Finite Group Databasebeta

← #11988433

Subgroups — #11988433

Order 1280.

366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#10608333C211yesmaximal, characteristic
2#10600478C211yesmaximal, characteristic
3#10599432C212yesmaximal
4C5×#1272C211yesmaximal, characteristic
5#10597969C212yesmaximal
6C5×#391C2211yescharacteristic
7#65519—21no—
8C2×#3967—21no—
9C2×#3950—22no—
10#65275—21no—
11C2×#3940—21no—
12#65224C2211yescharacteristic
13#65217C2212yes—
14#64950—22no—
15#64944—22no—
16C5×#336C2212yes—
17#64771—22no—
18#64744C2211yescharacteristic
19#7802—51nomaximal, Sylow
20C22×C5×Q8D411yescharacteristic
21C22×C5×C8—22no—
22C2×C5×C4⋊C4D411yescharacteristic
23C2×C42×C5C2311yescharacteristic
24C2×C4⋊Dic5—22no—
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—21no—
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5D412yes—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C2×C4×Dic5—21no—
32C22×#168—21no—
33C5×#95—22no—
34#3967—42no—
35#3963—21no—
36#3963—22no—
37#3963—22no—
38#3963—22no—
39#3950—44no—
40#3940—42no—
41#2809—51no—
42#2096—51no—
43#2083—52no—
44#1272D511yescharacteristic
45#1271—52no—
46C2×C5×Q8—21no—
47C2×C5×Q8—41no—
48C2×C5×Q8—41no—
49C2×C5×Q8Q1612yes—
50C22×C4×C5—21no—
51C22×C4×C5—21no—
52C22×C4×C5C2×D411yescharacteristic
53C22×C4×C5C2×D412yes—
54C22×Dic5—22no—
55C22×Dic5—22no—
56C22×Dic5—41no—
57C2×C5×C8—24no—
58C2×C5×C8—42no—
59C2×C5×C8—42no—
60C5×C4⋊C4—41no—
61C42×C5—41no—
62C4⋊Dic5—22no—
63C4⋊Dic5—22no—
64C4⋊Dic5—42no—
65C4⋊Dic5—41no—
66C4⋊Dic5—41no—
67C4⋊Dic5—42no—
68C4⋊Dic5—42no—
69C4⋊Dic5—81no—
70C4⋊Dic5—81no—
71#683—42no—
72#683—42no—
73C4×Dic5—81no—
74C2×#168—22no—
75C2×#168—41no—
76C2×#168—41no—
77C2×#107—102no—
78C2×#106—101no—
79C2×#103—101no—
80#400—101no—
81#398—102no—
82#391—101no—
83#391C2×D511yescharacteristic
84#389—52no—
85#387—102no—
86#384—51no—
87#340—102no—
88#336—51no—
89#336C2×D512yes—
90C23×C5#12011yescharacteristic
91C5×Q8—42no—
92C5×Q8—81no—
93C2×C4×C5—21no—
94C2×C4×C5—22no—
95C2×C4×C5—21no—
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—41no—
99C2×C4×C5—41no—
100C2×C4×C5—41no—
101C2×C4×C5—42no—
102C2×C4×C5C2×Q1611yescharacteristic
103C2×C4×C5#13512yes—
104C2×C4×C5AGL(1,ℤ/8)12yes—
105C2×C4×C5#13711yescharacteristic
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—82no—
113C2×Dic5—81no—
114C5×C8—44no—
115#168—42no—
116C22×Q8D2011yescharacteristic
117C22×C8—22no—
118C22×C8—101no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—102no—
122C2×C4⋊C4—101no—
123C2×C4⋊C4—102no—
124C2×C4⋊C4—101no—
125C2×C4⋊C4—101no—
126C2×C4⋊C4D2011yescharacteristic
127C2×C42—101no—
128C2×C42C22×D511yescharacteristic
129#107—204no—
130#106—202no—
131#103—202no—
132#95—22no—
133#95—101no—
134#95—102no—
135#95—102no—
136#95—102no—
137C22×C5#44912yes—
138C22×C5#45111yescharacteristic
139C22×C5#45311yescharacteristic
140C22×C5#45612yes—
141C22×C5#45811yescharacteristic
142C4×C5—22no—
143C4×C5—22no—
144C4×C5—21no—
145C4×C5—21no—
146C4×C5—42no—
147C4×C5—81no—
148Dic5—82no—
149Dic5—82no—
150Dic5—161no—
151C2×Q8—21no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8Dic2012yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—102no—
158C22×C4—102no—
159C22×C4—201no—
160C22×C4C2×D2011yescharacteristic
161C22×C4D4×D512yes—
162C2×C8—24no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—102no—
166C2×C8—201no—
167C2×C8—201no—
168C4⋊C4—41no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—202no—
172C4⋊C4—201no—
173C4⋊C4—201no—
174C4⋊C4—202no—
175C4⋊C4—202no—
176C4⋊C4—202no—
177C4⋊C4—202no—
178C4⋊C4—401no—
179C4⋊C4—401no—
180C42—41no—
181C42—401no—
182C2×C5#160912yes—
183C2×C5#161411yescharacteristic
184C2×C5#162411yescharacteristic
185C2×C5#164812yes—
186C2×C5#166011yescharacteristic
187C23#402811yescharacteristic
188Q8—42no—
189Q8—81no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—202no—
200C2×C4—202no—
201C2×C4—202no—
202C2×C4—202no—
203C2×C4—202no—
204C2×C4—202no—
205C2×C4—401no—
206C2×C4—402no—
207C2×C4C2×Dic2011yescharacteristic
208C2×C4#405511yescharacteristic
209C2×C4#406012yes—
210C2×C4#406512yes—
211C8—44no—
212C8—202no—
213C5#780211yescharacteristic, complemented, Sylow
214C22#6502811yescharacteristic
215C22#6503111yescharacteristic
216C22#6503611yescharacteristic
217C22#6510012yes—
218C22#6511512yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—81no—
225C4—402no—
226C4—402no—
227C4—801no—
228C2#1059891011yescharacteristic
229C2#1059904912yes—
230C2#1059912112yes—
231C2#1059914811yescharacteristic
232C2#1059928411yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1272C2
socle, prime radicalC23×C5#120
hypercenter#1272D5
hypocenterC5#7802
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
213. C5#7802semidirect

Maximal subgroups

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

subgroupindex
#106083332
#106004782
#105994322
C5×#12722
#105979692
#78025