Finite Group Databasebeta

← C3×#10598754 #14279418

Subgroups — C3×#10598754 #14279418

Order 1920.

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

normal subgroups only

This group has 196 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×#65375C211yesmaximal, characteristic
2C3×#64856C211yesmaximal, characteristic
3C3×#64854C211yesmaximal, characteristic
4#10598754C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C4⋊Q8C411yescharacteristic, complemented
6C2×C3×#689—21no—
7C2×C3×#688—21no—
8C3×#4021C2211yescharacteristic
9C3×#4005—21no—
10C3×#3999—21no—
11C3×#3935C411yescharacteristic, complemented
12C3×#1407—51nomaximal, Hall
13#65375C2×C311yescharacteristic
14#64856C2×C311yescharacteristic
15#64854C2×C311yescharacteristic
16C2×C3×C5×Q8—21no—
17C2×C3×D20D411yescharacteristic
18C2×C3×Dic10D411yescharacteristic
19C3×C22⋊AGL(1,𝔽5)—41no—
20C3×#704—41no—
21C3×C5×C4⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C3×#689—42no—
24C3×#688—42no—
25C3×#685—41no—
26C2×C3×#168—21no—
27C3×#497—51no—
28C3×#355—51no—
29C3×#354—51no—
30C5×C4⋊Q8C3×C411yescharacteristic, complemented
31C2×#689—21no—
32C2×#688—21no—
33#4021C22×C311yescharacteristic
34#4005—21no—
35#3999—21no—
36#3935C3×C411yescharacteristic, complemented
37#1407—51noSylow
38C22×C3×D5—21no—
39C2×C3×AGL(1,𝔽5)—81no—
40C3×C5×Q8—41no—
41C3×C5×Q8—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—41no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×Dic5—21no—
46C3×D20—41no—
47C3×Dic10—41no—
48C3×#170—81no—
49C3×#168—22no—
50C2×C3×Q16—101no—
51C2×C3×SD16—101no—
52C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
53C3×#124—51no—
54C3×#101—101no—
55C3×#99—101no—
56C3×#97—51no—
57C2×C5×Q8—21no—
58C2×D20C3×D411yescharacteristic
59C2×Dic10C3×D411yescharacteristic
60C22⋊AGL(1,𝔽5)—41no—
61#704—41no—
62C5×C4⋊C4—41no—
63C42×C5C2×C3×C411yescharacteristic
64#689—42no—
65#688—42no—
66#685—41no—
67C2×#168—21no—
68#497—51no—
69#355—51no—
70#354—51no—
71C22×C3×C5#9911yescharacteristic
72C2×C3×D5—41no—
73C2×C3×D5—81no—
74C3×AGL(1,𝔽5)—161no—
75C3×C4×C5—21no—
76C3×C4×C5—41no—
77C3×C4×C5—81no—
78C3×Dic5—41no—
79C2×C3×Q8—21no—
80C2×C3×Q8—51no—
81C2×C3×D4—51no—
82C3×Q16—202no—
83C3×SD16—202no—
84C3×M16—201no—
85C2×C3×C8—101no—
86C3×C4⋊C4—41no—
87C3×C22⋊C4—201no—
88C3×C22⋊C4—201no—
89C3×C42C2×AGL(1,𝔽5)11yescharacteristic
90C22×D5—21no—
91C2×AGL(1,𝔽5)—81no—
92C5×Q8—41no—
93C5×Q8—41no—
94C2×C4×C5—21no—
95C2×C4×C5—41no—
96C2×C4×C5C3×C22⋊C411yescharacteristic
97C2×Dic5—21no—
98D20—41no—
99Dic10—41no—
100#170—81no—
101#168—22no—
102C2×Q16—101no—
103C2×SD16—101no—
104C4⋊Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
105#124—51no—
106#101—101no—
107#99—101no—
108#97—51no—
109C2×C3×C5—21no—
110C2×C3×C5#35311yescharacteristic
111C3×D5—81no—
112C23×C3—101no—
113C3×Q8—41no—
114C3×Q8—41no—
115C3×Q8—201no—
116C3×D4—201no—
117C2×C3×C4—21no—
118C2×C3×C4—41no—
119C2×C3×C4—101no—
120C2×C3×C4—401no—
121C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
122C3×C8—102no—
123C3×C8—401no—
124C22×C5C3×#9911yescharacteristic
125C2×D5—41no—
126C2×D5—81no—
127AGL(1,𝔽5)—161no—
128C4×C5—21no—
129C4×C5—41no—
130C4×C5—81no—
131Dic5—41no—
132C2×Q8—21no—
133C2×Q8—51no—
134C2×D4—51no—
135Q16—202no—
136SD16—202no—
137M16—201no—
138C2×C8—101no—
139C4⋊C4—41no—
140C22⋊C4—201no—
141C22⋊C4—201no—
142C42C2×C3×AGL(1,𝔽5)11yescharacteristic
143C3×C5#140711yescharacteristic, complemented, Hall
144C22×C3—201no—
145C22×C3—401no—
146C22×C3#401111yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—81no—
150C3×C4—201no—
151C3×C4—801no—
152C2×C5—21no—
153C2×C5C3×#35311yescharacteristic
154D5—81no—
155C23—101no—
156Q8—41no—
157Q8—41no—
158Q8—201no—
159D4—201no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—101no—
163C2×C4—401no—
164C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
165C8—102no—
166C8—401no—
167C2×C3—21no—
168C2×C3—401no—
169C2×C3#6492211yescharacteristic
170C5C3×#140711yescharacteristic, complemented, Sylow
171C22—201no—
172C22—401no—
173C22C3×#401111yescharacteristic
174C4—21no—
175C4—41no—
176C4—81no—
177C4—201no—
178C4—801no—
179C3#1059875411yescharacteristic, direct product factor, Sylow
180C2—21no—
181C2—401no—
182C2C3×#6492211yescharacteristic
subgroupG/H
centerC2×C3#64922
commutatorC42×C5C2×C3×C4
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊Q8C4
socleC2×C3×C5#353
prime radicalC2×C3×D20D4
cosocle#4021C22×C3
hypercenterC3×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C3×#1407
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10598754C3direct (N × H)
5. C3×C5×C4⋊Q8C4semidirect
11. C3×#3935C4semidirect
30. C5×C4⋊Q8C3×C4semidirect
36. #3935C3×C4semidirect
52. C3×C4⋊Q8AGL(1,𝔽5)semidirect
104. C4⋊Q8C3×AGL(1,𝔽5)semidirect
143. C3×C5#1407semidirect
170. C5C3×#1407semidirect
179. C3#10598754direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653752
C3×#648562
C3×#648542
#105987543
C3×#14075