Finite Group Databasebeta

← #13023232

Subgroups — #13023232

Order 1280.

310 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 84 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#10610379C211yesmaximal, characteristic
2#10604710C211yesmaximal, characteristic, complemented
3#10604709C211yesmaximal, characteristic, complemented
4#10598831C212yesmaximal
5#10598782C212yesmaximal, complemented
6#41×Dic5C411yescharacteristic
7C5×#408C411yescharacteristic
8#65523C2211yescharacteristic
9#65408C2211yescharacteristic
10M16×Dic5C411yescharacteristic
11#65391C411yescharacteristic
12C2×C8×Dic5C2211yescharacteristic
13#65009—21no—
14#65009—21no—
15#65007—21no—
16#65007—21no—
17C22⋊#674C2212yes—
18C22⋊#674C2212yes—
19#64888—21no—
20#64888—21no—
21#64886—21no—
22#64885—21no—
23#11464—51nomaximal, Sylow
24C2×C5×#41C2×C411yescharacteristic
25C2×C5×M16C2×C411yescharacteristic
26C22×C5×C8C2×C411yescharacteristic
27Q8×Dic5C811yescharacteristic
28Q8×Dic5C811yescharacteristic
29D4×Dic5—21no—
30D4×Dic5—21no—
31D4×Dic5C811yescharacteristic
32D4×Dic5C811yescharacteristic
33#4072—21no—
34#4072C2×C411yescharacteristic
35C2×C4×Dic5—21no—
36C2×C4×Dic5C2×C411yescharacteristic
37C2×#681C2×C411yescharacteristic
38C22×#168C2311yescharacteristic
39C2×#674—22no—
40C2×#674—22no—
41C5×C22⋊C8—21no—
42C5×C22⋊C8—21no—
43C22⋊#168—21no—
44C22⋊#168—21no—
45#3947—21no—
46#3946—21no—
47#3946—21no—
48#3946—21no—
49#3946—21no—
50C8×Dic5—21no—
51C8×Dic5D411yescharacteristic
52C8×Dic5D411yescharacteristic
53C8×Dic5D411yescharacteristic
54C8×Dic5D411yescharacteristic
55#2922—51no—
56#2163—51no—
57#2162—51no—
58#1323—52no—
59#1315—52no—
60C5×#41—41no—
61C5×#41—41no—
62C2×C5×Q8C2×C811yescharacteristic
63C2×C5×D4—21no—
64C2×C5×D4C2×C811yescharacteristic
65C22×C4×C5—21no—
66C22×C4×C5C22×C411yescharacteristic
67C22×Dic5—21no—
68C22×Dic5—21no—
69C22×Dic5M1611yescharacteristic
70C22×Dic5M1611yescharacteristic
71C5×M16—41no—
72C2×C5×C8—21no—
73C2×C5×C8—41no—
74C2×C5×C8C22⋊C411yescharacteristic
75C2×C5×C8C22⋊C411yescharacteristic
76C22⋊Dic5—21no—
77C22⋊Dic5—21no—
78C22⋊Dic5—21no—
79C4⋊Dic5—21no—
80C4⋊Dic5—21no—
81C4⋊Dic5C2×C811yescharacteristic
82C4⋊Dic5C2×C811yescharacteristic
83C4×Dic5—21no—
84C4×Dic5—21no—
85C4×Dic5—21no—
86C4×Dic5C22⋊C411yescharacteristic
87C4×Dic5C22⋊C411yescharacteristic
88C4×Dic5C2×C811yescharacteristic
89C4×Dic5C2×C811yescharacteristic
90#681—41no—
91C2×#168—21no—
92C2×#168—41no—
93C2×#168C2×D411yescharacteristic
94C2×#168C2×D411yescharacteristic
95#674—42no—
96#674—42no—
97C4×#41—51no—
98#433—101no—
99#433—101no—
100#431—101no—
101#431—101no—
102#424—51no—
103#424—51no—
104#408—51no—
105#408AGL(1,𝔽5)11yescharacteristic
106C4×M16—51no—
107C2×C4×C8—51no—
108C4⋊C16—101no—
109C4⋊C16—101no—
110C22⋊C16—52no—
111C22⋊C16—52no—
112#346—101no—
113C4×C16—101no—
114C23×C5—21no—
115C23×C5C2×M1611yescharacteristic
116C5×Q8—41no—
117C5×D4—41no—
118C5×D4—42no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5C2×C22⋊C411yescharacteristic
125C2×C4×C5C22×C811yescharacteristic
126C2×Dic5—22no—
127C2×Dic5—21no—
128C2×Dic5—21no—
129C2×Dic5—41no—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5C22⋊C811yescharacteristic
133C2×Dic5C22⋊C811yescharacteristic
134C2×Dic5C22⋊C811yescharacteristic
135C2×Dic5C22⋊C811yescharacteristic
136C5×C8—21no—
137C5×C8—21no—
138C5×C8—41no—
139#168—21no—
140#168—21no—
141#168—41no—
142C2×#41C2×AGL(1,𝔽5)11yescharacteristic
143C2×M16—51no—
144C2×M16C2×AGL(1,𝔽5)11yescharacteristic
145C22×C8—51no—
146C22×C8C2×AGL(1,𝔽5)11yescharacteristic
147C4×Q8—51no—
148C4×Q8—51no—
149C4×D4—51no—
150C4×D4—51no—
151C4×D4—101no—
152C4×D4—101no—
153#117—51no—
154#117—101no—
155C2×C42—51no—
156C2×C42—101no—
157C2×C16—102no—
158C2×C16—102no—
159C4⋊C8—101no—
160C4⋊C8—101no—
161C4⋊C8—101no—
162C4⋊C8—101no—
163C22⋊C8—21no—
164C22⋊C8—21no—
165C22⋊C8—101no—
166C22⋊C8—101no—
167#97—101no—
168C4×C8—51no—
169C4×C8—51no—
170C4×C8—51no—
171C4×C8—51no—
172C4×C8—101no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—41no—
177C22×C5—41no—
178C22×C5—41no—
179C22×C5C2×C22⋊C811yescharacteristic
180C4×C5—21no—
181C4×C5—41no—
182C4×C5#41011yescharacteristic
183C4×C5#41311yescharacteristic
184Dic5—21no—
185Dic5—21no—
186Dic5—21no—
187Dic5—41no—
188Dic5—41no—
189Dic5#35012yes—
190#41—41no—
191#41—41no—
192C2×Q8D5⋊C811yescharacteristic
193C2×D4—21no—
194C2×D4D5⋊C811yescharacteristic
195C22×C4—21no—
196C22×C4—51no—
197C22×C4—51no—
198C22×C4—101no—
199C22×C4—101no—
200C22×C4C22×AGL(1,𝔽5)11yescharacteristic
201M16—41no—
202M16—201no—
203C2×C8—21no—
204C2×C8—41no—
205C2×C8—51no—
206C2×C8—51no—
207C2×C8—101no—
208C2×C8—201no—
209C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
210C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
211C4⋊C4—51no—
212C4⋊C4—51no—
213C4⋊C4—101no—
214C4⋊C4—101no—
215C22⋊C4—101no—
216C22⋊C4—101no—
217C22⋊C4—101no—
218C42—51no—
219C42—51no—
220C42—51no—
221C42—51no—
222C42—101no—
223C42—101no—
224C42—101no—
225C16—202no—
226C16—202no—
227C2×C5—41no—
228C2×C5—81no—
229C2×C5#145811yescharacteristic
230C2×C5C2×#35011yescharacteristic
231C2×C5#211711yescharacteristic
232C23—21no—
233C23D5⋊M1611yescharacteristic
234Q8—41no—
235D4—41no—
236D4—42no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—51no—
243C2×C4—51no—
244C2×C4—51no—
245C2×C4—51no—
246C2×C4—102no—
247C2×C4—101no—
248C2×C4—101no—
249C2×C4—202no—
250C2×C4—201no—
251C2×C4—202no—
252C2×C4C2×D5⋊C811yescharacteristic
253C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—101no—
258C8—101no—
259C8—201no—
260C5#1146411yescharacteristic, complemented, Sylow
261C22—21no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22D5⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—52no—
271C4—101no—
272C4—101no—
273C4—101no—
274C4—201no—
275C4—201no—
276C4#6577111yescharacteristic
277C4#6577711yescharacteristic
278C2—41no—
279C2—81no—
280C2#1060420011yescharacteristic
281C2D5⋊#35011yescharacteristic
282C2#1060477611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#408C4
socleC22×C5C2×C22⋊C8
prime radicalC2×C5×#41C2×C4
cosocleC22×#168C23
hypercenter#408AGL(1,𝔽5)
hypocenterC5#11464
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #10604710C2semidirect
3. #10604709C2semidirect
5. #10598782C2semidirect
260. C5#11464semidirect

Maximal subgroups

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

subgroupindex
#106103792
#106047102
#106047092
#105988312
#105987822
#114645