Finite Group Databasebeta

← #13100147

Subgroups — #13100147

Order 1600.

203 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 203 conjugacy classes of subgroups — too many to draw. Only its 61 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#11717425C211yesmaximal, characteristic
2D5⋊#681C211yesmaximal, characteristic
3C5×#4018C211yesmaximal, characteristic
4C2×C4×C5×D5C2211yescharacteristic
5C22⋊#1042—21no—
6#87853—21no—
7C4⋊#1042—21no—
8C4×#1042C412yescomplemented
9#87849—21no—
10D5⋊#168C412yescomplemented
11C42×C52C411yescharacteristic, complemented
12C5×#685—21no—
13C5×#683—21no—
14C4×C5×Dic5C411yescharacteristic, complemented
15#64863—51nomaximal
16#64751—51nomaximal
17C22×C5×D5D411yescharacteristic
18C2×#1042—22no—
19C2×C4×C52—21no—
20C2×C4×C52C2×C411yescharacteristic
21C2×C5×Dic5—21no—
22C2×C5×Dic5D411yescharacteristic
23C4×C5×D5C2×C411yescharacteristic
24C4×C5×D5C2×C411yescharacteristic
25C4×C5×D5D411yescharacteristic
26C4×C5×D5Q811yescharacteristic
27#6032—22no—
28#4130—51no—
29D5⋊M16—51no—
30C5×#117—51no—
31#4072—51no—
32C2×#681—51no—
33#4018D511yescharacteristic
34C22×C52C22⋊C411yescharacteristic
35C2×C5×D5—41no—
36C2×C5×D5C22⋊C411yescharacteristic
37C2×C5×D5C4⋊C411yescharacteristic
38#1042—42no—
39C4×C52—41no—
40C4×C52C4211yescharacteristic
41C4×C52C4⋊C411yescharacteristic
42C5×Dic5—41no—
43C5×Dic5C22⋊C411yescharacteristic
44C5×Dic5C4⋊C411yescharacteristic
45C22×C4×C5—51no—
46C2×C4×D5C2×D511yescharacteristic
47C22⋊AGL(1,𝔽5)—101no—
48#704—101no—
49C4⋊AGL(1,𝔽5)—101no—
50C4×AGL(1,𝔽5)—52no—
51#700—101no—
52D5⋊C8—52no—
53C5×C4⋊C4—101no—
54C5×C22⋊C4—101no—
55C42×C5—41no—
56C42×C5—51no—
57C42×C5Dic511yescharacteristic, complemented
58C42×C5AGL(1,𝔽5)11yescharacteristic, complemented
59C22⋊Dic5—101no—
60#685—21no—
61C4⋊Dic5—101no—
62#683—21no—
63C4×Dic5—52no—
64C4×Dic5Dic511yescharacteristic, complemented
65#681—101no—
66#681—101no—
67C2×#168—52no—
68H(3,ℤ/4)—251noSylow
69C2×C52—21no—
70C2×C52#9511yescharacteristic
71C5×D5—21no—
72C5×D5—21no—
73C23×C5—51no—
74C22×D5C22⋊D511yescharacteristic
75C2×AGL(1,𝔽5)—102no—
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—42no—
79C2×C4×C5—41no—
80C2×C4×C5—51no—
81C2×C4×C5—51no—
82C2×C4×C5—51no—
83C2×C4×C5—51no—
84C2×C4×C5—51no—
85C2×C4×C5—101no—
86C2×C4×C5C2×Dic511yescharacteristic
87C2×C4×C5C2×AGL(1,𝔽5)11yescharacteristic
88C2×Dic5—21no—
89C2×Dic5—102no—
90C2×Dic5C22⋊D511yescharacteristic
91C4×D5Dic1011yescharacteristic
92C4×D5C4×D511yescharacteristic
93C4×D5C4×D511yescharacteristic
94C4×D5D2011yescharacteristic
95#170—102no—
96#168—102no—
97C2×M16—251no—
98#117—51no—
99#117—251no—
100C52H(3,ℤ/4)11yescharacteristic, complemented, Sylow
101C22×C5—41no—
102C22×C5—51no—
103C22×C5—51no—
104C22×C5—201no—
105C22×C5C22⋊Dic511yescharacteristic
106C22×C5C22⋊AGL(1,𝔽5)11yescharacteristic
107C2×D5—41no—
108C2×D5#68311yescharacteristic
109C2×D5#68511yescharacteristic
110AGL(1,𝔽5)—202no—
111C4×C5—41no—
112C4×C5—41no—
113C4×C5—44no—
114C4×C5—41no—
115C4×C5—41no—
116C4×C5—51no—
117C4×C5—51no—
118C4×C5—201no—
119C4×C5C4×Dic511yescharacteristic
120C4×C5C4⋊Dic511yescharacteristic
121C4×C5C4×AGL(1,𝔽5)11yescharacteristic
122C4×C5C4⋊AGL(1,𝔽5)11yescharacteristic
123Dic5—41no—
124Dic5—202no—
125Dic5#68311yescharacteristic
126Dic5#68511yescharacteristic
127C22×C4—51no—
128M16—501no—
129M16—501no—
130C2×C8—252no—
131C4⋊C4—101no—
132C4⋊C4—501no—
133C22⋊C4—101no—
134C22⋊C4—501no—
135C42—51no—
136C42—252no—
137C42#104211yescharacteristic, complemented
138C2×C5—21no—
139C2×C5—21no—
140C2×C5—42no—
141C2×C5—41no—
142C2×C5—101no—
143C2×C5—101no—
144C2×C5#396311yescharacteristic
145C2×C5(C2×AGL(1,𝔽5))⋊C411yescharacteristic
146D5—21no—
147D5—21no—
148C23—51no—
149C2×C4—21no—
150C2×C4—51no—
151C2×C4—51no—
152C2×C4—51no—
153C2×C4—51no—
154C2×C4—51no—
155C2×C4—101no—
156C2×C4—502no—
157C2×C4C2×#104211yescharacteristic
158C8—502no—
159C5—41no—
160C5#6475111yescharacteristic, complemented
161C5#6486311yescharacteristic, complemented
162C22—51no—
163C22—51no—
164C22—201no—
165C22C22⋊#104211yescharacteristic
166C4—41no—
167C4—51no—
168C4—51no—
169C4—201no—
170C4—1002no—
171C4C4×#104211yescharacteristic
172C4C4⋊#104211yescharacteristic
173C2—21no—
174C2—101no—
175C2—101no—
176C2#1171684911yescharacteristic
subgroupG/H
centerC4C4×#1042
commutatorC4×C52C42
FrattiniC2×C4C2×#1042
FittingC42×C52C4
socleC2×C52#95
prime radicalC22×C5×D5D4
cosocleC2×C4×C5×D5C22
hypercenterC42#1042
hypocenterC52H(3,ℤ/4)
LCSG ▷ C4×C52 ▷ C52
UCSC1 ◁ C4 ◁ C42

Complements

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

NH ≅ G/Ntype
8. C4×#1042C4semidirect
10. D5⋊#168C4semidirect
11. C42×C52C4semidirect
14. C4×C5×Dic5C4semidirect
57. C42×C5Dic5semidirect
58. C42×C5AGL(1,𝔽5)semidirect
64. C4×Dic5Dic5semidirect
100. C52H(3,ℤ/4)semidirect
137. C42#1042semidirect
160. C5#64751semidirect
161. C5#64863semidirect

Maximal subgroups

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

subgroupindex
#117174252
D5⋊#6812
C5×#40182
#648635
#647515