Finite Group Databasebeta

← #13104923

Subgroups — #13104923

Order 1600.

456 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q8×C5⋊D5C211yesmaximal, characteristic
2#11717451C211yesmaximal, characteristic
3#11717448C211yesmaximal, characteristic
4#11716902C214yesmaximal, complemented
5C2×C52×Q8C411yescharacteristic, complemented
6Q8×C5⋊D5—21no—
7Q8×C5⋊D5—21no—
8Q8×C5⋊D5C412yescomplemented
9Q8×C5⋊D5C2212yes—
10C2×C4×C5⋊D5—21no—
11C2×C4×C5⋊D5C2211yescharacteristic
12C2×#6045—21no—
13C2×#6045C411yescharacteristic, complemented
14C22⋊#1044—21no—
15#87867—21no—
16C4⋊#1044C2212yes—
17C4×#1044—21no—
18#87863—21no—
19#87862C2212yes—
20#65782—52nomaximal
21C22×C5⋊D5D411yescharacteristic
22C2×#1044—22no—
23C52×Q8—21no—
24C52×Q8C2×C412yes—
25C2×C4×C52—21no—
26C2×C4×C52C2×C411yescharacteristic
27C2×#1039—21no—
28C2×#1039D411yescharacteristic
29C4×C5⋊D5—22no—
30C4×C5⋊D5—22no—
31C4×C5⋊D5C2×C411yescharacteristic
32C4×C5⋊D5D411yescharacteristic
33C4×C5⋊D5D411yescharacteristic
34C4×C5⋊D5C2311yescharacteristic
35#6045—21no—
36#6045—22no—
37#6045—22no—
38#6045C2×C412yes—
39#6034—22no—
40C2×Q8×D5—52no—
41C2×Q8×D5—102no—
42#4130—52no—
43D5⋊M16—52no—
44#4009—58no—
45C22×C52C22⋊C411yescharacteristic
46C2×C5⋊D5—22no—
47C2×C5⋊D5C22⋊C411yescharacteristic
48C2×C5⋊D5C2×D411yescharacteristic
49#1044—42no—
50C4×C52—22no—
51C4×C52C22⋊C411yescharacteristic
52C4×C52C22×C411yescharacteristic
53#1039—22no—
54#1039C22⋊C411yescharacteristic
55#1039C2×D411yescharacteristic
56C2×C5×Q8—22no—
57C2×C5×Q8AGL(1,𝔽5)12yescomplemented
58Q8×D5—54no—
59Q8×D5—54no—
60Q8×D5—104no—
61Q8×D5—104no—
62Q8×D5—102no—
63Q8×D5—102no—
64Q8×D5—104no—
65Q8×D5—104no—
66C2×C4×D5—52no—
67C2×C4×D5—102no—
68C2×C4×D5—102no—
69C2×C4×D5—104no—
70C2×Dic10—52no—
71C2×Dic10—102no—
72C2×Dic10—102no—
73C2×Dic10—104no—
74C22⋊AGL(1,𝔽5)—102no—
75#704—102no—
76C4⋊AGL(1,𝔽5)—54no—
77C4×AGL(1,𝔽5)—102no—
78#700—102no—
79D5⋊C8—54no—
80#419—251noSylow
81C2×C52—21no—
82C2×C52C2×C22⋊C411yescharacteristic
83C5⋊D5—21no—
84C5⋊D5#13712yes—
85C22×D5—52no—
86C22×D5—102no—
87C2×AGL(1,𝔽5)—104no—
88C5×Q8—24no—
89C5×Q8—22no—
90C5×Q8—24no—
91C5×Q8C2×AGL(1,𝔽5)14yes—
92C2×C4×C5—24no—
93C2×C4×C5—22no—
94C2×C4×C5—22no—
95C2×C4×C5C2×AGL(1,𝔽5)12yes—
96C2×Dic5—52no—
97C2×Dic5—102no—
98C2×Dic5—104no—
99C2×Dic5—102no—
100C4×D5—52no—
101C4×D5—52no—
102C4×D5—52no—
103C4×D5—52no—
104C4×D5—102no—
105C4×D5—102no—
106C4×D5—102no—
107C4×D5—102no—
108C4×D5—104no—
109C4×D5—104no—
110C4×D5—108no—
111C4×D5—108no—
112Dic10—54no—
113Dic10—104no—
114Dic10—104no—
115Dic10—104no—
116Dic10—108no—
117Dic10—108no—
118Dic10—104no—
119Dic10—102no—
120#170—104no—
121C22×Q8—251no—
122C2×M16—251no—
123#117—251no—
124#103—254no—
125C52#41911yescharacteristic, complemented, Sylow
126C22×C5—22no—
127C22×C5C22⋊AGL(1,𝔽5)12yes—
128C2×D5—52no—
129C2×D5—52no—
130C2×D5—102no—
131C2×D5—102no—
132C2×D5—104no—
133C2×D5—108no—
134AGL(1,𝔽5)—204no—
135C4×C5—28no—
136C4×C5—24no—
137C4×C5—22no—
138C4×C5—22no—
139C4×C5C22⋊AGL(1,𝔽5)12yes—
140C4×C5C22×AGL(1,𝔽5)12yes—
141Dic5—52no—
142Dic5—52no—
143Dic5—102no—
144Dic5—102no—
145Dic5—108no—
146Dic5—104no—
147C2×Q8—252no—
148C2×Q8—252no—
149C2×Q8—251no—
150C2×Q8—501no—
151C2×Q8—501no—
152C2×Q8—501no—
153C2×Q8#104411yescharacteristic, complemented
154C22×C4—251no—
155C22×C4—501no—
156M16—501no—
157M16—501no—
158C2×C8—252no—
159C4⋊C4—252no—
160C22⋊C4—501no—
161C42—501no—
162C2×C5—24no—
163C2×C5—22no—
164C2×C5—22no—
165C2×C5C2×C22⋊AGL(1,𝔽5)12yes—
166D5—54no—
167D5—104no—
168D5—104no—
169D5—102no—
170C23—251no—
171Q8—21no—
172Q8—252no—
173Q8—502no—
174Q8—502no—
175Q8—501no—
176Q8C2×#104412yes—
177C2×C4—21no—
178C2×C4—251no—
179C2×C4—251no—
180C2×C4—251no—
181C2×C4—251no—
182C2×C4—251no—
183C2×C4—502no—
184C2×C4—502no—
185C2×C4—501no—
186C2×C4—502no—
187C2×C4C2×#104411yescharacteristic
188C8—502no—
189C5—22no—
190C5#6578212yescomplemented
191C22—251no—
192C22—251no—
193C22—502no—
194C22C22⋊#104411yescharacteristic
195C4—22no—
196C4—251no—
197C4—251no—
198C4—502no—
199C4—1002no—
200C4C22⋊#104411yescharacteristic
201C4C22×#104411yescharacteristic
202C2—21no—
203C2—252no—
204C2—501no—
205C2C2×C22⋊#104411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#1044
commutatorC4×C52C22×C4
FrattiniC4C22×#1044
FittingC2×C52×Q8C4
socleC2×C52C2×C22⋊C4
prime radicalC22×C5⋊D5D4
cosocleC4×C5⋊D5C23
hypercenterC2×Q8#1044
hypocenterC52#419
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. #11716902C2semidirect
5. C2×C52×Q8C4semidirect
8. Q8×C5⋊D5C4semidirect
13. C2×#6045C4semidirect
57. C2×C5×Q8AGL(1,𝔽5)semidirect
125. C52#419semidirect
153. C2×Q8#1044semidirect
190. C5#65782semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C5⋊D52
#117174512
#117174482
#117169022
#657825