Finite Group Databasebeta

← #14315783

Subgroups — #14315783

Order 1920.

284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750818C211yesmaximal, characteristic
2C3×#65005C211yesmaximal, characteristic, complemented
3#11747560C211yesmaximal, characteristic
4C5×#4466C211yesmaximal, characteristic, complemented
5#11745937C211yesmaximal, characteristic, complemented
6#11745922C211yesmaximal, characteristic, complemented
7#11745913C211yesmaximal, characteristic
8#10599883—31nomaximal, Hall
9#91793C2211yescharacteristic
10#91790—21no—
11C2×C3×Dic20C2211yescharacteristic
12C3×C4×Dic10—21no—
13C3×C5×#97C2211yescharacteristic
14#91103C2211yescharacteristic
15#91089—21no—
16C5×#812C2211yescharacteristic
17C5×#812C2211yescharacteristic
18C3×#3949C2211yescharacteristic
19C3×#3948—21no—
20#90947C412yescomplemented
21#90943C412yescomplemented
22#70917—51nomaximal, Hall
23#65198—31no—
24#65006—31no—
25#65005D311yescharacteristic, complemented
26C5×#347—31no—
27#64738—31no—
28#64737—31no—
29#64733—31no—
30#6817—21no—
31C2×C3×Dic10—21no—
32C2×C3×C5×C8D411yescharacteristic
33C2×C3×C5×C8C2311yescharacteristic
34C3×C42×C5D411yescharacteristic
35#6710—21no—
36Dic60C2×C411yescharacteristic
37D120C2×C411yescharacteristic
38#6706—21no—
39#6705—41no—
40C8×D15—41no—
41C3×C4⋊Dic5—21no—
42C3×#683—41no—
43C3×C4×Dic5—41no—
44C3×Dic20—21no—
45C3×Dic20C2×C412yes—
46C5×C3⋊C16—21no—
47C5×C3⋊C16C2×C412yes—
48C3×#441—51no—
49#5179—51no—
50#4717—51no—
51#4565—51no—
52#4488—51no—
53#4487—51no—
54#4466D511yescharacteristic, complemented
55C2×Dic20C2×D311yescharacteristic
56#4050—31no—
57#4047—61no—
58C4×Dic10—21no—
59C5×M32—31no—
60C5×M32—31no—
61C5×#97C2×D311yescharacteristic
62#3951—31no—
63#3949C2×D311yescharacteristic
64#3948—21no—
65#3937—61no—
66Dic40—32no—
67#3932—32no—
68#2180—151noSylow
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C2×D411yescharacteristic
71#1220—41no—
72D60—21no—
73C4×D15—41no—
74Dic30—21no—
75C2×C3×Dic5—41no—
76C2×C3×Dic5—41no—
77C3×Dic10—22no—
78C3×Dic10—41no—
79C3×C5×C8—21no—
80C3×C5×C8C22×C411yescharacteristic
81C3×C5×C8#4111yescharacteristic
82C3⋊#168—41no—
83C2×C3×Q16—51no—
84C3×C4×Q8—101no—
85#904—51no—
86#901—101no—
87C3×#106—51no—
88C3×#103—101no—
89C3×#97C2×D511yescharacteristic
90#829—52no—
91#828—52no—
92#819—51no—
93#812C2×D511yescharacteristic
94#812C2×D511yescharacteristic
95#805—101no—
96#709—61no—
97C2×Dic10—21no—
98C2×C5×C8#6711yescharacteristic
99C2×C5×C8C22×D311yescharacteristic
100C42×C5#6711yescharacteristic
101C4⋊Dic5—21no—
102#683—41no—
103C4×Dic5—41no—
104#681—61no—
105Dic20—21no—
106Dic20—31no—
107Dic20C4×D312yes—
108D40—31no—
109#677—61no—
110#676—121no—
111C8×D5—121no—
112C5×C16—32no—
113C5×C16—61no—
114#510—151no—
115#444—151no—
116#441—51no—
117#365—151no—
118#362—151no—
119#360—151no—
120#347—31no—
121C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×D15—41no—
123C3×C4×C5—41no—
124C3×C4×C5C4×D411yescharacteristic
125C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
126Dic15—41no—
127C3×Dic5—42no—
128C3×Dic5—81no—
129C2×C3×Q8—101no—
130#235—101no—
131C3×Q16—52no—
132C3×Q16—101no—
133C2×C3×C8D2011yescharacteristic
134C2×C3×C8C22×D511yescharacteristic
135C3×C4⋊C4—101no—
136C3×C4⋊C4—201no—
137C3×C42—201no—
138C3×C42D2011yescharacteristic
139#208—101no—
140Dic12—51no—
141D24—51no—
142#204—101no—
143ΓL(1,𝔽25)—201no—
144D3×C8—201no—
145C3⋊C16—21no—
146C3⋊C16C4×D512yes—
147C2×C4×C5—21no—
148C2×C4×C5C2×#6711yescharacteristic
149C22⋊D5—121no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152D20—61no—
153C4×D5—121no—
154Dic10—22no—
155Dic10—41no—
156Dic10—61no—
157C5×C8—21no—
158C5×C8C2×C4×D311yescharacteristic
159C5×C8#23511yescharacteristic
160#168—121no—
161#135—151no—
162C2×Q16—51no—
163#131—301no—
164C4×Q8—101no—
165Q32—152no—
166SD32—152no—
167M32—31no—
168M32—31no—
169#108—151no—
170#106—51no—
171#104—301no—
172#103—101no—
173#97D3×D511yescharacteristic
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176D15—81no—
177C3×Q8—102no—
178C3×Q8—201no—
179C2×C3×C4—21no—
180C2×C3×C4—201no—
181C2×C3×C4—201no—
182C2×C3×C4C2×D2011yescharacteristic
183#67—201no—
184D12—101no—
185C4×D3—201no—
186Dic6—101no—
187C3×C8—21no—
188C3×C8C2×C4×D511yescharacteristic
189C3×C8#70911yescharacteristic
190C3⋊C8—201no—
191C22×C5#93211yescharacteristic
192C2×D5—121no—
193C4×C5—41no—
194C4×C5C4×#6711yescharacteristic
195C4×C5#94911yescharacteristic
196Dic5—42no—
197Dic5—81no—
198Dic5—121no—
199#41—301no—
200C2×Q8—101no—
201Q16—52no—
202Q16—101no—
203Q16—151no—
204SD16—301no—
205D8—151no—
206M16—301no—
207M16—601no—
208C2×C8—601no—
209C2×C8#120211yescharacteristic
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—101no—
212C4⋊C4—201no—
213C42—201no—
214C42#120211yescharacteristic
215C16—32no—
216C16—61no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3#405411yescharacteristic
219C2×D3—201no—
220C3×C4—41no—
221C3×C4—202no—
222C3×C4—401no—
223C3×C4C4×D2011yescharacteristic
224C3×C4#405411yescharacteristic
225Dic3—201no—
226C2×C5—21no—
227C2×C5#501411yescharacteristic
228D5—241no—
229Q8—102no—
230Q8—201no—
231Q8—301no—
232D4—301no—
233D4—601no—
234C2×C4—21no—
235C2×C4—201no—
236C2×C4—201no—
237C2×C4—601no—
238C2×C4C2×#120211yescharacteristic
239C8—21no—
240C8—601no—
241C8#677111yescharacteristic
242C8C4×D3×D511yescharacteristic
243C2×C3—21no—
244C2×C3#6500011yescharacteristic
245D3—401no—
246C5#7091711yescharacteristic, complemented, Sylow
247C22—601no—
248C22#9131211yescharacteristic
249C4—41no—
250C4—202no—
251C4—401no—
252C4—601no—
253C4#9130111yescharacteristic
254C4C4×#120211yescharacteristic
255C3#1059988311yescharacteristic, complemented, Sylow
256C2—21no—
257C2—1201no—
258C2#1174702311yescharacteristic
subgroupG/H
centerC2#11747023
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#97C22
socleC2×C3×C5#442
prime radical#91793C22
cosocleC2×C3×C5×C8C23
hypercenter#97D3×D5
hypocenterC3×C5#2180
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#65005C2semidirect
4. C5×#4466C2semidirect
5. #11745937C2semidirect
6. #11745922C2semidirect
20. #90947C4semidirect
21. #90943C4semidirect
25. #65005D3semidirect
54. #4466D5semidirect
217. C3×C5#2180semidirect
246. C5#70917semidirect
255. C3#10599883semidirect

Maximal subgroups

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

subgroupindex
#117508182
C3×#650052
#117475602
C5×#44662
#117459372
#117459222
#117459132
#105998833
#709175