Finite Group Databasebeta

← #14318209

Subgroups — #14318209

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
1C5×#4858C211yesmaximal, characteristic, complemented
2#11748068C211yesmaximal, characteristic
3#11746309C211yesmaximal, characteristic
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745936C211yesmaximal, characteristic, complemented
6#11745932C211yesmaximal, characteristic, complemented
7#11745914C211yesmaximal, characteristic
8#10602151—31nomaximal, Hall
9#91793C2211yescharacteristic
10C5×#890—21no—
11#91291—21no—
12C3×C5×#106C2211yescharacteristic
13#91096C2211yescharacteristic
14C5×#817C2211yescharacteristic
15C5×C8×Dic3C2211yescharacteristic
16C5×#807—21no—
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90980—21no—
20#69316—51nomaximal, Hall
21C5×#499—31no—
22#64989—31no—
23#64708—31no—
24#64708—31no—
25#64707—31no—
26#64707D311yescharacteristic, complemented
27#64683—31no—
28#6817—21no—
29C2×C3×C5×C8C2311yescharacteristic
30C3×C5×C4⋊C4—21no—
31Dic60Q811yescharacteristic
32D120Q811yescharacteristic
33#6706—21no—
34C5×C4⋊Dic3—21no—
35C5×C4⋊Dic3—41no—
36C5×Dic3⋊C4—41no—
37C4×C5×Dic3D411yescharacteristic
38C2×C5×C3⋊C8D411yescharacteristic
39C3×#681—21no—
40#6651—41no—
41#6648—41no—
42C3⋊#672—21no—
43C3×#672—21no—
44#4895—51no—
45#4858D511yescharacteristic, complemented
46C3×#365—51no—
47#4518—51no—
48#4511—51no—
49#4494—51no—
50#4488—51no—
51C5×#125—61no—
52#4050—31no—
53#4047—61no—
54C5×#107—61no—
55C5×#106—31no—
56C5×#106C2×D311yescharacteristic
57C4×C5×C8—31no—
58#3951C2×D311yescharacteristic
59#3944—31no—
60#3944C2×D311yescharacteristic
61#3937—61no—
62#2231—151noSylow
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65#1220—41no—
66D60—21no—
67C4×D15—41no—
68Dic30—21no—
69C2×C5×Dic3—21no—
70C2×C5×Dic3—41no—
71C3×C5×C8C2×Q811yescharacteristic
72C3×C5×C8#4111yescharacteristic
73C3×#168—41no—
74C5×C3⋊C8SD1611yescharacteristic
75C5×C3⋊C8SD1611yescharacteristic
76#907—101no—
77#904—51no—
78#890—21no—
79C3×M32—51no—
80C3×#108—51no—
81C3×#106C2×D511yescharacteristic
82#825—101no—
83#817C2×D511yescharacteristic
84C8×Dic3C2×D511yescharacteristic
85#812—51no—
86#807—21no—
87#709—61no—
88C2×C5×C8—31no—
89C2×C5×C8C22×D311yescharacteristic
90C5×C4⋊C4—21no—
91C5×C4⋊C4—61no—
92C5×C4⋊C4—121no—
93C5×C4⋊C4—121no—
94C42×C5—31no—
95#681—21no—
96Dic20—31no—
97D40—31no—
98#677—61no—
99#676—121no—
100C8×D5—121no—
101#672—21no—
102#672—61no—
103#499—31no—
104#443—151no—
105#365—51no—
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—
116C5×Dic3—41no—
117C5×Dic3—81no—
118#235—101no—
119C3×M16—101no—
120C2×C3×C8C22×D511yescharacteristic
121C3×C4⋊C4—21no—
122C4⋊Dic3—21no—
123C4⋊Dic3—41no—
124Dic3⋊C4—41no—
125C4×Dic3C22⋊D511yescharacteristic
126C2×C3⋊C8C22⋊D511yescharacteristic
127Dic12—51no—
128D24—51no—
129#204—101no—
130ΓL(1,𝔽25)—201no—
131D3×C8—201no—
132C3×C16—101no—
133C3⋊C16—101no—
134C2×C4×C5—41no—
135C2×C4×C5—61no—
136C2×C4×C5—121no—
137C2×C4×C5D3×D411yescharacteristic
138C22⋊D5—121no—
139D20—61no—
140C4×D5—121no—
141Dic10—61no—
142C5×C8—31no—
143C5×C8—31no—
144C5×C8#23511yescharacteristic
145C5×C8D3×Q811yescharacteristic
146#168—41no—
147#135—151no—
148#131—301no—
149#125—61no—
150M32—51no—
151M32—151no—
152#108—51no—
153#107—61no—
154#106—31no—
155#106D3×D511yescharacteristic
156#104—301no—
157C4×C8—31no—
158C2×C3×C5—21no—
159C2×C3×C5#47611yescharacteristic
160D15—81no—
161C2×C3×C4—41no—
162C2×C3×C4C2×C22⋊D511yescharacteristic
163#67—201no—
164C2×Dic3—21no—
165C2×Dic3—41no—
166D12—101no—
167C4×D3—201no—
168Dic6—101no—
169C3×C8—201no—
170C3×C8Q8×D511yescharacteristic
171C3×C8#71311yescharacteristic
172C3⋊C8#68811yescharacteristic
173C3⋊C8#68811yescharacteristic
174C22×C5#91411yescharacteristic
175C2×D5—121no—
176C4×C5—81no—
177C4×C5—121no—
178C4×C5—241no—
179C4×C5#89611yescharacteristic
180C4×C5D3×SD1611yescharacteristic
181Dic5—121no—
182#41—301no—
183Q16—151no—
184SD16—301no—
185D8—151no—
186M16—101no—
187M16—601no—
188C2×C8—31no—
189C2×C8—601no—
190C2×C8C2×D3×D511yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—61no—
193C4⋊C4—121no—
194C4⋊C4—121no—
195C42—31no—
196C16—101no—
197C16—301no—
198C3×C5#223111yescharacteristic, complemented, Hall
199C22×C3#407811yescharacteristic
200C2×D3—201no—
201C3×C4—81no—
202C3×C4C2×#68811yescharacteristic
203C3×C4#409211yescharacteristic
204Dic3—41no—
205Dic3—81no—
206Dic3—201no—
207C2×C5—21no—
208C2×C5#487011yescharacteristic
209D5—241no—
210Q8—301no—
211D4—301no—
212D4—601no—
213C2×C4—41no—
214C2×C4—61no—
215C2×C4—121no—
216C2×C4—601no—
217C2×C4D3×C22⋊D511yescharacteristic
218C8—31no—
219C8—31no—
220C8—201no—
221C8D15⋊Q811yescharacteristic
222C8#677311yescharacteristic
223C2×C3—21no—
224C2×C3#6537311yescharacteristic
225D3—401no—
226C5#6931611yescharacteristic, complemented, Sylow
227C22—601no—
228C22#9149611yescharacteristic
229C4—81no—
230C4—121no—
231C4—241no—
232C4—601no—
233C4#9142411yescharacteristic
234C4D3×#68811yescharacteristic
235C3#1060215111yescharacteristic, complemented, Sylow
236C2—21no—
237C2—1201no—
238C2#1174724811yescharacteristic
subgroupG/H
centerC2#11747248
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. C5×#4858C2semidirect
4. C3×#64707C2semidirect
5. #11745936C2semidirect
6. #11745932C2semidirect
26. #64707D3semidirect
45. #4858D5semidirect
198. C3×C5#2231semidirect
226. C5#69316semidirect
235. C3#10602151semidirect

Maximal subgroups

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

subgroupindex
C5×#48582
#117480682
#117463092
C3×#647072
#117459362
#117459322
#117459142
#106021513
#693165