Finite Group Databasebeta

← C4×C5×#997 #14511382

Subgroups — C4×C5×#997 #14511382

Order 1920.

690 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 58 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×#997C211yesmaximal, characteristic
2C4×C5×H(5,𝔽2)C311yesmaximal, characteristic, complemented, Hall
3C5×#997C411yescharacteristic, direct product factor
4C2×C4×C5×A4—43nomaximal
5C4×C5×SL(2,𝔽3)—42nomaximal
6C4×#997C511yesmaximal, characteristic, direct product factor, Hall
7C2×C5×H(5,𝔽2)C2×C311yescharacteristic
8C5×#520—32no—
9C5×#518—33no—
10C4×C5×#41—32no—
11C2×C4×C5×D4—33no—
12C22×C5×A4—43no—
13C2×C5×SL(2,𝔽3)—42no—
14C4×C5×A4—46no—
15C2×#997C2×C511yescharacteristic
16C5×H(5,𝔽2)—32no—
17C5×H(5,𝔽2)—33no—
18C5×H(5,𝔽2)C3×C411yescharacteristic, complemented
19C2×C5×#41—32no—
20C22×C5×D4—33no—
21C23×C4×C5—31no—
22C23×C4×C5A413yescomplemented
23C4×C5×Q8—32no—
24C4×C5×Q8A412yescomplemented
25C4×C5×D4—36no—
26C4×C5×D4—312no—
27C4×C5×D4—36no—
28C5×#117—36no—
29C2×C5×C4⋊C4—33no—
30C2×C5×C22⋊C4—33no—
31C2×C5×C22⋊C4—33no—
32C2×C42×C5—33no—
33C4×H(5,𝔽2)C3×C511yescharacteristic, complemented, Sylow
34C2×C5×A4—43no—
35C2×C5×A4—43no—
36C2×C5×A4—43no—
37C2×C3×C4×C5—161no—
38C5×SL(2,𝔽3)—42no—
39#997C4×C511yescharacteristic, direct product factor
40C2×C4×A4—43no—
41C4×SL(2,𝔽3)—42no—
42C24×C5—31no—
43C24×C5C2×A413yes—
44C5×#41—36no—
45C5×#41—36no—
46C5×#41—32no—
47C5×#41—32no—
48C2×C5×Q8C2×A412yes—
49C2×C5×D4—36no—
50C2×C5×D4—33no—
51C2×C5×D4—312no—
52C2×C5×D4—33no—
53C2×C5×D4—33no—
54C2×C5×D4—33no—
55C22×C4×C5—33no—
56C22×C4×C5—33no—
57C22×C4×C5—33no—
58C22×C4×C5—33no—
59C22×C4×C5—33no—
60C22×C4×C5—46no—
61C22×C4×C5—122no—
62C5×C4⋊C4—32no—
63C5×C4⋊C4—36no—
64C5×C22⋊C4—312no—
65C42×C5—36no—
66C42×C5—32no—
67C2×H(5,𝔽2)C2×C3×C511yescharacteristic
68#520—32no—
69#518—33no—
70C4×#41—32no—
71C2×C4×D4—33no—
72C22×C3×C5—161no—
73C5×A4—43no—
74C3×C4×C5—162no—
75C22×A4—43no—
76C2×SL(2,𝔽3)—42no—
77C4×A4—46no—
78C23×C5—33no—
79C23×C5—31no—
80C23×C5—33no—
81C23×C5—33no—
82C23×C5—43no—
83C23×C5—43no—
84C23×C5—121no—
85C23×C5—121no—
86C23×C5C4×A413yescomplemented
87C5×Q8—32no—
88C5×Q8C4×A412yescomplemented
89C5×D4—312no—
90C5×D4—36no—
91C5×D4—36no—
92C2×C4×C5—33no—
93C2×C4×C5—36no—
94C2×C4×C5—33no—
95C2×C4×C5—32no—
96C2×C4×C5—32no—
97C2×C4×C5—33no—
98C2×C4×C5—66no—
99C2×C4×C5—123no—
100C2×C4×C5—123no—
101C2×C4×C5—123no—
102C2×C4×C5C22⋊A411yescharacteristic
103H(5,𝔽2)—32no—
104H(5,𝔽2)—33no—
105H(5,𝔽2)C3×C4×C511yescharacteristic, complemented
106C2×#41—32no—
107C22×D4—33no—
108C23×C4—31no—
109C23×C4C5×A413yescomplemented
110C4×Q8—32no—
111C4×Q8C5×A412yescomplemented
112C4×D4—36no—
113C4×D4—312no—
114C4×D4—36no—
115#117—36no—
116C2×C4⋊C4—33no—
117C2×C22⋊C4—33no—
118C2×C22⋊C4—33no—
119C2×C42—33no—
120C2×C3×C5—161no—
121C2×C3×C5—161no—
122C2×C3×C5—161no—
123C2×A4—43no—
124C2×A4—43no—
125C2×A4—43no—
126C2×C3×C4—161no—
127SL(2,𝔽3)—42no—
128C22×C5—33no—
129C22×C5—33no—
130C22×C5—43no—
131C22×C5—63no—
132C22×C5—63no—
133C22×C5—123no—
134C22×C5—121no—
135C22×C5—123no—
136C22×C5C2×C22⋊A411yescharacteristic
137C4×C5—32no—
138C4×C5—32no—
139C4×C5—63no—
140C4×C5—62no—
141C4×C5#99712yesdirect product factor
142C24—31no—
143C24C2×C5×A413yes—
144#41—36no—
145#41—36no—
146#41—32no—
147#41—32no—
148C2×Q8C2×C5×A412yes—
149C2×D4—36no—
150C2×D4—33no—
151C2×D4—312no—
152C2×D4—33no—
153C2×D4—33no—
154C2×D4—33no—
155C22×C4—33no—
156C22×C4—33no—
157C22×C4—33no—
158C22×C4—33no—
159C22×C4—33no—
160C22×C4—46no—
161C22×C4—122no—
162C4⋊C4—32no—
163C4⋊C4—36no—
164C22⋊C4—312no—
165C42—36no—
166C42—32no—
167C3×C5—161noHall
168C22×C3—161no—
169A4—43no—
170C3×C4—162no—
171C2×C5—63no—
172C2×C5—63no—
173C2×C5C4×C22⋊A411yescharacteristic
174C2×C5C2×#99711yescharacteristic
175C2×C5#595011yescharacteristic
176C23—31no—
177C23—33no—
178C23—33no—
179C23—33no—
180C23—43no—
181C23—43no—
182C23—121no—
183C23—121no—
184C23C4×C5×A413yescomplemented
185Q8—32no—
186Q8C4×C5×A412yescomplemented
187D4—36no—
188D4—36no—
189D4—312no—
190C2×C4—33no—
191C2×C4—36no—
192C2×C4—33no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—33no—
196C2×C4—66no—
197C2×C4—123no—
198C2×C4—123no—
199C2×C4—123no—
200C2×C4C5×C22⋊A411yescharacteristic
201C2×C3—161no—
202C2×C3—161no—
203C2×C3—161no—
204C5C4×#99711yescharacteristic, direct product factor, Sylow
205C22—33no—
206C22—33no—
207C22—43no—
208C22—63no—
209C22—63no—
210C22—123no—
211C22—121no—
212C22—123no—
213C22C2×C5×C22⋊A411yescharacteristic
214C4—32no—
215C4—32no—
216C4—63no—
217C4—62no—
218C4C5×#99712yesdirect product factor
219C3—161noSylow
220C2—63no—
221C2—63no—
222C2C4×C5×C22⋊A411yescharacteristic
223C2C2×C5×#99711yescharacteristic
224C2C5×#595011yescharacteristic
subgroupG/H
center, hypercenterC2×C4×C5C22⋊A4
commutator, hypocenterH(5,𝔽2)C3×C4×C5
FrattiniC22C2×C5×C22⋊A4
FittingC4×C5×H(5,𝔽2)C3
socleC22×C5C2×C22⋊A4
prime radicalC2×C5×#997C2
cosocleC2×H(5,𝔽2)C2×C3×C5
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2×C4×C5

Complements

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

NH ≅ G/Ntype
2. C4×C5×H(5,𝔽2)C3semidirect
3. C5×#997C4direct (N × H)
6. C4×#997C5direct (N × H)
18. C5×H(5,𝔽2)C3×C4semidirect
22. C23×C4×C5A4semidirect
24. C4×C5×Q8A4semidirect
33. C4×H(5,𝔽2)C3×C5semidirect
39. #997C4×C5direct (N × H)
86. C23×C5C4×A4semidirect
88. C5×Q8C4×A4semidirect
105. H(5,𝔽2)C3×C4×C5semidirect
109. C23×C4C5×A4semidirect
111. C4×Q8C5×A4semidirect
141. C4×C5#997direct (N × H)
184. C23C4×C5×A4semidirect
186. Q8C4×C5×A4semidirect
204. C5C4×#997direct (N × H)
218. C4C5×#997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9972
C4×C5×H(5,𝔽2)3
C2×C4×C5×A44
C4×C5×SL(2,𝔽3)4
C4×#9975