Finite Group Databasebeta

← #11986327

Subgroups — #11986327

Order 1280.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C5×#1820C211yesmaximal, characteristic
2#10602375C211yesmaximal, characteristic
3#10602365C211yesmaximal, characteristic
4C2×C5×#117C2211yescharacteristic
5C5×#381—21no—
6C2×C22⋊#168—21no—
7#65215—21no—
8C2×#3935C411yescharacteristic, complemented
9C2×C4×#168C411yescharacteristic, complemented
10C5×#342—21no—
11C5×#342C412yes—
12#64748C412yescomplemented
13#64745—21no—
14#64744—21no—
15#7214—51nomaximal, Sylow
16C23×C4×C5D411yescharacteristic
17C5×#117—41no—
18C5×#117—41no—
19C2×C5×C4⋊C4C2×C411yescharacteristic
20C2×C5×C4⋊C4Q811yescharacteristic
21C2×C5×C22⋊C4—22no—
22C2×C5×C22⋊C4C2×C411yescharacteristic
23C2×C5×C22⋊C4D411yescharacteristic
24C2×C42×C5C2×C411yescharacteristic
25C2×C42×C5D411yescharacteristic
26C22×#168—21no—
27C22×#168—21no—
28C5×#95—41no—
29C5×#95—41no—
30C22⋊#168—24no—
31C22⋊#168—22no—
32C4⋊#168—41no—
33#3935—41no—
34#3935—41no—
35C4×#168—41no—
36#1820D511yescharacteristic
37#1750—51no—
38#1464—51no—
39C24×C5C22⋊C411yescharacteristic
40C22×C4×C5—22no—
41C22×C4×C5—21no—
42C22×C4×C5—21no—
43C22×C4×C5—41no—
44C22×C4×C5—42no—
45C22×C4×C5C4211yescharacteristic
46C22×C4×C5C22⋊C411yescharacteristic
47C22×C4×C5C22⋊C411yescharacteristic
48C22×C4×C5C4⋊C411yescharacteristic
49C22×C4×C5C4⋊C411yescharacteristic
50C22×C4×C5C4⋊C411yescharacteristic
51C5×C4⋊C4—41no—
52C5×C4⋊C4—41no—
53C5×C22⋊C4—41no—
54C5×C22⋊C4—41no—
55C5×C22⋊C4—42no—
56C5×C22⋊C4—42no—
57C42×C5—21no—
58C42×C5—21no—
59C42×C5—21no—
60C42×C5—21no—
61C2×#168—22no—
62C2×#168—22no—
63C2×#168—41no—
64C2×#168—41no—
65C2×#168—41no—
66C2×#168—41no—
67C2×#168—42no—
68C2×#117C2×D511yescharacteristic
69#432—101no—
70C2×C22⋊C8—101no—
71C2×#97—51no—
72C2×C4×C8—51no—
73#381—21no—
74#342—21no—
75#342Dic512yes—
76#336—101no—
77#324—52no—
78#323—101no—
79C23×C5—21no—
80C23×C5—21no—
81C23×C5—41no—
82C23×C5—41no—
83C23×C5#9511yescharacteristic
84C23×C5#10412yes—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—42no—
95C2×C4×C5—42no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5—41no—
99C2×C4×C5—41no—
100C2×C4×C5—82no—
101C2×C4×C5—82no—
102C2×C4×C5—82no—
103C2×C4×C5#9911yescharacteristic
104C2×C4×C5#9911yescharacteristic
105#168—42no—
106#168—42no—
107#168—82no—
108C23×C4C22⋊D511yescharacteristic
109C22×C8—101no—
110C22×C8—101no—
111#117—41no—
112#117—41no—
113C2×C4⋊C4Dic1011yescharacteristic
114C2×C4⋊C4C4×D511yescharacteristic
115C2×C22⋊C4—22no—
116C2×C22⋊C4C2×Dic511yescharacteristic
117C2×C22⋊C4C22⋊D511yescharacteristic
118C2×C42C4×D511yescharacteristic
119C2×C42D2011yescharacteristic
120C4⋊C8—201no—
121C22⋊C8—104no—
122C22⋊C8—102no—
123#97—201no—
124#97—201no—
125C4×C8—201no—
126#95—41no—
127#95—41no—
128C22×C5—21no—
129C22×C5—21no—
130C22×C5—22no—
131C22×C5—42no—
132C22×C5—41no—
133C22×C5—41no—
134C22×C5—81no—
135C22×C5H(3,ℤ/4)11yescharacteristic
136C22×C5#33911yescharacteristic
137C22×C5#34211yescharacteristic
138C4×C5—21no—
139C4×C5—21no—
140C4×C5—41no—
141C4×C5—41no—
142C4×C5—41no—
143C4×C5—41no—
144C4×C5—41no—
145C4×C5—162no—
146C24C22⋊Dic511yescharacteristic
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—41no—
151C22×C4—42no—
152C22×C4C4×Dic511yescharacteristic
153C22×C4#68311yescharacteristic
154C22×C4#68311yescharacteristic
155C22×C4C4⋊Dic511yescharacteristic
156C22×C4#68511yescharacteristic
157C22×C4#68511yescharacteristic
158C2×C8—102no—
159C2×C8—102no—
160C2×C8—201no—
161C2×C8—201no—
162C2×C8—201no—
163C2×C8—201no—
164C2×C8—202no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—21no—
172C42—21no—
173C42—21no—
174C42—21no—
175C2×C5—21no—
176C2×C5—21no—
177C2×C5—42no—
178C2×C5#128411yescharacteristic
179C2×C5#139111yescharacteristic
180C2×C5#139511yescharacteristic
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#396311yescharacteristic
186C23#396912yes—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4—82no—
205C2×C4#393811yescharacteristic
206C2×C4#393811yescharacteristic
207C8—202no—
208C8—202no—
209C8—402no—
210C5#721411yescharacteristic, complemented, Sylow
211C22—21no—
212C22—21no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22#6474711yescharacteristic
219C22#6475111yescharacteristic
220C22#6475211yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—162no—
229C2—21no—
230C2—21no—
231C2—42no—
232C2#1059811911yescharacteristic
233C2#1059818711yescharacteristic
234C2#1059818811yescharacteristic
subgroupG/H
centerC22#64747
commutatorC22×C4×C5C42
FrattiniC2×#117C2×D5
FittingC5×#1820C2
socleC22×C5#342
prime radicalC24×C5C22⋊C4
cosocleC2×C5×#117C22
hypercenter#1820D5
hypocenterC5#7214
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
8. C2×#3935C4semidirect
9. C2×C4×#168C4semidirect
12. #64748C4semidirect
210. C5#7214semidirect

Maximal subgroups

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

subgroupindex
C5×#18202
#106023752
#106023652
#72145