Finite Group Databasebeta

← D35×D273 #50304468

Subgroups — D35×D273 #50304468

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×C13×D35C211yesmaximal, characteristic, complemented
2C5×C7×D273C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4D35×D91—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D7×D273—51nomaximal, Hall
7C5⋊(C7⋊D91)—31no—
8C7×C13×D35D311yescharacteristic, complemented
9C5×C7×D91—31no—
10D35×D39—71nomaximal
11D5×D273—71nomaximal
12C3⋊(C7⋊D91)—51no—
13C7×D273D511yescharacteristic, complemented
14C3×C7×C13×D7—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D21×D35—131nomaximal, Hall
17D1365—71no—
18D1365—71no—
19D1365—143no—
20C5×D273D711yescharacteristic, complemented
21C5×C7×D39—71no—
22C3×C13×D35D711yescharacteristic, complemented
23C3×C7×D5×C13—71no—
24D7×D91—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26D5×D91—211no—
27D13×D35—211no—
28C3⋊(C5⋊(C7⋊D7))—131no—
29C5×C7×D21—131no—
30C3×C7×D35D1311yescharacteristic, complemented
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C2×D711yescharacteristic, complemented
34C7⋊D91—151no—
35C7×D91—31no—
36C7×C13×D7—51no—
37C2×D273—351no—
38D7×D39—351no—
39D7×D35—391noHall
40D455—211no—
41D455—211no—
42D455—423no—
43C13×D35D2111yescharacteristic, complemented
44C7×D5×C13—71no—
45C5×D91—31no—
46C5×C7×D13—211no—
47D5×D39—491noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50D7×D21—651noHall
51C2×C3×C7×C13—351no—
52D273—351no—
53D273—351no—
54D273—703no—
55D273D3511yescharacteristic, direct product factor
56C7×D39—71no—
57C3×C13×D7—51no—
58C5⋊(C7⋊D7)—391no—
59C7×D35D3911yescharacteristic, complemented
60C5×C7×D7—391no—
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64D3×D35—911no—
65D5×D21—911no—
66D195—491no—
67C5×D39—71no—
68C3×D5×C13—71no—
69C2×D91—1051no—
70D7×D13—1051no—
71C3⋊(C7⋊D7)—651no—
72C7×D21—131no—
73C3×C7×D7—51no—
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77D5×D13—1471noHall
78C5×C72C2×D3911yescharacteristic, complemented, Hall
79D105—911no—
80D105—911no—
81D105—1823no—
82C5×D21—131no—
83C5×D3×C7—911no—
84C3×D35D9111yescharacteristic, complemented
85C3×C7×D5—71no—
86D72—1951noHall
87C3×C5×C13D7211yescharacteristic, complemented, Hall
88C2×C7×C13—351no—
89D91—31no—
90D91—1051no—
91D91—1051no—
92D91—2103no—
93C7×D13—211no—
94C13×D7—51no—
95C2×D39—2451noHall
96C3×C72D5×D1311yescharacteristic, complemented, Hall
97C2×D35—2731no—
98D5×D7—2731no—
99D65—1471no—
100C5×D13—211no—
101D5×C13—71no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×D9111yescharacteristic, complemented
105C7⋊D7—1951no—
106C7×D7—51no—
107C7×D7—391no—
108C7×C13—23no—
109C7×C13D5×D2111yescharacteristic, complemented
110C7×C13D3×D3511yescharacteristic, complemented
111C2×D21—4551no—
112D3×D7—4551no—
113C2×C3×C13—351no—
114D39—71no—
115D39—2451no—
116C2×C5×C7—2731no—
117D35—2731no—
118D35—2731no—
119D35—5463no—
120D35D27311yescharacteristic, direct product factor
121C5×D7—391no—
122C7×D5—71no—
123C5×C13D7×D2111yescharacteristic, complemented, Hall
124D3×D5—6371noHall
125C2×D13—7351noHall
126C72D5×D3911yescharacteristic, complemented, Sylow
127C2×C3×C7—351no—
128D21—131no—
129D21—9103no—
130D21—4551no—
131D21—4551no—
132C3×D7—51no—
133D3×C7—911no—
134C3×C13D7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D7×D3911yescharacteristic, complemented
137C5×C7C2×D27311yescharacteristic, complemented
138D15—6371no—
139C3×D5—71no—
140C5×D3—911no—
141C2×D7—13651no—
142C2×D7—13651no—
143C2×C13—351no—
144D13—211no—
145D13—7351no—
146C3×C7—23no—
147C3×C7D13×D3511yescharacteristic, complemented
148C3×C7D5×D9111yescharacteristic, complemented
149C2×D5—19111noHall
150C3×C5D7×D9111yescharacteristic, complemented, Hall
151C2×C7—2731no—
152C2×C7—351no—
153D7—51no—
154D7—391no—
155D7—13651no—
156D7—13651no—
157D7—27303no—
158C13D21×D3511yescharacteristic, complemented, Sylow
159C2×D3—31851noHall
160C2×C5—2731no—
161D5—71no—
162D5—19111no—
163C7—23no—
164C7D5×D27311yescharacteristic, complemented
165C7D35×D3911yescharacteristic, complemented
166C2×C3—351no—
167D3—911no—
168D3—31851no—
169C5D7×D27311yescharacteristic, complemented, Sylow
170C22—95551noSylow
171C3D35×D9111yescharacteristic, complemented, Sylow
172C2—2731no—
173C2—351no—
174C2—95551no—
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×C13×D35C2semidirect
2. C5×C7×D273C2semidirect
3. C3⋊(C5⋊(C7⋊D91))C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C7×C13×D35D3semidirect
13. C7×D273D5semidirect
15. C5×C72×C13C2×D3semidirect
20. C5×D273D7semidirect
22. C3×C13×D35D7semidirect
25. C3×C72×C13C2×D5semidirect
30. C3×C7×D35D13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C2×D7semidirect
43. C13×D35D21semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13D3×D5semidirect
55. D273D35direct (N × H)
59. C7×D35D39semidirect
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D21semidirect
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×D39semidirect
84. C3×D35D91semidirect
87. C3×C5×C13D72semidirect
96. C3×C72D5×D13semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×D91semidirect
109. C7×C13D5×D21semidirect
110. C7×C13D3×D35semidirect
120. D35D273direct (N × H)
123. C5×C13D7×D21semidirect
126. C72D5×D39semidirect
134. C3×C13D7×D35semidirect
136. C5×C7D7×D39semidirect
137. C5×C7C2×D273semidirect
147. C3×C7D13×D35semidirect
148. C3×C7D5×D91semidirect
150. C3×C5D7×D91semidirect
158. C13D21×D35semidirect
164. C7D5×D273semidirect
165. C7D35×D39semidirect
169. C5D7×D273semidirect
171. C3D35×D91semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D352
C5×C7×D2732
C3⋊(C5⋊(C7⋊D91))2
D35×D913
D7×D2735
D35×D397
D5×D2737
D21×D3513