Finite Group Databasebeta

← C3×#10598043 #14279463

Subgroups — C3×#10598043 #14279463

Order 1920.

208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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×#65374C211yesmaximal, characteristic
2C3×C5×#356C211yesmaximal, characteristic, complemented
3C3×#64768C211yesmaximal, characteristic, complemented
4#10598043C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×C3×#688—21no—
7C2×C3×#688—21no—
8C3×#4020C411yescharacteristic
9C3×C5×#101—21no—
10C3×#3968—21no—
11C3×C4×#168C411yescharacteristic
12C3×#1410—51nomaximal, Hall
13#65374C2×C311yescharacteristic
14C5×#356C2×C311yescharacteristic, complemented
15#64768C2×C311yescharacteristic, complemented
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×C3×D20—21no—
19C2×C3×D20—41no—
20C3×C5×M16—41no—
21C3×C5×C4⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C3×#688—42no—
24C3×#688—42no—
25C3×#681—41no—
26C2×C3×#168—21no—
27C3×#492—51no—
28C3×#356—51no—
29C3×#356D511yescharacteristic, complemented
30C5×C4⋊Q8C22×C311yescharacteristic
31C2×#688—21no—
32C2×#688—21no—
33#4020C3×C411yescharacteristic
34C5×#101—21no—
35#3968—21no—
36C4×#168C3×C411yescharacteristic
37#1410—51noSylow
38C22×C3×D5—41no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3×C5×C8—81no—
49C3×#168—22no—
50C3×#168—81no—
51C2×C3×SD16—101no—
52C2×C3×SD16—101no—
53C3×C4⋊Q8C2×D511yescharacteristic
54C3×#127—51no—
55C3×#101—21no—
56C3×#101—101no—
57C3×C4×C8—51no—
58C2×C5×Q8C3×D411yescharacteristic
59C2×C5×Q8C3×D411yescharacteristic
60C2×D20—21no—
61C2×D20—41no—
62C5×M16—41no—
63C5×C4⋊C4—41no—
64C42×C5C2×C3×C411yescharacteristic
65#688—42no—
66#688—42no—
67#681—41no—
68C2×#168—21no—
69#492—51no—
70#356—51no—
71#356C3×D511yescharacteristic, complemented
72C22×C3×C5#9911yescharacteristic
73C2×C3×D5—82no—
74C2×C3×D5—81no—
75C3×C4×C5—22no—
76C3×C4×C5—21no—
77C3×C4×C5—41no—
78C3×C4×C5—41no—
79C2×C3×Q8D2011yescharacteristic
80C2×C3×Q8C22⋊D511yescharacteristic
81C2×C3×D4—101no—
82C2×C3×D4—201no—
83C3×SD16—202no—
84C3×SD16—202no—
85C3×M16—41no—
86C3×M16—201no—
87C2×C3×C8—101no—
88C3×C4⋊C4—41no—
89C3×C42C4×D511yescharacteristic
90C22×D5—41no—
91C5×Q8—41no—
92C5×Q8—41no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5C3×C22⋊C411yescharacteristic
97D20—41no—
98D20—41no—
99D20—82no—
100C5×C8—81no—
101#168—22no—
102#168—81no—
103C2×SD16—101no—
104C2×SD16—101no—
105C4⋊Q8C2×C3×D511yescharacteristic
106#127—51no—
107#101—21no—
108#101—101no—
109C4×C8—51no—
110C2×C3×C5—21no—
111C2×C3×C5#35311yescharacteristic
112C3×D5—161no—
113C23×C3—201no—
114C3×Q8—41no—
115C3×Q8—41no—
116C3×D4—201no—
117C3×D4—201no—
118C3×D4—402no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4#68511yescharacteristic
123C3×C8—81no—
124C3×C8—102no—
125C3×C8—401no—
126C22×C5C3×#9911yescharacteristic
127C2×D5—82no—
128C2×D5—81no—
129C4×C5—22no—
130C4×C5—21no—
131C4×C5—41no—
132C4×C5—41no—
133C2×Q8C3×D2011yescharacteristic
134C2×Q8C3×C22⋊D511yescharacteristic
135C2×D4—101no—
136C2×D4—201no—
137SD16—202no—
138SD16—202no—
139M16—41no—
140M16—201no—
141C2×C8—101no—
142C4⋊C4—41no—
143C42C3×C4×D511yescharacteristic
144C3×C5#141011yescharacteristic, complemented, Hall
145C22×C3—402no—
146C22×C3—401no—
147C22×C3#393811yescharacteristic
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—41no—
151C3×C4—41no—
152C2×C5—21no—
153C2×C5C3×#35311yescharacteristic
154D5—161no—
155C23—201no—
156Q8—41no—
157Q8—41no—
158D4—201no—
159D4—201no—
160D4—402no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4C3×#68511yescharacteristic
165C8—81no—
166C8—102no—
167C8—401no—
168C2×C3—21no—
169C2×C3—801no—
170C2×C3#6469411yescharacteristic
171C5C3×#141011yescharacteristic, complemented, Sylow
172C22—402no—
173C22—401no—
174C22C3×#393811yescharacteristic
175C4—22no—
176C4—21no—
177C4—41no—
178C4—41no—
179C3#1059804311yescharacteristic, direct product factor, Sylow
180C2—21no—
181C2—801no—
182C2C3×#6469411yescharacteristic
subgroupG/H
centerC2×C3#64694
commutatorC42×C5C2×C3×C4
FrattiniC4⋊Q8C2×C3×D5
FittingC3×C5×#356C2
socleC2×C3×C5#353
prime radicalC3×#4020C4
cosocleC5×C4⋊Q8C22×C3
hypercenterC3×#356D5
hypocenterC5C3×#1410
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊Q8 ◁ C3×#356

Complements

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

NH ≅ G/Ntype
2. C3×C5×#356C2semidirect
3. C3×#64768C2semidirect
4. #10598043C3direct (N × H)
14. C5×#356C2×C3semidirect
15. #64768C2×C3semidirect
29. C3×#356D5semidirect
71. #356C3×D5semidirect
144. C3×C5#1410semidirect
171. C5C3×#1410semidirect
179. C3#10598043direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653742
C3×C5×#3562
C3×#647682
#105980433
C3×#14105