Finite Group Databasebeta

← C5×D3×D285 #30685924

Subgroups — C5×D3×D285 #30685924

Order 17100.

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

normal subgroups only

This group has 212 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
1C5×C3⋊D285C211yesmaximal, characteristic, complemented
2C3×C5×D285C211yesmaximal, characteristic, complemented
3C3×C52×D3×C19C211yesmaximal, characteristic, complemented
4C2×C5×D285—31nomaximal
5C5×D3×D95—31nomaximal
6C32×C52×C19C2211yescharacteristic, complemented, Hall
7D3×D285C511yesmaximal, characteristic, direct product factor
8C5×D3×D57—51nomaximal
9C5×D285—31no—
10C5×D285—31no—
11C5×D285—61no—
12C5×D285D311yescharacteristic, direct product factor
13C52×D3×C19D311yescharacteristic, complemented
14C3×C5×D95—31no—
15C2×C3×C52×C19—31no—
16C2×C5×D95—91noHall
17C3⋊D285C2×C511yescharacteristic, complemented
18C5×C3⋊D57—51no—
19C3×D285C2×C511yescharacteristic, complemented
20C3×C5×D57—51no—
21C3×C5×D3×C19—22no—
22C3×C5×D3×C19D511yescharacteristic, complemented
23C3×C5×D3×C19C2×C511yescharacteristic, complemented
24C3×C52×C19—21no—
25C3×C52×C19C2×D311yescharacteristic, complemented
26C3×C52×C19C2×D311yescharacteristic, complemented
27C2×D285—31no—
28C2×C5×D57—151no—
29D3×D95—31no—
30C5×D3×D19—151no—
31C2×C52×C19—31no—
32C5×D95—31no—
33C5×D95—91no—
34C5×D3×D15—191nomaximal, Hall
35C32×C5×C19—22no—
36C32×C5×C19C2×D511yescharacteristic, complemented
37C32×C5×C19C22×C511yescharacteristic, complemented
38D3×D57—51noHall
39C2×C3×C5×C19—31no—
40C2×C3×C5×C19—31no—
41C2×C3×C5×C19—62no—
42D285—31no—
43D285—31no—
44D285—61no—
45D285C5×D311yescharacteristic, direct product factor
46C5×D57—51no—
47C5×D57—151no—
48C5×D57—151no—
49C5×D57—301no—
50C5×D3×C19—22no—
51C5×D3×C19C5×D311yescharacteristic, complemented
52C5×D3×C19D1511yescharacteristic, complemented
53C3×D95—31no—
54C3×C5×D19—151no—
55C52×C19D3211yescharacteristic, complemented, Hall
56C5×C3⋊D15—191no—
57C3×C5×D15—191no—
58C3×C52×D3D1911yescharacteristic, complemented
59C2×D95—91no—
60C2×C5×D19—451no—
61C3⋊D57—51no—
62C3×D57—51no—
63C3×D3×C19C5×D511yescharacteristic, complemented
64C2×C5×D15—571no—
65C5×D3×D5—571no—
66C3×C5×C19—22no—
67C3×C5×C19—22no—
68C3×C5×C19—21no—
69C3×C5×C19—21no—
70C3×C5×C19—42no—
71C3×C5×C19D3×D511yescharacteristic, complemented
72C3×C5×C19C2×C5×D311yescharacteristic, complemented
73C3×C5×C19C2×C5×D311yescharacteristic, complemented
74C3×C5×C19C2×D1511yescharacteristic, complemented
75C2×D57—151no—
76D3×D19—151no—
77C32×C52C2×D1911yescharacteristic, complemented, Hall
78C2×C5×C19—31no—
79C2×C5×C19—31no—
80C2×C5×C19—62no—
81D95—31no—
82D95—91no—
83C5×D19—151no—
84C5×D19—451no—
85D3×D15—191no—
86C5×D32—951no—
87C32×C19C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—31no—
89C5×D15—191no—
90C5×D15—571no—
91C5×D15—571no—
92C5×D15—1141no—
93C52×D3D5711yescharacteristic, complemented
94C3×C5×D5—571no—
95C2×C3×C19—31no—
96D57—51no—
97D57—151no—
98D57—151no—
99D57—301no—
100C3×D19—151no—
101D3×C19C5×D1511yescharacteristic, complemented
102C2×C5×D5—1711noHall
103C5×C19—22no—
104C5×C19C5×D3211yescharacteristic, complemented
105C5×C19D3×D1511yescharacteristic, complemented
106C3⋊D15—191no—
107C5×C3⋊D3—951no—
108C3×D15—191no—
109C3×C5×D3—22no—
110C3×C5×D3—951no—
111C3×C5×D3C5×D1911yescharacteristic, complemented
112C3×C5×D3D9511yescharacteristic, complemented
113C2×D19—451noHall
114C3×C52—21no—
115C3×C52D3×D1911yescharacteristic, complemented
116C3×C52C2×D5711yescharacteristic, complemented
117C2×D15—571no—
118C2×C5×D3—2851no—
119C2×C5×D3—2851no—
120D3×D5—571no—
121C3×C19—21no—
122C3×C19C5×D3×D511yescharacteristic, complemented
123C3×C19C2×C5×D1511yescharacteristic, complemented
124C2×C52—31no—
125C5×D5—571no—
126C5×D5—1711no—
127C32×C5—22no—
128C32×C5C2×C5×D1911yescharacteristic, complemented
129C32×C5C2×D9511yescharacteristic, complemented
130C2×C19—31no—
131D19—151no—
132D19—451no—
133D32—951noHall
134C2×C3×C5—31no—
135C2×C3×C5—31no—
136C2×C3×C5—62no—
137C2×C3×C5—2851no—
138D15—191no—
139D15—571no—
140D15—571no—
141D15—1141no—
142C3×D5—571no—
143C5×D3—22no—
144C5×D3—2851no—
145C5×D3—2851no—
146C5×D3—5701no—
147C5×D3—951no—
148C5×D3C5×D5711yescharacteristic, complemented
149C5×D3D28511yescharacteristic, direct product factor
150C52D3×D5711yescharacteristic, complemented, Sylow
151C22×C5—8551no—
152C2×D5—1711no—
153C19C5×D3×D1511yescharacteristic, complemented, Sylow
154C3⋊D3—951no—
155C3×D3—951no—
156C3×D3C5×D9511yescharacteristic, complemented
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D1911yescharacteristic, complemented
163C3×C5D3×D9511yescharacteristic, complemented
164C3×C5C2×C5×D5711yescharacteristic, complemented
165C3×C5C2×D28511yescharacteristic, complemented
166C2×D3—2851no—
167C2×D3—2851no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—2851no—
172C2×C5—8551no—
173D5—571no—
174D5—1711no—
175C32C2×C5×D9511yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—2851no—
178D3—2851no—
179D3—2851no—
180D3—5701no—
181D3—951no—
182D3C5×D28511yescharacteristic, direct product factor
183C5—22no—
184C5C5×D3×D5711yescharacteristic, complemented
185C5D3×D28511yescharacteristic, direct product factor
186C22—8551noSylow
187C3—21no—
188C3C5×D3×D9511yescharacteristic, complemented
189C3C2×C5×D28511yescharacteristic, complemented
190C2—31no—
191C2—2851no—
192C2—8551no—
subgroupG/H
center, hypercenterC5D3×D285
commutator, cosocle, hypocenterC32×C5×C19C22×C5
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C32×C5×C19
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D285C2semidirect
2. C3×C5×D285C2semidirect
3. C3×C52×D3×C19C2semidirect
6. C32×C52×C19C22semidirect
7. D3×D285C5direct (N × H)
12. C5×D285D3direct (N × H)
13. C52×D3×C19D3semidirect
17. C3⋊D285C2×C5semidirect
19. C3×D285C2×C5semidirect
22. C3×C5×D3×C19D5semidirect
23. C3×C5×D3×C19C2×C5semidirect
25. C3×C52×C19C2×D3semidirect
26. C3×C52×C19C2×D3semidirect
36. C32×C5×C19C2×D5semidirect
37. C32×C5×C19C22×C5semidirect
45. D285C5×D3direct (N × H)
51. C5×D3×C19C5×D3semidirect
52. C5×D3×C19D15semidirect
55. C52×C19D32semidirect
58. C3×C52×D3D19semidirect
63. C3×D3×C19C5×D5semidirect
71. C3×C5×C19D3×D5semidirect
72. C3×C5×C19C2×C5×D3semidirect
73. C3×C5×C19C2×C5×D3semidirect
74. C3×C5×C19C2×D15semidirect
77. C32×C52C2×D19semidirect
87. C32×C19C2×C5×D5semidirect
93. C52×D3D57semidirect
101. D3×C19C5×D15semidirect
104. C5×C19C5×D32semidirect
105. C5×C19D3×D15semidirect
111. C3×C5×D3C5×D19semidirect
112. C3×C5×D3D95semidirect
115. C3×C52D3×D19semidirect
116. C3×C52C2×D57semidirect
122. C3×C19C5×D3×D5semidirect
123. C3×C19C2×C5×D15semidirect
128. C32×C5C2×C5×D19semidirect
129. C32×C5C2×D95semidirect
148. C5×D3C5×D57semidirect
149. C5×D3D285direct (N × H)
150. C52D3×D57semidirect
153. C19C5×D3×D15semidirect
156. C3×D3C5×D95semidirect
162. C3×C5C5×D3×D19semidirect
163. C3×C5D3×D95semidirect
164. C3×C5C2×C5×D57semidirect
165. C3×C5C2×D285semidirect
175. C32C2×C5×D95semidirect
182. D3C5×D285direct (N × H)
184. C5C5×D3×D57semidirect
185. C5D3×D285direct (N × H)
188. C3C5×D3×D95semidirect
189. C3C2×C5×D285semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2852
C3×C5×D2852
C3×C52×D3×C192
C2×C5×D2853
C5×D3×D953
D3×D2855
C5×D3×D575
C5×D3×D1519