Finite Group Databasebeta

← #11988609

Subgroups — #11988609

Order 1280.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#10608333C211yesmaximal, characteristic
2C5×#2095C211yesmaximal, characteristic
3#10600365C212yesmaximal
4#10598133C211yesmaximal, characteristic
5#10597968C212yesmaximal
6C2×C5×#107—21no—
7C2×C5×#103—21no—
8C5×#391C2211yescharacteristic
9C5×#384C2211yescharacteristic
10#65519—21no—
11#65275—21no—
12#65217C2212yes—
13#64950—22no—
14#64944—22no—
15C5×#336C2211yescharacteristic
16#64749—22no—
17#64749—22no—
18#64744C2212yes—
19#7831—51nomaximal, Sylow
20C22×C5×Q8D411yescharacteristic
21C22×C5×C8—21no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4D411yescharacteristic
25C2×C42×C5C2311yescharacteristic
26C2×C4⋊Dic5—21no—
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5D412yes—
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#2809—51no—
41#2100—52no—
42#2095D511yescharacteristic
43#1272—51no—
44#1271—52no—
45C2×C5×Q8—21no—
46C2×C5×Q8—41no—
47C2×C5×Q8—41no—
48C2×C5×Q8Q1612yes—
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5—41no—
52C22×C4×C5C2×D412yes—
53C22×C4×C5C2×D411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5—22no—
56C2×C5×C8—22no—
57C2×C5×C8—41no—
58C2×C5×C8—41no—
59C5×C4⋊C4—41no—
60C5×C4⋊C4—44no—
61C5×C4⋊C4—41no—
62C5×C4⋊C4—41no—
63C42×C5—41no—
64C4⋊Dic5—22no—
65C4⋊Dic5—22no—
66C4⋊Dic5—42no—
67C4⋊Dic5—81no—
68C4⋊Dic5—81no—
69#683—42no—
70#683—42no—
71C4×Dic5—81no—
72C2×#168—42no—
73C2×#168—42no—
74C2×#168—42no—
75C2×#107—21no—
76C2×#103—21no—
77#400—101no—
78#398—102no—
79#391—101no—
80#391C2×D511yescharacteristic
81#389—52no—
82#387—102no—
83#384C2×D511yescharacteristic
84#340—102no—
85#340—102no—
86#336—52no—
87#336C2×D511yescharacteristic
88C23×C5#12011yescharacteristic
89C5×Q8—42no—
90C5×Q8—81no—
91C2×C4×C5—21no—
92C2×C4×C5—22no—
93C2×C4×C5—22no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5—41no—
99C2×C4×C5—42no—
100C2×C4×C5—81no—
101C2×C4×C5—82no—
102C2×C4×C5C2×Q1611yescharacteristic
103C2×C4×C5#13512yes—
104C2×C4×C5#13711yescharacteristic
105C2×C4×C5#13712yes—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C5×C8—42no—
113#168—82no—
114C22×Q8C22⋊D511yescharacteristic
115C22×C8—21no—
116C22×C8—102no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—102no—
122C2×C4⋊C4—101no—
123C2×C4⋊C4—101no—
124C2×C4⋊C4C22⋊D511yescharacteristic
125C2×C42—101no—
126C2×C42C22×D511yescharacteristic
127#107—42no—
128#103—42no—
129#95—22no—
130#95—101no—
131#95—102no—
132#95—102no—
133#95—102no—
134C22×C5#45111yescharacteristic
135C22×C5#45212yes—
136C22×C5#45311yescharacteristic
137C22×C5#45412yes—
138C22×C5#45811yescharacteristic
139C4×C5—21no—
140C4×C5—21no—
141C4×C5—22no—
142C4×C5—22no—
143C4×C5—42no—
144C4×C5—81no—
145C4×C5—161no—
146Dic5—82no—
147Dic5—82no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8#68912yes—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—102no—
156C22×C4—102no—
157C22×C4D4×D512yes—
158C22×C4C2×C22⋊D511yescharacteristic
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—202no—
163C2×C8—202no—
164C2×C8—202no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—44no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—202no—
172C4⋊C4—202no—
173C4⋊C4—202no—
174C4⋊C4—401no—
175C4⋊C4—401no—
176C42—41no—
177C42—401no—
178C2×C5#161411yescharacteristic
179C2×C5#161512yes—
180C2×C5#163411yescharacteristic
181C2×C5#163612yes—
182C2×C5#165711yescharacteristic
183C23#408311yescharacteristic
184Q8—42no—
185Q8—81no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—202no—
198C2×C4—202no—
199C2×C4—202no—
200C2×C4—202no—
201C2×C4—202no—
202C2×C4—202no—
203C2×C4#406412yes—
204C2×C4#406512yes—
205C2×C4C2×#68911yescharacteristic
206C2×C4#409711yescharacteristic
207C8—42no—
208C8—402no—
209C5#783111yescharacteristic, complemented, Sylow
210C22#6533911yescharacteristic
211C22#6534211yescharacteristic
212C22#6536611yescharacteristic
213C22#6547612yes—
214C22#6549012yes—
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—161no—
222C4—402no—
223C4—402no—
224C2#1060050911yescharacteristic
225C2#1060195112yes—
226C2#1060197112yes—
227C2#1060209711yescharacteristic
228C2#1060212111yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2095C2
socle, prime radicalC23×C5#120
hypercenter#2095D5
hypocenterC5#7831
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
209. C5#7831semidirect

Maximal subgroups

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

subgroupindex
#106083332
C5×#20952
#106003652
#105981332
#105979682
#78315