Finite Group Databasebeta

← #11993710

Subgroups — #11993710

Order 1280.

336 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 103 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#10615064C211yesmaximal, characteristic
2C5×#1526C211yesmaximal, characteristic
3#10602633C211yesmaximal, characteristic
4#10600644C212yesmaximal
5#10598156C212yesmaximal
6C5×#533C2211yescharacteristic
7C4×C5×M16C2212yes—
8#65313—22no—
9#65313—22no—
10#65289—22no—
11#65221C2211yescharacteristic
12#65215C2212yes—
13#65213C2211yescharacteristic
14C5×#330C411yescharacteristic, complemented
15C5×#330C412yescomplemented
16C5×#330C411yescharacteristic, complemented
17#64752—22no—
18#64678—22no—
19#64677—22no—
20#8919—51nomaximal, Sylow
21C2×C5×M16—22no—
22C5×C4⋊Q8Q812yes—
23C5×#125C2×C411yescharacteristic
24C5×#125C2×C411yescharacteristic
25C5×C22⋊Q8—22no—
26C4×C5×Q8—22no—
27C5×#117D412yes—
28C2×C42×C5C2311yescharacteristic
29C2×C4×Dic5—21no—
30C2×#681—21no—
31C5×#97C2×C412yes—
32C5×#97C2×C412yes—
33C4×C5×C8—22no—
34#3963—22no—
35C22⋊#168—22no—
36C4⋊#168—22no—
37C4⋊#168—22no—
38C4⋊#168—22no—
39C4⋊#168D412yes—
40C4⋊#168D412yes—
41#3935—22no—
42#3935—22no—
43C4×#168—22no—
44#2987—51no—
45#1995—51no—
46#1569—52no—
47#1526D511yescharacteristic
48#1300—52no—
49C2×C5×Q8—22no—
50C22×C4×C5C2×D411yescharacteristic
51C22×C4×C5#4112yes—
52C22×Dic5—41no—
53C5×M16—44no—
54C2×C5×C8—22no—
55C2×C5×C8—22no—
56C5×C4⋊C4—22no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4—22no—
59C5×C4⋊C4C4⋊C412yes—
60C5×C4⋊C4C4⋊C412yes—
61C5×C22⋊C4—22no—
62C42×C5—22no—
63C42×C5C22×C411yescharacteristic
64C42×C5C2×D412yes—
65C42×C5C2×Q811yescharacteristic
66C4×Dic5—22no—
67C4×Dic5—41no—
68#681—42no—
69C2×#168—22no—
70C2×#168—22no—
71C2×#168—41no—
72#533C2×D511yescharacteristic
73#446—102no—
74#446—102no—
75#433—102no—
76#432—52no—
77#423—51no—
78C4×M16C2×D512yes—
79#376—51no—
80#339—102no—
81#335—102no—
82#334—102no—
83#330Dic511yescharacteristic, complemented
84#330Dic512yescomplemented
85#330Dic511yescharacteristic, complemented
86C23×C5#12311yescharacteristic
87C5×Q8—82no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—42no—
93C2×C4×C5C2×C4⋊C411yescharacteristic
94C2×C4×C5C4×D412yes—
95C2×C4×C5#12011yescharacteristic
96C2×C4×C5C22⋊Q812yes—
97C2×Dic5—42no—
98C2×Dic5—82no—
99C5×C8—24no—
100C5×C8—42no—
101#168—42no—
102#168—42no—
103#168—81no—
104C2×M16—22no—
105C2×M16—101no—
106C4⋊Q8Dic1012yes—
107#125C2×Dic511yescharacteristic
108#125C2×Dic511yescharacteristic
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117D2012yes—
112C2×C42—101no—
113C2×C42C22×D511yescharacteristic
114C4⋊C8—52no—
115C4⋊C8—52no—
116C4⋊C8—102no—
117C4⋊C8—102no—
118C4⋊C8—102no—
119C22⋊C8—102no—
120#97—102no—
121#97—102no—
122#97C2×Dic512yes—
123#97C2×Dic512yes—
124C4×C8—22no—
125C4×C8—102no—
126#95—102no—
127C22×C5—21no—
128C22×C5—22no—
129C22×C5#38511yescharacteristic
130C4×C5—21no—
131C4×C5—22no—
132C4×C5—22no—
133C4×C5—42no—
134C4×C5—42no—
135C4×C5#45411yescharacteristic
136C4×C5#45611yescharacteristic
137Dic5—82no—
138C2×Q8—22no—
139C22×C4—201no—
140C22×C4C2×D2011yescharacteristic
141C22×C4#71112yes—
142M16—44no—
143M16—202no—
144C2×C8—22no—
145C2×C8—22no—
146C2×C8—102no—
147C2×C8—102no—
148C2×C8—201no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4C4⋊Dic512yes—
153C4⋊C4C4⋊Dic512yes—
154C22⋊C4—22no—
155C42—22no—
156C42—102no—
157C42—201no—
158C42C2×Dic1011yescharacteristic
159C42D4×D512yes—
160C42C22×Dic511yescharacteristic
161C2×C5—41no—
162C2×C5#185711yescharacteristic
163C2×C5#186112yes—
164C23#403211yescharacteristic
165Q8—82no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—202no—
172C2×C4—402no—
173C2×C4#402412yes—
174C2×C4#402811yescharacteristic
175C2×C4C2×C4⋊Dic511yescharacteristic
176C2×C4D4×Dic512yes—
177C8—24no—
178C8—42no—
179C8—202no—
180C8—202no—
181C8—401no—
182C5#891911yescharacteristic, complemented, Sylow
183C22—21no—
184C22—22no—
185C22#6523911yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—402no—
192C4#6504111yescharacteristic
193C4#6504211yescharacteristic
194C2—41no—
195C2#1060089511yescharacteristic
196C2#1060116812yes—
subgroupG/H
centerC2×C4#4028
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1526C2
socleC22×C5#385
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#1526D5
hypocenterC5#8919
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
14. C5×#330C4semidirect
15. C5×#330C4semidirect
16. C5×#330C4semidirect
83. #330Dic5semidirect
84. #330Dic5semidirect
85. #330Dic5semidirect
182. C5#8919semidirect

Maximal subgroups

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

subgroupindex
#106150642
C5×#15262
#106026332
#106006442
#105981562
#89195