Finite Group Databasebeta

← #11993770

Subgroups — #11993770

Order 1280.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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×#2369C211yesmaximal, characteristic
2#10602578C211yesmaximal, characteristic
3C2×#64766C211yesmaximal, characteristic
4#10600259C212yesmaximal
5#10598110C212yesmaximal
6C2×C5×C4⋊Q8C2211yescharacteristic
7C5×#391—22no—
8C5×#389—22no—
9C4×C5×C4⋊C4—22no—
10C4×C5×C4⋊C4C2212yes—
11C2×#3967—22no—
12C2×#3939—22no—
13#65224C2211yescharacteristic
14C2×C4⋊#168C2212yes—
15C2×C4×#168C2211yescharacteristic
16#64766C414yescomplemented
17#64749—22no—
18#8929—51nomaximal, Sylow
19C22×C5×Q8D412yes—
20C5×C4⋊Q8—22no—
21C5×C4⋊Q8C2×C412yes—
22C5×C4⋊Q8Q812yes—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4D412yes—
26C2×C5×C4⋊C4D412yes—
27C2×C42×C5—22no—
28C2×C42×C5—22no—
29C2×C42×C5C2311yescharacteristic
30C2×C4⋊Dic5—22no—
31C2×C4⋊Dic5—21no—
32C22×#168—21no—
33C22×#168—22no—
34C5×#95—24no—
35C5×#95—22no—
36#3967—44no—
37#3939—44no—
38C4⋊#168—22no—
39C4⋊#168C2×C414yes—
40C4×#168—22no—
41#2369D511yescharacteristic
42#1956—51no—
43#1947—52no—
44C2×#333—51no—
45#1279—52no—
46C2×C5×Q8—22no—
47C2×C5×Q8—42no—
48C2×C5×Q8—42no—
49C2×C5×Q8C4⋊C414yes—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5—22no—
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5C2×D412yes—
55C22×Dic5—41no—
56C5×C4⋊C4—24no—
57C5×C4⋊C4—24no—
58C5×C4⋊C4—22no—
59C5×C4⋊C4—22no—
60C5×C4⋊C4—22no—
61C5×C4⋊C4—82no—
62C5×C4⋊C4Q1614yes—
63C42×C5—42no—
64C42×C5—42no—
65C42×C5—82no—
66C42×C5C22×C411yescharacteristic
67C42×C5C2×Q811yescharacteristic
68C42×C5#4112yes—
69C4⋊Dic5—42no—
70C4⋊Dic5—42no—
71C4⋊Dic5—42no—
72C2×#168—22no—
73C2×#168—24no—
74C2×#168—41no—
75C2×#168—41no—
76C2×#168—42no—
77C2×#168—42no—
78C2×C4⋊Q8C2×D511yescharacteristic
79C2×#107—102no—
80C2×C4⋊C8—52no—
81C2×#103—102no—
82C2×C4×C8—51no—
83#391—22no—
84#389—22no—
85#384—51no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4C2×D512yes—
88#340—102no—
89#333—54no—
90C23×C5#12011yescharacteristic
91C5×Q8—44no—
92C5×Q8—82no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—24no—
96C2×C4×C5—24no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5C2×C4⋊C411yescharacteristic
105C2×C4×C5C4×D412yes—
106C2×C4×C5C22⋊Q812yes—
107C2×C4×C5#12311yescharacteristic
108C2×C4×C5C2×Q1612yes—
109C2×C4×C5#13512yes—
110C2×C4×C5AGL(1,ℤ/8)12yes—
111C2×C4×C5#13712yes—
112C2×Dic5—82no—
113C2×Dic5—81no—
114#168—42no—
115#168—44no—
116C22×Q8C22⋊D512yes—
117C22×C8—102no—
118C22×C8—101no—
119C4⋊Q8—22no—
120C4⋊Q8Dic1012yes—
121C4⋊Q8C4×D512yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—102no—
125C2×C4⋊C4—101no—
126C2×C4⋊C4C22⋊D512yes—
127C2×C4⋊C4C22⋊D512yes—
128C2×C42—22no—
129C2×C42—22no—
130C2×C42C22×D511yescharacteristic
131#107—204no—
132C4⋊C8—54no—
133C4⋊C8—102no—
134#103—204no—
135C4×C8—102no—
136#95—24no—
137#95—22no—
138C22×C5#38511yescharacteristic
139C22×C5#44912yes—
140C22×C5#45112yes—
141C22×C5#45311yescharacteristic
142C22×C5#45511yescharacteristic
143C4×C5—21no—
144C4×C5—21no—
145C4×C5—44no—
146C4×C5—44no—
147C4×C5—82no—
148C4×C5C4×Q1612yes—
149C4×C5#44012yes—
150C4×C5#47712yes—
151C4×C5#47912yes—
152Dic5—161no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8#68314yes—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—201no—
161C22×C4C2×C22⋊D511yescharacteristic
162C22×C4C2×C22⋊D512yes—
163C2×C8—102no—
164C2×C8—104no—
165C2×C8—201no—
166C2×C8—201no—
167C2×C8—202no—
168C2×C8—202no—
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—82no—
175C4⋊C4—202no—
176C4⋊C4—202no—
177C4⋊C4—202no—
178C4⋊C4#68914yes—
179C42—42no—
180C42—42no—
181C42—82no—
182C42C2×Dic1011yescharacteristic
183C42C2×C4×D511yescharacteristic
184C42#70912yes—
185C2×C5#162411yescharacteristic
186C2×C5#163311yescharacteristic
187C2×C5#164412yes—
188C2×C5#185611yescharacteristic
189C2×C5#186312yes—
190C23#409911yescharacteristic
191Q8—44no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—402no—
205C2×C4—401no—
206C2×C4C2×#68311yescharacteristic
207C2×C4#407012yes—
208C2×C4C4×C22⋊D512yes—
209C2×C4#407511yescharacteristic
210C2×C4#408812yes—
211C2×C4C2×#68912yes—
212C2×C4#409512yes—
213C2×C4#409612yes—
214C8—202no—
215C8—204no—
216C5#892911yescharacteristic, complemented, Sylow
217C22#6549911yescharacteristic
218C22#6551712yes—
219C22#6552712yes—
220C22#6553011yescharacteristic
221C22#6553111yescharacteristic
222C4—21no—
223C4—21no—
224C4—44no—
225C4—44no—
226C4—82no—
227C4—801no—
228C4#6531012yes—
229C4#6531112yes—
230C4#6531512yes—
231C4C4×#68912yes—
232C2#1060242112yes—
233C2#1060244011yescharacteristic
234C2#1060271912yes—
235C2#1060272011yescharacteristic
236C2#1060273311yescharacteristic
subgroupG/H
centerC23#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2369C2
socle, prime radicalC23×C5#120
cosocleC2×C42×C5C23
hypercenter#2369D5
hypocenterC5#8929
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2369

Complements

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

NH ≅ G/Ntype
16. #64766C4semidirect
216. C5#8929semidirect

Maximal subgroups

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

subgroupindex
C5×#23692
#106025782
C2×#647662
#106002592
#105981102
#89295