Finite Group Databasebeta

← #14318184

Subgroups — #14318184

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#11748066C211yesmaximal, characteristic
2#11748027C211yesmaximal, characteristic, complemented
3#11746334C211yesmaximal, characteristic, complemented
4C5×#4511C211yesmaximal, characteristic, complemented
5C3×#64738C211yesmaximal, characteristic
6#11745937C211yesmaximal, characteristic, complemented
7#11745910C211yesmaximal, characteristic
8#10600100—31nomaximal, Hall
9C3×#4050C2211yescharacteristic
10#91469—21no—
11#91283—21no—
12C3×C5×M32C2211yescharacteristic
13#91103C2211yescharacteristic
14#91101C2211yescharacteristic
15C5×C8×Dic3C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18#90987—21no—
19#90977—21no—
20#69246—51nomaximal, Hall
21#64989—31no—
22#64969—31no—
23C5×#364—31no—
24#64738—31no—
25#64738D311yescharacteristic
26#64733—31no—
27#64733—31no—
28C3×#709—21no—
29C2×#1204—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32#6710—21no—
33C4×C5×Dic3D411yescharacteristic
34C2×C5×C3⋊C8D411yescharacteristic
35C3×C4⋊Dic5—21no—
36C3×Dic20Q811yescharacteristic, complemented
37C3×D40Q811yescharacteristic, complemented
38C3×#677—21no—
39Dic3⋊Dic5—41no—
40#6649—41no—
41D5×C3⋊C8—41no—
42C3×C5×C16—21no—
43C5×C3⋊C16—21no—
44#5196—51no—
45#4855—51no—
46C3×#360—51no—
47#4566—51no—
48#4513—51no—
49#4511D511yescharacteristic, complemented
50#4487—51no—
51#4050C2×D311yescharacteristic
52#4047—61no—
53#4015—61no—
54C5×M32—31no—
55C5×M32C2×D311yescharacteristic
56C4×C5×C8—31no—
57#3951—31no—
58#3949—31no—
59#3949—61no—
60#3949C2×D311yescharacteristic
61#3937—61no—
62#2230—151noSylow
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×Dic15—41no—
65C2×C5×Dic3—21no—
66C3×C22⋊D5—41no—
67C2×C3×Dic5—41no—
68C3×D20—21no—
69C3×C4×D5—41no—
70C3×Dic10—21no—
71#1204—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3⋊#168—41no—
75C5×C3⋊C8SD1611yescharacteristic
76C5×C3⋊C8SD1611yescharacteristic
77C3×#135—51no—
78#948—101no—
79#888—101no—
80C3×M32C2×D511yescharacteristic
81C3×#106—51no—
82#837—101no—
83#819—51no—
84#817—51no—
85C8×Dic3C2×D511yescharacteristic
86#812C2×D511yescharacteristic
87#808—101no—
88#709—21no—
89C2×Dic10—121no—
90C2×C5×C8—31no—
91C2×C5×C8C22×D311yescharacteristic
92C42×C5—31no—
93C4⋊Dic5—21no—
94C4⋊Dic5—61no—
95C4⋊Dic5—121no—
96#681—61no—
97Dic20Dic611yescharacteristic, complemented
98D40Dic611yescharacteristic, complemented
99#677—21no—
100#676—121no—
101C8×D5—121no—
102C5×C16—21no—
103C5×C16—61no—
104#498—151no—
105#443—151no—
106#365—151no—
107#365—151no—
108#364—31no—
109#360—51no—
110#360—151no—
111C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
112C2×C3×D5—41no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—81no—
116C3×Dic5—41no—
117C3×Dic5—81no—
118C5×Dic3—22no—
119C3×#41—101no—
120C2×Dic6—201no—
121C3×Q16—51no—
122C3×SD16—101no—
123C3×D8—51no—
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—101no—
126C4⋊Dic3—101no—
127Dic3⋊C4—201no—
128C4×Dic3D2011yescharacteristic
129#208—101no—
130#208—201no—
131C2×C3⋊C8—201no—
132C2×C3⋊C8D2011yescharacteristic
133C3×C16—21no—
134C3⋊C16—21no—
135C2×C4×C5—61no—
136C2×C4×C5D3×D411yescharacteristic
137C22⋊D5—41no—
138C2×Dic5—41no—
139C2×Dic5—121no—
140D20—21no—
141C4×D5—41no—
142Dic10—21no—
143Dic10—242no—
144C5×C8—31no—
145C5×C8—31no—
146C5×C8C2×Dic611yescharacteristic
147C5×C8#23711yescharacteristic
148#168—121no—
149#135—51no—
150#131—301no—
151C4⋊Q8—301no—
152M32—31no—
153M32D3×D511yescharacteristic
154#108—151no—
155#106—51no—
156#106—151no—
157#106—301no—
158#104—301no—
159C4×C8—31no—
160C2×C3×C5—21no—
161C2×C3×C5#47611yescharacteristic
162C3×D5—81no—
163C3×Q8—101no—
164C3×D4—101no—
165C3×D4—201no—
166C2×C3×C4—201no—
167C2×C3×C4—201no—
168C2×C3×C4C2×D2011yescharacteristic
169C2×Dic3—21no—
170C2×Dic3—201no—
171Dic6—402no—
172C3×C8#71111yescharacteristic
173C3×C8Q8×D511yescharacteristic
174C3⋊C8—201no—
175C3⋊C8#67711yescharacteristic
176C3⋊C8#67711yescharacteristic
177C22×C5#91111yescharacteristic
178C2×D5—41no—
179C4×C5—62no—
180C4×C5#87811yescharacteristic
181C4×C5D3×SD1611yescharacteristic
182Dic5—41no—
183Dic5—81no—
184Dic5—241no—
185#41—101no—
186C2×Q8—601no—
187Q16—51no—
188SD16—101no—
189D8—51no—
190M16—301no—
191M16—601no—
192C2×C8—31no—
193C2×C8—601no—
194C2×C8C2×D3×D511yescharacteristic
195C4⋊C4—101no—
196C4⋊C4—301no—
197C4⋊C4—601no—
198C42—31no—
199C16—21no—
200C16—61no—
201C3×C5#223011yescharacteristic, complemented, Hall
202C22×C3—201no—
203C22×C3#405411yescharacteristic
204C3×C4—201no—
205C3×C4—401no—
206C3×C4#404311yescharacteristic
207C3×C4C2×#67711yescharacteristic
208Dic3—22no—
209Dic3—401no—
210C2×C5—21no—
211C2×C5#476111yescharacteristic
212D5—81no—
213Q8—101no—
214Q8—1202no—
215D4—101no—
216D4—201no—
217C2×C4—61no—
218C2×C4—201no—
219C2×C4—201no—
220C2×C4—601no—
221C2×C4D3×D2011yescharacteristic
222C8—31no—
223C8—31no—
224C8—601no—
225C8D5×Dic611yescharacteristic
226C8#678011yescharacteristic
227C2×C3—21no—
228C2×C3—401no—
229C2×C3#6513111yescharacteristic
230C5#6924611yescharacteristic, complemented, Sylow
231C22—201no—
232C22#9125411yescharacteristic
233C4—62no—
234C4—201no—
235C4—401no—
236C4—1201no—
237C4D3×#67711yescharacteristic
238C4#9142211yescharacteristic
239C3#1060010011yescharacteristic, complemented, Sylow
240C2—21no—
241C2—401no—
242C2#1174778111yescharacteristic
subgroupG/H
centerC2#11747781
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#476
prime radicalC3×#4050C22
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. #11748027C2semidirect
3. #11746334C2semidirect
4. C5×#4511C2semidirect
6. #11745937C2semidirect
36. C3×Dic20Q8semidirect
37. C3×D40Q8semidirect
49. #4511D5semidirect
97. Dic20Dic6semidirect
98. D40Dic6semidirect
201. C3×C5#2230semidirect
230. C5#69246semidirect
239. C3#10600100semidirect

Maximal subgroups

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

subgroupindex
#117480662
#117480272
#117463342
C5×#45112
C3×#647382
#117459372
#117459102
#106001003
#692465