Finite Group Databasebeta

← C2×#10613926 #12266750

Subgroups — C2×#10613926 #12266750

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4076C211yesmaximal, characteristic
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4040C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65502C211yesmaximal, characteristic, complemented
8C2×#65499C211yesmaximal, characteristic, complemented
9#10613926C2116yesmaximal, direct product factor
10C2×#65281C211yesmaximal, characteristic, complemented
11C2×#65282C211yesmaximal, characteristic, complemented
12C2×#65280C211yesmaximal, characteristic, complemented
13C2×#65278C211yesmaximal, characteristic, complemented
14C2×#65273C211yesmaximal, characteristic, complemented
15C2×#65279C211yesmaximal, characteristic, complemented
16C2×#65270C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C22⋊D5C2211yescharacteristic
22C23×D20C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4—28no—
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C22×C5×C4⋊C4C2218yescomplemented
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4076—28no—
33C2×#4076C2218yes—
34C2×C4×C22⋊D5—28no—
35C2×C4×C22⋊D5C2218yescomplemented
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×#685C2211yescharacteristic
44C22×#685C2211yescharacteristic
45C22×C4⋊Dic5C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4040—28no—
51C2×#4040C2218yescomplemented
52#65502C2218yescomplemented
53#65502C2218yescomplemented
54#65502C2218yescomplemented
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64#65282C2218yescomplemented
65#65281C2218yescomplemented
66#65280C2218yescomplemented
67#65279C2218yescomplemented
68#65278C2218yescomplemented
69#65273C2218yescomplemented
70#65270C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—24no—
82C23×C4×C5—42no—
83C23×C4×C5—42no—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2314yes—
87C23×C4×C5C2314yes—
88C23×C4×C5C2314yes—
89C23×C4×C5C2311yescharacteristic
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C23×C4×C5C2311yescharacteristic
93C22×C22⋊D5—24no—
94C22×C22⋊D5—24no—
95C22×C22⋊D5—24no—
96C22×C22⋊D5—24no—
97C22×C22⋊D5—24no—
98C22×C22⋊D5D418yes—
99C22×C22⋊D5C2314yes—
100C22×C22⋊D5C2314yes—
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×D20—24no—
108C22×D20—24no—
109C22×D20—42no—
110C22×D20C2314yes—
111C22×C4×D5—24no—
112C22×C4×D5—24no—
113C22×C4×D5—42no—
114C22×C4×D5C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—24no—
118C2×C5×C4⋊C4—232no—
119C2×C5×C4⋊C4D418yescomplemented
120C2×C5×C4⋊C4C2314yes—
121C2×C5×C4⋊C4C2314yes—
122C2×C5×C4⋊C4C2314yes—
123C2×C5×C4⋊C4C2314yes—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128#4076—232no—
129C4×C22⋊D5—232no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685—42no—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×#685C2314yes—
146C2×#685C2314yes—
147C2×#685C2314yes—
148C2×C4⋊Dic5—24no—
149C2×C4⋊Dic5C2314yes—
150C2×#683—24no—
151C2×#683—24no—
152C2×#683—42no—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158#4040—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4D511yescharacteristic, complemented
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×D414yes—
188C24×C5#4114yes—
189C24×C5#4114yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5C2×D414yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—232no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—28no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—28no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—28no—
225C22×C4×C5—28no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—28no—
229C22×C4×C5—28no—
230C22×C4×C5—44no—
231C22×C4×C5—44no—
232C22×C4×C5—416no—
233C22×C4×C5—416no—
234C22×C4×C5C2×D414yes—
235C22×C4×C5C2×D414yes—
236C22×C4×C5C2×D414yes—
237C22×C4×C5#4114yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C22×C4×C5C2412yes—
241C22×C4×C5C2412yes—
242C22×C4×C5C2412yes—
243C22×C4×C5C2412yes—
244C2×C22⋊D5—232no—
245C2×C22⋊D5—28no—
246C2×C22⋊D5—28no—
247C2×C22⋊D5—28no—
248C2×C22⋊D5—28no—
249C2×C22⋊D5—28no—
250C2×C22⋊D5—416no—
251C2×C22⋊D5C2×D4116yes—
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—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5—22no—
268C22×Dic5—22no—
269C22×Dic5C2×D414yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×D20—28no—
277C2×D20—28no—
278C2×D20—44no—
279C2×D20—416no—
280C2×C4×D5—28no—
281C2×C4×D5—28no—
282C2×C4×D5—44no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—28no—
286C5×C4⋊C4—28no—
287C5×C4⋊C4C2×D4116yescomplemented
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—28no—
297#685—28no—
298#685—44no—
299C4⋊Dic5—28no—
300#683—28no—
301#683—28no—
302#683—44no—
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C24×C4C2×D511yescharacteristic
310C24×C4C2×D511yescharacteristic
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—28no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C4⋊C4C2×D518yescomplemented
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4—51no—
336C22×C22⋊C4—51no—
337C22×C22⋊C4—51no—
338C22×C42—51no—
339#399—58no—
340#398—58no—
341#397—58no—
342#394—58no—
343#388—58no—
344#387—58no—
345#386—58no—
346#386—58no—
347#386—58no—
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95—51no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5#123116yescomplemented
369C23×C5C22×D414yes—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4114yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4114yes—
376C23×C5C2×#4112yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C52−1+412yes—
379C23×C5C2511yescharacteristic
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5C22×D414yes—
408C2×C4×C5—232no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—28no—
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—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—416no—
428C2×C4×C5—416no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C22×D414yes—
434C2×C4×C5C2×#4114yes—
435C22⋊D5—232no—
436C22⋊D5—416no—
437C2×Dic5—28no—
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—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—22no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5—44no—
460C2×Dic5C22×D414yes—
461D20—416no—
462C4×D5—416no—
463C25—51no—
464C25—51no—
465C25C22×D511yescharacteristic
466C22×D4—58no—
467C22×D4—54no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—202no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—42no—
486C23×C4—42no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4—54no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—202no—
497C23×C4C22×D514yes—
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D514yes—
501C23×C4C22×D514yes—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—232no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—202no—
521C2×C4⋊C4C22⋊D518yescomplemented
522C2×C4⋊C4C22×D514yes—
523C2×C4⋊C4C22×D514yes—
524C2×C4⋊C4C22×D514yes—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4—104no—
545C2×C22⋊C4—104no—
546C2×C22⋊C4—104no—
547C2×C22⋊C4—202no—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95—54no—
557#95—54no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—232no—
564C22×C5—24no—
565C22×C5C2×#12314yes—
566C22×C5C2×#12318yescomplemented
567C22×C5#52514yes—
568C22×C5#53914yes—
569C22×C5D4214yes—
570C22×C5#54714yes—
571C22×C5#54814yes—
572C22×C5#55314yes—
573C22×C5C23×D411yescharacteristic
574C22×C5C23×D411yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C22×#4111yescharacteristic
577C22×C5C22×#4111yescharacteristic
578C22×C5C2×H(5,𝔽2)11yescharacteristic
579C22×C5C2×2−1+411yescharacteristic
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—416no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—88no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—24no—
600C4×C5—42no—
601C4×C5—42no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—52no—
614C24—52no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#70914yes—
629C24D4×D514yes—
630C24#71314yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—516no—
634C2×D4—108no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—1032no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—204no—
643C2×D4—2016no—
644C2×D4—2016no—
645C22×C4—232no—
646C22×C4—28no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—416no—
671C22×C4—54no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—52no—
678C22×C4—108no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—102no—
696C22×C4—108no—
697C22×C4—204no—
698C22×C4—2016no—
699C22×C4#70914yes—
700C22×C4C2×C22⋊D514yes—
701C22×C4C2×C22⋊D514yes—
702C22×C4C2×C22⋊D514yes—
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—204no—
716C4⋊C4C2×C22⋊D5116yescomplemented
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—204no—
728C42—108no—
729C2×C5—28no—
730C2×C5#244318yescomplemented
731C2×C5C22×#12311yescharacteristic
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#53911yescharacteristic
734C2×C5C2×D4211yescharacteristic
735C2×C5C2×#54711yescharacteristic
736C2×C5C2×#54811yescharacteristic
737C2×C5C2×#55311yescharacteristic
738D5—44no—
739D5—82no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—54no—
751C23—108no—
752C23—108no—
753C23—108no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23#4040116yescomplemented
779C23C2×#70914yes—
780C23C2×#70912yes—
781C23C2×#70912yes—
782C23C2×D4×D514yes—
783C23C2×D4×D512yes—
784C23#414412yes—
785C23C2×#71314yes—
786C23C2×#71312yes—
787C23#414712yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790D4—1032no—
791D4—2016no—
792D4—2016no—
793C2×C4—232no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—416no—
813C2×C4—416no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—54no—
817C2×C4—108no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—2016no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4C2×#70914yes—
842C2×C4C22×C22⋊D514yes—
843C2×C4C22×C22⋊D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—232no—
852C22—24no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—2016no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—408no—
869C22C2×#404014yes—
870C22C2×#404018yescomplemented
871C22#6584114yes—
872C22#6584814yes—
873C22#6584914yes—
874C22#6612514yes—
875C22D4×C22⋊D514yes—
876C22#6615114yes—
877C22C22×#70911yescharacteristic
878C22C22×#70911yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C2×#414411yescharacteristic
881C22C22×#71311yescharacteristic
882C22C2×#414711yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—104no—
891C4—202no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—204no—
898C2—402no—
899C2#1061392618yesdirect product factor
900C2C22×#404011yescharacteristic
901C2C2×#6584911yescharacteristic
902C2C2×#6584111yescharacteristic
903C2C2×#6584811yescharacteristic
904C2C2×#6612511yescharacteristic
905C2C2×D4×C22⋊D511yescharacteristic
906C2C2×#6615111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC22×#4076C2
hypercenterC23×C4⋊C4D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C5×C4⋊C4C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4040C2semidirect
5. C2×#65502C2semidirect
6. C2×#65502C2semidirect
7. C2×#65502C2semidirect
8. C2×#65499C2semidirect
9. #10613926C2direct (N × H)
10. C2×#65281C2semidirect
11. C2×#65282C2semidirect
12. C2×#65280C2semidirect
13. C2×#65278C2semidirect
14. C2×#65273C2semidirect
15. C2×#65279C2semidirect
16. C2×#65270C2semidirect
29. C22×C5×C4⋊C4C22semidirect
35. C2×C4×C22⋊D5C22semidirect
51. C2×#4040C22semidirect
52. #65502C22semidirect
53. #65502C22semidirect
54. #65502C22semidirect
55. #65499C22semidirect
64. #65282C22semidirect
65. #65281C22semidirect
66. #65280C22semidirect
67. #65279C22semidirect
68. #65278C22semidirect
69. #65273C22semidirect
70. #65270C22semidirect
119. C2×C5×C4⋊C4D4semidirect
170. C23×C4⋊C4D5semidirect
287. C5×C4⋊C4C2×D4semidirect
326. C22×C4⋊C4C2×D5semidirect
368. C23×C5#123semidirect
521. C2×C4⋊C4C22⋊D5semidirect
566. C22×C5C2×#123semidirect
716. C4⋊C4C2×C22⋊D5semidirect
730. C2×C5#2443semidirect
778. C23#4040semidirect
845. C5C2×#2443semidirect
870. C22C2×#4040semidirect
899. C2#10613926direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C4⋊C42
C22×#40762
C22×C4×C22⋊D52
C22×#40402
C2×#655022
C2×#654992
#106139262
C2×#652812
C2×#652822
C2×#652802
C2×#652782
C2×#652732
C2×#652792
C2×#652702
C2×#24435