Finite Group Databasebeta

← #14318530

Subgroups — #14318530

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×#65448C211yesmaximal, characteristic
2#11748057C211yesmaximal, characteristic, complemented
3#11746384C211yesmaximal, characteristic, complemented
4C5×#4563C211yesmaximal, characteristic, complemented
5#11745937C211yesmaximal, characteristic, complemented
6#11745935C211yesmaximal, characteristic, complemented
7#11745882C211yesmaximal, characteristic, complemented
8#10600050—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10C3×#4084—21no—
11C2×C3×#676C2211yescharacteristic
12D5×#208—21no—
13#91103C2211yescharacteristic
14#91096C2211yescharacteristic
15C5×#819C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3964—21no—
18C3×#3949C2211yescharacteristic
19#90991—21no—
20#71088—51nomaximal, Hall
21#65448D311yescharacteristic
22#65182—31no—
23C5×#361—31no—
24#64783—31no—
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C3×C5×D4—21no—
29C2×C3×C22⋊D5—41no—
30C2×C3×C4×D5D411yescharacteristic
31C3×C5×D8—21no—
32C3×C5×D8—21no—
33C2×C3×C5×C8C2311yescharacteristic
34#6710—21no—
35C5×#208—21no—
36C3×C22⋊Dic5—41no—
37C3×C4⋊Dic5—21no—
38C2×C3×#168D411yescharacteristic
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#4563D511yescharacteristic, complemented
49#4553—51no—
50#4487—51no—
51#4487—51no—
52C2×C5×D8C2×D311yescharacteristic
53#4084—21no—
54D5×M16—61no—
55C2×#676C2×D311yescharacteristic
56C5×M32—31no—
57C5×#108—31no—
58#3964—21no—
59#3954—61no—
60#3951—31no—
61#3949C2×D311yescharacteristic
62#3944—31no—
63#2238—151noSylow
64C23×C3×C5—41no—
65C22×C3×D5SD1611yescharacteristic
66C3×C5×D4—41no—
67C3×C5×D4—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69C3×C22⋊D5—82no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5SD1611yescharacteristic
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×D8C2×D511yescharacteristic
80C2×C3×M16—51no—
81C3×#121—101no—
82C2×#208—101no—
83C3×#106—51no—
84C3×#102—101no—
85#819—51no—
86#819—101no—
87#819C2×D511yescharacteristic
88#812—51no—
89#812C2×D511yescharacteristic
90C2×C5×D4—21no—
91C2×C22⋊D5—41no—
92C2×C4×D5#6711yescharacteristic
93C5×D8—21no—
94C5×D8—21no—
95C5×M16—61no—
96C2×C5×C8C22×D311yescharacteristic
97C22⋊Dic5—41no—
98C4⋊Dic5—21no—
99#681—61no—
100C2×#168#6711yescharacteristic
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—151no—
110#365—151no—
111#361—31no—
112#361—151no—
113#349—151no—
114C22×C3×C5—81no—
115C22×C3×C5—81no—
116C22×C3×C5—81no—
117C22×C3×C5C2×SD1611yescharacteristic
118C2×C3×D5—21no—
119C2×C3×D5—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122C3×Dic5—21no—
123C3×Dic5—81no—
124C2×C3×D4—21no—
125C2×C3×D4—201no—
126C22×C3×C4—51no—
127C3×D8—21no—
128C3×D8—21no—
129C3×M16—101no—
130C3×M16—101no—
131C2×C3×C8—51no—
132C2×C3×C8C22×D511yescharacteristic
133C3×C4⋊C4—101no—
134C3×C22⋊C4—201no—
135#208—21no—
136#208—101no—
137#208—201no—
138C2×C3⋊C8—201no—
139C3⋊C16—21no—
140C3⋊C16—101no—
141C23×C5—41no—
142C22×D5#21411yescharacteristic
143C5×D4—41no—
144C5×D4—41no—
145C2×C4×C5C2×#6711yescharacteristic
146C22⋊D5—82no—
147C2×Dic5—41no—
148C2×Dic5#21411yescharacteristic
149C4×D5—21no—
150C4×D5—21no—
151C5×C8—121no—
152C5×C8#23711yescharacteristic
153C5×C8#23711yescharacteristic
154#168—21no—
155#168—121no—
156C2×D8D3×D511yescharacteristic
157C2×M16—51no—
158C2×M16—301no—
159#121—101no—
160M32—31no—
161M32—151no—
162#108—31no—
163#108—151no—
164#108—301no—
165#106—51no—
166#102—101no—
167C2×C3×C5—21no—
168C2×C3×C5—161no—
169C2×C3×C5#48111yescharacteristic
170C3×D5—41no—
171C23×C3—41no—
172C23×C3—51no—
173C3×D4—41no—
174C3×D4—41no—
175C3×D4—402no—
176C2×C3×C4—51no—
177C2×C3×C4—101no—
178C2×C3×C4—101no—
179C2×C3×C4—201no—
180C2×C3×C4D4×D511yescharacteristic
181C3×C8—101no—
182C3×C8#70911yescharacteristic
183C3×C8#71111yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—201no—
186C22×C5—81no—
187C22×C5—81no—
188C22×C5—81no—
189C22×C5C2×#21411yescharacteristic
190C2×D5—21no—
191C2×D5—41no—
192C4×C5#93511yescharacteristic
193C4×C5#94911yescharacteristic
194Dic5—21no—
195Dic5—81no—
196C2×D4—21no—
197C2×D4—201no—
198C22×C4—51no—
199D8—21no—
200D8—21no—
201M16—61no—
202M16—101no—
203M16—101no—
204M16—301no—
205M16—601no—
206C2×C8—51no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—101no—
210C22⋊C4—201no—
211C16—61no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—81no—
215C22×C3—81no—
216C22×C3—81no—
217C22×C3—101no—
218C22×C3—201no—
219C22×C3D5×SD1611yescharacteristic
220C3×C4—101no—
221C3×C4—401no—
222C3×C4#402911yescharacteristic
223C3×C4#405711yescharacteristic
224C2×C5—21no—
225C2×C5—161no—
226C2×C5#503411yescharacteristic
227D5—41no—
228C23—41no—
229C23—51no—
230D4—41no—
231D4—41no—
232D4—402no—
233C2×C4—51no—
234C2×C4—101no—
235C2×C4—101no—
236C2×C4—201no—
237C2×C4D5×#6711yescharacteristic
238C8—101no—
239C8—121no—
240C8—601no—
241C8#677911yescharacteristic
242C8#678011yescharacteristic
243C2×C3—21no—
244C2×C3—161no—
245C2×C3—201no—
246C2×C3#6506611yescharacteristic
247C5#7108811yescharacteristic, complemented, Sylow
248C22—81no—
249C22—81no—
250C22—81no—
251C22—101no—
252C22—201no—
253C22D5×#21411yescharacteristic
254C4—101no—
255C4—401no—
256C4#9147811yescharacteristic
257C4#9154811yescharacteristic
258C3#1060005011yescharacteristic, complemented, Sylow
259C2—21no—
260C2—161no—
261C2—201no—
262C2#1174895211yescharacteristic
subgroupG/H
centerC2#11748952
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5#481
prime radicalC3×#65448C2
hypercenterC2×D8D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11748057C2semidirect
3. #11746384C2semidirect
4. C5×#4563C2semidirect
5. #11745937C2semidirect
6. #11745935C2semidirect
7. #11745882C2semidirect
48. #4563D5semidirect
213. C3×C5#2238semidirect
247. C5#71088semidirect
258. C3#10600050semidirect

Maximal subgroups

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

subgroupindex
C3×#654482
#117480572
#117463842
C5×#45632
#117459372
#117459352
#117458822
#106000503
#710885