Finite Group Databasebeta

← #11987520

Subgroups — #11987520

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#10597968C214yesmaximal
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#7625—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—42no—
40C4×Dic10—42no—
41#3963—22no—
42#3963—22no—
43C4⋊#168—24no—
44#3935—42no—
45C4×C4⋊Q8—51no—
46#1839D511yescharacteristic
47#1767—51no—
48#1271—54no—
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×C4×C5C2×D411yescharacteristic
55C22×C4×C5C2×D411yescharacteristic
56C22×Dic5—22no—
57C22×Dic5—22no—
58C2×Dic10—24no—
59C2×Dic10—42no—
60C2×Dic10—42no—
61C2×C5×C8—42no—
62C2×C5×C8—42no—
63C2×C5×C8—42no—
64C42×C5—22no—
65C42×C5—22no—
66C42×C5—22no—
67C42×C5—22no—
68C42×C5—41no—
69C42×C5—41no—
70C42×C5D812yes—
71C42×C5SD1612yes—
72C4⋊Dic5—24no—
73C4⋊Dic5—22no—
74C4⋊Dic5—42no—
75C4⋊Dic5—42no—
76C4⋊Dic5—42no—
77C4⋊Dic5M1614yes—
78#683—42no—
79#683—42no—
80C4×Dic5—44no—
81C2×#168—24no—
82C2×#168—42no—
83C2×#168—42no—
84C2×C4⋊Q8—51no—
85C2×C4×Q8—101no—
86C2×C4⋊C8—101no—
87C2×#97—101no—
88#391—101no—
89#389—52no—
90#389—101no—
91#384—51no—
92C4×C4⋊C4—52no—
93C4×C4⋊C4—101no—
94C43C2×D511yescharacteristic
95#336—21no—
96#336—21no—
97#336—52no—
98#336C2×D512yes—
99C23×C5C2×C22⋊C411yescharacteristic
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—21no—
113C2×C4×C5—21no—
114C2×C4×C5#10112yes—
115C2×C4×C5#10212yes—
116C2×C4×C5#10212yes—
117C2×C4×C5#10412yes—
118C2×C4×C5C2×M1612yes—
119C2×C4×C5C2×D811yescharacteristic
120C2×C4×C5C2×SD1611yescharacteristic
121C2×C4×C5#13712yes—
122C2×Dic5—24no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128Dic10—48no—
129C5×C8—82no—
130#168—44no—
131C22×Q8—101no—
132C22×C8—22no—
133C22×C8—102no—
134C4⋊Q8—104no—
135C4×Q8—202no—
136C4×Q8—202no—
137C2×C4⋊C4—52no—
138C2×C4⋊C4—52no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—102no—
143C2×C42—102no—
144C2×C42C4×D511yescharacteristic
145C2×C42C4×D511yescharacteristic
146C2×C42D2011yescharacteristic
147C2×C42D2011yescharacteristic
148C2×C42C22⋊D511yescharacteristic
149C2×C42C22⋊D511yescharacteristic
150C2×C42C22×D511yescharacteristic
151C4⋊C8—104no—
152#97—202no—
153#95—102no—
154#95—102no—
155C22×C5#40711yescharacteristic
156C22×C5#41011yescharacteristic
157C22×C5C2×#10111yescharacteristic
158C22×C5C2×#10211yescharacteristic
159C22×C5#41911yescharacteristic
160C22×C5C2×#10411yescharacteristic
161C22×C5#42111yescharacteristic
162C4×C5—22no—
163C4×C5—22no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—21no—
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—22no—
170Dic5—44no—
171Dic5—82no—
172C2×Q8—104no—
173C2×Q8—202no—
174C2×Q8—202no—
175C22×C4—102no—
176C22×C4—102no—
177C22×C4#68511yescharacteristic
178C22×C4#68511yescharacteristic
179C22×C4#68511yescharacteristic
180C22×C4#68511yescharacteristic
181C22×C4C2×C4×D511yescharacteristic
182C22×C4C2×D2011yescharacteristic
183C22×C4C2×C22⋊D511yescharacteristic
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—104no—
188C2×C8—202no—
189C2×C8—202no—
190C4⋊C4—54no—
191C4⋊C4—104no—
192C4⋊C4—102no—
193C4⋊C4—202no—
194C4⋊C4—202no—
195C4⋊C4—202no—
196C4⋊C4—202no—
197C4⋊C4—202no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42—204no—
205C42#67712yes—
206C42D4012yes—
207C2×C5#146711yescharacteristic
208C2×C5#148611yescharacteristic
209C2×C5#149111yescharacteristic
210C2×C5#150211yescharacteristic
211C2×C5#151511yescharacteristic
212C2×C5#153111yescharacteristic
213C2×C5#154611yescharacteristic
214C23C2×#68511yescharacteristic
215Q8—208no—
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—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—104no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4#395312yes—
237C2×C4#395312yes—
238C2×C4#395612yes—
239C2×C4#395712yes—
240C2×C4C2×#67711yescharacteristic
241C2×C4C2×D4011yescharacteristic
242C2×C4D5×M1612yes—
243C2×C4#409712yes—
244C8—82no—
245C8—204no—
246C5#762511yescharacteristic, complemented, Sylow
247C22#6529311yescharacteristic
248C22#6529411yescharacteristic
249C22#6529511yescharacteristic
250C22C2×#395311yescharacteristic
251C22#6541511yescharacteristic
252C22C2×#395611yescharacteristic
253C22C2×#395711yescharacteristic
254C4—22no—
255C4—22no—
256C4—21no—
257C4—21no—
258C4—22no—
259C4—22no—
260C4—22no—
261C4—22no—
262C4—204no—
263C4—402no—
264C2#1060035911yescharacteristic
265C2#1060155511yescharacteristic
266C2#1060157111yescharacteristic
267C2#1060158211yescharacteristic
268C2#1060159511yescharacteristic
269C2#1060160611yescharacteristic
270C2#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#7625
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
246. C5#7625semidirect

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
#105979682
#76255