Finite Group Databasebeta

← C3×D3×D595 #36339486

Subgroups — C3×D3×D595 #36339486

Order 21420.

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

normal subgroups only

This group has 176 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
1C32×D595C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C17C211yesmaximal, characteristic, complemented
3C3×D1785C211yesmaximal, characteristic, complemented
4C2×C3×D595—31nomaximal
5D3×D595C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C3×D3×D119—51nomaximal, Hall
8D1785C2×C311yescharacteristic, complemented
9C5×D3×C7×C17C2×C311yescharacteristic, complemented
10C3×D595—21no—
11C3×D595—31no—
12C3×D595D311yescharacteristic, direct product factor
13C3×D595C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C17—31no—
15C3×D3×D85—71nomaximal, Hall
16C2×D595—31noHall
17C3×D357—51no—
18C3×D3×C7×C17D511yescharacteristic, complemented
19C32×D119—51no—
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C3×D255—71no—
24C3×C5×D3×C17D711yescharacteristic, complemented
25C32×D85—71no—
26C2×C3×D119—151no—
27D3×D119—51no—
28C3×D3×D35—171nomaximal, Hall
29C2×C5×C7×C17—31no—
30D595—31no—
31D595C3×D311yescharacteristic, direct product factor
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33C2×C3×D85—211no—
34D3×D85—71no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36C2×C3×C7×C17—31no—
37D357—51no—
38D3×C7×C17C3×D511yescharacteristic, complemented
39C3×D119—51no—
40C3×D119—51no—
41C3×D119—101no—
42C3×D119—151no—
43C3×D105—171no—
44C3×C5×D3×C7D1711yescharacteristic, complemented
45C32×D35—171no—
46C3×D3×D17—351noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×C5×C17—31no—
49D255—71no—
50C5×D3×C17C3×D711yescharacteristic, complemented
51C3×D85—71no—
52C3×D85—71no—
53C3×D85—141no—
54C3×D85—211no—
55C2×D119—151noHall
56C2×C3×D35—511no—
57D3×D35—171no—
58C3×C7×C17—21no—
59C3×C7×C17D3×D511yescharacteristic, complemented
60C3×C7×C17C2×C3×D511yescharacteristic, complemented
61C2×D85—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3×D51—351no—
64C3×D3×C17D3511yescharacteristic, complemented
65C32×D17—351no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17C2×C3×D711yescharacteristic, complemented
69C3×D3×D7—851noHall
70C2×C7×C17—31no—
71D119—51no—
72D119—151no—
73C2×C3×C5×C7—31no—
74D105—171no—
75C5×D3×C7C3×D1711yescharacteristic, complemented
76C3×D35—171no—
77C3×D35—171no—
78C3×D35—341no—
79C3×D35—511no—
80C2×C3×D17—1051no—
81D3×D17—351no—
82C3×D3×D5—1191noHall
83C2×C5×C17—31no—
84D85—71no—
85D85—211no—
86C32×C17C2×D3511yescharacteristic, complemented, Hall
87C2×D35—511noHall
88C3×D21—851no—
89C3×D3×C7D8511yescharacteristic, complemented
90C32×D7—851no—
91C7×C17C3×D3×D511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×C3×D1711yescharacteristic, complemented
95C2×C3×C17—31no—
96D51—351no—
97C3×D17—351no—
98C3×D17—351no—
99C3×D17—701no—
100C3×D17—1051no—
101D3×C17C3×D3511yescharacteristic, complemented
102C3×D15—1191no—
103C3×C5×D3D11911yescharacteristic, complemented
104C32×D5—1191no—
105C5×C17C3×D3×D711yescharacteristic, complemented, Hall
106C2×C3×D7—2551no—
107D3×D7—851no—
108C2×C5×C7—31no—
109D35—171no—
110D35—511no—
111C2×D17—1051noHall
112C32×C7C2×D8511yescharacteristic, complemented, Hall
113C2×C3×D5—3571no—
114D3×D5—1191no—
115C3×C17—21no—
116C3×C17D3×D3511yescharacteristic, complemented
117C3×C17C2×C3×D3511yescharacteristic, complemented
118C32×C5C2×D11911yescharacteristic, complemented, Hall
119C2×C3×C7—31no—
120D21—851no—
121C3×D7—851no—
122C3×D7—851no—
123C3×D7—1701no—
124C3×D7—2551no—
125D3×C7C3×D8511yescharacteristic, complemented
126C2×C3×D3—5951noHall
127C5×C7C3×D3×D1711yescharacteristic, complemented, Hall
128C2×C17—31no—
129D17—351no—
130D17—1051no—
131C2×C3×C5—31no—
132D15—1191no—
133C3×D5—3571no—
134C3×D5—1191no—
135C3×D5—1191no—
136C3×D5—2381no—
137C5×D3C3×D11911yescharacteristic, complemented
138C2×D7—2551noHall
139C3×C7—21no—
140C3×C7D3×D8511yescharacteristic, complemented
141C3×C7C2×C3×D8511yescharacteristic, complemented
142C2×D5—3571noHall
143C2×C32—5951no—
144C3×D3—5951no—
145C3×D3D59511yescharacteristic, direct product factor
146C17C3×D3×D3511yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D3×D11911yescharacteristic, complemented
149C3×C5C2×C3×D11911yescharacteristic, complemented
150C2×C7—31no—
151D7—851no—
152D7—2551no—
153C22×C3—17851no—
154C2×D3—5951no—
155C2×C5—31no—
156D5—3571no—
157D5—1191no—
158C32C2×D59511yescharacteristic, complemented, Sylow
159C7C3×D3×D8511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—5951no—
162C2×C3—5951no—
163C2×C3—11901no—
164C2×C3—17851no—
165D3—5951no—
166D3C3×D59511yescharacteristic, direct product factor
167C5C3×D3×D11911yescharacteristic, complemented, Sylow
168C22—17851noSylow
169C3—21no—
170C3D3×D59511yescharacteristic, direct product factor
171C3C2×C3×D59511yescharacteristic, complemented
172C2—31no—
173C2—5951no—
174C2—17851no—
subgroupG/H
center, hypercenterC3D3×D595
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×D595C2semidirect
2. C3×C5×D3×C7×C17C2semidirect
3. C3×D1785C2semidirect
5. D3×D595C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
8. D1785C2×C3semidirect
9. C5×D3×C7×C17C2×C3semidirect
12. C3×D595D3direct (N × H)
13. C3×D595C2×C3semidirect
18. C3×D3×C7×C17D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
24. C3×C5×D3×C17D7semidirect
31. D595C3×D3direct (N × H)
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
38. D3×C7×C17C3×D5semidirect
44. C3×C5×D3×C7D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
50. C5×D3×C17C3×D7semidirect
59. C3×C7×C17D3×D5semidirect
60. C3×C7×C17C2×C3×D5semidirect
62. C32×C5×C7C2×D17semidirect
64. C3×D3×C17D35semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17C2×C3×D7semidirect
75. C5×D3×C7C3×D17semidirect
86. C32×C17C2×D35semidirect
89. C3×D3×C7D85semidirect
91. C7×C17C3×D3×D5semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×C3×D17semidirect
101. D3×C17C3×D35semidirect
103. C3×C5×D3D119semidirect
105. C5×C17C3×D3×D7semidirect
112. C32×C7C2×D85semidirect
116. C3×C17D3×D35semidirect
117. C3×C17C2×C3×D35semidirect
118. C32×C5C2×D119semidirect
125. D3×C7C3×D85semidirect
127. C5×C7C3×D3×D17semidirect
137. C5×D3C3×D119semidirect
140. C3×C7D3×D85semidirect
141. C3×C7C2×C3×D85semidirect
145. C3×D3D595direct (N × H)
146. C17C3×D3×D35semidirect
148. C3×C5D3×D119semidirect
149. C3×C5C2×C3×D119semidirect
158. C32C2×D595semidirect
159. C7C3×D3×D85semidirect
166. D3C3×D595direct (N × H)
167. C5C3×D3×D119semidirect
170. C3D3×D595direct (N × H)
171. C3C2×C3×D595semidirect

Maximal subgroups

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

subgroupindex
C32×D5952
C3×C5×D3×C7×C172
C3×D17852
C2×C3×D5953
D3×D5953
C3×D3×D1195
C3×D3×D857
C3×D3×D3517