Finite Group Databasebeta

← #13021450

Subgroups — #13021450

Order 1280.

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

normal subgroups only

This group has 518 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
1#10607698C211yesmaximal, characteristic
2#10604185C211yesmaximal, characteristic
3C4×#4002C211yesmaximal, characteristic
4#10598721C212yesmaximal
5#10598721C212yesmaximal
6C2×#4034C411yescharacteristic
7C2×#4033—21no—
8C2×#4002—21no—
9C2×#4002—21no—
10C2×C4⋊#170C2212yes—
11C2×C4×#170C2212yes—
12C5×#389C411yescharacteristic
13#65265C411yescharacteristic
14C4⋊C4×Dic5C2211yescharacteristic
15C4⋊C4×Dic5C2211yescharacteristic
16#65261—21no—
17C42×Dic5C2211yescharacteristic
18#65217C411yescharacteristic
19#64938—21no—
20#64935—21no—
21#64918—21no—
22#64918—21no—
23#9877—51nomaximal, Sylow
24C22×Dic10—21no—
25C22×#170—22no—
26C22×#170—22no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C4⋊Dic5C2×C411yescharacteristic
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×#683—21no—
35C2×#683—21no—
36C2×#683—21no—
37C2×C4×Dic5—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—
47#4033—44no—
48#4002—24no—
49#4002—24no—
50C4⋊#170—24no—
51C4×#170—22no—
52C4×#170Q814yescomplemented
53C5×#95—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57C4×C4⋊Q8—51no—
58#1831—51no—
59C4×#97—51no—
60#1279—52no—
61#1279—52no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×Dic5—21no—
68C22×Dic5—21no—
69C22×Dic5C22⋊C411yescharacteristic
70C22×Dic5C22⋊C411yescharacteristic
71C22×Dic5C2×D411yescharacteristic
72C22×Dic5C2×D411yescharacteristic
73C2×Dic10—24no—
74C2×Dic10—42no—
75C2×Dic10—42no—
76C2×#170—24no—
77C2×#170—24no—
78C2×#170—24no—
79C2×#170—42no—
80C2×#170—42no—
81C2×#170—42no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—42no—
85C5×C4⋊C4M1612yes—
86C42×C5—22no—
87C4⋊Dic5—21no—
88C4⋊Dic5—22no—
89C4⋊Dic5M1612yes—
90#683—24no—
91#683—42no—
92#683—42no—
93#683—42no—
94C4×Dic5—21no—
95C4×Dic5—21no—
96C4×Dic5—22no—
97C4×Dic5—22no—
98C4×Dic5—22no—
99C4×Dic5—22no—
100C4×Dic5—42no—
101C4×Dic5—42no—
102C4×Dic5C2×Q812yes—
103C4×Dic5#4112yes—
104C2×C4⋊Q8—51no—
105C2×C4×Q8—101no—
106C2×C4⋊C8—52no—
107C2×#97—101no—
108C2×#97—101no—
109C2×C4×C8—52no—
110#391—101no—
111#389—51no—
112#389—101no—
113#389AGL(1,𝔽5)11yescharacteristic
114#384—51no—
115C4×C4⋊C4—51no—
116C4×C4⋊C4—51no—
117C4×C4⋊C4—101no—
118C43—51no—
119#336—101no—
120#336—101no—
121C23×C5C2×C22⋊C411yescharacteristic
122C2×C4×C5—22no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
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×C5C4×Q812yes—
135C2×C4×C5C2×M1611yescharacteristic
136C2×C4×C5C2×M1611yescharacteristic
137C2×C4×C5#13112yes—
138C2×Dic5—21no—
139C2×Dic5—21no—
140C2×Dic5—21no—
141C2×Dic5—21no—
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—22no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5#10412yes—
151C2×Dic5#10412yes—
152C2×Dic5C22⋊Q812yes—
153C2×Dic5#12411yescharacteristic
154C2×Dic5C4⋊Q811yescharacteristic
155C2×Dic5AGL(1,ℤ/8)12yes—
156C2×Dic5#13712yes—
157Dic10—48no—
158#170—28no—
159#170—82no—
160C22×Q8—101no—
161C22×C8—102no—
162C22×C8—102no—
163C4⋊Q8—102no—
164C4⋊Q8—102no—
165C4×Q8—204no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—51no—
168C2×C4⋊C4—51no—
169C2×C4⋊C4—101no—
170C2×C4⋊C4—101no—
171C2×C4⋊C4—101no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
174C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
175C2×C42—51no—
176C2×C42—51no—
177C2×C42—51no—
178C2×C42—51no—
179C2×C42—51no—
180C2×C42—51no—
181C2×C42—101no—
182C2×C42—101no—
183C2×C42C2×AGL(1,𝔽5)11yescharacteristic
184C4⋊C8—104no—
185#97—104no—
186#97—104no—
187C4×C8—54no—
188C4×C8—102no—
189#95—21no—
190#95—101no—
191#95—101no—
192#95—101no—
193C22×C5#39111yescharacteristic
194C22×C5#40711yescharacteristic
195C22×C5#40811yescharacteristic
196C22×C5#41811yescharacteristic
197C22×C5#41911yescharacteristic
198C22×C5C2×#10411yescharacteristic
199C22×C5C2×#10411yescharacteristic
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—42no—
203C4×C5—81no—
204C4×C5#44612yes—
205C4×C5#44612yes—
206Dic5—22no—
207Dic5—22no—
208Dic5—22no—
209Dic5—42no—
210Dic5—81no—
211Dic5#48912yes—
212Dic5#50112yes—
213C2×Q8—104no—
214C2×Q8—202no—
215C2×Q8—202no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—101no—
223C22×C4—101no—
224C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
225C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
226C22×C4C22×AGL(1,𝔽5)11yescharacteristic
227C2×C8—104no—
228C2×C8—104no—
229C2×C8—104no—
230C2×C8—202no—
231C2×C8—202no—
232C2×C8—202no—
233C4⋊C4—21no—
234C4⋊C4—22no—
235C4⋊C4—42no—
236C4⋊C4—52no—
237C4⋊C4—104no—
238C4⋊C4—101no—
239C4⋊C4—102no—
240C4⋊C4—202no—
241C4⋊C4—202no—
242C4⋊C4—202no—
243C4⋊C4#70012yes—
244C42—22no—
245C42—52no—
246C42—52no—
247C42—102no—
248C42—102no—
249C42—102no—
250C42—102no—
251C42—101no—
252C42—101no—
253C42—202no—
254C42—202no—
255C2×C5#148411yescharacteristic
256C2×C5#148511yescharacteristic
257C2×C5#149011yescharacteristic
258C2×C5#149111yescharacteristic
259C2×C5#198511yescharacteristic
260C2×C5#199311yescharacteristic
261C2×C5#199411yescharacteristic
262C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263Q8—208no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—52no—
277C2×C4—52no—
278C2×C4—51no—
279C2×C4—51no—
280C2×C4—52no—
281C2×C4—52no—
282C2×C4—52no—
283C2×C4—101no—
284C2×C4—101no—
285C2×C4—101no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—101no—
289C2×C4—102no—
290C2×C4—201no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4—201no—
294C2×C4—201no—
295C2×C4C2×#70011yescharacteristic
296C2×C4D5⋊M1611yescharacteristic
297C2×C4#413112yes—
298C2×C4Q8×AGL(1,𝔽5)12yes—
299C8—108no—
300C8—402no—
301C5#987711yescharacteristic, complemented, Sylow
302C22#6575611yescharacteristic
303C22#6576711yescharacteristic
304C22#6577511yescharacteristic
305C22#6578211yescharacteristic
306C22(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
307C22D5⋊#10411yescharacteristic
308C22D5⋊#10411yescharacteristic
309C4—42no—
310C4—41no—
311C4—41no—
312C4—52no—
313C4—52no—
314C4—81no—
315C4—102no—
316C4—102no—
317C4—102no—
318C4—202no—
319C4—401no—
320C4#6570712yes—
321C4#6570912yes—
322C2#1060433211yescharacteristic
323C2#1060440711yescharacteristic
324C2#1060444211yescharacteristic
325C2#1060448011yescharacteristic
326C2#1060451211yescharacteristic
327C2#1060458711yescharacteristic
328C2#1060467511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#389C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#389AGL(1,𝔽5)
hypocenterC5#9877
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
52. C4×#170Q8semidirect
301. C5#9877semidirect

Maximal subgroups

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

subgroupindex
#106076982
#106041852
C4×#40022
#105987212
#98775