Finite Group Databasebeta

← #12002411

Subgroups — #12002411

Order 1280.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#10605953C211yesmaximal, characteristic
2C5×#1518C211yesmaximal, characteristic
3#10602632C211yesmaximal, characteristic
4#10602631C211yesmaximal, characteristic
5#10598229C211yesmaximal, characteristic
6#10598227C211yesmaximal, characteristic
7#10598122C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C5×#382C2211yescharacteristic
11#65274—21no—
12#65262—21no—
13#65225C2211yescharacteristic
14C42×Dic5C2211yescharacteristic
15#65214C2211yescharacteristic
16#65213C2211yescharacteristic
17#64944—22no—
18#64943—22no—
19C5×#328—22no—
20#64758—22no—
21#64752—21no—
22#64752—21no—
23#10367—51nomaximal, Sylow
24C5×C4⋊Q8Q811yescharacteristic
25C5×C4⋊Q8Q811yescharacteristic
26C5×#125—21no—
27C5×C22⋊Q8—21no—
28C5×C22⋊Q8—21no—
29C4×C5×Q8—21no—
30C4×C5×Q8—21no—
31C5×#117—21no—
32C2×C5×C4⋊C4—21no—
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—21no—
36C2×#683—22no—
37C2×C4×Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×#681—21no—
42C5×C4⋊C8—21no—
43C5×C22⋊C8—21no—
44C4×C5×C8—21no—
45C5×#95—21no—
46C5×#95D412yes—
47#3963—22no—
48#3963—22no—
49#3963—21no—
50#3963D412yes—
51C22⋊#168—21no—
52C4⋊#168—21no—
53C4⋊#168—21no—
54C4⋊#168—21no—
55C4×#168—21no—
56#2864—51no—
57#1994—51no—
58#1518—51no—
59#1518D511yescharacteristic
60#1286—51no—
61#1286—51no—
62#1276—51no—
63C2×C5×Q8—21no—
64C2×C5×Q8—21no—
65C22×C4×C5—22no—
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—22no—
72C2×C5×C8—41no—
73C5×C4⋊C4—21no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4—21no—
76C5×C4⋊C4—21no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C5×C22⋊C4—41no—
82C42×C5—41no—
83C42×C5C2×Q811yescharacteristic
84C42×C5#4111yescharacteristic
85C42×C5#4111yescharacteristic
86C42×C5#4111yescharacteristic
87C4⋊Dic5—44no—
88C4⋊Dic5—41no—
89C4⋊Dic5—41no—
90#683—44no—
91C4×Dic5—21no—
92C4×Dic5—21no—
93C4×Dic5—21no—
94C4×Dic5—21no—
95C4×Dic5—42no—
96C4×Dic5—42no—
97#681—41no—
98#681—41no—
99C2×#168—41no—
100C2×#168—41no—
101#533C2×D511yescharacteristic
102#431—51no—
103#431C2×D511yescharacteristic
104#423—51no—
105#389—101no—
106#389—101no—
107#387—102no—
108#387—102no—
109#382—51no—
110#382C2×D511yescharacteristic
111C43—51no—
112#339—101no—
113#339—101no—
114#328—22no—
115#328—102no—
116C23×C5#12011yescharacteristic
117C5×Q8—81no—
118C5×Q8—81no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—42no—
126C2×C4×C5C22⋊Q811yescharacteristic
127C2×C4×C5C22⋊Q811yescharacteristic
128C2×C4×C5C22⋊Q811yescharacteristic
129C2×C4×C5#12411yescharacteristic
130C2×C4×C5#12411yescharacteristic
131C2×C4×C5#12411yescharacteristic
132C2×C4×C5#13511yescharacteristic
133C2×C4×C5#13511yescharacteristic
134C2×C4×C5#13711yescharacteristic
135C2×C4×C5#13711yescharacteristic
136C2×Dic5—22no—
137C2×Dic5—22no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—42no—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C5×C8—81no—
146#168—81no—
147#168—81no—
148C2×M16—101no—
149C4⋊Q8Dic1011yescharacteristic
150C4⋊Q8Dic1011yescharacteristic
151#125—21no—
152C22⋊Q8—21no—
153C22⋊Q8—21no—
154C4×Q8—21no—
155C4×Q8—21no—
156#117—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—102no—
159C2×C4⋊C4—102no—
160C2×C4⋊C4—101no—
161C2×C42—51no—
162C2×C42—51no—
163C2×C42—101no—
164C2×C42—101no—
165C2×C42C22×D511yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—101no—
168C4⋊C8—101no—
169C4⋊C8—101no—
170C22⋊C8—21no—
171C22⋊C8—101no—
172C4×C8—21no—
173C4×C8—101no—
174#95—21no—
175#95—52no—
176#95—102no—
177#95—102no—
178#95—101no—
179#95C22⋊D512yes—
180C22×C5—21no—
181C22×C5—21no—
182C22×C5#39311yescharacteristic
183C22×C5#45211yescharacteristic
184C22×C5#45211yescharacteristic
185C4×C5—21no—
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—21no—
189C4×C5—82no—
190C4×C5—81no—
191C4×C5—81no—
192C4×C5#47911yescharacteristic
193C4×C5#47911yescharacteristic
194C4×C5#48811yescharacteristic
195C4×C5#49111yescharacteristic
196Dic5—42no—
197Dic5—42no—
198Dic5—82no—
199C2×Q8—21no—
200C2×Q8—21no—
201C22×C4—22no—
202C22×C4—101no—
203C22×C4—101no—
204C22×C4—102no—
205C22×C4D4×D511yescharacteristic
206C22×C4D4×D511yescharacteristic
207C22×C4C2×C22⋊D511yescharacteristic
208M16—201no—
209M16—201no—
210C2×C8—41no—
211C2×C8—201no—
212C2×C8—201no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—204no—
222C4⋊C4—204no—
223C4⋊C4—201no—
224C4⋊C4—201no—
225C22⋊C4—41no—
226C42—41no—
227C42—101no—
228C42—101no—
229C42—101no—
230C42—101no—
231C42—202no—
232C42—202no—
233C42C2×Dic1011yescharacteristic
234C42#70911yescharacteristic
235C42#71111yescharacteristic
236C42#71111yescharacteristic
237C2×C5—21no—
238C2×C5—21no—
239C2×C5#202611yescharacteristic
240C2×C5#203111yescharacteristic
241C2×C5#203111yescharacteristic
242C23#408311yescharacteristic
243Q8—81no—
244Q8—81no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—102no—
253C2×C4—102no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—201no—
258C2×C4—202no—
259C2×C4—202no—
260C2×C4—202no—
261C2×C4#402411yescharacteristic
262C2×C4#402411yescharacteristic
263C2×C4#403111yescharacteristic
264C2×C4#403111yescharacteristic
265C2×C4#406111yescharacteristic
266C2×C4#406211yescharacteristic
267C2×C4#406411yescharacteristic
268C2×C4#406511yescharacteristic
269C2×C4#407011yescharacteristic
270C2×C4#408211yescharacteristic
271C8—81no—
272C8—401no—
273C8—401no—
274C5#1036711yescharacteristic, complemented, Sylow
275C22—21no—
276C22—21no—
277C22#6523611yescharacteristic
278C22#6546211yescharacteristic
279C22#6547611yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—82no—
285C4—81no—
286C4—81no—
287C4—202no—
288C4—202no—
289C4—402no—
290C4#6508511yescharacteristic
291C4#6508611yescharacteristic
292C4#6508811yescharacteristic
293C4#6508911yescharacteristic
294C2—21no—
295C2—21no—
296C2#1060083111yescharacteristic
297C2#1060102511yescharacteristic
298C2#1060118711yescharacteristic
subgroupG/H
centerC22#65236
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1518C2
socleC22×C5#393
prime radicalC23×C5#120
hypercenter#1518D5
hypocenterC5#10367
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
274. C5#10367semidirect

Maximal subgroups

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

subgroupindex
#106059532
C5×#15182
#106026322
#106026312
#105982292
#105982272
#105981222
#103675