Finite Group Databasebeta

← C2×#10614099 #12266823

Subgroups — C2×#10614099 #12266823

Order 1280.

3958 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×#4070C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4042C211yesmaximal, characteristic, complemented
5C2×#65512C211yesmaximal, characteristic
6C2×#65511C211yesmaximal, characteristic, complemented
7C2×#65502C211yesmaximal, characteristic, complemented
8C2×#65499C211yesmaximal, characteristic, complemented
9#10614099C2116yesmaximal, direct product factor
10C2×#65270C211yesmaximal, characteristic, complemented
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65250C211yesmaximal, characteristic, complemented
13C2×#65236C211yesmaximal, characteristic, complemented
14C2×#65234C211yesmaximal, 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
22C23×C4×D5C2211yescharacteristic
23C23×Dic10C2211yescharacteristic
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
34C22×C22⋊Dic5C2211yescharacteristic
35C22×C22⋊Dic5C2211yescharacteristic
36C2×C4×C22⋊D5—28no—
37C2×C4×C22⋊D5C2218yescomplemented
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C2×#4070—28no—
44C2×#4070C2218yescomplemented
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4042—28no—
51C2×#4042C2218yescomplemented
52#65512C2218yes—
53#65511C2218yescomplemented
54#65502C2218yescomplemented
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64#65270C2218yescomplemented
65#65250C2218yescomplemented
66#65245C2218yescomplemented
67#65236C2218yescomplemented
68#65234C2218yescomplemented
69#65229C2218yescomplemented
70#65222C2218yescomplemented
71C2×#2463—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
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×C5C2314yes—
87C23×C4×C5C2314yes—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
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×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C22×Dic10—24no—
112C22×Dic10—24no—
113C22×Dic10—42no—
114C22×Dic10C2314yes—
115C4×C5×D4—232no—
116C2×C5×C4⋊C4D418yescomplemented
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⋊Dic5—24no—
129C2×C22⋊Dic5—42no—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134C2×C22⋊Dic5C2314yes—
135C2×C22⋊Dic5C2314yes—
136C4×C22⋊D5—232no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685—24no—
140C2×#685—24no—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×C4⋊Dic5—24no—
146C2×C4⋊Dic5C2314yes—
147#4070—232no—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—24no—
151C2×#683D418yescomplemented
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158#4042—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×C22⋊Q8—51no—
168C22×C22⋊Q8—51no—
169C22×C4×D4—51no—
170C22×C4×D4D511yescharacteristic, complemented
171#2463—516no—
172C2×#394—51no—
173C2×#394—51no—
174C2×#393—51no—
175C2×#392—51no—
176C2×#388—51no—
177C2×#388—51no—
178C2×#387—51no—
179C2×#387—51no—
180C2×#386—51no—
181C2×#386—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×C5—22no—
194C24×C5—22no—
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#4114yes—
207C23×D5C2412yes—
208C2×C5×D4—232no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—28no—
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—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—28no—
224C22×C4×C5—28no—
225C22×C4×C5—28no—
226C22×C4×C5—28no—
227C22×C4×C5—44no—
228C22×C4×C5—44no—
229C22×C4×C5—416no—
230C22×C4×C5—416no—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2×D414yes—
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—232no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
244C2×C22⋊D5—28no—
245C2×C22⋊D5—28no—
246C2×C22⋊D5—44no—
247C2×C22⋊D5—416no—
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×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5C2×D414yes—
268C22×Dic5C2×D414yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—416no—
280C2×Dic10—28no—
281C2×Dic10—28no—
282C2×Dic10—44no—
283C2×Dic10—416no—
284C5×C4⋊C4C2×D4116yescomplemented
285C5×C22⋊C4—28no—
286C5×C22⋊C4—28no—
287C42×C5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292C22⋊Dic5—28no—
293C22⋊Dic5—44no—
294#685—28no—
295#685—28no—
296#685—28no—
297#685—28no—
298C4⋊Dic5—28no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683C2×D4116yescomplemented
303C4×Dic5—28no—
304C23×Q8—51no—
305C23×D4—51no—
306C23×D4—51no—
307C23×D4C2×D511yescharacteristic
308C24×C4—51no—
309C24×C4C2×D511yescharacteristic
310C24×C4C2×D511yescharacteristic
311C2×C22⋊Q8—58no—
312C2×C22⋊Q8—58no—
313C2×C22⋊Q8—108no—
314C2×C22⋊Q8—108no—
315C2×C4×D4—28no—
316C2×C4×D4—58no—
317C2×C4×D4—108no—
318C2×C4×D4C2×D518yescomplemented
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42C2×D511yescharacteristic
339#394—58no—
340#394—58no—
341#393—58no—
342#392—58no—
343#388—58no—
344#388—58no—
345#387—58no—
346#387—58no—
347#386—58no—
348#386—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—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5—44no—
384C23×C5C22×D412yes—
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—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5C2×#4114yes—
408C5×D4—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—416no—
425C2×C4×C5—416no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C22×D414yes—
431C22⋊D5—232no—
432C22⋊D5—416no—
433C2×Dic5—28no—
434C2×Dic5—28no—
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—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5C22×D414yes—
460C2×Dic5C22×D414yes—
461C4×D5—416no—
462Dic10—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×Q8—54no—
467C22×Q8—104no—
468C22×Q8—104no—
469C22×Q8—202no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—54no—
474C22×D4—54no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—104no—
479C22×D4—104no—
480C22×D4—202no—
481C22×D4C22×D514yes—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—42no—
487C23×C4—42no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4—51no—
494C23×C4—51no—
495C23×C4—54no—
496C23×C4—104no—
497C23×C4—104no—
498C23×C4—202no—
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D514yes—
501C23×C4C22×D514yes—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C22⋊Q8—1032no—
507C22⋊Q8—1032no—
508C4×D4—232no—
509C4×D4—1032no—
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—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4C22⋊D518yescomplemented
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
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—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
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—202no—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—24no—
547C2×C42—54no—
548C2×C42—104no—
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—24no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—416no—
573C22×C5—416no—
574C22×C5#52514yes—
575C22×C5#52514yes—
576C22×C5#53914yes—
577C22×C5D4214yes—
578C22×C5#54814yes—
579C22×C5#54814yes—
580C22×C5#55114yes—
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—24no—
589C2×D5—24no—
590C2×D5—24no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—416no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—24no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
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—22no—
619C24—22no—
620C24—54no—
621C24—52no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#70914yes—
629C24#70914yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×Q8—108no—
634C2×Q8—108no—
635C2×Q8—204no—
636C2×Q8—2016no—
637C2×D4—232no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—1032no—
644C2×D4—108no—
645C2×D4—108no—
646C2×D4—108no—
647C2×D4—204no—
648C2×D4—2016no—
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—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—416no—
667C22×C4—416no—
668C22×C4—54no—
669C22×C4—54no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—108no—
678C22×C4—102no—
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—102no—
697C22×C4—108no—
698C22×C4—204no—
699C22×C4—2016no—
700C22×C4D4×D514yes—
701C22×C4C2×C22⋊D514yes—
702C22×C4C2×C22⋊D514yes—
703C22×C4C2×C22⋊D514yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—516no—
710C4⋊C4—108no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4C2×C22⋊D5116yescomplemented
715C22⋊C4—28no—
716C22⋊C4—28no—
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—204no—
727C42—28no—
728C42—108no—
729C2×C5—44no—
730C2×C5—44no—
731C2×C5#246318yescomplemented
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#52511yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×D4211yescharacteristic
736C2×C5C2×#54811yescharacteristic
737C2×C5C2×#54811yescharacteristic
738C2×C5C2×#55111yescharacteristic
739D5—44no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—54no—
767C23—108no—
768C23—108no—
769C23—108no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—102no—
775C23—102no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23—204no—
780C23C2×#70914yes—
781C23C2×#70914yes—
782C23C2×#70912yes—
783C23C2×#70912yes—
784C23C2×D4×D512yes—
785C23#414412yes—
786C23D5×#4112yes—
787C23#415012yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790Q8—2016no—
791D4—232no—
792D4—1032no—
793D4—2016no—
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—416no—
810C2×C4—416no—
811C2×C4—44no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—108no—
815C2×C4—108no—
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—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×D4×D514yes—
842C2×C4C22×C22⋊D514yes—
843C2×C4C22×C22⋊D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#246311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—416no—
860C22—416no—
861C22—42no—
862C22—104no—
863C22—104no—
864C22—104no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—2016no—
869C22—202no—
870C22#6588114yes—
871C22#6588614yes—
872C22#6589014yes—
873C22#6589814yes—
874C22#6612514yes—
875C22D4×C22⋊D514yes—
876C22#6616514yes—
877C22C22×#70911yescharacteristic
878C22C22×#70911yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C2×#414411yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×#415011yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—202no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—44no—
898C2—204no—
899C2#1061409918yesdirect product factor
900C2C2×#6589811yescharacteristic
901C2C2×#6588611yescharacteristic
902C2C2×#6588111yescharacteristic
903C2C2×#6589011yescharacteristic
904C2C2×#6612511yescharacteristic
905C2C2×D4×C22⋊D511yescharacteristic
906C2C2×#6616511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×C4×D4D5
hypocenterC5C2×#2463
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×#4070C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4042C2semidirect
6. C2×#65511C2semidirect
7. C2×#65502C2semidirect
8. C2×#65499C2semidirect
9. #10614099C2direct (N × H)
10. C2×#65270C2semidirect
11. C2×#65245C2semidirect
12. C2×#65250C2semidirect
13. C2×#65236C2semidirect
14. C2×#65234C2semidirect
15. C2×#65229C2semidirect
16. C2×#65222C2semidirect
25. C2×C4×C5×D4C22semidirect
37. C2×C4×C22⋊D5C22semidirect
44. C2×#4070C22semidirect
51. C2×#4042C22semidirect
53. #65511C22semidirect
54. #65502C22semidirect
55. #65499C22semidirect
64. #65270C22semidirect
65. #65250C22semidirect
66. #65245C22semidirect
67. #65236C22semidirect
68. #65234C22semidirect
69. #65229C22semidirect
70. #65222C22semidirect
116. C2×C5×C4⋊C4D4semidirect
151. C2×#683D4semidirect
170. C22×C4×D4D5semidirect
284. C5×C4⋊C4C2×D4semidirect
302. #683C2×D4semidirect
318. C2×C4×D4C2×D5semidirect
520. C2×C4⋊C4C22⋊D5semidirect
714. C4⋊C4C2×C22⋊D5semidirect
731. C2×C5#2463semidirect
845. C5C2×#2463semidirect
899. C2#10614099direct (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×#40702
C22×C4×C22⋊D52
C22×#40422
C2×#655122
C2×#655112
C2×#655022
C2×#654992
#106140992
C2×#652702
C2×#652452
C2×#652502
C2×#652362
C2×#652342
C2×#652292
C2×#652222
C2×#24635