Finite Group Databasebeta

← #14318588

Subgroups — #14318588

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
1#11748057C211yesmaximal, characteristic
2#11747945C211yesmaximal, characteristic
3#11746334C211yesmaximal, characteristic, complemented
4C5×#4517C211yesmaximal, characteristic, complemented
5C3×#64734C211yesmaximal, characteristic
6#11745934C211yesmaximal, characteristic, complemented
7#11745924C211yesmaximal, characteristic, complemented
8#10600060—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C2×C3×#676C2211yescharacteristic
11#91359—21no—
12D5×#208—21no—
13C3×C5×M32C2211yescharacteristic
14#91103C2211yescharacteristic
15#91101C2211yescharacteristic
16C5×#819C2211yescharacteristic
17C3×#3944C2211yescharacteristic
18#90991—21no—
19#90973—21no—
20#69117—51nomaximal, Hall
21#65478—31no—
22#65182—31no—
23C5×#362—31no—
24#64785—31no—
25#64734D311yescharacteristic
26#64733—31no—
27#64714—31no—
28C2×C5×Dic6—21no—
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32#6710—21no—
33C5×#208—21no—
34C5×Dic12—21no—
35C5×Dic12—21no—
36C2×C3×#168D411yescharacteristic
37C3×#676—21no—
38C3×#676—21no—
39#6669—41no—
40#6665—41no—
41#6649—41no—
42D5×C3⋊C8—41no—
43C3×C5×C16—21no—
44C3×#672—21no—
45#5137—51no—
46#5125—51no—
47C3×#349—51no—
48#4517—51no—
49#4517D511yescharacteristic, complemented
50#4513—51no—
51#4513—51no—
52C2×C5×Q16—31no—
53#4092—61no—
54D5×M16—61no—
55C2×#676C2×D311yescharacteristic
56C5×M32C2×D311yescharacteristic
57C5×#108—31no—
58#3967—61no—
59#3954—61no—
60#3951—31no—
61#3949—31no—
62#3944C2×D311yescharacteristic
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#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—41no—
76C3×#168—21no—
77C5×C3⋊C8—41no—
78C2×C3×M16—51no—
79#924—101no—
80C2×#208—101no—
81C2×Dic12C2×D511yescharacteristic
82C3×M32—51no—
83C3×M32C2×D511yescharacteristic
84#819—51no—
85#819—101no—
86#819C2×D511yescharacteristic
87#817—51no—
88#816—101no—
89C2×C5×Q8—61no—
90C2×C4×D5D1211yescharacteristic
91C5×Q16—61no—
92C5×Q16—61no—
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95#685—121no—
96C4⋊Dic5—61no—
97#683—121no—
98#681—61no—
99C2×#168D1211yescharacteristic
100#676—21no—
101#676—21no—
102#676—121no—
103C8×D5—121no—
104C5×C16—21no—
105#672—21no—
106#470—151no—
107#430—151no—
108#365—151no—
109#365—151no—
110#362—31no—
111#362—151no—
112#349—51no—
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—101no—
124C3×M16—101no—
125C2×C3×C8—51no—
126C2×C3×C8C22×D511yescharacteristic
127#217—201no—
128C4⋊Dic3—101no—
129Dic3⋊C4—201no—
130#208—21no—
131#208—101no—
132#208—201no—
133C2×C3⋊C8—201no—
134Dic12—21no—
135Dic12—21no—
136C3×C16—21no—
137C3×C16—101no—
138C22×D5#20411yescharacteristic
139C5×Q8—121no—
140C5×Q8—121no—
141C2×C4×C5—121no—
142C2×C4×C5C2×D1211yescharacteristic
143C2×Dic5—121no—
144C2×Dic5#20411yescharacteristic
145C4×D5—21no—
146C4×D5—21no—
147C5×C8—121no—
148C5×C8#23711yescharacteristic
149C5×C8#23711yescharacteristic
150#168—21no—
151#168—121no—
152C2×Q16—31no—
153C2×M16—51no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—51no—
157M32D3×D511yescharacteristic
158#108—31no—
159#108—151no—
160#108—301no—
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—101no—
176C3×C8#70911yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—41no—
179C3⋊C8—201no—
180C22×C5C2×#20411yescharacteristic
181C2×D5—21no—
182C2×D5—41no—
183C4×C5—241no—
184C4×C5#88611yescharacteristic
185C4×C5#90811yescharacteristic
186Dic5—21no—
187Dic5—241no—
188C2×Q8—61no—
189C22×C4—51no—
190Q16—61no—
191Q16—61no—
192M16—61no—
193M16—101no—
194M16—101no—
195M16—301no—
196M16—601no—
197C2×C8—51no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—301no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—21no—
204C16—101no—
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#473511yescharacteristic
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×D1211yescharacteristic
226C8—101no—
227C8—121no—
228C8—601no—
229C8#676511yescharacteristic
230C8#678011yescharacteristic
231C2×C3—21no—
232C2×C3—201no—
233C2×C3#6506611yescharacteristic
234C5#6911711yescharacteristic, complemented, Sylow
235C22—101no—
236C22—201no—
237C22D5×#20411yescharacteristic
238C4—101no—
239C4—241no—
240C4—1201no—
241C4#9125011yescharacteristic
242C4#9141411yescharacteristic
243C3#1060006011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—201no—
246C2#1174761311yescharacteristic
subgroupG/H
centerC2#11747613
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radicalC22×C3×D5SD16
hypercenterM32D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
3. #11746334C2semidirect
4. C5×#4517C2semidirect
6. #11745934C2semidirect
7. #11745924C2semidirect
49. #4517D5semidirect
205. C3×C5#2239semidirect
234. C5#69117semidirect
243. C3#10600060semidirect

Maximal subgroups

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

subgroupindex
#117480572
#117479452
#117463342
C5×#45172
C3×#647342
#117459342
#117459242
#106000603
#691175