Finite Group Databasebeta

← #13014942

Subgroups — #13014942

Order 1280.

456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C4×#4034C211yesmaximal, characteristic
2#10604187C211yesmaximal, characteristic
3#10604187C211yesmaximal, characteristic
4#10598714C212yesmaximal
5#10598713C212yesmaximal
6C2×#4034C411yescharacteristic
7C2×C4×Dic10—21no—
8C2×C4⋊#170—21no—
9C2×C4⋊#170—21no—
10C4×C5×C4⋊C4C411yescharacteristic
11#65274C2211yescharacteristic
12#65265C411yescharacteristic
13#65262C2211yescharacteristic
14C4×C4⋊Dic5C411yescharacteristic
15C4×#683—21no—
16C42×Dic5C2211yescharacteristic
17#64936—21no—
18#64935—21no—
19#64918—21no—
20#64918—21no—
21#64918C2212yes—
22#64918C2212yes—
23#7652—51nomaximal, Sylow
24C22×Dic10—21no—
25C22×#170—22no—
26C22×#170—22no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C42×C5—21no—
30C2×C42×C5C2×C411yescharacteristic
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×#683—21no—
35C2×#683—21no—
36C2×#683—21no—
37C2×#683—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5C2311yescharacteristic
45#4034—22no—
46#4034—22no—
47C4×Dic10—42no—
48C4×Dic10—42no—
49C4⋊#170—42no—
50C4⋊#170—42no—
51C5×#95—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55C4×C4⋊Q8—51no—
56#1831—51no—
57#1831—51no—
58#1271—52no—
59#1271—52no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22×C411yescharacteristic
65C22×Dic5—21no—
66C22×Dic5—21no—
67C22×Dic5C22⋊C411yescharacteristic
68C22×Dic5C22⋊C411yescharacteristic
69C22×Dic5C2×D411yescharacteristic
70C22×Dic5C2×D411yescharacteristic
71C2×Dic10—24no—
72C2×Dic10—42no—
73C2×Dic10—42no—
74C2×#170—42no—
75C2×#170—42no—
76C2×#170—42no—
77C2×#170—42no—
78C2×#170—42no—
79C2×#170—42no—
80C5×C4⋊C4—21no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4M1612yes—
83C42×C5—22no—
84C42×C5—42no—
85C4⋊Dic5—21no—
86C4⋊Dic5—41no—
87C4⋊Dic5—41no—
88C4⋊Dic5—41no—
89C4⋊Dic5M1612yes—
90#683—24no—
91#683—42no—
92#683—42no—
93#683—41no—
94#683—41no—
95C4×Dic5—21no—
96C4×Dic5—21no—
97C4×Dic5—41no—
98C4×Dic5—41no—
99C4×Dic5—41no—
100C4×Dic5—42no—
101C4×Dic5D812yes—
102C4×Dic5SD1612yes—
103C4×Dic5SD1612yes—
104C4×Dic5Q1612yes—
105C2×C4⋊Q8—51no—
106C2×C4×Q8—101no—
107C2×C4⋊C8—101no—
108C2×C4⋊C8—101no—
109#391—101no—
110#389—51no—
111#389—51no—
112#389—101no—
113#384—51no—
114C4×C4⋊C4—51no—
115C4×C4⋊C4—101no—
116C4×C4⋊C4AGL(1,𝔽5)11yescharacteristic
117C43—51no—
118#336—52no—
119#336—52no—
120#336—101no—
121#336—101no—
122C23×C5C2×C22⋊C411yescharacteristic
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5#10112yes—
135C2×C4×C5#10212yes—
136C2×C4×C5#10312yes—
137C2×C4×C5C2×M1611yescharacteristic
138C2×C4×C5C2×M1611yescharacteristic
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—22no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5#10212yes—
154C2×Dic5#10312yes—
155C2×Dic5C2×D811yescharacteristic
156C2×Dic5C2×SD1611yescharacteristic
157C2×Dic5C2×SD1611yescharacteristic
158C2×Dic5C2×Q1611yescharacteristic
159Dic10—48no—
160#170—82no—
161#170—82no—
162C22×Q8—101no—
163C22×C8—102no—
164C22×C8—102no—
165C4⋊Q8—102no—
166C4⋊Q8—102no—
167C4×Q8—202no—
168C4×Q8—202no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—101no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4—101no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
177C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
178C2×C42—21no—
179C2×C42—51no—
180C2×C42—51no—
181C2×C42—51no—
182C2×C42—51no—
183C2×C42—51no—
184C2×C42—51no—
185C2×C42—101no—
186C2×C42C2×AGL(1,𝔽5)11yescharacteristic
187C4⋊C8—202no—
188C4⋊C8—202no—
189#95—21no—
190#95—101no—
191#95—101no—
192#95—101no—
193C22×C5#40711yescharacteristic
194C22×C5#41011yescharacteristic
195C22×C5C2×#10111yescharacteristic
196C22×C5C2×#10211yescharacteristic
197C22×C5C2×#10311yescharacteristic
198C22×C5#42111yescharacteristic
199C22×C5#42111yescharacteristic
200C4×C5—21no—
201C4×C5—21no—
202C4×C5—41no—
203C4×C5—42no—
204C4×C5—81no—
205C4×C5#33214yes—
206Dic5—22no—
207Dic5—22no—
208Dic5—21no—
209Dic5—21no—
210Dic5—21no—
211Dic5—21no—
212Dic5—42no—
213Dic5—81no—
214C2×Q8—104no—
215C2×Q8—202no—
216C2×Q8—202no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
226C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
227C22×C4C22×AGL(1,𝔽5)11yescharacteristic
228C2×C8—202no—
229C2×C8—202no—
230C2×C8—202no—
231C2×C8—202no—
232C2×C8—202no—
233C2×C8—202no—
234C4⋊C4—21no—
235C4⋊C4—41no—
236C4⋊C4—52no—
237C4⋊C4—104no—
238C4⋊C4—101no—
239C4⋊C4—201no—
240C4⋊C4—201no—
241C4⋊C4—201no—
242C4⋊C4—202no—
243C4⋊C4—201no—
244C4⋊C4—201no—
245C4⋊C4—202no—
246C4⋊C4#70012yes—
247C42—22no—
248C42—42no—
249C42—52no—
250C42—52no—
251C42—52no—
252C42—52no—
253C42—101no—
254C42—101no—
255C42—201no—
256C42—201no—
257C42—201no—
258C42—202no—
259C2×C5#146711yescharacteristic
260C2×C5#148611yescharacteristic
261C2×C5#148711yescharacteristic
262C2×C5#151711yescharacteristic
263C2×C5#151811yescharacteristic
264C2×C5#153711yescharacteristic
265C2×C5C2×#33211yescharacteristic
266C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
267Q8—208no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—51no—
280C2×C4—51no—
281C2×C4—52no—
282C2×C4—51no—
283C2×C4—52no—
284C2×C4—51no—
285C2×C4—101no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—102no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4#400512yes—
300C2×C4#400712yes—
301C2×C4#400912yes—
302C2×C4C2×#70011yescharacteristic
303C2×C4D5⋊M1611yescharacteristic
304C8—402no—
305C8—402no—
306C5#765211yescharacteristic, complemented, Sylow
307C22#6574511yescharacteristic
308C22#6575611yescharacteristic
309C22C2×#400511yescharacteristic
310C22C2×#400711yescharacteristic
311C22C2×#400911yescharacteristic
312C22#6579511yescharacteristic
313C22#6579511yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—42no—
318C4—81no—
319C4—101no—
320C4—101no—
321C4—102no—
322C4—101no—
323C4—101no—
324C4—102no—
325C4—202no—
326C4—401no—
327C4#6487314yes—
328C2#1060416411yescharacteristic
329C2C2×#6487311yescharacteristic
330C2#1060435211yescharacteristic
331C2#1060439411yescharacteristic
332C2#1060440411yescharacteristic
333C2#1060442911yescharacteristic
334C2#1060443911yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#7652
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
306. C5#7652semidirect

Maximal subgroups

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

subgroupindex
C4×#40342
#106041872
#105987142
#105987132
#76525