Finite Group Databasebeta

← #12024892

Subgroups — #12024892

Order 1280.

1586 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#399C211yesmaximal, characteristic
2C2×C4⋊C4×Dic5C212yesmaximal, complemented
3C2×#65240C212yesmaximal
4#10602362C212yesmaximal, complemented
5#10602357C212yesmaximal, complemented
6#10602341C211yesmaximal, characteristic
7#10602338C212yesmaximal
8#10602338C211yesmaximal, characteristic
9#10600200C212yesmaximal, complemented
10C22×C5×C4⋊C4C2212yes—
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic5C2212yes—
15C22×C22⋊Dic5C2211yescharacteristic
16C22×C22⋊Dic5C2211yescharacteristic
17C22×C4⋊Dic5C2212yes—
18C22×C4×Dic5C2212yes—
19C22×C4×Dic5C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C5×#399C418yescomplemented
22C2×C5×#95C2211yescharacteristic
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C4⋊C4×Dic5—28no—
33#65240—28no—
34#14194—51nomaximal, Sylow
35C25×C5C2311yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C23×C4×C5C2312yes—
38C23×C4×C5C2311yescharacteristic
39C23×C4×C5C2312yes—
40C23×Dic5C2312yes—
41C23×Dic5C2312yes—
42C23×Dic5C2312yes—
43C23×Dic5C2312yes—
44C2×C5×C4⋊C4—24no—
45C2×C5×C4⋊C4—24no—
46C2×C5×C4⋊C4—41no—
47C2×C5×C4⋊C4—41no—
48C2×C5×C4⋊C4C2×C418yes—
49C2×C5×C4⋊C4C2×C414yes—
50C2×C5×C22⋊C4—24no—
51C2×C5×C22⋊C4—24no—
52C2×C5×C22⋊C4—41no—
53C2×C5×C22⋊C4—41no—
54C2×C5×C22⋊C4C2×C418yes—
55C2×C5×C22⋊C4C2×C414yes—
56C2×C22⋊Dic5—24no—
57C2×C22⋊Dic5—24no—
58C2×C22⋊Dic5—24no—
59C2×C22⋊Dic5—24no—
60C2×C22⋊Dic5—24no—
61C2×C22⋊Dic5—41no—
62C2×C22⋊Dic5—41no—
63C2×C4⋊Dic5—24no—
64C2×C4⋊Dic5—24no—
65C2×C4⋊Dic5D418yes—
66C2×C4×Dic5—24no—
67C2×C4×Dic5—24no—
68C2×C4×Dic5—24no—
69C2×C4×Dic5—24no—
70C2×C4×Dic5—24no—
71C2×C4×Dic5—24no—
72C2×C4×Dic5—41no—
73C2×C4×Dic5—42no—
74C5×#95C2×C414yes—
75#3963—24no—
76#3963—24no—
77#3963—24no—
78#3963—24no—
79#3963—24no—
80#3963—24no—
81#3963—24no—
82#3963—42no—
83#3963—41no—
84C2×#399D511yescharacteristic
85C2×#388—52no—
86C2×C4×C4⋊C4—52no—
87#1445—52no—
88#1440—51no—
89#1437—51no—
90#1437—52no—
91#1436—52no—
92#1436—52no—
93C24×C5—22no—
94C24×C5—22no—
95C24×C5—22no—
96C24×C5—22no—
97C24×C5—22no—
98C24×C5—21no—
99C24×C5—21no—
100C24×C5—22no—
101C24×C5C22×C412yes—
102C24×C5C2411yescharacteristic
103C22×C4×C5—22no—
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—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5C22×C414yes—
122C22×C4×C5C22×C412yes—
123C22×C4×C5C22×C412yes—
124C22×C4×C5C22×C414yes—
125C22×C4×C5C2×D414yes—
126C22×C4×C5#4114yes—
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×Dic5C2×D414yes—
151C22×Dic5C2×D414yes—
152C22×Dic5#4114yes—
153C22×Dic5#4114yes—
154C22×Dic5#4114yes—
155C5×C4⋊C4—216no—
156C5×C4⋊C4—44no—
157C5×C22⋊C4—216no—
158C5×C22⋊C4—44no—
159C22⋊Dic5—44no—
160C22⋊Dic5—44no—
161C22⋊Dic5—48no—
162C4⋊Dic5—216no—
163C4×Dic5—216no—
164C4×Dic5—44no—
165C4×Dic5—48no—
166C22×C4⋊C4—52no—
167C22×C4⋊C4C2×D512yes—
168C22×C4⋊C4C2×D511yescharacteristic
169C22×C22⋊C4—52no—
170C22×C22⋊C4—51no—
171C22×C22⋊C4—51no—
172C22×C22⋊C4C2×D512yes—
173C22×C22⋊C4C2×D511yescharacteristic
174C22×C42—52no—
175C22×C42—52no—
176C22×C42—51no—
177#399Dic518yescomplemented
178#388—108no—
179C4×C4⋊C4—108no—
180C2×#95—52no—
181C2×#95—52no—
182C2×#95—52no—
183C2×#95—52no—
184C2×#95—52no—
185C2×#95—52no—
186C2×#95—52no—
187C2×#95—52no—
188C2×#95—51no—
189C2×#95C2×D511yescharacteristic
190C23×C5—24no—
191C23×C5—22no—
192C23×C5—24no—
193C23×C5—22no—
194C23×C5—22no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—42no—
198C23×C5—42no—
199C23×C5—42no—
200C23×C5—42no—
201C23×C5—41no—
202C23×C5—42no—
203C23×C5—42no—
204C23×C5—42no—
205C23×C5—41no—
206C23×C5—42no—
207C23×C5—42no—
208C23×C5—42no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5C23×C411yescharacteristic
212C23×C5C22×D412yes—
213C23×C5C2×#4112yes—
214C23×C5C2×#4112yes—
215C23×C5C2×#4112yes—
216C23×C5C2×#4112yes—
217C23×C5H(5,𝔽2)11yescharacteristic
218C23×C5H(5,𝔽2)11yescharacteristic
219C23×C52−1+412yes—
220C2×C4×C5—24no—
221C2×C4×C5—24no—
222C2×C4×C5—24no—
223C2×C4×C5—24no—
224C2×C4×C5—24no—
225C2×C4×C5—24no—
226C2×C4×C5—24no—
227C2×C4×C5—24no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—24no—
233C2×C4×C5—42no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—41no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—42no—
242C2×C4×C5—41no—
243C2×C4×C5C4×D418yes—
244C2×Dic5—24no—
245C2×Dic5—24no—
246C2×Dic5—24no—
247C2×Dic5—24no—
248C2×Dic5—24no—
249C2×Dic5—24no—
250C2×Dic5—24no—
251C2×Dic5—24no—
252C2×Dic5—24no—
253C2×Dic5—24no—
254C2×Dic5—24no—
255C2×Dic5—24no—
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#12318yes—
272C25C22×D511yescharacteristic
273C23×C4—52no—
274C23×C4—52no—
275C23×C4—52no—
276C23×C4—52no—
277C23×C4C22×D512yes—
278C23×C4C22×D511yescharacteristic
279C23×C4C22×D511yescharacteristic
280C23×C4C22×D512yes—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—58no—
286C2×C4⋊C4—104no—
287C2×C4⋊C4—104no—
288C2×C4⋊C4C2×Dic518yes—
289C2×C4⋊C4C2×Dic514yes—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—41no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—104no—
295C2×C22⋊C4—104no—
296C2×C22⋊C4—104no—
297C2×C22⋊C4—104no—
298C2×C22⋊C4—104no—
299C2×C22⋊C4—201no—
300C2×C22⋊C4—201no—
301C2×C22⋊C4C2×Dic518yes—
302C2×C22⋊C4C2×Dic514yes—
303C2×C42—104no—
304C2×C42—104no—
305C2×C42—104no—
306C2×C42—104no—
307C2×C42—104no—
308C2×C42—104no—
309C2×C42—201no—
310C2×C42—202no—
311#95—104no—
312#95—104no—
313#95—104no—
314#95—104no—
315#95—104no—
316#95—104no—
317#95—104no—
318#95—201no—
319#95—202no—
320#95C2×Dic514yes—
321C22×C5—42no—
322C22×C5—44no—
323C22×C5—42no—
324C22×C5—42no—
325C22×C5—44no—
326C22×C5—82no—
327C22×C5—82no—
328C22×C5—82no—
329C22×C5—82no—
330C22×C5C2×C4×D412yes—
331C22×C5C4×#4111yescharacteristic
332C22×C5C4×#4112yes—
333C22×C5#51811yescharacteristic
334C22×C5#51911yescharacteristic
335C22×C5C2×#12312yes—
336C22×C5#52512yes—
337C22×C5#52912yes—
338C22×C5#52912yes—
339C22×C5#53912yes—
340C22×C5#54212yes—
341C22×C5D4211yescharacteristic
342C22×C5#54712yes—
343C22×C5#54812yes—
344C22×C5#55012yes—
345C22×C5#55111yescharacteristic
346C22×C5#55212yes—
347C22×C5#55312yes—
348C22×C5#55612yes—
349C22×C5#55911yescharacteristic
350C22×C5#55911yescharacteristic
351C4×C5—28no—
352C4×C5—44no—
353C4×C5—42no—
354C4×C5—42no—
355Dic5—28no—
356Dic5—44no—
357Dic5—44no—
358Dic5—82no—
359C24—22no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24C22×Dic512yes—
368C24C23×D511yescharacteristic
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—54no—
388C22×C4—54no—
389C22×C4—54no—
390C22×C4—54no—
391C22×C4—54no—
392C22×C4—102no—
393C22×C4—102no—
394C22×C4—102no—
395C22×C4—102no—
396C22×C4—102no—
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×C4D4×D514yes—
416C22×C4#71114yes—
417C22×C4C22×Dic512yes—
418C22×C4C22×Dic514yes—
419C22×C4C22×Dic512yes—
420C22×C4C22×Dic514yes—
421C4⋊C4—216no—
422C4⋊C4—44no—
423C4⋊C4—1016no—
424C22⋊C4—216no—
425C22⋊C4—44no—
426C22⋊C4—208no—
427C22⋊C4—204no—
428C22⋊C4—204no—
429C42—1016no—
430C42—204no—
431C42—208no—
432C2×C5—82no—
433C2×C5C4×#12312yes—
434C2×C5#233211yescharacteristic
435C2×C5#236212yes—
436C2×C5#236611yescharacteristic
437C2×C5#237411yescharacteristic
438C2×C5#244312yes—
439C2×C5#244812yes—
440C2×C5#247912yes—
441C2×C5#259612yes—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—24no—
447C23—41no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23C2×D4×D512yes—
464C23C2×#71112yes—
465C23#414411yescharacteristic
466C23#414411yescharacteristic
467C23#414712yes—
468C23D5×#4112yes—
469C23D5×#4112yes—
470C23D5×#4112yes—
471C23C23×Dic511yescharacteristic
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—58no—
496C2×C4—104no—
497C2×C4—104no—
498C2×C4—104no—
499C2×C4—104no—
500C2×C4—104no—
501C2×C4—104no—
502C2×C4—104no—
503C2×C4—104no—
504C2×C4—104no—
505C2×C4—104no—
506C2×C4—104no—
507C2×C4—104no—
508C2×C4—202no—
509C2×C4—202no—
510C2×C4—202no—
511C2×C4—202no—
512C2×C4—202no—
513C2×C4—202no—
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×C4D4×Dic518yes—
524C5#1419411yescharacteristic, complemented, Sylow
525C22—44no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22#6596512yes—
535C22#6596712yes—
536C22#6597212yes—
537C22#6597312yes—
538C22#6597412yes—
539C22#6597512yes—
540C22#6598312yes—
541C22#6598312yes—
542C22D5×#12312yes—
543C22#6599012yes—
544C22#6599311yescharacteristic
545C22#6599512yes—
546C22#6599811yescharacteristic
547C22#6604711yescharacteristic
548C22#6605111yescharacteristic
549C22#6605212yes—
550C22C2×D4×Dic512yes—
551C22#6613211yescharacteristic
552C22#6614611yescharacteristic
553C22#41×Dic511yescharacteristic
554C22#41×Dic512yes—
555C4—28no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—108no—
560C4—204no—
561C4—204no—
562C4—402no—
563C2—82no—
564C2#1060975312yes—
565C2#1060975812yes—
566C2#1060977412yes—
567C2#1060983412yes—
568C2#1061447711yescharacteristic
569C2#1061447912yes—
570C2Dic5×#12312yes—
571C2#1061457011yescharacteristic
572C2#1061490411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#399C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#399D5
hypocenterC5#14194
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic5C2semidirect
4. #10602362C2semidirect
5. #10602357C2semidirect
9. #10600200C2semidirect
21. C5×#399C4semidirect
177. #399Dic5semidirect
524. C5#14194semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×C4⋊C4×Dic52
C2×#652402
#106023622
#106023572
#106023412
#106023382
#106002002
#141945