Finite Group Databasebeta

← #14318212

Subgroups — #14318212

Order 1920.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3×#65147C211yesmaximal, characteristic, complemented
2#11748064C211yesmaximal, characteristic
3#11746309C211yesmaximal, characteristic
4C5×#4487C211yesmaximal, characteristic, complemented
5#11745935C211yesmaximal, characteristic, complemented
6#11745930C211yesmaximal, characteristic, complemented
7#11745913C211yesmaximal, characteristic
8#10600109—31nomaximal, Hall
9#91793C2211yescharacteristic
10C3×#4036—21no—
11#91290—21no—
12C3×C5×#106C2211yescharacteristic
13#91096C2211yescharacteristic
14C5×#819C2211yescharacteristic
15C5×#812C2211yescharacteristic
16C3×#3949C2211yescharacteristic
17C3×C8×Dic5C2211yescharacteristic
18C3×#3939—21no—
19#90981—21no—
20#71358—51nomaximal, Hall
21#65184—31no—
22#65147D311yescharacteristic, complemented
23C5×#365—31no—
24#64738—31no—
25#64731—31no—
26#64714—31no—
27#64708—31no—
28#6817—21no—
29C2×C3×C5×C8C2311yescharacteristic
30C3×C5×C4⋊C4—21no—
31Dic60Q811yescharacteristic
32D120Q811yescharacteristic
33#6706—21no—
34C5×#208—21no—
35C3×C4⋊Dic5—21no—
36C3×C4⋊Dic5—41no—
37C3×#683—41no—
38C3×C4×Dic5D411yescharacteristic
39C2×C3×#168D411yescharacteristic
40#6651—41no—
41#6648—41no—
42C3⋊#672—21no—
43C5×C3⋊C16—21no—
44C3×#499—51no—
45#4700—51no—
46#4488—51no—
47#4488—51no—
48#4487—51no—
49#4487D511yescharacteristic, complemented
50#4463—51no—
51#4053—61no—
52#4050—31no—
53#4036—21no—
54C5×M32—31no—
55C5×#108—31no—
56C5×#106C2×D311yescharacteristic
57#3957—61no—
58#3949C2×D311yescharacteristic
59C8×Dic5C2×D311yescharacteristic
60#3944—31no—
61#3939—21no—
62#2231—151noSylow
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65#1220—41no—
66D60—21no—
67C4×D15—41no—
68Dic30—21no—
69C2×C3×Dic5—21no—
70C2×C3×Dic5—41no—
71C3×C5×C8C2×Q811yescharacteristic
72C3×C5×C8#4111yescharacteristic
73C3×#168SD1611yescharacteristic
74C3×#168SD1611yescharacteristic
75C5×C3⋊C8—41no—
76C3×#125—101no—
77#904—51no—
78#901—101no—
79C3×#107—101no—
80C3×#106—51no—
81C3×#106C2×D511yescharacteristic
82C3×C4×C8—51no—
83#819C2×D511yescharacteristic
84#812—51no—
85#812C2×D511yescharacteristic
86#805—101no—
87#709—61no—
88C5×M16—61no—
89C2×C5×C8C22×D311yescharacteristic
90C5×C4⋊C4—21no—
91C4⋊Dic5—21no—
92C4⋊Dic5—41no—
93#683—41no—
94C4×Dic5#6711yescharacteristic
95C2×#168#6711yescharacteristic
96Dic20—31no—
97D40—31no—
98#677—61no—
99#676—121no—
100C8×D5—121no—
101C5×C16—61no—
102#672—61no—
103#499—51no—
104#443—151no—
105#365—31no—
106#365—151no—
107#364—151no—
108#360—151no—
109#360—151no—
110C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
111C2×D15—41no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—41no—
116C3×Dic5—41no—
117C3×Dic5—81no—
118#235—101no—
119C2×C3×C8—51no—
120C2×C3×C8C22×D511yescharacteristic
121C3×C4⋊C4—21no—
122C3×C4⋊C4—101no—
123C3×C4⋊C4—201no—
124C3×C4⋊C4—201no—
125C3×C42—51no—
126#208—21no—
127Dic12—51no—
128D24—51no—
129#204—101no—
130ΓL(1,𝔽25)—201no—
131D3×C8—201no—
132C3⋊C16—21no—
133C3⋊C16—101no—
134C2×C4×C5—41no—
135C2×C4×C5C2×#6711yescharacteristic
136C22⋊D5—121no—
137C2×Dic5—21no—
138C2×Dic5—41no—
139D20—61no—
140C4×D5—121no—
141Dic10—61no—
142C5×C8—121no—
143C5×C8D3×Q811yescharacteristic
144C5×C8#23911yescharacteristic
145#168#21511yescharacteristic
146#168#21511yescharacteristic
147#135—151no—
148#131—301no—
149#125—101no—
150M32—31no—
151M32—151no—
152#108—31no—
153#107—101no—
154#106—51no—
155#106D3×D511yescharacteristic
156#104—301no—
157C4×C8—51no—
158C2×C3×C5—21no—
159C2×C3×C5#47611yescharacteristic
160D15—81no—
161C2×C3×C4—41no—
162C2×C3×C4—101no—
163C2×C3×C4—201no—
164C2×C3×C4D4×D511yescharacteristic
165#67—201no—
166D12—101no—
167C4×D3—201no—
168Dic6—101no—
169C3×C8—51no—
170C3×C8—51no—
171C3×C8#70911yescharacteristic
172C3×C8Q8×D511yescharacteristic
173C3⋊C8—41no—
174C22×C5#93211yescharacteristic
175C2×D5—121no—
176C4×C5—81no—
177C4×C5C2×#21511yescharacteristic
178C4×C5#94611yescharacteristic
179Dic5—41no—
180Dic5—81no—
181Dic5—121no—
182#41—301no—
183Q16—151no—
184SD16—301no—
185D8—151no—
186M16—61no—
187M16—601no—
188C2×C8—51no—
189C2×C8—601no—
190C2×C8C2×D3×D511yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—101no—
193C4⋊C4—201no—
194C4⋊C4—201no—
195C42—51no—
196C16—61no—
197C16—301no—
198C3×C5#223111yescharacteristic, complemented, Hall
199C22×C3#406011yescharacteristic
200C2×D3—201no—
201C3×C4—81no—
202C3×C4—201no—
203C3×C4—401no—
204C3×C4#404211yescharacteristic
205C3×C4D5×SD1611yescharacteristic
206Dic3—201no—
207C2×C5—21no—
208C2×C5#508411yescharacteristic
209D5—241no—
210Q8—301no—
211D4—301no—
212D4—601no—
213C2×C4—41no—
214C2×C4—101no—
215C2×C4—201no—
216C2×C4—601no—
217C2×C4D5×#6711yescharacteristic
218C8—51no—
219C8—51no—
220C8—121no—
221C8#676911yescharacteristic
222C8D15⋊Q811yescharacteristic
223C2×C3—21no—
224C2×C3#6515911yescharacteristic
225D3—401no—
226C5#7135811yescharacteristic, complemented, Sylow
227C22—601no—
228C22#9149111yescharacteristic
229C4—81no—
230C4—201no—
231C4—401no—
232C4—601no—
233C4#9141111yescharacteristic
234C4D5×#21511yescharacteristic
235C3#1060010911yescharacteristic, complemented, Sylow
236C2—21no—
237C2—1201no—
238C2#1174724011yescharacteristic
subgroupG/H
centerC2#11747240
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#476
prime radical#91793C22
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. C3×#65147C2semidirect
4. C5×#4487C2semidirect
5. #11745935C2semidirect
6. #11745930C2semidirect
22. #65147D3semidirect
49. #4487D5semidirect
198. C3×C5#2231semidirect
226. C5#71358semidirect
235. C3#10600109semidirect

Maximal subgroups

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

subgroupindex
C3×#651472
#117480642
#117463092
C5×#44872
#117459352
#117459302
#117459132
#106001093
#713585