Finite Group Databasebeta

← C5×C13×D7×D15 #41031973

Subgroups — C5×C13×D7×D15 #41031973

Order 27300.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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×C52×C13×D7C211yesmaximal, characteristic, complemented
2C5×C7×C13×D15C211yesmaximal, characteristic, complemented
3C5×C13×D105C211yesmaximal, characteristic, complemented
4C5×D5×C13×D7—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C13×D7×D15C511yesmaximal, characteristic, direct product factor
7C5×D3×C13×D7—51nomaximal
8C5×C13×D35—31no—
9C5×C7×D5×C13—31no—
10C52×C13×D7D311yescharacteristic, complemented
11C2×C5×C13×D15—71nomaximal, Hall
12C13×D105C2×C511yescharacteristic, complemented
13C7×C13×D15C2×C511yescharacteristic, complemented
14C5×C13×D21—51no—
15C5×D3×C7×C13—51no—
16C3×C5×C13×D7—22no—
17C3×C5×C13×D7D511yescharacteristic, complemented
18C3×C5×C13×D7C2×C511yescharacteristic, complemented
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C5×D7×D15C1311yesmaximal, characteristic, direct product factor, Hall
21C2×C3×C52×C13—71no—
22C5×C13×D15—71no—
23C5×C13×D15D711yescharacteristic, direct product factor
24C2×C5×C13×D7—151no—
25D5×C13×D7—31no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C22×C511yescharacteristic, complemented
29C2×C5×D5×C13—211noHall
30D3×C13×D7—51noHall
31C5×D105C2×C1311yescharacteristic, complemented
32C5×C7×D15C2×C1311yescharacteristic, complemented
33C3×C52×D7C2×C1311yescharacteristic, complemented
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—151no—
36C13×D35—31no—
37C7×D5×C13—31no—
38C5×C13×D7—22no—
39C5×C13×D7—151no—
40C5×C13×D7C5×D311yescharacteristic, complemented
41C5×C13×D7D1511yescharacteristic, direct product factor
42C2×C13×D15—71no—
43C2×C5×D3×C13—351no—
44C5×D5×D7—31noHall
45C2×C52×C13—71no—
46C5×D5×C13—31no—
47C5×D5×C13—211no—
48C13×D21—51no—
49D3×C7×C13—51no—
50C3×C13×D7C5×D511yescharacteristic, complemented
51C3×C52×C7C22×C1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13C2×C5×D311yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55D7×D15C5×C1311yescharacteristic, direct product factor
56C5×D3×D7—51no—
57C2×C3×C5×C13—71no—
58C2×C3×C5×C13—71no—
59C2×C3×C5×C13—142no—
60C13×D15—71no—
61C13×D15C5×D711yescharacteristic, direct product factor
62C5×D3×C13—51no—
63C5×D3×C13—351no—
64C2×C13×D7—151noHall
65C5×D35—31no—
66C5×C7×D5—31no—
67C52×D7D3×C1311yescharacteristic, complemented
68C52×C13D3×D711yescharacteristic, complemented, Hall
69C2×C5×D15—71noHall
70C3×C7×C13C2×C5×D511yescharacteristic, complemented, Hall
71C22×C5×C13—1051no—
72C2×D5×C13—211no—
73D105C2×C5×C1311yescharacteristic, complemented
74C7×D15C2×C5×C1311yescharacteristic, complemented
75C5×D21—51no—
76C5×D3×C7—51no—
77C3×C5×D7—22no—
78C3×C5×D7D5×C1311yescharacteristic, complemented
79C3×C5×D7C2×C5×C1311yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13D5×D711yescharacteristic, complemented
82C3×C5×C13C2×C5×D711yescharacteristic, complemented
83C2×C7×C13—151no—
84C13×D7—151no—
85C13×D7C5×D1511yescharacteristic, direct product factor
86C52×C7C2×D3×C1311yescharacteristic, complemented, Hall
87C2×D3×C13—351noHall
88C2×C3×C52—71no—
89C5×D15—71no—
90C5×D15C13×D711yescharacteristic, direct product factor
91C2×C5×D7—151no—
92D5×D7—31no—
93C2×C5×C13—71no—
94C2×C5×C13—71no—
95C2×C5×C13—142no—
96C2×C5×C13—151no—
97C2×C5×C13—1051no—
98D5×C13—31no—
99D5×C13—211no—
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1311yescharacteristic, complemented
102C3×C5×C7C22×C5×C1311yescharacteristic, complemented
103C2×C5×D5—211noHall
104C7×C13C2×C5×D1511yescharacteristic, complemented, Hall
105D3×D7—51noHall
106C2×C3×C13—71no—
107D3×C13—51no—
108D3×C13—351no—
109C3×C52C2×C13×D711yescharacteristic, complemented, Hall
110C2×C5×C7—151no—
111D35—31no—
112C5×D7—22no—
113C5×D7—151no—
114C5×D7C5×D3×C1311yescharacteristic, complemented
115C5×D7C13×D1511yescharacteristic, direct product factor
116C7×D5—31no—
117C5×C13—22no—
118C5×C13C5×D3×D711yescharacteristic, complemented
119C5×C13D7×D1511yescharacteristic, direct product factor
120C2×D15—71no—
121C2×C5×D3—351no—
122C22×C13—1051noHall
123C2×C52—71no—
124C5×D5—31no—
125C5×D5—211no—
126D21—51no—
127C3×D7C5×D5×C1311yescharacteristic, complemented
128D3×C7—51no—
129C3×C13C5×D5×D711yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7C2×C5×D3×C1311yescharacteristic, complemented
132C5×C7C2×C13×D1511yescharacteristic, complemented
133C2×C3×C5—71no—
134C2×C3×C5—71no—
135C2×C3×C5—142no—
136D15—71no—
137D15C5×C13×D711yescharacteristic, direct product factor
138C5×D3—51no—
139C5×D3—351no—
140C2×D7—151noHall
141C2×C13—71no—
142C2×C13—151no—
143C2×C13—1051no—
144C52D3×C13×D711yescharacteristic, complemented, Sylow
145C3×C7C2×C5×D5×C1311yescharacteristic, complemented, Hall
146C22×C5—1051no—
147C2×D5—211no—
148C3×C5—22no—
149C3×C5D5×C13×D711yescharacteristic, complemented
150C3×C5C2×C5×C13×D711yescharacteristic, complemented
151C2×C7—151no—
152D7—151no—
153D7C5×C13×D1511yescharacteristic, direct product factor
154C13C5×D7×D1511yescharacteristic, direct product factor, Sylow
155C2×D3—351noHall
156C2×C5—71no—
157C2×C5—71no—
158C2×C5—142no—
159C2×C5—151no—
160C2×C5—1051no—
161D5—31no—
162D5—211no—
163C7C2×C5×C13×D1511yescharacteristic, complemented, Sylow
164C2×C3—71no—
165D3—51no—
166D3—351no—
167C5—22no—
168C5C5×D3×C13×D711yescharacteristic, complemented
169C5C13×D7×D1511yescharacteristic, direct product factor
170C22—1051noSylow
171C3C5×D5×C13×D711yescharacteristic, complemented, Sylow
172C2—71no—
173C2—151no—
174C2—1051no—
subgroupG/H
center, hypercenterC5×C13D7×D15
commutator, cosocle, hypocenterC3×C5×C7C22×C5×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C13

Complements

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

NH ≅ G/Ntype
1. C3×C52×C13×D7C2semidirect
2. C5×C7×C13×D15C2semidirect
3. C5×C13×D105C2semidirect
5. C3×C52×C7×C13C22semidirect
6. C13×D7×D15C5direct (N × H)
10. C52×C13×D7D3semidirect
12. C13×D105C2×C5semidirect
13. C7×C13×D15C2×C5semidirect
17. C3×C5×C13×D7D5semidirect
18. C3×C5×C13×D7C2×C5semidirect
19. C52×C7×C13C2×D3semidirect
20. C5×D7×D15C13direct (N × H)
23. C5×C13×D15D7direct (N × H)
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C22×C5semidirect
31. C5×D105C2×C13semidirect
32. C5×C7×D15C2×C13semidirect
33. C3×C52×D7C2×C13semidirect
34. C3×C52×C13C2×D7semidirect
40. C5×C13×D7C5×D3semidirect
41. C5×C13×D7D15direct (N × H)
50. C3×C13×D7C5×D5semidirect
51. C3×C52×C7C22×C13semidirect
53. C5×C7×C13C2×C5×D3semidirect
54. C5×C7×C13C2×D15semidirect
55. D7×D15C5×C13direct (N × H)
61. C13×D15C5×D7direct (N × H)
67. C52×D7D3×C13semidirect
68. C52×C13D3×D7semidirect
70. C3×C7×C13C2×C5×D5semidirect
73. D105C2×C5×C13semidirect
74. C7×D15C2×C5×C13semidirect
78. C3×C5×D7D5×C13semidirect
79. C3×C5×D7C2×C5×C13semidirect
81. C3×C5×C13D5×D7semidirect
82. C3×C5×C13C2×C5×D7semidirect
85. C13×D7C5×D15direct (N × H)
86. C52×C7C2×D3×C13semidirect
90. C5×D15C13×D7direct (N × H)
101. C3×C5×C7C2×D5×C13semidirect
102. C3×C5×C7C22×C5×C13semidirect
104. C7×C13C2×C5×D15semidirect
109. C3×C52C2×C13×D7semidirect
114. C5×D7C5×D3×C13semidirect
115. C5×D7C13×D15direct (N × H)
118. C5×C13C5×D3×D7semidirect
119. C5×C13D7×D15direct (N × H)
127. C3×D7C5×D5×C13semidirect
129. C3×C13C5×D5×D7semidirect
131. C5×C7C2×C5×D3×C13semidirect
132. C5×C7C2×C13×D15semidirect
137. D15C5×C13×D7direct (N × H)
144. C52D3×C13×D7semidirect
145. C3×C7C2×C5×D5×C13semidirect
149. C3×C5D5×C13×D7semidirect
150. C3×C5C2×C5×C13×D7semidirect
153. D7C5×C13×D15direct (N × H)
154. C13C5×D7×D15direct (N × H)
163. C7C2×C5×C13×D15semidirect
168. C5C5×D3×C13×D7semidirect
169. C5C13×D7×D15direct (N × H)
171. C3C5×D5×C13×D7semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C13×D72
C5×C7×C13×D152
C5×C13×D1052
C5×D5×C13×D73
C13×D7×D155
C5×D3×C13×D75
C2×C5×C13×D157
C5×D7×D1513