Finite Group Databasebeta

← #12002553

Subgroups — #12002553

Order 1280.

542 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 75 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#10605575C211yesmaximal, characteristic
2C5×#1819C211yesmaximal, characteristic
3#10602335C212yesmaximal
4#10598114C211yesmaximal, characteristic
5#10598114C212yesmaximal
6C22×C5×C22⋊C4C2211yescharacteristic
7C5×#379C2211yescharacteristic
8C5×#379C2211yescharacteristic
9#65536C2212yes—
10#65536C2212yes—
11#65236—22no—
12#65236—24no—
13C5×#342—22no—
14#64746—24no—
15#10391—51nomaximal, Sylow
16C25×C5C2311yescharacteristic
17C23×C4×C5Q812yescomplemented
18C22×Dic10—22no—
19C2×C5×C22⋊C4—21no—
20C2×C5×C22⋊C4—22no—
21C2×C5×C22⋊C4—21no—
22C2×C5×C22⋊C4—22no—
23C2×C5×C22⋊C4—21no—
24C2×C5×C22⋊C4—22no—
25C2×C5×C22⋊C4—22no—
26C2×C5×C22⋊C4D412yes—
27C2×C22⋊Dic5—22no—
28C2×C22⋊Dic5—22no—
29C2×C22⋊Dic5—22no—
30C2×C22⋊Dic5—22no—
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5D414yes—
33#3963—26no—
34#2840—51no—
35#1819—52no—
36#1819D511yescharacteristic
37#1304—52no—
38#1304—51no—
39C24×C5—42no—
40C24×C5—82no—
41C24×C5C2×D412yes—
42C24×C5C2×D411yescharacteristic
43C24×C5C2×Q811yescharacteristic
44C24×C5#4111yescharacteristic
45C24×C5#4112yes—
46C22×C4×C5—22no—
47C22×C4×C5—22no—
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—41no—
51C22×C4×C5—82no—
52C22×Dic5—24no—
53C22×Dic5—42no—
54C2×Dic10—84no—
55C2×Dic10—82no—
56C5×C22⋊C4—41no—
57C5×C22⋊C4—42no—
58C5×C22⋊C4—41no—
59C5×C22⋊C4—42no—
60C5×C22⋊C4—42no—
61C5×C22⋊C4—82no—
62C5×C22⋊C4—82no—
63C22⋊Dic5—44no—
64C22⋊Dic5—44no—
65C22⋊Dic5—82no—
66C22⋊Dic5—82no—
67C22⋊Dic5—82no—
68C22⋊Dic5—82no—
69C22×C22⋊C4C2×D511yescharacteristic
70#393—104no—
71#393—102no—
72#379—52no—
73#379—52no—
74#379C2×D511yescharacteristic
75#379C2×D511yescharacteristic
76#342—22no—
77#342—104no—
78C23×C5—24no—
79C23×C5—22no—
80C23×C5—42no—
81C23×C5—41no—
82C23×C5—42no—
83C23×C5—42no—
84C23×C5—42no—
85C23×C5—42no—
86C23×C5—42no—
87C23×C5—42no—
88C23×C5—41no—
89C23×C5—42no—
90C23×C5—88no—
91C23×C5#12011yescharacteristic
92C23×C5C22⋊Q812yes—
93C23×C5C22⋊Q811yescharacteristic
94C23×C5#12412yes—
95C23×C5#12411yescharacteristic
96C2×C4×C5—44no—
97C2×C4×C5—42no—
98C2×C4×C5—42no—
99C2×C4×C5—82no—
100C2×C4×C5—82no—
101C2×C4×C5—82no—
102C2×C4×C5—81no—
103C2×C4×C5—82no—
104C2×Dic5—44no—
105C2×Dic5—44no—
106C2×Dic5—44no—
107C2×Dic5—82no—
108C2×Dic5—82no—
109C2×Dic5—82no—
110Dic10—88no—
111C25C22×D511yescharacteristic
112C22×Q8—102no—
113C23×C4Dic1012yescomplemented
114C2×C22⋊C4—21no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—54no—
122C2×C22⋊C4—102no—
123C2×C22⋊C4—102no—
124C2×C22⋊C4—102no—
125C2×C22⋊C4—102no—
126C2×C22⋊C4—102no—
127C2×C22⋊C4C22⋊D512yes—
128#95—106no—
129C22×C5—22no—
130C22×C5—22no—
131C22×C5—21no—
132C22×C5—22no—
133C22×C5—21no—
134C22×C5—22no—
135C22×C5—22no—
136C22×C5—22no—
137C22×C5—22no—
138C22×C5—22no—
139C22×C5—22no—
140C22×C5—44no—
141C22×C5—84no—
142C22×C5—82no—
143C22×C5—82no—
144C22×C5—84no—
145C22×C5#39311yescharacteristic
146C22×C5#45812yes—
147C4×C5—82no—
148C4×C5—82no—
149C4×C5—161no—
150Dic5—84no—
151Dic5—162no—
152C24—42no—
153C24—82no—
154C24C2×Dic1011yescharacteristic
155C24#70911yescharacteristic
156C24D4×D512yes—
157C24#71112yes—
158C24C2×C22⋊D511yescharacteristic
159C2×Q8—404no—
160C2×Q8—402no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4—82no—
167C22×C4—104no—
168C22×C4—202no—
169C22⋊C4—42no—
170C22⋊C4—41no—
171C22⋊C4—41no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—82no—
175C22⋊C4—82no—
176C22⋊C4—204no—
177C22⋊C4—204no—
178C22⋊C4—402no—
179C22⋊C4—402no—
180C22⋊C4—402no—
181C22⋊C4—402no—
182C2×C5—22no—
183C2×C5—42no—
184C2×C5—41no—
185C2×C5—42no—
186C2×C5—41no—
187C2×C5#203011yescharacteristic
188C2×C5#203212yes—
189C23—22no—
190C23—24no—
191C23—42no—
192C23—41no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—41no—
200C23—42no—
201C23—88no—
202C23#402412yes—
203C23#403112yes—
204C23#407011yescharacteristic
205C23#408211yescharacteristic
206C23#408311yescharacteristic
207Q8—408no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4—204no—
217C2×C4—204no—
218C2×C4—204no—
219C2×C4—402no—
220C2×C4—402no—
221C2×C4—402no—
222C5#1039111yescharacteristic, complemented, Sylow
223C22—22no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—22no—
232C22—22no—
233C22—21no—
234C22—44no—
235C22—82no—
236C22—84no—
237C22—84no—
238C22—82no—
239C22#6523611yescharacteristic
240C22#6534212yes—
241C4—82no—
242C4—82no—
243C4—161no—
244C4—404no—
245C4—802no—
246C2—22no—
247C2—41no—
248C2—42no—
249C2—42no—
250C2—41no—
251C2#1060032911yescharacteristic
252C2#1060081812yes—
subgroupG/H
centerC22#65236
commutator, prime radical, cosocleC25×C5C23
FrattiniC25C22×D5
FittingC5×#1819C2
socleC22×C5#393
hypercenter#1819D5
hypocenterC5#10391
LCSG ▷ C25×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
17. C23×C4×C5Q8semidirect
113. C23×C4Dic10semidirect
222. C5#10391semidirect

Maximal subgroups

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

subgroupindex
#106055752
C5×#18192
#106023352
#105981142
#103915