Finite Group Databasebeta

← #12002381

Subgroups — #12002381

Order 1280.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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#10605950C211yesmaximal, characteristic
2C5×#1960C211yesmaximal, characteristic
3#10602581C212yesmaximal
4#10598150C212yesmaximal
5#10598121C211yesmaximal, characteristic
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×C5×#103—22no—
8C2×C5×#97C2211yescharacteristic
9C5×#382C2211yescharacteristic
10#65273—22no—
11#65225C2212yes—
12C2×#3935C2212yes—
13#64950—22no—
14#64946—22no—
15#64749—22no—
16#64749—22no—
17#10361—51nomaximal, Sylow
18C22×C5×Q8—21no—
19C22×C5×C8—21no—
20C5×C4⋊Q8—22no—
21C5×C4⋊Q8—21no—
22C5×C4⋊Q8Q812yes—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D412yes—
25C2×C42×C5C2311yescharacteristic
26C2×C4⋊Dic5—22no—
27C2×C4⋊Dic5D412yes—
28C2×C4⋊Dic5D412yes—
29C2×#683—22no—
30C2×#683—22no—
31C22×#168—22no—
32C5×#103—44no—
33C5×#97—22no—
34C5×#95—22no—
35#3963—22no—
36#3963—22no—
37#3963—22no—
38#3935—22no—
39#3935—22no—
40#2845—51no—
41#1993—52no—
42#1960D511yescharacteristic
43#1295—52no—
44#1295—51no—
45C2×C5×Q8—22no—
46C2×C5×Q8—42no—
47C2×C5×Q8—42no—
48C2×C5×Q8—41no—
49C22×C4×C5—22no—
50C22×C4×C5—41no—
51C22×C4×C5C2×D412yes—
52C22×C4×C5C2×D411yescharacteristic
53C22×Dic5—22no—
54C22×Dic5—22no—
55C2×C5×C8—22no—
56C2×C5×C8—41no—
57C2×C5×C8—41no—
58C5×C4⋊C4—24no—
59C5×C4⋊C4—42no—
60C5×C4⋊C4—42no—
61C42×C5C2×Q811yescharacteristic
62C42×C5#4111yescharacteristic
63C42×C5#4112yes—
64C4⋊Dic5—42no—
65C4⋊Dic5—42no—
66C4⋊Dic5—82no—
67#683—82no—
68#683—82no—
69C2×#168—24no—
70C2×#168—42no—
71C2×#168—42no—
72C2×C4⋊Q8C2×D511yescharacteristic
73C2×#103—22no—
74C2×#97—52no—
75C2×#97C2×D511yescharacteristic
76#398—102no—
77#398—102no—
78#398—102no—
79#382—52no—
80#382C2×D511yescharacteristic
81#340—102no—
82#340—102no—
83C23×C5#12011yescharacteristic
84C5×Q8—44no—
85C5×Q8—82no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—22no—
89C2×C4×C5—22no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5—42no—
94C2×C4×C5—81no—
95C2×C4×C5—81no—
96C2×C4×C5C22⋊Q812yes—
97C2×C4×C5C22⋊Q811yescharacteristic
98C2×C4×C5#12412yes—
99C2×C4×C5#12411yescharacteristic
100C2×Dic5—42no—
101C2×Dic5—42no—
102C2×Dic5—42no—
103C2×Dic5—42no—
104C2×Dic5—42no—
105C2×Dic5—42no—
106C5×C8—42no—
107#168—44no—
108C22×Q8—21no—
109C22×C8—21no—
110C22×C8—102no—
111C4⋊Q8—21no—
112C4⋊Q8—22no—
113C4⋊Q8Dic1012yes—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4—52no—
117C2×C4⋊C4—102no—
118C2×C4⋊C4—102no—
119C2×C4⋊C4—102no—
120C2×C4⋊C4C22⋊D512yes—
121C2×C42C22×D511yescharacteristic
122#103—44no—
123#97—22no—
124#97—102no—
125#97—102no—
126#95—22no—
127#95—102no—
128#95—102no—
129#95—102no—
130C22×C5#39311yescharacteristic
131C22×C5#45311yescharacteristic
132C22×C5#45411yescharacteristic
133C22×C5#45512yes—
134C22×C5#45612yes—
135C4×C5—21no—
136C4×C5—21no—
137C4×C5—22no—
138C4×C5—22no—
139C4×C5—82no—
140C4×C5—82no—
141Dic5—82no—
142Dic5—82no—
143C2×Q8—22no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—41no—
147C22×C4—22no—
148C22×C4—41no—
149C22×C4—102no—
150C22×C4—102no—
151C22×C4D4×D512yes—
152C22×C4C2×C22⋊D511yescharacteristic
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—104no—
157C2×C8—202no—
158C2×C8—202no—
159C4⋊C4—24no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—202no—
163C4⋊C4—202no—
164C4⋊C4—402no—
165C4⋊C4—402no—
166C4⋊C4—402no—
167C42C2×Dic1011yescharacteristic
168C42#70911yescharacteristic
169C42#71112yes—
170C2×C5#166112yes—
171C2×C5#166211yescharacteristic
172C2×C5#166311yescharacteristic
173C2×C5#202711yescharacteristic
174C2×C5#202812yes—
175C23#408311yescharacteristic
176Q8—44no—
177Q8—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—202no—
189C2×C4—202no—
190C2×C4—202no—
191C2×C4—202no—
192C2×C4—202no—
193C2×C4—202no—
194C2×C4#402412yes—
195C2×C4#403112yes—
196C2×C4#407011yescharacteristic
197C2×C4#408211yescharacteristic
198C8—42no—
199C8—204no—
200C5#1036111yescharacteristic, complemented, Sylow
201C22#6523611yescharacteristic
202C22#6535111yescharacteristic
203C22#6536611yescharacteristic
204C22#6549112yes—
205C22#6549412yes—
206C4—22no—
207C4—22no—
208C4—21no—
209C4—21no—
210C4—82no—
211C4—82no—
212C4—402no—
213C4—402no—
214C2#1060043611yescharacteristic
215C2#1060112612yes—
216C2#1060204411yescharacteristic
217C2#1060204511yescharacteristic
218C2#1060212412yes—
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socle, prime radicalC23×C5#120
hypercenter#1960D5
hypocenterC5#10361
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
200. C5#10361semidirect

Maximal subgroups

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

subgroupindex
#106059502
C5×#19602
#106025812
#105981502
#105981212
#103615