Finite Group Databasebeta

← #13018307

Subgroups — #13018307

Order 1280.

486 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 106 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×#65014C211yesmaximal, characteristic
2#10604907C212yesmaximal
3#10604697C212yesmaximal, complemented
4#10598772C212yesmaximal, complemented
5C2×C4×C22⋊D5C2211yescharacteristic
6C23×#168C411yescharacteristic
7C22×C8×D5C411yescharacteristic
8C2×#4013—22no—
9#65758C2214yes—
10C2×C5×C22⋊C8C411yescharacteristic
11C2×#3952C411yescharacteristic
12C2×#3946C2211yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14#65014—22no—
15#65014—22no—
16#64919—22no—
17#64884—22no—
18#64882—22no—
19#8616—51nomaximal, Sylow
20C23×C4×C5C2×C411yescharacteristic
21C22×C22⋊D5D411yescharacteristic
22C22×C4×D5C2×C411yescharacteristic
23C2×#704—24no—
24C22×C5×C8C2×C411yescharacteristic
25C22×C5×C8C2×C411yescharacteristic
26C2×C22⋊Dic5Q811yescharacteristic
27C4×C22⋊D5—22no—
28C4×C22⋊D5—22no—
29C2×#685Q811yescharacteristic
30C2×#683D411yescharacteristic
31C2×C4×Dic5C2311yescharacteristic
32C22×#168—21no—
33C22×#168—21no—
34C22×#168—42no—
35C22×#168C2×C411yescharacteristic
36C22×#168C2×C411yescharacteristic
37C2×C8×D5—21no—
38C2×C8×D5—21no—
39C2×C8×D5—42no—
40#4013—44no—
41#4004—24no—
42C4⋊#170—24no—
43C5×C22⋊C8—22no—
44#3952—22no—
45#3946—22no—
46C8×Dic5D412yes—
47C8×Dic5D412yes—
48C2×C8×D4—51no—
49#1800—52no—
50#1567—52no—
51#1292—52no—
52C24×C5C4⋊C411yescharacteristic
53C23×D5C4⋊C411yescharacteristic
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—41no—
57C22×C4×C5—41no—
58C22×C4×C5C4⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C2×C22⋊D5—22no—
61C2×C22⋊D5—22no—
62C2×C22⋊D5D812yes—
63C2×C22⋊D5Q1612yes—
64C22×Dic5C4⋊C411yescharacteristic
65C22×Dic5C2×D411yescharacteristic
66C22×Dic5C2×Q811yescharacteristic
67C2×C4×D5—21no—
68C2×C4×D5—21no—
69C2×C4×D5—41no—
70C2×C4×D5—41no—
71#704—44no—
72#704—44no—
73C2×#170—44no—
74C2×C5×C8—21no—
75C2×C5×C8—41no—
76C2×C5×C8—41no—
77C2×C5×C8C22⋊C412yes—
78C22⋊Dic5—22no—
79#685—22no—
80#683—22no—
81C4×Dic5C2×D412yes—
82C4×Dic5#4112yes—
83C2×#168—22no—
84C2×#168—21no—
85C2×#168—42no—
86C2×#168—42no—
87C2×#168—41no—
88C2×#168C22⋊C411yescharacteristic
89C2×#168C22⋊C411yescharacteristic
90C8×D5—42no—
91C8×D5—42no—
92C23×C8—51no—
93C23×C8—51no—
94C2×C4×D4—51no—
95C8×D4—102no—
96C8×D4—102no—
97#423—54no—
98C2×C4⋊C8—51no—
99C2×#100—102no—
100C2×C22⋊C8—51no—
101C2×C22⋊C8AGL(1,𝔽5)11yescharacteristic
102C2×C4×C8—51no—
103#343—102no—
104#335—102no—
105#335—102no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5#10712yes—
111C23×C5C2×C4⋊C411yescharacteristic
112C22×D5—21no—
113C22×D5—21no—
114C22×D5—41no—
115C22×D5—41no—
116C22×D5#10712yes—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—42no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5C2×C22⋊C411yescharacteristic
125C2×C4×C5#11711yescharacteristic
126C22⋊D5—24no—
127C22⋊D5—24no—
128C2×Dic5—21no—
129C2×Dic5—41no—
130C2×Dic5—41no—
131C2×Dic5#12112yes—
132C2×Dic5C22⋊Q812yes—
133C2×Dic5C2×D811yescharacteristic
134C2×Dic5C2×Q1611yescharacteristic
135C2×Dic5#13512yes—
136C4×D5—42no—
137C4×D5—41no—
138C4×D5—41no—
139#170—84no—
140C5×C8—22no—
141C5×C8—41no—
142#168—21no—
143#168—41no—
144#168#10012yescomplemented
145C22×D4—51no—
146C23×C4—51no—
147C23×C4C2×AGL(1,𝔽5)11yescharacteristic
148C2×M16—104no—
149C22×C8—51no—
150C22×C8—51no—
151C22×C8—101no—
152C22×C8—101no—
153C22×C8—101no—
154C22×C8—101no—
155C22×C8—202no—
156C22×C8—202no—
157C22×C8C2×AGL(1,𝔽5)11yescharacteristic
158C22×C8C2×AGL(1,𝔽5)11yescharacteristic
159C4×D4—102no—
160C4×D4—102no—
161C2×C4⋊C4—51no—
162C2×C22⋊C4—51no—
163C2×C22⋊C4—51no—
164C2×C42—51no—
165C4⋊C8—102no—
166C4⋊C8—104no—
167C4⋊C8—104no—
168#100—204no—
169C22⋊C8—22no—
170C22⋊C8—102no—
171C4×C8—52no—
172C4×C8—52no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—22no—
176C22×C5—42no—
177C22×C5—42no—
178C22×C5—41no—
179C22×C5—41no—
180C22×C5#38011yescharacteristic
181C22×C5C2×#10711yescharacteristic
182C22×C5#42711yescharacteristic
183C2×D5—22no—
184C2×D5—42no—
185C2×D5—41no—
186C2×D5—41no—
187C2×D5—42no—
188C4×C5—21no—
189C4×C5—41no—
190C4×C5C2×#10011yescharacteristic
191C4×C5#41311yescharacteristic
192Dic5—22no—
193Dic5—41no—
194Dic5#46612yes—
195Dic5#46712yes—
196C24—51no—
197C24C4⋊AGL(1,𝔽5)11yescharacteristic
198C2×D4—52no—
199C2×D4—52no—
200C2×D4—102no—
201C2×D4—102no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—51no—
207C22×C4—51no—
208C22×C4—51no—
209C22×C4—101no—
210C22×C4—101no—
211C22×C4—201no—
212C22×C4—201no—
213C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
214C22×C4C22×AGL(1,𝔽5)11yescharacteristic
215M16—204no—
216M16—204no—
217C2×C8—21no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—51no—
221C2×C8—51no—
222C2×C8—102no—
223C2×C8—101no—
224C2×C8—202no—
225C2×C8—202no—
226C2×C8—202no—
227C2×C8—202no—
228C2×C8—201no—
229C2×C8—204no—
230C2×C8C22⋊AGL(1,𝔽5)12yes—
231C4⋊C4—102no—
232C22⋊C4—102no—
233C22⋊C4—102no—
234C42—52no—
235C42—52no—
236C2×C5—21no—
237C2×C5—21no—
238C2×C5—42no—
239C2×C5#180011yescharacteristic
240C2×C5#180811yescharacteristic
241C2×C5#181311yescharacteristic
242D5—42no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—52no—
248C23—101no—
249C23—101no—
250C23—201no—
251C23—201no—
252C23#399412yes—
253C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
254D4—104no—
255D4—104no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—51no—
264C2×C4—51no—
265C2×C4—52no—
266C2×C4—52no—
267C2×C4—52no—
268C2×C4—101no—
269C2×C4—202no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—201no—
273C2×C4—201no—
274C2×C4#413011yescharacteristic
275C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
276C8—22no—
277C8—41no—
278C8—52no—
279C8—101no—
280C8—201no—
281C8—404no—
282C5#861611yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—102no—
291C22—202no—
292C22—202no—
293C22—201no—
294C22—201no—
295C22C2×#399411yescharacteristic
296C22#6572111yescharacteristic
297C22#6576511yescharacteristic
298C4—21no—
299C4—41no—
300C4—52no—
301C4—52no—
302C4—102no—
303C4—201no—
304C4#6577711yescharacteristic
305C4D5⋊#10011yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—202no—
310C2#1060424611yescharacteristic
311C2#1060472311yescharacteristic
312C2#1060477311yescharacteristic
subgroupG/H
centerC22#65765
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C22⋊C8C4
socleC22×C5#380
prime radicalC22×C22⋊D5D4
cosocleC2×C4×Dic5C23
hypercenterC2×C22⋊C8AGL(1,𝔽5)
hypocenterC5#8616
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10604697C2semidirect
4. #10598772C2semidirect
144. #168#100semidirect
282. C5#8616semidirect

Maximal subgroups

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

subgroupindex
C2×#650142
#106049072
#106046972
#105987722
#86165