Finite Group Databasebeta

← C22×D5×#41⋊C3 #14514657

Subgroups — C22×D5×#41⋊C3 #14514657

Order 1920.

2790 conjugacy classes of subgroups; only the 311 normal subgroups are shown.

normal subgroups only

This group has 2790 conjugacy classes of subgroups — too many to draw. Only its 311 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×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×D5×#41⋊C3C2112yesmaximal, direct product factor
3C22×D5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4C22×C5⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
5C22×D5×#41C311yesmaximal, characteristic, complemented, Hall
6C22×C3×C4×D5—41nomaximal
7C2×C5×#41⋊C3C2216yescomplemented
8C22×C5×SL(2,𝔽3)C2211yescharacteristic, complemented
9D5×#41⋊C3C22116yesdirect product factor
10C2×D5×SL(2,𝔽3)C2216yescomplemented
11C2×C5⋊(#41⋊C3)C2216yescomplemented
12C23×#41⋊C3—51nomaximal, Hall
13C22×C5×#41C2×C311yescharacteristic, complemented
14C2×D5×#41—312no—
15C2×D5×#41C2×C3112yescomplemented
16C22×#713C2×C311yescharacteristic, complemented
17C22×Q8×D5C2×C311yescharacteristic
18C22×#711—31no—
19C22×D4×D5—31no—
20C22×#709—31no—
21C23×C4×D5—31no—
22C23×C3×D5—41no—
23C22×C3×C4×C5—41no—
24C22×C3×Dic5—41no—
25C2×C3×C4×D5—412no—
26C5×#41⋊C3C2314yescomplemented
27C2×C5×SL(2,𝔽3)C2313yescomplemented
28D5×SL(2,𝔽3)C2314yescomplemented
29C5⋊(#41⋊C3)C2314yescomplemented
30C22×#41⋊C3—512no—
31C22×#41⋊C3—51no—
32C22×#41⋊C3D511yescharacteristic, direct product factor
33C23×SL(2,𝔽3)—51no—
34C24×D5—31no—
35C2×C5×#41—36no—
36C2×C5×#41C22×C316yescomplemented
37C22×C5×Q8C22×C311yescharacteristic
38C22×C5×D4—31no—
39C23×C4×C5—31no—
40C22×C22⋊D5—32no—
41C23×Dic5—31no—
42D5×#41—332no—
43D5×#41—348no—
44D5×#41C22×C3116yescomplemented
45C2×#713—36no—
46C2×#713C22×C316yescomplemented
47C2×Q8×D5—36no—
48C2×Q8×D5C22×C316yes—
49C2×#711—312no—
50C2×#711—312no—
51C2×D4×D5—312no—
52C2×D4×D5—312no—
53C2×#709—312no—
54C2×#709—312no—
55C22×D20—31no—
56C22×C4×D5—31no—
57C22×C4×D5—31no—
58C22×C4×D5—31no—
59C22×C4×D5—312no—
60C22×C4×D5—312no—
61C22×C4×D5A411yescharacteristic
62C22×Dic10—31no—
63C23×#41—51noSylow
64C23×C3×C5—41no—
65C22×C3×D5—48no—
66C22×C3×D5—46no—
67C2×C3×C4×C5—46no—
68C2×C3×Dic5—46no—
69C3×C4×D5—416no—
70C5×SL(2,𝔽3)C2411yescharacteristic, complemented
71C23×C3×C4—201no—
72C2×#41⋊C3—516no—
73C2×#41⋊C3—56no—
74C2×#41⋊C3C2×D516yesdirect product factor
75C22×SL(2,𝔽3)—56no—
76C22×SL(2,𝔽3)C2×D511yescharacteristic, complemented
77C24×C5—31no—
78C23×D5—31no—
79C23×D5—312no—
80C23×D5—68no—
81C23×D5C2×A411yescharacteristic
82C5×#41—38no—
83C5×#41—312no—
84C5×#41C23×C314yescomplemented
85C2×C5×Q8—33no—
86C2×C5×Q8C23×C313yes—
87C2×C5×D4—36no—
88C2×C5×D4—36no—
89C22×C4×C5—31no—
90C22×C4×C5—36no—
91C22×C4×C5—36no—
92C22×C4×C5C2×A411yescharacteristic
93C2×C22⋊D5—324no—
94C22×Dic5—31no—
95C22×Dic5—312no—
96C22×Dic5C2×A411yescharacteristic
97#713—38no—
98#713—312no—
99#713C23×C314yescomplemented
100Q8×D5—38no—
101Q8×D5—312no—
102Q8×D5C23×C314yes—
103#711—348no—
104#711—316no—
105D4×D5—316no—
106D4×D5—348no—
107#709—348no—
108#709—316no—
109C2×D20—36no—
110C2×D20—36no—
111C2×C4×D5—36no—
112C2×C4×D5—36no—
113C2×C4×D5—312no—
114C2×C4×D5—36no—
115C2×C4×D5—36no—
116C2×C4×D5—348no—
117C2×C4×D5—316no—
118C2×C4×D5C2×A4112yes—
119C2×Dic10—36no—
120C2×Dic10—36no—
121C22×#41—512no—
122C22×#41—51no—
123C22×#41—151no—
124C22×#41—151no—
125C22×#41—1512no—
126C22×#41C3×D511yescharacteristic, complemented
127C23×Q8—51no—
128C23×D4—151no—
129C24×C4—151no—
130C22×C3×C5—44no—
131C22×C3×C5—43no—
132C2×C3×D5—424no—
133C2×C3×D5—44no—
134C3×C4×C5—44no—
135C3×Dic5—44no—
136C24×C3—201no—
137C22×C3×C4—41no—
138C22×C3×C4—2012no—
139C22×C3×C4—201no—
140#41⋊C3—54no—
141#41⋊C3C22×D514yesdirect product factor
142C2×SL(2,𝔽3)—54no—
143C2×SL(2,𝔽3)C22×D513yescomplemented
144C23×C5—36no—
145C23×C5—64no—
146C23×C5C22×A411yescharacteristic
147C22×D5—36no—
148C22×D5—316no—
149C22×D5—64no—
150C22×D5—648no—
151C22×D5#41⋊C318yesdirect product factor
152C22×D5C22×A416yes—
153C5×Q8—33no—
154C5×Q8—32no—
155C5×Q8C24×C311yescharacteristic
156C5×D4—34no—
157C5×D4—312no—
158C2×C4×C5—33no—
159C2×C4×C5—33no—
160C2×C4×C5—312no—
161C2×C4×C5—34no—
162C2×C4×C5C22×A416yes—
163C22⋊D5—332no—
164C2×Dic5—36no—
165C2×Dic5—316no—
166C2×Dic5C22×A416yes—
167D20—34no—
168D20—312no—
169C4×D5—312no—
170C4×D5—34no—
171C4×D5—316no—
172C4×D5—312no—
173C4×D5—34no—
174C4×D5C22×A4116yes—
175Dic10—312no—
176Dic10—34no—
177C25—151no—
178C2×#41—36no—
179C2×#41—516no—
180C2×#41—56no—
181C2×#41—1512no—
182C2×#41—1512no—
183C2×#41—1512no—
184C2×#41—1532no—
185C2×#41—1512no—
186C2×#41—156no—
187C2×#41—1548no—
188C2×#41C2×C3×D516yescomplemented
189C22×Q8—56no—
190C22×Q8—151no—
191C22×Q8—156no—
192C22×Q8C2×C3×D511yescharacteristic
193C22×D4—31no—
194C22×D4—151no—
195C22×D4—1512no—
196C22×D4—1512no—
197C22×D4—152no—
198C23×C4—31no—
199C23×C4—51no—
200C23×C4—151no—
201C23×C4—1512no—
202C23×C4—1512no—
203C23×C4—151no—
204C23×C4—151no—
205C23×C4—151no—
206C2×C3×C5—46no—
207C2×C3×C5—41no—
208C3×D5—48no—
209C23×C3—41no—
210C23×C3—206no—
211C23×C3—208no—
212C2×C3×C4—46no—
213C2×C3×C4—2016no—
214C2×C3×C4—206no—
215SL(2,𝔽3)C23×D511yescharacteristic, complemented
216C22×C5—34no—
217C22×C5—612no—
218C22×C5C2×#41⋊C314yescomplemented
219C22×C5C23×A413yes—
220C2×D5—34no—
221C2×D5—612no—
222C2×D5—632no—
223C2×D5C2×#41⋊C3124yesdirect product factor
224C2×D5C23×A414yes—
225C4×C5—33no—
226C4×C5—31no—
227C4×C5C23×A414yes—
228Dic5—34no—
229Dic5C23×A414yes—
230C24—31no—
231C24—51no—
232C24—1512no—
233C24—151no—
234C24—308no—
235#41—38no—
236#41—312no—
237#41—54no—
238#41—1548no—
239#41—1516no—
240#41—1548no—
241#41—158no—
242#41—1516no—
243#41—1512no—
244#41C22×C3×D514yescomplemented
245C2×Q8—33no—
246C2×Q8—54no—
247C2×Q8—156no—
248C2×Q8—156no—
249C2×Q8—158no—
250C2×Q8—1512no—
251C2×Q8C22×C3×D513yes—
252C2×D4—36no—
253C2×D4—36no—
254C2×D4—156no—
255C2×D4—156no—
256C2×D4—1516no—
257C2×D4—1548no—
258C2×D4—1524no—
259C22×C4—31no—
260C22×C4—36no—
261C22×C4—36no—
262C22×C4—51no—
263C22×C4—512no—
264C22×C4—156no—
265C22×C4—1516no—
266C22×C4—156no—
267C22×C4—1548no—
268C22×C4—156no—
269C22×C4—156no—
270C22×C4—1512no—
271C22×C4—151no—
272C22×C4—1512no—
273C22×C4D5×A411yescharacteristic
274C3×C5—41noHall
275C22×C3—44no—
276C22×C3—43no—
277C22×C3—204no—
278C22×C3—2024no—
279C3×C4—44no—
280C3×C4—204no—
281C2×C5—64no—
282C2×C5C22×#41⋊C316yescomplemented
283C2×C5C24×A411yescharacteristic
284D5—64no—
285D5C22×#41⋊C318yesdirect product factor
286C23—36no—
287C23—58no—
288C23—56no—
289C23—64no—
290C23—1516no—
291C23—156no—
292C23—3048no—
293C23—304no—
294C23C2×D5×A411yescharacteristic
295Q8—33no—
296Q8—32no—
297Q8—154no—
298Q8—1512no—
299Q8C23×C3×D511yescharacteristic
300D4—34no—
301D4—312no—
302D4—154no—
303D4—1512no—
304D4—1532no—
305C2×C4—33no—
306C2×C4—33no—
307C2×C4—34no—
308C2×C4—312no—
309C2×C4—56no—
310C2×C4—516no—
311C2×C4—154no—
312C2×C4—1512no—
313C2×C4—154no—
314C2×C4—1512no—
315C2×C4—1516no—
316C2×C4—156no—
317C2×C4—1516no—
318C2×C4C2×D5×A416yes—
319C2×C3—41no—
320C2×C3—46no—
321C2×C3—208no—
322C5C23×#41⋊C311yescharacteristic, complemented, Sylow
323C22—34no—
324C22—54no—
325C22—524no—
326C22—612no—
327C22—154no—
328C22—3032no—
329C22—3012no—
330C22D5×#41⋊C314yesdirect product factor
331C22C22×D5×A413yes—
332C4—31no—
333C4—33no—
334C4—54no—
335C4—154no—
336C4C22×D5×A414yes—
337C3—41noSylow
338C2—58no—
339C2—64no—
340C2—304no—
341C2C2×D5×#41⋊C316yesdirect product factor
342C2C23×D5×A411yescharacteristic
subgroupG/H
center, hypercenterC22×C4D5×A4
commutator, cosocle, hypocenterC5×Q8C24×C3
FrattiniC2C23×D5×A4
FittingC22×C5×#41C2×C3
socleC23×C5C22×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C2×D5×#41⋊C3C2direct (N × H)
3. C22×D5×SL(2,𝔽3)C2semidirect
4. C22×C5⋊(#41⋊C3)C2semidirect
5. C22×D5×#41C3semidirect
7. C2×C5×#41⋊C3C22semidirect
8. C22×C5×SL(2,𝔽3)C22semidirect
9. D5×#41⋊C3C22direct (N × H)
10. C2×D5×SL(2,𝔽3)C22semidirect
11. C2×C5⋊(#41⋊C3)C22semidirect
13. C22×C5×#41C2×C3semidirect
15. C2×D5×#41C2×C3semidirect
16. C22×#713C2×C3semidirect
26. C5×#41⋊C3C23semidirect
27. C2×C5×SL(2,𝔽3)C23semidirect
28. D5×SL(2,𝔽3)C23semidirect
29. C5⋊(#41⋊C3)C23semidirect
32. C22×#41⋊C3D5direct (N × H)
36. C2×C5×#41C22×C3semidirect
44. D5×#41C22×C3semidirect
46. C2×#713C22×C3semidirect
70. C5×SL(2,𝔽3)C24semidirect
74. C2×#41⋊C3C2×D5direct (N × H)
76. C22×SL(2,𝔽3)C2×D5semidirect
84. C5×#41C23×C3semidirect
99. #713C23×C3semidirect
126. C22×#41C3×D5semidirect
141. #41⋊C3C22×D5direct (N × H)
143. C2×SL(2,𝔽3)C22×D5semidirect
151. C22×D5#41⋊C3direct (N × H)
188. C2×#41C2×C3×D5semidirect
215. SL(2,𝔽3)C23×D5semidirect
218. C22×C5C2×#41⋊C3semidirect
223. C2×D5C2×#41⋊C3direct (N × H)
244. #41C22×C3×D5semidirect
282. C2×C5C22×#41⋊C3semidirect
285. D5C22×#41⋊C3direct (N × H)
322. C5C23×#41⋊C3semidirect
330. C22D5×#41⋊C3direct (N × H)
341. C2C2×D5×#41⋊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×#41⋊C32
C2×D5×#41⋊C32
C22×D5×SL(2,𝔽3)2
C22×C5⋊(#41⋊C3)2
C22×D5×#413
C22×C3×C4×D54
C23×#41⋊C35