Finite Group Databasebeta

← #13101829

Subgroups — #13101829

Order 1600.

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

normal subgroups only

This group has 352 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
1C5×#4147C211yesmaximal, characteristic
2#11717264C211yesmaximal, characteristic, complemented
3#11716949C212yesmaximal, complemented
4C5×#3968C211yesmaximal, characteristic, complemented
5#11716609C212yesmaximal, complemented
6C2×C52×Q8C2211yescharacteristic
7C2×#6045C2211yescharacteristic
8C5×#713—22no—
9C5×Q8×D5—22no—
10C5×#709—22no—
11C5×#709C2212yes—
12#87806—22no—
13C4×#1039C2211yescharacteristic
14C5×#681C2212yes—
15#87776—22no—
16#87773—22no—
17#65535—51nomaximal
18#65041—51nomaximal
19C52×Q8—22no—
20C2×C4×C52D412yes—
21C2×C4×C52C2311yescharacteristic
22C2×#1039—21no—
23C2×#1039—21no—
24#6045—22no—
25C5×C22⋊D5—22no—
26C5×D20—22no—
27C5×D20D412yes—
28C4×C5×D5—24no—
29C4×C5×D5—22no—
30C5×Dic10—22no—
31C5×Dic10D412yes—
32C5×#168—22no—
33C5×2−1+4—51no—
34#4147D511yescharacteristic
35#4097—52no—
36#4090—51no—
37#4090—51no—
38#4090—102no—
39#4055—52no—
40C5×#101—51no—
41#3969—52no—
42#3968D511yescharacteristic, complemented
43#3957—52no—
44C22×C52C2×D411yescharacteristic
45C2×C5×D5—22no—
46C4×C52—22no—
47C4×C52C2×D412yes—
48#1039—22no—
49#1039—41no—
50C5×Dic5—22no—
51C5×#41—52no—
52C5×#41—102no—
53C5×#41—102no—
54C2×C5×Q8—22no—
55C2×C5×Q8—102no—
56C2×C5×Q8C2×D511yescharacteristic
57C2×C5×Q8C2×D511yescharacteristic
58#713—22no—
59Q8×D5—22no—
60#709—22no—
61#709C2×D512yes—
62C2×Dic10—51no—
63C2×Dic10—51no—
64C2×Dic10—102no—
65C5×M16—52no—
66#689—102no—
67#687—102no—
68#683—108no—
69#683—102no—
70#683—102no—
71C4×Dic5—51no—
72C4×Dic5—51no—
73C4×Dic5—102no—
74#681C2×D512yes—
75Dic20—102no—
76#677—102no—
77#456—251noSylow
78C2×C52—21no—
79C2×C52#12011yescharacteristic
80C5×D5—42no—
81C5×Q8—22no—
82C5×Q8—22no—
83C5×Q8—44no—
84C5×Q8—52no—
85C5×Q8—102no—
86C5×D4—52no—
87C5×D4—102no—
88C5×D4—102no—
89C2×C4×C5—24no—
90C2×C4×C5—22no—
91C2×C4×C5—104no—
92C2×C4×C5—102no—
93C2×C4×C5D2012yes—
94C2×C4×C5C22⋊D512yes—
95C2×C4×C5C22×D511yescharacteristic
96C2×C4×C5C22×D511yescharacteristic
97C22⋊D5—22no—
98C2×Dic5—104no—
99C2×Dic5—101no—
100C2×Dic5—101no—
101C2×Dic5—104no—
102C2×Dic5—101no—
103C2×Dic5—101no—
104D20—22no—
105D20C22⋊D512yes—
106C4×D5—24no—
107C4×D5—22no—
108Dic10—22no—
109Dic10—102no—
110Dic10—102no—
111Dic10—204no—
112Dic10C22⋊D512yes—
113C5×C8—102no—
114#168—22no—
1152−1+4—51no—
116#137—252no—
117C4⋊Q8—251no—
118#104—252no—
119#101—51no—
120C52#45611yescharacteristic, complemented, Sylow
121C22×C5—22no—
122C22×C5—102no—
123C22×C5C2×D2011yescharacteristic
124C22×C5C2×C22⋊D511yescharacteristic
125C2×D5—22no—
126C4×C5—22no—
127C4×C5—22no—
128C4×C5—24no—
129C4×C5—44no—
130C4×C5—102no—
131C4×C5D4×D512yes—
132C4×C5C2×C22⋊D512yes—
133Dic5—22no—
134Dic5—108no—
135Dic5—102no—
136Dic5—102no—
137Dic5—204no—
138Dic5—201no—
139Dic5—201no—
140#41—52no—
141#41—102no—
142#41—102no—
143C2×Q8—102no—
144C2×Q8—251no—
145C2×Q8D5211yescharacteristic
146Q16—502no—
147SD16—502no—
148M16—52no—
149C4⋊C4—502no—
150C42—251no—
151C2×C5—24no—
152C2×C5—21no—
153C2×C5—21no—
154C2×C5—22no—
155C2×C5—202no—
156C2×C5#402811yescharacteristic
157C2×C5#409911yescharacteristic
158D5—42no—
159Q8—22no—
160Q8—52no—
161Q8—102no—
162Q8—502no—
163D4—52no—
164D4—102no—
165D4—102no—
166C2×C4—104no—
167C2×C4—102no—
168C2×C4—501no—
169C2×C4—501no—
170C2×C4#603812yes—
171C2×C4C2×D5211yescharacteristic
172C8—102no—
173C5—22no—
174C5#6504111yescharacteristic, complemented
175C5#6553511yescharacteristic, complemented
176C22—102no—
177C22C2×#603811yescharacteristic
178C4—22no—
179C4—102no—
180C4—502no—
181C4—1001no—
182C4D5×C22⋊D512yes—
183C2—21no—
184C2—202no—
185C2#1171709511yescharacteristic
subgroupG/H
centerC2#11717095
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC2×C52×Q8C22
socleC2×C52#120
prime radicalC5×#4147C2
hypercenterC2×Q8D52
hypocenterC52#456
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11717264C2semidirect
3. #11716949C2semidirect
4. C5×#3968C2semidirect
5. #11716609C2semidirect
42. #3968D5semidirect
120. C52#456semidirect
174. C5#65041semidirect
175. C5#65535semidirect

Maximal subgroups

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

subgroupindex
C5×#41472
#117172642
#117169492
C5×#39682
#117166092
#655355
#650415