Finite Group Databasebeta

← #12010357

Subgroups — #12010357

Order 1280.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#10614206C211yesmaximal, characteristic
2C5×#1801C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10597986C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4090—21no—
7C2×#4015C411yescharacteristic
8C5×#423—21no—
9C2×C5×#101—21no—
10#65272C412yes—
11#65272C2212yes—
12#65263—21no—
13C4×C4⋊Dic5C411yescharacteristic
14#65217—21no—
15#65217—21no—
16#65214—21no—
17C5×#343C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11883—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C2×C5×M16—22no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C2×C5×C4⋊C4C2×C411yescharacteristic
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C4⋊C4C2311yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32#4090—42no—
33#4090—42no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5C2×C412yes—
37C2×#683—22no—
38C2×#683—22no—
39C2×C4×Dic5—21no—
40#4015—41no—
41#4015—41no—
42C5×C4⋊C8—41no—
43C5×C4⋊C8—41no—
44C5×#101—42no—
45#3963—22no—
46#3963—22no—
47#3963C2×C412yes—
48C22⋊#168—22no—
49C4⋊#168—41no—
50C4×#168—41no—
51#2546—51no—
52#1801D511yescharacteristic
53#1461—51no—
54#1346—54no—
55C2×C5×Q8—41no—
56C2×C5×Q8—41no—
57C2×C5×Q8D812yes—
58C2×C5×Q8SD1612yes—
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×Dic5—22no—
67C22×Dic5—22no—
68C2×Dic10—42no—
69C2×Dic10—42no—
70C2×Dic10—42no—
71C5×M16—42no—
72C5×M16—42no—
73C2×C5×C8—42no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—41no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C4⋊Dic5—24no—
84C4⋊Dic5—41no—
85C4⋊Dic5—41no—
86C4⋊Dic5—42no—
87#683—44no—
88#683—42no—
89#683—42no—
90C4×Dic5—42no—
91C2×#168—42no—
92C2×C4⋊Q8—51no—
93C2×C4⋊Q8—101no—
94C2×C4×Q8C2×D511yescharacteristic
95#431—101no—
96#423—21no—
97C2×#101—21no—
98#398—52no—
99#398—52no—
100#391—101no—
101#389—101no—
102#389—101no—
103C4×C4⋊C4—51no—
104#343C2×D512yes—
105#324—52no—
106#324—101no—
107C23×C5C2×C22⋊C411yescharacteristic
108C5×Q8—42no—
109C5×Q8—42no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—22no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5#9911yescharacteristic
124C2×C4×C5#9911yescharacteristic
125C2×C4×C5#10212yes—
126C2×C4×C5#10212yes—
127C2×C4×C5C2×D811yescharacteristic
128C2×C4×C5C2×SD1611yescharacteristic
129C2×Dic5—24no—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135Dic10—84no—
136C5×C8—82no—
137#168—82no—
138C22×Q8—101no—
139C22×Q8C22⋊D511yescharacteristic
140C2×M16—22no—
141C4⋊Q8—201no—
142C4⋊Q8—201no—
143C4⋊Q8—202no—
144C4⋊Q8—202no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—52no—
148C2×C4⋊C4—101no—
149C2×C4⋊C4—102no—
150C2×C4⋊C4—101no—
151C2×C4⋊C4—102no—
152C2×C4⋊C4C4×D511yescharacteristic
153C2×C4⋊C4D2011yescharacteristic
154C2×C4⋊C4C22×D511yescharacteristic
155C2×C42—101no—
156C2×C42C4×D511yescharacteristic
157C2×C42D2011yescharacteristic
158C2×C42C22⋊D511yescharacteristic
159C4⋊C8—41no—
160C4⋊C8—41no—
161C4⋊C8—201no—
162#101—42no—
163C22⋊C8—102no—
164C4×C8—201no—
165#95—52no—
166#95—102no—
167#95—102no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5C2×#9911yescharacteristic
171C22×C5C2×#10211yescharacteristic
172C22×C5#42111yescharacteristic
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—22no—
176C4×C5—22no—
177C4×C5—21no—
178C4×C5—41no—
179C4×C5—41no—
180C4×C5—41no—
181C4×C5#35612yes—
182Dic5—44no—
183Dic5—82no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—202no—
187C2×Q8—202no—
188C2×Q8—202no—
189C2×Q8#68612yes—
190C2×Q8#68812yes—
191C22×C4—102no—
192C22×C4—102no—
193C22×C4#68511yescharacteristic
194C22×C4#68511yescharacteristic
195C22×C4#68511yescharacteristic
196C22×C4#68511yescharacteristic
197C22×C4C2×C4×D511yescharacteristic
198C22×C4C2×D2011yescharacteristic
199C22×C4C2×C22⋊D511yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—202no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—104no—
208C4⋊C4—202no—
209C4⋊C4—201no—
210C4⋊C4—201no—
211C4⋊C4—204no—
212C4⋊C4—202no—
213C4⋊C4—202no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—202no—
221C2×C5—21no—
222C2×C5—21no—
223C2×C5#151911yescharacteristic
224C2×C5#212311yescharacteristic
225C2×C5C2×#35611yescharacteristic
226C23C2×#68511yescharacteristic
227Q8—42no—
228Q8—42no—
229Q8—404no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—104no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—202no—
247C2×C4—202no—
248C2×C4—202no—
249C2×C4#393811yescharacteristic
250C2×C4#393811yescharacteristic
251C2×C4#394112yes—
252C2×C4#394112yes—
253C2×C4C2×#68611yescharacteristic
254C2×C4C2×#68811yescharacteristic
255C8—82no—
256C8—402no—
257C5#1188311yescharacteristic, complemented, Sylow
258C22—21no—
259C22—21no—
260C22C2×#393811yescharacteristic
261C22C2×#394111yescharacteristic
262C22#6529411yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—204no—
272C4—402no—
273C4#6469812yes—
274C2—21no—
275C2—21no—
276C2#1060030211yescharacteristic
277C2C2×#6469811yescharacteristic
278C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1801C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1801D5
hypocenterC5#11883
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
257. C5#11883semidirect

Maximal subgroups

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

subgroupindex
#106142062
C5×#18012
#106024172
#105979862
#118835