Finite Group Databasebeta

← #11992526

Subgroups — #11992526

Order 1280.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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#10610176C211yesmaximal, characteristic
2C5×#1835C211yesmaximal, characteristic
3#10600522C211yesmaximal, characteristic
4#10600339C212yesmaximal
5#10598122C212yesmaximal
6#65804C2211yescharacteristic
7C2×C4×C5×C8C2211yescharacteristic
8C5×#382C2212yes—
9#65391—21no—
10#65390—21no—
11#65214C2212yes—
12#65213C2211yescharacteristic
13#64968—21no—
14#64968C412yescomplemented
15C8×Dic10—21no—
16C8×Dic10C412yescomplemented
17C5×#340—21no—
18C5×#340—21no—
19#64678—21no—
20#64677—21no—
21#64672—24no—
22#8679—51nomaximal, Sylow
23C22×C5×C8D411yescharacteristic
24C22×C5×C8D411yescharacteristic
25C2×C5×C4⋊C4—22no—
26C2×C42×C5C2311yescharacteristic
27#4072—21no—
28#4070—21no—
29#4070D412yes—
30C2×#681—21no—
31#4016—21no—
32#4015Q811yescharacteristic
33#4015Q811yescharacteristic
34C4×Dic10—21no—
35C4×Dic10C2×C412yes—
36C4×C5×C8C2×C411yescharacteristic
37C4×C5×C8C2×C411yescharacteristic
38C4×C5×C8D411yescharacteristic
39C4×C5×C8D411yescharacteristic
40C5×#95—22no—
41C5×#95—22no—
42C22⋊#168—22no—
43#3947—22no—
44#3946—22no—
45#3946—22no—
46C8×Dic5—22no—
47C4⋊#168—21no—
48C4⋊#168—22no—
49C4⋊#168C2×C412yes—
50C4×#168—22no—
51#2960—51no—
52#1835D511yescharacteristic
53#1564—51no—
54#1518—52no—
55#1286—52no—
56C22×C4×C5—42no—
57C22×C4×C5C2×D411yescharacteristic
58C22×C4×C5C2×D411yescharacteristic
59C22×C4×C5#4111yescharacteristic
60C2×Dic10—21no—
61C2×Dic10C4⋊C412yes—
62C2×C5×C8—22no—
63C2×C5×C8—22no—
64C2×C5×C8C22⋊C411yescharacteristic
65C2×C5×C8C22⋊C411yescharacteristic
66C2×C5×C8C22⋊C411yescharacteristic
67C2×C5×C8C22⋊C411yescharacteristic
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C42×C5C22×C411yescharacteristic
71C42×C5C2×D411yescharacteristic
72C42×C5C2×Q811yescharacteristic
73C42×C5#4111yescharacteristic
74C22⋊Dic5—22no—
75C4⋊Dic5—21no—
76C4⋊Dic5—21no—
77C4⋊Dic5—21no—
78C4⋊Dic5C4⋊C412yes—
79#683—22no—
80#683—22no—
81C4×Dic5—22no—
82#681—42no—
83C2×#168—22no—
84C2×#168—42no—
85#533—51no—
86#446—52no—
87#446—101no—
88C8×Q8—52no—
89C8×Q8—101no—
90#431—52no—
91#424—101no—
92#423—51no—
93#405—101no—
94C2×C4×C8C2×D511yescharacteristic
95#382C2×D512yes—
96#340—21no—
97#340—21no—
98#335—101no—
99#334—101no—
100#328—104no—
101C23×C5#12111yescharacteristic
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5—82no—
105C2×C4×C5—82no—
106C2×C4×C5—82no—
107C2×C4×C5C2×C22⋊C411yescharacteristic
108C2×C4×C5C2×C4⋊C411yescharacteristic
109C2×C4×C5#11711yescharacteristic
110C2×C4×C5#12111yescharacteristic
111C2×C4×C5C22⋊Q811yescharacteristic
112C2×C4×C5C22⋊Q811yescharacteristic
113C2×C4×C5#13512yes—
114C2×C4×C5#13712yes—
115C2×Dic5—22no—
116C2×Dic5—22no—
117Dic10—42no—
118Dic10—42no—
119C5×C8—21no—
120C5×C8—21no—
121C5×C8—21no—
122C5×C8—21no—
123#168—42no—
124#168—82no—
125C2×M16—101no—
126C22×C8C22⋊D511yescharacteristic
127C22×C8C22⋊D511yescharacteristic
128C4⋊Q8—51no—
129C4⋊Q8—51no—
130#125—101no—
131C22⋊Q8—52no—
132C22⋊Q8—101no—
133C4×Q8—52no—
134C4×Q8—101no—
135#117—101no—
136C2×C4⋊C4—22no—
137C2×C42C22×D511yescharacteristic
138C4⋊C8—52no—
139C4⋊C8—102no—
140C4⋊C8—102no—
141C4⋊C8—101no—
142C4⋊C8—102no—
143C22⋊C8—102no—
144#97—102no—
145C4×C8—102no—
146C4×C8—102no—
147C4×C8C4×D511yescharacteristic
148C4×C8C4×D511yescharacteristic
149C4×C8D2011yescharacteristic
150C4×C8D2011yescharacteristic
151#95—22no—
152#95—22no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5#38011yescharacteristic
156C22×C5#46412yes—
157C4×C5—21no—
158C4×C5—21no—
159C4×C5—21no—
160C4×C5—21no—
161C4×C5—162no—
162C4×C5#41611yescharacteristic
163C4×C5#41911yescharacteristic
164C4×C5#47912yes—
165Dic5—42no—
166Dic5—42no—
167C2×Q8—52no—
168C2×Q8—101no—
169C22×C4—42no—
170C22×C4D4×D511yescharacteristic
171C22×C4#71111yescharacteristic
172C22×C4C2×C22⋊D511yescharacteristic
173M16—202no—
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—102no—
177C2×C8—202no—
178C2×C8#68511yescharacteristic
179C2×C8#68511yescharacteristic
180C2×C8#68511yescharacteristic
181C2×C8#68511yescharacteristic
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—52no—
185C4⋊C4—102no—
186C4⋊C4—102no—
187C4⋊C4—101no—
188C4⋊C4—101no—
189C4⋊C4—101no—
190C22⋊C4—102no—
191C42—102no—
192C42C2×C4×D511yescharacteristic
193C42C2×D2011yescharacteristic
194C42Q8×D511yescharacteristic
195C42#71311yescharacteristic
196C2×C5—22no—
197C2×C5#180511yescharacteristic
198C2×C5#181211yescharacteristic
199C2×C5#181411yescharacteristic
200C23#408411yescharacteristic
201Q8—202no—
202Q8—202no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4—82no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4D5×C4⋊C411yescharacteristic
211C2×C4#403811yescharacteristic
212C2×C4#404111yescharacteristic
213C2×C4#404311yescharacteristic
214C2×C4C2×#68511yescharacteristic
215C2×C4#409211yescharacteristic
216C2×C4#409612yes—
217C2×C4#409712yes—
218C8—21no—
219C8—21no—
220C8—21no—
221C8—21no—
222C8—202no—
223C8—402no—
224C5#867911yescharacteristic, complemented, Sylow
225C22—21no—
226C22—21no—
227C22#6527611yescharacteristic
228C22#6534312yes—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—162no—
234C4—202no—
235C4—202no—
236C4#6529111yescharacteristic
237C4#6529311yescharacteristic
238C4#6535212yes—
239C2—22no—
240C2#1060035211yescharacteristic
241C2#1060145711yescharacteristic
242C2#1060145811yescharacteristic
subgroupG/H
centerC22#65276
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1835C2
socleC22×C5#380
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1835D5
hypocenterC5#8679
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
14. #64968C4semidirect
16. C8×Dic10C4semidirect
224. C5#8679semidirect

Maximal subgroups

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

subgroupindex
#106101762
C5×#18352
#106005222
#106003392
#105981222
#86795