Finite Group Databasebeta

← C3×#10598035 #14279387

Subgroups — C3×#10598035 #14279387

Order 1920.

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

normal subgroups only

This group has 216 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×#65347C211yesmaximal, characteristic
2C3×C5×#354C211yesmaximal, characteristic, complemented
3C3×#64762C211yesmaximal, characteristic, complemented
4#10598035C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#124C2211yescharacteristic
6C2×C3×#688—21no—
7C2×C3×#686—21no—
8C3×#4020C411yescharacteristic, complemented
9C3×C5×#99—21no—
10C3×#3968—21no—
11C3×#3935C411yescharacteristic, complemented
12C3×#1406—51nomaximal, Hall
13#65347C2×C311yescharacteristic
14C5×#354C2×C311yescharacteristic, complemented
15#64762C2×C311yescharacteristic, complemented
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×D20—21no—
19C2×C3×D20—41no—
20C3×C5×C22⋊C4—41no—
21C3×C5×C22⋊C4—41no—
22C3×C42×C5C2×C411yescharacteristic
23C3×#688—42no—
24C3×#686—42no—
25C3×#681—41no—
26C2×C3×#168—21no—
27C3×#496—51no—
28C3×#355—51no—
29C3×#354D511yescharacteristic, complemented
30C5×#124C22×C311yescharacteristic
31C2×#688—21no—
32C2×#686—21no—
33#4020C3×C411yescharacteristic, complemented
34C5×#99—21no—
35#3968—21no—
36#3935C3×C411yescharacteristic, complemented
37#1406—51noSylow
38C23×C3×C5—21no—
39C22×C3×D5—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—81no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C3×D20—41no—
47C3×D20—41no—
48C3×D20—82no—
49C3×#168—22no—
50C3×#168—81no—
51C2×C3×SD16—101no—
52C2×C3×D8—101no—
53C3×#127—51no—
54C3×#124C2×D511yescharacteristic
55C3×#101—101no—
56C3×#99—21no—
57C3×#97—51no—
58C2×C5×Q8C3×D411yescharacteristic
59C2×C5×D4C3×D411yescharacteristic
60C2×D20—21no—
61C2×D20—41no—
62C5×C22⋊C4—41no—
63C5×C22⋊C4—41no—
64C42×C5C2×C3×C411yescharacteristic
65#688—42no—
66#686—42no—
67#681—41no—
68C2×#168—21no—
69#496—51no—
70#355—51no—
71#354C3×D511yescharacteristic, complemented
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5#9911yescharacteristic
75C2×C3×D5—82no—
76C2×C3×D5—81no—
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80C3×C4×C5—161no—
81C2×C3×Q8D2011yescharacteristic
82C2×C3×D4—101no—
83C2×C3×D4—201no—
84C2×C3×D4C22⋊D511yescharacteristic
85C3×SD16—202no—
86C3×D8—202no—
87C3×M16—201no—
88C2×C3×C8—101no—
89C3×C22⋊C4—41no—
90C3×C22⋊C4—41no—
91C3×C42C4×D511yescharacteristic
92C23×C5—21no—
93C22×D5—41no—
94C5×Q8—41no—
95C5×D4—41no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5—81no—
99C2×C4×C5C3×C22⋊C411yescharacteristic
100D20—41no—
101D20—41no—
102D20—82no—
103#168—22no—
104#168—81no—
105C2×SD16—101no—
106C2×D8—101no—
107#127—51no—
108#124C2×C3×D511yescharacteristic
109#101—101no—
110#99—21no—
111#97—51no—
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5#35311yescharacteristic
115C3×D5—161no—
116C23×C3—21no—
117C23×C3—201no—
118C3×Q8—41no—
119C3×D4—41no—
120C3×D4—201no—
121C3×D4—201no—
122C3×D4—402no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—81no—
126C2×C3×C4#68511yescharacteristic
127C3×C8—102no—
128C3×C8—401no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5C3×#9911yescharacteristic
132C2×D5—82no—
133C2×D5—81no—
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137C4×C5—161no—
138C2×Q8C3×D2011yescharacteristic
139C2×D4—101no—
140C2×D4—201no—
141C2×D4C3×C22⋊D511yescharacteristic
142SD16—202no—
143D8—202no—
144M16—201no—
145C2×C8—101no—
146C22⋊C4—41no—
147C22⋊C4—41no—
148C42C3×C4×D511yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3—402no—
153C22×C3—401no—
154C22×C3#393811yescharacteristic
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158C3×C4—161no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5C3×#35311yescharacteristic
162D5—161no—
163C23—21no—
164C23—201no—
165Q8—41no—
166D4—41no—
167D4—201no—
168D4—201no—
169D4—402no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—81no—
173C2×C4C3×#68511yescharacteristic
174C8—102no—
175C8—401no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3—801no—
179C2×C3#6469411yescharacteristic
180C5C3×#140611yescharacteristic, complemented, Sylow
181C22—41no—
182C22—81no—
183C22—402no—
184C22—401no—
185C22C3×#393811yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—161no—
190C3#1059803511yescharacteristic, direct product factor, Sylow
191C2—21no—
192C2—81no—
193C2—801no—
194C2C3×#6469411yescharacteristic
subgroupG/H
centerC2×C3#64694
commutatorC42×C5C2×C3×C4
Frattini#124C2×C3×D5
FittingC3×C5×#354C2
socleC2×C3×C5#353
prime radicalC3×#65347C2
cosocleC5×#124C22×C3
hypercenterC3×#354D5
hypocenterC5C3×#1406
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#124 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
2. C3×C5×#354C2semidirect
3. C3×#64762C2semidirect
4. #10598035C3direct (N × H)
8. C3×#4020C4semidirect
11. C3×#3935C4semidirect
14. C5×#354C2×C3semidirect
15. #64762C2×C3semidirect
29. C3×#354D5semidirect
33. #4020C3×C4semidirect
36. #3935C3×C4semidirect
71. #354C3×D5semidirect
149. C3×C5#1406semidirect
180. C5C3×#1406semidirect
190. C3#10598035direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653472
C3×C5×#3542
C3×#647622
#105980353
C3×#14065