Finite Group Databasebeta

← #14279459

Subgroups — #14279459

Order 1920.

220 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C5×#5076C211yesmaximal, characteristic
2#11746366C211yesmaximal, characteristic
3C3×#64765C211yesmaximal, characteristic
4#10598279—31nomaximal, Hall
5C3×C5×#127C2211yescharacteristic
6C2×C5×#214—21no—
7C2×C5×#214—21no—
8C5×#869C411yescharacteristic, complemented
9#91118—21no—
10C4×C5×C3⋊C8C411yescharacteristic, complemented
11C3×#3966—21no—
12#67540—51nomaximal, Hall
13C5×#492—31no—
14#64765—31no—
15#64765D311yescharacteristic
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×C5×Dic6—21no—
20C3×C42×C5C2×C411yescharacteristic
21#6719—41no—
22C5×#214—42no—
23C5×#214—42no—
24C5×C4⋊Dic3—41no—
25C2×C5×C3⋊C8—21no—
26C3×C22⋊Dic5—41no—
27#5076D511yescharacteristic
28C3×#353—51no—
29#4545—51no—
30C2×C5×SD16—61no—
31C2×C5×SD16—61no—
32C5×C4⋊Q8—31no—
33C5×#127C2×D311yescharacteristic
34C4×C5×C8—31no—
35#3966—21no—
36#3966—61no—
37#1409—151noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C3×C5×D4—41no—
41C3×C5×D4—41no—
42C3×C5×D4—82no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×Dic15—81no—
46C2×C5×Dic3—41no—
47C5×Dic6—41no—
48C5×Dic6—41no—
49C2×C3×Dic5—81no—
50C5×C3⋊C8—22no—
51C3×#127C2×D511yescharacteristic
52C2×#214—21no—
53C2×#214—21no—
54#869Dic511yescharacteristic, complemented
55C3×#99—101no—
56#834—101no—
57C4×C3⋊C8Dic511yescharacteristic, complemented
58C2×C5×Q8—61no—
59C2×C5×D4—41no—
60C2×C5×D4D1211yescharacteristic
61C2×C5×D4#6711yescharacteristic
62C5×SD16—122no—
63C5×SD16—122no—
64C2×C5×C8—61no—
65C5×C4⋊C4—121no—
66C42×C5C4×D311yescharacteristic
67C22⋊Dic5—41no—
68C22⋊Dic5—121no—
69#492—31no—
70#353—51no—
71#353—151no—
72C22×C3×C5—41no—
73C22×C3×C5—41no—
74C22×C3×C5—81no—
75C22×C3×C5—81no—
76C22×C3×C5#9911yescharacteristic
77C3×C4×C5—22no—
78C3×C4×C5—21no—
79Dic15—161no—
80C3×Dic5—161no—
81C5×Dic3—81no—
82C2×C3×D4—41no—
83C2×C3×D4C22⋊D511yescharacteristic
84C2×C3×D4C22⋊D511yescharacteristic
85C2×Dic6—21no—
86C3×C22⋊C4—201no—
87C3×C42C2×Dic511yescharacteristic
88#217—201no—
89#214—42no—
90#214—42no—
91C4⋊Dic3—41no—
92C2×C3⋊C8—21no—
93C23×C5—21no—
94C23×C5—21no—
95C5×Q8—121no—
96C5×Q8—121no—
97C5×D4—41no—
98C5×D4—41no—
99C5×D4—82no—
100C2×C4×C5—21no—
101C2×C4×C5—121no—
102C2×C4×C5(C2×D3)⋊C411yescharacteristic
103C2×Dic5—81no—
104C2×Dic5—241no—
105C5×C8—62no—
106C2×SD16—61no—
107C2×SD16—61no—
108C4⋊Q8—31no—
109#127D3×D511yescharacteristic
110#99—101no—
111#99—301no—
112C4×C8—31no—
113C2×C3×C5—21no—
114C2×C3×C5—81no—
115C2×C3×C5—81no—
116C2×C3×C5#35311yescharacteristic
117C23×C3—21no—
118C23×C3—21no—
119C3×D4—41no—
120C3×D4—41no—
121C3×D4—82no—
122C2×C3×C4—21no—
123C2×C3×C4—401no—
124C2×C3×C4C22⋊Dic511yescharacteristic
125C2×Dic3—41no—
126C2×Dic3—401no—
127Dic6—41no—
128Dic6—41no—
129C3⋊C8—22no—
130C22×C5—41no—
131C22×C5—41no—
132C22×C5—81no—
133C22×C5—81no—
134C22×C5#80611yescharacteristic
135C4×C5—22no—
136C4×C5—21no—
137C4×C5—241no—
138Dic5—161no—
139Dic5—481no—
140C2×Q8—61no—
141C2×D4—41no—
142C2×D4#120111yescharacteristic
143C2×D4#120311yescharacteristic
144SD16—122no—
145SD16—122no—
146C2×C8—61no—
147C4⋊C4—121no—
148C22⋊C4—201no—
149C22⋊C4—601no—
150C42D3×Dic511yescharacteristic
151C3×C5#140911yescharacteristic, complemented, Hall
152C22×C3—41no—
153C22×C3—41no—
154C22×C3—81no—
155C22×C3—81no—
156C22×C3#396611yescharacteristic
157C3×C4—22no—
158C3×C4—21no—
159C3×C4—801no—
160Dic3—81no—
161Dic3—801no—
162C2×C5—21no—
163C2×C5—81no—
164C2×C5—81no—
165C2×C5#447411yescharacteristic
166C23—21no—
167C23—21no—
168Q8—121no—
169Q8—121no—
170D4—41no—
171D4—41no—
172D4—82no—
173C2×C4—21no—
174C2×C4—121no—
175C2×C4—401no—
176C2×C4—1201no—
177C2×C4(C2×D3)⋊Dic511yescharacteristic
178C8—62no—
179C2×C3—21no—
180C2×C3—81no—
181C2×C3—81no—
182C2×C3#6476511yescharacteristic
183C5#6754011yescharacteristic, complemented, Sylow
184C22—41no—
185C22—41no—
186C22—81no—
187C22—81no—
188C22#9099611yescharacteristic
189C4—22no—
190C4—21no—
191C4—241no—
192C4—801no—
193C4—2401no—
194C3#1059827911yescharacteristic, complemented, Sylow
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1174600711yescharacteristic
subgroupG/H
centerC2#11746007
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#127D3×D5
Fitting, prime radical, cosocleC3×C5×#127C22
socleC2×C3×C5#353
hypocenterC3×C5#1409
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
8. C5×#869C4semidirect
10. C4×C5×C3⋊C8C4semidirect
54. #869Dic5semidirect
57. C4×C3⋊C8Dic5semidirect
151. C3×C5#1409semidirect
183. C5#67540semidirect
194. C3#10598279semidirect

Maximal subgroups

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

subgroupindex
C5×#50762
#117463662
C3×#647652
#105982793
#675405