Finite Group Databasebeta

← #13033822

Subgroups — #13033822

Order 1280.

998 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65737C212yesmaximal
2#10617184C211yesmaximal, characteristic, complemented
3#10617136C211yesmaximal, characteristic, complemented
4C4×#4062C211yesmaximal, characteristic
5#10604450C211yesmaximal, characteristic, complemented
6#10604416C211yesmaximal, characteristic, complemented
7#10604054C212yesmaximal, complemented
8#10603991C212yesmaximal, complemented
9#10603959C212yesmaximal, complemented
10C4×#3996C211yesmaximal, characteristic, complemented
11#10603838C211yesmaximal, characteristic, complemented
12C2×#4133C2212yes—
13C2×#4131C2212yes—
14C2×#4062C2211yescharacteristic
15C4×#713C2211yescharacteristic
16C4×#711C2211yescharacteristic
17C2×#4010C2212yes—
18C2×#4008C2212yes—
19C4×#704—21no—
20C2×#4002—21no—
21#65737C4116yescomplemented
22C2×#3996C2212yes—
23C2×#3992C2212yes—
24C2×C8×AGL(1,𝔽5)C2212yes—
25#65701—22no—
26#65701C2212yes—
27#65701C2212yes—
28#65691—22no—
29#65686C2211yescharacteristic
30C4×#700—21no—
31C4×#700C2211yescharacteristic
32C4×#700C2211yescharacteristic
33#65676—21no—
34#65676C2211yescharacteristic
35C4×C5×SD16C411yescharacteristic, complemented
36SD16×Dic5C411yescharacteristic, complemented
37C4×#689C411yescharacteristic, complemented
38C4×#686C411yescharacteristic, complemented
39#65149C2211yescharacteristic
40#65141C411yescharacteristic, complemented
41#65093C2211yescharacteristic
42#65079C411yescharacteristic, complemented
43#65061C2211yescharacteristic
44#65045C411yescharacteristic, complemented
45C4×#677C411yescharacteristic, complemented
46C4×C8×D5C2211yescharacteristic
47#64896C2212yes—
48#64875C2212yes—
49#64875C2212yes—
50#20513—51nomaximal, Sylow
51C2×#713C2311yescharacteristic
52C2×#711C2311yescharacteristic
53C2×#704—22no—
54C22×#170—22no—
55#4133—24no—
56#4133C2×C418yescomplemented
57#4131—24no—
58#4131C2×C418yescomplemented
59C2×C4×AGL(1,𝔽5)C2312yes—
60C2×#700—22no—
61C2×#700C2312yes—
62C2×#700C2312yes—
63C2×D5⋊C8—22no—
64C2×D5⋊C8C2312yes—
65C2×C5×SD16C2×C411yescharacteristic
66C4×C5×Q8C2×C411yescharacteristic
67C4×C5×D4C2×C411yescharacteristic
68Q8×Dic5C2×C411yescharacteristic
69C2×#689C2×C411yescharacteristic
70D4×Dic5C2×C411yescharacteristic
71C2×#686C2×C411yescharacteristic
72C4×C22⋊D5—21no—
73C2×C4×Dic5—21no—
74#4062C2×C418yes—
75C2×#677C2×C411yescharacteristic
76C2×C8×D5C2311yescharacteristic
77C2×C8×D5C2311yescharacteristic
78#4039—21no—
79#4039C2×C411yescharacteristic
80#4038—21no—
81#4038C2311yescharacteristic
82#4038C2311yescharacteristic
83#4033C2×C411yescharacteristic
84#4027—21no—
85#4023—21no—
86C4×D20—21no—
87C4×D20C2×C411yescharacteristic
88C42×D5—21no—
89C42×D5C2311yescharacteristic
90C4×Dic10C2×C411yescharacteristic
91#4010C2×C418yescomplemented
92#4008C2×C418yescomplemented
93(C2×AGL(1,𝔽5))⋊C4—21no—
94(C2×AGL(1,𝔽5))⋊C4—21no—
95#4002—22no—
96#4002—22no—
97#4002—21no—
98#4002—21no—
99#4002D411yescharacteristic
100#4002D411yescharacteristic
101#4002D412yes—
102C4×#170—22no—
103C4×#170—22no—
104C4×#170—21no—
105C4×#170—21no—
106#3996C2×C418yescomplemented
107#3992C2×C418yescomplemented
108C8×AGL(1,𝔽5)—24no—
109C5×#106C2×C411yescharacteristic
110C5×#103C2×C411yescharacteristic
111C5×#102C2×C411yescharacteristic
112C4×C5×C8C2×C411yescharacteristic
113#3967C2×C411yescharacteristic
114#3964C2×C411yescharacteristic
115#3953C2×C411yescharacteristic
116#3949C2×C411yescharacteristic
117#3948C2×C411yescharacteristic
118C8×Dic5C2×C411yescharacteristic
119C8×Dic5C2×C411yescharacteristic
120#3942C2×C411yescharacteristic
121#3941C2×C411yescharacteristic
122#3939C2×C411yescharacteristic
123#3939C2×C411yescharacteristic
124C4×#168C2×C411yescharacteristic
125C2×#444—52no—
126C4×#135—51no—
127#2875—51no—
128#2875—51no—
129C4×#108—51no—
130#1773—52no—
131#1764—52no—
132#1764—52no—
133#1759—51no—
134#1759—51no—
135#1726—51no—
136C22×AGL(1,𝔽5)—22no—
137C2×C5×Q8C22×C411yescharacteristic
138C2×C5×D4C22×C411yescharacteristic
139C22×C4×C5—21no—
140C2×C22⋊D5—21no—
141C22×Dic5—21no—
142C22×Dic5—21no—
143#713—22no—
144#713C22×C414yes—
145#711—22no—
146#711C22×C414yes—
147C2×D20—21no—
148C2×D20C22×C411yescharacteristic
149C2×C4×D5—21no—
150C2×C4×D5—21no—
151C2×C4×D5—21no—
152C2×C4×D5#4111yescharacteristic
153C2×C4×D5#4111yescharacteristic
154C2×C4×D5C2411yescharacteristic
155C2×Dic10C22×C411yescharacteristic
156#704—28no—
157C2×#170—22no—
158C2×#170—22no—
159C2×#170—28no—
160C2×#170C2×D412yes—
161C2×#170C2×D412yes—
162C4×AGL(1,𝔽5)—22no—
163C4×AGL(1,𝔽5)C22×C414yes—
164#700—22no—
165#700—22no—
166#700—28no—
167#700C22×C414yes—
168#700C22×C414yes—
169D5⋊C8—28no—
170D5⋊C8C22×C414yes—
171D5⋊C8#4114yes—
172C5×SD16C4214yes—
173C2×C5×C8C22×C411yescharacteristic
174C2×C5×C8C22×C411yescharacteristic
175C5×C4⋊C4—21no—
176C5×C4⋊C4C22×C411yescharacteristic
177C5×C4⋊C4C22×C411yescharacteristic
178C5×C22⋊C4—21no—
179C42×C5—21no—
180C42×C5C22×C411yescharacteristic
181C22⋊Dic5—21no—
182#689C4214yes—
183#686C4214yes—
184#685—21no—
185#685—21no—
186#685—21no—
187#685—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5C22×C411yescharacteristic
190C4⋊Dic5C22×C411yescharacteristic
191#683—21no—
192#683—21no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—21no—
197C4×Dic5—21no—
198C4×Dic5C22×C411yescharacteristic
199C4×Dic5C2×D411yescharacteristic
200C4×Dic5C2×D411yescharacteristic
201C2×#168C22×C411yescharacteristic
202C2×#168C22×C411yescharacteristic
203#677C4214yes—
204C8×D5—22no—
205C8×D5C22×C414yes—
206C2×#135—51no—
207C2×#131—52no—
208C2×#131—52no—
209C4×#41—51no—
210C4×#41—51no—
211#444—516no—
212C4×Q16—51no—
213C4×Q16—51no—
214C4×SD16—51no—
215C4×SD16—51no—
216C4×SD16—51no—
217C4×SD16AGL(1,𝔽5)11yescharacteristic, complemented
218C4×D8—51no—
219C4×D8—51no—
220C2×#108—52no—
221#427—51no—
222C2×#104—52no—
223C2×#104—52no—
224#416—51no—
225#416—51no—
226#405—52no—
227#405—52no—
228#405—102no—
229#405—102no—
230C4×M16—51no—
231C4×M16—51no—
232C4×M16—101no—
233C4×M16—101no—
234C2×#97—51no—
235C2×#97—52no—
236C2×#97—101no—
237C2×#97—101no—
238C2×C4×C8—51no—
239C2×C4×C8—52no—
240#376—51no—
241#341—52no—
242#339—52no—
243#339—52no—
244C23×C5—21no—
245C22×D5—21no—
246C22×D5C2×#4111yescharacteristic
247C2×AGL(1,𝔽5)—24no—
248C2×AGL(1,𝔽5)—42no—
249C2×AGL(1,𝔽5)—42no—
250C5×Q8—21no—
251C5×Q8C2×C4212yes—
252C5×D4—21no—
253C5×D4C2×C4212yes—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—81no—
258C2×C4×C5C4×D411yescharacteristic
259C2×C4×C5C4×D411yescharacteristic
260C2×C4×C5C23×C411yescharacteristic
261C22⋊D5—24no—
262C2×Dic5—21no—
263C2×Dic5—24no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—81no—
267C2×Dic5C4×D411yescharacteristic
268C2×Dic5C4×D411yescharacteristic
269C2×Dic5C22×D411yescharacteristic
270D20—24no—
271D20—21no—
272D20C2×C4212yes—
273C4×D5—24no—
274C4×D5—41no—
275C4×D5—41no—
276C4×D5—81no—
277C4×D5—81no—
278C4×D5C23×C412yes—
279C4×D5C2×#4112yes—
280Dic10—21no—
281Dic10C2×C4212yes—
282#170—24no—
283#170—24no—
284#170C4×D414yes—
285#170C4×D414yes—
286C5×C8—21no—
287C5×C8C2×C4212yes—
288#168—21no—
289#168C2×C4212yes—
290C2×#41—51no—
291C2×#41—51no—
292#135—58no—
293C2×Q16—51no—
294C2×SD16—51no—
295C2×SD16C2×AGL(1,𝔽5)11yescharacteristic
296C2×D8—51no—
297#131—58no—
298#131—58no—
299#131—104no—
300#131—104no—
301C2×M16—52no—
302C2×M16—52no—
303C2×M16—102no—
304C2×M16—102no—
305C22×C8—52no—
306C22×C8—51no—
307C22×C8—51no—
308C22×C8—102no—
309C22×C8—102no—
310C4×Q8—51no—
311C4×Q8—51no—
312C4×Q8—51no—
313C4×Q8C2×AGL(1,𝔽5)11yescharacteristic
314C4×D4—51no—
315C4×D4—51no—
316C4×D4—51no—
317C4×D4—101no—
318C4×D4—101no—
319C4×D4—101no—
320C4×D4—101no—
321C4×D4C2×AGL(1,𝔽5)11yescharacteristic
322#117—51no—
323#117—51no—
324#117—101no—
325#117—101no—
326C2×C42—51no—
327C2×C42—52no—
328C2×C42—101no—
329C2×C42—101no—
330#108—58no—
331#107—51no—
332#107—51no—
333#106—51no—
334#106C2×AGL(1,𝔽5)11yescharacteristic
335#104—58no—
336#104—58no—
337#103—51no—
338#103—51no—
339#103—51no—
340#103C2×AGL(1,𝔽5)11yescharacteristic
341#102—51no—
342#102—51no—
343#102—51no—
344#102C2×AGL(1,𝔽5)11yescharacteristic
345#97—51no—
346#97—51no—
347#97—52no—
348#97—58no—
349#97—101no—
350#97—101no—
351#97—102no—
352#97—102no—
353C4×C8—51no—
354C4×C8—51no—
355C4×C8—51no—
356C4×C8—101no—
357C4×C8—101no—
358C4×C8—104no—
359C4×C8—102no—
360C4×C8—102no—
361C4×C8C2×AGL(1,𝔽5)11yescharacteristic
362#95—101no—
363#95—101no—
364C22×C5—22no—
365C22×C5—41no—
366C22×C5—41no—
367C22×C5C2×C4×D411yescharacteristic
368C2×D5—21no—
369C2×D5—21no—
370C2×D5—22no—
371C2×D5—41no—
372C2×D5—41no—
373C2×D5C4×#4112yes—
374AGL(1,𝔽5)—44no—
375C4×C5—21no—
376C4×C5—21no—
377C4×C5—22no—
378C4×C5—41no—
379C4×C5—41no—
380C4×C5C22×C4211yescharacteristic
381C4×C5C4×#4111yescharacteristic
382Dic5—21no—
383Dic5—21no—
384Dic5—22no—
385Dic5—41no—
386Dic5—41no—
387Dic5C2×C4×D412yes—
388#41—54no—
389#41—54no—
390#41—102no—
391#41—102no—
392C2×Q8—51no—
393C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
394C2×D4—51no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4C22×AGL(1,𝔽5)11yescharacteristic
398C22×C4—21no—
399C22×C4—51no—
400C22×C4—51no—
401C22×C4—51no—
402C22×C4—101no—
403C22×C4—101no—
404C22×C4—101no—
405C22×C4—101no—
406C22×C4—102no—
407C22×C4—101no—
408Q16—54no—
409SD16—54no—
410SD16C4×AGL(1,𝔽5)14yes—
411D8—54no—
412M16—54no—
413M16—54no—
414M16—108no—
415M16—108no—
416M16—102no—
417M16—102no—
418C2×C8—52no—
419C2×C8—52no—
420C2×C8—54no—
421C2×C8—54no—
422C2×C8—51no—
423C2×C8—54no—
424C2×C8—51no—
425C2×C8—102no—
426C2×C8—108no—
427C2×C8—108no—
428C2×C8—102no—
429C2×C8—102no—
430C2×C8C22×AGL(1,𝔽5)11yescharacteristic
431C2×C8C22×AGL(1,𝔽5)11yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—51no—
434C4⋊C4—51no—
435C4⋊C4—101no—
436C4⋊C4—101no—
437C4⋊C4—101no—
438C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
439C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
440C22⋊C4—21no—
441C22⋊C4—101no—
442C22⋊C4—101no—
443C22⋊C4—101no—
444C22⋊C4—101no—
445C22⋊C4—101no—
446C42—21no—
447C42—51no—
448C42—51no—
449C42—51no—
450C42—54no—
451C42—101no—
452C42—101no—
453C42—101no—
454C42—101no—
455C42—102no—
456C42—101no—
457C42C22×AGL(1,𝔽5)11yescharacteristic
458C2×C5—42no—
459C2×C5C42×D411yescharacteristic
460C2×C5#295711yescharacteristic
461C2×C5#295711yescharacteristic
462D5—22no—
463D5—42no—
464C23—21no—
465C23—51no—
466C23—101no—
467Q8—21no—
468Q8—52no—
469Q8—101no—
470Q8C2×C4×AGL(1,𝔽5)12yes—
471D4—21no—
472D4—52no—
473D4—104no—
474D4—104no—
475D4—101no—
476D4C2×C4×AGL(1,𝔽5)12yes—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—51no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—81no—
486C2×C4—104no—
487C2×C4—104no—
488C2×C4—101no—
489C2×C4—104no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—201no—
493C2×C4—201no—
494C2×C4—202no—
495C2×C4—202no—
496C2×C4—401no—
497C2×C4—401no—
498C2×C4—401no—
499C2×C4D4×AGL(1,𝔽5)11yescharacteristic
500C2×C4D4×AGL(1,𝔽5)11yescharacteristic
501C2×C4C23×AGL(1,𝔽5)11yescharacteristic
502C8—21no—
503C8—54no—
504C8—54no—
505C8—52no—
506C8—104no—
507C8—104no—
508C8—101no—
509C8C2×C4×AGL(1,𝔽5)12yes—
510C5#2051311yescharacteristic, complemented, Sylow
511C22—22no—
512C22—41no—
513C22—41no—
514C22—52no—
515C22—101no—
516C22—101no—
517C22—102no—
518C22—201no—
519C22—201no—
520C22C2×D4×AGL(1,𝔽5)11yescharacteristic
521C4—22no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—52no—
527C4—102no—
528C4—101no—
529C4—101no—
530C4—204no—
531C4—201no—
532C4—201no—
533C4C22×C4×AGL(1,𝔽5)11yescharacteristic
534C4#41×AGL(1,𝔽5)11yescharacteristic
535C2—42no—
536C2—102no—
537C2—202no—
538C2C4×D4×AGL(1,𝔽5)11yescharacteristic
539C2#1061743111yescharacteristic
540C2#1061744511yescharacteristic
subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×SD16C4
socleC22×C5C2×C4×D4
prime radicalC2×#4062C22
cosocleC2×C4×D5C24
hypercenterC4×SD16AGL(1,𝔽5)
hypocenterC5#20513
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10617184C2semidirect
3. #10617136C2semidirect
5. #10604450C2semidirect
6. #10604416C2semidirect
7. #10604054C2semidirect
8. #10603991C2semidirect
9. #10603959C2semidirect
10. C4×#3996C2semidirect
11. #10603838C2semidirect
21. #65737C4semidirect
35. C4×C5×SD16C4semidirect
36. SD16×Dic5C4semidirect
37. C4×#689C4semidirect
38. C4×#686C4semidirect
40. #65141C4semidirect
42. #65079C4semidirect
44. #65045C4semidirect
45. C4×#677C4semidirect
56. #4133C2×C4semidirect
58. #4131C2×C4semidirect
91. #4010C2×C4semidirect
92. #4008C2×C4semidirect
106. #3996C2×C4semidirect
107. #3992C2×C4semidirect
217. C4×SD16AGL(1,𝔽5)semidirect
510. C5#20513semidirect

Maximal subgroups

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

subgroupindex
C2×#657372
#106171842
#106171362
C4×#40622
#106044502
#106044162
#106040542
#106039912
#106039592
C4×#39962
#106038382
#205135