Finite Group Databasebeta

← #12030387

Subgroups — #12030387

Order 1280.

1342 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×#65235C211yesmaximal, characteristic
2C5×#1439C211yesmaximal, characteristic
3#10602360C212yesmaximal, complemented
4#10602342C212yesmaximal
5#10602339C211yesmaximal, characteristic
6#10602337C212yesmaximal
7#10600214C212yesmaximal, complemented
8#10600211C212yesmaximal, complemented
9#10600203C212yesmaximal, complemented
10C24×Dic5C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic5C2211yescharacteristic
15C22×C22⋊Dic5C2212yes—
16C22×C4⋊Dic5C2211yescharacteristic
17C22×#683C2212yes—
18C2×C5×#95C2212yes—
19C2×C5×#95C2211yescharacteristic
20C2×#3963C2212yes—
21C2×#3963C2212yes—
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31#65235C418yescomplemented
32#14669—51nomaximal, Sylow
33C25×C5C2311yescharacteristic
34C23×C4×C5C2312yes—
35C23×C4×C5C2312yes—
36C23×C4×C5C2311yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C23×Dic5—41no—
39C23×Dic5—41no—
40C23×Dic5—42no—
41C23×Dic5—42no—
42C23×Dic5C2×C414yes—
43C23×Dic5C2312yes—
44C23×Dic5C2312yes—
45C23×Dic5C2312yes—
46C23×Dic5C2312yes—
47C2×C5×C4⋊C4—41no—
48C2×C5×C4⋊C4—42no—
49C2×C5×C22⋊C4—24no—
50C2×C5×C22⋊C4—41no—
51C2×C5×C22⋊C4—41no—
52C2×C5×C22⋊C4—42no—
53C2×C5×C22⋊C4—42no—
54C2×C5×C22⋊C4C2×C414yes—
55C2×C22⋊Dic5—22no—
56C2×C22⋊Dic5—22no—
57C2×C22⋊Dic5—24no—
58C2×C22⋊Dic5—42no—
59C2×C22⋊Dic5—42no—
60C2×C22⋊Dic5C2×C414yes—
61C2×C4⋊Dic5—42no—
62C2×C4⋊Dic5—41no—
63C2×#683—42no—
64C2×#683—42no—
65C2×#683C2×C418yes—
66C5×#95—41no—
67C5×#95—42no—
68#3963—42no—
69#3963—42no—
70#3963—42no—
71#3963—42no—
72#3963—42no—
73#3963—42no—
74#3963—42no—
75#3963—42no—
76#3963—42no—
77#3963—41no—
78#3963C2×C418yes—
79C2×#385—51no—
80#1445—52no—
81#1443—52no—
82#1442—52no—
83#1441—52no—
84#1440—52no—
85#1439—51no—
86#1439D511yescharacteristic
87C22⋊#95—52no—
88C24×C5—22no—
89C24×C5—22no—
90C24×C5—21no—
91C24×C5—21no—
92C24×C5—22no—
93C24×C5—21no—
94C24×C5—21no—
95C24×C5—22no—
96C24×C5C22×C412yes—
97C24×C5#4112yes—
98C24×C5#4112yes—
99C24×C5C2411yescharacteristic
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
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×C5C22×C412yes—
123C22×C4×C5C22×C412yes—
124C22×Dic5—22no—
125C22×Dic5—22no—
126C22×Dic5—22no—
127C22×Dic5—22no—
128C22×Dic5—22no—
129C22×Dic5—22no—
130C22×Dic5—22no—
131C22×Dic5—22no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
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—48no—
151C22×Dic5—44no—
152C22×Dic5—44no—
153C22×Dic5—48no—
154C22×Dic5—44no—
155C22×Dic5C22×C414yes—
156C22×Dic5C22×C414yes—
157C5×C4⋊C4—44no—
158C5×C22⋊C4—44no—
159C5×C22⋊C4—48no—
160C22⋊Dic5—28no—
161C22⋊Dic5—48no—
162C4⋊Dic5—44no—
163#683—48no—
164C24×C4—51no—
165C22×C4⋊C4—52no—
166C22×C4⋊C4—51no—
167C22×C4⋊C4C2×D511yescharacteristic
168C22×C22⋊C4—51no—
169C22×C22⋊C4—52no—
170C22×C22⋊C4C2×D512yes—
171C22×C22⋊C4C2×D511yescharacteristic
172#385—58no—
173C2×#95—52no—
174C2×#95—52no—
175C2×#95—52no—
176C2×#95—52no—
177C2×#95—52no—
178C2×#95—52no—
179C2×#95—51no—
180C2×#95—52no—
181C2×#95—52no—
182C2×#95—52no—
183C2×#95—52no—
184C2×#95C2×D512yes—
185C2×#95C2×D511yescharacteristic
186C23×C5—22no—
187C23×C5—24no—
188C23×C5—22no—
189C23×C5—24no—
190C23×C5—24no—
191C23×C5—24no—
192C23×C5—22no—
193C23×C5—22no—
194C23×C5—22no—
195C23×C5—22no—
196C23×C5—24no—
197C23×C5—24no—
198C23×C5—41no—
199C23×C5—42no—
200C23×C5—41no—
201C23×C5—41no—
202C23×C5—42no—
203C23×C5—42no—
204C23×C5—42no—
205C23×C5—42no—
206C23×C5—41no—
207C23×C5—42no—
208C23×C5#11714yes—
209C23×C5C23×C411yescharacteristic
210C23×C5C2×#4111yescharacteristic
211C23×C5C2×#4111yescharacteristic
212C23×C5H(5,𝔽2)12yes—
213C23×C5H(5,𝔽2)11yescharacteristic
214C23×C5H(5,𝔽2)11yescharacteristic
215C23×C5H(5,𝔽2)12yes—
216C23×C5H(5,𝔽2)12yes—
217C23×C52−1+411yescharacteristic
218C23×C52−1+411yescharacteristic
219C23×C52−1+412yes—
220C2×C4×C5—24no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—24no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—42no—
227C2×C4×C5—41no—
228C2×C4×C5—42no—
229C2×C4×C5—41no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×Dic5—24no—
245C2×Dic5—24no—
246C2×Dic5—24no—
247C2×Dic5—24no—
248C2×Dic5—24no—
249C2×Dic5—24no—
250C2×Dic5—416no—
251C2×Dic5—42no—
252C2×Dic5—42no—
253C2×Dic5—42no—
254C2×Dic5—42no—
255C2×Dic5—42no—
256C2×Dic5—42no—
257C2×Dic5—42no—
258C2×Dic5—42no—
259C2×Dic5—42no—
260C2×Dic5—42no—
261C2×Dic5—42no—
262C2×Dic5—42no—
263C2×Dic5—42no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C25C22×D511yescharacteristic
274C23×C4—52no—
275C23×C4—52no—
276C23×C4—54no—
277C23×C4—52no—
278C23×C4—52no—
279C23×C4—201no—
280C23×C4—201no—
281C23×C4—202no—
282C23×C4—202no—
283C23×C4C22×D512yes—
284C23×C4C22×D512yes—
285C23×C4C22×D511yescharacteristic
286C23×C4C22×D511yescharacteristic
287C2×C4⋊C4—42no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—58no—
290C2×C4⋊C4—202no—
291C2×C4⋊C4—202no—
292C2×C4⋊C4—201no—
293C2×C4⋊C4—202no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4—41no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—54no—
300C2×C22⋊C4—102no—
301C2×C22⋊C4—102no—
302C2×C22⋊C4—104no—
303C2×C22⋊C4—202no—
304C2×C22⋊C4—202no—
305C2×C22⋊C4C4×D514yes—
306#95—41no—
307#95—42no—
308#95—58no—
309#95—201no—
310#95—202no—
311#95—202no—
312#95—202no—
313#95—202no—
314#95—202no—
315#95—202no—
316#95—202no—
317#95—202no—
318#95—202no—
319C22×C5—24no—
320C22×C5—28no—
321C22×C5—42no—
322C22×C5—42no—
323C22×C5—44no—
324C22×C5—44no—
325C22×C5—42no—
326C22×C5—42no—
327C22×C5—42no—
328C22×C5—42no—
329C22×C5—44no—
330C22×C5C2×#11711yescharacteristic
331C22×C5#51811yescharacteristic
332C22×C5#51812yes—
333C22×C5#51911yescharacteristic
334C22×C5#52012yes—
335C22×C5#53812yes—
336C22×C5#53812yes—
337C22×C5#53911yescharacteristic
338C22×C5#53911yescharacteristic
339C22×C5#53911yescharacteristic
340C22×C5#53911yescharacteristic
341C22×C5#53912yes—
342C22×C5#53912yes—
343C22×C5#56011yescharacteristic
344C22×C5#56011yescharacteristic
345C22×C5#56012yes—
346C22×C5H(3,𝔽4)11yescharacteristic
347C22×C5#56212yes—
348C22×C5#56212yes—
349C22×C5#56212yes—
350C22×C5#56312yes—
351C22×C5#56311yescharacteristic
352C22×C5#56312yes—
353C4×C5—42no—
354C4×C5—42no—
355C4×C5—82no—
356C4×C5—82no—
357Dic5—44no—
358Dic5—44no—
359Dic5—82no—
360Dic5—82no—
361C24—22no—
362C24—21no—
363C24—21no—
364C24—22no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24C2×C4×D512yes—
370C24#71112yes—
371C24#71312yes—
372C24C23×D511yescharacteristic
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
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—54no—
396C22×C4—54no—
397C22×C4—102no—
398C22×C4—102no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4—102no—
403C22×C4—102no—
404C22×C4—102no—
405C22×C4—102no—
406C22×C4—102no—
407C22×C4—102no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—102no—
413C22×C4—102no—
414C22×C4—102no—
415C22×C4—102no—
416C22×C4—102no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—204no—
424C22×C4—208no—
425C22×C4—204no—
426C22×C4—208no—
427C22×C4—204no—
428C22×C4C2×C4×D512yes—
429C22×C4C2×C4×D512yes—
430C4⋊C4—44no—
431C4⋊C4—208no—
432C4⋊C4—204no—
433C22⋊C4—44no—
434C22⋊C4—48no—
435C22⋊C4—108no—
436C22⋊C4—208no—
437C2×C5—44no—
438C2×C5#231311yescharacteristic
439C2×C5#231812yes—
440C2×C5#237511yescharacteristic
441C2×C5#237611yescharacteristic
442C2×C5#237812yes—
443C2×C5#282411yescharacteristic
444C2×C5#282611yescharacteristic
445C2×C5#282712yes—
446C2×C5#282712yes—
447C2×C5#283411yescharacteristic
448C2×C5#283511yescharacteristic
449C23—22no—
450C23—22no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—22no—
458C23—22no—
459C23—24no—
460C23—24no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—41no—
467C23—42no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23#403814yes—
472C23C22×C4×D511yescharacteristic
473C23C2×#71111yescharacteristic
474C23#414411yescharacteristic
475C23#414412yes—
476C23#414411yescharacteristic
477C23#414412yes—
478C23C2×#71311yescharacteristic
479C23#414912yes—
480C23#415011yescharacteristic
481C23#415011yescharacteristic
482C23#415012yes—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
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—42no—
507C2×C4—104no—
508C2×C4—104no—
509C2×C4—104no—
510C2×C4—104no—
511C2×C4—104no—
512C2×C4—104no—
513C2×C4—2016no—
514C2×C4—202no—
515C2×C4—202no—
516C2×C4—202no—
517C2×C4—202no—
518C2×C4—202no—
519C2×C4—202no—
520C2×C4—202no—
521C2×C4—202no—
522C2×C4—202no—
523C2×C4—202no—
524C2×C4—202no—
525C2×C4—202no—
526C2×C4—202no—
527C2×C4—202no—
528C2×C4—202no—
529C2×C4—202no—
530C2×C4—202no—
531C2×C4—202no—
532C2×C4—202no—
533C2×C4—202no—
534C2×C4—202no—
535C2×C4—202no—
536C5#1466911yescharacteristic, complemented, Sylow
537C22—24no—
538C22—28no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—44no—
546C22—42no—
547C22—42no—
548C22#6582011yescharacteristic
549C22C2×#403811yescharacteristic
550C22#6585011yescharacteristic
551C22#6587912yes—
552C22#6588012yes—
553C22#6592712yes—
554C22#6592911yescharacteristic
555C22#6593611yescharacteristic
556C22#6593611yescharacteristic
557C22#6595412yes—
558C22#6595512yes—
559C22#6595512yes—
560C22#6597812yes—
561C22#6597911yescharacteristic
562C22#6597911yescharacteristic
563C22#6597912yes—
564C22#6598511yescharacteristic
565C22#6598512yes—
566C22#6599912yes—
567C22#6601711yescharacteristic
568C22#6601812yes—
569C22#6604612yes—
570C22#6605411yescharacteristic
571C4—42no—
572C4—42no—
573C4—82no—
574C4—82no—
575C4—204no—
576C4—204no—
577C4—402no—
578C4—402no—
579C2—44no—
580C2#1060559811yescharacteristic
581C2#1060611412yes—
582C2#1060641311yescharacteristic
583C2#1060722312yes—
584C2#1060816511yescharacteristic
585C2#1060847911yescharacteristic
586C2#1060861711yescharacteristic
587C2#1060882212yes—
588C2#1060918412yes—
589C2#1060939011yescharacteristic
590C2#1060982511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1439C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenter#1439D5
hypocenterC5#14669
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. #10602360C2semidirect
7. #10600214C2semidirect
8. #10600211C2semidirect
9. #10600203C2semidirect
31. #65235C4semidirect
536. C5#14669semidirect

Maximal subgroups

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

subgroupindex
C2×#652352
C5×#14392
#106023602
#106023422
#106023392
#106023372
#106002142
#106002112
#106002032
#146695