Finite Group Databasebeta

← C2×#10605626 #12267437

Subgroups — C2×#10605626 #12267437

Order 1280.

3894 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×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#4042C211yesmaximal, characteristic, complemented
3C22×#4030C211yesmaximal, characteristic
4C22×#4031C211yesmaximal, characteristic, complemented
5C2×C5×#380C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65282C211yesmaximal, characteristic, complemented
8C2×#65280C211yesmaximal, characteristic, complemented
9C2×#65261C211yesmaximal, characteristic, complemented
10C2×#65248C211yesmaximal, characteristic, complemented
11C2×#65241C211yesmaximal, characteristic, complemented
12#10605626C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic, complemented
14C2×#64956C211yesmaximal, characteristic, complemented
15C2×#64935C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×Dic10C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C2×C4×C22⋊D5—28no—
31C2×C4×C22⋊D5C2218yescomplemented
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4042—28no—
47C2×#4042C2218yescomplemented
48C2×#4031—28no—
49C2×#4031C2218yescomplemented
50C2×#4030—28no—
51C2×#4030C2218yes—
52C5×#380C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55#65502C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65282C2218yescomplemented
63#65280C2218yescomplemented
64#65261C2218yescomplemented
65#65248C2218yescomplemented
66#65241C2218yescomplemented
67#64956C2218yescomplemented
68#64955C2218yescomplemented
69#64954C2218yescomplemented
70#64935C2218yescomplemented
71C2×#2427—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—42no—
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2314yes—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—42no—
90C22×C22⋊D5D418yes—
91C22×C22⋊D5C2314yes—
92C22×C22⋊D5C2314yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—42no—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—42no—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C22×Dic10—24no—
112C22×Dic10—24no—
113C22×Dic10—24no—
114C22×Dic10C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4—42no—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C4×C22⋊D5—232no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—42no—
147C2×#683D418yescomplemented
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×C4×Dic5—24no—
153C2×C4×Dic5—24no—
154C2×C4×Dic5C2314yes—
155C2×C4×Dic5C2314yes—
156#4042—232no—
157#4031—232no—
158#4030—232no—
159C5×#95C2314yes—
160C5×#95C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×C22⋊Q8—51no—
169C22×#121—51no—
170C22×C4×D4—51no—
171#2427—516no—
172C2×#397—51no—
173C2×#397—51no—
174C2×#394—51no—
175C2×#394—51no—
176C2×#391—51no—
177C2×#389—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#380—51no—
181C2×#380D511yescharacteristic, complemented
182C2×C4×C22⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5C2×D414yes—
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×D5C2×D414yes—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
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—22no—
224C22×C4×C5—28no—
225C22×C4×C5—28no—
226C22×C4×C5—44no—
227C22×C4×C5—416no—
228C22×C4×C5C2×D414yes—
229C22×C4×C5#4114yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—232no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
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×Dic5C2×D414yes—
259C22×Dic5C2×D414yes—
260C22×Dic5C2×D414yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—28no—
269C2×D20—28no—
270C2×D20—44no—
271C2×D20—416no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—44no—
278C2×C4×D5—416no—
279C2×C4×D5—416no—
280C2×Dic10—28no—
281C2×Dic10—28no—
282C2×Dic10—28no—
283C2×Dic10—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—44no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4—28no—
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#683—28no—
299#683—28no—
300#683—44no—
301#683C2×D4116yescomplemented
302C4×Dic5—28no—
303C4×Dic5—28no—
304C23×Q8—51no—
305C23×D4—51no—
306C23×D4—51no—
307C23×D4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#124—58no—
312C2×#124—108no—
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—108no—
315C2×#121—58no—
316C2×#121—108no—
317C2×C4×D4—58no—
318C2×C4×D4—108no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4C2×D511yescharacteristic
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×C42—51no—
339#397—58no—
340#397—58no—
341#394—58no—
342#394—58no—
343#391—58no—
344#389—58no—
345#386—58no—
346#386—58no—
347#380—58no—
348#380C2×D518yescomplemented
349C4×C22⋊C4—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95C2×D511yescharacteristic
357C2×#95C2×D511yescharacteristic
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5C22×D414yes—
372C23×C5C22×D412yes—
373C23×C5C22×D412yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
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—28no—
384C22×D5—28no—
385C22×D5—28no—
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—22no—
397C22×D5—22no—
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×D5C22×D414yes—
407C22×D5C2×#4114yes—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
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—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—416no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C2×#4114yes—
433C22⋊D5—232no—
434C22⋊D5—416no—
435C2×Dic5—28no—
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—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5#121116yes—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C22×D414yes—
458C2×Dic5C2×#4114yes—
459D20—416no—
460C4×D5—416no—
461C4×D5—416no—
462Dic10—416no—
463C25—51no—
464C25—51no—
465C25C22×D511yescharacteristic
466C22×Q8—54no—
467C22×Q8—104no—
468C22×Q8—104no—
469C22×Q8—104no—
470C22×D4—58no—
471C22×D4—54no—
472C22×D4—54no—
473C22×D4—54no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—104no—
479C22×D4—104no—
480C22×D4—202no—
481C22×D4—202no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—42no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—54no—
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×D511yescharacteristic
503C23×C4C22×D514yes—
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#124—1032no—
507C22⋊Q8—1032no—
508#121—1032no—
509C4×D4—1032no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—58no—
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—202no—
520C2×C4⋊C4C22×D514yes—
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—104no—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—54no—
547C2×C42—54no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95C22×D514yes—
557#95C22×D514yes—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—42no—
562C22×C5—416no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5C2×#12114yes—
567C22×C5#52914yes—
568C22×C5#54214yes—
569C22×C5#54614yes—
570C22×C5#54614yes—
571C22×C5#54714yes—
572C22×C5#54814yes—
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—24no—
584C2×D5—24no—
585C2×D5—24no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—416no—
589C2×D5—416no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—42no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5C2×#12118yes—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—54no—
615C24—54no—
616C24—52no—
617C24—52no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24D4×D514yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×Q8—108no—
634C2×Q8—108no—
635C2×Q8—108no—
636C2×Q8—2016no—
637C2×D4—516no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—1032no—
642C2×D4—108no—
643C2×D4—108no—
644C2×D4—108no—
645C2×D4—204no—
646C2×D4—2016no—
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—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—44no—
668C22×C4—416no—
669C22×C4—54no—
670C22×C4—54no—
671C22×C4—54no—
672C22×C4—52no—
673C22×C4—54no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—52no—
678C22×C4—52no—
679C22×C4—108no—
680C22×C4—108no—
681C22×C4—108no—
682C22×C4—108no—
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×C4—2016no—
701C22×C4#70914yes—
702C22×C4D4×D514yes—
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—44no—
711C4⋊C4—516no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—204no—
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—108no—
727C42—108no—
728C42—108no—
729C2×C5—44no—
730C2×C5#242718yescomplemented
731C2×C5C22×#12111yescharacteristic
732C2×C5C2×#52911yescharacteristic
733C2×C5C2×#54211yescharacteristic
734C2×C5C2×#54611yescharacteristic
735C2×C5C2×#54611yescharacteristic
736C2×C5C2×#54711yescharacteristic
737C2×C5C2×#54811yescharacteristic
738D5—44no—
739D5—44no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—54no—
754C23—54no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—108no—
759C23—108no—
760C23—108no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23—204no—
780C23—204no—
781C23C2×#70912yes—
782C23C2×D4×D514yes—
783C23C2×D4×D512yes—
784C23C2×D4×D512yes—
785C23#414412yes—
786C23#414712yes—
787C23D5×#4112yes—
788C23D5×#4112yes—
789C23C24×D511yescharacteristic
790Q8—2016no—
791D4—1032no—
792D4—2016no—
793D4—2016no—
794C2×C4—28no—
795C2×C4—28no—
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—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—416no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—516no—
818C2×C4—54no—
819C2×C4—54no—
820C2×C4—54no—
821C2×C4—54no—
822C2×C4—108no—
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—2016no—
838C2×C4—2016no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×#70914yes—
844C2×C4C2×D4×D514yes—
845C5C2×#242711yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—416no—
853C22—42no—
854C22—104no—
855C22—104no—
856C22—104no—
857C22—104no—
858C22—104no—
859C22—104no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—2016no—
866C22—2016no—
867C22—202no—
868C22—202no—
869C22—202no—
870C22#6582414yes—
871C22#6584114yes—
872C22#6586214yes—
873C22D5×#12114yes—
874C22#6594414yes—
875C22#6596714yes—
876C22#6597414yes—
877C22C22×#70911yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C22×D4×D511yescharacteristic
880C22C2×#414411yescharacteristic
881C22C2×#414711yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×D5×#4111yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—58no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—204no—
898C2—204no—
899C2#1060562618yesdirect product factor
900C2C2×#6582411yescharacteristic
901C2C2×#6584111yescharacteristic
902C2C2×#6586211yescharacteristic
903C2C2×D5×#12111yescharacteristic
904C2C2×#6594411yescharacteristic
905C2C2×#6597411yescharacteristic
906C2C2×#6596711yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#380C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#380D5
hypocenterC5C2×#2427
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D5C2semidirect
2. C22×#4042C2semidirect
4. C22×#4031C2semidirect
5. C2×C5×#380C2semidirect
6. C2×#65502C2semidirect
7. C2×#65282C2semidirect
8. C2×#65280C2semidirect
9. C2×#65261C2semidirect
10. C2×#65248C2semidirect
11. C2×#65241C2semidirect
12. #10605626C2direct (N × H)
13. C2×#64954C2semidirect
14. C2×#64956C2semidirect
15. C2×#64935C2semidirect
16. C2×#64955C2semidirect
31. C2×C4×C22⋊D5C22semidirect
47. C2×#4042C22semidirect
49. C2×#4031C22semidirect
52. C5×#380C22semidirect
55. #65502C22semidirect
62. #65282C22semidirect
63. #65280C22semidirect
64. #65261C22semidirect
65. #65248C22semidirect
66. #65241C22semidirect
67. #64956C22semidirect
68. #64955C22semidirect
69. #64954C22semidirect
70. #64935C22semidirect
147. C2×#683D4semidirect
181. C2×#380D5semidirect
301. #683C2×D4semidirect
348. #380C2×D5semidirect
730. C2×C5#2427semidirect
845. C5C2×#2427semidirect
899. C2#10605626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40422
C22×#40302
C22×#40312
C2×C5×#3802
C2×#655022
C2×#652822
C2×#652802
C2×#652612
C2×#652482
C2×#652412
#106056262
C2×#649542
C2×#649562
C2×#649352
C2×#649552
C2×#24275