Finite Group Databasebeta

← #13098057

Subgroups — #13098057

Order 1600.

243 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 243 conjugacy classes of subgroups — too many to draw. Only its 57 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×#87746C211yesmaximal, characteristic, complemented
2C2×#87722C211yesmaximal, characteristic, complemented
3C2×#87713C211yesmaximal, characteristic, complemented
4#11716457C211yesmaximal, characteristic, complemented
5C25×#102C211yesmaximal, characteristic, complemented
6#11716368C211yesmaximal, characteristic, complemented
7#11716357C211yesmaximal, characteristic, complemented
8C2×D4×C25C2211yescharacteristic
9C2×C22⋊D25—21no—
10C22×Dic25—21no—
11#87746—22no—
12#87746—22no—
13C2×D100—21no—
14C2×D100C2211yescharacteristic
15C2×C4×D25C2211yescharacteristic
16C2×Dic50C2211yescharacteristic
17C2×C8×C25C2211yescharacteristic
18C4⋊C4×C25C2211yescharacteristic
19#87722—22no—
20#87720—21no—
21C2×#6014C2211yescharacteristic
22#87713—22no—
23#65070—51nomaximal
24C23×C25—21no—
25C22×D25—21no—
26C22×D25D411yescharacteristic
27D4×C25—21no—
28D4×C25D412yescomplemented
29C2×C4×C25—21no—
30C2×C4×C25C2311yescharacteristic
31C22⋊D25—24no—
32C2×Dic25—24no—
33C2×Dic25—21no—
34C2×Dic25D411yescharacteristic
35D100—21no—
36D100—21no—
37D100—42no—
38C4×D25—21no—
39C4×D25—21no—
40Dic50—21no—
41Dic50D412yescomplemented
42C8×C25—21no—
43#6014—21no—
44C2×#711—51no—
45C2×#686—51no—
46C2×#677—51no—
47#4041—51no—
48C5×#102D511yescharacteristic
49#3952—51no—
50#3942—51no—
51C22×C25—22no—
52C22×C25—41no—
53C22×C25—41no—
54C22×C25C2×D411yescharacteristic
55C2×D25—21no—
56C2×D25—21no—
57C2×D25—21no—
58C2×D25—41no—
59C2×D25—41no—
60C2×D25—41no—
61C4×C25—41no—
62C4×C25C2×D411yescharacteristic
63C4×C25C2×D411yescharacteristic
64Dic25—22no—
65Dic25—21no—
66C2×C5×D4C2×D511yescharacteristic
67C2×C22⋊D5—101no—
68C22×Dic5—101no—
69#711—102no—
70#711—102no—
71C2×D20—51no—
72C2×D20—101no—
73C2×C4×D5—51no—
74C2×Dic10—51no—
75C2×C5×C8C2×D511yescharacteristic
76C5×C4⋊C4C2×D511yescharacteristic
77#686—102no—
78#685—101no—
79C2×#168—51no—
80#677—102no—
81#449—251noSylow
82C2×C25—42no—
83C2×C25#12011yescharacteristic
84C2×C25#13511yescharacteristic
85C2×C25AGL(1,ℤ/8)11yescharacteristic
86D25—41no—
87D25—81no—
88C23×C5—21no—
89C22×D5—51no—
90C22×D5—101no—
91C5×D4—21no—
92C5×D4D2012yes—
93C2×C4×C5—21no—
94C2×C4×C5C22×D511yescharacteristic
95C22⋊D5—104no—
96C2×Dic5—51no—
97C2×Dic5—104no—
98C2×Dic5—101no—
99D20—101no—
100D20—101no—
101D20—202no—
102C4×D5—101no—
103C4×D5—101no—
104Dic10—52no—
105Dic10—101no—
106C5×C8—21no—
107#168—101no—
108C2×#41—251no—
109C2×SD16—251no—
110C2×D8—251no—
111#121—251no—
112#103—251no—
113#102D2511yescharacteristic, complemented
114C22⋊C8—251no—
115C25#44911yescharacteristic, complemented, Sylow
116C22×C5—22no—
117C22×C5—41no—
118C22×C5—41no—
119C22×C5D4×D511yescharacteristic
120C2×D5—101no—
121C2×D5—101no—
122C2×D5—101no—
123C2×D5—201no—
124C2×D5—201no—
125C2×D5—201no—
126C4×C5—41no—
127C4×C5C2×D2011yescharacteristic
128C4×C5D4×D511yescharacteristic
129Dic5—102no—
130Dic5—101no—
131#41—502no—
132#41—502no—
133C2×Q8—251no—
134C2×D4—251no—
135C2×D4—501no—
136C2×D4—501no—
137C2×D4C2×D2511yescharacteristic
138C22×C4—251no—
139C22×C4—501no—
140SD16—502no—
141D8—502no—
142C2×C8—251no—
143C2×C8C2×D2511yescharacteristic
144C4⋊C4C2×D2511yescharacteristic
145C22⋊C4—501no—
146C2×C5—42no—
147C2×C5#402811yescharacteristic
148C2×C5#405711yescharacteristic
149C2×C5#406211yescharacteristic
150D5—201no—
151D5—401no—
152C23—21no—
153C23—251no—
154C23—501no—
155Q8—252no—
156Q8—501no—
157D4—21no—
158D4—504no—
159D4—501no—
160D4—501no—
161D4—1002no—
162D4D10012yescomplemented
163C2×C4—21no—
164C2×C4—251no—
165C2×C4—504no—
166C2×C4—501no—
167C2×C4—501no—
168C2×C4—501no—
169C2×C4C22×D2511yescharacteristic
170C8—21no—
171C8—501no—
172C5#6507011yescharacteristic
173C22—22no—
174C22—41no—
175C22—41no—
176C22—501no—
177C22—501no—
178C22—501no—
179C22—1001no—
180C22—1001no—
181C22—1001no—
182C22D4×D2511yescharacteristic
183C4—41no—
184C4—501no—
185C4—502no—
186C4C2×D10011yescharacteristic
187C4D4×D2511yescharacteristic
188C2—42no—
189C2—1001no—
190C2—2001no—
191C2#1171644411yescharacteristic
192C2#1171647311yescharacteristic
193C2#1171647811yescharacteristic
subgroupG/H
centerC22D4×D25
commutator, cosocleC2×C4×C25C23
FrattiniC2×C4×C5C22×D5
FittingC25×#102C2
socleC22×C5D4×D5
hypercenter#102D25
hypocenterC25#449
LCSG ▷ C2×C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#87746C2semidirect
2. C2×#87722C2semidirect
3. C2×#87713C2semidirect
4. #11716457C2semidirect
5. C25×#102C2semidirect
6. #11716368C2semidirect
7. #11716357C2semidirect
28. D4×C25D4semidirect
41. Dic50D4semidirect
113. #102D25semidirect
115. C25#449semidirect
162. D4D100semidirect

Maximal subgroups

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

subgroupindex
C2×#877462
C2×#877222
C2×#877132
#117164572
C25×#1022
#117163682
#117163572
#650705