Finite Group Databasebeta

← #11996670

Subgroups — #11996670

Order 1280.

506 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 135 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×#2982C211yesmaximal, characteristic
2#10614206C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4#10601571C212yesmaximal
5#10598237C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090—21no—
8C2×#4015C2211yescharacteristic
9C5×C8×Q8—24no—
10C5×#431—22no—
11C5×#431C2212yes—
12C2×#3968—21no—
13#65272C414yes—
14#65263—21no—
15C4×C4⋊Dic5C2211yescharacteristic
16#65217—22no—
17#65213C2212yes—
18#64750—21no—
19#64706—24no—
20#9394—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C4×C5×Q8—22no—
24C4×C5×Q8—22no—
25C2×C5×C4⋊C4C2×C412yes—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C42×C5D412yes—
28C2×C42×C5C2311yescharacteristic
29#4090—42no—
30#4090—42no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C412yes—
34C2×#683—24no—
35C2×C4×Dic5—21no—
36C2×#681—22no—
37#4015—22no—
38#4015—22no—
39C5×C4⋊C8—24no—
40C5×C4⋊C8D414yes—
41C5×C22⋊C8—22no—
42C4×C5×C8—24no—
43C4×C5×C8—22no—
44#3968—42no—
45#3963—24no—
46#3963C2×C412yes—
47C4⋊#168—22no—
48C4⋊#168—22no—
49#2982D511yescharacteristic
50#2546—51no—
51#1801—51no—
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—
69C2×C5×C8—24no—
70C5×C4⋊C4—24no—
71C5×C4⋊C4—22no—
72C42×C5—22no—
73C42×C5—22no—
74C42×C5C2×D412yes—
75C42×C5#4112yes—
76C4⋊Dic5—24no—
77C4⋊Dic5—24no—
78C4⋊Dic5—41no—
79C4⋊Dic5—41no—
80#683—48no—
81C4×Dic5—41no—
82C4×Dic5—41no—
83#681—42no—
84#681—42no—
85C2×#168—42no—
86C2×C4⋊Q8—51no—
87C2×C4⋊Q8—101no—
88C2×C4×Q8C2×D511yescharacteristic
89C8×Q8—24no—
90#431—22no—
91#431C2×D512yes—
92#423—52no—
93C2×#101—101no—
94#398—54no—
95#391—101no—
96#389—102no—
97C4×C4⋊C4—51no—
98#343—101no—
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—44no—
126#168—82no—
127C22×Q8—101no—
128C22×Q8D2011yescharacteristic
129C2×M16—102no—
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⋊C4D2011yescharacteristic
142C2×C42—101no—
143C2×C42C22⋊D512yes—
144C2×C42C22×D511yescharacteristic
145C4⋊C8—24no—
146C4⋊C8—102no—
147C4⋊C8—102no—
148C4⋊C8C22⋊D514yes—
149#101—202no—
150C22⋊C8—22no—
151C4×C8—24no—
152C4×C8—22no—
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—201no—
172C2×Q8—201no—
173C2×Q8—202no—
174C2×Q8—202no—
175C2×Q8#67712yes—
176C2×Q8D4012yes—
177C22×C4—102no—
178C22×C4—102no—
179C22×C4#68512yes—
180C22×C4#68512yes—
181C22×C4C2×C4×D511yescharacteristic
182C22×C4C2×D2011yescharacteristic
183C22×C4C2×C22⋊D511yescharacteristic
184M16—202no—
185M16—202no—
186C2×C8—24no—
187C2×C8—202no—
188C4⋊C4—24no—
189C4⋊C4—22no—
190C4⋊C4—104no—
191C4⋊C4—104no—
192C4⋊C4—201no—
193C4⋊C4—208no—
194C4⋊C4—201no—
195C42—22no—
196C42—22no—
197C42—201no—
198C42—201no—
199C42#70912yes—
200C42C2×C22⋊D512yes—
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#395314yes—
224C2×C4C2×#67711yescharacteristic
225C2×C4C2×D4011yescharacteristic
226C2×C4#405012yes—
227C2×C4C4×C22⋊D512yes—
228C2×C4#407511yescharacteristic
229C2×C4#407612yes—
230C2×C4#409911yescharacteristic
231C8—44no—
232C8—402no—
233C5#939411yescharacteristic, complemented, Sylow
234C22—21no—
235C22—21no—
236C22C2×#395311yescharacteristic
237C22#6540211yescharacteristic
238C22#6550211yescharacteristic
239C4—24no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—204no—
244C4—402no—
245C4#6540312yes—
246C4#6540412yes—
247C4#6553512yes—
248C2—21no—
249C2—21no—
250C2#1060245311yescharacteristic
251C2#1060276611yescharacteristic
252C2#1060282411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2982C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2982D5
hypocenterC5#9394
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

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
C5×#29822
#106142062
#106024302
#106015712
#105982372
#93945