Finite Group Databasebeta

← C2×#10606124 #12258583

Subgroups — C2×#10606124 #12258583

Order 1280.

4718 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C23×#683C211yesmaximal, characteristic, complemented
3C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic
5C22×#4027C211yesmaximal, characteristic
6C2×C5×#385C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65261C211yesmaximal, characteristic, complemented
9C2×#65265C211yesmaximal, characteristic, complemented
10C2×#65239C211yesmaximal, characteristic, complemented
11C2×#65231C211yesmaximal, characteristic, complemented
12#10606124C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64956C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C2×C4×C22⋊D5—28no—
30C2×C4×C22⋊D5C2218yes—
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683—28no—
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2218yescomplemented
47C22×C4×Dic5C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×D5×C4⋊C4—28no—
51C2×D5×C4⋊C4C2218yescomplemented
52C2×#4027—28no—
53C2×#4027C4116yescomplemented
54C2×#4027C2218yes—
55C2×#4027C2218yes—
56C5×#385C2218yescomplemented
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65278C2218yescomplemented
64#65265C2218yescomplemented
65#65261C2218yescomplemented
66#65239C2218yescomplemented
67#65231C2218yescomplemented
68#64957C2218yescomplemented
69#64956C2218yescomplemented
70#64938C2218yescomplemented
71#64936C2218yescomplemented
72C2×D4×C4⋊C4—51nomaximal, Sylow
73C25×C5C2311yescharacteristic
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×C5C2314yes—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5C2×C418yes—
86C22×C22⋊D5D418yes—
87C22×C22⋊D5Q818yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—24no—
92C23×Dic5—24no—
93C23×Dic5—42no—
94C23×Dic5C2×C418yescomplemented
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2314yes—
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2314yes—
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—24no—
110C22×C4×D5—42no—
111C22×C4×D5—42no—
112C22×C4×D5C2×C418yescomplemented
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C22×C4×D5C2314yes—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—42no—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2314yes—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4C2×C418yescomplemented
122C2×C5×C22⋊C4C2314yes—
123C2×C5×C22⋊C4C2314yes—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5C2314yes—
126C4×C22⋊D5—232no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685C2×C418yescomplemented
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5—42no—
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683—232no—
145C2×#683C2×C418yescomplemented
146C2×#683D418yescomplemented
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5—24no—
158C2×C4×Dic5C2×C418yescomplemented
159C2×C4×Dic5C2314yes—
160C2×C4×Dic5C2314yes—
161C2×C4×Dic5C2314yes—
162D5×C4⋊C4—232no—
163#4027—232no—
164#4027C2×C4164yescomplemented
165C5×#95C2314yes—
166C5×#95C2314yes—
167#3963C2314yes—
168#3963C2314yes—
169#3963C2314yes—
170#3963C2314yes—
171C22×C4×D4—51no—
172C22×C4×D4—51no—
173C22×C4×D4—51no—
174C23×C4⋊C4—51no—
175C23×C4⋊C4—51no—
176D4×C4⋊C4—516no—
177C2×#389—51no—
178C2×#389—51no—
179C2×#385—51no—
180C2×#385—51no—
181C2×#385—51no—
182C2×#385D511yescharacteristic, complemented
183C2×#384—51no—
184C2×#380—51no—
185C2×#380—51no—
186C2×C4×C4⋊C4—51no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5C22×C414yes—
192C24×C5C2×D414yes—
193C24×C5C2×Q814yes—
194C24×C5C2412yes—
195C24×C5C2411yescharacteristic
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5C22×C414yes—
201C23×D5C2×D414yes—
202C23×D5C2×Q814yes—
203C23×D5C2412yes—
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—22no—
214C22×C4×C5—22no—
215C22×C4×C5—28no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—28no—
221C22×C4×C5—44no—
222C22×C4×C5—416no—
223C22×C4×C5C22×C414yes—
224C22×C4×C5C22×C414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5C4⋊C4164yescomplemented
233C2×C22⋊D5C22×C4116yes—
234C2×C22⋊D5C2×D4116yes—
235C2×C22⋊D5C2×Q8116yes—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—232no—
241C22×Dic5—28no—
242C22×Dic5—28no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—28no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—28no—
254C22×Dic5—44no—
255C22×Dic5—416no—
256C22×Dic5C22×C414yes—
257C22×Dic5C22×C414yes—
258C22×Dic5C22×C414yes—
259C22×Dic5C22×C4116yescomplemented
260C22×Dic5C2×D414yes—
261C22×Dic5C2×D414yes—
262C22×Dic5C2×D414yes—
263C22×Dic5C2×Q814yes—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×C4×D5—232no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—28no—
279C2×C4×D5—44no—
280C2×C4×D5—44no—
281C2×C4×D5—416no—
282C2×C4×D5—416no—
283C2×C4×D5C22×C4116yescomplemented
284C5×C4⋊C4—28no—
285C5×C4⋊C4—44no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4C22×C4116yescomplemented
288C22⋊Dic5—28no—
289#685—28no—
290#685—28no—
291#685C22×C4116yescomplemented
292C4⋊Dic5—28no—
293C4⋊Dic5—44no—
294#683—28no—
295#683—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301#683C22×C4116yescomplemented
302#683C2×D4116yescomplemented
303C4×Dic5—28no—
304C4×Dic5—28no—
305C4×Dic5C22×C4116yescomplemented
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4—51no—
311C24×C4—51no—
312C24×C4C2×D511yescharacteristic
313C2×C4×D4—58no—
314C2×C4×D4—516no—
315C2×C4×D4—58no—
316C2×C4×D4—58no—
317C2×C4×D4—108no—
318C2×C4×D4—108no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—58no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4—51no—
326C22×C4⋊C4—51no—
327C22×C4⋊C4—51no—
328C22×C4⋊C4—51no—
329C22×C4⋊C4—51no—
330C22×C4⋊C4—51no—
331C22×C4⋊C4—58no—
332C22×C4⋊C4—108no—
333C22×C4⋊C4—108no—
334C22×C4⋊C4C2×D511yescharacteristic
335C22×C4⋊C4C2×D511yescharacteristic
336C22×C22⋊C4—51no—
337C22×C22⋊C4—51no—
338C22×C22⋊C4—51no—
339C22×C22⋊C4—51no—
340C22×C22⋊C4C2×D511yescharacteristic
341C22×C22⋊C4C2×D511yescharacteristic
342C22×C42—51no—
343C22×C42—51no—
344C22×C42—51no—
345#389—58no—
346#389—58no—
347#385—58no—
348#385—58no—
349#385—58no—
350#385C2×D518yescomplemented
351#384—58no—
352#380—58no—
353#380—58no—
354C4×C4⋊C4—58no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95—51no—
358C2×#95—51no—
359C2×#95C2×D511yescharacteristic
360C2×#95C2×D511yescharacteristic
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—28no—
365C23×C5—28no—
366C23×C5—28no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5C2×C4⋊C4116yescomplemented
372C23×C5C23×C414yes—
373C23×C5C23×C412yes—
374C23×C5C22×D414yes—
375C23×C5C22×D412yes—
376C23×C5C22×D412yes—
377C23×C5C22×Q814yes—
378C23×C5C22×Q812yes—
379C23×C5C2×#4112yes—
380C23×C5H(5,𝔽2)12yes—
381C23×C52−1+412yes—
382C23×C5C2511yescharacteristic
383C22×D5—28no—
384C22×D5—28no—
385C22×D5—28no—
386C22×D5—28no—
387C22×D5—28no—
388C22×D5—28no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5C2×C4⋊C4116yescomplemented
394C22×D5C23×C414yes—
395C22×D5C22×D414yes—
396C22×D5C22×Q814yes—
397C2×C4×C5—28no—
398C2×C4×C5—28no—
399C2×C4×C5—28no—
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—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—416no—
416C2×C4×C5—44no—
417C2×C4×C5—44no—
418C2×C4×C5—44no—
419C2×C4×C5C23×C414yes—
420C2×C4×C5C23×C414yes—
421C2×C4×C5C22×D414yes—
422C22⋊D5C2×C4⋊C4164yescomplemented
423C2×Dic5—28no—
424C2×Dic5—28no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—232no—
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—416no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C2×C4⋊C4116yescomplemented
444C2×Dic5C4×D4116yescomplemented
445C2×Dic5C23×C414yes—
446C2×Dic5C23×C414yes—
447C2×Dic5C23×C414yes—
448C2×Dic5C22×D414yes—
449C2×Dic5C22×D414yes—
450C2×Dic5C22×D414yes—
451C2×Dic5C22×Q814yes—
452C2×Dic5C2×#4114yes—
453C4×D5—232no—
454C4×D5—416no—
455C4×D5—416no—
456C25—51no—
457C25C22×D511yescharacteristic
458C22×D4—58no—
459C22×D4—58no—
460C22×D4—58no—
461C22×D4—54no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—58no—
468C23×C4—54no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—58no—
472C23×C4—54no—
473C23×C4—51no—
474C23×C4—51no—
475C23×C4—51no—
476C23×C4—54no—
477C23×C4—54no—
478C23×C4—54no—
479C23×C4—104no—
480C23×C4—104no—
481C23×C4—104no—
482C23×C4—104no—
483C23×C4—104no—
484C23×C4—104no—
485C23×C4—104no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—202no—
490C23×C4—202no—
491C23×C4—202no—
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D514yes—
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C4×D4—564no—
500C4×D4—1032no—
501C4×D4—1032no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—58no—
505C2×C4⋊C4—58no—
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—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—1032no—
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—104no—
525C2×C4⋊C4—104no—
526C2×C4⋊C4—104no—
527C2×C4⋊C4—202no—
528C2×C4⋊C4C22×D514yes—
529C2×C4⋊C4C22×D514yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—58no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4C4×D518yescomplemented
540C2×C22⋊C4C22×D514yes—
541C2×C22⋊C4C22×D514yes—
542C2×C42—58no—
543C2×C42—54no—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—104no—
547C2×C42—104no—
548#95—54no—
549#95—54no—
550#95—54no—
551#95—54no—
552#95C22×D514yes—
553#95C22×D514yes—
554C22×C5—232no—
555C22×C5—24no—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5C22×C4⋊C414yes—
562C22×C5C22×C4⋊C418yescomplemented
563C22×C5C2×C4×D414yes—
564C22×C5#52014yes—
565C22×C5D4214yes—
566C22×C5#54714yes—
567C22×C5D4×Q814yes—
568C22×C5#55414yes—
569C22×C5C24×C411yescharacteristic
570C22×C5C23×D411yescharacteristic
571C22×C5C23×D411yescharacteristic
572C22×C5C23×Q811yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C2×H(5,𝔽2)11yescharacteristic
575C22×C5C2×2−1+411yescharacteristic
576C2×D5—232no—
577C2×D5—24no—
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5C22×C4⋊C418yescomplemented
584C4×C5—24no—
585C4×C5—24no—
586C4×C5—24no—
587C4×C5—42no—
588C4×C5—42no—
589C4×C5—42no—
590Dic5—24no—
591Dic5—24no—
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595Dic5C22×C4⋊C418yescomplemented
596Dic5C2×C4×D418yescomplemented
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—54no—
602C24—54no—
603C24—54no—
604C24—52no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24—102no—
609C24C2×C4×D514yes—
610C24D4×D514yes—
611C24Q8×D514yes—
612C24C23×D512yes—
613C24C23×D511yescharacteristic
614C2×D4—516no—
615C2×D4—516no—
616C2×D4—516no—
617C2×D4—564no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—28no—
635C22×C4—44no—
636C22×C4—416no—
637C22×C4—54no—
638C22×C4—54no—
639C22×C4—54no—
640C22×C4—54no—
641C22×C4—54no—
642C22×C4—54no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—54no—
646C22×C4—516no—
647C22×C4—54no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—516no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—108no—
655C22×C4—1032no—
656C22×C4—108no—
657C22×C4—108no—
658C22×C4—108no—
659C22×C4—108no—
660C22×C4—108no—
661C22×C4—1032no—
662C22×C4—108no—
663C22×C4—108no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—108no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—108no—
679C22×C4—204no—
680C22×C4—204no—
681C22×C4—2016no—
682C22×C4—2016no—
683C22×C4—204no—
684C22×C4—2016no—
685C22×C4C2×C4×D514yes—
686C22×C4C2×C4×D514yes—
687C22×C4D4×D514yes—
688C22×C4C23×D512yes—
689C22×C4C23×D512yes—
690C22×C4C23×D512yes—
691C22×C4C23×D512yes—
692C22×C4C23×D512yes—
693C22×C4C23×D512yes—
694C4⋊C4—28no—
695C4⋊C4—44no—
696C4⋊C4—516no—
697C4⋊C4—516no—
698C4⋊C4—108no—
699C4⋊C4—108no—
700C4⋊C4—108no—
701C4⋊C4—108no—
702C4⋊C4—108no—
703C4⋊C4—108no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—204no—
707C22⋊C4—28no—
708C22⋊C4—516no—
709C22⋊C4—108no—
710C22⋊C4—108no—
711C22⋊C4—108no—
712C22⋊C4C2×C4×D5116yescomplemented
713C42—516no—
714C42—108no—
715C42—108no—
716C2×C5—28no—
717C2×C5D4×C4⋊C418yescomplemented
718C2×C5C23×C4⋊C411yescharacteristic
719C2×C5C22×C4×D411yescharacteristic
720C2×C5C2×#52011yescharacteristic
721C2×C5C2×D4211yescharacteristic
722C2×C5C2×#54711yescharacteristic
723C2×C5C2×D4×Q811yescharacteristic
724C2×C5C2×#55411yescharacteristic
725D5—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—516no—
737C23—54no—
738C23—54no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—108no—
744C23—108no—
745C23—108no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23D5×C4⋊C4116yescomplemented
751C23C22×C4×D514yes—
752C23C22×C4×D512yes—
753C23C2×D4×D514yes—
754C23C2×D4×D512yes—
755C23C2×D4×D512yes—
756C23#414412yes—
757C23C2×Q8×D514yes—
758C23C2×Q8×D512yes—
759C23D5×#4112yes—
760C23#415012yes—
761C23C24×D511yescharacteristic
762D4—564no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
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—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—516no—
786C2×C4—516no—
787C2×C4—54no—
788C2×C4—54no—
789C2×C4—54no—
790C2×C4—54no—
791C2×C4—54no—
792C2×C4—54no—
793C2×C4—54no—
794C2×C4—54no—
795C2×C4—1032no—
796C2×C4—1032no—
797C2×C4—108no—
798C2×C4—108no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—2016no—
813C2×C4—2016no—
814C2×C4—2016no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4C22×C4×D514yes—
819C2×C4C22×C4×D514yes—
820C2×C4C2×D4×D514yes—
821C5C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
822C22—24no—
823C22—24no—
824C22—232no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—58no—
830C22—104no—
831C22—104no—
832C22—1032no—
833C22—104no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22C2×D5×C4⋊C414yes—
838C22C2×D5×C4⋊C418yescomplemented
839C22C4×D4×D514yes—
840C22#6588014yes—
841C22#6592414yes—
842C22#6596614yes—
843C22#6597014yes—
844C22#6598914yes—
845C22C23×C4×D511yescharacteristic
846C22C22×D4×D511yescharacteristic
847C22C22×D4×D511yescharacteristic
848C22C2×#414411yescharacteristic
849C22C22×Q8×D511yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C2×#415011yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—58no—
859C4—58no—
860C4—104no—
861C4—104no—
862C4—202no—
863C4—202no—
864C4—202no—
865C2—28no—
866C2—108no—
867C2#1060612418yesdirect product factor
868C2C22×D5×C4⋊C411yescharacteristic
869C2C2×#6588011yescharacteristic
870C2C2×C4×D4×D511yescharacteristic
871C2C2×#6592411yescharacteristic
872C2C2×#6596611yescharacteristic
873C2C2×#6597011yescharacteristic
874C2C2×#6598911yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
cosocleC23×C5C25
hypercenterC2×#385D5
hypocenterC5C2×D4×C4⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C23×#683C2semidirect
3. C22×D5×C4⋊C4C2semidirect
6. C2×C5×#385C2semidirect
7. C2×#65278C2semidirect
8. C2×#65261C2semidirect
9. C2×#65265C2semidirect
10. C2×#65239C2semidirect
11. C2×#65231C2semidirect
12. #10606124C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64956C2semidirect
15. C2×#64936C2semidirect
16. C2×#64938C2semidirect
46. C22×#683C22semidirect
51. C2×D5×C4⋊C4C22semidirect
53. C2×#4027C4semidirect
56. C5×#385C22semidirect
63. #65278C22semidirect
64. #65265C22semidirect
65. #65261C22semidirect
66. #65239C22semidirect
67. #65231C22semidirect
68. #64957C22semidirect
69. #64956C22semidirect
70. #64938C22semidirect
71. #64936C22semidirect
94. C23×Dic5C2×C4semidirect
112. C22×C4×D5C2×C4semidirect
121. C2×C5×C22⋊C4C2×C4semidirect
129. C2×#685C2×C4semidirect
145. C2×#683C2×C4semidirect
146. C2×#683D4semidirect
158. C2×C4×Dic5C2×C4semidirect
164. #4027C2×C4semidirect
182. C2×#385D5semidirect
232. C2×C22⋊D5C4⋊C4semidirect
259. C22×Dic5C22×C4semidirect
283. C2×C4×D5C22×C4semidirect
287. C5×C22⋊C4C22×C4semidirect
291. #685C22×C4semidirect
301. #683C22×C4semidirect
302. #683C2×D4semidirect
305. C4×Dic5C22×C4semidirect
350. #385C2×D5semidirect
371. C23×C5C2×C4⋊C4semidirect
393. C22×D5C2×C4⋊C4semidirect
422. C22⋊D5C2×C4⋊C4semidirect
443. C2×Dic5C2×C4⋊C4semidirect
444. C2×Dic5C4×D4semidirect
539. C2×C22⋊C4C4×D5semidirect
562. C22×C5C22×C4⋊C4semidirect
583. C2×D5C22×C4⋊C4semidirect
595. Dic5C22×C4⋊C4semidirect
596. Dic5C2×C4×D4semidirect
712. C22⋊C4C2×C4×D5semidirect
717. C2×C5D4×C4⋊C4semidirect
750. C23D5×C4⋊C4semidirect
821. C5C2×D4×C4⋊C4semidirect
838. C22C2×D5×C4⋊C4semidirect
867. C2#10606124direct (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
C23×#6832
C22×D5×C4⋊C42
C22×#40272
C2×C5×#3852
C2×#652782
C2×#652612
C2×#652652
C2×#652392
C2×#652312
#106061242
C2×#649572
C2×#649562
C2×#649362
C2×#649382
C2×D4×C4⋊C45