Finite Group Databasebeta

← #13105525

Subgroups — #13105525

Order 1600.

544 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C4⋊C4×C5⋊D5C211yesmaximal, characteristic
2C5×#4036C212yesmaximal, complemented
3#11717018C212yesmaximal
4#11717018C211yesmaximal, characteristic
5#11717001C212yesmaximal
6C4×#6036C211yesmaximal, characteristic
7#11716988C212yesmaximal, complemented
8#11716965C214yesmaximal, complemented
9C2×C4×C5⋊D5C2212yes—
10C2×C4×C5⋊D5C2211yescharacteristic
11C2×#6036C2211yescharacteristic
12C2×#6036C2211yescharacteristic
13C2×#6036C2212yes—
14C52×C4⋊C4C2211yescharacteristic
15C4⋊#1039C2211yescharacteristic
16#87806C2212yes—
17C5×C4⋊Dic5C2214yes—
18C5×C4⋊Dic5C2212yes—
19C5×#683C2214yes—
20C4×C5×Dic5C2212yes—
21#87781C2212yes—
22#87781C2214yes—
23#87780C2214yes—
24Dic52C2212yes—
25D5×#125—52nomaximal
26C22×C5⋊D5C2311yescharacteristic
27C2×C4×C52C2312yes—
28C2×C4×C52C2311yescharacteristic
29C2×#1039C2312yes—
30C2×#1039C2311yescharacteristic
31C4×C5⋊D5—24no—
32C4×C5⋊D5Q814yes—
33C2×C5×Dic5C2312yes—
34C2×C5×Dic5C2312yes—
35C2×C5×Dic5C2314yes—
36#6036—22no—
37#6036—24no—
38#6036—22no—
39C5×#125—52no—
40D5×C4⋊C4—52no—
41D5×C4⋊C4—54no—
42D5×C4⋊C4—52no—
43D5×C4⋊C4—54no—
44D5×C4⋊C4—102no—
45#4036—52no—
46#4036D512yescomplemented
47#4035—54no—
48#4035—54no—
49C42×D5—52no—
50#4016—52no—
51C22×C52C2411yescharacteristic
52C2×C5⋊D5C2×Q812yes—
53C2×C5⋊D5#4112yes—
54C2×C5⋊D5#4112yes—
55C4×C52—22no—
56C4×C52C2×Q812yes—
57#1039—22no—
58#1039C2×Q812yes—
59C5×Dic5—22no—
60C5×Dic5—24no—
61C5×Dic5—22no—
62C2×C4×D5—52no—
63C2×C4×D5—54no—
64C2×C4×D5—52no—
65C2×C4×D5—52no—
66C2×C4×D5—54no—
67C2×C4×D5—102no—
68C2×C4×D5—104no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—54no—
71C5×C4⋊C4—54no—
72C5×C4⋊C4—52no—
73C5×C4⋊C4C2×D512yes—
74C42×C5—52no—
75C4⋊Dic5—52no—
76C4⋊Dic5—54no—
77C4⋊Dic5—102no—
78C4⋊Dic5C2×D512yes—
79C4⋊Dic5C2×D514yes—
80#683—54no—
81#683—54no—
82#683—54no—
83#683—54no—
84#683—54no—
85#683—104no—
86#683C2×D514yes—
87C4×Dic5—52no—
88C4×Dic5—52no—
89C4×Dic5C2×D512yes—
90C2×#125—251noSylow
91C2×C52C22×Q811yescharacteristic
92C2×C52C2×#4111yescharacteristic
93C2×C52C2×#4111yescharacteristic
94C5⋊D5#12514yescomplemented
95C22×D5—52no—
96C22×D5—102no—
97C2×C4×C5—22no—
98C2×C4×C5—24no—
99C2×C4×C5—52no—
100C2×C4×C5—52no—
101C2×C4×C5—54no—
102C2×C4×C5C22×D514yes—
103C2×C4×C5C22×D512yes—
104C2×Dic5—52no—
105C2×Dic5—54no—
106C2×Dic5—102no—
107C2×Dic5—104no—
108C2×Dic5C22×D512yes—
109C2×Dic5C22×D512yes—
110C2×Dic5C22×D514yes—
111C4×D5—58no—
112C4×D5—108no—
113C4×D5—104no—
114C4×D5—104no—
115C4×D5—108no—
116C4×D5—108no—
117C4×D5—208no—
118#125—52no—
119#125—252no—
120#125—254no—
121C2×C4⋊C4—252no—
122C2×C4⋊C4—252no—
123C2×C4⋊C4—251no—
124C2×C4⋊C4—251no—
125C2×C42—251no—
126C52C2×#12511yescharacteristic, complemented, Sylow
127C22×C5—22no—
128C22×C5C23×D512yes—
129C2×D5—54no—
130C2×D5—54no—
131C2×D5—54no—
132C2×D5—104no—
133C2×D5—104no—
134C2×D5—104no—
135C4×C5—24no—
136C4×C5—24no—
137C4×C5—44no—
138C4×C5—102no—
139C4×C5—102no—
140C4×C5—104no—
141C4×C5Q8×D514yes—
142Dic5—22no—
143Dic5—22no—
144Dic5—24no—
145Dic5—54no—
146Dic5—104no—
147Dic5—104no—
148Dic5—204no—
149C22×C4—251no—
150C22×C4—251no—
151C22×C4—252no—
152C22×C4—251no—
153C22×C4—252no—
154C4⋊C4—54no—
155C4⋊C4—54no—
156C4⋊C4—52no—
157C4⋊C4—254no—
158C4⋊C4—252no—
159C4⋊C4—254no—
160C4⋊C4—252no—
161C4⋊C4—251no—
162C4⋊C4D5211yescharacteristic
163C42—52no—
164C42—252no—
165C2×C5—22no—
166C2×C5—22no—
167C2×C5—22no—
168C2×C5C2×Q8×D512yes—
169C2×C5D5×#4112yes—
170C2×C5D5×#4112yes—
171D5—58no—
172D5—108no—
173C23—251no—
174C2×C4—52no—
175C2×C4—52no—
176C2×C4—54no—
177C2×C4—251no—
178C2×C4—254no—
179C2×C4—252no—
180C2×C4—504no—
181C2×C4—502no—
182C2×C4—502no—
183C2×C4—504no—
184C2×C4C2×D5212yes—
185C2×C4C2×D5211yescharacteristic
186C5—22no—
187C5D5×#12512yescomplemented
188C22—252no—
189C22—252no—
190C22—252no—
191C22C22×D5211yescharacteristic
192C4—22no—
193C4—102no—
194C4—102no—
195C4—104no—
196C4—252no—
197C4—502no—
198C4#8787212yes—
199C2—254no—
200C2C2×#8787211yescharacteristic
201C2#1171747711yescharacteristic
202C2#1171748411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C4⋊C4C22
prime radicalC22×C5⋊D5C23
hypercenterC4⋊C4D52
hypocenterC52C2×#125
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#4036C2semidirect
7. #11716988C2semidirect
8. #11716965C2semidirect
46. #4036D5semidirect
94. C5⋊D5#125semidirect
126. C52C2×#125semidirect
187. C5D5×#125semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C5⋊D52
C5×#40362
#117170182
#117170012
C4×#60362
#117169882
#117169652
D5×#1255