Finite Group Databasebeta

← #14318585

Subgroups — #14318585

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#11750968C211yesmaximal, characteristic
2#11748061C211yesmaximal, characteristic
3C5×#4487C211yesmaximal, characteristic, complemented
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745926C211yesmaximal, characteristic, complemented
6#11745925C211yesmaximal, characteristic, complemented
7#11745884C211yesmaximal, characteristic
8#10600107—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×#6705C2211yescharacteristic
11#91786—21no—
12#91292—21no—
13C3×C5×#106C2211yescharacteristic
14#91094—21no—
15C5×#819C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90992—21no—
20#69314—51nomaximal, Hall
21#65182—31no—
22#65157—31no—
23C5×#365—31no—
24#64737—31no—
25#64734—31no—
26#64716—31no—
27#64707D311yescharacteristic, complemented
28C2×C4×D15D411yescharacteristic
29C2×Dic30—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32#6714—41no—
33C4⋊Dic15—41no—
34C2×C3⋊#168D411yescharacteristic
35Dic60—21no—
36Dic60—21no—
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#4893—51no—
46#4867—51no—
47C3×#365—51no—
48#4517—51no—
49#4514—51no—
50#4496—51no—
51#4487D511yescharacteristic, complemented
52D5×M16—61no—
53C2×Dic20—31no—
54C2×#676—31no—
55#4043—61no—
56C5×M32—31no—
57C5×#108—31no—
58C5×#106C2×D311yescharacteristic
59#3954—61no—
60#3951C2×D311yescharacteristic
61#3944C2×D311yescharacteristic
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#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—21no—
76C3×#168—41no—
77C5×C3⋊C8—41no—
78D3×M16—101no—
79C2×Dic12—51no—
80C2×ΓL(1,𝔽25)—51no—
81#897—101no—
82C3×M32—51no—
83C3×#108—51no—
84C3×#106C2×D511yescharacteristic
85#822—101no—
86#819C2×D511yescharacteristic
87#812C2×D511yescharacteristic
88#810—101no—
89C2×C4×D5—31no—
90C2×Dic10—61no—
91C5×M16—61no—
92C2×C5×C8C22×D311yescharacteristic
93C5×C4⋊C4—21no—
94#685—121no—
95C4⋊Dic5—121no—
96#681—21no—
97C2×#168—31no—
98Dic20—61no—
99Dic20—61no—
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—31no—
109#365—51no—
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—101no—
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—21no—
126(C2×D3)⋊C4—201no—
127C4⋊Dic3—201no—
128#208—21no—
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—101no—
137C3⋊C16—21no—
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—121no—
148C5×C8#23511yescharacteristic
149C5×C8#23911yescharacteristic
150#168—41no—
151#168—61no—
152C2×Q16—151no—
153C2×M16—151no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—31no—
157M32—51no—
158#108—31no—
159#108—51no—
160#108—301no—
161#106D3×D511yescharacteristic
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—201no—
176C3×C8#70911yescharacteristic
177C3×C8#71311yescharacteristic
178C3⋊C8—41no—
179C3⋊C8—101no—
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—61no—
193M16—101no—
194M16—301no—
195M16—301no—
196M16—601no—
197C2×C8—151no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—21no—
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#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×C4#679011yescharacteristic
226C8—121no—
227C8—201no—
228C8—301no—
229C8#676911yescharacteristic
230C8#677311yescharacteristic
231C2×C3—21no—
232C2×C3#6515211yescharacteristic
233D3—201no—
234C5#6931411yescharacteristic, complemented, Sylow
235C22—301no—
236C22—601no—
237C22#9148711yescharacteristic
238C4—81no—
239C4—301no—
240C4—1201no—
241C4#9143311yescharacteristic
242C4#9150611yescharacteristic
243C3#1060010711yescharacteristic, complemented, Sylow
244C2—21no—
245C2—601no—
246C2#1174720311yescharacteristic
subgroupG/H
centerC2#11747203
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radicalC22×D15SD16
hypercenter#106D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
3. C5×#4487C2semidirect
4. C3×#64707C2semidirect
5. #11745926C2semidirect
6. #11745925C2semidirect
27. #64707D3semidirect
51. #4487D5semidirect
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
#117509682
#117480612
C5×#44872
C3×#647072
#117459262
#117459252
#117458842
#106001073
#693145