Finite Group Databasebeta

← C3×D3×C7×D5×C23 #44394575

Subgroups — C3×D3×C7×D5×C23 #44394575

Order 28980.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C7×D5×C23C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C23C211yesmaximal, characteristic, complemented
3C3×C7×C23×D15C211yesmaximal, characteristic, complemented
4C2×C3×C7×D5×C23—31nomaximal
5D3×C7×D5×C23C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
7C2×C3×D3×C7×C23—51nomaximal, Hall
8C7×C23×D15C2×C311yescharacteristic, complemented
9C5×D3×C7×C23C2×C311yescharacteristic, complemented
10C3×C7×D5×C23—21no—
11C3×C7×D5×C23—31no—
12C3×C7×D5×C23D311yescharacteristic, direct product factor
13C3×C7×D5×C23C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C23—31no—
15C3×D3×D5×C23C711yesmaximal, characteristic, direct product factor, Hall
16C2×C7×D5×C23—31noHall
17C3×D3×C7×C23—51no—
18C3×D3×C7×C23D511yescharacteristic, direct product factor
19C2×C32×C7×C23—51no—
20C3×C5×C7×C23—21no—
21C3×C5×C7×C23C2×D311yescharacteristic, complemented
22C3×C5×C7×C23C22×C311yescharacteristic, complemented
23C3×C23×D15C2×C711yescharacteristic, complemented
24C3×C5×D3×C23C2×C711yescharacteristic, complemented
25C32×D5×C23C2×C711yescharacteristic, complemented
26C22×C3×C7×C23—151no—
27C2×D3×C7×C23—51no—
28C2×C5×C7×C23—31no—
29C7×D5×C23—31no—
30C7×D5×C23C3×D311yescharacteristic, direct product factor
31C32×C7×C23C2×D511yescharacteristic, complemented, Hall
32C2×C3×D5×C23—31no—
33D3×D5×C23C3×C711yescharacteristic, direct product factor
34C3×D3×C7×D5C2311yesmaximal, characteristic, direct product factor, Hall
35C32×C5×C23C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C23—31no—
37C2×C3×C7×C23—51no—
38C2×C3×C7×C23—51no—
39C2×C3×C7×C23—101no—
40C2×C3×C7×C23—151no—
41D3×C7×C23—51no—
42D3×C7×C23C3×D511yescharacteristic, direct product factor
43C2×C3×D3×C23—51noHall
44C5×C7×C23C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C23—31no—
46C23×D15C2×C3×C711yescharacteristic, complemented
47C5×D3×C23C2×C3×C711yescharacteristic, complemented
48C3×D5×C23—21no—
49C3×D5×C23—31no—
50C3×D5×C23D3×C711yescharacteristic, direct product factor
51C3×D5×C23C2×C3×C711yescharacteristic, complemented
52C22×C7×C23—151noHall
53C3×C7×D15C2×C2311yescharacteristic, complemented
54C3×C5×D3×C7C2×C2311yescharacteristic, complemented
55C32×C7×D5C2×C2311yescharacteristic, complemented
56C3×C7×C23—21no—
57C3×C7×C23D3×D511yescharacteristic, direct product factor
58C3×C7×C23C2×C3×D511yescharacteristic, complemented
59C2×D5×C23—31noHall
60C2×C3×C7×D5—31no—
61D3×C7×D5C3×C2311yescharacteristic, direct product factor
62C2×C32×C23—51no—
63C3×D3×C23—51no—
64C3×D3×C23C7×D511yescharacteristic, direct product factor
65C3×C5×C23—21no—
66C3×C5×C23C2×D3×C711yescharacteristic, complemented
67C3×C5×C23C22×C3×C711yescharacteristic, complemented
68C2×C7×C23—31no—
69C2×C7×C23—51no—
70C2×C7×C23—151no—
71C32×C5×C7C22×C2311yescharacteristic, complemented, Hall
72C22×C3×C23—151no—
73C2×D3×C23—51no—
74C2×C3×D3×C7—51noHall
75C2×C5×C23—31no—
76D5×C23—31no—
77D5×C23C3×D3×C711yescharacteristic, direct product factor
78C2×C3×C5×C7—31no—
79C7×D15C2×C3×C2311yescharacteristic, complemented
80C5×D3×C7C2×C3×C2311yescharacteristic, complemented
81C3×C7×D5—21no—
82C3×C7×D5—31no—
83C3×C7×D5D3×C2311yescharacteristic, direct product factor
84C3×C7×D5C2×C3×C2311yescharacteristic, complemented
85C32×C23C2×C7×D511yescharacteristic, complemented, Hall
86C3×D3×D5C7×C2311yescharacteristic, direct product factor, Hall
87C7×C23C3×D3×D511yescharacteristic, direct product factor, Hall
88C2×C7×D5—31noHall
89C2×C3×C23—31no—
90C2×C3×C23—51no—
91C2×C3×C23—51no—
92C2×C3×C23—101no—
93C2×C3×C23—151no—
94D3×C23—51no—
95D3×C23C3×C7×D511yescharacteristic, direct product factor
96C2×C32×C7—51no—
97C3×D3×C7—51no—
98C3×D3×C7D5×C2311yescharacteristic, direct product factor
99C5×C23C2×C3×D3×C711yescharacteristic, complemented, Hall
100C3×C5×C7—21no—
101C3×C5×C7C2×D3×C2311yescharacteristic, complemented
102C3×C5×C7C22×C3×C2311yescharacteristic, complemented
103C22×C23—151noHall
104C3×D15C2×C7×C2311yescharacteristic, complemented
105C3×C5×D3C2×C7×C2311yescharacteristic, complemented
106C32×D5C2×C7×C2311yescharacteristic, complemented
107C22×C3×C7—151no—
108C2×D3×C7—51no—
109C2×C5×C7—31no—
110C7×D5—31no—
111C7×D5C3×D3×C2311yescharacteristic, direct product factor
112C3×C23—21no—
113C3×C23D3×C7×D511yescharacteristic, direct product factor
114C3×C23C2×C3×C7×D511yescharacteristic, complemented
115C32×C7C2×D5×C2311yescharacteristic, complemented, Hall
116C2×C3×D5—31no—
117D3×D5C3×C7×C2311yescharacteristic, direct product factor
118C2×C23—31no—
119C2×C23—51no—
120C2×C23—151no—
121C32×C5C22×C7×C2311yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123C2×C3×C7—51no—
124C2×C3×C7—51no—
125C2×C3×C7—101no—
126C2×C3×C7—151no—
127D3×C7—51no—
128D3×C7C3×D5×C2311yescharacteristic, direct product factor
129C2×C3×D3—51noHall
130C5×C7C2×C3×D3×C2311yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15C2×C3×C7×C2311yescharacteristic, complemented
133C3×D5—21no—
134C3×D5—31no—
135C3×D5D3×C7×C2311yescharacteristic, direct product factor
136C3×D5C2×C3×C7×C2311yescharacteristic, complemented
137C5×D3C2×C3×C7×C2311yescharacteristic, complemented
138C22×C7—151noHall
139C23C3×D3×C7×D511yescharacteristic, direct product factor, Sylow
140C3×C7—21no—
141C3×C7D3×D5×C2311yescharacteristic, direct product factor
142C3×C7C2×C3×D5×C2311yescharacteristic, complemented
143C2×D5—31noHall
144C2×C32—51no—
145C3×D3—51no—
146C3×D3C7×D5×C2311yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5C2×D3×C7×C2311yescharacteristic, complemented
149C3×C5C22×C3×C7×C2311yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—51no—
152C2×C7—151no—
153C22×C3—151no—
154C2×D3—51no—
155C2×C5—31no—
156D5—31no—
157D5C3×D3×C7×C2311yescharacteristic, direct product factor
158C32C2×C7×D5×C2311yescharacteristic, complemented, Sylow
159C7C3×D3×D5×C2311yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—51no—
162C2×C3—51no—
163C2×C3—101no—
164C2×C3—151no—
165D3—51no—
166D3C3×C7×D5×C2311yescharacteristic, direct product factor
167C5C2×C3×D3×C7×C2311yescharacteristic, complemented, Sylow
168C22—151noSylow
169C3—21no—
170C3D3×C7×D5×C2311yescharacteristic, direct product factor
171C3C2×C3×C7×D5×C2311yescharacteristic, complemented
172C2—31no—
173C2—51no—
174C2—151no—
subgroupG/H
center, hypercenterC3×C7×C23D3×D5
commutator, cosocle, hypocenterC3×C5C22×C3×C7×C23
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C3×C5
UCSC1 ◁ C3×C7×C23

Complements

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

NH ≅ G/Ntype
1. C32×C7×D5×C23C2semidirect
2. C3×C5×D3×C7×C23C2semidirect
3. C3×C7×C23×D15C2semidirect
5. D3×C7×D5×C23C3direct (N × H)
6. C32×C5×C7×C23C22semidirect
8. C7×C23×D15C2×C3semidirect
9. C5×D3×C7×C23C2×C3semidirect
12. C3×C7×D5×C23D3direct (N × H)
13. C3×C7×D5×C23C2×C3semidirect
15. C3×D3×D5×C23C7direct (N × H)
18. C3×D3×C7×C23D5direct (N × H)
21. C3×C5×C7×C23C2×D3semidirect
22. C3×C5×C7×C23C22×C3semidirect
23. C3×C23×D15C2×C7semidirect
24. C3×C5×D3×C23C2×C7semidirect
25. C32×D5×C23C2×C7semidirect
30. C7×D5×C23C3×D3direct (N × H)
31. C32×C7×C23C2×D5semidirect
33. D3×D5×C23C3×C7direct (N × H)
34. C3×D3×C7×D5C23direct (N × H)
35. C32×C5×C23C22×C7semidirect
42. D3×C7×C23C3×D5direct (N × H)
44. C5×C7×C23C2×C3×D3semidirect
46. C23×D15C2×C3×C7semidirect
47. C5×D3×C23C2×C3×C7semidirect
50. C3×D5×C23D3×C7direct (N × H)
51. C3×D5×C23C2×C3×C7semidirect
53. C3×C7×D15C2×C23semidirect
54. C3×C5×D3×C7C2×C23semidirect
55. C32×C7×D5C2×C23semidirect
57. C3×C7×C23D3×D5direct (N × H)
58. C3×C7×C23C2×C3×D5semidirect
61. D3×C7×D5C3×C23direct (N × H)
64. C3×D3×C23C7×D5direct (N × H)
66. C3×C5×C23C2×D3×C7semidirect
67. C3×C5×C23C22×C3×C7semidirect
71. C32×C5×C7C22×C23semidirect
77. D5×C23C3×D3×C7direct (N × H)
79. C7×D15C2×C3×C23semidirect
80. C5×D3×C7C2×C3×C23semidirect
83. C3×C7×D5D3×C23direct (N × H)
84. C3×C7×D5C2×C3×C23semidirect
85. C32×C23C2×C7×D5semidirect
86. C3×D3×D5C7×C23direct (N × H)
87. C7×C23C3×D3×D5direct (N × H)
95. D3×C23C3×C7×D5direct (N × H)
98. C3×D3×C7D5×C23direct (N × H)
99. C5×C23C2×C3×D3×C7semidirect
101. C3×C5×C7C2×D3×C23semidirect
102. C3×C5×C7C22×C3×C23semidirect
104. C3×D15C2×C7×C23semidirect
105. C3×C5×D3C2×C7×C23semidirect
106. C32×D5C2×C7×C23semidirect
111. C7×D5C3×D3×C23direct (N × H)
113. C3×C23D3×C7×D5direct (N × H)
114. C3×C23C2×C3×C7×D5semidirect
115. C32×C7C2×D5×C23semidirect
117. D3×D5C3×C7×C23direct (N × H)
121. C32×C5C22×C7×C23semidirect
128. D3×C7C3×D5×C23direct (N × H)
130. C5×C7C2×C3×D3×C23semidirect
132. D15C2×C3×C7×C23semidirect
135. C3×D5D3×C7×C23direct (N × H)
136. C3×D5C2×C3×C7×C23semidirect
137. C5×D3C2×C3×C7×C23semidirect
139. C23C3×D3×C7×D5direct (N × H)
141. C3×C7D3×D5×C23direct (N × H)
142. C3×C7C2×C3×D5×C23semidirect
146. C3×D3C7×D5×C23direct (N × H)
148. C3×C5C2×D3×C7×C23semidirect
149. C3×C5C22×C3×C7×C23semidirect
157. D5C3×D3×C7×C23direct (N × H)
158. C32C2×C7×D5×C23semidirect
159. C7C3×D3×D5×C23direct (N × H)
166. D3C3×C7×D5×C23direct (N × H)
167. C5C2×C3×D3×C7×C23semidirect
170. C3D3×C7×D5×C23direct (N × H)
171. C3C2×C3×C7×D5×C23semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C232
C3×C5×D3×C7×C232
C3×C7×C23×D152
C2×C3×C7×D5×C233
D3×C7×D5×C233
C2×C3×D3×C7×C235
C3×D3×D5×C237
C3×D3×C7×D523