Finite Group Databasebeta

← C5×#73000 #14510724

Subgroups — C5×#73000 #14510724

Order 1920.

252 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 24 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
1C5×#5931C211yesmaximal, characteristic, complemented
2C5×#5930C211yesmaximal, characteristic, complemented
3C5×#393⋊C3C211yesmaximal, characteristic, complemented
4C5×#1606—31nomaximal, Hall
5C5×C22⋊SL(2,𝔽3)C2211yescharacteristic
6C5×GL(2,ℤ/4)—41nomaximal
7#73000C511yesmaximal, characteristic, direct product factor, Hall
8C5×#538—31no—
9C5×#451—31no—
10C5×#448—31no—
11C5×#393D311yescharacteristic, complemented
12C5×#328—31no—
13C5×#327—31no—
14C5×#323—31no—
15C22×C5×A4—41no—
16C2×C5×S4—41no—
17C5×SL(2,ℤ/4)—41no—
18C5×GL(2,𝔽3)—81no—
19C5×#226—81no—
20#5931C2×C511yescharacteristic, complemented
21#5930C2×C511yescharacteristic, complemented
22#393⋊C3C2×C511yescharacteristic, complemented
23C22×C5×Q8C2×D311yescharacteristic
24C2×C5×Q16—61no—
25C2×C5×SD16—61no—
26C5×#126—61no—
27C5×#124—61no—
28C5×#123—61no—
29C5×C22⋊Q8—31no—
30C5×#121—31no—
31C5×#121—61no—
32C5×#120—61no—
33C4×C5×D4—61no—
34C2×C5×C22⋊C4—31no—
35C5×#103—61no—
36C5×#103—61no—
37C5×C22⋊C8—31no—
38C5×C22⋊C8—31no—
39C5×#95—31no—
40#1606—31noSylow
41C2×C5×A4—41no—
42C2×C5×A4—81no—
43C5×S4—81no—
44C5×#67—161no—
45C5×SL(2,𝔽3)—81no—
46C5×SL(2,𝔽3)—81no—
47C22⋊SL(2,𝔽3)C22×C511yescharacteristic
48GL(2,ℤ/4)—41no—
49C24×C5S411yescharacteristic
50C2×C5×Q8—31no—
51C2×C5×Q8—61no—
52C2×C5×Q8—61no—
53C2×C5×D4—31no—
54C2×C5×D4—61no—
55C2×C5×D4—61no—
56C2×C5×D4—61no—
57C22×C4×C5—31no—
58C22×C4×C5—31no—
59C22×C4×C5—61no—
60C5×Q16—121no—
61C5×Q16—121no—
62C5×SD16—121no—
63C5×SD16—121no—
64C2×C5×C8—61no—
65C2×C5×C8—61no—
66C5×C4⋊C4—31no—
67C5×C4⋊C4—31no—
68C5×C4⋊C4—61no—
69C5×C4⋊C4—61no—
70C5×C22⋊C4—61no—
71C5×C22⋊C4—61no—
72C5×C22⋊C4—61no—
73C5×C22⋊C4—61no—
74C5×C22⋊C4—61no—
75C5×C22⋊C4—61no—
76C5×C22⋊C4—61no—
77C42×C5—61no—
78#538—31no—
79#451—31no—
80#448—31no—
81#393C5×D311yescharacteristic, complemented
82#328—31no—
83#327—31no—
84#323—31no—
85C22×C3×C5—161no—
86C2×C5×D3—161no—
87C5×A4—41no—
88C5×Dic3—161no—
89C22×A4—41no—
90C2×S4—41no—
91SL(2,ℤ/4)—41no—
92GL(2,𝔽3)—81no—
93#226—81no—
94C23×C5—21no—
95C23×C5—61no—
96C23×C5—61no—
97C23×C5—61no—
98C23×C5C2×S411yescharacteristic
99C5×Q8—21no—
100C5×Q8—21no—
101C5×Q8—61no—
102C5×Q8—61no—
103C5×Q8—121no—
104C5×D4—121no—
105C5×D4—121no—
106C5×D4—121no—
107C5×D4—241no—
108C5×D4—241no—
109C2×C4×C5—31no—
110C2×C4×C5—31no—
111C2×C4×C5—61no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C2×C4×C5—61no—
115C2×C4×C5—121no—
116C2×C4×C5—121no—
117C2×C4×C5—241no—
118C5×C8—121no—
119C5×C8—121no—
120C22×Q8C2×C5×D311yescharacteristic
121C2×Q16—61no—
122C2×SD16—61no—
123#126—61no—
124#124—61no—
125#123—61no—
126C22⋊Q8—31no—
127#121—31no—
128#121—61no—
129#120—61no—
130C4×D4—61no—
131C2×C22⋊C4—31no—
132#103—61no—
133#103—61no—
134C22⋊C8—31no—
135C22⋊C8—31no—
136#95—31no—
137C2×C3×C5—161no—
138C2×C3×C5—321no—
139C5×D3—321no—
140C2×A4—41no—
141C2×A4—81no—
142S4—81no—
143#67—161no—
144SL(2,𝔽3)—81no—
145SL(2,𝔽3)—81no—
146C22×C5—31no—
147C22×C5—31no—
148C22×C5—41no—
149C22×C5—121no—
150C22×C5—121no—
151C22×C5—121no—
152C22×C5—121no—
153C22×C5—121no—
154C22×C5#98311yescharacteristic
155C4×C5—61no—
156C4×C5—61no—
157C4×C5—121no—
158C4×C5—121no—
159C4×C5—121no—
160C4×C5—121no—
161C24C5×S411yescharacteristic
162C2×Q8—31no—
163C2×Q8—61no—
164C2×Q8—61no—
165C2×D4—31no—
166C2×D4—61no—
167C2×D4—61no—
168C2×D4—61no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—61no—
172Q16—121no—
173Q16—121no—
174SD16—121no—
175SD16—121no—
176C2×C8—61no—
177C2×C8—61no—
178C4⋊C4—31no—
179C4⋊C4—31no—
180C4⋊C4—61no—
181C4⋊C4—61no—
182C22⋊C4—61no—
183C22⋊C4—61no—
184C22⋊C4—61no—
185C22⋊C4—61no—
186C22⋊C4—61no—
187C22⋊C4—61no—
188C22⋊C4—61no—
189C42—61no—
190C3×C5—161noHall
191C22×C3—161no—
192C2×D3—161no—
193A4—41no—
194Dic3—161no—
195C2×C5—31no—
196C2×C5—31no—
197C2×C5—81no—
198C2×C5—241no—
199C2×C5#1020⋊C211yescharacteristic
200C23—21no—
201C23—61no—
202C23—61no—
203C23—61no—
204C23C2×C5×S411yescharacteristic
205Q8—21no—
206Q8—21no—
207Q8—61no—
208Q8—61no—
209Q8—121no—
210D4—121no—
211D4—121no—
212D4—121no—
213D4—241no—
214D4—241no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—61no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—121no—
222C2×C4—121no—
223C2×C4—241no—
224C8—121no—
225C8—121no—
226C2×C3—161no—
227C2×C3—321no—
228D3—321no—
229C5#7300011yescharacteristic, direct product factor, Sylow
230C22—31no—
231C22—31no—
232C22—41no—
233C22—121no—
234C22—121no—
235C22—121no—
236C22—121no—
237C22—121no—
238C22C5×#98311yescharacteristic
239C4—61no—
240C4—61no—
241C4—121no—
242C4—121no—
243C4—121no—
244C4—121no—
245C3—161noSylow
246C2—31no—
247C2—31no—
248C2—81no—
249C2—241no—
250C2C5×#1020⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2×C5#1020⋊C2
commutator, cosocle, hypocenterC22⋊SL(2,𝔽3)C22×C5
FrattiniC23C2×C5×S4
FittingC5×#393D3
socleC23×C5C2×S4
LCSG ▷ C22⋊SL(2,𝔽3)
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×#5931C2semidirect
2. C5×#5930C2semidirect
3. C5×#393⋊C3C2semidirect
7. #73000C5direct (N × H)
11. C5×#393D3semidirect
20. #5931C2×C5semidirect
21. #5930C2×C5semidirect
22. #393⋊C3C2×C5semidirect
81. #393C5×D3semidirect
229. C5#73000direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59312
C5×#59302
C5×#393⋊C32
C5×#16063
C5×GL(2,ℤ/4)4
#730005