Finite Group Databasebeta

← #11996715

Subgroups — #11996715

Order 1280.

570 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 119 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×#2975C211yesmaximal, characteristic
2#10614110C211yesmaximal, characteristic
3#10602410C211yesmaximal, characteristic
4#10601573C212yesmaximal, complemented
5#10598237C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4070—22no—
8C2×#4015C2211yescharacteristic
9C5×#436—24no—
10C5×#431C2212yes—
11C5×#407—22no—
12#65510—21no—
13C2×#3965—21no—
14#65265—21no—
15#65238C414yes—
16C4×C4⋊Dic5C2211yescharacteristic
17#65213C2212yes—
18#64750—21no—
19#64702—24no—
20#9403—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5D412yes—
23C22×Dic10—21no—
24C2×C5×M16—24no—
25C4×C5×D4—22no—
26C4×C5×D4—22no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C22⋊C4C2×C412yes—
29C2×C42×C5C2311yescharacteristic
30C2×C22⋊Dic5—24no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C412yes—
34#4070—48no—
35C2×#683—24no—
36C2×C4×Dic5—21no—
37C2×#681—22no—
38#4015—22no—
39#4015—22no—
40C5×C4⋊C8D414yes—
41C5×C22⋊C8—24no—
42C5×C22⋊C8—22no—
43C4×C5×C8—22no—
44#3965—42no—
45#3963C2×C412yes—
46C4⋊#168—22no—
47C4⋊#168—22no—
48#2975D511yescharacteristic
49#2542—51no—
50#1800—51no—
51#1549—52no—
52#1303—52no—
53C24×C5C22⋊C412yes—
54C2×C5×D4—22no—
55C2×C5×D4—21no—
56C2×C5×D4—22no—
57C2×C5×D4—21no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—44no—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22×C411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×Dic5—22no—
66C22×Dic5—22no—
67C2×Dic10—44no—
68C2×Dic10—41no—
69C2×Dic10—41no—
70C5×M16—84no—
71C2×C5×C8—24no—
72C5×C4⋊C4—22no—
73C5×C22⋊C4—24no—
74C42×C5C2×D412yes—
75C42×C5#4112yes—
76C22⋊Dic5—48no—
77C4⋊Dic5—24no—
78C4⋊Dic5—24no—
79C4⋊Dic5—42no—
80#683—48no—
81C4×Dic5—41no—
82C4×Dic5—41no—
83#681—42no—
84#681—42no—
85C2×#168—42no—
86C2×C4⋊Q8—51no—
87C2×C22⋊Q8—102no—
88C2×C4×D4C2×D511yescharacteristic
89#436—24no—
90#431C2×D512yes—
91#423—52no—
92C2×#100—101no—
93#407—22no—
94#399—54no—
95#390—101no—
96#384—101no—
97C4×C4⋊C4—51no—
98#343—101no—
99#332—104no—
100C23×C5—22no—
101C23×C5—22no—
102C23×C5—22no—
103C23×C5—42no—
104C23×C5—42no—
105C23×C5C2×C22⋊C411yescharacteristic
106C5×D4—42no—
107C5×D4—42no—
108C2×C4×C5—22no—
109C2×C4×C5—22no—
110C2×C4×C5—41no—
111C2×C4×C5—44no—
112C2×C4×C5—42no—
113C2×C4×C5—82no—
114C2×C4×C5C4×D412yes—
115C2×C4×C5#12011yescharacteristic
116C2×C4×C5#12112yes—
117C2×C4×C5#12311yescharacteristic
118C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C5#13712yes—
120C2×C4×C5#13711yescharacteristic
121C2×Dic5—24no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—44no—
125C2×Dic5—42no—
126Dic10—82no—
127Dic10—82no—
128C5×C8—44no—
129#168—82no—
130C22×Q8—101no—
131C22×D4D2011yescharacteristic
132C23×C4C22⋊D512yes—
133C2×M16—24no—
134C2×M16—102no—
135C4⋊Q8—102no—
136C4⋊Q8—102no—
137C22⋊Q8—208no—
138C4×D4—22no—
139C4×D4—22no—
140C2×C4⋊C4—52no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—104no—
143C2×C4⋊C4—101no—
144C2×C4⋊C4D2011yescharacteristic
145C2×C22⋊C4—104no—
146C2×C22⋊C4C4×D512yes—
147C2×C42—101no—
148C2×C42C22×D511yescharacteristic
149C4⋊C8—102no—
150C4⋊C8—102no—
151C4⋊C8C22⋊D514yes—
152#100—202no—
153C22⋊C8—24no—
154C22⋊C8—22no—
155C4×C8—22no—
156#95—52no—
157C22×C5—21no—
158C22×C5—21no—
159C22×C5—44no—
160C22×C5—42no—
161C22×C5—42no—
162C22×C5—42no—
163C22×C5—82no—
164C22×C5#38611yescharacteristic
165C22×C5#41711yescharacteristic
166C22×C5#41911yescharacteristic
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—42no—
170C4×C5#45312yes—
171C4×C5#46812yes—
172C4×C5#47012yes—
173Dic5—44no—
174Dic5—82no—
175C24#68512yes—
176C2×Q8—204no—
177C2×Q8—201no—
178C2×Q8—201no—
179C2×D4—21no—
180C2×D4—22no—
181C2×D4—21no—
182C2×D4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—44no—
186C22×C4—102no—
187C22×C4—102no—
188C22×C4#68512yes—
189C22×C4C2×C4×D511yescharacteristic
190C22×C4C2×D2011yescharacteristic
191C22×C4C2×C22⋊D511yescharacteristic
192M16—84no—
193M16—202no—
194M16—202no—
195C2×C8—24no—
196C2×C8—202no—
197C4⋊C4—22no—
198C4⋊C4—104no—
199C4⋊C4—104no—
200C4⋊C4—208no—
201C4⋊C4—202no—
202C22⋊C4—24no—
203C22⋊C4—208no—
204C42—201no—
205C42—201no—
206C42#70912yes—
207C42C2×C22⋊D512yes—
208C2×C5—21no—
209C2×C5—21no—
210C2×C5—82no—
211C2×C5#188711yescharacteristic
212C2×C5#189411yescharacteristic
213C2×C5#191511yescharacteristic
214C23—22no—
215C23—22no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23C2×#68511yescharacteristic
220Q8—402no—
221Q8—402no—
222D4—42no—
223D4—42no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4—104no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—204no—
234C2×C4—202no—
235C2×C4#405411yescharacteristic
236C2×C4#405512yes—
237C2×C4#405511yescharacteristic
238C2×C4C4×C22⋊D512yes—
239C2×C4#407511yescharacteristic
240C2×C4#407612yes—
241C2×C4#409911yescharacteristic
242C8—44no—
243C8—402no—
244C5#940311yescharacteristic, complemented, Sylow
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22#6540911yescharacteristic
253C22#6542211yescharacteristic
254C22#6550211yescharacteristic
255C4—22no—
256C4—21no—
257C4—42no—
258C4—204no—
259C4—402no—
260C4#6542312yes—
261C4#6542612yes—
262C4#6553012yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2#1060244311yescharacteristic
267C2#1060278211yescharacteristic
268C2#1060282411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2975C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#2975D5
hypocenterC5#9403
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
4. #10601573C2semidirect
5. #10598237C2semidirect
244. C5#9403semidirect

Maximal subgroups

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

subgroupindex
C5×#29752
#106141102
#106024102
#106015732
#105982372
#94035