Finite Group Databasebeta

← #11987507

Subgroups — #11987507

Order 1280.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#4015C211yesmaximal, characteristic
2C5×#1839C211yesmaximal, characteristic
3#10600184C211yesmaximal, characteristic
4#10597969C214yesmaximal
5C2×#4015C411yescharacteristic
6C2×C4×Dic10—21no—
7C43×C5C2211yescharacteristic
8#65224C411yescharacteristic
9C4×C4⋊Dic5—21no—
10C4×C4⋊Dic5C412yes—
11#65218—21no—
12#65217—21no—
13#65217C2212yes—
14C2×C4⋊#168—21no—
15C2×#3935—21no—
16C5×#336—21no—
17C5×#336—21no—
18C5×#336C2212yes—
19#64744C2212yes—
20#7622—51nomaximal, Sylow
21C22×Dic10—21no—
22C22×C5×C8—22no—
23C2×C42×C5C2×C411yescharacteristic
24C2×C42×C5C2×C411yescharacteristic
25C2×C42×C5D411yescharacteristic
26C2×C42×C5D411yescharacteristic
27C2×C42×C5D411yescharacteristic
28C2×C42×C5D411yescharacteristic
29C2×C42×C5C2311yescharacteristic
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C412yes—
34C2×C4⋊Dic5C2×C412yes—
35C2×#683—22no—
36C2×C4×Dic5—22no—
37C22×#168—22no—
38#4015—24no—
39C4×Dic10—44no—
40#3963—22no—
41#3963—22no—
42C4⋊#168—24no—
43#3935—42no—
44C4×C4⋊Q8—51no—
45#1839D511yescharacteristic
46#1767—51no—
47#1271—54no—
48C22×C4×C5C22⋊C411yescharacteristic
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22×C411yescharacteristic
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5C2×D411yescharacteristic
55C22×Dic5—22no—
56C22×Dic5—22no—
57C2×Dic10—24no—
58C2×Dic10—42no—
59C2×Dic10—42no—
60C2×C5×C8—42no—
61C2×C5×C8—42no—
62C2×C5×C8—42no—
63C42×C5—22no—
64C42×C5—22no—
65C42×C5—22no—
66C42×C5—22no—
67C42×C5—41no—
68C42×C5—41no—
69C42×C5SD1612yes—
70C42×C5Q1612yes—
71C4⋊Dic5—24no—
72C4⋊Dic5—22no—
73C4⋊Dic5—42no—
74C4⋊Dic5—42no—
75C4⋊Dic5—42no—
76C4⋊Dic5M1614yes—
77#683—44no—
78C4×Dic5—44no—
79C2×#168—24no—
80C2×#168—42no—
81C2×#168—42no—
82C2×C4⋊Q8—51no—
83C2×C4×Q8—101no—
84C2×C4⋊C8—101no—
85C2×#97—101no—
86#391—101no—
87#389—52no—
88#389—101no—
89#384—51no—
90C4×C4⋊C4—52no—
91C4×C4⋊C4—101no—
92C43C2×D511yescharacteristic
93#336—21no—
94#336—21no—
95#336—52no—
96#336C2×D512yes—
97C23×C5C2×C22⋊C411yescharacteristic
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5#10112yes—
113C2×C4×C5#10312yes—
114C2×C4×C5#10312yes—
115C2×C4×C5#10412yes—
116C2×C4×C5C2×M1612yes—
117C2×C4×C5C2×SD1611yescharacteristic
118C2×C4×C5C2×Q1611yescharacteristic
119C2×C4×C5AGL(1,ℤ/8)12yes—
120C2×Dic5—24no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126Dic10—48no—
127C5×C8—82no—
128#168—44no—
129C22×Q8—101no—
130C22×C8—22no—
131C22×C8—102no—
132C4⋊Q8—104no—
133C4×Q8—204no—
134C2×C4⋊C4—52no—
135C2×C4⋊C4—52no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4—101no—
139C2×C4⋊C4—102no—
140C2×C42—102no—
141C2×C42C4×D511yescharacteristic
142C2×C42C4×D511yescharacteristic
143C2×C42D2011yescharacteristic
144C2×C42D2011yescharacteristic
145C2×C42C22⋊D511yescharacteristic
146C2×C42C22⋊D511yescharacteristic
147C2×C42C22×D511yescharacteristic
148C4⋊C8—104no—
149#97—202no—
150#95—102no—
151#95—102no—
152C22×C5#40711yescharacteristic
153C22×C5#41011yescharacteristic
154C22×C5C2×#10111yescharacteristic
155C22×C5C2×#10311yescharacteristic
156C22×C5#41811yescharacteristic
157C22×C5C2×#10411yescharacteristic
158C22×C5#42111yescharacteristic
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—22no—
162C4×C5—22no—
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—22no—
167Dic5—44no—
168Dic5—82no—
169C2×Q8—104no—
170C2×Q8—202no—
171C2×Q8—202no—
172C22×C4—102no—
173C22×C4—102no—
174C22×C4#68511yescharacteristic
175C22×C4#68511yescharacteristic
176C22×C4#68511yescharacteristic
177C22×C4#68511yescharacteristic
178C22×C4C2×C4×D511yescharacteristic
179C22×C4C2×D2011yescharacteristic
180C22×C4C2×C22⋊D511yescharacteristic
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—104no—
185C2×C8—202no—
186C2×C8—202no—
187C4⋊C4—54no—
188C4⋊C4—104no—
189C4⋊C4—102no—
190C4⋊C4—202no—
191C4⋊C4—202no—
192C4⋊C4—202no—
193C4⋊C4—204no—
194C42—22no—
195C42—22no—
196C42—22no—
197C42—22no—
198C42—41no—
199C42—41no—
200C42—204no—
201C42#67712yes—
202C42Dic2012yes—
203C2×C5#146711yescharacteristic
204C2×C5#148711yescharacteristic
205C2×C5#149011yescharacteristic
206C2×C5#150311yescharacteristic
207C2×C5#151411yescharacteristic
208C2×C5#153111yescharacteristic
209C2×C5#154911yescharacteristic
210C23C2×#68511yescharacteristic
211Q8—208no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—104no—
227C2×C4—202no—
228C2×C4—202no—
229C2×C4—202no—
230C2×C4—202no—
231C2×C4—202no—
232C2×C4#394812yes—
233C2×C4#394812yes—
234C2×C4#395612yes—
235C2×C4#395712yes—
236C2×C4C2×#67711yescharacteristic
237C2×C4C2×Dic2011yescharacteristic
238C2×C4D5×M1612yes—
239C2×C4#409512yes—
240C8—82no—
241C8—204no—
242C5#762211yescharacteristic, complemented, Sylow
243C22#6529011yescharacteristic
244C22#6529411yescharacteristic
245C22#6529511yescharacteristic
246C22C2×#394811yescharacteristic
247C22#6541511yescharacteristic
248C22C2×#395611yescharacteristic
249C22C2×#395711yescharacteristic
250C4—22no—
251C4—22no—
252C4—21no—
253C4—21no—
254C4—22no—
255C4—22no—
256C4—22no—
257C4—22no—
258C4—204no—
259C4—402no—
260C2#1060035711yescharacteristic
261C2#1060156311yescharacteristic
262C2#1060157311yescharacteristic
263C2#1060158511yescharacteristic
264C2#1060159211yescharacteristic
265C2#1060160611yescharacteristic
266C2#1060162311yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1839C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1839D5
hypocenterC5#7622
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
242. C5#7622semidirect

Maximal subgroups

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

subgroupindex
C4×#40152
C5×#18392
#106001842
#105979692
#76225