Finite Group Databasebeta

← #14318542

Subgroups — #14318542

Order 1920.

268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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#11750994C211yesmaximal, characteristic, complemented
2#11747936C211yesmaximal, characteristic
3C5×#4494C211yesmaximal, characteristic, complemented
4C3×#64715C211yesmaximal, characteristic, complemented
5#11745933C211yesmaximal, characteristic, complemented
6#11745916C211yesmaximal, characteristic, complemented
7#11745884C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9M16×D15—21no—
10C2×#6705C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12#91465—21no—
13C3×C5×#108C2211yescharacteristic
14#91106—21no—
15#91103C2211yescharacteristic
16C5×#817C2211yescharacteristic
17C5×#812C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90964—21no—
20#69257—51nomaximal, Hall
21#65182—31no—
22#65154—31no—
23C5×#365—31no—
24#64736—31no—
25#64734—31no—
26#64715D311yescharacteristic, complemented
27#64707—31no—
28C2×C4×D15D411yescharacteristic
29C2×C3×D20—21no—
30C2×#1202—41no—
31C3×C5×M16—21no—
32C2×C3×C5×C8C2311yescharacteristic
33#6710—21no—
34C2×C3⋊#168D411yescharacteristic
35#6705—21no—
36#6705—21no—
37#6705—41no—
38C8×D15—41no—
39C5×C4⋊Dic3—21no—
40C3×D40—21no—
41C3×D40—21no—
42#6665—41no—
43C3×#672—21no—
44C5×C3⋊C16—21no—
45#5159—51no—
46#4893—51no—
47C3×#361—51no—
48#4563—51no—
49#4514—51no—
50#4513—51no—
51#4494D511yescharacteristic, complemented
52D5×M16—61no—
53C2×D40C2×D311yescharacteristic
54C2×#676—31no—
55#4041—61no—
56C5×M32—31no—
57C5×#108C2×D311yescharacteristic
58C5×#106—31no—
59#3954—61no—
60#3951—31no—
61#3944C2×D311yescharacteristic
62#3941—61no—
63#2238—151noSylow
64C22×D15SD1611yescharacteristic
65C22×C3×D5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15SD1611yescharacteristic
68C4×D15—21no—
69C4×D15—21no—
70C2×C5×Dic3—41no—
71C3×D20—41no—
72C3×D20—41no—
73#1202—82no—
74C3×C5×C8—41no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C3⋊#168—21no—
78C3⋊#168—41no—
79C2×C3×D8—51no—
80#938—101no—
81D3×M16—101no—
82C2×ΓL(1,𝔽25)—51no—
83C3×M32—51no—
84C3×#108C2×D511yescharacteristic
85#832—101no—
86#822—101no—
87#819—51no—
88#817C2×D511yescharacteristic
89#812C2×D511yescharacteristic
90C2×D20—21no—
91C2×D20—121no—
92C2×C4×D5—31no—
93C5×M16—21no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—61no—
96#685—121no—
97#681—61no—
98C2×#168—31no—
99D40—21no—
100D40—21no—
101#676—61no—
102#676—61no—
103#676—121no—
104C8×D5—121no—
105C5×C16—61no—
106#672—21no—
107#469—151no—
108#430—151no—
109#365—31no—
110#365—151no—
111#361—51no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—21no—
116C2×D15—41no—
117C2×C3×D5—81no—
118C2×C3×D5—81no—
119C2×C3×D5—81no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122Dic15—21no—
123C5×Dic3—81no—
124C2×C3×D4—101no—
125C2×#67—201no—
126C2×C4×D3—51no—
127C3×D8—101no—
128C3×D8—101no—
129C3×M16—21no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—21no—
133#208—101no—
134C2×C3⋊C8—51no—
135ΓL(1,𝔽25)—101no—
136ΓL(1,𝔽25)—101no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—101no—
140C3⋊C16—21no—
141C22×D5—31no—
142C22×D5—41no—
143C2×C4×C5—121no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146D20—41no—
147D20—41no—
148D20—242no—
149C4×D5—61no—
150C4×D5—61no—
151C5×C8—41no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—61no—
155#168—121no—
156C2×D8—51no—
157C2×M16—151no—
158C2×M16—301no—
159#121—301no—
160M32—31no—
161M32—51no—
162#108—151no—
163#108—301no—
164#108D3×D511yescharacteristic
165#106—31no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—41no—
170C3×D5—161no—
171C23×C3—201no—
172C22×D3—51no—
173C3×D4—201no—
174C3×D4—201no—
175C2×C3×C4D4×D511yescharacteristic
176#67—402no—
177C2×Dic3—41no—
178C2×Dic3—51no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8—41no—
182C3×C8#70911yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—101no—
185C3⋊C8—201no—
186C22×C5D3×SD1611yescharacteristic
187C2×D5—61no—
188C2×D5—81no—
189C2×D5—81no—
190C2×D5—81no—
191C2×D5—121no—
192C4×C5—241no—
193C4×C5#88311yescharacteristic
194C4×C5#91111yescharacteristic
195Dic5—61no—
196C2×D4—101no—
197C2×D4—601no—
198C22×C4—151no—
199D8—101no—
200D8—101no—
201M16—21no—
202M16—301no—
203M16—301no—
204M16—301no—
205M16—601no—
206C2×C8—151no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—61no—
210C22⋊C4—601no—
211C16—61no—
212C16—101no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—401no—
215C22×C3—401no—
216C22×C3—401no—
217C22×C3D5×SD1611yescharacteristic
218C2×D3—101no—
219C2×D3—201no—
220C3×C4#404011yescharacteristic
221C3×C4#406011yescharacteristic
222Dic3—81no—
223Dic3—101no—
224C2×C5—21no—
225C2×C5#477711yescharacteristic
226D5—121no—
227D5—161no—
228C23—151no—
229C23—201no—
230D4—201no—
231D4—201no—
232D4—1202no—
233C2×C4—121no—
234C2×C4—151no—
235C2×C4—301no—
236C2×C4—301no—
237C2×C4#679011yescharacteristic
238C8—41no—
239C8—301no—
240C8—601no—
241C8#676611yescharacteristic
242C8#677111yescharacteristic
243C2×C3—21no—
244C2×C3—801no—
245C2×C3#6515211yescharacteristic
246D3—201no—
247C5#6925711yescharacteristic, complemented, Sylow
248C22—301no—
249C22—401no—
250C22—401no—
251C22—401no—
252C22—601no—
253C22#9150511yescharacteristic
254C4—241no—
255C4—301no—
256C4#9135411yescharacteristic
257C4#9149811yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—601no—
261C2—801no—
262C2#1174733211yescharacteristic
subgroupG/H
centerC2#11747332
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5#481
prime radical#11747936C2
hypercenter#108D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #11750994C2semidirect
3. C5×#4494C2semidirect
4. C3×#64715C2semidirect
5. #11745933C2semidirect
6. #11745916C2semidirect
7. #11745884C2semidirect
26. #64715D3semidirect
51. #4494D5semidirect
213. C3×C5#2238semidirect
247. C5#69257semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
#117509942
#117479362
C5×#44942
C3×#647152
#117459332
#117459162
#117458842
#106001063
#692575