Finite Group Databasebeta

← #13100723

Subgroups — #13100723

Order 1600.

286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 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#11717207C211yesmaximal, characteristic
2#11716985C211yesmaximal, characteristic
3C2×#87776C212yesmaximal
4C5×#3942C212yesmaximal
5#11716613C211yesmaximal, characteristic
6C2×#6045C2211yescharacteristic
7C2×C5×Dic10C2212yes—
8C52×C4⋊C4C2211yescharacteristic
9#87806—21no—
10C4×#1039—21no—
11C4×#1039C2211yescharacteristic
12C2×C5×#168C2212yes—
13#87781—21no—
14#87781—21no—
15#87776—24no—
16#65082—52nomaximal
17C2×C4×C52—21no—
18C2×C4×C52C2311yescharacteristic
19C2×#1039—21no—
20C2×#1039D411yescharacteristic
21C2×#1039D411yescharacteristic
22#6045—21no—
23#6045D412yes—
24C2×C5×Dic5—22no—
25C5×Dic10—22no—
26C5×Dic10—22no—
27C5×#168—22no—
28#4090—52no—
29C2×#689—52no—
30C2×Dic20—52no—
31#4033—52no—
32#4033—102no—
33C5×#103—52no—
34#3946—52no—
35#3942D512yes—
36C22×C52C2×D411yescharacteristic
37C4×C52—41no—
38C4×C52C2×D411yescharacteristic
39C4×C52#4111yescharacteristic
40#1039—22no—
41#1039—21no—
42#1039Q1612yescomplemented
43C5×Dic5—42no—
44C2×C5×Q8—52no—
45C2×Dic10—52no—
46C2×Dic10—102no—
47C2×Dic10C2×D512yes—
48C2×C5×C8—52no—
49C5×C4⋊C4—22no—
50C5×C4⋊C4C2×D512yes—
51#689—104no—
52#683—102no—
53#683—102no—
54#683—102no—
55#683—104no—
56C4×Dic5—52no—
57C4×Dic5—102no—
58C4×Dic5—102no—
59C4×Dic5—104no—
60C2×#168C2×D512yes—
61Dic20—104no—
62#462—251noSylow
63C2×C52#12111yescharacteristic
64C2×C52C2×Q1611yescharacteristic
65C2×C52#13711yescharacteristic
66C5×Q8—102no—
67C5×Q8—102no—
68C2×C4×C5—24no—
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—102no—
72C2×C4×C5C22×D512yes—
73C2×Dic5—22no—
74C2×Dic5—52no—
75C2×Dic5—52no—
76C2×Dic5—102no—
77C2×Dic5—102no—
78C2×Dic5—104no—
79C2×Dic5—102no—
80Dic10—22no—
81Dic10—22no—
82Dic10—54no—
83Dic10—104no—
84Dic10—104no—
85Dic10—102no—
86C5×C8—102no—
87#168—22no—
88C2×Q16—252no—
89C4⋊Q8—251no—
90C4×Q8—251no—
91C4⋊C8—251no—
92#103—52no—
93C52#46211yescharacteristic, complemented, Sylow
94C22×C5—22no—
95C22×C5D4×D512yes—
96C4×C5—22no—
97C4×C5—22no—
98C4×C5—44no—
99C4×C5—42no—
100C4×C5—202no—
101C4×C5#70912yes—
102C4×C5D4×D512yes—
103Dic5—42no—
104Dic5—54no—
105Dic5—104no—
106Dic5—108no—
107Dic5—104no—
108Dic5—102no—
109Dic5—202no—
110C2×Q8—52no—
111C2×Q8—251no—
112Q16—504no—
113C2×C8—52no—
114C4⋊C4—501no—
115C4⋊C4—501no—
116C4⋊C4—501no—
117C4⋊C4D5211yescharacteristic
118C42—251no—
119C42—501no—
120C2×C5—22no—
121C2×C5—22no—
122C2×C5—22no—
123C2×C5#403012yes—
124C2×C5#406112yes—
125C2×C5D5×Q1612yes—
126Q8—102no—
127Q8—102no—
128Q8—252no—
129Q8—501no—
130C2×C4—21no—
131C2×C4—102no—
132C2×C4—251no—
133C2×C4—251no—
134C2×C4—501no—
135C2×C4C2×D5211yescharacteristic
136C8—102no—
137C5—22no—
138C5#6508212yescomplemented
139C22#8788611yescharacteristic
140C4—41no—
141C4—202no—
142C4—252no—
143C4—502no—
144C4—501no—
145C4#8787311yescharacteristic
146C4#8787711yescharacteristic
147C2#1171703011yescharacteristic
148C2#1171704911yescharacteristic
149C2#1171706211yescharacteristic
subgroupG/H
centerC22#87886
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC52×C4⋊C4C22
socle, prime radicalC22×C52C2×D4
hypercenterC4⋊C4D52
hypocenterC52#462
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
42. #1039Q16semidirect
93. C52#462semidirect
138. C5#65082semidirect

Maximal subgroups

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

subgroupindex
#117172072
#117169852
C2×#877762
C5×#39422
#117166132
#650825