Finite Group Databasebeta

← #13018243

Subgroups — #13018243

Order 1280.

478 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C2×#65122C211yesmaximal, characteristic
2C2×#64883C211yesmaximal, characteristic, complemented
3C2×#64881C211yesmaximal, characteristic, complemented
4#10604182C212yesmaximal
5#10598771C212yesmaximal, complemented
6C2×C42×D5C2211yescharacteristic
7C2×#4003—22no—
8C2×C4⋊#170C2212yes—
9C2×C4⋊#170C2212yes—
10C2×C5×C4⋊C8C411yescharacteristic
11C2×#3952C411yescharacteristic
12C2×#3952C411yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14C2×C8×Dic5C2211yescharacteristic
15C2×C4⋊#168C411yescharacteristic
16#65122—22no—
17#65122—22no—
18#64918—22no—
19#64883—22no—
20#64881—22no—
21#8598—51nomaximal, Sylow
22C22×C4×D5C2×C411yescharacteristic
23C22×C4×D5D411yescharacteristic
24C22×C4×D5Q811yescharacteristic
25C22×#170—22no—
26C22×#170—22no—
27C22×C5×C8C2×C411yescharacteristic
28C22×C5×C8C2×C411yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C4×Dic5D411yescharacteristic
31C2×C4×Dic5Q811yescharacteristic
32C2×C4×Dic5C2311yescharacteristic
33C22×#168C2×C411yescharacteristic
34C22×#168C2×C411yescharacteristic
35C42×D5—21no—
36C42×D5—21no—
37C42×D5—21no—
38C42×D5—21no—
39#4003—44no—
40C4⋊#170—22no—
41C4⋊#170—22no—
42C4⋊#170—22no—
43C4⋊#170—22no—
44C5×C4⋊C8—22no—
45#3952—22no—
46#3952—22no—
47C8×Dic5—21no—
48C8×Dic5—21no—
49C8×Dic5D412yes—
50C8×Dic5D412yes—
51C4⋊#168—22no—
52C2×#431—51no—
53#1797—52no—
54C2×#334—51no—
55C2×#334—51no—
56#1277—52no—
57C23×D5C4⋊C411yescharacteristic
58C22×C4×C5C4⋊C411yescharacteristic
59C22×C4×C5C4⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×Dic5C4⋊C411yescharacteristic
62C22×Dic5C2×D411yescharacteristic
63C22×Dic5C2×Q811yescharacteristic
64C2×C4×D5—21no—
65C2×C4×D5—21no—
66C2×C4×D5—22no—
67C2×C4×D5—21no—
68C2×C4×D5—21no—
69C2×C4×D5—22no—
70C2×C4×D5—22no—
71C2×C4×D5—21no—
72C2×C4×D5—21no—
73C2×C4×D5—42no—
74C2×C4×D5SD1614yes—
75C2×#170—42no—
76C2×#170—42no—
77C2×#170—42no—
78C2×#170—42no—
79C2×#170—42no—
80C2×#170—42no—
81C2×C5×C8—22no—
82C2×C5×C8—21no—
83C2×C5×C8—22no—
84C2×C5×C8C22⋊C412yes—
85C42×C5—21no—
86C42×C5—21no—
87C4×Dic5—21no—
88C4×Dic5—21no—
89C4×Dic5—21no—
90C4×Dic5—21no—
91C4×Dic5C2×D411yescharacteristic
92C4×Dic5C2×D411yescharacteristic
93C4×Dic5#4111yescharacteristic
94C4×Dic5#4111yescharacteristic
95C2×#168—22no—
96C2×#168—21no—
97C2×#168—22no—
98C2×#168C22⋊C412yes—
99C22×C42—51no—
100#431—102no—
101#431—102no—
102C2×C4⋊C8—52no—
103C2×C4⋊C8—52no—
104C2×C4⋊C8—51no—
105C2×C4⋊C8AGL(1,𝔽5)11yescharacteristic
106C2×C22⋊C8—51no—
107C2×C22⋊C8—51no—
108C2×C22⋊C8—102no—
109C2×C4×C8—51no—
110C2×C4×C8—51no—
111#336—102no—
112#334—102no—
113#334—102no—
114C23×C5C2×C4⋊C411yescharacteristic
115C22×D5—21no—
116C22×D5—22no—
117C22×D5—21no—
118C22×D5—22no—
119C22×D5#10612yes—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—22no—
124C2×C4×C5#10612yes—
125C2×C4×C5C2×C22⋊C411yescharacteristic
126C2×C4×C5#11711yescharacteristic
127C2×C4×C5#13112yes—
128C2×C4×C5#13112yes—
129C2×Dic5—22no—
130C2×Dic5—21no—
131C2×Dic5—22no—
132C2×Dic5#12111yescharacteristic
133C2×Dic5#12111yescharacteristic
134C2×Dic5C22⋊Q811yescharacteristic
135C2×Dic5C22⋊Q811yescharacteristic
136C2×Dic5C2×SD1612yes—
137C2×Dic5#13512yes—
138C4×D5—24no—
139C4×D5—24no—
140C4×D5—42no—
141C4×D5—42no—
142C4×D5—41no—
143C4×D5—41no—
144C4×D5—42no—
145#170—82no—
146#170—82no—
147C5×C8—22no—
148C5×C8—41no—
149#168—22no—
150#168—41no—
151C23×C4—51no—
152C23×C4—51no—
153C23×C4—51no—
154C22×C8—51no—
155C22×C8—51no—
156C22×C8—102no—
157C22×C8—102no—
158C22×C8C2×AGL(1,𝔽5)11yescharacteristic
159C22×C8C2×AGL(1,𝔽5)11yescharacteristic
160C2×C42—51no—
161C2×C42—51no—
162C2×C42—51no—
163C2×C42—101no—
164C2×C42—101no—
165C2×C42—101no—
166C2×C42—101no—
167C2×C42C2×AGL(1,𝔽5)11yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—102no—
170C4⋊C8—102no—
171C4⋊C8—102no—
172C4⋊C8—102no—
173C4⋊C8—102no—
174C22⋊C8—102no—
175C22⋊C8—102no—
176C22⋊C8—204no—
177C4×C8—52no—
178C4×C8—52no—
179C4×C8—101no—
180C4×C8—101no—
181C22×C5#38011yescharacteristic
182C22×C5#42412yes—
183C22×C5C2×#10611yescharacteristic
184C22×C5#42711yescharacteristic
185C22×C5#43012yes—
186C2×D5—22no—
187C2×D5—24no—
188C2×D5—41no—
189C2×D5—41no—
190C2×D5—42no—
191C4×C5—22no—
192C4×C5—41no—
193C4×C5#40811yescharacteristic
194C4×C5#40811yescharacteristic
195C4×C5#43312yes—
196Dic5—21no—
197Dic5—21no—
198Dic5—41no—
199Dic5#46512yes—
200Dic5#46512yes—
201C24—51no—
202C22×C4—51no—
203C22×C4—51no—
204C22×C4—54no—
205C22×C4—51no—
206C22×C4—101no—
207C22×C4—101no—
208C22×C4—102no—
209C22×C4—101no—
210C22×C4—101no—
211C22×C4—101no—
212C22×C4—102no—
213C22×C4—102no—
214C22×C4—101no—
215C22×C4—202no—
216C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
217C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
218C22×C4C22×AGL(1,𝔽5)11yescharacteristic
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—21no—
222C2×C8—52no—
223C2×C8—102no—
224C2×C8—102no—
225C2×C8—101no—
226C2×C8—202no—
227C2×C8—202no—
228C2×C8—202no—
229C2×C8—202no—
230C2×C8—202no—
231C2×C8—202no—
232C2×C8C22⋊AGL(1,𝔽5)12yes—
233C42—21no—
234C42—21no—
235C42—51no—
236C42—51no—
237C42—51no—
238C42—51no—
239C42—101no—
240C42—101no—
241C42—101no—
242C42—101no—
243C2×C5#157012yes—
244C2×C5#157212yes—
245C2×C5#179811yescharacteristic
246C2×C5#180711yescharacteristic
247C2×C5#181111yescharacteristic
248D5—42no—
249C23—52no—
250C23—102no—
251C23—101no—
252C23—102no—
253C23—101no—
254C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—52no—
260C2×C4—52no—
261C2×C4—51no—
262C2×C4—51no—
263C2×C4—51no—
264C2×C4—51no—
265C2×C4—104no—
266C2×C4—104no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4—101no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4—202no—
273C2×C4—201no—
274C2×C4—201no—
275C2×C4#399312yes—
276C2×C4#413011yescharacteristic
277C2×C4#413112yes—
278C2×C4#413312yes—
279C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
280C8—22no—
281C8—41no—
282C8—102no—
283C8—201no—
284C8—402no—
285C8—402no—
286C5#859811yescharacteristic, complemented, Sylow
287C22—102no—
288C22—104no—
289C22—201no—
290C22—201no—
291C22—202no—
292C22#6570812yes—
293C22C2×#399311yescharacteristic
294C22#6572111yescharacteristic
295C22#6572912yes—
296C22#6576511yescharacteristic
297C4—22no—
298C4—41no—
299C4—52no—
300C4—52no—
301C4—101no—
302C4—101no—
303C4—201no—
304C4#6570612yes—
305C4#6577511yescharacteristic
306C4#6578711yescharacteristic
307C2—202no—
308C2#1060401512yes—
309C2#1060401712yes—
310C2#1060431711yescharacteristic
311C2#1060472211yescharacteristic
312C2#1060477211yescharacteristic
subgroupG/H
centerC23C2×C4⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5C2×C4⋊C4
prime radicalC23×D5C4⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#8598
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#64883C2semidirect
3. C2×#64881C2semidirect
5. #10598771C2semidirect
286. C5#8598semidirect

Maximal subgroups

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

subgroupindex
C2×#651222
C2×#648832
C2×#648812
#106041822
#105987712
#85985