Finite Group Databasebeta

← #14279475

Subgroups — #14279475

Order 1920.

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

normal subgroups only

This group has 208 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#11747081C211yesmaximal, characteristic
2#11746726C211yesmaximal, characteristic, complemented
3C3×#64855C211yesmaximal, characteristic, complemented
4#10598749—31nomaximal, Hall
5C5×#874C411yescharacteristic
6C3×#4015C2211yescharacteristic
7C2×#6656—21no—
8C2×#6656—21no—
9#91234—21no—
10C3×#4005—21no—
11C4×C3⋊#168C411yescharacteristic
12#67552—51nomaximal, Hall
13#65365—31no—
14#64855—31no—
15#64855D311yescharacteristic, complemented
16C2×C5×D12—21no—
17C2×C5×D12—41no—
18C2×C3×Dic10D411yescharacteristic
19C2×C3×Dic10D411yescharacteristic
20#6762—41no—
21C3×#704—41no—
22C3×C42×C5C2×C411yescharacteristic
23C2×C3⋊#168—21no—
24C3×C4⋊Dic5—41no—
25#6656—42no—
26#6656—42no—
27#5085—51no—
28C3×#356—51no—
29#4548—51no—
30C5×#127—31no—
31C2×#687—61no—
32C2×#687—61no—
33#4015C2×D311yescharacteristic
34#4005—21no—
35#4005—61no—
36C4×#168—31no—
37#1410—151noSylow
38C22×C5×D3—41no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5C22⋊C411yescharacteristic
41C5×D12—41no—
42C5×D12—41no—
43C5×D12—82no—
44C2×C3×Dic5—21no—
45C2×C3×Dic5—21no—
46C3×Dic10—41no—
47C3×Dic10—41no—
48C3⋊#170—81no—
49C3×#170—81no—
50C3⋊#168—22no—
51C3×C4⋊Q8—51no—
52C2×#215—101no—
53C2×#215—101no—
54#874AGL(1,𝔽5)11yescharacteristic
55C3×#101—101no—
56#836—101no—
57C4×C3⋊C8—51no—
58C2×C5×D4—61no—
59C2×C5×D4—121no—
60C2×Dic10D1211yescharacteristic
61C2×Dic10#6711yescharacteristic
62#704—41no—
63#704—121no—
64C42×C5C4×D311yescharacteristic
65#687—122no—
66#687—122no—
67C4⋊Dic5—41no—
68C2×#168—61no—
69#492—151no—
70#356—51no—
71#356—151no—
72C22×C3×C5#9911yescharacteristic
73C2×C5×D3—82no—
74C2×C5×D3—81no—
75C3×C4×C5—22no—
76C3×C4×C5—21no—
77C3×Dic5—41no—
78C3×Dic5—41no—
79C2×C3×Q8—51no—
80C2×C3×Q8—51no—
81C2×D12—21no—
82C2×D12—41no—
83C3×M16—201no—
84C3×C4⋊C4—201no—
85C3×C42C2×AGL(1,𝔽5)11yescharacteristic
86#215—202no—
87#215—202no—
88#208—201no—
89C2×C3⋊C8—101no—
90C23×C5—121no—
91C5×D4—121no—
92C5×D4—121no—
93C5×D4—242no—
94C2×C4×C5—21no—
95C2×C4×C5(C2×D3)⋊C411yescharacteristic
96C2×Dic5—21no—
97C2×Dic5—21no—
98Dic10—41no—
99Dic10—41no—
100#170—81no—
101#170—241no—
102#168—62no—
103C2×SD16—301no—
104C2×SD16—301no—
105C4⋊Q8—51no—
106#127—31no—
107#101—101no—
108#101—301no—
109C4×C8—151no—
110C2×C3×C5—21no—
111C2×C3×C5#35311yescharacteristic
112C5×D3—161no—
113C22×D3—41no—
114C3×Q8—201no—
115C3×Q8—201no—
116C2×C3×C4—21no—
117C2×C3×C4—101no—
118C2×C3×C4—101no—
119C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
120D12—41no—
121D12—41no—
122D12—82no—
123C3×C8—401no—
124C3⋊C8—102no—
125C3⋊C8—401no—
126C22×C5—242no—
127C22×C5—241no—
128C22×C5#80611yescharacteristic
129C4×C5—22no—
130C4×C5—21no—
131Dic5—41no—
132Dic5—41no—
133C2×Q8—51no—
134C2×Q8—51no—
135C2×D4—61no—
136C2×D4—121no—
137SD16—602no—
138SD16—602no—
139M16—201no—
140M16—601no—
141C2×C8—301no—
142C4⋊C4—201no—
143C42D3×AGL(1,𝔽5)11yescharacteristic
144C3×C5#141011yescharacteristic, complemented, Hall
145C22×C3#401111yescharacteristic
146C2×D3—82no—
147C2×D3—81no—
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—201no—
151C3×C4—201no—
152C2×C5—21no—
153C2×C5—481no—
154C2×C5#447411yescharacteristic
155C23—121no—
156Q8—201no—
157Q8—201no—
158D4—121no—
159D4—121no—
160D4—242no—
161C2×C4—21no—
162C2×C4—101no—
163C2×C4—101no—
164C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
165C8—302no—
166C8—401no—
167C8—1201no—
168C2×C3—21no—
169C2×C3#6492211yescharacteristic
170D3—161no—
171C5#6755211yescharacteristic, complemented, Sylow
172C22—242no—
173C22—241no—
174C22#9117211yescharacteristic
175C4—22no—
176C4—21no—
177C4—201no—
178C4—201no—
179C3#1059874911yescharacteristic, complemented, Sylow
180C2—21no—
181C2—481no—
182C2#1174655411yescharacteristic
subgroupG/H
centerC2#11746554
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radicalC5×#874C4
cosocleC3×#4015C22
hypocenterC3×C5#1410
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. #11746726C2semidirect
3. C3×#64855C2semidirect
15. #64855D3semidirect
144. C3×C5#1410semidirect
171. C5#67552semidirect
179. C3#10598749semidirect

Maximal subgroups

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

subgroupindex
#117470812
#117467262
C3×#648552
#105987493
#675525