Finite Group Databasebeta

← C2×C5×#458⋊C3 #14510982

Subgroups — C2×C5×#458⋊C3 #14510982

Order 1920.

358 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 40 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×#997C211yesmaximal, characteristic
2C5×#458⋊C3C212yesmaximal, direct product factor
3C2×C5×#458C311yesmaximal, characteristic, complemented, Hall
4C5×#997C2211yescharacteristic
5C2×C4×C5×A4—41nomaximal
6C2×#458⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C2×C5×H(5,𝔽2)C2×C311yescharacteristic
8C2×C5×#123—31no—
9C5×#458—32no—
10C5×#458C2×C312yescomplemented
11C2×C5×#99—31no—
12C22×C5×A4—41no—
13C22×C5×A4—81no—
14C2×C5×SL(2,𝔽3)—81no—
15C4×C5×A4—42no—
16C2×#997C2×C511yescharacteristic
17#458⋊C3C2×C512yesdirect product factor
18C5×H(5,𝔽2)—31no—
19C5×H(5,𝔽2)—61no—
20C5×H(5,𝔽2)—61no—
21C5×H(5,𝔽2)C22×C311yescharacteristic
22C2×C5×#41—61no—
23C22×C5×D4—31no—
24C22×C5×D4—61no—
25C23×C4×C5A411yescharacteristic, complemented
26C5×#123—32no—
27C5×#123—32no—
28C5×#123—61no—
29C5×#123—61no—
30C2×C5×C4⋊C4—61no—
31C2×C5×C22⋊C4—31no—
32C2×C5×C22⋊C4—61no—
33C5×#99—32no—
34C5×#99—32no—
35C2×#458C3×C511yescharacteristic, complemented, Sylow
36C2×C5×A4—42no—
37C2×C5×A4—41no—
38C2×C5×A4—81no—
39C2×C5×A4—82no—
40C2×C3×C4×C5—161no—
41C5×SL(2,𝔽3)—81no—
42#997C22×C511yescharacteristic
43C2×C4×A4—41no—
44C24×C5—21no—
45C24×C5—31no—
46C24×C5C2×A411yescharacteristic
47C5×#41—61no—
48C5×#41—62no—
49C5×#41—61no—
50C5×#41—61no—
51C5×#41—62no—
52C5×#41—61no—
53C2×C5×Q8—21no—
54C2×C5×D4—31no—
55C2×C5×D4—31no—
56C2×C5×D4—31no—
57C2×C5×D4—31no—
58C2×C5×D4—61no—
59C2×C5×D4—62no—
60C2×C5×D4—62no—
61C2×C5×D4—62no—
62C2×C5×D4—61no—
63C2×C5×D4—61no—
64C2×C5×D4—62no—
65C2×C5×D4—61no—
66C2×C5×D4—61no—
67C22×C4×C5—31no—
68C22×C4×C5—61no—
69C22×C4×C5—61no—
70C22×C4×C5—61no—
71C22×C4×C5—61no—
72C22×C4×C5C2×A412yescomplemented
73C5×C4⋊C4—62no—
74C5×C4⋊C4—62no—
75C5×C22⋊C4—32no—
76C5×C22⋊C4—61no—
77C5×C22⋊C4—62no—
78C5×C22⋊C4—62no—
79C2×H(5,𝔽2)C2×C3×C511yescharacteristic
80C2×#123—31no—
81#458—32no—
82#458C2×C3×C512yescomplemented
83C2×#99—31no—
84C22×C3×C5—161no—
85C5×A4—41no—
86C5×A4—81no—
87C3×C4×C5—162no—
88C22×A4—41no—
89C22×A4—81no—
90C2×SL(2,𝔽3)—81no—
91C4×A4—42no—
92C23×C5—21no—
93C23×C5—31no—
94C23×C5—31no—
95C23×C5—31no—
96C23×C5—31no—
97C23×C5—42no—
98C23×C5—61no—
99C23×C5—61no—
100C23×C5—61no—
101C23×C5—82no—
102C23×C5—122no—
103C23×C5C22×A411yescharacteristic
104C5×Q8—21no—
105C5×Q8—61no—
106C5×D4—62no—
107C5×D4—62no—
108C5×D4—62no—
109C5×D4—62no—
110C5×D4—61no—
111C5×D4—61no—
112C5×D4—62no—
113C2×C4×C5—31no—
114C2×C4×C5—31no—
115C2×C4×C5—41no—
116C2×C4×C5—62no—
117C2×C4×C5—61no—
118C2×C4×C5—62no—
119C2×C4×C5—61no—
120C2×C4×C5—61no—
121C2×C4×C5—61no—
122C2×C4×C5—62no—
123C2×C4×C5—121no—
124C2×C4×C5—122no—
125H(5,𝔽2)—31no—
126H(5,𝔽2)—61no—
127H(5,𝔽2)—61no—
128H(5,𝔽2)C22×C3×C511yescharacteristic
129C2×#41—61no—
130C22×D4—31no—
131C22×D4—61no—
132C23×C4C5×A411yescharacteristic, complemented
133#123—32no—
134#123—32no—
135#123—61no—
136#123—61no—
137C2×C4⋊C4—61no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—61no—
140#99—32no—
141#99—32no—
142C2×C3×C5—162no—
143C2×C3×C5—161no—
144C2×A4—42no—
145C2×A4—41no—
146C2×A4—81no—
147C2×A4—82no—
148C2×C3×C4—161no—
149SL(2,𝔽3)—81no—
150C22×C5—31no—
151C22×C5—31no—
152C22×C5—41no—
153C22×C5—62no—
154C22×C5—61no—
155C22×C5—61no—
156C22×C5—81no—
157C22×C5—121no—
158C22×C5—121no—
159C22×C5—121no—
160C22×C5—122no—
161C22×C5—241no—
162C22×C5—241no—
163C22×C5#120⋊C311yescharacteristic
164C4×C5—42no—
165C4×C5—61no—
166C4×C5—61no—
167C4×C5—122no—
168C24—21no—
169C24—31no—
170C24C2×C5×A411yescharacteristic
171#41—61no—
172#41—62no—
173#41—61no—
174#41—61no—
175#41—62no—
176#41—61no—
177C2×Q8—21no—
178C2×D4—31no—
179C2×D4—31no—
180C2×D4—31no—
181C2×D4—31no—
182C2×D4—61no—
183C2×D4—62no—
184C2×D4—62no—
185C2×D4—62no—
186C2×D4—61no—
187C2×D4—61no—
188C2×D4—62no—
189C2×D4—61no—
190C2×D4—61no—
191C22×C4—31no—
192C22×C4—61no—
193C22×C4—61no—
194C22×C4—61no—
195C22×C4—61no—
196C22×C4C2×C5×A412yescomplemented
197C4⋊C4—62no—
198C4⋊C4—62no—
199C22⋊C4—32no—
200C22⋊C4—61no—
201C22⋊C4—62no—
202C22⋊C4—62no—
203C3×C5—161noHall
204C22×C3—161no—
205A4—41no—
206A4—81no—
207C3×C4—162no—
208C2×C5—61no—
209C2×C5—61no—
210C2×C5—121no—
211C2×C5—121no—
212C2×C5#458⋊C312yesdirect product factor
213C2×C5C2×#120⋊C311yescharacteristic
214C23—21no—
215C23—31no—
216C23—31no—
217C23—31no—
218C23—31no—
219C23—42no—
220C23—61no—
221C23—61no—
222C23—61no—
223C23—82no—
224C23—122no—
225C23C22×C5×A411yescharacteristic
226Q8—21no—
227Q8—61no—
228D4—62no—
229D4—62no—
230D4—62no—
231D4—62no—
232D4—61no—
233D4—61no—
234D4—62no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—41no—
238C2×C4—62no—
239C2×C4—61no—
240C2×C4—62no—
241C2×C4—61no—
242C2×C4—61no—
243C2×C4—61no—
244C2×C4—62no—
245C2×C4—121no—
246C2×C4—122no—
247C2×C3—162no—
248C2×C3—161no—
249C5C2×#458⋊C311yescharacteristic, direct product factor, Sylow
250C22—31no—
251C22—31no—
252C22—41no—
253C22—62no—
254C22—61no—
255C22—61no—
256C22—81no—
257C22—121no—
258C22—121no—
259C22—121no—
260C22—122no—
261C22—241no—
262C22—241no—
263C22C5×#120⋊C311yescharacteristic
264C4—42no—
265C4—61no—
266C4—61no—
267C4—122no—
268C3—161noSylow
269C2—61no—
270C2—61no—
271C2—121no—
272C2—121no—
273C2C5×#458⋊C312yesdirect product factor
274C2C2×C5×#120⋊C311yescharacteristic
subgroupG/H
center, socle, hypercenterC22×C5#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C3×C5
FrattiniC23C22×C5×A4
FittingC2×C5×#458C3
prime radicalC2×C5×#997C2
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
2. C5×#458⋊C3C2direct (N × H)
3. C2×C5×#458C3semidirect
6. C2×#458⋊C3C5direct (N × H)
10. C5×#458C2×C3semidirect
17. #458⋊C3C2×C5direct (N × H)
25. C23×C4×C5A4semidirect
35. C2×#458C3×C5semidirect
72. C22×C4×C5C2×A4semidirect
82. #458C2×C3×C5semidirect
132. C23×C4C5×A4semidirect
196. C22×C4C2×C5×A4semidirect
212. C2×C5#458⋊C3direct (N × H)
249. C5C2×#458⋊C3direct (N × H)
273. C2C5×#458⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9972
C5×#458⋊C32
C2×C5×#4583
C2×C4×C5×A44
C2×#458⋊C35