Finite Group Databasebeta

← C5×D15⋊D93 #42124931

Subgroups — C5×D15⋊D93 #42124931

Order 27900.

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

normal subgroups only

This group has 224 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×C5×D15×C31C211yesmaximal, characteristic, complemented
2C3×C5×D465C211yesmaximal, characteristic, complemented
3C52×C3⋊D93C211yesmaximal, characteristic, complemented
4C5×D15⋊D31—31nomaximal
5C5×D5×D93—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D15⋊D93C511yesmaximal, characteristic, direct product factor
8C5×D3×D93—51nomaximal
9C5×D465D311yescharacteristic, complemented
10C5×D15×C31D311yescharacteristic, complemented
11C52×D93—31no—
12C52×D93—31no—
13C52×D93—61no—
14C3×C5×D155—31no—
15C3×C5×D5×C31—31no—
16C5×D5×D31—91noHall
17C5×C3⋊D93—22no—
18C5×C3⋊D93D511yescharacteristic, complemented
19C5×C3⋊D93C2×C511yescharacteristic, complemented
20C3×D465C2×C511yescharacteristic, complemented
21C3×D15×C31C2×C511yescharacteristic, complemented
22C3×C5×D93—51no—
23C3×C5×D3×C31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C2×D311yescharacteristic, complemented
27C2×C5×D93—151no—
28D15⋊D31—31no—
29D5×D93—31no—
30C5×D3×D31—151no—
31C5×D155—31no—
32C5×D5×C31—31no—
33C52×D31—91no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C22×C511yescharacteristic, complemented
37D3×D93—51noHall
38C2×C3×C5×C31—151no—
39D465C5×D311yescharacteristic, complemented
40D15×C31C5×D311yescharacteristic, complemented
41C5×D93—31no—
42C5×D93—31no—
43C5×D93—31no—
44C5×D93—31no—
45C5×D93—51no—
46C5×D93—62no—
47C5×D93—62no—
48C5×D93—61no—
49C5×D93—61no—
50C5×D93—64no—
51C5×D3×C31—51no—
52C3×D155—31no—
53C3×D5×C31—31no—
54C3×C5×D31—151no—
55C5×(C3⋊D3)⋊D5—311nomaximal, Hall
56C52×C31D3211yescharacteristic, complemented, Hall
57C2×C5×D31—451no—
58D5×D31—91no—
59C3⋊D93C5×D511yescharacteristic, complemented
60C3×D93—51no—
61C3×D3×C31—51no—
62C3×C5×C31—24no—
63C3×C5×C31—21no—
64C3×C5×C31—21no—
65C3×C5×C31—22no—
66C3×C5×C31—22no—
67C3×C5×C31D3×D511yescharacteristic, complemented
68C3×C5×C31D3×D511yescharacteristic, complemented
69C3×C5×C31C2×C5×D311yescharacteristic, complemented
70C3×C5×C31C2×C5×D311yescharacteristic, complemented
71C52×C3⋊D3—311no—
72C3×C5×D15—311no—
73C3×C5×D15D3111yescharacteristic, complemented
74C2×D93—151no—
75D3×D31—151no—
76C2×C5×C31—151no—
77D155—31no—
78C5×D31—91no—
79C5×D31—91no—
80C5×D31—151no—
81C5×D31—182no—
82D5×C31—31no—
83C5×D3×D5—931no—
84C5×D3×D5—931no—
85C32×C31C2×C5×D511yescharacteristic, complemented, Hall
86C32×C52C2×D3111yescharacteristic, complemented, Hall
87C2×C3×C31—151no—
88D93—31no—
89D93—31no—
90D93—51no—
91D93—61no—
92C3×D31—151no—
93D3×C31—51no—
94(C3⋊D3)⋊D5—311no—
95C5×D32—1551no—
96C5×C31—22no—
97C5×C31C5×D3211yescharacteristic, complemented
98C5×C31(C3⋊D3)⋊D511yescharacteristic, complemented
99C5×D15—311no—
100C5×D15D9311yescharacteristic, complemented
101C52×D3—931no—
102C52×D3—931no—
103C52×D3—1861no—
104C3×C5×D5—31no—
105C3×C5×D5—931no—
106C2×D31—451noHall
107C2×C5×D5—2791noHall
108C3×C31—21no—
109C3×C31C5×D3×D511yescharacteristic, complemented
110C3×C31C5×D3×D511yescharacteristic, complemented
111C5×C3⋊D3—311no—
112C5×C3⋊D3—311no—
113C5×C3⋊D3—622no—
114C3×D15—311no—
115C3×D15C5×D3111yescharacteristic, complemented
116C3×C5×D3—51no—
117C3×C5×D3—1551no—
118C3×C52—21no—
119C3×C52D3×D3111yescharacteristic, complemented
120C3×C52C2×D9311yescharacteristic, complemented
121C2×C31—151no—
122D31—91no—
123D31—151no—
124C2×C5×D3—4651no—
125C2×C5×D3—4651no—
126D3×D5—931no—
127D3×D5—931no—
128C2×C52—2791no—
129C5×D5—31no—
130C5×D5—931no—
131C32×C5—22no—
132C32×C5D5×D3111yescharacteristic, complemented
133C32×C5C2×C5×D3111yescharacteristic, complemented
134D32—1551noHall
135C31C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
136C2×C3×C5—151no—
137C2×C3×C5—4651no—
138D15—311no—
139D15C5×D9311yescharacteristic, complemented
140C3×D5—31no—
141C3×D5—931no—
142C5×D3—51no—
143C5×D3—931no—
144C5×D3—931no—
145C5×D3—931no—
146C5×D3—931no—
147C5×D3—1551no—
148C5×D3—1862no—
149C5×D3—1862no—
150C5×D3—1861no—
151C5×D3—1861no—
152C5×D3—1864no—
153C52D3×D9311yescharacteristic, complemented, Sylow
154C22×C5—13951no—
155C2×D5—2791no—
156C3⋊D3—311no—
157C3×D3—51no—
158C3×D3—1551no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5C5×D3×D3111yescharacteristic, complemented
165C3×C5D5×D9311yescharacteristic, complemented
166C3×C5D15⋊D3111yescharacteristic, complemented
167C3×C5C2×C5×D9311yescharacteristic, complemented
168C2×D3—4651no—
169C2×D3—4651no—
170C2×C5—151no—
171C2×C5—2791no—
172C2×C5—2791no—
173C2×C5—5582no—
174C2×C5—4651no—
175D5—31no—
176D5—931no—
177C32C5×D5×D3111yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—4651no—
180D3—51no—
181D3—931no—
182D3—931no—
183D3—1551no—
184D3—1861no—
185C5—22no—
186C5C5×D3×D9311yescharacteristic, complemented
187C5D15⋊D9311yescharacteristic, direct product factor
188C22—13951noSylow
189C3—21no—
190C3C5×D5×D9311yescharacteristic, complemented
191C3C5×D15⋊D3111yescharacteristic, complemented
192C2—151no—
193C2—2791no—
194C2—4651no—
subgroupG/H
center, hypercenterC5D15⋊D93
commutator, cosocle, hypocenterC32×C5×C31C22×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C31C2semidirect
2. C3×C5×D465C2semidirect
3. C52×C3⋊D93C2semidirect
6. C32×C52×C31C22semidirect
7. D15⋊D93C5direct (N × H)
9. C5×D465D3semidirect
10. C5×D15×C31D3semidirect
18. C5×C3⋊D93D5semidirect
19. C5×C3⋊D93C2×C5semidirect
20. C3×D465C2×C5semidirect
21. C3×D15×C31C2×C5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C2×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C22×C5semidirect
39. D465C5×D3semidirect
40. D15×C31C5×D3semidirect
56. C52×C31D32semidirect
59. C3⋊D93C5×D5semidirect
67. C3×C5×C31D3×D5semidirect
68. C3×C5×C31D3×D5semidirect
69. C3×C5×C31C2×C5×D3semidirect
70. C3×C5×C31C2×C5×D3semidirect
73. C3×C5×D15D31semidirect
85. C32×C31C2×C5×D5semidirect
86. C32×C52C2×D31semidirect
97. C5×C31C5×D32semidirect
98. C5×C31(C3⋊D3)⋊D5semidirect
100. C5×D15D93semidirect
109. C3×C31C5×D3×D5semidirect
110. C3×C31C5×D3×D5semidirect
115. C3×D15C5×D31semidirect
119. C3×C52D3×D31semidirect
120. C3×C52C2×D93semidirect
132. C32×C5D5×D31semidirect
133. C32×C5C2×C5×D31semidirect
135. C31C5×(C3⋊D3)⋊D5semidirect
139. D15C5×D93semidirect
153. C52D3×D93semidirect
164. C3×C5C5×D3×D31semidirect
165. C3×C5D5×D93semidirect
166. C3×C5D15⋊D31semidirect
167. C3×C5C2×C5×D93semidirect
177. C32C5×D5×D31semidirect
186. C5C5×D3×D93semidirect
187. C5D15⋊D93direct (N × H)
190. C3C5×D5×D93semidirect
191. C3C5×D15⋊D31semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C312
C3×C5×D4652
C52×C3⋊D932
C5×D15⋊D313
C5×D5×D933
D15⋊D935
C5×D3×D935
C5×(C3⋊D3)⋊D531