Finite Group Databasebeta

← #11992245

Subgroups — #11992245

Order 1280.

450 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#65123C211yesmaximal, characteristic
2#10601620C212yesmaximal
3#10601587C212yesmaximal, complemented
4C5×#1290C211yesmaximal, characteristic, complemented
5#10598199C211yesmaximal, characteristic, complemented
6C22×C8×D5C412yes—
7C2×C4×D20C2211yescharacteristic
8C5×#432C2212yes—
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×#3952C412yes—
11#65215C2212yes—
12C2×C4×#168C2211yescharacteristic
13#65123—22no—
14#65123—22no—
15#64700—22no—
16#64699—22no—
17#64688—24no—
18#8620—51nomaximal, Sylow
19C22×D20Q811yescharacteristic
20C22×C4×D5C2×C412yes—
21C22×C5×C8C2×C412yes—
22C2×C42×C5C2311yescharacteristic
23C2×#685D412yes—
24C2×C4⋊Dic5Q811yescharacteristic
25C22×#168C2×C411yescharacteristic
26C22×#168C2×C411yescharacteristic
27C2×C8×D5—22no—
28C2×C8×D5—22no—
29C2×C8×D5—44no—
30C4×D20—22no—
31C4×D20—22no—
32C5×C4⋊C8—22no—
33C5×C4⋊C8—22no—
34C5×C22⋊C8—22no—
35C5×#97—22no—
36C22⋊#168—22no—
37#3952—24no—
38C4⋊#168—22no—
39#3935—22no—
40C4×#168D412yes—
41C4×#168D412yes—
42C2×C8×D4—51no—
43#1568—52no—
44#1466—52no—
45#1290—51no—
46#1290D511yescharacteristic, complemented
47C23×D5C4⋊C412yes—
48C22×C4×C5C22×C411yescharacteristic
49C22×C4×C5C2×D411yescharacteristic
50C22×C4×C5C2×Q811yescharacteristic
51C22×Dic5C4⋊C412yes—
52C2×D20—24no—
53C2×D20—22no—
54C2×C4×D5—22no—
55C2×C4×D5—22no—
56C2×C4×D5—42no—
57C2×C4×D5—42no—
58C2×C5×C8—22no—
59C2×C5×C8—42no—
60C2×C5×C8—42no—
61C42×C5C2×D412yes—
62C42×C5#4112yes—
63#685—24no—
64C4⋊Dic5—22no—
65C2×#168—22no—
66C2×#168—41no—
67C2×#168—42no—
68C2×#168C22⋊C412yes—
69C2×#168C22⋊C411yescharacteristic
70C2×#168C22⋊C411yescharacteristic
71C8×D5—44no—
72C8×D5—44no—
73C23×C8—52no—
74C2×C4×D4—51no—
75C8×D4—102no—
76C8×D4—102no—
77#432—52no—
78#432C2×D512yes—
79C2×C4⋊C8C2×D511yescharacteristic
80C2×C22⋊C8—52no—
81C2×C4×C8—51no—
82#335—102no—
83#334—102no—
84#323—104no—
85C23×C5C2×C4⋊C411yescharacteristic
86C22×D5—22no—
87C22×D5—22no—
88C22×D5—42no—
89C22×D5—42no—
90C22×D5#10814yes—
91C2×C4×C5—22no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—41no—
95C2×C4×C5C2×C22⋊C411yescharacteristic
96C2×C4×C5#11711yescharacteristic
97C2×C4×C5#12112yes—
98C2×C4×C5C22⋊Q812yes—
99C2×Dic5—22no—
100C2×Dic5—42no—
101D20—28no—
102C4×D5—44no—
103C4×D5—42no—
104C4×D5—42no—
105C5×C8—42no—
106C5×C8—82no—
107#168—21no—
108#168—22no—
109#168—82no—
110#168#10012yes—
111C22×D4—51no—
112C23×C4—52no—
113C22×C8—51no—
114C22×C8—51no—
115C22×C8—102no—
116C22×C8—102no—
117C22×C8—204no—
118C22×C8C4×D512yes—
119C4×D4—102no—
120C4×D4—102no—
121C2×C4⋊C4—51no—
122C2×C22⋊C4—52no—
123C2×C42C22×D511yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—22no—
126C4⋊C8—102no—
127C22⋊C8—22no—
128C22⋊C8—104no—
129C22⋊C8—102no—
130#97—22no—
131#97—102no—
132C4×C8—52no—
133C4×C8—52no—
134C22×C5—21no—
135C22×C5—21no—
136C22×C5#38011yescharacteristic
137C22×C5C2×#10812yes—
138C2×D5—24no—
139C2×D5—44no—
140C2×D5—42no—
141C2×D5—42no—
142C2×D5—44no—
143C4×C5—21no—
144C4×C5—22no—
145C4×C5—22no—
146C4×C5C2×#10011yescharacteristic
147C4×C5#41311yescharacteristic
148Dic5—42no—
149C24—52no—
150C2×D4—104no—
151C2×D4—102no—
152C22×C4—52no—
153C22×C4—102no—
154C22×C4—102no—
155C22×C4—202no—
156C22×C4—202no—
157C22×C4C2×C4×D511yescharacteristic
158C22×C4D4×D511yescharacteristic
159C22×C4Q8×D511yescharacteristic
160C2×C8—22no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—51no—
164C2×C8—52no—
165C2×C8—51no—
166C2×C8—102no—
167C2×C8—204no—
168C2×C8—204no—
169C2×C8—201no—
170C2×C8—202no—
171C4⋊C4—102no—
172C22⋊C4—104no—
173C42#70912yes—
174C42D4×D512yes—
175C2×C5—22no—
176C2×C5#180011yescharacteristic
177C2×C5#181011yescharacteristic
178C2×C5#181211yescharacteristic
179D5—44no—
180C23—54no—
181C23—102no—
182C23—102no—
183C23—202no—
184C23—202no—
185C23D5×C4⋊C411yescharacteristic
186D4—108no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—102no—
192C2×C4—204no—
193C2×C4—202no—
194C2×C4—202no—
195C2×C4—202no—
196C2×C4#401811yescharacteristic
197C2×C4D5×C22⋊C411yescharacteristic
198C2×C4#403012yes—
199C2×C4#404212yes—
200C8—42no—
201C8—52no—
202C8—82no—
203C8—101no—
204C8—102no—
205C8—402no—
206C5#862011yescharacteristic, complemented, Sylow
207C22—21no—
208C22—21no—
209C22—104no—
210C22—204no—
211C22—204no—
212C22—202no—
213C22—202no—
214C22#6495611yescharacteristic
215C22D5×#10812yes—
216C4—22no—
217C4—22no—
218C4—21no—
219C4—202no—
220C4D5×#10011yescharacteristic
221C4#6504011yescharacteristic
222C2—22no—
223C2—204no—
224C2#1059950311yescharacteristic
225C2#1059973211yescharacteristic
226C2#1059978711yescharacteristic
subgroupG/H
centerC22#64956
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1290C2
socleC22×C5#380
prime radicalC22×D20Q8
cosocleC2×C42×C5C23
hypercenter#1290D5
hypocenterC5#8620
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
3. #10601587C2semidirect
4. C5×#1290C2semidirect
5. #10598199C2semidirect
46. #1290D5semidirect
206. C5#8620semidirect

Maximal subgroups

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

subgroupindex
C2×#651232
#106016202
#106015872
C5×#12902
#105981992
#86205