Finite Group Databasebeta

← #12963832

Subgroups — #12963832

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#10618174C211yesmaximal, characteristic
2C5×#2961C211yesmaximal, characteristic, complemented
3#10615059C211yesmaximal, characteristic, complemented
4#10611671C218yesmaximal, complemented
5#10611670C218yesmaximal, complemented
6#10610804C212yesmaximal, complemented
7#10610802C212yesmaximal, complemented
8#10610772C211yesmaximal, characteristic, complemented
9#10610770C211yesmaximal, characteristic, complemented
10#10610285C212yesmaximal, complemented
11#10610280C212yesmaximal, complemented
12#10610222C211yesmaximal, characteristic, complemented
13C2×#64997C211yesmaximal, characteristic, complemented
14C5×#533C2211yescharacteristic
15C2×#4053C2212yes—
16C2×#4047C2212yes—
17C22×#676C2211yescharacteristic
18C22×C8×D5C2211yescharacteristic
19#66067C414yes—
20#66032C412yes—
21#66031C412yes—
22#65979C414yes—
23#65978C414yes—
24#65914C2218yes—
25#65858C2212yes—
26#65856C2212yes—
27#65811C2211yescharacteristic
28C2×#4018C2211yescharacteristic
29C5×#446C2218yescomplemented
30C5×#424C2212yes—
31C5×#423C2211yescharacteristic
32C5×#405C2212yes—
33C2×C5×#97C2211yescharacteristic
34#65418C2212yes—
35#65415C2212yes—
36M16×Dic5C2212yes—
37#65399C2212yes—
38C2×#3947C2211yescharacteristic
39C2×C8×Dic5C2211yescharacteristic
40#65313C2214yescomplemented
41Q8×#168C2214yescomplemented
42#65288C2212yes—
43#65286C2212yes—
44#65213C2211yescharacteristic
45C2×C4×#168C2211yescharacteristic
46#65129C2218yes—
47#65129C2218yescomplemented
48#65127C2214yescomplemented
49#65125C2218yes—
50#65124C2218yescomplemented
51#65123C2218yes—
52#65123C2214yescomplemented
53#64997C2214yes—
54#64997C2214yes—
55#64997C2214yescomplemented
56#64996C2214yescomplemented
57#64995C2218yes—
58#64995C2218yescomplemented
59#64978C2214yescomplemented
60#64977C2218yes—
61C4×C8×D5C2214yescomplemented
62#60206—51nomaximal, Sylow
63C2×#709C2312yes—
64C22×C4×D5C2311yescharacteristic
65C2×C5×M16C2312yes—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C5×C4⋊Q8C2×C412yes—
69C5×#125C2×C412yes—
70C5×C22⋊Q8C2×C414yes—
71C4×C5×Q8C2314yes—
72C5×#117C2312yes—
73C2×C42×C5C2311yescharacteristic
74#4093C2×C418yes—
75#4092C2×C418yes—
76#4076C2×C414yes—
77C2×#685C2×C412yes—
78C2×#683C2×C412yes—
79C2×C4×Dic5C2311yescharacteristic
80C2×#681C2312yes—
81C22×#168C2311yescharacteristic
82C22×#168C2311yescharacteristic
83#4053—28no—
84#4047—28no—
85C2×#676—24no—
86C2×#676C2314yes—
87C2×#676C2314yes—
88C2×#676C2314yes—
89C2×C8×D5—24no—
90C2×C8×D5C2312yes—
91C2×C8×D5C2312yes—
92C2×C8×D5C2314yes—
93C2×C8×D5C2314yes—
94#4044C2×C418yes—
95#4044C2×C418yes—
96#4043C2×C414yes—
97#4041C2×C414yes—
98#4041C2×C418yes—
99#4040C2×C418yes—
100#4040C2×C418yes—
101#4039C2×C414yes—
102#4036C2×C418yes—
103#4033C2×C414yes—
104#4032C2×C414yes—
105#4028C2×C414yes—
106#4027C2×C418yes—
107#4021C2×C412yes—
108#4020C2×C411yescharacteristic
109C4×D20C2314yes—
110C4×D20C2318yes—
111#4018C2×C412yes—
112#4018C2×C412yes—
113#4018C2314yes—
114#4018C2314yes—
115C42×D5C2314yes—
116#4015C2×C411yescharacteristic
117C5×C4⋊C8C2314yes—
118C5×C4⋊C8C2318yes—
119C5×#97C2314yes—
120C5×#97C2314yes—
121C4×C5×C8C2314yes—
122#3952C2318yes—
123#3952C2318yes—
124#3952C2318yes—
125#3947C2314yes—
126#3947C2314yes—
127C8×Dic5C2314yes—
128C8×Dic5C2312yes—
129C8×Dic5C2312yes—
130C4⋊#168C2318yes—
131C4⋊#168C2314yes—
132#3935C2314yes—
133C4×#168C2314yes—
134C4×#168C2312yes—
135C4×#168C2312yes—
136#3455—51no—
137#2967—58no—
138#2966—58no—
139#2961D511yescharacteristic, complemented
140#2960—51no—
141#2932—51no—
142#2931—51no—
143#2930—52no—
144#2929—52no—
145#2923—52no—
146#2921—51no—
147C4×#131—52no—
148C2×#405—51no—
149C23×D5C22×C411yescharacteristic
150C2×C5×Q8C22×C414yes—
151C22×C4×C5C22×C412yes—
152C22×C4×C5C2411yescharacteristic
153C2×C22⋊D5C22×C414yes—
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C412yes—
156#709—24no—
157#709—24no—
158C2×D20C22×C412yes—
159C2×D20C22×C414yes—
160C2×D20C22×C418yes—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5C22×C412yes—
164C2×C4×D5C22×C418yes—
165C2×C4×D5C2412yes—
166C2×C4×D5C2414yes—
167C2×Dic10C22×C412yes—
168C5×M16—24no—
169C2×C5×C8—22no—
170C2×C5×C8#4114yes—
171C2×C5×C8C2412yes—
172C2×C5×C8C2414yes—
173C2×C5×C8C2412yes—
174C5×C4⋊C4C22×C414yes—
175C5×C4⋊C4C22×C418yes—
176C5×C4⋊C4C22×C414yes—
177C5×C22⋊C4C22×C414yes—
178C42×C5C22×C411yescharacteristic
179C42×C5C22×C411yescharacteristic
180C42×C5C2412yes—
181C42×C5C2414yes—
182#685C22×C414yes—
183#685C22×C414yes—
184#685C22×C418yes—
185#685C22×C418yes—
186#685C22×C418yes—
187#685C22×C418yes—
188C4⋊Dic5C22×C414yes—
189C4⋊Dic5C22×C418yes—
190#683C22×C414yes—
191#683C22×C414yes—
192#683C22×C418yes—
193C4×Dic5C22×C418yes—
194C4×Dic5C22×C412yes—
195C4×Dic5C2412yes—
196#681—24no—
197C2×#168—22no—
198C2×#168#4114yes—
199C2×#168C2412yes—
200C2×#168C2414yes—
201C2×#168C2411yescharacteristic
202C2×#168C2411yescharacteristic
203#676—28no—
204#676—28no—
205#676—28no—
206C8×D5—28no—
207C8×D5—24no—
208C8×D5—24no—
209C8×D5—28no—
210C2×#131—52no—
211C2×#131—52no—
212C22×M16—51no—
213C23×C8—51no—
214#542—54no—
215#541—52no—
216#540—52no—
217#539—54no—
218#538—54no—
219#533C2×D511yescharacteristic
220#532—51no—
221#529—58no—
222#525—52no—
223C4×#41—52no—
224C2×#117—51no—
225#446—54no—
226#446C2×D518yescomplemented
227C8×Q8—54no—
228#436—54no—
229#436—58no—
230#435—58no—
231#435—58no—
232#435—58no—
233C8×D4—58no—
234C8×D4—54no—
235#433—58no—
236#433—58no—
237#432—58no—
238#424—52no—
239#424C2×D512yes—
240#423—51no—
241#423C2×D511yescharacteristic
242#408—52no—
243#408—52no—
244#407—52no—
245#405—52no—
246#405—54no—
247#405—54no—
248#405—54no—
249#405—54no—
250#405C2×D512yes—
251C4×M16—52no—
252C4×M16—54no—
253C2×#97—51no—
254C2×#97C2×D511yescharacteristic
255C2×C4×C8—51no—
256C2×C4×C8—51no—
257C2×C4×C8—54no—
258C23×C5C23×C411yescharacteristic
259C22×D5—22no—
260C22×D5—42no—
261C22×D5C23×C412yes—
262C22×D5C23×C414yes—
263C5×Q8—44no—
264C2×C4×C5—42no—
265C2×C4×C5C23×C418yes—
266C2×C4×C5C23×C412yes—
267C2×C4×C5C23×C412yes—
268C2×C4×C5C23×C411yescharacteristic
269C2×C4×C5C2×#4112yes—
270C2×C4×C5C2×#4112yes—
271C2×C4×C5C2511yescharacteristic
272C22⋊D5—28no—
273C2×Dic5—22no—
274C2×Dic5—42no—
275C2×Dic5C23×C414yes—
276C2×Dic5C23×C414yes—
277C2×Dic5C23×C412yes—
278D20—24no—
279D20—48no—
280D20—44no—
281C4×D5—24no—
282C4×D5—22no—
283C4×D5—24no—
284C4×D5—24no—
285C4×D5—22no—
286C4×D5—48no—
287Dic10—24no—
288C5×C8—22no—
289C5×C8—24no—
290C5×C8C2×#4114yes—
291#168—24no—
292#168—22no—
293#168C2×#4112yes—
294#168C2×#4112yes—
295C2×#41—52no—
296C23×C4—51no—
297#131—108no—
298#131—108no—
299C2×M16—52no—
300C2×M16—54no—
301C2×M16—54no—
302C2×M16—54no—
303C2×M16—104no—
304C2×M16C22×D512yes—
305C22×C8—51no—
306C22×C8—51no—
307C22×C8—52no—
308C22×C8—52no—
309C22×C8—54no—
310C22×C8—54no—
311C22×C8—104no—
312C22×C8C22×D511yescharacteristic
313C22×C8C22×D511yescharacteristic
314C4⋊Q8—51no—
315C4⋊Q8C4×D512yes—
316#127—51no—
317#126—58no—
318#126—58no—
319#125—58no—
320#125C4×D512yes—
321#124—58no—
322#124—52no—
323#123—58no—
324#123—58no—
325#123—54no—
326C22⋊Q8—58no—
327C22⋊Q8—54no—
328C22⋊Q8C4×D514yes—
329#121—54no—
330#121—54no—
331#121—58no—
332#120—54no—
333C4×Q8—54no—
334C4×Q8C22×D514yes—
335C4×D4—54no—
336C4×D4—58no—
337C4×D4—58no—
338C4×D4—54no—
339#117—52no—
340#117—52no—
341#117—54no—
342#117—54no—
343#117C22×D512yes—
344C2×C4⋊C4—52no—
345C2×C22⋊C4—52no—
346C2×C42—51no—
347C2×C42—54no—
348C2×C42C22×D511yescharacteristic
349C4⋊C8—54no—
350C4⋊C8—58no—
351C4⋊C8C22×D514yes—
352C4⋊C8C22×D518yes—
353C22⋊C8—58no—
354C22⋊C8—58no—
355C22⋊C8—58no—
356#97—54no—
357#97—54no—
358#97—54no—
359#97C22×D514yes—
360#97C22×D514yes—
361C4×C8—52no—
362C4×C8—52no—
363C4×C8—54no—
364C4×C8—52no—
365C4×C8—54no—
366C4×C8—52no—
367C4×C8C22×D514yes—
368C22×C5—22no—
369C22×C5C4×#4112yes—
370C22×C5C24×C411yescharacteristic
371C2×D5—22no—
372C2×D5—24no—
373C2×D5—28no—
374C2×D5—24no—
375C2×D5—44no—
376C4×C5—28no—
377C4×C5—22no—
378C4×C5—22no—
379C4×C5C4×#4112yes—
380C4×C5C22×#4111yescharacteristic
381C4×C5C22×#4111yescharacteristic
382Dic5—24no—
383Dic5—22no—
384Dic5—24no—
385C24—51no—
386#41—104no—
387#41—104no—
388C2×Q8—52no—
389C2×Q8C2×C4×D514yes—
390C2×D4—54no—
391C2×D4—52no—
392C2×D4—58no—
393C2×D4—54no—
394C22×C4—51no—
395C22×C4—52no—
396C22×C4—52no—
397C22×C4—54no—
398C22×C4—52no—
399C22×C4—58no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4C2×C4×D512yes—
403C22×C4C23×D511yescharacteristic
404M16—24no—
405M16—108no—
406M16—104no—
407M16—108no—
408M16—108no—
409C2×C8—22no—
410C2×C8—54no—
411C2×C8—51no—
412C2×C8—51no—
413C2×C8—54no—
414C2×C8—52no—
415C2×C8—104no—
416C2×C8—104no—
417C2×C8—108no—
418C2×C8—102no—
419C2×C8—108no—
420C2×C8#71314yes—
421C2×C8C23×D514yes—
422C2×C8C23×D512yes—
423C2×C8C23×D512yes—
424C4⋊C4—54no—
425C4⋊C4—54no—
426C4⋊C4—58no—
427C4⋊C4—54no—
428C4⋊C4—58no—
429C4⋊C4C2×C4×D514yes—
430C4⋊C4C2×C4×D518yes—
431C4⋊C4C2×C4×D514yes—
432C22⋊C4—54no—
433C22⋊C4—54no—
434C22⋊C4—58no—
435C22⋊C4—58no—
436C22⋊C4—58no—
437C22⋊C4—58no—
438C22⋊C4C2×C4×D514yes—
439C42—52no—
440C42—58no—
441C42—52no—
442C42C2×C4×D511yescharacteristic
443C42C2×C4×D511yescharacteristic
444C42C23×D512yes—
445C42C23×D514yes—
446C2×C5—22no—
447C2×C5C2×C4×#4111yescharacteristic
448C2×C5#357312yes—
449D5—44no—
450D5—42no—
451C23—52no—
452C23—54no—
453C23—102no—
454C23—202no—
455C23C22×C4×D511yescharacteristic
456Q8—44no—
457Q8—104no—
458D4—108no—
459D4—104no—
460D4—204no—
461D4—208no—
462C2×C4—42no—
463C2×C4—54no—
464C2×C4—54no—
465C2×C4—52no—
466C2×C4—102no—
467C2×C4—104no—
468C2×C4—104no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—104no—
472C2×C4—208no—
473C2×C4—202no—
474C2×C4C22×C4×D518yes—
475C2×C4C22×C4×D512yes—
476C2×C4C22×C4×D512yes—
477C2×C4C22×C4×D511yescharacteristic
478C2×C4C2×#71312yes—
479C2×C4D5×#4112yes—
480C2×C4C24×D511yescharacteristic
481C8—22no—
482C8—24no—
483C8—52no—
484C8—52no—
485C8—102no—
486C8—104no—
487C8C2×#71314yes—
488C5#6020611yescharacteristic, complemented, Sylow
489C22—22no—
490C22—102no—
491C22—104no—
492C22—108no—
493C22—104no—
494C22—204no—
495C22C4×#71312yes—
496C22C23×C4×D511yescharacteristic
497C4—22no—
498C4—22no—
499C4—28no—
500C4—102no—
501C4—104no—
502C4—104no—
503C4C4×#71312yes—
504C4C22×#71311yescharacteristic
505C4C2×D5×#4111yescharacteristic
506C2—22no—
507C2—202no—
508C2—204no—
509C2C2×C4×#71311yescharacteristic
510C2#1061906712yes—
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
FittingC5×#2961C2
prime radical#10618174C2
cosocleC2×C4×C5C25
hypercenter#2961D5
hypocenterC5#60206
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. C5×#2961C2semidirect
3. #10615059C2semidirect
4. #10611671C2semidirect
5. #10611670C2semidirect
6. #10610804C2semidirect
7. #10610802C2semidirect
8. #10610772C2semidirect
9. #10610770C2semidirect
10. #10610285C2semidirect
11. #10610280C2semidirect
12. #10610222C2semidirect
13. C2×#64997C2semidirect
29. C5×#446C22semidirect
40. #65313C22semidirect
41. Q8×#168C22semidirect
47. #65129C22semidirect
48. #65127C22semidirect
50. #65124C22semidirect
52. #65123C22semidirect
55. #64997C22semidirect
56. #64996C22semidirect
58. #64995C22semidirect
59. #64978C22semidirect
61. C4×C8×D5C22semidirect
139. #2961D5semidirect
226. #446C2×D5semidirect
488. C5#60206semidirect

Maximal subgroups

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

subgroupindex
#106181742
C5×#29612
#106150592
#106116712
#106116702
#106108042
#106108022
#106107722
#106107702
#106102852
#106102802
#106102222
C2×#649972
#602065