Finite Group Databasebeta

← #14318541

Subgroups — #14318541

Order 1920.

268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4893C211yesmaximal, characteristic, complemented
2#11747920C211yesmaximal, characteristic
3#11746316C211yesmaximal, characteristic, complemented
4C3×#64714C211yesmaximal, characteristic, complemented
5#11745935C211yesmaximal, characteristic, complemented
6#11745920C211yesmaximal, characteristic, complemented
7#11745883C211yesmaximal, characteristic, complemented
8#10601516—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C5×D3×M16—21no—
11C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
12#91460—21no—
13C3×C5×#108C2211yescharacteristic
14#91096C2211yescharacteristic
15C5×#822—21no—
16C5×#819C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90968—21no—
20#69313—51nomaximal, Hall
21C5×#430—31no—
22#65424—31no—
23#64773—31no—
24#64715—31no—
25#64715—31no—
26#64714—31no—
27#64714D311yescharacteristic, complemented
28C2×D60—21no—
29C2×C4×C5×D3D411yescharacteristic
30C2×#1203—41no—
31C3×C5×M16—21no—
32C2×C3×C5×C8C2311yescharacteristic
33D120—21no—
34D120—21no—
35C5×#208—21no—
36C2×C5×C3⋊C8D411yescharacteristic
37C5×ΓL(1,𝔽25)—21no—
38C5×ΓL(1,𝔽25)—21no—
39C5×ΓL(1,𝔽25)—41no—
40C5×D3×C8—41no—
41C3×C4⋊Dic5—21no—
42#6667—41no—
43C3⋊#672—21no—
44C3×#672—21no—
45#4893D511yescharacteristic, complemented
46#4865—51no—
47C3×#365—51no—
48#4516—51no—
49#4514—51no—
50#4495—51no—
51#4487—51no—
52C2×C5×M16—31no—
53C2×C5×M16—61no—
54#4076—61no—
55C2×D40—31no—
56C5×#108—31no—
57C5×#108—61no—
58C5×#108C2×D311yescharacteristic
59#3953—61no—
60#3949C2×D311yescharacteristic
61#3944—31no—
62#3944C2×D311yescharacteristic
63#2238—151noSylow
64C22×D15—41no—
65C22×C5×D3SD1611yescharacteristic
66C2×C3×C4×C5C2×D411yescharacteristic
67D60—41no—
68D60—41no—
69C2×C5×Dic3SD1611yescharacteristic
70C4×C5×D3—21no—
71C4×C5×D3—21no—
72C2×C3×Dic5—41no—
73#1203—82no—
74C3×C5×C8—41no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C5×C3⋊C8—21no—
78C5×C3⋊C8—41no—
79D3×M16—21no—
80C2×D24—51no—
81C2×ΓL(1,𝔽25)C2×D511yescharacteristic
82#895—101no—
83C3×M32—51no—
84C3×#108C2×D511yescharacteristic
85C3×#106—51no—
86#822—21no—
87#819C2×D511yescharacteristic
88#812—51no—
89#809—101no—
90C22×C4×C5—31no—
91C2×C22⋊D5—121no—
92C2×D20—61no—
93C5×M16—21no—
94C5×M16—61no—
95C5×M16—61no—
96C5×M16—61no—
97C5×M16—121no—
98C2×C5×C8—31no—
99C2×C5×C8—121no—
100C2×C5×C8C22×D311yescharacteristic
101#685—121no—
102C4⋊Dic5—21no—
103D40—61no—
104D40—61no—
105#672—21no—
106#672—61no—
107#469—151no—
108#430—31no—
109#365—51no—
110#365—151no—
111#361—151no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—81no—
116C2×D15—81no—
117C2×D15—81no—
118C2×C5×D3—21no—
119C2×C5×D3—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122C3×Dic5—81no—
123C5×Dic3—21no—
124C2×D12—101no—
125C2×D12—201no—
126C2×C4×D3C22⋊D511yescharacteristic
127C3×M16—21no—
128C2×C3×C8C22×D511yescharacteristic
129C3×C4⋊C4—101no—
130(C2×D3)⋊C4—201no—
131#208—21no—
132C2×C3⋊C8C22⋊D511yescharacteristic
133D24—101no—
134D24—101no—
135ΓL(1,𝔽25)—21no—
136ΓL(1,𝔽25)—21no—
137ΓL(1,𝔽25)—41no—
138D3×C8—41no—
139C3×C16—101no—
140C3⋊C16—101no—
141C23×C5—31no—
142C22×D5—121no—
143C2×C4×C5—31no—
144C2×C4×C5—61no—
145C2×C4×C5—61no—
146C2×C4×C5D3×D411yescharacteristic
147C22⋊D5—242no—
148C2×Dic5—41no—
149D20—121no—
150D20—121no—
151C5×C8—41no—
152C5×C8—61no—
153C5×C8—121no—
154C5×C8#23511yescharacteristic
155C5×C8#23911yescharacteristic
156C2×D8—151no—
157C2×M16—31no—
158C2×M16—61no—
159#121—301no—
160M32—51no—
161M32—151no—
162#108—31no—
163#108—61no—
164#108D3×D511yescharacteristic
165#106—51no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—161no—
170C5×D3—41no—
171C22×D3—201no—
172C22×D3#68811yescharacteristic
173C2×C3×C4—201no—
174C2×C3×C4C2×C22⋊D511yescharacteristic
175C2×Dic3#68811yescharacteristic
176D12—201no—
177D12—201no—
178D12—402no—
179C4×D3—21no—
180C4×D3—21no—
181C3×C8—41no—
182C3×C8#70911yescharacteristic
183C3×C8#70911yescharacteristic
184C3⋊C8—21no—
185C3⋊C8—41no—
186C22×C5—61no—
187C22×C5—121no—
188C22×C5D3×SD1611yescharacteristic
189C2×D5—241no—
190C2×D5—241no—
191C2×D5—241no—
192C4×C5—61no—
193C4×C5#89411yescharacteristic
194C4×C5#91411yescharacteristic
195Dic5—81no—
196C2×D4—301no—
197C2×D4—601no—
198C22×C4—31no—
199D8—301no—
200D8—301no—
201M16—21no—
202M16—61no—
203M16—61no—
204M16—61no—
205M16—121no—
206C2×C8—31no—
207C2×C8—121no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—101no—
210C22⋊C4—601no—
211C16—101no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3C2×#68811yescharacteristic
215C2×D3—21no—
216C2×D3—41no—
217C2×D3—401no—
218C2×D3—401no—
219C2×D3—401no—
220C3×C4—401no—
221C3×C4#407511yescharacteristic
222C3×C4#407811yescharacteristic
223Dic3—21no—
224C2×C5—21no—
225C2×C5—121no—
226C2×C5#486311yescharacteristic
227D5—481no—
228C23—31no—
229C23—601no—
230D4—601no—
231D4—601no—
232D4—1202no—
233C2×C4—31no—
234C2×C4—61no—
235C2×C4—61no—
236C2×C4—201no—
237C2×C4D3×C22⋊D511yescharacteristic
238C8—41no—
239C8—61no—
240C8—121no—
241C8#676911yescharacteristic
242C8#677111yescharacteristic
243C2×C3—21no—
244C2×C3#6525711yescharacteristic
245D3—41no—
246D3—801no—
247C5#6931311yescharacteristic, complemented, Sylow
248C22—61no—
249C22—121no—
250C22—1201no—
251C22—1201no—
252C22—1201no—
253C22D3×#68811yescharacteristic
254C4—61no—
255C4—401no—
256C4#9135111yescharacteristic
257C4#9149611yescharacteristic
258C3#1060151611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—121no—
261C2—2401no—
262C2#1174717311yescharacteristic
subgroupG/H
centerC2#11747173
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5#481
prime radical#11747920C2
hypercenter#108D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
1. C5×#4893C2semidirect
3. #11746316C2semidirect
4. C3×#64714C2semidirect
5. #11745935C2semidirect
6. #11745920C2semidirect
7. #11745883C2semidirect
27. #64714D3semidirect
45. #4893D5semidirect
213. C3×C5#2238semidirect
247. C5#69313semidirect
258. C3#10601516semidirect

Maximal subgroups

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

subgroupindex
C5×#48932
#117479202
#117463162
C3×#647142
#117459352
#117459202
#117458832
#106015163
#693135