Finite Group Databasebeta

← #13014947

Subgroups — #13014947

Order 1280.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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#10606051C211yesmaximal, characteristic
2#10604186C212yesmaximal
3#10598715C214yesmaximal
4C2×#4033C412yes—
5C2×#4015C411yescharacteristic
6C2×#4004—22no—
7C5×#384C411yescharacteristic
8C4⋊C4×Dic5—22no—
9#65263C2212yes—
10#65262—22no—
11C42×Dic5C2211yescharacteristic
12#64918—22no—
13#64918C2214yes—
14#7653—51nomaximal, Sylow
15C22×Dic10C2×C412yes—
16C22×#170—24no—
17C2×C5×C4⋊C4—22no—
18C2×C5×C4⋊C4C2×C412yes—
19C2×C42×C5C2×C411yescharacteristic
20C2×C4⋊Dic5—22no—
21C2×#683—22no—
22C2×C4×Dic5—22no—
23C2×C4×Dic5C2×C411yescharacteristic
24C2×C4×Dic5D412yes—
25C2×C4×Dic5D412yes—
26C2×C4×Dic5C2311yescharacteristic
27#4033—44no—
28#4015—24no—
29#4004—44no—
30#3963—24no—
31C4×C4⋊Q8—51no—
32#1831—52no—
33#1272—54no—
34C22×C4×C5—22no—
35C22×C4×C5C22⋊C412yes—
36C22×C4×C5C22×C411yescharacteristic
37C22×Dic5—22no—
38C22×Dic5C22⋊C411yescharacteristic
39C22×Dic5C22⋊C411yescharacteristic
40C22×Dic5C2×D412yes—
41C2×Dic10—22no—
42C2×Dic10—42no—
43C2×Dic10—42no—
44C2×Dic10M1614yes—
45C2×#170—44no—
46C2×#170—44no—
47C2×#170—44no—
48C5×C4⋊C4—42no—
49C5×C4⋊C4—44no—
50C42×C5—22no—
51C4⋊Dic5—28no—
52#683—44no—
53C4×Dic5—22no—
54C4×Dic5—42no—
55C4×Dic5—41no—
56C4×Dic5—44no—
57C4×Dic5SD1614yes—
58C4×Dic5Q1614yes—
59C2×C4⋊Q8—51no—
60C2×C4×Q8—52no—
61C2×C4⋊C8—102no—
62#391—52no—
63#389—102no—
64#384AGL(1,𝔽5)11yescharacteristic
65C4×C4⋊C4—102no—
66C43—51no—
67#336—54no—
68#336—102no—
69C23×C5C2×C22⋊C411yescharacteristic
70C2×C4×C5—22no—
71C2×C4×C5—21no—
72C2×C4×C5—21no—
73C2×C4×C5—22no—
74C2×C4×C5—42no—
75C2×C4×C5—44no—
76C2×C4×C5#10314yes—
77C2×C4×C5C2×M1612yes—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—24no—
81C2×Dic5—21no—
82C2×Dic5—22no—
83C2×Dic5—42no—
84C2×Dic5—42no—
85C2×Dic5#10012yes—
86C2×Dic5#10314yes—
87C2×Dic5C2×SD1612yes—
88C2×Dic5C2×Q1612yes—
89Dic10—44no—
90Dic10—44no—
91#170—84no—
92C22×Q8—52no—
93C22×C8—104no—
94C4⋊Q8—104no—
95C4×Q8—204no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—102no—
98C2×C4⋊C4—102no—
99C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
100C2×C42—52no—
101C2×C42—51no—
102C2×C42—52no—
103C2×C42—51no—
104C2×C42—102no—
105C2×C42C2×AGL(1,𝔽5)11yescharacteristic
106C4⋊C8—204no—
107#95—104no—
108C22×C5#40711yescharacteristic
109C22×C5#41011yescharacteristic
110C22×C5C2×#10011yescharacteristic
111C22×C5C2×#10312yes—
112C22×C5#42112yes—
113C4×C5—22no—
114C4×C5—24no—
115C4×C5—82no—
116Dic5—22no—
117Dic5—22no—
118Dic5—41no—
119Dic5—44no—
120Dic5#33314yes—
121C2×Q8—54no—
122C2×Q8—102no—
123C2×Q8—202no—
124C2×Q8—202no—
125C22×C4—22no—
126C22×C4—51no—
127C22×C4—52no—
128C22×C4—51no—
129C22×C4—102no—
130C22×C4C22⋊AGL(1,𝔽5)12yes—
131C22×C4C22×AGL(1,𝔽5)11yescharacteristic
132C2×C8—204no—
133C2×C8—204no—
134C2×C8—204no—
135C4⋊C4—42no—
136C4⋊C4—44no—
137C4⋊C4—108no—
138C4⋊C4—204no—
139C42—22no—
140C42—54no—
141C42—54no—
142C42—102no—
143C42—202no—
144C42—201no—
145C42—204no—
146C2×C5#146611yescharacteristic
147C2×C5#148712yes—
148C2×C5#151812yes—
149C2×C5#153611yescharacteristic
150C2×C5C2×#33311yescharacteristic
151C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
152Q8—204no—
153Q8—204no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—44no—
159C2×C4—42no—
160C2×C4—52no—
161C2×C4—54no—
162C2×C4—52no—
163C2×C4—52no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—104no—
167C2×C4—102no—
168C2×C4—101no—
169C2×C4—202no—
170C2×C4—202no—
171C2×C4#400914yes—
172C2×C4D5⋊M1612yes—
173C8—404no—
174C5#765311yescharacteristic, complemented, Sylow
175C22#6575511yescharacteristic
176C22#6576912yes—
177C22D5⋊#10011yescharacteristic
178C22C2×#400912yes—
179C22#6578511yescharacteristic
180C4—22no—
181C4—24no—
182C4—54no—
183C4—82no—
184C4—102no—
185C4—102no—
186C4—204no—
187C4—201no—
188C2#1060427312yes—
189C2#1060429411yescharacteristic
190C2#1060459911yescharacteristic
191C2#1060463112yes—
192C2D5⋊#33311yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#384C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#384AGL(1,𝔽5)
hypocenterC5#7653
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
174. C5#7653semidirect

Maximal subgroups

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

subgroupindex
#106060512
#106041862
#105987152
#76535