Finite Group Databasebeta

← #11995383

Subgroups — #11995383

Order 1280.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C8×#41C211yesmaximal, characteristic
2#10614238C211yesmaximal, characteristic
3#10602439C211yesmaximal, characteristic
4#10601585C211yesmaximal, characteristic, complemented
5#10600531C211yesmaximal, characteristic, complemented
6#10598236C211yesmaximal, characteristic, complemented
7#10598146C211yesmaximal, characteristic, complemented
8C4×C5×#41C2211yescharacteristic
9#65804C2211yescharacteristic
10C5×C8×Q8—21no—
11C5×C8×D4—22no—
12C5×C8×D4—21no—
13C5×#431—21no—
14C5×#431C2211yescharacteristic
15C2×C4×C5×C8—21no—
16C2×C4×C5×C8C2211yescharacteristic
17C2×#3969—21no—
18#65522—21no—
19#65311—21no—
20#65310C411yescharacteristic, complemented
21#65309C411yescharacteristic, complemented
22#65298—21no—
23#65297C411yescharacteristic, complemented
24#65296C411yescharacteristic, complemented
25#65287—21no—
26C4×C4⋊Dic5C2211yescharacteristic
27#65213C2211yescharacteristic
28C2×C4⋊#168C2211yescharacteristic
29#64752—21no—
30#64687—22no—
31#64676—21no—
32#64676—21no—
33#9207—51nomaximal, Sylow
34C2×C5×#41D411yescharacteristic
35C22×C5×C8—22no—
36C22×C5×C8—21no—
37C4×C5×Q8C2×C411yescharacteristic
38C4×C5×Q8D411yescharacteristic
39C4×C5×D4—21no—
40C4×C5×D4—21no—
41C4×C5×D4C2×C411yescharacteristic
42C4×C5×D4D411yescharacteristic
43C5×#117—21no—
44C5×#117D411yescharacteristic
45C2×C42×C5—21no—
46C2×C42×C5C2311yescharacteristic
47#4072—21no—
48C2×C4⋊Dic5—21no—
49#4070—21no—
50#4070—21no—
51C2×C4×Dic5—21no—
52C2×#681—21no—
53C22×#168—21no—
54#4016—21no—
55#4015C2×C411yescharacteristic
56#4015C2×C411yescharacteristic
57C4×Dic10—21no—
58C4×Dic10—21no—
59C5×C4⋊C8—22no—
60C5×C4⋊C8—21no—
61C5×C22⋊C8—22no—
62C5×C22⋊C8D412yes—
63C4×C5×C8—22no—
64C4×C5×C8—21no—
65C4×C5×C8—21no—
66C4×C5×C8D411yescharacteristic
67C4×C5×C8D411yescharacteristic
68#3969—42no—
69#3967—21no—
70#3967—21no—
71#3964—21no—
72#3964—21no—
73#3963—21no—
74#3940—21no—
75#3940—21no—
76#3939—21no—
77#3939—21no—
78C4⋊#168—21no—
79C4⋊#168—21no—
80C4⋊#168—21no—
81C4⋊#168C2×C411yescharacteristic
82C4⋊#168C2×C411yescharacteristic
83#3076—51no—
84C8×#41D511yescharacteristic
85#1806—51no—
86#1503—51no—
87#1493—51no—
88#1301—51no—
89#1279—51no—
90C5×#41—21no—
91C5×#41—21no—
92C5×#41SD1612yes—
93C5×#41Q1612yes—
94C2×C5×Q8C22⋊C411yescharacteristic
95C2×C5×D4—21no—
96C2×C5×D4C22⋊C411yescharacteristic
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5#4111yescharacteristic
103C22×Dic5—41no—
104C2×Dic10—21no—
105C2×Dic10—21no—
106C2×C5×C8—21no—
107C2×C5×C8—22no—
108C2×C5×C8—21no—
109C2×C5×C8—42no—
110C2×C5×C8—44no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4C22⋊C411yescharacteristic
114C5×C4⋊C4C22⋊C411yescharacteristic
115C5×C22⋊C4—21no—
116C5×C22⋊C4—21no—
117C5×C22⋊C4—21no—
118C42×C5—21no—
119C42×C5—21no—
120C42×C5—21no—
121C42×C5C22×C411yescharacteristic
122C42×C5C2×D411yescharacteristic
123C42×C5C2×D411yescharacteristic
124C42×C5#4111yescharacteristic
125C22⋊Dic5—41no—
126C4⋊Dic5—22no—
127C4⋊Dic5—21no—
128C4⋊Dic5—21no—
129C4⋊Dic5—21no—
130C4⋊Dic5—21no—
131C4⋊Dic5—41no—
132#683—41no—
133#683—41no—
134C4×Dic5—41no—
135C4×Dic5—41no—
136C4×Dic5—41no—
137#681—41no—
138#681—41no—
139C2×#168—21no—
140C2×#168—21no—
141C2×#168—41no—
142C2×#168—41no—
143C2×#168—41no—
144#533—51no—
145C4×#41C2×D511yescharacteristic
146#479—101no—
147#478—101no—
148#477—51no—
149#476—51no—
150#475—51no—
151#474—51no—
152C8×Q8—21no—
153C8×D4—21no—
154C8×D4—22no—
155#431—21no—
156#431C2×D511yescharacteristic
157#427—101no—
158#423—51no—
159C2×C4⋊C8—51no—
160C2×#104—101no—
161#416—101no—
162C2×C4×C8—21no—
163C2×C4×C8C2×D511yescharacteristic
164C4×C4⋊C4—51no—
165#339—101no—
166#328—102no—
167Q8⋊C8—101no—
168Q8⋊C8—101no—
169C23×C5—21no—
170C23×C5#12111yescharacteristic
171C5×Q8—21no—
172C5×Q8#10312yes—
173C5×D4—22no—
174C5×D4—22no—
175C5×D4—21no—
176C5×D4#10312yes—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—22no—
181C2×C4×C5—22no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—41no—
185C2×C4×C5—42no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5C2×C22⋊C411yescharacteristic
189C2×C4×C5C4×D411yescharacteristic
190C2×C4×C5C4×D411yescharacteristic
191C2×C4×C5#12011yescharacteristic
192C2×C4×C5#12111yescharacteristic
193C2×C4×C5#12311yescharacteristic
194C2×C4×C5C2×SD1611yescharacteristic
195C2×C4×C5C2×Q1611yescharacteristic
196C2×C4×C5#13511yescharacteristic
197C2×C4×C5#13511yescharacteristic
198C2×Dic5—42no—
199C2×Dic5—41no—
200C2×Dic5—41no—
201C2×Dic5—81no—
202C2×Dic5—81no—
203Dic10—41no—
204Dic10—41no—
205Dic10—81no—
206C5×C8—22no—
207C5×C8—42no—
208C5×C8—41no—
209#168—41no—
210#168—41no—
211#168—81no—
212C2×#41D2011yescharacteristic
213C2×M16—101no—
214C22×C8—22no—
215C22×C8—21no—
216C22×C8—101no—
217C4⋊Q8—51no—
218C4⋊Q8—51no—
219#125—101no—
220C22⋊Q8—101no—
221C22⋊Q8—101no—
222C4×Q8—101no—
223C4×Q8—101no—
224C4×Q8C4×D511yescharacteristic
225C4×Q8C22⋊D511yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4C4×D511yescharacteristic
229C4×D4C22⋊D511yescharacteristic
230#117—21no—
231#117—101no—
232#117D2011yescharacteristic
233C2×C4⋊C4—101no—
234C2×C42—21no—
235C2×C42—101no—
236C2×C42C22×D511yescharacteristic
237#107—101no—
238#107—101no—
239#106—101no—
240#106—101no—
241C4⋊C8—22no—
242C4⋊C8—21no—
243C4⋊C8—51no—
244C4⋊C8—51no—
245C4⋊C8—101no—
246C4⋊C8—101no—
247C4⋊C8—101no—
248#104—202no—
249#103—101no—
250#103—101no—
251#102—101no—
252#102—101no—
253C22⋊C8—22no—
254C22⋊C8C22⋊D512yes—
255C4×C8—22no—
256C4×C8—21no—
257C4×C8—21no—
258C4×C8C22⋊D511yescharacteristic
259C4×C8C22⋊D511yescharacteristic
260#95—101no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—22no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5#38611yescharacteristic
267C22×C5#46511yescharacteristic
268C22×C5#46711yescharacteristic
269C4×C5—21no—
270C4×C5—22no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—41no—
274C4×C5—41no—
275C4×C5C2×#10311yescharacteristic
276C4×C5#41611yescharacteristic
277C4×C5#44311yescharacteristic
278C4×C5#44411yescharacteristic
279C4×C5#46511yescharacteristic
280C4×C5#46711yescharacteristic
281Dic5—82no—
282Dic5—81no—
283Dic5—81no—
284#41—21no—
285#41—21no—
286#41#67712yes—
287#41Dic2012yes—
288C2×Q8—101no—
289C2×Q8—101no—
290C2×Q8#68511yescharacteristic
291C2×D4—21no—
292C2×D4#68511yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—201no—
297C22×C4C2×D2011yescharacteristic
298C22×C4#70911yescharacteristic
299C22×C4C2×C22⋊D511yescharacteristic
300M16—201no—
301M16—201no—
302C2×C8—21no—
303C2×C8—22no—
304C2×C8—21no—
305C2×C8—42no—
306C2×C8—44no—
307C2×C8—101no—
308C2×C8—101no—
309C2×C8—201no—
310C2×C8—201no—
311C2×C8—201no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—102no—
315C4⋊C4—101no—
316C4⋊C4—101no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C4⋊C4—201no—
320C4⋊C4—201no—
321C4⋊C4—201no—
322C4⋊C4#68511yescharacteristic
323C4⋊C4#68511yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—201no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—201no—
332C42—201no—
333C42—201no—
334C42C2×C4×D511yescharacteristic
335C42#70911yescharacteristic
336C42C2×C22⋊D511yescharacteristic
337C42C2×C22⋊D511yescharacteristic
338C2×C5—21no—
339C2×C5—21no—
340C2×C5—42no—
341C2×C5#187611yescharacteristic
342C2×C5#189211yescharacteristic
343C2×C5#190611yescharacteristic
344C23—21no—
345C23#407611yescharacteristic
346Q8—21no—
347Q8—201no—
348Q8—201no—
349Q8—401no—
350Q8#394812yes—
351D4—22no—
352D4—22no—
353D4—21no—
354D4#394812yes—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—202no—
367C2×C4—201no—
368C2×C4—201no—
369C2×C4—401no—
370C2×C4—401no—
371C2×C4C2×#67711yescharacteristic
372C2×C4#405011yescharacteristic
373C2×C4#405011yescharacteristic
374C2×C4C2×Dic2011yescharacteristic
375C2×C4C2×#68511yescharacteristic
376C2×C4C4×C22⋊D511yescharacteristic
377C2×C4C4×C22⋊D511yescharacteristic
378C2×C4#407511yescharacteristic
379C2×C4#407611yescharacteristic
380C2×C4#409911yescharacteristic
381C8—22no—
382C8—42no—
383C8—41no—
384C8—201no—
385C8—201no—
386C8—401no—
387C5#920711yescharacteristic, complemented, Sylow
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#6540311yescharacteristic
394C22#6540511yescharacteristic
395C22#6550211yescharacteristic
396C4—22no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—402no—
403C4—401no—
404C4—401no—
405C4C2×#394811yescharacteristic
406C4#6540211yescharacteristic
407C4#6540311yescharacteristic
408C4#6540511yescharacteristic
409C4#6543311yescharacteristic
410C4#6543411yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#1060243811yescharacteristic
415C2#1060276511yescharacteristic
416C2#1060280311yescharacteristic
subgroupG/H
centerC2×C4#4076
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×C8×#41C2
socleC22×C5#386
prime radicalC2×C5×#41D4
cosocleC2×C42×C5C23
hypercenterC8×#41D5
hypocenterC5#9207
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
4. #10601585C2semidirect
5. #10600531C2semidirect
6. #10598236C2semidirect
7. #10598146C2semidirect
20. #65310C4semidirect
21. #65309C4semidirect
23. #65297C4semidirect
24. #65296C4semidirect
387. C5#9207semidirect

Maximal subgroups

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

subgroupindex
C5×C8×#412
#106142382
#106024392
#106015852
#106005312
#105982362
#105981462
#92075