Finite Group Databasebeta

← #11993708

Subgroups — #11993708

Order 1280.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2987C211yesmaximal, characteristic
2#10602633C211yesmaximal, characteristic
3#10602614C211yesmaximal, characteristic
4#10601588C212yesmaximal
5#10598239C212yesmaximal
6C5×#533C2211yescharacteristic
7C5×#446—22no—
8C5×#446—22no—
9C5×#433—22no—
10C5×#432C2212yes—
11#65221C2211yescharacteristic
12#65213C2211yescharacteristic
13C4×#681C2212yes—
14#64763C411yescharacteristic, complemented
15#64763C412yescomplemented
16#64763C411yescharacteristic, complemented
17#64752—22no—
18#64700—22no—
19#64699—22no—
20#8919—51nomaximal, Sylow
21C5×C4⋊Q8Q812yes—
22C5×#125C2×C411yescharacteristic
23C5×#125C2×C411yescharacteristic
24C5×C22⋊Q8—22no—
25C4×C5×Q8—22no—
26C5×#117D412yes—
27C2×C42×C5C2311yescharacteristic
28C2×C4×Dic5—21no—
29C2×#681—22no—
30C2×#681—21no—
31C5×C4⋊C8—22no—
32C5×C4⋊C8—22no—
33C5×C4⋊C8D412yes—
34C5×C4⋊C8D412yes—
35C5×C22⋊C8—22no—
36C5×#97—22no—
37C5×#97—22no—
38C4×C5×C8—22no—
39#3963—22no—
40C4⋊#168—22no—
41#3935C2×C412yes—
42#3935C2×C412yes—
43C4×#168—22no—
44#2987D511yescharacteristic
45#1995—51no—
46#1569—52no—
47#1526—51no—
48#1300—52no—
49C2×C5×Q8—22no—
50C22×C4×C5C2×D411yescharacteristic
51C22×C4×C5#4112yes—
52C22×Dic5—41no—
53C2×C5×C8—22no—
54C2×C5×C8—22no—
55C5×C4⋊C4—22no—
56C5×C4⋊C4—22no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4C4⋊C412yes—
59C5×C4⋊C4C4⋊C412yes—
60C5×C22⋊C4—22no—
61C42×C5—22no—
62C42×C5C22×C411yescharacteristic
63C42×C5C2×D412yes—
64C42×C5C2×Q811yescharacteristic
65C4×Dic5—22no—
66C4×Dic5—41no—
67#681—44no—
68#681—42no—
69C2×#168—22no—
70C2×#168—22no—
71C2×#168—41no—
72#533C2×D511yescharacteristic
73#446—22no—
74#446—22no—
75#433—22no—
76#432C2×D512yes—
77#423—51no—
78C4×M16—52no—
79#376—51no—
80#339—102no—
81#335—102no—
82#334—102no—
83#330—51no—
84#330—52no—
85#330—51no—
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—42no—
100C5×C8—42no—
101#168—24no—
102#168—42no—
103#168—81no—
104C2×M16—102no—
105C2×M16—101no—
106C4⋊Q8Dic1012yes—
107#125C4×D511yescharacteristic
108#125C4×D511yescharacteristic
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117C22⋊D512yes—
112C2×C42—101no—
113C2×C42C22×D511yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—102no—
117C4⋊C8C22⋊D512yes—
118C4⋊C8C22⋊D512yes—
119C22⋊C8—22no—
120#97—22no—
121#97—22no—
122#97—52no—
123#97—52no—
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×C4#70912yes—
141C22×C4C2×C22⋊D511yescharacteristic
142M16—204no—
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⋊C4#68312yes—
153C4⋊C4#68312yes—
154C22⋊C4—22no—
155C42—22no—
156C42—102no—
157C42—201no—
158C42C2×Dic1011yescharacteristic
159C42C2×C4×D511yescharacteristic
160C42C2×C22⋊D512yes—
161C2×C5—41no—
162C2×C5#185711yescharacteristic
163C2×C5#186112yes—
164C23#407511yescharacteristic
165Q8—82no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—202no—
172C2×C4—402no—
173C2×C4C2×#68311yescharacteristic
174C2×C4#407012yes—
175C2×C4C4×C22⋊D512yes—
176C2×C4#409911yescharacteristic
177C8—42no—
178C8—42no—
179C8—104no—
180C8—202no—
181C8—401no—
182C5#891911yescharacteristic, complemented, Sylow
183C22—22no—
184C22—21no—
185C22#6549911yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—42no—
190C4—42no—
191C4—402no—
192C4#6553411yescharacteristic
193C4#6553511yescharacteristic
194C2—41no—
195C2#1060245111yescharacteristic
196C2#1060282112yes—
subgroupG/H
centerC2×C4#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2987C2
socleC22×C5#385
prime radicalC23×C5#123
cosocleC2×C42×C5C23
hypercenter#2987D5
hypocenterC5#8919
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
14. #64763C4semidirect
15. #64763C4semidirect
16. #64763C4semidirect
182. C5#8919semidirect

Maximal subgroups

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

subgroupindex
C5×#29872
#106026332
#106026142
#106015882
#105982392
#89195