Finite Group Databasebeta

← #12018985

Subgroups — #12018985

Order 1280.

416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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#10608335C211yesmaximal, characteristic
2C5×#1857C211yesmaximal, characteristic
3#10602451C212yesmaximal
4#10598190C212yesmaximal
5#10598135C211yesmaximal, characteristic
6C5×#519C2211yescharacteristic
7C5×#428—21no—
8C2×C5×#101C2211yescharacteristic
9C5×#391C2211yescharacteristic
10#65519C2212yes—
11C2×#3968C2212yes—
12#65284—22no—
13#65268—21no—
14#65218—21no—
15#64945—22no—
16#64935—22no—
17C5×#339—21no—
18#64752—22no—
19#13464—51nomaximal, Sylow
20C22×C5×Q8C2311yescharacteristic
21C22×Dic10—21no—
22C22×Dic10—21no—
23C2×C5×M16—21no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C5×#117—22no—
27C5×#117—21no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5D412yes—
32C2×#683—22no—
33C2×C4×Dic5D412yes—
34C2×#681—22no—
35C5×#107—41no—
36C5×#106—41no—
37C5×#101—21no—
38C5×#101Q812yescomplemented
39C5×#95—22no—
40#3968—22no—
41#3968Q814yescomplemented
42#3963—21no—
43#3963—22no—
44#3963—22no—
45#3963—22no—
46#3940—42no—
47#3939—42no—
48#2811—51no—
49#1857—52no—
50#1857D511yescharacteristic
51#1394—52no—
52#1394—51no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8C2×Q811yescharacteristic
56C2×C5×Q8C2×Q812yes—
57C2×C5×Q8#4111yescharacteristic
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5C2×D412yes—
61C22×C4×C5C2×D411yescharacteristic
62C22×Dic5—22no—
63C22×Dic5—22no—
64C2×Dic10—24no—
65C2×Dic10—81no—
66C2×Dic10—81no—
67C2×Dic10—82no—
68C2×Dic10—81no—
69C5×M16—22no—
70C5×M16—41no—
71C2×C5×C8—41no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4—22no—
74C5×C4⋊C4—21no—
75C5×C4⋊C4—21no—
76C5×C4⋊C4—41no—
77C5×C22⋊C4—41no—
78C42×C5—41no—
79C42×C5—42no—
80C42×C5—41no—
81C4⋊Dic5—42no—
82C4⋊Dic5—81no—
83#683—82no—
84C4×Dic5—42no—
85#681—24no—
86#681—42no—
87C2×#168—42no—
88#519C2×D511yescharacteristic
89#428—21no—
90#428—102no—
91C2×#101—52no—
92C2×#101C2×D511yescharacteristic
93#395—102no—
94#395—101no—
95#391—52no—
96#391—102no—
97#391—101no—
98#391C2×D511yescharacteristic
99#339—21no—
100#339—102no—
101C23×C5#12011yescharacteristic
102C5×Q8—41no—
103C5×Q8—42no—
104C5×Q8—41no—
105C2×C4×C5—22no—
106C2×C4×C5—21no—
107C2×C4×C5—22no—
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5C22⋊Q812yes—
117C2×C4×C5C22⋊Q811yescharacteristic
118C2×C4×C5C4⋊Q812yes—
119C2×C4×C5C4⋊Q811yescharacteristic
120C2×Dic5—24no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126Dic10—84no—
127Dic10—84no—
128C5×C8—42no—
129#168—44no—
130C22×Q8—101no—
131C22×Q8—101no—
132C22×Q8C22×D511yescharacteristic
133C2×M16—21no—
134C2×M16—102no—
135C4×Q8—41no—
136C4×Q8—41no—
137#117—22no—
138#117—21no—
139C2×C4⋊C4—52no—
140C2×C4⋊C4—102no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4C22⋊D511yescharacteristic
143C2×C42—52no—
144C2×C42C22⋊D511yescharacteristic
145#107—41no—
146#107—202no—
147#106—41no—
148#106—202no—
149#101—21no—
150#101—54no—
151#101—102no—
152#101Dic1012yescomplemented
153#95—22no—
154#95—102no—
155#95—101no—
156#95—102no—
157#95—102no—
158C22×C5—21no—
159C22×C5—21no—
160C22×C5#39511yescharacteristic
161C22×C5B(4,𝔽2)11yescharacteristic
162C22×C5#45811yescharacteristic
163C4×C5—22no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—21no—
167C4×C5—42no—
168C4×C5—81no—
169C4×C5—81no—
170C4×C5—81no—
171Dic5—44no—
172Dic5—82no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—104no—
176C2×Q8—401no—
177C2×Q8—401no—
178C2×Q8—402no—
179C2×Q8—401no—
180C2×Q8C2×Dic1011yescharacteristic
181C2×Q8#70911yescharacteristic
182C2×Q8Q8×D512yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—102no—
186C22×C4—102no—
187C22×C4D4×D512yes—
188C22×C4C2×C22⋊D511yescharacteristic
189M16—22no—
190M16—41no—
191M16—104no—
192M16—202no—
193C2×C8—41no—
194C2×C8—202no—
195C4⋊C4—21no—
196C4⋊C4—22no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—202no—
201C4⋊C4—402no—
202C4⋊C4—401no—
203C22⋊C4—41no—
204C42—41no—
205C42—41no—
206C42—42no—
207C42—202no—
208C2×C5—21no—
209C2×C5—21no—
210C2×C5#206211yescharacteristic
211C2×C5#220211yescharacteristic
212C2×C5#220511yescharacteristic
213C23#408311yescharacteristic
214Q8—41no—
215Q8—41no—
216Q8—42no—
217Q8—404no—
218Q8—404no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—104no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4#403412yes—
237C2×C4#404212yes—
238C2×C4#407011yescharacteristic
239C2×C4#409011yescharacteristic
240C8—42no—
241C8—204no—
242C5#1346411yescharacteristic, complemented, Sylow
243C22—21no—
244C22—21no—
245C22#6526811yescharacteristic
246C22#6532111yescharacteristic
247C22#6534211yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—21no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—81no—
256C4—204no—
257C4—402no—
258C2—21no—
259C2—21no—
260C2#1060038711yescharacteristic
261C2#1060178011yescharacteristic
262C2#1060178811yescharacteristic
subgroupG/H
centerC22#65321
commutator, cosocleC22×C5×Q8C23
FrattiniC22×Q8C22×D5
FittingC5×#1857C2
socleC22×C5B(4,𝔽2)
prime radicalC23×C5#120
hypercenter#1857D5
hypocenterC5#13464
LCSG ▷ C22×C5×Q8 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
38. C5×#101Q8semidirect
41. #3968Q8semidirect
152. #101Dic10semidirect
242. C5#13464semidirect

Maximal subgroups

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

subgroupindex
#106083352
C5×#18572
#106024512
#105981902
#105981352
#134645