Finite Group Databasebeta

← D5×D1365 #41032014

Subgroups — D5×D1365 #41032014

Order 27300.

192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 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×D1365C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊D455)C211yesmaximal, characteristic, complemented
4D5×D455—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C2×D1365—51nomaximal
7D5×D273—51nomaximal
8C5⋊D455—31no—
9C5×D455—31no—
10C5×C7×D5×C13D311yescharacteristic, complemented
11D5×D195—71nomaximal, Hall
12D1365—51no—
13D1365—51no—
14D1365—102no—
15D1365D511yescharacteristic, direct product factor
16C5×D273—51no—
17C3×C7×D5×C13D511yescharacteristic, complemented
18C2×C3×C5×C7×C13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20D5×D105—131nomaximal, Hall
21C3⋊(C5⋊D65)—71no—
22C5×D195—71no—
23C3×C5×D5×C13D711yescharacteristic, complemented
24C2×D455—151no—
25D5×D91—151no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C2×D511yescharacteristic, complemented
29D5×D65—211noHall
30C2×D273—251noHall
31C3⋊(C5⋊D35)—131no—
32C5×D105—131no—
33C3×C5×C7×D5D1311yescharacteristic, complemented
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—51no—
36D455—31no—
37D455—151no—
38D455—151no—
39D455—302no—
40C7×D5×C13D1511yescharacteristic, complemented
41C5×D91—151no—
42C2×D195—351no—
43D5×D39—351no—
44D5×D35—391noHall
45C5⋊D65—211no—
46C5×D65—211no—
47C5×D5×C13D2111yescharacteristic, complemented
48C2×C3×C7×C13—51no—
49D273—51no—
50D273—251no—
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55C2×D105—651no—
56D5×D21—651no—
57C2×C3×C5×C13—51no—
58D195—71no—
59D195—351no—
60D195—351no—
61D195—702no—
62C5×D39—351no—
63C3×D5×C13D3511yescharacteristic, complemented
64C2×D91—751noHall
65C5⋊D35—391no—
66C5×D35—391no—
67C5×C7×D5D3911yescharacteristic, complemented
68C52×C13C2×D2111yescharacteristic, complemented, Hall
69D5×D15—911noHall
70C3×C7×C13D5211yescharacteristic, complemented, Hall
71C2×D65—1051no—
72D5×D13—1051no—
73C2×C3×C5×C7—51no—
74D105—131no—
75D105—651no—
76D105—651no—
77D105—1302no—
78C5×D21—651no—
79C3×C7×D5D6511yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13D5×D711yescharacteristic, complemented
82C3×C5×C13C2×D3511yescharacteristic, complemented
83C2×C7×C13—51no—
84D91—151no—
85D91—751no—
86C52×C7C2×D3911yescharacteristic, complemented, Hall
87C2×D39—1751noHall
88C3⋊(C5⋊D5)—911no—
89C5×D15—911no—
90C3×C5×D5D9111yescharacteristic, complemented
91C2×D35—1951no—
92D5×D7—1951no—
93C2×C5×C13—51no—
94D65—211no—
95D65—1051no—
96D65—1051no—
97D65—2102no—
98C5×D13—1051no—
99D5×C13D10511yescharacteristic, complemented
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7C2×D6511yescharacteristic, complemented
103D52—2731noHall
104C7×C13D5×D1511yescharacteristic, complemented, Hall
105C2×D21—3251noHall
106C2×C3×C13—51no—
107D39—351no—
108D39—1751no—
109C3×C52C2×D9111yescharacteristic, complemented, Hall
110C2×C5×C7—51no—
111D35—391no—
112D35—3902no—
113D35—1951no—
114D35—1951no—
115C5×D7—1951no—
116C7×D5D19511yescharacteristic, complemented
117C5×C13—22no—
118C5×C13D5×D2111yescharacteristic, complemented
119C5×C13C2×D10511yescharacteristic, complemented
120C2×D15—4551no—
121D3×D5—4551no—
122C2×D13—5251noHall
123C5⋊D5—2731no—
124C5×D5—2731no—
125C5×D5D27311yescharacteristic, complemented
126C2×C3×C7—51no—
127D21—651no—
128D21—3251no—
129C3×C13D5×D3511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D5×D3911yescharacteristic, complemented
132C5×C7C2×D19511yescharacteristic, complemented
133C2×C3×C5—51no—
134D15—911no—
135D15—9102no—
136D15—4551no—
137D15—4551no—
138C3×D5D45511yescharacteristic, complemented
139C5×D3—4551no—
140C2×D7—9751noHall
141C2×C13—51no—
142D13—5251no—
143D13—1051no—
144C52C2×D27311yescharacteristic, complemented, Sylow
145C3×C7D5×D6511yescharacteristic, complemented, Hall
146C2×D5—13651no—
147C2×D5—13651no—
148C3×C5—22no—
149C3×C5D5×D9111yescharacteristic, complemented
150C3×C5C2×D45511yescharacteristic, complemented
151C2×C7—51no—
152D7—1951no—
153D7—9751no—
154C13D5×D10511yescharacteristic, complemented, Sylow
155C2×D3—22751noHall
156C2×C5—51no—
157C2×C5—13651no—
158D5—2731no—
159D5—13651no—
160D5—13651no—
161D5—27302no—
162D5D136511yescharacteristic, direct product factor
163C7D5×D19511yescharacteristic, complemented, Sylow
164C2×C3—51no—
165D3—4551no—
166D3—22751no—
167C5—22no—
168C5D5×D27311yescharacteristic, complemented
169C5C2×D136511yescharacteristic, complemented
170C22—68251noSylow
171C3D5×D45511yescharacteristic, complemented, Sylow
172C2—51no—
173C2—13651no—
174C2—68251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C13C22
LCSG ▷ C3×C52×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C13C2semidirect
2. C5×D1365C2semidirect
3. C3⋊(C5⋊D455)C2semidirect
5. C3×C52×C7×C13C22semidirect
10. C5×C7×D5×C13D3semidirect
15. D1365D5direct (N × H)
17. C3×C7×D5×C13D5semidirect
19. C52×C7×C13C2×D3semidirect
23. C3×C5×D5×C13D7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C2×D5semidirect
33. C3×C5×C7×D5D13semidirect
34. C3×C52×C13C2×D7semidirect
40. C7×D5×C13D15semidirect
47. C5×D5×C13D21semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×D15semidirect
63. C3×D5×C13D35semidirect
67. C5×C7×D5D39semidirect
68. C52×C13C2×D21semidirect
70. C3×C7×C13D52semidirect
79. C3×C7×D5D65semidirect
81. C3×C5×C13D5×D7semidirect
82. C3×C5×C13C2×D35semidirect
86. C52×C7C2×D39semidirect
90. C3×C5×D5D91semidirect
99. D5×C13D105semidirect
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×D65semidirect
104. C7×C13D5×D15semidirect
109. C3×C52C2×D91semidirect
116. C7×D5D195semidirect
118. C5×C13D5×D21semidirect
119. C5×C13C2×D105semidirect
125. C5×D5D273semidirect
129. C3×C13D5×D35semidirect
131. C5×C7D5×D39semidirect
132. C5×C7C2×D195semidirect
138. C3×D5D455semidirect
144. C52C2×D273semidirect
145. C3×C7D5×D65semidirect
149. C3×C5D5×D91semidirect
150. C3×C5C2×D455semidirect
154. C13D5×D105semidirect
162. D5D1365direct (N × H)
163. C7D5×D195semidirect
168. C5D5×D273semidirect
169. C5C2×D1365semidirect
171. C3D5×D455semidirect

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×D13652
C3⋊(C5⋊D455)2
D5×D4553
C2×D13655
D5×D2735
D5×D1957
D5×D10513