Finite Group Databasebeta

← C2×#10606184 #12266912

Subgroups — C2×#10606184 #12266912

Order 1280.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#685C211yesmaximal, characteristic
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic, complemented
4C2×#65501C211yesmaximal, characteristic, complemented
5C2×#65282C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×#65244C211yesmaximal, characteristic
9C2×#65244C211yesmaximal, characteristic
10C2×#65235C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10606184C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64963C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic, complemented
21C22×C5×C4⋊C4C2211yescharacteristic, complemented
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×#685—28no—
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2218yes—
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic, complemented
41C22×C4⋊Dic5C2211yescharacteristic, complemented
42C22×#683C2211yescharacteristic, complemented
43C22×#683C2211yescharacteristic, complemented
44C22×C4×Dic5C2211yescharacteristic, complemented
45C22×C4×Dic5C2211yescharacteristic, complemented
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C5×#385C2218yescomplemented
49C2×C5×#95C2211yescharacteristic, complemented
50C2×C5×#95C2211yescharacteristic, complemented
51#65501C2218yescomplemented
52C2×#3963C2211yescharacteristic, complemented
53C2×#3963C2211yescharacteristic, complemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57C2×#3963C2211yescharacteristic, complemented
58#65283C2218yescomplemented
59#65282C2218yescomplemented
60#65279C2218yescomplemented
61#65244C2218yes—
62#65244C2218yes—
63#65235C2218yescomplemented
64C22⋊C4×Dic5C2218yescomplemented
65#64964C2218yescomplemented
66#64963C2218yescomplemented
67#64959C2218yescomplemented
68#64958C2218yescomplemented
69C2×#2480—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5—24no—
72C24×D5—24no—
73C24×D5—24no—
74C24×D5—24no—
75C24×D5—24no—
76C24×D5—42no—
77C24×D5—42no—
78C24×D5C2311yescharacteristic
79C24×D5C2311yescharacteristic
80C24×D5C2314yes—
81C23×C4×C5—24no—
82C23×C4×C5—24no—
83C23×C4×C5—42no—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2314yes—
90C23×C4×C5C2311yescharacteristic
91C23×Dic5—24no—
92C23×Dic5—24no—
93C23×Dic5—42no—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2314yes—
100C23×Dic5C2311yescharacteristic
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—42no—
103C2×C5×C4⋊C4C2314yescomplemented
104C2×C5×C4⋊C4C2314yescomplemented
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—232no—
121C2×#685—42no—
122C2×#685—42no—
123C2×#685—42no—
124C2×#685—42no—
125C2×#685D418yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5—42no—
140C2×C4⋊Dic5C2314yescomplemented
141C2×C4⋊Dic5C2314yescomplemented
142C2×#683—24no—
143C2×#683—42no—
144C2×#683C2314yescomplemented
145C2×#683C2314yescomplemented
146C2×C4×Dic5—24no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yescomplemented
149C2×C4×Dic5C2314yescomplemented
150#4044—232no—
151C5×#95C2314yescomplemented
152C5×#95C2314yescomplemented
153#3963C2314yescomplemented
154#3963C2314yescomplemented
155#3963C2314yescomplemented
156#3963C2314yescomplemented
157#3963C2314yescomplemented
158#3963C2314yescomplemented
159C22×#126—51no—
160C23×C22⋊C4—51no—
161#2480—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#397—51no—
165C2×#396—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#385—51no—
170C2×#385D511yescharacteristic, complemented
171C2×#380—51no—
172C2×#379—51no—
173C2×#379—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5#4114yes—
180C24×C5#4114yes—
181C24×C5#4114yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—232no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—28no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—28no—
199C23×D5—28no—
200C23×D5—28no—
201C23×D5—28no—
202C23×D5—44no—
203C23×D5—44no—
204C23×D5—416no—
205C23×D5—416no—
206C23×D5—416no—
207C23×D5—416no—
208C23×D5—416no—
209C23×D5—416no—
210C23×D5C2×D414yes—
211C23×D5#4114yes—
212C23×D5C2412yes—
213C23×D5C2412yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—28no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—28no—
233C22×C4×C5—44no—
234C22×C4×C5—416no—
235C22×C4×C5C2×D414yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C22×C4×C5C2412yes—
241C22×C4×C5C2412yes—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—28no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—28no—
261C22×Dic5—44no—
262C22×Dic5—416no—
263C22×Dic5C2×D414yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C5×C4⋊C4—28no—
271C5×C4⋊C4—44no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—28no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—44no—
284#685—44no—
285#685—44no—
286#685—44no—
287#685C2×D4116yes—
288C4⋊Dic5—28no—
289C4⋊Dic5—44no—
290#683—28no—
291#683—44no—
292C4×Dic5—28no—
293C4×Dic5—44no—
294C26—51no—
295C24×C4—51no—
296C24×C4C2×D511yescharacteristic
297C2×#126—58no—
298C2×#126—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic, complemented
304C22×C4⋊C4C2×D511yescharacteristic, complemented
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×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—58no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—51no—
318C22×C22⋊C4—51no—
319C22×C22⋊C4—51no—
320C22×C22⋊C4—108no—
321C22×C22⋊C4C2×D511yescharacteristic
322C22×C22⋊C4C2×D511yescharacteristic
323C22×C42—51no—
324C22×C42—51no—
325#397—58no—
326#397—58no—
327#397—58no—
328#396—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#385—58no—
333#385C2×D518yescomplemented
334#380—58no—
335#379—58no—
336#379—58no—
337C4×C22⋊C4—58no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95C2×D511yescharacteristic, complemented
345C2×#95C2×D511yescharacteristic, complemented
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
349C23×C5—28no—
350C23×C5—28no—
351C23×C5—28no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5#126116yescomplemented
357C23×C5C22×D412yes—
358C23×C5C2×#4114yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4114yes—
361C23×C5C2×#4112yes—
362C23×C5C2×#4114yes—
363C23×C5C2×#4112yes—
364C23×C5C2×#4112yes—
365C23×C5H(5,𝔽2)12yes—
366C23×C5H(5,𝔽2)12yes—
367C23×C5C2511yescharacteristic
368C22×D5—232no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—28no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—416no—
388C22×D5—416no—
389C22×D5—416no—
390C22×D5—416no—
391C22×D5—416no—
392C22×D5—4128no—
393C22×D5—44no—
394C22×D5—44no—
395C22×D5—416no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5C22×D414yes—
403C22×D5C2×#4114yes—
404C2×C4×C5—28no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—416no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5C22×D414yes—
429C2×Dic5—28no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—416no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5C22×D414yes—
454C25—51no—
455C25—51no—
456C25—54no—
457C25—104no—
458C25—104no—
459C25—104no—
460C25—104no—
461C25—104no—
462C25—202no—
463C25—202no—
464C25C22×D511yescharacteristic
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—42no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—54no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—202no—
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D514yes—
484C23×C4C22×D511yescharacteristic
485#126—1032no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—202no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4C22×D514yescomplemented
497C2×C4⋊C4C22×D514yescomplemented
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—58no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—54no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—54no—
514C2×C22⋊C4—54no—
515C2×C22⋊C4—1032no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—104no—
518C2×C22⋊C4—104no—
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×C22⋊C4—202no—
527C2×C22⋊C4—202no—
528C2×C22⋊C4—202no—
529C2×C22⋊C4C22×D514yes—
530C2×C22⋊C4C22×D514yes—
531C2×C42—54no—
532C2×C42—54no—
533C2×C42—104no—
534C2×C42—202no—
535#95—54no—
536#95—54no—
537#95—54no—
538#95—54no—
539#95—54no—
540#95—54no—
541#95C22×D514yescomplemented
542#95C22×D514yescomplemented
543C22×C5—24no—
544C22×C5—24no—
545C22×C5—24no—
546C22×C5—24no—
547C22×C5—24no—
548C22×C5—24no—
549C22×C5—232no—
550C22×C5#52514yes—
551C22×C5C2×#12614yes—
552C22×C5C2×#12618yescomplemented
553C22×C5#53814yes—
554C22×C5#54614yes—
555C22×C5#54614yes—
556C22×C5#55114yes—
557C22×C5#55114yes—
558C22×C5C23×D411yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C2×H(5,𝔽2)11yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C2×D5—24no—
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—24no—
570C2×D5—24no—
571C2×D5—464no—
572C2×D5—42no—
573C2×D5—42no—
574C2×D5—42no—
575C2×D5—42no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—416no—
581C2×D5—416no—
582C4×C5—24no—
583C4×C5—42no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5—42no—
588Dic5—24no—
589Dic5—42no—
590Dic5—42no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—54no—
599C24—54no—
600C24—52no—
601C24—52no—
602C24—108no—
603C24—108no—
604C24—1032no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24—102no—
610C24—102no—
611C24—102no—
612C24—108no—
613C24—102no—
614C24—102no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—108no—
619C24—108no—
620C24—204no—
621C24—204no—
622C24—2016no—
623C24—2016no—
624C24—2016no—
625C24—2016no—
626C24—2016no—
627C24—2016no—
628C24#70914yes—
629C24#71114yes—
630C24#71314yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—28no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—44no—
653C22×C4—416no—
654C22×C4—54no—
655C22×C4—52no—
656C22×C4—52no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—108no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—108no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—204no—
681C22×C4—2016no—
682C22×C4D4×D514yes—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—28no—
690C4⋊C4—44no—
691C4⋊C4—108no—
692C4⋊C4—108no—
693C4⋊C4—204no—
694C4⋊C4—204no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—516no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—108no—
702C22⋊C4—108no—
703C22⋊C4—108no—
704C22⋊C4—108no—
705C22⋊C4—108no—
706C22⋊C4—108no—
707C22⋊C4—204no—
708C22⋊C4—204no—
709C22⋊C4—204no—
710C22⋊C4—204no—
711C42—108no—
712C42—204no—
713C2×C5—28no—
714C2×C5#248018yescomplemented
715C2×C5C2×#52511yescharacteristic
716C2×C5C22×#12611yescharacteristic
717C2×C5C2×#53811yescharacteristic
718C2×C5C2×#54611yescharacteristic
719C2×C5C2×#54611yescharacteristic
720C2×C5C2×#55111yescharacteristic
721C2×C5C2×#55111yescharacteristic
722D5—44no—
723D5—44no—
724C23—28no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—54no—
735C23—54no—
736C23—1032no—
737C23—108no—
738C23—108no—
739C23—108no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—102no—
754C23—102no—
755C23—2016no—
756C23—2016no—
757C23—2016no—
758C23—2016no—
759C23—2016no—
760C23—20128no—
761C23—204no—
762C23—204no—
763C23—2016no—
764C23—204no—
765C23—204no—
766C23—204no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23#4044116yescomplemented
771C23C2×#70914yes—
772C23C2×#70912yes—
773C23C2×D4×D512yes—
774C23C2×#71114yes—
775C23C2×#71112yes—
776C23#414412yes—
777C23C2×#71314yes—
778C23C2×#71312yes—
779C23D5×#4112yes—
780C23#414912yes—
781C23C24×D511yescharacteristic
782C2×C4—28no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—416no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—54no—
807C2×C4—108no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—2016no—
826C2×C4—204no—
827C2×C4—204no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4—204no—
831C2×C4C2×D4×D514yes—
832C5C2×#248011yescharacteristic, complemented, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—232no—
839C22—24no—
840C22—104no—
841C22—104no—
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—2064no—
847C22—202no—
848C22—202no—
849C22—202no—
850C22—202no—
851C22—202no—
852C22—202no—
853C22—202no—
854C22—2016no—
855C22—2016no—
856C22—202no—
857C22C2×#404414yes—
858C22C2×#404418yescomplemented
859C22#6588414yes—
860C22#6589014yes—
861C22#6592514yes—
862C22#6596114yes—
863C22#6597814yes—
864C22#6599214yes—
865C22C22×#70911yescharacteristic
866C22C22×D4×D511yescharacteristic
867C22C22×#71111yescharacteristic
868C22C2×#414411yescharacteristic
869C22C22×#71311yescharacteristic
870C22C2×D5×#4111yescharacteristic
871C22C2×#414911yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—104no—
879C4—202no—
880C4—202no—
881C4—202no—
882C4—202no—
883C4—202no—
884C2—28no—
885C2—204no—
886C2—204no—
887C2#1060618418yesdirect product factor
888C2C22×#404411yescharacteristic
889C2C2×#6588411yescharacteristic
890C2C2×#6589011yescharacteristic
891C2C2×#6592511yescharacteristic
892C2C2×#6596111yescharacteristic
893C2C2×#6597811yescharacteristic
894C2C2×#6599211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC2×#385D5
hypocenterC5C2×#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#4044C2semidirect
3. C2×C5×#385C2semidirect
4. C2×#65501C2semidirect
5. C2×#65282C2semidirect
6. C2×#65283C2semidirect
7. C2×#65279C2semidirect
10. C2×#65235C2semidirect
11. C2×C22⋊C4×Dic5C2semidirect
12. #10606184C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64963C2semidirect
15. C2×#64959C2semidirect
16. C2×#64958C2semidirect
20. C22×C5×C4⋊C4C22semidirect
21. C22×C5×C4⋊C4C22semidirect
40. C22×C4⋊Dic5C22semidirect
41. C22×C4⋊Dic5C22semidirect
42. C22×#683C22semidirect
43. C22×#683C22semidirect
44. C22×C4×Dic5C22semidirect
45. C22×C4×Dic5C22semidirect
47. C2×#4044C22semidirect
48. C5×#385C22semidirect
49. C2×C5×#95C22semidirect
50. C2×C5×#95C22semidirect
51. #65501C22semidirect
52. C2×#3963C22semidirect
53. C2×#3963C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. C2×#3963C22semidirect
57. C2×#3963C22semidirect
58. #65283C22semidirect
59. #65282C22semidirect
60. #65279C22semidirect
63. #65235C22semidirect
64. C22⋊C4×Dic5C22semidirect
65. #64964C22semidirect
66. #64963C22semidirect
67. #64959C22semidirect
68. #64958C22semidirect
103. C2×C5×C4⋊C4C23semidirect
104. C2×C5×C4⋊C4C23semidirect
140. C2×C4⋊Dic5C23semidirect
141. C2×C4⋊Dic5C23semidirect
144. C2×#683C23semidirect
145. C2×#683C23semidirect
148. C2×C4×Dic5C23semidirect
149. C2×C4×Dic5C23semidirect
151. C5×#95C23semidirect
152. C5×#95C23semidirect
153. #3963C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
170. C2×#385D5semidirect
303. C22×C4⋊C4C2×D5semidirect
304. C22×C4⋊C4C2×D5semidirect
333. #385C2×D5semidirect
344. C2×#95C2×D5semidirect
345. C2×#95C2×D5semidirect
356. C23×C5#126semidirect
496. C2×C4⋊C4C22×D5semidirect
497. C2×C4⋊C4C22×D5semidirect
541. #95C22×D5semidirect
542. #95C22×D5semidirect
552. C22×C5C2×#126semidirect
714. C2×C5#2480semidirect
770. C23#4044semidirect
832. C5C2×#2480semidirect
858. C22C2×#4044semidirect
887. C2#10606184direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6852
C22×#40442
C2×C5×#3852
C2×#655012
C2×#652822
C2×#652832
C2×#652792
C2×#652442
C2×#652352
C2×C22⋊C4×Dic52
#106061842
C2×#649642
C2×#649632
C2×#649592
C2×#649582
C2×#24805