Finite Group Databasebeta

← D5×C13×D105 #41032013

Subgroups — D5×C13×D105 #41032013

Order 27300.

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C5×C13×D105C211yesmaximal, characteristic, complemented
3C13×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D5×C13×D35—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C2×C13×D105—51nomaximal
7D5×C13×D21—51nomaximal
8C13×C5⋊D35—31no—
9C5×C13×D35—31no—
10C5×C7×D5×C13D311yescharacteristic, complemented
11D5×C13×D15—71nomaximal, Hall
12C13×D105—51no—
13C13×D105—51no—
14C13×D105—102no—
15C13×D105D511yescharacteristic, direct product factor
16C5×C13×D21—51no—
17C3×C7×D5×C13D511yescharacteristic, complemented
18C2×C3×C5×C7×C13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20D5×D105C1311yesmaximal, characteristic, direct product factor, Hall
21C13×C3⋊(C5⋊D5)—71no—
22C5×C13×D15—71no—
23C3×C5×D5×C13D711yescharacteristic, complemented
24C2×C13×D35—151no—
25D5×C13×D7—151no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C2×D511yescharacteristic, complemented
29D52×C13—211noHall
30C2×C13×D21—251noHall
31C3⋊(C5⋊D35)C2×C1311yescharacteristic, complemented
32C5×D105C2×C1311yescharacteristic, complemented
33C3×C5×C7×D5C2×C1311yescharacteristic, complemented
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—51no—
36C13×D35—31no—
37C13×D35—151no—
38C13×D35—151no—
39C13×D35—302no—
40C7×D5×C13D1511yescharacteristic, complemented
41C5×C13×D7—151no—
42C2×C13×D15—351no—
43D3×D5×C13—351no—
44D5×D35—31noHall
45C13×C5⋊D5—211no—
46C5×D5×C13—211no—
47C5×D5×C13D2111yescharacteristic, complemented
48C2×C3×C7×C13—51no—
49C13×D21—51no—
50C13×D21—251no—
51C3×C52×C7C22×C1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55C2×D105—51no—
56D5×D21—51no—
57C2×C3×C5×C13—51no—
58C13×D15—71no—
59C13×D15—351no—
60C13×D15—351no—
61C13×D15—702no—
62C5×D3×C13—351no—
63C3×D5×C13D3511yescharacteristic, complemented
64C2×C13×D7—751noHall
65C5⋊D35—31no—
66C5×D35—31no—
67C5×C7×D5D3×C1311yescharacteristic, complemented
68C52×C13C2×D2111yescharacteristic, complemented, Hall
69D5×D15—71noHall
70C3×C7×C13D5211yescharacteristic, complemented, Hall
71C2×D5×C13—1051no—
72C2×D5×C13—1051no—
73C2×C3×C5×C7—51no—
74D105—51no—
75D105—51no—
76D105—102no—
77D105D5×C1311yescharacteristic, direct product factor
78C5×D21—51no—
79C3×C7×D5D5×C1311yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13D5×D711yescharacteristic, complemented
82C3×C5×C13C2×D3511yescharacteristic, complemented
83C2×C7×C13—51no—
84C13×D7—151no—
85C13×D7—751no—
86C52×C7C2×D3×C1311yescharacteristic, complemented, Hall
87C2×D3×C13—1751noHall
88C3⋊(C5⋊D5)—71no—
89C5×D15—71no—
90C3×C5×D5C13×D711yescharacteristic, complemented
91C2×D35—151no—
92D5×D7—151no—
93C2×C5×C13—51no—
94C2×C5×C13—1051no—
95D5×C13—211no—
96D5×C13—1051no—
97D5×C13—1051no—
98D5×C13—2102no—
99D5×C13D10511yescharacteristic, direct product factor
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1311yescharacteristic, complemented
102C3×C5×C7C2×D5×C1311yescharacteristic, complemented
103D52—211noHall
104C7×C13D5×D1511yescharacteristic, complemented, Hall
105C2×D21—251noHall
106C2×C3×C13—51no—
107D3×C13—351no—
108D3×C13—1751no—
109C3×C52C2×C13×D711yescharacteristic, complemented, Hall
110C2×C5×C7—51no—
111D35—31no—
112D35—151no—
113D35—151no—
114D35—302no—
115C5×D7—151no—
116C7×D5C13×D1511yescharacteristic, complemented
117C5×C13—22no—
118C5×C13D5×D2111yescharacteristic, complemented
119C5×C13C2×D10511yescharacteristic, complemented
120C2×D15—351no—
121D3×D5—351no—
122C22×C13—5251noHall
123C5⋊D5—211no—
124C5×D5—211no—
125C5×D5C13×D2111yescharacteristic, complemented
126C2×C3×C7—51no—
127D21—51no—
128D21—251no—
129C3×C13D5×D3511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D3×D5×C1311yescharacteristic, complemented
132C5×C7C2×C13×D1511yescharacteristic, complemented
133C2×C3×C5—51no—
134D15—71no—
135D15—351no—
136D15—351no—
137D15—702no—
138C3×D5C13×D3511yescharacteristic, complemented
139C5×D3—351no—
140C2×D7—751noHall
141C2×C13—51no—
142C2×C13—5251no—
143C2×C13—1051no—
144C52C2×C13×D2111yescharacteristic, complemented, Sylow
145C3×C7D52×C1311yescharacteristic, complemented, Hall
146C2×D5—1051no—
147C2×D5—1051no—
148C3×C5—22no—
149C3×C5D5×C13×D711yescharacteristic, complemented
150C3×C5C2×C13×D3511yescharacteristic, complemented
151C2×C7—51no—
152D7—151no—
153D7—751no—
154C13D5×D10511yescharacteristic, direct product factor, Sylow
155C2×D3—1751noHall
156C2×C5—51no—
157C2×C5—1051no—
158D5—211no—
159D5—1051no—
160D5—1051no—
161D5—2102no—
162D5C13×D10511yescharacteristic, direct product factor
163C7D5×C13×D1511yescharacteristic, complemented, Sylow
164C2×C3—51no—
165D3—351no—
166D3—1751no—
167C5—22no—
168C5D5×C13×D2111yescharacteristic, complemented
169C5C2×C13×D10511yescharacteristic, complemented
170C22—5251noSylow
171C3D5×C13×D3511yescharacteristic, complemented, Sylow
172C2—51no—
173C2—5251no—
174C2—1051no—
subgroupG/H
center, hypercenterC13D5×D105
commutator, cosocle, hypocenterC3×C52×C7C22×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C13C2semidirect
2. C5×C13×D105C2semidirect
3. C13×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C13C22semidirect
10. C5×C7×D5×C13D3semidirect
15. C13×D105D5direct (N × H)
17. C3×C7×D5×C13D5semidirect
19. C52×C7×C13C2×D3semidirect
20. D5×D105C13direct (N × H)
23. C3×C5×D5×C13D7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C2×D5semidirect
31. C3⋊(C5⋊D35)C2×C13semidirect
32. C5×D105C2×C13semidirect
33. C3×C5×C7×D5C2×C13semidirect
34. C3×C52×C13C2×D7semidirect
40. C7×D5×C13D15semidirect
47. C5×D5×C13D21semidirect
51. C3×C52×C7C22×C13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×D15semidirect
63. C3×D5×C13D35semidirect
67. C5×C7×D5D3×C13semidirect
68. C52×C13C2×D21semidirect
70. C3×C7×C13D52semidirect
77. D105D5×C13direct (N × H)
79. C3×C7×D5D5×C13semidirect
81. C3×C5×C13D5×D7semidirect
82. C3×C5×C13C2×D35semidirect
86. C52×C7C2×D3×C13semidirect
90. C3×C5×D5C13×D7semidirect
99. D5×C13D105direct (N × H)
101. C3×C5×C7C2×D5×C13semidirect
102. C3×C5×C7C2×D5×C13semidirect
104. C7×C13D5×D15semidirect
109. C3×C52C2×C13×D7semidirect
116. C7×D5C13×D15semidirect
118. C5×C13D5×D21semidirect
119. C5×C13C2×D105semidirect
125. C5×D5C13×D21semidirect
129. C3×C13D5×D35semidirect
131. C5×C7D3×D5×C13semidirect
132. C5×C7C2×C13×D15semidirect
138. C3×D5C13×D35semidirect
144. C52C2×C13×D21semidirect
145. C3×C7D52×C13semidirect
149. C3×C5D5×C13×D7semidirect
150. C3×C5C2×C13×D35semidirect
154. C13D5×D105direct (N × H)
162. D5C13×D105direct (N × H)
163. C7D5×C13×D15semidirect
168. C5D5×C13×D21semidirect
169. C5C2×C13×D105semidirect
171. C3D5×C13×D35semidirect

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
C5×C13×D1052
C13×C3⋊(C5⋊D35)2
D5×C13×D353
C2×C13×D1055
D5×C13×D215
D5×C13×D157
D5×D10513