Finite Group Databasebeta

← #14279405

Subgroups — #14279405

Order 1920.

216 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 34 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
1#11747042C211yesmaximal, characteristic
2#11746727C211yesmaximal, characteristic, complemented
3C3×#64854C211yesmaximal, characteristic, complemented
4#10598748—31nomaximal, Hall
5C5×#874C411yescharacteristic, complemented
6C3×#4021C2211yescharacteristic
7C2×#6656—21no—
8C2×#6652—21no—
9#91234—21no—
10C3×#3999—21no—
11#91087C411yescharacteristic, complemented
12#67544—51nomaximal, Hall
13#65363—31no—
14#64856—31no—
15#64854D311yescharacteristic, complemented
16C2×C5×D12—21no—
17C2×C5×D12—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×Dic10D411yescharacteristic
20#6762—41no—
21C3×C22⋊AGL(1,𝔽5)—41no—
22C3×C42×C5C2×C411yescharacteristic
23C2×C3⋊#168—21no—
24C3×#685—41no—
25#6656—42no—
26#6652—42no—
27#5058—51no—
28C3×#354—51no—
29#4542—51no—
30C5×#127—31no—
31C2×#687—61no—
32C2×#686—61no—
33#4021C2×D311yescharacteristic
34#4005—61no—
35#3999—21no—
36#3935—31no—
37#1406—151noSylow
38C22×C5×D3—41no—
39C22×C3×D5—21no—
40C2×C3×AGL(1,𝔽5)—81no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C5×D12—41no—
44C5×D12—41no—
45C5×D12—82no—
46C2×C3×Dic5—21no—
47C3×D20—41no—
48C3×Dic10—41no—
49C3⋊#170—81no—
50C3⋊#168—22no—
51C3×#124—51no—
52C2×#215—101no—
53C2×#213—101no—
54#874AGL(1,𝔽5)11yescharacteristic, complemented
55C3×#99—101no—
56#836—101no—
57#803—51no—
58C2×C5×D4—61no—
59C2×C5×D4—121no—
60C2×D20#6711yescharacteristic
61C2×Dic10D1211yescharacteristic
62C22⋊AGL(1,𝔽5)—41no—
63#704—121no—
64C42×C5C4×D311yescharacteristic
65#687—122no—
66#686—122no—
67#685—41no—
68C2×#168—61no—
69#496—151no—
70#355—151no—
71#354—51no—
72C22×C3×C5#9911yescharacteristic
73C2×C5×D3—82no—
74C2×C5×D3—81no—
75C2×C3×D5—41no—
76C2×C3×D5—81no—
77C3×AGL(1,𝔽5)—161no—
78C3×C4×C5—21no—
79C3×C4×C5—41no—
80C3×Dic5—41no—
81C2×C3×Q8—51no—
82C2×C3×D4—51no—
83C2×D12—21no—
84C2×D12—41no—
85C3×C22⋊C4—201no—
86C3×C22⋊C4—201no—
87C3×C42C2×AGL(1,𝔽5)11yescharacteristic
88#215—202no—
89#213—202no—
90#208—201no—
91C2×C3⋊C8—101no—
92C23×C5—121no—
93C22×D5—21no—
94C2×AGL(1,𝔽5)—81no—
95C5×D4—121no—
96C5×D4—121no—
97C5×D4—242no—
98C2×C4×C5—21no—
99C2×C4×C5(C2×D3)⋊C411yescharacteristic
100C2×Dic5—21no—
101D20—41no—
102Dic10—41no—
103#170—241no—
104#168—62no—
105C2×SD16—301no—
106C2×D8—301no—
107#127—31no—
108#124—51no—
109#101—301no—
110#99—101no—
111#97—151no—
112C2×C3×C5—21no—
113C2×C3×C5#35311yescharacteristic
114C3×D5—81no—
115C5×D3—161no—
116C23×C3—101no—
117C22×D3—41no—
118C3×Q8—201no—
119C3×D4—201no—
120C2×C3×C4—21no—
121C2×C3×C4—101no—
122C2×C3×C4—401no—
123C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
124D12—41no—
125D12—41no—
126D12—82no—
127C3⋊C8—102no—
128C3⋊C8—401no—
129C22×C5—242no—
130C22×C5—241no—
131C22×C5#80611yescharacteristic
132C2×D5—41no—
133C2×D5—81no—
134AGL(1,𝔽5)—161no—
135C4×C5—21no—
136C4×C5—41no—
137Dic5—41no—
138C2×Q8—51no—
139C2×D4—51no—
140C2×D4—61no—
141C2×D4—121no—
142SD16—602no—
143D8—602no—
144M16—601no—
145C2×C8—301no—
146C22⋊C4—201no—
147C22⋊C4—201no—
148C42D3×AGL(1,𝔽5)11yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—201no—
151C22×C3—401no—
152C22×C3#401111yescharacteristic
153C2×D3—82no—
154C2×D3—81no—
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—201no—
158C3×C4—801no—
159C2×C5—21no—
160C2×C5—481no—
161C2×C5#447411yescharacteristic
162D5—81no—
163C23—101no—
164C23—121no—
165Q8—201no—
166D4—121no—
167D4—121no—
168D4—201no—
169D4—242no—
170C2×C4—21no—
171C2×C4—101no—
172C2×C4—401no—
173C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
174C8—302no—
175C8—1201no—
176C2×C3—21no—
177C2×C3—401no—
178C2×C3#6492211yescharacteristic
179D3—161no—
180C5#6754411yescharacteristic, complemented, Sylow
181C22—201no—
182C22—242no—
183C22—241no—
184C22—401no—
185C22#9117211yescharacteristic
186C4—21no—
187C4—41no—
188C4—201no—
189C4—801no—
190C3#1059874811yescharacteristic, complemented, Sylow
191C2—21no—
192C2—401no—
193C2—481no—
194C2#1174655411yescharacteristic
subgroupG/H
centerC2#11746554
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radical#11747042C2
cosocleC3×#4021C22
hypocenterC3×C5#1406
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11746727C2semidirect
3. C3×#64854C2semidirect
5. C5×#874C4semidirect
11. #91087C4semidirect
15. #64854D3semidirect
54. #874AGL(1,𝔽5)semidirect
149. C3×C5#1406semidirect
180. C5#67544semidirect
190. C3#10598748semidirect

Maximal subgroups

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

subgroupindex
#117470422
#117467272
C3×#648542
#105987483
#675445