Finite Group Databasebeta

← C5×C7×D5×D39 #41031978

Subgroups — C5×C7×D5×D39 #41031978

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×C5×C7×D5×C13C211yesmaximal, characteristic, complemented
2C52×C7×D39C211yesmaximal, characteristic, complemented
3C5×C7×D195C211yesmaximal, characteristic, complemented
4C5×C7×D5×D13—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C2×C5×C7×D39—51nomaximal
7C7×D5×D39C511yesmaximal, characteristic, direct product factor
8C5×C7×D65—31no—
9C5×C7×D5×C13D311yescharacteristic, complemented
10C52×C7×D13—31no—
11C5×D5×D39C711yesmaximal, characteristic, direct product factor, Hall
12C7×D195C2×C511yescharacteristic, complemented
13C5×C7×D39—22no—
14C5×C7×D39—51no—
15C5×C7×D39D511yescharacteristic, direct product factor
16C5×C7×D39C2×C511yescharacteristic, complemented
17C3×C7×D5×C13C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C5×D3×C7×D5—131nomaximal, Hall
21C5×D195C2×C711yescharacteristic, complemented
22C52×D39C2×C711yescharacteristic, complemented
23C3×C5×D5×C13C2×C711yescharacteristic, complemented
24C2×C5×C7×D13—151no—
25C7×D5×D13—31no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C22×C511yescharacteristic, complemented
29C5×D5×D13—31noHall
30C2×C7×D39—51noHall
31C5×C7×D15—131no—
32C52×D3×C7—131no—
33C3×C5×C7×D5D1311yescharacteristic, complemented
34C3×C52×C13C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—51no—
36C7×D65—31no—
37C7×D5×C13C5×D311yescharacteristic, complemented
38C5×C7×D13—31no—
39C5×C7×D13—31no—
40C5×C7×D13—62no—
41C5×C7×D13—151no—
42C2×C5×D39—51no—
43D5×D39C5×C711yescharacteristic, direct product factor
44C2×C5×C7×D5—391noHall
45C5×D65—31no—
46C5×D5×C13D3×C711yescharacteristic, complemented
47C52×D13—31no—
48C2×C3×C7×C13—51no—
49C7×D39—51no—
50C7×D39C5×D511yescharacteristic, direct product factor
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, complemented
54C5×C7×C13C2×C5×D311yescharacteristic, complemented
55C2×C5×D3×C7—651no—
56D3×C7×D5—131no—
57C2×C3×C5×C13—51no—
58D195C2×C5×C711yescharacteristic, complemented
59C5×D39—22no—
60C5×D39—51no—
61C5×D39C7×D511yescharacteristic, direct product factor
62C5×D39C2×C5×C711yescharacteristic, complemented
63C3×D5×C13C2×C5×C711yescharacteristic, complemented
64C2×C7×D13—151noHall
65C2×C52×C7—391no—
66C5×C7×D5—391no—
67C5×C7×D5D3911yescharacteristic, direct product factor
68C52×C13C2×D3×C711yescharacteristic, complemented, Hall
69C5×D3×D5—131noHall
70C3×C7×C13C2×C5×D511yescharacteristic, complemented, Hall
71C2×C5×D13—151no—
72D5×D13—31no—
73C2×C3×C5×C7—51no—
74C7×D15—131no—
75C5×D3×C7—131no—
76C5×D3×C7—131no—
77C5×D3×C7—262no—
78C5×D3×C7—651no—
79C3×C7×D5C5×D1311yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13C2×C7×D511yescharacteristic, complemented
82C3×C5×C13C22×C5×C711yescharacteristic, complemented
83C2×C7×C13—51no—
84C7×D13—31no—
85C7×D13—151no—
86C52×C7C2×D3911yescharacteristic, complemented, Hall
87C2×D39—51noHall
88C5×D15—131no—
89C52×D3—131no—
90C3×C5×D5C7×D1311yescharacteristic, complemented
91C22×C5×C7—1951no—
92C2×C7×D5—391no—
93C2×C5×C13—51no—
94D65—31no—
95C5×D13—31no—
96C5×D13—31no—
97C5×D13—62no—
98C5×D13—151no—
99D5×C13C5×D3×C711yescharacteristic, complemented
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7C2×C5×D1311yescharacteristic, complemented
103C2×C5×D5—391noHall
104C7×C13C5×D3×D511yescharacteristic, complemented, Hall
105C2×D3×C7—651noHall
106C2×C3×C13—51no—
107D39—51no—
108D39C5×C7×D511yescharacteristic, direct product factor
109C3×C52C2×C7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—51no—
111C2×C5×C7—391no—
112C2×C5×C7—391no—
113C2×C5×C7—782no—
114C2×C5×C7—1951no—
115C7×D5—391no—
116C7×D5C5×D3911yescharacteristic, direct product factor
117C5×C13—22no—
118C5×C13D3×C7×D511yescharacteristic, complemented
119C5×C13C2×C5×D3×C711yescharacteristic, complemented
120C2×C5×D3—651no—
121D3×D5—131no—
122C2×D13—151noHall
123C2×C52—391no—
124C5×D5—391no—
125C5×D5C7×D3911yescharacteristic, direct product factor
126C2×C3×C7—51no—
127D3×C7—131no—
128D3×C7—651no—
129C3×C13C2×C5×C7×D511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D5×D3911yescharacteristic, direct product factor
132C5×C7C2×C5×D3911yescharacteristic, complemented
133C2×C3×C5—51no—
134D15—131no—
135C3×D5C5×C7×D1311yescharacteristic, complemented
136C5×D3—131no—
137C5×D3—131no—
138C5×D3—262no—
139C5×D3—651no—
140C22×C7—1951noHall
141C2×C13—51no—
142D13—31no—
143D13—151no—
144C52C2×C7×D3911yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1311yescharacteristic, complemented, Hall
146C22×C5—1951no—
147C2×D5—391no—
148C3×C5—22no—
149C3×C5C7×D5×D1311yescharacteristic, complemented
150C3×C5C2×C5×C7×D1311yescharacteristic, complemented
151C2×C7—51no—
152C2×C7—391no—
153C2×C7—1951no—
154C13C5×D3×C7×D511yescharacteristic, complemented, Sylow
155C2×D3—651noHall
156C2×C5—51no—
157C2×C5—391no—
158C2×C5—391no—
159C2×C5—782no—
160C2×C5—1951no—
161D5—391no—
162D5C5×C7×D3911yescharacteristic, direct product factor
163C7C5×D5×D3911yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—131no—
166D3—651no—
167C5—22no—
168C5C7×D5×D3911yescharacteristic, direct product factor
169C5C2×C5×C7×D3911yescharacteristic, complemented
170C22—1951noSylow
171C3C5×C7×D5×D1311yescharacteristic, complemented, Sylow
172C2—51no—
173C2—391no—
174C2—1951no—
subgroupG/H
center, hypercenterC5×C7D5×D39
commutator, cosocle, hypocenterC3×C5×C13C22×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C13C2semidirect
2. C52×C7×D39C2semidirect
3. C5×C7×D195C2semidirect
5. C3×C52×C7×C13C22semidirect
7. C7×D5×D39C5direct (N × H)
9. C5×C7×D5×C13D3semidirect
11. C5×D5×D39C7direct (N × H)
12. C7×D195C2×C5semidirect
15. C5×C7×D39D5direct (N × H)
16. C5×C7×D39C2×C5semidirect
17. C3×C7×D5×C13C2×C5semidirect
19. C52×C7×C13C2×D3semidirect
21. C5×D195C2×C7semidirect
22. C52×D39C2×C7semidirect
23. C3×C5×D5×C13C2×C7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C22×C5semidirect
33. C3×C5×C7×D5D13semidirect
34. C3×C52×C13C22×C7semidirect
37. C7×D5×C13C5×D3semidirect
43. D5×D39C5×C7direct (N × H)
46. C5×D5×C13D3×C7semidirect
50. C7×D39C5×D5direct (N × H)
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×C5×D3semidirect
58. D195C2×C5×C7semidirect
61. C5×D39C7×D5direct (N × H)
62. C5×D39C2×C5×C7semidirect
63. C3×D5×C13C2×C5×C7semidirect
67. C5×C7×D5D39direct (N × H)
68. C52×C13C2×D3×C7semidirect
70. C3×C7×C13C2×C5×D5semidirect
79. C3×C7×D5C5×D13semidirect
81. C3×C5×C13C2×C7×D5semidirect
82. C3×C5×C13C22×C5×C7semidirect
86. C52×C7C2×D39semidirect
90. C3×C5×D5C7×D13semidirect
99. D5×C13C5×D3×C7semidirect
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×C5×D13semidirect
104. C7×C13C5×D3×D5semidirect
108. D39C5×C7×D5direct (N × H)
109. C3×C52C2×C7×D13semidirect
116. C7×D5C5×D39direct (N × H)
118. C5×C13D3×C7×D5semidirect
119. C5×C13C2×C5×D3×C7semidirect
125. C5×D5C7×D39direct (N × H)
129. C3×C13C2×C5×C7×D5semidirect
131. C5×C7D5×D39direct (N × H)
132. C5×C7C2×C5×D39semidirect
135. C3×D5C5×C7×D13semidirect
144. C52C2×C7×D39semidirect
145. C3×C7C5×D5×D13semidirect
149. C3×C5C7×D5×D13semidirect
150. C3×C5C2×C5×C7×D13semidirect
154. C13C5×D3×C7×D5semidirect
162. D5C5×C7×D39direct (N × H)
163. C7C5×D5×D39direct (N × H)
168. C5C7×D5×D39direct (N × H)
169. C5C2×C5×C7×D39semidirect
171. C3C5×C7×D5×D13semidirect

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×C7×D392
C5×C7×D1952
C5×C7×D5×D133
C2×C5×C7×D395
C7×D5×D395
C5×D5×D397
C5×D3×C7×D513