Finite Group Databasebeta

← #14279327

Subgroups — #14279327

Order 1920.

224 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C3×#65531C211yesmaximal, characteristic
2#11746794C211yesmaximal, characteristic, complemented
3#11746792C211yesmaximal, characteristic, complemented
4#10598834—31nomaximal, Hall
5C3×C5×H(5,𝔽2)C411yescharacteristic
6C3×#4097—21no—
7C3×#4082C2211yescharacteristic
8#91234—21no—
9#91231—21no—
10C3×#3969—21no—
11C3×#3965C411yescharacteristic
12#67772—51nomaximal, Hall
13#65531D311yescharacteristic
14#64923—31no—
15#64921—31no—
16C3×C5×#41—21no—
17C3×C5×#41—41no—
18C2×C3×C5×D4—41no—
19C2×C3×C5×D4—41no—
20C2×C3×C5×D4C2×C411yescharacteristic
21C2×C3×Dic10D411yescharacteristic
22#6762—41no—
23C2×C3⋊#170—41no—
24C3×C22⋊Dic5—41no—
25C3×#689—41no—
26C3×#687—41no—
27C3×C4×Dic5D411yescharacteristic
28C3×#681—21no—
29C3×#455—51no—
30#4542—51no—
31#4540—51no—
32C5×H(5,𝔽2)Dic311yescharacteristic
33#4097—21no—
34#4082C2×D311yescharacteristic
35#4005—61no—
36#4002—61no—
37#3969—21no—
38#3965Dic311yescharacteristic
39#1403—151noSylow
40C23×C3×C5—21no—
41C23×C3×C5—41no—
42C3×C5×Q8—21no—
43C3×C5×D4—21no—
44C3×C5×D4—41no—
45C3×C5×D4—42no—
46C3×C5×D4—41no—
47C2×C3×C4×C5—41no—
48C2×C3×C4×C5—41no—
49C2×C3×C4×C5C22⋊C411yescharacteristic
50C2×C3×Dic5—21no—
51C2×C3×Dic5—21no—
52C3×Dic10—41no—
53C3⋊#170—42no—
54C3⋊#170—81no—
55C3×#168—41no—
56C3×H(5,𝔽2)AGL(1,𝔽5)11yescharacteristic
57C3×#137—101no—
58C3×#124—51no—
59C3×#104—101no—
60C3×#100—51no—
61#836—101no—
62#803—101no—
63C5×#41—21no—
64C5×#41—41no—
65C2×C5×D4—41no—
66C2×C5×D4—41no—
67C2×C5×D4C2×Dic311yescharacteristic
68C2×Dic10#6711yescharacteristic
69#704—121no—
70C2×#170—121no—
71C22⋊Dic5—41no—
72#689—41no—
73#687—41no—
74C4×Dic5#6711yescharacteristic
75#681—21no—
76#455—51no—
77#355—151no—
78#329—151no—
79C22×C3×C5—41no—
80C22×C3×C5—41no—
81C22×C3×C5—81no—
82C22×C3×C5—161no—
83C22×C3×C5#9911yescharacteristic
84C3×C4×C5—21no—
85C3×C4×C5—41no—
86C3×Dic5—41no—
87C3×Dic5—41no—
88C3×#41—21no—
89C3×#41—41no—
90C2×C3×Q8—51no—
91C2×C3×D4—41no—
92C2×C3×D4—41no—
93C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
94C3×Q16—201no—
95C3×SD16—201no—
96C3×M16—101no—
97C3×C22⋊C4—201no—
98C3×C42—51no—
99#208—201no—
100C2×C3⋊C8—201no—
101C23×C5—21no—
102C23×C5—41no—
103C5×Q8—21no—
104C5×D4—21no—
105C5×D4—41no—
106C5×D4—42no—
107C5×D4—41no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×C4×C5#21711yescharacteristic
111C2×Dic5—21no—
112C2×Dic5—21no—
113Dic10—41no—
114#170—122no—
115#170—241no—
116#168—41no—
117H(5,𝔽2)ΓL(1,𝔽16)11yescharacteristic
118#137—101no—
119#124—51no—
120#104—101no—
121#101—301no—
122#100—51no—
123#97—301no—
124C2×C3×C5—21no—
125C2×C3×C5—81no—
126C2×C3×C5—81no—
127C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
128C23×C3—21no—
129C23×C3—41no—
130C3×Q8—21no—
131C3×Q8—201no—
132C3×D4—21no—
133C3×D4—41no—
134C3×D4—42no—
135C3×D4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—101no—
139C2×C3×C4—101no—
140C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
141C3×C8—201no—
142C3⋊C8—202no—
143C3⋊C8—401no—
144C22×C5—41no—
145C22×C5—41no—
146C22×C5—81no—
147C22×C5—161no—
148C22×C5#83411yescharacteristic
149C4×C5—21no—
150C4×C5—41no—
151Dic5—41no—
152Dic5—41no—
153#41—21no—
154#41—41no—
155C2×Q8—51no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
159Q16—201no—
160SD16—201no—
161M16—101no—
162M16—601no—
163C2×C8—601no—
164C22⋊C4—201no—
165C42—51no—
166C3×C5#140311yescharacteristic, complemented, Hall
167C22×C3—41no—
168C22×C3—41no—
169C22×C3—81no—
170C22×C3—161no—
171C22×C3#401111yescharacteristic
172C3×C4—21no—
173C3×C4—41no—
174C3×C4—201no—
175C3×C4—201no—
176C2×C5—21no—
177C2×C5—81no—
178C2×C5—81no—
179C2×C5#453611yescharacteristic
180C23—21no—
181C23—41no—
182Q8—21no—
183Q8—201no—
184D4—21no—
185D4—41no—
186D4—42no—
187D4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4#676311yescharacteristic
193C8—201no—
194C8—602no—
195C8—1201no—
196C2×C3—21no—
197C2×C3—81no—
198C2×C3—81no—
199C2×C3#6493411yescharacteristic
200C5#6777211yescharacteristic, complemented, Sylow
201C22—41no—
202C22—41no—
203C22—81no—
204C22—161no—
205C22#9124011yescharacteristic
206C4—21no—
207C4—41no—
208C4—201no—
209C4—201no—
210C3#1059883411yescharacteristic, complemented, Sylow
211C2—21no—
212C2—81no—
213C2—81no—
214C2#1174680511yescharacteristic
subgroupG/H
centerC2#11746805
commutatorC2×C3×C5×D4C2×C4
FrattiniC2×D4C2×ΓL(1,𝔽16)
Fitting, prime radicalC3×C5×H(5,𝔽2)C4
socleC2×C3×C5AΣL(1,𝔽16)
cosocleC3×#4082C22
hypercenterH(5,𝔽2)ΓL(1,𝔽16)
hypocenterC3×C5#1403
LCSG ▷ C2×C3×C5×D4 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. #11746794C2semidirect
3. #11746792C2semidirect
166. C3×C5#1403semidirect
200. C5#67772semidirect
210. C3#10598834semidirect

Maximal subgroups

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

subgroupindex
C3×#655312
#117467942
#117467922
#105988343
#677725