Finite Group Databasebeta

← #14279461

Subgroups — #14279461

Order 1920.

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

normal subgroups only

This group has 220 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#11747071C211yesmaximal, characteristic
2#11746724C211yesmaximal, characteristic
3C3×#64853C211yesmaximal, characteristic
4#10598517—31nomaximal, Hall
5#91758C411yescharacteristic, complemented
6C3×#4020C2211yescharacteristic
7C2×#6657—21no—
8C2×#6657—21no—
9#91228—21no—
10C3×#3999—21no—
11C4×C5×C3⋊C8C411yescharacteristic, complemented
12#67540—51nomaximal, Hall
13#64982—31no—
14#64853—31no—
15#64853D311yescharacteristic
16C2×Dic30—21no—
17C2×C3×D20—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×D20D411yescharacteristic
20#6763—41no—
21C3×C22⋊AGL(1,𝔽5)—41no—
22C3×C42×C5C2×C411yescharacteristic
23C4⋊Dic15—41no—
24C2×C5×C3⋊C8—21no—
25#6657—42no—
26#6657—42no—
27#5076—51no—
28C3×#353—51no—
29#4545—51no—
30C2×#677—61no—
31C2×#677—61no—
32#4020C2×D311yescharacteristic
33#4015—31no—
34#3999—21no—
35#3999—61no—
36C4×C5×C8—31no—
37#1409—151noSylow
38C22×C3×D5—21no—
39C22×C3×D5—21no—
40C2×ΓL(1,𝔽16)—81no—
41C2×C3×AGL(1,𝔽5)—81no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×Dic15—41no—
45Dic30—41no—
46Dic30—41no—
47C3×D20—41no—
48C3×D20—41no—
49C3×D20—82no—
50C5×C3⋊C8—22no—
51C3×#127—51no—
52C2×#214—101no—
53C2×#214—101no—
54#869—51no—
55C3×#99—101no—
56#834—101no—
57C4×C3⋊C8AGL(1,𝔽5)11yescharacteristic, complemented
58C2×D20—41no—
59C2×D20D1211yescharacteristic
60C2×D20#6711yescharacteristic
61C2×Dic10—61no—
62C22⋊AGL(1,𝔽5)—41no—
63C22⋊AGL(1,𝔽5)—121no—
64C2×C5×C8—61no—
65C42×C5C4×D311yescharacteristic
66C4⋊Dic5—121no—
67#677—122no—
68#677—122no—
69#492—151no—
70#353—51no—
71#353—151no—
72C22×C3×C5#9911yescharacteristic
73C2×C3×D5—41no—
74C2×C3×D5—41no—
75C2×C3×D5—81no—
76C2×C3×D5—81no—
77ΓL(1,𝔽16)—161no—
78C3×AGL(1,𝔽5)—161no—
79C3×C4×C5—22no—
80C3×C4×C5—21no—
81Dic15—81no—
82C2×C3×D4—51no—
83C2×C3×D4—51no—
84C2×C3×D4—201no—
85C2×Dic6—101no—
86C3×C22⋊C4—201no—
87C3×C42C2×AGL(1,𝔽5)11yescharacteristic
88#217—201no—
89#214—202no—
90#214—202no—
91C4⋊Dic3—201no—
92C2×C3⋊C8—21no—
93C22×D5—21no—
94C22×D5—21no—
95C2×AGL(1,𝔽5)—81no—
96C2×AGL(1,𝔽5)—241no—
97C2×C4×C5—21no—
98C2×C4×C5(C2×D3)⋊C411yescharacteristic
99C2×Dic5—121no—
100D20—41no—
101D20—41no—
102D20—82no—
103Dic10—121no—
104Dic10—121no—
105C5×C8—62no—
106C2×SD16—301no—
107C2×SD16—301no—
108C4⋊Q8—151no—
109#127—51no—
110#99—101no—
111#99—301no—
112C4×C8—31no—
113C2×C3×C5—21no—
114C2×C3×C5#35311yescharacteristic
115C3×D5—81no—
116C3×D5—81no—
117C23×C3—101no—
118C23×C3—101no—
119C3×D4—201no—
120C3×D4—201no—
121C3×D4—402no—
122C2×C3×C4—21no—
123C2×C3×C4—401no—
124C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
125C2×Dic3—201no—
126C2×Dic3—401no—
127Dic6—201no—
128Dic6—201no—
129C3⋊C8—22no—
130C22×C5#80611yescharacteristic
131C2×D5—41no—
132C2×D5—41no—
133C2×D5—81no—
134C2×D5—81no—
135AGL(1,𝔽5)—161no—
136AGL(1,𝔽5)—481no—
137C4×C5—22no—
138C4×C5—21no—
139Dic5—241no—
140C2×Q8—301no—
141C2×D4—51no—
142C2×D4—51no—
143C2×D4—201no—
144SD16—602no—
145SD16—602no—
146C2×C8—61no—
147C4⋊C4—601no—
148C22⋊C4—201no—
149C22⋊C4—601no—
150C42D3×AGL(1,𝔽5)11yescharacteristic
151C3×C5#140911yescharacteristic, complemented, Hall
152C22×C3—201no—
153C22×C3—201no—
154C22×C3—401no—
155C22×C3—401no—
156C22×C3#399911yescharacteristic
157C3×C4—22no—
158C3×C4—21no—
159C3×C4—801no—
160Dic3—401no—
161Dic3—801no—
162C2×C5—21no—
163C2×C5#447411yescharacteristic
164D5—81no—
165D5—81no—
166C23—101no—
167C23—101no—
168Q8—601no—
169Q8—601no—
170D4—201no—
171D4—201no—
172D4—402no—
173C2×C4—21no—
174C2×C4—401no—
175C2×C4—601no—
176C2×C4—1201no—
177C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
178C8—62no—
179C2×C3—21no—
180C2×C3—401no—
181C2×C3—401no—
182C2×C3#6485311yescharacteristic
183C5#6754011yescharacteristic, complemented, Sylow
184C22—201no—
185C22—201no—
186C22—401no—
187C22—401no—
188C22#9117311yescharacteristic
189C4—22no—
190C4—21no—
191C4—801no—
192C4—1201no—
193C4—2401no—
194C3#1059851711yescharacteristic, complemented, Sylow
195C2—21no—
196C2—401no—
197C2—401no—
198C2#1174655511yescharacteristic
subgroupG/H
centerC2#11746555
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radical, cosocleC3×#4020C22
hypocenterC3×C5#1409
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
5. #91758C4semidirect
11. C4×C5×C3⋊C8C4semidirect
57. C4×C3⋊C8AGL(1,𝔽5)semidirect
151. C3×C5#1409semidirect
183. C5#67540semidirect
194. C3#10598517semidirect

Maximal subgroups

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

subgroupindex
#117470712
#117467242
C3×#648532
#105985173
#675405