Finite Group Databasebeta

← #11996708

Subgroups — #11996708

Order 1280.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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
2#10614167C211yesmaximal, characteristic
3C5×#1801C211yesmaximal, characteristic
4#10601299C212yesmaximal
5#10598206C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090—21no—
8C2×#4015C2211yescharacteristic
9C5×#423C2212yes—
10C2×C5×#101—21no—
11#65313—24no—
12#65272C414yes—
13#65263—21no—
14C4×C4⋊Dic5C2211yescharacteristic
15#65217—22no—
16#65215—22no—
17#65214C2212yes—
18C5×#343—21no—
19#64702—24no—
20#9402—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10—21no—
23C2×C5×M16—22no—
24C4×C5×Q8—22no—
25C4×C5×Q8—22no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C42×C5D412yes—
29C2×C42×C5C2311yescharacteristic
30#4090—44no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C412yes—
34C2×#683—24no—
35C2×C4×Dic5—21no—
36#4015—22no—
37#4015—22no—
38C5×C4⋊C8—22no—
39C5×C4⋊C8—22no—
40C5×#101—42no—
41#3963—24no—
42#3963C2×C412yes—
43C22⋊#168—22no—
44C4⋊#168—24no—
45C4⋊#168D414yes—
46#3935—24no—
47C4×#168—22no—
48#2983—51no—
49#2546—51no—
50#1801D511yescharacteristic
51#1546—52no—
52#1303—52no—
53C2×C5×Q8—22no—
54C2×C5×Q8—21no—
55C2×C5×Q8—22no—
56C2×C5×Q8—21no—
57C22×C4×C5C22⋊C412yes—
58C22×C4×C5C22⋊C412yes—
59C22×C4×C5C22×C411yescharacteristic
60C22×C4×C5C2×D411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×Dic5—22no—
63C22×Dic5—22no—
64C2×Dic10—42no—
65C2×Dic10—41no—
66C2×Dic10—42no—
67C2×Dic10—41no—
68C5×M16—42no—
69C5×M16—42no—
70C2×C5×C8—42no—
71C5×C4⋊C4—24no—
72C5×C4⋊C4—22no—
73C42×C5—22no—
74C42×C5—22no—
75C42×C5C2×D412yes—
76C42×C5#4112yes—
77C4⋊Dic5—24no—
78C4⋊Dic5—24no—
79C4⋊Dic5—41no—
80C4⋊Dic5—41no—
81#683—48no—
82C4×Dic5—42no—
83C2×#168—24no—
84C2×C4⋊Q8—51no—
85C2×C4⋊Q8—101no—
86C2×C4×Q8C2×D511yescharacteristic
87#446—104no—
88#432—102no—
89#431—52no—
90#423C2×D512yes—
91C2×#101—21no—
92#398—54no—
93#391—101no—
94#389—102no—
95C4×C4⋊C4—51no—
96#343—21no—
97#332—104no—
98C23×C5C2×C22⋊C411yescharacteristic
99C5×Q8—42no—
100C5×Q8—42no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—41no—
107C2×C4×C5—42no—
108C2×C4×C5C4×D412yes—
109C2×C4×C5#12011yescharacteristic
110C2×C4×C5#12112yes—
111C2×C4×C5#12311yescharacteristic
112C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C5AGL(1,ℤ/8)12yes—
114C2×C4×C5#13711yescharacteristic
115C2×Dic5—24no—
116C2×Dic5—42no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121Dic10—82no—
122Dic10—82no—
123C5×C8—82no—
124#168—44no—
125C22×Q8—101no—
126C22×Q8C22⋊D511yescharacteristic
127C2×M16—22no—
128C4⋊Q8—102no—
129C4⋊Q8—102no—
130C4⋊Q8—204no—
131C4×Q8—22no—
132C4×Q8—22no—
133C2×C4⋊C4—52no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4—104no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4C4×D512yes—
138C2×C4⋊C4C22⋊D511yescharacteristic
139C2×C42—101no—
140C2×C42D2012yes—
141C2×C42C22×D511yescharacteristic
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—54no—
145C4⋊C8—104no—
146#101—42no—
147C22⋊C8—102no—
148#97—104no—
149C4×C8—102no—
150#95—52no—
151#95—104no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5#38611yescharacteristic
155C22×C5#41711yescharacteristic
156C22×C5#41811yescharacteristic
157C4×C5—21no—
158C4×C5—22no—
159C4×C5—42no—
160C4×C5—42no—
161C4×C5#45612yes—
162C4×C5#46812yes—
163C4×C5#46912yes—
164Dic5—44no—
165Dic5—82no—
166C2×Q8—21no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—22no—
170C2×Q8—201no—
171C2×Q8—202no—
172C2×Q8—201no—
173C2×Q8—202no—
174C22×C4—102no—
175C22×C4—102no—
176C22×C4#68512yes—
177C22×C4#68512yes—
178C22×C4C2×C4×D511yescharacteristic
179C22×C4C2×D2011yescharacteristic
180C22×C4C2×C22⋊D511yescharacteristic
181M16—42no—
182M16—42no—
183C2×C8—42no—
184C2×C8—104no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—104no—
188C4⋊C4—104no—
189C4⋊C4—208no—
190C4⋊C4—201no—
191C4⋊C4—201no—
192C42—22no—
193C42—22no—
194C42—202no—
195C42D4×D512yes—
196C42#71112yes—
197C2×C5—21no—
198C2×C5—21no—
199C2×C5#188611yescharacteristic
200C2×C5#189511yescharacteristic
201C2×C5#191511yescharacteristic
202C23C2×#68511yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—402no—
206Q8—402no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—104no—
215C2×C4—202no—
216C2×C4—202no—
217C2×C4—202no—
218C2×C4—202no—
219C2×C4—202no—
220C2×C4#402712yes—
221C2×C4#402811yescharacteristic
222C2×C4#403211yescharacteristic
223C2×C4#407811yescharacteristic
224C2×C4#408512yes—
225C2×C4#408811yescharacteristic
226C2×C4#409512yes—
227C8—82no—
228C8—204no—
229C5#940211yescharacteristic, complemented, Sylow
230C22—21no—
231C22—21no—
232C22#6524711yescharacteristic
233C22#6525511yescharacteristic
234C22#6529011yescharacteristic
235C4—21no—
236C4—22no—
237C4—42no—
238C4—42no—
239C4—204no—
240C4—402no—
241C4#6504112yes—
242C4#6532812yes—
243C4#6533812yes—
244C2—21no—
245C2—21no—
246C2#1060031011yescharacteristic
247C2#1060089611yescharacteristic
248C2#1060093111yescharacteristic
subgroupG/H
centerC22#65247
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1801C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1801D5
hypocenterC5#9402
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
229. C5#9402semidirect

Maximal subgroups

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

subgroupindex
#106142062
#106141672
C5×#18012
#106012992
#105982062
#94025