Finite Group Databasebeta

← #14279401

Subgroups — #14279401

Order 1920.

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

normal subgroups only

This group has 216 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×#5058C211yesmaximal, characteristic
2#11746363C211yesmaximal, characteristic, complemented
3C3×#64761C211yesmaximal, characteristic, complemented
4#10598288—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×C5×#215—21no—
7C2×C5×#213—21no—
8C5×#874C411yescharacteristic, complemented
9#91120—21no—
10C5×#803C411yescharacteristic, complemented
11C3×#3966—21no—
12#67544—51nomaximal, Hall
13C5×#496—31no—
14#64762—31no—
15#64761D311yescharacteristic, complemented
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C5×D12—21no—
19C2×C5×D12—41no—
20C3×C5×C22⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6710—41no—
23C5×#215—42no—
24C5×#213—42no—
25C2×C5×C3⋊C8—21no—
26C3×C22⋊Dic5—41no—
27#5058D511yescharacteristic
28C3×#354—51no—
29#4542—51no—
30C2×C5×SD16—61no—
31C2×C5×D8—61no—
32C5×#127—31no—
33C5×#124C2×D311yescharacteristic
34C5×#97—31no—
35#3968—61no—
36#3966—21no—
37#1406—151noSylow
38C23×C3×C5—21no—
39C22×C5×D3—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C5×D12—41no—
46C5×D12—41no—
47C5×D12—82no—
48C2×C3×Dic5—81no—
49C3⋊#168—81no—
50C5×C3⋊C8—22no—
51C3×#124C2×D511yescharacteristic
52C2×#215—21no—
53C2×#213—21no—
54#874Dic511yescharacteristic, complemented
55C3×#99—101no—
56#836—101no—
57#803Dic511yescharacteristic, complemented
58C2×C5×Q8D1211yescharacteristic
59C2×C5×D4—61no—
60C2×C5×D4—121no—
61C2×C5×D4#6711yescharacteristic
62C5×SD16—122no—
63C5×D8—122no—
64C2×C5×C8—61no—
65C5×C22⋊C4—41no—
66C42×C5C4×D311yescharacteristic
67C22⋊Dic5—41no—
68#681—121no—
69#496—31no—
70#355—151no—
71#354—51no—
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5#9911yescharacteristic
75C2×C5×D3—82no—
76C2×C5×D3—81no—
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80C3×Dic5—161no—
81C2×C3×Q8C22⋊D511yescharacteristic
82C2×C3×D4C22⋊D511yescharacteristic
83C2×D12—21no—
84C2×D12—41no—
85C3×C22⋊C4—41no—
86C3×C22⋊C4—201no—
87C3×C42C2×Dic511yescharacteristic
88#215—42no—
89#213—42no—
90#208—201no—
91C2×C3⋊C8—21no—
92C23×C5—21no—
93C23×C5—121no—
94C5×Q8—41no—
95C5×D4—41no—
96C5×D4—121no—
97C5×D4—121no—
98C5×D4—242no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5(C2×D3)⋊C411yescharacteristic
102C2×Dic5—81no—
103C5×C8—62no—
104#168—241no—
105C2×SD16—61no—
106C2×D8—61no—
107#127—31no—
108#124D3×D511yescharacteristic
109#101—301no—
110#99—101no—
111#97—31no—
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5#35311yescharacteristic
115C5×D3—161no—
116C23×C3—21no—
117C22×D3—41no—
118C3×Q8—41no—
119C3×D4—41no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—401no—
123C2×C3×C4C22⋊Dic511yescharacteristic
124D12—41no—
125D12—41no—
126D12—82no—
127C3⋊C8—22no—
128C3⋊C8—401no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5—242no—
132C22×C5—241no—
133C22×C5#80611yescharacteristic
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137Dic5—161no—
138C2×Q8#120311yescharacteristic
139C2×D4—61no—
140C2×D4—121no—
141C2×D4#120111yescharacteristic
142SD16—122no—
143D8—122no—
144M16—601no—
145C2×C8—61no—
146C22⋊C4—41no—
147C22⋊C4—201no—
148C42D3×Dic511yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3#396611yescharacteristic
153C2×D3—82no—
154C2×D3—81no—
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158C3×C4—801no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5—481no—
162C2×C5#447411yescharacteristic
163C23—21no—
164C23—121no—
165Q8—41no—
166D4—41no—
167D4—121no—
168D4—121no—
169D4—242no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—401no—
173C2×C4(C2×D3)⋊Dic511yescharacteristic
174C8—62no—
175C8—1201no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3#6476511yescharacteristic
179D3—161no—
180C5#6754411yescharacteristic, complemented, Sylow
181C22—41no—
182C22—81no—
183C22—242no—
184C22—241no—
185C22#9099611yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—801no—
190C3#1059828811yescharacteristic, complemented, Sylow
191C2—21no—
192C2—81no—
193C2—481no—
194C2#1174600711yescharacteristic
subgroupG/H
centerC2#11746007
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#353
prime radicalC5×#5058C2
hypocenterC3×C5#1406
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
2. #11746363C2semidirect
3. C3×#64761C2semidirect
8. C5×#874C4semidirect
10. C5×#803C4semidirect
15. #64761D3semidirect
54. #874Dic5semidirect
57. #803Dic5semidirect
149. C3×C5#1406semidirect
180. C5#67544semidirect
190. C3#10598288semidirect

Maximal subgroups

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

subgroupindex
C5×#50582
#117463632
C3×#647612
#105982883
#675445