Finite Group Databasebeta

← #13014944

Subgroups — #13014944

Order 1280.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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#10606051C211yesmaximal, characteristic
2#10604186C211yesmaximal, characteristic
3#10604186C211yesmaximal, characteristic
4#10598714C214yesmaximal
5C2×#4033—21no—
6C2×#4015C411yescharacteristic
7C2×#4004—21no—
8C2×#4004—21no—
9C5×#384C411yescharacteristic
10C4⋊C4×Dic5—21no—
11C4⋊C4×Dic5C412yes—
12#65263—21no—
13#65262—21no—
14#65262C2212yes—
15C42×Dic5C2211yescharacteristic
16#64918—21no—
17#64918—21no—
18#64918C2212yes—
19#64918C2212yes—
20#7652—51nomaximal, Sylow
21C22×Dic10—21no—
22C22×#170—22no—
23C22×#170—22no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C42×C5C2×C411yescharacteristic
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5C2×C412yes—
30C2×#683—22no—
31C2×C4×Dic5—22no—
32C2×C4×Dic5C2×C411yescharacteristic
33C2×C4×Dic5D411yescharacteristic
34C2×C4×Dic5D411yescharacteristic
35C2×C4×Dic5D411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5C2311yescharacteristic
38#4033—42no—
39#4033—42no—
40#4015—24no—
41#4004—42no—
42#4004—42no—
43#3963—22no—
44#3963—22no—
45C4×C4⋊Q8—51no—
46#1831—51no—
47#1831—51no—
48#1271—54no—
49C22×C4×C5—22no—
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22×C411yescharacteristic
53C22×Dic5—22no—
54C22×Dic5C22⋊C411yescharacteristic
55C22×Dic5C22⋊C411yescharacteristic
56C22×Dic5C2×D411yescharacteristic
57C22×Dic5C2×D411yescharacteristic
58C2×Dic10—24no—
59C2×Dic10—42no—
60C2×Dic10—42no—
61C2×#170—42no—
62C2×#170—42no—
63C2×#170—42no—
64C2×#170—42no—
65C2×#170—42no—
66C2×#170—42no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C42×C5—22no—
71C4⋊Dic5—24no—
72C4⋊Dic5—22no—
73C4⋊Dic5M1614yes—
74#683—42no—
75#683—42no—
76C4×Dic5—22no—
77C4×Dic5—41no—
78C4×Dic5—41no—
79C4×Dic5—41no—
80C4×Dic5—44no—
81C4×Dic5D812yes—
82C4×Dic5SD1612yes—
83C4×Dic5SD1612yes—
84C4×Dic5Q1612yes—
85C2×C4⋊Q8—51no—
86C2×C4×Q8—101no—
87C2×C4⋊C8—101no—
88C2×C4⋊C8—101no—
89#391—101no—
90#389—52no—
91#389—101no—
92#384AGL(1,𝔽5)11yescharacteristic
93C4×C4⋊C4—52no—
94C4×C4⋊C4—101no—
95C43—51no—
96#336—52no—
97#336—52no—
98#336—101no—
99#336—101no—
100C23×C5C2×C22⋊C411yescharacteristic
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5#10212yes—
111C2×C4×C5#10312yes—
112C2×C4×C5C2×M1612yes—
113C2×Dic5—21no—
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—21no—
117C2×Dic5—24no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5#10112yes—
124C2×Dic5#10212yes—
125C2×Dic5#10312yes—
126C2×Dic5C2×D811yescharacteristic
127C2×Dic5C2×SD1611yescharacteristic
128C2×Dic5C2×SD1611yescharacteristic
129C2×Dic5C2×Q1611yescharacteristic
130Dic10—48no—
131#170—82no—
132#170—82no—
133C22×Q8—101no—
134C22×C8—102no—
135C22×C8—102no—
136C4⋊Q8—104no—
137C4×Q8—202no—
138C4×Q8—202no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—52no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4—102no—
144C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
145C2×C42—51no—
146C2×C42—51no—
147C2×C42—51no—
148C2×C42—51no—
149C2×C42—51no—
150C2×C42—51no—
151C2×C42—102no—
152C2×C42C2×AGL(1,𝔽5)11yescharacteristic
153C4⋊C8—202no—
154C4⋊C8—202no—
155#95—102no—
156#95—102no—
157C22×C5#40711yescharacteristic
158C22×C5#41011yescharacteristic
159C22×C5C2×#10111yescharacteristic
160C22×C5C2×#10211yescharacteristic
161C22×C5C2×#10311yescharacteristic
162C22×C5#42111yescharacteristic
163C22×C5#42111yescharacteristic
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—82no—
168Dic5—21no—
169Dic5—21no—
170Dic5—21no—
171Dic5—21no—
172Dic5—41no—
173Dic5—44no—
174Dic5#33214yes—
175C2×Q8—104no—
176C2×Q8—202no—
177C2×Q8—202no—
178C22×C4—22no—
179C22×C4—51no—
180C22×C4—51no—
181C22×C4—51no—
182C22×C4—51no—
183C22×C4—102no—
184C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
185C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
186C22×C4C22×AGL(1,𝔽5)11yescharacteristic
187C2×C8—202no—
188C2×C8—202no—
189C2×C8—202no—
190C2×C8—202no—
191C2×C8—202no—
192C2×C8—202no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—54no—
197C4⋊C4—104no—
198C4⋊C4—102no—
199C4⋊C4—202no—
200C4⋊C4—202no—
201C42—22no—
202C42—52no—
203C42—52no—
204C42—52no—
205C42—52no—
206C42—102no—
207C42—201no—
208C42—201no—
209C42—201no—
210C42—204no—
211C2×C5#146711yescharacteristic
212C2×C5#148611yescharacteristic
213C2×C5#148711yescharacteristic
214C2×C5#151711yescharacteristic
215C2×C5#151811yescharacteristic
216C2×C5#153711yescharacteristic
217C2×C5C2×#33211yescharacteristic
218C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
219Q8—208no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—52no—
230C2×C4—52no—
231C2×C4—52no—
232C2×C4—51no—
233C2×C4—51no—
234C2×C4—51no—
235C2×C4—51no—
236C2×C4—101no—
237C2×C4—101no—
238C2×C4—101no—
239C2×C4—101no—
240C2×C4—104no—
241C2×C4—101no—
242C2×C4—101no—
243C2×C4—101no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4#400712yes—
247C2×C4#400912yes—
248C2×C4D5⋊M1612yes—
249C8—402no—
250C8—402no—
251C5#765211yescharacteristic, complemented, Sylow
252C22#6575511yescharacteristic
253C22C2×#400711yescharacteristic
254C22#6576911yescharacteristic
255C22#6577111yescharacteristic
256C22C2×#400911yescharacteristic
257C22#6578411yescharacteristic
258C22D5⋊#10111yescharacteristic
259C4—22no—
260C4—22no—
261C4—22no—
262C4—54no—
263C4—82no—
264C4—101no—
265C4—101no—
266C4—101no—
267C4—101no—
268C4—201no—
269C4—204no—
270C2#1060427211yescharacteristic
271C2#1060427311yescharacteristic
272C2#1060429511yescharacteristic
273C2#1060459611yescharacteristic
274C2#1060463211yescharacteristic
275C2#1060463911yescharacteristic
276C2D5⋊#33211yescharacteristic
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#7652
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
251. C5#7652semidirect

Maximal subgroups

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

subgroupindex
#106060512
#106041862
#105987142
#76525