Finite Group Databasebeta

← #13014628

Subgroups — #13014628

Order 1280.

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

normal subgroups only

This group has 462 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
1#10607693C211yesmaximal, characteristic
2C4×#4004C211yesmaximal, characteristic
3#10604174C211yesmaximal, characteristic
4#10598715C212yesmaximal
5#10598713C212yesmaximal
6C2×#4033C411yescharacteristic
7C2×#4004—21no—
8C2×C4×#170—21no—
9C2×C4×#170—21no—
10C5×#389C411yescharacteristic
11#65274C2211yescharacteristic
12#65267—21no—
13C4⋊C4×Dic5—21no—
14C4⋊C4×Dic5C411yescharacteristic
15#65263C2211yescharacteristic
16C42×Dic5C2211yescharacteristic
17#65218C411yescharacteristic
18#64944—21no—
19#64937—21no—
20#64918—21no—
21#64918C2212yes—
22#64918C2212yes—
23#7562—51nomaximal, Sylow
24C22×Dic10C2×C411yescharacteristic
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⋊Dic5—21no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5—21no—
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5C2311yescharacteristic
42#4033—22no—
43#4033C814yescomplemented
44#4004—24no—
45C4×#170—24no—
46C4×#170—42no—
47C5×#95—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#2295—51no—
55C4×C4⋊C8—51no—
56#1744—51no—
57#1272—52no—
58#1271—52no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×Dic5—21no—
65C22×Dic5—21no—
66C22×Dic5C22⋊C411yescharacteristic
67C22×Dic5C22⋊C411yescharacteristic
68C22×Dic5C2×D411yescharacteristic
69C22×Dic5C2×D411yescharacteristic
70C2×Dic10—21no—
71C2×Dic10—41no—
72C2×Dic10—41no—
73C2×Dic10C2×C812yes—
74C2×#170—24no—
75C2×#170—24no—
76C2×#170—42no—
77C2×#170—42no—
78C2×#170—42no—
79C2×#170—42no—
80C5×C4⋊C4—21no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4C2×C812yes—
84C42×C5—41no—
85C4⋊Dic5—42no—
86C4⋊Dic5—41no—
87#683—24no—
88C4×Dic5—22no—
89C4×Dic5—24no—
90C4×Dic5—22no—
91C4×Dic5—22no—
92C4×Dic5—41no—
93C4×Dic5—42no—
94C4×Dic5C2×C812yes—
95C4×Dic5M1612yes—
96C4×Dic5SD1612yes—
97C4×Dic5Q1612yes—
98C2×C4×Q8—51no—
99C2×C4⋊C8—101no—
100C2×C4×C8—101no—
101C2×C4×C8—101no—
102#391—51no—
103#391—51no—
104#389—51no—
105#389AGL(1,𝔽5)11yescharacteristic
106#387—101no—
107#387—101no—
108C4×C4⋊C4—51no—
109C4×C4⋊C4—101no—
110#376—101no—
111C43—51no—
112#336—52no—
113#336—52no—
114#336—101no—
115C23×C5C2×C22⋊C411yescharacteristic
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—22no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5#10312yes—
129C2×C4×C5#10412yes—
130C2×C4×C5C22×C811yescharacteristic
131C2×C4×C5C2×M1611yescharacteristic
132C2×Dic5—21no—
133C2×Dic5—21no—
134C2×Dic5—21no—
135C2×Dic5—21no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—22no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5C22⋊C812yes—
145C2×Dic5C22⋊C812yes—
146C2×Dic5#10312yes—
147C2×Dic5#10412yes—
148C2×Dic5C2×SD1611yescharacteristic
149C2×Dic5C2×Q1611yescharacteristic
150C2×Dic5#13512yes—
151Dic10—42no—
152Dic10—42no—
153#170—44no—
154#170—44no—
155C22×Q8—51no—
156C22×C8—102no—
157C22×C8—102no—
158C4×Q8—54no—
159C4×Q8—102no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—101no—
163C2×C4⋊C4—101no—
164C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
165C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
166C2×C42—51no—
167C2×C42—51no—
168C2×C42—51no—
169C2×C42—51no—
170C2×C42—51no—
171C2×C42—51no—
172C2×C42—101no—
173C2×C42—101no—
174C2×C42C2×AGL(1,𝔽5)11yescharacteristic
175C4⋊C8—104no—
176C4×C8—104no—
177C4×C8—202no—
178#95—21no—
179#95—101no—
180#95—101no—
181#95—101no—
182#95—101no—
183#95—101no—
184#95—101no—
185C22×C5C2×C22⋊C811yescharacteristic
186C22×C5#41011yescharacteristic
187C22×C5#41311yescharacteristic
188C22×C5C2×#10311yescharacteristic
189C22×C5#41611yescharacteristic
190C22×C5C2×#10411yescharacteristic
191C22×C5C2×#10411yescharacteristic
192C4×C5—22no—
193C4×C5—21no—
194C4×C5—21no—
195C4×C5—22no—
196C4×C5—42no—
197C4×C5—81no—
198Dic5—22no—
199Dic5—22no—
200Dic5—21no—
201Dic5—21no—
202Dic5—42no—
203Dic5—81no—
204Dic5Q8⋊C814yes—
205C2×Q8—52no—
206C2×Q8—101no—
207C2×Q8—201no—
208C2×Q8—201no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—51no—
212C22×C4—51no—
213C22×C4—51no—
214C22×C4—51no—
215C22×C4—101no—
216C22×C4—101no—
217C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
218C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
219C22×C4C22×AGL(1,𝔽5)11yescharacteristic
220C2×C8—104no—
221C2×C8—104no—
222C2×C8—202no—
223C2×C8—202no—
224C2×C8—202no—
225C2×C8—202no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—104no—
230C4⋊C4—201no—
231C4⋊C4—202no—
232C4⋊C4D5⋊C812yes—
233C42—41no—
234C42—52no—
235C42—52no—
236C42—52no—
237C42—52no—
238C42—102no—
239C42—102no—
240C42—104no—
241C42—102no—
242C42—201no—
243C42—202no—
244C2×C5#145811yescharacteristic
245C2×C5C2×Q8⋊C811yescharacteristic
246C2×C5#147611yescharacteristic
247C2×C5#150011yescharacteristic
248C2×C5#150311yescharacteristic
249C2×C5#152411yescharacteristic
250C2×C5#154211yescharacteristic
251C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
252Q8—202no—
253Q8—202no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—52no—
267C2×C4—52no—
268C2×C4—52no—
269C2×C4—52no—
270C2×C4—52no—
271C2×C4—51no—
272C2×C4—51no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—102no—
280C2×C4—201no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4#400812yes—
286C2×C4#400912yes—
287C2×C4C2×D5⋊C811yescharacteristic
288C2×C4D5⋊M1611yescharacteristic
289C8—204no—
290C8—204no—
291C5#756211yescharacteristic, complemented, Sylow
292C22D5⋊(C22⋊C8)11yescharacteristic
293C22C2×#400811yescharacteristic
294C22#6577711yescharacteristic
295C22C2×#400911yescharacteristic
296C22#6578511yescharacteristic
297C22D5⋊#10411yescharacteristic
298C22#6579411yescharacteristic
299C4—21no—
300C4—21no—
301C4—22no—
302C4—22no—
303C4—42no—
304C4—54no—
305C4—81no—
306C4—102no—
307C4—101no—
308C4—101no—
309C4—102no—
310C4—202no—
311C4—401no—
312C2#1060428911yescharacteristic
313C2#1060440111yescharacteristic
314C2D5⋊(Q8⋊C8)11yescharacteristic
315C2#1060447311yescharacteristic
316C2#1060451711yescharacteristic
317C2#1060457311yescharacteristic
318C2#1060462211yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#389C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#389AGL(1,𝔽5)
hypocenterC5#7562
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
43. #4033C8semidirect
291. C5#7562semidirect

Maximal subgroups

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

subgroupindex
#106076932
C4×#40042
#106041742
#105987152
#105987132
#75625