Finite Group Databasebeta

← #12021974

Subgroups — #12021974

Order 1280.

1630 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65261C212yesmaximal
2C2×C4×#683C211yesmaximal, characteristic
3C2×#64936C212yesmaximal
4C2×#64939C211yesmaximal, characteristic
5C2×#64938C211yesmaximal, characteristic
6C5×C4⋊#95C211yesmaximal, characteristic
7#10602361C212yesmaximal
8#10602328C211yesmaximal, characteristic
9#10600213C212yesmaximal
10#10600197C211yesmaximal, characteristic
11#10600197C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2212yes—
13C22×C42×C5C2211yescharacteristic
14C22×C4⋊Dic5C2212yes—
15C22×#683C2212yes—
16C22×#683C2212yes—
17C22×#683C2212yes—
18C22×#683C2212yes—
19C22×#683C2211yescharacteristic
20C22×#683C2211yescharacteristic
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C22×C4×Dic5C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2211yescharacteristic
30C2×#3963C2211yescharacteristic
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35#65261—28no—
36C4×#683C418yescomplemented
37#64939—24no—
38#64938—24no—
39#64936—28no—
40#13954—51nomaximal, Sylow
41C23×C4×C5C2312yes—
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—42no—
55C2×C42×C5—42no—
56C2×C42×C5C2×C414yes—
57C2×C4⋊Dic5—24no—
58C2×C4⋊Dic5—24no—
59C2×C4⋊Dic5—42no—
60C2×#683—24no—
61C2×#683—24no—
62C2×#683—24no—
63C2×#683—24no—
64C2×#683—24no—
65C2×#683—24no—
66C2×#683—24no—
67C2×#683—24no—
68C2×#683—24no—
69C2×#683—24no—
70C2×#683—42no—
71C2×#683—42no—
72C2×#683C2×C414yes—
73C2×#683C2×C414yes—
74C2×#683D414yes—
75C2×#683D414yes—
76C2×#683Q814yes—
77C2×#683Q814yes—
78C2×C4×Dic5—24no—
79C2×C4×Dic5—24no—
80C2×C4×Dic5—24no—
81C2×C4×Dic5—42no—
82C2×C4×Dic5C2×C414yes—
83C2×C4×Dic5C2×C414yes—
84C2×C4×Dic5D414yes—
85C2×C4×Dic5Q814yes—
86C5×#95—24no—
87C5×#95—22no—
88C5×#95—22no—
89#3963—22no—
90#3963—22no—
91#3963—24no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963C2×C414yes—
96#3963C2×C414yes—
97C2×#389—52no—
98C2×#389—52no—
99C2×#382—51no—
100C2×C4×C4⋊C4—51no—
101C2×C4×C4⋊C4—51no—
102#1444—52no—
103#1444—52no—
104C4⋊#95—51no—
105C4⋊#95—51no—
106C4⋊#95—51no—
107C4⋊#95D511yescharacteristic
108C24×C5C2411yescharacteristic
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
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—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5C22×C412yes—
129C22×C4×C5C22×C412yes—
130C22×C4×C5C22×C412yes—
131C22×C4×C5C2×D412yes—
132C22×C4×C5C2×D412yes—
133C22×C4×C5C2×D412yes—
134C22×C4×C5C2×Q812yes—
135C22×C4×C5C2×Q812yes—
136C22×C4×C5C2×Q812yes—
137C22×C4×C5#4114yes—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5C22×C412yes—
158C22×Dic5C22×C412yes—
159C22×Dic5C22×C412yes—
160C22×Dic5C22×C412yes—
161C22×Dic5C2×D412yes—
162C22×Dic5C2×D412yes—
163C22×Dic5C2×D412yes—
164C22×Dic5C2×D412yes—
165C22×Dic5C2×D412yes—
166C22×Dic5C2×D412yes—
167C22×Dic5C2×Q812yes—
168C22×Dic5C2×Q812yes—
169C22×Dic5C2×Q812yes—
170C22×Dic5C2×Q812yes—
171C22×Dic5C2×Q812yes—
172C22×Dic5C2×Q812yes—
173C22×Dic5#4114yes—
174C5×C4⋊C4—48no—
175C42×C5—44no—
176C4⋊Dic5—48no—
177#683—216no—
178#683—48no—
179#683—48no—
180#683—48no—
181#683C4⋊C4116yescomplemented
182#683C4⋊C4116yescomplemented
183C4×Dic5—44no—
184C4×Dic5—48no—
185C4×Dic5C4⋊C4116yescomplemented
186C22×C4⋊C4—51no—
187C22×C4⋊C4—51no—
188C22×C4⋊C4—52no—
189C22×C4⋊C4—52no—
190C22×C4⋊C4—52no—
191C22×C4⋊C4—52no—
192C22×C4⋊C4—52no—
193C22×C4⋊C4C2×D512yes—
194C22×C42—51no—
195C22×C42—51no—
196C22×C42—52no—
197C22×C42C2×D511yescharacteristic
198#389—108no—
199#389—108no—
200#382—104no—
201C4×C4⋊C4—58no—
202C4×C4⋊C4—104no—
203C2×#95—51no—
204C2×#95—51no—
205C2×#95—51no—
206C2×#95—51no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95—52no—
211C2×#95C2×D511yescharacteristic
212C2×#95C2×D511yescharacteristic
213C2×#95C2×D512yes—
214C23×C5C23×C411yescharacteristic
215C23×C5C22×D411yescharacteristic
216C23×C5C22×D411yescharacteristic
217C23×C5C22×D411yescharacteristic
218C23×C5C22×Q811yescharacteristic
219C23×C5C22×Q811yescharacteristic
220C23×C5C22×Q811yescharacteristic
221C23×C5C2×#4112yes—
222C23×C5C2×#4112yes—
223C23×C5H(5,𝔽2)12yes—
224C23×C52−1+412yes—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—24no—
232C2×C4×C5—24no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—24no—
237C2×C4×C5—24no—
238C2×C4×C5—24no—
239C2×C4×C5—24no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5C2×C4⋊C414yes—
252C2×C4×C5C2×C4⋊C414yes—
253C2×C4×C5C2×C4⋊C414yes—
254C2×Dic5—22no—
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—22no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—24no—
263C2×Dic5—24no—
264C2×Dic5—24no—
265C2×Dic5—24no—
266C2×Dic5—24no—
267C2×Dic5—24no—
268C2×Dic5—24no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—42no—
274C2×Dic5—42no—
275C2×Dic5—42no—
276C2×Dic5—42no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5C2×C4⋊C414yes—
281C2×Dic5C2×C4⋊C414yes—
282C2×Dic5C2×C4⋊C414yes—
283C2×Dic5C2×C4⋊C414yes—
284C2×Dic5C2×C4⋊C414yes—
285C2×Dic5C2×C4⋊C414yes—
286C2×Dic5#12714yes—
287C2×Dic5C4⋊Q814yes—
288C2×Dic5C4⋊Q814yes—
289C2×Dic5C4⋊Q814yes—
290C23×C4—51no—
291C23×C4—51no—
292C23×C4—51no—
293C23×C4—51no—
294C23×C4—52no—
295C23×C4—52no—
296C23×C4C22×D512yes—
297C23×C4C22×D512yes—
298C23×C4C22×D511yescharacteristic
299C23×C4C22×D511yescharacteristic
300C23×C4C22×D511yescharacteristic
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—54no—
305C2×C4⋊C4—54no—
306C2×C4⋊C4—54no—
307C2×C4⋊C4—54no—
308C2×C4⋊C4—54no—
309C2×C4⋊C4—54no—
310C2×C4⋊C4—104no—
311C2×C4⋊C4—104no—
312C2×C4⋊C4—104no—
313C2×C4⋊C4—104no—
314C2×C4⋊C4—104no—
315C2×C4⋊C4—104no—
316C2×C4⋊C4—104no—
317C2×C4⋊C4—104no—
318C2×C4⋊C4—104no—
319C2×C4⋊C4—104no—
320C2×C4⋊C4—104no—
321C2×C4⋊C4—104no—
322C2×C4⋊C4—202no—
323C2×C4⋊C4—202no—
324C2×C4⋊C4—202no—
325C2×C42—42no—
326C2×C42—54no—
327C2×C42—54no—
328C2×C42—54no—
329C2×C42—54no—
330C2×C42—104no—
331C2×C42—104no—
332C2×C42—104no—
333C2×C42—202no—
334C2×C42C4×D514yes—
335#95—22no—
336#95—22no—
337#95—24no—
338#95—54no—
339#95—54no—
340#95—104no—
341#95—104no—
342#95—104no—
343#95—102no—
344#95—102no—
345#95—104no—
346C22×C5C22×C4⋊C411yescharacteristic
347C22×C5C22×C4⋊C411yescharacteristic
348C22×C5C22×C4⋊C411yescharacteristic
349C22×C5C4×#4111yescharacteristic
350C22×C5C4×#4111yescharacteristic
351C22×C5#51811yescharacteristic
352C22×C5#51911yescharacteristic
353C22×C5#52512yes—
354C22×C5C2×#12711yescharacteristic
355C22×C5C2×C4⋊Q811yescharacteristic
356C22×C5C2×C4⋊Q811yescharacteristic
357C22×C5C2×C4⋊Q811yescharacteristic
358C22×C5#53312yes—
359C22×C5#53712yes—
360C22×C5#54412yes—
361C22×C5#54612yes—
362C22×C5#54612yes—
363C22×C5#54812yes—
364C22×C5#54812yes—
365C22×C5#55412yes—
366C22×C5#55412yes—
367C22×C5#55712yes—
368C22×C5#55712yes—
369C4×C5—24no—
370C4×C5—24no—
371C4×C5—24no—
372C4×C5—44no—
373C4×C5—82no—
374Dic5—24no—
375Dic5—24no—
376Dic5—24no—
377Dic5—44no—
378Dic5—82no—
379Dic5#38418yes—
380C24C23×D511yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—52no—
401C22×C4—52no—
402C22×C4—52no—
403C22×C4—52no—
404C22×C4—52no—
405C22×C4—52no—
406C22×C4—52no—
407C22×C4—52no—
408C22×C4—52no—
409C22×C4—52no—
410C22×C4—52no—
411C22×C4—52no—
412C22×C4—52no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—52no—
416C22×C4—54no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4C2×C4×D512yes—
437C22×C4C2×C4×D512yes—
438C22×C4C2×C4×D512yes—
439C22×C4#70914yes—
440C22×C4D4×D512yes—
441C22×C4D4×D512yes—
442C22×C4D4×D512yes—
443C22×C4Q8×D512yes—
444C22×C4Q8×D512yes—
445C22×C4Q8×D512yes—
446C4⋊C4—48no—
447C4⋊C4—516no—
448C4⋊C4—516no—
449C4⋊C4—1016no—
450C4⋊C4—208no—
451C4⋊C4—208no—
452C4⋊C4—208no—
453C4⋊C4—208no—
454C42—44no—
455C42—516no—
456C42—204no—
457C42—208no—
458C2×C5C2×#38411yescharacteristic
459C2×C5#229611yescharacteristic
460C2×C5#231611yescharacteristic
461C2×C5#234911yescharacteristic
462C2×C5#234911yescharacteristic
463C2×C5#235111yescharacteristic
464C2×C5#235111yescharacteristic
465C2×C5#254012yes—
466C2×C5#255012yes—
467C2×C5#255012yes—
468C2×C5#258412yes—
469C23C22×C4×D511yescharacteristic
470C23C2×#70912yes—
471C23C2×D4×D511yescharacteristic
472C23C2×D4×D511yescharacteristic
473C23C2×D4×D511yescharacteristic
474C23#414412yes—
475C23C2×Q8×D511yescharacteristic
476C23C2×Q8×D511yescharacteristic
477C23C2×Q8×D511yescharacteristic
478C23D5×#4112yes—
479C23#415012yes—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—54no—
507C2×C4—54no—
508C2×C4—54no—
509C2×C4—54no—
510C2×C4—54no—
511C2×C4—54no—
512C2×C4—54no—
513C2×C4—54no—
514C2×C4—54no—
515C2×C4—54no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—104no—
521C2×C4—104no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—104no—
525C2×C4—104no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—104no—
529C2×C4—104no—
530C2×C4—104no—
531C2×C4—202no—
532C2×C4—202no—
533C2×C4—202no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4—202no—
537C2×C4—202no—
538C2×C4—202no—
539C2×C4—202no—
540C2×C4—202no—
541C2×C4—202no—
542C2×C4D5×C4⋊C414yes—
543C2×C4D5×C4⋊C414yes—
544C2×C4D5×C4⋊C414yes—
545C5#1395411yescharacteristic, complemented, Sylow
546C22C4×#70911yescharacteristic
547C22#6582011yescharacteristic
548C22#6582412yes—
549C22C2×D5×C4⋊C411yescharacteristic
550C22C2×D5×C4⋊C411yescharacteristic
551C22C2×D5×C4⋊C411yescharacteristic
552C22#6584512yes—
553C22#6585011yescharacteristic
554C22#6585611yescharacteristic
555C22#6588112yes—
556C22#6588612yes—
557C22#6590112yes—
558C22#6591212yes—
559C22#6593112yes—
560C22#6594412yes—
561C22#6595712yes—
562C22#6597012yes—
563C22#6601112yes—
564C22#6601912yes—
565C22D5×#12711yescharacteristic
566C22D5×C4⋊Q811yescharacteristic
567C22D5×C4⋊Q811yescharacteristic
568C22D5×C4⋊Q811yescharacteristic
569C4—24no—
570C4—24no—
571C4—24no—
572C4—44no—
573C4—58no—
574C4—82no—
575C4—104no—
576C4—104no—
577C4—104no—
578C4—204no—
579C4—402no—
580C2#1060510011yescharacteristic
581C2#1060536811yescharacteristic
582C2#1060548611yescharacteristic
583C2#1060560011yescharacteristic
584C2#1060574211yescharacteristic
585C2#1060588811yescharacteristic
586C2D5×#38411yescharacteristic
587C2#1060779412yes—
588C2#1060781112yes—
589C2#1060807812yes—
590C2#1060826812yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, prime radical, cosocleC24×C5C24
hypercenterC4⋊#95D5
hypocenterC5#13954
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
36. C4×#683C4semidirect
181. #683C4⋊C4semidirect
182. #683C4⋊C4semidirect
185. C4×Dic5C4⋊C4semidirect
545. C5#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#652612
C2×C4×#6832
C2×#649362
C2×#649392
C2×#649382
C5×C4⋊#952
#106023612
#106023282
#106002132
#106001972
#139545