Finite Group Databasebeta

← C2×#10609835 #12266791

Subgroups — C2×#10609835 #12266791

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×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#4024C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic
5C2×C5×#399C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65269C211yesmaximal, characteristic, complemented
8C2×#65268C211yesmaximal, characteristic, complemented
9C2×#65262C211yesmaximal, characteristic, complemented
10C2×#65245C211yesmaximal, characteristic
11C2×#65245C211yesmaximal, characteristic
12C2×#65237C211yesmaximal, characteristic, complemented
13C2×#65235C211yesmaximal, characteristic, complemented
14#10609835C2116yesmaximal, direct product factor
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4042—28no—
45C2×#4042C2218yescomplemented
46C2×D5×C4⋊C4—28no—
47C2×D5×C4⋊C4C2218yescomplemented
48C2×#4027—28no—
49C2×#4027C2218yes—
50C2×#4024—28no—
51C2×#4024C2218yescomplemented
52C5×#399C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65278C2218yescomplemented
62#65269C2218yescomplemented
63#65268C2218yescomplemented
64#65262C2218yescomplemented
65#65245C2218yes—
66#65245C2218yes—
67#65237C2218yescomplemented
68#65235C2218yescomplemented
69#64957C2218yescomplemented
70#64942C2218yescomplemented
71C2×#2449—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5Q818yescomplemented
83C22×C22⋊D5C2314yes—
84C23×Dic5—24no—
85C23×Dic5—24no—
86C23×Dic5—42no—
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2314yes—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—42no—
103C22×C4×D5—42no—
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⋊C4—24no—
113C2×C5×C4⋊C4—42no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—42no—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685D418yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5D418yescomplemented
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×C4×Dic5—24no—
152C2×C4×Dic5C2314yes—
153#4042—232no—
154D5×C4⋊C4—232no—
155#4027—232no—
156#4024—232no—
157C5×#95C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
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×#399D511yescharacteristic, complemented
171C2×#398—51no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#389—51no—
175C2×#387—51no—
176C2×#386—51no—
177C2×#386—51no—
178C2×#385—51no—
179C2×#385—51no—
180C2×#385—51no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×Q814yes—
188C24×C5C2412yes—
189C24×C5C2411yescharacteristic
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5C2×D414yes—
195C23×D5C2×Q814yes—
196C23×D5#4114yes—
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×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C2×C22⋊D5—232no—
223C2×C22⋊D5—28no—
224C2×C22⋊D5—28no—
225C2×C22⋊D5C2×Q8116yescomplemented
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×Dic5—28no—
243C22×Dic5—28no—
244C22×Dic5—44no—
245C22×Dic5—416no—
246C22×Dic5C2×D414yes—
247C22×Dic5C2×D414yes—
248C22×Dic5C2×D414yes—
249C22×Dic5C2×Q814yes—
250C22×Dic5#4114yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C2×C4×D5—232no—
259C2×C4×D5—28no—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—44no—
267C2×C4×D5—44no—
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⋊C4—28no—
276C5×C4⋊C4—44no—
277C5×C22⋊C4—28no—
278C5×C22⋊C4—28no—
279C5×C22⋊C4—44no—
280C22⋊Dic5—28no—
281C22⋊Dic5—28no—
282#685—28no—
283#685—28no—
284#685C2×D4116yes—
285C4⋊Dic5—28no—
286C4⋊Dic5C2×D4116yescomplemented
287#683—28no—
288#683—28no—
289#683—28no—
290#683—28no—
291#683—28no—
292#683—28no—
293#683—28no—
294C4×Dic5—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—58no—
317C22×C4⋊C4—108no—
318C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
327C22×C22⋊C4C2×D511yescharacteristic
328C22×C22⋊C4C2×D511yescharacteristic
329C22×C42—51no—
330#399C2×D518yescomplemented
331#398—58no—
332#396—58no—
333#395—58no—
334#389—58no—
335#387—58no—
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×#95—51no—
346C2×#95—51no—
347C2×#95—51no—
348C2×#95C2×D511yescharacteristic
349C23×C5—28no—
350C23×C5—28no—
351C23×C5—28no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—44no—
359C23×C5—44no—
360C23×C5—44no—
361C23×C5—44no—
362C23×C5C22×D412yes—
363C23×C5C22×D412yes—
364C23×C5C22×Q814yes—
365C23×C5C22×Q812yes—
366C23×C5C2×#4112yes—
367C23×C5C2×#4112yes—
368C23×C5H(5,𝔽2)12yes—
369C23×C52−1+412yes—
370C23×C5C2511yescharacteristic
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—28no—
375C22×D5—28no—
376C22×D5—28no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5C22⋊Q8116yescomplemented
382C22×D5C22×D414yes—
383C22×D5C22×Q814yes—
384C22×D5C2×#4114yes—
385C2×C4×C5—28no—
386C2×C4×C5—28no—
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—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—44no—
404C2×C4×C5—44no—
405C2×C4×C5—44no—
406C2×C4×C5—44no—
407C2×C4×C5C22×D414yes—
408C2×C4×C5C22×D414yes—
409C22⋊D5—232no—
410C2×Dic5—28no—
411C2×Dic5—28no—
412C2×Dic5—28no—
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—416no—
432C2×Dic5—44no—
433C2×Dic5—44no—
434C2×Dic5C22×D414yes—
435C2×Dic5C22×D414yes—
436C2×Dic5C22×D414yes—
437C2×Dic5C22×Q814yes—
438C2×Dic5C2×#4114yes—
439C4×D5—232no—
440C4×D5—416no—
441C4×D5—416no—
442Dic10—416no—
443C25—51no—
444C25C22×D511yescharacteristic
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—51no—
460C23×C4—54no—
461C23×C4—54no—
462C23×C4—54no—
463C23×C4—54no—
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—104no—
473C23×C4—202no—
474C23×C4—202no—
475C23×C4—202no—
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—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—58no—
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—54no—
497C2×C4⋊C4—54no—
498C2×C4⋊C4—1032no—
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—104no—
506C2×C4⋊C4—104no—
507C2×C4⋊C4C22×D514yes—
508C2×C4⋊C4C22×D514yes—
509C2×C4⋊C4C22×D514yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—58no—
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⋊C4C22×D514yes—
524C2×C22⋊C4C22×D514yes—
525C2×C22⋊C4C22×D514yes—
526C2×C42—54no—
527C2×C42—104no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95C22×D514yes—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—416no—
544C22×C5C2×C22⋊Q814yes—
545C22×C5#52514yes—
546C22×C5#53914yes—
547C22×C5D4214yes—
548C22×C5#54714yes—
549C22×C5D4×Q814yes—
550C22×C5#55414yes—
551C22×C5C23×D411yescharacteristic
552C22×C5C23×D411yescharacteristic
553C22×C5C23×Q811yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C22×#4111yescharacteristic
556C22×C5C2×H(5,𝔽2)11yescharacteristic
557C22×C5C2×2−1+411yescharacteristic
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—24no—
562C2×D5—24no—
563C2×D5—24no—
564C2×D5—232no—
565C2×D5C2×C22⋊Q818yescomplemented
566C4×C5—24no—
567C4×C5—24no—
568C4×C5—42no—
569C4×C5—42no—
570C4×C5—42no—
571C4×C5—42no—
572Dic5—24no—
573Dic5—24no—
574Dic5—24no—
575Dic5—24no—
576Dic5—24no—
577Dic5—42no—
578Dic5—42no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—54no—
586C24—54no—
587C24—54no—
588C24—52no—
589C24—102no—
590C24—102no—
591C24—102no—
592C24—102no—
593C24Q8×D514yes—
594C24C23×D512yes—
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—54no—
623C22×C4—54no—
624C22×C4—54no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—52no—
628C22×C4—52no—
629C22×C4—52no—
630C22×C4—52no—
631C22×C4—52no—
632C22×C4—108no—
633C22×C4—108no—
634C22×C4—108no—
635C22×C4—108no—
636C22×C4—1032no—
637C22×C4—108no—
638C22×C4—108no—
639C22×C4—108no—
640C22×C4—108no—
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—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—204no—
659C22×C4—204no—
660C22×C4—2016no—
661C22×C4—2016no—
662C22×C4—204no—
663C22×C4—2016no—
664C22×C4D4×D514yes—
665C22×C4D4×D514yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D512yes—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—44no—
675C4⋊C4—516no—
676C4⋊C4—108no—
677C4⋊C4—108no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—108no—
683C4⋊C4—108no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—516no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C42—108no—
693C2×C5—44no—
694C2×C5#244918yescomplemented
695C2×C5C22×C22⋊Q811yescharacteristic
696C2×C5C2×#52511yescharacteristic
697C2×C5C2×#53911yescharacteristic
698C2×C5C2×D4211yescharacteristic
699C2×C5C2×#54711yescharacteristic
700C2×C5C2×D4×Q811yescharacteristic
701C2×C5C2×#55411yescharacteristic
702D5—28no—
703C23—28no—
704C23—28no—
705C23—28no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—516no—
717C23—54no—
718C23—54no—
719C23—54no—
720C23—108no—
721C23—108no—
722C23—108no—
723C23—108no—
724C23—108no—
725C23—108no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23C2×D4×D512yes—
731C23C2×D4×D512yes—
732C23#414412yes—
733C23C2×Q8×D514yes—
734C23C2×Q8×D512yes—
735C23D5×#4112yes—
736C23D5×#4112yes—
737C23#415012yes—
738C23C24×D511yescharacteristic
739Q8—2016no—
740D4—1032no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
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—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—54no—
764C2×C4—54no—
765C2×C4—54no—
766C2×C4—54no—
767C2×C4—54no—
768C2×C4—1032no—
769C2×C4—108no—
770C2×C4—108no—
771C2×C4—108no—
772C2×C4—108no—
773C2×C4—108no—
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—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—2016no—
791C2×C4—2016no—
792C2×C4—2016no—
793C2×C4—204no—
794C2×C4—204no—
795C2×C4C2×D4×D514yes—
796C2×C4C2×D4×D514yes—
797C5C2×#244911yescharacteristic, complemented, Sylow
798C22—24no—
799C22—24no—
800C22—24no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—416no—
805C22—42no—
806C22—58no—
807C22—104no—
808C22—104no—
809C22—104no—
810C22—104no—
811C22—104no—
812C22—1032no—
813C22—104no—
814C22D5×C22⋊Q814yes—
815C22#6596614yes—
816C22#6597014yes—
817C22#6598914yes—
818C22#6599014yes—
819C22#6599414yes—
820C22#6605114yes—
821C22C22×D4×D511yescharacteristic
822C22C22×D4×D511yescharacteristic
823C22C2×#414411yescharacteristic
824C22C22×Q8×D511yescharacteristic
825C22C2×D5×#4111yescharacteristic
826C22C2×D5×#4111yescharacteristic
827C22C2×#415011yescharacteristic
828C4—24no—
829C4—24no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—104no—
835C4—104no—
836C4—104no—
837C4—104no—
838C4—104no—
839C4—202no—
840C4—202no—
841C2—44no—
842C2—108no—
843C2#1060983518yesdirect product factor
844C2C2×#6596611yescharacteristic
845C2C2×#6597011yescharacteristic
846C2C2×D5×C22⋊Q811yescharacteristic
847C2C2×#6599011yescharacteristic
848C2C2×#6599411yescharacteristic
849C2C2×#6598911yescharacteristic
850C2C2×#6605111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#399C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#399D5
hypocenterC5C2×#2449
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
2. C22×D5×C4⋊C4C2semidirect
3. C22×#4024C2semidirect
5. C2×C5×#399C2semidirect
6. C2×#65278C2semidirect
7. C2×#65269C2semidirect
8. C2×#65268C2semidirect
9. C2×#65262C2semidirect
12. C2×#65237C2semidirect
13. C2×#65235C2semidirect
14. #10609835C2direct (N × H)
15. C2×#64957C2semidirect
16. C2×#64942C2semidirect
45. C2×#4042C22semidirect
47. C2×D5×C4⋊C4C22semidirect
51. C2×#4024C22semidirect
52. C5×#399C22semidirect
61. #65278C22semidirect
62. #65269C22semidirect
63. #65268C22semidirect
64. #65262C22semidirect
67. #65237C22semidirect
68. #65235C22semidirect
69. #64957C22semidirect
70. #64942C22semidirect
82. C22×C22⋊D5Q8semidirect
134. C2×C4⋊Dic5D4semidirect
170. C2×#399D5semidirect
225. C2×C22⋊D5C2×Q8semidirect
286. C4⋊Dic5C2×D4semidirect
330. #399C2×D5semidirect
381. C22×D5C22⋊Q8semidirect
565. C2×D5C2×C22⋊Q8semidirect
694. C2×C5#2449semidirect
797. C5C2×#2449semidirect
843. C2#10609835direct (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×D5×C4⋊C42
C22×#40242
C22×#40272
C2×C5×#3992
C2×#652782
C2×#652692
C2×#652682
C2×#652622
C2×#652452
C2×#652372
C2×#652352
#106098352
C2×#649572
C2×#649422
C2×#24495