Finite Group Databasebeta

← #14318547

Subgroups — #14318547

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
1#11748059C211yesmaximal, characteristic, complemented
2#11747921C211yesmaximal, characteristic
3#11746334C211yesmaximal, characteristic, complemented
4C5×#4514C211yesmaximal, characteristic, complemented
5C3×#64736C211yesmaximal, characteristic, complemented
6#11745938C211yesmaximal, characteristic, complemented
7#11745916C211yesmaximal, characteristic, complemented
8#10599909—31nomaximal, Hall
9C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
10C2×C3×D40C2211yescharacteristic
11#91456—21no—
12D3×#681—21no—
13C3×C5×M32C2211yescharacteristic
14#91103C2211yescharacteristic
15#91101C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18#90993—21no—
19#90965—21no—
20#69257—51nomaximal, Hall
21#65424—31no—
22#65414—31no—
23C5×#349—31no—
24#64736—31no—
25#64736D311yescharacteristic, complemented
26#64733—31no—
27#64733—31no—
28C2×C4×C5×D3D411yescharacteristic
29C2×C3×D20—21no—
30C2×#1201—41no—
31C2×C3×C5×C8C2311yescharacteristic
32C4⋊Dic15—21no—
33#6710—21no—
34C2×C5×C3⋊C8D411yescharacteristic
35C5×ΓL(1,𝔽25)—21no—
36C5×ΓL(1,𝔽25)—21no—
37C3×#681—21no—
38C3×D40—21no—
39C3×D40—21no—
40#6665—41no—
41#6650—41no—
42D3×#168—41no—
43C3×C5×C16—21no—
44C5×C3⋊C16—21no—
45#5159—51no—
46#4893—51no—
47C3×#361—51no—
48#4563—51no—
49#4514D511yescharacteristic, complemented
50#4513—51no—
51#4494—51no—
52C2×C5×M16—31no—
53#4076—61no—
54C2×#681—61no—
55C2×D40C2×D311yescharacteristic
56C5×M32—31no—
57C5×M32C2×D311yescharacteristic
58#3953—61no—
59#3951—31no—
60#3951—61no—
61#3951C2×D311yescharacteristic
62#3949—31no—
63#2238—151noSylow
64C22×C5×D3SD1611yescharacteristic
65C22×C3×D5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15—41no—
68C2×C5×Dic3SD1611yescharacteristic
69C4×C5×D3—21no—
70C4×C5×D3—21no—
71C3×D20—41no—
72C3×D20—41no—
73#1201—82no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—41no—
77C3×#168—41no—
78C5×C3⋊C8—21no—
79C2×C3×D8—51no—
80#938—101no—
81D3×M16—101no—
82C2×ΓL(1,𝔽25)C2×D511yescharacteristic
83C3×M32C2×D511yescharacteristic
84C3×#108—51no—
85#832—101no—
86#822—101no—
87#819—51no—
88#817—51no—
89#812C2×D511yescharacteristic
90C22×C4×C5—31no—
91C2×C22⋊D5—121no—
92C2×D20—21no—
93C5×M16—61no—
94C5×M16—61no—
95C2×C5×C8—31no—
96C2×C5×C8C22×D311yescharacteristic
97#685—121no—
98C4⋊Dic5—61no—
99#681—21no—
100#681—61no—
101#681—121no—
102C2×#168—121no—
103D40—21no—
104D40—21no—
105C5×C16—21no—
106C5×C16—61no—
107#469—151no—
108#430—151no—
109#365—151no—
110#365—151no—
111#361—51no—
112#361—151no—
113#349—31no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×C5×D3—21no—
116C2×C5×D3—41no—
117C2×C3×D5—81no—
118C2×C3×D5—81no—
119C2×C3×D5—81no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122Dic15—81no—
123C5×Dic3—21no—
124C2×C3×D4—101no—
125C2×#67—201no—
126C2×C4×D3D2011yescharacteristic
127C3×D8—101no—
128C3×D8—101no—
129C3×M16—101no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—101no—
133#208—101no—
134C2×C3⋊C8D2011yescharacteristic
135ΓL(1,𝔽25)—21no—
136ΓL(1,𝔽25)—21no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—21no—
140C3⋊C16—21no—
141C23×C5—31no—
142C22×D5—41no—
143C2×C4×C5—31no—
144C2×C4×C5—61no—
145C2×C4×C5—61no—
146C2×C4×C5D3×D411yescharacteristic
147C22⋊D5—242no—
148C2×Dic5—121no—
149D20—41no—
150D20—41no—
151C5×C8—61no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—41no—
155#168—121no—
156C2×D8—51no—
157C2×M16—31no—
158C2×M16—301no—
159#121—301no—
160M32—31no—
161M32D3×D511yescharacteristic
162#108—51no—
163#108—151no—
164#108—301no—
165#106—151no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169C3×D5—161no—
170C5×D3—41no—
171C23×C3—201no—
172C22×D3#67711yescharacteristic
173C3×D4—201no—
174C3×D4—201no—
175C2×C3×C4C2×D2011yescharacteristic
176#67—402no—
177C2×Dic3—201no—
178C2×Dic3#67711yescharacteristic
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×C5D3×SD1611yescharacteristic
189C2×D5—81no—
190C2×D5—81no—
191C2×D5—81no—
192C4×C5—61no—
193C4×C5#88311yescharacteristic
194C4×C5#91111yescharacteristic
195Dic5—241no—
196C2×D4—101no—
197C2×D4—601no—
198C22×C4—31no—
199D8—101no—
200D8—101no—
201M16—61no—
202M16—61no—
203M16—101no—
204M16—301no—
205M16—601no—
206C2×C8—31no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—301no—
210C22⋊C4—601no—
211C16—21no—
212C16—61no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—401no—
215C22×C3—401no—
216C22×C3—401no—
217C22×C3C2×#67711yescharacteristic
218C2×D3—21no—
219C2×D3—41no—
220C3×C4#403211yescharacteristic
221C3×C4#405411yescharacteristic
222Dic3—21no—
223Dic3—401no—
224C2×C5—21no—
225C2×C5—121no—
226C2×C5#477711yescharacteristic
227D5—161no—
228C23—31no—
229C23—201no—
230D4—201no—
231D4—201no—
232D4—1202no—
233C2×C4—31no—
234C2×C4—61no—
235C2×C4—61no—
236C2×C4—601no—
237C2×C4D3×D2011yescharacteristic
238C8—61no—
239C8—201no—
240C8—601no—
241C8#677211yescharacteristic
242C8#678011yescharacteristic
243C2×C3—21no—
244C2×C3—801no—
245C2×C3#6502411yescharacteristic
246D3—41no—
247C5#6925711yescharacteristic, complemented, Sylow
248C22—61no—
249C22—121no—
250C22—401no—
251C22—401no—
252C22—401no—
253C22D3×#67711yescharacteristic
254C4—61no—
255C4—1201no—
256C4#9125411yescharacteristic
257C4#9145711yescharacteristic
258C3#1059990911yescharacteristic, complemented, Sylow
259C2—21no—
260C2—121no—
261C2—801no—
262C2#1174791311yescharacteristic
subgroupG/H
centerC2#11747913
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radical#11747921C2
hypercenterM32D3×D5
hypocenterC3×C5#2238
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
1. #11748059C2semidirect
3. #11746334C2semidirect
4. C5×#4514C2semidirect
5. C3×#64736C2semidirect
6. #11745938C2semidirect
7. #11745916C2semidirect
25. #64736D3semidirect
49. #4514D5semidirect
213. C3×C5#2238semidirect
247. C5#69257semidirect
258. C3#10599909semidirect

Maximal subgroups

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

subgroupindex
#117480592
#117479212
#117463342
C5×#45142
C3×#647362
#117459382
#117459162
#105999093
#692575