Finite Group Databasebeta

← #14278221

Subgroups — #14278221

Order 1920.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C3×#65172C211yesmaximal, characteristic
2#11746767C211yesmaximal, characteristic, complemented
3#11746758C211yesmaximal, characteristic, complemented
4#10598613—31nomaximal, Hall
5C2×#6758—21no—
6C2×C3×D40C411yescharacteristic
7C2×C3×C8×D5C2211yescharacteristic
8C3×#4041—21no—
9C2×C3⋊#674—21no—
10C3×C5×#107C411yescharacteristic
11C3×#3941—21no—
12#67775—51nomaximal, Hall
13#65172D311yescharacteristic
14#64896—31no—
15#64887—31no—
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×C4×D5D411yescharacteristic
19C2×C3⋊#170—41no—
20#6758—22no—
21#6758—41no—
22C2×C3×C5×C8C2×C411yescharacteristic
23C3×C5×C4⋊C4—21no—
24C3×#685—41no—
25C2×C3×#168D411yescharacteristic
26C3×D40—41no—
27C3×C8×D5—41no—
28C3⋊#674—41no—
29C3×#466—51no—
30#4552—51no—
31#4549—51no—
32C2×#700—61no—
33C2×D40Dic311yescharacteristic
34C2×C8×D5C2×D311yescharacteristic
35#4041—21no—
36C2×#674—61no—
37C5×#107Dic311yescharacteristic
38#3941—21no—
39#1349—151noSylow
40C22×C3×D5—41no—
41C22×C3×D5SD1611yescharacteristic
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×Dic5D811yescharacteristic
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3×C4×D5—21no—
49C3×C4×D5—21no—
50C3⋊#170—42no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×D8—51no—
54C22×C3×C8—51no—
55C3×#121—101no—
56C2×#208—101no—
57C3×#107AGL(1,𝔽5)11yescharacteristic
58C3×#102—101no—
59C2×C3⋊C16—101no—
60C2×D20—21no—
61C2×D20—41no—
62C2×C4×D5#6711yescharacteristic
63C2×#170—121no—
64#700—62no—
65#700—121no—
66C2×C5×C8C2×Dic311yescharacteristic
67C5×C4⋊C4—21no—
68#685—41no—
69C2×#168#6711yescharacteristic
70D40—41no—
71C8×D5—41no—
72#674—121no—
73#466—51no—
74C22⋊C16—151no—
75#341—151no—
76C22×C3×C5#10211yescharacteristic
77C2×C3×D5—21no—
78C2×C3×D5—21no—
79C2×C3×D5—21no—
80C2×C3×D5—81no—
81C2×C3×D5—81no—
82C2×C3×D5—81no—
83C3×C4×C5—81no—
84C3×C4×C5#9911yescharacteristic
85C3×C4×C5#10411yescharacteristic
86C3×Dic5—21no—
87C2×C3×D4—101no—
88C2×C3×D4—201no—
89C22×C3×C4—51no—
90C3×D8—201no—
91C2×C3×C8—51no—
92C2×C3×C8—201no—
93C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
94C3×C4⋊C4—21no—
95C3×C22⋊C4—201no—
96#208—102no—
97#208—201no—
98C2×C3⋊C8—201no—
99C3⋊C16—201no—
100C22×D5—41no—
101C22×D5#21411yescharacteristic
102C2×C4×C5—41no—
103C2×C4×C5#21711yescharacteristic
104C2×Dic5#21311yescharacteristic
105D20—41no—
106D20—41no—
107D20—82no—
108C4×D5—21no—
109C4×D5—21no—
110#170—122no—
111C5×C8—21no—
112#168—21no—
113C2×D8—51no—
114C2×M16—301no—
115C22×C8—51no—
116#121—101no—
117C2×C16—301no—
118#107ΓL(1,𝔽16)11yescharacteristic
119#102—101no—
120C2×C3×C5#32711yescharacteristic
121C2×C3×C5#35911yescharacteristic
122C2×C3×C5#36111yescharacteristic
123C3×D5—41no—
124C3×D5—161no—
125C23×C3—51no—
126C23×C3—201no—
127C3×D4—201no—
128C3×D4—201no—
129C3×D4—402no—
130C2×C3×C4—41no—
131C2×C3×C4—51no—
132C2×C3×C4—101no—
133C2×C3×C4—101no—
134C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
135C3×C8—21no—
136C3×C8—101no—
137C3⋊C8—202no—
138C22×C5#83211yescharacteristic
139C2×D5—21no—
140C2×D5—21no—
141C2×D5—21no—
142C2×D5—81no—
143C2×D5—81no—
144C2×D5—81no—
145C4×C5—81no—
146C4×C5#83411yescharacteristic
147C4×C5#83711yescharacteristic
148Dic5—21no—
149C2×D4—101no—
150C2×D4—201no—
151C22×C4—51no—
152D8—201no—
153M16—302no—
154M16—601no—
155C2×C8—51no—
156C2×C8—201no—
157C2×C8—601no—
158C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
159C4⋊C4—21no—
160C22⋊C4—201no—
161C16—601no—
162C3×C5#134911yescharacteristic, complemented, Hall
163C22×C3—101no—
164C22×C3—101no—
165C22×C3—101no—
166C22×C3—401no—
167C22×C3—401no—
168C22×C3—401no—
169C22×C3#400711yescharacteristic
170C3×C4—81no—
171C3×C4—101no—
172C3×C4#399911yescharacteristic
173C3×C4#401011yescharacteristic
174C2×C5#453711yescharacteristic
175C2×C5#456311yescharacteristic
176C2×C5#456711yescharacteristic
177D5—41no—
178D5—161no—
179C23—51no—
180C23—201no—
181D4—201no—
182D4—201no—
183D4—402no—
184C2×C4—41no—
185C2×C4—51no—
186C2×C4—101no—
187C2×C4—101no—
188C2×C4#676311yescharacteristic
189C8—21no—
190C8—101no—
191C8—602no—
192C2×C3—201no—
193C2×C3—801no—
194C2×C3#6486811yescharacteristic
195C2×C3#6490611yescharacteristic
196C2×C3#6490911yescharacteristic
197C5#6777511yescharacteristic, complemented, Sylow
198C22—101no—
199C22—101no—
200C22—101no—
201C22—401no—
202C22—401no—
203C22—401no—
204C22#9123611yescharacteristic
205C4—81no—
206C4—101no—
207C4#9122811yescharacteristic
208C4#9123911yescharacteristic
209C3#1059861311yescharacteristic, complemented, Sylow
210C2—201no—
211C2—801no—
212C2#1174673911yescharacteristic
213C2#1174677711yescharacteristic
214C2#1174678011yescharacteristic
subgroupG/H
centerC22#91236
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC3×C5×#107C4
socleC22×C3×C5#102
prime radicalC3×#65172C2
cosocleC2×C3×C8×D5C22
hypercenter#107ΓL(1,𝔽16)
hypocenterC3×C5#1349
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11746767C2semidirect
3. #11746758C2semidirect
162. C3×C5#1349semidirect
197. C5#67775semidirect
209. C3#10598613semidirect

Maximal subgroups

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

subgroupindex
C3×#651722
#117467672
#117467582
#105986133
#677755