Finite Group Databasebeta

← C2×C3×C5×D105 #20263164

Subgroups — C2×C3×C5×D105 #20263164

Order 6300.

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×D105C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C5×D105C311yesmaximal, characteristic, direct product factor
4C2×C3×C5×D35—31nomaximal
5C32×C52×C7C2211yescharacteristic, complemented, Hall
6C2×C3×D105C511yesmaximal, characteristic, direct product factor
7C2×C3×C5×D21—51nomaximal
8C2×C3×C52×C7—21no—
9C2×C3×C52×C7D311yescharacteristic, complemented
10C2×C3×C52×C7C2×C311yescharacteristic, complemented
11C5×D105C2×C312yesdirect product factor
12C3×C5×D35—32no—
13C2×C3×C5×D15—71nomaximal, Hall
14C2×C5×D35—31noHall
15C2×C32×C5×C7—22no—
16C2×C32×C5×C7D511yescharacteristic, complemented
17C2×C32×C5×C7C2×C511yescharacteristic, complemented
18C3×D105C2×C512yesdirect product factor
19C3×C5×D21—52no—
20C3×C52×C7—21no—
21C3×C52×C7C2×D311yescharacteristic, complemented
22C3×C52×C7C22×C311yescharacteristic, complemented
23C2×C32×C52D711yescharacteristic, complemented
24C3×C5×D15—72no—
25C2×D105C3×C511yescharacteristic, direct product factor
26C2×C5×D21—51no—
27C2×C3×D35—31no—
28C2×C3×C5×D7—151no—
29C2×C52×C7C3×D311yescharacteristic, complemented
30C5×D35—32no—
31C32×C5×C7—22no—
32C32×C5×C7C2×D511yescharacteristic, complemented
33C32×C5×C7C22×C511yescharacteristic, complemented
34C2×C5×D15—71no—
35C2×C3×C5×D5—211no—
36C2×C3×D21—51noHall
37C32×C52C2×D711yescharacteristic, complemented, Hall
38C2×C3×C5×C7—24no—
39C2×C3×C5×C7—22no—
40C2×C3×C5×C7—22no—
41C2×C3×C5×C7—21no—
42C2×C3×C5×C7—21no—
43C2×C3×C5×C7C5×D311yescharacteristic, complemented
44C2×C3×C5×C7C3×D511yescharacteristic, complemented
45C2×C3×C5×C7D1511yescharacteristic, complemented
46C2×C3×C5×C7C2×C3×C511yescharacteristic, complemented
47D105C2×C3×C512yesdirect product factor
48C5×D21—52no—
49C3×D35—32no—
50C3×C5×D7—152no—
51C2×C3×D15—71no—
52C2×C3×C5×D3—351no—
53C52×C7C2×C3×D311yescharacteristic, complemented, Hall
54C2×C3×C52—21no—
55C2×C3×C52C3×D711yescharacteristic, complemented
56C2×C3×C52D2111yescharacteristic, complemented
57C5×D15—72no—
58C3×C5×D5—212no—
59C2×D35—31no—
60C2×C5×D7—151no—
61C2×C32×C7C5×D511yescharacteristic, complemented
62C3×D21—52no—
63C3×C5×C7—24no—
64C3×C5×C7—21no—
65C3×C5×C7—21no—
66C3×C5×C7—22no—
67C3×C5×C7—22no—
68C3×C5×C7C2×C3×D511yescharacteristic, complemented
69C3×C5×C7C2×C5×D311yescharacteristic, complemented
70C3×C5×C7C2×D1511yescharacteristic, complemented
71C3×C5×C7C22×C3×C511yescharacteristic, complemented
72C2×C5×D5—211noHall
73C2×C32×C5—22no—
74C2×C32×C5C5×D711yescharacteristic, complemented
75C2×C32×C5D3511yescharacteristic, complemented
76C3×D15—72no—
77C3×C5×D3—352no—
78C2×D21—51no—
79C2×C3×D7—151no—
80C3×C52—21no—
81C3×C52C2×C3×D711yescharacteristic, complemented
82C3×C52C2×D2111yescharacteristic, complemented
83C2×C5×C7—22no—
84C2×C5×C7C3×C5×D311yescharacteristic, complemented
85C2×C5×C7C3×D1511yescharacteristic, complemented
86D35—32no—
87C5×D7—152no—
88C32×C7C2×C5×D511yescharacteristic, complemented, Hall
89C22×C3×C5—1051no—
90C2×D15—71no—
91C2×C5×D3—351no—
92C2×C3×D5—211no—
93C2×C52C3×D2111yescharacteristic, complemented
94C5×D5—212no—
95C32×C5—22no—
96C32×C5C2×C5×D711yescharacteristic, complemented
97C32×C5C2×D3511yescharacteristic, complemented
98C2×C3×C7—21no—
99C2×C3×C7C3×C5×D511yescharacteristic, complemented
100C2×C3×C7C5×D1511yescharacteristic, complemented
101D21—52no—
102C3×D7—152no—
103C2×C3×D3—351noHall
104C5×C7—22no—
105C5×C7C2×C3×C5×D311yescharacteristic, complemented
106C5×C7C2×C3×D1511yescharacteristic, complemented
107C2×C3×C5—24no—
108C2×C3×C5—21no—
109C2×C3×C5—21no—
110C2×C3×C5—22no—
111C2×C3×C5—22no—
112C2×C3×C5—1052no—
113C2×C3×C5C3×C5×D711yescharacteristic, complemented
114C2×C3×C5C3×D3511yescharacteristic, complemented
115C2×C3×C5C5×D2111yescharacteristic, complemented
116C2×C3×C5D10511yescharacteristic, direct product factor
117D15—72no—
118C3×D5—212no—
119C5×D3—352no—
120C2×D7—151noHall
121C52C2×C3×D2111yescharacteristic, complemented, Sylow
122C3×C7—21no—
123C3×C7C2×C3×C5×D511yescharacteristic, complemented
124C3×C7C2×C5×D1511yescharacteristic, complemented
125C22×C5—1051no—
126C2×D5—211no—
127C2×C32C5×D3511yescharacteristic, complemented
128C3×D3—352no—
129C3×C5—24no—
130C3×C5—21no—
131C3×C5—21no—
132C3×C5—22no—
133C3×C5—22no—
134C3×C5C2×C3×C5×D711yescharacteristic, complemented
135C3×C5C2×C3×D3511yescharacteristic, complemented
136C3×C5C2×C5×D2111yescharacteristic, complemented
137C3×C5C2×D10511yescharacteristic, direct product factor
138C2×C7C3×C5×D1511yescharacteristic, complemented
139D7—152no—
140C22×C3—1051no—
141C2×D3—351no—
142C2×C5—22no—
143C2×C5—1052no—
144C2×C5C3×C5×D2111yescharacteristic, complemented
145C2×C5C3×D10511yescharacteristic, direct product factor
146D5—212no—
147C32C2×C5×D3511yescharacteristic, complemented, Sylow
148C7C2×C3×C5×D1511yescharacteristic, complemented, Sylow
149C2×C3—21no—
150C2×C3—1052no—
151C2×C3C3×C5×D3511yescharacteristic, complemented
152C2×C3C5×D10511yescharacteristic, direct product factor
153D3—352no—
154C5—22no—
155C5C2×C3×C5×D2111yescharacteristic, complemented
156C5C2×C3×D10511yescharacteristic, direct product factor
157C22—1051noSylow
158C3—21no—
159C3C2×C3×C5×D3511yescharacteristic, complemented
160C3C2×C5×D10511yescharacteristic, direct product factor
161C2—1052no—
162C2C3×C5×D10511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5D105
commutator, hypocenterC3×C5×C7C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D105C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
3. C2×C5×D105C3direct (N × H)
5. C32×C52×C7C22semidirect
6. C2×C3×D105C5direct (N × H)
9. C2×C3×C52×C7D3semidirect
10. C2×C3×C52×C7C2×C3semidirect
11. C5×D105C2×C3direct (N × H)
16. C2×C32×C5×C7D5semidirect
17. C2×C32×C5×C7C2×C5semidirect
18. C3×D105C2×C5direct (N × H)
21. C3×C52×C7C2×D3semidirect
22. C3×C52×C7C22×C3semidirect
23. C2×C32×C52D7semidirect
25. C2×D105C3×C5direct (N × H)
29. C2×C52×C7C3×D3semidirect
32. C32×C5×C7C2×D5semidirect
33. C32×C5×C7C22×C5semidirect
37. C32×C52C2×D7semidirect
43. C2×C3×C5×C7C5×D3semidirect
44. C2×C3×C5×C7C3×D5semidirect
45. C2×C3×C5×C7D15semidirect
46. C2×C3×C5×C7C2×C3×C5semidirect
47. D105C2×C3×C5direct (N × H)
53. C52×C7C2×C3×D3semidirect
55. C2×C3×C52C3×D7semidirect
56. C2×C3×C52D21semidirect
61. C2×C32×C7C5×D5semidirect
68. C3×C5×C7C2×C3×D5semidirect
69. C3×C5×C7C2×C5×D3semidirect
70. C3×C5×C7C2×D15semidirect
71. C3×C5×C7C22×C3×C5semidirect
74. C2×C32×C5C5×D7semidirect
75. C2×C32×C5D35semidirect
81. C3×C52C2×C3×D7semidirect
82. C3×C52C2×D21semidirect
84. C2×C5×C7C3×C5×D3semidirect
85. C2×C5×C7C3×D15semidirect
88. C32×C7C2×C5×D5semidirect
93. C2×C52C3×D21semidirect
96. C32×C5C2×C5×D7semidirect
97. C32×C5C2×D35semidirect
99. C2×C3×C7C3×C5×D5semidirect
100. C2×C3×C7C5×D15semidirect
105. C5×C7C2×C3×C5×D3semidirect
106. C5×C7C2×C3×D15semidirect
113. C2×C3×C5C3×C5×D7semidirect
114. C2×C3×C5C3×D35semidirect
115. C2×C3×C5C5×D21semidirect
116. C2×C3×C5D105direct (N × H)
121. C52C2×C3×D21semidirect
123. C3×C7C2×C3×C5×D5semidirect
124. C3×C7C2×C5×D15semidirect
127. C2×C32C5×D35semidirect
134. C3×C5C2×C3×C5×D7semidirect
135. C3×C5C2×C3×D35semidirect
136. C3×C5C2×C5×D21semidirect
137. C3×C5C2×D105direct (N × H)
138. C2×C7C3×C5×D15semidirect
144. C2×C5C3×C5×D21semidirect
145. C2×C5C3×D105direct (N × H)
147. C32C2×C5×D35semidirect
148. C7C2×C3×C5×D15semidirect
151. C2×C3C3×C5×D35semidirect
152. C2×C3C5×D105direct (N × H)
155. C5C2×C3×C5×D21semidirect
156. C5C2×C3×D105direct (N × H)
159. C3C2×C3×C5×D35semidirect
160. C3C2×C5×D105direct (N × H)
162. C2C3×C5×D105direct (N × H)