Finite Group Databasebeta

← C5×D91⋊D15 #41031976

Subgroups — C5×D91⋊D15 #41031976

Order 27300.

192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 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×D91C211yesmaximal, characteristic, complemented
2C5×C7×D195C211yesmaximal, characteristic, complemented
3C5×C13×D105C211yesmaximal, characteristic, complemented
4C5×D35⋊D13—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6D91⋊D15C511yesmaximal, characteristic, direct product factor
7C5×D21⋊D13—51nomaximal
8C5×C13×D35—31no—
9C5×C7×D65—31no—
10C52×D91D311yescharacteristic, complemented
11C5×D13×D15—71nomaximal, Hall
12C13×D105C2×C511yescharacteristic, complemented
13C7×D195C2×C511yescharacteristic, complemented
14C5×C13×D21—51no—
15C5×C7×D39—51no—
16C3×C5×D91—22no—
17C3×C5×D91D511yescharacteristic, complemented
18C3×C5×D91C2×C511yescharacteristic, complemented
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C5×D7×D15—131nomaximal, Hall
21C5×D195D711yescharacteristic, complemented
22C5×C13×D15—71no—
23C3×C52×D13—71no—
24D35⋊D13—31no—
25C5×D7×D13—151no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C22×C511yescharacteristic, complemented
29C5×D5×D13—211noHall
30D21⋊D13—51noHall
31C5×D105D1311yescharacteristic, complemented
32C5×C7×D15—131no—
33C3×C52×D7—131no—
34C3×C52×C13C2×D711yescharacteristic, complemented, Hall
35C13×D35—31no—
36C7×D65—31no—
37C5×D91—22no—
38C5×D91C5×D311yescharacteristic, complemented
39C5×D91D1511yescharacteristic, complemented
40C5×C13×D7—151no—
41C5×C7×D13—151no—
42D13×D15—71no—
43C5×D3×D13—351no—
44C5×D5×D7—391noHall
45C5×D65—31no—
46C5×D5×C13—211no—
47C52×D13—71no—
48C13×D21—51no—
49C7×D39—51no—
50C3×D91C5×D511yescharacteristic, complemented
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13C2×C5×D311yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55D7×D15—131no—
56C5×D3×D7—651no—
57D195C5×D711yescharacteristic, complemented
58C13×D15—71no—
59C5×D39—51no—
60C5×D3×C13—351no—
61C3×C5×D13—71no—
62C3×C5×D13—71no—
63C3×C5×D13—142no—
64D7×D13—151noHall
65C5×D35—31no—
66C5×C7×D5—391no—
67C52×D7—131no—
68C52×C13D3×D711yescharacteristic, complemented, Hall
69C2×C5×D15—911noHall
70C3×C7×C13C2×C5×D511yescharacteristic, complemented, Hall
71C2×C5×D13—1051no—
72D5×D13—211no—
73D105C5×D1311yescharacteristic, complemented
74C7×D15—131no—
75C5×D21—51no—
76C5×D3×C7—651no—
77C3×C5×D7—131no—
78C3×C5×D7—131no—
79C3×C5×D7—262no—
80C3×C5×C13—22no—
81C3×C5×C13D5×D711yescharacteristic, complemented
82C3×C5×C13C2×C5×D711yescharacteristic, complemented
83D91C5×D1511yescharacteristic, complemented
84C7×D13—151no—
85C13×D7—151no—
86C52×C7D3×D1311yescharacteristic, complemented, Hall
87D3×D13—351noHall
88C2×C3×C52—911no—
89C5×D15—71no—
90C5×D15—131no—
91C2×C5×D7—1951no—
92D5×D7—391no—
93C2×C5×C13—1051no—
94D65—31no—
95C5×D13—71no—
96C5×D13—71no—
97C5×D13—142no—
98C5×D13—151no—
99D5×C13—211no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7C2×C5×D1311yescharacteristic, complemented
103C2×C5×D5—2731noHall
104C7×C13C2×C5×D1511yescharacteristic, complemented, Hall
105D3×D7—651noHall
106D39—51no—
107C3×D13—71no—
108D3×C13—351no—
109C3×C52D7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—1951no—
111D35—31no—
112C5×D7—131no—
113C5×D7—131no—
114C5×D7—151no—
115C5×D7—262no—
116C7×D5—391no—
117C5×C13—22no—
118C5×C13C5×D3×D711yescharacteristic, complemented
119C5×C13D7×D1511yescharacteristic, complemented
120C2×D15—911no—
121C2×C5×D3—4551no—
122C2×D13—1051noHall
123C2×C52—911no—
124C5×D5—211no—
125C5×D5—391no—
126D21—51no—
127C3×D7—131no—
128D3×C7—651no—
129C3×C13C5×D5×D711yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7C5×D3×D1311yescharacteristic, complemented
132C5×C7D13×D1511yescharacteristic, complemented
133C2×C3×C5—911no—
134C2×C3×C5—911no—
135C2×C3×C5—1822no—
136D15—71no—
137D15—131no—
138C5×D3—351no—
139C5×D3—651no—
140C2×D7—1951noHall
141C2×C13—1051no—
142D13—71no—
143D13—151no—
144C52D21⋊D1311yescharacteristic, complemented, Sylow
145C3×C7C5×D5×D1311yescharacteristic, complemented, Hall
146C22×C5—13651no—
147C2×D5—2731no—
148C3×C5—22no—
149C3×C5C5×D7×D1311yescharacteristic, complemented
150C3×C5D35⋊D1311yescharacteristic, complemented
151C2×C7—1951no—
152D7—131no—
153D7—151no—
154C13C5×D7×D1511yescharacteristic, complemented, Sylow
155C2×D3—4551noHall
156C2×C5—911no—
157C2×C5—911no—
158C2×C5—1051no—
159C2×C5—1822no—
160C2×C5—1951no—
161D5—211no—
162D5—391no—
163C7C5×D13×D1511yescharacteristic, complemented, Sylow
164C2×C3—911no—
165D3—351no—
166D3—651no—
167C5—22no—
168C5C5×D21⋊D1311yescharacteristic, complemented
169C5D91⋊D1511yescharacteristic, direct product factor
170C22—13651noSylow
171C3C5×D35⋊D1311yescharacteristic, complemented, Sylow
172C2—911no—
173C2—1051no—
174C2—1951no—
subgroupG/H
center, hypercenterC5D91⋊D15
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×D91C2semidirect
2. C5×C7×D195C2semidirect
3. C5×C13×D105C2semidirect
5. C3×C52×C7×C13C22semidirect
6. D91⋊D15C5direct (N × H)
10. C52×D91D3semidirect
12. C13×D105C2×C5semidirect
13. C7×D195C2×C5semidirect
17. C3×C5×D91D5semidirect
18. C3×C5×D91C2×C5semidirect
19. C52×C7×C13C2×D3semidirect
21. C5×D195D7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C22×C5semidirect
31. C5×D105D13semidirect
34. C3×C52×C13C2×D7semidirect
38. C5×D91C5×D3semidirect
39. C5×D91D15semidirect
50. C3×D91C5×D5semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13C2×C5×D3semidirect
54. C5×C7×C13C2×D15semidirect
57. D195C5×D7semidirect
68. C52×C13D3×D7semidirect
70. C3×C7×C13C2×C5×D5semidirect
73. D105C5×D13semidirect
81. C3×C5×C13D5×D7semidirect
82. C3×C5×C13C2×C5×D7semidirect
83. D91C5×D15semidirect
86. C52×C7D3×D13semidirect
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×C5×D13semidirect
104. C7×C13C2×C5×D15semidirect
109. C3×C52D7×D13semidirect
118. C5×C13C5×D3×D7semidirect
119. C5×C13D7×D15semidirect
129. C3×C13C5×D5×D7semidirect
131. C5×C7C5×D3×D13semidirect
132. C5×C7D13×D15semidirect
144. C52D21⋊D13semidirect
145. C3×C7C5×D5×D13semidirect
149. C3×C5C5×D7×D13semidirect
150. C3×C5D35⋊D13semidirect
154. C13C5×D7×D15semidirect
163. C7C5×D13×D15semidirect
168. C5C5×D21⋊D13semidirect
169. C5D91⋊D15direct (N × H)
171. C3C5×D35⋊D13semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D912
C5×C7×D1952
C5×C13×D1052
C5×D35⋊D133
D91⋊D155
C5×D21⋊D135
C5×D13×D157
C5×D7×D1513