Finite Group Databasebeta

← C3×D15×D119 #36339474

Subgroups — C3×D15×D119 #36339474

Order 21420.

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

normal subgroups only

This group has 176 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
1C32×C5×D119C211yesmaximal, characteristic, complemented
2C3×C7×C17×D15C211yesmaximal, characteristic, complemented
3C3×D1785C211yesmaximal, characteristic, complemented
4D15×D119C311yesmaximal, characteristic, direct product factor
5C3×D5×D119—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C3×D3×D119—51nomaximal, Hall
8D1785C2×C311yescharacteristic, complemented
9C7×C17×D15C2×C311yescharacteristic, complemented
10C3×D595—31no—
11C3×C7×D5×C17—31no—
12C3×C5×D119—21no—
13C3×C5×D119D311yescharacteristic, complemented
14C3×C5×D119C2×C311yescharacteristic, complemented
15C3×D15×D17—71nomaximal, Hall
16D5×D119—31noHall
17C3×D357—51no—
18C3×D3×C7×C17—51no—
19C32×D119D511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C3×D255—71no—
24C3×C17×D15D711yescharacteristic, complemented
25C32×C5×D17—71no—
26C2×C3×D119—151no—
27D3×D119—51no—
28C3×D7×D15—171nomaximal, Hall
29D595—31no—
30C7×D5×C17—31no—
31C5×D119C3×D311yescharacteristic, complemented
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33D15×D17—71no—
34C3×D5×D17—211no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C17—151no—
37D357—51no—
38D3×C7×C17—51no—
39C3×D119—21no—
40C3×D119—151no—
41C3×D119C3×D511yescharacteristic, complemented
42C3×D119D1511yescharacteristic, direct product factor
43C3×D105—171no—
44C3×C7×D15D1711yescharacteristic, complemented
45C32×C5×D7—171no—
46C3×D3×D17—351noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48D255—71no—
49C17×D15C3×D711yescharacteristic, complemented
50C3×D85—211no—
51C3×D5×C17—31no—
52C3×C5×D17—71no—
53C3×C5×D17—71no—
54C3×C5×D17—141no—
55C2×D119—151noHall
56D7×D15—171no—
57C3×D5×D7—511no—
58C3×C7×C17—21no—
59C3×C7×C17C2×C3×D511yescharacteristic, complemented
60C3×C7×C17C2×D1511yescharacteristic, complemented
61D5×D17—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3×D51—351no—
64C3×D3×C17—51no—
65C32×D17—71no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17C2×C3×D711yescharacteristic, complemented
69C3×D3×D7—851noHall
70C2×C7×C17—151no—
71D119—151no—
72D119C3×D1511yescharacteristic, direct product factor
73D105—171no—
74C7×D15C3×D1711yescharacteristic, complemented
75C3×D35—511no—
76C3×C7×D5—31no—
77C3×C5×D7—171no—
78C3×C5×D7—171no—
79C3×C5×D7—341no—
80C2×C3×D17—1051no—
81D3×D17—351no—
82C2×C3×D15—1191noHall
83D85—211no—
84C5×D17—71no—
85D5×C17—31no—
86C32×C17D5×D711yescharacteristic, complemented, Hall
87D5×D7—511noHall
88C3×D21—851no—
89C3×D3×C7—51no—
90C32×D7—171no—
91C7×C17C2×C3×D1511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×C3×D1711yescharacteristic, complemented
95C2×C3×C17—151no—
96D51—351no—
97C3×D17—71no—
98C3×D17—71no—
99C3×D17—141no—
100C3×D17—1051no—
101D3×C17—51no—
102C2×C32×C5—1191no—
103C3×D15—1191no—
104C3×D15D11911yescharacteristic, direct product factor
105C5×C17C3×D3×D711yescharacteristic, complemented, Hall
106C2×C3×D7—2551no—
107D3×D7—851no—
108D35—511no—
109C5×D7—171no—
110C7×D5—31no—
111C2×D17—1051noHall
112C32×C7D5×D1711yescharacteristic, complemented, Hall
113C2×D15—1191no—
114C2×C3×D5—3571no—
115C3×C17—21no—
116C3×C17C3×D5×D711yescharacteristic, complemented
117C3×C17D7×D1511yescharacteristic, complemented
118C32×C5C2×D11911yescharacteristic, complemented, Hall
119C2×C3×C7—151no—
120D21—851no—
121C3×D7—171no—
122C3×D7—171no—
123C3×D7—341no—
124C3×D7—2551no—
125D3×C7—51no—
126C2×C3×D3—5951noHall
127C5×C7C3×D3×D1711yescharacteristic, complemented, Hall
128C2×C17—151no—
129D17—71no—
130D17—1051no—
131C2×C3×C5—1191no—
132C2×C3×C5—1191no—
133C2×C3×C5—2381no—
134D15—1191no—
135D15C3×D11911yescharacteristic, direct product factor
136C3×D5—31no—
137C3×D5—3571no—
138C2×D7—2551noHall
139C3×C7—21no—
140C3×C7C3×D5×D1711yescharacteristic, complemented
141C3×C7D15×D1711yescharacteristic, complemented
142C2×D5—3571noHall
143C2×C32—1191no—
144C3×D3—51no—
145C3×D3—5951no—
146C17C3×D7×D1511yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D3×D11911yescharacteristic, complemented
149C3×C5C2×C3×D11911yescharacteristic, complemented
150C2×C7—151no—
151D7—171no—
152D7—2551no—
153C22×C3—17851no—
154C2×D3—5951no—
155C2×C5—1191no—
156D5—31no—
157D5—3571no—
158C32D5×D11911yescharacteristic, complemented, Sylow
159C7C3×D15×D1711yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—1191no—
162C2×C3—1191no—
163C2×C3—2381no—
164C2×C3—17851no—
165D3—51no—
166D3—5951no—
167C5C3×D3×D11911yescharacteristic, complemented, Sylow
168C22—17851noSylow
169C3—21no—
170C3C3×D5×D11911yescharacteristic, complemented
171C3D15×D11911yescharacteristic, direct product factor
172C2—151no—
173C2—1191no—
174C2—17851no—
subgroupG/H
center, hypercenterC3D15×D119
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×D119C2semidirect
2. C3×C7×C17×D15C2semidirect
3. C3×D1785C2semidirect
4. D15×D119C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
8. D1785C2×C3semidirect
9. C7×C17×D15C2×C3semidirect
13. C3×C5×D119D3semidirect
14. C3×C5×D119C2×C3semidirect
19. C32×D119D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
24. C3×C17×D15D7semidirect
31. C5×D119C3×D3semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
41. C3×D119C3×D5semidirect
42. C3×D119D15direct (N × H)
44. C3×C7×D15D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
49. C17×D15C3×D7semidirect
59. C3×C7×C17C2×C3×D5semidirect
60. C3×C7×C17C2×D15semidirect
62. C32×C5×C7C2×D17semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17C2×C3×D7semidirect
72. D119C3×D15direct (N × H)
74. C7×D15C3×D17semidirect
86. C32×C17D5×D7semidirect
91. C7×C17C2×C3×D15semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×C3×D17semidirect
104. C3×D15D119direct (N × H)
105. C5×C17C3×D3×D7semidirect
112. C32×C7D5×D17semidirect
116. C3×C17C3×D5×D7semidirect
117. C3×C17D7×D15semidirect
118. C32×C5C2×D119semidirect
127. C5×C7C3×D3×D17semidirect
135. D15C3×D119direct (N × H)
140. C3×C7C3×D5×D17semidirect
141. C3×C7D15×D17semidirect
146. C17C3×D7×D15semidirect
148. C3×C5D3×D119semidirect
149. C3×C5C2×C3×D119semidirect
158. C32D5×D119semidirect
159. C7C3×D15×D17semidirect
167. C5C3×D3×D119semidirect
170. C3C3×D5×D119semidirect
171. C3D15×D119direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1192
C3×C7×C17×D152
C3×D17852
D15×D1193
C3×D5×D1193
C3×D3×D1195
C3×D15×D177
C3×D7×D1517