4×D514yes—
641C22×C4C2×C4×D514yes—
642C22×C4D4×D514yes—
643C22×C4C23×D512yes—
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D512yes—
647C22×C4C23×D512yes—
648C22×C4C23×D512yes—
649C22×C4C23×D512yes—
650C4⋊C4—28no—
651C4⋊C4—516no—
652C4⋊C4—108no—
653C4⋊C4—108no—
654C4⋊C4—108no—
655C4⋊C4—108no—
656C4⋊C4—204no—
657C4⋊C4—204no—
658C4⋊C4C2×C4×D5116yescomplemented
659C22⋊C4—516no—
660C22⋊C4—516no—
661C22⋊C4—516no—
662C22⋊C4—108no—
663C22⋊C4—108no—
664C22⋊C4—108no—
665C22⋊C4—204no—
666C22⋊C4—204no—
667C42—28no—
668C42—204no—
669C42—204no—
670C2×C5#232218yescomplemented
671C2×C5C22×C4×D411yescharacteristic
672C2×C5C2×#52011yescharacteristic
673C2×C5C2×#52011yescharacteristic
674C2×C5C2×#53411yescharacteristic
675C2×C5C2×#53611yescharacteristic
676C2×C5C2×#53911yescharacteristic
677C2×C5C2×#53911yescharacteristic
678D5—28no—
679D5—44no—
680C23—516no—
681C23—54no—
682C23—54no—
683C23—54no—
684C23—54no—
685C23—108no—
686C23—108no—
687C23—108no—
688C23—108no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23—108no—
693C23—102no—
694C23—108no—
695C23—108no—
696C23—108no—
697C23—108no—
698C23—102no—
699C23—102no—
700C23—102no—
701C23—102no—
702C23—102no—
703C23—102no—
704C23—204no—
705C23—204no—
706C23—204no—
707C23—204no—
708C23C22×C4×D512yes—
709C23C2×D4×D512yes—
710C23#414712yes—
711C23D5×#4112yes—
712C23#414912yes—
713C23#414912yes—
714C23#415012yes—
715C23C24×D511yescharacteristic
716D4—1032no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—54no—
742C2×C4—54no—
743C2×C4—54no—
744C2×C4—1032no—
745C2×C4—108no—
746C2×C4—108no—
747C2×C4—108no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—2016no—
764C2×C4—2016no—
765C2×C4—2016no—
766C2×C4—204no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4C22×C4×D514yes—
770C2×C4C22×C4×D514yes—
771C2×C4C22×C4×D514yes—
772C2×C4C2×D4×D514yes—
773C5C2×#232211yescharacteristic, complemented, Sylow
774C22—58no—
775C22—104no—
776C22—104no—
777C22—104no—
778C22—104no—
779C22—104no—
780C22—104no—
781C22—1032no—
782C22—104no—
783C22—104no—
784C22—104no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—202no—
789C22—2016no—
790C22#6585714yes—
791C22C4×D4×D514yes—
792C22#6590814yes—
793C22#6596214yes—
794C22#6598714yes—
795C22#6602614yes—
796C22#6604114yes—
797C22C23×C4×D511yescharacteristic
798C22C22×D4×D511yescharacteristic
799C22C2×#414711yescharacteristic
800C22C2×D5×#4111yescharacteristic
801C22C2×#414911yescharacteristic
802C22C2×#414911yescharacteristic
803C22C2×#415011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—104no—
812C4—104no—
813C4—104no—
814C4—202no—
815C4—202no—
816C4—202no—
817C2—108no—
818C2—204no—
819C2#1060702818yesdirect product factor
820C2C2×#6585711yescharacteristic
821C2C2×C4×D4×D511yescharacteristic
822C2C2×#6590811yescharacteristic
823C2C2×#6596211yescharacteristic
824C2C2×#6598711yescharacteristic
825C2C2×#6602611yescharacteristic
826C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
cosocleC23×C5C25
hypercenterC2×#387D5
hypocenterC5C2×#2322
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×D5×C4⋊C4C2semidirect
4. C2×C5×#387C2semidirect
5. C2×#65278C2semidirect
6. C2×#65274C2semidirect
7. C2×#65222C2semidirect
8. #10607028C2direct (N × H)
10. C2×#64957C2semidirect
11. C2×#64957C2semidirect
12. C2×#64953C2semidirect
13. C2×#64936C2semidirect
14. C2×#64959C2semidirect
15. C2×#64958C2semidirect
16. C2×#64955C2semidirect
42. C2×#4040C4semidirect
45. C2×D5×C4⋊C4C22semidirect
48. C5×#387C22semidirect
59. #65278C22semidirect
60. #65274C22semidirect
61. #65222C22semidirect
62. #64959C22semidirect
63. #64958C22semidirect
64. #64957C22semidirect
65. #64957C22semidirect
66. #64955C22semidirect
68. #64953C22semidirect
69. #64936C22semidirect
100. C22×C4×D5C2×C4semidirect
107. C2×C5×C4⋊C4C2×C4semidirect
117. C2×#685C2×C4semidirect
118. C2×#685C2×C4semidirect
119. C2×#685C2×C4semidirect
137. C2×#683C2×C4semidirect
146. #4040C2×C4semidirect
168. C2×#387D5semidirect
262. C2×C4×D5C22×C4semidirect
265. C5×C4⋊C4C22×C4semidirect
272. #685C22×C4semidirect
273. #685C22×C4semidirect
274. #685C22×C4semidirect
281. #683C22×C4semidirect
320. #387C2×D5semidirect
483. C2×C4⋊C4C4×D5semidirect
658. C4⋊C4C2×C4×D5semidirect
670. C2×C5#2322semidirect
773. C5C2×#2322semidirect
819. C2#10607028direct (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×D5×C4⋊C42
C22×C4×D202
C2×C5×#3872
C2×#652782
C2×#652742
C2×#652222
#106070282
C2×#649542
C2×#649572
C2×#649532
C2×#649362
C2×#649592
C2×#649582
C2×#649552
C2×#23225