Finite Group Databasebeta

← #14279424

Subgroups — #14279424

Order 1920.

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

normal subgroups only

This group has 196 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×#5060C211yesmaximal, characteristic
2#11746363C211yesmaximal, characteristic
3C3×#64761C211yesmaximal, characteristic
4#10598289—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×C5×#216—21no—
7C2×C5×#214—21no—
8C5×#869C411yescharacteristic, complemented
9#91120—21no—
10C5×#803C411yescharacteristic, complemented
11C3×#3966—21no—
12#67545—51nomaximal, Hall
13C5×#497—31no—
14#64762—31no—
15#64761D311yescharacteristic
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C5×Dic6—21no—
19C3×C5×C22⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21#6710—41no—
22C5×#216—42no—
23C5×#214—42no—
24C5×C4⋊Dic3—41no—
25C2×C5×C3⋊C8—21no—
26C3×C22⋊Dic5—41no—
27#5060D511yescharacteristic
28C3×#354—51no—
29#4542—51no—
30C2×C5×Q16—61no—
31C2×C5×SD16—61no—
32C5×C4⋊Q8—31no—
33C5×#124C2×D311yescharacteristic
34C5×#97—31no—
35#3968—61no—
36#3966—21no—
37#1407—151noSylow
38C23×C3×C5—21no—
39C3×C5×Q8—41no—
40C3×C5×D4—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C5×Dic3—41no—
45C5×Dic6—41no—
46C5×Dic6—41no—
47C2×C3×Dic5—81no—
48C3⋊#168—81no—
49C5×C3⋊C8—22no—
50C3×#124C2×D511yescharacteristic
51C2×#216—21no—
52C2×#214—21no—
53#869Dic511yescharacteristic, complemented
54C3×#99—101no—
55#836—101no—
56#803Dic511yescharacteristic, complemented
57C2×C5×Q8—61no—
58C2×C5×Q8D1211yescharacteristic
59C2×C5×D4#6711yescharacteristic
60C5×Q16—122no—
61C5×SD16—122no—
62C2×C5×C8—61no—
63C5×C4⋊C4—121no—
64C5×C22⋊C4—41no—
65C42×C5C4×D311yescharacteristic
66C22⋊Dic5—41no—
67#681—121no—
68#497—31no—
69#355—151no—
70#354—51no—
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#9911yescharacteristic
74C3×C4×C5—21no—
75C3×C4×C5—41no—
76C3×C4×C5—41no—
77C3×Dic5—161no—
78C5×Dic3—81no—
79C2×C3×Q8C22⋊D511yescharacteristic
80C2×C3×D4C22⋊D511yescharacteristic
81C2×Dic6—21no—
82C3×C22⋊C4—41no—
83C3×C22⋊C4—201no—
84C3×C42C2×Dic511yescharacteristic
85#216—42no—
86#214—42no—
87C4⋊Dic3—41no—
88#208—201no—
89C2×C3⋊C8—21no—
90C23×C5—21no—
91C5×Q8—41no—
92C5×Q8—121no—
93C5×Q8—121no—
94C5×D4—41no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—121no—
98C2×C4×C5(C2×D3)⋊C411yescharacteristic
99C2×Dic5—81no—
100C5×C8—62no—
101#168—241no—
102C2×Q16—61no—
103C2×SD16—61no—
104C4⋊Q8—31no—
105#124D3×D511yescharacteristic
106#101—301no—
107#99—101no—
108#97—31no—
109C2×C3×C5—21no—
110C2×C3×C5—81no—
111C2×C3×C5#35311yescharacteristic
112C23×C3—21no—
113C3×Q8—41no—
114C3×D4—41no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—401no—
118C2×C3×C4C22⋊Dic511yescharacteristic
119C2×Dic3—41no—
120Dic6—41no—
121Dic6—41no—
122C3⋊C8—22no—
123C3⋊C8—401no—
124C22×C5—41no—
125C22×C5—81no—
126C22×C5#80611yescharacteristic
127C4×C5—21no—
128C4×C5—41no—
129C4×C5—41no—
130C4×C5—241no—
131Dic5—161no—
132C2×Q8—61no—
133C2×Q8#120311yescharacteristic
134C2×D4#120111yescharacteristic
135Q16—122no—
136SD16—122no—
137M16—601no—
138C2×C8—61no—
139C4⋊C4—121no—
140C22⋊C4—41no—
141C22⋊C4—201no—
142C42D3×Dic511yescharacteristic
143C3×C5#140711yescharacteristic, complemented, Hall
144C22×C3—41no—
145C22×C3—81no—
146C22×C3#396611yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—801no—
151Dic3—81no—
152C2×C5—21no—
153C2×C5—81no—
154C2×C5#447411yescharacteristic
155C23—21no—
156Q8—41no—
157Q8—121no—
158Q8—121no—
159D4—41no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—121no—
163C2×C4—401no—
164C2×C4(C2×D3)⋊Dic511yescharacteristic
165C8—62no—
166C8—1201no—
167C2×C3—21no—
168C2×C3—81no—
169C2×C3#6476511yescharacteristic
170C5#6754511yescharacteristic, complemented, Sylow
171C22—41no—
172C22—81no—
173C22#9099611yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—241no—
178C4—801no—
179C3#1059828911yescharacteristic, complemented, Sylow
180C2—21no—
181C2—81no—
182C2#1174600711yescharacteristic
subgroupG/H
centerC2#11746007
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#353
prime radicalC2×C3×C5×D4D4
hypocenterC3×C5#1407
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
8. C5×#869C4semidirect
10. C5×#803C4semidirect
53. #869Dic5semidirect
56. #803Dic5semidirect
143. C3×C5#1407semidirect
170. C5#67545semidirect
179. C3#10598289semidirect

Maximal subgroups

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

subgroupindex
C5×#50602
#117463632
C3×#647612
#105982893
#675455