Finite Group Databasebeta

← #12010027

Subgroups — #12010027

Order 1280.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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#10613995C211yesmaximal, characteristic
2C5×#1464C211yesmaximal, characteristic
3#10602387C211yesmaximal, characteristic
4#10597940C214yesmaximal
5C2×C5×#117C2211yescharacteristic
6C2×#4015C411yescharacteristic, complemented
7C5×#432—21no—
8#65501—21no—
9#65500—21no—
10#65275—21no—
11#65268C412yescomplemented
12#65238—21no—
13#65236C2212yes—
14#65225C411yescharacteristic, complemented
15#65217—21no—
16C5×#324—21no—
17C5×#323C2212yes—
18#64746—21no—
19#64746C2212yes—
20#11812—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C22×Dic10C2×C412yes—
23C5×#117—41no—
24C5×#117—41no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C22⋊C4D411yescharacteristic
28C2×C5×C22⋊C4C2311yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×#683—22no—
37#4015—41no—
38#4015—41no—
39C5×C4⋊C8—41no—
40C5×C22⋊C8—22no—
41C5×#97—41no—
42#3963—21no—
43#3963—22no—
44#3963—22no—
45#3963—41no—
46#3963—41no—
47#3963C2×C412yes—
48#2628—51no—
49#1820—51no—
50#1464D511yescharacteristic
51#1351—54no—
52C24×C5C2×D411yescharacteristic
53C22×C4×C5—22no—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—41no—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22×C411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—22no—
64C22×Dic5—22no—
65C22×Dic5—42no—
66C2×Dic10—42no—
67C2×Dic10—82no—
68C2×C5×C8—42no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C22⋊C4—41no—
72C5×C22⋊C4—41no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C22⋊Dic5—42no—
78C22⋊Dic5—42no—
79C22⋊Dic5—82no—
80C4⋊Dic5—42no—
81C4⋊Dic5—42no—
82C4⋊Dic5—41no—
83C4⋊Dic5—41no—
84#683—82no—
85C2×C4⋊Q8—51no—
86C2×#117C2×D511yescharacteristic
87#432—21no—
88#400—101no—
89#399—101no—
90#395—52no—
91#393—52no—
92#389—101no—
93#382—51no—
94#381—101no—
95#380—101no—
96#342—52no—
97#342—101no—
98#324—21no—
99#323C2×D512yes—
100C23×C5—21no—
101C23×C5—21no—
102C23×C5—41no—
103C23×C5—41no—
104C23×C5C2×C22⋊C411yescharacteristic
105C23×C5#13712yes—
106C2×C4×C5—21no—
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—21no—
114C2×C4×C5—21no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#9911yescharacteristic
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—82no—
130C2×Dic5—82no—
131C2×Dic5—82no—
132Dic10—84no—
133C5×C8—82no—
134C22×Q8—52no—
135C23×C4D2011yescharacteristic
136C4⋊Q8—201no—
137C4⋊Q8—201no—
138#117—41no—
139#117—41no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4—102no—
144C2×C4⋊C4C4×D511yescharacteristic
145C2×C4⋊C4C22⋊D511yescharacteristic
146C2×C22⋊C4—102no—
147C2×C22⋊C4—102no—
148C2×C22⋊C4D2011yescharacteristic
149C2×C22⋊C4C22×D511yescharacteristic
150C2×C42C4×D511yescharacteristic
151C2×C42C22⋊D511yescharacteristic
152C4⋊C8—41no—
153C22⋊C8—22no—
154#97—41no—
155#95—52no—
156#95—102no—
157#95—101no—
158#95—102no—
159#95—201no—
160#95—201no—
161C22×C5—21no—
162C22×C5—21no—
163C22×C5—22no—
164C22×C5—42no—
165C22×C5—41no—
166C22×C5—41no—
167C22×C5—81no—
168C22×C5C2×#9911yescharacteristic
169C22×C5#41911yescharacteristic
170C22×C5#42111yescharacteristic
171C4×C5—21no—
172C4×C5—21no—
173C4×C5—41no—
174C4×C5—41no—
175C4×C5—41no—
176C4×C5—41no—
177C4×C5—41no—
178Dic5—82no—
179Dic5—82no—
180Dic5—162no—
181C24C2×D2011yescharacteristic
182C2×Q8—202no—
183C2×Q8—402no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—102no—
189C22×C4—102no—
190C22×C4—202no—
191C22×C4#68511yescharacteristic
192C22×C4#68511yescharacteristic
193C22×C4#68511yescharacteristic
194C22×C4#68511yescharacteristic
195C22×C4C2×C4×D511yescharacteristic
196C22×C4C2×C22⋊D511yescharacteristic
197C2×C8—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—202no—
201C4⋊C4—202no—
202C4⋊C4—201no—
203C4⋊C4—201no—
204C4⋊C4—402no—
205C22⋊C4—41no—
206C22⋊C4—41no—
207C22⋊C4—202no—
208C22⋊C4—202no—
209C22⋊C4—402no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C2×C5—21no—
215C2×C5—21no—
216C2×C5—42no—
217C2×C5#151111yescharacteristic
218C2×C5#212211yescharacteristic
219C2×C5#212911yescharacteristic
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23#405512yes—
225C23C2×#68511yescharacteristic
226Q8—404no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—202no—
243C2×C4—202no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—202no—
247C2×C4—202no—
248C2×C4—402no—
249C2×C4—402no—
250C2×C4—402no—
251C2×C4#393811yescharacteristic
252C2×C4#393811yescharacteristic
253C8—82no—
254C5#1181211yescharacteristic, complemented, Sylow
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#393811yescharacteristic
263C22#6540911yescharacteristic
264C22#6542811yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—402no—
273C4—402no—
274C4—802no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2#1060077411yescharacteristic
279C2#1060085211yescharacteristic
280C2#1060093911yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1464C2
socleC22×C5C2×#99
prime radicalC24×C5C2×D4
cosocleC2×C5×C22⋊C4C23
hypercenter#1464D5
hypocenterC5#11812
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
6. C2×#4015C4semidirect
11. #65268C4semidirect
14. #65225C4semidirect
254. C5#11812semidirect

Maximal subgroups

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

subgroupindex
#106139952
C5×#14642
#106023872
#105979402
#118125