Finite Group Databasebeta

← #12002560

Subgroups — #12002560

Order 1280.

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

normal subgroups only

This group has 526 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×#2842C211yesmaximal, characteristic
2#10600288C211yesmaximal, characteristic
3#10600288C212yesmaximal
4#10598114C211yesmaximal, characteristic
5#10598114C212yesmaximal
6C22×C22⋊Dic5C2211yescharacteristic
7C5×#399—22no—
8C5×#396—24no—
9C5×#379C2211yescharacteristic
10C5×#379C2212yes—
11#65536C2212yes—
12#65536C2211yescharacteristic
13#64747—24no—
14#64747—22no—
15#10393—51nomaximal, Sylow
16C25×C5C2311yescharacteristic
17C23×Dic5Q812yes—
18C2×C5×C4⋊C4—24no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C22⋊C4—22no—
21C2×C5×C22⋊C4—22no—
22C2×C5×C22⋊C4—22no—
23C2×C5×C22⋊C4D414yes—
24C2×C5×C22⋊C4D412yes—
25C2×C22⋊Dic5—22no—
26C2×C22⋊Dic5—21no—
27C2×C22⋊Dic5—21no—
28C2×C22⋊Dic5—22no—
29C2×C22⋊Dic5—22no—
30C2×C22⋊Dic5—21no—
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34C5×#95—22no—
35#2842D511yescharacteristic
36#1819—52no—
37#1819—51no—
38#1304—51no—
39#1304—52no—
40C24×C5—42no—
41C24×C5—82no—
42C24×C5C2×D412yes—
43C24×C5C2×D411yescharacteristic
44C24×C5C2×Q811yescharacteristic
45C24×C5#4112yes—
46C24×C5#4111yescharacteristic
47C22×C4×C5—22no—
48C22×C4×C5—24no—
49C22×Dic5—22no—
50C22×Dic5—22no—
51C22×Dic5—22no—
52C22×Dic5—42no—
53C22×Dic5—41no—
54C22×Dic5—82no—
55C5×C4⋊C4—84no—
56C5×C4⋊C4—82no—
57C5×C22⋊C4—44no—
58C5×C22⋊C4—42no—
59C5×C22⋊C4—82no—
60C5×C22⋊C4—82no—
61C5×C22⋊C4—82no—
62C22⋊Dic5—41no—
63C22⋊Dic5—42no—
64C22⋊Dic5—41no—
65C22⋊Dic5—44no—
66C22⋊Dic5—42no—
67C22⋊Dic5—82no—
68C22⋊Dic5—82no—
69C22⋊Dic5—82no—
70C22×C22⋊C4—51no—
71#399—22no—
72#396—24no—
73#379—52no—
74#379—51no—
75#379C2×D511yescharacteristic
76#379C2×D512yes—
77#342—104no—
78#342—102no—
79C23×C5—24no—
80C23×C5—22no—
81C23×C5—42no—
82C23×C5—41no—
83C23×C5—42no—
84C23×C5—42no—
85C23×C5—42no—
86C23×C5—42no—
87C23×C5—42no—
88C23×C5—42no—
89C23×C5—41no—
90C23×C5—42no—
91C23×C5—88no—
92C23×C5#12011yescharacteristic
93C23×C5C22⋊Q812yes—
94C23×C5C22⋊Q811yescharacteristic
95C23×C5#12412yes—
96C23×C5#12411yescharacteristic
97C2×C4×C5—44no—
98C2×C4×C5—44no—
99C2×C4×C5—44no—
100C2×C4×C5—44no—
101C2×C4×C5—42no—
102C2×Dic5—42no—
103C2×Dic5—82no—
104C2×Dic5—82no—
105C2×Dic5—82no—
106C2×Dic5—82no—
107C2×Dic5—81no—
108C2×Dic5—82no—
109C2×Dic5—82no—
110C2×Dic5—82no—
111C25C22×D511yescharacteristic
112C23×C4—52no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—22no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—101no—
119C2×C22⋊C4—102no—
120C2×C22⋊C4—102no—
121C2×C22⋊C4—101no—
122C2×C22⋊C4—102no—
123C2×C22⋊C4—101no—
124C2×C22⋊C4—102no—
125C2×C22⋊C4—102no—
126C2×C22⋊C4—102no—
127C2×C22⋊C4C22⋊D514yes—
128C2×C22⋊C4C22⋊D512yes—
129#95—22no—
130C22×C5—22no—
131C22×C5—22no—
132C22×C5—21no—
133C22×C5—22no—
134C22×C5—21no—
135C22×C5—22no—
136C22×C5—22no—
137C22×C5—22no—
138C22×C5—22no—
139C22×C5—22no—
140C22×C5—22no—
141C22×C5—44no—
142C22×C5—84no—
143C22×C5—82no—
144C22×C5—82no—
145C22×C5—84no—
146C22×C5#39311yescharacteristic
147C22×C5#45812yes—
148C4×C5—82no—
149C4×C5—84no—
150Dic5—82no—
151Dic5—162no—
152Dic5—161no—
153C24—42no—
154C24—82no—
155C24Q8×D511yescharacteristic
156C24#71312yes—
157C24#71311yescharacteristic
158C24C2×C22⋊D512yes—
159C24C2×C22⋊D511yescharacteristic
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—102no—
163C22×C4—102no—
164C22×C4—102no—
165C22×C4—202no—
166C22×C4—201no—
167C22×C4—402no—
168C4⋊C4—84no—
169C4⋊C4—82no—
170C22⋊C4—44no—
171C22⋊C4—42no—
172C22⋊C4—82no—
173C22⋊C4—82no—
174C22⋊C4—82no—
175C22⋊C4—201no—
176C22⋊C4—202no—
177C22⋊C4—201no—
178C22⋊C4—204no—
179C22⋊C4—202no—
180C22⋊C4—402no—
181C22⋊C4—402no—
182C22⋊C4—402no—
183C2×C5—22no—
184C2×C5—42no—
185C2×C5—41no—
186C2×C5—42no—
187C2×C5—41no—
188C2×C5#203011yescharacteristic
189C2×C5#203212yes—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—41no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—41no—
201C23—42no—
202C23—88no—
203C23#409212yes—
204C23#409211yescharacteristic
205C23#409312yes—
206C23#409311yescharacteristic
207C23#409911yescharacteristic
208C2×C4—44no—
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—202no—
214C2×C4—402no—
215C2×C4—402no—
216C2×C4—402no—
217C2×C4—402no—
218C2×C4—401no—
219C2×C4—402no—
220C2×C4—402no—
221C2×C4—402no—
222C5#1039311yescharacteristic, complemented, Sylow
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#6552011yescharacteristic
240C22#6553212yes—
241C4—82no—
242C4—84no—
243C4—402no—
244C4—802no—
245C4—801no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#1060268711yescharacteristic
252C2#1060268912yes—
subgroupG/H
centerC22#65520
commutator, prime radical, cosocleC25×C5C23
FrattiniC25C22×D5
FittingC5×#2842C2
socleC22×C5#393
hypercenter#2842D5
hypocenterC5#10393
LCSG ▷ C25×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #2842

Complements

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

NH ≅ G/Ntype
222. C5#10393semidirect

Maximal subgroups

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

subgroupindex
C5×#28422
#106002882
#105981142
#103935