Finite Group Databasebeta

← #14279474

Subgroups — #14279474

Order 1920.

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

normal subgroups only

This group has 208 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×#5085C211yesmaximal, characteristic
2#11746369C211yesmaximal, characteristic, complemented
3C3×#64768C211yesmaximal, characteristic, complemented
4#10598280—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×C5×#215—21no—
7C2×C5×#215—21no—
8C5×#874C411yescharacteristic
9#91120—21no—
10C4×C5×C3⋊C8C411yescharacteristic
11C3×#3968—21no—
12#67552—51nomaximal, Hall
13C5×#492—31no—
14#64768—31no—
15#64768D311yescharacteristic, complemented
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×C5×D12—21no—
19C2×C5×D12—41no—
20C3×C5×C4⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6710—41no—
23C5×#215—42no—
24C5×#215—42no—
25C2×C5×C3⋊C8—21no—
26C3×#681—41no—
27#5085D511yescharacteristic
28C3×#356—51no—
29#4548—51no—
30C2×C5×SD16—61no—
31C2×C5×SD16—61no—
32C5×C4⋊Q8C2×D311yescharacteristic
33C5×#127—31no—
34C4×C5×C8—31no—
35#3968—21no—
36#3968—61no—
37#1410—151noSylow
38C22×C5×D3—41no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C5×D12—41no—
46C5×D12—41no—
47C5×D12—82no—
48C3⋊#168—81no—
49C3×#168—81no—
50C5×C3⋊C8—22no—
51C3×C4⋊Q8C2×D511yescharacteristic
52C2×#215—21no—
53C2×#215—21no—
54#874Dic511yescharacteristic
55C3×#101—101no—
56#836—101no—
57C4×C3⋊C8Dic511yescharacteristic
58C2×C5×Q8D1211yescharacteristic
59C2×C5×Q8#6711yescharacteristic
60C2×C5×D4—61no—
61C2×C5×D4—121no—
62C5×SD16—122no—
63C5×SD16—122no—
64C2×C5×C8—61no—
65C5×C4⋊C4—41no—
66C42×C5C4×D311yescharacteristic
67#681—41no—
68#681—121no—
69#492—31no—
70#356—51no—
71#356—151no—
72C22×C3×C5#9911yescharacteristic
73C2×C5×D3—82no—
74C2×C5×D3—81no—
75C3×C4×C5—22no—
76C3×C4×C5—21no—
77C3×C4×C5—41no—
78C3×C4×C5—41no—
79C2×C3×Q8C22⋊D511yescharacteristic
80C2×C3×Q8C22⋊D511yescharacteristic
81C2×D12—21no—
82C2×D12—41no—
83C3×M16—201no—
84C3×C4⋊C4—41no—
85C3×C42C2×Dic511yescharacteristic
86#215—42no—
87#215—42no—
88#208—201no—
89C2×C3⋊C8—21no—
90C23×C5—121no—
91C5×Q8—41no—
92C5×Q8—41no—
93C5×D4—121no—
94C5×D4—121no—
95C5×D4—242no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5(C2×D3)⋊C411yescharacteristic
100C5×C8—62no—
101#168—81no—
102#168—241no—
103C2×SD16—61no—
104C2×SD16—61no—
105C4⋊Q8D3×D511yescharacteristic
106#127—31no—
107#101—101no—
108#101—301no—
109C4×C8—31no—
110C2×C3×C5—21no—
111C2×C3×C5#35311yescharacteristic
112C5×D3—161no—
113C22×D3—41no—
114C3×Q8—41no—
115C3×Q8—41no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4C22⋊Dic511yescharacteristic
120D12—41no—
121D12—41no—
122D12—82no—
123C3×C8—401no—
124C3⋊C8—22no—
125C3⋊C8—401no—
126C22×C5—242no—
127C22×C5—241no—
128C22×C5#80611yescharacteristic
129C4×C5—22no—
130C4×C5—21no—
131C4×C5—41no—
132C4×C5—41no—
133C2×Q8#120111yescharacteristic
134C2×Q8#120311yescharacteristic
135C2×D4—61no—
136C2×D4—121no—
137SD16—122no—
138SD16—122no—
139M16—201no—
140M16—601no—
141C2×C8—61no—
142C4⋊C4—41no—
143C42D3×Dic511yescharacteristic
144C3×C5#141011yescharacteristic, complemented, Hall
145C22×C3#396611yescharacteristic
146C2×D3—82no—
147C2×D3—81no—
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—41no—
151C3×C4—41no—
152C2×C5—21no—
153C2×C5—481no—
154C2×C5#447411yescharacteristic
155C23—121no—
156Q8—41no—
157Q8—41no—
158D4—121no—
159D4—121no—
160D4—242no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4(C2×D3)⋊Dic511yescharacteristic
165C8—62no—
166C8—401no—
167C8—1201no—
168C2×C3—21no—
169C2×C3#6476511yescharacteristic
170D3—161no—
171C5#6755211yescharacteristic, complemented, Sylow
172C22—242no—
173C22—241no—
174C22#9099611yescharacteristic
175C4—22no—
176C4—21no—
177C4—41no—
178C4—41no—
179C3#1059828011yescharacteristic, complemented, Sylow
180C2—21no—
181C2—481no—
182C2#1174600711yescharacteristic
subgroupG/H
centerC2#11746007
commutatorC3×C42×C5C2×C4
Frattini, hypercenterC4⋊Q8D3×D5
Fitting, cosocleC3×C5×C4⋊Q8C22
socleC2×C3×C5#353
prime radicalC5×#874C4
hypocenterC3×C5#1410
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11746369C2semidirect
3. C3×#64768C2semidirect
15. #64768D3semidirect
144. C3×C5#1410semidirect
171. C5#67552semidirect
179. C3#10598280semidirect

Maximal subgroups

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

subgroupindex
C5×#50852
#117463692
C3×#647682
#105982803
#675525