Finite Group Databasebeta

← D21×D455 #50304469

Subgroups — D21×D455 #50304469

Order 38220.

208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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×C7×D455C211yesmaximal, characteristic, complemented
2C5×C7×C13×D21C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4D7×D455—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D21×D91—51nomaximal, Hall
7C5⋊(C7⋊D91)—31no—
8C7×D455D311yescharacteristic, complemented
9C5×C7×C13×D7—31no—
10D3×D455—71nomaximal
11D21×D65—71nomaximal
12C3⋊(C7⋊D91)—51no—
13C7×C13×D21D511yescharacteristic, complemented
14C3×C7×D91—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D21×D35—131nomaximal, Hall
17D1365—71no—
18D1365—71no—
19D1365—143no—
20C5×C13×D21D711yescharacteristic, complemented
21C5×D3×C7×C13—71no—
22C3×D455D711yescharacteristic, complemented
23C3×C7×D65—71no—
24D7×D91—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26C2×D455—211no—
27D7×D65—211no—
28C3⋊(C5⋊(C7⋊D7))—131no—
29C5×C7×D21D1311yescharacteristic, complemented
30C3×C7×D35—131no—
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C2×D711yescharacteristic, complemented
34C7⋊D91—151no—
35C7×D91—51no—
36C7×C13×D7—31no—
37D3×D91—351no—
38D13×D21—351no—
39D7×D35—391noHall
40C2×C5×C7×C13—211no—
41D455—211no—
42D455—211no—
43D455—423no—
44D455D2111yescharacteristic, direct product factor
45C7×D65—71no—
46C5×C13×D7—31no—
47D3×D65—491noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50D7×D21—651noHall
51D273—351no—
52D273—351no—
53D273—703no—
54C13×D21D3511yescharacteristic, complemented
55D3×C7×C13—71no—
56C3×D91—51no—
57C3×C7×D13—351no—
58C5⋊(C7⋊D7)—391no—
59C7×D35—131no—
60C5×C7×D7—31no—
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64D3×D35—911no—
65D5×D21—911no—
66D195—491no—
67C5×D3×C13—71no—
68C3×D65—71no—
69C2×D91—1051no—
70D7×D13—1051no—
71C3⋊(C7⋊D7)—651no—
72C7×D21D6511yescharacteristic, complemented
73C3×C7×D7—651no—
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77C2×D65—1471noHall
78C5×C72D3×D1311yescharacteristic, complemented, Hall
79D105—911no—
80D105—911no—
81D105—1823no—
82C5×D21D9111yescharacteristic, complemented
83C5×D3×C7—71no—
84C3×D35—131no—
85C3×C7×D5—911no—
86D72—1951noHall
87C3×C5×C13D7211yescharacteristic, complemented, Hall
88C2×C7×C13—211no—
89D91—51no—
90D91—1051no—
91D91—1051no—
92D91—2103no—
93C7×D13—351no—
94C13×D7—31no—
95D3×D13—2451noHall
96C3×C72C2×D6511yescharacteristic, complemented, Hall
97C2×D35—2731no—
98D5×D7—2731no—
99C2×C5×C13—211no—
100D65—71no—
101D65—1471no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×D9111yescharacteristic, complemented
105C7⋊D7—1951no—
106C7×D7—31no—
107C7×D7—651no—
108C7×C13—23no—
109C7×C13D5×D2111yescharacteristic, complemented
110C7×C13D3×D3511yescharacteristic, complemented
111C2×D21—4551no—
112D3×D7—4551no—
113D39—2451no—
114C3×D13—351no—
115D3×C13—71no—
116C2×C5×C7—211no—
117D35—131no—
118D35—2731no—
119D35—2731no—
120D35—5463no—
121C5×D7—31no—
122C7×D5—911no—
123C5×C13D7×D2111yescharacteristic, complemented, Hall
124D3×D5—6371noHall
125C2×D13—7351noHall
126C72D3×D6511yescharacteristic, complemented, Sylow
127C2×C3×C7—4551no—
128D21—9103no—
129D21—4551no—
130D21—4551no—
131D21D45511yescharacteristic, direct product factor
132C3×D7—651no—
133D3×C7—71no—
134C3×C13D7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D13×D2111yescharacteristic, complemented
137C5×C7D3×D9111yescharacteristic, complemented
138D15—6371no—
139C3×D5—911no—
140C5×D3—71no—
141C2×D7—13651no—
142C2×D7—13651no—
143C2×C13—211no—
144D13—351no—
145D13—7351no—
146C3×C7—23no—
147C3×C7D7×D6511yescharacteristic, complemented
148C3×C7C2×D45511yescharacteristic, complemented
149C2×D5—19111noHall
150C3×C5D7×D9111yescharacteristic, complemented, Hall
151C2×C7—211no—
152C2×C7—4551no—
153D7—31no—
154D7—651no—
155D7—13651no—
156D7—13651no—
157D7—27303no—
158C13D21×D3511yescharacteristic, complemented, Sylow
159C2×D3—31851noHall
160C2×C5—211no—
161D5—911no—
162D5—19111no—
163C7—23no—
164C7D21×D6511yescharacteristic, complemented
165C7D3×D45511yescharacteristic, complemented
166C2×C3—4551no—
167D3—71no—
168D3—31851no—
169C5D21×D9111yescharacteristic, complemented, Sylow
170C22—95551noSylow
171C3D7×D45511yescharacteristic, complemented, Sylow
172C2—211no—
173C2—95551no—
174C2—4551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×D455C2semidirect
2. C5×C7×C13×D21C2semidirect
3. C3⋊(C5⋊(C7⋊D91))C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C7×D455D3semidirect
13. C7×C13×D21D5semidirect
15. C5×C72×C13C2×D3semidirect
20. C5×C13×D21D7semidirect
22. C3×D455D7semidirect
25. C3×C72×C13C2×D5semidirect
29. C5×C7×D21D13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C2×D7semidirect
44. D455D21direct (N × H)
48. C3×C5×C72C2×D13semidirect
49. C72×C13D3×D5semidirect
54. C13×D21D35semidirect
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D21semidirect
72. C7×D21D65semidirect
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72D3×D13semidirect
82. C5×D21D91semidirect
87. C3×C5×C13D72semidirect
96. C3×C72C2×D65semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×D91semidirect
109. C7×C13D5×D21semidirect
110. C7×C13D3×D35semidirect
123. C5×C13D7×D21semidirect
126. C72D3×D65semidirect
131. D21D455direct (N × H)
134. C3×C13D7×D35semidirect
136. C5×C7D13×D21semidirect
137. C5×C7D3×D91semidirect
147. C3×C7D7×D65semidirect
148. C3×C7C2×D455semidirect
150. C3×C5D7×D91semidirect
158. C13D21×D35semidirect
164. C7D21×D65semidirect
165. C7D3×D455semidirect
169. C5D21×D91semidirect
171. C3D7×D455semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D4552
C5×C7×C13×D212
C3⋊(C5⋊(C7⋊D91))2
D7×D4553
D21×D915
D3×D4557
D21×D657
D21×D3513