Finite Group Databasebeta

← #12008918

Subgroups — #12008918

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#10614104C211yesmaximal, characteristic
2C5×#1465C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10597936C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4081C412yes—
7C22×C4⋊Dic5C411yescharacteristic
8C5×#407—21no—
9#65501—21no—
10#65501C411yescharacteristic
11#65272—21no—
12#65242—21no—
13#65232C2212yes—
14#65217—21no—
15#65214—21no—
16C5×#324—21no—
17C5×#323C2212yes—
18#64745—21no—
19#64745C2212yes—
20#11562—51nomaximal, Sylow
21C22×C5×D4C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5C2×C412yes—
25C2×C5×M16—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5C2×C412yes—
34#4081—44no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—41no—
39C2×C4⋊Dic5—41no—
40C2×#683—22no—
41C5×C22⋊C8—22no—
42C5×C22⋊C8—41no—
43#3963—21no—
44#3963—22no—
45#3963—22no—
46C22⋊#168—22no—
47C4⋊#168—41no—
48C4×#168—41no—
49#2486—51no—
50#1465D511yescharacteristic
51#1460—51no—
52#1317—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—
71C22×Dic5—24no—
72C22×Dic5—42no—
73C22×Dic5—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—42no—
83C4⋊Dic5—42no—
84C4⋊Dic5—42no—
85C4⋊Dic5—41no—
86C4⋊Dic5—41no—
87#683—44no—
88C2×#168—42no—
89C2×#123—52no—
90C2×C4×D4C2×D511yescharacteristic
91C22×C4⋊C4—51no—
92#431—101no—
93#407—21no—
94#398—101no—
95#397—101no—
96#389—101no—
97#381—52no—
98#380—51no—
99#380—101no—
100#324—21no—
101#323—52no—
102#323—101no—
103#323C2×D512yes—
104C23×C5—21no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—41no—
110C23×C5—41no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5C2×C22⋊C411yescharacteristic
114C23×C5#13112yes—
115C5×D4—44no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—22no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—42no—
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#9911yescharacteristic
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#10012yes—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—84no—
139C5×C8—82no—
140#168—82no—
141C22×D4C4×D511yescharacteristic
142C23×C4—52no—
143C23×C4C4×D511yescharacteristic
144C23×C4C22⋊D511yescharacteristic
145C2×M16—41no—
146#123—204no—
147C4×D4—41no—
148C4×D4—41no—
149C2×C4⋊C4—101no—
150C2×C4⋊C4—102no—
151C2×C4⋊C4—101no—
152C2×C4⋊C4—101no—
153C2×C4⋊C4—201no—
154C2×C4⋊C4—201no—
155C2×C4⋊C4C22⋊D511yescharacteristic
156C2×C22⋊C4—52no—
157C2×C22⋊C4—102no—
158C2×C22⋊C4D2011yescharacteristic
159C2×C22⋊C4C22×D511yescharacteristic
160C2×C42D2011yescharacteristic
161C4⋊C8—201no—
162C22⋊C8—22no—
163C22⋊C8—41no—
164C22⋊C8—102no—
165C4×C8—201no—
166#95—101no—
167#95—102no—
168#95—102no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5—22no—
172C22×C5—42no—
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#40811yescharacteristic
182C22×C5C2×#9911yescharacteristic
183C22×C5C2×#10011yescharacteristic
184C4×C5—21no—
185C4×C5—22no—
186C4×C5—41no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5#35212yes—
190Dic5—82no—
191Dic5—82no—
192C24#68511yescharacteristic
193C24C2×C4×D511yescharacteristic
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—41no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—102no—
204C22×C4—102no—
205C22×C4—104no—
206C22×C4—202no—
207C22×C4—202no—
208C22×C4#68511yescharacteristic
209C22×C4#68511yescharacteristic
210C22×C4#68511yescharacteristic
211C22×C4C2×D2011yescharacteristic
212C22×C4C2×C22⋊D511yescharacteristic
213M16—82no—
214C2×C8—42no—
215C2×C8—202no—
216C4⋊C4—41no—
217C4⋊C4—202no—
218C4⋊C4—202no—
219C4⋊C4—201no—
220C4⋊C4—201no—
221C4⋊C4—204no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—204no—
225C22⋊C4—202no—
226C42—21no—
227C42—21no—
228C2×C5—21no—
229C2×C5—21no—
230C2×C5—42no—
231C2×C5—81no—
232C2×C5#147111yescharacteristic
233C2×C5C2×#35211yescharacteristic
234C2×C5#212311yescharacteristic
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23#405312yes—
245C23C2×#68511yescharacteristic
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—81no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4—202no—
263C2×C4—202no—
264C2×C4—202no—
265C2×C4—202no—
266C2×C4—404no—
267C2×C4#393811yescharacteristic
268C2×C4#393811yescharacteristic
269C2×C4#395512yes—
270C8—82no—
271C8—402no—
272C5#1156211yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C2×#393811yescharacteristic
286C22#6541811yescharacteristic
287C22C2×#395511yescharacteristic
288C4—22no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—402no—
294C4—402no—
295C4#6469212yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2#1060076311yescharacteristic
301C2C2×#6469211yescharacteristic
302C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1465C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C22⋊C4C23
hypercenter#1465D5
hypocenterC5#11562
LCSG ▷ C24×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. #10597936C2semidirect
272. C5#11562semidirect

Maximal subgroups

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

subgroupindex
#106141042
C5×#14652
#106023942
#105979362
#115625