Finite Group Databasebeta

← D5×#16838452 #50304205

Subgroups — D5×#16838452 #50304205

Order 38220.

200 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 35 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
1D5×C13⋊#3862C211yesmaximal, characteristic, complemented
2C5⋊#16838452C211yesmaximal, characteristic, complemented
3C5×#16838452C211yesmaximal, characteristic, complemented
4D5×C7⋊D91C311yesmaximal, characteristic, complemented, Hall
5C5×C13⋊#3862C2211yescharacteristic, complemented, Hall
6C2×#16838452—51nomaximal, Hall
7C5⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10D5×#10587723—71nomaximal
11D5×#10587722—71nomaximal
12C2×C13⋊#3862—51no—
13#16838452—51no—
14#16838452D511yescharacteristic, direct product factor
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16D5×#64425—131nomaximal, Hall
17C5⋊#10587723—71no—
18C5⋊#10587722—71no—
19D5×#63271—71no—
20D5×#63270—71no—
21C5×#10587723—71no—
22C5×#10587722—71no—
23C2×C7⋊D91—51noHall
24C13⋊#3862C2×D511yescharacteristic, complemented, Hall
25D5×D91—71no—
26D5×D91—71no—
27D5×D91—212no—
28D5×#3862—131no—
29C5⋊#64425—131no—
30C5×#64425—131no—
31C5×#63270—71no—
32C5×#63271—71no—
33C2×C72×C13—51no—
34C7⋊D91—51no—
35C7⋊D91C3×D511yescharacteristic, complemented
36C2×#10587723—351no—
37C2×#10587722—351no—
38D5×C7⋊D7—131noHall
39D455—71no—
40D455—71no—
41D455—212no—
42C7×D5×C13—32no—
43C7×D5×C13AGL(1,𝔽7)11yescharacteristic, complemented
44C7×D5×C13AGL(1,𝔽7)11yescharacteristic, complemented
45C5×D91—71no—
46C5×D91—71no—
47C5×D91—212no—
48D5×D13⋊C3—491noHall
49C5×#3862—131noHall
50C72×C13C2×C3×D511yescharacteristic, complemented, Hall
51C2×#64425—651noHall
52C2×#63271—351no—
53C2×#63270—351no—
54#10587723—71no—
55#10587723—351no—
56#10587722—71no—
57#10587722—351no—
58C5⋊(C7⋊D7)—131no—
59C72×D5D13⋊C311yescharacteristic, complemented
60C5×C7⋊D7—131no—
61C5×C7×C13—32no—
62C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
63C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
64D5×AGL(1,𝔽7)—911no—
65D5×AGL(1,𝔽7)—911no—
66C5⋊(D13⋊C3)—491no—
67D5×C13⋊C3—491no—
68C5×D13⋊C3—491no—
69C2×D91—351no—
70C2×D91—351no—
71C2×D91—1052no—
72C2×#3862—651no—
73#64425—131no—
74#64425—651no—
75#63271—71no—
76#63270—71no—
77D5×D13—491noHall
78C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
79C5⋊AGL(1,𝔽7)—911no—
80C5⋊AGL(1,𝔽7)—911no—
81D5×ΓL(1,𝔽8)—911no—
82D5×ΓL(1,𝔽8)—911no—
83C5×AGL(1,𝔽7)—911no—
84C5×AGL(1,𝔽7)—911no—
85C2×C7⋊D7—651noHall
86C5×C13⋊C3—491noHall
87C2×C7×C13—51no—
88C2×C7×C13—51no—
89C2×C7×C13—152no—
90D91—71no—
91D91—71no—
92D91—212no—
93D91—351no—
94D91—351no—
95D91—1052no—
96C2×D13⋊C3—2451noHall
97#3862—131noHall
98D5×D7—2732no—
99D5×D7—911no—
100D5×D7—911no—
101D65—491no—
102C5×D13—491no—
103D5×C13#6442511yescharacteristic, complemented
104C5×ΓL(1,𝔽8)—911no—
105C5×ΓL(1,𝔽8)—911no—
106C2×C72—51no—
107C7⋊D7—131no—
108C7⋊D7—651no—
109C7×C13—32no—
110C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
111C7×C13D5×AGL(1,𝔽7)11yescharacteristic, complemented
112C2×AGL(1,𝔽7)—4551no—
113C2×AGL(1,𝔽7)—4551no—
114C2×C13⋊C3—2451no—
115D13⋊C3—491no—
116D13⋊C3—2451no—
117D35—2732no—
118D35—911no—
119D35—911no—
120C5×D7—2732no—
121C5×D7—911no—
122C5×D7—911no—
123C7×D5—32no—
124C7×D5#1058772211yescharacteristic, complemented
125C7×D5#1058772311yescharacteristic, complemented
126C5×C13C2×#6442511yescharacteristic, complemented, Hall
127C2×C3×D5—6371noHall
128C2×D13—2451noHall
129C72D5×D13⋊C311yescharacteristic, complemented, Sylow
130C2×ΓL(1,𝔽8)—4551no—
131C2×ΓL(1,𝔽8)—4551no—
132AGL(1,𝔽7)—911no—
133AGL(1,𝔽7)—911no—
134AGL(1,𝔽7)—4551no—
135AGL(1,𝔽7)—4551no—
136C13⋊C3—491noHall
137C5×C7—32no—
138C5×C7C2×#1058772211yescharacteristic, complemented
139C5×C7C2×#1058772311yescharacteristic, complemented
140C2×C3×C5—6371no—
141C3×D5—6371no—
142C3×D5—6371no—
143C2×D7—13652no—
144C2×D7—4551no—
145C2×D7—4551no—
146C2×C13—51no—
147D13—491no—
148D13—2451no—
149ΓL(1,𝔽8)—911no—
150ΓL(1,𝔽8)—911no—
151C2×D5—6371noHall
152C3×C5—6371noHall
153C2×C7—51no—
154C2×C7—51no—
155C2×C7—152no—
156D7—2732no—
157D7—13652no—
158D7—911no—
159D7—911no—
160D7—4551no—
161D7—4551no—
162C13D5×#6442511yescharacteristic, complemented, Sylow
163C22×C3—31851noHall
164C2×C5—6371no—
165D5—6371no—
166D5#1683845211yescharacteristic, direct product factor
167C7—32no—
168C7D5×#1058772211yescharacteristic, complemented
169C7D5×#1058772311yescharacteristic, complemented
170C2×C3—31851no—
171C2×C3—31851no—
172C2×C3—6371no—
173C5C2×#1683845211yescharacteristic, complemented, Sylow
174C22—31851noSylow
175C3—6371noSylow
176C2—51no—
177C2—31851no—
178C2—6371no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D5×C13⋊#3862C2semidirect
2. C5⋊#16838452C2semidirect
3. C5×#16838452C2semidirect
4. D5×C7⋊D91C3semidirect
5. C5×C13⋊#3862C22semidirect
7. C5⋊(C7⋊D91)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
14. #16838452D5direct (N × H)
15. C5×C72×C13C22×C3semidirect
24. C13⋊#3862C2×D5semidirect
35. C7⋊D91C3×D5semidirect
43. C7×D5×C13AGL(1,𝔽7)semidirect
44. C7×D5×C13AGL(1,𝔽7)semidirect
50. C72×C13C2×C3×D5semidirect
59. C72×D5D13⋊C3semidirect
62. C5×C7×C13C2×AGL(1,𝔽7)semidirect
63. C5×C7×C13C2×AGL(1,𝔽7)semidirect
78. C5×C72C2×D13⋊C3semidirect
103. D5×C13#64425semidirect
110. C7×C13D5×AGL(1,𝔽7)semidirect
111. C7×C13D5×AGL(1,𝔽7)semidirect
124. C7×D5#10587722semidirect
125. C7×D5#10587723semidirect
126. C5×C13C2×#64425semidirect
129. C72D5×D13⋊C3semidirect
138. C5×C7C2×#10587722semidirect
139. C5×C7C2×#10587723semidirect
162. C13D5×#64425semidirect
166. D5#16838452direct (N × H)
168. C7D5×#10587722semidirect
169. C7D5×#10587723semidirect
173. C5C2×#16838452semidirect

Maximal subgroups

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

subgroupindex
D5×C13⋊#38622
C5⋊#168384522
C5×#168384522
D5×C7⋊D913
C2×#168384525
D5×#105877237
D5×#105877227
D5×#6442513