Finite Group Databasebeta

← #11996905

Subgroups — #11996905

Order 1280.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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×#3139C211yesmaximal, characteristic
2#10615063C211yesmaximal, characteristic
3#10602627C211yesmaximal, characteristic
4#10602568C212yesmaximal
5#10598160C212yesmaximal
6C5×#533C2211yescharacteristic
7C2×C5×C4⋊Q8C2211yescharacteristic
8C5×#491C414yes—
9C5×#487—22no—
10C5×#419—22no—
11C4×C5×M16C2211yescharacteristic
12#65313—22no—
13Q8×#168—22no—
14#65289—22no—
15#65214C2212yes—
16#65213C2212yes—
17#64767—22no—
18#64767—22no—
19#64767—22no—
20#9436—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C2×C5×M16—21no—
23C5×C4⋊Q8—22no—
24C5×C4⋊Q8—21no—
25C5×C4⋊Q8C2×C412yes—
26C5×C4⋊Q8D412yes—
27C5×#125C2×C412yes—
28C5×C22⋊Q8—22no—
29C4×C5×Q8—22no—
30C5×#117D412yes—
31C2×C5×C4⋊C4—22no—
32C2×C42×C5C2311yescharacteristic
33C2×#681—22no—
34C5×#103—28no—
35C5×#97C2×C412yes—
36C4×C5×C8—21no—
37C22⋊#168—22no—
38C4⋊#168—24no—
39C4⋊#168—22no—
40C4⋊#168—22no—
41C4⋊#168D412yes—
42C4⋊#168D412yes—
43#3935—22no—
44C4×#168—22no—
45C4×#168—22no—
46#3139D511yescharacteristic
47#2986—51no—
48#1561—51no—
49#1549—52no—
50#1299—52no—
51C2×C5×Q8—22no—
52C2×C5×Q8—22no—
53C2×C5×Q8—44no—
54C2×C5×Q8—41no—
55C22×C4×C5—41no—
56C22×C4×C5C2×D411yescharacteristic
57C22×C4×C5#4112yes—
58C5×M16—42no—
59C2×C5×C8—22no—
60C5×C4⋊C4—24no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4—24no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4C22⋊C414yes—
65C5×C22⋊C4—22no—
66C42×C5—22no—
67C42×C5C22×C411yescharacteristic
68C42×C5C2×D412yes—
69C42×C5C2×D411yescharacteristic
70#681—82no—
71C2×#168—22no—
72C2×#168—22no—
73C2×#168—42no—
74#533C2×D511yescharacteristic
75C2×C4⋊Q8C2×D511yescharacteristic
76#491Dic514yes—
77#487—22no—
78#446—102no—
79C8×Q8—102no—
80#433—102no—
81#431—52no—
82#423—52no—
83#419—22no—
84C4×M16C2×D511yescharacteristic
85#332—102no—
86#332—102no—
87#332—102no—
88C23×C5#12311yescharacteristic
89C5×Q8—44no—
90C5×Q8—42no—
91C5×Q8—42no—
92C5×Q8—82no—
93C2×C4×C5—22no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5—24no—
97C2×C4×C5—42no—
98C2×C4×C5—82no—
99C2×C4×C5C2×C22⋊C411yescharacteristic
100C2×C4×C5C4×D412yes—
101C2×C4×C5#12011yescharacteristic
102C2×C4×C5#12112yes—
103C5×C8—42no—
104#168—42no—
105#168—42no—
106#168—82no—
107C22×Q8—21no—
108C2×M16—21no—
109C2×M16—102no—
110C4⋊Q8—22no—
111C4⋊Q8—21no—
112C4⋊Q8C2×Dic512yes—
113C4⋊Q8C22⋊D512yes—
114#125C2×Dic512yes—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117C22⋊D512yes—
118C2×C4⋊C4—22no—
119C2×C42C22×D511yescharacteristic
120C4⋊C8—52no—
121C4⋊C8—52no—
122C4⋊C8—104no—
123C4⋊C8—102no—
124C4⋊C8—102no—
125#103—28no—
126C22⋊C8—102no—
127#97—102no—
128#97C2×Dic512yes—
129C4×C8—21no—
130C4×C8—102no—
131C4×C8—102no—
132C22×C5—21no—
133C22×C5—22no—
134C22×C5#38611yescharacteristic
135C4×C5—21no—
136C4×C5—22no—
137C4×C5—44no—
138C4×C5—82no—
139C4×C5#45412yes—
140C4×C5#47112yes—
141C4×C5#47312yes—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—44no—
145C2×Q8—41no—
146C22×C4—41no—
147C22×C4#71112yes—
148C22×C4C2×C22⋊D511yescharacteristic
149M16—42no—
150M16—402no—
151C2×C8—22no—
152C2×C8—102no—
153C2×C8—102no—
154C2×C8—202no—
155C4⋊C4—24no—
156C4⋊C4—22no—
157C4⋊C4—24no—
158C4⋊C4—42no—
159C4⋊C4C22⋊Dic514yes—
160C22⋊C4—22no—
161C42—22no—
162C42D4×D512yes—
163C42C22×Dic511yescharacteristic
164C42C2×C22⋊D511yescharacteristic
165C2×C5—41no—
166C2×C5#188811yescharacteristic
167C2×C5#190812yes—
168C23#408111yescharacteristic
169Q8—44no—
170Q8—42no—
171Q8—42no—
172Q8—82no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—42no—
178C2×C4—82no—
179C2×C4D4×Dic512yes—
180C2×C4#408311yescharacteristic
181C2×C4#408512yes—
182C2×C4C2×C22⋊Dic511yescharacteristic
183C8—42no—
184C8—202no—
185C8—202no—
186C8—402no—
187C5#943611yescharacteristic, complemented, Sylow
188C22—21no—
189C22—22no—
190C22#6550911yescharacteristic
191C4—21no—
192C4—22no—
193C4—44no—
194C4—82no—
195C4#6535112yes—
196C4#6549212yes—
197C4#6549312yes—
198C2—41no—
199C2#1060251711yescharacteristic
200C2#1060289612yes—
subgroupG/H
centerC22#65509
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3139C2
socleC22×C5#386
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#3139D5
hypocenterC5#9436
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

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×#31392
#106150632
#106026272
#106025682
#105981602
#94365