Finite Group Databasebeta

← D5×#4621 #14511616

Subgroups — D5×#4621 #14511616

Order 1920.

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

normal subgroups only

This group has 276 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
1D5×#95⋊C3C211yesmaximal, characteristic
2C5⋊#4621C211yesmaximal, characteristic, complemented
3C5×#4621C211yesmaximal, characteristic, complemented
4D5×#328—31nomaximal, Hall
5D5×SL(2,ℤ/4)—41nomaximal
6C5×#95⋊C3C2211yescharacteristic
7C2×#4621—51nomaximal, Hall
8D5×C22⋊Q8—31no—
9D5×C22⋊C8—31no—
10D5×#95D311yescharacteristic
11C5×#328—31no—
12#64758—31no—
13#64687—31no—
14#64672—31no—
15C2×D5×A4—41no—
16A4⋊Dic5—41no—
17C5×SL(2,ℤ/4)—41no—
18C2×#95⋊C3—51no—
19#4621—51no—
20#4621D511yescharacteristic, direct product factor
21C2×Q8×D5—31no—
22C22×C4×D5—31no—
23C5×C22⋊Q8—31no—
24#4092—31no—
25#4070—31no—
26C2×C8×D5—61no—
27#4043—31no—
28#4042—61no—
29D5×C4⋊C4—31no—
30D5×C4⋊C4—61no—
31D5×C22⋊C4—61no—
32#4024—61no—
33C5×C22⋊C8—31no—
34C5×#95C2×D311yescharacteristic
35#3963—31no—
36C22⋊#168—31no—
37#3952—61no—
38C2×#328—151noSylow
39C2×C5×A4—41no—
40D5×A4—42no—
41D5×Dic3—161no—
42C2×SL(2,ℤ/4)—201no—
43#95⋊C3C2×D511yescharacteristic
44C23×D5S411yescharacteristic
45C2×C5×Q8—31no—
46C22×C4×C5—31no—
47C22×Dic5—31no—
48Q8×D5—122no—
49C2×C4×D5—31no—
50C2×C4×D5—31no—
51C2×C4×D5—31no—
52C2×C4×D5—31no—
53C2×C4×D5—61no—
54C2×C4×D5—61no—
55C2×C4×D5—122no—
56C2×Dic10—31no—
57C2×Dic10—61no—
58C2×C5×C8—61no—
59C5×C4⋊C4—31no—
60C5×C4⋊C4—61no—
61C5×C22⋊C4—61no—
62C22⋊Dic5—61no—
63#685—61no—
64#685—61no—
65C4⋊Dic5—31no—
66C4⋊Dic5—61no—
67#683—61no—
68#683—61no—
69#683—61no—
70C2×#168—61no—
71C8×D5—122no—
72C2×C22⋊Q8—151no—
73C2×C22⋊C8—151no—
74C2×#95—51no—
75#328—31no—
76#328—151no—
77#328—151no—
78#328—151no—
79C2×C3×D5—161no—
80C5×A4—41no—
81Dic15—161no—
82C5×Dic3—161no—
83C22×A4—201no—
84SL(2,ℤ/4)—41no—
85SL(2,ℤ/4)—201no—
86C23×C5C2×S411yescharacteristic
87C22×D5—31no—
88C22×D5—31no—
89C22×D5—32no—
90C22×D5#22612yes—
91C5×Q8—121no—
92C2×C4×C5—31no—
93C2×C4×C5—31no—
94C2×C4×C5—61no—
95C2×C4×C5—61no—
96C2×C4×C5—121no—
97C2×Dic5—31no—
98C2×Dic5—31no—
99C2×Dic5—61no—
100C2×Dic5—61no—
101C2×Dic5—121no—
102C4×D5—62no—
103C4×D5—62no—
104C4×D5—121no—
105C4×D5—121no—
106C4×D5—121no—
107C4×D5—122no—
108C4×D5—121no—
109Dic10—122no—
110Dic10—121no—
111C5×C8—121no—
112#168—121no—
113C22×Q8—151no—
114C23×C4—151no—
115C22×C8—301no—
116C22⋊Q8—31no—
117C22⋊Q8—151no—
118C22⋊Q8—151no—
119C22⋊Q8—151no—
120C22⋊Q8—301no—
121C22⋊Q8—301no—
122C2×C4⋊C4—151no—
123C2×C4⋊C4—301no—
124C2×C22⋊C4—301no—
125C22⋊C8—31no—
126C22⋊C8—151no—
127C22⋊C8—301no—
128#95—151no—
129#95D3×D511yescharacteristic
130C2×C3×C5—161no—
131C3×D5—162no—
132C2×A4—41no—
133C2×A4—202no—
134C2×Dic3—801no—
135C22×C5—31no—
136C22×C5—31no—
137C22×C5C2×#22611yescharacteristic
138C2×D5—31no—
139C2×D5—32no—
140C2×D5—32no—
141C2×D5—32no—
142C2×D5—61no—
143C2×D5#85711yescharacteristic
144C4×C5—61no—
145C4×C5—61no—
146C4×C5—121no—
147C4×C5—121no—
148Dic5—61no—
149Dic5—61no—
150Dic5—121no—
151Dic5—121no—
152C24—51no—
153C2×Q8—31no—
154C2×Q8—151no—
155C2×Q8—301no—
156C2×Q8—602no—
157C22×C4—31no—
158C22×C4—151no—
159C22×C4—151no—
160C22×C4—151no—
161C22×C4—151no—
162C22×C4—151no—
163C22×C4—301no—
164C22×C4—301no—
165C22×C4—602no—
166C2×C8—61no—
167C2×C8—301no—
168C2×C8—602no—
169C4⋊C4—31no—
170C4⋊C4—61no—
171C4⋊C4—151no—
172C4⋊C4—301no—
173C4⋊C4—301no—
174C4⋊C4—301no—
175C4⋊C4—301no—
176C22⋊C4—61no—
177C22⋊C4—301no—
178C22⋊C4—301no—
179C22⋊C4—301no—
180C3×C5—161noHall
181C22×C3—801no—
182A4—41no—
183Dic3—161no—
184Dic3—801no—
185C2×C5—31no—
186C2×C5—31no—
187C2×C5C2×#85711yescharacteristic
188D5—32no—
189D5#462112yesdirect product factor
190C23—52no—
191C23—151no—
192C23—151no—
193C23—152no—
194C23D5×S411yescharacteristic
195Q8—121no—
196Q8—601no—
197Q8—602no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—121no—
203C2×C4—151no—
204C2×C4—151no—
205C2×C4—302no—
206C2×C4—302no—
207C2×C4—301no—
208C2×C4—301no—
209C2×C4—601no—
210C2×C4—601no—
211C2×C4—601no—
212C2×C4—602no—
213C2×C4—601no—
214C2×C4—601no—
215C8—121no—
216C8—601no—
217C2×C3—161no—
218C2×C3—802no—
219C5C2×#462111yescharacteristic, complemented, Sylow
220C22—31no—
221C22—31no—
222C22—51no—
223C22—152no—
224C22—152no—
225C22—152no—
226C22—151no—
227C22—301no—
228C22D5×#22611yescharacteristic
229C4—61no—
230C4—61no—
231C4—121no—
232C4—121no—
233C4—301no—
234C4—301no—
235C4—601no—
236C4—601no—
237C3—161noSylow
238C2—31no—
239C2—31no—
240C2—52no—
241C2—152no—
242C2D5×#85711yescharacteristic
subgroupG/H
center, hypercenterC2D5×#857
commutator, cosocle, hypocenterC5×#95⋊C3C22
FrattiniC23D5×S4
FittingC5×#95C2×D3
socleC23×C5C2×S4
prime radicalD5×#95⋊C3C2
LCSG ▷ C5×#95⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C5⋊#4621C2semidirect
3. C5×#4621C2semidirect
20. #4621D5direct (N × H)
189. D5#4621direct (N × H)
219. C5C2×#4621semidirect

Maximal subgroups

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

subgroupindex
D5×#95⋊C32
C5⋊#46212
C5×#46212
D5×#3283
D5×SL(2,ℤ/4)4
C2×#46215