Finite Group Databasebeta

← #14279494

Subgroups — #14279494

Order 1920.

188 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 41 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#11751172C211yesmaximal, characteristic
2C3×C5×#353C211yesmaximal, characteristic
3#11746366C211yesmaximal, characteristic
4#10598030—31nomaximal, Hall
5C3×C5×#127C2211yescharacteristic
6#91759C411yescharacteristic, complemented
7C3×C5×#99—21no—
8#91118—21no—
9#91116—21no—
10#91116—21no—
11#91087C411yescharacteristic, complemented
12#67539—51nomaximal, Hall
13#65360—31no—
14C5×#353D311yescharacteristic
15#64765—31no—
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C3×C5×C22⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21#6719—41no—
22C4⋊Dic15—21no—
23#6712—41no—
24C2×C3⋊#168—21no—
25#5071—51no—
26C3×#353D511yescharacteristic
27#4545—51no—
28C5×#127C2×D311yescharacteristic
29#4016—31no—
30C5×#99—21no—
31#3966—61no—
32#3964—61no—
33#3964—61no—
34#3935—31no—
35#1412—151noSylow
36C23×C3×C5—21no—
37C23×C3×C5—21no—
38C3×C5×D4—41no—
39C3×C5×D4—41no—
40C3×C5×D4—82no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—81no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×Dic15—41no—
45C2×Dic15—81no—
46C3⋊#168—41no—
47C3×#127C2×D511yescharacteristic
48#870—51no—
49C3×#99—21no—
50#834—101no—
51#832—101no—
52#832—101no—
53#803—51no—
54C2×C5×D4—41no—
55C2×C5×D4D1211yescharacteristic
56C2×C5×D4#6711yescharacteristic
57C5×C22⋊C4—41no—
58C42×C5C4×D311yescharacteristic
59C22⋊Dic5—121no—
60C4⋊Dic5—61no—
61#683—121no—
62C2×#168—61no—
63#490—151no—
64#353—151no—
65#353D1511yescharacteristic
66C22×C3×C5—41no—
67C22×C3×C5—41no—
68C22×C3×C5—81no—
69C22×C3×C5—81no—
70C22×C3×C5#9911yescharacteristic
71C3×C4×C5—21no—
72C3×C4×C5—41no—
73C3×C4×C5—161no—
74Dic15—81no—
75Dic15—161no—
76C2×C3×D4—41no—
77C2×C3×D4D2011yescharacteristic
78C2×C3×D4C22⋊D511yescharacteristic
79C3×C22⋊C4—41no—
80C3×C42C4×D511yescharacteristic
81#217—201no—
82C4⋊Dic3—101no—
83Dic3⋊C4—201no—
84C2×C3⋊C8—101no—
85C23×C5—21no—
86C23×C5—21no—
87C5×D4—41no—
88C5×D4—41no—
89C5×D4—82no—
90C2×C4×C5—21no—
91C2×C4×C5—81no—
92C2×C4×C5(C2×D3)⋊C411yescharacteristic
93C2×Dic5—121no—
94C2×Dic5—241no—
95#168—121no—
96#127C2×D1511yescharacteristic
97#125—151no—
98#102—301no—
99#102—301no—
100#99—21no—
101#99—301no—
102#97—151no—
103C2×C3×C5—21no—
104C2×C3×C5—81no—
105C2×C3×C5—81no—
106C2×C3×C5#35411yescharacteristic
107C23×C3—21no—
108C23×C3—21no—
109C3×D4—41no—
110C3×D4—41no—
111C3×D4—82no—
112C2×C3×C4—21no—
113C2×C3×C4—81no—
114C2×C3×C4#68511yescharacteristic
115C2×Dic3—201no—
116C2×Dic3—401no—
117C3⋊C8—201no—
118C22×C5—41no—
119C22×C5—41no—
120C22×C5—81no—
121C22×C5—81no—
122C22×C5#80611yescharacteristic
123C4×C5—21no—
124C4×C5—41no—
125C4×C5—161no—
126Dic5—241no—
127Dic5—481no—
128C2×D4—41no—
129C2×D4D6011yescharacteristic
130C2×D4#122011yescharacteristic
131C2×C8—301no—
132C4⋊C4—301no—
133C4⋊C4—601no—
134C22⋊C4—41no—
135C22⋊C4—601no—
136C42C4×D1511yescharacteristic
137C3×C5#141211yescharacteristic, complemented, Hall
138C22×C3—41no—
139C22×C3—41no—
140C22×C3—81no—
141C22×C3—81no—
142C22×C3#393811yescharacteristic
143C3×C4—21no—
144C3×C4—41no—
145C3×C4—161no—
146Dic3—401no—
147Dic3—801no—
148C2×C5—21no—
149C2×C5—81no—
150C2×C5—81no—
151C2×C5#447311yescharacteristic
152C23—21no—
153C23—21no—
154D4—41no—
155D4—41no—
156D4—82no—
157C2×C4—21no—
158C2×C4—81no—
159C2×C4—601no—
160C2×C4—1201no—
161C2×C4#671411yescharacteristic
162C8—601no—
163C2×C3—21no—
164C2×C3—81no—
165C2×C3—81no—
166C2×C3#6469311yescharacteristic
167C5#6753911yescharacteristic, complemented, Sylow
168C22—41no—
169C22—41no—
170C22—81no—
171C22—81no—
172C22#9109011yescharacteristic
173C4—21no—
174C4—41no—
175C4—161no—
176C4—1201no—
177C4—2401no—
178C3#1059803011yescharacteristic, complemented, Sylow
179C2—21no—
180C2—81no—
181C2—81no—
182C2#1174629411yescharacteristic
subgroupG/H
centerC2#11746294
commutatorC3×C42×C5C2×C4
Frattini#127C2×D15
FittingC3×C5×#353C2
socleC2×C3×C5#354
prime radical, cosocleC3×C5×#127C22
hypercenter#353D15
hypocenterC3×C5#1412
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #91759C4semidirect
11. #91087C4semidirect
137. C3×C5#1412semidirect
167. C5#67539semidirect
178. C3#10598030semidirect

Maximal subgroups

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

subgroupindex
#117511722
C3×C5×#3532
#117463662
#105980303
#675395