Finite Group Databasebeta

← #13100709

Subgroups — #13100709

Order 1600.

216 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C5×#4036C211yesmaximal, characteristic
2#11717036C211yesmaximal, characteristic
3#11716675C211yesmaximal, characteristic
4C5×#3940C211yesmaximal, characteristic
5#11716617C211yesmaximal, characteristic
6#11716616C211yesmaximal, characteristic
7#11716595C211yesmaximal, characteristic
8C2×#6039—21no—
9C52×C4⋊C4C2211yescharacteristic
10C4⋊#1039C2211yescharacteristic
11C2×#6029C2211yescharacteristic
12C5×C4⋊Dic5—21no—
13C5×C4⋊Dic5C2211yescharacteristic
14C5×C4⋊Dic5C2211yescharacteristic
15C5×#683—21no—
16C4×C5×Dic5C2211yescharacteristic
17C2×C5×#168C2211yescharacteristic
18#87780—21no—
19#65354—51nomaximal
20#65145—51nomaximal
21C2×C4×C52—21no—
22C2×C4×C52C2311yescharacteristic
23C2×#1039—21no—
24C2×C5×Dic5—21no—
25C2×C5×Dic5—21no—
26C2×C5×Dic5D411yescharacteristic
27C2×C5×Dic5D411yescharacteristic
28#6039—42no—
29#6029Q812yescomplemented
30C5×#168Q812yescomplemented
31C5×#125—51no—
32#4036D511yescharacteristic
33#4034—51no—
34#4015—51no—
35C5×#106—51no—
36#3950—51no—
37#3947—51no—
38#3940—51no—
39#3940—51no—
40#3940—102no—
41#3940D511yescharacteristic
42#3939—51no—
43#3939—51no—
44#3939—51no—
45#3935—51no—
46C22×C52C2×D411yescharacteristic
47C4×C52—41no—
48C4×C52C2×Q811yescharacteristic
49C4×C52C2×Q811yescharacteristic
50#1039—41no—
51C5×Dic5—21no—
52C5×Dic5—21no—
53C5×Dic5—41no—
54C5×Dic5—41no—
55C2×Dic10—101no—
56C2×Dic10—101no—
57C2×C5×C8—51no—
58C5×C4⋊C4—22no—
59C5×C4⋊C4—51no—
60C5×C4⋊C4—51no—
61C5×C4⋊C4—101no—
62C5×C4⋊C4—101no—
63C5×C4⋊C4C2×D511yescharacteristic
64C5×C4⋊C4C2×D511yescharacteristic
65C42×C5—51no—
66C4⋊Dic5—21no—
67C4⋊Dic5—51no—
68C4⋊Dic5—51no—
69C4⋊Dic5—102no—
70C4⋊Dic5—101no—
71C4⋊Dic5C2×D511yescharacteristic
72C4⋊Dic5C2×D511yescharacteristic
73#683—21no—
74#683—101no—
75C4×Dic5C2×D511yescharacteristic
76C2×#168—51no—
77C2×#168—51no—
78C2×#168—102no—
79C2×#168C2×D511yescharacteristic
80#501—251noSylow
81C2×C52C4⋊Q811yescharacteristic
82C2×C52AGL(1,ℤ/8)11yescharacteristic
83C2×C52#13711yescharacteristic
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—42no—
88C2×C4×C5—51no—
89C2×C4×C5—51no—
90C2×C4×C5—101no—
91C2×C4×C5—101no—
92C2×C4×C5C22×D511yescharacteristic
93C2×C4×C5C22×D511yescharacteristic
94C2×Dic5—21no—
95C2×Dic5—21no—
96C2×Dic5—101no—
97C2×Dic5—101no—
98C2×Dic5—202no—
99C2×Dic5C22⋊D511yescharacteristic
100C2×Dic5C22⋊D511yescharacteristic
101Dic10—202no—
102Dic10—202no—
103C5×C8—52no—
104#168—52no—
105#168—52no—
106#168—104no—
107#168Dic1012yescomplemented
108C4⋊Q8—251no—
109#125—51no—
110#107—251no—
111#107—251no—
112#106—51no—
113#106—251no—
114#97—251no—
115C52#50111yescharacteristic, complemented, Sylow
116C22×C5—22no—
117C22×C5D4×D511yescharacteristic
118C22×C5C2×C22⋊D511yescharacteristic
119C4×C5—22no—
120C4×C5—22no—
121C4×C5—41no—
122C4×C5—41no—
123C4×C5—82no—
124C4×C5—101no—
125C4×C5—101no—
126C4×C5—201no—
127C4×C5—201no—
128C4×C5C2×Dic1011yescharacteristic
129C4×C5Q8×D511yescharacteristic
130C4×C5Q8×D511yescharacteristic
131C4×C5Q8×D511yescharacteristic
132Dic5—21no—
133Dic5—21no—
134Dic5—41no—
135Dic5—41no—
136Dic5—201no—
137Dic5—201no—
138Dic5—402no—
139C2×Q8—501no—
140C2×C8—51no—
141C2×C8—251no—
142C4⋊C4—51no—
143C4⋊C4—51no—
144C4⋊C4—101no—
145C4⋊C4—101no—
146C4⋊C4—251no—
147C4⋊C4—501no—
148C4⋊C4D5211yescharacteristic
149C42—51no—
150C2×C5—22no—
151C2×C5—22no—
152C2×C5—22no—
153C2×C5#403411yescharacteristic
154C2×C5#406011yescharacteristic
155C2×C5#406111yescharacteristic
156C2×C5#409011yescharacteristic
157C2×C5#409511yescharacteristic
158C2×C5#409711yescharacteristic
159Q8—1002no—
160C2×C4—21no—
161C2×C4—51no—
162C2×C4—51no—
163C2×C4—101no—
164C2×C4—101no—
165C2×C4—501no—
166C2×C4C2×D5211yescharacteristic
167C8—52no—
168C8—252no—
169C5—22no—
170C5#6514511yescharacteristic, complemented
171C5#6535411yescharacteristic, complemented
172C22D5×C22⋊D511yescharacteristic
173C4—41no—
174C4—101no—
175C4—101no—
176C4—201no—
177C4—201no—
178C4—1001no—
179C4D5×Dic1011yescharacteristic
180C4#8787211yescharacteristic
181C2#1171695711yescharacteristic
182C2#1171704711yescharacteristic
183C2#1171705711yescharacteristic
subgroupG/H
centerC22D5×C22⋊D5
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC52×C4⋊C4C22
socle, prime radicalC22×C52C2×D4
hypercenterC4⋊C4D52
hypocenterC52#501
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
29. #6029Q8semidirect
30. C5×#168Q8semidirect
107. #168Dic10semidirect
115. C52#501semidirect
170. C5#65145semidirect
171. C5#65354semidirect

Maximal subgroups

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

subgroupindex
C5×#40362
#117170362
#117166752
C5×#39402
#117166172
#117166162
#117165952
#653545
#651455