Finite Group Databasebeta

← #13014312

Subgroups — #13014312

Order 1280.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#10600383C211yesmaximal, characteristic
2#10598694C211yesmaximal, characteristic
3#10598687C211yesmaximal, characteristic
4C2×#4005—21no—
5C5×#384C411yescharacteristic
6C2×#3942—21no—
7C2×#3939—21no—
8#65218C2211yescharacteristic
9#64913—21no—
10#64744C411yescharacteristic
11#7436—51nomaximal, Sylow
12C22×Dic10D411yescharacteristic
13C2×#704—41no—
14C2×C5×C4⋊C4—21no—
15C2×C5×C4⋊C4—41no—
16C2×C42×C5C2×C411yescharacteristic
17C2×C4⋊Dic5D411yescharacteristic
18C22×#168—21no—
19C22⋊#170—41no—
20#4005—22no—
21#4005—41no—
22#3963—41no—
23#3942—42no—
24#3939—42no—
25#2095—51no—
26#1394—51no—
27#1319—51no—
28C22×C4×C5—21no—
29C22×C4×C5—41no—
30C22×C4×C5C22⋊C411yescharacteristic
31C22×Dic5—21no—
32C22×Dic5—21no—
33C2×Dic10—21no—
34C2×Dic10—41no—
35C2×Dic10—41no—
36C2×Dic10SD1611yescharacteristic
37C2×Dic10Q1611yescharacteristic
38#704—42no—
39#704—81no—
40C2×#170—81no—
41C2×#170—81no—
42C5×C4⋊C4—41no—
43C5×C4⋊C4—41no—
44C5×C4⋊C4—82no—
45C42×C5—41no—
46C4⋊Dic5—41no—
47C2×#168—22no—
48C2×#168—41no—
49C2×#168—41no—
50C2×#107—101no—
51C2×#103—101no—
52C2×#101—101no—
53#391—51no—
54#384AGL(1,𝔽5)11yescharacteristic
55#336—51no—
56#324—101no—
57C23×C5#9911yescharacteristic
58C2×C4×C5—21no—
59C2×C4×C5—21no—
60C2×C4×C5—22no—
61C2×C4×C5—41no—
62C2×C4×C5—41no—
63C2×C4×C5—82no—
64C2×C4×C5—81no—
65C2×C4×C5#10311yescharacteristic
66C2×C4×C5#10411yescharacteristic
67C2×Dic5—21no—
68C2×Dic5—21no—
69C2×Dic5—41no—
70C2×Dic5—41no—
71C2×Dic5—41no—
72C2×Dic5—81no—
73Dic10—41no—
74Dic10—41no—
75Dic10—81no—
76#170—82no—
77#170—161no—
78#168—42no—
79C22×Q8—51no—
80C2×M16—201no—
81C22×C8—101no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—51no—
85C2×C42C2×AGL(1,𝔽5)11yescharacteristic
86#107—202no—
87#103—202no—
88#101—102no—
89#101—201no—
90C22⋊C8—201no—
91#95—201no—
92C22×C5—21no—
93C22×C5—21no—
94C22×C5#32811yescharacteristic
95C22×C5#35211yescharacteristic
96C22×C5#35311yescharacteristic
97C4×C5—21no—
98C4×C5—21no—
99C4×C5—42no—
100C4×C5—161no—
101Dic5—41no—
102Dic5—41no—
103Dic5—81no—
104C2×Q8—51no—
105C2×Q8—51no—
106C2×Q8—101no—
107C2×Q8—201no—
108C2×Q8—201no—
109C22×C4—21no—
110C22×C4—41no—
111C22×C4—101no—
112C22×C4—101no—
113C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
114M16—202no—
115M16—401no—
116C2×C8—102no—
117C2×C8—201no—
118C2×C8—201no—
119C2×C8—401no—
120C2×C8—401no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—82no—
124C4⋊C4—201no—
125C42—41no—
126C2×C5—21no—
127C2×C5—21no—
128C2×C5#135211yescharacteristic
129C2×C5#140611yescharacteristic
130C2×C5#141111yescharacteristic
131C23#401111yescharacteristic
132Q8—201no—
133Q8—201no—
134Q8—401no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—82no—
141C2×C4—81no—
142C2×C4—101no—
143C2×C4—101no—
144C2×C4—201no—
145C2×C4—201no—
146C2×C4—201no—
147C2×C4—401no—
148C2×C4#400911yescharacteristic
149C2×C4#401011yescharacteristic
150C8—202no—
151C8—402no—
152C8—801no—
153C5#743611yescharacteristic, complemented, Sylow
154C22—21no—
155C22—21no—
156C22#6491611yescharacteristic
157C22#6492211yescharacteristic
158C22#6492611yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—161no—
163C4—201no—
164C4—201no—
165C4—401no—
166C2—21no—
167C2—21no—
168C2#1059871711yescharacteristic
169C2#1059874811yescharacteristic
170C2#1059875511yescharacteristic
subgroupG/H
centerC22#64922
commutatorC2×C42×C5C2×C4
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC5×#384C4
socleC22×C5#353
prime radicalC23×C5#99
cosocle#65218C22
hypercenter#384AGL(1,𝔽5)
hypocenterC5#7436
LCSG ▷ C2×C42×C5 ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
153. C5#7436semidirect

Maximal subgroups

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

subgroupindex
#106003832
#105986942
#105986872
#74365