Finite Group Databasebeta

← #11995852

Subgroups — #11995852

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2962C211yesmaximal, characteristic, complemented
2#10615086C211yesmaximal, characteristic
3#10602623C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600669C211yesmaximal, characteristic
6#10598198C211yesmaximal, characteristic, complemented
7#10598159C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×#4020C2211yescharacteristic
10C5×#446—21no—
11C5×#446—22no—
12C5×C8×Q8—21no—
13C5×#424—21no—
14C2×C5×C4⋊C8C2211yescharacteristic
15C5×#405—21no—
16C4×C5×M16C2211yescharacteristic
17C2×#3955—21no—
18C2×#3955—21no—
19#65377—21no—
20#65374—21no—
21#65335C414yes—
22#65316—22no—
23#65214C2211yescharacteristic
24#65213C2211yescharacteristic
25C2×C4⋊#168C2211yescharacteristic
26#64767—21no—
27#64766—21no—
28#64705—21no—
29#64705—21no—
30#9274—51nomaximal, Sylow
31C22×D20—21no—
32C22×D20—21no—
33C22×D20C2×C412yes—
34C2×C5×M16D411yescharacteristic
35C2×C5×M16D411yescharacteristic
36C22×C5×C8—21no—
37C5×C4⋊Q8D411yescharacteristic
38C5×C4⋊Q8D411yescharacteristic
39C5×#125—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8C2×C412yes—
42C4×C5×Q8—21no—
43C4×C5×Q8D412yes—
44C5×#117—21no—
45C2×C42×C5C2311yescharacteristic
46C2×#688—24no—
47C2×#681—21no—
48C22×#168—21no—
49#4020—21no—
50#4020—21no—
51#4020—21no—
52#4020—21no—
53C5×C4⋊C8—22no—
54C5×C4⋊C8—22no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8D411yescharacteristic
57C5×C4⋊C8D411yescharacteristic
58C5×#97—22no—
59C5×#97—21no—
60C4×C5×C8—22no—
61C4×C5×C8—21no—
62C22⋊#168C2×C412yes—
63#3955—42no—
64#3955—42no—
65#3941—24no—
66C4⋊#168—21no—
67C4⋊#168—21no—
68C4⋊#168—21no—
69C4⋊#168—21no—
70C4⋊#168—21no—
71C4×#168—21no—
72#3208—51no—
73#2962D511yescharacteristic, complemented
74#1965—51no—
75#1550—51no—
76C2×#331—51no—
77#1301—51no—
78#1283—51no—
79C23×D5—22no—
80C2×C5×Q8—21no—
81C2×C5×Q8C22⋊C412yes—
82C22×C4×C5C22×C411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5#4111yescharacteristic
85C2×D20—22no—
86C2×D20—22no—
87C2×D20—41no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×D20—41no—
94C2×D20—41no—
95C2×D20—82no—
96C2×D20—81no—
97C2×D20—81no—
98C5×M16—21no—
99C5×M16—21no—
100C5×M16—21no—
101C5×M16SD1612yescomplemented
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4C22⋊C412yes—
114C5×C22⋊C4—22no—
115C42×C5—22no—
116C42×C5C2×D411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5#4111yescharacteristic
120#688—84no—
121#681—41no—
122#681—41no—
123C2×#168—22no—
124C2×#168—41no—
125C2×#168—41no—
126C2×#168—81no—
127#533C2×D511yescharacteristic
128C2×#127—51no—
129#492—101no—
130#486—101no—
131#460—102no—
132#450—54no—
133#446—22no—
134#446—21no—
135C8×Q8—21no—
136#431—51no—
137#424—21no—
138#423—51no—
139C2×C4⋊C8—51no—
140C2×C4⋊C8C2×D511yescharacteristic
141C2×#100—101no—
142C2×#100—101no—
143#405—21no—
144C4×M16C2×D511yescharacteristic
145#333—101no—
146#332—101no—
147#331—101no—
148#331—101no—
149C23×C5C4×D411yescharacteristic
150C22×D5—42no—
151C22×D5—42no—
152C22×D5—42no—
153C22×D5—82no—
154C22×D5—82no—
155C5×Q8—42no—
156C5×Q8—41no—
157C5×Q8—41no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—41no—
163C2×C4×C5C2×C22⋊C411yescharacteristic
164C2×C4×C5C4×D411yescharacteristic
165C2×C4×C5#12011yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5#12111yescharacteristic
168C2×C4×C5#12311yescharacteristic
169C2×C4×C5C2×SD1611yescharacteristic
170C2×C4×C5#13511yescharacteristic
171C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C5#13711yescharacteristic
173D20—44no—
174D20—82no—
175D20—82no—
176D20—81no—
177D20—81no—
178D20—81no—
179D20—81no—
180D20—81no—
181D20—81no—
182C5×C8—22no—
183C5×C8—41no—
184C5×C8—41no—
185C5×C8—41no—
186#168—42no—
187#168—81no—
188#168—81no—
189C22×D4—52no—
190C22×D4—101no—
191C22×D4—101no—
192C2×SD16—104no—
193C2×M16—101no—
194C2×M16C22⋊D511yescharacteristic
195C2×M16C22⋊D511yescharacteristic
196C22×C8—21no—
197C22×C8—101no—
198C4⋊Q8D2011yescharacteristic
199C4⋊Q8D2011yescharacteristic
200#127—101no—
201#127—101no—
202#127—101no—
203#127—101no—
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8C4×D512yes—
207C4×Q8—21no—
208C4×Q8C22⋊D512yes—
209#117—21no—
210C2×C42C22×D511yescharacteristic
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—21no—
214C4⋊C8—101no—
215C4⋊C8—101no—
216C4⋊C8—101no—
217C4⋊C8—101no—
218C4⋊C8—101no—
219C4⋊C8C22⋊D511yescharacteristic
220C4⋊C8C22⋊D511yescharacteristic
221#102—104no—
222#100—202no—
223#100—202no—
224C22⋊C8—52no—
225#97—22no—
226#97—21no—
227C4×C8—22no—
228C4×C8—21no—
229C4×C8—101no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5#38611yescharacteristic
233C22×C5C4×SD1611yescharacteristic
234C22×C5#44011yescharacteristic
235C2×D5—82no—
236C2×D5—82no—
237C2×D5—82no—
238C2×D5—162no—
239C2×D5—162no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—42no—
244C4×C5—42no—
245C4×C5#44811yescharacteristic
246C4×C5#44911yescharacteristic
247C4×C5#46011yescharacteristic
248C4×C5#46411yescharacteristic
249C4×C5#47111yescharacteristic
250C4×C5#47211yescharacteristic
251C24—102no—
252C2×Q8—21no—
253C2×Q8#68512yes—
254C2×D4—102no—
255C2×D4—102no—
256C2×D4—201no—
257C2×D4—201no—
258C2×D4—201no—
259C2×D4—201no—
260C2×D4—201no—
261C2×D4—201no—
262C2×D4—201no—
263C2×D4—201no—
264C2×D4—401no—
265C2×D4—401no—
266C2×D4—402no—
267C22×C4C2×C4×D511yescharacteristic
268C22×C4#70911yescharacteristic
269C22×C4C2×C22⋊D511yescharacteristic
270SD16—404no—
271M16—21no—
272M16—21no—
273M16—21no—
274M16—201no—
275M16—201no—
276M16#68812yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—102no—
284C2×C8—201no—
285C2×C8—201no—
286C2×C8—401no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4#68512yes—
293C22⋊C4—22no—
294C42—22no—
295C42C2×D2011yescharacteristic
296C42#70911yescharacteristic
297C42C2×C22⋊D511yescharacteristic
298C42C2×C22⋊D511yescharacteristic
299C2×C5—21no—
300C2×C5—21no—
301C2×C5#188011yescharacteristic
302C2×C5#190711yescharacteristic
303C2×C5#191411yescharacteristic
304D5—162no—
305C23—202no—
306C23—202no—
307C23—202no—
308C23—402no—
309C23—402no—
310C23C4×C22⋊D511yescharacteristic
311Q8—42no—
312Q8—41no—
313Q8—41no—
314D4—204no—
315D4—402no—
316D4—402no—
317D4—401no—
318D4—401no—
319D4—401no—
320D4—401no—
321D4—401no—
322D4—401no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4C2×#68511yescharacteristic
329C2×C4C4×C22⋊D511yescharacteristic
330C2×C4#407511yescharacteristic
331C2×C4#407611yescharacteristic
332C2×C4#407611yescharacteristic
333C2×C4C2×#68811yescharacteristic
334C2×C4#408811yescharacteristic
335C2×C4#409511yescharacteristic
336C2×C4#409611yescharacteristic
337C2×C4#409911yescharacteristic
338C8—22no—
339C8—41no—
340C8—41no—
341C8—41no—
342C8—202no—
343C8—401no—
344C8—401no—
345C5#927411yescharacteristic, complemented, Sylow
346C22—21no—
347C22—21no—
348C22—402no—
349C22—402no—
350C22—402no—
351C22—802no—
352C22—802no—
353C22C4×#68811yescharacteristic
354C22#6531511yescharacteristic
355C22#6550211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4#6531611yescharacteristic
362C4#6531711yescharacteristic
363C4#6543011yescharacteristic
364C4#6543111yescharacteristic
365C4#6551611yescharacteristic
366C4#6552711yescharacteristic
367C2—21no—
368C2—21no—
369C2—802no—
370C2#1060242611yescharacteristic
371C2#1060281111yescharacteristic
372C2#1060282311yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2962C2
socleC22×C5#386
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenter#2962D5
hypocenterC5#9274
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. C5×#2962C2semidirect
3. #10602623C2semidirect
6. #10598198C2semidirect
7. #10598159C2semidirect
73. #2962D5semidirect
101. C5×M16SD16semidirect
276. M16#688semidirect
345. C5#9274semidirect

Maximal subgroups

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

subgroupindex
C5×#29622
#106150862
#106026232
C2×#647052
#106006692
#105981982
#105981592
#92745