Finite Group Databasebeta

← #14315791

Subgroups — #14315791

Order 1920.

284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5179C211yesmaximal, characteristic
2C3×#65473C211yesmaximal, characteristic, complemented
3#11748063C211yesmaximal, characteristic
4#11746386C211yesmaximal, characteristic, complemented
5#11745937C211yesmaximal, characteristic, complemented
6#11745911C211yesmaximal, characteristic
7#11745876C211yesmaximal, characteristic, complemented
8#10602314—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C5×#904C2211yescharacteristic
11C3×Q8×Dic5—21no—
12#91286—21no—
13#91103C2211yescharacteristic
14#91096C2211yescharacteristic
15C5×#829C412yescomplemented
16C5×#828C412yescomplemented
17C5×#812C2211yescharacteristic
18C3×#3967—21no—
19C3×#3949C2211yescharacteristic
20C3×#3947C2211yescharacteristic
21#90979—21no—
22#70917—51nomaximal, Hall
23C5×#510—31no—
24#65486—31no—
25#65473D311yescharacteristic, complemented
26#64786—31no—
27#64785—31no—
28#64733—31no—
29#64732—31no—
30C2×C3×C5×Q8—21no—
31C5×#235—21no—
32C3×C5×Q16—21no—
33C3×C5×Q16C2×C412yes—
34C2×C3×C5×C8C2311yescharacteristic
35#6710—21no—
36C5×Dic12C2×C411yescharacteristic
37C5×D24C2×C411yescharacteristic
38C5×#204—21no—
39C3×C4⋊Dic5—21no—
40C3×C4⋊Dic5—41no—
41C3×C4×Dic5—41no—
42C3×C4×Dic5D411yescharacteristic
43C2×C3×#168D411yescharacteristic
44#6650—41no—
45D3×#168—41no—
46C3⋊#672—21no—
47C5×C3⋊C16C2×C412yes—
48C3×#441—51no—
49#5179D511yescharacteristic
50#4717—51no—
51#4565—51no—
52#4488—51no—
53#4487—51no—
54#4466—51no—
55C5×#135—31no—
56C2×C5×Q16C2×D311yescharacteristic
57#4094—61no—
58Q8×Dic5—21no—
59C5×Q32—32no—
60C5×SD32—32no—
61C5×M32—31no—
62#3969—61no—
63#3967—21no—
64#3951—31no—
65#3949C2×D311yescharacteristic
66#3947C2×D311yescharacteristic
67#3944—31no—
68#2180—151noSylow
69C3×C5×Q8—22no—
70C3×C5×Q8—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C5×#67—41no—
74C5×D12—21no—
75C4×C5×D3—41no—
76C5×Dic6—21no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—41no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C3⋊#168—41no—
82C3×#168—21no—
83C2×C3×Q16C2×D511yescharacteristic
84C3×C4×Q8—101no—
85#904C2×D511yescharacteristic
86#901—101no—
87C3×#106—51no—
88C3×#103—101no—
89C3×#97—51no—
90#829Dic512yescomplemented
91#828Dic512yescomplemented
92#819—51no—
93#812—51no—
94#812C2×D511yescharacteristic
95#805—101no—
96C5×#41—61no—
97C2×C5×Q8—21no—
98C5×Q16—21no—
99C5×Q16—31no—
100C5×Q16C4×D312yes—
101C5×SD16—61no—
102C5×D8—31no—
103C2×C5×C8C22×D311yescharacteristic
104C4⋊Dic5—21no—
105C4⋊Dic5—41no—
106C4×Dic5—41no—
107C4×Dic5#6711yescharacteristic
108#681—61no—
109#681—121no—
110C2×#168—121no—
111C2×#168#6711yescharacteristic
112C5×C16—32no—
113#672—61no—
114#510—31no—
115#444—151no—
116#441—51no—
117#365—151no—
118#362—151no—
119#360—151no—
120#347—151no—
121C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×C5×D3—41no—
123C3×C4×C5—42no—
124C3×C4×C5C4×D411yescharacteristic
125C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
126C3×Dic5—41no—
127C3×Dic5—81no—
128C5×Dic3—41no—
129C2×C3×Q8—21no—
130#235—21no—
131C3×Q16—21no—
132C3×Q16C2×Dic512yes—
133C2×C3×C8—51no—
134C2×C3×C8C22×D511yescharacteristic
135C3×C4⋊C4—101no—
136C3×C4⋊C4—201no—
137C3×C42—51no—
138C3×C42—201no—
139#208—101no—
140Dic12C2×Dic511yescharacteristic
141D24C2×Dic511yescharacteristic
142#204—21no—
143ΓL(1,𝔽25)—201no—
144D3×C8—201no—
145C3⋊C16—101no—
146C3⋊C16C2×Dic512yes—
147C5×Q8—22no—
148C5×Q8—41no—
149C5×Q8—61no—
150C5×D4—61no—
151C5×D4—121no—
152C2×C4×C5—41no—
153C2×C4×C5—121no—
154C2×C4×C5C2×#6711yescharacteristic
155C2×Dic5—21no—
156C2×Dic5—41no—
157C5×C8C2×C4×D311yescharacteristic
158C5×C8#23511yescharacteristic
159#168—21no—
160#168—121no—
161#135—31no—
162C2×Q16D3×D511yescharacteristic
163#131—301no—
164C4×Q8—101no—
165Q32—32no—
166SD32—32no—
167M32—31no—
168M32—151no—
169#108—151no—
170#106—51no—
171#104—301no—
172#103—101no—
173#97—51no—
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176C5×D3—81no—
177C3×Q8—22no—
178C3×Q8—41no—
179C2×C3×C4—41no—
180C2×C3×C4—101no—
181C2×C3×C4—201no—
182C2×C3×C4D4×D511yescharacteristic
183#67—41no—
184D12—21no—
185C4×D3—41no—
186Dic6—21no—
187C3×C8—101no—
188C3×C8#71111yescharacteristic
189C3×C8C22×Dic511yescharacteristic
190C3⋊C8—201no—
191C22×C5—121no—
192C22×C5#93211yescharacteristic
193C4×C5—42no—
194C4×C5—121no—
195C4×C5C4×#6711yescharacteristic
196C4×C5#94911yescharacteristic
197Dic5—41no—
198Dic5—81no—
199#41—61no—
200C2×Q8—21no—
201Q16—21no—
202Q16—31no—
203Q16D3×Dic512yes—
204SD16—61no—
205D8—31no—
206M16—301no—
207M16—601no—
208C2×C8—51no—
209C2×C8—601no—
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—101no—
212C4⋊C4—201no—
213C42—51no—
214C42—201no—
215C16—32no—
216C16—301no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3#405711yescharacteristic
219C2×D3—41no—
220C3×C4—42no—
221C3×C4—201no—
222C3×C4—401no—
223C3×C4#405711yescharacteristic
224C3×C4D4×Dic511yescharacteristic
225Dic3—41no—
226C2×C5—21no—
227C2×C5—241no—
228C2×C5#501411yescharacteristic
229Q8—22no—
230Q8—41no—
231Q8—61no—
232D4—61no—
233D4—121no—
234C2×C4—41no—
235C2×C4—101no—
236C2×C4—121no—
237C2×C4—201no—
238C2×C4D5×#6711yescharacteristic
239C8—101no—
240C8—601no—
241C8C2×D3×Dic511yescharacteristic
242C8#678211yescharacteristic
243C2×C3—21no—
244C2×C3#6544111yescharacteristic
245D3—81no—
246C5#7091711yescharacteristic, complemented, Sylow
247C22—121no—
248C22#9148911yescharacteristic
249C4—42no—
250C4—121no—
251C4—201no—
252C4—401no—
253C4#9147811yescharacteristic
254C4Dic5×#6711yescharacteristic
255C3#1060231411yescharacteristic, complemented, Sylow
256C2—21no—
257C2—241no—
258C2#1174897711yescharacteristic
subgroupG/H
centerC2#11748977
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5#442
prime radicalC5×#904C22
cosocleC2×C3×C5×C8C23
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2180
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C3×#65473C2semidirect
4. #11746386C2semidirect
5. #11745937C2semidirect
7. #11745876C2semidirect
15. C5×#829C4semidirect
16. C5×#828C4semidirect
25. #65473D3semidirect
90. #829Dic5semidirect
91. #828Dic5semidirect
217. C3×C5#2180semidirect
246. C5#70917semidirect
255. C3#10602314semidirect

Maximal subgroups

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

subgroupindex
C5×#51792
C3×#654732
#117480632
#117463862
#117459372
#117459112
#117458762
#106023143
#709175