Finite Group Databasebeta

← #11996668

Subgroups — #11996668

Order 1280.

506 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 131 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#10614206C211yesmaximal, characteristic
2#10614166C211yesmaximal, characteristic
3C5×#1801C211yesmaximal, characteristic
4#10601299C212yesmaximal
5#10598206C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090—21no—
8C2×#4015C2211yescharacteristic
9C5×#423C2212yes—
10C2×C5×#101—21no—
11Q8×#168—24no—
12#65272C414yes—
13#65263—21no—
14C4×C4⋊Dic5C2211yescharacteristic
15#65217—22no—
16#65214—22no—
17#65214C2212yes—
18C5×#343—21no—
19#64702—24no—
20#9394—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C2×C5×M16—22no—
24C4×C5×Q8—22no—
25C4×C5×Q8—22no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C42×C5D412yes—
29C2×C42×C5C2311yescharacteristic
30#4090—42no—
31#4090—42no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C412yes—
35C2×#683—24no—
36C2×C4×Dic5—21no—
37#4015—22no—
38#4015—22no—
39C5×C4⋊C8—22no—
40C5×C4⋊C8—22no—
41C5×#101—42no—
42#3963—24no—
43#3963C2×C412yes—
44C22⋊#168—22no—
45C4⋊#168—24no—
46C4⋊#168D414yes—
47C4×#168—24no—
48C4×#168—22no—
49#2982—51no—
50#2546—51no—
51#1801D511yescharacteristic
52#1546—52no—
53#1303—52no—
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8D812yes—
57C2×C5×Q8SD1612yes—
58C22×C4×C5C22⋊C412yes—
59C22×C4×C5C22⋊C412yes—
60C22×C4×C5C22×C411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—22no—
64C22×Dic5—22no—
65C2×Dic10—42no—
66C2×Dic10—41no—
67C2×Dic10—41no—
68C2×Dic10—42no—
69C5×M16—42no—
70C5×M16—42no—
71C2×C5×C8—42no—
72C5×C4⋊C4—24no—
73C5×C4⋊C4—22no—
74C42×C5—22no—
75C42×C5—22no—
76C42×C5C2×D412yes—
77C42×C5#4112yes—
78C4⋊Dic5—24no—
79C4⋊Dic5—24no—
80C4⋊Dic5—41no—
81C4⋊Dic5—41no—
82#683—48no—
83C4×Dic5—41no—
84C4×Dic5—41no—
85C2×#168—24no—
86C2×C4⋊Q8—51no—
87C2×C4⋊Q8—101no—
88C2×C4×Q8C2×D511yescharacteristic
89C8×Q8—104no—
90#431—52no—
91#431—102no—
92#423C2×D512yes—
93C2×#101—21no—
94#398—54no—
95#391—101no—
96#389—102no—
97C4×C4⋊C4—51no—
98#343—21no—
99#332—104no—
100C23×C5C2×C22⋊C411yescharacteristic
101C5×Q8—24no—
102C5×Q8—24no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5#10214yes—
110C2×C4×C5C4×D412yes—
111C2×C4×C5#12011yescharacteristic
112C2×C4×C5#12112yes—
113C2×C4×C5#12311yescharacteristic
114C2×C4×C5C2×D811yescharacteristic
115C2×C4×C5C2×SD1611yescharacteristic
116C2×C4×C5#13512yes—
117C2×Dic5—24no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123Dic10—82no—
124Dic10—82no—
125C5×C8—82no—
126#168—44no—
127C22×Q8—101no—
128C22×Q8C22⋊D511yescharacteristic
129C2×M16—22no—
130C4⋊Q8—102no—
131C4⋊Q8—102no—
132C4⋊Q8—202no—
133C4⋊Q8—202no—
134C4×Q8—22no—
135C4×Q8—22no—
136C2×C4⋊C4—52no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4—104no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4C4×D512yes—
141C2×C4⋊C4C22⋊D511yescharacteristic
142C2×C42—101no—
143C2×C42D2012yes—
144C2×C42C22×D511yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—22no—
147C4⋊C8—54no—
148C4⋊C8—104no—
149#101—42no—
150C22⋊C8—102no—
151C4×C8—104no—
152C4×C8—102no—
153#95—52no—
154#95—104no—
155C22×C5—21no—
156C22×C5—21no—
157C22×C5#38611yescharacteristic
158C22×C5C2×#10211yescharacteristic
159C22×C5#41611yescharacteristic
160C4×C5—21no—
161C4×C5—24no—
162C4×C5—22no—
163C4×C5—42no—
164C4×C5#45612yes—
165C4×C5#46512yes—
166C4×C5#46612yes—
167Dic5—44no—
168Dic5—82no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—202no—
172C2×Q8—201no—
173C2×Q8—202no—
174C2×Q8—201no—
175C2×Q8#68612yes—
176C2×Q8#68812yes—
177C22×C4—102no—
178C22×C4—102no—
179C22×C4#68512yes—
180C22×C4#68512yes—
181C22×C4C2×C4×D511yescharacteristic
182C22×C4C2×D2011yescharacteristic
183C22×C4C2×C22⋊D511yescharacteristic
184M16—42no—
185M16—42no—
186C2×C8—42no—
187C2×C8—104no—
188C4⋊C4—24no—
189C4⋊C4—22no—
190C4⋊C4—104no—
191C4⋊C4—104no—
192C4⋊C4—208no—
193C4⋊C4—201no—
194C4⋊C4—201no—
195C42—22no—
196C42—22no—
197C42—201no—
198C42—201no—
199C42D4×D512yes—
200C42#71112yes—
201C2×C5—21no—
202C2×C5—21no—
203C2×C5#188611yescharacteristic
204C2×C5#189311yescharacteristic
205C2×C5#191511yescharacteristic
206C23C2×#68511yescharacteristic
207Q8—24no—
208Q8—24no—
209Q8—402no—
210Q8—402no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—104no—
218C2×C4—202no—
219C2×C4—202no—
220C2×C4—202no—
221C2×C4—202no—
222C2×C4—202no—
223C2×C4#394114yes—
224C2×C4#402712yes—
225C2×C4#402811yescharacteristic
226C2×C4#403211yescharacteristic
227C2×C4C2×#68611yescharacteristic
228C2×C4#408512yes—
229C2×C4C2×#68811yescharacteristic
230C2×C4#409612yes—
231C8—82no—
232C8—204no—
233C5#939411yescharacteristic, complemented, Sylow
234C22—21no—
235C22—21no—
236C22#6524711yescharacteristic
237C22C2×#394111yescharacteristic
238C22#6529111yescharacteristic
239C4—24no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—204no—
244C4—402no—
245C4#6504112yes—
246C4#6532712yes—
247C4#6533712yes—
248C2—21no—
249C2—21no—
250C2#1060030811yescharacteristic
251C2#1060089611yescharacteristic
252C2#1060093111yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1801C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1801D5
hypocenterC5#9394
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
233. C5#9394semidirect

Maximal subgroups

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

subgroupindex
#106142062
#106141662
C5×#18012
#106012992
#105982062
#93945