Finite Group Databasebeta

← #12008635

Subgroups — #12008635

Order 1280.

342 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#65119C211yesmaximal, characteristic
2#10599885C212yesmaximal
3C5×#1322C211yesmaximal, characteristic
4#10598200C211yesmaximal, characteristic
5#10598015C212yesmaximal
6C2×C4×Dic10C411yescharacteristic
7C2×C5×C4⋊C8C2211yescharacteristic
8C2×#3946C411yescharacteristic
9C2×#3946C2211yescharacteristic
10C2×C8×Dic5C411yescharacteristic
11C2×C8×Dic5C2211yescharacteristic
12C2×C4×#168C411yescharacteristic
13#65119—22no—
14#65119—22no—
15C5×C22⋊C16C2212yes—
16C22⋊#672C2212yes—
17#64721—22no—
18C16×Dic5—22no—
19#11493—51nomaximal, Sylow
20C22×Dic10C811yescharacteristic
21C22×C5×C8C2×C411yescharacteristic
22C22×C5×C8C2311yescharacteristic
23C2×C42×C5C2×C411yescharacteristic
24C2×C4⋊Dic5C811yescharacteristic
25C2×#683C811yescharacteristic
26C2×#683C811yescharacteristic
27C2×C4×Dic5C2×C411yescharacteristic
28C2×C4×Dic5C2×C411yescharacteristic
29C22×#168C2×C411yescharacteristic
30C22×#168C2×C411yescharacteristic
31C4×Dic10—22no—
32C4×Dic10—22no—
33C2×C5×C16—22no—
34C5×C4⋊C8—22no—
35#3946—22no—
36#3946—22no—
37C8×Dic5—21no—
38C8×Dic5—21no—
39C8×Dic5D412yes—
40C8×Dic5D412yes—
41C2×#672—22no—
42C4×#168—21no—
43C4×#168—21no—
44C2×C8×Q8—51no—
45#2162—52no—
46#1322—51no—
47#1322—52no—
48#1322D511yescharacteristic
49C22×C4×C5C2×C811yescharacteristic
50C22×C4×C5C2×C811yescharacteristic
51C22×C4×C5C22×C411yescharacteristic
52C22×Dic5C2×C811yescharacteristic
53C22×Dic5C2×C811yescharacteristic
54C22×Dic5C2×C811yescharacteristic
55C22×Dic5C2×C811yescharacteristic
56C2×Dic10—22no—
57C2×Dic10—22no—
58C2×Dic10C1614yescomplemented
59C2×C5×C8—21no—
60C2×C5×C8—41no—
61C2×C5×C8—41no—
62C2×C5×C8C2×D412yes—
63C42×C5—21no—
64C42×C5—21no—
65C4⋊Dic5—22no—
66#683—22no—
67#683—22no—
68C4×Dic5—21no—
69C4×Dic5—21no—
70C4×Dic5C22⋊C412yes—
71C4×Dic5M1612yes—
72C2×#168—22no—
73C2×#168—21no—
74C2×#168—41no—
75C2×#168C22⋊C411yescharacteristic
76C2×#168C22⋊C411yescharacteristic
77C5×C16—42no—
78#672—42no—
79C2×C4×Q8—51no—
80C8×Q8—102no—
81C8×Q8—102no—
82C2×C4⋊C8—51no—
83C2×C4⋊C8—51no—
84C2×C4⋊C8C2×D511yescharacteristic
85C2×C4×C8—51no—
86C2×C4×C8—51no—
87C2×C4×C8—51no—
88C4⋊C16—102no—
89C22⋊C16—52no—
90C22⋊C16C2×D512yes—
91C4×C16—102no—
92C23×C5C22×C811yescharacteristic
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—41no—
99C2×C4×C5C2×C1612yes—
100C2×C4×C5C2×C22⋊C411yescharacteristic
101C2×C4×C5C2×M1611yescharacteristic
102C2×Dic5—21no—
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—41no—
106C2×Dic5—41no—
107C2×Dic5C22⋊C812yes—
108C2×Dic5C22⋊C812yes—
109C2×Dic5C2×C1612yes—
110C2×Dic5C2×C1612yes—
111C2×Dic5M3212yes—
112Dic10—28no—
113C5×C8—22no—
114C5×C8—41no—
115#168—21no—
116#168—41no—
117#168#10112yes—
118C22×Q8—51no—
119C22×C8—51no—
120C22×C8—51no—
121C22×C8C4×D511yescharacteristic
122C22×C8C22×D511yescharacteristic
123C4×Q8—102no—
124C4×Q8—102no—
125C2×C4⋊C4—51no—
126C2×C4⋊C4—51no—
127C2×C4⋊C4—51no—
128C2×C42—51no—
129C2×C42—51no—
130C2×C42C4×D511yescharacteristic
131C2×C16—22no—
132C2×C16—102no—
133C4⋊C8—22no—
134C4⋊C8—102no—
135C4⋊C8—102no—
136C4×C8—52no—
137C4×C8—52no—
138C4×C8—101no—
139C4×C8—101no—
140C4×C8—101no—
141C4×C8—101no—
142C22×C5—21no—
143C22×C5—21no—
144C22×C5C2×C22⋊C811yescharacteristic
145C22×C5C22×C1611yescharacteristic
146C22×C5C2×M3211yescharacteristic
147C4×C5—22no—
148C4×C5—21no—
149C4×C5—41no—
150C4×C5#41011yescharacteristic
151C4×C5C2×#10111yescharacteristic
152Dic5—22no—
153Dic5—22no—
154Dic5—41no—
155Dic5C22⋊C1614yes—
156C2×Q8—54no—
157C2×Q8—102no—
158C2×Q8—102no—
159C22×C4—51no—
160C22×C4—51no—
161C22×C4—51no—
162C22×C4—51no—
163C22×C4C8×D511yescharacteristic
164C22×C4C8×D511yescharacteristic
165C22×C4C2×C4×D511yescharacteristic
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—51no—
170C2×C8—51no—
171C2×C8—102no—
172C2×C8—101no—
173C2×C8—201no—
174C2×C8D4×D512yes—
175C4⋊C4—102no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C42—21no—
179C42—21no—
180C42—52no—
181C42—52no—
182C42—101no—
183C42—101no—
184C16—42no—
185C16—202no—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#146111yescharacteristic
189C2×C5C2×C22⋊C1611yescharacteristic
190C2×C5#211511yescharacteristic
191C23C2×C8×D511yescharacteristic
192Q8—108no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—52no—
200C2×C4—52no—
201C2×C4—52no—
202C2×C4—52no—
203C2×C4—52no—
204C2×C4—101no—
205C2×C4—101no—
206C2×C4—101no—
207C2×C4—201no—
208C2×C4—201no—
209C2×C4D5×C1612yes—
210C2×C4D5×C22⋊C411yescharacteristic
211C2×C4D5×M1611yescharacteristic
212C8—22no—
213C8—41no—
214C8—52no—
215C8—101no—
216C8—201no—
217C5#1149311yescharacteristic, complemented, Sylow
218C22—21no—
219C22—21no—
220C22D5×C22⋊C811yescharacteristic
221C22C2×D5×C1611yescharacteristic
222C22D5×M3211yescharacteristic
223C4—21no—
224C4—22no—
225C4—41no—
226C4—54no—
227C4—102no—
228C4—102no—
229C4—201no—
230C4#6502911yescharacteristic
231C4D5×#10111yescharacteristic
232C2—21no—
233C2—21no—
234C2#1059891811yescharacteristic
235C2D5×C22⋊C1611yescharacteristic
236C2#1059991211yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC22×C5C22×C16
FrattiniC22×C8C22×D5
FittingC5×#1322C2
socleC22×C5C2×C22⋊C8
prime radicalC23×C5C22×C8
cosocleC22×C5×C8C23
hypercenter#1322D5
hypocenterC5#11493
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
58. C2×Dic10C16semidirect
217. C5#11493semidirect

Maximal subgroups

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

subgroupindex
C2×#651192
#105998852
C5×#13222
#105982002
#105980152
#114935