Finite Group Databasebeta

← #11993655

Subgroups — #11993655

Order 1280.

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

normal subgroups only

This group has 500 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
1C5×#2379C211yesmaximal, characteristic
2#10602519C211yesmaximal, characteristic
3C2×#64760C211yesmaximal, characteristic
4#10600343C212yesmaximal, complemented
5#10598121C212yesmaximal, complemented
6C2×C5×#124C2211yescharacteristic
7C5×#391—21no—
8C5×#388—22no—
9C5×#386—21no—
10C5×#385—22no—
11C5×#382C2212yes—
12C2×#3967—21no—
13C2×#3964—21no—
14C2×#3940—22no—
15C2×#3939—22no—
16#65224C2211yescharacteristic
17C2×#3935C2211yescharacteristic
18C2×#3935C2212yes—
19#64760C414yescomplemented
20#8910—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×C5×D4D411yescharacteristic
23C23×C4×C5—21no—
24C5×#124—22no—
25C5×#124C2×C412yes—
26C5×#124Q812yes—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4D412yes—
29C2×C5×C4⋊C4D412yes—
30C2×C5×C22⋊C4—22no—
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4—21no—
33C2×C42×C5—21no—
34C2×C42×C5C2311yescharacteristic
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—22no—
37C22×#168—22no—
38C22×#168—21no—
39C5×#95—22no—
40C5×#95—22no—
41C5×#95—22no—
42#3967—42no—
43#3964—42no—
44#3940—44no—
45#3939—44no—
46#3935—22no—
47#3935—22no—
48#3935C2×C414yescomplemented
49#2379D511yescharacteristic
50#1959—51no—
51#1847—52no—
52C2×#329—51no—
53#1295—52no—
54C24×C5—21no—
55C2×C5×Q8—21no—
56C2×C5×Q8—41no—
57C2×C5×Q8—41no—
58C2×C5×Q8C4⋊C412yes—
59C2×C5×D4—21no—
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C2×C5×D4C4⋊C412yes—
63C22×C4×C5—21no—
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—82no—
67C22×C4×C5—81no—
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D412yes—
70C22×Dic5—41no—
71C5×C4⋊C4—42no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—81no—
74C5×C22⋊C4—24no—
75C5×C22⋊C4—24no—
76C5×C22⋊C4—82no—
77C5×C22⋊C4—81no—
78C42×C5—81no—
79C42×C5C22×C411yescharacteristic
80C42×C5C2×Q811yescharacteristic
81C42×C5#4112yes—
82C4⋊Dic5—42no—
83C4⋊Dic5—42no—
84C4⋊Dic5—41no—
85C4⋊Dic5—41no—
86C2×#168—24no—
87C2×#168—24no—
88C2×#168—24no—
89C2×#168—22no—
90C2×#168—41no—
91C2×#168—41no—
92C2×#124C2×D511yescharacteristic
93C2×#107—102no—
94C2×#106—102no—
95C2×#103—101no—
96C2×#102—101no—
97C2×#97—52no—
98C2×#97—51no—
99#391—21no—
100#388—22no—
101#386—21no—
102#385—22no—
103#384—51no—
104#382C2×D512yes—
105#329—54no—
106C23×C5—22no—
107C23×C5—42no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—42no—
111C23×C5#12011yescharacteristic
112C5×Q8—42no—
113C5×Q8—81no—
114C5×D4—42no—
115C5×D4—81no—
116C2×C4×C5—22no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—84no—
130C2×C4×C5C2×C4⋊C411yescharacteristic
131C2×C4×C5C4×D412yes—
132C2×C4×C5C22⋊Q812yes—
133C2×C4×C5#12311yescharacteristic
134C2×Dic5—81no—
135C2×Dic5—82no—
136#168—28no—
137#168—42no—
138C22×Q8C22⋊D511yescharacteristic
139C22×D4C22⋊D511yescharacteristic
140C23×C4—21no—
141C22×C8—102no—
142C22×C8—101no—
143#124—22no—
144#124Dic1012yes—
145#124C4×D512yes—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—101no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4C22⋊D512yes—
150C2×C4⋊C4C22⋊D512yes—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—21no—
154C2×C42—21no—
155C2×C42C22×D511yescharacteristic
156#107—204no—
157#106—204no—
158#103—202no—
159#102—202no—
160#97—54no—
161#97—102no—
162#97—102no—
163#95—22no—
164#95—22no—
165#95—22no—
166C22×C5—42no—
167C22×C5—44no—
168C22×C5—81no—
169C22×C5—81no—
170C22×C5—82no—
171C22×C5#38511yescharacteristic
172C22×C5#45311yescharacteristic
173C22×C5#45312yes—
174C22×C5#45511yescharacteristic
175C22×C5#45612yes—
176C4×C5—21no—
177C4×C5—21no—
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—42no—
181C4×C5—82no—
182C4×C5—82no—
183Dic5—161no—
184C24—21no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#68312yes—
189C2×D4—21no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4#68312yes—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—82no—
197C22×C4—81no—
198C22×C4—201no—
199C22×C4C2×C22⋊D511yescharacteristic
200C22×C4C2×C22⋊D512yes—
201C2×C8—104no—
202C2×C8—104no—
203C2×C8—104no—
204C2×C8—102no—
205C2×C8—201no—
206C2×C8—201no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—201no—
211C4⋊C4—201no—
212C4⋊C4—202no—
213C4⋊C4—202no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—82no—
217C22⋊C4—81no—
218C42—81no—
219C42C2×Dic1011yescharacteristic
220C42C2×C4×D511yescharacteristic
221C42#70912yes—
222C2×C5—82no—
223C2×C5#165511yescharacteristic
224C2×C5#166011yescharacteristic
225C2×C5#166112yes—
226C2×C5#185611yescharacteristic
227C2×C5#185912yes—
228C23—22no—
229C23—42no—
230C23—41no—
231C23—41no—
232C23—42no—
233C23#409911yescharacteristic
234Q8—42no—
235Q8—81no—
236D4—42no—
237D4—81no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—401no—
253C2×C4—402no—
254C2×C4C2×#68311yescharacteristic
255C2×C4#407012yes—
256C2×C4C4×C22⋊D512yes—
257C2×C4#407511yescharacteristic
258C8—108no—
259C8—202no—
260C5#891011yescharacteristic, complemented, Sylow
261C22—42no—
262C22—44no—
263C22—81no—
264C22—82no—
265C22—81no—
266C22#6549911yescharacteristic
267C22#6553011yescharacteristic
268C22#6553012yes—
269C22#6553111yescharacteristic
270C22#6553512yes—
271C4—21no—
272C4—21no—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—82no—
277C4—82no—
278C4—801no—
279C2—82no—
280C2#1060244011yescharacteristic
281C2#1060245712yes—
282C2#1060274111yescharacteristic
283C2#1060274612yes—
284C2#1060274911yescharacteristic
subgroupG/H
centerC23#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2379C2
socleC23×C5#120
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#2379D5
hypocenterC5#8910
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2379

Complements

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

NH ≅ G/Ntype
4. #10600343C2semidirect
5. #10598121C2semidirect
19. #64760C4semidirect
48. #3935C2×C4semidirect
260. C5#8910semidirect

Maximal subgroups

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

subgroupindex
C5×#23792
#106025192
C2×#647602
#106003432
#105981212
#89105