Finite Group Databasebeta

← #14318544

Subgroups — #14318544

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×#4865C211yesmaximal, characteristic
2#11748059C211yesmaximal, characteristic, complemented
3#11746308C211yesmaximal, characteristic, complemented
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745918C211yesmaximal, characteristic, complemented
6#11745917C211yesmaximal, characteristic, complemented
7#11745883C211yesmaximal, characteristic, complemented
8#10601881—31nomaximal, Hall
9C2×C5×D24C2211yescharacteristic
10C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
11C5×#895—21no—
12D3×#681—21no—
13C3×C5×#106C2211yescharacteristic
14#91103C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#809—21no—
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90993—21no—
20#69313—51nomaximal, Hall
21C5×#469—31no—
22#65414—31no—
23#64783—31no—
24#64783—31no—
25#64773—31no—
26#64707—31no—
27#64707D311yescharacteristic, complemented
28C2×C5×D12—21no—
29C2×C5×D12—41no—
30C2×C4×C5×D3D411yescharacteristic
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33#6710—21no—
34C5×(C2×D3)⋊C4—41no—
35C2×C5×C3⋊C8D411yescharacteristic
36C5×D24—21no—
37C5×D24—21no—
38C5×ΓL(1,𝔽25)—21no—
39C5×ΓL(1,𝔽25)—21no—
40C3×#681—21no—
41#6650—41no—
42D3×#168—41no—
43C3⋊#672—21no—
44C3×#672—21no—
45#4893—51no—
46#4865D511yescharacteristic
47C3×#365—51no—
48#4516—51no—
49#4514—51no—
50#4495—51no—
51#4487—51no—
52C2×C5×D8—31no—
53C2×C5×M16—31no—
54C5×#121—61no—
55C2×#681—61no—
56C5×#106C2×D311yescharacteristic
57C5×#102—61no—
58#3951—31no—
59#3951—61no—
60#3951C2×D311yescharacteristic
61#3944—31no—
62#3944C2×D311yescharacteristic
63#2238—151noSylow
64C22×C5×D3—41no—
65C22×C5×D3SD1611yescharacteristic
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C5×Dic3SD1611yescharacteristic
69C5×D12—41no—
70C5×D12—41no—
71C5×D12—82no—
72C4×C5×D3—21no—
73C4×C5×D3—21no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—41no—
77C3×#168—41no—
78C5×C3⋊C8—21no—
79D3×M16—101no—
80C2×D24C2×D511yescharacteristic
81C2×ΓL(1,𝔽25)C2×D511yescharacteristic
82#895—21no—
83C3×M32—51no—
84C3×#108—51no—
85C3×#106C2×D511yescharacteristic
86#822—101no—
87#819—51no—
88#812—51no—
89#809—21no—
90C2×C5×D4—61no—
91C2×C5×D4—121no—
92C22×C4×C5—31no—
93C5×D8—61no—
94C5×D8—61no—
95C5×M16—61no—
96C5×M16—61no—
97C2×C5×C8—31no—
98C2×C5×C8C22×D311yescharacteristic
99C5×C4⋊C4—21no—
100C5×C22⋊C4—121no—
101#681—21no—
102#681—61no—
103#681—121no—
104C2×#168—121no—
105#672—21no—
106#672—61no—
107#469—31no—
108#430—151no—
109#365—51no—
110#365—151no—
111#361—151no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×C5×D3—21no—
116C2×C5×D3—41no—
117C2×C5×D3—81no—
118C2×C5×D3—81no—
119C2×C5×D3—81no—
120C3×C4×C5—81no—
121C3×C4×C5#12311yescharacteristic
122C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
123C5×Dic3—21no—
124C2×D12—21no—
125C2×D12—41no—
126C2×C4×D3C22⋊D511yescharacteristic
127C3×M16—101no—
128C2×C3×C8C22×D511yescharacteristic
129C3×C4⋊C4—21no—
130(C2×D3)⋊C4—41no—
131#208—101no—
132C2×C3⋊C8C22⋊D511yescharacteristic
133D24—21no—
134D24—21no—
135ΓL(1,𝔽25)—21no—
136ΓL(1,𝔽25)—21no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—101no—
140C3⋊C16—101no—
141C23×C5—31no—
142C23×C5—121no—
143C5×D4—121no—
144C5×D4—121no—
145C5×D4—242no—
146C2×C4×C5—31no—
147C2×C4×C5—41no—
148C2×C4×C5—61no—
149C2×C4×C5—61no—
150C2×C4×C5D3×D411yescharacteristic
151C5×C8—61no—
152C5×C8#23511yescharacteristic
153C5×C8#23911yescharacteristic
154#168—41no—
155#168—121no—
156C2×D8—31no—
157C2×M16—31no—
158C2×M16—301no—
159#121—61no—
160M32—51no—
161M32—151no—
162#108—51no—
163#108—151no—
164#108—301no—
165#106D3×D511yescharacteristic
166#102—61no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169C5×D3—41no—
170C5×D3—161no—
171C22×D3—41no—
172C22×D3#68711yescharacteristic
173C2×C3×C4—41no—
174C2×C3×C4C2×C22⋊D511yescharacteristic
175C2×Dic3#68711yescharacteristic
176D12—41no—
177D12—41no—
178D12—82no—
179C4×D3—21no—
180C4×D3—21no—
181C3×C8—201no—
182C3×C8#71111yescharacteristic
183C3×C8#71111yescharacteristic
184C3⋊C8—21no—
185C3⋊C8—201no—
186C22×C5—61no—
187C22×C5—121no—
188C22×C5—241no—
189C22×C5—241no—
190C22×C5—241no—
191C22×C5D3×SD1611yescharacteristic
192C4×C5—61no—
193C4×C5—81no—
194C4×C5#89411yescharacteristic
195C4×C5#91411yescharacteristic
196C2×D4—61no—
197C2×D4—121no—
198C22×C4—31no—
199D8—61no—
200D8—61no—
201M16—61no—
202M16—61no—
203M16—101no—
204M16—301no—
205M16—601no—
206C2×C8—31no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—21no—
210C22⋊C4—121no—
211C16—101no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3C2×#68711yescharacteristic
215C2×D3—21no—
216C2×D3—41no—
217C2×D3—81no—
218C2×D3—81no—
219C2×D3—81no—
220C3×C4—81no—
221C3×C4#408111yescharacteristic
222C3×C4#409511yescharacteristic
223Dic3—21no—
224C2×C5—21no—
225C2×C5—121no—
226C2×C5—481no—
227C2×C5#486311yescharacteristic
228C23—31no—
229C23—121no—
230D4—121no—
231D4—121no—
232D4—242no—
233C2×C4—31no—
234C2×C4—41no—
235C2×C4—61no—
236C2×C4—61no—
237C2×C4D3×C22⋊D511yescharacteristic
238C8—61no—
239C8—201no—
240C8—601no—
241C8#676811yescharacteristic
242C8#677211yescharacteristic
243C2×C3—21no—
244C2×C3#6532311yescharacteristic
245D3—41no—
246D3—161no—
247C5#6931311yescharacteristic, complemented, Sylow
248C22—61no—
249C22—121no—
250C22—241no—
251C22—241no—
252C22—241no—
253C22D3×#68711yescharacteristic
254C4—61no—
255C4—81no—
256C4#9142311yescharacteristic
257C4#9150411yescharacteristic
258C3#1060188111yescharacteristic, complemented, Sylow
259C2—21no—
260C2—121no—
261C2—481no—
262C2#1174719911yescharacteristic
subgroupG/H
centerC2#11747199
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radicalC5×#4865C2
hypercenter#106D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11748059C2semidirect
3. #11746308C2semidirect
4. C3×#64707C2semidirect
5. #11745918C2semidirect
6. #11745917C2semidirect
7. #11745883C2semidirect
27. #64707D3semidirect
213. C3×C5#2238semidirect
247. C5#69313semidirect
258. C3#10601881semidirect

Maximal subgroups

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

subgroupindex
C5×#48652
#117480592
#117463082
C3×#647072
#117459182
#117459172
#117458832
#106018813
#693135