Finite Group Databasebeta

← #12008534

Subgroups — #12008534

Order 1280.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#10610386C211yesmaximal, characteristic
2D5×C22⋊C16C212yesmaximal, complemented
3C5×#1315C211yesmaximal, characteristic, complemented
4#10598180C211yesmaximal, characteristic, complemented
5#10598016C212yesmaximal, complemented
6#66162C411yescharacteristic
7C2×#4094C411yescharacteristic
8C22×C8×D5C2211yescharacteristic
9C5×#408C2211yescharacteristic
10#65415C411yescharacteristic
11#65411C411yescharacteristic
12#65391C2211yescharacteristic
13C2×D5×C16—22no—
14#65017—22no—
15#65014—22no—
16C5×C22⋊C16C2212yes—
17C22⋊#672C2212yes—
18#64727—22no—
19#11468—51nomaximal, Sylow
20C2×C5×#41C2×C411yescharacteristic
21C22×C4×D5C2×C411yescharacteristic
22C2×C5×M16C2×C411yescharacteristic
23C22×C5×C8C2311yescharacteristic
24#4094—42no—
25#4092C812yes—
26#4084C812yes—
27#4083—21no—
28#4081—21no—
29C4×C22⋊D5—22no—
30#4072C2×C411yescharacteristic
31C2×#681—21no—
32C2×#681C2×C411yescharacteristic
33C22×#168—21no—
34C22×#168C2×C411yescharacteristic
35C2×C8×D5—42no—
36C2×C8×D5D412yes—
37C2×C8×D5D412yes—
38C2×C5×C16—22no—
39C5×C22⋊C8—22no—
40#3952—22no—
41#3947—21no—
42#3946—22no—
43C8×Dic5—21no—
44C2×#672—22no—
45D5×C16—44no—
46#2929—51no—
47C2×C22⋊C16—52no—
48#1323—52no—
49#1315—51no—
50#1315D511yescharacteristic, complemented
51C23×D5M1611yescharacteristic
52C5×#41—41no—
53C5×#41—41no—
54C2×C5×Q8C2×C811yescharacteristic
55C2×C5×D4—21no—
56C2×C5×D4C2×C811yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5C22×C411yescharacteristic
59C2×C22⋊D5—22no—
60C22×Dic5M1611yescharacteristic
61C2×C4×D5—41no—
62C2×C4×D5—41no—
63C2×C4×D5C22⋊C412yes—
64C2×C4×D5C2×C812yes—
65C5×M16—41no—
66C2×C5×C8—21no—
67C2×C5×C8—41no—
68C2×C5×C8C2×D412yes—
69C22⋊Dic5—21no—
70C22⋊Dic5—22no—
71#685—22no—
72C4⋊Dic5C2×C812yes—
73#683—22no—
74C4×Dic5—21no—
75#681—42no—
76#681—41no—
77C2×#168—22no—
78C2×#168—21no—
79C2×#168—42no—
80C2×#168C22⋊C411yescharacteristic
81C2×#168C22⋊C411yescharacteristic
82C8×D5—24no—
83C8×D5—42no—
84C5×C16—42no—
85#672—42no—
86C2×#131—51no—
87C23×C8—51no—
88#525—51no—
89C22×C16—102no—
90#435—102no—
91C8×D4—102no—
92#424—51no—
93#408C2×D511yescharacteristic
94#407—51no—
95#405—51no—
96C22⋊C16—52no—
97C22⋊C16—102no—
98C22⋊C16C2×D512yes—
99C23×C5—21no—
100C23×C5C2×M1611yescharacteristic
101C22×D5—24no—
102C22×D5—41no—
103C22×D5C22⋊C812yes—
104C5×Q8—41no—
105C5×D4—41no—
106C5×D4—42no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5C2×C22⋊C411yescharacteristic
113C2×C4×C5C22×C811yescharacteristic
114C22⋊D5—44no—
115C2×Dic5—22no—
116C2×Dic5—41no—
117C2×Dic5C22⋊C812yes—
118C4×D5—22no—
119C4×D5—22no—
120C4×D5—42no—
121C5×C8—22no—
122C5×C8—41no—
123#168—21no—
124#168—41no—
125#168#9912yes—
126C2×#41C4×D511yescharacteristic
127C23×C4—51no—
128#131—202no—
129C2×M16—51no—
130C2×M16—101no—
131C2×M16C4×D511yescharacteristic
132C22×C8—51no—
133C22×C8—52no—
134C22×C8—52no—
135C22×C8—101no—
136C22×C8—202no—
137C22×C8C22×D511yescharacteristic
138#123—101no—
139C22⋊Q8—52no—
140#121—52no—
141#120—101no—
142C4×D4—102no—
143#117—51no—
144C2×C16—22no—
145C2×C16—102no—
146C2×C16—204no—
147C4⋊C8—102no—
148C22⋊C8—22no—
149C22⋊C8—102no—
150#97—101no—
151C4×C8—101no—
152C22×C5—22no—
153C22×C5—21no—
154C22×C5—42no—
155C22×C5—41no—
156C22×C5C2×C22⋊C811yescharacteristic
157C2×D5—22no—
158C2×D5—22no—
159C2×D5—44no—
160C2×D5#35014yes—
161C4×C5—21no—
162C4×C5—41no—
163C4×C5C2×#9911yescharacteristic
164C4×C5#41311yescharacteristic
165Dic5—22no—
166Dic5—42no—
167C24—51no—
168#41—41no—
169#41—41no—
170C2×Q8C8×D511yescharacteristic
171C2×D4—21no—
172C2×D4—102no—
173C2×D4C8×D511yescharacteristic
174C22×C4—21no—
175C22×C4—51no—
176C22×C4—52no—
177C22×C4—52no—
178C22×C4—201no—
179C22×C4—201no—
180C22×C4C2×C4×D511yescharacteristic
181M16—41no—
182M16—202no—
183M16—201no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—51no—
187C2×C8—51no—
188C2×C8—104no—
189C2×C8—102no—
190C2×C8—101no—
191C2×C8—202no—
192C2×C8—202no—
193C2×C8D4×D512yes—
194C4⋊C4—52no—
195C4⋊C4—102no—
196C22⋊C4—102no—
197C22⋊C4—102no—
198C22⋊C4—101no—
199C42—101no—
200C16—42no—
201C16—202no—
202C2×C5—41no—
203C2×C5—81no—
204C2×C5#145911yescharacteristic
205C2×C5C2×#35012yes—
206D5—24no—
207C23—21no—
208C23—52no—
209C23—104no—
210C23—201no—
211C23D5×M1611yescharacteristic
212Q8—41no—
213D4—41no—
214D4—42no—
215D4—204no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—52no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—102no—
225C2×C4—202no—
226C2×C4—201no—
227C2×C4D5×C22⋊C411yescharacteristic
228C2×C4C2×C8×D511yescharacteristic
229C8—22no—
230C8—41no—
231C8—52no—
232C8—101no—
233C8—201no—
234C5#1146811yescharacteristic, complemented, Sylow
235C22—21no—
236C22—22no—
237C22—41no—
238C22—42no—
239C22—54no—
240C22—102no—
241C22—102no—
242C22—204no—
243C22D5×C22⋊C811yescharacteristic
244C4—21no—
245C4—41no—
246C4—102no—
247C4—202no—
248C4D5×#9911yescharacteristic
249C4#6503411yescharacteristic
250C2—41no—
251C2—81no—
252C2—104no—
253C2#1059891211yescharacteristic
254C2D5×#35012yes—
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1315C2
socleC22×C5C2×C22⋊C8
prime radical#66162C4
cosocleC22×C5×C8C23
hypercenter#1315D5
hypocenterC5#11468
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. D5×C22⋊C16C2semidirect
3. C5×#1315C2semidirect
4. #10598180C2semidirect
5. #10598016C2semidirect
50. #1315D5semidirect
234. C5#11468semidirect

Maximal subgroups

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

subgroupindex
#106103862
D5×C22⋊C162
C5×#13152
#105981802
#105980162
#114685