Finite Group Databasebeta

← #12008510

Subgroups — #12008510

Order 1280.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#10610801C211yesmaximal, characteristic
2#10599885C212yesmaximal, complemented
3C5×#1323C211yesmaximal, characteristic, complemented
4#10598209C211yesmaximal, characteristic, complemented
5#10598014C212yesmaximal
6#65856C411yescharacteristic
7C5×#424C2211yescharacteristic
8#65418C411yescharacteristic
9M16×Dic5C411yescharacteristic
10#65399C2211yescharacteristic
11C2×C8×Dic5C2211yescharacteristic
12#65288C411yescharacteristic
13#65129—22no—
14#65122—22no—
15C5×C22⋊C16C2212yes—
16C22⋊#672C2212yes—
17#64721—22no—
18C16×Dic5—22no—
19#11462—51nomaximal, Sylow
20C2×#709C2×C411yescharacteristic
21C2×C5×M16C2×C411yescharacteristic
22C22×C5×C8C2311yescharacteristic
23C5×#117C2×C411yescharacteristic
24C2×C4×Dic5C2×C411yescharacteristic
25C2×#681C2×C411yescharacteristic
26C22×#168C2×C411yescharacteristic
27#4039C812yes—
28#4033C812yes—
29#4027—22no—
30#4018—21no—
31C42×D5—21no—
32C2×C5×C16—22no—
33C5×C4⋊C8—22no—
34#3952—22no—
35#3952—22no—
36#3947—21no—
37C8×Dic5—21no—
38C8×Dic5D412yes—
39C8×Dic5D412yes—
40C2×#672—22no—
41C4⋊#168—22no—
42#2922—51no—
43#2162—52no—
44#1323—51no—
45#1323D511yescharacteristic, complemented
46#1315—52no—
47C22×C4×C5C22×C411yescharacteristic
48C2×C22⋊D5—21no—
49C22×Dic5M1612yes—
50#709—41no—
51#709—41no—
52C2×D20C2×C811yescharacteristic
53C2×C4×D5—21no—
54C2×C4×D5—22no—
55C2×Dic10C2×C811yescharacteristic
56C5×M16—41no—
57C2×C5×C8—21no—
58C2×C5×C8—41no—
59C2×C5×C8C2×D412yes—
60C5×C4⋊C4C2×C812yes—
61C5×C22⋊C4—21no—
62C42×C5—21no—
63#685—22no—
64#683—22no—
65C4×Dic5—22no—
66C4×Dic5C22⋊C411yescharacteristic
67C4×Dic5C22⋊C411yescharacteristic
68C4×Dic5C2×C812yes—
69#681—41no—
70C2×#168—21no—
71C2×#168—41no—
72C2×#168C22⋊C412yes—
73C5×C16—42no—
74#672—42no—
75C4×#41—51no—
76#433—102no—
77#431—102no—
78#424—51no—
79#424C2×D511yescharacteristic
80#408—51no—
81#408—51no—
82C4×M16—51no—
83C2×C4×C8—51no—
84C4⋊C16—102no—
85C22⋊C16—52no—
86C22⋊C16C2×D512yes—
87C4×C16—102no—
88C23×C5C2×M1611yescharacteristic
89C22×D5—21no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5—22no—
93C2×C4×C5C2×C22⋊C411yescharacteristic
94C2×C4×C5C22×C811yescharacteristic
95C22⋊D5—42no—
96C2×Dic5—24no—
97C2×Dic5—21no—
98C2×Dic5C22⋊C812yes—
99C2×Dic5C22⋊C812yes—
100D20—41no—
101C4×D5—41no—
102C4×D5—41no—
103C4×D5—44no—
104Dic10—41no—
105C5×C8—22no—
106C5×C8—41no—
107#168—22no—
108#168—41no—
109C2×#41—51no—
110C2×M16—51no—
111C2×M16C4×D511yescharacteristic
112C22×C8—51no—
113C22×C8C22×D511yescharacteristic
114C4×Q8—52no—
115C4×D4—52no—
116C4×D4—102no—
117#117—101no—
118#117C4×D511yescharacteristic
119C2×C42—51no—
120C2×C42—101no—
121C2×C16—22no—
122C2×C16—102no—
123C4⋊C8—22no—
124C4⋊C8—102no—
125C22⋊C8—102no—
126C22⋊C8—102no—
127#97—101no—
128C4×C8—52no—
129C4×C8—52no—
130C4×C8—101no—
131C22×C5—22no—
132C22×C5—21no—
133C22×C5C2×C22⋊C811yescharacteristic
134C2×D5—42no—
135C2×D5—41no—
136C4×C5—21no—
137C4×C5—42no—
138C4×C5#41011yescharacteristic
139C4×C5#41311yescharacteristic
140Dic5—22no—
141Dic5—41no—
142Dic5#35014yes—
143#41—201no—
144#41—201no—
145C2×Q8—51no—
146C2×D4—51no—
147C2×D4—101no—
148C22×C4—52no—
149C22×C4—102no—
150C22×C4—101no—
151C22×C4C2×C4×D511yescharacteristic
152M16—41no—
153M16—201no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—52no—
157C2×C8—101no—
158C2×C8—201no—
159C2×C8D4×D512yes—
160C4⋊C4—102no—
161C4⋊C4C8×D512yes—
162C22⋊C4—21no—
163C22⋊C4—102no—
164C42—21no—
165C42—51no—
166C42—51no—
167C42—52no—
168C42—102no—
169C16—42no—
170C16—202no—
171C2×C5—41no—
172C2×C5#145811yescharacteristic
173C2×C5C2×#35012yes—
174D5—81no—
175C23—101no—
176C23D5×M1611yescharacteristic
177Q8—201no—
178D4—201no—
179D4—202no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—52no—
184C2×C4—52no—
185C2×C4—104no—
186C2×C4—101no—
187C2×C4—204no—
188C2×C4—201no—
189C2×C4—201no—
190C2×C4D5×C22⋊C411yescharacteristic
191C2×C4C2×C8×D511yescharacteristic
192C8—22no—
193C8—41no—
194C8—102no—
195C8—201no—
196C5#1146211yescharacteristic, complemented, Sylow
197C22—21no—
198C22—22no—
199C22—201no—
200C22—202no—
201C22D5×C22⋊C811yescharacteristic
202C4—21no—
203C4—42no—
204C4—54no—
205C4—102no—
206C4—201no—
207C4#6502911yescharacteristic
208C4#6504011yescharacteristic
209C2—41no—
210C2—401no—
211C2#1059891711yescharacteristic
212C2D5×#35012yes—
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#1323C2
socleC22×C5C2×C22⋊C8
prime radicalC2×#709C2×C4
cosocleC22×C5×C8C23
hypercenter#1323D5
hypocenterC5#11462
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #10599885C2semidirect
3. C5×#1323C2semidirect
4. #10598209C2semidirect
45. #1323D5semidirect
196. C5#11462semidirect

Maximal subgroups

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

subgroupindex
#106108012
#105998852
C5×#13232
#105982092
#105980142
#114625