Finite Group Databasebeta

← #14318567

Subgroups — #14318567

Order 1920.

248 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 67 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#11750994C211yesmaximal, characteristic
2#11750968C211yesmaximal, characteristic
3C3×C5×#365C211yesmaximal, characteristic, complemented
4#11746338C211yesmaximal, characteristic, complemented
5#11746335C211yesmaximal, characteristic
6#11746317C211yesmaximal, characteristic, complemented
7#11746308C211yesmaximal, characteristic, complemented
8#10600107—31nomaximal, Hall
9M16×D15—21no—
10C2×Dic60C2211yescharacteristic
11C2×#6705C2211yescharacteristic
12#91786—21no—
13C3×C5×M32C2211yescharacteristic
14C3×C5×#108C2211yescharacteristic
15C3×C5×#106C2211yescharacteristic
16#91106—21no—
17#91103C2211yescharacteristic
18#91096C2211yescharacteristic
19#91094—21no—
20#69314—51nomaximal, Hall
21#65182—31no—
22#65157—31no—
23C5×#365D311yescharacteristic, complemented
24#64737—31no—
25#64734—31no—
26#64716—31no—
27#64707—31no—
28C2×C4×D15D411yescharacteristic
29C2×Dic30—21no—
30C3×C5×M16—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33#6714—41no—
34C4⋊Dic15—41no—
35#6710—21no—
36C2×C3⋊#168D411yescharacteristic
37Dic60—21no—
38Dic60—21no—
39#6705—21no—
40#6705—21no—
41#6705—41no—
42C8×D15—41no—
43C3×C5×C16—21no—
44C3⋊#672—21no—
45#4893—51no—
46#4867—51no—
47C3×#365D511yescharacteristic, complemented
48#4517—51no—
49#4514—51no—
50#4496—51no—
51#4487—51no—
52D5×M16—61no—
53C2×Dic20—31no—
54C2×#676—31no—
55#4043—61no—
56C5×M32C2×D311yescharacteristic
57C5×#108C2×D311yescharacteristic
58C5×#106C2×D311yescharacteristic
59#3954—61no—
60#3951—31no—
61#3944—31no—
62#3942—61no—
63#2239—151noSylow
64C22×D15SD1611yescharacteristic
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15—41no—
68C2×Dic15SD1611yescharacteristic
69C4×D15—21no—
70C4×D15—21no—
71Dic30—41no—
72Dic30—41no—
73C3×C5×C8—41no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—21no—
77C3⋊#168—41no—
78D3×M16—101no—
79C2×Dic12—51no—
80C2×ΓL(1,𝔽25)—51no—
81#897—101no—
82C3×M32C2×D511yescharacteristic
83C3×#108C2×D511yescharacteristic
84C3×#106C2×D511yescharacteristic
85#822—101no—
86#819—51no—
87#812—51no—
88#810—101no—
89C2×C4×D5—31no—
90C2×Dic10—61no—
91C5×M16—21no—
92C2×C5×C8C22×D311yescharacteristic
93C5×C4⋊C4—21no—
94#685—121no—
95C4⋊Dic5—121no—
96#681—61no—
97C2×#168—31no—
98Dic20—61no—
99Dic20—61no—
100#676—61no—
101#676—61no—
102#676—121no—
103C8×D5—121no—
104C5×C16—21no—
105#672—61no—
106#470—151no—
107#430—151no—
108#365—151no—
109#365D1511yescharacteristic, complemented
110#362—151no—
111#362—151no—
112#349—151no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×D15—21no—
115C2×D15—41no—
116C3×C4×C5—81no—
117C3×C4×C5#12311yescharacteristic
118C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
119Dic15—21no—
120Dic15—81no—
121C2×C4×D3—51no—
122C2×Dic6—101no—
123C3×M16—21no—
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—21no—
126(C2×D3)⋊C4—201no—
127C4⋊Dic3—201no—
128#208—101no—
129C2×C3⋊C8—51no—
130Dic12—101no—
131Dic12—101no—
132ΓL(1,𝔽25)—101no—
133ΓL(1,𝔽25)—101no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—21no—
137C3⋊C16—101no—
138C22×D5—31no—
139C2×C4×C5—41no—
140C2×C4×C5D3×D411yescharacteristic
141C2×Dic5—31no—
142C2×Dic5—121no—
143C4×D5—61no—
144C4×D5—61no—
145Dic10—121no—
146Dic10—121no—
147C5×C8—41no—
148C5×C8#23511yescharacteristic
149C5×C8#23911yescharacteristic
150#168—61no—
151#168—121no—
152C2×Q16—151no—
153C2×M16—151no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—151no—
157M32C2×D1511yescharacteristic
158#108—151no—
159#108—301no—
160#108C2×D1511yescharacteristic
161#106C2×D1511yescharacteristic
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165D15—41no—
166C22×D3—51no—
167C2×C3×C4—41no—
168C2×C3×C4D4×D511yescharacteristic
169C2×Dic3—51no—
170C2×Dic3—201no—
171C4×D3—101no—
172C4×D3—101no—
173Dic6—201no—
174Dic6—201no—
175C3×C8—41no—
176C3×C8#70911yescharacteristic
177C3×C8#71311yescharacteristic
178C3⋊C8—101no—
179C3⋊C8—201no—
180C22×C5D3×SD1611yescharacteristic
181C2×D5—61no—
182C2×D5—121no—
183C4×C5—81no—
184C4×C5#89411yescharacteristic
185C4×C5#91411yescharacteristic
186Dic5—61no—
187Dic5—241no—
188C2×Q8—301no—
189C22×C4—151no—
190Q16—301no—
191Q16—301no—
192M16—21no—
193M16—301no—
194M16—301no—
195M16—301no—
196M16—601no—
197C2×C8—151no—
198C2×C8—601no—
199C2×C8C22×D1511yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—21no—
204C16—301no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3D5×SD1611yescharacteristic
207C2×D3—101no—
208C2×D3—201no—
209C3×C4—81no—
210C3×C4#404011yescharacteristic
211C3×C4#406011yescharacteristic
212Dic3—101no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5#486311yescharacteristic
216D5—121no—
217C23—151no—
218Q8—601no—
219Q8—601no—
220C2×C4—41no—
221C2×C4—151no—
222C2×C4—301no—
223C2×C4—301no—
224C2×C4—601no—
225C2×C4D4×D1511yescharacteristic
226C8—41no—
227C8—301no—
228C8—601no—
229C8#681711yescharacteristic
230C8#682111yescharacteristic
231C2×C3—21no—
232C2×C3#6515211yescharacteristic
233D3—201no—
234C5#6931411yescharacteristic, complemented, Sylow
235C22—301no—
236C22—601no—
237C22SD16×D1511yescharacteristic
238C4—81no—
239C4—301no—
240C4—1201no—
241C4#9178311yescharacteristic
242C4#9180311yescharacteristic
243C3#1060010711yescharacteristic, complemented, Sylow
244C2—21no—
245C2—601no—
246C2#1175096411yescharacteristic
subgroupG/H
centerC2#11750964
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#365C2
socleC2×C3×C5#481
prime radicalC22×D15SD16
hypercenter#365D15
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
3. C3×C5×#365C2semidirect
4. #11746338C2semidirect
6. #11746317C2semidirect
7. #11746308C2semidirect
23. C5×#365D3semidirect
47. C3×#365D5semidirect
109. #365D15semidirect
205. C3×C5#2239semidirect
234. C5#69314semidirect
243. C3#10600107semidirect

Maximal subgroups

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

subgroupindex
#117509942
#117509682
C3×C5×#3652
#117463382
#117463352
#117463172
#117463082
#106001073
#693145