Finite Group Databasebeta

← Dic5×C5⋊S4 #72231438

Subgroups — Dic5×C5⋊S4 #72231438

Order 2400.

262 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 38 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×C5⋊S4C211yesmaximal, characteristic
2C5×A4×Dic5C211yesmaximal, characteristic, complemented
3A4⋊#1039C211yesmaximal, characteristic, complemented
4Dic5×C22⋊D5—31nomaximal, Hall
5C2×C52×A4C2211yescharacteristic
6C5×C5⋊S4C412yescomplemented
7Dic5×D15—41nomaximal
8C4×C5⋊S4—51nomaximal
9Dic5×S4—51nomaximal
10C2×C5×C22⋊D5—31no—
11C22×C5×Dic5D311yescharacteristic, complemented
12C2×D5×Dic5—31no—
13C22⋊#1039—31no—
14#87780—31no—
15#87778—31no—
16Dic52—31no—
17C2×C5×D15—41no—
18C52×A4C2×C411yescharacteristic, complemented
19C3⋊#1039—41no—
20C3×C5×Dic5—41no—
21C2×C5⋊S4D511yescharacteristic
22C2×C5×S4—51no—
23C4×C5×A4—51no—
24A4×Dic5D511yescharacteristic, complemented
25A4⋊Dic5—51no—
26A4⋊Dic5—51no—
27A4⋊Dic5—102no—
28C23×C52C2×D311yescharacteristic
29C22×C5×D5—31no—
30C2×#1039—31no—
31C2×#1039—31no—
32C5×C22⋊D5—32no—
33C5×C22⋊D5—32no—
34C2×C5×Dic5—31no—
35C2×C5×Dic5—31no—
36C2×C5×Dic5—31no—
37D5×Dic5—61no—
38D5×Dic5—61no—
39D4×Dic5—151no—
40C4×C22⋊D5—151no—
41C2×C3×C52—41no—
42C5×D15—42no—
43C2×C5×A4—22no—
44C2×C5×A4C2×D511yescharacteristic
45C2×C5×A4C2×D511yescharacteristic
46C5⋊S4Dic512yesdirect product factor
47C5×S4—52no—
48C4×D15—201no—
49D3×Dic5—201no—
50C22×C52—31no—
51C22×C52—31no—
52C22×C52C4×D311yescharacteristic, complemented
53C2×C5×D5—32no—
54C2×C5×D5—61no—
55C2×C5×D5—61no—
56#1039—61no—
57#1039—61no—
58C5×Dic5—32no—
59C5×Dic5—31no—
60C5×Dic5S411yescharacteristic, complemented
61C4×S4—251noHall
62C2×C5×D4—151no—
63C22×C4×C5—51no—
64C2×C22⋊D5—31no—
65C22×Dic5—151no—
66C22×Dic5D1511yescharacteristic, complemented
67C2×C4×D5—151no—
68C22⋊Dic5—151no—
69C22⋊Dic5—151no—
70C22⋊Dic5—151no—
71C22⋊Dic5—302no—
72#685—151no—
73C4⋊Dic5—151no—
74#683—151no—
75C4×Dic5—151no—
76C4×Dic5—151no—
77C3×C52—41noHall
78C2×D15—41no—
79C2×C5×D3—201no—
80C5×A4—22no—
81C5×A4C4×D511yescharacteristic, complemented
82C5×A4C2×Dic511yescharacteristic, complemented
83C3×C4×C5—201no—
84Dic15—201no—
85Dic15—201no—
86Dic15—402no—
87C3×Dic5—41no—
88C2×C52—31no—
89C2×C52—31no—
90C2×C52C2×S411yescharacteristic
91C5×D5—62no—
92C2×S4—51no—
93C4×A4—51no—
94SL(2,ℤ/4)—251no—
95C23×C5—22no—
96C23×C5—151no—
97C23×C5D3×D511yescharacteristic
98C23×C5C2×D1511yescharacteristic
99C22×D5—31no—
100C5×D4—152no—
101C5×D4—152no—
102C2×C4×C5—151no—
103C2×C4×C5—151no—
104C2×C4×C5—151no—
105C22⋊D5—32no—
106C22⋊D5—32no—
107C2×Dic5—31no—
108C2×Dic5—31no—
109C2×Dic5—31no—
110C2×Dic5—151no—
111C2×Dic5—151no—
112C2×Dic5—151no—
113C2×Dic5—151no—
114C2×Dic5—302no—
115C2×Dic5—302no—
116C2×Dic5—301no—
117C2×Dic5—301no—
118C4×D5—301no—
119C4×D5—301no—
120C4×D4—751noSylow
121C2×C3×C5—41no—
122C2×C3×C5—41no—
123C2×C3×C5—82no—
124D15—42no—
125C5×D3—202no—
126C52C4×S411yescharacteristic, complemented, Sylow
127C2×A4D5211yescharacteristic
128S4—52no—
129C4×D3—1001no—
130C22×C5—22no—
131C22×C5—31no—
132C22×C5—31no—
133C22×C5—31no—
134C22×C5—31no—
135C22×C5—62no—
136C22×C5—62no—
137C22×C5—152no—
138C22×C5—301no—
139C22×C5—301no—
140C22×C5D3×Dic511yescharacteristic, complemented
141C22×C5C4×D1511yescharacteristic, complemented
142C2×D5—32no—
143C2×D5—61no—
144C2×D5—61no—
145C4×C5—51no—
146C4×C5—152no—
147C4×C5—151no—
148Dic5—32no—
149Dic5—31no—
150Dic5—301no—
151Dic5—301no—
152Dic5—301no—
153Dic5—301no—
154Dic5—602no—
155Dic5—602no—
156Dic5C5⋊S411yescharacteristic, direct product factor
157C2×D4—151no—
158C22×C4—51no—
159C22×C4—751no—
160C4⋊C4—751no—
161C22⋊C4—751no—
162C22⋊C4—751no—
163C42—751no—
164C3×C5—41no—
165C3×C5—41no—
166C3×C5—82no—
167C2×D3—201no—
168A4D5×Dic511yescharacteristic, complemented
169C3×C4—201no—
170Dic3—1001no—
171C2×C5—22no—
172C2×C5—31no—
173C2×C5—31no—
174C2×C5—31no—
175C2×C5—31no—
176C2×C5—62no—
177C2×C5—62no—
178C2×C5—302no—
179C2×C5D5×S411yescharacteristic
180C2×C5C2×C5⋊S411yescharacteristic
181D5—62no—
182C23—151no—
183C23D5×D1511yescharacteristic
184D4—152no—
185D4—152no—
186C2×C4—151no—
187C2×C4—151no—
188C2×C4—151no—
189C2×C4—751no—
190C2×C4—751no—
191C2×C4—1501no—
192C2×C4—1501no—
193C2×C3—41no—
194D3—202no—
195C5—22no—
196C5Dic5×S411yescharacteristic, complemented
197C5C4×C5⋊S411yescharacteristic, complemented
198C22—31no—
199C22—31no—
200C22—152no—
201C22—301no—
202C22—301no—
203C22Dic5×D1511yescharacteristic, complemented
204C4—51no—
205C4—152no—
206C4—151no—
207C4—1501no—
208C4—1501no—
209C3—41noSylow
210C2—31no—
211C2—31no—
212C2—302no—
213C2D5×C5⋊S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D5×C5⋊S4
commutator, hypocenterC52×A4C2×C4
Fitting, socleC23×C52C2×D3
prime radicalC2×C5×C5⋊S4C2
cosocleC2×C52×A4C22
LCSG ▷ C52×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C5×A4×Dic5C2semidirect
3. A4⋊#1039C2semidirect
6. C5×C5⋊S4C4semidirect
11. C22×C5×Dic5D3semidirect
18. C52×A4C2×C4semidirect
24. A4×Dic5D5semidirect
46. C5⋊S4Dic5direct (N × H)
52. C22×C52C4×D3semidirect
60. C5×Dic5S4semidirect
66. C22×Dic5D15semidirect
81. C5×A4C4×D5semidirect
82. C5×A4C2×Dic5semidirect
126. C52C4×S4semidirect
140. C22×C5D3×Dic5semidirect
141. C22×C5C4×D15semidirect
156. Dic5C5⋊S4direct (N × H)
168. A4D5×Dic5semidirect
196. C5Dic5×S4semidirect
197. C5C4×C5⋊S4semidirect
203. C22Dic5×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C5⋊S42
C5×A4×Dic52
A4⋊#10392
Dic5×C22⋊D53
Dic5×D154
C4×C5⋊S45
Dic5×S45