Finite Group Databasebeta

← #13021084

Subgroups — #13021084

Order 1280.

538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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#10606087C211yesmaximal, characteristic
2C2×#64873C214yesmaximal
3#10604186C211yesmaximal, characteristic
4#10604180C211yesmaximal, characteristic
5C2×#4034—21no—
6C2×#4034—21no—
7C2×#4034C2212yes—
8C2×#4004C2212yes—
9C2×#4004C2212yes—
10C2×#4002—21no—
11C5×#384C411yescharacteristic
12#65265—21no—
13#65265—21no—
14#65265C412yes—
15#65224C411yescharacteristic
16C42×Dic5C2211yescharacteristic
17#64918—21no—
18#64918—21no—
19#64918—21no—
20#64873—28no—
21#9703—51nomaximal, Sylow
22C22×Dic10—22no—
23C22×#170—22no—
24C22×#170—22no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4C2×C412yes—
28C2×C42×C5C2×C411yescharacteristic
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5C2×C412yes—
32C2×#683—22no—
33C2×#683—22no—
34C2×#683—22no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5D411yescharacteristic
39C2×C4×Dic5D411yescharacteristic
40C2×C4×Dic5C2311yescharacteristic
41#4034—24no—
42#4034—24no—
43#4034—44no—
44#4034—44no—
45#4004—24no—
46#4004—22no—
47#4004D414yes—
48#4002—42no—
49#2868—51no—
50#1831—51no—
51#1767—51no—
52C2×#332—54no—
53C22×C4×C5—22no—
54C22×C4×C5C22⋊C411yescharacteristic
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22×C411yescharacteristic
57C22×Dic5—22no—
58C22×Dic5C22⋊C411yescharacteristic
59C22×Dic5C22⋊C411yescharacteristic
60C22×Dic5C2×D411yescharacteristic
61C22×Dic5C2×D411yescharacteristic
62C2×Dic10—42no—
63C2×Dic10—42no—
64C2×Dic10—44no—
65C2×Dic10—44no—
66C2×#170—24no—
67C2×#170—42no—
68C2×#170—42no—
69C2×#170—42no—
70C2×#170—42no—
71C2×#170—42no—
72C5×C4⋊C4—24no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C42×C5—22no—
76C4⋊Dic5—24no—
77C4⋊Dic5—42no—
78C4⋊Dic5—42no—
79#683—44no—
80#683—44no—
81#683—44no—
82C4×Dic5—22no—
83C4×Dic5—22no—
84C4×Dic5—22no—
85C4×Dic5—22no—
86C4×Dic5SD1612yes—
87C4×Dic5Q1612yes—
88C4×Dic5C2×D412yes—
89C4×Dic5#4112yes—
90C2×C4⋊Q8—52no—
91C2×C4⋊Q8—101no—
92C2×C4⋊Q8—101no—
93C2×C4⋊C8—52no—
94C2×C4⋊C8—52no—
95C2×#97—101no—
96#384—52no—
97#384—51no—
98#384—101no—
99#384—101no—
100#384AGL(1,𝔽5)11yescharacteristic
101C43—51no—
102#336—101no—
103#336—101no—
104#336—101no—
105#332—108no—
106C23×C5C2×C22⋊C411yescharacteristic
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5#10112yes—
117C2×C4×C5#10312yes—
118C2×C4×C5C4×D412yes—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—21no—
122C2×Dic5—21no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5#10112yes—
127C2×Dic5#10312yes—
128C2×Dic5#12112yes—
129C2×Dic5#12411yescharacteristic
130C2×Dic5#12711yescharacteristic
131C2×Dic5C2×SD1611yescharacteristic
132C2×Dic5C2×Q1611yescharacteristic
133C2×Dic5AGL(1,ℤ/8)12yes—
134C2×Dic5AGL(1,ℤ/8)12yes—
135C2×Dic5#13712yes—
136Dic10—84no—
137Dic10—84no—
138#170—44no—
139#170—82no—
140C22×Q8—102no—
141C22×C8—102no—
142C22×C8—102no—
143C4⋊Q8—104no—
144C4⋊Q8—104no—
145C4⋊Q8—204no—
146C4⋊Q8—204no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—52no—
150C2×C4⋊C4—102no—
151C2×C4⋊C4—102no—
152C2×C4⋊C4—102no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
156C2×C42—51no—
157C2×C42—51no—
158C2×C42—51no—
159C2×C42—51no—
160C2×C42—51no—
161C2×C42—51no—
162C2×C42C2×AGL(1,𝔽5)11yescharacteristic
163C4⋊C8—54no—
164C4⋊C8—102no—
165C4⋊C8—104no—
166#97—202no—
167C22×C5#39011yescharacteristic
168C22×C5C2×#10111yescharacteristic
169C22×C5C2×#10111yescharacteristic
170C22×C5C2×#10311yescharacteristic
171C22×C5#41811yescharacteristic
172C22×C5#41811yescharacteristic
173C22×C5#41911yescharacteristic
174C4×C5—22no—
175C4×C5—22no—
176C4×C5—22no—
177C4×C5—82no—
178Dic5—22no—
179Dic5—22no—
180Dic5—82no—
181Dic5#46112yes—
182Dic5#46212yes—
183Dic5#49012yes—
184Dic5#49612yes—
185C2×Q8—202no—
186C2×Q8—202no—
187C2×Q8—204no—
188C2×Q8—204no—
189C22×C4—22no—
190C22×C4—51no—
191C22×C4—51no—
192C22×C4—51no—
193C22×C4—51no—
194C22×C4—102no—
195C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C22×C4C22×AGL(1,𝔽5)11yescharacteristic
198C2×C8—104no—
199C2×C8—202no—
200C2×C8—202no—
201C2×C8—202no—
202C2×C8—202no—
203C2×C8—202no—
204C4⋊C4—24no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—104no—
208C4⋊C4—202no—
209C4⋊C4—202no—
210C4⋊C4—204no—
211C4⋊C4—204no—
212C4⋊C4—204no—
213C42—22no—
214C42—52no—
215C42—52no—
216C42—52no—
217C42—52no—
218C42—102no—
219C42—102no—
220C42—102no—
221C42—102no—
222C2×C5#154911yescharacteristic
223C2×C5#154911yescharacteristic
224C2×C5#155611yescharacteristic
225C2×C5#155611yescharacteristic
226C2×C5#196111yescharacteristic
227C2×C5#196611yescharacteristic
228C2×C5#198111yescharacteristic
229C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
230Q8—404no—
231Q8—404no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—52no—
242C2×C4—52no—
243C2×C4—52no—
244C2×C4—51no—
245C2×C4—51no—
246C2×C4—51no—
247C2×C4—51no—
248C2×C4—52no—
249C2×C4—52no—
250C2×C4—52no—
251C2×C4—101no—
252C2×C4—101no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—202no—
256C2×C4—202no—
257C2×C4—202no—
258C2×C4#400512yes—
259C2×C4#400912yes—
260C2×C4D4×AGL(1,𝔽5)12yes—
261C8—204no—
262C8—402no—
263C5#970311yescharacteristic, complemented, Sylow
264C22C2×#400511yescharacteristic
265C22#6576711yescharacteristic
266C22#6576711yescharacteristic
267C22#6578011yescharacteristic
268C22C2×#400911yescharacteristic
269C22#6578211yescharacteristic
270C22D5⋊#10111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—52no—
275C4—52no—
276C4—52no—
277C4—52no—
278C4—82no—
279C4—102no—
280C4—102no—
281C4—402no—
282C2#1060427811yescharacteristic
283C2#1060427911yescharacteristic
284C2#1060433911yescharacteristic
285C2#1060461711yescharacteristic
286C2#1060466011yescharacteristic
287C2#1060466111yescharacteristic
288C2#1060466711yescharacteristic
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#9703
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
263. C5#9703semidirect

Maximal subgroups

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

subgroupindex
#106060872
C2×#648732
#106041862
#106041802
#97035