Finite Group Databasebeta

← #14318577

Subgroups — #14318577

Order 1920.

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

normal subgroups only

This group has 248 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
2#11747945C211yesmaximal, characteristic
3#11746315C211yesmaximal, characteristic, complemented
4C5×#4496C211yesmaximal, characteristic, complemented
5#11745938C211yesmaximal, characteristic, complemented
6#11745923C211yesmaximal, characteristic, complemented
7#11745882C211yesmaximal, characteristic
8#10600060—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C3×D5×M16—21no—
11C2×C3×#676C2211yescharacteristic
12#91359—21no—
13C3×C5×#108C2211yescharacteristic
14#91101C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3954—21no—
18C3×#3951C2211yescharacteristic
19#90973—21no—
20#70724—51nomaximal, Hall
21#65478—31no—
22#65182D311yescharacteristic
23C5×#362—31no—
24#64785—31no—
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C5×Dic6—21no—
29C2×C3×C4×D5D411yescharacteristic
30C3×C5×M16—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C4⋊Dic15—21no—
33C5×Dic12—21no—
34C5×Dic12—21no—
35C3×#681—21no—
36C2×C3×#168D411yescharacteristic
37C3×#676—21no—
38C3×#676—21no—
39C3×#676—41no—
40C3×C8×D5—41no—
41#6669—41no—
42#6665—41no—
43C3⋊#672—21no—
44C5×C3⋊C16—21no—
45C3×#430—51no—
46#5137—51no—
47#4553—51no—
48#4496—51no—
49#4496D511yescharacteristic, complemented
50#4494—51no—
51#4494—51no—
52C2×C5×Q16—31no—
53#4092—61no—
54D5×M16—21no—
55C2×#676C2×D311yescharacteristic
56C5×M32—31no—
57C5×#108C2×D311yescharacteristic
58#3967—61no—
59#3954—21no—
60#3951C2×D311yescharacteristic
61#3949—31no—
62#3944—31no—
63#2239—151noSylow
64C22×C3×D5SD1611yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15—41no—
67C2×C5×Dic3—41no—
68C5×Dic6—41no—
69C5×Dic6—41no—
70C2×C3×Dic5SD1611yescharacteristic
71C3×C4×D5—21no—
72C3×C4×D5—21no—
73C3×C5×C8—41no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3×#168—21no—
77C3×#168—41no—
78C2×C3×M16—51no—
79C2×C3×M16—101no—
80#924—101no—
81C2×Dic12C2×D511yescharacteristic
82C3×#108—51no—
83C3×#108—101no—
84C3×#108C2×D511yescharacteristic
85#817—51no—
86#816—101no—
87#812—51no—
88#812C2×D511yescharacteristic
89C2×C5×Q8—61no—
90C2×C4×D5#6711yescharacteristic
91C5×Q16—61no—
92C5×Q16—61no—
93C5×M16—21no—
94C2×C5×C8C22×D311yescharacteristic
95#685—121no—
96C4⋊Dic5—61no—
97#683—121no—
98#681—21no—
99C2×#168#6711yescharacteristic
100#676—21no—
101#676—21no—
102#676—41no—
103C8×D5—41no—
104C5×C16—61no—
105#672—61no—
106#470—151no—
107#430—51no—
108#365—151no—
109#365—151no—
110#362—31no—
111#362—151no—
112#349—151no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×C3×D5—21no—
115C2×C3×D5—41no—
116C3×C4×C5#12311yescharacteristic
117C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
118Dic15—81no—
119C3×Dic5—21no—
120C5×Dic3—81no—
121C22×C3×C4—51no—
122C2×Dic6—21no—
123C3×M16—21no—
124C3×M16—101no—
125C3×M16—101no—
126C3×M16—101no—
127C3×M16—201no—
128C2×C3×C8—51no—
129C2×C3×C8—201no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—101no—
133Dic3⋊C4—201no—
134Dic12—21no—
135Dic12—21no—
136C3⋊C16—21no—
137C3⋊C16—101no—
138C22×D5#21511yescharacteristic
139C5×Q8—121no—
140C5×Q8—121no—
141C2×C4×C5—121no—
142C2×C4×C5C2×#6711yescharacteristic
143C2×Dic5—121no—
144C2×Dic5#21511yescharacteristic
145C4×D5—21no—
146C4×D5—21no—
147C5×C8—41no—
148C5×C8#23511yescharacteristic
149C5×C8#23511yescharacteristic
150#168—21no—
151#168—41no—
152C2×Q16—31no—
153C2×M16—51no—
154C2×M16—101no—
155C22⋊Q8—301no—
156M32—31no—
157M32—151no—
158#108—51no—
159#108—101no—
160#108D3×D511yescharacteristic
161#106—151no—
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165C3×D5—41no—
166C23×C3—51no—
167C2×C3×C4—51no—
168C2×C3×C4—101no—
169C2×C3×C4—101no—
170C2×C3×C4D4×D511yescharacteristic
171C2×Dic3—41no—
172C2×Dic3—201no—
173Dic6—41no—
174Dic6—41no—
175C3×C8—41no—
176C3×C8—101no—
177C3×C8—201no—
178C3×C8#70911yescharacteristic
179C3×C8#71111yescharacteristic
180C22×C5C2×#21511yescharacteristic
181C2×D5—21no—
182C2×D5—41no—
183C4×C5—241no—
184C4×C5#92911yescharacteristic
185C4×C5#93211yescharacteristic
186Dic5—21no—
187Dic5—241no—
188C2×Q8—61no—
189C22×C4—51no—
190Q16—61no—
191Q16—61no—
192M16—21no—
193M16—101no—
194M16—101no—
195M16—101no—
196M16—201no—
197C2×C8—51no—
198C2×C8—201no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—301no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—61no—
204C16—301no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3—101no—
207C22×C3—201no—
208C22×C3D5×SD1611yescharacteristic
209C3×C4—101no—
210C3×C4#402911yescharacteristic
211C3×C4#405711yescharacteristic
212Dic3—81no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5#496811yescharacteristic
216D5—41no—
217C23—51no—
218Q8—121no—
219Q8—121no—
220C2×C4—51no—
221C2×C4—101no—
222C2×C4—101no—
223C2×C4—121no—
224C2×C4—601no—
225C2×C4D5×#6711yescharacteristic
226C8—41no—
227C8—101no—
228C8—201no—
229C8#677111yescharacteristic
230C8#677211yescharacteristic
231C2×C3—21no—
232C2×C3—201no—
233C2×C3#6506611yescharacteristic
234C5#7072411yescharacteristic, complemented, Sylow
235C22—101no—
236C22—201no—
237C22D5×#21511yescharacteristic
238C4—101no—
239C4—241no—
240C4—1201no—
241C4#9144711yescharacteristic
242C4#9148911yescharacteristic
243C3#1060006011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—201no—
246C2#1174730811yescharacteristic
subgroupG/H
centerC2#11747308
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5#481
prime radicalC22×C3×D5SD16
hypercenter#108D3×D5
hypocenterC3×C5#2239
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
3. #11746315C2semidirect
4. C5×#4496C2semidirect
5. #11745938C2semidirect
6. #11745923C2semidirect
49. #4496D5semidirect
205. C3×C5#2239semidirect
234. C5#70724semidirect
243. C3#10600060semidirect

Maximal subgroups

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

subgroupindex
C3×#651822
#117479452
#117463152
C5×#44962
#117459382
#117459232
#117458822
#106000603
#707245