Finite Group Databasebeta

← #12002791

Subgroups — #12002791

Order 1280.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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×#2822C211yesmaximal, characteristic
2#10602534C212yesmaximal
3C2×#64763C212yesmaximal
4#10600341C211yesmaximal, characteristic
5#10598121C211yesmaximal, characteristic
6C2×C5×#125C2212yes—
7C5×#400—22no—
8C5×#398—22no—
9C5×#398—22no—
10C5×#382C2211yescharacteristic
11#65224C2211yescharacteristic
12C2×#3935C2212yes—
13C2×#3935C2211yescharacteristic
14#64763—24no—
15#64749—22no—
16#64749—22no—
17#64749—22no—
18#10428—51nomaximal, Sylow
19C5×#125—22no—
20C5×#125—22no—
21C5×#125—22no—
22C5×#125—22no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4—22no—
25C2×C5×C4⋊C4—22no—
26C2×C5×C4⋊C4D412yes—
27C2×C5×C4⋊C4D412yes—
28C2×C5×C4⋊C4D412yes—
29C2×C42×C5C2311yescharacteristic
30C2×C4⋊Dic5—22no—
31C2×C4⋊Dic5—21no—
32C22×#168—22no—
33C22×#168—21no—
34C5×#95—24no—
35C5×#95—22no—
36C5×#95—22no—
37#3935—21no—
38#3935—22no—
39#3935—22no—
40#3935D412yes—
41#2822D511yescharacteristic
42#1992—52no—
43#1836—51no—
44C2×#330—52no—
45#1295—51no—
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5C2×D412yes—
50C22×C4×C5C2×D411yescharacteristic
51C22×Dic5—41no—
52C5×C4⋊C4—22no—
53C5×C4⋊C4—22no—
54C5×C4⋊C4—22no—
55C5×C4⋊C4—22no—
56C5×C4⋊C4—42no—
57C5×C4⋊C4—42no—
58C5×C4⋊C4—42no—
59C5×C4⋊C4—42no—
60C5×C4⋊C4—42no—
61C5×C4⋊C4—82no—
62C42×C5C2×D411yescharacteristic
63C42×C5#4111yescharacteristic
64C42×C5#4112yes—
65C4⋊Dic5—42no—
66C4⋊Dic5—44no—
67C2×#168—24no—
68C2×#168—22no—
69C2×#168—42no—
70C2×#168—41no—
71C2×#168—41no—
72C2×#168—42no—
73C2×#125C2×D512yes—
74C2×#97—51no—
75C2×#97—52no—
76#400—22no—
77#398—22no—
78#398—22no—
79#384—51no—
80#382C2×D511yescharacteristic
81#340—102no—
82#340—102no—
83#340—102no—
84#330—104no—
85C23×C5#12011yescharacteristic
86C2×C4×C5—22no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—42no—
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#12111yescharacteristic
100C2×C4×C5#12112yes—
101C2×C4×C5#12312yes—
102C2×C4×C5#12411yescharacteristic
103C2×Dic5—81no—
104C2×Dic5—82no—
105#168—44no—
106#168—42no—
107C22×C8—102no—
108C22×C8—101no—
109#125—22no—
110#125—22no—
111#125—22no—
112#125—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—102no—
117C2×C4⋊C4—101no—
118C2×C4⋊C4C22⋊D512yes—
119C2×C4⋊C4C22⋊D512yes—
120C2×C4⋊C4C22⋊D512yes—
121C2×C42C22×D511yescharacteristic
122#97—52no—
123#97—102no—
124#97—101no—
125#97—102no—
126#95—24no—
127#95—22no—
128#95—22no—
129C22×C5#39411yescharacteristic
130C22×C5#45411yescharacteristic
131C22×C5#45412yes—
132C22×C5#45511yescharacteristic
133C22×C5#45612yes—
134C4×C5—22no—
135C4×C5—22no—
136C4×C5—21no—
137C4×C5—21no—
138C4×C5—82no—
139C4×C5—82no—
140C4×C5—82no—
141Dic5—161no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—201no—
146C22×C4C2×C22⋊D512yes—
147C22×C4C2×C22⋊D511yescharacteristic
148C2×C8—104no—
149C2×C8—102no—
150C2×C8—201no—
151C2×C8—202no—
152C2×C8—201no—
153C2×C8—202no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—82no—
164C4⋊C4—204no—
165C4⋊C4—202no—
166C42D4×D511yescharacteristic
167C42#71111yescharacteristic
168C42#71112yes—
169C2×C5#165811yescharacteristic
170C2×C5#166311yescharacteristic
171C2×C5#166412yes—
172C2×C5#203812yes—
173C2×C5#204011yescharacteristic
174C23#409911yescharacteristic
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—401no—
189C2×C4—402no—
190C2×C4#408112yes—
191C2×C4#408211yescharacteristic
192C2×C4#408411yescharacteristic
193C2×C4#408512yes—
194C8—204no—
195C8—202no—
196C5#1042811yescharacteristic, complemented, Sylow
197C22#6551111yescharacteristic
198C22#6553111yescharacteristic
199C22#6553411yescharacteristic
200C22#6553412yes—
201C22#6553512yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—801no—
210C2#1060265612yes—
211C2#1060267011yescharacteristic
212C2#1060275012yes—
213C2#1060275311yescharacteristic
214C2#1060275411yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2822C2
socle, prime radicalC23×C5#120
hypercenter#2822D5
hypocenterC5#10428
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
196. C5#10428semidirect

Maximal subgroups

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

subgroupindex
C5×#28222
#106025342
C2×#647632
#106003412
#105981212
#104285