Finite Group Databasebeta

← #14279361

Subgroups — #14279361

Order 1920.

224 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 34 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#11749386C211yesmaximal, characteristic
2#11746799C211yesmaximal, characteristic, complemented
3C3×#64927C211yesmaximal, characteristic, complemented
4#10598835—31nomaximal, Hall
5C5×#1007C411yescharacteristic, complemented
6C3×#4093C2211yescharacteristic
7#91298—21no—
8#91228—21no—
9C3×#4002—21no—
10#91120C411yescharacteristic, complemented
11#90979—21no—
12#67460—51nomaximal, Hall
13#65534—31no—
14#64928—31no—
15#64927D311yescharacteristic, complemented
16C2×C3×C5×Q8C2×C411yescharacteristic
17C5×#239—41no—
18C5×D3×Q8—41no—
19C5×#235—21no—
20C5×#235—41no—
21C2×C3×D20D411yescharacteristic
22#6763—41no—
23C2×C3×#170—41no—
24#6710—21no—
25C3×#685—41no—
26C3×C4×Dic5D411yescharacteristic
27#6655—41no—
28#6652—41no—
29#5062—51no—
30C3×#329—51no—
31#4541—51no—
32C5×2−1+4—31no—
33#4095—61no—
34#4093C2×D311yescharacteristic
35#4002—21no—
36#3999—61no—
37#3969—61no—
38#3968—31no—
39#1404—151noSylow
40C22×C3×D5—21no—
41C2×ΓL(1,𝔽16)—81no—
42C3×C5×Q8—41no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C5×#67—41no—
46C5×D12—21no—
47C5×D12—41no—
48C4×C5×D3—41no—
49C4×C5×D3—42no—
50C5×Dic6—21no—
51C5×Dic6—41no—
52C2×C3×Dic5—21no—
53C3×D20—41no—
54C3×#170—42no—
55C3⋊#168—41no—
56#1007AGL(1,𝔽5)11yescharacteristic, complemented
57C3×#124—51no—
58#932—101no—
59C3×#97—101no—
60#836—51no—
61#834—101no—
62#805—101no—
63C5×#41—61no—
64C5×#41—121no—
65C5×#41—121no—
66C2×C5×Q8—121no—
67C2×C5×Q8C4×D311yescharacteristic
68C2×D20D1211yescharacteristic
69C22⋊AGL(1,𝔽5)—121no—
70C2×#170—41no—
71#688—121no—
72#686—121no—
73#685—41no—
74C4×Dic5#6711yescharacteristic
75#681—61no—
76#454—151no—
77#354—151no—
78#329—51no—
79C22×C3×C5#9911yescharacteristic
80C2×C5×D3—41no—
81C2×C3×D5—41no—
82C2×C3×D5—81no—
83ΓL(1,𝔽16)—161no—
84C3×C4×C5—21no—
85C3×C4×C5—41no—
86C3×Dic5—41no—
87C5×Dic3—41no—
88C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
89C2×C3×D4—51no—
90#239—41no—
91D3×Q8—41no—
92#235—21no—
93#235—41no—
94C2×C3×C8—201no—
95C3×C22⋊C4—201no—
96C3×C42—51no—
97#217—201no—
98#214—201no—
99#213—201no—
100#208—101no—
101C22×D5—21no—
102C2×AGL(1,𝔽5)—241no—
103C5×Q8—41no—
104C5×Q8—61no—
105C5×Q8—121no—
106C5×D4—61no—
107C5×D4—121no—
108C5×D4—121no—
109C2×C4×C5—21no—
110C2×C4×C5—121no—
111C2×C4×C5—122no—
112C2×C4×C5(C2×D3)⋊C411yescharacteristic
113C2×Dic5—21no—
114D20—41no—
115#170—42no—
116#168—121no—
1172−1+4—31no—
118AGL(1,ℤ/8)—301no—
119#124—51no—
120#104—301no—
121#101—151no—
122#99—301no—
123#97—101no—
124C2×C3×C5—21no—
125C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
126C3×D5—81no—
127C5×D3—81no—
128C23×C3—101no—
129C3×Q8—41no—
130C3×D4—201no—
131C2×C3×C4—21no—
132C2×C3×C4—101no—
133C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
134#67—41no—
135C2×Dic3—401no—
136D12—21no—
137D12—41no—
138C4×D3—41no—
139C4×D3—42no—
140Dic6—21no—
141Dic6—41no—
142C3×C8—202no—
143C3⋊C8—201no—
144C22×C5—121no—
145C22×C5#80611yescharacteristic
146C2×D5—41no—
147C2×D5—81no—
148AGL(1,𝔽5)—481no—
149C4×C5—21no—
150C4×C5—41no—
151C4×C5—121no—
152Dic5—41no—
153#41—61no—
154#41—121no—
155#41—121no—
156C2×Q8—121no—
157C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
158C2×D4—51no—
159SD16—601no—
160D8—601no—
161M16—301no—
162C2×C8—201no—
163C22⋊C4—201no—
164C22⋊C4—601no—
165C42—51no—
166C3×C5#140411yescharacteristic, complemented, Hall
167C22×C3—201no—
168C22×C3—401no—
169C22×C3#401111yescharacteristic
170C2×D3—41no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—201no—
174Dic3—41no—
175Dic3—801no—
176C2×C5—21no—
177C2×C5—241no—
178C2×C5#447511yescharacteristic
179D5—81no—
180C23—101no—
181Q8—41no—
182Q8—61no—
183Q8—121no—
184D4—61no—
185D4—121no—
186D4—121no—
187D4—201no—
188C2×C4—21no—
189C2×C4—101no—
190C2×C4—121no—
191C2×C4—122no—
192C2×C4—1201no—
193C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
194C8—202no—
195C8—601no—
196C2×C3—21no—
197C2×C3—401no—
198C2×C3#6493411yescharacteristic
199D3—81no—
200C5#6746011yescharacteristic, complemented, Sylow
201C22—121no—
202C22—201no—
203C22—401no—
204C22#9117211yescharacteristic
205C4—21no—
206C4—41no—
207C4—121no—
208C4—201no—
209C4—2401no—
210C3#1059883511yescharacteristic, complemented, Sylow
211C2—21no—
212C2—241no—
213C2—401no—
214C2#1174657811yescharacteristic
subgroupG/H
centerC2#11746578
commutator, FittingC2×C3×C5×Q8C2×C4
Frattini, hypercenterC2×Q8D3×AGL(1,𝔽5)
socleC2×C3×C5AΣL(1,𝔽16)
prime radical#11749386C2
cosocleC3×#4093C22
hypocenterC3×C5#1404
LCSG ▷ C2×C3×C5×Q8 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11746799C2semidirect
3. C3×#64927C2semidirect
5. C5×#1007C4semidirect
10. #91120C4semidirect
15. #64927D3semidirect
56. #1007AGL(1,𝔽5)semidirect
166. C3×C5#1404semidirect
200. C5#67460semidirect
210. C3#10598835semidirect

Maximal subgroups

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

subgroupindex
#117493862
#117467992
C3×#649272
#105988353
#674605