Finite Group Databasebeta

← #12020687

Subgroups — #12020687

Order 1280.

2782 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C22×#4038C211yesmaximal, characteristic
3C22×#4018C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5#10602356C211yesmaximal, characteristic, complemented
6#10602356C211yesmaximal, characteristic, complemented
7#10602328C211yesmaximal, characteristic, complemented
8#10600218C214yesmaximal
9#10600197C214yesmaximal, complemented
10C23×C4×D5C2212yes—
11C23×C4×D5C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×#685C2212yes—
16C22×#685C2212yes—
17C22×C4⋊Dic5C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×#683C2212yes—
20C22×#683C2212yes—
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C2×#4038—24no—
24C2×#4038—24no—
25C2×#4038C418yescomplemented
26C2×D5×C4⋊C4—24no—
27C2×D5×C4⋊C4—24no—
28C2×D5×C4⋊C4C418yescomplemented
29C2×#4018—24no—
30C2×#4018—24no—
31C2×#4018C418yescomplemented
32C2×C5×#95C2214yes—
33C2×#3963C2214yes—
34C2×#3963C2214yes—
35C2×#3963C2214yes—
36#13795—51nomaximal, Sylow
37C24×D5C2311yescharacteristic
38C23×C4×C5C2312yes—
39C23×C4×C5C2312yes—
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×Dic5C2312yes—
43C23×Dic5C2312yes—
44C23×Dic5C2312yes—
45C23×Dic5C2311yescharacteristic
46C22×C4×D5—24no—
47C22×C4×D5—24no—
48C22×C4×D5—44no—
49C22×C4×D5—44no—
50C22×C4×D5C2×C418yes—
51C22×C4×D5C2×C414yes—
52C22×C4×D5C2×C414yes—
53C22×C4×D5C2×C414yes—
54C22×C4×D5D414yes—
55C22×C4×D5D414yes—
56C22×C4×D5D414yes—
57C22×C4×D5Q814yes—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4C2×C414yes—
63C2×C5×C4⋊C4C2×C414yescomplemented
64C2×C42×C5—22no—
65C2×C42×C5—22no—
66C2×C42×C5C2×C414yescomplemented
67C2×#685—24no—
68C2×#685—24no—
69C2×#685—24no—
70C2×#685—24no—
71C2×#685C2×C418yes—
72C2×#685C2×C418yes—
73C2×C4⋊Dic5—22no—
74C2×C4⋊Dic5—22no—
75C2×C4⋊Dic5—22no—
76C2×C4⋊Dic5—22no—
77C2×C4⋊Dic5C2×C414yes—
78C2×C4⋊Dic5C2×C414yescomplemented
79C2×#683—24no—
80C2×#683—24no—
81C2×#683—24no—
82C2×#683—24no—
83C2×#683C2×C418yes—
84C2×#683C2×C418yescomplemented
85C2×C4×Dic5—22no—
86C2×C4×Dic5—22no—
87C2×C4×Dic5—24no—
88C2×C4×Dic5—24no—
89C2×C4×Dic5C2×C414yescomplemented
90C2×C4×Dic5C2×C418yescomplemented
91#4038—232no—
92D5×C4⋊C4—232no—
93#4018—232no—
94C5×#95—44no—
95#3963—44no—
96#3963—44no—
97#3963—44no—
98C22×#117—51no—
99C22×#117—51no—
100C23×C4⋊C4—51no—
101C4⋊#95—51no—
102C4⋊#95—54no—
103C4⋊#95—51no—
104C4⋊#95—51no—
105C4⋊#95D511yescharacteristic, complemented
106C22⋊#95—54no—
107C24×C5C2411yescharacteristic
108C23×D5—22no—
109C23×D5—22no—
110C23×D5—22no—
111C23×D5—22no—
112C23×D5C22×C412yes—
113C23×D5C22×C412yes—
114C23×D5C22×C412yes—
115C23×D5C2×D412yes—
116C23×D5C2×D412yes—
117C23×D5C2×D412yes—
118C23×D5C2×Q812yes—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—24no—
126C22×C4×C5—24no—
127C22×C4×C5—22no—
128C22×C4×C5—24no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—24no—
132C22×C4×C5—22no—
133C22×C4×C5C22×C414yes—
134C22×C4×C5C22×C414yes—
135C22×C4×C5C22×C414yes—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C22×C412yes—
138C22×C4×C5C22×C412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×D412yes—
141C22×C4×C5C2×D412yes—
142C22×C4×C5C2×Q812yes—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—24no—
150C22×Dic5—24no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—24no—
154C22×Dic5—22no—
155C22×Dic5—24no—
156C22×Dic5—22no—
157C22×Dic5C22×C414yes—
158C22×Dic5C22×C414yes—
159C22×Dic5C22×C414yes—
160C22×Dic5C22×C412yes—
161C22×Dic5C22×C412yes—
162C22×Dic5C22×C412yes—
163C22×Dic5C2×D412yes—
164C22×Dic5C2×D412yes—
165C22×Dic5C2×D412yes—
166C22×Dic5C2×Q812yes—
167C2×C4×D5—216no—
168C2×C4×D5—416no—
169C2×C4×D5—48no—
170C2×C4×D5—416no—
171C2×C4×D5—48no—
172C2×C4×D5C42116yes—
173C2×C4×D5C22⋊C4116yes—
174C2×C4×D5C22⋊C4116yes—
175C2×C4×D5C22⋊C4116yes—
176C2×C4×D5C4⋊C4116yes—
177C2×C4×D5C4⋊C4116yes—
178C2×C4×D5C4⋊C4116yes—
179C5×C4⋊C4—28no—
180C5×C4⋊C4—28no—
181C42×C5—28no—
182#685—216no—
183#685—216no—
184C4⋊Dic5—28no—
185C4⋊Dic5—28no—
186#683—216no—
187#683—216no—
188C4×Dic5—28no—
189C4×Dic5—216no—
190C24×C4—51no—
191C24×C4—52no—
192C2×#117—58no—
193C2×#117—58no—
194C2×#117—104no—
195C2×#117—104no—
196C2×#117—104no—
197C2×#117—104no—
198C22×C4⋊C4—52no—
199C22×C4⋊C4—52no—
200C22×C4⋊C4—51no—
201C22×C4⋊C4—51no—
202C22×C4⋊C4—58no—
203C22×C4⋊C4—104no—
204C22×C4⋊C4—104no—
205C22×C4⋊C4C2×D511yescharacteristic
206C22×C4⋊C4C2×D511yescharacteristic
207C22×C22⋊C4—52no—
208C22×C22⋊C4—52no—
209C22×C42—52no—
210C22×C42—51no—
211C22×C42C2×D511yescharacteristic
212C2×#95—54no—
213C2×#95—54no—
214C2×#95—54no—
215C2×#95C2×D514yes—
216C23×C5C23×C411yescharacteristic
217C23×C5C23×C411yescharacteristic
218C23×C5C23×C411yescharacteristic
219C23×C5C22×D411yescharacteristic
220C23×C5C22×D411yescharacteristic
221C23×C5C22×D411yescharacteristic
222C23×C5C22×Q811yescharacteristic
223C23×C5H(5,𝔽2)12yes—
224C23×C5H(5,𝔽2)12yes—
225C23×C52−1+412yes—
226C23×C52−1+412yes—
227C22×D5—24no—
228C22×D5—24no—
229C22×D5—24no—
230C22×D5—24no—
231C22×D5—24no—
232C22×D5—24no—
233C22×D5—22no—
234C22×D5—24no—
235C22×D5—22no—
236C22×D5—22no—
237C22×D5—24no—
238C22×D5—22no—
239C22×D5—24no—
240C22×D5—24no—
241C22×D5—24no—
242C22×D5—24no—
243C22×D5C2×C4214yes—
244C22×D5C2×C22⋊C414yes—
245C22×D5C2×C22⋊C414yes—
246C22×D5C2×C22⋊C414yes—
247C22×D5C2×C4⋊C414yes—
248C22×D5C2×C4⋊C414yes—
249C22×D5C2×C4⋊C414yes—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—28no—
254C2×C4×C5—24no—
255C2×C4×C5—24no—
256C2×C4×C5—28no—
257C2×C4×C5—42no—
258C2×C4×C5—44no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—44no—
266C2×C4×C5—42no—
267C2×C4×C5C2×C4214yes—
268C2×C4×C5C2×C22⋊C414yes—
269C2×C4×C5C2×C22⋊C414yes—
270C2×C4×C5C2×C22⋊C414yes—
271C2×C4×C5C2×C4⋊C414yes—
272C2×C4×C5C2×C4⋊C414yes—
273C2×C4×C5C2×C4⋊C414yes—
274C2×Dic5—24no—
275C2×Dic5—24no—
276C2×Dic5—24no—
277C2×Dic5—28no—
278C2×Dic5—24no—
279C2×Dic5—24no—
280C2×Dic5—28no—
281C2×Dic5—42no—
282C2×Dic5—44no—
283C2×Dic5—42no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—44no—
291C2×Dic5C2×C4214yes—
292C2×Dic5C2×C22⋊C414yes—
293C2×Dic5C2×C22⋊C414yes—
294C2×Dic5C2×C22⋊C414yes—
295C2×Dic5C2×C4⋊C414yes—
296C2×Dic5C2×C4⋊C414yes—
297C2×Dic5C2×C4⋊C414yes—
298C4×D5—432no—
299C4×D5#95164yescomplemented
300C25—51no—
301C23×C4—51no—
302C23×C4—54no—
303C23×C4—54no—
304C23×C4—54no—
305C23×C4—54no—
306C23×C4—54no—
307C23×C4—54no—
308C23×C4—54no—
309C23×C4—52no—
310C23×C4—52no—
311C23×C4—52no—
312C23×C4—58no—
313C23×C4—104no—
314C23×C4—104no—
315C23×C4—204no—
316C23×C4—204no—
317C23×C4C22×D512yes—
318C23×C4C22×D512yes—
319C23×C4C22×D512yes—
320C23×C4C22×D511yescharacteristic
321#117—1032no—
322#117—1032no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—58no—
328C2×C4⋊C4—54no—
329C2×C4⋊C4—58no—
330C2×C4⋊C4—54no—
331C2×C4⋊C4—1032no—
332C2×C4⋊C4—104no—
333C2×C4⋊C4—104no—
334C2×C4⋊C4—104no—
335C2×C4⋊C4—104no—
336C2×C4⋊C4—102no—
337C2×C4⋊C4—102no—
338C2×C4⋊C4—102no—
339C2×C4⋊C4—102no—
340C2×C4⋊C4C4×D514yes—
341C2×C4⋊C4C4×D514yescomplemented
342C2×C22⋊C4—58no—
343C2×C22⋊C4—58no—
344C2×C22⋊C4—104no—
345C2×C22⋊C4—104no—
346C2×C22⋊C4—104no—
347C2×C22⋊C4—104no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—58no—
351C2×C42—54no—
352C2×C42—104no—
353C2×C42—104no—
354C2×C42—102no—
355C2×C42—102no—
356C2×C42C4×D514yescomplemented
357#95—44no—
358#95—204no—
359#95—204no—
360#95—204no—
361C22×C5C22×C4211yescharacteristic
362C22×C5C22×C22⋊C411yescharacteristic
363C22×C5C22×C22⋊C411yescharacteristic
364C22×C5C22×C22⋊C411yescharacteristic
365C22×C5C22×C4⋊C411yescharacteristic
366C22×C5C22×C4⋊C411yescharacteristic
367C22×C5C22×C4⋊C411yescharacteristic
368C22×C5#51812yes—
369C22×C5#51912yes—
370C22×C5#52012yes—
371C22×C5#52012yes—
372C22×C5#52012yes—
373C22×C5#52012yes—
374C22×C5#53511yescharacteristic
375C22×C5#53512yes—
376C22×C5#53511yescharacteristic
377C22×C5#53611yescharacteristic
378C22×C5#53612yes—
379C22×C5#53611yescharacteristic
380C22×C5#53712yes—
381C22×C5#53712yes—
382C22×C5#54412yes—
383C22×C5#54412yes—
384C2×D5—24no—
385C2×D5—24no—
386C2×D5—24no—
387C2×D5—24no—
388C2×D5—28no—
389C2×D5—28no—
390C2×D5—24no—
391C2×D5—28no—
392C2×D5—24no—
393C2×D5—28no—
394C2×D5C2×#9518yes—
395C4×C5—44no—
396C4×C5—44no—
397C4×C5—44no—
398C4×C5C2×#9518yes—
399Dic5—44no—
400Dic5—44no—
401Dic5—44no—
402Dic5C2×#9518yes—
403C24—52no—
404C24—52no—
405C24—52no—
406C24—52no—
407C24—52no—
408C24—52no—
409C24—52no—
410C24—102no—
411C24—102no—
412C24—102no—
413C24—102no—
414C24C23×D511yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—52no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—52no—
434C22×C4—52no—
435C22×C4—52no—
436C22×C4—516no—
437C22×C4—516no—
438C22×C4—516no—
439C22×C4—516no—
440C22×C4—516no—
441C22×C4—516no—
442C22×C4—516no—
443C22×C4—54no—
444C22×C4—54no—
445C22×C4—54no—
446C22×C4—1016no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—104no—
455C22×C4—102no—
456C22×C4—104no—
457C22×C4—102no—
458C22×C4—104no—
459C22×C4—104no—
460C22×C4—102no—
461C22×C4—2016no—
462C22×C4—208no—
463C22×C4—2016no—
464C22×C4—208no—
465C22×C4C2×C4×D514yes—
466C22×C4C2×C4×D514yes—
467C22×C4C2×C4×D514yes—
468C22×C4C2×C4×D512yes—
469C22×C4C2×C4×D512yes—
470C22×C4C2×C4×D512yes—
471C22×C4D4×D512yes—
472C22×C4D4×D512yes—
473C22×C4D4×D512yes—
474C22×C4Q8×D512yes—
475C4⋊C4—28no—
476C4⋊C4—28no—
477C4⋊C4—1016no—
478C4⋊C4—1016no—
479C4⋊C4—108no—
480C4⋊C4—108no—
481C22⋊C4—1016no—
482C22⋊C4—1016no—
483C42—28no—
484C42—1016no—
485C42—108no—
486C2×C5C22×#9511yescharacteristic
487C2×C5#227412yes—
488C2×C5#230911yescharacteristic
489C2×C5#231011yescharacteristic
490C2×C5#231111yescharacteristic
491C2×C5#231111yescharacteristic
492C2×C5#231112yes—
493C2×C5#231612yes—
494C2×C5#231711yescharacteristic
495C2×C5#231712yes—
496C2×C5#231711yescharacteristic
497D5—28no—
498C23—54no—
499C23—54no—
500C23—54no—
501C23—54no—
502C23—54no—
503C23—54no—
504C23—54no—
505C23—102no—
506C23—102no—
507C23—104no—
508C23—104no—
509C23—104no—
510C23—104no—
511C23—104no—
512C23—104no—
513C23—104no—
514C23—104no—
515C23—104no—
516C23—104no—
517C23—104no—
518C23—102no—
519C23—102no—
520C23—104no—
521C23C22×C4×D511yescharacteristic
522C23C22×C4×D511yescharacteristic
523C23C22×C4×D511yescharacteristic
524C23C2×D4×D511yescharacteristic
525C23C2×D4×D511yescharacteristic
526C23C2×D4×D511yescharacteristic
527C23#414412yes—
528C23C2×Q8×D511yescharacteristic
529C23#414712yes—
530C23#414912yes—
531C23#415012yes—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—28no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—54no—
550C2×C4—54no—
551C2×C4—54no—
552C2×C4—54no—
553C2×C4—54no—
554C2×C4—54no—
555C2×C4—54no—
556C2×C4—564no—
557C2×C4—104no—
558C2×C4—104no—
559C2×C4—104no—
560C2×C4—104no—
561C2×C4—104no—
562C2×C4—108no—
563C2×C4—108no—
564C2×C4—2032no—
565C2×C4—202no—
566C2×C4—202no—
567C2×C4—204no—
568C2×C4—202no—
569C2×C4—202no—
570C2×C4—202no—
571C2×C4—204no—
572C2×C4—202no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4C42×D514yes—
576C2×C4D5×C22⋊C414yes—
577C2×C4D5×C22⋊C414yes—
578C2×C4D5×C22⋊C414yes—
579C2×C4D5×C4⋊C414yes—
580C2×C4D5×C4⋊C414yes—
581C2×C4D5×C4⋊C414yes—
582C5#1379511yescharacteristic, complemented, Sylow
583C22—58no—
584C22—104no—
585C22—104no—
586C22—108no—
587C22—108no—
588C22—104no—
589C22—104no—
590C22—104no—
591C22—108no—
592C22—108no—
593C22—104no—
594C22C2×C42×D511yescharacteristic
595C22C2×D5×C22⋊C411yescharacteristic
596C22C2×D5×C22⋊C411yescharacteristic
597C22C2×D5×C22⋊C411yescharacteristic
598C22C2×D5×C4⋊C411yescharacteristic
599C22C2×D5×C4⋊C411yescharacteristic
600C22C2×D5×C4⋊C411yescharacteristic
601C22#6583812yes—
602C22#6585712yes—
603C22#6587912yes—
604C22#6588012yes—
605C22#6590612yes—
606C22#6590812yes—
607C22#6594112yes—
608C22#6594212yes—
609C22#6596212yes—
610C22#6596312yes—
611C22#6600811yescharacteristic
612C22#6600911yescharacteristic
613C22#6602312yes—
614C22#6604911yescharacteristic
615C22#6605811yescharacteristic
616C22#6606312yes—
617C4—44no—
618C4—44no—
619C4—44no—
620C4—58no—
621C4—204no—
622C4—204no—
623C4—204no—
624C4D5×#9518yes—
625C2—108no—
626C2C2×D5×#9511yescharacteristic
627C2#1060548112yes—
628C2#1060573412yes—
629C2#1060595611yescharacteristic
630C2#1060609011yescharacteristic
631C2#1060769912yes—
632C2#1060792612yes—
633C2#1060802511yescharacteristic
634C2#1060815911yescharacteristic
635C2#1060821311yescharacteristic
636C2#1060834111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13795
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C5×C4⋊#95C2semidirect
5. #10602356C2semidirect
6. #10602356C2semidirect
7. #10602328C2semidirect
9. #10600197C2semidirect
25. C2×#4038C4semidirect
28. C2×D5×C4⋊C4C4semidirect
31. C2×#4018C4semidirect
63. C2×C5×C4⋊C4C2×C4semidirect
66. C2×C42×C5C2×C4semidirect
78. C2×C4⋊Dic5C2×C4semidirect
84. C2×#683C2×C4semidirect
89. C2×C4×Dic5C2×C4semidirect
90. C2×C4×Dic5C2×C4semidirect
105. C4⋊#95D5semidirect
299. C4×D5#95semidirect
341. C2×C4⋊C4C4×D5semidirect
356. C2×C42C4×D5semidirect
582. C5#13795semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×#40382
C22×#40182
C5×C4⋊#952
#106023562
#106023282
#106002182
#106001972
#137955