Finite Group Databasebeta

← #13018309

Subgroups — #13018309

Order 1280.

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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#10604697C212yesmaximal
3#10604194C212yesmaximal
4#10598772C212yesmaximal
5C2×C4×Dic10C2211yescharacteristic
6C2×#4005—22no—
7#65758C2214yes—
8C2×C5×C4⋊C8C411yescharacteristic
9C2×#3946C411yescharacteristic
10C2×#3946C2211yescharacteristic
11C2×C8×Dic5C411yescharacteristic
12C2×C8×Dic5C2211yescharacteristic
13C2×C4×#168C411yescharacteristic
14#65119—22no—
15#65119—22no—
16#64919—22no—
17#64884—22no—
18#64882—22no—
19#8617—51nomaximal, Sylow
20C22×Dic10D411yescharacteristic
21C2×#704—24no—
22C22×C5×C8C2×C411yescharacteristic
23C22×C5×C8C2×C411yescharacteristic
24C2×C42×C5C2×C411yescharacteristic
25C2×C4⋊Dic5Q811yescharacteristic
26C2×#683D411yescharacteristic
27C2×#683Q811yescharacteristic
28C2×C4×Dic5C2×C411yescharacteristic
29C2×C4×Dic5C2311yescharacteristic
30C22×#168C2×C411yescharacteristic
31C22×#168C2×C411yescharacteristic
32C4×Dic10—22no—
33C4×Dic10—22no—
34#4005—44no—
35#4004—24no—
36C4⋊#170—24no—
37C5×C4⋊C8—22no—
38#3946—22no—
39#3946—22no—
40C8×Dic5—21no—
41C8×Dic5—21no—
42C8×Dic5D412yes—
43C8×Dic5D412yes—
44C4×#168—21no—
45C4×#168—21no—
46C2×C8×Q8—51no—
47#1801—52no—
48#1567—52no—
49#1292—52no—
50C22×C4×C5C4⋊C411yescharacteristic
51C22×C4×C5C4⋊C411yescharacteristic
52C22×C4×C5C22×C411yescharacteristic
53C22×Dic5C4⋊C411yescharacteristic
54C22×Dic5C4⋊C411yescharacteristic
55C22×Dic5C2×D411yescharacteristic
56C22×Dic5C2×Q811yescharacteristic
57C2×Dic10—22no—
58C2×Dic10—22no—
59C2×Dic10D812yes—
60C2×Dic10Q1612yes—
61#704—44no—
62#704—44no—
63C2×#170—44no—
64C2×C5×C8—21no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C2×C5×C8C22⋊C412yes—
68C42×C5—21no—
69C42×C5—21no—
70C4⋊Dic5—22no—
71#683—22no—
72#683—22no—
73C4×Dic5—21no—
74C4×Dic5—21no—
75C4×Dic5C2×D412yes—
76C4×Dic5#4112yes—
77C2×#168—22no—
78C2×#168—21no—
79C2×#168—41no—
80C2×#168C22⋊C411yescharacteristic
81C2×#168C22⋊C411yescharacteristic
82C2×C4×Q8—51no—
83C8×Q8—102no—
84C8×Q8—102no—
85#423—54no—
86C2×C4⋊C8—51no—
87C2×C4⋊C8—51no—
88C2×C4⋊C8AGL(1,𝔽5)11yescharacteristic
89C2×#101—102no—
90C2×C4×C8—51no—
91C2×C4×C8—51no—
92C2×C4×C8—51no—
93#343—102no—
94#335—102no—
95#335—102no—
96C23×C5C2×C4⋊C411yescharacteristic
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—41no—
103C2×C4×C5#10712yes—
104C2×C4×C5C2×C22⋊C411yescharacteristic
105C2×C4×C5#11711yescharacteristic
106C2×Dic5—21no—
107C2×Dic5—21no—
108C2×Dic5—21no—
109C2×Dic5—41no—
110C2×Dic5—41no—
111C2×Dic5#10712yes—
112C2×Dic5#12112yes—
113C2×Dic5C22⋊Q812yes—
114C2×Dic5C2×D811yescharacteristic
115C2×Dic5C2×Q1611yescharacteristic
116C2×Dic5#13512yes—
117Dic10—24no—
118Dic10—24no—
119#170—84no—
120C5×C8—22no—
121C5×C8—41no—
122#168—21no—
123#168—41no—
124#168#10112yescomplemented
125C22×Q8—51no—
126C2×M16—104no—
127C22×C8—51no—
128C22×C8—51no—
129C22×C8C2×AGL(1,𝔽5)11yescharacteristic
130C22×C8C2×AGL(1,𝔽5)11yescharacteristic
131C4×Q8—102no—
132C4×Q8—102no—
133C2×C4⋊C4—51no—
134C2×C4⋊C4—51no—
135C2×C4⋊C4—51no—
136C2×C42—51no—
137C2×C42—51no—
138C2×C42C2×AGL(1,𝔽5)11yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—102no—
141C4⋊C8—104no—
142C4⋊C8—104no—
143C4⋊C8—102no—
144#101—204no—
145C4×C8—52no—
146C4×C8—52no—
147C4×C8—101no—
148C4×C8—101no—
149C4×C8—101no—
150C4×C8—101no—
151C22×C5—21no—
152C22×C5—21no—
153C22×C5#38011yescharacteristic
154C22×C5C2×#10711yescharacteristic
155C22×C5#42711yescharacteristic
156C4×C5—21no—
157C4×C5—22no—
158C4×C5—41no—
159C4×C5C2×#10111yescharacteristic
160C4×C5#41311yescharacteristic
161Dic5—22no—
162Dic5—22no—
163Dic5—41no—
164Dic5#46612yes—
165Dic5#46712yes—
166C2×Q8—52no—
167C2×Q8—52no—
168C2×Q8—102no—
169C2×Q8—102no—
170C22×C4—51no—
171C22×C4—51no—
172C22×C4—51no—
173C22×C4—51no—
174C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
175C22×C4C4⋊AGL(1,𝔽5)11yescharacteristic
176C22×C4C22×AGL(1,𝔽5)11yescharacteristic
177M16—204no—
178M16—204no—
179C2×C8—21no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—51no—
183C2×C8—51no—
184C2×C8—102no—
185C2×C8—101no—
186C2×C8—201no—
187C2×C8—204no—
188C2×C8C22⋊AGL(1,𝔽5)12yes—
189C4⋊C4—102no—
190C4⋊C4—102no—
191C4⋊C4—102no—
192C42—21no—
193C42—21no—
194C42—52no—
195C42—52no—
196C42—101no—
197C42—101no—
198C2×C5—21no—
199C2×C5—21no—
200C2×C5#180111yescharacteristic
201C2×C5#180811yescharacteristic
202C2×C5#181311yescharacteristic
203C23C2×C4⋊AGL(1,𝔽5)11yescharacteristic
204Q8—104no—
205Q8—104no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—51no—
213C2×C4—51no—
214C2×C4—52no—
215C2×C4—52no—
216C2×C4—52no—
217C2×C4—52no—
218C2×C4—101no—
219C2×C4—101no—
220C2×C4—101no—
221C2×C4—201no—
222C2×C4—201no—
223C2×C4#399412yes—
224C2×C4#413011yescharacteristic
225C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
226C8—22no—
227C8—41no—
228C8—52no—
229C8—101no—
230C8—201no—
231C8—404no—
232C5#861711yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22C2×#399411yescharacteristic
236C22#6572111yescharacteristic
237C22#6576511yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—52no—
242C4—52no—
243C4—102no—
244C4—102no—
245C4—201no—
246C4#6577711yescharacteristic
247C4D5⋊#10111yescharacteristic
248C2—21no—
249C2—21no—
250C2#1060433611yescharacteristic
251C2#1060472311yescharacteristic
252C2#1060477311yescharacteristic
subgroupG/H
centerC22#65765
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC22×C5#380
prime radicalC23×C5C2×C4⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#8617
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
124. #168#101semidirect
232. C5#8617semidirect

Maximal subgroups

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

subgroupindex
C2×#651192
#106046972
#106041942
#105987722
#86175