Finite Group Databasebeta

← #12018693

Subgroups — #12018693

Order 1280.

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

normal subgroups only

This group has 436 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×#64988C211yesmaximal, characteristic
2C2×#64737C212yesmaximal
3#10602238C212yesmaximal
4#10600587C211yesmaximal, characteristic
5C5×#1376C211yesmaximal, characteristic
6C22×Dic20—21no—
7C22×Dic20C2212yes—
8C2×#4015—21no—
9C2×C5×M32C2212yes—
10C2×C4×C5×C8C2211yescharacteristic
11C2×#3951C2211yescharacteristic
12#65395C2211yescharacteristic
13#65391—21no—
14#64988—24no—
15#64743—21no—
16#64737—24no—
17#64723—24no—
18#13415—51nomaximal, Sylow
19C22×Dic10—22no—
20C22×C5×C8D411yescharacteristic
21C22×C5×C8C2311yescharacteristic
22C2×C42×C5D411yescharacteristic
23#4072—21no—
24C2×C4⋊Dic5—42no—
25C2×#681—21no—
26C2×Dic20—22no—
27C2×Dic20—22no—
28C2×Dic20—22no—
29C2×Dic20—22no—
30C2×Dic20—24no—
31C2×Dic20—22no—
32C2×Dic20—42no—
33C2×Dic20—42no—
34C2×Dic20D414yes—
35#4015—24no—
36#4015—42no—
37C5×M32—22no—
38C5×M32—22no—
39C2×C5×C16—22no—
40C4×C5×C8—22no—
41#3951—22no—
42#3950D412yes—
43#3949—21no—
44#3946—42no—
45C2×#494—51no—
46C2×#362—52no—
47#2141—52no—
48#1945—51no—
49#1376D511yescharacteristic
50C22×C4×C5—21no—
51C22×C4×C5C2×D411yescharacteristic
52C22×Dic5—42no—
53C2×Dic10—24no—
54C2×Dic10—42no—
55C2×Dic10—42no—
56C2×Dic10—42no—
57C2×Dic10—42no—
58C2×Dic10—42no—
59C2×C5×C8—21no—
60C2×C5×C8—21no—
61C2×C5×C8D812yes—
62C2×C5×C8C2×D411yescharacteristic
63C2×C5×C8C2×D412yes—
64C2×C5×C8#4112yes—
65C2×C5×C8#4111yescharacteristic
66C42×C5—21no—
67C42×C5SD1612yes—
68C22⋊Dic5—41no—
69C4⋊Dic5—22no—
70C4⋊Dic5—48no—
71C4×Dic5—41no—
72#681—41no—
73#681—41no—
74C2×#168—41no—
75Dic20—24no—
76Dic20—24no—
77Dic20—48no—
78Dic20—42no—
79Dic20—42no—
80C5×C16—42no—
81C22×Q16—52no—
82C22×Q16—101no—
83C2×C4⋊Q8—101no—
84C2×M32C2×D512yes—
85#494—104no—
86C2×#108—51no—
87#427—51no—
88#424—101no—
89C2×C4×C8C2×D511yescharacteristic
90#362—104no—
91#358—104no—
92#339—101no—
93C23×C5AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C5—24no—
95C2×C4×C5—22no—
96C2×C4×C5#12011yescharacteristic
97C2×C4×C5#12111yescharacteristic
98C2×C4×C5#12411yescharacteristic
99C2×C4×C5C2×D811yescharacteristic
100C2×C4×C5C2×SD1611yescharacteristic
101C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
102C2×Dic5—44no—
103C2×Dic5—42no—
104C2×Dic5—82no—
105C2×Dic5—82no—
106Dic10—44no—
107Dic10—44no—
108Dic10—82no—
109Dic10—82no—
110C5×C8—22no—
111C5×C8#12112yes—
112C5×C8#12312yes—
113#168—81no—
114C22×Q8—102no—
115C2×Q16—54no—
116C2×Q16—104no—
117C2×Q16—102no—
118C2×Q16—102no—
119C2×Q16—102no—
120C2×Q16—102no—
121C2×Q16—102no—
122C2×Q16—202no—
123C2×Q16—202no—
124C2×M16—101no—
125C22×C8D2011yescharacteristic
126C22×C8C22×D511yescharacteristic
127C4⋊Q8—104no—
128C4⋊Q8—202no—
129#117—101no—
130C2×C4⋊C4—202no—
131C2×C42D2011yescharacteristic
132M32—22no—
133M32—22no—
134C2×C16—22no—
135#108—102no—
136#107—52no—
137#106—101no—
138C4⋊C8—202no—
139C4×C8—22no—
140C22×C5—22no—
141C22×C5#45011yescharacteristic
142C22×C5#45911yescharacteristic
143C22×C5#49011yescharacteristic
144C4×C5—24no—
145C4×C5#39411yescharacteristic
146C4×C5#44711yescharacteristic
147C4×C5#46011yescharacteristic
148C4×C5#48611yescharacteristic
149Dic5—82no—
150Dic5—84no—
151C2×Q8—104no—
152C2×Q8—202no—
153C2×Q8—202no—
154C2×Q8—202no—
155C2×Q8—202no—
156C2×Q8—202no—
157C22×C4—21no—
158C22×C4—202no—
159C22×C4C2×D2011yescharacteristic
160Q16—104no—
161Q16—104no—
162Q16—208no—
163Q16—202no—
164Q16—202no—
165M16—201no—
166M16—201no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—201no—
170C2×C8D4012yes—
171C2×C8#70912yes—
172C2×C8D4×D511yescharacteristic
173C2×C8D4×D512yes—
174C2×C8#71311yescharacteristic
175C4⋊C4—102no—
176C4⋊C4—208no—
177C22⋊C4—201no—
178C42—21no—
179C42—201no—
180C42#67712yes—
181C16—42no—
182C2×C5—21no—
183C2×C5—21no—
184C2×C5#204111yescharacteristic
185C2×C5#221412yes—
186C23#405411yescharacteristic
187Q8—204no—
188Q8—204no—
189Q8—402no—
190Q8—402no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—202no—
194C2×C4—204no—
195C2×C4—402no—
196C2×C4—402no—
197C2×C4#402111yescharacteristic
198C2×C4#402811yescharacteristic
199C2×C4#404111yescharacteristic
200C2×C4C2×#67711yescharacteristic
201C2×C4C2×D4011yescharacteristic
202C2×C4#405411yescharacteristic
203C8—22no—
204C8—401no—
205C8#403012yes—
206C8#404012yes—
207C5#1341511yescharacteristic, complemented, Sylow
208C22—22no—
209C22#6500211yescharacteristic
210C22#6502011yescharacteristic
211C22#6513211yescharacteristic
212C4—24no—
213C4—402no—
214C4—404no—
215C4#6496111yescharacteristic
216C4#6498311yescharacteristic
217C4#6502111yescharacteristic
218C4#6513711yescharacteristic
219C2—21no—
220C2—21no—
221C2#1059942211yescharacteristic
222C2#1060009912yes—
subgroupG/H
centerC22#65132
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC5×#1376C2
socleC22×C5#459
prime radicalC23×C5AGL(1,ℤ/8)
hypercenter#1376D5
hypocenterC5#13415
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
207. C5#13415semidirect

Maximal subgroups

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

subgroupindex
C2×#649882
C2×#647372
#106022382
#106005872
C5×#13762
#134155