Finite Group Databasebeta

← C3×C5×#1414 #14274448

Subgroups — C3×C5×#1414 #14274448

Order 1920.

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

normal subgroups only

This group has 168 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×#488C211yesmaximal, characteristic
2C3×C5×#355C211yesmaximal, characteristic
3C3×C5×#354C211yesmaximal, characteristic
4C5×#1414C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#125C411yescharacteristic, complemented
6C3×C5×#124C2211yescharacteristic
7C3×C5×#103—21no—
8C3×C5×#102—21no—
9C3×C5×#101—21no—
10C3×C5×#99—21no—
11C3×C4×C5×C8C411yescharacteristic, complemented
12C3×#1414C511yesmaximal, characteristic, direct product factor, Hall
13C5×#488C2×C311yescharacteristic
14C5×#355C2×C311yescharacteristic
15C5×#354C2×C311yescharacteristic
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C3×C5×M16—41no—
19C2×C3×C5×C8—21no—
20C3×C5×C4⋊C4—21no—
21C3×C5×C4⋊C4—41no—
22C3×C5×C22⋊C4—41no—
23C3×C5×C22⋊C4—41no—
24C3×C42×C5C2×C411yescharacteristic
25C3×#488C2×C511yescharacteristic
26C3×#355C2×C511yescharacteristic
27C3×#354C2×C511yescharacteristic
28C5×#125C3×C411yescharacteristic, complemented
29C5×#124C22×C311yescharacteristic
30C5×#103—21no—
31C5×#102—21no—
32C5×#101—21no—
33C5×#99—21no—
34C4×C5×C8C3×C411yescharacteristic, complemented
35#1414C3×C511yescharacteristic, direct product factor, Sylow
36C23×C3×C5—21no—
37C3×C5×Q8—41no—
38C3×C5×D4—41no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—81no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C3×C5×C8—41no—
45C3×C5×C8—81no—
46C3×#125C4×C511yescharacteristic, complemented
47C3×#124C22×C511yescharacteristic
48C3×#103—21no—
49C3×#102—21no—
50C3×#101—21no—
51C3×#99—21no—
52C3×C4×C8C4×C511yescharacteristic, complemented
53C2×C5×Q8C3×D411yescharacteristic
54C2×C5×D4C3×D411yescharacteristic
55C5×M16—41no—
56C2×C5×C8—21no—
57C5×C4⋊C4—21no—
58C5×C4⋊C4—41no—
59C5×C22⋊C4—41no—
60C5×C22⋊C4—41no—
61C42×C5C2×C3×C411yescharacteristic
62#488C2×C3×C511yescharacteristic
63#355C2×C3×C511yescharacteristic
64#354C2×C3×C511yescharacteristic
65C22×C3×C5—41no—
66C22×C3×C5—81no—
67C22×C3×C5#9911yescharacteristic
68C3×C4×C5—21no—
69C3×C4×C5—41no—
70C3×C4×C5—41no—
71C3×C4×C5—81no—
72C3×C4×C5—161no—
73C2×C3×Q8C5×D411yescharacteristic
74C2×C3×D4C5×D411yescharacteristic
75C3×M16—41no—
76C2×C3×C8—21no—
77C3×C4⋊C4—21no—
78C3×C4⋊C4—41no—
79C3×C22⋊C4—41no—
80C3×C22⋊C4—41no—
81C3×C42C2×C4×C511yescharacteristic
82C23×C5—21no—
83C5×Q8—41no—
84C5×D4—41no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—41no—
88C2×C4×C5—81no—
89C2×C4×C5C3×C22⋊C411yescharacteristic
90C5×C8—41no—
91C5×C8—81no—
92#125C3×C4×C511yescharacteristic, complemented
93#124C22×C3×C511yescharacteristic
94#103—21no—
95#102—21no—
96#101—21no—
97#99—21no—
98C4×C8C3×C4×C511yescharacteristic, complemented
99C2×C3×C5—21no—
100C2×C3×C5—81no—
101C2×C3×C5#35411yescharacteristic
102C23×C3—21no—
103C3×Q8—41no—
104C3×D4—41no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—41no—
108C2×C3×C4—81no—
109C2×C3×C4C5×C22⋊C411yescharacteristic
110C3×C8—41no—
111C3×C8—81no—
112C22×C5—41no—
113C22×C5—81no—
114C22×C5C3×#9911yescharacteristic
115C4×C5—21no—
116C4×C5—41no—
117C4×C5—41no—
118C4×C5—81no—
119C4×C5—161no—
120C2×Q8C3×C5×D411yescharacteristic
121C2×D4C3×C5×D411yescharacteristic
122M16—41no—
123C2×C8—21no—
124C4⋊C4—21no—
125C4⋊C4—41no—
126C22⋊C4—41no—
127C22⋊C4—41no—
128C42C2×C3×C4×C511yescharacteristic
129C3×C5#141411yescharacteristic, direct product factor, Hall
130C22×C3—41no—
131C22×C3—81no—
132C22×C3C5×#9911yescharacteristic
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—41no—
136C3×C4—81no—
137C3×C4—161no—
138C2×C5—21no—
139C2×C5—81no—
140C2×C5C3×#35411yescharacteristic
141C23—21no—
142Q8—41no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—81no—
148C2×C4C3×C5×C22⋊C411yescharacteristic
149C8—41no—
150C8—81no—
151C2×C3—21no—
152C2×C3—81no—
153C2×C3C5×#35411yescharacteristic
154C5C3×#141411yescharacteristic, direct product factor, Sylow
155C22—41no—
156C22—81no—
157C22C3×C5×#9911yescharacteristic
158C4—21no—
159C4—41no—
160C4—41no—
161C4—81no—
162C4—161no—
163C3C5×#141411yescharacteristic, direct product factor, Sylow
164C2—21no—
165C2—81no—
166C2C3×C5×#35411yescharacteristic
subgroupG/H
center, socleC2×C3×C5#354
commutatorC42C2×C3×C4×C5
Frattini, cosocle#124C22×C3×C5
prime radicalC2×C3×C5×D4D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#124 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1414C3direct (N × H)
5. C3×C5×#125C4semidirect
11. C3×C4×C5×C8C4semidirect
12. C3×#1414C5direct (N × H)
28. C5×#125C3×C4semidirect
34. C4×C5×C8C3×C4semidirect
35. #1414C3×C5direct (N × H)
46. C3×#125C4×C5semidirect
52. C3×C4×C8C4×C5semidirect
92. #125C3×C4×C5semidirect
98. C4×C8C3×C4×C5semidirect
129. C3×C5#1414direct (N × H)
154. C5C3×#1414direct (N × H)
163. C3C5×#1414direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4882
C3×C5×#3552
C3×C5×#3542
C5×#14143
C3×#14145