Finite Group Databasebeta

← C3×#10598834 #14279326

Subgroups — C3×#10598834 #14279326

Order 1920.

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

normal subgroups only

This group has 224 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
1C3×#65531C211yesmaximal, characteristic
2C3×#64923C211yesmaximal, characteristic, complemented
3C3×#64921C211yesmaximal, characteristic, complemented
4#10598834C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×H(5,𝔽2)C411yescharacteristic
6C3×#4097—21no—
7C3×#4082C2211yescharacteristic
8C3×#4005—21no—
9C3×#4002—21no—
10C3×#3969—21no—
11C3×#3965C411yescharacteristic
12C3×#1403—51nomaximal, Hall
13#65531C2×C311yescharacteristic
14#64923C2×C311yescharacteristic, complemented
15#64921C2×C311yescharacteristic, complemented
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
22C3×#704—41no—
23C2×C3×#170—41no—
24C3×C22⋊Dic5—41no—
25C3×#689—41no—
26C3×#687—41no—
27C3×C4×Dic5D411yescharacteristic
28C3×#681—21no—
29C3×#455—51no—
30C3×#355—51no—
31C3×#329—51no—
32C5×H(5,𝔽2)C3×C411yescharacteristic
33#4097—21no—
34#4082C22×C311yescharacteristic
35#4005—21no—
36#4002—21no—
37#3969—21no—
38#3965C3×C411yescharacteristic
39#1403—51noSylow
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×#101—101no—
61C3×#100—51no—
62C3×#97—101no—
63C5×#41—21no—
64C5×#41—41no—
65C2×C5×D4—41no—
66C2×C5×D4—41no—
67C2×C5×D4C2×C3×C411yescharacteristic
68C2×Dic10C3×D411yescharacteristic
69#704—41no—
70C2×#170—41no—
71C22⋊Dic5—41no—
72#689—41no—
73#687—41no—
74C4×Dic5C3×D411yescharacteristic
75#681—21no—
76#455—51no—
77#355—51no—
78#329—51no—
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×M16—201no—
98C2×C3×C8—201no—
99C3×C22⋊C4—201no—
100C3×C42—51no—
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×C5C3×C22⋊C411yescharacteristic
111C2×Dic5—21no—
112C2×Dic5—21no—
113Dic10—41no—
114#170—42no—
115#170—81no—
116#168—41no—
117H(5,𝔽2)C3×AGL(1,𝔽5)11yescharacteristic
118#137—101no—
119#124—51no—
120#104—101no—
121#101—101no—
122#100—51no—
123#97—101no—
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×C5C3×#9911yescharacteristic
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×C3×AGL(1,𝔽5)11yescharacteristic
159Q16—201no—
160SD16—201no—
161M16—101no—
162M16—201no—
163C2×C8—201no—
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×C5C3×AΣL(1,𝔽16)11yescharacteristic
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×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
193C8—201no—
194C8—202no—
195C8—401no—
196C2×C3—21no—
197C2×C3—81no—
198C2×C3—81no—
199C2×C3#6493411yescharacteristic
200C5C3×#140311yescharacteristic, complemented, Sylow
201C22—41no—
202C22—41no—
203C22—81no—
204C22—161no—
205C22C3×#401111yescharacteristic
206C4—21no—
207C4—41no—
208C4—201no—
209C4—201no—
210C3#1059883411yescharacteristic, direct product factor, Sylow
211C2—21no—
212C2—81no—
213C2—81no—
214C2C3×#6493411yescharacteristic
subgroupG/H
centerC2×C3#64934
commutatorC2×C5×D4C2×C3×C4
FrattiniC2×D4C2×C3×AGL(1,𝔽5)
Fitting, prime radicalC3×C5×H(5,𝔽2)C4
socleC2×C3×C5AΣL(1,𝔽16)
cosocle#4082C22×C3
hypercenterC3×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C3×#1403
LCSG ▷ C2×C5×D4 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4 ◁ C3×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C3×#64923C2semidirect
3. C3×#64921C2semidirect
4. #10598834C3direct (N × H)
14. #64923C2×C3semidirect
15. #64921C2×C3semidirect
166. C3×C5#1403semidirect
200. C5C3×#1403semidirect
210. C3#10598834direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#655312
C3×#649232
C3×#649212
#105988343
C3×#14035