Finite Group Databasebeta

← #12010055

Subgroups — #12010055

Order 1280.

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

normal subgroups only

This group has 368 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×#1822C211yesmaximal, characteristic
3#10602365C211yesmaximal, characteristic
4#10597985C214yesmaximal, complemented
5C2×C5×#117C2211yescharacteristic
6C2×#4015C411yescharacteristic
7C5×#407—21no—
8#65501—21no—
9#65275—21no—
10#65268C2212yes—
11#65238—21no—
12#65236C412yes—
13#65225C411yescharacteristic
14#65217—21no—
15#65215—21no—
16C5×#343—21no—
17C5×#343C2212yes—
18#64748C2212yes—
19#64745—21no—
20#11819—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C22×Dic10C2×C412yes—
23C2×C5×M16—22no—
24C5×#117—41no—
25C5×#117—41no—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C4⋊C4C2311yescharacteristic
28C2×C5×C22⋊C4C2×C411yescharacteristic
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
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×C22⋊C8—41no—
40C5×C22⋊C8—41no—
41#3963—22no—
42#3963—21no—
43#3963—22no—
44#3963C2×C412yes—
45C22⋊#168—22no—
46C4⋊#168—41no—
47#3935—41no—
48#2628—51no—
49#1822D511yescharacteristic
50#1464—51no—
51#1354—54no—
52C24×C5C22⋊C411yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—22no—
56C22×C4×C5—41no—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—22no—
64C22×Dic5—22no—
65C2×Dic10—42no—
66C2×Dic10—82no—
67C5×M16—42no—
68C5×M16—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C22⋊C4—41no—
73C5×C22⋊C4—41no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—21no—
78C22⋊Dic5—82no—
79C4⋊Dic5—42no—
80C4⋊Dic5—42no—
81C4⋊Dic5—41no—
82C4⋊Dic5—41no—
83#683—82no—
84C2×#168—42no—
85C2×C4⋊Q8—51no—
86C2×#117C2×D511yescharacteristic
87#432—101no—
88#407—21no—
89#400—101no—
90#399—101no—
91#395—52no—
92#393—52no—
93#389—101no—
94#382—51no—
95#380—101no—
96#343—21no—
97#343C2×D512yes—
98#324—52no—
99#323—101no—
100C23×C5—21no—
101C23×C5—21no—
102C23×C5—21no—
103C23×C5—41no—
104C23×C5—41no—
105C23×C5C2×C22⋊C411yescharacteristic
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—42no—
115C2×C4×C5—42no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5#9911yescharacteristic
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#13712yes—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129Dic10—84no—
130C5×C8—82no—
131#168—82no—
132C22×Q8—52no—
133C23×C4C22⋊D511yescharacteristic
134C2×M16—22no—
135C4⋊Q8—201no—
136C4⋊Q8—201no—
137#117—41no—
138#117—41no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4—102no—
143C2×C4⋊C4C22⋊D511yescharacteristic
144C2×C4⋊C4C22×D511yescharacteristic
145C2×C22⋊C4—102no—
146C2×C22⋊C4C4×D511yescharacteristic
147C2×C22⋊C4D2011yescharacteristic
148C2×C42C4×D511yescharacteristic
149C2×C42D2011yescharacteristic
150C4⋊C8—201no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—102no—
154#97—201no—
155#95—52no—
156#95—101no—
157#95—102no—
158#95—102no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5—42no—
162C22×C5—41no—
163C22×C5—41no—
164C22×C5—41no—
165C22×C5—81no—
166C22×C5C2×#9911yescharacteristic
167C22×C5#41911yescharacteristic
168C22×C5#42111yescharacteristic
169C4×C5—22no—
170C4×C5—21no—
171C4×C5—21no—
172C4×C5—41no—
173C4×C5—41no—
174C4×C5—41no—
175C4×C5—41no—
176Dic5—82no—
177Dic5—82no—
178C24#68511yescharacteristic
179C2×Q8—202no—
180C2×Q8—402no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—102no—
186C22×C4—102no—
187C22×C4#68511yescharacteristic
188C22×C4#68511yescharacteristic
189C22×C4#68511yescharacteristic
190C22×C4C2×C4×D511yescharacteristic
191C22×C4C2×D2011yescharacteristic
192C22×C4C2×C22⋊D511yescharacteristic
193M16—42no—
194M16—42no—
195C2×C8—42no—
196C2×C8—202no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—202no—
200C4⋊C4—202no—
201C4⋊C4—201no—
202C4⋊C4—201no—
203C4⋊C4—402no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—402no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C2×C5—21no—
212C2×C5—21no—
213C2×C5—81no—
214C2×C5#151111yescharacteristic
215C2×C5#212211yescharacteristic
216C2×C5#213511yescharacteristic
217C23—21no—
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23C2×#68511yescharacteristic
223Q8—404no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—202no—
239C2×C4—202no—
240C2×C4—202no—
241C2×C4—202no—
242C2×C4—202no—
243C2×C4—202no—
244C2×C4#393811yescharacteristic
245C2×C4#393811yescharacteristic
246C2×C4#409712yes—
247C8—82no—
248C8—402no—
249C5#1181911yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#393811yescharacteristic
258C22#6529311yescharacteristic
259C22#6529411yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—402no—
268C4—402no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1060032611yescharacteristic
273C2#1060093911yescharacteristic
274C2#1060094311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1822C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1822D5
hypocenterC5#11819
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
4. #10597985C2semidirect
249. C5#11819semidirect

Maximal subgroups

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

subgroupindex
#106139952
C5×#18222
#106023652
#105979852
#118195