Finite Group Databasebeta

← #13105083

Subgroups — #13105083

Order 1600.

768 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 200 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×C4×D52C211yesmaximal, characteristic
2C42×C5⋊D5C211yesmaximal, characteristic, complemented
3C5×#4018C212yesmaximal, complemented
4#11717039C212yesmaximal
5#11717001C212yesmaximal, complemented
6C4×#6036C211yesmaximal, characteristic, complemented
7#11716996C214yesmaximal, complemented
8#11716973C212yesmaximal, complemented
9C22×D52C2211yescharacteristic
10C2×C4×C5⋊D5C2212yes—
11C2×C4×C5⋊D5C2211yescharacteristic
12C2×C4×C5×D5C2212yes—
13C2×#6036C2212yes—
14C2×#6036C2211yescharacteristic
15C2×D5×Dic5C2212yes—
16C4×D52C418yescomplemented
17C42×C52C2211yescharacteristic, complemented
18C4×#1039C2211yescharacteristic, complemented
19C4×#1039C2212yescomplemented
20C5×#685C2214yes—
21C5×#683C2214yescomplemented
22C4×C5×Dic5C2212yescomplemented
23#87780C2214yescomplemented
24#87778C2214yes—
25Dic52C2212yescomplemented
26D5×#117—52nomaximal
27C22×C5⋊D5C2311yescharacteristic
28C22×C5×D5C2312yes—
29C2×D52—24no—
30C2×D52C2×C414yes—
31C2×C4×C52C2312yes—
32C2×C4×C52C2311yescharacteristic
33C2×#1039C2312yes—
34C2×#1039C2311yescharacteristic
35C4×C5⋊D5—24no—
36C4×C5⋊D5C2×C414yes—
37C2×C5×Dic5C2314yes—
38C2×C5×Dic5C2312yes—
39C4×C5×D5C2×C418yescomplemented
40#6036—24no—
41#6036C2×C414yes—
42D5×Dic5C2×C418yescomplemented
43C22×C4×D5—52no—
44C5×#117—52no—
45#4072—52no—
46#4038—54no—
47D5×C4⋊C4—54no—
48D5×C22⋊C4—54no—
49#4023—54no—
50#4018—52no—
51#4018D512yescomplemented
52C42×D5—52no—
53C42×D5—52no—
54C42×D5—102no—
55C22×C52C2411yescharacteristic
56C2×C5⋊D5C22×C412yes—
57C2×C5⋊D5#4114yes—
58C2×C5×D5—24no—
59C2×C5×D5C22×C414yes—
60D52—28no—
61C4×C52—22no—
62C4×C52C22×C412yes—
63#1039—22no—
64#1039C22×C412yes—
65C5×Dic5—24no—
66C5×Dic5C22×C414yes—
67C23×D5—52no—
68C22×C4×C5—52no—
69C22×Dic5—52no—
70C2×C4×D5—52no—
71C2×C4×D5—52no—
72C2×C4×D5—52no—
73C2×C4×D5—516no—
74C2×C4×D5—54no—
75C2×C4×D5—54no—
76C2×C4×D5—102no—
77C2×C4×D5—104no—
78C2×C4×D5C2×D512yes—
79C5×C4⋊C4—54no—
80C5×C22⋊C4—54no—
81C42×C5—22no—
82C42×C5—52no—
83C42×C5C2×D512yescomplemented
84C22⋊Dic5—54no—
85#685—54no—
86#685C2×D514yes—
87C4⋊Dic5—54no—
88#683—54no—
89#683C2×D514yescomplemented
90C4×Dic5—52no—
91C4×Dic5—54no—
92C4×Dic5—54no—
93C4×Dic5—104no—
94C4×Dic5—102no—
95C4×Dic5C2×D512yescomplemented
96C2×#117—251noSylow
97C2×C52C23×C411yescharacteristic
98C2×C52C2×#4112yes—
99C5⋊D5#11714yescomplemented
100C5×D5—24no—
101C23×C5—52no—
102C22×D5—52no—
103C22×D5—58no—
104C22×D5—102no—
105C22×D5—108no—
106C22×D5C22×D512yes—
107C2×C4×C5—24no—
108C2×C4×C5—22no—
109C2×C4×C5—52no—
110C2×C4×C5—58no—
111C2×C4×C5—54no—
112C2×C4×C5C22×D514yes—
113C2×C4×C5C22×D512yes—
114C2×Dic5—52no—
115C2×Dic5—58no—
116C2×Dic5—54no—
117C2×Dic5—102no—
118C2×Dic5—104no—
119C2×Dic5C22×D514yes—
120C2×Dic5C22×D512yes—
121C4×D5—58no—
122C4×D5—58no—
123C4×D5—58no—
124C4×D5—108no—
125C4×D5—108no—
126C4×D5—108no—
127C4×D5—1016no—
128C4×D5C4×D518yescomplemented
129C23×C4—251no—
130#117—52no—
131#117—252no—
132#117—254no—
133C2×C4⋊C4—252no—
134C2×C22⋊C4—252no—
135C2×C42—251no—
136C2×C42—251no—
137C52C2×#11711yescharacteristic, complemented, Sylow
138C22×C5—22no—
139C22×C5—54no—
140C22×C5—104no—
141C22×C5C23×D512yes—
142C2×D5—24no—
143C2×D5—54no—
144C2×D5—58no—
145C2×D5—104no—
146C2×D5—108no—
147C2×D5—1016no—
148C2×D5C2×C4×D514yes—
149C4×C5—28no—
150C4×C5—24no—
151C4×C5—24no—
152C4×C5—54no—
153C4×C5—104no—
154C4×C5C2×C4×D514yes—
155Dic5—24no—
156Dic5—54no—
157Dic5—104no—
158Dic5—108no—
159Dic5—104no—
160Dic5C2×C4×D514yes—
161C24—251no—
162C22×C4—52no—
163C22×C4—251no—
164C22×C4—258no—
165C22×C4—252no—
166C22×C4—252no—
167C22×C4—251no—
168C22×C4—252no—
169C4⋊C4—54no—
170C4⋊C4—254no—
171C22⋊C4—54no—
172C22⋊C4—254no—
173C42—52no—
174C42—252no—
175C42—252no—
176C42—251no—
177C42D5211yescharacteristic, complemented
178C2×C5—22no—
179C2×C5—24no—
180C2×C5—104no—
181C2×C5C22×C4×D512yes—
182C2×C5D5×#4114yes—
183D5—24no—
184D5—58no—
185D5—108no—
186C23—52no—
187C23—254no—
188C23—251no—
189C23—504no—
190C2×C4—52no—
191C2×C4—58no—
192C2×C4—54no—
193C2×C4—254no—
194C2×C4—258no—
195C2×C4—251no—
196C2×C4—254no—
197C2×C4—252no—
198C2×C4—504no—
199C2×C4—504no—
200C2×C4C2×D5212yes—
201C2×C4C2×D5211yescharacteristic
202C5—22no—
203C5D5×#11712yescomplemented
204C22—54no—
205C22—104no—
206C22—252no—
207C22—254no—
208C22—508no—
209C22C22×D5211yescharacteristic
210C4—22no—
211C4—54no—
212C4—104no—
213C4—252no—
214C4—502no—
215C4C4×D5212yes—
216C2—104no—
217C2—254no—
218C2C2×C4×D5211yescharacteristic
219C2#1171747112yes—
subgroupG/H
centerC2×C4C2×D52
commutatorC2×C52C23×C4
FrattiniC22C22×D52
FittingC42×C52C22
socle, cosocleC22×C52C24
prime radicalC22×D52C22
hypercenterC42D52
hypocenterC52C2×#117
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C42×C5⋊D5C2semidirect
3. C5×#4018C2semidirect
5. #11717001C2semidirect
6. C4×#6036C2semidirect
7. #11716996C2semidirect
8. #11716973C2semidirect
16. C4×D52C4semidirect
17. C42×C52C22semidirect
18. C4×#1039C22semidirect
19. C4×#1039C22semidirect
21. C5×#683C22semidirect
22. C4×C5×Dic5C22semidirect
23. #87780C22semidirect
25. Dic52C22semidirect
39. C4×C5×D5C2×C4semidirect
42. D5×Dic5C2×C4semidirect
51. #4018D5semidirect
83. C42×C5C2×D5semidirect
89. #683C2×D5semidirect
95. C4×Dic5C2×D5semidirect
99. C5⋊D5#117semidirect
128. C4×D5C4×D5semidirect
137. C52C2×#117semidirect
177. C42D52semidirect
203. C5D5×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D522
C42×C5⋊D52
C5×#40182
#117170392
#117170012
C4×#60362
#117169962
#117169732
D5×#1175