Finite Group Databasebeta

← #12013533

Subgroups — #12013533

Order 1280.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2169C211yesmaximal, characteristic, complemented
2#10601643C211yesmaximal, characteristic, complemented
3#10601640C211yesmaximal, characteristic
4#10599854C211yesmaximal, characteristic, complemented
5#10598052C211yesmaximal, characteristic, complemented
6#10598051C211yesmaximal, characteristic, complemented
7#10597991C211yesmaximal, characteristic, complemented
8C2×C5×M32—21no—
9C5×C8×D4C2211yescharacteristic
10#65304—21no—
11#65296—21no—
12C2×#3932—21no—
13C2×#3932—21no—
14#64988C2211yescharacteristic
15#64984C2211yescharacteristic
16C5×C4⋊C16C2211yescharacteristic
17C5×C22⋊C16—21no—
18C4×C5×C16C2211yescharacteristic
19#64705—21no—
20#64702—21no—
21#64678C2211yescharacteristic
22#64678C2211yescharacteristic
23#12435—51nomaximal, Sylow
24C22×C5×C8—21no—
25C4×C5×D4D411yescharacteristic
26C2×#686—41no—
27C2×Dic20—21no—
28C2×Dic20—21no—
29C2×D40—21no—
30C2×D40—21no—
31#4020—21no—
32#4015—21no—
33C5×M32—42no—
34C2×C5×C16—21no—
35C2×C5×C16D411yescharacteristic
36C2×C5×C16D411yescharacteristic
37C5×C4⋊C8D411yescharacteristic
38C5×C22⋊C8—21no—
39C4×C5×C8C2311yescharacteristic
40#3964—41no—
41#3941—41no—
42#3939—41no—
43C4⋊#168—21no—
44C4⋊#168—21no—
45#3932—42no—
46#3932—42no—
47#2248—51no—
48#2169D511yescharacteristic, complemented
49#1669—51no—
50#1667—51no—
51#1371—51no—
52#1362—51no—
53#1361—51no—
54C2×C5×D4D811yescharacteristic
55C22×C4×C5—21no—
56C2×D20—41no—
57C2×D20—41no—
58C2×D20—41no—
59C2×Dic10—41no—
60C2×C5×C8—21no—
61C2×C5×C8—41no—
62C2×C5×C8—41no—
63C2×C5×C8C2×D411yescharacteristic
64C2×C5×C8#4111yescharacteristic
65C5×C4⋊C4D811yescharacteristic
66C5×C22⋊C4—21no—
67C42×C5C2×D411yescharacteristic
68#686—82no—
69C4⋊Dic5—41no—
70C4⋊Dic5—41no—
71C2×#168—41no—
72C2×#168—41no—
73Dic20—41no—
74Dic20—41no—
75Dic20—81no—
76D40—41no—
77D40—41no—
78D40—81no—
79C5×C16—21no—
80C5×C16—41no—
81C5×C16D812yescomplemented
82C2×SD32—101no—
83C2×SD32—101no—
84C2×M32—21no—
85#494—51no—
86#493—51no—
87#474—101no—
88#459—101no—
89C8×D4C2×D511yescharacteristic
90C4⋊C16C2×D511yescharacteristic
91C22⋊C16—21no—
92C4×C16C2×D511yescharacteristic
93#335—51no—
94#335—51no—
95#332—101no—
96#331—101no—
97C23×C5—21no—
98C22×D5—81no—
99C5×D4—21no—
100C5×D4—21no—
101C2×C4×C5—21no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5#12111yescharacteristic
105C2×C4×C5C2×D811yescharacteristic
106C2×C4×C5#13511yescharacteristic
107C2×Dic5—81no—
108D20—81no—
109D20—81no—
110D20—81no—
111D20—81no—
112D20—161no—
113Dic10—81no—
114Dic10—81no—
115C5×C8—21no—
116C5×C8—41no—
117C5×C8C2×D811yescharacteristic
118C5×C8AGL(1,ℤ/8)11yescharacteristic
119#168—81no—
120#168—81no—
121C2×Q16—101no—
122C2×Q16—101no—
123C2×D8—101no—
124C2×D8—101no—
125C2×D8—201no—
126C22×C8—21no—
127C4⋊Q8—101no—
128#127—101no—
129C4×D4D2011yescharacteristic
130SD32—202no—
131SD32—202no—
132M32—42no—
133C2×C16—21no—
134C2×C16C22⋊D511yescharacteristic
135C2×C16C22⋊D511yescharacteristic
136#107—201no—
137C4⋊C8—101no—
138C4⋊C8—101no—
139C4⋊C8D2011yescharacteristic
140#102—201no—
141#102—201no—
142C22⋊C8—21no—
143C4×C8C22×D511yescharacteristic
144C22×C5—41no—
145C22×C5—41no—
146C22×C5—41no—
147C22×C5#46611yescharacteristic
148C2×D5—161no—
149C2×D5—161no—
150C2×D5—161no—
151C4×C5—21no—
152C4×C5—41no—
153C4×C5#45911yescharacteristic
154C4×C5#47211yescharacteristic
155C4×C5#50911yescharacteristic
156C4×C5#51011yescharacteristic
157Dic5—161no—
158C2×Q8—201no—
159C2×D4—201no—
160C2×D4—201no—
161C2×D4—201no—
162C2×D4D4011yescharacteristic
163C22×C4—21no—
164Q16—201no—
165Q16—201no—
166Q16—401no—
167D8—201no—
168D8—201no—
169D8—401no—
170D8—402no—
171C2×C8—21no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—201no—
175C2×C8—201no—
176C2×C8#70911yescharacteristic
177C2×C8C2×C22⋊D511yescharacteristic
178C4⋊C4—201no—
179C4⋊C4—201no—
180C4⋊C4D4011yescharacteristic
181C22⋊C4—21no—
182C42C2×D2011yescharacteristic
183C16—21no—
184C16—41no—
185C16#68612yescomplemented
186C2×C5—81no—
187C2×C5#166711yescharacteristic
188C2×C5#222011yescharacteristic
189C2×C5#222311yescharacteristic
190D5—321no—
191C23—21no—
192C23—401no—
193Q8—401no—
194Q8—401no—
195D4—21no—
196D4—21no—
197D4—401no—
198D4—401no—
199D4—401no—
200D4—401no—
201D4—801no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—401no—
206C2×C4C2×D4011yescharacteristic
207C2×C4#405011yescharacteristic
208C2×C4#407611yescharacteristic
209C8—21no—
210C8—41no—
211C8—401no—
212C8—401no—
213C8C2×#68611yescharacteristic
214C8#409511yescharacteristic
215C5#1243511yescharacteristic, complemented, Sylow
216C22—41no—
217C22—41no—
218C22—41no—
219C22—801no—
220C22—801no—
221C22—801no—
222C22#6540411yescharacteristic
223C4—21no—
224C4—41no—
225C4—801no—
226C4#6519711yescharacteristic
227C4#6519811yescharacteristic
228C4#6530411yescharacteristic
229C4#6543111yescharacteristic
230C2—81no—
231C2—1601no—
232C2#1060164011yescharacteristic
233C2#1060223711yescharacteristic
234C2#1060224811yescharacteristic
subgroupG/H
centerC22#65404
commutator, cosocleC4×C5×C8C23
FrattiniC4×C8C22×D5
FittingC5×#2169C2
socleC22×C5#466
prime radical#10601640C2
hypercenter#2169D5
hypocenterC5#12435
LCSG ▷ C4×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. C5×#2169C2semidirect
2. #10601643C2semidirect
4. #10599854C2semidirect
5. #10598052C2semidirect
6. #10598051C2semidirect
7. #10597991C2semidirect
48. #2169D5semidirect
81. C5×C16D8semidirect
185. C16#686semidirect
215. C5#12435semidirect

Maximal subgroups

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

subgroupindex
C5×#21692
#106016432
#106016402
#105998542
#105980522
#105980512
#105979912
#124355