Finite Group Databasebeta

← C22×C5×#127⋊C3 #14511329

Subgroups — C22×C5×#127⋊C3 #14511329

Order 1920.

1160 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 106 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⋊C3C216yesmaximal, direct product factor
2C22×C5×C42⋊C3C211yesmaximal, characteristic, complemented
3C22×C5×#127C311yesmaximal, characteristic, complemented, Hall
4C23×C5×A4—41nomaximal
5C5×#127⋊C3C2214yesdirect product factor
6C2×C5×C42⋊C3C2213yescomplemented
7C22×#127⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C23×C5×D4—31no—
9C23×C5×D4—31no—
10C2×C5×#127—36no—
11C2×C5×#127C2×C316yescomplemented
12C22×C42×C5C2×C311yescharacteristic, complemented
13C22×C5×A4—41no—
14C22×C5×A4—46no—
15C5×C42⋊C3C2311yescharacteristic, complemented
16C2×#127⋊C3C2×C516yesdirect product factor
17C22×C42⋊C3C2×C511yescharacteristic, complemented
18C25×C5—31no—
19C25×C5A411yescharacteristic
20C22×C5×D4—36no—
21C22×C5×D4—36no—
22C22×C5×D4—36no—
23C22×C5×D4—36no—
24C22×C5×D4—62no—
25C22×C5×D4—66no—
26C22×C5×D4—66no—
27C22×C5×D4—62no—
28C23×C4×C5—31no—
29C5×#127—312no—
30C5×#127—38no—
31C5×#127C22×C314yescomplemented
32C2×C42×C5—33no—
33C2×C42×C5C22×C313yescomplemented
34C22×#127C3×C511yescharacteristic, complemented, Sylow
35C23×C3×C5—161no—
36C2×C5×A4—43no—
37C2×C5×A4—44no—
38C23×A4—41no—
39#127⋊C3C22×C514yesdirect product factor
40C2×C42⋊C3C22×C513yescomplemented
41C24×C5—36no—
42C24×C5—61no—
43C24×C5—63no—
44C24×C5—63no—
45C24×C5—66no—
46C24×C5—61no—
47C24×C5—62no—
48C24×C5C2×A411yescharacteristic
49C24×C5C2×A416yes—
50C2×C5×D4—34no—
51C2×C5×D4—312no—
52C2×C5×D4—34no—
53C2×C5×D4—312no—
54C2×C5×D4—612no—
55C2×C5×D4—612no—
56C2×C5×D4—612no—
57C2×C5×D4—612no—
58C2×C5×D4—612no—
59C2×C5×D4—612no—
60C2×C5×D4—612no—
61C2×C5×D4—612no—
62C22×C4×C5—36no—
63C22×C4×C5—32no—
64C22×C4×C5—33no—
65C22×C4×C5—33no—
66C42×C5—33no—
67C42×C5—32no—
68C42×C5C23×C311yescharacteristic, complemented
69C23×D4—31no—
70C23×D4—31no—
71C2×#127—36no—
72C2×#127C2×C3×C516yescomplemented
73C22×C42C2×C3×C511yescharacteristic, complemented
74C22×C3×C5—166no—
75C22×C3×C5—161no—
76C5×A4—41no—
77C22×A4—41no—
78C22×A4—46no—
79C42⋊C3C23×C511yescharacteristic, complemented
80C23×C5—33no—
81C23×C5—31no—
82C23×C5—34no—
83C23×C5—41no—
84C23×C5—66no—
85C23×C5—66no—
86C23×C5—66no—
87C23×C5—612no—
88C23×C5—66no—
89C23×C5—612no—
90C23×C5—123no—
91C23×C5—122no—
92C23×C5—126no—
93C23×C5—126no—
94C23×C5—123no—
95C23×C5—121no—
96C23×C5C22×A413yes—
97C23×C5C22×A414yes—
98C5×D4—68no—
99C5×D4—624no—
100C5×D4—68no—
101C5×D4—624no—
102C2×C4×C5—36no—
103C2×C4×C5—36no—
104C2×C4×C5—36no—
105C2×C4×C5—36no—
106C2×C4×C5—31no—
107C2×C4×C5—33no—
108C25—31no—
109C25C5×A411yescharacteristic
110C22×D4—36no—
111C22×D4—36no—
112C22×D4—36no—
113C22×D4—36no—
114C22×D4—62no—
115C22×D4—66no—
116C22×D4—66no—
117C22×D4—62no—
118C23×C4—31no—
119#127—312no—
120#127—38no—
121#127C22×C3×C514yescomplemented
122C2×C42—33no—
123C2×C42C22×C3×C513yescomplemented
124C2×C3×C5—164no—
125C2×C3×C5—163no—
126C23×C3—161no—
127C2×A4—43no—
128C2×A4—44no—
129C22×C5—33no—
130C22×C5—32no—
131C22×C5—33no—
132C22×C5—33no—
133C22×C5—46no—
134C22×C5—64no—
135C22×C5—64no—
136C22×C5—68no—
137C22×C5—126no—
138C22×C5—1212no—
139C22×C5—126no—
140C22×C5—126no—
141C22×C5#127⋊C311yescharacteristic, direct product factor
142C22×C5C23×A411yescharacteristic
143C4×C5—32no—
144C4×C5—36no—
145C24—36no—
146C24—61no—
147C24—63no—
148C24—63no—
149C24—66no—
150C24—61no—
151C24—62no—
152C24C2×C5×A411yescharacteristic
153C24C2×C5×A416yes—
154C2×D4—34no—
155C2×D4—312no—
156C2×D4—34no—
157C2×D4—312no—
158C2×D4—612no—
159C2×D4—612no—
160C2×D4—612no—
161C2×D4—612no—
162C2×D4—612no—
163C2×D4—612no—
164C2×D4—612no—
165C2×D4—612no—
166C22×C4—36no—
167C22×C4—32no—
168C22×C4—33no—
169C22×C4—33no—
170C42—33no—
171C42—32no—
172C42C23×C3×C511yescharacteristic, complemented
173C3×C5—161noHall
174C22×C3—166no—
175C22×C3—161no—
176A4—41no—
177C2×C5—31no—
178C2×C5—33no—
179C2×C5—44no—
180C2×C5—124no—
181C2×C5C2×#127⋊C313yesdirect product factor
182C23—33no—
183C23—31no—
184C23—34no—
185C23—41no—
186C23—66no—
187C23—66no—
188C23—66no—
189C23—612no—
190C23—66no—
191C23—612no—
192C23—123no—
193C23—122no—
194C23—126no—
195C23—126no—
196C23—123no—
197C23—121no—
198C23C22×C5×A413yes—
199C23C22×C5×A414yes—
200D4—68no—
201D4—624no—
202D4—68no—
203D4—624no—
204C2×C4—36no—
205C2×C4—36no—
206C2×C4—36no—
207C2×C4—36no—
208C2×C4—31no—
209C2×C4—33no—
210C2×C3—164no—
211C2×C3—163no—
212C5C22×#127⋊C311yescharacteristic, direct product factor, Sylow
213C22—33no—
214C22—32no—
215C22—33no—
216C22—33no—
217C22—46no—
218C22—64no—
219C22—64no—
220C22—68no—
221C22—126no—
222C22—1212no—
223C22—126no—
224C22—126no—
225C22C5×#127⋊C311yescharacteristic, direct product factor
226C22C23×C5×A411yescharacteristic
227C4—32no—
228C4—36no—
229C3—161noSylow
230C2—31no—
231C2—33no—
232C2—44no—
233C2—124no—
234C2C2×C5×#127⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C5#127⋊C3
commutator, cosocle, hypocenterC42C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#127C3
socleC24×C5C2×A4
LCSG ▷ C42
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#127⋊C3C2direct (N × H)
2. C22×C5×C42⋊C3C2semidirect
3. C22×C5×#127C3semidirect
5. C5×#127⋊C3C22direct (N × H)
6. C2×C5×C42⋊C3C22semidirect
7. C22×#127⋊C3C5direct (N × H)
11. C2×C5×#127C2×C3semidirect
12. C22×C42×C5C2×C3semidirect
15. C5×C42⋊C3C23semidirect
16. C2×#127⋊C3C2×C5direct (N × H)
17. C22×C42⋊C3C2×C5semidirect
31. C5×#127C22×C3semidirect
33. C2×C42×C5C22×C3semidirect
34. C22×#127C3×C5semidirect
39. #127⋊C3C22×C5direct (N × H)
40. C2×C42⋊C3C22×C5semidirect
68. C42×C5C23×C3semidirect
72. C2×#127C2×C3×C5semidirect
73. C22×C42C2×C3×C5semidirect
79. C42⋊C3C23×C5semidirect
121. #127C22×C3×C5semidirect
123. C2×C42C22×C3×C5semidirect
141. C22×C5#127⋊C3direct (N × H)
172. C42C23×C3×C5semidirect
181. C2×C5C2×#127⋊C3direct (N × H)
212. C5C22×#127⋊C3direct (N × H)
225. C22C5×#127⋊C3direct (N × H)
234. C2C2×C5×#127⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#127⋊C32
C22×C5×C42⋊C32
C22×C5×#1273
C23×C5×A44
C22×#127⋊C35