Finite Group Databasebeta

← C2×#10606449 #12267165

Subgroups — C2×#10606449 #12267165

Order 1280.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4070C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C22×#4029C211yesmaximal, characteristic, complemented
4C22×#4031C211yesmaximal, characteristic, complemented
5C2×C5×#386C211yesmaximal, characteristic, complemented
6C2×#65512C211yesmaximal, characteristic
7C2×#65510C211yesmaximal, characteristic, complemented
8C2×#65248C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65234C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12#10606449C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64945C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×C4×C22⋊D5—28no—
33C2×C4×C22⋊D5C2218yescomplemented
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C2×#4070—28no—
42C2×#4070C2218yescomplemented
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4031—28no—
51C2×#4031C2218yescomplemented
52C2×#4029—28no—
53C2×#4029C2218yescomplemented
54C5×#386C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57#65512C2218yes—
58#65510C2218yescomplemented
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65248C2218yescomplemented
64#65240C2218yescomplemented
65#65237C2218yescomplemented
66#65234C2218yescomplemented
67#64959C2218yescomplemented
68#64957C2218yescomplemented
69#64945C2218yescomplemented
70#64938C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5—42no—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—42no—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C4×C22⋊D5—232no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685D418yescomplemented
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—42no—
141C2×C4⋊Dic5C2314yes—
142C2×C4⋊Dic5C2314yes—
143C2×C4⋊Dic5C2314yes—
144#4070—232no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683D418yescomplemented
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159#4031—232no—
160#4029—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123—51no—
169C22×C22⋊Q8—51no—
170C22×C4×D4—51no—
171#2461—516no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#386D511yescharacteristic, complemented
181C2×#385—51no—
182C2×C4×C4⋊C4—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—22no—
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×D5C2×D414yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—44no—
211C2×C5×D4—416no—
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×C5C2×D414yes—
230C22×C4×C5#4114yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—44no—
243C2×C22⋊D5—416no—
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×Dic5C2×D414yes—
262C22×Dic5C2×D414yes—
263C22×Dic5C2×D414yes—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—44no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C22⋊C4—28no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C22⋊Dic5—28no—
284C22⋊Dic5—28no—
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685C2×D4116yescomplemented
293C4⋊Dic5—28no—
294C4⋊Dic5—28no—
295C4⋊Dic5—44no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683C2×D4116yescomplemented
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8—51no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—58no—
312C2×#123—108no—
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
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—51no—
324C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388—58no—
348#386C2×D518yescomplemented
349#385—58no—
350C4×C4⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
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—44no—
374C23×C5—44no—
375C23×C5—44no—
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×#4112yes—
387C23×C5C2×#4114yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5H(5,𝔽2)12yes—
391C23×C52−1+412yes—
392C23×C5C2511yescharacteristic
393C22×D5—28no—
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C22×D414yes—
407C5×D4—416no—
408C2×C4×C5—28no—
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—416no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C2×#4114yes—
429C22⋊D5—232no—
430C22⋊D5—416no—
431C2×Dic5—28no—
432C2×Dic5—28no—
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—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C22×D414yes—
458C2×Dic5C2×#4114yes—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25C22×D511yescharacteristic
463C25C22×D511yescharacteristic
464C22×Q8—54no—
465C22×Q8—104no—
466C22×Q8—104no—
467C22×Q8—202no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—54no—
472C22×D4—54no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4C22×D514yes—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—202no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D514yes—
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—1032no—
502C22⋊Q8—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—58no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—202no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—58no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
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—104no—
533C2×C22⋊C4—104no—
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⋊C4C22×D514yes—
542C2×C22⋊C4C22×D514yes—
543C2×C22⋊C4C22×D514yes—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—416no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—88no—
572C22×C5#52514yes—
573C22×C5#53214yes—
574C22×C5#54214yes—
575C22×C5D4214yes—
576C22×C5#54714yes—
577C22×C5#54814yes—
578C22×C5#55114yes—
579C22×C5C23×D411yescharacteristic
580C22×C5C23×D411yescharacteristic
581C22×C5C22×#4111yescharacteristic
582C22×C5C22×#4111yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C2×H(5,𝔽2)11yescharacteristic
585C22×C5C2×2−1+411yescharacteristic
586C2×D5—24no—
587C2×D5—24no—
588C2×D5—24no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—416no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—42no—
598C4×C5—42no—
599Dic5—24no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—54no—
620C24—52no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24#71114yes—
628C24C23×D512yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—44no—
638C2×D4—416no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—1032no—
643C2×D4—108no—
644C2×D4—108no—
645C2×D4—204no—
646C2×D4—2016no—
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—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—44no—
662C22×C4—416no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
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—108no—
693C22×C4—204no—
694C22×C4—2016no—
695C22×C4#70914yes—
696C22×C4D4×D514yes—
697C22×C4D4×D514yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—516no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—204no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—516no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C42—108no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5—82no—
728C2×C5#246118yescomplemented
729C2×C5C2×#52511yescharacteristic
730C2×C5C2×#53211yescharacteristic
731C2×C5C2×#54211yescharacteristic
732C2×C5C2×D4211yescharacteristic
733C2×C5C2×#54711yescharacteristic
734C2×C5C2×#54811yescharacteristic
735C2×C5C2×#55111yescharacteristic
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—54no—
765C23—108no—
766C23—108no—
767C23—108no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C2×#70912yes—
779C23C2×D4×D512yes—
780C23C2×D4×D512yes—
781C23C2×#71114yes—
782C23C2×#71112yes—
783C23#414412yes—
784C23D5×#4112yes—
785C23#415012yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—416no—
789D4—1032no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
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—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—54no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—108no—
814C2×C4—108no—
815C2×C4—108no—
816C2×C4—108no—
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—2016no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4C2×#70914yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×D4×D514yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—104no—
859C22—104no—
860C22—104no—
861C22—202no—
862C22—202no—
863C22—2016no—
864C22—202no—
865C22—202no—
866C22#6582914yes—
867C22#6588214yes—
868C22#6588514yes—
869C22#6592414yes—
870C22#6593214yes—
871C22#6594014yes—
872C22#6599614yes—
873C22C22×#70911yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×D4×D511yescharacteristic
876C22C22×#71111yescharacteristic
877C22C2×#414411yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×#415011yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—104no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—82no—
894C2—204no—
895C2#1060644918yesdirect product factor
896C2C2×#6582911yescharacteristic
897C2C2×#6588211yescharacteristic
898C2C2×#6588511yescharacteristic
899C2C2×#6592411yescharacteristic
900C2C2×#6594011yescharacteristic
901C2C2×#6593211yescharacteristic
902C2C2×#6599611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#4070C2semidirect
2. C22×C4×C22⋊D5C2semidirect
3. C22×#4029C2semidirect
4. C22×#4031C2semidirect
5. C2×C5×#386C2semidirect
7. C2×#65510C2semidirect
8. C2×#65248C2semidirect
9. C2×#65237C2semidirect
10. C2×#65234C2semidirect
11. C2×#65240C2semidirect
12. #10606449C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64945C2semidirect
15. C2×#64959C2semidirect
16. C2×#64938C2semidirect
33. C2×C4×C22⋊D5C22semidirect
42. C2×#4070C22semidirect
51. C2×#4031C22semidirect
53. C2×#4029C22semidirect
54. C5×#386C22semidirect
58. #65510C22semidirect
63. #65248C22semidirect
64. #65240C22semidirect
65. #65237C22semidirect
66. #65234C22semidirect
67. #64959C22semidirect
68. #64957C22semidirect
69. #64945C22semidirect
70. #64938C22semidirect
133. C2×#685D4semidirect
148. C2×#683D4semidirect
180. C2×#386D5semidirect
292. #685C2×D4semidirect
299. #683C2×D4semidirect
348. #386C2×D5semidirect
728. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10606449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40702
C22×C4×C22⋊D52
C22×#40292
C22×#40312
C2×C5×#3862
C2×#655122
C2×#655102
C2×#652482
C2×#652372
C2×#652342
C2×#652402
#106064492
C2×#649572
C2×#649452
C2×#649592
C2×#649382
C2×#24615