Finite Group Databasebeta

← #14279312

Subgroups — #14279312

Order 1920.

244 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 42 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×#65366C211yesmaximal, characteristic
2#11746366C211yesmaximal, characteristic, complemented
3C5×#4544C211yesmaximal, characteristic, complemented
4#10597953—31nomaximal, Hall
5C3×#4144C411yescharacteristic, complemented
6C3×C5×#127C2211yescharacteristic
7C3×#4078—21no—
8#91118—21no—
9C5×C4⋊(C3⋊C8)—21no—
10C3×#3965C411yescharacteristic, complemented
11C3×#3937—21no—
12#67770—51nomaximal, Hall
13#65366D311yescharacteristic
14C5×#331—31no—
15#64765—31no—
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4C2×C411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×C3×C22⋊D5—41no—
20C3×#711—41no—
21C3×D4×D5—41no—
22C3×#709—21no—
23C3×C42×C5D411yescharacteristic
24#6719—41no—
25C2×C5×C3⋊C8—41no—
26C3×#687—41no—
27C3×#686—41no—
28C3×#681—21no—
29C3×#453—51no—
30#4545—51no—
31#4544D511yescharacteristic, complemented
32#4144Dic311yescharacteristic, complemented
33C5×#127C2×D311yescharacteristic
34#4078—21no—
35C5×C4⋊C8—61no—
36#3966—61no—
37#3965Dic311yescharacteristic, complemented
38#3937—21no—
39#1402—151noSylow
40C23×C3×C5—21no—
41C23×C3×C5—21no—
42C22×C3×D5—41no—
43C3×C5×D4—41no—
44C3×C5×D4—41no—
45C3×C5×D4—81no—
46C3×C5×D4—81no—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5C22⋊C411yescharacteristic
49C2×Dic15—81no—
50C3×C22⋊D5—42no—
51C3×C22⋊D5—41no—
52C2×C3×Dic5—41no—
53C3×D20—21no—
54C3×C4×D5—41no—
55C3×Dic10—21no—
56C3×#168—41no—
57C5×C3⋊C8—81no—
58C3×H(5,𝔽2)—51no—
59C3×AGL(1,ℤ/8)—101no—
60C3×#127C2×D511yescharacteristic
61C3×#104—101no—
62C3×#100—51no—
63#834—101no—
64C4⋊(C3⋊C8)—21no—
65C2×C5×D4—41no—
66C2×C5×D4C2×Dic311yescharacteristic
67C2×C5×D4#6711yescharacteristic
68C2×C22⋊D5—41no—
69#711—41no—
70D4×D5—41no—
71#709—21no—
72C2×C5×C8—121no—
73C42×C5#6711yescharacteristic
74C22⋊Dic5—121no—
75#687—41no—
76#686—41no—
77#681—21no—
78#453—51no—
79#353—151no—
80#331—31no—
81C22×C3×C5—41no—
82C22×C3×C5—41no—
83C22×C3×C5—81no—
84C22×C3×C5—81no—
85C22×C3×C5#9911yescharacteristic
86C2×C3×D5—41no—
87C2×C3×D5—161no—
88C3×C4×C5—21no—
89C3×C4×C5—21no—
90C3×C4×C5—21no—
91Dic15—161no—
92C3×Dic5—41no—
93C3×#41—101no—
94C3×#41—201no—
95C2×C3×D4—41no—
96C2×C3×D4—201no—
97C2×C3×D4—201no—
98C2×C3×D4C4×D511yescharacteristic
99C2×C3×D4D2011yescharacteristic
100C3×SD16—201no—
101C3×D8—201no—
102C3×M16—101no—
103C3×C42C22⋊D511yescharacteristic
104#217—201no—
105C2×C3⋊C8—41no—
106C23×C5—21no—
107C23×C5—21no—
108C22×D5—41no—
109C5×D4—41no—
110C5×D4—41no—
111C5×D4—81no—
112C5×D4—81no—
113C2×C4×C5—21no—
114C2×C4×C5#21711yescharacteristic
115C22⋊D5—42no—
116C22⋊D5—41no—
117C2×Dic5—41no—
118C2×Dic5—241no—
119D20—21no—
120C4×D5—41no—
121Dic10—21no—
122C5×C8—241no—
123#168—41no—
124H(5,𝔽2)—51no—
125AGL(1,ℤ/8)—101no—
126#127D3×D511yescharacteristic
127C4⋊C8—61no—
128#104—101no—
129#100—51no—
130#99—301no—
131C2×C3×C5—21no—
132C2×C3×C5—81no—
133C2×C3×C5—81no—
134C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
135C3×D5—81no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—201no—
139C3×Q8—101no—
140C3×D4—41no—
141C3×D4—41no—
142C3×D4—81no—
143C3×D4—81no—
144C3×D4—101no—
145C3×D4—202no—
146C3×D4—201no—
147C2×C3×C4—21no—
148C2×C3×C4—201no—
149C2×C3×C4—201no—
150C2×C3×C4#68511yescharacteristic
151C2×Dic3—401no—
152C3×C8—201no—
153C3⋊C8—81no—
154C22×C5—41no—
155C22×C5—41no—
156C22×C5—81no—
157C22×C5—81no—
158C22×C5#83411yescharacteristic
159C2×D5—41no—
160C2×D5—161no—
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—21no—
164Dic5—41no—
165Dic5—481no—
166#41—101no—
167#41—201no—
168C2×D4—41no—
169C2×D4—201no—
170C2×D4—201no—
171C2×D4D5×Dic311yescharacteristic
172C2×D4#120211yescharacteristic
173SD16—201no—
174D8—201no—
175M16—101no—
176C2×C8—121no—
177C22⋊C4—601no—
178C42#120111yescharacteristic
179C3×C5#140211yescharacteristic, complemented, Hall
180C22×C3—41no—
181C22×C3—41no—
182C22×C3—81no—
183C22×C3—81no—
184C22×C3—201no—
185C22×C3—801no—
186C22×C3#393811yescharacteristic
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—201no—
191Dic3—801no—
192C2×C5—21no—
193C2×C5—81no—
194C2×C5—81no—
195C2×C5#453611yescharacteristic
196D5—81no—
197C23—21no—
198C23—21no—
199C23—201no—
200Q8—101no—
201D4—41no—
202D4—41no—
203D4—81no—
204D4—81no—
205D4—101no—
206D4—202no—
207D4—201no—
208C2×C4—21no—
209C2×C4—201no—
210C2×C4—201no—
211C2×C4—1201no—
212C2×C4#666511yescharacteristic
213C8—201no—
214C8—241no—
215C2×C3—21no—
216C2×C3—81no—
217C2×C3—81no—
218C2×C3—401no—
219C2×C3#6469511yescharacteristic
220C5#6777011yescharacteristic, complemented, Sylow
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—201no—
226C22—801no—
227C22#9099511yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—201no—
232C4—2401no—
233C3#1059795311yescharacteristic, complemented, Sylow
234C2—21no—
235C2—81no—
236C2—81no—
237C2—401no—
238C2#1174599511yescharacteristic
subgroupG/H
centerC2#11745995
commutatorC2×C3×C5×D4C2×C4
Frattini, hypercenter#127D3×D5
Fitting, cosocleC3×C5×#127C22
socleC2×C3×C5AΣL(1,𝔽16)
prime radicalC3×#65366C2
hypocenterC3×C5#1402
LCSG ▷ C2×C3×C5×D4 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746366C2semidirect
3. C5×#4544C2semidirect
5. C3×#4144C4semidirect
10. C3×#3965C4semidirect
31. #4544D5semidirect
32. #4144Dic3semidirect
37. #3965Dic3semidirect
179. C3×C5#1402semidirect
220. C5#67770semidirect
233. C3#10597953semidirect

Maximal subgroups

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

subgroupindex
C3×#653662
#117463662
C5×#45442
#105979533
#677705