Finite Group Databasebeta

← C22×C5×#120⋊C3 #14511320

Subgroups — C22×C5×#120⋊C3 #14511320

Order 1920.

1708 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C22×C5×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C5×#120⋊C3C216yesmaximal, direct product factor
3C22×C5×#120C311yesmaximal, characteristic, complemented, Hall
4C2×C5×C22⋊A4C2213yescomplemented
5C23×C5×A4—41nomaximal
6C5×#120⋊C3C2214yesdirect product factor
7C22×#120⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C26×C5C2×C311yescharacteristic, complemented
9C23×C5×D4—31no—
10C2×C5×#120—36no—
11C2×C5×#120C2×C316yescomplemented
12C22×C5×C22⋊C4—31no—
13C5×C22⋊A4C2311yescharacteristic, complemented
14C22×C5×A4—41no—
15C22×C5×A4—46no—
16C22×C5×A4—82no—
17C22×C22⋊A4C2×C511yescharacteristic, complemented
18C2×#120⋊C3C2×C516yesdirect product factor
19C25×C5—31no—
20C25×C5—33no—
21C25×C5—62no—
22C25×C5—66no—
23C25×C5A411yescharacteristic, complemented
24C25×C5C22×C313yescomplemented
25C22×C5×D4—36no—
26C22×C5×D4—36no—
27C22×C5×D4—62no—
28C22×C5×D4—66no—
29C23×C4×C5—31no—
30C5×#120—38no—
31C5×#120—312no—
32C5×#120C22×C314yescomplemented
33C2×C5×C22⋊C4—36no—
34C2×C5×C22⋊C4—36no—
35C22×#120C3×C511yescharacteristic, complemented, Sylow
36C23×C3×C5—161no—
37C2×C5×A4—43no—
38C2×C5×A4—44no—
39C2×C5×A4—86no—
40C2×C22⋊A4C22×C513yescomplemented
41C23×A4—41no—
42#120⋊C3C22×C514yesdirect product factor
43C24×C5—22no—
44C24×C5—36no—
45C24×C5—32no—
46C24×C5—33no—
47C24×C5—33no—
48C24×C5—32no—
49C24×C5—33no—
50C24×C5—66no—
51C24×C5—66no—
52C24×C5—61no—
53C24×C5—66no—
54C24×C5—66no—
55C24×C5—62no—
56C24×C5—66no—
57C24×C5—612no—
58C24×C5—612no—
59C24×C5—66no—
60C24×C5—63no—
61C24×C5—66no—
62C24×C5—62no—
63C24×C5—64no—
64C24×C5—612no—
65C24×C5—612no—
66C24×C5C2×A411yescharacteristic
67C24×C5C2×A416yescomplemented
68C24×C5C23×C311yescharacteristic, complemented
69C2×C5×D4—34no—
70C2×C5×D4—312no—
71C2×C5×D4—612no—
72C2×C5×D4—612no—
73C2×C5×D4—612no—
74C2×C5×D4—612no—
75C22×C4×C5—36no—
76C22×C4×C5—63no—
77C22×C4×C5—61no—
78C5×C22⋊C4—312no—
79C5×C22⋊C4—34no—
80C26C2×C3×C511yescharacteristic, complemented
81C23×D4—31no—
82C2×#120—36no—
83C2×#120C2×C3×C516yescomplemented
84C22×C22⋊C4—31no—
85C22×C3×C5—166no—
86C22×C3×C5—161no—
87C5×A4—41no—
88C5×A4—82no—
89C22⋊A4C23×C511yescharacteristic, complemented
90C22×A4—41no—
91C22×A4—46no—
92C22×A4—82no—
93C23×C5—26no—
94C23×C5—33no—
95C23×C5—31no—
96C23×C5—36no—
97C23×C5—36no—
98C23×C5—36no—
99C23×C5—36no—
100C23×C5—33no—
101C23×C5—31no—
102C23×C5—41no—
103C23×C5—62no—
104C23×C5—66no—
105C23×C5—66no—
106C23×C5—66no—
107C23×C5—66no—
108C23×C5—612no—
109C23×C5—66no—
110C23×C5—66no—
111C23×C5—612no—
112C23×C5—66no—
113C23×C5—66no—
114C23×C5—612no—
115C23×C5—612no—
116C23×C5—66no—
117C23×C5—66no—
118C23×C5—66no—
119C23×C5—66no—
120C23×C5—66no—
121C23×C5—612no—
122C23×C5—612no—
123C23×C5—624no—
124C23×C5—624no—
125C23×C5—612no—
126C23×C5—612no—
127C23×C5—62no—
128C23×C5—123no—
129C23×C5—122no—
130C23×C5C22×A413yes—
131C23×C5C22×A414yescomplemented
132C5×D4—68no—
133C5×D4—624no—
134C2×C4×C5—34no—
135C2×C4×C5—66no—
136C2×C4×C5—66no—
137C25—31no—
138C25—33no—
139C25—62no—
140C25—66no—
141C25C5×A411yescharacteristic, complemented
142C25C22×C3×C513yescomplemented
143C22×D4—36no—
144C22×D4—36no—
145C22×D4—62no—
146C22×D4—66no—
147C23×C4—31no—
148#120—38no—
149#120—312no—
150#120C22×C3×C514yescomplemented
151C2×C22⋊C4—36no—
152C2×C22⋊C4—36no—
153C2×C3×C5—164no—
154C2×C3×C5—163no—
155C23×C3—161no—
156C2×A4—43no—
157C2×A4—44no—
158C2×A4—86no—
159C22×C5—22no—
160C22×C5—33no—
161C22×C5—32no—
162C22×C5—33no—
163C22×C5—33no—
164C22×C5—32no—
165C22×C5—36no—
166C22×C5—46no—
167C22×C5—64no—
168C22×C5—62no—
169C22×C5—66no—
170C22×C5—612no—
171C22×C5—66no—
172C22×C5—612no—
173C22×C5—66no—
174C22×C5—66no—
175C22×C5—62no—
176C22×C5—66no—
177C22×C5—612no—
178C22×C5—64no—
179C22×C5—612no—
180C22×C5—66no—
181C22×C5—66no—
182C22×C5—126no—
183C22×C5#120⋊C311yescharacteristic, direct product factor
184C22×C5C23×A411yescharacteristic
185C4×C5—64no—
186C24—22no—
187C24—36no—
188C24—32no—
189C24—33no—
190C24—33no—
191C24—32no—
192C24—33no—
193C24—66no—
194C24—66no—
195C24—61no—
196C24—66no—
197C24—66no—
198C24—62no—
199C24—66no—
200C24—612no—
201C24—66no—
202C24—612no—
203C24—63no—
204C24—66no—
205C24—62no—
206C24—64no—
207C24—612no—
208C24—612no—
209C24C2×C5×A411yescharacteristic
210C24C2×C5×A416yescomplemented
211C24C23×C3×C511yescharacteristic, complemented
212C2×D4—34no—
213C2×D4—312no—
214C2×D4—612no—
215C2×D4—612no—
216C2×D4—612no—
217C2×D4—612no—
218C22×C4—36no—
219C22×C4—63no—
220C22×C4—61no—
221C22⋊C4—312no—
222C22⋊C4—34no—
223C3×C5—161noHall
224C22×C3—166no—
225C22×C3—161no—
226A4—41no—
227A4—82no—
228C2×C5—31no—
229C2×C5—33no—
230C2×C5—44no—
231C2×C5—62no—
232C2×C5—66no—
233C2×C5C2×#120⋊C313yesdirect product factor
234C23—26no—
235C23—33no—
236C23—31no—
237C23—36no—
238C23—36no—
239C23—36no—
240C23—36no—
241C23—31no—
242C23—33no—
243C23—41no—
244C23—62no—
245C23—66no—
246C23—66no—
247C23—66no—
248C23—66no—
249C23—612no—
250C23—66no—
251C23—66no—
252C23—612no—
253C23—66no—
254C23—66no—
255C23—612no—
256C23—612no—
257C23—66no—
258C23—66no—
259C23—66no—
260C23—66no—
261C23—66no—
262C23—612no—
263C23—612no—
264C23—624no—
265C23—624no—
266C23—612no—
267C23—612no—
268C23—62no—
269C23—123no—
270C23—122no—
271C23C22×C5×A413yes—
272C23C22×C5×A414yescomplemented
273D4—68no—
274D4—624no—
275C2×C4—34no—
276C2×C4—66no—
277C2×C4—66no—
278C2×C3—164no—
279C2×C3—163no—
280C5C22×#120⋊C311yescharacteristic, direct product factor, Sylow
281C22—22no—
282C22—33no—
283C22—32no—
284C22—33no—
285C22—33no—
286C22—32no—
287C22—36no—
288C22—46no—
289C22—64no—
290C22—62no—
291C22—66no—
292C22—612no—
293C22—66no—
294C22—612no—
295C22—66no—
296C22—66no—
297C22—62no—
298C22—66no—
299C22—612no—
300C22—64no—
301C22—612no—
302C22—66no—
303C22—66no—
304C22—126no—
305C22C5×#120⋊C311yescharacteristic, direct product factor
306C22C23×C5×A411yescharacteristic
307C4—64no—
308C3—161noSylow
309C2—31no—
310C2—33no—
311C2—44no—
312C2—62no—
313C2—66no—
314C2C2×C5×#120⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C5#120⋊C3
commutator, cosocle, hypocenterC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#120C3
socleC24×C5C2×A4
LCSG ▷ C24
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C22×C5×C22⋊A4C2semidirect
2. C2×C5×#120⋊C3C2direct (N × H)
3. C22×C5×#120C3semidirect
4. C2×C5×C22⋊A4C22semidirect
6. C5×#120⋊C3C22direct (N × H)
7. C22×#120⋊C3C5direct (N × H)
8. C26×C5C2×C3semidirect
11. C2×C5×#120C2×C3semidirect
13. C5×C22⋊A4C23semidirect
17. C22×C22⋊A4C2×C5semidirect
18. C2×#120⋊C3C2×C5direct (N × H)
23. C25×C5A4semidirect
24. C25×C5C22×C3semidirect
32. C5×#120C22×C3semidirect
35. C22×#120C3×C5semidirect
40. C2×C22⋊A4C22×C5semidirect
42. #120⋊C3C22×C5direct (N × H)
67. C24×C5C2×A4semidirect
68. C24×C5C23×C3semidirect
80. C26C2×C3×C5semidirect
83. C2×#120C2×C3×C5semidirect
89. C22⋊A4C23×C5semidirect
131. C23×C5C22×A4semidirect
141. C25C5×A4semidirect
142. C25C22×C3×C5semidirect
150. #120C22×C3×C5semidirect
183. C22×C5#120⋊C3direct (N × H)
210. C24C2×C5×A4semidirect
211. C24C23×C3×C5semidirect
233. C2×C5C2×#120⋊C3direct (N × H)
272. C23C22×C5×A4semidirect
280. C5C22×#120⋊C3direct (N × H)
305. C22C5×#120⋊C3direct (N × H)
314. C2C2×C5×#120⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊A42
C2×C5×#120⋊C32
C22×C5×#1203
C23×C5×A44
C22×#120⋊C35