Finite Group Databasebeta

← #14318570

Subgroups — #14318570

Order 1920.

248 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 64 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#11751290C211yesmaximal, characteristic
2#11748061C211yesmaximal, characteristic
3C5×#4565C211yesmaximal, characteristic, complemented
4C3×#64785C211yesmaximal, characteristic, complemented
5#11745938C211yesmaximal, characteristic, complemented
6#11745934C211yesmaximal, characteristic, complemented
7#11745884C211yesmaximal, characteristic
8#10600060—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91835—21no—
11C2×#6705C2211yescharacteristic
12#91292—21no—
13#91119—21no—
14#91101C2211yescharacteristic
15C5×#819C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90992—21no—
20#69267—51nomaximal, Hall
21#65478—31no—
22#65182—31no—
23C5×#362—31no—
24#64785D311yescharacteristic, complemented
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C3×C5×Q8—21no—
29C2×C4×D15D411yescharacteristic
30C3×C5×Q16—21no—
31C3×C5×Q16—21no—
32C2×C3×C5×C8C2311yescharacteristic
33#6714—41no—
34C4⋊Dic15—21no—
35#6712—41no—
36C2×C3⋊#168D411yescharacteristic
37#6705—21no—
38#6705—21no—
39C5×#208—21no—
40C3×#681—21no—
41#6651—41no—
42#6648—41no—
43C3×#672—21no—
44C5×C3⋊C16—21no—
45#5189—51no—
46#4893—51no—
47C3×#362—51no—
48#4565D511yescharacteristic, complemented
49#4514—51no—
50#4513—51no—
51#4494—51no—
52C2×C5×Q16C2×D311yescharacteristic
53#4092—61no—
54D5×M16—61no—
55C2×#676—31no—
56C5×M32—31no—
57C5×#108—31no—
58#3967—61no—
59#3954—61no—
60#3951C2×D311yescharacteristic
61#3949—31no—
62#3944C2×D311yescharacteristic
63#2239—151noSylow
64C22×D15SD1611yescharacteristic
65C3×C5×Q8—41no—
66C3×C5×Q8—41no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69C2×Dic15—41no—
70C2×Dic15SD1611yescharacteristic
71C4×D15—21no—
72C4×D15—21no—
73C3×C5×C8#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—21no—
76C3×#168—41no—
77C5×C3⋊C8—41no—
78C2×C3×Q16C2×D511yescharacteristic
79#946—101no—
80D3×M16—101no—
81C2×ΓL(1,𝔽25)—51no—
82C3×M32—51no—
83C3×#108—51no—
84#835—101no—
85#822—101no—
86#819C2×D511yescharacteristic
87#817—51no—
88#812C2×D511yescharacteristic
89C2×C5×Q8—21no—
90C2×C4×D5—31no—
91C5×Q16—21no—
92C5×Q16—21no—
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95#685—121no—
96C4⋊Dic5—61no—
97#683—121no—
98#681—21no—
99C2×#168—31no—
100#676—61no—
101#676—61no—
102#676—121no—
103C8×D5—121no—
104C5×C16—61no—
105#672—21no—
106#470—151no—
107#430—151no—
108#365—151no—
109#365—151no—
110#362—31no—
111#362—51no—
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×C3×Q8—21no—
122C2×C4×D3—51no—
123C3×Q16—21no—
124C3×Q16—21no—
125C3×M16—101no—
126C2×C3×C8C22×D511yescharacteristic
127(C2×D3)⋊C4—201no—
128C4⋊Dic3—101no—
129Dic3⋊C4—201no—
130#208—21no—
131C2×C3⋊C8—51no—
132ΓL(1,𝔽25)—101no—
133ΓL(1,𝔽25)—101no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—101no—
137C3⋊C16—21no—
138C22×D5—31no—
139C5×Q8—41no—
140C5×Q8—41no—
141C2×C4×C5—41no—
142C2×C4×C5D3×D411yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—121no—
145C4×D5—61no—
146C4×D5—61no—
147C5×C8—121no—
148C5×C8#23511yescharacteristic
149C5×C8#23711yescharacteristic
150#168—41no—
151#168—61no—
152C2×Q16D3×D511yescharacteristic
153C2×M16—151no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—31no—
157M32—51no—
158#108—31no—
159#108—51no—
160#108—301no—
161#106—151no—
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165D15—41no—
166C22×D3—51no—
167C3×Q8—41no—
168C3×Q8—41no—
169C2×C3×C4—41no—
170C2×C3×C4D4×D511yescharacteristic
171C2×Dic3—51no—
172C2×Dic3—201no—
173C4×D3—101no—
174C4×D3—101no—
175C3×C8—201no—
176C3×C8#70911yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—41no—
179C3⋊C8—101no—
180C22×C5D3×SD1611yescharacteristic
181C2×D5—61no—
182C2×D5—121no—
183C4×C5—81no—
184C4×C5#88311yescharacteristic
185C4×C5#91111yescharacteristic
186Dic5—61no—
187Dic5—241no—
188C2×Q8—21no—
189C22×C4—151no—
190Q16—21no—
191Q16—21no—
192M16—61no—
193M16—101no—
194M16—301no—
195M16—301no—
196M16—601no—
197C2×C8—151no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—301no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—61no—
204C16—101no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3D5×SD1611yescharacteristic
207C2×D3—101no—
208C2×D3—201no—
209C3×C4—81no—
210C3×C4#402911yescharacteristic
211C3×C4#405711yescharacteristic
212Dic3—101no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5#477711yescharacteristic
216D5—121no—
217C23—151no—
218Q8—41no—
219Q8—41no—
220C2×C4—41no—
221C2×C4—151no—
222C2×C4—301no—
223C2×C4—301no—
224C2×C4—601no—
225C2×C4#679011yescharacteristic
226C8—121no—
227C8—201no—
228C8—301no—
229C8#677911yescharacteristic
230C8#678211yescharacteristic
231C2×C3—21no—
232C2×C3#6506611yescharacteristic
233D3—201no—
234C5#6926711yescharacteristic, complemented, Sylow
235C22—301no—
236C22—601no—
237C22#9148711yescharacteristic
238C4—81no—
239C4—301no—
240C4—1201no—
241C4#9148211yescharacteristic
242C4#9156211yescharacteristic
243C3#1060006011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—601no—
246C2#1174896011yescharacteristic
subgroupG/H
centerC2#11748960
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5#481
prime radicalC22×D15SD16
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. C5×#4565C2semidirect
4. C3×#64785C2semidirect
5. #11745938C2semidirect
6. #11745934C2semidirect
24. #64785D3semidirect
48. #4565D5semidirect
205. C3×C5#2239semidirect
234. C5#69267semidirect
243. C3#10600060semidirect

Maximal subgroups

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

subgroupindex
#117512902
#117480612
C5×#45652
C3×#647852
#117459382
#117459342
#117458842
#106000603
#692675