Finite Group Databasebeta

← C5×D3×C7×D5×C13 #41031977

Subgroups — C5×D3×C7×D5×C13 #41031977

Order 27300.

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

normal subgroups only

This group has 192 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
1C3×C5×C7×D5×C13C211yesmaximal, characteristic, complemented
2C52×D3×C7×C13C211yesmaximal, characteristic, complemented
3C5×C7×C13×D15C211yesmaximal, characteristic, complemented
4C2×C5×C7×D5×C13—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C2×C5×D3×C7×C13—51nomaximal
7D3×C7×D5×C13C511yesmaximal, characteristic, direct product factor
8C5×C7×D5×C13—31no—
9C5×C7×D5×C13D311yescharacteristic, direct product factor
10C2×C52×C7×C13—31no—
11C5×D3×D5×C13C711yesmaximal, characteristic, direct product factor, Hall
12C7×C13×D15C2×C511yescharacteristic, complemented
13C5×D3×C7×C13—22no—
14C5×D3×C7×C13—51no—
15C5×D3×C7×C13D511yescharacteristic, direct product factor
16C5×D3×C7×C13C2×C511yescharacteristic, complemented
17C3×C7×D5×C13C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C5×D3×C7×D5C1311yesmaximal, characteristic, direct product factor, Hall
21C5×C13×D15C2×C711yescharacteristic, complemented
22C52×D3×C13C2×C711yescharacteristic, complemented
23C3×C5×D5×C13C2×C711yescharacteristic, complemented
24C22×C5×C7×C13—151no—
25C2×C7×D5×C13—31no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C22×C511yescharacteristic, complemented
29C2×C5×D5×C13—31noHall
30C2×D3×C7×C13—51noHall
31C5×C7×D15C2×C1311yescharacteristic, complemented
32C52×D3×C7C2×C1311yescharacteristic, complemented
33C3×C5×C7×D5C2×C1311yescharacteristic, complemented
34C3×C52×C13C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—31no—
36C2×C5×C7×C13—31no—
37C2×C5×C7×C13—51no—
38C2×C5×C7×C13—62no—
39C2×C5×C7×C13—151no—
40C7×D5×C13—31no—
41C7×D5×C13C5×D311yescharacteristic, direct product factor
42C2×C5×D3×C13—51no—
43D3×D5×C13C5×C711yescharacteristic, direct product factor
44C2×C5×C7×D5—31noHall
45C2×C52×C13—31no—
46C5×D5×C13—31no—
47C5×D5×C13D3×C711yescharacteristic, direct product factor
48C2×C3×C7×C13—51no—
49D3×C7×C13—51no—
50D3×C7×C13C5×D511yescharacteristic, direct product factor
51C3×C52×C7C22×C1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, direct product factor
54C5×C7×C13C2×C5×D311yescharacteristic, complemented
55C2×C5×D3×C7—51no—
56D3×C7×D5C5×C1311yescharacteristic, direct product factor
57C2×C3×C5×C13—51no—
58C13×D15C2×C5×C711yescharacteristic, complemented
59C5×D3×C13—22no—
60C5×D3×C13—51no—
61C5×D3×C13C7×D511yescharacteristic, direct product factor
62C5×D3×C13C2×C5×C711yescharacteristic, complemented
63C3×D5×C13C2×C5×C711yescharacteristic, complemented
64C22×C7×C13—151noHall
65C2×C52×C7—31no—
66C5×C7×D5—31no—
67C5×C7×D5D3×C1311yescharacteristic, direct product factor
68C52×C13C2×D3×C711yescharacteristic, complemented, Hall
69C5×D3×D5C7×C1311yescharacteristic, direct product factor, Hall
70C3×C7×C13C2×C5×D511yescharacteristic, complemented, Hall
71C22×C5×C13—151no—
72C2×D5×C13—31no—
73C2×C3×C5×C7—51no—
74C7×D15C2×C5×C1311yescharacteristic, complemented
75C5×D3×C7—22no—
76C5×D3×C7—51no—
77C5×D3×C7D5×C1311yescharacteristic, direct product factor
78C5×D3×C7C2×C5×C1311yescharacteristic, complemented
79C3×C7×D5C2×C5×C1311yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13C2×C7×D511yescharacteristic, complemented
82C3×C5×C13C22×C5×C711yescharacteristic, complemented
83C2×C7×C13—31no—
84C2×C7×C13—51no—
85C2×C7×C13—151no—
86C52×C7C2×D3×C1311yescharacteristic, complemented, Hall
87C2×D3×C13—51noHall
88C5×D15C2×C7×C1311yescharacteristic, complemented
89C52×D3C2×C7×C1311yescharacteristic, complemented
90C3×C5×D5C2×C7×C1311yescharacteristic, complemented
91C22×C5×C7—151no—
92C2×C7×D5—31no—
93C2×C5×C13—31no—
94C2×C5×C13—31no—
95C2×C5×C13—51no—
96C2×C5×C13—62no—
97C2×C5×C13—151no—
98D5×C13—31no—
99D5×C13C5×D3×C711yescharacteristic, direct product factor
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1311yescharacteristic, complemented
102C3×C5×C7C22×C5×C1311yescharacteristic, complemented
103C2×C5×D5—31noHall
104C7×C13C5×D3×D511yescharacteristic, direct product factor, Hall
105C2×D3×C7—51noHall
106C2×C3×C13—51no—
107D3×C13—51no—
108D3×C13C5×C7×D511yescharacteristic, direct product factor
109C3×C52C22×C7×C1311yescharacteristic, complemented, Hall
110C2×C5×C7—31no—
111C2×C5×C7—31no—
112C2×C5×C7—51no—
113C2×C5×C7—62no—
114C2×C5×C7—151no—
115C7×D5—31no—
116C7×D5C5×D3×C1311yescharacteristic, direct product factor
117C5×C13—22no—
118C5×C13D3×C7×D511yescharacteristic, direct product factor
119C5×C13C2×C5×D3×C711yescharacteristic, complemented
120C2×C5×D3—51no—
121D3×D5C5×C7×C1311yescharacteristic, direct product factor
122C22×C13—151noHall
123C2×C52—31no—
124C5×D5—31no—
125C5×D5D3×C7×C1311yescharacteristic, direct product factor
126C2×C3×C7—51no—
127D3×C7—51no—
128D3×C7C5×D5×C1311yescharacteristic, direct product factor
129C3×C13C2×C5×C7×D511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D3×D5×C1311yescharacteristic, direct product factor
132C5×C7C2×C5×D3×C1311yescharacteristic, complemented
133C2×C3×C5—51no—
134D15C2×C5×C7×C1311yescharacteristic, complemented
135C3×D5C2×C5×C7×C1311yescharacteristic, complemented
136C5×D3—22no—
137C5×D3—51no—
138C5×D3C7×D5×C1311yescharacteristic, direct product factor
139C5×D3C2×C5×C7×C1311yescharacteristic, complemented
140C22×C7—151noHall
141C2×C13—31no—
142C2×C13—51no—
143C2×C13—151no—
144C52C2×D3×C7×C1311yescharacteristic, complemented, Sylow
145C3×C7C2×C5×D5×C1311yescharacteristic, complemented, Hall
146C22×C5—151no—
147C2×D5—31no—
148C3×C5—22no—
149C3×C5C2×C7×D5×C1311yescharacteristic, complemented
150C3×C5C22×C5×C7×C1311yescharacteristic, complemented
151C2×C7—31no—
152C2×C7—51no—
153C2×C7—151no—
154C13C5×D3×C7×D511yescharacteristic, direct product factor, Sylow
155C2×D3—51noHall
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—51no—
159C2×C5—62no—
160C2×C5—151no—
161D5—31no—
162D5C5×D3×C7×C1311yescharacteristic, direct product factor
163C7C5×D3×D5×C1311yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—51no—
166D3C5×C7×D5×C1311yescharacteristic, direct product factor
167C5—22no—
168C5D3×C7×D5×C1311yescharacteristic, direct product factor
169C5C2×C5×D3×C7×C1311yescharacteristic, complemented
170C22—151noSylow
171C3C2×C5×C7×D5×C1311yescharacteristic, complemented, Sylow
172C2—31no—
173C2—51no—
174C2—151no—
subgroupG/H
center, hypercenterC5×C7×C13D3×D5
commutator, cosocle, hypocenterC3×C5C22×C5×C7×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C5
UCSC1 ◁ C5×C7×C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C13C2semidirect
2. C52×D3×C7×C13C2semidirect
3. C5×C7×C13×D15C2semidirect
5. C3×C52×C7×C13C22semidirect
7. D3×C7×D5×C13C5direct (N × H)
9. C5×C7×D5×C13D3direct (N × H)
11. C5×D3×D5×C13C7direct (N × H)
12. C7×C13×D15C2×C5semidirect
15. C5×D3×C7×C13D5direct (N × H)
16. C5×D3×C7×C13C2×C5semidirect
17. C3×C7×D5×C13C2×C5semidirect
19. C52×C7×C13C2×D3semidirect
20. C5×D3×C7×D5C13direct (N × H)
21. C5×C13×D15C2×C7semidirect
22. C52×D3×C13C2×C7semidirect
23. C3×C5×D5×C13C2×C7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C22×C5semidirect
31. C5×C7×D15C2×C13semidirect
32. C52×D3×C7C2×C13semidirect
33. C3×C5×C7×D5C2×C13semidirect
34. C3×C52×C13C22×C7semidirect
41. C7×D5×C13C5×D3direct (N × H)
43. D3×D5×C13C5×C7direct (N × H)
47. C5×D5×C13D3×C7direct (N × H)
50. D3×C7×C13C5×D5direct (N × H)
51. C3×C52×C7C22×C13semidirect
53. C5×C7×C13D3×D5direct (N × H)
54. C5×C7×C13C2×C5×D3semidirect
56. D3×C7×D5C5×C13direct (N × H)
58. C13×D15C2×C5×C7semidirect
61. C5×D3×C13C7×D5direct (N × H)
62. C5×D3×C13C2×C5×C7semidirect
63. C3×D5×C13C2×C5×C7semidirect
67. C5×C7×D5D3×C13direct (N × H)
68. C52×C13C2×D3×C7semidirect
69. C5×D3×D5C7×C13direct (N × H)
70. C3×C7×C13C2×C5×D5semidirect
74. C7×D15C2×C5×C13semidirect
77. C5×D3×C7D5×C13direct (N × H)
78. C5×D3×C7C2×C5×C13semidirect
79. C3×C7×D5C2×C5×C13semidirect
81. C3×C5×C13C2×C7×D5semidirect
82. C3×C5×C13C22×C5×C7semidirect
86. C52×C7C2×D3×C13semidirect
88. C5×D15C2×C7×C13semidirect
89. C52×D3C2×C7×C13semidirect
90. C3×C5×D5C2×C7×C13semidirect
99. D5×C13C5×D3×C7direct (N × H)
101. C3×C5×C7C2×D5×C13semidirect
102. C3×C5×C7C22×C5×C13semidirect
104. C7×C13C5×D3×D5direct (N × H)
108. D3×C13C5×C7×D5direct (N × H)
109. C3×C52C22×C7×C13semidirect
116. C7×D5C5×D3×C13direct (N × H)
118. C5×C13D3×C7×D5direct (N × H)
119. C5×C13C2×C5×D3×C7semidirect
121. D3×D5C5×C7×C13direct (N × H)
125. C5×D5D3×C7×C13direct (N × H)
128. D3×C7C5×D5×C13direct (N × H)
129. C3×C13C2×C5×C7×D5semidirect
131. C5×C7D3×D5×C13direct (N × H)
132. C5×C7C2×C5×D3×C13semidirect
134. D15C2×C5×C7×C13semidirect
135. C3×D5C2×C5×C7×C13semidirect
138. C5×D3C7×D5×C13direct (N × H)
139. C5×D3C2×C5×C7×C13semidirect
144. C52C2×D3×C7×C13semidirect
145. C3×C7C2×C5×D5×C13semidirect
149. C3×C5C2×C7×D5×C13semidirect
150. C3×C5C22×C5×C7×C13semidirect
154. C13C5×D3×C7×D5direct (N × H)
162. D5C5×D3×C7×C13direct (N × H)
163. C7C5×D3×D5×C13direct (N × H)
166. D3C5×C7×D5×C13direct (N × H)
168. C5D3×C7×D5×C13direct (N × H)
169. C5C2×C5×D3×C7×C13semidirect
171. C3C2×C5×C7×D5×C13semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C132
C52×D3×C7×C132
C5×C7×C13×D152
C2×C5×C7×D5×C133
C2×C5×D3×C7×C135
D3×C7×D5×C135
C5×D3×D5×C137
C5×D3×C7×D513