Finite Group Databasebeta

← C5×#72985 #14510709

Subgroups — C5×#72985 #14510709

Order 1920.

274 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 26 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
1C2×C5×#95⋊C3C211yesmaximal, characteristic, complemented
2C5×#4622C211yesmaximal, characteristic, complemented
3C5×#4621C211yesmaximal, characteristic, complemented
4C5×#1504—31nomaximal, Hall
5C5×GL(2,ℤ/4)—41nomaximal
6C5×#95⋊C3C2211yescharacteristic
7#72985C511yesmaximal, characteristic, direct product factor, Hall
8C5×#525—31no—
9C5×#407—31no—
10C2×C5×#95D311yescharacteristic, complemented
11C5×#328—31no—
12C5×#328—31no—
13C5×#327—31no—
14C5×#327—31no—
15C22×C5×A4—41no—
16C2×C5×S4—41no—
17C5×SL(2,ℤ/4)—41no—
18C2×#95⋊C3C2×C511yescharacteristic, complemented
19#4622C2×C511yescharacteristic, complemented
20#4621C2×C511yescharacteristic, complemented
21C2×C5×#41—31no—
22C23×C4×C5—31no—
23C2×C5×M16—61no—
24C5×#123—61no—
25C5×C22⋊Q8—31no—
26C5×C22⋊Q8—31no—
27C5×#121—31no—
28C5×#121—31no—
29C5×#120—61no—
30C4×C5×D4—61no—
31C4×C5×D4—61no—
32C5×#117—31no—
33C5×C22⋊C8—31no—
34C5×C22⋊C8—31no—
35C5×C22⋊C8—61no—
36C5×#95—31no—
37C5×#95C2×D311yescharacteristic
38#1504—31noSylow
39C2×C5×A4—41no—
40C2×C5×A4—81no—
41C5×S4—81no—
42C5×#67—161no—
43GL(2,ℤ/4)—41no—
44#95⋊C3C22×C511yescharacteristic
45C24×C5S411yescharacteristic
46C5×#41—122no—
47C2×C5×Q8—31no—
48C2×C5×D4—31no—
49C2×C5×D4—61no—
50C2×C5×D4—61no—
51C2×C5×D4—61no—
52C22×C4×C5—31no—
53C22×C4×C5—31no—
54C22×C4×C5—31no—
55C22×C4×C5—31no—
56C22×C4×C5—31no—
57C22×C4×C5—31no—
58C22×C4×C5—61no—
59C22×C4×C5—122no—
60C5×M16—122no—
61C2×C5×C8—61no—
62C2×C5×C8—61no—
63C5×C4⋊C4—31no—
64C5×C4⋊C4—31no—
65C5×C4⋊C4—61no—
66C5×C4⋊C4—61no—
67C5×C22⋊C4—61no—
68C5×C22⋊C4—61no—
69C5×C22⋊C4—61no—
70C5×C22⋊C4—61no—
71C5×C22⋊C4—61no—
72C42×C5—61no—
73#525—31no—
74#407—31no—
75C2×#95C5×D311yescharacteristic, complemented
76#328—31no—
77#328—31no—
78#327—31no—
79#327—31no—
80C22×C3×C5—161no—
81C2×C5×D3—161no—
82C5×A4—41no—
83C5×Dic3—161no—
84C22×A4—41no—
85C2×S4—41no—
86SL(2,ℤ/4)—41no—
87C23×C5—21no—
88C23×C5—31no—
89C23×C5—31no—
90C23×C5—61no—
91C23×C5—61no—
92C23×C5C2×S411yescharacteristic
93C5×Q8—121no—
94C5×D4—121no—
95C5×D4—121no—
96C5×D4—121no—
97C5×D4—122no—
98C5×D4—121no—
99C5×D4—121no—
100C2×C4×C5—31no—
101C2×C4×C5—31no—
102C2×C4×C5—31no—
103C2×C4×C5—31no—
104C2×C4×C5—62no—
105C2×C4×C5—62no—
106C2×C4×C5—61no—
107C2×C4×C5—61no—
108C2×C4×C5—61no—
109C2×C4×C5—121no—
110C2×C4×C5—121no—
111C2×C4×C5—121no—
112C2×C4×C5—121no—
113C2×C4×C5—122no—
114C5×C8—121no—
115C5×C8—121no—
116C2×#41—31no—
117C23×C4—31no—
118C2×M16—61no—
119#123—61no—
120C22⋊Q8—31no—
121C22⋊Q8—31no—
122#121—31no—
123#121—31no—
124#120—61no—
125C4×D4—61no—
126C4×D4—61no—
127#117—31no—
128C22⋊C8—31no—
129C22⋊C8—31no—
130C22⋊C8—61no—
131#95—31no—
132#95C2×C5×D311yescharacteristic
133C2×C3×C5—161no—
134C2×C3×C5—321no—
135C5×D3—321no—
136C2×A4—41no—
137C2×A4—81no—
138S4—81no—
139#67—161no—
140C22×C5—31no—
141C22×C5—31no—
142C22×C5—32no—
143C22×C5—31no—
144C22×C5—61no—
145C22×C5—61no—
146C22×C5—61no—
147C22×C5—121no—
148C22×C5—121no—
149C22×C5—121no—
150C22×C5#85711yescharacteristic
151C22×C5#98311yescharacteristic
152C4×C5—61no—
153C4×C5—61no—
154C4×C5—61no—
155C4×C5—61no—
156C4×C5—121no—
157C4×C5—121no—
158C4×C5—121no—
159C24C5×S411yescharacteristic
160#41—122no—
161C2×Q8—31no—
162C2×D4—31no—
163C2×D4—61no—
164C2×D4—61no—
165C2×D4—61no—
166C22×C4—31no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—61no—
173C22×C4—122no—
174M16—122no—
175C2×C8—61no—
176C2×C8—61no—
177C4⋊C4—31no—
178C4⋊C4—31no—
179C4⋊C4—61no—
180C4⋊C4—61no—
181C22⋊C4—61no—
182C22⋊C4—61no—
183C22⋊C4—61no—
184C22⋊C4—61no—
185C22⋊C4—61no—
186C42—61no—
187C3×C5—161noHall
188C22×C3—161no—
189C2×D3—161no—
190A4—41no—
191Dic3—161no—
192C2×C5—21no—
193C2×C5—31no—
194C2×C5—31no—
195C2×C5—61no—
196C2×C5—241no—
197C2×C5C2×#85711yescharacteristic
198C23—21no—
199C23—31no—
200C23—31no—
201C23—61no—
202C23—61no—
203C23C2×C5×S411yescharacteristic
204Q8—121no—
205D4—121no—
206D4—122no—
207D4—121no—
208D4—121no—
209D4—121no—
210D4—121no—
211C2×C4—31no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—62no—
216C2×C4—62no—
217C2×C4—61no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—121no—
221C2×C4—121no—
222C2×C4—121no—
223C2×C4—121no—
224C2×C4—122no—
225C8—121no—
226C8—121no—
227C2×C3—161no—
228C2×C3—321no—
229D3—321no—
230C5#7298511yescharacteristic, direct product factor, Sylow
231C22—31no—
232C22—31no—
233C22—32no—
234C22—31no—
235C22—61no—
236C22—61no—
237C22—61no—
238C22—121no—
239C22—121no—
240C22—121no—
241C22C5×#85711yescharacteristic
242C22C5×#98311yescharacteristic
243C4—61no—
244C4—61no—
245C4—61no—
246C4—61no—
247C4—121no—
248C4—121no—
249C4—121no—
250C3—161noSylow
251C2—21no—
252C2—31no—
253C2—31no—
254C2—61no—
255C2—241no—
256C2C2×C5×#85711yescharacteristic
subgroupG/H
centerC2×C5C2×#857
commutator, cosocle, hypocenter#95⋊C3C22×C5
FrattiniC23C2×C5×S4
FittingC2×C5×#95D3
socleC23×C5C2×S4
hypercenterC22×C5#857
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C5 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#95⋊C3C2semidirect
2. C5×#4622C2semidirect
3. C5×#4621C2semidirect
7. #72985C5direct (N × H)
10. C2×C5×#95D3semidirect
18. C2×#95⋊C3C2×C5semidirect
19. #4622C2×C5semidirect
20. #4621C2×C5semidirect
75. C2×#95C5×D3semidirect
230. C5#72985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#95⋊C32
C5×#46222
C5×#46212
C5×#15043
C5×GL(2,ℤ/4)4
#729855