Finite Group Databasebeta

← #11987558

Subgroups — #11987558

Order 1280.

520 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 107 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#10608023C211yesmaximal, characteristic
2#10599396C212yesmaximal, complemented
3C5×#1270C211yesmaximal, characteristic
4#10598130C211yesmaximal, characteristic
5#10597971C212yesmaximal, complemented
6C2×#4082C411yescharacteristic
7C2×D4×Dic5C411yescharacteristic
8C2×#4033C411yescharacteristic
9C5×#390C2211yescharacteristic
10C2×#3947—22no—
11C2×#3946—22no—
12#65266C411yescharacteristic
13#65233—22no—
14C22⋊C4×Dic5—22no—
15C42×Dic5C2211yescharacteristic
16#65218C2211yescharacteristic
17C5×#336C2212yes—
18#64744C2212yes—
19#7635—51nomaximal, Sylow
20C22×C5×D4C2×C411yescharacteristic
21C23×Dic5—21no—
22C22×Dic10C2×C411yescharacteristic
23C22×C5×C8—22no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C5×C22⋊C4—22no—
26C2×C42×C5C2311yescharacteristic
27C2×C22⋊Dic5—22no—
28C2×C22⋊Dic5—21no—
29#4082—22no—
30#4082—22no—
31D4×Dic5—42no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5D412yes—
38C2×C4×Dic5D412yes—
39C22×#168—22no—
40#4033—42no—
41#3963—22no—
42#3963—22no—
43#3947—44no—
44#3946—28no—
45C4×#124—51no—
46#1767—52no—
47#1272—52no—
48#1270—51no—
49#1270D511yescharacteristic
50C24×C5—21no—
51C2×C5×D4—21no—
52C2×C5×D4—41no—
53C2×C5×D4—41no—
54C2×C5×D4M1612yes—
55C22×C4×C5—21no—
56C22×C4×C5C22×C411yescharacteristic
57C22×C4×C5C2×D412yes—
58C22×Dic5—21no—
59C22×Dic5—21no—
60C22×Dic5—42no—
61C22×Dic5—44no—
62C22×Dic5C22⋊C412yes—
63C22×Dic5C22⋊C411yescharacteristic
64C22×Dic5C22⋊C411yescharacteristic
65C2×Dic10—21no—
66C2×Dic10—41no—
67C2×Dic10—41no—
68C2×Dic10M1612yes—
69C2×C5×C8—24no—
70C2×C5×C8—42no—
71C2×C5×C8—42no—
72C5×C4⋊C4—41no—
73C5×C22⋊C4—42no—
74C5×C22⋊C4—42no—
75C42×C5—41no—
76C22⋊Dic5—28no—
77C22⋊Dic5—42no—
78C4⋊Dic5—41no—
79#683—42no—
80C4×Dic5—21no—
81C4×Dic5—21no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5—22no—
85C4×Dic5—24no—
86C4×Dic5—42no—
87C2×#168—24no—
88C2×#168—42no—
89C2×#168—42no—
90C2×#124—51no—
91C2×C4×Q8—51no—
92C2×C4×D4—51no—
93C2×C4⋊C8—102no—
94C2×#97—102no—
95#391—51no—
96#390C2×D511yescharacteristic
97#388—102no—
98#382—51no—
99C4×C22⋊C4—102no—
100C43—51no—
101#336—52no—
102#336C2×D512yes—
103C23×C5—22no—
104C23×C5—41no—
105C23×C5—41no—
106C23×C5—42no—
107C23×C5—42no—
108C23×C5C2×C22⋊C411yescharacteristic
109C5×D4—42no—
110C5×D4—42no—
111C2×C4×C5—22no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—22no—
115C2×C4×C5—41no—
116C2×C4×C5—42no—
117C2×C4×C5C2×M1611yescharacteristic
118C2×C4×C5C2×M1611yescharacteristic
119C2×C4×C5AGL(1,ℤ/8)12yes—
120C2×C4×C5#13712yes—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—21no—
124C2×Dic5—22no—
125C2×Dic5—22no—
126C2×Dic5—22no—
127C2×Dic5—41no—
128C2×Dic5—41no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5—84no—
132C2×Dic5#10012yes—
133C2×Dic5#10414yes—
134Dic10—42no—
135Dic10—42no—
136C5×C8—44no—
137#168—44no—
138C22×Q8—51no—
139C22×D4C4×D511yescharacteristic
140C23×C4—101no—
141C22×C8—22no—
142C22×C8—102no—
143#124—102no—
144#124—102no—
145C4×Q8—202no—
146C4×D4—202no—
147C2×C4⋊C4—51no—
148C2×C4⋊C4—101no—
149C2×C4⋊C4C4×D511yescharacteristic
150C2×C22⋊C4—22no—
151C2×C22⋊C4—102no—
152C2×C22⋊C4—101no—
153C2×C42—51no—
154C2×C42—51no—
155C2×C42—52no—
156C2×C42—52no—
157C2×C42—101no—
158C2×C42C22×D511yescharacteristic
159C4⋊C8—108no—
160#97—204no—
161#95—102no—
162#95—102no—
163C22×C5—42no—
164C22×C5—44no—
165C22×C5—81no—
166C22×C5—82no—
167C22×C5—81no—
168C22×C5#40711yescharacteristic
169C22×C5#41011yescharacteristic
170C22×C5C2×#10011yescharacteristic
171C22×C5#41712yes—
172C22×C5C2×#10412yes—
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—22no—
176C4×C5—22no—
177C4×C5—81no—
178Dic5—41no—
179Dic5—42no—
180Dic5—42no—
181Dic5—81no—
182Dic5#32914yes—
183C24—21no—
184C2×Q8—52no—
185C2×Q8—101no—
186C2×Q8—201no—
187C2×Q8—201no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4#67612yes—
192C22×C4—21no—
193C22×C4—51no—
194C22×C4—52no—
195C22×C4—51no—
196C22×C4—101no—
197C22×C4—101no—
198C22×C4—202no—
199C22×C4—204no—
200C22×C4C2×C4×D511yescharacteristic
201C22×C4D4×D512yes—
202C2×C8—24no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—104no—
206C2×C8—202no—
207C2×C8—202no—
208C4⋊C4—41no—
209C4⋊C4—201no—
210C4⋊C4—202no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—108no—
214C22⋊C4—202no—
215C42—41no—
216C42—104no—
217C42—102no—
218C42—101no—
219C42—101no—
220C42—102no—
221C42—102no—
222C42—202no—
223C2×C5—82no—
224C2×C5#146611yescharacteristic
225C2×C5#148912yes—
226C2×C5#150912yes—
227C2×C5C2×#32911yescharacteristic
228C2×C5#156011yescharacteristic
229C23—22no—
230C23—41no—
231C23—41no—
232C23—42no—
233C23—42no—
234C23D5×C22⋊C411yescharacteristic
235Q8—202no—
236Q8—202no—
237D4—42no—
238D4—42no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—52no—
246C2×C4—54no—
247C2×C4—101no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—102no—
251C2×C4—102no—
252C2×C4—102no—
253C2×C4—201no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—202no—
257C2×C4—404no—
258C2×C4C2×#67611yescharacteristic
259C2×C4D5×M1611yescharacteristic
260C2×C4#405712yes—
261C2×C4#406112yes—
262C8—44no—
263C8—204no—
264C5#763511yescharacteristic, complemented, Sylow
265C22—44no—
266C22—42no—
267C22—81no—
268C22—82no—
269C22—81no—
270C22#6501511yescharacteristic
271C22#6502911yescharacteristic
272C22D5×#10011yescharacteristic
273C22#6506012yes—
274C22D5×#10412yes—
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—54no—
280C4—81no—
281C4—201no—
282C4—202no—
283C4—202no—
284C4—401no—
285C2—82no—
286C2#1059889611yescharacteristic
287C2#1059896712yes—
288C2#1059907212yes—
289C2D5×#32911yescharacteristic
290C2#1059918211yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1270C2
socleC23×C5C2×C22⋊C4
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenter#1270D5
hypocenterC5#7635
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #10599396C2semidirect
5. #10597971C2semidirect
264. C5#7635semidirect

Maximal subgroups

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

subgroupindex
#106080232
#105993962
C5×#12702
#105981302
#105979712
#76355