Finite Group Databasebeta

← #12010467

Subgroups — #12010467

Order 1280.

388 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C5×#2567C211yesmaximal, characteristic
2#10602430C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10598139C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×Q8C2211yescharacteristic
7C5×#395C412yes—
8C5×#395C2212yes—
9C5×#391—21no—
10C5×#389—21no—
11C5×#389—21no—
12C5×#384—21no—
13C4×C5×C4⋊C4C411yescharacteristic
14C2×#3968—21no—
15#65214—21no—
16#65213—21no—
17#64750C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11908—51nomaximal, Sylow
21C22×C5×Q8C2×C412yes—
22C22×C5×Q8D411yescharacteristic
23C5×C4⋊Q8—41no—
24C5×C4⋊Q8—41no—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4C2311yescharacteristic
35C2×C42×C5—21no—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5D411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×#681—22no—
40C5×#95—22no—
41C5×#95—22no—
42C5×#95C2×C412yes—
43#3968—42no—
44C22⋊#168—22no—
45C4⋊#168—41no—
46C4⋊#168—41no—
47C4⋊#168—41no—
48C4×#168—41no—
49#2567D511yescharacteristic
50#1801—51no—
51#1461—51no—
52#1354—54no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8—42no—
56C2×C5×Q8—82no—
57C2×C5×Q8SD1612yes—
58C2×C5×Q8Q1612yes—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C5×C4⋊C4—24no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—82no—
76C5×C4⋊C4—82no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—42no—
84#681—42no—
85#681—42no—
86C2×#168—42no—
87C2×#168—42no—
88C2×C4⋊Q8Dic511yescharacteristic
89C2×C4×Q8C2×D511yescharacteristic
90#431—101no—
91#423—101no—
92C2×#101—101no—
93#395Dic512yes—
94#395C2×D512yes—
95#391—21no—
96#389—21no—
97#389—21no—
98#384—21no—
99C4×C4⋊C4Dic511yescharacteristic
100#343—52no—
101#324—52no—
102#324—101no—
103C23×C5C2×C22⋊C411yescharacteristic
104C5×Q8—42no—
105C5×Q8—42no—
106C5×Q8—84no—
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—22no—
114C2×C4×C5—24no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5#9911yescharacteristic
127C2×C4×C5#9911yescharacteristic
128C2×C4×C5#10312yes—
129C2×C4×C5#10312yes—
130C2×C4×C5C2×SD1611yescharacteristic
131C2×C4×C5C2×Q1611yescharacteristic
132#168—82no—
133#168—82no—
134C22×Q8C2×Dic512yes—
135C22×Q8C22⋊D511yescharacteristic
136C2×M16—102no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C2×Dic511yescharacteristic
147C2×C4⋊C4C22⋊D511yescharacteristic
148C2×C4⋊C4C22×D511yescharacteristic
149C2×C42—21no—
150C2×C42C2×Dic511yescharacteristic
151C2×C42C22⋊D511yescharacteristic
152C2×C42C22⋊D511yescharacteristic
153C4⋊C8—201no—
154C4⋊C8—201no—
155C4⋊C8—201no—
156#101—202no—
157C22⋊C8—102no—
158C4×C8—201no—
159#95—22no—
160#95—22no—
161#95C2×Dic512yes—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5C2×#9911yescharacteristic
165C22×C5C2×#10311yescharacteristic
166C22×C5#42111yescharacteristic
167C4×C5—21no—
168C4×C5—21no—
169C4×C5—22no—
170C4×C5—22no—
171C4×C5—21no—
172C4×C5—44no—
173C4×C5—41no—
174C4×C5—41no—
175C4×C5—41no—
176C4×C5—82no—
177C4×C5#35612yes—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8—82no—
182C2×Q8#68812yes—
183C2×Q8#68912yes—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic511yescharacteristic
187C22×C4C22⋊Dic511yescharacteristic
188C22×C4C22⋊Dic511yescharacteristic
189C22×C4C22⋊Dic511yescharacteristic
190C22×C4C22×Dic511yescharacteristic
191C22×C4C2×C22⋊D511yescharacteristic
192C22×C4C2×C22⋊D511yescharacteristic
193M16—202no—
194M16—202no—
195C2×C8—202no—
196C2×C8—202no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—42no—
213C2×C5—21no—
214C2×C5—21no—
215C2×C5#152011yescharacteristic
216C2×C5#212211yescharacteristic
217C2×C5C2×#35611yescharacteristic
218C23C2×C22⋊Dic511yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—84no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#396611yescharacteristic
242C2×C4#396611yescharacteristic
243C2×C4#396712yes—
244C2×C4#396712yes—
245C2×C4C2×#68811yescharacteristic
246C2×C4C2×#68911yescharacteristic
247C8—402no—
248C8—402no—
249C5#1190811yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22C2×#396611yescharacteristic
253C22C2×#396711yescharacteristic
254C22#6552511yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#6476812yes—
266C2—21no—
267C2—21no—
268C2#1060248311yescharacteristic
269C2C2×#6476811yescharacteristic
270C2#1060265211yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2567C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2567D5
hypocenterC5#11908
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
249. C5#11908semidirect

Maximal subgroups

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

subgroupindex
C5×#25672
#106024302
#106024172
#105981392
#119085