Finite Group Databasebeta

← #14318543

Subgroups — #14318543

Order 1920.

268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#65182C211yesmaximal, characteristic, complemented
2#11747904C211yesmaximal, characteristic
3#11746316C211yesmaximal, characteristic, complemented
4C5×#4494C211yesmaximal, characteristic, complemented
5#11745936C211yesmaximal, characteristic, complemented
6#11745919C211yesmaximal, characteristic, complemented
7#11745882C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C3×D5×M16—21no—
11C2×C3×#676C2211yescharacteristic
12#91450—21no—
13C3×C5×#108C2211yescharacteristic
14#91096C2211yescharacteristic
15C5×#817C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3954—21no—
18C3×#3951C2211yescharacteristic
19#90969—21no—
20#70723—51nomaximal, Hall
21#65182D311yescharacteristic, complemented
22#65154—31no—
23C5×#365—31no—
24#64736—31no—
25#64734—31no—
26#64715—31no—
27#64707—31no—
28C2×D60—21no—
29C2×C3×C4×D5D411yescharacteristic
30C2×#1202—41no—
31C3×C5×M16—21no—
32C2×C3×C5×C8C2311yescharacteristic
33D120—21no—
34D120—21no—
35C5×C4⋊Dic3—21no—
36C3×#681—21no—
37C2×C3×#168D411yescharacteristic
38C3×#676—21no—
39C3×#676—21no—
40C3×#676—41no—
41C3×C8×D5—41no—
42#6667—41no—
43C3⋊#672—21no—
44C5×C3⋊C16—21no—
45C3×#430—51no—
46#5135—51no—
47#4553—51no—
48#4495—51no—
49#4495—51no—
50#4494—51no—
51#4494D511yescharacteristic, complemented
52D5×M16—21no—
53C2×D40—31no—
54C2×#676C2×D311yescharacteristic
55#4041—61no—
56C5×M32—31no—
57C5×#108C2×D311yescharacteristic
58C5×#106—31no—
59#3954—21no—
60#3951C2×D311yescharacteristic
61#3944—31no—
62#3941—61no—
63#2238—151noSylow
64C22×D15—41no—
65C22×C3×D5SD1611yescharacteristic
66C2×C3×C4×C5C2×D411yescharacteristic
67D60—41no—
68D60—41no—
69C2×C5×Dic3—41no—
70C2×C3×Dic5SD1611yescharacteristic
71C3×C4×D5—21no—
72C3×C4×D5—21no—
73#1202—82no—
74C3×C5×C8—41no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C3×#168—21no—
78C3×#168—41no—
79C2×C3×M16—51no—
80C2×C3×M16—101no—
81#930—101no—
82C2×D24—51no—
83C3×#108—51no—
84C3×#108—101no—
85C3×#108C2×D511yescharacteristic
86#821—101no—
87#817C2×D511yescharacteristic
88#812—51no—
89#812C2×D511yescharacteristic
90C2×D20—61no—
91C2×D20—121no—
92C2×C4×D5#6711yescharacteristic
93C5×M16—21no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—61no—
96#685—121no—
97#681—21no—
98C2×#168#6711yescharacteristic
99D40—61no—
100D40—61no—
101#676—21no—
102#676—21no—
103#676—41no—
104C8×D5—41no—
105C5×C16—61no—
106#672—61no—
107#469—151no—
108#430—51no—
109#365—31no—
110#365—151no—
111#361—151no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—81no—
116C2×D15—81no—
117C2×D15—81no—
118C2×C3×D5—21no—
119C2×C3×D5—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122C3×Dic5—21no—
123C5×Dic3—81no—
124C22×C3×C4—51no—
125C2×#67—201no—
126C2×D12—101no—
127C3×M16—21no—
128C3×M16—101no—
129C3×M16—101no—
130C3×M16—101no—
131C3×M16—201no—
132C2×C3×C8—51no—
133C2×C3×C8—201no—
134C2×C3×C8C22×D511yescharacteristic
135(C2×D3)⋊C4—201no—
136C4⋊Dic3—21no—
137D24—101no—
138D24—101no—
139C3⋊C16—21no—
140C3⋊C16—101no—
141C22×D5—121no—
142C22×D5#21511yescharacteristic
143C2×C4×C5—121no—
144C2×C4×C5C2×#6711yescharacteristic
145C2×Dic5#21511yescharacteristic
146D20—121no—
147D20—121no—
148D20—242no—
149C4×D5—21no—
150C4×D5—21no—
151C5×C8—41no—
152C5×C8#23511yescharacteristic
153C5×C8#23511yescharacteristic
154#168—21no—
155#168—41no—
156C2×D8—151no—
157C2×M16—51no—
158C2×M16—101no—
159#121—301no—
160M32—31no—
161M32—151no—
162#108—51no—
163#108—101no—
164#108D3×D511yescharacteristic
165#106—31no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—161no—
170C3×D5—41no—
171C23×C3—51no—
172C22×D3—201no—
173C2×C3×C4—51no—
174C2×C3×C4—101no—
175C2×C3×C4—101no—
176C2×C3×C4D4×D511yescharacteristic
177#67—402no—
178C2×Dic3—41no—
179D12—201no—
180D12—201no—
181C3×C8—41no—
182C3×C8—101no—
183C3×C8—201no—
184C3×C8#70911yescharacteristic
185C3×C8#71311yescharacteristic
186C22×C5C2×#21511yescharacteristic
187C2×D5—21no—
188C2×D5—41no—
189C2×D5—241no—
190C2×D5—241no—
191C2×D5—241no—
192C4×C5—241no—
193C4×C5#92911yescharacteristic
194C4×C5#93211yescharacteristic
195Dic5—21no—
196C2×D4—301no—
197C2×D4—601no—
198C22×C4—51no—
199D8—301no—
200D8—301no—
201M16—21no—
202M16—101no—
203M16—101no—
204M16—101no—
205M16—201no—
206C2×C8—51no—
207C2×C8—201no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—61no—
210C22⋊C4—601no—
211C16—61no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—101no—
215C22×C3—201no—
216C22×C3D5×SD1611yescharacteristic
217C2×D3—401no—
218C2×D3—401no—
219C2×D3—401no—
220C3×C4—101no—
221C3×C4#404011yescharacteristic
222C3×C4#406011yescharacteristic
223Dic3—81no—
224C2×C5—21no—
225C2×C5#496811yescharacteristic
226D5—41no—
227D5—481no—
228C23—51no—
229C23—601no—
230D4—601no—
231D4—601no—
232D4—1202no—
233C2×C4—51no—
234C2×C4—101no—
235C2×C4—101no—
236C2×C4—121no—
237C2×C4D5×#6711yescharacteristic
238C8—41no—
239C8—101no—
240C8—201no—
241C8#677111yescharacteristic
242C8#677311yescharacteristic
243C2×C3—21no—
244C2×C3—201no—
245C2×C3#6515211yescharacteristic
246D3—801no—
247C5#7072311yescharacteristic, complemented, Sylow
248C22—101no—
249C22—201no—
250C22—1201no—
251C22—1201no—
252C22—1201no—
253C22D5×#21511yescharacteristic
254C4—101no—
255C4—241no—
256C4#9134811yescharacteristic
257C4#9149111yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—201no—
261C2—2401no—
262C2#1174716511yescharacteristic
subgroupG/H
centerC2#11747165
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5#481
prime radical#11747904C2
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. C3×#65182C2semidirect
3. #11746316C2semidirect
4. C5×#4494C2semidirect
5. #11745936C2semidirect
6. #11745919C2semidirect
7. #11745882C2semidirect
21. #65182D3semidirect
51. #4494D5semidirect
213. C3×C5#2238semidirect
247. C5#70723semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
C3×#651822
#117479042
#117463162
C5×#44942
#117459362
#117459192
#117458822
#106001063
#707235