Finite Group Databasebeta

← #13102748

Subgroups — #13102748

Order 1600.

424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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#11717215C211yesmaximal, characteristic
2#11717212C211yesmaximal, characteristic, complemented
3C52×#107C211yesmaximal, characteristic, complemented
4#11716688C211yesmaximal, characteristic, complemented
5#11716687C211yesmaximal, characteristic, complemented
6#11716676C211yesmaximal, characteristic, complemented
7#11716675C211yesmaximal, characteristic, complemented
8C2×C4⋊(C5⋊D5)—21no—
9C2×C4⋊(C5⋊D5)C2211yescharacteristic
10C2×C4×C5⋊D5C2211yescharacteristic
11C2×C52×C8C2211yescharacteristic
12C52×C4⋊C4C2211yescharacteristic
13C52×C4⋊C4C2211yescharacteristic
14#87808—21no—
15#87808—21no—
16C4⋊#1039C2211yescharacteristic
17C4×#1039—21no—
18C2×#6029C2211yescharacteristic
19#65174—56nomaximal
20C22×C5⋊D5—21no—
21C22×C5⋊D5D411yescharacteristic
22C2×C4×C52—21no—
23C2×C4×C52—21no—
24C2×C4×C52C2311yescharacteristic
25C2×#1039—21no—
26C2×#1039D411yescharacteristic
27C4⋊(C5⋊D5)—21no—
28C4⋊(C5⋊D5)—21no—
29C4⋊(C5⋊D5)—42no—
30C4×C5⋊D5—21no—
31C4×C5⋊D5—21no—
32C52×C8—21no—
33#6029—21no—
34#4041—56no—
35#4038—56no—
36C5×#107D516yescomplemented
37#3953—56no—
38#3952—56no—
39#3941—56no—
40#3940—56no—
41C22×C52C2×D411yescharacteristic
42C2×C5⋊D5—21no—
43C2×C5⋊D5—21no—
44C2×C5⋊D5—21no—
45C2×C5⋊D5—41no—
46C2×C5⋊D5—41no—
47C2×C5⋊D5—41no—
48C4×C52—41no—
49C4×C52—41no—
50C4×C52#4111yescharacteristic
51C4×C52#4111yescharacteristic
52#1039—21no—
53#1039—41no—
54C2×D20—56no—
55C2×D20—106no—
56C2×C4×D5—56no—
57C2×C5×C8C2×D516yes—
58C5×C4⋊C4C2×D516yes—
59C5×C4⋊C4C2×D516yes—
60#685—106no—
61#685—106no—
62C4⋊Dic5—56no—
63C4×Dic5—106no—
64C2×#168—56no—
65#482—251noSylow
66C2×C52#12311yescharacteristic
67C2×C52#13511yescharacteristic
68C2×C52AGL(1,ℤ/8)11yescharacteristic
69C5⋊D5—41no—
70C5⋊D5—81no—
71C22×D5—56no—
72C22×D5—106no—
73C2×C4×C5—26no—
74C2×C4×C5—26no—
75C2×C4×C5C22×D516yes—
76C2×Dic5—56no—
77C2×Dic5—106no—
78D20—106no—
79D20—106no—
80D20—2012no—
81C4×D5—106no—
82C4×D5—106no—
83C5×C8—26no—
84#168—106no—
85#121—251no—
86#117—251no—
87#107C5⋊D511yescharacteristic, complemented
88#106—251no—
89#102—251no—
90#102—251no—
91C22⋊C8—251no—
92C52#48211yescharacteristic, complemented, Sylow
93C22×C5D4×D516yes—
94C2×D5—106no—
95C2×D5—106no—
96C2×D5—106no—
97C2×D5—206no—
98C2×D5—206no—
99C2×D5—206no—
100C4×C5—46no—
101C4×C5—46no—
102C4×C5#70916yes—
103C4×C5#71316yes—
104Dic5—106no—
105Dic5—206no—
106C2×D4—251no—
107C2×D4—501no—
108C22×C4—251no—
109C2×C8—251no—
110C2×C8C2×C5⋊D511yescharacteristic
111C4⋊C4—251no—
112C4⋊C4C2×C5⋊D511yescharacteristic
113C4⋊C4C2×C5⋊D511yescharacteristic
114C22⋊C4—501no—
115C22⋊C4—501no—
116C42—501no—
117C2×C5#404016yes—
118C2×C5#405716yes—
119C2×C5#406516yes—
120D5—206no—
121D5—406no—
122C23—251no—
123C23—501no—
124D4—501no—
125D4—501no—
126D4—1002no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—251no—
130C2×C4—501no—
131C2×C4—501no—
132C2×C4—501no—
133C2×C4C22×C5⋊D511yescharacteristic
134C8—21no—
135C8—501no—
136C5#6517416yescomplemented
137C22—501no—
138C22—501no—
139C22—501no—
140C22—1001no—
141C22—1001no—
142C22—1001no—
143C22D4×C5⋊D511yescharacteristic
144C4—41no—
145C4—41no—
146C4—501no—
147C4—1001no—
148C4#8790011yescharacteristic
149C4#8790411yescharacteristic
150C2—1001no—
151C2—2001no—
152C2#1171721411yescharacteristic
153C2#1171723111yescharacteristic
154C2#1171723911yescharacteristic
subgroupG/H
centerC22D4×C5⋊D5
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C22×C5⋊D5
FittingC52×#107C2
socleC22×C52C2×D4
prime radical#11717215C2
hypercenter#107C5⋊D5
hypocenterC52#482
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11717212C2semidirect
3. C52×#107C2semidirect
4. #11716688C2semidirect
5. #11716687C2semidirect
6. #11716676C2semidirect
7. #11716675C2semidirect
36. C5×#107D5semidirect
87. #107C5⋊D5semidirect
92. C52#482semidirect
136. C5#65174semidirect

Maximal subgroups

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

subgroupindex
#117172152
#117172122
C52×#1072
#117166882
#117166872
#117166762
#117166752
#651745