Finite Group Databasebeta

← C3×C5×#489 #11751464

Subgroups — C3×C5×#489 #11751464

Order 960.

200 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 100 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×C5×#124C211yesmaximal, characteristic
3C3×C5×#103C212yesmaximal, complemented
4C3×C5×#102C212yesmaximal
5C3×C5×#97C211yesmaximal, characteristic, complemented
6C5×#489C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q8—21no—
8C2×C3×C5×Q8C2211yescharacteristic
9C2×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×C8C2212yes—
11C3×C5×C4⋊C4—21no—
12C3×C5×C4⋊C4C2212yes—
13C3×C5×C22⋊C4—21no—
14C3×C5×C22⋊C4—21no—
15C3×C42×C5C2211yescharacteristic
16C3×#489C511yesmaximal, characteristic, direct product factor, Hall
17C5×C4⋊Q8C2×C311yescharacteristic, complemented
18C5×#124C2×C311yescharacteristic
19C5×#103C2×C312yescomplemented
20C5×#102C2×C312yes—
21C5×#97C2×C311yescharacteristic, complemented
22C23×C3×C5—21no—
23C3×C5×Q8—22no—
24C3×C5×Q8—42no—
25C3×C5×D4—22no—
26C2×C3×C4×C5—21no—
27C2×C3×C4×C5—22no—
28C2×C3×C4×C5D411yescharacteristic
29C2×C3×C4×C5D411yescharacteristic
30C2×C3×C4×C5C2311yescharacteristic
31C3×C5×C8—22no—
32C3×C4⋊Q8C2×C511yescharacteristic, complemented
33C3×#124C2×C511yescharacteristic
34C3×#103C2×C512yescomplemented
35C3×#102C2×C512yes—
36C3×#97C2×C511yescharacteristic, complemented
37C2×C5×Q8—21no—
38C2×C5×Q8C22×C311yescharacteristic
39C2×C5×D4C22×C311yescharacteristic
40C2×C5×C8C22×C312yes—
41C5×C4⋊C4—21no—
42C5×C4⋊C4C22×C312yes—
43C5×C22⋊C4—21no—
44C5×C22⋊C4—21no—
45C42×C5C22×C311yescharacteristic
46#489C3×C511yescharacteristic, direct product factor, Sylow
47C22×C3×C5—41no—
48C22×C3×C5—41no—
49C22×C3×C5—41no—
50C22×C3×C5C2×D411yescharacteristic
51C3×C4×C5—21no—
52C3×C4×C5—21no—
53C3×C4×C5—41no—
54C3×C4×C5—42no—
55C3×C4×C5#4112yes—
56C2×C3×Q8—21no—
57C2×C3×Q8C22×C511yescharacteristic
58C2×C3×D4C22×C511yescharacteristic
59C2×C3×C8C22×C512yes—
60C3×C4⋊C4—21no—
61C3×C4⋊C4C22×C512yes—
62C3×C22⋊C4—21no—
63C3×C22⋊C4—21no—
64C3×C42C22×C511yescharacteristic
65C23×C5—21no—
66C5×Q8—22no—
67C5×Q8—42no—
68C5×D4—22no—
69C2×C4×C5—21no—
70C2×C4×C5—22no—
71C2×C4×C5C3×D411yescharacteristic
72C2×C4×C5C3×D411yescharacteristic
73C2×C4×C5C23×C311yescharacteristic
74C5×C8—22no—
75C4⋊Q8C2×C3×C511yescharacteristic, complemented
76#124C2×C3×C511yescharacteristic
77#103C2×C3×C512yescomplemented
78#102C2×C3×C512yes—
79#97C2×C3×C511yescharacteristic, complemented
80C2×C3×C5—81no—
81C2×C3×C5#12411yescharacteristic
82C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
83C2×C3×C5#13711yescharacteristic
84C23×C3—21no—
85C3×Q8—22no—
86C3×Q8—42no—
87C3×D4—22no—
88C2×C3×C4—21no—
89C2×C3×C4—22no—
90C2×C3×C4C5×D411yescharacteristic
91C2×C3×C4C5×D411yescharacteristic
92C2×C3×C4C23×C511yescharacteristic
93C3×C8—22no—
94C22×C5—41no—
95C22×C5—41no—
96C22×C5—41no—
97C22×C5C2×C3×D411yescharacteristic
98C4×C5—21no—
99C4×C5—21no—
100C4×C5—41no—
101C4×C5—42no—
102C4×C5C3×#4112yes—
103C2×Q8—21no—
104C2×Q8C22×C3×C511yescharacteristic
105C2×D4C22×C3×C511yescharacteristic
106C2×C8C22×C3×C512yes—
107C4⋊C4—21no—
108C4⋊C4C22×C3×C512yes—
109C22⋊C4—21no—
110C22⋊C4—21no—
111C42C22×C3×C511yescharacteristic
112C3×C5#48911yescharacteristic, direct product factor, Hall
113C22×C3—41no—
114C22×C3—41no—
115C22×C3—41no—
116C22×C3C2×C5×D411yescharacteristic
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—41no—
120C3×C4—42no—
121C3×C4C5×#4112yes—
122C2×C5—81no—
123C2×C5C3×#12411yescharacteristic
124C2×C5C3×AGL(1,ℤ/8)11yescharacteristic
125C2×C5C3×#13711yescharacteristic
126C23—21no—
127Q8—22no—
128Q8—42no—
129D4—22no—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4C3×C5×D411yescharacteristic
133C2×C4C3×C5×D411yescharacteristic
134C2×C4C23×C3×C511yescharacteristic
135C8—22no—
136C2×C3—81no—
137C2×C3C5×#12411yescharacteristic
138C2×C3C5×AGL(1,ℤ/8)11yescharacteristic
139C2×C3C5×#13711yescharacteristic
140C5C3×#48911yescharacteristic, direct product factor, Sylow
141C22—41no—
142C22—41no—
143C22—41no—
144C22C2×C3×C5×D411yescharacteristic
145C4—21no—
146C4—21no—
147C4—41no—
148C4—42no—
149C4C3×C5×#4112yes—
150C3C5×#48911yescharacteristic, direct product factor, Sylow
151C2—81no—
152C2C3×C5×#12411yescharacteristic
153C2C3×C5×AGL(1,ℤ/8)11yescharacteristic
154C2C3×C5×#13711yescharacteristic
subgroupG/H
center, socleC22×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C23×C3×C5
prime radicalC2×C3×C5×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×C4⋊Q8C2semidirect
3. C3×C5×#103C2semidirect
5. C3×C5×#97C2semidirect
6. C5×#489C3direct (N × H)
16. C3×#489C5direct (N × H)
17. C5×C4⋊Q8C2×C3semidirect
19. C5×#103C2×C3semidirect
21. C5×#97C2×C3semidirect
32. C3×C4⋊Q8C2×C5semidirect
34. C3×#103C2×C5semidirect
36. C3×#97C2×C5semidirect
46. #489C3×C5direct (N × H)
75. C4⋊Q8C2×C3×C5semidirect
77. #103C2×C3×C5semidirect
79. #97C2×C3×C5semidirect
112. C3×C5#489direct (N × H)
140. C5C3×#489direct (N × H)
150. C3C5×#489direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C4⋊Q82
C3×C5×#1242
C3×C5×#1032
C3×C5×#1022
C3×C5×#972
C5×#4893
C3×#4895