Finite Group Databasebeta

← #11993808

Subgroups — #11993808

Order 1280.

412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2979C211yesmaximal, characteristic
2#10602608C211yesmaximal, characteristic
3#10602598C211yesmaximal, characteristic
4#10601541C212yesmaximal, complemented
5#10598227C212yesmaximal, complemented
6C5×#532C2211yescharacteristic
7C5×#436—22no—
8C5×C8×D4—22no—
9C5×#431C2212yes—
10C5×#408—22no—
11C2×#3969—22no—
12C42×Dic5C2211yescharacteristic
13#65214C2212yes—
14#65213C2211yescharacteristic
15#64766C411yescharacteristic, complemented
16#64766C411yescharacteristic, complemented
17#64764C412yescomplemented
18#64700—22no—
19#64699—22no—
20#8935—51nomaximal, Sylow
21C2×C5×#41D412yes—
22C2×C5×M16—22no—
23C22×C5×C8—22no—
24C5×C4⋊Q8C2×C411yescharacteristic
25C5×#127C2×C411yescharacteristic
26C5×#124Q812yes—
27C5×#121—22no—
28C4×C5×D4—22no—
29C2×C42×C5C2311yescharacteristic
30C2×C4×Dic5—21no—
31C2×C4×Dic5—22no—
32C2×#681—21no—
33C5×C4⋊C8D412yes—
34C5×C4⋊C8D412yes—
35C5×C22⋊C8—24no—
36C5×C22⋊C8—22no—
37C4×C5×C8—22no—
38#3969—44no—
39C22⋊#168—22no—
40C4⋊#168—22no—
41C4⋊#168C2×C412yes—
42C4⋊#168C2×C412yes—
43C4×#168—22no—
44#2979D511yescharacteristic
45#1962—51no—
46#1574—52no—
47#1543—51no—
48#1276—52no—
49C5×#41—42no—
50C5×#41—42no—
51C2×C5×Q8C4⋊C412yes—
52C2×C5×D4—22no—
53C2×C5×D4—22no—
54C2×C5×D4C4⋊C412yes—
55C22×C4×C5—22no—
56C22×C4×C5C2×D411yescharacteristic
57C22×C4×C5#4112yes—
58C22×Dic5—41no—
59C5×M16—82no—
60C2×C5×C8—22no—
61C2×C5×C8—22no—
62C2×C5×C8—82no—
63C5×C4⋊C4—22no—
64C5×C22⋊C4—24no—
65C42×C5C22×C411yescharacteristic
66C42×C5C2×D412yes—
67C42×C5C2×Q811yescharacteristic
68C4×Dic5—22no—
69C4×Dic5—24no—
70C4×Dic5—42no—
71C4×Dic5—41no—
72#681—42no—
73C2×#168—22no—
74C2×#168—22no—
75C2×#168—41no—
76#532C2×D511yescharacteristic
77#436—22no—
78C8×D4—22no—
79#431—52no—
80#431C2×D512yes—
81#423—51no—
82C2×#104—102no—
83#408—22no—
84C43—51no—
85#335—102no—
86#334—102no—
87#333—51no—
88#333—51no—
89#331—52no—
90C23×C5—22no—
91C23×C5#12311yescharacteristic
92C5×Q8—42no—
93C5×D4—42no—
94C5×D4—42no—
95C5×D4—42no—
96C5×D4—82no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—22no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5C2×C4⋊C411yescharacteristic
105C2×C4×C5C4×D412yes—
106C2×C4×C5#12011yescharacteristic
107C2×C4×C5C22⋊Q812yes—
108C2×Dic5—42no—
109C2×Dic5—44no—
110C5×C8—42no—
111C5×C8—42no—
112#168—42no—
113#168—42no—
114#168—81no—
115C2×#41C22⋊D512yes—
116C2×M16—22no—
117C2×M16—101no—
118C22×C8—22no—
119C4⋊Q8C4×D511yescharacteristic
120#127C4×D511yescharacteristic
121#124Dic1012yes—
122#121—22no—
123C4×D4—22no—
124C2×C42—102no—
125C2×C42—101no—
126C2×C42C22×D511yescharacteristic
127C4⋊C8—52no—
128C4⋊C8—52no—
129C4⋊C8—102no—
130C4⋊C8C22⋊D512yes—
131C4⋊C8C22⋊D512yes—
132#104—204no—
133C22⋊C8—24no—
134C22⋊C8—22no—
135C22⋊C8—102no—
136C4×C8—22no—
137C4×C8—102no—
138C22×C5—21no—
139C22×C5—22no—
140C22×C5—42no—
141C22×C5—44no—
142C22×C5#38511yescharacteristic
143C4×C5—21no—
144C4×C5—22no—
145C4×C5—42no—
146C4×C5#44312yes—
147C4×C5#44412yes—
148C4×C5#45311yescharacteristic
149C4×C5#45511yescharacteristic
150Dic5—44no—
151#41—42no—
152#41—42no—
153C2×Q8#68312yes—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4#68312yes—
157C22×C4—22no—
158C22×C4—201no—
159C22×C4#70912yes—
160C22×C4C2×C22⋊D511yescharacteristic
161M16—82no—
162M16—202no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—82no—
166C2×C8—102no—
167C2×C8—102no—
168C2×C8—201no—
169C4⋊C4—22no—
170C22⋊C4—24no—
171C42—102no—
172C42—104no—
173C42—202no—
174C42—201no—
175C42C2×Dic1011yescharacteristic
176C42C2×C4×D511yescharacteristic
177C42C2×C22⋊D512yes—
178C2×C5—41no—
179C2×C5—82no—
180C2×C5#185611yescharacteristic
181C2×C5#186612yes—
182C23—22no—
183C23#407511yescharacteristic
184Q8—42no—
185D4—42no—
186D4—42no—
187D4—42no—
188D4—82no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—204no—
197C2×C4—202no—
198C2×C4C2×#68311yescharacteristic
199C2×C4#407012yes—
200C2×C4C4×C22⋊D512yes—
201C2×C4#409911yescharacteristic
202C8—42no—
203C8—42no—
204C8—202no—
205C8—202no—
206C8—401no—
207C5#893511yescharacteristic, complemented, Sylow
208C22—22no—
209C22—21no—
210C22—44no—
211C22—42no—
212C22#6549911yescharacteristic
213C4—22no—
214C4—21no—
215C4—42no—
216C4—204no—
217C4#6543312yes—
218C4#6543412yes—
219C4#6553011yescharacteristic
220C4#6553111yescharacteristic
221C2—41no—
222C2—82no—
223C2#1060244011yescharacteristic
224C2#1060281012yes—
subgroupG/H
centerC2×C4#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2979C2
socleC22×C5#385
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#2979D5
hypocenterC5#8935
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2979

Complements

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

NH ≅ G/Ntype
4. #10601541C2semidirect
5. #10598227C2semidirect
15. #64766C4semidirect
16. #64766C4semidirect
17. #64764C4semidirect
207. C5#8935semidirect

Maximal subgroups

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

subgroupindex
C5×#29792
#106026082
#106025982
#106015412
#105982272
#89355