Finite Group Databasebeta

← #13021026

Subgroups — #13021026

Order 1280.

552 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 138 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
1Dic5×C4⋊Q8C211yesmaximal, characteristic
2C2×Q8⋊#170C214yesmaximal
3#10604181C211yesmaximal, characteristic
4C4×#4004C211yesmaximal, characteristic
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×Q8×Dic5C2212yes—
7C2×#4004—21no—
8C2×#4002—21no—
9C2×C4⋊#170C2212yes—
10C2×C4×#170C2212yes—
11#65519C412yes—
12#65274—21no—
13#65274—21no—
14C4⋊C4×Dic5—21no—
15C4⋊C4×Dic5—21no—
16#65224C411yescharacteristic
17C42×Dic5C2211yescharacteristic
18Q8⋊#170—28no—
19#64918—21no—
20#64918—21no—
21#9677—51nomaximal, Sylow
22C22×C5×Q8C2×C412yes—
23C22×#170—22no—
24C22×#170—22no—
25C5×C4⋊Q8—24no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—21no—
28C2×C42×C5C2×C411yescharacteristic
29Q8×Dic5—24no—
30Q8×Dic5—24no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—22no—
34C2×C4⋊Dic5C2×C412yes—
35C2×C4×Dic5—22no—
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5C2311yescharacteristic
42#4004—24no—
43#4002—42no—
44C4⋊#170—22no—
45C4⋊#170D414yes—
46C4×#170—24no—
47#3963—22no—
48#3963—22no—
49C4×C4⋊Q8—51no—
50#1767—51no—
51C4×C4⋊C8—51no—
52C2×Q8⋊C8—54no—
53C2×C5×Q8—22no—
54C2×C5×Q8—24no—
55C2×C5×Q8—24no—
56C2×C5×Q8M1614yes—
57C22×C4×C5—22no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×Dic5—22no—
62C22×Dic5C22⋊C411yescharacteristic
63C22×Dic5C22⋊C411yescharacteristic
64C22×Dic5C2×D411yescharacteristic
65C22×Dic5C2×D411yescharacteristic
66C2×#170—24no—
67C2×#170—24no—
68C2×#170—42no—
69C2×#170—42no—
70C2×#170—42no—
71C2×#170—42no—
72C5×C4⋊C4—24no—
73C5×C4⋊C4—24no—
74C42×C5—22no—
75C4⋊Dic5—24no—
76C4⋊Dic5—42no—
77C4⋊Dic5—42no—
78C4⋊Dic5—42no—
79C4⋊Dic5—42no—
80C4×Dic5—22no—
81C4×Dic5—22no—
82C4×Dic5—22no—
83C4×Dic5—41no—
84C4×Dic5—44no—
85C4×Dic5SD1612yes—
86C4×Dic5Q1612yes—
87C4×Dic5C2×D412yes—
88C4×Dic5#4112yes—
89C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
90C2×C4×Q8—52no—
91C2×C4⋊C8—52no—
92C2×C4⋊C8—101no—
93C2×#97—101no—
94C2×C4×C8—52no—
95#391—52no—
96#389—101no—
97#389—101no—
98#384—51no—
99C4×C4⋊C4—101no—
100C4×C4⋊C4—101no—
101C43—51no—
102#336—101no—
103#336—101no—
104Q8⋊C8—108no—
105C23×C5C2×C22⋊C411yescharacteristic
106C5×Q8—28no—
107C5×Q8—44no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—24no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5#10312yes—
116C2×C4×C5#10412yes—
117C2×C4×C5C4×D412yes—
118C2×C4×C5C2×M1612yes—
119C2×C4×C5#13112yes—
120C2×Dic5—21no—
121C2×Dic5—21no—
122C2×Dic5—21no—
123C2×Dic5—21no—
124C2×Dic5—21no—
125C2×Dic5—21no—
126C2×Dic5—21no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130C2×Dic5#10312yes—
131C2×Dic5#12112yes—
132C2×Dic5#12411yescharacteristic
133C2×Dic5#12711yescharacteristic
134C2×Dic5C2×SD1611yescharacteristic
135C2×Dic5C2×Q1611yescharacteristic
136C2×Dic5#13712yes—
137#170—44no—
138#170—44no—
139C22×Q8C2×AGL(1,𝔽5)12yes—
140C22×C8—102no—
141C22×C8—102no—
142C4⋊Q8—24no—
143C4×Q8—104no—
144C4×Q8—104no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—52no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4—101no—
150C2×C4⋊C4—101no—
151C2×C42—51no—
152C2×C42—51no—
153C2×C42—51no—
154C2×C42—51no—
155C2×C42—51no—
156C2×C42—51no—
157C2×C42—102no—
158C2×C42C2×AGL(1,𝔽5)11yescharacteristic
159C4⋊C8—54no—
160C4⋊C8—102no—
161C4⋊C8—104no—
162#97—202no—
163C4×C8—104no—
164#95—102no—
165#95—102no—
166C22×C5#39011yescharacteristic
167C22×C5#40711yescharacteristic
168C22×C5#40811yescharacteristic
169C22×C5C2×#10311yescharacteristic
170C22×C5#41911yescharacteristic
171C22×C5C2×#10411yescharacteristic
172C22×C5#42111yescharacteristic
173C4×C5—22no—
174C4×C5—22no—
175C4×C5—44no—
176C4×C5#43514yes—
177Dic5—21no—
178Dic5—21no—
179Dic5—22no—
180Dic5—41no—
181Dic5—82no—
182Dic5#46112yes—
183Dic5#46212yes—
184C2×Q8—22no—
185C2×Q8—24no—
186C2×Q8—24no—
187C2×Q8#70414yes—
188C22×C4—22no—
189C22×C4—51no—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—51no—
193C22×C4—102no—
194C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
195C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C22×C4C22×AGL(1,𝔽5)11yescharacteristic
197C2×C8—104no—
198C2×C8—104no—
199C2×C8—202no—
200C2×C8—202no—
201C2×C8—202no—
202C2×C8—202no—
203C4⋊C4—24no—
204C4⋊C4—24no—
205C4⋊C4—104no—
206C4⋊C4—202no—
207C4⋊C4—202no—
208C4⋊C4—202no—
209C4⋊C4—202no—
210C42—22no—
211C42—52no—
212C42—52no—
213C42—52no—
214C42—52no—
215C42—102no—
216C42—102no—
217C42—102no—
218C42—201no—
219C42—204no—
220C2×C5#148711yescharacteristic
221C2×C5#149111yescharacteristic
222C2×C5#149311yescharacteristic
223C2×C5#149711yescharacteristic
224C2×C5#195511yescharacteristic
225C2×C5#198011yescharacteristic
226C2×C5#198111yescharacteristic
227C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
228Q8—28no—
229Q8—44no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—52no—
238C2×C4—51no—
239C2×C4—51no—
240C2×C4—52no—
241C2×C4—51no—
242C2×C4—51no—
243C2×C4—52no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—101no—
247C2×C4—101no—
248C2×C4—101no—
249C2×C4—101no—
250C2×C4—101no—
251C2×C4—202no—
252C2×C4—202no—
253C2×C4—202no—
254C2×C4#400912yes—
255C2×C4#401012yes—
256C2×C4#413112yes—
257C2×C4D4×AGL(1,𝔽5)12yes—
258C2×C4C2×#70412yes—
259C8—204no—
260C8—204no—
261C5#967711yescharacteristic, complemented, Sylow
262C22#6577611yescharacteristic
263C22#6578011yescharacteristic
264C22C2×#400911yescharacteristic
265C22#6578211yescharacteristic
266C22C2×#401011yescharacteristic
267C22#6578411yescharacteristic
268C22#6579811yescharacteristic
269C4—22no—
270C4—22no—
271C4—44no—
272C4—52no—
273C4—52no—
274C4—102no—
275C4—101no—
276C4—101no—
277C4—201no—
278C4—402no—
279C4#6577314yes—
280C2#1060465111yescharacteristic
281C2#1060465411yescharacteristic
282C2#1060466711yescharacteristic
283C2#1060467811yescharacteristic
284C2#1060494911yescharacteristic
285C2#1060496811yescharacteristic
286C2#1060496911yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#9677
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
261. C5#9677semidirect

Maximal subgroups

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

subgroupindex
Dic5×C4⋊Q82
C2×Q8⋊#1702
#106041812
C4×#40042
#96775