Finite Group Databasebeta

← #13015196

Subgroups — #13015196

Order 1280.

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

normal subgroups only

This group has 404 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#10614983C211yesmaximal, characteristic
2#10604189C211yesmaximal, characteristic
3#10604186C211yesmaximal, characteristic
4#10598715C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×#4015C411yescharacteristic
7C2×#4004—21no—
8#65519—21no—
9#65519—21no—
10#65266—21no—
11#65266—21no—
12#65263C412yes—
13#65263C2212yes—
14C42×Dic5C2211yescharacteristic
15#64918—21no—
16#64918—21no—
17#64918—21no—
18#64918C2212yes—
19#64918C2212yes—
20#7722—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×Dic10C2×C412yes—
23C22×#170—22no—
24C22×#170—22no—
25C5×C4⋊Q8—42no—
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×C411yescharacteristic
32C2×C4×Dic5D411yescharacteristic
33C2×C4×Dic5D411yescharacteristic
34C2×C4×Dic5D411yescharacteristic
35C2×C4×Dic5D411yescharacteristic
36C2×C4×Dic5C2311yescharacteristic
37#4015—42no—
38#4004—42no—
39#3963—22no—
40#3963—22no—
41#3963—22no—
42#3963—22no—
43#2862—51no—
44#1839—51no—
45#1831—51no—
46#1272—54no—
47C2×C5×Q8—42no—
48C2×C5×Q8—42no—
49C2×C5×Q8—42no—
50C22×C4×C5—22no—
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5C22⋊C411yescharacteristic
56C22×Dic5C22⋊C411yescharacteristic
57C22×Dic5C2×D411yescharacteristic
58C22×Dic5C2×D411yescharacteristic
59C2×Dic10—24no—
60C2×Dic10—42no—
61C2×Dic10—42no—
62C2×#170—42no—
63C2×#170—42no—
64C2×#170—42no—
65C2×#170—42no—
66C2×#170—42no—
67C2×#170—42no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C42×C5—22no—
71C4⋊Dic5—42no—
72C4⋊Dic5—42no—
73C4×Dic5—22no—
74C4×Dic5—22no—
75C4×Dic5—41no—
76C4×Dic5—41no—
77C4×Dic5—41no—
78C4×Dic5SD1612yes—
79C4×Dic5Q1612yes—
80C2×C4⋊Q8—51no—
81C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
82C2×C4⋊C8—101no—
83#391—52no—
84#391—52no—
85#391—101no—
86#391—101no—
87#382—101no—
88#382—101no—
89C43—51no—
90#336—52no—
91#336—52no—
92#336—101no—
93#336—101no—
94#336—101no—
95C23×C5C2×C22⋊C411yescharacteristic
96C5×Q8—84no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—42no—
106C2×C4×C5#10012yes—
107C2×C4×C5#10312yes—
108C2×C4×C5#13112yes—
109C2×Dic5—21no—
110C2×Dic5—21no—
111C2×Dic5—21no—
112C2×Dic5—21no—
113C2×Dic5—21no—
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—21no—
117C2×Dic5—21no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5#10312yes—
122C2×Dic5C2×SD1611yescharacteristic
123C2×Dic5C2×Q1611yescharacteristic
124C2×Dic5#13712yes—
125Dic10—84no—
126#170—82no—
127#170—82no—
128C22×Q8—21no—
129C22×Q8—52no—
130C22×C8—102no—
131C22×C8—102no—
132C4⋊Q8—42no—
133C4⋊Q8—202no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—101no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
138C2×C42—51no—
139C2×C42—51no—
140C2×C42—51no—
141C2×C42—51no—
142C2×C42—51no—
143C2×C42—51no—
144C2×C42C2×AGL(1,𝔽5)11yescharacteristic
145C4⋊C8—202no—
146#95—102no—
147#95—102no—
148#95—102no—
149#95—102no—
150C22×C5#40811yescharacteristic
151C22×C5#41011yescharacteristic
152C22×C5C2×#10011yescharacteristic
153C22×C5C2×#10311yescharacteristic
154C22×C5#41911yescharacteristic
155C22×C5#42111yescharacteristic
156C22×C5#42111yescharacteristic
157C4×C5—22no—
158C4×C5—22no—
159C4×C5—22no—
160C4×C5—82no—
161Dic5—22no—
162Dic5—22no—
163Dic5—21no—
164Dic5—21no—
165Dic5—41no—
166Dic5—82no—
167C2×Q8—42no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8—104no—
171C2×Q8—202no—
172C2×Q8—202no—
173C22×C4—22no—
174C22×C4—51no—
175C22×C4—51no—
176C22×C4—51no—
177C22×C4—51no—
178C22×C4—102no—
179C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
180C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
181C22×C4C22×AGL(1,𝔽5)11yescharacteristic
182C2×C8—202no—
183C2×C8—202no—
184C2×C8—202no—
185C2×C8—202no—
186C2×C8—202no—
187C2×C8—202no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—202no—
191C4⋊C4—202no—
192C42—22no—
193C42—52no—
194C42—52no—
195C42—102no—
196C42—102no—
197C42—201no—
198C42—201no—
199C42—201no—
200C2×C5#146911yescharacteristic
201C2×C5#148111yescharacteristic
202C2×C5#149711yescharacteristic
203C2×C5#151511yescharacteristic
204C2×C5#151811yescharacteristic
205C2×C5#153311yescharacteristic
206C2×C5#154811yescharacteristic
207C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
208Q8—84no—
209Q8—404no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—51no—
220C2×C4—52no—
221C2×C4—51no—
222C2×C4—52no—
223C2×C4—101no—
224C2×C4—101no—
225C2×C4—101no—
226C2×C4—101no—
227C2×C4—101no—
228C2×C4—101no—
229C2×C4—101no—
230C2×C4—101no—
231C2×C4—101no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4#400912yes—
236C2×C4#401312yes—
237C2×C4#413312yes—
238C8—402no—
239C8—402no—
240C5#772211yescharacteristic, complemented, Sylow
241C22#6576911yescharacteristic
242C22#6576911yescharacteristic
243C22C2×#400911yescharacteristic
244C22#6578211yescharacteristic
245C22#6578511yescharacteristic
246C22#6578711yescharacteristic
247C22C2×#401311yescharacteristic
248C4—22no—
249C4—22no—
250C4—22no—
251C4—82no—
252C4—102no—
253C4—101no—
254C4—101no—
255C4—102no—
256C4—201no—
257C4—402no—
258C2#1060462811yescharacteristic
259C2#1060463111yescharacteristic
260C2#1060464611yescharacteristic
261C2#1060465511yescharacteristic
262C2#1060491611yescharacteristic
263C2#1060497111yescharacteristic
264C2#1060497811yescharacteristic
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#7722
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
240. C5#7722semidirect

Maximal subgroups

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

subgroupindex
#106149832
#106041892
#106041862
#105987152
#77225