Finite Group Databasebeta

← #12963830

Subgroups — #12963830

Order 1280.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10618137C211yesmaximal, characteristic
2C5×#2931C211yesmaximal, characteristic, complemented
3#10615525C212yesmaximal, complemented
4Dic5×#131C212yesmaximal, complemented
5#10615007C211yesmaximal, characteristic, complemented
6#10611250C218yesmaximal, complemented
7#10611131C218yesmaximal, complemented
8#10610776C211yesmaximal, characteristic, complemented
9#10610770C211yesmaximal, characteristic, complemented
10#10610387C212yesmaximal, complemented
11#10610380C212yesmaximal, complemented
12C2×#64978C211yesmaximal, characteristic, complemented
13#10610176C211yesmaximal, characteristic, complemented
14C2×C5×#131C2212yes—
15C5×#532C2211yescharacteristic
16#66162C2212yes—
17#41×Dic5C2212yes—
18C2×#4094C2212yes—
19C22×#676C2211yescharacteristic
20C22×C8×D5C2211yescharacteristic
21#66065C412yes—
22#66053C412yes—
23#66016C414yes—
24#65951C414yes—
25#65936C414yes—
26#65872C2218yes—
27C2×#4018C2211yescharacteristic
28#65804C2211yescharacteristic
29C5×#436C2214yescomplemented
30C5×C8×D4C2214yescomplemented
31C5×#423C2211yescharacteristic
32C5×#408C2212yes—
33C2×C4×C5×C8C2211yescharacteristic
34#65523C2212yes—
35#65416C2218yes—
36#65415C2212yes—
37#65411C2212yes—
38#65411C2214yescomplemented
39#65408C2212yes—
40M16×Dic5C2212yes—
41M16×Dic5C2214yescomplemented
42C8×C22⋊D5C2218yes—
43#65391C2212yes—
44#65390C2212yes—
45#65390C2214yescomplemented
46C2×#3947C2211yescharacteristic
47C2×C8×Dic5C2211yescharacteristic
48C2×C8×Dic5C2214yescomplemented
49#65300C2218yescomplemented
50#65213C2211yescharacteristic
51C2×#3935C2211yescharacteristic
52#65129C2218yes—
53#65117C2218yescomplemented
54#65019C2218yes—
55#65018C2218yes—
56#65009C2218yescomplemented
57#65008C2218yescomplemented
58#64978C2214yes—
59#64978C2214yes—
60#64968C2214yescomplemented
61C8×Dic10C2214yescomplemented
62#60206—51nomaximal, Sylow
63C2×C5×#41C2312yes—
64C22×C4×D5C2311yescharacteristic
65C5×#131—28no—
66C2×C5×M16C2312yes—
67C2×C5×M16C2314yes—
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2314yes—
70C22×C5×C8C2311yescharacteristic
71C5×C4⋊Q8C2×C411yescharacteristic
72C5×#127C2×C411yescharacteristic
73C5×#124C2×C412yes—
74C5×#121C2×C414yes—
75C4×C5×D4C2314yes—
76C2×C42×C5C2311yescharacteristic
77#4094—28no—
78#4092C2×C414yes—
79Q8×Dic5C2×C414yes—
80#4085C2×C418yes—
81#4084C2×C414yes—
82#4083C2×C414yes—
83#4081C2×C418yes—
84#4081C2×C414yes—
85D4×Dic5C2×C414yes—
86D4×Dic5C2×C418yes—
87C4×C22⋊D5C2318yes—
88C2×#685C2×C412yes—
89#4072C2312yes—
90#4072C2314yes—
91#4070C2×C414yes—
92C2×#683C2×C412yes—
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2314yes—
95C2×#681C2314yes—
96C2×#681C2312yes—
97C22×#168C2314yes—
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C2×#676—24no—
101C2×#676C2314yes—
102C2×C8×D5—24no—
103C2×C8×D5C2312yes—
104C2×C8×D5C2312yes—
105#4044C2×C418yes—
106#4035C2×C418yes—
107#4032C2×C418yes—
108#4031C2×C418yes—
109#4025C2×C418yes—
110#4024C2×C418yes—
111#4018C2×C412yes—
112#4018C2×C412yes—
113#4018C2314yes—
114#4016C2×C412yes—
115#4015C2×C412yes—
116C4×Dic10C2314yes—
117C5×C4⋊C8C2314yes—
118C5×C22⋊C8C2318yes—
119C4×C5×C8C2312yes—
120C4×C5×C8C2312yes—
121C22⋊#168C2318yes—
122#3952C2318yes—
123#3947C2314yes—
124#3947C2314yes—
125#3947C2314yes—
126#3947C2314yes—
127#3946C2318yes—
128#3946C2318yes—
129C8×Dic5C2314yes—
130C8×Dic5C2314yes—
131C8×Dic5C2312yes—
132C8×Dic5C2312yes—
133C8×Dic5C2314yes—
134C4⋊#168C2314yes—
135#3935C2314yes—
136#3455—51no—
137#2967—58no—
138#2966—58no—
139#2961—51no—
140#2960—51no—
141#2932—51no—
142#2931D511yescharacteristic, complemented
143#2930—52no—
144#2929—52no—
145#2923—52no—
146#2921—51no—
147C4×#131—52no—
148C2×#405—51no—
149C23×D5C22×C411yescharacteristic
150C5×#41—24no—
151C5×#41—24no—
152C2×C5×Q8C22×C412yes—
153C2×C5×D4C22×C414yes—
154C2×C5×D4C22×C412yes—
155C2×C5×D4C22×C414yes—
156C22×C4×C5C22×C412yes—
157C22×C4×C5C2414yes—
158C22×C4×C5C2411yescharacteristic
159C2×C22⋊D5C22×C418yes—
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C418yes—
162C22×Dic5C22×C412yes—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5C22×C412yes—
166C2×C4×D5C2412yes—
167C2×Dic10C22×C414yes—
168C5×M16—24no—
169C5×M16—28no—
170C2×C5×C8—22no—
171C2×C5×C8—28no—
172C2×C5×C8#4114yes—
173C2×C5×C8C2414yes—
174C2×C5×C8C2412yes—
175C2×C5×C8C2411yescharacteristic
176C2×C5×C8C2411yescharacteristic
177C5×C4⋊C4C22×C414yes—
178C5×C22⋊C4C22×C418yes—
179C42×C5C22×C411yescharacteristic
180C42×C5C22×C411yescharacteristic
181C42×C5C2412yes—
182C22⋊Dic5C22×C418yes—
183C22⋊Dic5C22×C418yes—
184C22⋊Dic5C22×C414yes—
185#685C22×C414yes—
186#685C22×C414yes—
187#685C22×C418yes—
188C4⋊Dic5C22×C414yes—
189C4⋊Dic5C22×C414yes—
190C4⋊Dic5C22×C418yes—
191#683C22×C418yes—
192#683C22×C414yes—
193#683C22×C414yes—
194#683C22×C418yes—
195C4×Dic5C22×C412yes—
196C4×Dic5C22×C418yes—
197C4×Dic5C2412yes—
198C4×Dic5C2414yes—
199#681—24no—
200#681—28no—
201C2×#168—22no—
202C2×#168—28no—
203C2×#168#4114yes—
204C2×#168C2412yes—
205C2×#168C2414yes—
206C2×#168C2412yes—
207#676—28no—
208C8×D5—24no—
209C8×D5—24no—
210C2×#131—52no—
211C2×#131C2×D512yes—
212C22×M16—51no—
213C23×C8—51no—
214#542—54no—
215#541—52no—
216#540—52no—
217#539—54no—
218#538—54no—
219#533—51no—
220#532C2×D511yescharacteristic
221#529—58no—
222#525—52no—
223C4×#41—52no—
224C2×#117—51no—
225#446—58no—
226#446—54no—
227C8×Q8—54no—
228#436—58no—
229#436C2×D514yescomplemented
230#435—58no—
231#435—58no—
232#435—58no—
233C8×D4—58no—
234C8×D4C2×D514yescomplemented
235#433—58no—
236#433—58no—
237#432—58no—
238#424—52no—
239#424—52no—
240#423—51no—
241#423C2×D511yescharacteristic
242#408—52no—
243#408C2×D512yes—
244#407—52no—
245#405—52no—
246#405—54no—
247#405—52no—
248#405—54no—
249#405—54no—
250#405—54no—
251C4×M16—52no—
252C4×M16—54no—
253C2×#97—51no—
254C2×#97—51no—
255C2×C4×C8—51no—
256C2×C4×C8—54no—
257C2×C4×C8C2×D511yescharacteristic
258C23×C5C23×C414yes—
259C23×C5C23×C411yescharacteristic
260C22×D5—22no—
261C22×D5—42no—
262C22×D5C23×C412yes—
263C5×Q8—24no—
264C5×D4—28no—
265C5×D4—24no—
266C5×D4—44no—
267C2×C4×C5—24no—
268C2×C4×C5—24no—
269C2×C4×C5—42no—
270C2×C4×C5C23×C414yes—
271C2×C4×C5C23×C412yes—
272C2×C4×C5C23×C412yes—
273C2×C4×C5C23×C411yescharacteristic
274C2×C4×C5C2×#4112yes—
275C2×C4×C5C2×#4112yes—
276C2×C4×C5C2511yescharacteristic
277C22⋊D5—48no—
278C2×Dic5—22no—
279C2×Dic5—48no—
280C2×Dic5—42no—
281C2×Dic5C23×C414yes—
282C2×Dic5C23×C418yes—
283C2×Dic5C23×C412yes—
284C4×D5—24no—
285C4×D5—22no—
286C4×D5—22no—
287Dic10—44no—
288C5×C8—22no—
289C5×C8—24no—
290C5×C8C2×#4112yes—
291C5×C8C2×#4112yes—
292#168—22no—
293#168—24no—
294#168C2×#4114yes—
295C2×#41C22×D512yes—
296C23×C4—51no—
297#131—28no—
298#131—108no—
299C2×M16—52no—
300C2×M16—54no—
301C2×M16—54no—
302C2×M16—104no—
303C2×M16C22×D512yes—
304C2×M16C22×D514yes—
305C22×C8—51no—
306C22×C8—51no—
307C22×C8—54no—
308C22×C8—52no—
309C22×C8—52no—
310C22×C8—104no—
311C22×C8C22×D511yescharacteristic
312C22×C8C22×D514yes—
313C22×C8C22×D511yescharacteristic
314C4⋊Q8—52no—
315C4⋊Q8C4×D511yescharacteristic
316#127C4×D511yescharacteristic
317#126—58no—
318#126—58no—
319#125—58no—
320#125—52no—
321#124—58no—
322#124C4×D512yes—
323#123—54no—
324#123—58no—
325#123—58no—
326C22⋊Q8—54no—
327C22⋊Q8—54no—
328C22⋊Q8—58no—
329#121—54no—
330#121—58no—
331#121C4×D514yes—
332#120—54no—
333C4×Q8—54no—
334C4×Q8—54no—
335C4×D4—58no—
336C4×D4—54no—
337C4×D4—58no—
338C4×D4C22×D514yes—
339#117—52no—
340#117—54no—
341#117—52no—
342#117—52no—
343#117—54no—
344C2×C4⋊C4—52no—
345C2×C22⋊C4—52no—
346C2×C42—51no—
347C2×C42—54no—
348C2×C42C22×D511yescharacteristic
349C4⋊C8—58no—
350C4⋊C8—58no—
351C4⋊C8—54no—
352C4⋊C8C22×D514yes—
353C22⋊C8—58no—
354C22⋊C8—58no—
355C22⋊C8C22×D518yes—
356#97—54no—
357#97—54no—
358#97—54no—
359#97—54no—
360#97—54no—
361C4×C8—52no—
362C4×C8—54no—
363C4×C8—54no—
364C4×C8—52no—
365C4×C8—54no—
366C4×C8C22×D512yes—
367C4×C8C22×D512yes—
368C22×C5—22no—
369C22×C5—24no—
370C22×C5—28no—
371C22×C5C4×#4112yes—
372C22×C5C24×C411yescharacteristic
373C2×D5—22no—
374C2×D5—24no—
375C2×D5—44no—
376C4×C5—24no—
377C4×C5—22no—
378C4×C5—22no—
379C4×C5C4×#4112yes—
380C4×C5C22×#4111yescharacteristic
381C4×C5C22×#4111yescharacteristic
382Dic5—22no—
383Dic5—28no—
384Dic5—24no—
385C24—51no—
386#41—24no—
387#41—24no—
388C2×Q8—54no—
389C2×Q8C2×C4×D512yes—
390C2×D4—58no—
391C2×D4C2×C4×D514yes—
392C2×D4C2×C4×D512yes—
393C2×D4C2×C4×D514yes—
394C22×C4—51no—
395C22×C4—52no—
396C22×C4—58no—
397C22×C4—52no—
398C22×C4—52no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4C2×C4×D512yes—
402C22×C4C23×D514yes—
403C22×C4C23×D511yescharacteristic
404M16—24no—
405M16—28no—
406M16—108no—
407M16—108no—
408M16—104no—
409C2×C8—22no—
410C2×C8—28no—
411C2×C8—54no—
412C2×C8—52no—
413C2×C8—54no—
414C2×C8—52no—
415C2×C8—108no—
416C2×C8—102no—
417C2×C8—104no—
418C2×C8—104no—
419C2×C8#71114yes—
420C2×C8C23×D514yes—
421C2×C8C23×D512yes—
422C2×C8C23×D511yescharacteristic
423C2×C8C23×D511yescharacteristic
424C4⋊C4—54no—
425C4⋊C4—54no—
426C4⋊C4—54no—
427C4⋊C4—58no—
428C4⋊C4—58no—
429C4⋊C4—58no—
430C4⋊C4—54no—
431C4⋊C4C2×C4×D514yes—
432C22⋊C4—54no—
433C22⋊C4—58no—
434C22⋊C4—58no—
435C22⋊C4—54no—
436C22⋊C4—54no—
437C22⋊C4—58no—
438C22⋊C4C2×C4×D518yes—
439C42—52no—
440C42—58no—
441C42—52no—
442C42—54no—
443C42C2×C4×D511yescharacteristic
444C42C2×C4×D511yescharacteristic
445C42C23×D512yes—
446C2×C5—22no—
447C2×C5—44no—
448C2×C5C2×C4×#4111yescharacteristic
449C2×C5#357312yes—
450D5—42no—
451C23—52no—
452C23—102no—
453C23—202no—
454C23C22×C4×D514yes—
455C23C22×C4×D511yescharacteristic
456Q8—24no—
457Q8—204no—
458D4—28no—
459D4—24no—
460D4—44no—
461D4—208no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—42no—
465C2×C4—54no—
466C2×C4—58no—
467C2×C4—52no—
468C2×C4—102no—
469C2×C4—104no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—202no—
473C2×C4—208no—
474C2×C4C22×C4×D514yes—
475C2×C4C22×C4×D512yes—
476C2×C4C22×C4×D512yes—
477C2×C4C22×C4×D511yescharacteristic
478C2×C4C2×#71112yes—
479C2×C4D5×#4112yes—
480C2×C4C24×D511yescharacteristic
481C8—24no—
482C8—22no—
483C8—54no—
484C8—102no—
485C8—104no—
486C8C2×#71112yes—
487C8C2×#71112yes—
488C5#6020611yescharacteristic, complemented, Sylow
489C22—22no—
490C22—24no—
491C22—28no—
492C22—102no—
493C22—104no—
494C22—204no—
495C22C4×#71112yes—
496C22C23×C4×D511yescharacteristic
497C4—24no—
498C4—22no—
499C4—22no—
500C4—102no—
501C4—104no—
502C4—108no—
503C4C4×#71112yes—
504C4C22×#71111yescharacteristic
505C4C2×D5×#4111yescharacteristic
506C2—22no—
507C2—44no—
508C2—202no—
509C2C2×C4×#71111yescharacteristic
510C2#1061906112yes—
subgroupG/H
centerC2×C8C23×D5
commutator, socleC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC5×#2931C2
prime radical#10618137C2
cosocleC2×C4×C5C25
hypercenter#2931D5
hypocenterC5#60206
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. C5×#2931C2semidirect
3. #10615525C2semidirect
4. Dic5×#131C2semidirect
5. #10615007C2semidirect
6. #10611250C2semidirect
7. #10611131C2semidirect
8. #10610776C2semidirect
9. #10610770C2semidirect
10. #10610387C2semidirect
11. #10610380C2semidirect
12. C2×#64978C2semidirect
13. #10610176C2semidirect
29. C5×#436C22semidirect
30. C5×C8×D4C22semidirect
38. #65411C22semidirect
41. M16×Dic5C22semidirect
45. #65390C22semidirect
48. C2×C8×Dic5C22semidirect
49. #65300C22semidirect
53. #65117C22semidirect
56. #65009C22semidirect
57. #65008C22semidirect
60. #64968C22semidirect
61. C8×Dic10C22semidirect
142. #2931D5semidirect
229. #436C2×D5semidirect
234. C8×D4C2×D5semidirect
488. C5#60206semidirect

Maximal subgroups

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

subgroupindex
#106181372
C5×#29312
#106155252
Dic5×#1312
#106150072
#106112502
#106111312
#106107762
#106107702
#106103872
#106103802
C2×#649782
#106101762
#602065