Finite Group Databasebeta

← #13021471

Subgroups — #13021471

Order 1280.

600 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 126 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×#65274C211yesmaximal, characteristic
2#10604900C211yesmaximal, characteristic
3#10604897C211yesmaximal, characteristic
4#10598821C214yesmaximal
5C22×C5×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic5C412yes—
7C22×C4⋊Dic5C411yescharacteristic
8C22×C4×Dic5C2211yescharacteristic
9C2×C22⋊#170C2212yes—
10C2×C22⋊#170C2212yes—
11C2×#4004—21no—
12C2×#4002—21no—
13C2×#3963C2212yes—
14#65274—21no—
15#65274—21no—
16#65274—21no—
17#65274—21no—
18#64918—21no—
19#64918—21no—
20#9883—51nomaximal, Sylow
21C23×C4×C5C2×C412yes—
22C23×C4×C5C2×C411yescharacteristic
23C23×Dic5C2×C411yescharacteristic
24C23×Dic5C2×C412yes—
25C23×Dic5C2311yescharacteristic
26C22×#170—22no—
27C22×#170—22no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—24no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—22no—
34C2×C4⋊Dic5—22no—
35C2×C4⋊Dic5—44no—
36C2×C4⋊Dic5—42no—
37C2×C4×Dic5—42no—
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C22⋊#170—22no—
43C22⋊#170—24no—
44C22⋊#170Q814yes—
45#4004—42no—
46#4002—42no—
47#3963—22no—
48#3963—22no—
49C2×#389—51no—
50#1797—51no—
51#1749—51no—
52#1280—54no—
53C24×C5C22×C411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—42no—
60C22×C4×C5—42no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5M1614yes—
64C22×Dic5—22no—
65C22×Dic5—22no—
66C22×Dic5—22no—
67C22×Dic5—24no—
68C22×Dic5—41no—
69C22×Dic5—41no—
70C22×Dic5—41no—
71C22×Dic5—42no—
72C22×Dic5—42no—
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C22⋊C411yescharacteristic
75C22×Dic5C2×D411yescharacteristic
76C22×Dic5C2×D411yescharacteristic
77C22×Dic5C2×Q812yes—
78C22×Dic5#4112yes—
79C2×#170—24no—
80C2×#170—42no—
81C2×#170—42no—
82C2×#170—42no—
83C2×#170—42no—
84C2×#170—42no—
85C5×C4⋊C4—24no—
86C5×C4⋊C4—24no—
87C4⋊Dic5—44no—
88C4⋊Dic5—42no—
89C4⋊Dic5—42no—
90C4⋊Dic5—44no—
91C4×Dic5—22no—
92C4×Dic5—22no—
93C4×Dic5—41no—
94C4×Dic5—41no—
95C22×C4⋊C4—52no—
96C22×C4⋊C4—51no—
97C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
98C22×C42—51no—
99C2×C4⋊C8—101no—
100C2×C22⋊C8—52no—
101C2×C22⋊C8—52no—
102C2×#97—101no—
103#389—101no—
104#389—101no—
105#389—101no—
106#389—101no—
107C2×#95—52no—
108#336—101no—
109#336—101no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5C2×C22⋊C411yescharacteristic
115C23×C5C4×Q812yes—
116C23×C5C2×M1612yes—
117C23×C5#13112yes—
118C2×C4×C5—28no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—24no—
124C2×C4×C5—44no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—44no—
128C2×C4×C5#9912yes—
129C2×C4×C5#10112yes—
130C2×Dic5—21no—
131C2×Dic5—21no—
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—21no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—44no—
142C2×Dic5—42no—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—84no—
146C2×Dic5#10012yes—
147C2×Dic5C22⋊Q812yes—
148C2×Dic5#12411yescharacteristic
149C2×Dic5C4⋊Q811yescharacteristic
150#170—44no—
151#170—82no—
152C23×C4—51no—
153C23×C4—51no—
154C23×C4—52no—
155C23×C4C2×AGL(1,𝔽5)12yes—
156C23×C4C2×AGL(1,𝔽5)11yescharacteristic
157C22×C8—102no—
158C22×C8—102no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—102no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—101no—
166C2×C4⋊C4—202no—
167C2×C4⋊C4—204no—
168C2×C42—51no—
169C2×C42—51no—
170C2×C42—51no—
171C2×C42—51no—
172C2×C42—202no—
173C4⋊C8—202no—
174C22⋊C8—54no—
175C22⋊C8—102no—
176C22⋊C8—104no—
177#97—202no—
178#95—102no—
179#95—102no—
180C22×C5—22no—
181C22×C5—22no—
182C22×C5—22no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—22no—
186C22×C5#39111yescharacteristic
187C22×C5#40711yescharacteristic
188C22×C5#40811yescharacteristic
189C22×C5C2×#9911yescharacteristic
190C22×C5#41011yescharacteristic
191C22×C5C2×#10011yescharacteristic
192C22×C5C2×#10111yescharacteristic
193C22×C5#44614yes—
194C4×C5—22no—
195C4×C5—22no—
196C4×C5—44no—
197Dic5—22no—
198Dic5—22no—
199Dic5—21no—
200Dic5—21no—
201Dic5—41no—
202Dic5—82no—
203C24C22×AGL(1,𝔽5)11yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—51no—
212C22×C4—51no—
213C22×C4—51no—
214C22×C4—52no—
215C22×C4—52no—
216C22×C4—51no—
217C22×C4—102no—
218C22×C4—102no—
219C22×C4—102no—
220C22×C4—104no—
221C22×C4—201no—
222C22×C4—201no—
223C22×C4—201no—
224C22×C4—202no—
225C22×C4—202no—
226C22×C4#70414yes—
227C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
228C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
229C2×C8—104no—
230C2×C8—202no—
231C2×C8—202no—
232C2×C8—202no—
233C2×C8—202no—
234C2×C8—202no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—202no—
238C4⋊C4—204no—
239C4⋊C4—204no—
240C4⋊C4—202no—
241C42—102no—
242C42—102no—
243C42—201no—
244C42—201no—
245C2×C5—24no—
246C2×C5#146311yescharacteristic
247C2×C5#146611yescharacteristic
248C2×C5#147011yescharacteristic
249C2×C5#147111yescharacteristic
250C2×C5#198511yescharacteristic
251C2×C5#199611yescharacteristic
252C2×C5#199711yescharacteristic
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#413312yes—
258C23Q8×AGL(1,𝔽5)12yes—
259C23C2×#70412yes—
260C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—24no—
267C2×C4—44no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—44no—
271C2×C4—52no—
272C2×C4—52no—
273C2×C4—51no—
274C2×C4—51no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—101no—
280C2×C4—101no—
281C2×C4—101no—
282C2×C4—101no—
283C2×C4—101no—
284C2×C4—202no—
285C2×C4—202no—
286C2×C4—204no—
287C2×C4—202no—
288C2×C4—202no—
289C2×C4—202no—
290C2×C4—404no—
291C2×C4#399912yes—
292C2×C4#400512yes—
293C8—204no—
294C8—402no—
295C5#988311yescharacteristic, complemented, Sylow
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22C2×#399911yescharacteristic
303C22C2×#400511yescharacteristic
304C22#6577111yescharacteristic
305C22D5⋊#10011yescharacteristic
306C22#6578711yescharacteristic
307C22#6578814yes—
308C22(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
309C22#6579811yescharacteristic
310C4—22no—
311C4—22no—
312C4—44no—
313C4—102no—
314C4—102no—
315C4—101no—
316C4—101no—
317C4—201no—
318C4—402no—
319C2—24no—
320C2#1060429911yescharacteristic
321C2#1060430011yescharacteristic
322C2#1060431011yescharacteristic
323C2#1060434011yescharacteristic
324C2#1060488111yescharacteristic
325C2#1060493411yescharacteristic
326C2#1060498511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutator, prime radicalC24×C5C22×C4
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
cosocleC23×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#9883
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
295. C5#9883semidirect

Maximal subgroups

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

subgroupindex
C2×#652742
#106049002
#106048972
#105988212
#98835