Finite Group Databasebeta

← C22×C5⋊(#127⋊C3) #14513974

Subgroups — C22×C5⋊(#127⋊C3) #14513974

Order 1920.

1160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C22×C5×C42⋊C3C211yesmaximal, characteristic, complemented
2C2×C5⋊(#127⋊C3)C216yesmaximal, direct product factor
3C22×#4020C311yesmaximal, characteristic, complemented, Hall
4C22×D5×A4—41nomaximal
5C2×C5×C42⋊C3C2213yescomplemented
6C5⋊(#127⋊C3)C2214yesdirect product factor
7C22×#127⋊C3—51nomaximal, Hall
8C23×D20—31no—
9C23×D20—31no—
10C22×C42×C5C2×C311yescharacteristic, complemented
11C2×#4020—36no—
12C2×#4020C2×C316yescomplemented
13C22×C5×A4—41no—
14C2×D5×A4—46no—
15C5×C42⋊C3C2311yescharacteristic, complemented
16C2×#127⋊C3—56no—
17C22×C42⋊C3D511yescharacteristic, complemented
18C24×D5—31no—
19C24×D5A411yescharacteristic
20C23×C4×C5—31no—
21C22×D20—36no—
22C22×D20—36no—
23C22×D20—36no—
24C22×D20—36no—
25C22×D20—62no—
26C22×D20—66no—
27C22×D20—62no—
28C22×D20—66no—
29C2×C42×C5—33no—
30C2×C42×C5C22×C313yescomplemented
31#4020—312no—
32#4020—38no—
33#4020C22×C314yescomplemented
34C22×#127—51noSylow
35C22×C3×D5—161no—
36C2×C5×A4—43no—
37D5×A4—44no—
38C23×A4—201no—
39#127⋊C3—54no—
40C2×C42⋊C3C2×D513yescomplemented
41C24×C5C2×A411yescharacteristic
42C23×D5—36no—
43C23×D5—61no—
44C23×D5—66no—
45C23×D5—63no—
46C23×D5—61no—
47C23×D5—62no—
48C23×D5—63no—
49C23×D5C2×A416yes—
50C22×C4×C5—36no—
51C22×C4×C5—32no—
52C22×C4×C5—33no—
53C22×C4×C5—33no—
54C2×D20—34no—
55C2×D20—312no—
56C2×D20—312no—
57C2×D20—34no—
58C2×D20—612no—
59C2×D20—612no—
60C2×D20—612no—
61C2×D20—612no—
62C2×D20—612no—
63C2×D20—612no—
64C2×D20—612no—
65C2×D20—612no—
66C42×C5—33no—
67C42×C5—32no—
68C42×C5C23×C311yescharacteristic, complemented
69C23×D4—151no—
70C23×D4—151no—
71C2×#127—56no—
72C2×#127—156no—
73C22×C42C3×D511yescharacteristic, complemented
74C22×C3×C5—161no—
75C2×C3×D5—166no—
76C5×A4—41no—
77C22×A4—41no—
78C22×A4—206no—
79C42⋊C3C22×D511yescharacteristic, complemented
80C23×C5—33no—
81C23×C5—31no—
82C23×C5C22×A413yes—
83C22×D5—34no—
84C22×D5—41no—
85C22×D5—66no—
86C22×D5—612no—
87C22×D5—66no—
88C22×D5—66no—
89C22×D5—612no—
90C22×D5—66no—
91C22×D5—123no—
92C22×D5—122no—
93C22×D5—126no—
94C22×D5—123no—
95C22×D5—126no—
96C22×D5—121no—
97C22×D5C22×A414yes—
98C2×C4×C5—36no—
99C2×C4×C5—36no—
100C2×C4×C5—36no—
101C2×C4×C5—36no—
102C2×C4×C5—31no—
103C2×C4×C5—33no—
104D20—624no—
105D20—68no—
106D20—68no—
107D20—624no—
108C25—51no—
109C25—151no—
110C22×D4—156no—
111C22×D4—156no—
112C22×D4—156no—
113C22×D4—156no—
114C22×D4—302no—
115C22×D4—306no—
116C22×D4—306no—
117C22×D4—302no—
118C23×C4—31no—
119#127—54no—
120#127—1512no—
121#127—158no—
122C2×C42—33no—
123C2×C42C2×C3×D513yescomplemented
124C2×C3×C5—163no—
125C3×D5—164no—
126C23×C3—801no—
127C2×A4—43no—
128C2×A4—204no—
129C22×C5—33no—
130C22×C5—32no—
131C22×C5—33no—
132C22×C5—33no—
133C22×C5#127⋊C311yescharacteristic, complemented
134C22×C5C23×A411yescharacteristic
135C2×D5—46no—
136C2×D5—64no—
137C2×D5—64no—
138C2×D5—68no—
139C2×D5—126no—
140C2×D5—126no—
141C2×D5—1212no—
142C2×D5—126no—
143C4×C5—32no—
144C4×C5—36no—
145C24—56no—
146C24—156no—
147C24—301no—
148C24—303no—
149C24—303no—
150C24—306no—
151C24—301no—
152C24—302no—
153C24D5×A411yescharacteristic
154C2×D4—154no—
155C2×D4—1512no—
156C2×D4—154no—
157C2×D4—1512no—
158C2×D4—3012no—
159C2×D4—3012no—
160C2×D4—3012no—
161C2×D4—3012no—
162C2×D4—3012no—
163C2×D4—3012no—
164C2×D4—3012no—
165C2×D4—3012no—
166C22×C4—36no—
167C22×C4—32no—
168C22×C4—33no—
169C22×C4—33no—
170C42—33no—
171C42—32no—
172C42C22×C3×D511yescharacteristic, complemented
173C3×C5—161noHall
174C22×C3—161no—
175C22×C3—806no—
176A4—41no—
177C2×C5—31no—
178C2×C5—33no—
179C2×C5C2×#127⋊C313yescomplemented
180D5—44no—
181D5—124no—
182C23—33no—
183C23—31no—
184C23—54no—
185C23—154no—
186C23—201no—
187C23—306no—
188C23—306no—
189C23—306no—
190C23—3012no—
191C23—306no—
192C23—3012no—
193C23—603no—
194C23—602no—
195C23—606no—
196C23—606no—
197C23—603no—
198C23—601no—
199C23C2×D5×A413yes—
200D4—308no—
201D4—3024no—
202D4—308no—
203D4—3024no—
204C2×C4—36no—
205C2×C4—36no—
206C2×C4—36no—
207C2×C4—36no—
208C2×C4—31no—
209C2×C4—33no—
210C2×C3—163no—
211C2×C3—804no—
212C5C22×#127⋊C311yescharacteristic, complemented, Sylow
213C22—33no—
214C22—32no—
215C22—33no—
216C22—33no—
217C22—206no—
218C22—304no—
219C22—304no—
220C22—308no—
221C22—606no—
222C22—6012no—
223C22—606no—
224C22—606no—
225C22C5⋊(#127⋊C3)11yescharacteristic, direct product factor
226C22C22×D5×A411yescharacteristic
227C4—32no—
228C4—36no—
229C3—161noSylow
230C2—31no—
231C2—33no—
232C2—204no—
233C2—604no—
234C2C2×C5⋊(#127⋊C3)13yesdirect product factor
subgroupG/H
center, hypercenterC22C5⋊(#127⋊C3)
commutator, cosocle, hypocenterC42×C5C23×C3
FrattiniC22C22×D5×A4
FittingC22×C42×C5C2×C3
socleC24×C5C2×A4
LCSG ▷ C42×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C5×C42⋊C3C2semidirect
2. C2×C5⋊(#127⋊C3)C2direct (N × H)
3. C22×#4020C3semidirect
5. C2×C5×C42⋊C3C22semidirect
6. C5⋊(#127⋊C3)C22direct (N × H)
10. C22×C42×C5C2×C3semidirect
12. C2×#4020C2×C3semidirect
15. C5×C42⋊C3C23semidirect
17. C22×C42⋊C3D5semidirect
30. C2×C42×C5C22×C3semidirect
33. #4020C22×C3semidirect
40. C2×C42⋊C3C2×D5semidirect
68. C42×C5C23×C3semidirect
73. C22×C42C3×D5semidirect
79. C42⋊C3C22×D5semidirect
123. C2×C42C2×C3×D5semidirect
133. C22×C5#127⋊C3semidirect
172. C42C22×C3×D5semidirect
179. C2×C5C2×#127⋊C3semidirect
212. C5C22×#127⋊C3semidirect
225. C22C5⋊(#127⋊C3)direct (N × H)
234. C2C2×C5⋊(#127⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C42⋊C32
C2×C5⋊(#127⋊C3)2
C22×#40203
C22×D5×A44
C22×#127⋊C35