Finite Group Databasebeta

← #14318211

Subgroups — #14318211

Order 1920.

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

normal subgroups only

This group has 240 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#11750959C211yesmaximal, characteristic, complemented
2#11748072C211yesmaximal, characteristic
3C5×#4488C211yesmaximal, characteristic
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745938C211yesmaximal, characteristic, complemented
6#11745931C211yesmaximal, characteristic, complemented
7#11745912C211yesmaximal, characteristic
8#10600040—31nomaximal, Hall
9#91779—21no—
10C5×#904C2211yescharacteristic
11#91288—21no—
12C3×C5×#106C2211yescharacteristic
13#91101C2211yescharacteristic
14C8×Dic15C2211yescharacteristic
15#91091—21no—
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90978—21no—
20#69316—51nomaximal, Hall
21#65485—31no—
22#65147—31no—
23C5×#360—31no—
24#64786—31no—
25#64733—31no—
26#64731—31no—
27#64707D311yescharacteristic, complemented
28C5×#235—21no—
29C2×C3×C5×C8C2311yescharacteristic
30C3×C5×C4⋊C4—21no—
31C4⋊Dic15—21no—
32C4⋊Dic15—41no—
33#6712—41no—
34C4×Dic15D411yescharacteristic
35C2×C3⋊#168D411yescharacteristic
36C5×Dic12Q811yescharacteristic
37C5×D24Q811yescharacteristic
38C5×#204—21no—
39C3×#681—21no—
40#6650—41no—
41D3×#168—41no—
42C3×#672—21no—
43C5×C3⋊C16—21no—
44#4895—51no—
45#4858—51no—
46C3×#365—51no—
47#4518—51no—
48#4511—51no—
49#4494—51no—
50#4488D511yescharacteristic
51C5×#135—31no—
52#4094—61no—
53#4036—61no—
54C5×M32—31no—
55C5×#106C2×D311yescharacteristic
56#3969—61no—
57#3951C2×D311yescharacteristic
58#3949—31no—
59C8×Dic5—31no—
60#3944C2×D311yescharacteristic
61#3939—61no—
62#2231—151noSylow
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×Dic15—21no—
66C2×Dic15—41no—
67C5×#67—41no—
68C5×D12—21no—
69C4×C5×D3—41no—
70C5×Dic6—21no—
71C3×C5×C8C2×Q811yescharacteristic
72C3×C5×C8#4111yescharacteristic
73C3⋊#168SD1611yescharacteristic
74C3⋊#168SD1611yescharacteristic
75C3×#168—41no—
76#907—101no—
77#904C2×D511yescharacteristic
78#890—101no—
79C3×M32—51no—
80C3×#108—51no—
81C3×#106C2×D511yescharacteristic
82#825—101no—
83#817—51no—
84C8×Dic3—51no—
85#812C2×D511yescharacteristic
86#807—101no—
87C5×#41—61no—
88C5×Q16—31no—
89C5×SD16—61no—
90C5×D8—31no—
91C2×C5×C8C22×D311yescharacteristic
92C5×C4⋊C4—21no—
93C4⋊Dic5—61no—
94C4⋊Dic5—121no—
95#683—121no—
96C4×Dic5—31no—
97#681—21no—
98#681—121no—
99C2×#168—31no—
100C2×#168—121no—
101C5×C16—61no—
102#672—21no—
103#499—151no—
104#443—151no—
105#365—51no—
106#365—151no—
107#364—151no—
108#360—31no—
109#360—151no—
110C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
111C2×C5×D3—41no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—41no—
116Dic15—81no—
117C5×Dic3—41no—
118#235—21no—
119C3×M16—101no—
120C2×C3×C8C22×D511yescharacteristic
121C3×C4⋊C4—21no—
122C4⋊Dic3—101no—
123C4⋊Dic3—201no—
124Dic3⋊C4—201no—
125C4×Dic3—51no—
126C2×C3⋊C8—51no—
127Dic12Dic1011yescharacteristic
128D24Dic1011yescharacteristic
129#204—21no—
130ΓL(1,𝔽25)—201no—
131D3×C8—201no—
132C3×C16—101no—
133C3⋊C16—21no—
134C5×Q8—61no—
135C5×D4—61no—
136C5×D4—121no—
137C2×C4×C5—41no—
138C2×C4×C5—121no—
139C2×C4×C5D3×D411yescharacteristic
140C2×Dic5—61no—
141C2×Dic5—121no—
142C5×C8#23511yescharacteristic
143C5×C8D3×Q811yescharacteristic
144#168—31no—
145#168—31no—
146#168—41no—
147#135—31no—
148#131—301no—
149#125—301no—
150M32—31no—
151M32—51no—
152#108—51no—
153#107—301no—
154#106—151no—
155#106D3×D511yescharacteristic
156#104—301no—
157C4×C8—151no—
158C2×C3×C5—21no—
159C2×C3×C5#47611yescharacteristic
160C5×D3—81no—
161C2×C3×C4—41no—
162C2×C3×C4D4×D511yescharacteristic
163#67—41no—
164C2×Dic3—101no—
165C2×Dic3—201no—
166D12—21no—
167C4×D3—41no—
168Dic6—21no—
169C3×C8—201no—
170C3×C8C2×Dic1011yescharacteristic
171C3×C8#71111yescharacteristic
172C3⋊C8—51no—
173C3⋊C8—51no—
174C22×C5—121no—
175C22×C5#91411yescharacteristic
176C4×C5—81no—
177C4×C5—121no—
178C4×C5#89611yescharacteristic
179C4×C5D3×SD1611yescharacteristic
180Dic5—121no—
181Dic5—241no—
182#41—61no—
183Q16—31no—
184SD16—61no—
185D8—31no—
186M16—101no—
187M16—601no—
188C2×C8—151no—
189C2×C8—601no—
190C2×C8C2×D3×D511yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—301no—
193C4⋊C4—601no—
194C4⋊C4—601no—
195C42—151no—
196C16—61no—
197C16—101no—
198C3×C5#223111yescharacteristic, complemented, Hall
199C22×C3#405711yescharacteristic
200C2×D3—41no—
201C3×C4—81no—
202C3×C4#402411yescharacteristic
203C3×C4D5×SD1611yescharacteristic
204Dic3—41no—
205Dic3—201no—
206Dic3—401no—
207C2×C5—21no—
208C2×C5—241no—
209C2×C5#487011yescharacteristic
210Q8—61no—
211D4—61no—
212D4—121no—
213C2×C4—41no—
214C2×C4—121no—
215C2×C4—301no—
216C2×C4—601no—
217C2×C4#679011yescharacteristic
218C8—151no—
219C8—151no—
220C8—201no—
221C8D3×Dic1011yescharacteristic
222C8#677211yescharacteristic
223C2×C3—21no—
224C2×C3#6505011yescharacteristic
225D3—81no—
226C5#6931611yescharacteristic, complemented, Sylow
227C22—121no—
228C22#9150011yescharacteristic
229C4—81no—
230C4—121no—
231C4—601no—
232C4—1201no—
233C4#9143211yescharacteristic
234C4#9150511yescharacteristic
235C3#1060004011yescharacteristic, complemented, Sylow
236C2—21no—
237C2—241no—
238C2#1174725611yescharacteristic
subgroupG/H
centerC2#11747256
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#476
prime radicalC5×#904C22
hypercenter#106D3×D5
hypocenterC3×C5#2231
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
1. #11750959C2semidirect
4. C3×#64707C2semidirect
5. #11745938C2semidirect
6. #11745931C2semidirect
27. #64707D3semidirect
198. C3×C5#2231semidirect
226. C5#69316semidirect
235. C3#10600040semidirect

Maximal subgroups

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

subgroupindex
#117509592
#117480722
C5×#44882
C3×#647072
#117459382
#117459312
#117459122
#106000403
#693165