Finite Group Databasebeta

← #12003438

Subgroups — #12003438

Order 1280.

386 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 75 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×#1849C211yesmaximal, characteristic, complemented
3#10601297C212yesmaximal, complemented
4#10600591C212yesmaximal, complemented
5#10598207C211yesmaximal, characteristic, complemented
6#65811C2212yes—
7C2×C5×#108—22no—
8C5×#423C2211yescharacteristic
9C5×#423C2211yescharacteristic
10C2×C5×#97C2211yescharacteristic
11#65424—22no—
12#65215C2212yes—
13#65132—22no—
14#65131—22no—
15#64706—22no—
16#64705—22no—
17#64684—24no—
18#10524—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×D40—22no—
27#4021—22no—
28#4020D412yes—
29C4×D20—22no—
30C4×D20—22no—
31#4015D412yes—
32C5×#108—44no—
33C5×C4⋊C8—22no—
34C5×C4⋊C8—22no—
35C5×#97—21no—
36C5×#97D412yes—
37C22⋊#168—22no—
38#3953—24no—
39#3949—22no—
40C4⋊#168—22no—
41#3935—22no—
42#3253—51no—
43#1849D511yescharacteristic, complemented
44#1557—52no—
45#1530—52no—
46#1307—51no—
47C22×C4×C5C2×D411yescharacteristic
48C22×C4×C5#4112yes—
49C2×C22⋊D5—42no—
50#709—84no—
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—22no—
61C2×C5×C8—22no—
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—
70C2×#168—42no—
71D40—82no—
72#532—52no—
73#476—102no—
74#469—102no—
75#459—102no—
76#432—52no—
77C2×#108—22no—
78#423C2×D511yescharacteristic
79#423C2×D511yescharacteristic
80C2×#97C2×D511yescharacteristic
81#332—102no—
82#331—102no—
83#329—104no—
84C23×C5#12411yescharacteristic
85C22×D5—42no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—42no—
89C2×C4×C5#12011yescharacteristic
90C2×C4×C5#12112yes—
91C2×C4×C5#12111yescharacteristic
92C2×C4×C5#12312yes—
93C22⋊D5—84no—
94C2×Dic5—42no—
95D20—42no—
96D20—42no—
97D20—82no—
98D20—82no—
99C4×D5—84no—
100Dic10—82no—
101C5×C8—24no—
102C5×C8—42no—
103C5×C8—81no—
104#168—82no—
105C2×#41—102no—
106C2×D8—102no—
107C2×M16—21no—
108C2×M16C22⋊D512yes—
109C22×C8—21no—
110C4⋊Q8—52no—
111#127—52no—
112#124—102no—
113#121—102no—
114#121—102no—
115C4×D4—102no—
116C4×D4—102no—
117C2×C42C22×D511yescharacteristic
118#108—44no—
119#106—102no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—102no—
123#102—104no—
124C22⋊C8—102no—
125#97—21no—
126#97—102no—
127#97D2012yes—
128C22×C5—22no—
129C22×C5—21no—
130C22×C5#39411yescharacteristic
131C2×D5—82no—
132C2×D5—82no—
133C2×D5—82no—
134C4×C5—22no—
135C4×C5—22no—
136C4×C5—21no—
137C4×C5#45311yescharacteristic
138C4×C5#45611yescharacteristic
139Dic5—82no—
140#41—404no—
141C2×Q8—102no—
142C2×D4—102no—
143C2×D4—102no—
144C2×D4—102no—
145C2×D4—202no—
146C22×C4—202no—
147C22×C4#71312yes—
148C22×C4C2×C22⋊D511yescharacteristic
149D8—402no—
150M16—42no—
151M16—42no—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—202no—
158C4⋊C4—102no—
159C4⋊C4—102no—
160C22⋊C4—202no—
161C22⋊C4—202no—
162C42C2×D2011yescharacteristic
163C42#70911yescharacteristic
164C42D4×D512yes—
165C2×C5—41no—
166C2×C5#203911yescharacteristic
167C2×C5#204812yes—
168D5—162no—
169C23—202no—
170C23#409311yescharacteristic
171Q8—402no—
172D4—202no—
173D4—202no—
174D4—402no—
175D4—402no—
176D4—404no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—202no—
181C2×C4—404no—
182C2×C4#404012yes—
183C2×C4#404112yes—
184C2×C4#407611yescharacteristic
185C2×C4#408311yescharacteristic
186C8—24no—
187C8—42no—
188C8—81no—
189C8—402no—
190C5#1052411yescharacteristic, complemented, Sylow
191C22—22no—
192C22—21no—
193C22—402no—
194C22—402no—
195C22—402no—
196C22#6528011yescharacteristic
197C4—22no—
198C4—22no—
199C4—21no—
200C4—402no—
201C4#6536611yescharacteristic
202C4#6538411yescharacteristic
203C2—41no—
204C2—802no—
205C2#1060038611yescharacteristic
206C2#1060152912yes—
subgroupG/H
centerC22#65280
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1849C2
socleC22×C5#394
prime radical#10610795C2
hypercenter#1849D5
hypocenterC5#10524
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
2. C5×#1849C2semidirect
3. #10601297C2semidirect
4. #10600591C2semidirect
5. #10598207C2semidirect
43. #1849D5semidirect
190. C5#10524semidirect

Maximal subgroups

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

subgroupindex
#106107952
C5×#18492
#106012972
#106005912
#105982072
#105245