Finite Group Databasebeta

← #14318186

Subgroups — #14318186

Order 1920.

252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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#11748062C211yesmaximal, characteristic
2#11748016C211yesmaximal, characteristic, complemented
3#11746334C211yesmaximal, characteristic, complemented
4C5×#4518C211yesmaximal, characteristic
5C3×#64731C211yesmaximal, characteristic, complemented
6#11745933C211yesmaximal, characteristic, complemented
7#11745912C211yesmaximal, characteristic
8#10600039—31nomaximal, Hall
9C5×#904C2211yescharacteristic
10#91468—21no—
11#91286—21no—
12C3×C5×M32C2211yescharacteristic
13#91103C2211yescharacteristic
14#91101C2211yescharacteristic
15C5×#817C2211yescharacteristic
16C3×C8×Dic5C2211yescharacteristic
17C3×#3944C2211yescharacteristic
18#90985—21no—
19#90979—21no—
20#69307—51nomaximal, Hall
21#65485—31no—
22#65144—31no—
23C5×#360—31no—
24#64786—31no—
25#64733—31no—
26#64731D311yescharacteristic, complemented
27#64707—31no—
28C5×#235—21no—
29C2×#1204—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32#6710—21no—
33C5×C4⋊Dic3—21no—
34C5×Dic12Q811yescharacteristic, complemented
35C5×D24Q811yescharacteristic, complemented
36C5×#204—21no—
37C3×C4×Dic5D411yescharacteristic
38C2×C3×#168D411yescharacteristic
39#6668—41no—
40#6650—41no—
41D3×#168—41no—
42C3×C5×C16—21no—
43C3×#672—21no—
44#4700—51no—
45#4680—51no—
46C3×#364—51no—
47#4518—51no—
48#4518D511yescharacteristic
49#4513—51no—
50#4513—51no—
51C5×#135—31no—
52#4094—61no—
53#4034—61no—
54C5×M32C2×D311yescharacteristic
55C5×#106—31no—
56#3969—61no—
57#3951—31no—
58#3949—31no—
59C8×Dic5C2×D311yescharacteristic
60#3944C2×D311yescharacteristic
61#3940—61no—
62#2230—151noSylow
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×Dic15—41no—
65C5×#67—41no—
66C2×C5×Dic3—41no—
67C5×D12—21no—
68C4×C5×D3—41no—
69C5×Dic6—21no—
70C2×C3×Dic5—21no—
71#1204—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3⋊#168—41no—
75C3×#168SD1611yescharacteristic
76C3×#168SD1611yescharacteristic
77#904C2×D511yescharacteristic
78#901—101no—
79#869—101no—
80C3×M32—51no—
81C3×M32C2×D511yescharacteristic
82C3×C4×C8—51no—
83#819—51no—
84#817—51no—
85#817—101no—
86#817C2×D511yescharacteristic
87#805—101no—
88C5×#41—61no—
89C2×Dic10—121no—
90C5×Q16—31no—
91C5×SD16—61no—
92C5×D8—31no—
93C2×C5×C8C22×D311yescharacteristic
94C5×C4⋊C4—61no—
95C4⋊Dic5—61no—
96#683—121no—
97C4×Dic5D1211yescharacteristic
98#681—61no—
99#681—121no—
100C2×#168—121no—
101C2×#168D1211yescharacteristic
102C5×C16—21no—
103#672—21no—
104#498—151no—
105#443—151no—
106#365—151no—
107#365—151no—
108#364—51no—
109#360—31no—
110#360—151no—
111C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
112C2×C5×D3—41no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—81no—
116C3×Dic5—22no—
117C5×Dic3—41no—
118C5×Dic3—81no—
119#235—21no—
120C2×Dic6—201no—
121C2×C3×C8—51no—
122C2×C3×C8C22×D511yescharacteristic
123C3×C42—51no—
124C4⋊Dic3—21no—
125C4⋊Dic3—101no—
126C4⋊Dic3—201no—
127#208—101no—
128Dic12Dic1011yescharacteristic, complemented
129D24Dic1011yescharacteristic, complemented
130#204—21no—
131ΓL(1,𝔽25)—201no—
132D3×C8—201no—
133C3×C16—21no—
134C3×C16—101no—
135C5×Q8—61no—
136C5×D4—61no—
137C5×D4—121no—
138C2×C4×C5—121no—
139C2×C4×C5—121no—
140C2×C4×C5C2×D1211yescharacteristic
141C2×Dic5—21no—
142C2×Dic5—121no—
143Dic10—242no—
144C5×C8#23711yescharacteristic
145C5×C8D3×Q811yescharacteristic
146#168—121no—
147#168#20411yescharacteristic
148#168#20411yescharacteristic
149#135—31no—
150#131—301no—
151C4⋊Q8—301no—
152M32—51no—
153M32D3×D511yescharacteristic
154#108—151no—
155#106—31no—
156#106—151no—
157#106—301no—
158#104—301no—
159C4×C8—51no—
160C2×C3×C5—21no—
161C2×C3×C5#47611yescharacteristic
162C5×D3—81no—
163C2×C3×C4—101no—
164C2×C3×C4D4×D511yescharacteristic
165#67—41no—
166C2×Dic3—41no—
167C2×Dic3—201no—
168D12—21no—
169C4×D3—41no—
170Dic6—21no—
171Dic6—402no—
172C3×C8—51no—
173C3×C8—51no—
174C3×C8C2×Dic1011yescharacteristic
175C3×C8#71111yescharacteristic
176C3⋊C8—201no—
177C22×C5—121no—
178C22×C5#90811yescharacteristic
179C4×C5—121no—
180C4×C5—241no—
181C4×C5#89711yescharacteristic
182C4×C5C2×#20411yescharacteristic
183Dic5—22no—
184Dic5—241no—
185#41—61no—
186C2×Q8—601no—
187Q16—31no—
188SD16—61no—
189D8—31no—
190M16—301no—
191M16—601no—
192C2×C8—51no—
193C2×C8—601no—
194C2×C8C2×D3×D511yescharacteristic
195C4⋊C4—61no—
196C4⋊C4—301no—
197C4⋊C4—601no—
198C42—51no—
199C16—21no—
200C16—101no—
201C3×C5#223011yescharacteristic, complemented, Hall
202C22×C3#405711yescharacteristic
203C2×D3—41no—
204C3×C4—102no—
205C3×C4#402411yescharacteristic
206C3×C4D5×SD1611yescharacteristic
207Dic3—41no—
208Dic3—81no—
209Dic3—401no—
210C2×C5—21no—
211C2×C5—241no—
212C2×C5#484211yescharacteristic
213Q8—61no—
214Q8—1202no—
215D4—61no—
216D4—121no—
217C2×C4—101no—
218C2×C4—121no—
219C2×C4—121no—
220C2×C4—601no—
221C2×C4D5×D1211yescharacteristic
222C8—51no—
223C8—51no—
224C8—601no—
225C8D3×Dic1011yescharacteristic
226C8#678011yescharacteristic
227C2×C3—21no—
228C2×C3#6505011yescharacteristic
229D3—81no—
230C5#6930711yescharacteristic, complemented, Sylow
231C22—121no—
232C22#9125011yescharacteristic
233C4—102no—
234C4—121no—
235C4—241no—
236C4—1201no—
237C4D5×#20411yescharacteristic
238C4#9141711yescharacteristic
239C3#1060003911yescharacteristic, complemented, Sylow
240C2—21no—
241C2—241no—
242C2#1174775811yescharacteristic
subgroupG/H
centerC2#11747758
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#476
prime radicalC5×#904C22
hypercenterM32D3×D5
hypocenterC3×C5#2230
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
2. #11748016C2semidirect
3. #11746334C2semidirect
5. C3×#64731C2semidirect
6. #11745933C2semidirect
26. #64731D3semidirect
34. C5×Dic12Q8semidirect
35. C5×D24Q8semidirect
128. Dic12Dic10semidirect
129. D24Dic10semidirect
201. C3×C5#2230semidirect
230. C5#69307semidirect
239. C3#10600039semidirect

Maximal subgroups

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

subgroupindex
#117480622
#117480162
#117463342
C5×#45182
C3×#647312
#117459332
#117459122
#106000393
#693075