Finite Group Databasebeta

← C5×C4⋊(#127⋊C3) #14510945

Subgroups — C5×C4⋊(#127⋊C3) #14510945

Order 1920.

504 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C2×C5×#127⋊C3C212yesmaximal, complemented
2C4×C5×C42⋊C3C211yesmaximal, characteristic, complemented
3C5×#2867C311yesmaximal, characteristic, complemented, Hall
4C5×D4×A4—41nomaximal
5C5×#127⋊C3—22no—
6C2×C5×C42⋊C3C2211yescharacteristic
7C4⋊(#127⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
8C2×C5×#127—32no—
9C2×C5×#127—31no—
10C2×C5×#127—31no—
11C2×C5×#127C2×C312yescomplemented
12C43×C5C2×C311yescharacteristic, complemented
13C22×C5×A4—42no—
14C4×C5×A4—41no—
15C5×C42⋊C3D411yescharacteristic, complemented
16C2×#127⋊C3C2×C512yescomplemented
17C4×C42⋊C3C2×C511yescharacteristic, complemented
18C22×C5×D4—32no—
19C22×C5×D4—32no—
20C22×C5×D4—32no—
21C22×C5×D4—32no—
22C22×C5×D4—31no—
23C22×C5×D4A411yescharacteristic
24C5×#127—22no—
25C5×#127—62no—
26C5×#127—62no—
27C5×#127—68no—
28C5×#127—62no—
29C5×#127—62no—
30C5×#127—62no—
31C2×C42×C5—31no—
32C2×C42×C5—31no—
33C2×C42×C5C22×C311yescharacteristic
34#2867C3×C511yescharacteristic, complemented, Sylow
35C2×C5×A4—41no—
36C2×C5×A4—82no—
37C3×C5×D4—161no—
38D4×A4—41no—
39#127⋊C3—22no—
40C2×C42⋊C3C22×C511yescharacteristic
41C24×C5—32no—
42C24×C5C2×A412yes—
43C2×C5×D4—61no—
44C2×C5×D4—62no—
45C2×C5×D4—62no—
46C2×C5×D4—62no—
47C2×C5×D4—62no—
48C2×C5×D4—64no—
49C2×C5×D4—64no—
50C2×C5×D4—68no—
51C2×C5×D4—64no—
52C2×C5×D4—64no—
53C2×C5×D4—64no—
54C2×C5×D4—68no—
55C2×C5×D4—64no—
56C2×C5×D4—61no—
57C2×C5×D4—62no—
58C2×C5×D4—62no—
59C2×C5×D4—61no—
60C2×C5×D4—61no—
61C22×C4×C5—31no—
62C22×C4×C5—31no—
63C22×C4×C5C2×A411yescharacteristic
64C42×C5—31no—
65C42×C5—34no—
66C42×C5—32no—
67C42×C5—32no—
68C42×C5C3×D411yescharacteristic, complemented
69C2×#127—32no—
70C2×#127—31no—
71C2×#127—31no—
72C2×#127C2×C3×C512yescomplemented
73C43C2×C3×C511yescharacteristic, complemented
74C22×C3×C5—162no—
75C5×A4—41no—
76C3×C4×C5—161no—
77C22×A4—42no—
78C4×A4—41no—
79C42⋊C3C5×D411yescharacteristic, complemented
80C23×C5—22no—
81C23×C5—62no—
82C23×C5—62no—
83C23×C5—64no—
84C23×C5—62no—
85C23×C5—62no—
86C23×C5—64no—
87C23×C5—62no—
88C23×C5C22×A411yescharacteristic
89C5×D4—41no—
90C5×D4—121no—
91C5×D4—124no—
92C5×D4—124no—
93C5×D4—128no—
94C5×D4—124no—
95C5×D4—124no—
96C5×D4—128no—
97C5×D4—121no—
98C5×D4—122no—
99C5×D4—121no—
100C2×C4×C5—32no—
101C2×C4×C5—34no—
102C2×C4×C5—32no—
103C2×C4×C5—32no—
104C2×C4×C5—31no—
105C2×C4×C5—31no—
106C2×C4×C5—31no—
107C2×C4×C5—31no—
108C22×D4—32no—
109C22×D4—32no—
110C22×D4—32no—
111C22×D4—32no—
112C22×D4—31no—
113C22×D4C5×A411yescharacteristic
114#127—22no—
115#127—62no—
116#127—62no—
117#127—68no—
118#127—62no—
119#127—62no—
120#127—62no—
121C2×C42—31no—
122C2×C42—31no—
123C2×C42C22×C3×C511yescharacteristic
124C2×C3×C5—161no—
125C2×C3×C5—322no—
126C2×A4—41no—
127C2×A4—82no—
128C3×D4—161no—
129C22×C5—31no—
130C22×C5—31no—
131C22×C5—42no—
132C22×C5—122no—
133C22×C5—122no—
134C22×C5—122no—
135C22×C5—124no—
136C22×C5—122no—
137C22×C5—124no—
138C22×C5—122no—
139C22×C5D4×A411yescharacteristic
140C4×C5—34no—
141C4×C5—32no—
142C4×C5—32no—
143C4×C5—31no—
144C4×C5#127⋊C311yescharacteristic, complemented
145C24—32no—
146C24C2×C5×A412yes—
147C2×D4—61no—
148C2×D4—62no—
149C2×D4—62no—
150C2×D4—62no—
151C2×D4—62no—
152C2×D4—64no—
153C2×D4—64no—
154C2×D4—64no—
155C2×D4—68no—
156C2×D4—64no—
157C2×D4—64no—
158C2×D4—68no—
159C2×D4—64no—
160C2×D4—61no—
161C2×D4—62no—
162C2×D4—62no—
163C2×D4—61no—
164C2×D4—61no—
165C22×C4—31no—
166C22×C4—31no—
167C22×C4C2×C5×A411yescharacteristic
168C42—31no—
169C42—34no—
170C42—32no—
171C42—32no—
172C42C3×C5×D411yescharacteristic, complemented
173C3×C5—161noHall
174C22×C3—162no—
175A4—41no—
176C3×C4—161no—
177C2×C5—31no—
178C2×C5—31no—
179C2×C5—82no—
180C2×C5—242no—
181C2×C5C2×#127⋊C311yescharacteristic
182C23—22no—
183C23—62no—
184C23—62no—
185C23—62no—
186C23—64no—
187C23—62no—
188C23—64no—
189C23—62no—
190C23C22×C5×A411yescharacteristic
191D4—41no—
192D4—121no—
193D4—124no—
194D4—124no—
195D4—128no—
196D4—124no—
197D4—124no—
198D4—128no—
199D4—121no—
200D4—122no—
201D4—121no—
202C2×C4—32no—
203C2×C4—34no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—31no—
210C2×C3—161no—
211C2×C3—322no—
212C5C4⋊(#127⋊C3)11yescharacteristic, direct product factor, Sylow
213C22—31no—
214C22—31no—
215C22—42no—
216C22—122no—
217C22—122no—
218C22—122no—
219C22—124no—
220C22—122no—
221C22—124no—
222C22—122no—
223C22C5×D4×A411yescharacteristic
224C4—32no—
225C4—32no—
226C4—34no—
227C4—31no—
228C4C5×#127⋊C311yescharacteristic, complemented
229C3—161noSylow
230C2—31no—
231C2—31no—
232C2—82no—
233C2—242no—
234C2C2×C5×#127⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#127⋊C3
commutator, cosocleC2×C42C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2867C3
socleC23×C5C22×A4
hypercenterC4×C5#127⋊C3
hypocenterC42C3×C5×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C5 ◁ C4×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×#127⋊C3C2semidirect
2. C4×C5×C42⋊C3C2semidirect
3. C5×#2867C3semidirect
7. C4⋊(#127⋊C3)C5direct (N × H)
11. C2×C5×#127C2×C3semidirect
12. C43×C5C2×C3semidirect
15. C5×C42⋊C3D4semidirect
16. C2×#127⋊C3C2×C5semidirect
17. C4×C42⋊C3C2×C5semidirect
34. #2867C3×C5semidirect
68. C42×C5C3×D4semidirect
72. C2×#127C2×C3×C5semidirect
73. C43C2×C3×C5semidirect
79. C42⋊C3C5×D4semidirect
144. C4×C5#127⋊C3semidirect
172. C42C3×C5×D4semidirect
212. C5C4⋊(#127⋊C3)direct (N × H)
228. C4C5×#127⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#127⋊C32
C4×C5×C42⋊C32
C5×#28673
C5×D4×A44
C4⋊(#127⋊C3)5