Finite Group Databasebeta

← #11988612

Subgroups — #11988612

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
2#10600477C211yesmaximal, characteristic
3#10599436C212yesmaximal
4C5×#1272C211yesmaximal, characteristic
5#10597969C212yesmaximal
6C5×#391C2211yescharacteristic
7#65519—21no—
8C2×#3967—21no—
9#65275—21no—
10C2×#3939—21no—
11#65224C2211yescharacteristic
12#65217C2212yes—
13#64950—22no—
14#64944—22no—
15C5×#336C2212yes—
16#64771—22no—
17#64771—22no—
18#64744C2211yescharacteristic
19#7831—51nomaximal, Sylow
20C22×C5×Q8D411yescharacteristic
21C22×C5×C8—22no—
22C2×C5×C4⋊C4D411yescharacteristic
23C2×C42×C5C2311yescharacteristic
24C2×C4⋊Dic5—22no—
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—21no—
27C2×C4⋊Dic5—21no—
28C2×C4⋊Dic5D412yes—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C2×C4×Dic5—21no—
32C22×#168—21no—
33C5×#95—22no—
34#3967—42no—
35#3963—21no—
36#3963—22no—
37#3963—22no—
38#3963—22no—
39#3939—42no—
40#2809—51no—
41#2100—52no—
42#2095—51no—
43#1272D511yescharacteristic
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×C5C2×D411yescharacteristic
52C22×C4×C5C2×D412yes—
53C22×Dic5—22no—
54C22×Dic5—22no—
55C22×Dic5—41no—
56C2×C5×C8—42no—
57C2×C5×C8—42no—
58C2×C5×C8—42no—
59C5×C4⋊C4—41no—
60C42×C5—41no—
61C4⋊Dic5—22no—
62C4⋊Dic5—22no—
63C4⋊Dic5—42no—
64C4⋊Dic5—41no—
65C4⋊Dic5—41no—
66C4⋊Dic5—44no—
67C4⋊Dic5—81no—
68C4⋊Dic5—81no—
69#683—42no—
70#683—42no—
71C4×Dic5—81no—
72C2×#168—22no—
73C2×#168—41no—
74C2×#168—41no—
75C2×#107—101no—
76C2×#103—101no—
77#400—101no—
78#398—102no—
79#391—101no—
80#391C2×D511yescharacteristic
81#389—52no—
82#387—102no—
83#384—51no—
84#340—102no—
85#340—102no—
86#336—51no—
87#336C2×D512yes—
88C23×C5#12011yescharacteristic
89C5×Q8—42no—
90C5×Q8—81no—
91C2×C4×C5—21no—
92C2×C4×C5—22no—
93C2×C4×C5—21no—
94C2×C4×C5—22no—
95C2×C4×C5—22no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5—41no—
99C2×C4×C5—42no—
100C2×C4×C5C2×Q1611yescharacteristic
101C2×C4×C5#13512yes—
102C2×C4×C5#13711yescharacteristic
103C2×C4×C5#13712yes—
104C2×Dic5—42no—
105C2×Dic5—42no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110C2×Dic5—81no—
111C2×Dic5—82no—
112C5×C8—82no—
113#168—42no—
114C22×Q8D2011yescharacteristic
115C22×C8—22no—
116C22×C8—101no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4—52no—
119C2×C4⋊C4—102no—
120C2×C4⋊C4—101no—
121C2×C4⋊C4—102no—
122C2×C4⋊C4—101no—
123C2×C4⋊C4—101no—
124C2×C4⋊C4D2011yescharacteristic
125C2×C42—101no—
126C2×C42C22×D511yescharacteristic
127#107—202no—
128#103—202no—
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—
145Dic5—82no—
146Dic5—82no—
147Dic5—161no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8Dic2012yes—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—102no—
155C22×C4—102no—
156C22×C4—201no—
157C22×C4C2×D2011yescharacteristic
158C22×C4D4×D512yes—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—102no—
163C2×C8—201no—
164C2×C8—201no—
165C4⋊C4—41no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C4⋊C4—202no—
169C4⋊C4—201no—
170C4⋊C4—201no—
171C4⋊C4—204no—
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#402811yescharacteristic
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—202no—
196C2×C4—202no—
197C2×C4—202no—
198C2×C4—202no—
199C2×C4—202no—
200C2×C4—202no—
201C2×C4—401no—
202C2×C4—402no—
203C2×C4C2×Dic2011yescharacteristic
204C2×C4#405511yescharacteristic
205C2×C4#406212yes—
206C2×C4#406412yes—
207C8—82no—
208C8—202no—
209C5#783111yescharacteristic, complemented, Sylow
210C22#6502811yescharacteristic
211C22#6503111yescharacteristic
212C22#6503611yescharacteristic
213C22#6509912yes—
214C22#6511612yes—
215C4—22no—
216C4—22no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—81no—
221C4—402no—
222C4—402no—
223C4—801no—
224C2#1059891011yescharacteristic
225C2#1059904612yes—
226C2#1059912312yes—
227C2#1059914711yescharacteristic
228C2#1059928611yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1272C2
socle, prime radicalC23×C5#120
hypercenter#1272D5
hypocenterC5#7831
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

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
#106004772
#105994362
C5×#12722
#105979692
#78315