Finite Group Databasebeta

← #14279491

Subgroups — #14279491

Order 1920.

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

normal subgroups only

This group has 188 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#11747100C211yesmaximal, characteristic
2#11746726C211yesmaximal, characteristic
3C3×#64855C211yesmaximal, characteristic
4#10598521—31nomaximal, Hall
5#91758C411yescharacteristic
6C3×#4015C2211yescharacteristic
7C2×#6662—21no—
8C2×#6662—21no—
9#91234—21no—
10C3×#4005—21no—
11C4×C5×C3⋊C8C411yescharacteristic
12#67553—51nomaximal, Hall
13#64988—31no—
14#64855—31no—
15#64855D311yescharacteristic
16C2×Dic30—21no—
17C2×C3×Dic10D411yescharacteristic
18C2×C3×Dic10D411yescharacteristic
19#6762—41no—
20C3×#704—41no—
21C3×C42×C5C2×C411yescharacteristic
22C4⋊Dic15—41no—
23C2×C5×C3⋊C8—21no—
24C3×C4⋊Dic5—41no—
25#6662—42no—
26#6662—42no—
27#5092—51no—
28C3×#356—51no—
29#4548—51no—
30C2×Dic20—61no—
31C2×Dic20—61no—
32#4015—31no—
33#4015C2×D311yescharacteristic
34#4005—21no—
35#4005—61no—
36C4×C5×C8—31no—
37#1411—151noSylow
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5C22⋊C411yescharacteristic
40C2×Dic15—41no—
41Dic30—41no—
42Dic30—41no—
43C2×C3×Dic5—21no—
44C2×C3×Dic5—21no—
45C3×Dic10—41no—
46C3×Dic10—41no—
47C3⋊#170—81no—
48C3×#170—81no—
49C5×C3⋊C8—22no—
50C3×C4⋊Q8—51no—
51C2×#216—101no—
52C2×#216—101no—
53#869—51no—
54C3×#101—101no—
55#836—101no—
56C4×C3⋊C8AGL(1,𝔽5)11yescharacteristic
57C2×Dic10—61no—
58C2×Dic10D1211yescharacteristic
59C2×Dic10#6711yescharacteristic
60#704—41no—
61#704—121no—
62C2×C5×C8—61no—
63C42×C5C4×D311yescharacteristic
64C4⋊Dic5—41no—
65C4⋊Dic5—121no—
66Dic20—122no—
67Dic20—122no—
68#494—151no—
69#356—51no—
70#356—151no—
71C22×C3×C5#9911yescharacteristic
72C3×C4×C5—22no—
73C3×C4×C5—21no—
74Dic15—81no—
75C3×Dic5—41no—
76C3×Dic5—41no—
77C2×C3×Q8—51no—
78C2×C3×Q8—51no—
79C2×Dic6—101no—
80C3×M16—201no—
81C3×C4⋊C4—201no—
82C3×C42C2×AGL(1,𝔽5)11yescharacteristic
83#216—202no—
84#216—202no—
85C4⋊Dic3—201no—
86#208—201no—
87C2×C3⋊C8—21no—
88C2×C4×C5—21no—
89C2×C4×C5(C2×D3)⋊C411yescharacteristic
90C2×Dic5—21no—
91C2×Dic5—21no—
92C2×Dic5—121no—
93Dic10—41no—
94Dic10—41no—
95Dic10—121no—
96Dic10—121no—
97#170—81no—
98#170—241no—
99C5×C8—62no—
100C2×Q16—301no—
101C2×Q16—301no—
102C4⋊Q8—51no—
103C4⋊Q8—151no—
104#101—101no—
105#101—301no—
106C4×C8—31no—
107C2×C3×C5—21no—
108C2×C3×C5#35311yescharacteristic
109C3×Q8—201no—
110C3×Q8—201no—
111C2×C3×C4—21no—
112C2×C3×C4—101no—
113C2×C3×C4—101no—
114C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
115C2×Dic3—201no—
116Dic6—201no—
117Dic6—201no—
118C3×C8—401no—
119C3⋊C8—22no—
120C3⋊C8—401no—
121C22×C5#80611yescharacteristic
122C4×C5—22no—
123C4×C5—21no—
124Dic5—41no—
125Dic5—41no—
126Dic5—241no—
127C2×Q8—51no—
128C2×Q8—51no—
129C2×Q8—301no—
130Q16—602no—
131Q16—602no—
132M16—201no—
133M16—601no—
134C2×C8—61no—
135C4⋊C4—201no—
136C4⋊C4—601no—
137C42D3×AGL(1,𝔽5)11yescharacteristic
138C3×C5#141111yescharacteristic, complemented, Hall
139C22×C3#399911yescharacteristic
140C3×C4—22no—
141C3×C4—21no—
142C3×C4—201no—
143C3×C4—201no—
144Dic3—401no—
145C2×C5—21no—
146C2×C5#447411yescharacteristic
147Q8—201no—
148Q8—201no—
149Q8—601no—
150Q8—601no—
151C2×C4—21no—
152C2×C4—101no—
153C2×C4—101no—
154C2×C4—601no—
155C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
156C8—62no—
157C8—401no—
158C8—1201no—
159C2×C3—21no—
160C2×C3#6485311yescharacteristic
161C5#6755311yescharacteristic, complemented, Sylow
162C22#9117311yescharacteristic
163C4—22no—
164C4—21no—
165C4—201no—
166C4—201no—
167C4—1201no—
168C3#1059852111yescharacteristic, complemented, Sylow
169C2—21no—
170C2#1174655511yescharacteristic
subgroupG/H
centerC2#11746555
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radicalC22×C3×C5#99
cosocleC3×#4015C22
hypocenterC3×C5#1411
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
138. C3×C5#1411semidirect
161. C5#67553semidirect
168. C3#10598521semidirect

Maximal subgroups

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

subgroupindex
#117471002
#117467262
C3×#648552
#105985213
#675535