Finite Group Databasebeta

← #11986885

Subgroups — #11986885

Order 1280.

226 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 43 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×#2025C211yesmaximal, characteristic
2#10598132C211yesmaximal, characteristic
3#10598131C211yesmaximal, characteristic
4C2×C5×#125C411yescharacteristic, complemented
5C2×C5×#102—21no—
6C5×#390C2211yescharacteristic
7C2×#3966—21no—
8C5×#340—21no—
9C5×#336C411yescharacteristic, complemented
10#64748—21no—
11#7428—51nomaximal, Sylow
12C22×C5×D4D411yescharacteristic
13C22×C5×C8—21no—
14C5×#125—42no—
15C2×C5×C4⋊C4—21no—
16C2×C5×C4⋊C4—41no—
17C2×C5×C4⋊C4D411yescharacteristic
18C2×C5×C22⋊C4—41no—
19C2×C42×C5C2×C411yescharacteristic
20C2×C22⋊Dic5—41no—
21C5×#102—42no—
22#3966—22no—
23#3966—41no—
24C22⋊#168—41no—
25#2025D511yescharacteristic
26#1393—51no—
27#1318—51no—
28C24×C5—21no—
29C2×C5×D4—21no—
30C2×C5×D4—41no—
31C2×C5×D4—41no—
32C2×C5×D4SD1611yescharacteristic
33C2×C5×D4Q1611yescharacteristic
34C22×C4×C5—21no—
35C22×C4×C5—21no—
36C22×C4×C5—41no—
37C22×C4×C5C22⋊C411yescharacteristic
38C22×Dic5—81no—
39C2×C5×C8—41no—
40C2×C5×C8—41no—
41C2×C5×C8—41no—
42C5×C4⋊C4—22no—
43C5×C4⋊C4—41no—
44C5×C4⋊C4—41no—
45C5×C4⋊C4—42no—
46C5×C4⋊C4—42no—
47C5×C22⋊C4—82no—
48C42×C5—41no—
49C22⋊Dic5—42no—
50C22⋊Dic5—81no—
51C2×#168—81no—
52C2×#125Dic511yescharacteristic, complemented
53C2×#102—21no—
54C2×#99—101no—
55#390C2×D511yescharacteristic
56#340—21no—
57#336Dic511yescharacteristic, complemented
58#324—101no—
59C23×C5—21no—
60C23×C5—21no—
61C23×C5—41no—
62C23×C5—41no—
63C23×C5—81no—
64C23×C5—81no—
65C23×C5#9911yescharacteristic
66C5×D4—41no—
67C5×D4—41no—
68C5×D4—81no—
69C2×C4×C5—21no—
70C2×C4×C5—21no—
71C2×C4×C5—41no—
72C2×C4×C5—41no—
73C2×C4×C5—41no—
74C2×C4×C5—42no—
75C2×C4×C5—41no—
76C2×C4×C5—81no—
77C2×C4×C5—81no—
78C2×C4×C5—81no—
79C2×C4×C5#10311yescharacteristic
80C2×C4×C5#10411yescharacteristic
81C2×Dic5—82no—
82C2×Dic5—161no—
83C2×Dic5—161no—
84C5×C8—81no—
85#168—161no—
86C22×D4C22⋊D511yescharacteristic
87C22×C8—21no—
88#125—42no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4C22⋊D511yescharacteristic
92C2×C22⋊C4—41no—
93C2×C22⋊C4—201no—
94C2×C42C2×Dic511yescharacteristic
95#102—42no—
96#99—102no—
97#99—201no—
98C22⋊C8—201no—
99C22×C5—21no—
100C22×C5—21no—
101C22×C5—41no—
102C22×C5—41no—
103C22×C5—81no—
104C22×C5—81no—
105C22×C5—81no—
106C22×C5—81no—
107C22×C5—161no—
108C22×C5#32811yescharacteristic
109C22×C5AΣL(1,𝔽16)11yescharacteristic
110C22×C5#35411yescharacteristic
111C4×C5—21no—
112C4×C5—21no—
113C4×C5—81no—
114C4×C5—82no—
115C4×C5—81no—
116Dic5—162no—
117C24—21no—
118C2×D4—21no—
119C2×D4—41no—
120C2×D4—41no—
121C2×D4#68811yescharacteristic
122C2×D4#68911yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—401no—
127C22×C4C22⋊Dic511yescharacteristic
128C2×C8—41no—
129C2×C8—41no—
130C2×C8—41no—
131C2×C8—401no—
132C4⋊C4—22no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C22⋊C4—82no—
138C22⋊C4—202no—
139C22⋊C4—401no—
140C42—41no—
141C2×C5—21no—
142C2×C5—21no—
143C2×C5—81no—
144C2×C5—81no—
145C2×C5#135111yescharacteristic
146C2×C5#141211yescharacteristic
147C2×C5#141411yescharacteristic
148C23—21no—
149C23—21no—
150C23—41no—
151C23—41no—
152C23—81no—
153C23—81no—
154C23#396611yescharacteristic
155D4—41no—
156D4—41no—
157D4—81no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—402no—
169C2×C4—801no—
170C2×C4—801no—
171C2×C4#396711yescharacteristic
172C2×C4#396911yescharacteristic
173C8—81no—
174C8—801no—
175C5#742811yescharacteristic, complemented, Sylow
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#6475611yescharacteristic
186C22#6475811yescharacteristic
187C22#6476111yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—81no—
193C4—802no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1059813711yescharacteristic
199C2#1059827311yescharacteristic
200C2#1059827511yescharacteristic
subgroupG/H
centerC22#64761
commutatorC2×C42×C5C2×C4
Frattini#390C2×D5
FittingC5×#2025C2
socleC22×C5#354
prime radicalC22×C5×D4D4
cosocleC5×#390C22
hypercenter#2025D5
hypocenterC5#7428
LCSG ▷ C2×C42×C5 ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #2025

Complements

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

NH ≅ G/Ntype
4. C2×C5×#125C4semidirect
9. C5×#336C4semidirect
52. C2×#125Dic5semidirect
57. #336Dic5semidirect
175. C5#7428semidirect

Maximal subgroups

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

subgroupindex
C5×#20252
#105981322
#105981312
#74285