Finite Group Databasebeta

← #11987738

Subgroups — #11987738

Order 1280.

396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10607924C211yesmaximal, characteristic
2#10599395C211yesmaximal, characteristic
3#10599390C211yesmaximal, characteristic
4C5×#1271C211yesmaximal, characteristic
5#10598129C211yesmaximal, characteristic
6#10597969C211yesmaximal, characteristic
7#10597968C211yesmaximal, characteristic
8C5×#389C2211yescharacteristic
9C2×#3947—21no—
10C2×#3946—21no—
11C2×C8×Dic5—21no—
12#65274C411yescharacteristic
13#65270—21no—
14#65267—21no—
15#65266C411yescharacteristic
16#65266C411yescharacteristic
17#65262C411yescharacteristic
18C42×Dic5C2211yescharacteristic
19#65217C2211yescharacteristic
20#64942—21no—
21#64941—21no—
22C5×#336C2211yescharacteristic
23C5×#336C2211yescharacteristic
24#64770—21no—
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7677—51nomaximal, Sylow
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C22×#168—21no—
46C22×#168—21no—
47C5×#95—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3947—24no—
56#3946—24no—
57C8×Dic5—42no—
58#2864—51no—
59C4×C4⋊C8—51no—
60#1745—51no—
61#1271—51no—
62#1271—51no—
63#1271—51no—
64#1271D511yescharacteristic
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5C22⋊C411yescharacteristic
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C22⋊C411yescharacteristic
75C22×Dic5C22⋊C411yescharacteristic
76C2×C5×C8—22no—
77C2×C5×C8—22no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4—21no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C42×C5—41no—
88C4⋊Dic5—21no—
89C4⋊Dic5—21no—
90C4⋊Dic5—42no—
91C4⋊Dic5—41no—
92#683—41no—
93#683—41no—
94#683—42no—
95C4×Dic5—21no—
96C4×Dic5—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5—22no—
102C4×Dic5—22no—
103C4×Dic5—22no—
104C2×#168—22no—
105C2×#168—22no—
106C2×#168—41no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×C4⋊C8—101no—
111C2×#97—101no—
112C2×C4×C8—101no—
113#389—51no—
114#389—51no—
115#389—51no—
116#389C2×D511yescharacteristic
117#387—101no—
118#387—101no—
119#387—101no—
120#387—101no—
121#382—51no—
122#382—51no—
123C43—51no—
124#336—51no—
125#336—51no—
126#336—101no—
127#336C2×D511yescharacteristic
128#336C2×D511yescharacteristic
129C23×C5C2×C22⋊C411yescharacteristic
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5#13111yescharacteristic
143C2×C4×C5#13111yescharacteristic
144C2×C4×C5#13511yescharacteristic
145C2×C4×C5#13511yescharacteristic
146C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C5#13711yescharacteristic
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5#10112yes—
164C2×Dic5#10412yes—
165C2×Dic5#10412yes—
166C5×C8—42no—
167C5×C8—42no—
168#168—42no—
169#168—42no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—101no—
173C22×C8—101no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4C4×D511yescharacteristic
181C2×C4⋊C4C4×D511yescharacteristic
182C2×C42—51no—
183C2×C42—51no—
184C2×C42—51no—
185C2×C42—51no—
186C2×C42—51no—
187C2×C42—51no—
188C2×C42C22×D511yescharacteristic
189C4⋊C8—104no—
190#97—104no—
191C4×C8—202no—
192#95—21no—
193#95—101no—
194#95—101no—
195#95—101no—
196#95—101no—
197#95—101no—
198#95—101no—
199#95—101no—
200C22×C5#40811yescharacteristic
201C22×C5#41011yescharacteristic
202C22×C5C2×#10111yescharacteristic
203C22×C5#41611yescharacteristic
204C22×C5#41711yescharacteristic
205C22×C5C2×#10411yescharacteristic
206C22×C5C2×#10411yescharacteristic
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—81no—
214C4×C5—81no—
215Dic5—22no—
216Dic5—22no—
217Dic5—22no—
218Dic5—41no—
219Dic5—81no—
220Dic5—81no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—101no—
228C22×C4—101no—
229C22×C4C2×C4×D511yescharacteristic
230C22×C4D4×D511yescharacteristic
231C22×C4D4×D511yescharacteristic
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—102no—
239C2×C8—102no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C2×C8—201no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—101no—
250C4⋊C4—101no—
251C4⋊C4—201no—
252C4⋊C4—202no—
253C4⋊C4—202no—
254C4⋊C4—201no—
255C4⋊C4—201no—
256C42—41no—
257C42—102no—
258C42—102no—
259C42—102no—
260C42—101no—
261C42—101no—
262C42—101no—
263C42—101no—
264C42—101no—
265C42—101no—
266C2×C5#147011yescharacteristic
267C2×C5#148311yescharacteristic
268C2×C5#149411yescharacteristic
269C2×C5#150011yescharacteristic
270C2×C5#150911yescharacteristic
271C2×C5#152611yescharacteristic
272C2×C5#155211yescharacteristic
273C23D5×C22⋊C411yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—52no—
287C2×C4—52no—
288C2×C4—52no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—101no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4#404711yescharacteristic
305C2×C4#405311yescharacteristic
306C2×C4#405711yescharacteristic
307C2×C4#406111yescharacteristic
308C2×C4#406211yescharacteristic
309C2×C4#406511yescharacteristic
310C8—42no—
311C8—42no—
312C8—202no—
313C8—202no—
314C5#767711yescharacteristic, complemented, Sylow
315C22#6501611yescharacteristic
316C22#6502911yescharacteristic
317C22D5×#10111yescharacteristic
318C22#6506011yescharacteristic
319C22#6509311yescharacteristic
320C22D5×#10411yescharacteristic
321C22D5×#10411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—102no—
331C4—102no—
332C4—102no—
333C4—201no—
334C4—401no—
335C4—401no—
336C2#1059892111yescharacteristic
337C2#1059896311yescharacteristic
338C2#1059903411yescharacteristic
339C2#1059907211yescharacteristic
340C2#1059910111yescharacteristic
341C2#1059915511yescharacteristic
342C2#1059921811yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1271C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1271D5
hypocenterC5#7677
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
314. C5#7677semidirect

Maximal subgroups

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

subgroupindex
#106079242
#105993952
#105993902
C5×#12712
#105981292
#105979692
#105979682
#76775