Finite Group Databasebeta

← #13023220

Subgroups — #13023220

Order 1280.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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×#65009C211yesmaximal, characteristic
2#10604710C211yesmaximal, characteristic, complemented
3#10604709C211yesmaximal, characteristic, complemented
4#10598817C212yesmaximal
5#10598761C212yesmaximal, complemented
6C2×#4072C411yescharacteristic
7C2×C5×C22⋊C8C411yescharacteristic
8C2×C22⋊#168C2211yescharacteristic
9C2×#3947C411yescharacteristic
10C2×#3946C411yescharacteristic
11C2×#3946C2211yescharacteristic
12C2×C8×Dic5C2211yescharacteristic
13#65009—21no—
14#65009—21no—
15#65009—21no—
16#65009—21no—
17C22⋊#674C2212yes—
18C22⋊#674C2212yes—
19#64888—21no—
20#64888—21no—
21#64886—21no—
22#64885—21no—
23#11461—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C22×C5×C8C2×C411yescharacteristic
26C22×C5×C8C2×C411yescharacteristic
27C2×C22⋊Dic5C811yescharacteristic
28C2×C22⋊Dic5C811yescharacteristic
29#4072—21no—
30#4072—21no—
31#4072—21no—
32#4072—21no—
33C2×C4⋊Dic5C811yescharacteristic
34C2×C4⋊Dic5C811yescharacteristic
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5C2×C411yescharacteristic
37C22×#168C2×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#3947—21no—
47#3946—21no—
48#3946—21no—
49#3946—21no—
50#3946—21no—
51C8×Dic5D411yescharacteristic
52C8×Dic5D411yescharacteristic
53C8×Dic5D411yescharacteristic
54C8×Dic5D411yescharacteristic
55C2×#433—51no—
56#2163—51no—
57#2162—51no—
58#1322—52no—
59#1314—52no—
60C24×C5C2×C811yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5C2×C811yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×Dic5C2×C811yescharacteristic
68C22×Dic5C2×C811yescharacteristic
69C22×Dic5C2×C811yescharacteristic
70C22×Dic5C2×C811yescharacteristic
71C2×C5×C8—21no—
72C2×C5×C8—41no—
73C2×C5×C8—41no—
74C2×C5×C8C22⋊C411yescharacteristic
75C2×C5×C8C22⋊C411yescharacteristic
76C22⋊Dic5—21no—
77C22⋊Dic5—21no—
78C22⋊Dic5—21no—
79C22⋊Dic5—21no—
80C4⋊Dic5—21no—
81C4⋊Dic5—21no—
82C4⋊Dic5—21no—
83C4⋊Dic5—21no—
84C4×Dic5—21no—
85C4×Dic5—21no—
86C4×Dic5C22⋊C411yescharacteristic
87C4×Dic5C22⋊C411yescharacteristic
88C4×Dic5M1611yescharacteristic
89C4×Dic5M1611yescharacteristic
90C2×#168—21no—
91C2×#168—41no—
92C2×#168—41no—
93C2×#168C2×D411yescharacteristic
94C2×#168C2×D411yescharacteristic
95#674—42no—
96#674—42no—
97C2×#117—51no—
98#433—101no—
99#433—101no—
100#433—101no—
101#433—101no—
102C2×C4⋊C8—51no—
103C2×C4⋊C8—51no—
104C2×C22⋊C8—51no—
105C2×C22⋊C8AGL(1,𝔽5)11yescharacteristic
106C2×#97—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×C5—22no—
116C23×C5—41no—
117C23×C5—41no—
118C23×C5C22×C811yescharacteristic
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5C2×C22⋊C411yescharacteristic
127C2×C4×C5C2×M1611yescharacteristic
128C2×Dic5—22no—
129C2×Dic5—21no—
130C2×Dic5—21no—
131C2×Dic5—22no—
132C2×Dic5—41no—
133C2×Dic5—41no—
134C2×Dic5C22⋊C811yescharacteristic
135C2×Dic5C22⋊C811yescharacteristic
136C2×Dic5C22⋊C811yescharacteristic
137C2×Dic5C22⋊C811yescharacteristic
138C5×C8—21no—
139C5×C8—21no—
140C5×C8—41no—
141#168—21no—
142#168—21no—
143#168—41no—
144C23×C4C2×AGL(1,𝔽5)11yescharacteristic
145C22×C8—51no—
146C22×C8—51no—
147C22×C8C2×AGL(1,𝔽5)11yescharacteristic
148C22×C8C2×AGL(1,𝔽5)11yescharacteristic
149#117—101no—
150#117—101no—
151#117—101no—
152#117—101no—
153C2×C4⋊C4—51no—
154C2×C4⋊C4—51no—
155C2×C22⋊C4—51no—
156C2×C22⋊C4—51no—
157C2×C42—51no—
158C2×C42—51no—
159C2×C16—102no—
160C2×C16—102no—
161C4⋊C8—101no—
162C4⋊C8—101no—
163C4⋊C8—101no—
164C4⋊C8—101no—
165C22⋊C8—21no—
166C22⋊C8—21no—
167C22⋊C8—101no—
168C22⋊C8—101no—
169#97—101no—
170#97—101no—
171C4×C8—51no—
172C4×C8—51no—
173C4×C8—51no—
174C4×C8—51no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—41no—
178C22×C5—41no—
179C22×C5—41no—
180C22×C5—82no—
181C22×C5C2×C22⋊C811yescharacteristic
182C22×C5#50412yes—
183C4×C5—21no—
184C4×C5—41no—
185C4×C5#41011yescharacteristic
186C4×C5#41311yescharacteristic
187Dic5—21no—
188Dic5—21no—
189Dic5—21no—
190Dic5—21no—
191Dic5—41no—
192Dic5—41no—
193C24D5⋊C811yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—51no—
201C22×C4—51no—
202C22×C4D5⋊C811yescharacteristic
203C22×C4C22×AGL(1,𝔽5)11yescharacteristic
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—51no—
208C2×C8—51no—
209C2×C8—101no—
210C2×C8—201no—
211C2×C8—201no—
212C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
213C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
214C4⋊C4—101no—
215C4⋊C4—101no—
216C4⋊C4—101no—
217C4⋊C4—101no—
218C22⋊C4—101no—
219C22⋊C4—101no—
220C22⋊C4—101no—
221C22⋊C4—101no—
222C42—51no—
223C42—51no—
224C42—51no—
225C42—51no—
226C42—101no—
227C42—101no—
228C16—202no—
229C16—202no—
230C2×C5—22no—
231C2×C5—81no—
232C2×C5#145811yescharacteristic
233C2×C5#211311yescharacteristic
234C2×C5#211511yescharacteristic
235C23—21no—
236C23—22no—
237C23—41no—
238C23—41no—
239C23C2×D5⋊C811yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—51no—
248C2×C4—51no—
249C2×C4—51no—
250C2×C4—51no—
251C2×C4—102no—
252C2×C4—102no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4D5⋊M1611yescharacteristic
258C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
259C8—21no—
260C8—21no—
261C8—41no—
262C8—101no—
263C8—101no—
264C8—201no—
265C5#1146111yescharacteristic, complemented, Sylow
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—82no—
272C22#6572512yes—
273C22D5⋊(C22⋊C8)11yescharacteristic
274C4—21no—
275C4—41no—
276C4—101no—
277C4—101no—
278C4—101no—
279C4—101no—
280C4—201no—
281C4—201no—
282C4#6577111yescharacteristic
283C4#6577711yescharacteristic
284C2—22no—
285C2—81no—
286C2#1060420011yescharacteristic
287C2#1060471311yescharacteristic
288C2#1060474311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C22⋊C8C4
socleC22×C5C2×C22⋊C8
prime radicalC24×C5C2×C8
cosocleC22×#168C23
hypercenterC2×C22⋊C8AGL(1,𝔽5)
hypocenterC5#11461
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10604710C2semidirect
3. #10604709C2semidirect
5. #10598761C2semidirect
265. C5#11461semidirect

Maximal subgroups

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

subgroupindex
C2×#650092
#106047102
#106047092
#105988172
#105987612
#114615