Finite Group Databasebeta

← #11986621

Subgroups — #11986621

Order 1280.

374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 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×#1445C211yesmaximal, characteristic
2#10602345C212yesmaximal
3C22×C5×C4⋊C4C2211yescharacteristic
4C2×C5×#95—22no—
5C2×C5×#95C411yescharacteristic
6C2×C5×#95C411yescharacteristic
7#65496—22no—
8#64748—22no—
9#64748C414yescomplemented
10#7326—51nomaximal, Sylow
11C23×C4×C5—21no—
12C23×C4×C5—21no—
13C23×C4×C5C2×C411yescharacteristic
14C23×C4×C5D412yes—
15C2×C5×C4⋊C4—41no—
16C2×C5×C4⋊C4—41no—
17C2×C5×C4⋊C4C2×C412yes—
18C2×C5×C4⋊C4D411yescharacteristic
19C2×C5×C4⋊C4Q811yescharacteristic
20C2×#681—42no—
21C5×#95—41no—
22C5×#95—41no—
23C5×#95—44no—
24C22⋊#168—24no—
25C22⋊#168—42no—
26#1463—52no—
27#1445D511yescharacteristic
28C24×C5C22⋊C411yescharacteristic
29C22×C4×C5—21no—
30C22×C4×C5—21no—
31C22×C4×C5—22no—
32C22×C4×C5—22no—
33C22×C4×C5—22no—
34C22×C4×C5—22no—
35C22×C4×C5—42no—
36C22×C4×C5—42no—
37C22×C4×C5—42no—
38C22×C4×C5—42no—
39C22×C4×C5—42no—
40C22×C4×C5—41no—
41C22×C4×C5—41no—
42C22×C4×C5—42no—
43C22×C4×C5—42no—
44C22×C4×C5—41no—
45C22×C4×C5—41no—
46C22×C4×C5C4211yescharacteristic
47C22×C4×C5C22⋊C412yes—
48C22×C4×C5C4⋊C412yes—
49C22×C4×C5C4⋊C411yescharacteristic
50C5×C4⋊C4—42no—
51C5×C4⋊C4—41no—
52C5×C4⋊C4—41no—
53#681—82no—
54#681—82no—
55C2×#168—44no—
56C22×C4⋊C4C2×D511yescharacteristic
57#407—102no—
58C2×#95—22no—
59C2×#95Dic511yescharacteristic
60C2×#95Dic511yescharacteristic
61#324—54no—
62#324—102no—
63C23×C5—22no—
64C23×C5—21no—
65C23×C5—21no—
66C23×C5—21no—
67C23×C5—21no—
68C23×C5#9511yescharacteristic
69C23×C5#9911yescharacteristic
70C23×C5#9911yescharacteristic
71C2×C4×C5—22no—
72C2×C4×C5—21no—
73C2×C4×C5—22no—
74C2×C4×C5—21no—
75C2×C4×C5—22no—
76C2×C4×C5—22no—
77C2×C4×C5—42no—
78C2×C4×C5—42no—
79C2×C4×C5—42no—
80C2×C4×C5—42no—
81C2×C4×C5—42no—
82C2×C4×C5—42no—
83C2×C4×C5—44no—
84C2×C4×C5—44no—
85C2×C4×C5—42no—
86C2×C4×C5—42no—
87C2×C4×C5—82no—
88C2×C4×C5—82no—
89C2×C4×C5—82no—
90C2×C4×C5—81no—
91C2×C4×C5—81no—
92C2×C4×C5—81no—
93C2×C4×C5—81no—
94#168—84no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4C2×Dic511yescharacteristic
98C23×C4C22⋊D512yes—
99C2×M16—202no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4Dic1011yescharacteristic
103C2×C4⋊C4C4×D512yes—
104C2×C4⋊C4D2011yescharacteristic
105C22⋊C8—104no—
106C22⋊C8—202no—
107#95—41no—
108#95—41no—
109#95—44no—
110C22×C5—22no—
111C22×C5—22no—
112C22×C5—22no—
113C22×C5—22no—
114C22×C5—21no—
115C22×C5—21no—
116C22×C5—21no—
117C22×C5—21no—
118C22×C5—21no—
119C22×C5—21no—
120C22×C5#34211yescharacteristic
121C22×C5#34412yes—
122C22×C5#35311yescharacteristic
123C22×C5#35411yescharacteristic
124C22×C5#35511yescharacteristic
125C22×C5#35611yescharacteristic
126C4×C5—41no—
127C4×C5—41no—
128C4×C5—42no—
129C4×C5—42no—
130C4×C5—82no—
131C4×C5—82no—
132C24C22⋊Dic511yescharacteristic
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4C4×Dic511yescharacteristic
151C22×C4#68312yes—
152C22×C4C4⋊Dic511yescharacteristic
153C22×C4#68512yes—
154M16—402no—
155M16—402no—
156C2×C8—204no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C2×C5—21no—
161C2×C5—21no—
162C2×C5—22no—
163C2×C5—21no—
164C2×C5—21no—
165C2×C5#130611yescharacteristic
166C2×C5#139311yescharacteristic
167C2×C5#139411yescharacteristic
168C23—21no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#396311yescharacteristic
174C23#396611yescharacteristic
175C23#396611yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4—44no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C8—404no—
200C5#732611yescharacteristic, complemented, Sylow
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#6474611yescharacteristic
212C22#6475312yes—
213C22#6476111yescharacteristic
214C22#6476211yescharacteristic
215C22#6476511yescharacteristic
216C22#6476811yescharacteristic
217C4—41no—
218C4—41no—
219C4—42no—
220C4—42no—
221C4—82no—
222C4—82no—
223C2—21no—
224C2—21no—
225C2—21no—
226C2—22no—
227C2—21no—
228C2#1059812011yescharacteristic
229C2#1059813211yescharacteristic
230C2#1059813511yescharacteristic
subgroupG/H
centerC22#64746
commutatorC22×C4×C5C42
FrattiniC22×C4⋊C4C2×D5
FittingC5×#1445C2
socleC22×C5#342
prime radicalC24×C5C22⋊C4
cosocleC22×C5×C4⋊C4C22
hypercenter#1445D5
hypocenterC5#7326
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
9. #64748C4semidirect
200. C5#7326semidirect

Maximal subgroups

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

subgroupindex
C5×#14452
#106023452
#73265