Finite Group Databasebeta

← #14318545

Subgroups — #14318545

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×#65154C211yesmaximal, characteristic
2#11748057C211yesmaximal, characteristic, complemented
3#11746308C211yesmaximal, characteristic, complemented
4C5×#4487C211yesmaximal, characteristic, complemented
5#11745916C211yesmaximal, characteristic, complemented
6#11745915C211yesmaximal, characteristic, complemented
7#11745882C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9C2×C3×D40C2211yescharacteristic
10C2×C3×#676C2211yescharacteristic
11C3×#4041—21no—
12D5×#208—21no—
13C3×C5×#106C2211yescharacteristic
14#91103C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#819C2211yescharacteristic
17C5×#812C2211yescharacteristic
18C3×#3941—21no—
19#90991—21no—
20#71088—51nomaximal, Hall
21#65182—31no—
22#65154D311yescharacteristic
23C5×#365—31no—
24#64736—31no—
25#64734—31no—
26#64715—31no—
27#64707—31no—
28C2×C3×D20—21no—
29C2×C3×D20—41no—
30C2×C3×C4×D5D411yescharacteristic
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33#6710—21no—
34C5×#208—21no—
35C3×#685—41no—
36C2×C3×#168D411yescharacteristic
37C3×D40—21no—
38C3×D40—21no—
39C3×#676—21no—
40C3×#676—21no—
41#6649—41no—
42D5×C3⋊C8—41no—
43C3⋊#672—21no—
44C5×C3⋊C16—21no—
45C3×#469—51no—
46#5125—51no—
47#4563—51no—
48#4563—51no—
49#4553—51no—
50#4487—51no—
51#4487D511yescharacteristic, complemented
52D5×M16—61no—
53C2×D40C2×D311yescharacteristic
54C2×#676C2×D311yescharacteristic
55#4041—21no—
56C5×M32—31no—
57C5×#108—31no—
58C5×#106C2×D311yescharacteristic
59#3954—61no—
60#3951—31no—
61#3944—31no—
62#3941—21no—
63#2238—151noSylow
64C22×C3×D5—41no—
65C22×C3×D5SD1611yescharacteristic
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×Dic5SD1611yescharacteristic
69C3×D20—41no—
70C3×D20—41no—
71C3×D20—82no—
72C3×C4×D5—21no—
73C3×C4×D5—21no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—41no—
77C3×#168—21no—
78C5×C3⋊C8—41no—
79C2×C3×D8—51no—
80C2×C3×M16—51no—
81C3×#121—101no—
82C2×#208—101no—
83C3×#106C2×D511yescharacteristic
84C3×#102—101no—
85#819—51no—
86#819—101no—
87#819C2×D511yescharacteristic
88#812—51no—
89#812C2×D511yescharacteristic
90C2×D20—21no—
91C2×D20—41no—
92C2×C4×D5#6711yescharacteristic
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—21no—
96#685—41no—
97#681—61no—
98C2×#168#6711yescharacteristic
99D40—21no—
100D40—21no—
101#676—21no—
102#676—21no—
103#676—121no—
104C8×D5—121no—
105C5×C16—61no—
106#672—61no—
107#469—51no—
108#430—151no—
109#365—31no—
110#365—151no—
111#361—151no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×C3×D5—21no—
116C2×C3×D5—41no—
117C2×C3×D5—81no—
118C2×C3×D5—81no—
119C2×C3×D5—81no—
120C3×C4×C5—81no—
121C3×C4×C5#12311yescharacteristic
122C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
123C3×Dic5—21no—
124C2×C3×D4—101no—
125C2×C3×D4—201no—
126C22×C3×C4—51no—
127C3×D8—101no—
128C3×D8—101no—
129C3×M16—101no—
130C3×M16—101no—
131C2×C3×C8—51no—
132C2×C3×C8C22×D511yescharacteristic
133C3×C4⋊C4—21no—
134C3×C22⋊C4—201no—
135#208—21no—
136#208—101no—
137#208—201no—
138C2×C3⋊C8—201no—
139C3⋊C16—21no—
140C3⋊C16—101no—
141C22×D5—41no—
142C22×D5#21411yescharacteristic
143C2×C4×C5—41no—
144C2×C4×C5C2×#6711yescharacteristic
145C2×Dic5#21411yescharacteristic
146D20—41no—
147D20—41no—
148D20—82no—
149C4×D5—21no—
150C4×D5—21no—
151C5×C8—121no—
152C5×C8#23711yescharacteristic
153C5×C8#23711yescharacteristic
154#168—21no—
155#168—121no—
156C2×D8—51no—
157C2×M16—51no—
158C2×M16—301no—
159#121—101no—
160M32—31no—
161M32—151no—
162#108—31no—
163#108—151no—
164#108—301no—
165#106D3×D511yescharacteristic
166#102—101no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169C3×D5—41no—
170C3×D5—161no—
171C23×C3—51no—
172C23×C3—201no—
173C3×D4—201no—
174C3×D4—201no—
175C3×D4—402no—
176C2×C3×C4—41no—
177C2×C3×C4—51no—
178C2×C3×C4—101no—
179C2×C3×C4—101no—
180C2×C3×C4D4×D511yescharacteristic
181C3×C8—101no—
182C3×C8#70911yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—201no—
186C22×C5C2×#21411yescharacteristic
187C2×D5—21no—
188C2×D5—41no—
189C2×D5—81no—
190C2×D5—81no—
191C2×D5—81no—
192C4×C5—81no—
193C4×C5#93511yescharacteristic
194C4×C5#94911yescharacteristic
195Dic5—21no—
196C2×D4—101no—
197C2×D4—201no—
198C22×C4—51no—
199D8—101no—
200D8—101no—
201M16—61no—
202M16—101no—
203M16—101no—
204M16—301no—
205M16—601no—
206C2×C8—51no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—21no—
210C22⋊C4—201no—
211C16—61no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—101no—
215C22×C3—201no—
216C22×C3—401no—
217C22×C3—401no—
218C22×C3—401no—
219C22×C3D5×SD1611yescharacteristic
220C3×C4—81no—
221C3×C4—101no—
222C3×C4#404011yescharacteristic
223C3×C4#406011yescharacteristic
224C2×C5—21no—
225C2×C5#503411yescharacteristic
226D5—41no—
227D5—161no—
228C23—51no—
229C23—201no—
230D4—201no—
231D4—201no—
232D4—402no—
233C2×C4—41no—
234C2×C4—51no—
235C2×C4—101no—
236C2×C4—101no—
237C2×C4D5×#6711yescharacteristic
238C8—101no—
239C8—121no—
240C8—601no—
241C8#676511yescharacteristic
242C8#676611yescharacteristic
243C2×C3—21no—
244C2×C3—201no—
245C2×C3—801no—
246C2×C3#6515211yescharacteristic
247C5#7108811yescharacteristic, complemented, Sylow
248C22—101no—
249C22—201no—
250C22—401no—
251C22—401no—
252C22—401no—
253C22D5×#21411yescharacteristic
254C4—81no—
255C4—101no—
256C4#9140711yescharacteristic
257C4#9150211yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—201no—
261C2—801no—
262C2#1174719511yescharacteristic
subgroupG/H
centerC2#11747195
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radicalC3×#65154C2
hypercenter#106D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11748057C2semidirect
3. #11746308C2semidirect
4. C5×#4487C2semidirect
5. #11745916C2semidirect
6. #11745915C2semidirect
7. #11745882C2semidirect
51. #4487D5semidirect
213. C3×C5#2238semidirect
247. C5#71088semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
C3×#651542
#117480572
#117463082
C5×#44872
#117459162
#117459152
#117458822
#106001063
#710885