Finite Group Databasebeta

← #12016769

Subgroups — #12016769

Order 1280.

454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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×#3407C211yesmaximal, characteristic
2#10615538C211yesmaximal, characteristic
3#10602807C211yesmaximal, characteristic
4C2×#64737C212yesmaximal, complemented
5#10598313C212yesmaximal, complemented
6C2×C5×#131C2211yescharacteristic
7#66159—21no—
8C22×Dic20C2211yescharacteristic
9C5×#504—24no—
10C2×C5×M32—22no—
11C2×C5×M32C2212yes—
12#65526—21no—
13#65426C414yes—
14#65409—21no—
15#65405—22no—
16C2×#3951C2212yes—
17#65395C2211yescharacteristic
18#64780—21no—
19#64737—24no—
20#13078—51nomaximal, Sylow
21C2×C5×#41D411yescharacteristic
22C22×Dic10—21no—
23C5×#131—22no—
24C5×#131—22no—
25C2×C5×M16C2×C412yes—
26C2×C5×M16D411yescharacteristic
27C22×C5×C8D412yes—
28C22×C5×C8C2311yescharacteristic
29#4090—41no—
30#4082—41no—
31#4081—42no—
32#4072—21no—
33#4070—24no—
34C2×#681—22no—
35C2×Dic20—22no—
36C2×Dic20—22no—
37C2×Dic20—21no—
38C2×Dic20C2×C412yes—
39C5×M32—24no—
40C5×M32—22no—
41C5×M32D414yes—
42C2×C5×C16—24no—
43C2×C5×C16—22no—
44#3968—41no—
45#3965—41no—
46#3951—22no—
47#3951—22no—
48#3950—21no—
49#3949C2×C412yes—
50#3948—24no—
51#3407D511yescharacteristic
52#3059—51no—
53C2×#362—52no—
54#1813—51no—
55#1389—52no—
56C5×#41—22no—
57C5×#41—22no—
58C2×C5×Q8D811yescharacteristic
59C2×C5×D4D811yescharacteristic
60C2×C5×D4SD1612yes—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—41no—
64C2×Dic10—22no—
65C2×Dic10—42no—
66C2×Dic10—42no—
67C2×Dic10—41no—
68C5×M16—22no—
69C5×M16—24no—
70C2×C5×C8—22no—
71C2×C5×C8—22no—
72C2×C5×C8C22⋊C412yes—
73C2×C5×C8C22×C411yescharacteristic
74C2×C5×C8C2×D412yes—
75C2×C5×C8C2×D411yescharacteristic
76C2×C5×C8#4112yes—
77C22⋊Dic5—44no—
78C22⋊Dic5—41no—
79C4⋊Dic5—22no—
80#683—44no—
81C4×Dic5—41no—
82#681—42no—
83#681—42no—
84C2×#168—42no—
85Dic20—24no—
86Dic20—41no—
87Dic20—41no—
88C5×C16—24no—
89C22×Q16—51no—
90C2×#131C2×D511yescharacteristic
91#536—101no—
92#504—24no—
93C2×M32—22no—
94C2×M32C2×D512yes—
95#470—54no—
96#467—102no—
97C2×#108—52no—
98#427—51no—
99#419—101no—
100#413—101no—
101#362—104no—
102#338—101no—
103C23×C5#10212yes—
104C23×C5C2×SD1611yescharacteristic
105C5×Q8—22no—
106C5×D4—24no—
107C5×D4—22no—
108C2×C4×C5—22no—
109C2×C4×C5—22no—
110C2×C4×C5#10212yes—
111C2×C4×C5C2×C22⋊C411yescharacteristic
112C2×C4×C5#12112yes—
113C2×C4×C5C2×D811yescharacteristic
114C2×C4×C5#13512yes—
115C2×Dic5—42no—
116C2×Dic5—42no—
117C2×Dic5—82no—
118Dic10—42no—
119Dic10—42no—
120Dic10—82no—
121C5×C8—22no—
122C5×C8C4×D412yes—
123C5×C8#12011yescharacteristic
124C5×C8#12311yescharacteristic
125#168—82no—
126C2×#41D2011yescharacteristic
127C22×Q8—101no—
128C2×Q16—52no—
129C2×Q16—102no—
130C2×Q16—102no—
131C2×Q16—101no—
132#131—22no—
133#131—22no—
134C2×M16—102no—
135C2×M16C4×D512yes—
136C2×M16D2011yescharacteristic
137C22×C8C22⋊D512yes—
138C22×C8C22×D511yescharacteristic
139C4⋊Q8—201no—
140#124—201no—
141#123—202no—
142C22⋊Q8—104no—
143#117—101no—
144M32—24no—
145M32—22no—
146M32C22⋊D514yes—
147C2×C16—24no—
148C2×C16—22no—
149#108—102no—
150#108—102no—
151#107—101no—
152#106—52no—
153#103—104no—
154#101—201no—
155#100—201no—
156C22×C5—22no—
157C22×C5—41no—
158C22×C5—42no—
159C22×C5C2×#10211yescharacteristic
160C22×C5#46512yes—
161C4×C5—22no—
162C4×C5#38611yescharacteristic
163C4×C5#41611yescharacteristic
164C4×C5#46612yes—
165Dic5—82no—
166Dic5—82no—
167#41—22no—
168#41—22no—
169C2×Q8—102no—
170C2×Q8—201no—
171C2×Q8—202no—
172C2×Q8—202no—
173C2×Q8D4011yescharacteristic
174C2×D4#67712yes—
175C2×D4D4011yescharacteristic
176C22×C4—201no—
177C22×C4#68512yes—
178C22×C4C2×D2011yescharacteristic
179Q16—104no—
180Q16—201no—
181Q16—201no—
182M16—22no—
183M16—24no—
184M16—202no—
185M16—202no—
186C2×C8—22no—
187C2×C8—22no—
188C2×C8—202no—
189C2×C8#68512yes—
190C2×C8C2×C4×D511yescharacteristic
191C2×C8#70912yes—
192C2×C8C2×C22⋊D512yes—
193C2×C8C2×C22⋊D511yescharacteristic
194C4⋊C4—102no—
195C4⋊C4—204no—
196C22⋊C4—204no—
197C22⋊C4—201no—
198C42—201no—
199C16—24no—
200C2×C5—21no—
201C2×C5—22no—
202C2×C5—42no—
203C2×C5#189311yescharacteristic
204C23#395312yes—
205C23C2×#67711yescharacteristic
206Q8—22no—
207Q8—202no—
208Q8—202no—
209Q8—402no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4—402no—
217C2×C4#395312yes—
218C2×C4C2×D4011yescharacteristic
219C2×C4#405012yes—
220C2×C4C2×#68511yescharacteristic
221C2×C4#407612yes—
222C8—22no—
223C8—402no—
224C8C4×C22⋊D512yes—
225C8#407511yescharacteristic
226C8#409911yescharacteristic
227C5#1307811yescharacteristic, complemented, Sylow
228C22—22no—
229C22—41no—
230C22—42no—
231C22C2×#395311yescharacteristic
232C22#6540312yes—
233C4—22no—
234C4—402no—
235C4—402no—
236C4#6540211yescharacteristic
237C4#6540412yes—
238C4#6550211yescharacteristic
239C2—21no—
240C2—22no—
241C2—42no—
242C2#1060276611yescharacteristic
subgroupG/H
centerC2#10602766
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#3407C2
socleC2×C5#1893
prime radicalC2×C5×#41D4
cosocleC22×C5×C8C23
hypercenter#3407D5
hypocenterC5#13078
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
4. C2×#64737C2semidirect
5. #10598313C2semidirect
227. C5#13078semidirect

Maximal subgroups

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

subgroupindex
C5×#34072
#106155382
#106028072
C2×#647372
#105983132
#130785