Finite Group Databasebeta

← C2×C3×C5×D285 #30685973

Subgroups — C2×C3×C5×D285 #30685973

Order 17100.

224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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×D285C212yesmaximal, direct product factor
2C2×C32×C52×C19C211yesmaximal, characteristic, complemented
3C2×C5×D285C311yesmaximal, characteristic, direct product factor
4C2×C3×C5×D95—31nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6C2×C3×C5×D57—51nomaximal
7C2×C3×D285C511yesmaximal, characteristic, direct product factor
8C5×D285C2×C312yesdirect product factor
9C3×C5×D95—32no—
10C2×C3×C52×C19—21no—
11C2×C3×C52×C19D311yescharacteristic, complemented
12C2×C3×C52×C19C2×C311yescharacteristic, complemented
13C2×C5×D95—31noHall
14C2×C32×C5×C19—22no—
15C2×C32×C5×C19D511yescharacteristic, complemented
16C2×C32×C5×C19C2×C511yescharacteristic, complemented
17C3×D285C2×C512yesdirect product factor
18C3×C5×D57—52no—
19C3×C52×C19—21no—
20C3×C52×C19C2×D311yescharacteristic, complemented
21C3×C52×C19C22×C311yescharacteristic, complemented
22C2×D285C3×C511yescharacteristic, direct product factor
23C2×C5×D57—51no—
24C2×C3×D95—31no—
25C2×C3×C5×D19—151no—
26C2×C52×C19C3×D311yescharacteristic, complemented
27C5×D95—32no—
28C2×C3×C5×D15—191nomaximal, Hall
29C32×C5×C19—22no—
30C32×C5×C19C2×D511yescharacteristic, complemented
31C32×C5×C19C22×C511yescharacteristic, complemented
32C2×C3×D57—51noHall
33C2×C3×C5×C19—24no—
34C2×C3×C5×C19—22no—
35C2×C3×C5×C19—22no—
36C2×C3×C5×C19—21no—
37C2×C3×C5×C19—21no—
38C2×C3×C5×C19C5×D311yescharacteristic, complemented
39C2×C3×C5×C19C3×D511yescharacteristic, complemented
40C2×C3×C5×C19D1511yescharacteristic, complemented
41C2×C3×C5×C19C2×C3×C511yescharacteristic, complemented
42D285C2×C3×C512yesdirect product factor
43C5×D57—52no—
44C3×D95—32no—
45C3×C5×D19—152no—
46C52×C19C2×C3×D311yescharacteristic, complemented, Hall
47C2×C32×C52D1911yescharacteristic, complemented
48C3×C5×D15—192no—
49C2×D95—31no—
50C2×C5×D19—151no—
51C2×C32×C19C5×D511yescharacteristic, complemented
52C3×D57—52no—
53C2×C5×D15—191no—
54C2×C3×C5×D5—571no—
55C3×C5×C19—24no—
56C3×C5×C19—22no—
57C3×C5×C19—22no—
58C3×C5×C19—21no—
59C3×C5×C19—21no—
60C3×C5×C19C2×C3×D511yescharacteristic, complemented
61C3×C5×C19C2×C5×D311yescharacteristic, complemented
62C3×C5×C19C2×D1511yescharacteristic, complemented
63C3×C5×C19C22×C3×C511yescharacteristic, complemented
64C2×D57—51no—
65C2×C3×D19—151no—
66C32×C52C2×D1911yescharacteristic, complemented, Hall
67C2×C5×C19—22no—
68C2×C5×C19C3×C5×D311yescharacteristic, complemented
69C2×C5×C19C3×D1511yescharacteristic, complemented
70D95—32no—
71C5×D19—152no—
72C2×C3×D15—191no—
73C2×C3×C5×D3—951no—
74C32×C19C2×C5×D511yescharacteristic, complemented, Hall
75C2×C3×C52—21no—
76C2×C3×C52C3×D1911yescharacteristic, complemented
77C2×C3×C52D5711yescharacteristic, complemented
78C5×D15—192no—
79C3×C5×D5—572no—
80C2×C3×C19—21no—
81C2×C3×C19C3×C5×D511yescharacteristic, complemented
82C2×C3×C19C5×D1511yescharacteristic, complemented
83D57—52no—
84C3×D19—152no—
85C2×C5×D5—571noHall
86C5×C19—22no—
87C5×C19C2×C3×C5×D311yescharacteristic, complemented
88C5×C19C2×C3×D1511yescharacteristic, complemented
89C2×C32×C5—22no—
90C2×C32×C5C5×D1911yescharacteristic, complemented
91C2×C32×C5D9511yescharacteristic, complemented
92C3×D15—192no—
93C3×C5×D3—952no—
94C2×D19—151noHall
95C3×C52—21no—
96C3×C52C2×C3×D1911yescharacteristic, complemented
97C3×C52C2×D5711yescharacteristic, complemented
98C22×C3×C5—2851no—
99C2×D15—191no—
100C2×C5×D3—951no—
101C2×C3×D5—571no—
102C3×C19—21no—
103C3×C19C2×C3×C5×D511yescharacteristic, complemented
104C3×C19C2×C5×D1511yescharacteristic, complemented
105C2×C52C3×D5711yescharacteristic, complemented
106C5×D5—572no—
107C32×C5—22no—
108C32×C5C2×C5×D1911yescharacteristic, complemented
109C32×C5C2×D9511yescharacteristic, complemented
110C2×C19C3×C5×D1511yescharacteristic, complemented
111D19—152no—
112C2×C3×D3—951noHall
113C2×C3×C5—24no—
114C2×C3×C5—21no—
115C2×C3×C5—21no—
116C2×C3×C5—22no—
117C2×C3×C5—22no—
118C2×C3×C5—2852no—
119C2×C3×C5C3×C5×D1911yescharacteristic, complemented
120C2×C3×C5C3×D9511yescharacteristic, complemented
121C2×C3×C5C5×D5711yescharacteristic, complemented
122C2×C3×C5D28511yescharacteristic, direct product factor
123D15—192no—
124C3×D5—572no—
125C5×D3—952no—
126C52C2×C3×D5711yescharacteristic, complemented, Sylow
127C22×C5—2851no—
128C2×D5—571no—
129C19C2×C3×C5×D1511yescharacteristic, complemented, Sylow
130C2×C32C5×D9511yescharacteristic, complemented
131C3×D3—952no—
132C3×C5—24no—
133C3×C5—21no—
134C3×C5—21no—
135C3×C5—22no—
136C3×C5—22no—
137C3×C5C2×C3×C5×D1911yescharacteristic, complemented
138C3×C5C2×C3×D9511yescharacteristic, complemented
139C3×C5C2×C5×D5711yescharacteristic, complemented
140C3×C5C2×D28511yescharacteristic, direct product factor
141C22×C3—2851no—
142C2×D3—951no—
143C2×C5—22no—
144C2×C5—2852no—
145C2×C5C3×C5×D5711yescharacteristic, complemented
146C2×C5C3×D28511yescharacteristic, direct product factor
147D5—572no—
148C32C2×C5×D9511yescharacteristic, complemented, Sylow
149C2×C3—21no—
150C2×C3—2852no—
151C2×C3C3×C5×D9511yescharacteristic, complemented
152C2×C3C5×D28511yescharacteristic, direct product factor
153D3—952no—
154C5—22no—
155C5C2×C3×D28511yescharacteristic, direct product factor
156C5C2×C3×C5×D5711yescharacteristic, complemented
157C22—2851noSylow
158C3—21no—
159C3C2×C3×C5×D9511yescharacteristic, complemented
160C3C2×C5×D28511yescharacteristic, direct product factor
161C2—2852no—
162C2C3×C5×D28511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D285
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C19C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D285C2direct (N × H)
2. C2×C32×C52×C19C2semidirect
3. C2×C5×D285C3direct (N × H)
5. C32×C52×C19C22semidirect
7. C2×C3×D285C5direct (N × H)
8. C5×D285C2×C3direct (N × H)
11. C2×C3×C52×C19D3semidirect
12. C2×C3×C52×C19C2×C3semidirect
15. C2×C32×C5×C19D5semidirect
16. C2×C32×C5×C19C2×C5semidirect
17. C3×D285C2×C5direct (N × H)
20. C3×C52×C19C2×D3semidirect
21. C3×C52×C19C22×C3semidirect
22. C2×D285C3×C5direct (N × H)
26. C2×C52×C19C3×D3semidirect
30. C32×C5×C19C2×D5semidirect
31. C32×C5×C19C22×C5semidirect
38. C2×C3×C5×C19C5×D3semidirect
39. C2×C3×C5×C19C3×D5semidirect
40. C2×C3×C5×C19D15semidirect
41. C2×C3×C5×C19C2×C3×C5semidirect
42. D285C2×C3×C5direct (N × H)
46. C52×C19C2×C3×D3semidirect
47. C2×C32×C52D19semidirect
51. C2×C32×C19C5×D5semidirect
60. C3×C5×C19C2×C3×D5semidirect
61. C3×C5×C19C2×C5×D3semidirect
62. C3×C5×C19C2×D15semidirect
63. C3×C5×C19C22×C3×C5semidirect
66. C32×C52C2×D19semidirect
68. C2×C5×C19C3×C5×D3semidirect
69. C2×C5×C19C3×D15semidirect
74. C32×C19C2×C5×D5semidirect
76. C2×C3×C52C3×D19semidirect
77. C2×C3×C52D57semidirect
81. C2×C3×C19C3×C5×D5semidirect
82. C2×C3×C19C5×D15semidirect
87. C5×C19C2×C3×C5×D3semidirect
88. C5×C19C2×C3×D15semidirect
90. C2×C32×C5C5×D19semidirect
91. C2×C32×C5D95semidirect
96. C3×C52C2×C3×D19semidirect
97. C3×C52C2×D57semidirect
103. C3×C19C2×C3×C5×D5semidirect
104. C3×C19C2×C5×D15semidirect
105. C2×C52C3×D57semidirect
108. C32×C5C2×C5×D19semidirect
109. C32×C5C2×D95semidirect
110. C2×C19C3×C5×D15semidirect
119. C2×C3×C5C3×C5×D19semidirect
120. C2×C3×C5C3×D95semidirect
121. C2×C3×C5C5×D57semidirect
122. C2×C3×C5D285direct (N × H)
126. C52C2×C3×D57semidirect
129. C19C2×C3×C5×D15semidirect
130. C2×C32C5×D95semidirect
137. C3×C5C2×C3×C5×D19semidirect
138. C3×C5C2×C3×D95semidirect
139. C3×C5C2×C5×D57semidirect
140. C3×C5C2×D285direct (N × H)
145. C2×C5C3×C5×D57semidirect
146. C2×C5C3×D285direct (N × H)
148. C32C2×C5×D95semidirect
151. C2×C3C3×C5×D95semidirect
152. C2×C3C5×D285direct (N × H)
155. C5C2×C3×D285direct (N × H)
156. C5C2×C3×C5×D57semidirect
159. C3C2×C3×C5×D95semidirect
160. C3C2×C5×D285direct (N × H)
162. C2C3×C5×D285direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D2852
C2×C32×C52×C192
C2×C5×D2853
C2×C3×C5×D953
C2×C3×C5×D575
C2×C3×D2855
C2×C3×C5×D1519