Finite Group Databasebeta

← C3×C5×#1407 #14274441

Subgroups — C3×C5×#1407 #14274441

Order 1920.

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

normal subgroups only

This group has 196 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×#497C211yesmaximal, characteristic
2C3×C5×#355C211yesmaximal, characteristic
3C3×C5×#354C211yesmaximal, characteristic
4C5×#1407C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C5×Q16—21no—
6C2×C3×C5×SD16—21no—
7C3×C5×C4⋊Q8C411yescharacteristic, complemented
8C3×C5×#124C2211yescharacteristic
9C3×C5×#101—21no—
10C3×C5×#99—21no—
11C3×C5×#97C411yescharacteristic, complemented
12C3×#1407C511yesmaximal, characteristic, direct product factor, Hall
13C5×#497C2×C311yescharacteristic
14C5×#355C2×C311yescharacteristic
15C5×#354C2×C311yescharacteristic
16C2×C3×C5×Q8—21no—
17C2×C3×C5×Q8D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C3×C5×Q16—42no—
20C3×C5×SD16—42no—
21C3×C5×M16—41no—
22C2×C3×C5×C8—21no—
23C3×C5×C4⋊C4—41no—
24C3×C5×C22⋊C4—41no—
25C3×C5×C22⋊C4—41no—
26C3×C42×C5C2×C411yescharacteristic
27C3×#497C2×C511yescharacteristic
28C3×#355C2×C511yescharacteristic
29C3×#354C2×C511yescharacteristic
30C2×C5×Q16—21no—
31C2×C5×SD16—21no—
32C5×C4⋊Q8C3×C411yescharacteristic, complemented
33C5×#124C22×C311yescharacteristic
34C5×#101—21no—
35C5×#99—21no—
36C5×#97C3×C411yescharacteristic, complemented
37#1407C3×C511yescharacteristic, direct product factor, Sylow
38C23×C3×C5—21no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C3×C5×Q8—41no—
42C3×C5×D4—41no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—41no—
46C2×C3×C4×C5—81no—
47C2×C3×C4×C5C22⋊C411yescharacteristic
48C3×C5×C8—22no—
49C3×C5×C8—81no—
50C2×C3×Q16—21no—
51C2×C3×SD16—21no—
52C3×C4⋊Q8C4×C511yescharacteristic, complemented
53C3×#124C22×C511yescharacteristic
54C3×#101—21no—
55C3×#99—21no—
56C3×#97C4×C511yescharacteristic, complemented
57C2×C5×Q8—21no—
58C2×C5×Q8C3×D411yescharacteristic
59C2×C5×D4C3×D411yescharacteristic
60C5×Q16—42no—
61C5×SD16—42no—
62C5×M16—41no—
63C2×C5×C8—21no—
64C5×C4⋊C4—41no—
65C5×C22⋊C4—41no—
66C5×C22⋊C4—41no—
67C42×C5C2×C3×C411yescharacteristic
68#497C2×C3×C511yescharacteristic
69#355C2×C3×C511yescharacteristic
70#354C2×C3×C511yescharacteristic
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#9911yescharacteristic
74C3×C4×C5—21no—
75C3×C4×C5—41no—
76C3×C4×C5—41no—
77C3×C4×C5—81no—
78C3×C4×C5—161no—
79C2×C3×Q8—21no—
80C2×C3×Q8C5×D411yescharacteristic
81C2×C3×D4C5×D411yescharacteristic
82C3×Q16—42no—
83C3×SD16—42no—
84C3×M16—41no—
85C2×C3×C8—21no—
86C3×C4⋊C4—41no—
87C3×C22⋊C4—41no—
88C3×C22⋊C4—41no—
89C3×C42C2×C4×C511yescharacteristic
90C23×C5—21no—
91C5×Q8—41no—
92C5×Q8—41no—
93C5×Q8—41no—
94C5×D4—41no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—41no—
98C2×C4×C5—81no—
99C2×C4×C5C3×C22⋊C411yescharacteristic
100C5×C8—22no—
101C5×C8—81no—
102C2×Q16—21no—
103C2×SD16—21no—
104C4⋊Q8C3×C4×C511yescharacteristic, complemented
105#124C22×C3×C511yescharacteristic
106#101—21no—
107#99—21no—
108#97C3×C4×C511yescharacteristic, complemented
109C2×C3×C5—21no—
110C2×C3×C5—81no—
111C2×C3×C5#35311yescharacteristic
112C23×C3—21no—
113C3×Q8—41no—
114C3×Q8—41no—
115C3×Q8—41no—
116C3×D4—41no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—41no—
120C2×C3×C4—81no—
121C2×C3×C4C5×C22⋊C411yescharacteristic
122C3×C8—22no—
123C3×C8—81no—
124C22×C5—41no—
125C22×C5—81no—
126C22×C5C3×#9911yescharacteristic
127C4×C5—21no—
128C4×C5—41no—
129C4×C5—41no—
130C4×C5—81no—
131C4×C5—161no—
132C2×Q8—21no—
133C2×Q8C3×C5×D411yescharacteristic
134C2×D4C3×C5×D411yescharacteristic
135Q16—42no—
136SD16—42no—
137M16—41no—
138C2×C8—21no—
139C4⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C42C2×C3×C4×C511yescharacteristic
143C3×C5#140711yescharacteristic, direct product factor, Hall
144C22×C3—41no—
145C22×C3—81no—
146C22×C3C5×#9911yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—81no—
151C3×C4—161no—
152C2×C5—21no—
153C2×C5—81no—
154C2×C5C3×#35311yescharacteristic
155C23—21no—
156Q8—41no—
157Q8—41no—
158Q8—41no—
159D4—41no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—81no—
164C2×C4C3×C5×C22⋊C411yescharacteristic
165C8—22no—
166C8—81no—
167C2×C3—21no—
168C2×C3—81no—
169C2×C3C5×#35311yescharacteristic
170C5C3×#140711yescharacteristic, direct product factor, Sylow
171C22—41no—
172C22—81no—
173C22C3×C5×#9911yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—161no—
179C3C5×#140711yescharacteristic, direct product factor, Sylow
180C2—21no—
181C2—81no—
182C2C3×C5×#35311yescharacteristic
subgroupG/H
center, socleC2×C3×C5#353
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×#1407C3direct (N × H)
7. C3×C5×C4⋊Q8C4semidirect
11. C3×C5×#97C4semidirect
12. C3×#1407C5direct (N × H)
32. C5×C4⋊Q8C3×C4semidirect
36. C5×#97C3×C4semidirect
37. #1407C3×C5direct (N × H)
52. C3×C4⋊Q8C4×C5semidirect
56. C3×#97C4×C5semidirect
104. C4⋊Q8C3×C4×C5semidirect
108. #97C3×C4×C5semidirect
143. C3×C5#1407direct (N × H)
170. C5C3×#1407direct (N × H)
179. C3C5×#1407direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4972
C3×C5×#3552
C3×C5×#3542
C5×#14073
C3×#14075