Finite Group Databasebeta

← #11996904

Subgroups — #11996904

Order 1280.

400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2986C211yesmaximal, characteristic
2#10615068C211yesmaximal, characteristic
3#10602627C211yesmaximal, characteristic
4#10601573C212yesmaximal
5#10598234C212yesmaximal
6C5×#533C2211yescharacteristic
7C2×#4015C2211yescharacteristic
8C5×#446—22no—
9C5×C8×Q8—22no—
10C5×#433—22no—
11C5×#431C2212yes—
12#65382—22no—
13#65358C414yes—
14#65293—22no—
15#65213C2212yes—
16C4×#681C2211yescharacteristic
17#64767—22no—
18#64702—22no—
19#64702—22no—
20#9436—51nomaximal, Sylow
21C22×Dic10—21no—
22C5×C4⋊Q8D412yes—
23C5×#125C2×C412yes—
24C5×C22⋊Q8—22no—
25C4×C5×Q8—22no—
26C5×#117D412yes—
27C2×C42×C5C2311yescharacteristic
28C2×C4⋊Dic5—22no—
29C2×#681—21no—
30C2×#681—22no—
31#4015—22no—
32#4015—21no—
33#4015C2×C412yes—
34C5×C4⋊C8—24no—
35C5×C4⋊C8D412yes—
36C5×C4⋊C8D412yes—
37C5×C22⋊C8—22no—
38C5×#97—22no—
39C4×C5×C8—22no—
40C4×C5×C8—22no—
41#3942—28no—
42C4⋊#168—22no—
43C4⋊#168—22no—
44#3935C2×C412yes—
45C4×#168—21no—
46#3139—51no—
47#2986D511yescharacteristic
48#1561—51no—
49#1549—52no—
50#1299—52no—
51C2×C5×Q8—22no—
52C22×C4×C5C2×D411yescharacteristic
53C22×C4×C5#4112yes—
54C22×Dic5—41no—
55C2×Dic10—22no—
56C2×Dic10—44no—
57C2×Dic10—41no—
58C2×C5×C8—22no—
59C2×C5×C8—22no—
60C5×C4⋊C4—24no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4C22⋊C414yes—
63C5×C22⋊C4—22no—
64C42×C5—22no—
65C42×C5C22×C411yescharacteristic
66C42×C5C2×D411yescharacteristic
67C42×C5C2×D412yes—
68C4⋊Dic5—24no—
69C4⋊Dic5—42no—
70#681—42no—
71#681—82no—
72C2×#168—22no—
73C2×#168—42no—
74#533C2×D511yescharacteristic
75C2×C4⋊Q8—51no—
76#491—54no—
77#487—102no—
78#446—22no—
79C8×Q8—22no—
80#433—22no—
81#431C2×D512yes—
82#423—52no—
83#419—102no—
84C4×M16—51no—
85#332—102no—
86#332—102no—
87#332—102no—
88C23×C5#12311yescharacteristic
89C5×Q8—42no—
90C5×Q8—42no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5—22no—
94C2×C4×C5—24no—
95C2×C4×C5C2×C22⋊C411yescharacteristic
96C2×C4×C5C4×D412yes—
97C2×C4×C5#12011yescharacteristic
98C2×C4×C5#12112yes—
99C2×Dic5—42no—
100C2×Dic5—82no—
101Dic10—44no—
102Dic10—82no—
103C5×C8—42no—
104C5×C8—42no—
105#168—42no—
106#168—82no—
107C22×Q8—101no—
108C2×M16—101no—
109C2×M16—102no—
110C4⋊Q8—52no—
111C4⋊Q8—101no—
112C4⋊Q8—102no—
113C4⋊Q8D2012yes—
114#125C4×D512yes—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117C22⋊D512yes—
118C2×C4⋊C4—102no—
119C2×C42C22×D511yescharacteristic
120C4⋊C8—24no—
121C4⋊C8—102no—
122C4⋊C8—102no—
123C4⋊C8C22⋊D512yes—
124C4⋊C8C22⋊D512yes—
125#103—108no—
126C22⋊C8—22no—
127#97—22no—
128#97—52no—
129C4×C8—22no—
130C4×C8—22no—
131C4×C8—101no—
132C22×C5—21no—
133C22×C5—22no—
134C22×C5#38611yescharacteristic
135C4×C5—21no—
136C4×C5—22no—
137C4×C5—44no—
138C4×C5#45412yes—
139C4×C5#47112yes—
140C4×C5#47312yes—
141Dic5—82no—
142C2×Q8—22no—
143C2×Q8—102no—
144C2×Q8—204no—
145C2×Q8—201no—
146C22×C4—201no—
147C22×C4#70912yes—
148C22×C4C2×C22⋊D511yescharacteristic
149M16—202no—
150M16—402no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—102no—
154C2×C8—202no—
155C4⋊C4—24no—
156C4⋊C4—22no—
157C4⋊C4—104no—
158C4⋊C4—202no—
159C4⋊C4#68514yes—
160C22⋊C4—22no—
161C42—22no—
162C42C2×C4×D511yescharacteristic
163C42C2×D2011yescharacteristic
164C42C2×C22⋊D512yes—
165C2×C5—41no—
166C2×C5#188811yescharacteristic
167C2×C5#190812yes—
168C23#407511yescharacteristic
169Q8—42no—
170Q8—42no—
171Q8—204no—
172Q8—402no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—202no—
178C2×C4—402no—
179C2×C4C2×#68511yescharacteristic
180C2×C4C4×C22⋊D512yes—
181C2×C4#407612yes—
182C2×C4#409911yescharacteristic
183C8—42no—
184C8—42no—
185C8—202no—
186C8—402no—
187C5#943611yescharacteristic, complemented, Sylow
188C22—22no—
189C22—21no—
190C22#6550211yescharacteristic
191C4—22no—
192C4—21no—
193C4—44no—
194C4—402no—
195C4#6543012yes—
196C4#6543212yes—
197C4#6553412yes—
198C2—41no—
199C2#1060245411yescharacteristic
200C2#1060281212yes—
subgroupG/H
centerC22#65502
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2986C2
socleC22×C5#386
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#2986D5
hypocenterC5#9436
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
187. C5#9436semidirect

Maximal subgroups

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

subgroupindex
C5×#29862
#106150682
#106026272
#106015732
#105982342
#94365