Finite Group Databasebeta

← #12002544

Subgroups — #12002544

Order 1280.

406 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 77 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×#2608C211yesmaximal, characteristic
2#10600327C211yesmaximal, characteristic
3#10600235C212yesmaximal
4#10598120C211yesmaximal, characteristic
5#10598107C212yesmaximal
6C2×#4072C2211yescharacteristic
7C5×#396—22no—
8C5×#389—22no—
9C5×#387—22no—
10C5×#381C2211yescharacteristic
11C4×C5×C22⋊C4C2212yes—
12#65500C2211yescharacteristic
13#65496C2212yes—
14#64747—22no—
15#64743—22no—
16#64743—22no—
17#10389—51nomaximal, Sylow
18C23×C4×C5C2311yescharacteristic
19C2×C5×C4⋊C4—22no—
20C2×C5×C4⋊C4—22no—
21C2×C5×C4⋊C4—22no—
22C2×C5×C22⋊C4—22no—
23C2×C5×C22⋊C4D412yes—
24C2×C42×C5D412yes—
25C2×C42×C5D412yes—
26C2×C22⋊Dic5—21no—
27C2×C22⋊Dic5—21no—
28#4072—22no—
29#4072—22no—
30C2×C4⋊Dic5Q812yes—
31C2×C4×Dic5—21no—
32C2×#681—22no—
33C5×#95—22no—
34C5×#95—22no—
35C5×#95—22no—
36#3963—22no—
37C22⋊#168—22no—
38C22⋊#168—22no—
39#2608D511yescharacteristic
40#1826—52no—
41#1820—51no—
42#1306—51no—
43#1284—52no—
44C24×C5C2×D411yescharacteristic
45C22×C4×C5—22no—
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—42no—
49C22×C4×C5C2×D412yes—
50C22×C4×C5C2×Q811yescharacteristic
51C22×C4×C5#4112yes—
52C22×C4×C5#4111yescharacteristic
53C22×Dic5—22no—
54C22×Dic5—41no—
55C5×C4⋊C4—44no—
56C5×C4⋊C4—44no—
57C5×C4⋊C4—82no—
58C5×C22⋊C4—44no—
59C5×C22⋊C4—42no—
60C42×C5—42no—
61C42×C5—42no—
62C22⋊Dic5—41no—
63C22⋊Dic5—41no—
64C22⋊Dic5—42no—
65C4⋊Dic5—24no—
66C4×Dic5—42no—
67#681—42no—
68#681—42no—
69C2×#168—42no—
70C2×#117—51no—
71#407—52no—
72#396—22no—
73#389—22no—
74#387—22no—
75#381—51no—
76#381C2×D511yescharacteristic
77C4×C22⋊C4C2×D512yes—
78#342—102no—
79#339—102no—
80#339—102no—
81C23×C5—22no—
82C23×C5—42no—
83C23×C5#12011yescharacteristic
84C23×C5C22⋊Q811yescharacteristic
85C23×C5#12411yescharacteristic
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—24no—
89C2×C4×C5—41no—
90C2×C4×C5—41no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5—42no—
94C2×C4×C5—42no—
95C2×C4×C5—42no—
96C2×C4×C5—42no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5C22⋊Q812yes—
101C2×C4×C5#12412yes—
102C2×Dic5—42no—
103C2×Dic5—82no—
104C2×Dic5—81no—
105C2×Dic5—82no—
106#168—82no—
107C23×C4C22×D511yescharacteristic
108C2×M16—102no—
109#117—102no—
110#117—102no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—52no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—101no—
117C2×C22⋊C4—101no—
118C2×C22⋊C4C22⋊D512yes—
119C2×C42—101no—
120C2×C42C22⋊D512yes—
121C2×C42C22⋊D512yes—
122C22⋊C8—102no—
123C22⋊C8—102no—
124#95—22no—
125#95—22no—
126#95—22no—
127#95—102no—
128C22×C5—22no—
129C22×C5—21no—
130C22×C5—21no—
131C22×C5—22no—
132C22×C5—22no—
133C22×C5—82no—
134C22×C5#39311yescharacteristic
135C22×C5#45812yes—
136C4×C5—22no—
137C4×C5—22no—
138C4×C5—44no—
139C4×C5—82no—
140C4×C5—82no—
141Dic5—82no—
142Dic5—161no—
143C24C2×C22⋊D511yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4—102no—
149C22×C4—201no—
150C22×C4Q8×D511yescharacteristic
151C22×C4#71312yes—
152C22×C4#71311yescharacteristic
153C22×C4C2×C22⋊D512yes—
154M16—202no—
155M16—202no—
156C2×C8—202no—
157C4⋊C4—44no—
158C4⋊C4—44no—
159C4⋊C4—82no—
160C4⋊C4—104no—
161C22⋊C4—44no—
162C22⋊C4—42no—
163C22⋊C4—201no—
164C22⋊C4—201no—
165C22⋊C4—202no—
166C42—42no—
167C42—42no—
168C42—202no—
169C2×C5—22no—
170C2×C5—41no—
171C2×C5—41no—
172C2×C5#203011yescharacteristic
173C2×C5#203112yes—
174C23—22no—
175C23—42no—
176C23#409211yescharacteristic
177C23#409311yescharacteristic
178C23#409911yescharacteristic
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—202no—
194C2×C4—402no—
195C2×C4—401no—
196C2×C4—402no—
197C2×C4#409212yes—
198C2×C4#409312yes—
199C8—402no—
200C5#1038911yescharacteristic, complemented, Sylow
201C22—22no—
202C22—22no—
203C22—22no—
204C22—21no—
205C22—21no—
206C22—82no—
207C22#6552011yescharacteristic
208C22#6553212yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—402no—
215C4—801no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#1060263512yes—
220C2#1060268711yescharacteristic
subgroupG/H
centerC22#65520
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2608C2
socleC22×C5#393
prime radicalC24×C5C2×D4
hypercenter#2608D5
hypocenterC5#10389
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
200. C5#10389semidirect

Maximal subgroups

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

subgroupindex
C5×#26082
#106003272
#106002352
#105981202
#105981072
#103895