Finite Group Databasebeta

← #14318586

Subgroups — #14318586

Order 1920.

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

normal subgroups only

This group has 248 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
1#11748059C211yesmaximal, characteristic
2#11747953C211yesmaximal, characteristic
3#11746334C211yesmaximal, characteristic, complemented
4C5×#4514C211yesmaximal, characteristic
5C3×#64737C211yesmaximal, characteristic, complemented
6#11745938C211yesmaximal, characteristic, complemented
7#11745922C211yesmaximal, characteristic, complemented
8#10599910—31nomaximal, Hall
9C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11#91369—21no—
12D3×#681—21no—
13C3×C5×M32C2211yescharacteristic
14#91103C2211yescharacteristic
15#91101C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18#90993—21no—
19#90971—21no—
20#69267—51nomaximal, Hall
21#65426—31no—
22#65414—31no—
23C5×#349—31no—
24#64737—31no—
25#64737D311yescharacteristic, complemented
26#64733—31no—
27#64733—31no—
28C2×C4×C5×D3D411yescharacteristic
29C2×C3×Dic10—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32#6710—21no—
33C2×C5×C3⋊C8D411yescharacteristic
34C5×ΓL(1,𝔽25)—21no—
35C5×ΓL(1,𝔽25)—21no—
36C3×#681—21no—
37C3×Dic20—21no—
38C3×Dic20—21no—
39#6669—41no—
40(C2×D3)⋊Dic5—41no—
41#6650—41no—
42D3×#168—41no—
43C3×C5×C16—21no—
44C5×C3⋊C16—21no—
45#5189—51no—
46#4893—51no—
47C3×#362—51no—
48#4565—51no—
49#4514D511yescharacteristic
50#4513—51no—
51#4494—51no—
52C2×C5×M16—31no—
53#4070—61no—
54C2×#681—61no—
55C2×Dic20C2×D311yescharacteristic
56C5×M32—31no—
57C5×M32C2×D311yescharacteristic
58#3951—31no—
59#3951—61no—
60#3951C2×D311yescharacteristic
61#3949—31no—
62#3948—61no—
63#2239—151noSylow
64C22×C5×D3SD1611yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15—41no—
67C2×C5×Dic3SD1611yescharacteristic
68C4×C5×D3—21no—
69C4×C5×D3—21no—
70C2×C3×Dic5—41no—
71C3×Dic10—41no—
72C3×Dic10—41no—
73C3×C5×C8#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—41no—
76C3×#168—41no—
77C5×C3⋊C8—21no—
78C2×C3×Q16—51no—
79#946—101no—
80D3×M16—101no—
81C2×ΓL(1,𝔽25)C2×D511yescharacteristic
82C3×M32C2×D511yescharacteristic
83C3×#108—51no—
84#835—101no—
85#822—101no—
86#819—51no—
87#817—51no—
88#812C2×D511yescharacteristic
89C22×C4×C5—31no—
90C2×Dic10—21no—
91C5×M16—61no—
92C5×M16—61no—
93C2×C5×C8—31no—
94C2×C5×C8C22×D311yescharacteristic
95C22⋊Dic5—121no—
96C4⋊Dic5—61no—
97#683—121no—
98#681—21no—
99#681—61no—
100#681—121no—
101C2×#168—121no—
102Dic20—21no—
103Dic20—21no—
104C5×C16—21no—
105C5×C16—61no—
106#470—151no—
107#430—151no—
108#365—151no—
109#365—151no—
110#362—51no—
111#362—151no—
112#349—31no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×C5×D3—21no—
115C2×C5×D3—41no—
116C3×C4×C5#12311yescharacteristic
117C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
118Dic15—81no—
119C3×Dic5—81no—
120C5×Dic3—21no—
121C2×C3×Q8—101no—
122C2×C4×D3D2011yescharacteristic
123C3×Q16—101no—
124C3×Q16—101no—
125C3×M16—101no—
126C2×C3×C8C22×D511yescharacteristic
127(C2×D3)⋊C4—201no—
128C4⋊Dic3—101no—
129Dic3⋊C4—201no—
130#208—101no—
131C2×C3⋊C8D2011yescharacteristic
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—21no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—21no—
137C3⋊C16—21no—
138C23×C5—31no—
139C2×C4×C5—31no—
140C2×C4×C5—61no—
141C2×C4×C5—61no—
142C2×C4×C5D3×D411yescharacteristic
143C2×Dic5—41no—
144C2×Dic5—121no—
145Dic10—41no—
146Dic10—41no—
147C5×C8—61no—
148C5×C8#23511yescharacteristic
149C5×C8#23711yescharacteristic
150#168—41no—
151#168—121no—
152C2×Q16—51no—
153C2×M16—31no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—31no—
157M32D3×D511yescharacteristic
158#108—51no—
159#108—151no—
160#108—301no—
161#106—151no—
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165C5×D3—41no—
166C22×D3#67711yescharacteristic
167C3×Q8—201no—
168C3×Q8—201no—
169C2×C3×C4—201no—
170C2×C3×C4C2×D2011yescharacteristic
171C2×Dic3—201no—
172C2×Dic3#67711yescharacteristic
173C4×D3—21no—
174C4×D3—21no—
175C3×C8—201no—
176C3×C8#71111yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—21no—
179C3⋊C8—201no—
180C22×C5—61no—
181C22×C5—121no—
182C22×C5D3×SD1611yescharacteristic
183C4×C5—61no—
184C4×C5#88311yescharacteristic
185C4×C5#91111yescharacteristic
186Dic5—81no—
187Dic5—241no—
188C2×Q8—101no—
189C22×C4—31no—
190Q16—101no—
191Q16—101no—
192M16—61no—
193M16—61no—
194M16—101no—
195M16—301no—
196M16—601no—
197C2×C8—31no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—301no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—21no—
204C16—61no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3C2×#67711yescharacteristic
207C2×D3—21no—
208C2×D3—41no—
209C3×C4—401no—
210C3×C4#403211yescharacteristic
211C3×C4#405411yescharacteristic
212Dic3—21no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5—121no—
216C2×C5#477711yescharacteristic
217C23—31no—
218Q8—201no—
219Q8—201no—
220C2×C4—31no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—201no—
224C2×C4—601no—
225C2×C4D3×D2011yescharacteristic
226C8—61no—
227C8—201no—
228C8—601no—
229C8#677211yescharacteristic
230C8#678011yescharacteristic
231C2×C3—21no—
232C2×C3#6502411yescharacteristic
233D3—41no—
234C5#6926711yescharacteristic, complemented, Sylow
235C22—61no—
236C22—121no—
237C22D3×#67711yescharacteristic
238C4—61no—
239C4—401no—
240C4—1201no—
241C4#9125411yescharacteristic
242C4#9145711yescharacteristic
243C3#1059991011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—121no—
246C2#1174791311yescharacteristic
subgroupG/H
centerC2#11747913
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radicalC22×C5×D3SD16
hypercenterM32D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
3. #11746334C2semidirect
5. C3×#64737C2semidirect
6. #11745938C2semidirect
7. #11745922C2semidirect
25. #64737D3semidirect
205. C3×C5#2239semidirect
234. C5#69267semidirect
243. C3#10599910semidirect

Maximal subgroups

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

subgroupindex
#117480592
#117479532
#117463342
C5×#45142
C3×#647372
#117459382
#117459222
#105999103
#692675