Finite Group Databasebeta

← #12016754

Subgroups — #12016754

Order 1280.

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

normal subgroups only

This group has 458 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#10602805C211yesmaximal, characteristic
4#10602238C212yesmaximal, complemented
5#10598309C212yesmaximal, complemented
6C2×C5×#131C2211yescharacteristic
7#66159—21no—
8C22×Dic20C2211yescharacteristic
9C5×#504—24no—
10C2×C5×M32—22no—
11C2×C5×M32C2212yes—
12#65529—21no—
13#65426C414yescomplemented
14#65409—21no—
15#65405—22no—
16#65395C2212yes—
17#65395C2211yescharacteristic
18#64777—21no—
19#64723—24no—
20#13075—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#4072—22no—
34#4070—24no—
35C2×Dic20—22no—
36C2×Dic20—22no—
37C2×Dic20—21no—
38C2×Dic20C2×C412yes—
39C5×M32—24no—
40C5×M32—22no—
41C5×M32—22no—
42C2×C5×C16—24no—
43C2×C5×C16D414yes—
44#3966—42no—
45#3950—21no—
46#3950—22no—
47#3949—22no—
48#3949C2×C412yes—
49#3948—24no—
50#3407D511yescharacteristic
51#3059—51no—
52#2141—52no—
53#1812—51no—
54#1384—52no—
55C5×#41—22no—
56C5×#41—22no—
57C2×C5×Q8SD1611yescharacteristic
58C2×C5×D4D812yes—
59C2×C5×D4SD1611yescharacteristic
60C22×C4×C5C22⋊C412yes—
61C22×C4×C5C2×D411yescharacteristic
62C22×Dic5—41no—
63C2×Dic10—22no—
64C2×Dic10—42no—
65C2×Dic10—42no—
66C2×Dic10—41no—
67C5×M16—22no—
68C5×M16—24no—
69C2×C5×C8—22no—
70C2×C5×C8—22no—
71C2×C5×C8C22⋊C412yes—
72C2×C5×C8C22×C411yescharacteristic
73C2×C5×C8C2×D412yes—
74C2×C5×C8C2×D411yescharacteristic
75C2×C5×C8#4112yes—
76C22⋊Dic5—44no—
77C22⋊Dic5—41no—
78C22⋊Dic5—42no—
79C4⋊Dic5—22no—
80C4⋊Dic5—42no—
81#683—44no—
82C4×Dic5—41no—
83C4×Dic5—42no—
84Dic20—24no—
85Dic20—41no—
86Dic20—41no—
87C5×C16—24no—
88C22×Q16—51no—
89C2×#131C2×D511yescharacteristic
90#536—101no—
91#504—24no—
92C2×M32—22no—
93C2×M32C2×D512yes—
94#470—54no—
95#467—102no—
96#427—51no—
97#427—52no—
98#419—101no—
99#410—101no—
100#358—104no—
101H(3,ℤ/4)—101no—
102C23×C5#10212yes—
103C23×C5C2×D811yescharacteristic
104C5×Q8—22no—
105C5×D4—24no—
106C5×D4—22no—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5#10212yes—
110C2×C4×C5C2×C22⋊C411yescharacteristic
111C2×C4×C5#12112yes—
112C2×C4×C5C2×SD1611yescharacteristic
113C2×C4×C5#13512yes—
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5—82no—
117C2×Dic5—82no—
118Dic10—42no—
119Dic10—42no—
120Dic10—82no—
121C5×C8—22no—
122C5×C8C4×D412yes—
123C5×C8#12011yescharacteristic
124C5×C8#12311yescharacteristic
125C2×#41D2011yescharacteristic
126C22×Q8—101no—
127C2×Q16—52no—
128C2×Q16—102no—
129C2×Q16—102no—
130C2×Q16—101no—
131#131—22no—
132#131—22no—
133C2×M16C4×D512yes—
134C2×M16D2011yescharacteristic
135C22×C8C22⋊D512yes—
136C22×C8C22×D511yescharacteristic
137C4⋊Q8—201no—
138#124—201no—
139#123—202no—
140C22⋊Q8—104no—
141#117—101no—
142#117—102no—
143M32—24no—
144M32—22no—
145M32—22no—
146C2×C16—24no—
147C2×C16C22⋊D514yes—
148#107—101no—
149#107—102no—
150#106—52no—
151#106—102no—
152#103—104no—
153#99—202no—
154C22×C5—22no—
155C22×C5—41no—
156C22×C5—42no—
157C22×C5C2×#10211yescharacteristic
158C22×C5#46612yes—
159C4×C5—22no—
160C4×C5#38611yescharacteristic
161C4×C5#41611yescharacteristic
162C4×C5#46512yes—
163Dic5—82no—
164Dic5—82no—
165Dic5—162no—
166#41—22no—
167#41—22no—
168C2×Q8—102no—
169C2×Q8—201no—
170C2×Q8—202no—
171C2×Q8—202no—
172C2×Q8#67711yescharacteristic
173C2×D4#67711yescharacteristic
174C2×D4D4012yes—
175C22×C4—201no—
176C22×C4#68512yes—
177C22×C4C2×D2011yescharacteristic
178Q16—104no—
179Q16—201no—
180Q16—201no—
181M16—22no—
182M16—24no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8#68512yes—
186C2×C8C2×C4×D511yescharacteristic
187C2×C8#70912yes—
188C2×C8C2×C22⋊D512yes—
189C2×C8C2×C22⋊D511yescharacteristic
190C4⋊C4—102no—
191C4⋊C4—204no—
192C4⋊C4—202no—
193C22⋊C4—204no—
194C22⋊C4—201no—
195C22⋊C4—202no—
196C42—201no—
197C42—202no—
198C16—24no—
199C2×C5—21no—
200C2×C5—22no—
201C2×C5—42no—
202C2×C5#189311yescharacteristic
203C23#395312yes—
204C23C2×D4011yescharacteristic
205Q8—22no—
206Q8—202no—
207Q8—202no—
208Q8—402no—
209D4—24no—
210D4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—202no—
214C2×C4—202no—
215C2×C4—402no—
216C2×C4—402no—
217C2×C4#395312yes—
218C2×C4C2×#67711yescharacteristic
219C2×C4#405012yes—
220C2×C4C2×#68511yescharacteristic
221C2×C4#407612yes—
222C8—22no—
223C8C4×C22⋊D512yes—
224C8#407511yescharacteristic
225C8#409911yescharacteristic
226C5#1307511yescharacteristic, complemented, Sylow
227C22—22no—
228C22—41no—
229C22—42no—
230C22C2×#395311yescharacteristic
231C22#6540412yes—
232C4—22no—
233C4—402no—
234C4—402no—
235C4—802no—
236C4#6540211yescharacteristic
237C4#6540312yes—
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#13075
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. #10602238C2semidirect
5. #10598309C2semidirect
13. #65426C4semidirect
226. C5#13075semidirect

Maximal subgroups

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

subgroupindex
C5×#34072
#106155382
#106028052
#106022382
#105983092
#130755