Finite Group Databasebeta

← #12004201

Subgroups — #12004201

Order 1280.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#10601618C211yesmaximal, characteristic
2#10601613C211yesmaximal, characteristic
3#10601564C211yesmaximal, characteristic
4#10601542C211yesmaximal, characteristic
5C5×#1287C211yesmaximal, characteristic
6#10598249C211yesmaximal, characteristic
7#10598246C211yesmaximal, characteristic
8#65804C2211yescharacteristic
9C5×#432C2211yescharacteristic
10C5×#432C2211yescharacteristic
11C5×#431C2211yescharacteristic
12#65215C2211yescharacteristic
13#65213C2211yescharacteristic
14C2×C4⋊#168C2211yescharacteristic
15#64706—21no—
16#64706—21no—
17#64702—21no—
18#64701—21no—
19#64677—22no—
20#64676—22no—
21#10648—51nomaximal, Sylow
22C2×C42×C5C2311yescharacteristic
23#4072—21no—
24#4070—21no—
25#4070—21no—
26C2×#681—21no—
27C22×#168—21no—
28#4016—21no—
29#4015D411yescharacteristic
30#4015D411yescharacteristic
31C4×Dic10—21no—
32C4×Dic10—21no—
33C5×C4⋊C8—21no—
34C5×C4⋊C8—21no—
35C5×C4⋊C8—21no—
36C5×C22⋊C8—21no—
37C5×C22⋊C8—21no—
38C5×C22⋊C8—21no—
39C5×#97—21no—
40C5×#97—21no—
41C4×C5×C8D412yes—
42C22⋊#168—21no—
43C4⋊#168—21no—
44C4⋊#168—21no—
45C4⋊#168—21no—
46C4⋊#168—21no—
47C4⋊#168—21no—
48#3935—21no—
49#1570—51no—
50#1559—51no—
51#1552—51no—
52#1497—51no—
53#1307—51no—
54#1290—51no—
55#1287D511yescharacteristic
56C22×C4×C5#4111yescharacteristic
57C22×C4×C5#4111yescharacteristic
58C22×C4×C5#4111yescharacteristic
59C2×Dic10—21no—
60C2×Dic10—21no—
61C2×C5×C8—22no—
62C2×C5×C8—41no—
63C2×C5×C8—41no—
64C42×C5C2×D411yescharacteristic
65C42×C5C2×D411yescharacteristic
66C42×C5#4111yescharacteristic
67C42×C5#4111yescharacteristic
68C22⋊Dic5—41no—
69C4⋊Dic5—21no—
70C4⋊Dic5—21no—
71C4⋊Dic5—21no—
72C4⋊Dic5—21no—
73#683—41no—
74#683—41no—
75C4×Dic5—41no—
76#681—81no—
77C2×#168—41no—
78C2×#168—41no—
79C2×#168—41no—
80C2×#168—81no—
81#533—51no—
82#432—51no—
83#432C2×D511yescharacteristic
84#432C2×D511yescharacteristic
85#431C2×D511yescharacteristic
86#423—51no—
87C2×C4⋊C8—51no—
88#334—102no—
89#333—101no—
90#332—101no—
91#332—101no—
92#332—101no—
93Q8⋊C8—102no—
94C23×C5#12611yescharacteristic
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—41no—
98C2×C4×C5—41no—
99C2×C4×C5#12111yescharacteristic
100C2×C4×C5#12311yescharacteristic
101C2×C4×C5#12311yescharacteristic
102C2×C4×C5#12311yescharacteristic
103C2×C4×C5#12411yescharacteristic
104C2×C4×C5#12611yescharacteristic
105C2×Dic5—41no—
106C2×Dic5—41no—
107Dic10—41no—
108Dic10—41no—
109Dic10—81no—
110C5×C8—42no—
111C5×C8—81no—
112C5×C8—81no—
113#168—81no—
114#168—81no—
115#168—81no—
116C2×M16—101no—
117C22×C8—101no—
118C4⋊Q8—51no—
119C4⋊Q8—51no—
120#125—101no—
121C22⋊Q8—101no—
122C22⋊Q8—101no—
123C4×Q8—101no—
124C4×Q8—101no—
125#117—101no—
126C2×C42C22×D511yescharacteristic
127C4⋊C8—21no—
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—101no—
131C4⋊C8—101no—
132C4⋊C8—101no—
133C4⋊C8—101no—
134C4⋊C8—101no—
135C22⋊C8—21no—
136C22⋊C8—21no—
137C22⋊C8—21no—
138C22⋊C8—101no—
139#97—21no—
140#97—21no—
141#97—101no—
142C4×C8D2012yes—
143C22×C5—21no—
144C22×C5—21no—
145C22×C5—21no—
146C22×C5#39711yescharacteristic
147C4×C5—21no—
148C4×C5—21no—
149C4×C5—21no—
150C4×C5—21no—
151C4×C5—21no—
152C4×C5#47111yescharacteristic
153C4×C5#47111yescharacteristic
154Dic5—81no—
155Dic5—81no—
156C2×Q8—101no—
157C2×Q8—101no—
158C22×C4#70911yescharacteristic
159C22×C4#71111yescharacteristic
160C22×C4#71311yescharacteristic
161M16—401no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—201no—
166C2×C8—201no—
167C2×C8—201no—
168C2×C8—401no—
169C4⋊C4—101no—
170C4⋊C4—101no—
171C4⋊C4—101no—
172C4⋊C4—101no—
173C4⋊C4—201no—
174C4⋊C4—201no—
175C22⋊C4—201no—
176C42—201no—
177C42C2×D2011yescharacteristic
178C42#70911yescharacteristic
179C42D4×D511yescharacteristic
180C42#71111yescharacteristic
181C2×C5—41no—
182C2×C5#207911yescharacteristic
183C2×C5#208011yescharacteristic
184C2×C5#208211yescharacteristic
185C23#404411yescharacteristic
186Q8—201no—
187Q8—201no—
188Q8—401no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—201no—
194C2×C4—201no—
195C2×C4#402111yescharacteristic
196C2×C4#402911yescharacteristic
197C2×C4#402911yescharacteristic
198C2×C4#403211yescharacteristic
199C2×C4#404111yescharacteristic
200C2×C4#404411yescharacteristic
201C8—42no—
202C8—81no—
203C8—81no—
204C8—401no—
205C8—401no—
206C8—401no—
207C5#1064811yescharacteristic, complemented, Sylow
208C22—21no—
209C22—21no—
210C22—21no—
211C22#6496311yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—401no—
218C4—401no—
219C4#6518711yescharacteristic
220C4#6518711yescharacteristic
221C2—41no—
222C2#1059949311yescharacteristic
223C2#1059971511yescharacteristic
224C2#1059981511yescharacteristic
subgroupG/H
centerC22#64963
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1287C2
socleC22×C5#397
prime radicalC23×C5#126
hypercenter#1287D5
hypocenterC5#10648
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
207. C5#10648semidirect

Maximal subgroups

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

subgroupindex
#106016182
#106016132
#106015642
#106015422
C5×#12872
#105982492
#105982462
#106485