Finite Group Databasebeta

← #14315794

Subgroups — #14315794

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
2C5×#5184C211yesmaximal, characteristic, complemented
3#11748069C211yesmaximal, characteristic
4C3×#64785C211yesmaximal, characteristic, complemented
5#11745936C211yesmaximal, characteristic, complemented
6#11745914C211yesmaximal, characteristic
7#11745877C211yesmaximal, characteristic, complemented
8#10601710—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91793C2211yescharacteristic
11C5×Q8×Dic3—21no—
12#91291—21no—
13#91113C412yescomplemented
14#91112C412yescomplemented
15#91096C2211yescharacteristic
16C5×#835—21no—
17C5×#817C2211yescharacteristic
18C5×#815C2211yescharacteristic
19C3×#3951C2211yescharacteristic
20C3×#3944C2211yescharacteristic
21#90980—21no—
22#69264—51nomaximal, Hall
23C5×#441—31no—
24#65468—31no—
25#65006—31no—
26#64785D311yescharacteristic, complemented
27#64708—31no—
28#64707—31no—
29#64686—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×C4⋊Dic3—21no—
39C5×C4⋊Dic3—41no—
40C4×C5×Dic3—41no—
41C4×C5×Dic3D411yescharacteristic
42C2×C5×C3⋊C8D411yescharacteristic
43C3×#681—21no—
44#6651—41no—
45#6648—41no—
46C3⋊#672C2×C412yes—
47C3×#672—21no—
48#5184D511yescharacteristic, complemented
49#5179—51no—
50#4894—51no—
51C3×#362—51no—
52#4518—51no—
53#4512—51no—
54#4494—51no—
55C2×C5×Q16C2×D311yescharacteristic
56C4×C5×Q8—61no—
57#4050—31no—
58#4047—61no—
59C5×#106—31no—
60C5×#103—61no—
61C5×#97—31no—
62#3961—32no—
63#3960—32no—
64#3951C2×D311yescharacteristic
65#3944—31no—
66#3944C2×D311yescharacteristic
67#3937—61no—
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×C5×Dic3—21no—
78C2×C5×Dic3—41no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C3×#168—41no—
82C5×C3⋊C8—21no—
83C2×C3×Q16C2×D511yescharacteristic
84Q8×Dic3—21no—
85#907—101no—
86#904—51no—
87C3×M32—51no—
88C3×#108—51no—
89#835—21no—
90#829—52no—
91#828—52no—
92#825—101no—
93#817C2×D511yescharacteristic
94#815C2×D511yescharacteristic
95#812—51no—
96C2×C5×Q8—21no—
97#709—61no—
98C5×Q16—21no—
99C5×Q16C4×D312yes—
100C2×C5×C8—31no—
101C2×C5×C8C22×D311yescharacteristic
102C5×C4⋊C4—61no—
103C5×C4⋊C4—121no—
104C42×C5—31no—
105C42×C5—121no—
106#681—21no—
107Dic20—31no—
108D40—31no—
109#677—61no—
110#676—121no—
111C8×D5—121no—
112#672—21no—
113#672—32no—
114#510—151no—
115#444—151no—
116#441—31no—
117#365—151no—
118#362—51no—
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—
127C5×Dic3—41no—
128C5×Dic3—81no—
129C2×C3×Q8—21no—
130#235—101no—
131C3×Q16—21no—
132C3×Q16C4×D512yes—
133C3×M16—101no—
134C2×C3×C8C22×D511yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—41no—
137C4×Dic3—41no—
138C4×Dic3C22⋊D511yescharacteristic
139C2×C3⋊C8C22⋊D511yescharacteristic
140Dic12—51no—
141D24—51no—
142#204—101no—
143ΓL(1,𝔽25)—201no—
144D3×C8—201no—
145C3×C16—101no—
146C3⋊C16—52no—
147C5×Q8—22no—
148C5×Q8—41no—
149C2×C4×C5—41no—
150C2×C4×C5—61no—
151C2×C4×C5—121no—
152C2×C4×C5D3×D411yescharacteristic
153C22⋊D5—121no—
154D20—61no—
155C4×D5—121no—
156Dic10—61no—
157C5×C8—61no—
158C5×C8C2×C4×D311yescharacteristic
159C5×C8#23711yescharacteristic
160#168—41no—
161#135—151no—
162C2×Q16D3×D511yescharacteristic
163#131—301no—
164C4×Q8—61no—
165Q32—152no—
166SD32—152no—
167M32—51no—
168M32—151no—
169#108—51no—
170#106—31no—
171#104—301no—
172#103—61no—
173#97—31no—
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176D15—81no—
177C3×Q8—22no—
178C3×Q8—41no—
179C2×C3×C4—41no—
180C2×C3×C4C2×C22⋊D511yescharacteristic
181#67—201no—
182C2×Dic3—21no—
183C2×Dic3—41no—
184D12—101no—
185C4×D3—201no—
186Dic6—101no—
187C3×C8—201no—
188C3×C8C2×C4×D511yescharacteristic
189C3×C8#70911yescharacteristic
190C3⋊C8—21no—
191C22×C5#91411yescharacteristic
192C2×D5—121no—
193C4×C5—42no—
194C4×C5—121no—
195C4×C5—241no—
196C4×C5#67⋊C411yescharacteristic
197C4×C5#91111yescharacteristic
198Dic5—121no—
199#41—301no—
200C2×Q8—21no—
201Q16—21no—
202Q16—151no—
203Q16#120012yes—
204SD16—301no—
205D8—151no—
206M16—101no—
207M16—601no—
208C2×C8—31no—
209C2×C8—601no—
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—61no—
212C4⋊C4—121no—
213C42—31no—
214C42—121no—
215C16—101no—
216C16—152no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3#407811yescharacteristic
219C2×D3—201no—
220C3×C4—42no—
221C3×C4C4×C22⋊D511yescharacteristic
222C3×C4#409511yescharacteristic
223Dic3—41no—
224Dic3—81no—
225Dic3—201no—
226C2×C5—21no—
227C2×C5#478511yescharacteristic
228D5—241no—
229Q8—22no—
230Q8—41no—
231Q8—301no—
232D4—301no—
233D4—601no—
234C2×C4—41no—
235C2×C4—61no—
236C2×C4—121no—
237C2×C4—601no—
238C2×C4D3×C22⋊D511yescharacteristic
239C8—61no—
240C8—201no—
241C8#677911yescharacteristic
242C8C2×#120011yescharacteristic
243C2×C3—21no—
244C2×C3#6530311yescharacteristic
245D3—401no—
246C5#6926411yescharacteristic, complemented, Sylow
247C22—601no—
248C22#9149611yescharacteristic
249C4—42no—
250C4—121no—
251C4—241no—
252C4—601no—
253C4#9148011yescharacteristic
254C4#9155611yescharacteristic
255C3#1060171011yescharacteristic, complemented, Sylow
256C2—21no—
257C2—1201no—
258C2#1174898911yescharacteristic
subgroupG/H
centerC2#11748989
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. C5×#5184C2semidirect
4. C3×#64785C2semidirect
5. #11745936C2semidirect
7. #11745877C2semidirect
13. #91113C4semidirect
14. #91112C4semidirect
26. #64785D3semidirect
48. #5184D5semidirect
217. C3×C5#2180semidirect
246. C5#69264semidirect
255. C3#10601710semidirect

Maximal subgroups

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

subgroupindex
#117512802
C5×#51842
#117480692
C3×#647852
#117459362
#117459142
#117458772
#106017103
#692645