Finite Group Databasebeta

← C3×C5×#1409 #14274443

Subgroups — C3×C5×#1409 #14274443

Order 1920.

220 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 56 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×C5×#492C211yesmaximal, characteristic
2C3×C5×#353C212yesmaximal
3C5×#1409C311yesmaximal, characteristic, direct product factor, Hall
4C2×C3×C5×SD16—22no—
5C3×C5×C4⋊Q8C411yescharacteristic, complemented
6C3×C5×#127C2211yescharacteristic
7C3×C5×#99—22no—
8C3×C4×C5×C8C411yescharacteristic, complemented
9C3×#1409C511yesmaximal, characteristic, direct product factor, Hall
10C5×#492C2×C311yescharacteristic
11C5×#353C2×C312yes—
12C2×C3×C5×Q8—21no—
13C2×C3×C5×D4—41no—
14C2×C3×C5×D4D412yes—
15C3×C5×SD16—44no—
16C2×C3×C5×C8—21no—
17C3×C5×C4⋊C4—41no—
18C3×C5×C22⋊C4—42no—
19C3×C42×C5C2×C411yescharacteristic
20C3×#492C2×C511yescharacteristic
21C3×#353C2×C512yes—
22C2×C5×SD16—22no—
23C5×C4⋊Q8C3×C411yescharacteristic, complemented
24C5×#127C22×C311yescharacteristic
25C5×#99—22no—
26C4×C5×C8C3×C411yescharacteristic, complemented
27#1409C3×C511yescharacteristic, direct product factor, Sylow
28C23×C3×C5—22no—
29C3×C5×Q8—42no—
30C3×C5×D4—42no—
31C3×C5×D4—82no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—41no—
34C2×C3×C4×C5—82no—
35C2×C3×C4×C5C22⋊C411yescharacteristic
36C3×C5×C8—22no—
37C2×C3×SD16—22no—
38C3×C4⋊Q8C4×C511yescharacteristic, complemented
39C3×#127C22×C511yescharacteristic
40C3×#99—22no—
41C3×C4×C8C4×C511yescharacteristic, complemented
42C2×C5×Q8—21no—
43C2×C5×D4—41no—
44C2×C5×D4C3×D412yes—
45C5×SD16—44no—
46C2×C5×C8—21no—
47C5×C4⋊C4—41no—
48C5×C22⋊C4—42no—
49C42×C5C2×C3×C411yescharacteristic
50#492C2×C3×C511yescharacteristic
51#353C2×C3×C512yes—
52C22×C3×C5—42no—
53C22×C3×C5—82no—
54C22×C3×C5#9911yescharacteristic
55C3×C4×C5—22no—
56C3×C4×C5—21no—
57C3×C4×C5—81no—
58C3×C4×C5—162no—
59C2×C3×Q8—21no—
60C2×C3×D4—41no—
61C2×C3×D4C5×D412yes—
62C3×SD16—44no—
63C2×C3×C8—21no—
64C3×C4⋊C4—41no—
65C3×C22⋊C4—42no—
66C3×C42C2×C4×C511yescharacteristic
67C23×C5—22no—
68C5×Q8—42no—
69C5×D4—42no—
70C5×D4—82no—
71C2×C4×C5—21no—
72C2×C4×C5—41no—
73C2×C4×C5—82no—
74C2×C4×C5C3×C22⋊C411yescharacteristic
75C5×C8—22no—
76C2×SD16—22no—
77C4⋊Q8C3×C4×C511yescharacteristic, complemented
78#127C22×C3×C511yescharacteristic
79#99—22no—
80C4×C8C3×C4×C511yescharacteristic, complemented
81C2×C3×C5—21no—
82C2×C3×C5—82no—
83C2×C3×C5#35311yescharacteristic
84C23×C3—22no—
85C3×Q8—42no—
86C3×D4—42no—
87C3×D4—82no—
88C2×C3×C4—21no—
89C2×C3×C4—41no—
90C2×C3×C4—82no—
91C2×C3×C4C5×C22⋊C411yescharacteristic
92C3×C8—22no—
93C22×C5—42no—
94C22×C5—82no—
95C22×C5C3×#9911yescharacteristic
96C4×C5—22no—
97C4×C5—21no—
98C4×C5—81no—
99C4×C5—162no—
100C2×Q8—21no—
101C2×D4—41no—
102C2×D4C3×C5×D412yes—
103SD16—44no—
104C2×C8—21no—
105C4⋊C4—41no—
106C22⋊C4—42no—
107C42C2×C3×C4×C511yescharacteristic
108C3×C5#140911yescharacteristic, direct product factor, Hall
109C22×C3—42no—
110C22×C3—82no—
111C22×C3C5×#9911yescharacteristic
112C3×C4—22no—
113C3×C4—21no—
114C3×C4—81no—
115C3×C4—162no—
116C2×C5—21no—
117C2×C5—82no—
118C2×C5C3×#35311yescharacteristic
119C23—22no—
120Q8—42no—
121D4—42no—
122D4—82no—
123C2×C4—21no—
124C2×C4—41no—
125C2×C4—82no—
126C2×C4C3×C5×C22⋊C411yescharacteristic
127C8—22no—
128C2×C3—21no—
129C2×C3—82no—
130C2×C3C5×#35311yescharacteristic
131C5C3×#140911yescharacteristic, direct product factor, Sylow
132C22—42no—
133C22—82no—
134C22C3×C5×#9911yescharacteristic
135C4—22no—
136C4—21no—
137C4—81no—
138C4—162no—
139C3C5×#140911yescharacteristic, direct product factor, Sylow
140C2—21no—
141C2—82no—
142C2C3×C5×#35311yescharacteristic
subgroupG/H
center, socleC2×C3×C5#353
commutatorC42C2×C3×C4×C5
Frattini, cosocle#127C22×C3×C5
prime radicalC3×C5×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1409C3direct (N × H)
5. C3×C5×C4⋊Q8C4semidirect
8. C3×C4×C5×C8C4semidirect
9. C3×#1409C5direct (N × H)
23. C5×C4⋊Q8C3×C4semidirect
26. C4×C5×C8C3×C4semidirect
27. #1409C3×C5direct (N × H)
38. C3×C4⋊Q8C4×C5semidirect
41. C3×C4×C8C4×C5semidirect
77. C4⋊Q8C3×C4×C5semidirect
80. C4×C8C3×C4×C5semidirect
108. C3×C5#1409direct (N × H)
131. C5C3×#1409direct (N × H)
139. C3C5×#1409direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4922
C3×C5×#3532
C5×#14093
C3×#14095