Finite Group Databasebeta

← #14315796

Subgroups — #14315796

Order 1920.

284 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 80 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#11751280C211yesmaximal, characteristic
2C3×#65473C211yesmaximal, characteristic, complemented
3#11748065C211yesmaximal, characteristic
4C5×#4565C211yesmaximal, characteristic, complemented
5#11745935C211yesmaximal, characteristic, complemented
6#11745913C211yesmaximal, characteristic
7#11745876C211yesmaximal, characteristic, complemented
8#10600057—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91793C2211yescharacteristic
11C3×Q8×Dic5—21no—
12#91290—21no—
13#91113C412yescomplemented
14#91112C412yescomplemented
15#91096C2211yescharacteristic
16C5×#819C2211yescharacteristic
17C5×#812C2211yescharacteristic
18C3×#3967—21no—
19C3×#3949C2211yescharacteristic
20C3×#3947C2211yescharacteristic
21#90981—21no—
22#70917—51nomaximal, Hall
23#65473D311yescharacteristic, complemented
24#65468—31no—
25#65183—31no—
26C5×#362—31no—
27#64738—31no—
28#64732—31no—
29#64714—31no—
30C2×C3×C5×Q8—21no—
31#6817—21no—
32C3×C5×Q16—21no—
33C3×C5×Q16C2×C412yes—
34C2×C3×C5×C8C2311yescharacteristic
35Dic60C2×C411yescharacteristic
36D120C2×C411yescharacteristic
37#6706—21no—
38C5×#208—21no—
39C3×C4⋊Dic5—21no—
40C3×C4⋊Dic5—41no—
41C3×C4×Dic5—41no—
42C3×C4×Dic5D411yescharacteristic
43C2×C3×#168D411yescharacteristic
44#6651—41no—
45#6648—41no—
46C3⋊#672C2×C412yes—
47C5×C3⋊C16—21no—
48C3×#441—51no—
49#5179—51no—
50#4717—51no—
51#4565D511yescharacteristic, complemented
52#4488—51no—
53#4487—51no—
54#4466—51no—
55C2×C5×Q16C2×D311yescharacteristic
56Q8×Dic5—21no—
57#4053—61no—
58#4050—31no—
59C5×M32—31no—
60C5×#108—31no—
61#3967—21no—
62#3961—32no—
63#3960—32no—
64#3957—61no—
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
73#1220—41no—
74D60—21no—
75C4×D15—41no—
76Dic30—21no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—41no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C3×#168—21no—
82C5×C3⋊C8—41no—
83C2×C3×Q16C2×D511yescharacteristic
84C3×C4×Q8—101no—
85#904—51no—
86#901—101no—
87C3×#106—51no—
88C3×#103—101no—
89C3×#97—51no—
90#829—52no—
91#828—52no—
92#819C2×D511yescharacteristic
93#812—51no—
94#812C2×D511yescharacteristic
95#805—101no—
96C2×C5×Q8—21no—
97#709—61no—
98C5×Q16—21no—
99C5×Q16C4×D312yes—
100C5×M16—61no—
101C2×C5×C8C22×D311yescharacteristic
102C4⋊Dic5—21no—
103C4⋊Dic5—41no—
104C4×Dic5—41no—
105C4×Dic5#6711yescharacteristic
106C2×#168#6711yescharacteristic
107Dic20—31no—
108D40—31no—
109#677—61no—
110#676—121no—
111C8×D5—121no—
112C5×C16—61no—
113#672—32no—
114#510—151no—
115#444—151no—
116#441—51no—
117#365—151no—
118#362—31no—
119#360—151no—
120#347—151no—
121C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×D15—41no—
123C3×C4×C5—42no—
124C3×C4×C5C4×D411yescharacteristic
125C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
126Dic15—41no—
127C3×Dic5—41no—
128C3×Dic5—81no—
129C2×C3×Q8—21no—
130#235—101no—
131C3×Q16—21no—
132C3×Q16C4×D512yes—
133C2×C3×C8—51no—
134C2×C3×C8C22×D511yescharacteristic
135C3×C4⋊C4—101no—
136C3×C4⋊C4—201no—
137C3×C42—51no—
138C3×C42—201no—
139#208—21no—
140Dic12—51no—
141D24—51no—
142#204—101no—
143ΓL(1,𝔽25)—201no—
144D3×C8—201no—
145C3⋊C16—21no—
146C3⋊C16—52no—
147C5×Q8—22no—
148C5×Q8—41no—
149C2×C4×C5—41no—
150C2×C4×C5C2×#6711yescharacteristic
151C22⋊D5—121no—
152C2×Dic5—21no—
153C2×Dic5—41no—
154D20—61no—
155C4×D5—121no—
156Dic10—61no—
157C5×C8—121no—
158C5×C8C2×C4×D311yescharacteristic
159C5×C8#23511yescharacteristic
160#168—21no—
161#135—151no—
162C2×Q16D3×D511yescharacteristic
163#131—301no—
164C4×Q8—101no—
165Q32—152no—
166SD32—152no—
167M32—31no—
168M32—151no—
169#108—31no—
170#106—51no—
171#104—301no—
172#103—101no—
173#97—51no—
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176D15—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—201no—
184D12—101no—
185C4×D3—201no—
186Dic6—101no—
187C3×C8—101no—
188C3×C8C2×C4×D511yescharacteristic
189C3×C8#71111yescharacteristic
190C3⋊C8—41no—
191C22×C5#93211yescharacteristic
192C2×D5—121no—
193C4×C5—42no—
194C4×C5C4×#6711yescharacteristic
195C4×C5#94911yescharacteristic
196Dic5—41no—
197Dic5—81no—
198Dic5—121no—
199#41—301no—
200C2×Q8—21no—
201Q16—21no—
202Q16—151no—
203Q16#120012yes—
204SD16—301no—
205D8—151no—
206M16—61no—
207M16—601no—
208C2×C8—51no—
209C2×C8—601no—
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—101no—
212C4⋊C4—201no—
213C42—51no—
214C42—201no—
215C16—61no—
216C16—152no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3#406011yescharacteristic
219C2×D3—201no—
220C3×C4—42no—
221C3×C4—201no—
222C3×C4—401no—
223C3×C4#402711yescharacteristic
224C3×C4#405711yescharacteristic
225Dic3—201no—
226C2×C5—21no—
227C2×C5#501411yescharacteristic
228D5—241no—
229Q8—22no—
230Q8—41no—
231Q8—301no—
232D4—301no—
233D4—601no—
234C2×C4—41no—
235C2×C4—101no—
236C2×C4—201no—
237C2×C4—601no—
238C2×C4D5×#6711yescharacteristic
239C8—101no—
240C8—121no—
241C8#678211yescharacteristic
242C8C2×#120011yescharacteristic
243C2×C3—21no—
244C2×C3#6507411yescharacteristic
245D3—401no—
246C5#7091711yescharacteristic, complemented, Sylow
247C22—601no—
248C22#9149111yescharacteristic
249C4—42no—
250C4—201no—
251C4—401no—
252C4—601no—
253C4#9147811yescharacteristic
254C4#9155211yescharacteristic
255C3#1060005711yescharacteristic, complemented, Sylow
256C2—21no—
257C2—1201no—
258C2#1174897911yescharacteristic
subgroupG/H
centerC2#11748979
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5#442
prime radical#91793C22
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. C5×#4565C2semidirect
5. #11745935C2semidirect
7. #11745876C2semidirect
13. #91113C4semidirect
14. #91112C4semidirect
23. #65473D3semidirect
51. #4565D5semidirect
217. C3×C5#2180semidirect
246. C5#70917semidirect
255. C3#10600057semidirect

Maximal subgroups

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

subgroupindex
#117512802
C3×#654732
#117480652
C5×#45652
#117459352
#117459132
#117458762
#106000573
#709175