Finite Group Databasebeta

← C3×#10598540 #14279397

Subgroups — C3×#10598540 #14279397

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
1C3×#65001C211yesmaximal, characteristic
2C3×#64856C211yesmaximal, characteristic, complemented
3C3×#64854C211yesmaximal, characteristic, complemented
4#10598540C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×D40—21no—
6C2×C3×#677—21no—
7C3×#4021C2211yescharacteristic
8C3×#4020C411yescharacteristic, complemented
9C3×#4005—21no—
10C3×#3999—21no—
11C3×C5×#97C411yescharacteristic, complemented
12C3×#1406—51nomaximal, Hall
13#65001C2×C311yescharacteristic
14#64856C2×C311yescharacteristic, complemented
15#64854C2×C311yescharacteristic, complemented
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×Dic10D411yescharacteristic
20C3×C22⋊AGL(1,𝔽5)—41no—
21C3×#704—41no—
22C2×C3×C5×C8—21no—
23C3×C42×C5C2×C411yescharacteristic
24C3×#685—41no—
25C3×D40—42no—
26C3×#677—42no—
27C3×#496—51no—
28C3×#355—51no—
29C3×#354—51no—
30C2×D40—21no—
31C2×#677—21no—
32#4021C22×C311yescharacteristic
33#4020C3×C411yescharacteristic, complemented
34#4005—21no—
35#3999—21no—
36C5×#97C3×C411yescharacteristic, complemented
37#1406—51noSylow
38C22×C3×D5—21no—
39C22×C3×D5—41no—
40C2×C3×AGL(1,𝔽5)—81no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C2×C3×Dic5—21no—
44C3×D20—41no—
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3×Dic10—41no—
49C3×#170—81no—
50C3×C5×C8—22no—
51C2×C3×SD16—101no—
52C2×C3×D8—101no—
53C3×#127—51no—
54C3×#124—51no—
55C3×#101—101no—
56C3×#99—101no—
57C3×#97AGL(1,𝔽5)11yescharacteristic, complemented
58C2×D20—21no—
59C2×D20—41no—
60C2×D20C3×D411yescharacteristic
61C2×Dic10C3×D411yescharacteristic
62C22⋊AGL(1,𝔽5)—41no—
63#704—41no—
64C2×C5×C8—21no—
65C42×C5C2×C3×C411yescharacteristic
66#685—41no—
67D40—42no—
68#677—42no—
69#496—51no—
70#355—51no—
71#354—51no—
72C22×C3×C5#9911yescharacteristic
73C2×C3×D5—41no—
74C2×C3×D5—81no—
75C2×C3×D5—82no—
76C2×C3×D5—81no—
77C3×AGL(1,𝔽5)—161no—
78C3×C4×C5—21no—
79C3×C4×C5—41no—
80C3×Dic5—41no—
81C2×C3×Q8—51no—
82C2×C3×D4—51no—
83C2×C3×D4—101no—
84C2×C3×D4—201no—
85C3×SD16—202no—
86C3×D8—202no—
87C3×M16—201no—
88C2×C3×C8—21no—
89C3×C22⋊C4—201no—
90C3×C22⋊C4—201no—
91C3×C42C2×AGL(1,𝔽5)11yescharacteristic
92C22×D5—21no—
93C22×D5—41no—
94C2×AGL(1,𝔽5)—81no—
95C2×C4×C5—21no—
96C2×C4×C5C3×C22⋊C411yescharacteristic
97C2×Dic5—21no—
98D20—41no—
99D20—41no—
100D20—41no—
101D20—82no—
102Dic10—41no—
103#170—81no—
104C5×C8—22no—
105C2×SD16—101no—
106C2×D8—101no—
107#127—51no—
108#124—51no—
109#101—101no—
110#99—101no—
111#97C3×AGL(1,𝔽5)11yescharacteristic, complemented
112C2×C3×C5—21no—
113C2×C3×C5#35311yescharacteristic
114C3×D5—81no—
115C3×D5—161no—
116C23×C3—101no—
117C23×C3—201no—
118C3×Q8—201no—
119C3×D4—201no—
120C3×D4—201no—
121C3×D4—201no—
122C3×D4—402no—
123C2×C3×C4—21no—
124C2×C3×C4—101no—
125C2×C3×C4—401no—
126C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
127C3×C8—22no—
128C3×C8—401no—
129C22×C5C3×#9911yescharacteristic
130C2×D5—41no—
131C2×D5—81no—
132C2×D5—82no—
133C2×D5—81no—
134AGL(1,𝔽5)—161no—
135C4×C5—21no—
136C4×C5—41no—
137Dic5—41no—
138C2×Q8—51no—
139C2×D4—51no—
140C2×D4—101no—
141C2×D4—201no—
142SD16—202no—
143D8—202no—
144M16—201no—
145C2×C8—21no—
146C22⋊C4—201no—
147C22⋊C4—201no—
148C42C2×C3×AGL(1,𝔽5)11yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—201no—
151C22×C3—401no—
152C22×C3—402no—
153C22×C3—401no—
154C22×C3#399911yescharacteristic
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—201no—
158C3×C4—801no—
159C2×C5—21no—
160C2×C5C3×#35311yescharacteristic
161D5—81no—
162D5—161no—
163C23—101no—
164C23—201no—
165Q8—201no—
166D4—201no—
167D4—201no—
168D4—201no—
169D4—402no—
170C2×C4—21no—
171C2×C4—101no—
172C2×C4—401no—
173C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
174C8—22no—
175C8—401no—
176C2×C3—21no—
177C2×C3—401no—
178C2×C3—801no—
179C2×C3#6485311yescharacteristic
180C5C3×#140611yescharacteristic, complemented, Sylow
181C22—201no—
182C22—401no—
183C22—402no—
184C22—401no—
185C22C3×#399911yescharacteristic
186C4—21no—
187C4—41no—
188C4—201no—
189C4—801no—
190C3#1059854011yescharacteristic, direct product factor, Sylow
191C2—21no—
192C2—401no—
193C2—801no—
194C2C3×#6485311yescharacteristic
subgroupG/H
centerC2×C3#64853
commutatorC42×C5C2×C3×C4
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×#97C4
socleC2×C3×C5#353
prime radicalC3×#65001C2
cosocle#4021C22×C3
hypercenterC3×#97AGL(1,𝔽5)
hypocenterC5C3×#1406
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×#97

Complements

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

NH ≅ G/Ntype
2. C3×#64856C2semidirect
3. C3×#64854C2semidirect
4. #10598540C3direct (N × H)
8. C3×#4020C4semidirect
11. C3×C5×#97C4semidirect
14. #64856C2×C3semidirect
15. #64854C2×C3semidirect
33. #4020C3×C4semidirect
36. C5×#97C3×C4semidirect
57. C3×#97AGL(1,𝔽5)semidirect
111. #97C3×AGL(1,𝔽5)semidirect
149. C3×C5#1406semidirect
180. C5C3×#1406semidirect
190. C3#10598540direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#650012
C3×#648562
C3×#648542
#105985403
C3×#14065