Finite Group Databasebeta

← #14511617

Subgroups — #14511617

Order 1920.

224 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 21 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⋊(#399⋊C3)C211yesmaximal, characteristic
2C5⋊#4621C211yesmaximal, characteristic, complemented
3C5×#4621C211yesmaximal, characteristic, complemented
4#10599115—31nomaximal, Hall
5D5×SL(2,ℤ/4)—41nomaximal
6C5×#95⋊C3C2211yescharacteristic
7#73004—51nomaximal, Hall
8#65968—31no—
9#65333—31no—
10#65011—31no—
11#64966D311yescharacteristic
12C5×#328—31no—
13#64688—31no—
14#64672—31no—
15C2×D5×A4—41no—
16A4⋊Dic5—41no—
17C5×SL(2,ℤ/4)—41no—
18#399⋊C3—51no—
19#4621—51no—
20#4621D511yescharacteristic, complemented
21C5×C22⋊Q8—31no—
22#4092—61no—
23C2×#685—31no—
24C2×C4⋊Dic5—31no—
25#4070—31no—
26#4043—61no—
27#4042—61no—
28#4042—61no—
29D5×C22⋊C4—61no—
30#4024—61no—
31C5×C22⋊C8—31no—
32C5×#95C2×D311yescharacteristic
33#3967—61no—
34C22⋊#168—31no—
35#3950—61no—
36#3948—61no—
37#3939—61no—
38#1614—151noSylow
39C2×C5×A4—41no—
40D5×A4—42no—
41D5×Dic3—161no—
42C2×SL(2,ℤ/4)—201no—
43#95⋊C3C2×D511yescharacteristic
44C23×D5S411yescharacteristic
45C2×C5×Q8—31no—
46C22×C4×C5—31no—
47C22×Dic5—31no—
48C2×C4×D5—61no—
49C2×C4×D5—61no—
50C2×Dic10—31no—
51C2×Dic10—61no—
52C2×C5×C8—61no—
53C5×C4⋊C4—31no—
54C5×C4⋊C4—61no—
55C5×C22⋊C4—61no—
56C22⋊Dic5—61no—
57#685—61no—
58#685—61no—
59#685—61no—
60#685—61no—
61C4⋊Dic5—31no—
62C4⋊Dic5—61no—
63C4⋊Dic5—61no—
64C4⋊Dic5—61no—
65#683—61no—
66#683—61no—
67#683—61no—
68C2×#168—61no—
69#543—151no—
70#484—151no—
71#484—151no—
72#399—51no—
73#328—31no—
74#328—151no—
75#323—151no—
76C2×C3×D5—161no—
77C5×A4—41no—
78Dic15—161no—
79C5×Dic3—161no—
80C22×A4—201no—
81SL(2,ℤ/4)—41no—
82SL(2,ℤ/4)—201no—
83C23×C5C2×S411yescharacteristic
84C22×D5—61no—
85C22×D5—61no—
86C22×D5#22612yes—
87C5×Q8—121no—
88C2×C4×C5—31no—
89C2×C4×C5—31no—
90C2×C4×C5—61no—
91C2×C4×C5—61no—
92C2×C4×C5—121no—
93C2×Dic5—61no—
94C2×Dic5—61no—
95C2×Dic5—61no—
96C2×Dic5—121no—
97C4×D5—241no—
98C4×D5—241no—
99Dic10—121no—
100Dic10—241no—
101C5×C8—121no—
102#168—121no—
103C22⋊Q8—31no—
104C22⋊Q8—151no—
105C22⋊Q8—301no—
106C22⋊Q8—301no—
107C22⋊Q8—301no—
108C22⋊Q8—301no—
109C22⋊Q8—301no—
110C2×C4⋊C4—151no—
111C2×C22⋊C4—151no—
112C2×C22⋊C4—301no—
113#107—301no—
114#107—301no—
115#103—301no—
116#103—301no—
117C22⋊C8—31no—
118C22⋊C8—151no—
119#95D3×D511yescharacteristic
120C2×C3×C5—161no—
121C3×D5—162no—
122C2×A4—41no—
123C2×A4—202no—
124C2×Dic3—801no—
125C22×C5—31no—
126C22×C5—31no—
127C22×C5C2×#22611yescharacteristic
128C2×D5—41no—
129C2×D5—62no—
130C2×D5—121no—
131C4×C5—61no—
132C4×C5—61no—
133C4×C5—121no—
134C4×C5—121no—
135Dic5—121no—
136Dic5—121no—
137Dic5—121no—
138C24—51no—
139C2×Q8—31no—
140C2×Q8—151no—
141C2×Q8—301no—
142C22×C4—31no—
143C22×C4—151no—
144C22×C4—301no—
145C22×C4—301no—
146C2×C8—61no—
147C2×C8—301no—
148C4⋊C4—31no—
149C4⋊C4—61no—
150C4⋊C4—151no—
151C4⋊C4—301no—
152C4⋊C4—301no—
153C4⋊C4—301no—
154C4⋊C4—301no—
155C4⋊C4—301no—
156C4⋊C4—301no—
157C22⋊C4—61no—
158C22⋊C4—301no—
159C22⋊C4—301no—
160C22⋊C4—301no—
161C22⋊C4—301no—
162C22⋊C4—301no—
163C3×C5—161noHall
164C22×C3—801no—
165A4—41no—
166Dic3—161no—
167Dic3—801no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5#857⋊C211yescharacteristic
171D5—42no—
172C23—52no—
173C23—301no—
174C23—301no—
175C23D5×S411yescharacteristic
176Q8—121no—
177Q8—601no—
178Q8—1201no—
179C2×C4—31no—
180C2×C4—31no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—121no—
184C2×C4—301no—
185C2×C4—301no—
186C2×C4—301no—
187C2×C4—601no—
188C2×C4—1201no—
189C2×C4—1201no—
190C8—121no—
191C8—601no—
192C2×C3—161no—
193C2×C3—802no—
194C5#7300411yescharacteristic, complemented, Sylow
195C22—31no—
196C22—31no—
197C22—201no—
198C22—302no—
199C22—601no—
200C22D5×#22611yescharacteristic
201C4—61no—
202C4—61no—
203C4—121no—
204C4—121no—
205C4—601no—
206C4—601no—
207C4—601no—
208C3—161noSylow
209C2—31no—
210C2—31no—
211C2—202no—
212C2#857⋊D511yescharacteristic
subgroupG/H
center, hypercenterC2#857⋊D5
commutator, cosocle, hypocenterC5×#95⋊C3C22
FrattiniC23D5×S4
FittingC5×#95C2×D3
socleC23×C5C2×S4
prime radicalC5⋊(#399⋊C3)C2
LCSG ▷ C5×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C5⋊#4621C2semidirect
3. C5×#4621C2semidirect
20. #4621D5semidirect
194. C5#73004semidirect

Maximal subgroups

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

subgroupindex
C5⋊(#399⋊C3)2
C5⋊#46212
C5×#46212
#105991153
D5×SL(2,ℤ/4)4
#730045