Finite Group Databasebeta

← #12003477

Subgroups — #12003477

Order 1280.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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#10610795C211yesmaximal, characteristic
2C5×#1837C211yesmaximal, characteristic, complemented
3#10601298C212yesmaximal, complemented
4#10600528C212yesmaximal, complemented
5#10598203C211yesmaximal, characteristic, complemented
6#65811C2212yes—
7C5×#423C2211yescharacteristic
8C5×#423C2211yescharacteristic
9C2×C4×C5×C8C2211yescharacteristic
10#65424—22no—
11#65213C2212yes—
12#65132—22no—
13#65131—22no—
14C5×#341—22no—
15#64705—22no—
16#64701—22no—
17#64679—24no—
18#10531—51nomaximal, Sylow
19C2×#709—22no—
20C2×C5×M16—21no—
21C2×C5×M16D412yes—
22C22×C5×C8—21no—
23C2×C42×C5C2311yescharacteristic
24#4076—22no—
25#4076—22no—
26C2×#681—22no—
27C2×D40—22no—
28#4021—22no—
29#4020D412yes—
30C4×D20—22no—
31C4×D20—22no—
32#4015D412yes—
33C5×C4⋊C8—22no—
34C5×C4⋊C8—22no—
35C4×C5×C8—21no—
36C4×C5×C8D412yes—
37#3953—24no—
38#3949—22no—
39C4⋊#168—22no—
40C4⋊#168—22no—
41#3253—51no—
42#1837D511yescharacteristic, complemented
43#1560—52no—
44#1492—52no—
45#1309—51no—
46C22×C4×C5C2×D411yescharacteristic
47C22×C4×C5#4112yes—
48C2×C22⋊D5—42no—
49#709—82no—
50#709—82no—
51C2×D20—22no—
52C2×D20—22no—
53C2×D20—22no—
54C2×C4×D5—42no—
55C2×Dic10—22no—
56C5×M16—42no—
57C5×M16—42no—
58C2×C5×C8—22no—
59C2×C5×C8—22no—
60C2×C5×C8—41no—
61C2×C5×C8—41no—
62C2×C5×C8—41no—
63C42×C5C2×D411yescharacteristic
64C42×C5C2×D412yes—
65C42×C5#4111yescharacteristic
66#685—42no—
67#685—42no—
68C4⋊Dic5—22no—
69C4⋊Dic5—22no—
70#681—82no—
71C2×#168—42no—
72D40—82no—
73#532—52no—
74#476—102no—
75#469—102no—
76#459—102no—
77#423—52no—
78#423C2×D511yescharacteristic
79#423C2×D511yescharacteristic
80C2×C4×C8C2×D511yescharacteristic
81#341—22no—
82#333—102no—
83#331—102no—
84D4⋊C8—104no—
85C23×C5#12411yescharacteristic
86C22×D5—42no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—22no—
91C2×C4×C5#12011yescharacteristic
92C2×C4×C5#12112yes—
93C2×C4×C5#12111yescharacteristic
94C2×C4×C5#12312yes—
95C22⋊D5—84no—
96C2×Dic5—42no—
97D20—42no—
98D20—42no—
99D20—42no—
100D20—42no—
101D20—82no—
102C4×D5—82no—
103C4×D5—82no—
104Dic10—82no—
105C5×C8—42no—
106C5×C8—42no—
107C5×C8—81no—
108#168—82no—
109C2×#41—102no—
110C2×D8—102no—
111C2×M16—21no—
112C2×M16—102no—
113C2×M16C22⋊D512yes—
114C22×C8—21no—
115C4⋊Q8—52no—
116#127—52no—
117#124—102no—
118#121—102no—
119#121—102no—
120C4×D4—102no—
121C4×D4—102no—
122C2×C42C22×D511yescharacteristic
123#106—102no—
124C4⋊C8—22no—
125C4⋊C8—22no—
126C4⋊C8—102no—
127C4⋊C8—102no—
128#102—104no—
129C4×C8—21no—
130C4×C8D2012yes—
131C22×C5—22no—
132C22×C5—21no—
133C22×C5#39411yescharacteristic
134C2×D5—82no—
135C2×D5—82no—
136C2×D5—82no—
137C4×C5—22no—
138C4×C5—21no—
139C4×C5#45411yescharacteristic
140C4×C5#45511yescharacteristic
141C4×C5#47112yes—
142C4×C5#47212yes—
143Dic5—82no—
144#41—402no—
145#41—402no—
146C2×Q8—102no—
147C2×D4—102no—
148C2×D4—102no—
149C2×D4—102no—
150C2×D4—202no—
151C22×C4—202no—
152C22×C4#71312yes—
153C22×C4C2×C22⋊D511yescharacteristic
154D8—402no—
155M16—42no—
156M16—42no—
157M16—402no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—202no—
164C4⋊C4—102no—
165C4⋊C4—102no—
166C22⋊C4—202no—
167C22⋊C4—202no—
168C42C2×D2011yescharacteristic
169C42#70911yescharacteristic
170C42D4×D512yes—
171C2×C5—41no—
172C2×C5#204011yescharacteristic
173C2×C5#205112yes—
174D5—162no—
175C23—202no—
176C23#409311yescharacteristic
177Q8—402no—
178D4—202no—
179D4—202no—
180D4—202no—
181D4—202no—
182D4—402no—
183D4—404no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—202no—
189C2×C4—402no—
190C2×C4—402no—
191C2×C4#404012yes—
192C2×C4#404112yes—
193C2×C4#407611yescharacteristic
194C2×C4#408311yescharacteristic
195C8—42no—
196C8—42no—
197C8—81no—
198C8—402no—
199C5#1053111yescharacteristic, complemented, Sylow
200C22—22no—
201C22—21no—
202C22—402no—
203C22—402no—
204C22—402no—
205C22#6528011yescharacteristic
206C4—22no—
207C4—21no—
208C4—402no—
209C4#6518612yes—
210C4#6518712yes—
211C4#6535011yescharacteristic
212C4#6535111yescharacteristic
213C2—41no—
214C2—802no—
215C2#1060035611yescharacteristic
216C2#1060150712yes—
subgroupG/H
centerC22#65280
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1837C2
socleC22×C5#394
prime radical#10610795C2
hypercenter#1837D5
hypocenterC5#10531
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
2. C5×#1837C2semidirect
3. #10601298C2semidirect
4. #10600528C2semidirect
5. #10598203C2semidirect
42. #1837D5semidirect
199. C5#10531semidirect

Maximal subgroups

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

subgroupindex
#106107952
C5×#18372
#106012982
#106005282
#105982032
#105315