Finite Group Databasebeta

← #12015309

Subgroups — #12015309

Order 1280.

432 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 101 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#10614958C211yesmaximal, characteristic
2C2×C5×#356C211yesmaximal, characteristic
3C2×#64768C211yesmaximal, characteristic
4#10600890C212yesmaximal
5#10598190C212yesmaximal
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×Q8×Dic5C411yescharacteristic
8C2×Q8×Dic5C2211yescharacteristic
9C2×C5×#101C2212yes—
10#65519C411yescharacteristic
11#65519C2211yescharacteristic
12C2×#3968C2212yes—
13#65407—22no—
14#65270—22no—
15#65270—22no—
16#65225C411yescharacteristic
17#65221C411yescharacteristic
18C5×#356—22no—
19#64774—22no—
20#64768—22no—
21#12804—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×C5×Q8C2311yescharacteristic
24C2×C5×M16—22no—
25C5×C4⋊Q8—22no—
26C5×C4⋊Q8D412yes—
27C5×C4⋊Q8Q812yes—
28C2×C5×C4⋊C4—22no—
29C2×C42×C5C2×C411yescharacteristic
30Q8×Dic5—42no—
31Q8×Dic5—42no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5D412yes—
36C2×C4×Dic5—21no—
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5C2×C411yescharacteristic
39C2×C4×Dic5D412yes—
40C2×#681—22no—
41C5×#101—22no—
42C5×#101—22no—
43#3968—22no—
44#3968—22no—
45#3963—22no—
46#3963—21no—
47#3963—21no—
48#3963—22no—
49#3963—22no—
50#3946—44no—
51#2327—51no—
52C2×#356—51no—
53C2×#356D511yescharacteristic
54#1801—52no—
55#1394—52no—
56C2×C5×Q8—21no—
57C2×C5×Q8—41no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8C4⋊C412yes—
62C2×C5×Q8C2×D411yescharacteristic
63C2×C5×Q8C2×Q811yescharacteristic
64C2×C5×Q8#4112yes—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D412yes—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5C22⋊C412yes—
72C22×Dic5C22⋊C411yescharacteristic
73C22×Dic5C22⋊C411yescharacteristic
74C5×M16—42no—
75C5×M16—42no—
76C2×C5×C8—42no—
77C5×C4⋊C4—24no—
78C5×C4⋊C4—24no—
79C42×C5—21no—
80C42×C5C4⋊C412yes—
81C4⋊Dic5—41no—
82C4⋊Dic5—42no—
83C4⋊Dic5—42no—
84C4⋊Dic5—41no—
85C4×Dic5—24no—
86C4×Dic5—22no—
87C4×Dic5—42no—
88C4×Dic5—41no—
89#681—42no—
90#681—42no—
91C2×#168—42no—
92C2×C4⋊Q8C2×D511yescharacteristic
93C2×C4×Q8—51no—
94C2×C4×Q8—51no—
95#423—102no—
96C2×#101—52no—
97C2×#101C2×D512yes—
98#391—51no—
99#391—51no—
100#387—102no—
101#387—102no—
102#382—51no—
103#376—51no—
104#356—22no—
105#356—102no—
106#343—102no—
107C23×C5C2×C22⋊C411yescharacteristic
108C5×Q8—41no—
109C5×Q8—41no—
110C5×Q8—42no—
111C5×Q8—42no—
112C5×Q8—42no—
113C2×C4×C5—22no—
114C2×C4×C5—21no—
115C2×C4×C5—22no—
116C2×C4×C5—21no—
117C2×C4×C5—22no—
118C2×C4×C5—22no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5C2×C4⋊C411yescharacteristic
124C2×C4×C5#11711yescharacteristic
125C2×C4×C5#12112yes—
126C2×C4×C5C22⋊Q812yes—
127C2×Dic5—21no—
128C2×Dic5—22no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5—41no—
132C2×Dic5—41no—
133C2×Dic5—41no—
134C2×Dic5—42no—
135C2×Dic5—41no—
136C2×Dic5—41no—
137C2×Dic5#9912yes—
138C5×C8—82no—
139#168—82no—
140C22×Q8C4×D511yescharacteristic
141C22×Q8C22×D511yescharacteristic
142C2×M16—22no—
143C2×M16—102no—
144C4⋊Q8—22no—
145C4⋊Q8Dic1012yes—
146C4⋊Q8C22⋊D512yes—
147C4×Q8—202no—
148C4×Q8—202no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—51no—
151C2×C4⋊C4—52no—
152C2×C4⋊C4—51no—
153C2×C4⋊C4—101no—
154C2×C42—51no—
155C2×C42—52no—
156C2×C42—51no—
157C2×C42—101no—
158C2×C42C4×D511yescharacteristic
159C4⋊C8—204no—
160#101—22no—
161#101—22no—
162#101—102no—
163#101—102no—
164#95—101no—
165#95—101no—
166#95—102no—
167#95—102no—
168#95—102no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5#38011yescharacteristic
172C22×C5C2×#9911yescharacteristic
173C22×C5#41011yescharacteristic
174C4×C5—22no—
175C4×C5—21no—
176C4×C5—21no—
177C4×C5—22no—
178C4×C5—42no—
179C4×C5—42no—
180Dic5—22no—
181Dic5—41no—
182Dic5—42no—
183Dic5—81no—
184Dic5—81no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8#68312yes—
191C2×Q8C2×Dic1011yescharacteristic
192C2×Q8#71112yes—
193C2×Q8C2×C22⋊D511yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—51no—
197C22×C4—52no—
198C22×C4—51no—
199C22×C4—101no—
200C22×C4—101no—
201C22×C4C2×C4×D511yescharacteristic
202C22×C4D4×D512yes—
203M16—42no—
204M16—42no—
205M16—202no—
206M16—202no—
207C2×C8—42no—
208C2×C8—202no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—201no—
212C4⋊C4—202no—
213C4⋊C4—201no—
214C4⋊C4—202no—
215C42—21no—
216C42—104no—
217C42—102no—
218C42—201no—
219C42—202no—
220C42#68312yes—
221C2×C5—21no—
222C2×C5—21no—
223C2×C5#179911yescharacteristic
224C2×C5#213311yescharacteristic
225C2×C5#213511yescharacteristic
226C23D5×C22⋊C411yescharacteristic
227Q8—41no—
228Q8—42no—
229Q8—41no—
230Q8—42no—
231Q8—42no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—52no—
243C2×C4—101no—
244C2×C4—102no—
245C2×C4—201no—
246C2×C4—202no—
247C2×C4—201no—
248C2×C4—201no—
249C2×C4—201no—
250C2×C4—202no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4#402311yescharacteristic
254C2×C4#402412yes—
255C2×C4C2×#68311yescharacteristic
256C2×C4#408512yes—
257C8—82no—
258C8—402no—
259C5#1280411yescharacteristic, complemented, Sylow
260C22—21no—
261C22—21no—
262C22#6502911yescharacteristic
263C22D5×#9911yescharacteristic
264C22#6523111yescharacteristic
265C4—22no—
266C4—21no—
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—102no—
272C4—201no—
273C4—202no—
274C4—401no—
275C4—401no—
276C2—21no—
277C2—21no—
278C2#1059996411yescharacteristic
279C2#1059996611yescharacteristic
280C2#1060082111yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC2×C5×#356C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×C5×Q8C23
hypercenterC2×#356D5
hypocenterC5#12804
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
259. C5#12804semidirect

Maximal subgroups

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

subgroupindex
#106149582
C2×C5×#3562
C2×#647682
#106008902
#105981902
#128045