Finite Group Databasebeta

← #14279403

Subgroups — #14279403

Order 1920.

216 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 40 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#11751159C211yesmaximal, characteristic
2C5×#4542C211yesmaximal, characteristic, complemented
3C3×#64761C211yesmaximal, characteristic, complemented
4#10598039—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×#6717—21no—
7C2×#6715—21no—
8#91763C411yescharacteristic, complemented
9#91087C411yescharacteristic, complemented
10C5×#836—21no—
11C3×#3966—21no—
12#67544—51nomaximal, Hall
13#65347—31no—
14C5×#355—31no—
15#64761D311yescharacteristic, complemented
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×D60—21no—
19C2×D60—41no—
20C3×C5×C22⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6717—42no—
23#6715—42no—
24C2×C3⋊#168—21no—
25C5×#208—41no—
26C3×C22⋊Dic5—41no—
27#5058—51no—
28C3×#354—51no—
29#4542D511yescharacteristic, complemented
30C5×#124C2×D311yescharacteristic
31C2×#688—61no—
32C2×#686—61no—
33#4020—31no—
34C5×#101—61no—
35#3966—21no—
36#3935—31no—
37#1406—151noSylow
38C23×C3×C5—21no—
39C22×D15—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45D60—41no—
46D60—41no—
47D60—82no—
48C2×C3×Dic5—81no—
49C3⋊#168—22no—
50C5×C3⋊C8—81no—
51C3×#124C2×D511yescharacteristic
52C2×#215—101no—
53C2×#213—101no—
54#874—51no—
55C3×#99—101no—
56#836—21no—
57#803—51no—
58C2×C5×Q8D1211yescharacteristic
59C2×C5×D4#6711yescharacteristic
60C2×D20—61no—
61C2×D20—121no—
62C5×M16—121no—
63C5×C22⋊C4—41no—
64C42×C5C4×D311yescharacteristic
65C22⋊Dic5—41no—
66#688—122no—
67#686—122no—
68C2×#168—61no—
69#496—151no—
70#355—31no—
71#354—51no—
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5#9911yescharacteristic
75C2×D15—82no—
76C2×D15—81no—
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80C3×Dic5—161no—
81C2×C3×Q8C22⋊D511yescharacteristic
82C2×C3×D4D2011yescharacteristic
83C2×D12—101no—
84C2×D12—201no—
85C3×C22⋊C4—41no—
86C3×C22⋊C4—201no—
87C3×C42C4×D511yescharacteristic
88#215—202no—
89#213—202no—
90#208—41no—
91C2×C3⋊C8—101no—
92C23×C5—21no—
93C22×D5—121no—
94C5×Q8—41no—
95C5×D4—41no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5(C2×D3)⋊C411yescharacteristic
99C2×Dic5—81no—
100D20—121no—
101D20—121no—
102D20—242no—
103C5×C8—241no—
104#168—62no—
105C2×SD16—301no—
106C2×D8—301no—
107#127—151no—
108#124D3×D511yescharacteristic
109#101—61no—
110#99—101no—
111#97—151no—
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5#35311yescharacteristic
115D15—161no—
116C23×C3—21no—
117C22×D3—201no—
118C3×Q8—41no—
119C3×D4—41no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—401no—
123C2×C3×C4#68511yescharacteristic
124D12—201no—
125D12—201no—
126D12—402no—
127C3⋊C8—81no—
128C3⋊C8—102no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5#80611yescharacteristic
132C2×D5—242no—
133C2×D5—241no—
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137Dic5—161no—
138C2×Q8#120311yescharacteristic
139C2×D4—301no—
140C2×D4—601no—
141C2×D4#120211yescharacteristic
142SD16—602no—
143D8—602no—
144M16—121no—
145C2×C8—301no—
146C22⋊C4—41no—
147C22⋊C4—201no—
148C42#120011yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3#393811yescharacteristic
153C2×D3—402no—
154C2×D3—401no—
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158C3×C4—801no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5#447411yescharacteristic
162D5—481no—
163C23—21no—
164C23—601no—
165Q8—41no—
166D4—41no—
167D4—601no—
168D4—601no—
169D4—1202no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—401no—
173C2×C4#666711yescharacteristic
174C8—241no—
175C8—302no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3#6469411yescharacteristic
179D3—801no—
180C5#6754411yescharacteristic, complemented, Sylow
181C22—41no—
182C22—81no—
183C22—1202no—
184C22—1201no—
185C22#9099711yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—801no—
190C3#1059803911yescharacteristic, complemented, Sylow
191C2—21no—
192C2—81no—
193C2—2401no—
194C2#1174600811yescharacteristic
subgroupG/H
centerC2#11746008
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#353
prime radical#11751159C2
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. C5×#4542C2semidirect
3. C3×#64761C2semidirect
8. #91763C4semidirect
9. #91087C4semidirect
15. #64761D3semidirect
29. #4542D5semidirect
149. C3×C5#1406semidirect
180. C5#67544semidirect
190. C3#10598039semidirect

Maximal subgroups

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

subgroupindex
#117511592
C5×#45422
C3×#647612
#105980393
#675445