Finite Group Databasebeta

← #12009896

Subgroups — #12009896

Order 1280.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1467C211yesmaximal, characteristic
3C4×#3968C211yesmaximal, characteristic
4#10597949C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4090—21no—
7C2×#4015C411yescharacteristic
8C5×#432—21no—
9C2×#3968—21no—
10#65272C412yes—
11#65272C2212yes—
12#65263—21no—
13C4×C4⋊Dic5C411yescharacteristic
14#65217—21no—
15#65217—21no—
16C4×#681—21no—
17C5×#324—21no—
18C5×#324C2212yes—
19#64750C2212yes—
20#11782—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C4×C5×Q8—41no—
24C4×C5×Q8—41no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C4⋊C4C2311yescharacteristic
28C2×C42×C5C2×C411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C42×C5D411yescharacteristic
31#4090—44no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C412yes—
35C2×#683—22no—
36C2×#683—22no—
37C2×C4×Dic5—21no—
38C2×#681—22no—
39#4015—41no—
40#4015—41no—
41C5×C4⋊C8—41no—
42C5×C22⋊C8—22no—
43C5×#97—41no—
44#3968—24no—
45#3963—22no—
46#3963—22no—
47#3963C2×C412yes—
48#3935—41no—
49C4×#168—41no—
50#2546—51no—
51C4×#101—51no—
52#1467D511yescharacteristic
53#1346—54no—
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—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×C4×C5C2×D411yescharacteristic
64C22×Dic5—22no—
65C22×Dic5—22no—
66C2×Dic10—42no—
67C2×Dic10—42no—
68C2×Dic10—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—21no—
78C42×C5—21no—
79C4⋊Dic5—24no—
80C4⋊Dic5—41no—
81C4⋊Dic5—41no—
82C4⋊Dic5—42no—
83#683—44no—
84#683—44no—
85C4×Dic5—42no—
86#681—24no—
87#681—42no—
88C2×#168—42no—
89C2×C4⋊Q8—51no—
90C2×C4⋊Q8—101no—
91C2×C4×Q8C2×D511yescharacteristic
92#432—21no—
93C2×#101—101no—
94C4×M16—101no—
95#398—52no—
96#398—52no—
97#391—101no—
98#389—101no—
99#389—101no—
100C4×C4⋊C4—51no—
101#343—52no—
102#324—21no—
103#324C2×D512yes—
104C23×C5C2×C22⋊C411yescharacteristic
105C5×Q8—44no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—22no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—41no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5#9911yescharacteristic
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#10412yes—
123C2×C4×C5AGL(1,ℤ/8)12yes—
124C2×Dic5—24no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128C2×Dic5—42no—
129C2×Dic5—42no—
130Dic10—84no—
131C5×C8—82no—
132#168—44no—
133C22×Q8—101no—
134C22×Q8D2011yescharacteristic
135C2×M16—102no—
136C4⋊Q8—201no—
137C4⋊Q8—201no—
138C4⋊Q8—204no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—52no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4—102no—
144C2×C4⋊C4—101no—
145C2×C4⋊C4—102no—
146C2×C4⋊C4C4×D511yescharacteristic
147C2×C4⋊C4C22⋊D511yescharacteristic
148C2×C4⋊C4C22×D511yescharacteristic
149C2×C42—101no—
150C2×C42C4×D511yescharacteristic
151C2×C42D2011yescharacteristic
152C2×C42C22⋊D511yescharacteristic
153C4⋊C8—41no—
154#101—104no—
155C22⋊C8—22no—
156#97—41no—
157#97—201no—
158C4×C8—201no—
159#95—52no—
160#95—102no—
161#95—102no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5C2×#9911yescharacteristic
165C22×C5#41811yescharacteristic
166C22×C5C2×#10411yescharacteristic
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—22no—
170C4×C5—41no—
171C4×C5—41no—
172C4×C5—41no—
173C4×C5—41no—
174C4×C5#35612yes—
175Dic5—44no—
176Dic5—82no—
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—202no—
181C2×Q8—202no—
182C2×Q8—202no—
183C22×C4—102no—
184C22×C4—102no—
185C22×C4#68511yescharacteristic
186C22×C4#68511yescharacteristic
187C22×C4#68511yescharacteristic
188C22×C4#68511yescharacteristic
189C22×C4C2×C4×D511yescharacteristic
190C22×C4C2×D2011yescharacteristic
191C22×C4C2×C22⋊D511yescharacteristic
192M16—104no—
193M16—202no—
194C2×C8—42no—
195C2×C8—202no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—104no—
200C4⋊C4—202no—
201C4⋊C4—204no—
202C4⋊C4—201no—
203C4⋊C4—201no—
204C4⋊C4—204no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—202no—
212C2×C5—21no—
213C2×C5—21no—
214C2×C5#150711yescharacteristic
215C2×C5#212311yescharacteristic
216C2×C5C2×#35611yescharacteristic
217C23C2×#68511yescharacteristic
218Q8—44no—
219Q8—404no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—104no—
235C2×C4—202no—
236C2×C4—202no—
237C2×C4—202no—
238C2×C4—202no—
239C2×C4—202no—
240C2×C4#393811yescharacteristic
241C2×C4#393811yescharacteristic
242C2×C4#395712yes—
243C2×C4#405412yes—
244C8—82no—
245C8—204no—
246C5#1178211yescharacteristic, complemented, Sylow
247C22—21no—
248C22—21no—
249C22C2×#393811yescharacteristic
250C22#6542011yescharacteristic
251C22C2×#395711yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—204no—
260C4—402no—
261C4#6469812yes—
262C2—21no—
263C2—21no—
264C2#1060077011yescharacteristic
265C2#1060085111yescharacteristic
266C2C2×#6469811yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1467C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1467D5
hypocenterC5#11782
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
246. C5#11782semidirect

Maximal subgroups

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

subgroupindex
#106142062
C5×#14672
C4×#39682
#105979492
#117825