Finite Group Databasebeta

← #14318519

Subgroups — #14318519

Order 1920.

268 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 67 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#11751260C211yesmaximal, characteristic
2#11750994C211yesmaximal, characteristic, complemented
3C3×C5×#361C211yesmaximal, characteristic, complemented
4#11746384C211yesmaximal, characteristic, complemented
5#11746335C211yesmaximal, characteristic, complemented
6#11746334C211yesmaximal, characteristic, complemented
7#11746315C211yesmaximal, characteristic, complemented
8#10600050—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10#91827—21no—
11M16×D15—21no—
12C2×#6705C2211yescharacteristic
13C3×C5×M32C2211yescharacteristic
14C3×C5×#108C2211yescharacteristic
15#91116—21no—
16#91106—21no—
17#91103C2211yescharacteristic
18#91101C2211yescharacteristic
19#91096C2211yescharacteristic
20#69257—51nomaximal, Hall
21#65448—31no—
22#65182—31no—
23C5×#361D311yescharacteristic, complemented
24#64783—31no—
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C3×C5×D4—21no—
29C2×#1220—41no—
30C2×C4×D15D411yescharacteristic
31C3×C5×D8—21no—
32C3×C5×D8—21no—
33C3×C5×M16—21no—
34C2×C3×C5×C8C2311yescharacteristic
35#6719—41no—
36C4⋊Dic15—21no—
37#6710—21no—
38C2×C3⋊#168D411yescharacteristic
39#6705—21no—
40#6705—21no—
41#6705—41no—
42C8×D15—41no—
43C3×C5×C16—21no—
44C3⋊#672—21no—
45#5159—51no—
46#4893—51no—
47C3×#361D511yescharacteristic, complemented
48#4563—51no—
49#4514—51no—
50#4513—51no—
51#4494—51no—
52C2×C5×D8C2×D311yescharacteristic
53#4084—61no—
54D5×M16—61no—
55C2×#676—31no—
56C5×M32C2×D311yescharacteristic
57C5×#108C2×D311yescharacteristic
58#3964—61no—
59#3954—61no—
60#3951—31no—
61#3949—31no—
62#3944—31no—
63#2238—151noSylow
64C23×C3×C5—41no—
65C22×D15SD1611yescharacteristic
66C3×C5×D4—41no—
67C3×C5×D4—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69#1220—82no—
70C2×Dic15—41no—
71C2×Dic15SD1611yescharacteristic
72C4×D15—21no—
73C4×D15—21no—
74C3×C5×C8—41no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C3⋊#168—21no—
78C3⋊#168—41no—
79C2×C3×D8C2×D511yescharacteristic
80#938—101no—
81D3×M16—101no—
82C2×ΓL(1,𝔽25)—51no—
83C3×M32C2×D511yescharacteristic
84C3×#108C2×D511yescharacteristic
85#832—101no—
86#822—101no—
87#819—51no—
88#817—51no—
89#812—51no—
90C2×C5×D4—21no—
91C2×C22⋊D5—121no—
92C2×C4×D5—31no—
93C5×D8—21no—
94C5×D8—21no—
95C5×M16—21no—
96C2×C5×C8C22×D311yescharacteristic
97C22⋊Dic5—121no—
98C4⋊Dic5—61no—
99#681—61no—
100C2×#168—31no—
101#676—61no—
102#676—61no—
103#676—121no—
104C8×D5—121no—
105C5×C16—21no—
106#672—61no—
107#469—151no—
108#430—151no—
109#365—151no—
110#365—151no—
111#361—151no—
112#361D1511yescharacteristic, complemented
113#349—151no—
114C22×C3×C5—81no—
115C22×C3×C5—81no—
116C22×C3×C5—81no—
117C22×C3×C5C2×SD1611yescharacteristic
118C2×D15—21no—
119C2×D15—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122Dic15—21no—
123Dic15—81no—
124C2×C3×D4—21no—
125C2×#67—201no—
126C2×C4×D3—51no—
127C3×D8—21no—
128C3×D8—21no—
129C3×M16—21no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—101no—
133#208—101no—
134C2×C3⋊C8—51no—
135ΓL(1,𝔽25)—101no—
136ΓL(1,𝔽25)—101no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—21no—
140C3⋊C16—101no—
141C23×C5—41no—
142C22×D5—31no—
143C5×D4—41no—
144C5×D4—41no—
145C2×C4×C5D3×D411yescharacteristic
146C22⋊D5—242no—
147C2×Dic5—31no—
148C2×Dic5—121no—
149C4×D5—61no—
150C4×D5—61no—
151C5×C8—41no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—61no—
155#168—121no—
156C2×D8C2×D1511yescharacteristic
157C2×M16—151no—
158C2×M16—301no—
159#121—301no—
160M32—151no—
161M32C2×D1511yescharacteristic
162#108—151no—
163#108—301no—
164#108C2×D1511yescharacteristic
165#106—151no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5—161no—
169C2×C3×C5#48111yescharacteristic
170D15—41no—
171C23×C3—41no—
172C22×D3—51no—
173C3×D4—41no—
174C3×D4—41no—
175C2×C3×C4D4×D511yescharacteristic
176#67—402no—
177C2×Dic3—51no—
178C2×Dic3—201no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8—41no—
182C3×C8#70911yescharacteristic
183C3×C8#71111yescharacteristic
184C3⋊C8—101no—
185C3⋊C8—201no—
186C22×C5—81no—
187C22×C5—81no—
188C22×C5—81no—
189C22×C5D3×SD1611yescharacteristic
190C2×D5—61no—
191C2×D5—121no—
192C4×C5#88311yescharacteristic
193C4×C5#91111yescharacteristic
194Dic5—61no—
195Dic5—241no—
196C2×D4—21no—
197C2×D4—601no—
198C22×C4—151no—
199D8—21no—
200D8—21no—
201M16—21no—
202M16—301no—
203M16—301no—
204M16—301no—
205M16—601no—
206C2×C8—151no—
207C2×C8—601no—
208C2×C8C22×D1511yescharacteristic
209C4⋊C4—301no—
210C22⋊C4—601no—
211C16—21no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—81no—
215C22×C3—81no—
216C22×C3—81no—
217C22×C3D5×SD1611yescharacteristic
218C2×D3—101no—
219C2×D3—201no—
220C3×C4#402911yescharacteristic
221C3×C4#405711yescharacteristic
222Dic3—101no—
223Dic3—401no—
224C2×C5—21no—
225C2×C5—161no—
226C2×C5#477711yescharacteristic
227D5—121no—
228C23—41no—
229C23—151no—
230D4—41no—
231D4—41no—
232D4—1202no—
233C2×C4—151no—
234C2×C4—301no—
235C2×C4—301no—
236C2×C4—601no—
237C2×C4D4×D1511yescharacteristic
238C8—41no—
239C8—301no—
240C8—601no—
241C8#681711yescharacteristic
242C8#681911yescharacteristic
243C2×C3—21no—
244C2×C3—161no—
245C2×C3#6506611yescharacteristic
246D3—201no—
247C5#6925711yescharacteristic, complemented, Sylow
248C22—81no—
249C22—81no—
250C22—81no—
251C22—301no—
252C22—601no—
253C22SD16×D1511yescharacteristic
254C4—301no—
255C4—1201no—
256C4#9177211yescharacteristic
257C4#9180011yescharacteristic
258C3#1060005011yescharacteristic, complemented, Sylow
259C2—21no—
260C2—161no—
261C2—601no—
262C2#1175087811yescharacteristic
subgroupG/H
centerC2#11750878
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#361C2
socleC2×C3×C5#481
prime radical#11751260C2
hypercenter#361D15
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #11750994C2semidirect
3. C3×C5×#361C2semidirect
4. #11746384C2semidirect
5. #11746335C2semidirect
6. #11746334C2semidirect
7. #11746315C2semidirect
23. C5×#361D3semidirect
47. C3×#361D5semidirect
112. #361D15semidirect
213. C3×C5#2238semidirect
247. C5#69257semidirect
258. C3#10600050semidirect

Maximal subgroups

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

subgroupindex
#117512602
#117509942
C3×C5×#3612
#117463842
#117463352
#117463342
#117463152
#106000503
#692575