Finite Group Databasebeta

← #13105404

Subgroups — #13105404

Order 1600.

400 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 120 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#11717210C211yesmaximal, characteristic
2C5×#4035C212yesmaximal
3#11716989C211yesmaximal, characteristic
4#11716989C211yesmaximal, characteristic
5#11716988C212yesmaximal
6#11716986C212yesmaximal
7#11716965C212yesmaximal
8#11716963C212yesmaximal
9#11716963C212yesmaximal
10C52×C4⋊C4C2211yescharacteristic
11C4⋊#1039C2211yescharacteristic
12C4⋊#1039C2212yes—
13#87806C2212yes—
14C4×#1039C2211yescharacteristic
15C5×C4⋊Dic5C2212yes—
16C5×#683C2212yes—
17C5×#683C2212yes—
18C5×#683C2212yes—
19C5×#683C2212yes—
20C4×C5×Dic5C2212yes—
21#87781C2211yescharacteristic
22#87781C2212yes—
23#87781C2211yescharacteristic
24#87781C2211yescharacteristic
25#87781C2211yescharacteristic
26#87780C2212yes—
27#87780C2212yes—
28#87780C2212yes—
29#87780C2212yes—
30Dic52C2212yes—
31C5⋊#564—52nomaximal
32C2×C4×C52C2312yes—
33C2×C4×C52C2311yescharacteristic
34C2×#1039C2312yes—
35C2×#1039C2311yescharacteristic
36C2×#1039C2311yescharacteristic
37C2×C5×Dic5C2312yes—
38C2×C5×Dic5C2312yes—
39C2×C5×Dic5C2312yes—
40C2×C5×Dic5C2312yes—
41C5×#125—52no—
42#4036—52no—
43#4036—52no—
44#4036—52no—
45#4036—52no—
46#4036—102no—
47#4035—52no—
48#4035—52no—
49#4035—52no—
50#4035—52no—
51#4035—52no—
52#4035—52no—
53#4035—52no—
54#4035D512yes—
55#4016—52no—
56#4016—52no—
57C22×C52C2411yescharacteristic
58C4×C52—21no—
59C4×C52—22no—
60#1039—22no—
61#1039—21no—
62#1039—21no—
63C5×Dic5—22no—
64C5×Dic5—22no—
65C5×Dic5—22no—
66C5×Dic5—22no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—52no—
69C5×C4⋊C4—52no—
70C5×C4⋊C4—52no—
71C5×C4⋊C4—52no—
72C5×C4⋊C4—52no—
73C5×C4⋊C4C2×D512yes—
74C42×C5—52no—
75C4⋊Dic5—52no—
76C4⋊Dic5—52no—
77C4⋊Dic5—52no—
78C4⋊Dic5—52no—
79C4⋊Dic5—52no—
80C4⋊Dic5—52no—
81C4⋊Dic5—52no—
82C4⋊Dic5—104no—
83C4⋊Dic5—102no—
84C4⋊Dic5C2×D512yes—
85#683—52no—
86#683—52no—
87#683—52no—
88#683—52no—
89#683—52no—
90#683—52no—
91#683—52no—
92#683—52no—
93#683—52no—
94#683—52no—
95#683—52no—
96#683—52no—
97#683—104no—
98#683C2×D512yes—
99#683C2×D512yes—
100#683C2×D512yes—
101#683C2×D512yes—
102C4×Dic5—52no—
103C4×Dic5—52no—
104C4×Dic5—52no—
105C4×Dic5—102no—
106C4×Dic5C2×D512yes—
107#564—251noSylow
108C2×C522−1+411yescharacteristic
109C2×C522−1+411yescharacteristic
110C2×C522−1+411yescharacteristic
111C2×C4×C5—22no—
112C2×C4×C5—24no—
113C2×C4×C5—52no—
114C2×C4×C5—52no—
115C2×C4×C5—52no—
116C2×C4×C5—52no—
117C2×C4×C5C22×D512yes—
118C2×C4×C5C22×D512yes—
119C2×C4×C5C22×D512yes—
120C2×Dic5—52no—
121C2×Dic5—52no—
122C2×Dic5—52no—
123C2×Dic5—52no—
124C2×Dic5—102no—
125C2×Dic5—102no—
126C2×Dic5—104no—
127C2×Dic5C22×D512yes—
128C2×Dic5C22×D512yes—
129C2×Dic5C22×D512yes—
130C2×Dic5C22×D512yes—
131#125—52no—
132#125—252no—
133#125—252no—
134#125—252no—
135#125—251no—
136#125—251no—
137#125—252no—
138#125—252no—
139#125—251no—
140C52#56411yescharacteristic, complemented, Sylow
141C22×C5—22no—
142C22×C5C23×D512yes—
143C4×C5—24no—
144C4×C5—22no—
145C4×C5—22no—
146C4×C5—22no—
147C4×C5—44no—
148C4×C5—102no—
149C4×C5—102no—
150C4×C5—102no—
151C4×C5—102no—
152Dic5—22no—
153Dic5—22no—
154Dic5—22no—
155Dic5—22no—
156Dic5—102no—
157Dic5—102no—
158Dic5—102no—
159Dic5—102no—
160Dic5—202no—
161Dic5—202no—
162Dic5—204no—
163C4⋊C4—52no—
164C4⋊C4—52no—
165C4⋊C4—52no—
166C4⋊C4—52no—
167C4⋊C4—52no—
168C4⋊C4—251no—
169C4⋊C4—251no—
170C4⋊C4—252no—
171C4⋊C4—251no—
172C4⋊C4—251no—
173C4⋊C4—252no—
174C4⋊C4—252no—
175C4⋊C4—252no—
176C4⋊C4—252no—
177C4⋊C4—252no—
178C4⋊C4—252no—
179C4⋊C4—251no—
180C4⋊C4D5211yescharacteristic
181C42—52no—
182C42—252no—
183C42—251no—
184C2×C5—22no—
185C2×C5—22no—
186C2×C5—22no—
187C2×C5#414712yes—
188C2×C5#415012yes—
189C2×C5#415012yes—
190C2×C4—52no—
191C2×C4—52no—
192C2×C4—52no—
193C2×C4—52no—
194C2×C4—251no—
195C2×C4—252no—
196C2×C4—251no—
197C2×C4C2×D5212yes—
198C2×C4C2×D5211yescharacteristic
199C5—22no—
200C5C5⋊#56412yescomplemented
201C22C22×D5211yescharacteristic
202C4—21no—
203C4—22no—
204C4—102no—
205C4—102no—
206C4—102no—
207C4—102no—
208C4—501no—
209C4—502no—
210C4—501no—
211C2#1171746311yescharacteristic
212C2#1171747411yescharacteristic
213C2#1171748111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, prime radical, cosocleC22×C52C24
FittingC52×C4⋊C4C22
hypercenterC4⋊C4D52
hypocenterC52#564
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
140. C52#564semidirect
200. C5C5⋊#564semidirect

Maximal subgroups

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

subgroupindex
#117172102
C5×#40352
#117169892
#117169882
#117169862
#117169652
#117169632
C5⋊#5645