Finite Group Databasebeta

← C2×#10607271 #12266909

Subgroups — C2×#10607271 #12266909

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
1C22×D5×C22⋊C4C211yesmaximal, characteristic
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65244C211yesmaximal, characteristic
7C2×#65244C211yesmaximal, characteristic
8C2×#65242C211yesmaximal, characteristic, complemented
9C2×#65242C211yesmaximal, characteristic, complemented
10C2×#65229C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607271C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64963C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic, complemented
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic, complemented
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic, complemented
39C22×C4⋊Dic5C2211yescharacteristic, complemented
40C22×C4⋊Dic5C2211yescharacteristic, complemented
41C22×#683C2211yescharacteristic, complemented
42C22×#683C2211yescharacteristic, complemented
43C22×C4×Dic5C2211yescharacteristic, complemented
44C2×D5×C22⋊C4—28no—
45C2×D5×C22⋊C4C2218yes—
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48C5×#388C2218yescomplemented
49C2×C5×#95C2211yescharacteristic, complemented
50C2×C5×#95C2211yescharacteristic, complemented
51C2×#3963C2211yescharacteristic, complemented
52C2×#3963C2211yescharacteristic, complemented
53C2×#3963C2211yescharacteristic, complemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57#65283C2218yescomplemented
58#65276C2218yescomplemented
59#65244C2218yes—
60#65244C2218yes—
61#65242C2218yescomplemented
62#65242C2218yescomplemented
63#65229C2218yescomplemented
64C4×#685C2218yescomplemented
65#64963C2218yescomplemented
66#64959C2218yescomplemented
67#64957C2218yescomplemented
68#64957C2218yescomplemented
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×D5C2314yes—
80C24×D5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4C2314yescomplemented
103C2×C5×C22⋊C4—42no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4D418yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C42×C5—42no—
110C2×C42×C5C2314yescomplemented
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—42no—
126C2×#685—42no—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5—42no—
139C2×C4⋊Dic5—42no—
140C2×C4⋊Dic5C2314yescomplemented
141C2×C4⋊Dic5C2314yescomplemented
142C2×C4⋊Dic5C2314yescomplemented
143C2×#683—24no—
144C2×#683—24no—
145C2×#683C2314yescomplemented
146C2×#683C2314yescomplemented
147C2×C4×Dic5—24no—
148C2×C4×Dic5C2314yescomplemented
149D5×C22⋊C4—232no—
150#4025—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×#388D511yescharacteristic, complemented
169C2×#385—51no—
170C2×#385—51no—
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—22no—
180C24×C5—22no—
181C24×C5C2×D414yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—232no—
189C23×D5—28no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—28no—
197C23×D5—28no—
198C23×D5—28no—
199C23×D5—28no—
200C23×D5—44no—
201C23×D5—44no—
202C23×D5—416no—
203C23×D5—416no—
204C23×D5—416no—
205C23×D5—416no—
206C23×D5—416no—
207C23×D5—416no—
208C23×D5#4114yes—
209C23×D5#4114yes—
210C23×D5#4114yes—
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—22no—
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×C5C2×D414yes—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
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—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
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—
270C5×C4⋊C4—44no—
271C5×C22⋊C4—44no—
272C5×C22⋊C4—44no—
273C5×C22⋊C4C2×D4116yes—
274C42×C5—44no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—28no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—44no—
287#685—44no—
288C4⋊Dic5—28no—
289C4⋊Dic5—44no—
290C4⋊Dic5—44no—
291#683—28no—
292#683—28no—
293C4×Dic5—28no—
294C26—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×#126—58no—
298C2×#126—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
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—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—51no—
318C22×C22⋊C4—58no—
319C22×C22⋊C4—108no—
320C22×C22⋊C4C2×D511yescharacteristic
321C22×C22⋊C4C2×D511yescharacteristic
322C22×C22⋊C4C2×D511yescharacteristic
323C22×C42—51no—
324C22×C42C2×D511yescharacteristic, complemented
325#397—58no—
326#397—58no—
327#397—58no—
328#396—58no—
329#388—58no—
330#388—58no—
331#388C2×D518yescomplemented
332#385—58no—
333#385—58no—
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—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5C22×D414yes—
360C23×C5C22×D412yes—
361C23×C5C2×#4112yes—
362C23×C5C2×#4112yes—
363C23×C5C2×#4112yes—
364C23×C5C2×#4112yes—
365C23×C5H(5,𝔽2)12yes—
366C23×C5H(5,𝔽2)12yes—
367C23×C5C2511yescharacteristic
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—232no—
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—416no—
389C22×D5—416no—
390C22×D5—416no—
391C22×D5—416no—
392C22×D5—416no—
393C22×D5—4128no—
394C22×D5—44no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—416no—
399C22×D5#126116yescomplemented
400C22×D5C2×#4114yes—
401C22×D5C2×#4114yes—
402C22×D5C2×#4114yes—
403C22×D5C2×#4114yes—
404C2×C4×C5—28no—
405C2×C4×C5—28no—
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—44no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×Dic5—22no—
429C2×Dic5—22no—
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—44no—
447C2×Dic5—44no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C4×D5—416no—
453C4×D5—416no—
454C25—51no—
455C25—51no—
456C25—54no—
457C25—104no—
458C25—104no—
459C25—104no—
460C25—104no—
461C25—104no—
462C25—202no—
463C25—202no—
464C25C22×D511yescharacteristic
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—54no—
472C23×C4—54no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—202no—
478C23×C4—202no—
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485#126—1032no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—54no—
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—104no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4C22×D514yescomplemented
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—54no—
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—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
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—1032no—
525C2×C22⋊C4—202no—
526C2×C22⋊C4—202no—
527C2×C22⋊C4D2018yes—
528C2×C22⋊C4C22×D514yes—
529C2×C22⋊C4C22×D514yes—
530C2×C22⋊C4C22×D514yes—
531C2×C42—42no—
532C2×C42—54no—
533C2×C42—104no—
534C2×C42C22×D514yescomplemented
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—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—416no—
551C22×C5#52514yes—
552C22×C5C2×#12614yes—
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—232no—
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—464no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—416no—
581C2×D5C2×#12618yescomplemented
582C4×C5—24no—
583C4×C5—24no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5—42no—
588Dic5—42no—
589Dic5—42no—
590Dic5—42no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—54no—
601C24—54no—
602C24—54no—
603C24—52no—
604C24—54no—
605C24—52no—
606C24—108no—
607C24—108no—
608C24—108no—
609C24—108no—
610C24—1032no—
611C24—102no—
612C24—102no—
613C24—102no—
614C24—102no—
615C24—108no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—204no—
623C24—204no—
624C24—2016no—
625C24—2016no—
626C24—2016no—
627C24—2016no—
628C24—2016no—
629C24—2016no—
630C24C2×D2014yes—
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—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—108no—
656C22×C4—108no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
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—108no—
676C22×C4—108no—
677C22×C4—204no—
678C22×C4—204no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4C2×D2014yes—
682C22×C4C2×D2014yes—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—44no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—108no—
693C4⋊C4—204no—
694C4⋊C4—204no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—108no—
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—108no—
708C22⋊C4—204no—
709C22⋊C4—204no—
710C22⋊C4C2×D20116yes—
711C42—44no—
712C42—108no—
713C2×C5—44no—
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—28no—
723D5—44no—
724C23—28no—
725C23—28no—
726C23—28no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—54no—
738C23—54no—
739C23—54no—
740C23—516no—
741C23—54no—
742C23—1032no—
743C23—108no—
744C23—108no—
745C23—108no—
746C23—108no—
747C23—108no—
748C23—108no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—108no—
754C23—108no—
755C23—108no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—2016no—
763C23—2016no—
764C23—2016no—
765C23—2016no—
766C23—2016no—
767C23—20128no—
768C23—2016no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23C22×D2014yes—
774C23C22×D2012yes—
775C23#414412yes—
776C23#414412yes—
777C23D5×#4112yes—
778C23D5×#4112yes—
779C23D5×#4112yes—
780C23D5×#4112yes—
781C23C24×D511yescharacteristic
782C2×C4—28no—
783C2×C4—28no—
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—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
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—2016no—
823C2×C4—2016no—
824C2×C4—204no—
825C2×C4—204no—
826C2×C4—204no—
827C2×C4—204no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4C22×D2014yes—
831C2×C4C22×D2014yes—
832C5C2×#248011yescharacteristic, complemented, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—416no—
840C22—42no—
841C22—58no—
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—104no—
847C22—1032no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—104no—
852C22—2064no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—2016no—
857C22—202no—
858C22#6585814yes—
859C22#6588814yes—
860C22#6588814yes—
861C22#6594714yes—
862C22#6599314yes—
863C22#6601314yes—
864C22D5×#12614yes—
865C22C23×D2011yescharacteristic
866C22C2×#414411yescharacteristic
867C22C2×#414411yescharacteristic
868C22C2×D5×#4111yescharacteristic
869C22C2×D5×#4111yescharacteristic
870C22C2×D5×#4111yescharacteristic
871C22C2×D5×#4111yescharacteristic
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—202no—
879C4—202no—
880C4—202no—
881C4—202no—
882C4—202no—
883C4—202no—
884C2—44no—
885C2—108no—
886C2—204no—
887C2#1060727118yesdirect product factor
888C2C2×#6585811yescharacteristic
889C2C2×#6588811yescharacteristic
890C2C2×#6588811yescharacteristic
891C2C2×#6594711yescharacteristic
892C2C2×#6599311yescharacteristic
893C2C2×#6601311yescharacteristic
894C2C2×D5×#12611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#4025C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65283C2semidirect
5. C2×#65276C2semidirect
8. C2×#65242C2semidirect
9. C2×#65242C2semidirect
10. C2×#65229C2semidirect
11. C2×C4×#685C2semidirect
12. #10607271C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64957C2semidirect
15. C2×#64963C2semidirect
16. C2×#64959C2semidirect
20. C22×C5×C4⋊C4C22semidirect
24. C22×C42×C5C22semidirect
38. C22×C4⋊Dic5C22semidirect
39. C22×C4⋊Dic5C22semidirect
40. C22×C4⋊Dic5C22semidirect
41. C22×#683C22semidirect
42. C22×#683C22semidirect
43. C22×C4×Dic5C22semidirect
47. C2×#4025C22semidirect
48. C5×#388C22semidirect
49. C2×C5×#95C22semidirect
50. C2×C5×#95C22semidirect
51. C2×#3963C22semidirect
52. C2×#3963C22semidirect
53. C2×#3963C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. C2×#3963C22semidirect
57. #65283C22semidirect
58. #65276C22semidirect
61. #65242C22semidirect
62. #65242C22semidirect
63. #65229C22semidirect
64. C4×#685C22semidirect
65. #64963C22semidirect
66. #64959C22semidirect
67. #64957C22semidirect
68. #64957C22semidirect
102. C2×C5×C4⋊C4C23semidirect
110. C2×C42×C5C23semidirect
140. C2×C4⋊Dic5C23semidirect
141. C2×C4⋊Dic5C23semidirect
142. C2×C4⋊Dic5C23semidirect
145. C2×#683C23semidirect
146. C2×#683C23semidirect
148. C2×C4×Dic5C23semidirect
151. C5×#95C23semidirect
152. C5×#95C23semidirect
153. #3963C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
168. C2×#388D5semidirect
304. C22×C4⋊C4C2×D5semidirect
324. C22×C42C2×D5semidirect
331. #388C2×D5semidirect
344. C2×#95C2×D5semidirect
345. C2×#95C2×D5semidirect
399. C22×D5#126semidirect
497. C2×C4⋊C4C22×D5semidirect
534. C2×C42C22×D5semidirect
541. #95C22×D5semidirect
542. #95C22×D5semidirect
581. C2×D5C2×#126semidirect
714. C2×C5#2480semidirect
832. C5C2×#2480semidirect
887. C2#10607271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C22⋊C42
C22×#40252
C2×C5×#3882
C2×#652832
C2×#652762
C2×#652442
C2×#652422
C2×#652292
C2×C4×#6852
#106072712
C2×#649572
C2×#649632
C2×#649592
C2×#24805