Finite Group Databasebeta

← #12008793

Subgroups — #12008793

Order 1280.

376 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 75 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#10608216C211yesmaximal, characteristic
2#10598920C212yesmaximal
3C5×#1319C211yesmaximal, characteristic
4#10598134C211yesmaximal, characteristic
5#10597943C212yesmaximal
6C2×Q8×Dic5C411yescharacteristic
7C2×#4090C411yescharacteristic
8C2×#4033C2211yescharacteristic
9C5×#391C2211yescharacteristic
10#65266C2211yescharacteristic
11#65221C411yescharacteristic
12#65218C411yescharacteristic
13#65008—22no—
14#64944—22no—
15#64941—22no—
16C5×#324C2212yes—
17#64748C2212yes—
18#64689—22no—
19#11536—51nomaximal, Sylow
20C22×C5×Q8C2×C411yescharacteristic
21C22×Dic10C2×C411yescharacteristic
22C2×C5×C4⋊C4C2311yescharacteristic
23C2×C42×C5C2×C411yescharacteristic
24Q8×Dic5—42no—
25#4090—22no—
26#4090—22no—
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5C2×C411yescharacteristic
29C2×#683—22no—
30C2×#683D412yes—
31C2×C4×Dic5—21no—
32C2×C4×Dic5C2×C411yescharacteristic
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35#4033—42no—
36C5×C22⋊C8—22no—
37C5×#95—22no—
38#3963—22no—
39#3963—21no—
40#3963—22no—
41#3963—21no—
42C22⋊#168—22no—
43#3947—42no—
44#3946—42no—
45#2327—51no—
46#1467—52no—
47#1324—52no—
48#1319—51no—
49#1319D511yescharacteristic
50C2×C5×Q8—21no—
51C2×C5×Q8—41no—
52C2×C5×Q8—41no—
53C2×C5×Q8M1612yes—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5C22×C411yescharacteristic
57C22×C4×C5C2×D412yes—
58C22×Dic5—21no—
59C22×Dic5—21no—
60C22×Dic5C22⋊C412yes—
61C22×Dic5C22⋊C411yescharacteristic
62C22×Dic5C22⋊C411yescharacteristic
63C2×Dic10—21no—
64C2×Dic10—21no—
65C2×Dic10—41no—
66C2×Dic10—41no—
67C2×C5×C8—42no—
68C5×C4⋊C4—41no—
69C42×C5—41no—
70C4⋊Dic5—42no—
71C4⋊Dic5—41no—
72#683—28no—
73#683—42no—
74C4×Dic5—21no—
75C4×Dic5—22no—
76C4×Dic5—22no—
77C4×Dic5—22no—
78C4×Dic5—42no—
79C4×Dic5M1612yes—
80C2×#168—42no—
81C2×C4⋊Q8—51no—
82C2×C4×Q8—51no—
83C2×C4×Q8—51no—
84#432—102no—
85#391—51no—
86#391C2×D511yescharacteristic
87#387—102no—
88#387—102no—
89#382—51no—
90#376—51no—
91#324—52no—
92#324—102no—
93#324C2×D512yes—
94C23×C5C2×C22⋊C411yescharacteristic
95C5×Q8—42no—
96C5×Q8—42no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—42no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5—41no—
107C2×C4×C5C2×M1611yescharacteristic
108C2×C4×C5C2×M1611yescharacteristic
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—21no—
112C2×Dic5—22no—
113C2×Dic5—22no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5—41no—
117C2×Dic5—41no—
118C2×Dic5—42no—
119C2×Dic5—41no—
120C2×Dic5#9912yes—
121Dic10—42no—
122Dic10—42no—
123C5×C8—82no—
124#168—82no—
125C22×Q8—51no—
126C22×Q8C4×D511yescharacteristic
127C4⋊Q8—102no—
128C4⋊Q8—102no—
129C4×Q8—202no—
130C4×Q8—202no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4—51no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4C22×D511yescharacteristic
136C2×C42—51no—
137C2×C42—51no—
138C2×C42—52no—
139C2×C42—101no—
140C2×C42C4×D511yescharacteristic
141C4⋊C8—202no—
142C22⋊C8—22no—
143C22⋊C8—102no—
144#97—202no—
145#95—22no—
146#95—101no—
147#95—101no—
148#95—102no—
149#95—102no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5#40711yescharacteristic
153C22×C5C2×#9911yescharacteristic
154C22×C5#41311yescharacteristic
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—42no—
158C4×C5—42no—
159C4×C5—81no—
160Dic5—22no—
161Dic5—42no—
162Dic5—41no—
163Dic5—42no—
164Dic5—81no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—101no—
169C2×Q8—101no—
170C2×Q8—201no—
171C2×Q8—201no—
172C2×Q8#67612yes—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—51no—
176C22×C4—52no—
177C22×C4—51no—
178C22×C4—101no—
179C22×C4—101no—
180C22×C4C2×C4×D511yescharacteristic
181C22×C4D4×D512yes—
182C2×C8—42no—
183C2×C8—202no—
184C4⋊C4—41no—
185C4⋊C4—108no—
186C4⋊C4—202no—
187C4⋊C4—201no—
188C4⋊C4—202no—
189C42—41no—
190C42—52no—
191C42—102no—
192C42—102no—
193C42—102no—
194C42—101no—
195C42—202no—
196C2×C5—21no—
197C2×C5—21no—
198C2×C5#146511yescharacteristic
199C2×C5#212911yescharacteristic
200C2×C5#213311yescharacteristic
201C23D5×C22⋊C411yescharacteristic
202Q8—42no—
203Q8—42no—
204Q8—202no—
205Q8—202no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—52no—
217C2×C4—101no—
218C2×C4—102no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—201no—
223C2×C4—201no—
224C2×C4—201no—
225C2×C4—201no—
226C2×C4—202no—
227C2×C4—201no—
228C2×C4C2×#67611yescharacteristic
229C2×C4D5×M1611yescharacteristic
230C8—82no—
231C8—402no—
232C5#1153611yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22#6501511yescharacteristic
236C22D5×#9911yescharacteristic
237C22#6503411yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—102no—
244C4—202no—
245C4—202no—
246C4—201no—
247C4—401no—
248C2—21no—
249C2—21no—
250C2#1059891411yescharacteristic
251C2#1059995211yescharacteristic
252C2#1059996411yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1319C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1319D5
hypocenterC5#11536
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
232. C5#11536semidirect

Maximal subgroups

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

subgroupindex
#106082162
#105989202
C5×#13192
#105981342
#105979432
#115365