Finite Group Databasebeta

← #13098918

Subgroups — #13098918

Order 1600.

378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C25×#120C211yesmaximal, characteristic, complemented
2#11716515C212yesmaximal, complemented
3#11716502C211yesmaximal, characteristic, complemented
4#11716501C212yesmaximal, complemented
5#11716500C212yesmaximal, complemented
6#11716497C211yesmaximal, characteristic, complemented
7#11716446C212yesmaximal, complemented
8#11716445C212yesmaximal, complemented
9#11716441C212yesmaximal, complemented
10C24×C25C2211yescharacteristic
11C2×D4×C25C2211yescharacteristic
12C2×D4×C25C2212yes—
13C2×C22⋊D25C2212yes—
14C2×C22⋊D25C2212yes—
15C2×C22⋊D25C2212yes—
16C2×C22⋊D25C2212yescomplemented
17C22×Dic25C2211yescharacteristic, complemented
18C2×D100C2211yescharacteristic, complemented
19C2×C4×D25C2212yescomplemented
20C22⋊C4×C25C2212yes—
21C22⋊C4×C25C2211yescharacteristic
22C22⋊Dic25C2212yes—
23C22⋊Dic25C2212yes—
24C22⋊Dic25C2212yes—
25C22⋊Dic25C2211yescharacteristic, complemented
26#87720C2212yescomplemented
27C4⋊Dic25C2212yescomplemented
28#87718C2212yescomplemented
29#87718C2212yescomplemented
30C4×Dic25C2211yescharacteristic, complemented
31#65929—51nomaximal
32C23×C25—42no—
33C23×C25—41no—
34C23×C25C2312yes—
35C23×C25C2311yescharacteristic
36C23×C25C2311yescharacteristic
37C22×D25C2312yes—
38D4×C25—42no—
39D4×C25—41no—
40C2×C4×C25C2311yescharacteristic
41C2×C4×C25C2312yes—
42C22⋊D25—42no—
43C22⋊D25—42no—
44C22⋊D25—42no—
45C22⋊D25—42no—
46C2×Dic25—41no—
47C2×Dic25C2312yes—
48C2×Dic25C2312yes—
49C2×Dic25C2312yes—
50D100—41no—
51C4×D25—42no—
52C5×#120D511yescharacteristic
53#4099—52no—
54#4086—51no—
55#4085—52no—
56#4084—52no—
57#4081—51no—
58#4030—52no—
59#4029—52no—
60#4025—52no—
61C22×C25—21no—
62C22×C25—22no—
63C22×C25—22no—
64C22×C25—22no—
65C22×C25—22no—
66C22×C25—22no—
67C22×C25—21no—
68C22×C25—44no—
69C22×C25C2411yescharacteristic
70C2×D25—22no—
71C2×D25—22no—
72C2×D25—22no—
73C4×C25—22no—
74C4×C25—21no—
75Dic25—22no—
76Dic25—22no—
77Dic25—22no—
78C24×C5C2×D511yescharacteristic
79C2×C5×D4C2×D511yescharacteristic
80C2×C5×D4C2×D512yes—
81C2×C22⋊D5—52no—
82C2×C22⋊D5—52no—
83C2×C22⋊D5—52no—
84C2×C22⋊D5—52no—
85C22×Dic5—51no—
86C2×D20—51no—
87C2×C4×D5—52no—
88C5×C22⋊C4C2×D512yes—
89C5×C22⋊C4C2×D511yescharacteristic
90C22⋊Dic5—52no—
91C22⋊Dic5—52no—
92C22⋊Dic5—52no—
93C22⋊Dic5—51no—
94#685—52no—
95C4⋊Dic5—52no—
96#683—52no—
97#683—52no—
98C4×Dic5—51no—
99#560—251noSylow
100C2×C25—41no—
101C2×C25—42no—
102C2×C25—41no—
103C2×C25H(5,𝔽2)12yes—
104C2×C25H(5,𝔽2)11yescharacteristic
105D25—42no—
106C23×C5—42no—
107C23×C5—41no—
108C23×C5C22×D512yes—
109C23×C5C22×D511yescharacteristic
110C23×C5C22×D511yescharacteristic
111C22×D5—52no—
112C5×D4—42no—
113C5×D4—41no—
114C2×C4×C5C22×D511yescharacteristic
115C2×C4×C5C22×D512yes—
116C22⋊D5—202no—
117C22⋊D5—202no—
118C22⋊D5—202no—
119C22⋊D5—202no—
120C2×Dic5—52no—
121C2×Dic5—52no—
122C2×Dic5—52no—
123C2×Dic5—201no—
124D20—201no—
125C4×D5—202no—
126#127—251no—
127#126—252no—
128#123—251no—
129#123—252no—
130#121—252no—
131#121—252no—
132#121—252no—
133#120—252no—
134#120D2511yescharacteristic, complemented
135C25#56011yescharacteristic, complemented, Sylow
136C22×C5—21no—
137C22×C5—22no—
138C22×C5—22no—
139C22×C5—22no—
140C22×C5—22no—
141C22×C5—22no—
142C22×C5—21no—
143C22×C5—44no—
144C22×C5C23×D511yescharacteristic
145C2×D5—102no—
146C2×D5—102no—
147C2×D5—102no—
148C4×C5—22no—
149C4×C5—21no—
150Dic5—102no—
151Dic5—102no—
152Dic5—102no—
153C24C2×D2511yescharacteristic
154C2×D4—252no—
155C2×D4—252no—
156C2×D4—252no—
157C2×D4—252no—
158C2×D4—251no—
159C2×D4C2×D2512yes—
160C2×D4C2×D2511yescharacteristic
161C22×C4—251no—
162C22×C4—252no—
163C4⋊C4—252no—
164C4⋊C4—252no—
165C4⋊C4—252no—
166C22⋊C4—252no—
167C22⋊C4—252no—
168C22⋊C4—252no—
169C22⋊C4—251no—
170C22⋊C4—252no—
171C22⋊C4C2×D2512yes—
172C22⋊C4C2×D2511yescharacteristic
173C42—251no—
174C2×C5—42no—
175C2×C5—41no—
176C2×C5—41no—
177C2×C5#414412yes—
178C2×C5#414411yescharacteristic
179D5—202no—
180C23—42no—
181C23—41no—
182C23—252no—
183C23C22×D2512yes—
184C23C22×D2511yescharacteristic
185C23C22×D2511yescharacteristic
186D4—42no—
187D4—41no—
188D4—1001no—
189D4—1002no—
190D4—1002no—
191D4—1002no—
192D4—1002no—
193C2×C4—252no—
194C2×C4—252no—
195C2×C4—252no—
196C2×C4—1002no—
197C2×C4—1001no—
198C2×C4C22×D2511yescharacteristic
199C2×C4C22×D2512yes—
200C5#6592911yescharacteristic
201C22—21no—
202C22—22no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—44no—
209C22—502no—
210C22—502no—
211C22—502no—
212C22C23×D2511yescharacteristic
213C4—22no—
214C4—21no—
215C4—502no—
216C4—502no—
217C4—502no—
218C2—42no—
219C2—41no—
220C2—41no—
221C2—1002no—
222C2#1171656312yes—
223C2#1171656311yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#120C2
hypercenter#120D25
hypocenterC25#560
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C25×#120C2semidirect
2. #11716515C2semidirect
3. #11716502C2semidirect
4. #11716501C2semidirect
5. #11716500C2semidirect
6. #11716497C2semidirect
7. #11716446C2semidirect
8. #11716445C2semidirect
9. #11716441C2semidirect
16. C2×C22⋊D25C22semidirect
17. C22×Dic25C22semidirect
18. C2×D100C22semidirect
19. C2×C4×D25C22semidirect
25. C22⋊Dic25C22semidirect
26. #87720C22semidirect
27. C4⋊Dic25C22semidirect
28. #87718C22semidirect
29. #87718C22semidirect
30. C4×Dic25C22semidirect
134. #120D25semidirect
135. C25#560semidirect

Maximal subgroups

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

subgroupindex
C25×#1202
#117165152
#117165022
#117165012
#117165002
#117164972
#117164462
#117164452
#117164412
#659295