Finite Group Databasebeta

← C2×#10614143 #12267411

Subgroups — C2×#10614143 #12267411

Order 1280.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic, complemented
3C2×#65512C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65500C211yesmaximal, characteristic, complemented
8C2×#65501C211yesmaximal, characteristic, complemented
9#10614143C2116yesmaximal, direct product factor
10C2×#65283C211yesmaximal, characteristic, complemented
11C2×#65275C211yesmaximal, characteristic, complemented
12C2×#65245C211yesmaximal, characteristic, complemented
13C2×#65234C211yesmaximal, characteristic, complemented
14C2×#65240C211yesmaximal, characteristic, complemented
15C2×#65222C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C22⋊D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C2×C4×C5×D4—28no—
24C2×C4×C5×D4C2218yescomplemented
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4029—28no—
45C2×#4029C2218yescomplemented
46#65512C2218yes—
47#65511C2218yescomplemented
48#65502C2218yescomplemented
49#65502C2218yescomplemented
50#65501C2218yescomplemented
51#65500C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65283C2218yescomplemented
63#65275C2218yescomplemented
64#65245C2218yescomplemented
65#65240C2218yescomplemented
66#65234C2218yescomplemented
67C4×#685C2218yescomplemented
68#65222C2218yescomplemented
69C2×#2457—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4C2314yes—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5—42no—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5—42no—
95C22×C22⋊D5—42no—
96C22×C22⋊D5C2314yes—
97C22×C22⋊D5C2314yes—
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C4×C5×D4—232no—
110C2×C5×C4⋊C4—24no—
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4D418yescomplemented
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C42×C5—24no—
117C2×C42×C5C2314yes—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5—42no—
122C2×C22⋊Dic5—42no—
123C2×C22⋊Dic5—42no—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—42no—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5—42no—
140C2×C4⋊Dic5C2314yes—
141C2×C4⋊Dic5C2314yes—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148#4029—232no—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×C4×D4D511yescharacteristic, complemented
161#2457—516no—
162C2×#400—51no—
163C2×#396—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#387—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#381—51no—
173C2×#380—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×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×D414yes—
188C24×C5#4114yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5#4114yes—
199C23×D5C2412yes—
200C2×C5×D4—232no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
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—28no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—28no—
217C22×C4×C5—28no—
218C22×C4×C5—28no—
219C22×C4×C5—44no—
220C22×C4×C5—44no—
221C22×C4×C5—416no—
222C22×C4×C5—416no—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5#4114yes—
226C22×C4×C5#4114yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—416no—
239C2×C22⋊D5—416no—
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×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—44no—
271C2×C4×D5—416no—
272C5×C4⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4C2×D4116yescomplemented
275C42×C5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—28no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280C22⋊Dic5—44no—
281C22⋊Dic5—44no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—44no—
286C4⋊Dic5—28no—
287C4⋊Dic5—44no—
288#683—28no—
289#683—28no—
290C4×Dic5—44no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C24×C4C2×D511yescharacteristic
296C24×C4C2×D511yescharacteristic
297C2×#123—58no—
298C2×#123—108no—
299C2×C4×D4—28no—
300C2×C4×D4C2×D518yescomplemented
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42C2×D511yescharacteristic
320#400—58no—
321#396—58no—
322#394—58no—
323#392—58no—
324#388—58no—
325#388—58no—
326#387—58no—
327#386—58no—
328#386—58no—
329#386—58no—
330#381—58no—
331#380—58no—
332C4×C22⋊C4—58no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
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—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5C22×D414yes—
370C23×C5C22×D412yes—
371C23×C5C2×#4114yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C5C2511yescharacteristic
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—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5C2×#4114yes—
393C5×D4—232no—
394C2×C4×C5—28no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
397C2×C4×C5—28no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—416no—
410C2×C4×C5—416no—
411C2×C4×C5—44no—
412C2×C4×C5C22×D414yes—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C2×#4114yes—
415C2×C4×C5C2×#4114yes—
416C22⋊D5—416no—
417C22⋊D5—416no—
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—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5—44no—
444C2×Dic5—44no—
445C2×Dic5—44no—
446C4×D5—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—54no—
454C22×D4—54no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—202no—
460C22×D4—202no—
461C22×D4C22×D514yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—51no—
475C23×C4—54no—
476C23×C4—104no—
477C23×C4—104no—
478C23×C4—202no—
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D514yes—
481C23×C4C22×D514yes—
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486#123—1032no—
487C4×D4—232no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—54no—
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—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4C22⋊D518yescomplemented
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—24no—
523C2×C42—54no—
524C2×C42—202no—
525C2×C42C22×D514yes—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—54no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—416no—
551C22×C5—416no—
552C22×C5#52514yes—
553C22×C5#52914yes—
554C22×C5#54014yes—
555C22×C5#54614yes—
556C22×C5#54614yes—
557C22×C5#55114yes—
558C22×C5#55314yes—
559C22×C5C23×D411yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C22×C5C2×H(5,𝔽2)11yescharacteristic
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—416no—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—24no—
577C4×C5—24no—
578C4×C5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—54no—
599C24—52no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24#70914yes—
607C24C2×C22⋊D514yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—232no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—108no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—2016no—
622C2×D4—2016no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—416no—
641C22×C4—416no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—108no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
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—108no—
672C22×C4—204no—
673C22×C4—2016no—
674C22×C4#70914yes—
675C22×C4#71114yes—
676C22×C4C2×C22⋊D514yes—
677C22×C4C2×C22⋊D514yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—28no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C4⋊C4—108no—
687C4⋊C4—204no—
688C22⋊C4—28no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4C2×C22⋊D5116yescomplemented
700C42—28no—
701C42—204no—
702C2×C5—44no—
703C2×C5—44no—
704C2×C5#245718yescomplemented
705C2×C5C2×#52511yescharacteristic
706C2×C5C2×#52911yescharacteristic
707C2×C5C2×#54011yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#54611yescharacteristic
710C2×C5C2×#55111yescharacteristic
711C2×C5C2×#55311yescharacteristic
712D5—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23C2×#70914yes—
754C23C2×#70912yes—
755C23C2×#70912yes—
756C23C2×#71112yes—
757C23#414412yes—
758C23D5×#4112yes—
759C23#414912yes—
760C23C22×C22⋊D514yes—
761C23C22×C22⋊D512yes—
762C23C24×D511yescharacteristic
763D4—232no—
764D4—2016no—
765D4—2016no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—2016no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4C2×#70914yes—
814C2×C4C2×#71114yes—
815C2×C4C22×C22⋊D514yes—
816C2×C4C22×C22⋊D514yes—
817C5C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—416no—
832C22—416no—
833C22—42no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—202no—
838C22—202no—
839C22—2016no—
840C22—202no—
841C22—202no—
842C22#6589014yes—
843C22#6589114yes—
844C22#6589614yes—
845C22#6589914yes—
846C22#6612514yes—
847C22#6614014yes—
848C22#6616314yes—
849C22C22×#70911yescharacteristic
850C22C22×#70911yescharacteristic
851C22C22×#71111yescharacteristic
852C22C2×#414411yescharacteristic
853C22C2×D5×#4111yescharacteristic
854C22C2×#414911yescharacteristic
855C22C23×C22⋊D511yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—202no—
862C4—202no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—44no—
870C2—204no—
871C2#1061414318yesdirect product factor
872C2C2×#6589911yescharacteristic
873C2C2×#6589111yescharacteristic
874C2C2×#6589611yescharacteristic
875C2C2×#6589011yescharacteristic
876C2C2×#6612511yescharacteristic
877C2C2×#6614011yescharacteristic
878C2C2×#6616311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×C4×D4D5
hypocenterC5C2×#2457
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
2. C22×#4029C2semidirect
4. C2×#65511C2semidirect
5. C2×#65502C2semidirect
6. C2×#65502C2semidirect
7. C2×#65500C2semidirect
8. C2×#65501C2semidirect
9. #10614143C2direct (N × H)
10. C2×#65283C2semidirect
11. C2×#65275C2semidirect
12. C2×#65245C2semidirect
13. C2×#65234C2semidirect
14. C2×#65240C2semidirect
15. C2×#65222C2semidirect
16. C2×C4×#685C2semidirect
24. C2×C4×C5×D4C22semidirect
45. C2×#4029C22semidirect
47. #65511C22semidirect
48. #65502C22semidirect
49. #65502C22semidirect
50. #65501C22semidirect
51. #65500C22semidirect
62. #65283C22semidirect
63. #65275C22semidirect
64. #65245C22semidirect
65. #65240C22semidirect
66. #65234C22semidirect
67. C4×#685C22semidirect
68. #65222C22semidirect
113. C2×C5×C22⋊C4D4semidirect
160. C22×C4×D4D5semidirect
274. C5×C22⋊C4C2×D4semidirect
300. C2×C4×D4C2×D5semidirect
519. C2×C22⋊C4C22⋊D5semidirect
699. C22⋊C4C2×C22⋊D5semidirect
704. C2×C5#2457semidirect
817. C5C2×#2457semidirect
871. C2#10614143direct (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×#40292
C2×#655122
C2×#655112
C2×#655022
C2×#655002
C2×#655012
#106141432
C2×#652832
C2×#652752
C2×#652452
C2×#652342
C2×#652402
C2×#652222
C2×C4×#6852
C2×#24575