Finite Group Databasebeta

← #12008926

Subgroups — #12008926

Order 1280.

444 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 87 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#10614113C211yesmaximal, characteristic
2C5×#1465C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10597946C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4082C412yes—
7C2×#4015C411yescharacteristic
8C5×#407—21no—
9#65501—21no—
10#65501—21no—
11C2×C22⋊#168—21no—
12#65263C2212yes—
13#65242—21no—
14#65242—21no—
15C4×C4⋊Dic5C411yescharacteristic
16C5×#324C2212yes—
17C5×#323—21no—
18#64748C2212yes—
19#64745—21no—
20#11564—51nomaximal, Sylow
21C22×C5×D4C2×C411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C22×Dic10C2×C412yes—
25C2×C5×M16—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4C2311yescharacteristic
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34#4082—44no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4×Dic5C2×C412yes—
39C22×#168—41no—
40#4015—41no—
41#4015—41no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8—41no—
44#3963—21no—
45#3963—22no—
46#3963—22no—
47C22⋊#168—22no—
48C22⋊#168—41no—
49#2547—51no—
50#1465D511yescharacteristic
51#1459—51no—
52#1319—54no—
53C24×C5C22⋊C411yescharacteristic
54C24×C5C22⋊C411yescharacteristic
55C2×C5×D4—22no—
56C2×C5×D4—22no—
57C2×C5×D4—41no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×Dic5—22no—
70C22×Dic5—22no—
71C2×Dic10—24no—
72C2×Dic10—42no—
73C2×Dic10—42no—
74C5×M16—82no—
75C2×C5×C8—42no—
76C5×C4⋊C4—41no—
77C5×C22⋊C4—41no—
78C5×C22⋊C4—41no—
79C42×C5—21no—
80C42×C5—21no—
81C22⋊Dic5—44no—
82C22⋊Dic5—44no—
83C4⋊Dic5—42no—
84C4⋊Dic5—42no—
85C4⋊Dic5—41no—
86C4⋊Dic5—41no—
87C4×Dic5—42no—
88C2×#168—42no—
89C2×#168—82no—
90C2×C4⋊Q8—51no—
91C2×#124—52no—
92C2×C4×D4C2×D511yescharacteristic
93#407—21no—
94C2×C22⋊C8—101no—
95#397—101no—
96#397—101no—
97#391—52no—
98#380—101no—
99#380—101no—
100C4×C4⋊C4—51no—
101#324—52no—
102#324C2×D512yes—
103#323—21no—
104#323—101no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—41no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5#10012yes—
115C23×C5C2×C22⋊C411yescharacteristic
116C5×D4—44no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—22no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—81no—
129C2×C4×C5—81no—
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#9911yescharacteristic
132C2×C4×C5#13112yes—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139Dic10—84no—
140C5×C8—82no—
141#168—82no—
142C22×Q8—52no—
143C22×D4C4×D511yescharacteristic
144C23×C4D2011yescharacteristic
145C23×C4C22⋊D511yescharacteristic
146C2×M16—41no—
147C22×C8—201no—
148C4⋊Q8—201no—
149C4⋊Q8—201no—
150#124—204no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4C22×D511yescharacteristic
157C2×C22⋊C4—102no—
158C2×C22⋊C4—102no—
159C2×C22⋊C4D2011yescharacteristic
160C2×C22⋊C4C22⋊D511yescharacteristic
161C2×C42—52no—
162C2×C42C4×D511yescharacteristic
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—102no—
166C22⋊C8—201no—
167#95—101no—
168#95—102no—
169#95—102no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5—22no—
173C22×C5—42no—
174C22×C5—42no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5—41no—
178C22×C5—41no—
179C22×C5—41no—
180C22×C5—81no—
181C22×C5—81no—
182C22×C5#40811yescharacteristic
183C22×C5C2×#9911yescharacteristic
184C22×C5C2×#10011yescharacteristic
185C4×C5—21no—
186C4×C5—22no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5—41no—
190C4×C5#35412yes—
191Dic5—82no—
192Dic5—82no—
193C24#68511yescharacteristic
194C24#68511yescharacteristic
195C2×Q8—104no—
196C2×Q8—202no—
197C2×Q8—202no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—102no—
208C22×C4—102no—
209C22×C4#68511yescharacteristic
210C22×C4#68511yescharacteristic
211C22×C4C2×C4×D511yescharacteristic
212C22×C4C2×D2011yescharacteristic
213C22×C4C2×C22⋊D511yescharacteristic
214M16—82no—
215C2×C8—42no—
216C2×C8—202no—
217C2×C8—402no—
218C4⋊C4—41no—
219C4⋊C4—202no—
220C4⋊C4—202no—
221C4⋊C4—201no—
222C4⋊C4—201no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—204no—
226C22⋊C4—204no—
227C42—21no—
228C42—21no—
229C42—202no—
230C2×C5—21no—
231C2×C5—21no—
232C2×C5—42no—
233C2×C5—81no—
234C2×C5#147111yescharacteristic
235C2×C5C2×#35411yescharacteristic
236C2×C5#213511yescharacteristic
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23#395512yes—
247C23C2×#68511yescharacteristic
248Q8—404no—
249D4—44no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—202no—
264C2×C4—202no—
265C2×C4—202no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4#393811yescharacteristic
270C2×C4#393811yescharacteristic
271C2×C4#405312yes—
272C8—82no—
273C8—402no—
274C5#1156411yescharacteristic, complemented, Sylow
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22C2×#393811yescharacteristic
288C22#6541811yescharacteristic
289C22C2×#395511yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—402no—
296C4—402no—
297C4#6469312yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2#1060076311yescharacteristic
303C2C2×#6469311yescharacteristic
304C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1465C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1465D5
hypocenterC5#11564
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #10597946C2semidirect
274. C5#11564semidirect

Maximal subgroups

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

subgroupindex
#106141132
C5×#14652
#106023932
#105979462
#115645