Finite Group Databasebeta

← #14279528

Subgroups — #14279528

Order 1920.

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

normal subgroups only

This group has 156 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#11746925C211yesmaximal, characteristic
2#11746726C211yesmaximal, characteristic
3C3×#64855C211yesmaximal, characteristic
4#10598743—31nomaximal, Hall
5C5×#870C411yescharacteristic
6C3×#4015C2211yescharacteristic
7#91234—21no—
8C3×#4005—21no—
9#91087C411yescharacteristic
10#90970—21no—
11#90970—21no—
12#67551—51nomaximal, Hall
13#65358—31no—
14#64855—31no—
15#64855D311yescharacteristic
16C2×C3×Dic10D411yescharacteristic
17C2×C3×Dic10D411yescharacteristic
18#6762—41no—
19C3×#704—41no—
20C3×C42×C5C2×C411yescharacteristic
21C2×C3⋊#168—21no—
22C5×C4⋊Dic3—21no—
23C5×Dic3⋊C4—41no—
24C3×C4⋊Dic5—41no—
25#5082—51no—
26C3×#356—51no—
27#4548—51no—
28C5×#125—31no—
29#4015C2×D311yescharacteristic
30#4005—21no—
31#4005—61no—
32#3942—61no—
33#3942—61no—
34#3935—31no—
35#1413—151noSylow
36C2×C3×C4×C5—21no—
37C2×C3×C4×C5C22⋊C411yescharacteristic
38C2×C5×Dic3—41no—
39C2×C3×Dic5—21no—
40C2×C3×Dic5—21no—
41C3×Dic10—41no—
42C3×Dic10—41no—
43C3⋊#170—81no—
44C3×#170—81no—
45C3⋊#168—41no—
46C3×C4⋊Q8—51no—
47#870AGL(1,𝔽5)11yescharacteristic
48C3×#101—101no—
49#836—101no—
50#835—101no—
51#835—101no—
52#803—51no—
53C2×Dic10D1211yescharacteristic
54C2×Dic10#6711yescharacteristic
55#704—41no—
56#704—121no—
57C5×C4⋊C4—61no—
58C5×C4⋊C4—121no—
59C42×C5C4×D311yescharacteristic
60C4⋊Dic5—41no—
61C2×#168—61no—
62#491—151no—
63#356—51no—
64#356—151no—
65C22×C3×C5#9911yescharacteristic
66C3×C4×C5—21no—
67C3×C4×C5—41no—
68C3×Dic5—41no—
69C3×Dic5—41no—
70C5×Dic3—81no—
71C2×C3×Q8—51no—
72C2×C3×Q8—51no—
73C3×M16—201no—
74C3×C4⋊C4—201no—
75C3×C42C2×AGL(1,𝔽5)11yescharacteristic
76C4⋊Dic3—21no—
77Dic3⋊C4—41no—
78#208—201no—
79C2×C3⋊C8—101no—
80C2×C4×C5—21no—
81C2×C4×C5—121no—
82C2×C4×C5(C2×D3)⋊C411yescharacteristic
83C2×Dic5—21no—
84C2×Dic5—21no—
85Dic10—41no—
86Dic10—41no—
87#170—81no—
88#170—241no—
89#168—121no—
90C4⋊Q8—51no—
91#125—31no—
92#103—301no—
93#103—301no—
94#101—101no—
95#101—301no—
96#97—151no—
97C2×C3×C5—21no—
98C2×C3×C5#35411yescharacteristic
99C3×Q8—201no—
100C3×Q8—201no—
101C2×C3×C4—21no—
102C2×C3×C4—101no—
103C2×C3×C4—101no—
104C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
105C2×Dic3—41no—
106C3×C8—401no—
107C3⋊C8—201no—
108C3⋊C8—401no—
109C22×C5#80611yescharacteristic
110C4×C5—21no—
111C4×C5—41no—
112C4×C5—241no—
113Dic5—41no—
114Dic5—41no—
115C2×Q8—51no—
116C2×Q8—51no—
117M16—201no—
118M16—601no—
119C2×C8—301no—
120C4⋊C4—61no—
121C4⋊C4—121no—
122C4⋊C4—201no—
123C42D3×AGL(1,𝔽5)11yescharacteristic
124C3×C5#141311yescharacteristic, complemented, Hall
125C22×C3#401111yescharacteristic
126C3×C4—21no—
127C3×C4—41no—
128C3×C4—201no—
129C3×C4—201no—
130Dic3—81no—
131C2×C5—21no—
132C2×C5#447311yescharacteristic
133Q8—201no—
134Q8—201no—
135C2×C4—21no—
136C2×C4—101no—
137C2×C4—101no—
138C2×C4—121no—
139C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
140C8—401no—
141C8—601no—
142C8—1201no—
143C2×C3—21no—
144C2×C3#6492811yescharacteristic
145C5#6755111yescharacteristic, complemented, Sylow
146C22#9117211yescharacteristic
147C4—21no—
148C4—41no—
149C4—201no—
150C4—201no—
151C4—241no—
152C3#1059874311yescharacteristic, complemented, Sylow
153C2—21no—
154C2#1174655611yescharacteristic
subgroupG/H
centerC2#11746556
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#354
prime radicalC22×C3×C5#99
cosocleC3×#4015C22
hypocenterC3×C5#1413
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
124. C3×C5#1413semidirect
145. C5#67551semidirect
152. C3#10598743semidirect

Maximal subgroups

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

subgroupindex
#117469252
#117467262
C3×#648552
#105987433
#675515