Finite Group Databasebeta

← C3×C5×D13×D35 #41031908

Subgroups — C3×C5×D13×D35 #41031908

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×C7×D13C211yesmaximal, characteristic, complemented
2C3×C5×C13×D35C211yesmaximal, characteristic, complemented
3C3×C5×D455C211yesmaximal, characteristic, complemented
4C5×D13×D35C311yesmaximal, characteristic, direct product factor, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C3×D13×D35C511yesmaximal, characteristic, direct product factor
7C3×C5×D7×D13—51nomaximal
8C5×D455C2×C311yescharacteristic, complemented
9C5×C13×D35C2×C311yescharacteristic, complemented
10C52×C7×D13C2×C311yescharacteristic, complemented
11C3×C5×D5×D13—71nomaximal, Hall
12C3×D455C2×C511yescharacteristic, complemented
13C3×C13×D35C2×C511yescharacteristic, complemented
14C3×C5×D91—51no—
15C3×C5×C13×D7—51no—
16C3×C5×C7×D13—22no—
17C3×C5×C7×D13D511yescharacteristic, complemented
18C3×C5×C7×D13C2×C511yescharacteristic, complemented
19C52×C7×C13C22×C311yescharacteristic, complemented, Hall
20C2×C3×C5×D35—131nomaximal, Hall
21C3×C5×D65—71no—
22C3×C5×D5×C13—71no—
23C3×C52×D13D711yescharacteristic, complemented
24D13×D35C3×C511yescharacteristic, direct product factor
25C5×D7×D13—51no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C22×C511yescharacteristic, complemented
29C5×D5×D13—71noHall
30C3×D7×D13—51noHall
31C2×C3×C52×C7—131no—
32C3×C5×D35—131no—
33C3×C5×D35D1311yescharacteristic, direct product factor
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35D455C2×C3×C511yescharacteristic, complemented
36C13×D35C2×C3×C511yescharacteristic, complemented
37C5×D91—51no—
38C5×C13×D7—51no—
39C5×C7×D13—22no—
40C5×C7×D13C3×D511yescharacteristic, complemented
41C5×C7×D13C2×C3×C511yescharacteristic, complemented
42C2×C3×C5×D13—351no—
43C3×D5×D13—71no—
44C2×C5×D35—131noHall
45C5×D65—71no—
46C5×D5×C13—71no—
47C52×D13C3×D711yescharacteristic, complemented
48C3×D91—51no—
49C3×C13×D7—51no—
50C3×C7×D13C5×D511yescharacteristic, complemented
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13C2×C3×D511yescharacteristic, complemented
54C5×C7×C13C22×C3×C511yescharacteristic, complemented
55C2×C3×D35—131no—
56C2×C3×C5×D7—651no—
57C2×C3×C5×C13—351no—
58C3×D65—71no—
59C3×D5×C13—71no—
60C3×C5×D13—22no—
61C3×C5×D13—351no—
62C3×C5×D13C5×D711yescharacteristic, complemented
63C3×C5×D13D3511yescharacteristic, direct product factor
64D7×D13—51noHall
65C2×C52×C7—131no—
66C5×D35—131no—
67C5×D35C3×D1311yescharacteristic, direct product factor
68C52×C13C2×C3×D711yescharacteristic, complemented, Hall
69C2×C3×C5×D5—911noHall
70C3×C7×C13C2×C5×D511yescharacteristic, complemented, Hall
71C2×C5×D13—351no—
72D5×D13—71no—
73C2×C3×C5×C7—131no—
74C2×C3×C5×C7—131no—
75C2×C3×C5×C7—262no—
76C3×D35—131no—
77C3×D35C5×D1311yescharacteristic, direct product factor
78C3×C5×D7—51no—
79C3×C5×D7—651no—
80C3×C5×C13—22no—
81C3×C5×C13C2×C5×D711yescharacteristic, complemented
82C3×C5×C13C2×D3511yescharacteristic, complemented
83D91—51no—
84C7×D13C3×C5×D511yescharacteristic, complemented
85C13×D7—51no—
86C52×C7C2×C3×D1311yescharacteristic, complemented, Hall
87C2×C3×D13—351noHall
88C2×C3×C52—131no—
89C3×C5×D5—71no—
90C3×C5×D5—911no—
91C2×D35—131no—
92C2×C5×D7—651no—
93C2×C5×C13—351no—
94D65—71no—
95C5×D13—22no—
96C5×D13—351no—
97C5×D13C3×C5×D711yescharacteristic, complemented
98C5×D13C3×D3511yescharacteristic, direct product factor
99D5×C13—71no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7C2×C5×D1311yescharacteristic, complemented
103C2×C5×D5—911noHall
104C7×C13C2×C3×C5×D511yescharacteristic, complemented, Hall
105C2×C3×D7—651noHall
106C2×C3×C13—351no—
107C3×D13—351no—
108C3×D13C5×D3511yescharacteristic, direct product factor
109C3×C52D7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—131no—
111C2×C5×C7—131no—
112C2×C5×C7—262no—
113D35—131no—
114D35C3×C5×D1311yescharacteristic, direct product factor
115C5×D7—51no—
116C5×D7—651no—
117C5×C13—22no—
118C5×C13C2×C3×C5×D711yescharacteristic, complemented
119C5×C13C2×C3×D3511yescharacteristic, complemented
120C22×C3×C5—4551no—
121C2×C3×D5—911no—
122C2×D13—351noHall
123C2×C52—131no—
124C5×D5—71no—
125C5×D5—911no—
126C2×C3×C7—131no—
127C3×D7—51no—
128C3×D7—651no—
129C3×C13C2×C5×D3511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7C3×D5×D1311yescharacteristic, complemented
132C5×C7C2×C3×C5×D1311yescharacteristic, complemented
133C2×C3×C5—131no—
134C2×C3×C5—131no—
135C2×C3×C5—262no—
136C2×C3×C5—351no—
137C2×C3×C5—4551no—
138C3×D5—71no—
139C3×D5—911no—
140C2×D7—651noHall
141C2×C13—351no—
142D13—351no—
143D13C3×C5×D3511yescharacteristic, direct product factor
144C52C3×D7×D1311yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1311yescharacteristic, complemented, Hall
146C22×C5—4551no—
147C2×D5—911no—
148C3×C5—22no—
149C3×C5C5×D7×D1311yescharacteristic, complemented
150C3×C5D13×D3511yescharacteristic, direct product factor
151C2×C7—131no—
152D7—51no—
153D7—651no—
154C13C2×C3×C5×D3511yescharacteristic, complemented, Sylow
155C22×C3—4551noHall
156C2×C5—131no—
157C2×C5—131no—
158C2×C5—262no—
159C2×C5—351no—
160C2×C5—4551no—
161D5—71no—
162D5—911no—
163C7C3×C5×D5×D1311yescharacteristic, complemented, Sylow
164C2×C3—131no—
165C2×C3—351no—
166C2×C3—4551no—
167C5—22no—
168C5C3×C5×D7×D1311yescharacteristic, complemented
169C5C3×D13×D3511yescharacteristic, direct product factor
170C22—4551noSylow
171C3C5×D13×D3511yescharacteristic, direct product factor, Sylow
172C2—131no—
173C2—351no—
174C2—4551no—
subgroupG/H
center, hypercenterC3×C5D13×D35
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×C7×D13C2semidirect
2. C3×C5×C13×D35C2semidirect
3. C3×C5×D455C2semidirect
4. C5×D13×D35C3direct (N × H)
5. C3×C52×C7×C13C22semidirect
6. C3×D13×D35C5direct (N × H)
8. C5×D455C2×C3semidirect
9. C5×C13×D35C2×C3semidirect
10. C52×C7×D13C2×C3semidirect
12. C3×D455C2×C5semidirect
13. C3×C13×D35C2×C5semidirect
17. C3×C5×C7×D13D5semidirect
18. C3×C5×C7×D13C2×C5semidirect
19. C52×C7×C13C22×C3semidirect
23. C3×C52×D13D7semidirect
24. D13×D35C3×C5direct (N × H)
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C22×C5semidirect
33. C3×C5×D35D13direct (N × H)
34. C3×C52×C13C2×D7semidirect
35. D455C2×C3×C5semidirect
36. C13×D35C2×C3×C5semidirect
40. C5×C7×D13C3×D5semidirect
41. C5×C7×D13C2×C3×C5semidirect
47. C52×D13C3×D7semidirect
50. C3×C7×D13C5×D5semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13C2×C3×D5semidirect
54. C5×C7×C13C22×C3×C5semidirect
62. C3×C5×D13C5×D7semidirect
63. C3×C5×D13D35direct (N × H)
67. C5×D35C3×D13direct (N × H)
68. C52×C13C2×C3×D7semidirect
70. C3×C7×C13C2×C5×D5semidirect
77. C3×D35C5×D13direct (N × H)
81. C3×C5×C13C2×C5×D7semidirect
82. C3×C5×C13C2×D35semidirect
84. C7×D13C3×C5×D5semidirect
86. C52×C7C2×C3×D13semidirect
97. C5×D13C3×C5×D7semidirect
98. C5×D13C3×D35direct (N × H)
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×C5×D13semidirect
104. C7×C13C2×C3×C5×D5semidirect
108. C3×D13C5×D35direct (N × H)
109. C3×C52D7×D13semidirect
114. D35C3×C5×D13direct (N × H)
118. C5×C13C2×C3×C5×D7semidirect
119. C5×C13C2×C3×D35semidirect
129. C3×C13C2×C5×D35semidirect
131. C5×C7C3×D5×D13semidirect
132. C5×C7C2×C3×C5×D13semidirect
143. D13C3×C5×D35direct (N × H)
144. C52C3×D7×D13semidirect
145. C3×C7C5×D5×D13semidirect
149. C3×C5C5×D7×D13semidirect
150. C3×C5D13×D35direct (N × H)
154. C13C2×C3×C5×D35semidirect
163. C7C3×C5×D5×D13semidirect
168. C5C3×C5×D7×D13semidirect
169. C5C3×D13×D35direct (N × H)
171. C3C5×D13×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C7×D132
C3×C5×C13×D352
C3×C5×D4552
C5×D13×D353
C3×D13×D355
C3×C5×D7×D135
C3×C5×D5×D137
C2×C3×C5×D3513