Finite Group Databasebeta

← C2×#10614087 #12266754

Subgroups — C2×#10614087 #12266754

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
1C22×C4×C5×D4C211yesmaximal, characteristic, complemented
2C22×#4085C211yesmaximal, characteristic
3C22×#4075C211yesmaximal, characteristic, complemented
4C23×#683C211yesmaximal, characteristic, complemented
5C2×#65509C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65499C211yesmaximal, characteristic, complemented
8#10614087C2116yesmaximal, direct product factor
9C2×#65281C211yesmaximal, characteristic, complemented
10C2×#65269C211yesmaximal, characteristic, complemented
11C2×#65248C211yesmaximal, characteristic, complemented
12C2×#65241C211yesmaximal, characteristic, complemented
13C2×#65247C211yesmaximal, characteristic, complemented
14C2×#65235C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×#65222C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C22⋊D5C2211yescharacteristic
22C24×Dic5C2211yescharacteristic
23C24×Dic5C2211yescharacteristic
24C2×C4×C5×D4—28no—
25C2×C4×C5×D4C2218yescomplemented
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C2×#4085—28no—
35C2×#4085C2218yes—
36C2×#4075—28no—
37C2×#4075C2218yescomplemented
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×#683—28no—
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×#683C2211yescharacteristic
50C22×#683C2211yescharacteristic
51C22×#683C2218yescomplemented
52#65509C2218yescomplemented
53#65502C2218yescomplemented
54#65499C2218yescomplemented
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65281C2218yescomplemented
64#65269C2218yescomplemented
65#65248C2218yescomplemented
66#65247C2218yescomplemented
67#65241C2218yescomplemented
68#65235C2218yescomplemented
69#65229C2218yescomplemented
70#65222C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4D418yes—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—24no—
82C23×C4×C5—24no—
83C23×C4×C5—42no—
84C23×C4×C5—42no—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2314yes—
89C23×C4×C5C2314yes—
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5—24no—
95C22×C22⋊D5—24no—
96C22×C22⋊D5—24no—
97C22×C22⋊D5—42no—
98C22×C22⋊D5C2314yes—
99C22×C22⋊D5C2314yes—
100C23×Dic5—24no—
101C23×Dic5—24no—
102C23×Dic5—24no—
103C23×Dic5—24no—
104C23×Dic5—24no—
105C23×Dic5—42no—
106C23×Dic5C2311yescharacteristic
107C23×Dic5C2311yescharacteristic
108C23×Dic5C2311yescharacteristic
109C23×Dic5C2311yescharacteristic
110C23×Dic5C2314yes—
111C23×Dic5C2314yes—
112C23×Dic5C2311yescharacteristic
113C23×Dic5C2311yescharacteristic
114C23×Dic5C2311yescharacteristic
115C4×C5×D4—232no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C42×C5—24no—
123C2×C42×C5C2314yes—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132#4085—232no—
133#4075—232no—
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×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683—232no—
150C2×#683—42no—
151C2×#683D418yescomplemented
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×#683C2314yes—
157C2×#683C2314yes—
158C2×#683C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4D511yescharacteristic, complemented
170C23×C4⋊C4—51no—
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×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5C2×D414yes—
194C24×C5C2×D414yes—
195C24×C5#4114yes—
196C24×C5#4114yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5C2412yes—
208C2×C5×D4—232no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4C2×D4116yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—28no—
220C22×C4×C5—28no—
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—28no—
228C22×C4×C5—28no—
229C22×C4×C5—44no—
230C22×C4×C5—44no—
231C22×C4×C5—416no—
232C22×C4×C5—416no—
233C22×C4×C5C2×D414yes—
234C22×C4×C5C2×D414yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
244C2×C22⋊D5—28no—
245C2×C22⋊D5—44no—
246C2×C22⋊D5—416no—
247C2×C22⋊D5—416no—
248C22×Dic5—232no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—28no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—28no—
257C22×Dic5—28no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—28no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5—22no—
268C22×Dic5—22no—
269C22×Dic5—22no—
270C22×Dic5—22no—
271C22×Dic5—28no—
272C22×Dic5—44no—
273C22×Dic5—416no—
274C22×Dic5C2×D414yes—
275C22×Dic5C2×D414yes—
276C22×Dic5#4114yes—
277C22×Dic5C2412yes—
278C22×Dic5C2412yes—
279C22×Dic5C2412yes—
280C22×Dic5C2412yes—
281C22×Dic5C2412yes—
282C22×Dic5C2412yes—
283C22×Dic5C2412yes—
284C5×C4⋊C4—28no—
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C42×C5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—44no—
297#683—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683—44no—
303#683C2×D4116yescomplemented
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4C2×D511yescharacteristic
310C24×C4C2×D511yescharacteristic
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—28no—
316C2×C4×D4C2×D518yescomplemented
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—58no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4—108no—
326C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42C2×D511yescharacteristic
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—28no—
369C23×C5—28no—
370C23×C5—28no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5#123116yescomplemented
382C23×C5C22×D412yes—
383C23×C5C22×D414yes—
384C23×C5C22×D414yes—
385C23×C5C22×D412yes—
386C23×C5C2×#4114yes—
387C23×C5C2×#4114yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C52−1+412yes—
393C23×C5C2511yescharacteristic
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5—44no—
408C5×D4—232no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
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—22no—
423C2×C4×C5—22no—
424C2×C4×C5—416no—
425C2×C4×C5—416no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C22×D414yes—
431C22⋊D5—416no—
432C22⋊D5—416no—
433C2×Dic5—232no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
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—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—22no—
455C2×Dic5—416no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5—44no—
460C2×Dic5C22×D414yes—
461C2×Dic5C22×D414yes—
462C2×Dic5C2×#4114yes—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—202no—
476C22×D4C22⋊D518yes—
477C22×D4C22×D514yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—54no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—54no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—202no—
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D514yes—
503C23×C4C22×D514yes—
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—232no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—58no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—1032no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—104no—
522C2×C4⋊C4—104no—
523C2×C4⋊C4—104no—
524C2×C4⋊C4—202no—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
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—202no—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—24no—
549C2×C42C22×D514yes—
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×C5—24no—
566C22×C5—24no—
567C22×C5—24no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—416no—
572C22×C5—42no—
573C22×C5C2×#12314yes—
574C22×C5C2×#12318yescomplemented
575C22×C5#52514yes—
576C22×C5#53914yes—
577C22×C5D4214yes—
578C22×C5#54714yes—
579C22×C5#54814yes—
580C22×C5#55314yes—
581C22×C5C23×D411yescharacteristic
582C22×C5C23×D411yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C22×C5C2×H(5,𝔽2)11yescharacteristic
587C22×C5C2×2−1+411yescharacteristic
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—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—52no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24#70914yes—
627C24#70914yes—
628C24C2×C22⋊D514yes—
629C24C2×C22⋊D514yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—232no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—204no—
642C2×D4—2016no—
643C2×D4—2016no—
644C2×D4C2×C22⋊D5116yes—
645C22×C4—22no—
646C22×C4—22no—
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—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—416no—
665C22×C4—416no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—108no—
677C22×C4—108no—
678C22×C4—108no—
679C22×C4—1032no—
680C22×C4—108no—
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—102no—
697C22×C4—102no—
698C22×C4—102no—
699C22×C4—108no—
700C22×C4—204no—
701C22×C4—2016no—
702C22×C4D4×D514yes—
703C22×C4C2×C22⋊D514yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—516no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—204no—
717C22⋊C4—28no—
718C22⋊C4—28no—
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—28no—
729C2×C5—28no—
730C2×C5—44no—
731C2×C5#244318yescomplemented
732C2×C5C22×#12311yescharacteristic
733C2×C5C2×#52511yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×D4211yescharacteristic
736C2×C5C2×#54711yescharacteristic
737C2×C5C2×#54811yescharacteristic
738C2×C5C2×#55311yescharacteristic
739D5—82no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23#4075116yescomplemented
778C23C2×#70914yes—
779C23C2×#70914yes—
780C23C2×#70912yes—
781C23C2×#70912yes—
782C23C2×D4×D512yes—
783C23#414412yes—
784C23D5×#4112yes—
785C23#415012yes—
786C23C22×C22⋊D514yes—
787C23C22×C22⋊D514yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790D4—232no—
791D4—2016no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
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—416no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—1032no—
817C2×C4—108no—
818C2×C4—108no—
819C2×C4—108no—
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—102no—
836C2×C4—102no—
837C2×C4—102no—
838C2×C4—2016no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—232no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—416no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—408no—
869C22#6587414yes—
870C22#6588114yes—
871C22#6588614yes—
872C22#6589814yes—
873C22C2×#407514yes—
874C22C2×#407518yescomplemented
875C22D4×C22⋊D514yes—
876C22#6615814yes—
877C22C22×#70911yescharacteristic
878C22C22×#70911yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C2×#414411yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×#415011yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—44no—
898C2—402no—
899C2#1061408718yesdirect product factor
900C2C2×#6589811yescharacteristic
901C2C2×#6588611yescharacteristic
902C2C2×#6587411yescharacteristic
903C2C2×#6588111yescharacteristic
904C2C22×#407511yescharacteristic
905C2C2×D4×C22⋊D511yescharacteristic
906C2C2×#6615811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC22×C4×D4D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×D4C2semidirect
3. C22×#4075C2semidirect
4. C23×#683C2semidirect
5. C2×#65509C2semidirect
6. C2×#65502C2semidirect
7. C2×#65499C2semidirect
8. #10614087C2direct (N × H)
9. C2×#65281C2semidirect
10. C2×#65269C2semidirect
11. C2×#65248C2semidirect
12. C2×#65241C2semidirect
13. C2×#65247C2semidirect
14. C2×#65235C2semidirect
15. C2×#65229C2semidirect
16. C2×#65222C2semidirect
25. C2×C4×C5×D4C22semidirect
37. C2×#4075C22semidirect
51. C22×#683C22semidirect
52. #65509C22semidirect
53. #65502C22semidirect
54. #65499C22semidirect
63. #65281C22semidirect
64. #65269C22semidirect
65. #65248C22semidirect
66. #65247C22semidirect
67. #65241C22semidirect
68. #65235C22semidirect
69. #65229C22semidirect
70. #65222C22semidirect
151. C2×#683D4semidirect
169. C22×C4×D4D5semidirect
303. #683C2×D4semidirect
316. C2×C4×D4C2×D5semidirect
381. C23×C5#123semidirect
574. C22×C5C2×#123semidirect
731. C2×C5#2443semidirect
777. C23#4075semidirect
845. C5C2×#2443semidirect
874. C22C2×#4075semidirect
899. C2#10614087direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C22×#40852
C22×#40752
C23×#6832
C2×#655092
C2×#655022
C2×#654992
#106140872
C2×#652812
C2×#652692
C2×#652482
C2×#652412
C2×#652472
C2×#652352
C2×#652292
C2×#652222
C2×#24435