Finite Group Databasebeta

← #11988642

Subgroups — #11988642

Order 1280.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#10608335C211yesmaximal, characteristic
2C5×#2095C211yesmaximal, characteristic
3#10600383C212yesmaximal
4#10598133C211yesmaximal, characteristic
5#10597971C212yesmaximal
6C2×C5×#107—21no—
7C2×C5×#103—21no—
8C5×#391C2211yescharacteristic
9C5×#384C2211yescharacteristic
10#65519—21no—
11#65268—21no—
12C2×#3942—22no—
13C2×#3939—22no—
14#65218C2212yes—
15#64945—22no—
16#64935—22no—
17C5×#336C2211yescharacteristic
18#64744C2212yes—
19#7837—51nomaximal, Sylow
20C22×C5×Q8D411yescharacteristic
21C22×Dic10—21no—
22C22×Dic10D412yes—
23C22×C5×C8—21no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—22no—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C42×C5C2311yescharacteristic
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C2×C4×Dic5—21no—
32C22×#168—22no—
33C5×#107—42no—
34C5×#103—42no—
35C5×#95—22no—
36#3963—21no—
37#3963—22no—
38#3963—22no—
39#3963—22no—
40#3942—44no—
41#3939—44no—
42#2811—51no—
43#2095—52no—
44#2095D511yescharacteristic
45#1272—51no—
46#1272—52no—
47C2×C5×Q8—21no—
48C2×C5×Q8—41no—
49C2×C5×Q8—41no—
50C2×C5×Q8Q1612yes—
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5—41no—
54C22×C4×C5C2×D412yes—
55C22×C4×C5C2×D411yescharacteristic
56C22×Dic5—22no—
57C22×Dic5—22no—
58C2×Dic10—22no—
59C2×Dic10—42no—
60C2×Dic10—42no—
61C2×Dic10—82no—
62C2×Dic10—81no—
63C2×Dic10Q1614yes—
64C2×C5×C8—22no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C5×C4⋊C4—41no—
68C5×C4⋊C4—42no—
69C5×C4⋊C4—42no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C42×C5—41no—
73C4⋊Dic5—42no—
74C4⋊Dic5—81no—
75#683—82no—
76C4×Dic5—81no—
77C2×#168—24no—
78C2×#168—42no—
79C2×#168—42no—
80C2×#107—21no—
81C2×#107—102no—
82C2×#103—21no—
83C2×#103—102no—
84#395—102no—
85#395—101no—
86#391—52no—
87#391—102no—
88#391—101no—
89#391C2×D511yescharacteristic
90#384C2×D511yescharacteristic
91#336—52no—
92#336C2×D511yescharacteristic
93C23×C5#12011yescharacteristic
94C5×Q8—42no—
95C5×Q8—81no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5—21no—
100C2×C4×C5—22no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—42no—
104C2×C4×C5—41no—
105C2×C4×C5—81no—
106C2×C4×C5—82no—
107C2×C4×C5C2×Q1612yes—
108C2×C4×C5C2×Q1611yescharacteristic
109C2×C4×C5#13711yescharacteristic
110C2×C4×C5#13712yes—
111C2×Dic5—24no—
112C2×Dic5—42no—
113C2×Dic5—42no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5—42no—
117Dic10—44no—
118Dic10—82no—
119Dic10—84no—
120C5×C8—42no—
121#168—44no—
122C22×Q8—52no—
123C22×Q8—101no—
124C22×Q8C22⋊D511yescharacteristic
125C22×C8—21no—
126C22×C8—102no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—52no—
130C2×C4⋊C4—102no—
131C2×C4⋊C4—101no—
132C2×C4⋊C4C22⋊D511yescharacteristic
133C2×C42—101no—
134C2×C42C22×D511yescharacteristic
135#107—42no—
136#107—204no—
137#103—42no—
138#103—204no—
139#95—22no—
140#95—102no—
141#95—101no—
142#95—102no—
143#95—102no—
144C22×C5#45111yescharacteristic
145C22×C5#45112yes—
146C22×C5#45311yescharacteristic
147C22×C5#45312yes—
148C22×C5#45811yescharacteristic
149C4×C5—22no—
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—21no—
153C4×C5—42no—
154C4×C5—81no—
155C4×C5—161no—
156Dic5—44no—
157Dic5—82no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—54no—
162C2×Q8—102no—
163C2×Q8—202no—
164C2×Q8—202no—
165C2×Q8—401no—
166C2×Q8—402no—
167C2×Q8#68912yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—41no—
171C22×C4—102no—
172C22×C4—102no—
173C22×C4D4×D512yes—
174C22×C4C2×C22⋊D511yescharacteristic
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—104no—
179C2×C8—202no—
180C2×C8—202no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—202no—
187C4⋊C4—402no—
188C4⋊C4—401no—
189C42—41no—
190C42—401no—
191C2×C5#161411yescharacteristic
192C2×C5#161412yes—
193C2×C5#163311yescharacteristic
194C2×C5#163312yes—
195C2×C5#165511yescharacteristic
196C23#408311yescharacteristic
197Q8—42no—
198Q8—81no—
199Q8—204no—
200Q8—402no—
201Q8—404no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—82no—
213C2×C4—104no—
214C2×C4—202no—
215C2×C4—202no—
216C2×C4—202no—
217C2×C4—202no—
218C2×C4—202no—
219C2×C4D5×Q1612yes—
220C2×C4#406412yes—
221C2×C4C2×#68911yescharacteristic
222C2×C4#409711yescharacteristic
223C8—42no—
224C8—204no—
225C5#783711yescharacteristic, complemented, Sylow
226C22#6533911yescharacteristic
227C22#6534211yescharacteristic
228C22#6536611yescharacteristic
229C22#6547512yes—
230C22#6548712yes—
231C4—21no—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—161no—
238C4—204no—
239C4—402no—
240C2#1060050911yescharacteristic
241C2#1060195412yes—
242C2#1060196912yes—
243C2#1060210011yescharacteristic
244C2#1060211911yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2095C2
socle, prime radicalC23×C5#120
hypercenter#2095D5
hypocenterC5#7837
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
225. C5#7837semidirect

Maximal subgroups

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

subgroupindex
#106083352
C5×#20952
#106003832
#105981332
#105979712
#78375