Finite Group Databasebeta

← #13014773

Subgroups — #13014773

Order 1280.

608 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 110 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#10606050C211yesmaximal, characteristic
2#10604188C212yesmaximal, complemented
3#10598712C214yesmaximal, complemented
4C2×#4039—22no—
5C2×#4039C412yes—
6C2×#4020C411yescharacteristic
7C5×#384C411yescharacteristic
8#65277—22no—
9#65277C2212yes—
10C42×Dic5C2211yescharacteristic
11#64918—22no—
12#64918—22no—
13#64918C2214yes—
14#7603—51nomaximal, Sylow
15C22×D20—22no—
16C22×D20C2×C412yes—
17C22×C4×D5—22no—
18C22×#170—24no—
19C2×C5×C4⋊C4—22no—
20C2×C5×C4⋊C4C2×C412yes—
21C2×C42×C5C2×C411yescharacteristic
22C2×#685—22no—
23C2×#685—24no—
24C2×C4×Dic5C2×C411yescharacteristic
25C2×C4×Dic5D412yes—
26C2×C4×Dic5D412yes—
27C2×C4×Dic5C2311yescharacteristic
28#4039—48no—
29#4039—44no—
30#4020—22no—
31#4020C814yescomplemented
32C4×#127—51no—
33#1839—52no—
34#1270—54no—
35C23×D5—22no—
36C22×C4×C5—22no—
37C22×C4×C5C22⋊C412yes—
38C22×C4×C5C22×C411yescharacteristic
39C22×Dic5C22⋊C411yescharacteristic
40C22×Dic5C22⋊C411yescharacteristic
41C22×Dic5C2×D412yes—
42C2×D20—28no—
43C2×D20—22no—
44C2×D20—42no—
45C2×D20—42no—
46C2×D20—44no—
47C2×D20—44no—
48C2×D20C2×C814yes—
49C2×C4×D5—48no—
50C2×C4×D5—44no—
51C2×#170—44no—
52C2×#170—44no—
53C2×#170—44no—
54C5×C4⋊C4—42no—
55C5×C4⋊C4—44no—
56C42×C5C2×C812yes—
57C42×C5M1612yes—
58#685—44no—
59#685—48no—
60C4×Dic5—22no—
61C4×Dic5—24no—
62C4×Dic5—42no—
63C4×Dic5—41no—
64C2×#127—51no—
65C2×C4×D4—52no—
66C2×C4×D4—102no—
67#390—52no—
68#390—102no—
69#384AGL(1,𝔽5)11yescharacteristic
70C43—51no—
71#336—54no—
72#336—102no—
73#336—102no—
74C23×C5C2×C22⋊C411yescharacteristic
75C22×D5—24no—
76C22×D5—42no—
77C22×D5—42no—
78C22×D5—44no—
79C22×D5—44no—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—42no—
85C2×C4×C5—44no—
86C2×C4×C5C22⋊C814yes—
87C2×C4×C5C22×C811yescharacteristic
88C2×C4×C5C2×M1611yescharacteristic
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—21no—
93C2×Dic5—22no—
94C2×Dic5#10012yes—
95C2×Dic5AGL(1,ℤ/8)14yes—
96D20—44no—
97D20—44no—
98D20—416no—
99C4×D5—88no—
100#170—84no—
101C22×D4—52no—
102C22×D4—102no—
103C23×C4—102no—
104C22×C8—104no—
105#127—54no—
106#127—102no—
107C4×D4—208no—
108C4×D4—204no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
111C2×C22⋊C4—102no—
112C2×C22⋊C4—104no—
113C2×C42—52no—
114C2×C42—51no—
115C2×C42—52no—
116C2×C42—51no—
117C2×C42C2×AGL(1,𝔽5)11yescharacteristic
118C22×C5C2×C22⋊C811yescharacteristic
119C22×C5#41011yescharacteristic
120C22×C5C2×#10011yescharacteristic
121C22×C5#41812yes—
122C22×C5#42112yes—
123C2×D5—44no—
124C2×D5—48no—
125C2×D5—82no—
126C2×D5—82no—
127C2×D5—84no—
128C4×C5—21no—
129C4×C5—21no—
130C4×C5—24no—
131C4×C5—82no—
132Dic5—22no—
133Dic5—24no—
134Dic5—41no—
135C24—102no—
136C2×D4—54no—
137C2×D4—102no—
138C2×D4—108no—
139C2×D4—202no—
140C2×D4—202no—
141C2×D4—204no—
142C2×D4—204no—
143C22×C4—22no—
144C22×C4—52no—
145C22×C4—51no—
146C22×C4—51no—
147C22×C4—204no—
148C22×C4—208no—
149C22×C4C22⋊AGL(1,𝔽5)12yes—
150C22×C4C22×AGL(1,𝔽5)11yescharacteristic
151C2×C8—204no—
152C2×C8—204no—
153C2×C8—204no—
154C4⋊C4—42no—
155C4⋊C4—44no—
156C22⋊C4—208no—
157C22⋊C4—204no—
158C42—104no—
159C42—102no—
160C42—202no—
161C42—201no—
162C42D5⋊C812yes—
163C42#70012yes—
164C2×C5#146011yescharacteristic
165C2×C5#147812yes—
166C2×C5#151412yes—
167C2×C5#153611yescharacteristic
168C2×C5#155511yescharacteristic
169D5—84no—
170C23—104no—
171C23—204no—
172C23—202no—
173C23—204no—
174C23—202no—
175C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
176D4—204no—
177D4—204no—
178D4—2016no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—54no—
186C2×C4—52no—
187C2×C4—102no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—101no—
191C2×C4—102no—
192C2×C4—408no—
193C2×C4#400314yes—
194C2×C4C2×D5⋊C811yescharacteristic
195C2×C4C2×#70011yescharacteristic
196C8—404no—
197C5#760311yescharacteristic, complemented, Sylow
198C22—204no—
199C22—208no—
200C22—402no—
201C22—404no—
202C22—402no—
203C22C2×#400311yescharacteristic
204C22#6576712yes—
205C22D5⋊#10011yescharacteristic
206C22#6578412yes—
207C22#6578511yescharacteristic
208C4—21no—
209C4—21no—
210C4—24no—
211C4—82no—
212C4—102no—
213C4—104no—
214C4—201no—
215C2—404no—
216C2#1060427012yes—
217C2#1060429011yescharacteristic
218C2#1060461011yescharacteristic
219C2#1060462712yes—
220C2#1060463811yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#384C4
socleC23×C5C2×C22⋊C4
prime radicalC2×#4020C4
cosocleC2×C4×Dic5C23
hypercenter#384AGL(1,𝔽5)
hypocenterC5#7603
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #10604188C2semidirect
3. #10598712C2semidirect
31. #4020C8semidirect
197. C5#7603semidirect

Maximal subgroups

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

subgroupindex
#106060502
#106041882
#105987122
#76035