Finite Group Databasebeta

← #14277989

Subgroups — #14277989

Order 1920.

228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 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×#65448C211yesmaximal, characteristic
2#11746766C211yesmaximal, characteristic, complemented
3#11746762C211yesmaximal, characteristic, complemented
4#10598803—31nomaximal, Hall
5#91989—21no—
6C2×C3×C5×D8C411yescharacteristic, complemented
7C3×#4084—21no—
8C2×C3×#676C2211yescharacteristic
9#91227—21no—
10C3×#3964—21no—
11C3×#3949C411yescharacteristic, complemented
12#67778—51nomaximal, Hall
13#65448D311yescharacteristic
14#64895—31no—
15#64891—31no—
16C2×C3×C5×D4—21no—
17C2×C3×C22⋊D5—41no—
18C2×C3×C4×D5D411yescharacteristic
19#6763—41no—
20C4⋊ΓL(1,𝔽16)—41no—
21C4×ΓL(1,𝔽16)—22no—
22C3×C5×D8—41no—
23C2×C3×C5×C8C2×C411yescharacteristic
24C3×C22⋊Dic5—41no—
25C3×C4⋊Dic5—21no—
26C2×C3×#168D411yescharacteristic
27C3×#676—41no—
28C3⋊#674—41no—
29C3×#469—51no—
30#4557—51no—
31#4553—51no—
32#4130—61no—
33C2×C5×D8Dic311yescharacteristic, complemented
34#4084—21no—
35C2×#676C2×D311yescharacteristic
36#3998—61no—
37#3964—21no—
38#3949Dic311yescharacteristic, complemented
39#1339—151noSylow
40C23×C3×C5—41no—
41C22×C3×D5D811yescharacteristic
42C2×ΓL(1,𝔽16)—42no—
43C3×C5×D4—41no—
44C3×C5×D4—41no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C3×C22⋊D5—82no—
47C2×C3×Dic5—41no—
48C2×C3×Dic5SD1611yescharacteristic
49C3×C4×D5—21no—
50C3×C4×D5—21no—
51C3×C5×C8—21no—
52C3×#168—21no—
53C2×C3×D8AGL(1,𝔽5)11yescharacteristic, complemented
54C2×C3×M16—51no—
55C3×#121—101no—
56#926—101no—
57C3×#106—51no—
58C3×#102—101no—
59#812—101no—
60C2×C5×D4—21no—
61C2×C22⋊D5—41no—
62C2×C4×D5#6711yescharacteristic
63C22⋊AGL(1,𝔽5)—121no—
64C4⋊AGL(1,𝔽5)—121no—
65C4×AGL(1,𝔽5)—62no—
66C5×D8—41no—
67C2×C5×C8C2×Dic311yescharacteristic
68C22⋊Dic5—41no—
69C4⋊Dic5—21no—
70C2×#168#6711yescharacteristic
71#676—41no—
72#674—121no—
73#469—51no—
74#349—151no—
75H(3,ℤ/4)—151no—
76C22×C3×C5—81no—
77C22×C3×C5—81no—
78C22×C3×C5—81no—
79C22×C3×C5#10211yescharacteristic
80C2×C3×D5—21no—
81C2×C3×D5—41no—
82ΓL(1,𝔽16)—82no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85C3×Dic5—21no—
86C3×Dic5—81no—
87C2×C3×D4—21no—
88C2×C3×D4—201no—
89C22×C3×C4—51no—
90C3×D8—41no—
91C3×M16—201no—
92C2×C3×C8—51no—
93C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
94C3×C4⋊C4—101no—
95C3×C22⋊C4—201no—
96#217—201no—
97C4⋊Dic3—201no—
98C4×Dic3—102no—
99C3⋊C16—201no—
100C23×C5—41no—
101C22×D5#21311yescharacteristic
102C2×AGL(1,𝔽5)—122no—
103C5×D4—41no—
104C5×D4—41no—
105C2×C4×C5#21711yescharacteristic
106C22⋊D5—82no—
107C2×Dic5—41no—
108C2×Dic5#21411yescharacteristic
109C4×D5—21no—
110C4×D5—21no—
111C5×C8—21no—
112#168—21no—
113C2×D8ΓL(1,𝔽16)11yescharacteristic, complemented
114C2×M16—51no—
115#121—101no—
116#117—301no—
117M32—301no—
118#106—51no—
119#102—101no—
120C2×C3×C5—21no—
121C2×C3×C5—161no—
122C2×C3×C5#32711yescharacteristic
123C3×D5—41no—
124C23×C3—41no—
125C23×C3—51no—
126C3×D4—41no—
127C3×D4—41no—
128C3×D4—402no—
129C2×C3×C4—51no—
130C2×C3×C4—101no—
131C2×C3×C4—101no—
132C2×C3×C4—201no—
133C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
134C2×Dic3—202no—
135C3×C8—21no—
136C3×C8—101no—
137C22×C5—81no—
138C22×C5—81no—
139C22×C5—81no—
140C22×C5#83211yescharacteristic
141C2×D5—21no—
142C2×D5—41no—
143AGL(1,𝔽5)—242no—
144C4×C5#83411yescharacteristic
145C4×C5#83711yescharacteristic
146Dic5—21no—
147Dic5—81no—
148C2×D4—21no—
149C2×D4—201no—
150C22×C4—51no—
151D8—41no—
152M16—201no—
153C2×C8—51no—
154C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
155C4⋊C4—101no—
156C4⋊C4—601no—
157C22⋊C4—201no—
158C22⋊C4—601no—
159C42—302no—
160C16—601no—
161C3×C5#133911yescharacteristic, complemented, Hall
162C22×C3—81no—
163C22×C3—81no—
164C22×C3—81no—
165C22×C3—101no—
166C22×C3—201no—
167C22×C3#400711yescharacteristic
168C3×C4—101no—
169C3×C4—401no—
170C3×C4#400811yescharacteristic
171C3×C4#401111yescharacteristic
172Dic3—402no—
173C2×C5—21no—
174C2×C5—161no—
175C2×C5#453711yescharacteristic
176D5—41no—
177C23—41no—
178C23—51no—
179D4—41no—
180D4—41no—
181D4—402no—
182C2×C4—51no—
183C2×C4—101no—
184C2×C4—101no—
185C2×C4—201no—
186C2×C4—602no—
187C2×C4#676311yescharacteristic
188C8—21no—
189C8—101no—
190C2×C3—21no—
191C2×C3—161no—
192C2×C3—201no—
193C2×C3#6492011yescharacteristic
194C5#6777811yescharacteristic, complemented, Sylow
195C22—81no—
196C22—81no—
197C22—81no—
198C22—101no—
199C22—201no—
200C22#9123611yescharacteristic
201C4—101no—
202C4—401no—
203C4—1202no—
204C4#9123711yescharacteristic
205C4#9124011yescharacteristic
206C3#1059880311yescharacteristic, complemented, Sylow
207C2—21no—
208C2—161no—
209C2—201no—
210C2#1174679111yescharacteristic
subgroupG/H
centerC2#11746791
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC2×C3×C5×D8C4
socleC2×C3×C5#327
prime radicalC3×#65448C2
cosocleC2×C3×#676C22
hypercenterC2×D8ΓL(1,𝔽16)
hypocenterC3×C5#1339
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11746766C2semidirect
3. #11746762C2semidirect
6. C2×C3×C5×D8C4semidirect
11. C3×#3949C4semidirect
33. C2×C5×D8Dic3semidirect
38. #3949Dic3semidirect
53. C2×C3×D8AGL(1,𝔽5)semidirect
113. C2×D8ΓL(1,𝔽16)semidirect
161. C3×C5#1339semidirect
194. C5#67778semidirect
206. C3#10598803semidirect

Maximal subgroups

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

subgroupindex
C3×#654482
#117467662
#117467622
#105988033
#677785