Finite Group Databasebeta

← #14277619

Subgroups — #14277619

Order 1920.

256 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 54 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#11748346C211yesmaximal, characteristic
2#11746783C211yesmaximal, characteristic, complemented
3C3×#64912C211yesmaximal, characteristic, complemented
4#10598818—31nomaximal, Hall
5C22×C4×C5×D3C411yescharacteristic
6C2×#6710C411yescharacteristic
7C2×C3×#681C2211yescharacteristic
8#91227—21no—
9C3×#3998—21no—
10(C2×D3)⋊#168—21no—
11(C2×D3)⋊#168—21no—
12#67530—51nomaximal, Hall
13#65496—31no—
14#64912—31no—
15#64912D311yescharacteristic, complemented
16C23×C5×D3C811yescharacteristic
17C22×C3×C4×C5C2×C411yescharacteristic
18C22×C5×Dic3C811yescharacteristic
19C2×C4×C5×D3—21no—
20C2×C4×C5×D3—21no—
21C2×C4×C5×D3—41no—
22C2×C4×C5×D3—41no—
23#6710—41no—
24C2×C3⋊#168—21no—
25C3×#681—41no—
26C2×C3×#168D411yescharacteristic
27C2×C3×#168D411yescharacteristic
28C3⋊#674—41no—
29C3×#674—41no—
30#5126—51no—
31C3×#349—51no—
32#4553—51no—
33C23×C4×C5—31no—
34C2×#681—31no—
35C2×#681C2×D311yescharacteristic
36#3998—21no—
37#3998—61no—
38C22⋊#168—61no—
39C22⋊#168—61no—
40#1320—151noSylow
41C23×C3×C5C2×C811yescharacteristic
42C22×C5×D3—21no—
43C22×C5×D3—42no—
44C22×C5×D3—41no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5C22⋊C411yescharacteristic
48C2×C3×C4×C5M1611yescharacteristic
49C2×C5×Dic3—21no—
50C2×C5×Dic3—41no—
51C4×C5×D3—42no—
52C4×C5×D3—41no—
53C4×C5×D3—41no—
54C3⋊#168—41no—
55C3×#168—21no—
56C3×#168—21no—
57C22×C4×D3AGL(1,𝔽5)11yescharacteristic
58C2×C3×M16—51no—
59C2×#208—51no—
60C3×M32—101no—
61(C2×D3)⋊C8—101no—
62(C2×D3)⋊C8—101no—
63#812—101no—
64C24×C5—31no—
65C22×C4×C5—31no—
66C22×C4×C5—61no—
67C22×C4×C5—61no—
68C22×C4×C5—121no—
69C22×C4×C5—121no—
70C22×C4×C5C4×D311yescharacteristic
71#681—41no—
72#681—121no—
73C2×#168—61no—
74C2×#168D1211yescharacteristic
75C2×#168#6711yescharacteristic
76#674—41no—
77#674—121no—
78#407—151no—
79#349—51no—
80#349—151no—
81C22×C3×C5—21no—
82C22×C3×C5—41no—
83C22×C3×C5C22⋊C811yescharacteristic
84C2×C5×D3—22no—
85C2×C5×D3—41no—
86C2×C5×D3—42no—
87C2×C5×D3—41no—
88C2×C5×D3—42no—
89C3×C4×C5—21no—
90C3×C4×C5#9911yescharacteristic
91C3×C4×C5#10011yescharacteristic
92C5×Dic3—41no—
93C23×D3#17011yescharacteristic
94C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
95C22×Dic3#17011yescharacteristic
96C2×C4×D3—21no—
97C2×C4×D3—21no—
98C2×C4×D3—41no—
99C2×C4×D3—41no—
100C3×M16—201no—
101C2×C3×C8—51no—
102C2×C3×C8—51no—
103#208—201no—
104C2×C3⋊C8—101no—
105C3×C16—201no—
106C3⋊C16—201no—
107C23×C5—61no—
108C23×C5—121no—
109C23×C5—122no—
110C23×C5D3×C811yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—61no—
114C2×C4×C5—122no—
115C2×C4×C5—121no—
116C2×C4×C5—121no—
117C2×C4×C5—121no—
118C2×C4×C5ΓL(1,𝔽25)11yescharacteristic
119C2×C4×C5(C2×D3)⋊C411yescharacteristic
120#168—21no—
121#168—21no—
122#168—121no—
123C23×C4—31no—
124C2×M16—51no—
125C2×M16—151no—
126M32—101no—
127M32—301no—
128C22⋊C8—301no—
129C22⋊C8—301no—
130C2×C3×C5—21no—
131C2×C3×C5—41no—
132C2×C3×C5#32311yescharacteristic
133C5×D3—42no—
134C23×C3C2×#17011yescharacteristic
135C22×D3—21no—
136C22×D3—42no—
137C22×D3—41no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4#70411yescharacteristic
141C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
142C2×Dic3—21no—
143C2×Dic3—41no—
144C4×D3—42no—
145C4×D3—41no—
146C4×D3—41no—
147C3×C8—101no—
148C3×C8—101no—
149C3⋊C8—201no—
150C22×C5—21no—
151C22×C5—41no—
152C22×C5—62no—
153C22×C5—121no—
154C22×C5—122no—
155C22×C5—122no—
156C22×C5—121no—
157C22×C5(C2×D3)⋊C811yescharacteristic
158C4×C5—21no—
159C4×C5—121no—
160C4×C5#80611yescharacteristic
161C4×C5#82311yescharacteristic
162C24—31no—
163C22×C4—31no—
164C22×C4—61no—
165C22×C4—61no—
166C22×C4—121no—
167C22×C4—121no—
168C22×C4D3×AGL(1,𝔽5)11yescharacteristic
169M16—201no—
170M16—601no—
171C2×C8—51no—
172C2×C8—51no—
173C2×C8—301no—
174C16—201no—
175C16—601no—
176C3×C5#132011yescharacteristic, complemented, Hall
177C22×C3—21no—
178C22×C3—41no—
179C22×C3C22⋊#17011yescharacteristic
180C2×D3—22no—
181C2×D3—41no—
182C2×D3—42no—
183C2×D3—41no—
184C2×D3—42no—
185C3×C4—21no—
186C3×C4#401111yescharacteristic
187C3×C4#401311yescharacteristic
188Dic3—41no—
189C2×C5—21no—
190C2×C5—41no—
191C2×C5—122no—
192C2×C5#446811yescharacteristic
193C23—61no—
194C23—121no—
195C23—122no—
196C23D3×#17011yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—61no—
200C2×C4—122no—
201C2×C4—121no—
202C2×C4—121no—
203C2×C4—121no—
204C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
205C2×C4#673911yescharacteristic
206C8—101no—
207C8—101no—
208C8—601no—
209C2×C3—21no—
210C2×C3—41no—
211C2×C3#6493311yescharacteristic
212D3—42no—
213C5#6753011yescharacteristic, complemented, Sylow
214C22—21no—
215C22—41no—
216C22—62no—
217C22—121no—
218C22—122no—
219C22—122no—
220C22—121no—
221C22(C2×D3)⋊#17011yescharacteristic
222C4—21no—
223C4—121no—
224C4#9117211yescharacteristic
225C4#9117411yescharacteristic
226C3#1059881811yescharacteristic, complemented, Sylow
227C2—21no—
228C2—41no—
229C2—122no—
230C2#1174656611yescharacteristic
subgroupG/H
centerC4#91172
commutatorC23×C3×C5C2×C8
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5#323
prime radicalC23×C5×D3C8
cosocleC2×C3×#681C22
hypocenterC3×C5#1320
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11746783C2semidirect
3. C3×#64912C2semidirect
15. #64912D3semidirect
176. C3×C5#1320semidirect
213. C5#67530semidirect
226. C3#10598818semidirect

Maximal subgroups

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

subgroupindex
#117483462
#117467832
C3×#649122
#105988183
#675305