Finite Group Databasebeta

← #12002434

Subgroups — #12002434

Order 1280.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#10605128C211yesmaximal, characteristic
2#10601585C212yesmaximal
3#10600234C211yesmaximal, characteristic
4C5×#1274C211yesmaximal, characteristic
5#10598237C212yesmaximal
6#65804C2211yescharacteristic
7C2×C4×Dic10—21no—
8C5×#431C2212yes—
9C5×#376C2211yescharacteristic
10C4×C4⋊Dic5—21no—
11C4×C4⋊Dic5C2212yes—
12#65213C2211yescharacteristic
13#64950—22no—
14#64945—22no—
15#64743—21no—
16#64743—21no—
17#64687—22no—
18#64687—22no—
19#10371—51nomaximal, Sylow
20C22×Dic10—21no—
21C2×C42×C5D411yescharacteristic
22C2×C42×C5D411yescharacteristic
23C2×C42×C5C2311yescharacteristic
24#4072—21no—
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—22no—
27C2×C4⋊Dic5—22no—
28#4070—22no—
29C2×#683—22no—
30C2×C4×Dic5—22no—
31C2×#681—21no—
32#4016—21no—
33#4015Q812yescomplemented
34C4×Dic10—22no—
35C4×Dic10—42no—
36C4×Dic10—42no—
37C5×C4⋊C8—22no—
38C5×C22⋊C8—22no—
39C4×C5×C8—22no—
40C5×#95—22no—
41#3963—21no—
42#3963—21no—
43#3963D412yes—
44#3963D412yes—
45C4⋊#168—22no—
46#2399—51no—
47#1995—51no—
48#1503—52no—
49#1303—52no—
50#1274D511yescharacteristic
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5C2×D412yes—
55C22×Dic5—22no—
56C22×Dic5—22no—
57C2×Dic10—22no—
58C2×Dic10—44no—
59C2×Dic10—42no—
60C2×C5×C8—42no—
61C42×C5—21no—
62C42×C5—21no—
63C42×C5SD1612yes—
64C42×C5Q1612yes—
65C42×C5C2×Q811yescharacteristic
66C42×C5#4112yes—
67C42×C5#4111yescharacteristic
68C22⋊Dic5—41no—
69C4⋊Dic5—22no—
70C4⋊Dic5—22no—
71C4⋊Dic5—44no—
72C4⋊Dic5—44no—
73C4⋊Dic5—42no—
74#683—44no—
75#683—42no—
76C4×Dic5—41no—
77C4×Dic5—42no—
78C4×Dic5—42no—
79#681—41no—
80#681—41no—
81C2×#168—41no—
82#533—51no—
83C2×C4×Q8—101no—
84#431C2×D512yes—
85#423—51no—
86#398—102no—
87#395—102no—
88C4×C4⋊C4—52no—
89C4×C4⋊C4—101no—
90#376C2×D511yescharacteristic
91#339—101no—
92#339—101no—
93#328—102no—
94#328—102no—
95C23×C5#12011yescharacteristic
96C2×C4×C5—22no—
97C2×C4×C5—22no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5C22⋊Q812yes—
102C2×C4×C5C22⋊Q811yescharacteristic
103C2×C4×C5#12411yescharacteristic
104C2×C4×C5#12412yes—
105C2×C4×C5C2×SD1611yescharacteristic
106C2×C4×C5C2×Q1611yescharacteristic
107C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C5#13711yescharacteristic
109C2×Dic5—24no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—42no—
113C2×Dic5—42no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116Dic10—48no—
117Dic10—82no—
118C5×C8—82no—
119#168—81no—
120C22×Q8—101no—
121C2×M16—101no—
122C4⋊Q8—52no—
123#125—101no—
124C22⋊Q8—102no—
125C4×Q8—102no—
126C4×Q8—202no—
127C4×Q8—202no—
128#117—101no—
129C2×C4⋊C4—102no—
130C2×C4⋊C4—101no—
131C2×C4⋊C4—102no—
132C2×C4⋊C4—102no—
133C2×C42—102no—
134C2×C42D2011yescharacteristic
135C2×C42D2011yescharacteristic
136C2×C42C22×D511yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—102no—
139C22⋊C8—22no—
140C4×C8—22no—
141#95—22no—
142#95—52no—
143#95—52no—
144#95—101no—
145#95—101no—
146C22×C5—22no—
147C22×C5#39311yescharacteristic
148C22×C5#45011yescharacteristic
149C22×C5#45111yescharacteristic
150C4×C5—22no—
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—42no—
154C4×C5#47511yescharacteristic
155C4×C5#47711yescharacteristic
156C4×C5#48711yescharacteristic
157C4×C5#48911yescharacteristic
158Dic5—44no—
159Dic5—82no—
160Dic5—82no—
161C2×Q8—102no—
162C2×Q8—202no—
163C2×Q8—204no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—102no—
167C22×C4—102no—
168C22×C4C2×D2011yescharacteristic
169C22×C4D4×D512yes—
170M16—201no—
171M16—201no—
172C2×C8—42no—
173C2×C8—201no—
174C4⋊C4—102no—
175C4⋊C4—102no—
176C4⋊C4—204no—
177C4⋊C4—202no—
178C4⋊C4—204no—
179C4⋊C4—204no—
180C4⋊C4—202no—
181C22⋊C4—201no—
182C42—21no—
183C42—21no—
184C42—201no—
185C42—202no—
186C42—202no—
187C42#67712yes—
188C42Dic2012yes—
189C42#70912yes—
190C42#71111yescharacteristic
191C42Q8×D511yescharacteristic
192C2×C5—21no—
193C2×C5—21no—
194C2×C5#202411yescharacteristic
195C2×C5#203112yes—
196C23#402811yescharacteristic
197Q8—208no—
198Q8—402no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—104no—
205C2×C4—202no—
206C2×C4—202no—
207C2×C4—202no—
208C2×C4—202no—
209C2×C4—202no—
210C2×C4—202no—
211C2×C4#402111yescharacteristic
212C2×C4#403112yes—
213C2×C4#404212yes—
214C2×C4#404311yescharacteristic
215C2×C4C2×#67711yescharacteristic
216C2×C4C2×Dic2011yescharacteristic
217C2×C4#405411yescharacteristic
218C2×C4#405511yescharacteristic
219C8—82no—
220C8—401no—
221C5#1037111yescharacteristic, complemented, Sylow
222C22—22no—
223C22#6496211yescharacteristic
224C22#6502011yescharacteristic
225C22#6502811yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—204no—
231C4—402no—
232C4—402no—
233C4#6497011yescharacteristic
234C4#6500311yescharacteristic
235C4#6513911yescharacteristic
236C4#6514011yescharacteristic
237C2—21no—
238C2—21no—
239C2#1059948211yescharacteristic
240C2#1059950712yes—
subgroupG/H
centerC2×C4#4021
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1274C2
socleC22×C5#393
prime radicalC23×C5#120
hypercenter#1274D5
hypocenterC5#10371
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
33. #4015Q8semidirect
221. C5#10371semidirect

Maximal subgroups

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

subgroupindex
#106051282
#106015852
#106002342
C5×#12742
#105982372
#103715