Finite Group Databasebeta

← #13100843

Subgroups — #13100843

Order 1600.

244 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 64 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
1D5×C4⋊Dic5C211yesmaximal, characteristic
2#11716974C211yesmaximal, characteristic
3#11716684C211yesmaximal, characteristic, complemented
4C5×#3952C211yesmaximal, characteristic
5C5×#3948C211yesmaximal, characteristic, complemented
6#11716614C211yesmaximal, characteristic, complemented
7#11716607C211yesmaximal, characteristic, complemented
8C2×C4×C5×D5C2211yescharacteristic
9C2×C5×Dic10C2211yescharacteristic
10C2×D5×Dic5—21no—
11C2×C52×C8C2211yescharacteristic
12C4⋊#1039C2211yescharacteristic
13C4⋊#1039C2211yescharacteristic
14C5×C4⋊Dic5C2211yescharacteristic
15C2×C5×#168C2211yescharacteristic
16#87781—21no—
17#87780—21no—
18#87778—21no—
19#65094—51nomaximal
20#65010—51nomaximal
21C22×C5×D5D411yescharacteristic
22C2×C4×C52C2311yescharacteristic
23C2×#1039—21no—
24C2×#1039—21no—
25C2×C5×Dic5—21no—
26C2×C5×Dic5—21no—
27C2×C5×Dic5D411yescharacteristic
28C4×C5×D5—21no—
29C4×C5×D5—21no—
30C5×Dic10—21no—
31C5×Dic10—21no—
32D5×Dic5—42no—
33C52×C8—21no—
34C5×#168—21no—
35#4092—51no—
36C2×C4⋊Dic5—51no—
37#4070—51no—
38D5×C4⋊C4—51no—
39C5×#103—51no—
40C5×C22⋊C8—51no—
41#3967—51no—
42#3952D511yescharacteristic
43#3949—51no—
44#3949—51no—
45#3949—51no—
46#3949—102no—
47#3948—51no—
48#3948D511yescharacteristic, complemented
49#3940—51no—
50C22×C52C2×D411yescharacteristic
51C2×C5×D5—21no—
52C2×C5×D5—21no—
53C2×C5×D5SD1612yes—
54C4×C52#4111yescharacteristic
55C4×C52#4111yescharacteristic
56#1039—41no—
57#1039—41no—
58C5×Dic5—21no—
59C5×Dic5—41no—
60C5×Dic5—41no—
61C2×C5×Q8—51no—
62C22×C4×C5—51no—
63C22×Dic5—101no—
64C2×C4×D5—101no—
65C2×C4×D5C2×D511yescharacteristic
66C2×Dic10C2×D511yescharacteristic
67C2×C5×C8—22no—
68C2×C5×C8—51no—
69C2×C5×C8C2×D511yescharacteristic
70C2×C5×C8C2×D511yescharacteristic
71C5×C4⋊C4—51no—
72C22⋊Dic5—101no—
73#685—101no—
74C4⋊Dic5—51no—
75C4⋊Dic5—51no—
76C4⋊Dic5—51no—
77C4⋊Dic5—51no—
78C4⋊Dic5—102no—
79C4⋊Dic5—102no—
80C4⋊Dic5—101no—
81C4⋊Dic5C2×D511yescharacteristic
82#683—101no—
83#683—101no—
84#683—101no—
85C2×#168C2×D511yescharacteristic
86#483—251noSylow
87C2×C52#12311yescharacteristic
88C2×C52C2×SD1611yescharacteristic
89C2×C52#13711yescharacteristic
90C5×D5—22no—
91C23×C5—51no—
92C22×D5D2011yescharacteristic
93C5×Q8—101no—
94C5×Q8—101no—
95C2×C4×C5—22no—
96C2×C4×C5—51no—
97C2×C4×C5—101no—
98C2×C4×C5—101no—
99C2×C4×C5—101no—
100C2×C4×C5—101no—
101C2×C4×C5C22×D511yescharacteristic
102C2×C4×C5C22×D511yescharacteristic
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—101no—
106C2×Dic5—101no—
107C2×Dic5—101no—
108C2×Dic5—101no—
109C2×Dic5—202no—
110C2×Dic5—202no—
111C2×Dic5—202no—
112C2×Dic5D2011yescharacteristic
113C4×D5—21no—
114C4×D5—21no—
115C4×D5—202no—
116Dic10—21no—
117Dic10—21no—
118C5×C8—24no—
119C5×C8—21no—
120C5×C8—21no—
121C5×C8—101no—
122#168—21no—
123C22⋊Q8—251no—
124C2×C4⋊C4—251no—
125#106—251no—
126#106—251no—
127#103—51no—
128#103—251no—
129C22⋊C8—51no—
130C52#48311yescharacteristic, complemented, Sylow
131C22×C5—22no—
132C22×C5—52no—
133C22×C5—101no—
134C22×C5—101no—
135C22×C5C2×D2011yescharacteristic
136C22×C5D4×D511yescharacteristic
137C2×D5—21no—
138C2×D5—21no—
139C2×D5#67712yes—
140C4×C5—22no—
141C4×C5—22no—
142C4×C5—101no—
143C4×C5—201no—
144C4×C5—201no—
145C4×C5#70911yescharacteristic
146C4×C5#71111yescharacteristic
147C4×C5#71111yescharacteristic
148C4×C5#71111yescharacteristic
149Dic5—21no—
150Dic5—41no—
151Dic5—41no—
152Dic5—201no—
153Dic5—201no—
154Dic5—201no—
155Dic5—201no—
156Dic5—402no—
157Dic5—402no—
158C2×Q8—51no—
159C22×C4—51no—
160C22×C4—501no—
161C2×C8—51no—
162C2×C8D5211yescharacteristic
163C4⋊C4—51no—
164C4⋊C4—251no—
165C4⋊C4—251no—
166C4⋊C4—501no—
167C4⋊C4—501no—
168C22⋊C4—501no—
169C2×C5—22no—
170C2×C5—22no—
171C2×C5—22no—
172C2×C5—102no—
173C2×C5#402911yescharacteristic
174C2×C5#403211yescharacteristic
175C2×C5C2×#67711yescharacteristic
176C2×C5#405511yescharacteristic
177C2×C5D5×SD1611yescharacteristic
178C2×C5#406411yescharacteristic
179D5—22no—
180C23—51no—
181Q8—101no—
182Q8—101no—
183C2×C4—51no—
184C2×C4—101no—
185C2×C4—101no—
186C2×C4—101no—
187C2×C4—101no—
188C2×C4—501no—
189C2×C4—501no—
190C2×C4—1002no—
191C2×C4C2×D5211yescharacteristic
192C8—21no—
193C8—101no—
194C5—22no—
195C5#6501011yescharacteristic, complemented
196C5#6509411yescharacteristic, complemented
197C22—52no—
198C22—101no—
199C22—101no—
200C22D5×D2011yescharacteristic
201C4—101no—
202C4—201no—
203C4—201no—
204C4—1001no—
205C4—1001no—
206C4#8787011yescharacteristic
207C4#8788011yescharacteristic
208C2—102no—
209C2D5×#67711yescharacteristic
210C2#1171691911yescharacteristic
211C2#1171700311yescharacteristic
subgroupG/H
centerC22D5×D20
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC2×C52×C8C22
socleC22×C52C2×D4
prime radicalC22×C5×D5D4
hypercenterC2×C8D52
hypocenterC52#483
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. #11716684C2semidirect
5. C5×#3948C2semidirect
6. #11716614C2semidirect
7. #11716607C2semidirect
48. #3948D5semidirect
130. C52#483semidirect
195. C5#65010semidirect
196. C5#65094semidirect

Maximal subgroups

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

subgroupindex
D5×C4⋊Dic52
#117169742
#117166842
C5×#39522
C5×#39482
#117166142
#117166072
#650945
#650105