Finite Group Databasebeta

← C2×#10607052 #12266785

Subgroups — C2×#10607052 #12266785

Order 1280.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×#4043C211yesmaximal, characteristic, complemented
3C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×C4×D20C211yesmaximal, characteristic
5C2×C5×#387C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65217C211yesmaximal, characteristic, complemented
8#10607052C2116yesmaximal, direct product factor
9C2×#64966C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64950C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C2×#4043—28no—
45C2×#4043C2218yescomplemented
46C2×#4042—28no—
47C2×#4042C2218yescomplemented
48C2×D5×C4⋊C4—28no—
49C2×D5×C4⋊C4C2218yescomplemented
50C2×C4×D20—28no—
51C2×C4×D20C2218yes—
52C5×#387C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65217C2218yescomplemented
63#64966C2218yescomplemented
64#64957C2218yescomplemented
65#64957C2218yescomplemented
66#64957C2218yescomplemented
67#64954C2218yes—
68#64954C2218yes—
69#64950C2218yescomplemented
70#64945C2218yescomplemented
71C2×#2449—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×D20—24no—
88C22×D20—24no—
89C22×D20Q818yescomplemented
90C22×D20C2314yes—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—42no—
101C22×C4×D5—42no—
102C22×C4×D5—42no—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C22×C4×D5C2314yes—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4D418yescomplemented
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C4⋊C4C2314yes—
115C2×C42×C5—24no—
116C2×C42×C5C2314yes—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—42no—
124C2×#685D418yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—24no—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5—42no—
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2314yes—
141C2×C4⋊Dic5C2314yes—
142C2×C4⋊Dic5C2314yes—
143C2×C4⋊Dic5C2314yes—
144C2×C4⋊Dic5C2314yes—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153#4043—232no—
154#4042—232no—
155D5×C4⋊C4—232no—
156C4×D20—232no—
157C5×#95C2314yes—
158C5×#95C2314yes—
159C5×#95C2314yes—
160C5×#95C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165C22×C22⋊Q8—51no—
166C22×C22⋊Q8—51no—
167C22×C4×D4—51no—
168C23×C4⋊C4—51no—
169#2449—516no—
170C2×#399—51no—
171C2×#398—51no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#389—51no—
175C2×#387D511yescharacteristic, complemented
176C2×#386—51no—
177C2×#386—51no—
178C2×#385—51no—
179C2×#385—51no—
180C2×#385—51no—
181C24×C5C2411yescharacteristic
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5C2×D414yes—
193C23×D5C2×Q814yes—
194C23×D5C2×Q814yes—
195C23×D5#4114yes—
196C23×D5C2412yes—
197C23×D5C2412yes—
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×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5C2×D414yes—
215C22×C4×C5C2×D414yes—
216C22×C4×C5C2×D414yes—
217C22×C4×C5C2×D414yes—
218C22×C4×C5C2×Q814yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
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×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5C2×D414yes—
243C22×Dic5#4114yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C2×D20—232no—
251C2×D20—28no—
252C2×D20—28no—
253C2×D20C2×Q8116yescomplemented
254C2×C4×D5—232no—
255C2×C4×D5—28no—
256C2×C4×D5—28no—
257C2×C4×D5—28no—
258C2×C4×D5—28no—
259C2×C4×D5—28no—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—44no—
265C2×C4×D5—44no—
266C2×C4×D5—44no—
267C2×C4×D5—416no—
268C2×C4×D5—416no—
269C2×C4×D5—416no—
270C2×Dic10—28no—
271C2×Dic10—28no—
272C2×Dic10—44no—
273C2×Dic10—416no—
274C5×C4⋊C4—28no—
275C5×C4⋊C4C2×D4116yescomplemented
276C42×C5—28no—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—44no—
284#685C2×D4116yes—
285C4⋊Dic5—28no—
286C4⋊Dic5—28no—
287C4⋊Dic5—28no—
288C4⋊Dic5—28no—
289C4⋊Dic5—28no—
290C4⋊Dic5—44no—
291#683—28no—
292#683—28no—
293#683—28no—
294#683—28no—
295C23×Q8—51no—
296C23×D4—51no—
297C24×C4—51no—
298C24×C4—51no—
299C24×C4—51no—
300C24×C4—51no—
301C2×C22⋊Q8—58no—
302C2×C22⋊Q8—58no—
303C2×C22⋊Q8—108no—
304C2×C22⋊Q8—108no—
305C2×C4×D4—58no—
306C2×C4×D4—108no—
307C22×C4⋊C4—51no—
308C22×C4⋊C4—51no—
309C22×C4⋊C4—51no—
310C22×C4⋊C4—51no—
311C22×C4⋊C4—51no—
312C22×C4⋊C4—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4—51no—
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—58no—
318C22×C4⋊C4—108no—
319C22×C4⋊C4C2×D511yescharacteristic
320C22×C4⋊C4C2×D511yescharacteristic
321C22×C22⋊C4—51no—
322C22×C22⋊C4—51no—
323C22×C22⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C42C2×D511yescharacteristic
330#399—58no—
331#398—58no—
332#396—58no—
333#395—58no—
334#389—58no—
335#387C2×D518yescomplemented
336#386—58no—
337#386—58no—
338#385—58no—
339#385—58no—
340#385—58no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95C2×D511yescharacteristic
346C2×#95C2×D511yescharacteristic
347C2×#95C2×D511yescharacteristic
348C2×#95C2×D511yescharacteristic
349C23×C5C22×D412yes—
350C23×C5C22×D412yes—
351C23×C5C22×Q812yes—
352C23×C5C2×#4112yes—
353C23×C5C2×#4112yes—
354C23×C5H(5,𝔽2)12yes—
355C23×C52−1+412yes—
356C23×C5C2511yescharacteristic
357C22×D5—28no—
358C22×D5—28no—
359C22×D5—28no—
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—44no—
377C22×D5—44no—
378C22×D5—44no—
379C22×D5—44no—
380C22×D5C22⋊Q8116yescomplemented
381C22×D5C22×D414yes—
382C22×D5C22×Q814yes—
383C22×D5C22×Q814yes—
384C22×D5C2×#4114yes—
385C2×C4×C5—28no—
386C2×C4×C5—28no—
387C2×C4×C5—28no—
388C2×C4×C5—28no—
389C2×C4×C5—28no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—44no—
407C2×C4×C5—44no—
408C2×C4×C5C22×D414yes—
409C2×C4×C5C22×D414yes—
410C2×C4×C5C22×D414yes—
411C2×C4×C5C22×D414yes—
412C2×C4×C5C22×Q814yes—
413C2×Dic5—28no—
414C2×Dic5—28no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—44no—
432C2×Dic5—44no—
433C2×Dic5—44no—
434C2×Dic5—44no—
435C2×Dic5C22×D414yes—
436C2×Dic5C2×#4114yes—
437D20—232no—
438C4×D5—232no—
439C4×D5—416no—
440C4×D5—416no—
441C4×D5—416no—
442Dic10—416no—
443C25—51no—
444C25—51no—
445C22×Q8—54no—
446C22×Q8—104no—
447C22×Q8—104no—
448C22×Q8—202no—
449C22×D4—58no—
450C22×D4—54no—
451C22×D4—104no—
452C22×D4—104no—
453C23×C4—51no—
454C23×C4—51no—
455C23×C4—51no—
456C23×C4—51no—
457C23×C4—51no—
458C23×C4—51no—
459C23×C4—54no—
460C23×C4—54no—
461C23×C4—54no—
462C23×C4—54no—
463C23×C4—104no—
464C23×C4—104no—
465C23×C4—104no—
466C23×C4—104no—
467C23×C4—104no—
468C23×C4—104no—
469C23×C4—104no—
470C23×C4—104no—
471C23×C4—104no—
472C23×C4—202no—
473C23×C4—202no—
474C23×C4—202no—
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C22⋊Q8—1032no—
483C22⋊Q8—1032no—
484C4×D4—1032no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—54no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—104no—
497C2×C4⋊C4—104no—
498C2×C4⋊C4—104no—
499C2×C4⋊C4—104no—
500C2×C4⋊C4—104no—
501C2×C4⋊C4—104no—
502C2×C4⋊C4—104no—
503C2×C4⋊C4—104no—
504C2×C4⋊C4—104no—
505C2×C4⋊C4—1032no—
506C2×C4⋊C4—202no—
507C2×C4⋊C4D2018yescomplemented
508C2×C4⋊C4C22×D514yes—
509C2×C4⋊C4C22×D514yes—
510C2×C22⋊C4—58no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—54no—
514C2×C22⋊C4—54no—
515C2×C22⋊C4—54no—
516C2×C22⋊C4—54no—
517C2×C22⋊C4—54no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—104no—
520C2×C22⋊C4—104no—
521C2×C22⋊C4—104no—
522C2×C22⋊C4—104no—
523C2×C22⋊C4—104no—
524C2×C22⋊C4—104no—
525C2×C22⋊C4—202no—
526C2×C42—24no—
527C2×C42C22×D514yes—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95C22×D514yes—
533#95C22×D514yes—
534#95C22×D514yes—
535#95C22×D514yes—
536C22×C5C2×C22⋊Q814yes—
537C22×C5#52514yes—
538C22×C5#53914yes—
539C22×C5D4214yes—
540C22×C5#54714yes—
541C22×C5D4×Q814yes—
542C22×C5#55414yes—
543C22×C5C23×D411yescharacteristic
544C22×C5C23×D411yescharacteristic
545C22×C5C23×Q811yescharacteristic
546C22×C5C22×#4111yescharacteristic
547C22×C5C22×#4111yescharacteristic
548C22×C5C2×H(5,𝔽2)11yescharacteristic
549C22×C5C2×2−1+411yescharacteristic
550C2×D5—24no—
551C2×D5—24no—
552C2×D5—24no—
553C2×D5—24no—
554C2×D5—24no—
555C2×D5—24no—
556C2×D5—232no—
557C2×D5—24no—
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—416no—
565C2×D5C2×C22⋊Q818yescomplemented
566C4×C5—24no—
567C4×C5—24no—
568C4×C5—24no—
569C4×C5—24no—
570C4×C5—24no—
571C4×C5—42no—
572C4×C5—42no—
573Dic5—24no—
574Dic5—24no—
575Dic5—42no—
576Dic5—42no—
577Dic5—42no—
578Dic5—42no—
579C24—54no—
580C24—54no—
581C24—54no—
582C24—52no—
583C24—54no—
584C24—52no—
585C24—102no—
586C24—102no—
587C24—102no—
588C24—102no—
589C24—102no—
590C24—102no—
591C24—102no—
592C24—102no—
593C24—102no—
594C24—102no—
595C24C23×D511yescharacteristic
596C2×Q8—108no—
597C2×Q8—108no—
598C2×Q8—204no—
599C2×Q8—2016no—
600C2×D4—516no—
601C2×D4—108no—
602C2×D4—1032no—
603C2×D4—108no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—54no—
621C22×C4—54no—
622C22×C4—52no—
623C22×C4—52no—
624C22×C4—52no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—52no—
628C22×C4—108no—
629C22×C4—108no—
630C22×C4—108no—
631C22×C4—1032no—
632C22×C4—108no—
633C22×C4—108no—
634C22×C4—102no—
635C22×C4—102no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—108no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—102no—
645C22×C4—102no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—108no—
652C22×C4—108no—
653C22×C4—108no—
654C22×C4—204no—
655C22×C4—204no—
656C22×C4—204no—
657C22×C4—2016no—
658C22×C4—2016no—
659C22×C4—2016no—
660C22×C4C2×D2014yes—
661C22×C4C2×D2014yes—
662C22×C4C2×D2014yes—
663C22×C4D4×D514yes—
664C22×C4Q8×D514yes—
665C22×C4C23×D512yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D512yes—
672C4⋊C4—28no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4—108no—
677C4⋊C4—108no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—204no—
683C4⋊C4C2×D20116yescomplemented
684C22⋊C4—516no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—204no—
692C42—28no—
693C2×C5#244918yescomplemented
694C2×C5C22×C22⋊Q811yescharacteristic
695C2×C5C2×#52511yescharacteristic
696C2×C5C2×#53911yescharacteristic
697C2×C5C2×D4211yescharacteristic
698C2×C5C2×#54711yescharacteristic
699C2×C5C2×D4×Q811yescharacteristic
700C2×C5C2×#55411yescharacteristic
701D5—28no—
702D5—44no—
703C23—516no—
704C23—54no—
705C23—54no—
706C23—54no—
707C23—54no—
708C23—108no—
709C23—108no—
710C23—108no—
711C23—108no—
712C23—102no—
713C23—108no—
714C23—102no—
715C23—102no—
716C23—102no—
717C23—108no—
718C23—108no—
719C23—108no—
720C23—102no—
721C23—102no—
722C23—108no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23—204no—
728C23—204no—
729C23—204no—
730C23—204no—
731C23C22×D2012yes—
732C23C2×D4×D512yes—
733C23C2×Q8×D512yes—
734C23D5×#4112yes—
735C23D5×#4112yes—
736C23#414912yes—
737C23#415012yes—
738C23C24×D511yescharacteristic
739Q8—2016no—
740D4—1032no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—54no—
765C2×C4—54no—
766C2×C4—1032no—
767C2×C4—108no—
768C2×C4—108no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—2016no—
786C2×C4—2016no—
787C2×C4—2016no—
788C2×C4—204no—
789C2×C4—204no—
790C2×C4—204no—
791C2×C4—204no—
792C2×C4C22×D2014yes—
793C2×C4C22×D2014yes—
794C2×C4C22×D2014yes—
795C2×C4C2×D4×D514yes—
796C2×C4C2×Q8×D514yes—
797C5C2×#244911yescharacteristic, complemented, Sylow
798C22—58no—
799C22—104no—
800C22—104no—
801C22—104no—
802C22—104no—
803C22—104no—
804C22—104no—
805C22—1032no—
806C22—104no—
807C22—104no—
808C22—104no—
809C22—202no—
810C22—202no—
811C22—202no—
812C22—202no—
813C22—2016no—
814C22#6585814yes—
815C22D4×D2014yes—
816C22Q8×D2014yes—
817C22D5×C22⋊Q814yes—
818C22#6598914yes—
819C22#6602414yes—
820C22#6604114yes—
821C22C23×D2011yescharacteristic
822C22C22×D4×D511yescharacteristic
823C22C22×Q8×D511yescharacteristic
824C22C2×D5×#4111yescharacteristic
825C22C2×D5×#4111yescharacteristic
826C22C2×#414911yescharacteristic
827C22C2×#415011yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—104no—
836C4—104no—
837C4—202no—
838C4—202no—
839C4—202no—
840C4—202no—
841C2—108no—
842C2—204no—
843C2#1060705218yesdirect product factor
844C2C2×#6585811yescharacteristic
845C2C2×D4×D2011yescharacteristic
846C2C2×Q8×D2011yescharacteristic
847C2C2×D5×C22⋊Q811yescharacteristic
848C2C2×#6598911yescharacteristic
849C2C2×#6602411yescharacteristic
850C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2449
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
2. C22×#4043C2semidirect
3. C22×D5×C4⋊C4C2semidirect
5. C2×C5×#387C2semidirect
6. C2×#65283C2semidirect
7. C2×#65217C2semidirect
8. #10607052C2direct (N × H)
9. C2×#64966C2semidirect
12. C2×#64957C2semidirect
13. C2×#64957C2semidirect
14. C2×#64957C2semidirect
15. C2×#64950C2semidirect
16. C2×#64945C2semidirect
45. C2×#4043C22semidirect
47. C2×#4042C22semidirect
49. C2×D5×C4⋊C4C22semidirect
52. C5×#387C22semidirect
61. #65283C22semidirect
62. #65217C22semidirect
63. #64966C22semidirect
64. #64957C22semidirect
65. #64957C22semidirect
66. #64957C22semidirect
69. #64950C22semidirect
70. #64945C22semidirect
89. C22×D20Q8semidirect
112. C2×C5×C4⋊C4D4semidirect
175. C2×#387D5semidirect
253. C2×D20C2×Q8semidirect
275. C5×C4⋊C4C2×D4semidirect
335. #387C2×D5semidirect
380. C22×D5C22⋊Q8semidirect
507. C2×C4⋊C4D20semidirect
565. C2×D5C2×C22⋊Q8semidirect
683. C4⋊C4C2×D20semidirect
693. C2×C5#2449semidirect
797. C5C2×#2449semidirect
843. C2#10607052direct (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×#40432
C22×D5×C4⋊C42
C22×C4×D202
C2×C5×#3872
C2×#652832
C2×#652172
#106070522
C2×#649662
C2×#649542
C2×#649572
C2×#649502
C2×#649452
C2×#24495