Finite Group Databasebeta

← #41032020

Subgroups — #41032020

Order 27300.

192 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 43 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×D455C211yesmaximal, characteristic, complemented
2C5×C7×D195C211yesmaximal, characteristic, complemented
3C13×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D65⋊D35—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6D39⋊D35—51nomaximal
7D91⋊D15—51nomaximal
8C13×C5⋊D35—31no—
9C5×D455D311yescharacteristic, complemented
10C5×C7×D65—31no—
11D65⋊D15—71nomaximal, Hall
12C13×D105—51no—
13C13×D105—51no—
14C13×D105—102no—
15C7×D195D511yescharacteristic, complemented
16C5×C7×D39—51no—
17C3×D455D511yescharacteristic, complemented
18C3×C5×D91—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20D15×D35—131nomaximal, Hall
21C13×C3⋊(C5⋊D5)—71no—
22C5×D195D711yescharacteristic, complemented
23C3×C5×D65—71no—
24D35⋊D13—151no—
25D13×D35—151no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C2×D511yescharacteristic, complemented
29(C5⋊D5)⋊D13—211noHall
30D21⋊D13—251noHall
31C3⋊(C5⋊D35)D1311yescharacteristic, complemented
32C5×C7×D15—131no—
33C3×C5×D35—131no—
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35D455D1511yescharacteristic, complemented
36C13×D35—151no—
37C13×D35—151no—
38C13×D35—302no—
39C7×D65—31no—
40C5×D91—51no—
41C5×C7×D13—151no—
42D15⋊D13—351no—
43D13×D15—351no—
44D5×D35—391noHall
45C13×C5⋊D5—211no—
46C5×D65—31no—
47C5×D65—71no—
48C13×D21—251no—
49C7×D39—51no—
50C3×D91—51no—
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55D3×D35—651no—
56D7×D15—651no—
57D195D3511yescharacteristic, complemented
58C13×D15—351no—
59C13×D15—351no—
60C13×D15—702no—
61C5×D39—51no—
62C3×D65—71no—
63C3×C5×D13—351no—
64D7×D13—751noHall
65C5⋊D35—31no—
66C5×D35—131no—
67C5×C7×D5—391no—
68C52×C13D3×D711yescharacteristic, complemented, Hall
69D5×D15—911noHall
70C3×C7×C13D5211yescharacteristic, complemented, Hall
71D5×D13—1051no—
72D5×D13—1051no—
73D105—51no—
74D105—51no—
75D105—102no—
76C7×D15—131no—
77C5×D3×C7—651no—
78C3×D35—131no—
79C3×C5×D7—651no—
80C3×C5×C13—22no—
81C3×C5×C13D5×D711yescharacteristic, complemented
82C3×C5×C13C2×D3511yescharacteristic, complemented
83D91—51no—
84C7×D13—151no—
85C13×D7—751no—
86C52×C7D3×D1311yescharacteristic, complemented, Hall
87D3×D13—1751noHall
88C3⋊(C5⋊D5)—71no—
89C5×D15—131no—
90C3×C5×D5—911no—
91C2×D35—1951no—
92D5×D7—1951no—
93D65—31no—
94D65—71no—
95C5×D13—151no—
96C5×D13—351no—
97D5×C13—1051no—
98D5×C13—1051no—
99D5×C13—2102no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7D5×D1311yescharacteristic, complemented
103D52—2731noHall
104C7×C13D5×D1511yescharacteristic, complemented, Hall
105D3×D7—3251noHall
106D39—51no—
107C3×D13—351no—
108D3×C13—1751no—
109C3×C52D7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—1951no—
111D35—131no—
112D35—151no—
113D35—151no—
114D35—302no—
115C5×D7—651no—
116C7×D5—391no—
117C5×C13—22no—
118C5×C13D7×D1511yescharacteristic, complemented
119C5×C13D3×D3511yescharacteristic, complemented
120C2×D15—4551no—
121D3×D5—4551no—
122C2×D13—5251noHall
123C5⋊D5—211no—
124C5×D5—391no—
125C5×D5—911no—
126D21—251no—
127C3×D7—651no—
128D3×C7—651no—
129C3×C13D5×D3511yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D13×D1511yescharacteristic, complemented
132C5×C7D15⋊D1311yescharacteristic, complemented
133C2×C3×C5—4551no—
134D15—131no—
135D15—351no—
136D15—351no—
137D15—702no—
138C3×D5—911no—
139C5×D3—651no—
140C2×D7—9751noHall
141C2×C13—5251no—
142D13—151no—
143D13—351no—
144C52D21⋊D1311yescharacteristic, complemented, Sylow
145C3×C7(C5⋊D5)⋊D1311yescharacteristic, complemented, Hall
146C2×D5—13651no—
147C2×D5—13651no—
148C3×C5—22no—
149C3×C5D13×D3511yescharacteristic, complemented
150C3×C5D35⋊D1311yescharacteristic, complemented
151C2×C7—1951no—
152D7—651no—
153D7—751no—
154C13D15×D3511yescharacteristic, complemented, Sylow
155C2×D3—22751noHall
156C2×C5—1951no—
157C2×C5—4551no—
158D5—391no—
159D5—911no—
160D5—1051no—
161D5—1051no—
162D5—2102no—
163C7D65⋊D1511yescharacteristic, complemented, Sylow
164C2×C3—4551no—
165D3—651no—
166D3—1751no—
167C5—22no—
168C5D91⋊D1511yescharacteristic, complemented
169C5D39⋊D3511yescharacteristic, complemented
170C22—68251noSylow
171C3D65⋊D3511yescharacteristic, complemented, Sylow
172C2—5251no—
173C2—1951no—
174C2—4551no—
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×D455C2semidirect
2. C5×C7×D195C2semidirect
3. C13×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C13C22semidirect
9. C5×D455D3semidirect
15. C7×D195D5semidirect
17. C3×D455D5semidirect
19. C52×C7×C13C2×D3semidirect
22. C5×D195D7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C2×D5semidirect
31. C3⋊(C5⋊D35)D13semidirect
34. C3×C52×C13C2×D7semidirect
35. D455D15semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×D15semidirect
57. D195D35semidirect
68. C52×C13D3×D7semidirect
70. C3×C7×C13D52semidirect
81. C3×C5×C13D5×D7semidirect
82. C3×C5×C13C2×D35semidirect
86. C52×C7D3×D13semidirect
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7D5×D13semidirect
104. C7×C13D5×D15semidirect
109. C3×C52D7×D13semidirect
118. C5×C13D7×D15semidirect
119. C5×C13D3×D35semidirect
129. C3×C13D5×D35semidirect
131. C5×C7D13×D15semidirect
132. C5×C7D15⋊D13semidirect
144. C52D21⋊D13semidirect
145. C3×C7(C5⋊D5)⋊D13semidirect
149. C3×C5D13×D35semidirect
150. C3×C5D35⋊D13semidirect
154. C13D15×D35semidirect
163. C7D65⋊D15semidirect
168. C5D91⋊D15semidirect
169. C5D39⋊D35semidirect
171. C3D65⋊D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4552
C5×C7×D1952
C13×C3⋊(C5⋊D35)2
D65⋊D353
D39⋊D355
D91⋊D155
D65⋊D157
D15×D3513