Finite Group Databasebeta

← #13015199

Subgroups — #13015199

Order 1280.

388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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#10606086C211yesmaximal, characteristic
2#10604189C211yesmaximal, characteristic
3#10604186C211yesmaximal, characteristic
4#10598714C214yesmaximal
5C2×#4036—21no—
6C2×#4004—21no—
7C5×#384C411yescharacteristic
8#65274—21no—
9#65274C412yes—
10#65266—21no—
11#65262—21no—
12#65262C2212yes—
13#65224C411yescharacteristic
14C42×Dic5C2211yescharacteristic
15#64918—21no—
16#64918—21no—
17#64918—21no—
18#64918C2212yes—
19#64918C2212yes—
20#7723—51nomaximal, Sylow
21C22×#170—22no—
22C22×#170—22no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4C2×C412yes—
26C2×C42×C5C2×C411yescharacteristic
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5—22no—
30C2×C4⋊Dic5C2×C412yes—
31C2×#683—22no—
32C2×C4×Dic5C2×C411yescharacteristic
33C2×C4×Dic5D411yescharacteristic
34C2×C4×Dic5D411yescharacteristic
35C2×C4×Dic5D411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5C2311yescharacteristic
38#4036—42no—
39#4036—42no—
40#4004—42no—
41#3963—22no—
42#3963—22no—
43#2859—51no—
44#1839—51no—
45#1831—51no—
46#1271—54no—
47C22×C4×C5—22no—
48C22×C4×C5C22⋊C411yescharacteristic
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C22×C411yescharacteristic
51C22×Dic5—22no—
52C22×Dic5C22⋊C411yescharacteristic
53C22×Dic5C22⋊C411yescharacteristic
54C22×Dic5C2×D411yescharacteristic
55C22×Dic5C2×D411yescharacteristic
56C2×#170—42no—
57C2×#170—42no—
58C2×#170—42no—
59C2×#170—42no—
60C2×#170—42no—
61C2×#170—42no—
62C5×C4⋊C4—42no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4—42no—
65C42×C5—22no—
66C4⋊Dic5—24no—
67C4⋊Dic5—42no—
68C4⋊Dic5—42no—
69C4⋊Dic5—44no—
70#683—42no—
71#683—42no—
72C4×Dic5—22no—
73C4×Dic5—22no—
74C4×Dic5—41no—
75C4×Dic5—41no—
76C4×Dic5—41no—
77C4×Dic5D812yes—
78C4×Dic5SD1612yes—
79C2×#125—101no—
80C2×C4⋊C8—101no—
81#389—52no—
82#389—52no—
83#389—101no—
84#389—101no—
85#384—51no—
86#384AGL(1,𝔽5)11yescharacteristic
87#382—101no—
88C43—51no—
89#336—52no—
90#336—52no—
91#336—101no—
92#336—101no—
93#336—101no—
94C23×C5C2×C22⋊C411yescharacteristic
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5#10112yes—
105C2×C4×C5#10212yes—
106C2×C4×C5#13112yes—
107C2×Dic5—21no—
108C2×Dic5—21no—
109C2×Dic5—21no—
110C2×Dic5—21no—
111C2×Dic5—21no—
112C2×Dic5—21no—
113C2×Dic5—21no—
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—42no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5#10212yes—
120C2×Dic5C2×D811yescharacteristic
121C2×Dic5C2×SD1611yescharacteristic
122C2×Dic5#13712yes—
123#170—82no—
124#170—82no—
125C22×C8—102no—
126C22×C8—102no—
127#125—202no—
128#125—202no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—52no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4—101no—
136C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
137C2×C42—51no—
138C2×C42—51no—
139C2×C42—51no—
140C2×C42—51no—
141C2×C42—51no—
142C2×C42—51no—
143C2×C42C2×AGL(1,𝔽5)11yescharacteristic
144C4⋊C8—202no—
145#95—102no—
146#95—102no—
147C22×C5#40811yescharacteristic
148C22×C5#41011yescharacteristic
149C22×C5C2×#10111yescharacteristic
150C22×C5C2×#10211yescharacteristic
151C22×C5#41911yescharacteristic
152C22×C5#42111yescharacteristic
153C22×C5#42111yescharacteristic
154C4×C5—22no—
155C4×C5—22no—
156C4×C5—22no—
157C4×C5—82no—
158Dic5—22no—
159Dic5—22no—
160Dic5—21no—
161Dic5—21no—
162Dic5—41no—
163Dic5—82no—
164C22×C4—22no—
165C22×C4—51no—
166C22×C4—51no—
167C22×C4—51no—
168C22×C4—51no—
169C22×C4—102no—
170C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
171C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
172C22×C4C22×AGL(1,𝔽5)11yescharacteristic
173C2×C8—202no—
174C2×C8—202no—
175C2×C8—202no—
176C2×C8—202no—
177C2×C8—202no—
178C2×C8—202no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—104no—
183C4⋊C4—202no—
184C4⋊C4—202no—
185C4⋊C4—202no—
186C4⋊C4—204no—
187C4⋊C4—202no—
188C42—22no—
189C42—52no—
190C42—52no—
191C42—102no—
192C42—102no—
193C42—201no—
194C42—201no—
195C42—201no—
196C2×C5#147011yescharacteristic
197C2×C5#148011yescharacteristic
198C2×C5#149711yescharacteristic
199C2×C5#151511yescharacteristic
200C2×C5#151711yescharacteristic
201C2×C5#153411yescharacteristic
202C2×C5#154611yescharacteristic
203C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—51no—
214C2×C4—52no—
215C2×C4—51no—
216C2×C4—52no—
217C2×C4—101no—
218C2×C4—101no—
219C2×C4—101no—
220C2×C4—101no—
221C2×C4—101no—
222C2×C4—101no—
223C2×C4—101no—
224C2×C4—101no—
225C2×C4—101no—
226C2×C4—202no—
227C2×C4—202no—
228C2×C4—202no—
229C2×C4#400512yes—
230C2×C4#400712yes—
231C2×C4#413312yes—
232C8—402no—
233C8—402no—
234C5#772311yescharacteristic, complemented, Sylow
235C22C2×#400511yescharacteristic
236C22C2×#400711yescharacteristic
237C22#6576911yescharacteristic
238C22#6577111yescharacteristic
239C22#6578211yescharacteristic
240C22#6578411yescharacteristic
241C22#6578711yescharacteristic
242C4—22no—
243C4—22no—
244C4—22no—
245C4—82no—
246C4—101no—
247C4—101no—
248C4—102no—
249C4—102no—
250C4—201no—
251C4—402no—
252C2#1060426711yescharacteristic
253C2#1060427711yescharacteristic
254C2#1060429911yescharacteristic
255C2#1060459611yescharacteristic
256C2#1060462911yescharacteristic
257C2#1060464411yescharacteristic
258C2#1060465511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#384C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#384AGL(1,𝔽5)
hypocenterC5#7723
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
234. C5#7723semidirect

Maximal subgroups

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

subgroupindex
#106060862
#106041892
#106041862
#105987142
#77235