Finite Group Databasebeta

← #12015305

Subgroups — #12015305

Order 1280.

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

normal subgroups only

This group has 480 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#10614684C211yesmaximal, characteristic
2C2×C5×#355C211yesmaximal, characteristic
3C2×#64762C211yesmaximal, characteristic
4#10600890C212yesmaximal, complemented
5#10598190C212yesmaximal, complemented
6C2×C5×#124C2211yescharacteristic
7C2×Q8×Dic5C2211yescharacteristic
8C2×D4×Dic5C411yescharacteristic
9C2×C5×#101C2212yes—
10#65519C2211yescharacteristic
11C2×#3968C2212yes—
12#65510C411yescharacteristic
13#65407—22no—
14#65240—22no—
15#65239—22no—
16#65224C411yescharacteristic
17#65221C411yescharacteristic
18C5×#355—22no—
19#64774—22no—
20#64762—22no—
21#12803—51nomaximal, Sylow
22C22×C5×Q8C2311yescharacteristic
23C22×C5×D4C2×C411yescharacteristic
24C23×Dic5—21no—
25C2×C5×M16—22no—
26C5×#124—22no—
27C5×#124D412yes—
28C5×#124Q812yes—
29C2×C5×C22⋊C4—22no—
30C2×C42×C5C2×C411yescharacteristic
31C2×C22⋊Dic5—21no—
32C2×C22⋊Dic5—22no—
33Q8×Dic5—42no—
34D4×Dic5—42no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×C4⋊Dic5D412yes—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D412yes—
42C2×#681—22no—
43C5×#101—22no—
44C5×#101—22no—
45#3968—22no—
46#3968—22no—
47#3963—22no—
48#3963—21no—
49#3963—21no—
50#3946—44no—
51#2326—51no—
52C2×#355—51no—
53C2×#355D511yescharacteristic
54#1801—52no—
55#1394—52no—
56C24×C5—21no—
57C2×C5×Q8—41no—
58C2×C5×Q8—41no—
59C2×C5×Q8C2×D411yescharacteristic
60C2×C5×Q8C2×Q811yescharacteristic
61C2×C5×Q8#4112yes—
62C2×C5×D4—21no—
63C2×C5×D4—41no—
64C2×C5×D4—41no—
65C2×C5×D4C4⋊C412yes—
66C22×C4×C5—21no—
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D412yes—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—42no—
72C22×Dic5—82no—
73C22×Dic5C22⋊C412yes—
74C22×Dic5C22⋊C411yescharacteristic
75C22×Dic5C22⋊C411yescharacteristic
76C5×M16—42no—
77C5×M16—42no—
78C2×C5×C8—42no—
79C5×C22⋊C4—24no—
80C5×C22⋊C4—24no—
81C42×C5—21no—
82C42×C5C4⋊C412yes—
83C22⋊Dic5—42no—
84C22⋊Dic5—82no—
85C4⋊Dic5—41no—
86C4⋊Dic5—42no—
87C4⋊Dic5—41no—
88C4⋊Dic5—82no—
89C4×Dic5—24no—
90C4×Dic5—22no—
91C4×Dic5—41no—
92#681—42no—
93#681—42no—
94C2×#168—42no—
95C2×#124C2×D511yescharacteristic
96C2×C4×Q8—51no—
97C2×C4×D4—51no—
98#423—102no—
99C2×#101—52no—
100C2×#101C2×D512yes—
101#391—51no—
102#390—51no—
103#388—102no—
104#385—102no—
105#384—51no—
106#376—51no—
107#355—22no—
108#355—102no—
109#343—102no—
110C23×C5—22no—
111C23×C5—42no—
112C23×C5—42no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5C2×C22⋊C411yescharacteristic
116C5×Q8—41no—
117C5×Q8—41no—
118C5×Q8—42no—
119C5×D4—42no—
120C5×D4—42no—
121C2×C4×C5—22no—
122C2×C4×C5—21no—
123C2×C4×C5—22no—
124C2×C4×C5—21no—
125C2×C4×C5—22no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5C2×C4⋊C411yescharacteristic
129C2×C4×C5#11711yescharacteristic
130C2×C4×C5#12112yes—
131C2×C4×C5C22⋊Q812yes—
132C2×Dic5—21no—
133C2×Dic5—22no—
134C2×Dic5—41no—
135C2×Dic5—42no—
136C2×Dic5—41no—
137C2×Dic5—42no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—84no—
143C2×Dic5#9912yes—
144C5×C8—82no—
145#168—82no—
146C22×Q8C22×D511yescharacteristic
147C22×D4C4×D511yescharacteristic
148C23×C4—101no—
149C2×M16—22no—
150C2×M16—102no—
151#124—22no—
152#124Dic1012yes—
153#124C22⋊D512yes—
154C4×Q8—202no—
155C4×D4—202no—
156C2×C4⋊C4—51no—
157C2×C4⋊C4—52no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—102no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—101no—
162C2×C22⋊C4—102no—
163C2×C42—51no—
164C2×C42—52no—
165C2×C42—51no—
166C2×C42C4×D511yescharacteristic
167C4⋊C8—204no—
168#101—22no—
169#101—22no—
170#101—102no—
171#101—102no—
172#95—101no—
173#95—101no—
174#95—102no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—44no—
178C22×C5—42no—
179C22×C5—82no—
180C22×C5—81no—
181C22×C5—81no—
182C22×C5#38011yescharacteristic
183C22×C5C2×#9911yescharacteristic
184C22×C5#41011yescharacteristic
185C4×C5—22no—
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—22no—
189C4×C5—42no—
190Dic5—22no—
191Dic5—42no—
192Dic5—41no—
193Dic5—81no—
194Dic5—81no—
195C24—21no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8C2×Dic1011yescharacteristic
199C2×Q8#71112yes—
200C2×Q8C2×C22⋊D511yescharacteristic
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4#68312yes—
205C22×C4—21no—
206C22×C4—51no—
207C22×C4—51no—
208C22×C4—52no—
209C22×C4—101no—
210C22×C4—101no—
211C22×C4—202no—
212C22×C4—402no—
213C22×C4C2×C4×D511yescharacteristic
214C22×C4D4×D512yes—
215M16—42no—
216M16—42no—
217M16—202no—
218M16—202no—
219C2×C8—42no—
220C2×C8—202no—
221C4⋊C4—201no—
222C4⋊C4—202no—
223C4⋊C4—201no—
224C4⋊C4—402no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C22⋊C4—202no—
228C22⋊C4—402no—
229C42—21no—
230C42—104no—
231C42—102no—
232C42—201no—
233C42#68312yes—
234C2×C5—21no—
235C2×C5—21no—
236C2×C5—82no—
237C2×C5#179911yescharacteristic
238C2×C5#213311yescharacteristic
239C2×C5#213411yescharacteristic
240C23—22no—
241C23—42no—
242C23—42no—
243C23—41no—
244C23—41no—
245C23D5×C22⋊C411yescharacteristic
246Q8—41no—
247Q8—42no—
248Q8—41no—
249D4—42no—
250D4—42no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—52no—
259C2×C4—101no—
260C2×C4—102no—
261C2×C4—201no—
262C2×C4—202no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4—202no—
266C2×C4—201no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—404no—
270C2×C4#402311yescharacteristic
271C2×C4#402412yes—
272C2×C4C2×#68311yescharacteristic
273C2×C4#408512yes—
274C8—82no—
275C8—402no—
276C5#1280311yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22—44no—
280C22—42no—
281C22—82no—
282C22—81no—
283C22—81no—
284C22#6502911yescharacteristic
285C22D5×#9911yescharacteristic
286C22#6523111yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—21no—
291C4—42no—
292C4—102no—
293C4—201no—
294C4—202no—
295C4—401no—
296C4—401no—
297C2—21no—
298C2—21no—
299C2—82no—
300C2#1059995711yescharacteristic
301C2#1059995911yescharacteristic
302C2#1060082111yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC2×C5×#355C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC22×C5×Q8C23
hypercenterC2×#355D5
hypocenterC5#12803
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
4. #10600890C2semidirect
5. #10598190C2semidirect
276. C5#12803semidirect

Maximal subgroups

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

subgroupindex
#106146842
C2×C5×#3552
C2×#647622
#106008902
#105981902
#128035