Finite Group Databasebeta

← #12018409

Subgroups — #12018409

Order 1280.

402 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#64969C211yesmaximal, characteristic, complemented
2C2×#64738C212yesmaximal
3#10600588C211yesmaximal, characteristic
4C5×#1376C211yesmaximal, characteristic, complemented
5#10598307C212yesmaximal, complemented
6C2×#4050C2211yescharacteristic
7C2×#4015—21no—
8C2×C5×M32C2212yes—
9C2×C4×C5×C8C2211yescharacteristic
10#65399—21no—
11C2×#3951C2211yescharacteristic
12C2×#3949—21no—
13C2×#3949C2212yes—
14C2×#3937—21no—
15#64969—24no—
16#64738—24no—
17#13371—51nomaximal, Sylow
18C2×#709—21no—
19C22×Dic10—41no—
20C22×C5×C8D411yescharacteristic
21C22×C5×C8C2311yescharacteristic
22C2×C42×C5D411yescharacteristic
23C2×C4⋊Dic5—22no—
24C2×C4⋊Dic5—41no—
25C2×#681—21no—
26C2×Dic20Q811yescharacteristic, complemented
27#4050—22no—
28#4050—22no—
29C2×D40Q811yescharacteristic, complemented
30C2×#677—21no—
31#4015—24no—
32#4015—42no—
33C5×M32—22no—
34C5×M32—22no—
35C2×C5×C16—22no—
36C4×C5×C8—22no—
37#3952—42no—
38#3951—22no—
39#3949—24no—
40#3949—22no—
41#3949D414yes—
42#3937—42no—
43C2×#498—51no—
44C2×#360—52no—
45#1974—51no—
46#1383—52no—
47#1376D511yescharacteristic, complemented
48C22×C4×C5—21no—
49C22×C4×C5C2×D411yescharacteristic
50C2×C22⋊D5—41no—
51C22×Dic5—42no—
52#709—41no—
53#709—41no—
54#709—41no—
55#709—41no—
56C2×D20—21no—
57C2×C4×D5—41no—
58C2×Dic10—21no—
59C2×Dic10—44no—
60C2×Dic10—84no—
61C2×C5×C8—21no—
62C2×C5×C8—21no—
63C2×C5×C8SD1612yes—
64C2×C5×C8C2×D412yes—
65C2×C5×C8C2×Q811yescharacteristic
66C2×C5×C8#4112yes—
67C2×C5×C8#4111yescharacteristic
68C42×C5—21no—
69C42×C5D812yes—
70C4⋊Dic5—24no—
71C4⋊Dic5—44no—
72C4⋊Dic5—42no—
73#681—41no—
74#681—41no—
75C2×#168—41no—
76Dic20—22no—
77D40—22no—
78#677—42no—
79C5×C16—42no—
80C2×#135—51no—
81C2×C4⋊Q8—101no—
82C2×M32C2×D512yes—
83#498—104no—
84C2×#108—51no—
85C2×#106—52no—
86C2×#106—101no—
87C2×#104—101no—
88#408—101no—
89C2×C4×C8C2×D511yescharacteristic
90#360—104no—
91C23×C5AGL(1,ℤ/8)11yescharacteristic
92C22×D5—41no—
93C2×C4×C5—24no—
94C2×C4×C5—22no—
95C2×C4×C5#12011yescharacteristic
96C2×C4×C5C22⋊Q811yescharacteristic
97C2×C4×C5#12411yescharacteristic
98C2×C4×C5C2×D811yescharacteristic
99C2×C4×C5C2×SD1611yescharacteristic
100C2×C4×C5#13711yescharacteristic
101C22⋊D5—81no—
102C22⋊D5—81no—
103C2×Dic5—44no—
104C2×Dic5—41no—
105C2×Dic5—84no—
106D20—41no—
107D20—41no—
108C4×D5—81no—
109C4×D5—81no—
110Dic10—41no—
111Dic10—41no—
112Dic10—88no—
113C5×C8—22no—
114C5×C8C22⋊Q812yes—
115C5×C8#12412yes—
116#168—81no—
117C2×#41—101no—
118C22×Q8—201no—
119#135—102no—
120#135—102no—
121C2×Q16—51no—
122C2×SD16—101no—
123C2×D8—51no—
124C2×M16—101no—
125C22×C8D2011yescharacteristic
126C22×C8C22×D511yescharacteristic
127C4⋊Q8—104no—
128C4⋊Q8—202no—
129C2×C4⋊C4—102no—
130C2×C4⋊C4—201no—
131C2×C42D2011yescharacteristic
132M32—22no—
133M32—22no—
134C2×C16—22no—
135#108—102no—
136#106—54no—
137#106—104no—
138#106—102no—
139#104—202no—
140C22⋊C8—202no—
141C4×C8—22no—
142C22×C5—22no—
143C22×C5#44711yescharacteristic
144C22×C5#47611yescharacteristic
145C22×C5#48911yescharacteristic
146C2×D5—82no—
147C2×D5—81no—
148C4×C5—24no—
149C4×C5#39311yescharacteristic
150C4×C5#44811yescharacteristic
151C4×C5#47411yescharacteristic
152C4×C5#48611yescharacteristic
153Dic5—84no—
154Dic5—81no—
155#41—201no—
156#41—201no—
157#41—201no—
158#41—201no—
159C2×Q8—101no—
160C2×Q8—204no—
161C2×Q8—404no—
162C2×D4—101no—
163C2×D4—201no—
164C22×C4—21no—
165C22×C4—202no—
166C22×C4—201no—
167C22×C4C2×D2011yescharacteristic
168Q16—102no—
169SD16—202no—
170D8—102no—
171M16—201no—
172M16—201no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—201no—
176C2×C8#67712yes—
177C2×C8#70912yes—
178C2×C8D4×D512yes—
179C2×C8#71111yescharacteristic
180C2×C8Q8×D511yescharacteristic
181C4⋊C4—104no—
182C4⋊C4—204no—
183C4⋊C4—202no—
184C42—21no—
185C42D4012yes—
186C16—42no—
187C2×C5—21no—
188C2×C5—21no—
189C2×C5#202311yescharacteristic
190C2×C5#223012yes—
191D5—161no—
192C23—201no—
193C23#405411yescharacteristic
194Q8—201no—
195Q8—201no—
196Q8—408no—
197D4—201no—
198D4—201no—
199D4—401no—
200D4—401no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—201no—
204C2×C4—204no—
205C2×C4—404no—
206C2×C4—401no—
207C2×C4—401no—
208C2×C4#402111yescharacteristic
209C2×C4#402811yescharacteristic
210C2×C4#404311yescharacteristic
211C2×C4C2×#67711yescharacteristic
212C2×C4C2×D4011yescharacteristic
213C2×C4#405511yescharacteristic
214C8—22no—
215C8—401no—
216C8#403112yes—
217C8#404212yes—
218C5#1337111yescharacteristic, complemented, Sylow
219C22—22no—
220C22—401no—
221C22—402no—
222C22#6500311yescharacteristic
223C22#6502111yescharacteristic
224C22#6513111yescharacteristic
225C4—24no—
226C4—404no—
227C4—401no—
228C4#6496211yescharacteristic
229C4#6498311yescharacteristic
230C4#6502711yescharacteristic
231C4#6513511yescharacteristic
232C2—21no—
233C2—21no—
234C2—801no—
235C2#1059947111yescharacteristic
236C2#1060010012yes—
subgroupG/H
centerC22#65131
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC5×#1376C2
socleC22×C5#476
prime radicalC2×#4050C22
hypercenter#1376D5
hypocenterC5#13371
LCSG ▷ C22×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
1. C2×#64969C2semidirect
4. C5×#1376C2semidirect
5. #10598307C2semidirect
26. C2×Dic20Q8semidirect
29. C2×D40Q8semidirect
47. #1376D5semidirect
218. C5#13371semidirect

Maximal subgroups

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

subgroupindex
C2×#649692
C2×#647382
#106005882
C5×#13762
#105983072
#133715