Finite Group Databasebeta

← #11994113

Subgroups — #11994113

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65376C211yesmaximal, characteristic
2#10605369C211yesmaximal, characteristic
3C5×#1981C211yesmaximal, characteristic, complemented
4#10602580C211yesmaximal, characteristic, complemented
5C2×#64703C211yesmaximal, characteristic
6#10598193C211yesmaximal, characteristic, complemented
7#10598110C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4038—21no—
10C2×C4×D20C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×#103—21no—
13C2×C5×#103—21no—
14C4×C5×C4⋊C4C2211yescharacteristic
15#65376—22no—
16#65376C414yescomplemented
17#65276—21no—
18C2×#3941—21no—
19C2×#3939—21no—
20#65228—21no—
21#65224C2211yescharacteristic
22C4×C4⋊Dic5—21no—
23C2×C4⋊#168C2211yescharacteristic
24C2×C4×#168C2211yescharacteristic
25#64959—22no—
26#64749—22no—
27#64703—22no—
28#8984—51nomaximal, Sylow
29C22×C5×Q8—21no—
30C22×D20D411yescharacteristic
31C22×C4×D5—21no—
32C22×C5×C8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8C2×C412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C42×C5—21no—
42C2×C42×C5C2311yescharacteristic
43C2×#685—21no—
44C2×#685—22no—
45C2×#685—22no—
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5—21no—
48C2×C4⋊Dic5D411yescharacteristic
49C2×C4⋊Dic5D412yes—
50C2×C4×Dic5—22no—
51C22×#168—21no—
52C22×#168—21no—
53#4038—42no—
54#4038—42no—
55C4×D20—21no—
56C4×D20—21no—
57C4×D20C2×C412yes—
58C4×D20D412yes—
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×#103—42no—
62C5×#103—42no—
63C5×#95—21no—
64#3963—22no—
65#3941—24no—
66#3939—24no—
67C4⋊#168—21no—
68C4⋊#168C2×C412yes—
69C4×#168—21no—
70C4×#168—21no—
71C2×#474—51no—
72#2354—51no—
73#1990—51no—
74#1981D511yescharacteristic, complemented
75C2×D4⋊C8—51no—
76#1296—51no—
77#1279—51no—
78C23×D5—21no—
79C2×C5×Q8—22no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C2×C5×Q8—41no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—41no—
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×Dic5—21no—
92C22×Dic5—22no—
93C2×D20—21no—
94C2×D20—21no—
95C2×D20—21no—
96C2×D20—21no—
97C2×D20—21no—
98C2×D20C22⋊C412yes—
99C2×C4×D5—22no—
100C2×C4×D5—22no—
101C2×C4×D5—41no—
102C2×C4×D5—41no—
103C2×C4×D5—41no—
104C2×C4×D5—41no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4D812yes—
116C42×C5—41no—
117C42×C5—41no—
118C42×C5C22×C411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C42×C5#4111yescharacteristic
121C42×C5#4111yescharacteristic
122#685—22no—
123#685—22no—
124#685—44no—
125#685—82no—
126C4⋊Dic5—21no—
127C4⋊Dic5—41no—
128C4⋊Dic5—41no—
129C4⋊Dic5—41no—
130C4⋊Dic5—41no—
131C4⋊Dic5—42no—
132C4⋊Dic5C22⋊C412yes—
133C4×Dic5—44no—
134C2×#168—22no—
135C2×#168—22no—
136C2×#168—41no—
137C2×#168—41no—
138C2×#168—41no—
139C2×#168—41no—
140C2×C4⋊Q8C2×D511yescharacteristic
141C2×C4×D4—51no—
142C2×#117—101no—
143#474—54no—
144#474—102no—
145C2×#107—101no—
146C2×C4⋊C8—51no—
147C2×C4⋊C8C2×D511yescharacteristic
148C2×#103—21no—
149C2×#103—21no—
150C2×#102—101no—
151C2×C4×C8—51no—
152#390—101no—
153#388—102no—
154#384—51no—
155#380—101no—
156C4×C4⋊C4—101no—
157C4×C4⋊C4C2×D511yescharacteristic
158#340—102no—
159D4⋊C8—102no—
160C23×C5#12011yescharacteristic
161C22×D5—22no—
162C22×D5—41no—
163C22×D5—41no—
164C22×D5—41no—
165C22×D5—41no—
166C22×D5—41no—
167C22×D5—41no—
168C5×Q8—42no—
169C5×Q8—42no—
170C5×Q8—81no—
171C5×Q8—81no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—81no—
182C2×C4×C5—81no—
183C2×C4×C5C2×C22⋊C411yescharacteristic
184C2×C4×C5C4×D411yescharacteristic
185C2×C4×C5C4×D411yescharacteristic
186C2×C4×C5#12111yescharacteristic
187C2×C4×C5#12111yescharacteristic
188C2×C4×C5#12311yescharacteristic
189C2×C4×C5C2×D811yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5#13511yescharacteristic
192C2×C4×C5#13511yescharacteristic
193C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C5#13711yescharacteristic
196C2×C4×C5#13711yescharacteristic
197C2×Dic5—22no—
198C2×Dic5—41no—
199C2×Dic5—41no—
200C2×Dic5—42no—
201C2×Dic5—42no—
202C2×Dic5—42no—
203D20—22no—
204D20—22no—
205D20—41no—
206D20—41no—
207C4×D5—42no—
208C4×D5—42no—
209C4×D5—42no—
210C4×D5—42no—
211C5×C8—81no—
212#168—42no—
213#168—42no—
214C22×Q8—21no—
215C22×D4—51no—
216C23×C4—101no—
217C22×C8—21no—
218C22×C8—101no—
219C22×C8—101no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8C4×D512yes—
224C4×D4—52no—
225C4×D4—52no—
226C4×D4—101no—
227C4×D4—101no—
228#117—202no—
229#117—202no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—51no—
233C2×C4⋊C4—52no—
234C2×C4⋊C4—101no—
235C2×C4⋊C4—101no—
236C2×C4⋊C4C22⋊D511yescharacteristic
237C2×C4⋊C4C22⋊D511yescharacteristic
238C2×C22⋊C4—101no—
239C2×C22⋊C4—102no—
240C2×C22⋊C4—102no—
241C2×C42—21no—
242C2×C42—102no—
243C2×C42C22×D511yescharacteristic
244#107—104no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—52no—
248C4⋊C8—101no—
249#103—42no—
250#103—42no—
251#102—104no—
252C4×C8—101no—
253C4×C8—101no—
254#95—21no—
255#95—102no—
256C22×C5#38611yescharacteristic
257C22×C5#44711yescharacteristic
258C22×C5#44911yescharacteristic
259C22×C5#45211yescharacteristic
260C22×C5#45211yescharacteristic
261C22×C5#45511yescharacteristic
262C22×C5#45611yescharacteristic
263C2×D5—42no—
264C2×D5—42no—
265C2×D5—42no—
266C2×D5—81no—
267C2×D5—81no—
268C2×D5—81no—
269C2×D5—81no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—42no—
273C4×C5—82no—
274C4×C5—81no—
275C4×C5#41611yescharacteristic
276C4×C5#41911yescharacteristic
277C4×C5C4×D811yescharacteristic
278C4×C5#44211yescharacteristic
279C4×C5#45911yescharacteristic
280C4×C5#46311yescharacteristic
281C4×C5#48511yescharacteristic
282C4×C5#48511yescharacteristic
283Dic5—42no—
284Dic5—82no—
285C24—101no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—52no—
293C2×D4—101no—
294C2×D4—101no—
295C2×D4—101no—
296C2×D4—101no—
297C2×D4—101no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—101no—
302C22×C4—102no—
303C22×C4—102no—
304C22×C4—102no—
305C22×C4—201no—
306C22×C4—201no—
307C22×C4—201no—
308C22×C4—201no—
309C22×C4D4×D511yescharacteristic
310C22×C4D4×D511yescharacteristic
311C22×C4C2×C22⋊D511yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—102no—
316C2×C8—102no—
317C2×C8—201no—
318C2×C8—201no—
319C2×C8—201no—
320C2×C8—201no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—52no—
329C4⋊C4—101no—
330C4⋊C4—202no—
331C4⋊C4—201no—
332C4⋊C4—201no—
333C4⋊C4—201no—
334C4⋊C4—201no—
335C4⋊C4#68612yes—
336C22⋊C4—102no—
337C22⋊C4—102no—
338C22⋊C4—204no—
339C22⋊C4—402no—
340C42—41no—
341C42—41no—
342C42—204no—
343C42C2×C4×D511yescharacteristic
344C42#70911yescharacteristic
345C42D4×D511yescharacteristic
346C42#71111yescharacteristic
347C2×C5#164111yescharacteristic
348C2×C5#164611yescharacteristic
349C2×C5#164711yescharacteristic
350C2×C5#165211yescharacteristic
351C2×C5#187311yescharacteristic
352C2×C5#187911yescharacteristic
353C2×C5#188211yescharacteristic
354D5—82no—
355C23—102no—
356C23—201no—
357C23—201no—
358C23—201no—
359C23—201no—
360C23—201no—
361C23—201no—
362C23#408311yescharacteristic
363Q8—42no—
364Q8—42no—
365Q8—81no—
366Q8—81no—
367D4—102no—
368D4—102no—
369D4—201no—
370D4—201no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—102no—
383C2×C4—201no—
384C2×C4—201no—
385C2×C4—202no—
386C2×C4—202no—
387C2×C4—202no—
388C2×C4—202no—
389C2×C4—202no—
390C2×C4—202no—
391C2×C4—202no—
392C2×C4D5×C22⋊C411yescharacteristic
393C2×C4#402711yescharacteristic
394C2×C4#402911yescharacteristic
395C2×C4#403011yescharacteristic
396C2×C4#406111yescharacteristic
397C2×C4#406211yescharacteristic
398C2×C4#406411yescharacteristic
399C2×C4#406511yescharacteristic
400C2×C4C4×C22⋊D511yescharacteristic
401C2×C4C2×#68611yescharacteristic
402C2×C4#407811yescharacteristic
403C2×C4#408411yescharacteristic
404C2×C4#409511yescharacteristic
405C2×C4#409611yescharacteristic
406C8—81no—
407C8—202no—
408C8—202no—
409C5#898411yescharacteristic, complemented, Sylow
410C22—202no—
411C22—202no—
412C22—202no—
413C22—401no—
414C22—401no—
415C22—401no—
416C22—401no—
417C22#6524511yescharacteristic
418C22#6532511yescharacteristic
419C22#6532611yescharacteristic
420C22#6546211yescharacteristic
421C22#6547611yescharacteristic
422C22#6549111yescharacteristic
423C22#6549411yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—81no—
429C4—202no—
430C4—402no—
431C4#6509111yescharacteristic
432C4#6509311yescharacteristic
433C4#6510311yescharacteristic
434C4#6510411yescharacteristic
435C4C4×#68611yescharacteristic
436C4#6530311yescharacteristic
437C4#6534611yescharacteristic
438C4#6536111yescharacteristic
439C2—402no—
440C2#1060045011yescharacteristic
441C2#1060106211yescharacteristic
442C2#1060114111yescharacteristic
443C2#1060184011yescharacteristic
444C2#1060184111yescharacteristic
445C2#1060185411yescharacteristic
446C2#1060185911yescharacteristic
subgroupG/H
centerC23#4083
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1981C2
socleC23×C5#120
prime radicalC22×D20D4
cosocleC2×C42×C5C23
hypercenter#1981D5
hypocenterC5#8984
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. C5×#1981C2semidirect
4. #10602580C2semidirect
6. #10598193C2semidirect
7. #10598110C2semidirect
16. #65376C4semidirect
74. #1981D5semidirect
409. C5#8984semidirect

Maximal subgroups

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

subgroupindex
C2×#653762
#106053692
C5×#19812
#106025802
C2×#647032
#105981932
#105981102
#89845