Finite Group Databasebeta

← #12104192

Subgroups — #12104192

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65124C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic
4C5×#1948C211yesmaximal, characteristic, complemented
5#10601372C212yesmaximal
6#10601346C212yesmaximal, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600361C211yesmaximal, characteristic, complemented
9#10600259C211yesmaximal, characteristic, complemented
10#10599667C212yesmaximal
11#10599579C212yesmaximal, complemented
12C2×#4038—21no—
13C2×D5×C4⋊C4C2211yescharacteristic
14C2×D5×C4⋊C4C2211yescharacteristic
15C2×C42×D5—21no—
16C2×C42×D5C2211yescharacteristic
17C2×C5×#106C2212yes—
18C2×C5×C4⋊C8C2211yescharacteristic
19C5×#384C2211yescharacteristic
20C4×C5×C4⋊C4C2211yescharacteristic
21C2×#3952C2212yes—
22C2×#3950C2212yes—
23C2×#3947C2212yes—
24#65276—21no—
25#65276C2212yes—
26#65266—21no—
27C4⋊C4×Dic5—21no—
28C4⋊C4×Dic5C2211yescharacteristic
29C4⋊C4×Dic5C2212yes—
30C4⋊C4×Dic5C2211yescharacteristic
31C2×#3940C2212yes—
32C2×#3939C2212yes—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35C4×#683—21no—
36C2×C4⋊#168C2211yescharacteristic
37#65124C418yescomplemented
38D5×#95—21no—
39#64938—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21365—51nomaximal, Sylow
45C22×C4×D5—21no—
46C22×C4×D5—21no—
47C22×C4×D5D411yescharacteristic
48C22×C4×D5D411yescharacteristic
49C22×C4×D5C2311yescharacteristic
50C22×C5×C8C2312yes—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4C2312yes—
54C2×C5×C4⋊C4C2311yescharacteristic
55C2×C5×C4⋊C4C2311yescharacteristic
56C2×C42×C5—21no—
57C2×C42×C5C2311yescharacteristic
58C2×#685—22no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5C2312yes—
62C2×C4⋊Dic5C2311yescharacteristic
63C2×C4⋊Dic5C2311yescharacteristic
64C2×#683—21no—
65C2×#683—21no—
66C2×C4×Dic5—21no—
67C2×C4×Dic5—21no—
68C2×C4×Dic5—21no—
69C2×C4×Dic5—22no—
70C2×C4×Dic5D411yescharacteristic
71C2×C4×Dic5D411yescharacteristic
72C2×C4×Dic5C2311yescharacteristic
73C22×#168C2312yes—
74#4038—44no—
75D5×C4⋊C4—22no—
76D5×C4⋊C4—22no—
77D5×C4⋊C4—22no—
78D5×C4⋊C4—22no—
79C42×D5—44no—
80C42×D5C2×C414yes—
81C42×D5Q814yes—
82C5×#106—24no—
83C5×C4⋊C8C2×C414yescomplemented
84C5×#95—21no—
85#3963—21no—
86#3963—21no—
87#3963—21no—
88#3963—22no—
89#3963—22no—
90#3952C2×C418yes—
91#3950—24no—
92#3947C2×C418yescomplemented
93#3940—24no—
94#3939—24no—
95C4⋊#168C2×C414yescomplemented
96C2×#432—51no—
97#2285—51no—
98C2×C4×C4⋊C4—51no—
99#1948—51no—
100#1948D511yescharacteristic, complemented
101#1947—51no—
102#1947—51no—
103#1853—52no—
104#1852—52no—
105#1776—52no—
106#1776—52no—
107C23×D5C2×D411yescharacteristic
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—22no—
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2411yescharacteristic
114C22×Dic5—21no—
115C22×Dic5—21no—
116C22×Dic5—22no—
117C22×Dic5C2×D411yescharacteristic
118C22×Dic5C2×D411yescharacteristic
119C22×Dic5C2×D411yescharacteristic
120C2×C4×D5—22no—
121C2×C4×D5—22no—
122C2×C4×D5—22no—
123C2×C4×D5—22no—
124C2×C4×D5—21no—
125C2×C4×D5—21no—
126C2×C4×D5—21no—
127C2×C4×D5—21no—
128C2×C4×D5—24no—
129C2×C4×D5—24no—
130C2×C4×D5—42no—
131C2×C4×D5—42no—
132C2×C4×D5—42no—
133C2×C4×D5—42no—
134C2×C4×D5C4⋊C414yes—
135C2×C4×D5C4⋊C414yes—
136C2×C4×D5C22×C412yes—
137C2×C4×D5C2×Q812yes—
138C2×C5×C8—22no—
139C2×C5×C8—22no—
140C2×C5×C8C22×C414yes—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—22no—
144C5×C4⋊C4—22no—
145C5×C4⋊C4—42no—
146C5×C4⋊C4—42no—
147C5×C4⋊C4#4112yes—
148C5×C4⋊C4#4112yes—
149C42×C5—42no—
150C42×C5C22×C412yes—
151C42×C5C2×Q812yes—
152#685—44no—
153C4⋊Dic5—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5—22no—
156C4⋊Dic5—22no—
157C4⋊Dic5—42no—
158C4⋊Dic5—42no—
159C4⋊Dic5#4112yes—
160C4⋊Dic5#4112yes—
161#683—24no—
162#683—24no—
163C4×Dic5—42no—
164C4×Dic5—42no—
165C4×Dic5—44no—
166C4×Dic5—42no—
167C4×Dic5C4⋊C414yes—
168C4×Dic5C4⋊C414yes—
169C4×Dic5C22×C412yes—
170C4×Dic5C2×Q812yes—
171C2×#168—22no—
172C2×#168—22no—
173C2×#168C22×C414yes—
174C2×#117—101no—
175C22×C4⋊C4—51no—
176C22×C4⋊C4—51no—
177C22×C42—51no—
178C22×C42—101no—
179#432—58no—
180C2×#107—52no—
181C2×#107—52no—
182C2×#106—52no—
183C2×#106C2×D512yes—
184C2×C4⋊C8—51no—
185C2×C4⋊C8C2×D511yescharacteristic
186C2×C22⋊C8—52no—
187C2×#97—52no—
188#384—51no—
189#384C2×D511yescharacteristic
190#382—101no—
191#380—52no—
192#380—101no—
193C4×C4⋊C4—51no—
194C4×C4⋊C4—51no—
195C4×C4⋊C4—52no—
196C4×C4⋊C4—51no—
197C4×C4⋊C4—101no—
198C4×C4⋊C4—101no—
199C4×C4⋊C4—101no—
200C4×C4⋊C4C2×D511yescharacteristic
201C2×#95—101no—
202#340—52no—
203#340—52no—
204#340—52no—
205#340C2×D512yes—
206C23×C5C22×D411yescharacteristic
207C22×D5—21no—
208C22×D5—21no—
209C22×D5—21no—
210C22×D5—21no—
211C22×D5C2×C4⋊C412yes—
212C22×D5AGL(1,ℤ/8)12yes—
213C22×D5#13712yes—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5C2×C4⋊C412yes—
226C2×C4×C5C2×C4⋊C412yes—
227C2×C4×C5AGL(1,ℤ/8)12yes—
228C2×C4×C5#13712yes—
229C2×C4×C5C23×C411yescharacteristic
230C2×C4×C5C22×Q811yescharacteristic
231C2×C4×C5C2×#4111yescharacteristic
232C2×C4×C5C2×#4111yescharacteristic
233C2×C4×C5C2×#4111yescharacteristic
234C2×C4×C5C2×#4111yescharacteristic
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240C2×Dic5—21no—
241C2×Dic5—22no—
242C2×Dic5—22no—
243C2×Dic5—41no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—41no—
247C2×Dic5—42no—
248C2×Dic5—42no—
249C2×Dic5—42no—
250C2×Dic5C2×C4⋊C412yes—
251C2×Dic5C2×C4⋊C412yes—
252C2×Dic5C2×C4⋊C412yes—
253C4×D5—28no—
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—22no—
257C4×D5—22no—
258C4×D5—28no—
259C4×D5—48no—
260C4×D5—48no—
261C5×C8—24no—
262#168—24no—
263C23×C4—51no—
264C23×C4—51no—
265C23×C4—51no—
266C23×C4—101no—
267C23×C4—101no—
268C22×C8—52no—
269C22×C8C22×D512yes—
270#117—204no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—51no—
274C2×C4⋊C4—51no—
275C2×C4⋊C4—52no—
276C2×C4⋊C4—102no—
277C2×C4⋊C4—102no—
278C2×C4⋊C4—101no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—102no—
281C2×C4⋊C4—102no—
282C2×C4⋊C4—101no—
283C2×C4⋊C4—101no—
284C2×C4⋊C4C22×D512yes—
285C2×C4⋊C4C22×D511yescharacteristic
286C2×C4⋊C4C22×D511yescharacteristic
287C2×C22⋊C4—102no—
288C2×C42—21no—
289C2×C42—51no—
290C2×C42—51no—
291C2×C42—51no—
292C2×C42—54no—
293C2×C42—54no—
294C2×C42—102no—
295C2×C42—101no—
296C2×C42—101no—
297C2×C42—101no—
298C2×C42—204no—
299C2×C42C22×D511yescharacteristic
300#107—104no—
301#107—104no—
302#106—24no—
303#106—104no—
304C4⋊C8—54no—
305C4⋊C8C4×D514yescomplemented
306C22⋊C8—58no—
307#97—58no—
308#95—21no—
309#95—101no—
310#95—101no—
311#95—102no—
312#95—102no—
313#95—101no—
314C22×C5C22×C4⋊C411yescharacteristic
315C22×C5#52511yescharacteristic
316C22×C5#52511yescharacteristic
317C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C5C2×#13711yescharacteristic
320C22×C5C2×#13711yescharacteristic
321C2×D5—22no—
322C2×D5—22no—
323C2×D5—22no—
324C2×D5—22no—
325C2×D5—22no—
326C2×D5—22no—
327C2×D5#42814yes—
328C4×C5—22no—
329C4×C5—42no—
330C4×C5—42no—
331C4×C5—82no—
332C4×C5#42814yes—
333C4×C5C4×#4111yescharacteristic
334C4×C5C4×#4111yescharacteristic
335C4×C5#53311yescharacteristic
336C4×C5#53311yescharacteristic
337Dic5—22no—
338Dic5—22no—
339Dic5—22no—
340Dic5—42no—
341Dic5—42no—
342Dic5—82no—
343C24—51no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—51no—
348C22×C4—51no—
349C22×C4—51no—
350C22×C4—52no—
351C22×C4—52no—
352C22×C4—54no—
353C22×C4—54no—
354C22×C4—102no—
355C22×C4—102no—
356C22×C4—104no—
357C22×C4—104no—
358C22×C4—101no—
359C22×C4—101no—
360C22×C4—101no—
361C22×C4—101no—
362C22×C4—102no—
363C22×C4—102no—
364C22×C4—101no—
365C22×C4—101no—
366C22×C4—102no—
367C22×C4—202no—
368C22×C4—202no—
369C22×C4—202no—
370C22×C4—202no—
371C22×C4D4×D511yescharacteristic
372C22×C4D4×D511yescharacteristic
373C22×C4C23×D511yescharacteristic
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—54no—
377C2×C8—102no—
378C2×C8—102no—
379C2×C8C2×C4×D514yes—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—52no—
387C4⋊C4—52no—
388C4⋊C4—104no—
389C4⋊C4—104no—
390C4⋊C4—101no—
391C4⋊C4—101no—
392C4⋊C4—102no—
393C4⋊C4—102no—
394C4⋊C4—202no—
395C4⋊C4—202no—
396C4⋊C4#71112yes—
397C4⋊C4#71312yes—
398C22⋊C4—204no—
399C42—42no—
400C42—52no—
401C42—52no—
402C42—54no—
403C42—54no—
404C42—202no—
405C42—202no—
406C42—204no—
407C42—202no—
408C42C2×C4×D512yes—
409C42Q8×D512yes—
410C2×C5#229611yescharacteristic
411C2×C5C2×#42811yescharacteristic
412C2×C5C2×#42811yescharacteristic
413C2×C5#310911yescharacteristic
414C2×C5#311011yescharacteristic
415C2×C5#311211yescharacteristic
416C2×C5#311311yescharacteristic
417D5—24no—
418C23—52no—
419C23—52no—
420C23—52no—
421C23—101no—
422C23—101no—
423C23—101no—
424C23—101no—
425C23C2×D4×D511yescharacteristic
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—52no—
440C2×C4—108no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—101no—
445C2×C4—101no—
446C2×C4—101no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—108no—
451C2×C4—102no—
452C2×C4—102no—
453C2×C4—102no—
454C2×C4—208no—
455C2×C4—208no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—201no—
459C2×C4—201no—
460C2×C4—202no—
461C2×C4—202no—
462C2×C4—202no—
463C2×C4D5×C4⋊C412yes—
464C2×C4D5×C4⋊C412yes—
465C2×C4#406012yes—
466C2×C4#406112yes—
467C2×C4C22×C4×D511yescharacteristic
468C2×C4C2×#71111yescharacteristic
469C2×C4C2×Q8×D511yescharacteristic
470C2×C4C2×#71311yescharacteristic
471C2×C4D5×#4111yescharacteristic
472C2×C4D5×#4111yescharacteristic
473C8—24no—
474C8—104no—
475C5#2136511yescharacteristic, complemented, Sylow
476C22—54no—
477C22—102no—
478C22—102no—
479C22—102no—
480C22—102no—
481C22—102no—
482C22—102no—
483C22C2×D5×C4⋊C411yescharacteristic
484C22#6594011yescharacteristic
485C22#6596111yescharacteristic
486C22C2×#406011yescharacteristic
487C22C2×#406111yescharacteristic
488C22D5×AGL(1,ℤ/8)11yescharacteristic
489C22D5×#13711yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—102no—
495C4—102no—
496C4—102no—
497C4—202no—
498C4—202no—
499C4—402no—
500C4#6515014yes—
501C4C4×#71111yescharacteristic
502C4C4×#71311yescharacteristic
503C4#6602211yescharacteristic
504C4#6606211yescharacteristic
505C2—104no—
506C2#1060769411yescharacteristic
507C2C2×#6515011yescharacteristic
508C2D5×#42811yescharacteristic
509C2#1061209311yescharacteristic
510C2#1061214111yescharacteristic
511C2#1061272911yescharacteristic
512C2#1061277711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1948C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1948D5
hypocenterC5#21365
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. C5×#1948C2semidirect
6. #10601346C2semidirect
7. #10601246C2semidirect
8. #10600361C2semidirect
9. #10600259C2semidirect
11. #10599579C2semidirect
37. #65124C4semidirect
83. C5×C4⋊C8C2×C4semidirect
92. #3947C2×C4semidirect
95. C4⋊#168C2×C4semidirect
100. #1948D5semidirect
305. C4⋊C8C4×D5semidirect
475. C5#21365semidirect

Maximal subgroups

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

subgroupindex
C2×#651242
#106060492
C4×D5×C4⋊C42
C5×#19482
#106013722
#106013462
#106012462
#106003612
#106002592
#105996672
#105995792
#213655