Finite Group Databasebeta

← #11990228

Subgroups — #11990228

Order 1280.

444 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 141 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
1Dic5×#125C211yesmaximal, characteristic
2C2×C5×#330C211yesmaximal, characteristic
3C2×#64763C211yesmaximal, characteristic
4#10600598C212yesmaximal
5#10598150C212yesmaximal
6C2×C5×#125C2211yescharacteristic
7C2×C5×#97C2212yes—
8#65274C412yes—
9#65270—22no—
10C4⋊C4×Dic5—22no—
11C4⋊C4×Dic5C412yes—
12#65225C2211yescharacteristic
13C42×Dic5C2211yescharacteristic
14C2×#3935C2212yes—
15C5×#330C414yescomplemented
16#64770—22no—
17#64770—22no—
18#64763C414yescomplemented
19#8225—51nomaximal, Sylow
20C22×C5×C8—22no—
21C5×#125—22no—
22C5×#125C2×C412yes—
23C5×#125C2×C412yes—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4C2×C412yes—
26C2×C42×C5C2311yescharacteristic
27C2×C4⋊Dic5—22no—
28C2×C4⋊Dic5C2×C412yes—
29C2×C4×Dic5—22no—
30C2×C4×Dic5C2×C411yescharacteristic
31C2×C4×Dic5C2×C411yescharacteristic
32C2×C4×Dic5D412yes—
33C2×C4×Dic5D412yes—
34C22×#168—22no—
35C5×#97—22no—
36C5×#97C2×C414yes—
37#3963—22no—
38#3963—22no—
39#3963—22no—
40#3935—22no—
41#3935C2×C414yes—
42C4×#125—51no—
43#1745—52no—
44C2×#330—51no—
45C2×#330D511yescharacteristic
46#1295—52no—
47C22×C4×C5—22no—
48C22×C4×C5C22×C411yescharacteristic
49C22×C4×C5C2×D412yes—
50C22×Dic5—22no—
51C22×Dic5C22⋊C411yescharacteristic
52C22×Dic5C22⋊C412yes—
53C22×Dic5C22⋊C411yescharacteristic
54C2×C5×C8—24no—
55C2×C5×C8—42no—
56C2×C5×C8—42no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4—24no—
59C5×C4⋊C4—24no—
60C5×C4⋊C4C4214yes—
61C42×C5C22×C411yescharacteristic
62C42×C5C22×C411yescharacteristic
63C42×C5#4112yes—
64C4⋊Dic5—44no—
65C4⋊Dic5—42no—
66C4×Dic5—22no—
67C4×Dic5—41no—
68C4×Dic5—42no—
69C4×Dic5—42no—
70C4×Dic5—44no—
71C2×#168—24no—
72C2×#168—42no—
73C2×#168—42no—
74C2×#125C2×D511yescharacteristic
75C2×#97—52no—
76C2×#97C2×D512yes—
77#389—52no—
78#387—102no—
79#382—51no—
80C4×C4⋊C4—52no—
81C4×C4⋊C4—102no—
82C43—51no—
83#336—102no—
84#336—102no—
85#330—54no—
86#330Dic514yescomplemented
87C23×C5C2×C22⋊C411yescharacteristic
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—24no—
93C2×C4×C5—42no—
94C2×C4×C5—42no—
95C2×C4×C5C2×C4211yescharacteristic
96C2×C4×C5#11711yescharacteristic
97C2×C4×C5C4×D412yes—
98C2×C4×C5C4×D412yes—
99C2×Dic5—22no—
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5—22no—
103C2×Dic5—22no—
104C2×Dic5—22no—
105C2×Dic5—42no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5#10112yes—
109C5×C8—44no—
110#168—44no—
111C22×C8—22no—
112C22×C8—102no—
113#125—22no—
114#125C4×D512yes—
115#125C2×Dic512yes—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4—102no—
119C2×C4⋊C4C4×D512yes—
120C2×C42—51no—
121C2×C42—51no—
122C2×C42—52no—
123C2×C42—52no—
124C2×C42—102no—
125C2×C42C22×D511yescharacteristic
126#97—22no—
127#97—54no—
128#97—102no—
129#97C2×Dic514yes—
130#95—102no—
131#95—102no—
132#95—102no—
133C22×C5C4×C22⋊C411yescharacteristic
134C22×C5C2×#10111yescharacteristic
135C22×C5#41311yescharacteristic
136C22×C5#42112yes—
137C22×C5#42112yes—
138C4×C5—21no—
139C4×C5—21no—
140C4×C5—22no—
141C4×C5—22no—
142C4×C5—44no—
143Dic5—22no—
144Dic5—41no—
145Dic5—42no—
146Dic5—82no—
147C22×C4—22no—
148C22×C4—51no—
149C22×C4—51no—
150C22×C4—52no—
151C22×C4—102no—
152C22×C4C2×C4×D511yescharacteristic
153C22×C4D4×D512yes—
154C2×C8—24no—
155C2×C8—42no—
156C2×C8—42no—
157C2×C8—104no—
158C2×C8—202no—
159C2×C8—202no—
160C4⋊C4—22no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—202no—
164C4⋊C4—204no—
165C4⋊C4C4×Dic514yes—
166C42—102no—
167C42—201no—
168C42—202no—
169C42—202no—
170C42—204no—
171C42C2×C4×D511yescharacteristic
172C42#71112yes—
173C42C22×Dic511yescharacteristic
174C2×C5#153411yescharacteristic
175C2×C5#153512yes—
176C2×C5#153711yescharacteristic
177C2×C5C4×#10111yescharacteristic
178C2×C5#175912yes—
179C23D5×C22⋊C411yescharacteristic
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—52no—
188C2×C4—102no—
189C2×C4—101no—
190C2×C4—102no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4—202no—
195C2×C4—202no—
196C2×C4—202no—
197C2×C4#402311yescharacteristic
198C2×C4#402712yes—
199C2×C4C2×C4×Dic511yescharacteristic
200C2×C4D4×Dic512yes—
201C8—44no—
202C8—204no—
203C5#822511yescharacteristic, complemented, Sylow
204C22D5×#10111yescharacteristic
205C22#6504011yescharacteristic
206C22#6511012yes—
207C22#6511012yes—
208C22C22⋊C4×Dic511yescharacteristic
209C4—21no—
210C4—21no—
211C4—22no—
212C4—22no—
213C4—44no—
214C4—102no—
215C4—202no—
216C4—201no—
217C4—402no—
218C2#1059916011yescharacteristic
219C2#1059916112yes—
220C2#1059916211yescharacteristic
221C2Dic5×#10111yescharacteristic
222C2#1060114712yes—
subgroupG/H
centerC23D5×C22⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC2×C5×#330C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenterC2×#330D5
hypocenterC5#8225
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
15. C5×#330C4semidirect
18. #64763C4semidirect
86. #330Dic5semidirect
203. C5#8225semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1252
C2×C5×#3302
C2×#647632
#106005982
#105981502
#82255