Finite Group Databasebeta

← D5×#520⋊C3 #14514055

Subgroups — D5×#520⋊C3 #14514055

Order 1920.

790 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 790 conjugacy classes of subgroups — too many to draw. Only its 119 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×D5×#41⋊C3C211yesmaximal, characteristic
2C5×#520⋊C3C211yesmaximal, characteristic, complemented
3#66161⋊C3C211yesmaximal, characteristic, complemented
4C4×D5×SL(2,𝔽3)C212yesmaximal, complemented
5#65908⋊C3C212yesmaximal, complemented
6D5×#520C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8D5×#41⋊C3C414yescomplemented
9C2×D5×SL(2,𝔽3)C2211yescharacteristic
10C2×C5⋊(#41⋊C3)C2211yescharacteristic
11C3×D5×C4⋊C4—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yescomplemented
13Dic5×SL(2,𝔽3)C2212yescomplemented
14C2×#520⋊C3—51nomaximal, Hall
15C2×D5×#41C2×C311yescharacteristic
16C5×#520C2×C311yescharacteristic, complemented
17#66161C2×C311yescharacteristic, complemented
18#65908C2×C312yescomplemented
19C4×Q8×D5C2×C312yes—
20#65880—32no—
21C4×D4×D5—32no—
22#65857—31no—
23D5×#117—31no—
24#65838—31no—
25C2×D5×C4⋊C4—31no—
26C2×C3×C4×D5—41no—
27C2×C3×C4×D5—42no—
28C5×#41⋊C3C2×C412yescomplemented
29C2×C5×SL(2,𝔽3)C2311yescharacteristic
30D5×SL(2,𝔽3)C2×C412yescomplemented
31C5⋊(#41⋊C3)C2×C412yescomplemented
32C3×C5×C4⋊C4—41no—
33C3×C4⋊Dic5—41no—
34C3×#683—42no—
35C22×#41⋊C3—51no—
36#520⋊C3—51no—
37#520⋊C3—52no—
38#520⋊C3D511yescharacteristic, direct product factor
39C2×C4×SL(2,𝔽3)—52no—
40C2×C5×#41C22×C311yescharacteristic
41D5×#41—34no—
42D5×#41C3×C414yescomplemented
43C2×#713C22×C311yescharacteristic
44C2×Q8×D5C22×C311yescharacteristic
45C2×#711—31no—
46C2×D4×D5—31no—
47C2×#709—31no—
48C22×C4×D5—31no—
49C22×C4×D5—32no—
50C4×C5×Q8C22×C312yes—
51C4×C5×D4—32no—
52C5×#117—31no—
53C2×C5×C4⋊C4—31no—
54Q8×Dic5C22×C312yes—
55D4×Dic5—32no—
56C4×C22⋊D5—34no—
57#4072—31no—
58C2×C4⋊Dic5—31no—
59C2×#683—32no—
60#4039—32no—
61#4038—31no—
62#4038—31no—
63D5×C4⋊C4—32no—
64D5×C4⋊C4—32no—
65D5×C4⋊C4—31no—
66D5×C4⋊C4—32no—
67D5×C4⋊C4A411yescharacteristic
68#4033—32no—
69#4027—34no—
70D5×C22⋊C4—32no—
71#4023—32no—
72C4×D20—32no—
73#4018—32no—
74C42×D5—32no—
75C4×Dic10—32no—
76C2×#520—51noSylow
77C22×C3×D5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—42no—
80C2×C3×Dic5—41no—
81C2×C3×Dic5—42no—
82C3×C4×D5—44no—
83C3×C4×D5—84no—
84C5×SL(2,𝔽3)C22×C411yescharacteristic, complemented
85C2×#41⋊C3—54no—
86C2×#41⋊C3—51no—
87C2×#41⋊C3C2×D511yescharacteristic
88C22×SL(2,𝔽3)—51no—
89C2×C3×C4⋊C4—201no—
90C4×SL(2,𝔽3)—52no—
91C4×SL(2,𝔽3)C2×D512yescomplemented
92C23×D5—31no—
93C5×#41—32no—
94C5×#41C2×C3×C412yescomplemented
95C2×C5×Q8C23×C311yescharacteristic
96C2×C5×D4—31no—
97C22×C4×C5—31no—
98C22×C4×C5—32no—
99C2×C22⋊D5—32no—
100C22×Dic5—31no—
101C22×Dic5—32no—
102#713—32no—
103#713C2×C3×C412yescomplemented
104Q8×D5—32no—
105Q8×D5C2×C3×C412yes—
106#711—34no—
107#711—34no—
108D4×D5—34no—
109D4×D5—34no—
110#709—34no—
111#709—34no—
112C2×D20—31no—
113C2×C4×D5—31no—
114C2×C4×D5—31no—
115C2×C4×D5—31no—
116C2×C4×D5—34no—
117C2×C4×D5—34no—
118C2×C4×D5—32no—
119C2×C4×D5—34no—
120C2×C4×D5—124no—
121C2×C4×D5C2×A412yes—
122C2×C4×D5C2×A411yescharacteristic
123C2×Dic10—31no—
124C5×C4⋊C4—32no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4C2×A411yescharacteristic
127C5×C22⋊C4—32no—
128C42×C5—32no—
129C22⋊Dic5—32no—
130#685—32no—
131#685—32no—
132C4⋊Dic5—31no—
133C4⋊Dic5—32no—
134C4⋊Dic5C2×A411yescharacteristic
135#683—34no—
136#683—32no—
137#683C2×A412yes—
138C4×Dic5—32no—
139C4×Dic5—32no—
140C4×Dic5—32no—
141C22×#41—51no—
142#520—51no—
143#520—52no—
144#520—151no—
145#520—151no—
146#520—152no—
147#520C3×D511yescharacteristic, complemented
148C2×C4×Q8—52no—
149C2×C4×D4—152no—
150C2×#117—151no—
151C22×C4⋊C4—151no—
152C22×C3×C5—41no—
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C3×C4×C5—42no—
157C3×C4×C5—82no—
158C3×Dic5—42no—
159C3×Dic5—82no—
160C22×C3×C4—201no—
161C22×C3×C4—202no—
162#41⋊C3—52no—
163#41⋊C3C4×D512yescomplemented
164C2×SL(2,𝔽3)—52no—
165C2×SL(2,𝔽3)C22×D511yescharacteristic
166C3×C4⋊C4—41no—
167C3×C4⋊C4—202no—
168C3×C4⋊C4—201no—
169C23×C5—31no—
170C22×D5—31no—
171C22×D5—34no—
172C22×D5—62no—
173C22×D5—62no—
174C22×D5C22×A411yescharacteristic
175C5×Q8—31no—
176C5×Q8C22×C3×C411yescharacteristic
177C5×D4—32no—
178C5×D4—32no—
179C2×C4×C5—31no—
180C2×C4×C5—32no—
181C2×C4×C5—32no—
182C2×C4×C5—32no—
183C2×C4×C5—122no—
184C2×C4×C5C22×A412yes—
185C2×C4×C5C22×A411yescharacteristic
186C22⋊D5—38no—
187C2×Dic5—31no—
188C2×Dic5—34no—
189C2×Dic5—32no—
190C2×Dic5—122no—
191C2×Dic5C22×A412yes—
192C2×Dic5C22×A411yescharacteristic
193D20—32no—
194D20—32no—
195C4×D5—24no—
196C4×D5—32no—
197C4×D5—32no—
198C4×D5—34no—
199C4×D5—32no—
200C4×D5—32no—
201C4×D5—64no—
202C4×D5—124no—
203C4×D5C4×A414yes—
204Dic10—32no—
205Dic10—32no—
206C2×#41—54no—
207C2×#41—51no—
208C2×#41—151no—
209C2×#41—151no—
210C2×#41—154no—
211C2×#41C2×C3×D511yescharacteristic
212C22×Q8—51no—
213C22×D4—151no—
214C23×C4—151no—
215C23×C4—152no—
216C4×Q8—52no—
217C4×Q8—152no—
218C4×Q8—152no—
219C4×Q8C2×C3×D512yes—
220C4×D4—32no—
221C4×D4—152no—
222C4×D4—154no—
223C4×D4—154no—
224C4×D4—152no—
225C4×D4—152no—
226#117—31no—
227#117—152no—
228#117—152no—
229#117—151no—
230#117—151no—
231#117—151no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—51no—
234C2×C4⋊C4—151no—
235C2×C4⋊C4—152no—
236C2×C4⋊C4—152no—
237C2×C4⋊C4—152no—
238C2×C4⋊C4—152no—
239C2×C4⋊C4—151no—
240C2×C22⋊C4—152no—
241C2×C42—152no—
242C2×C3×C5—41no—
243C2×C3×C5—41no—
244C2×C3×C5—41no—
245C3×D5—44no—
246C23×C3—201no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—204no—
250C2×C3×C4—201no—
251C2×C3×C4—202no—
252C2×C3×C4—404no—
253SL(2,𝔽3)C2×C4×D511yescharacteristic, complemented
254C22×C5—32no—
255C22×C5—61no—
256C22×C5—61no—
257C22×C5C23×A411yescharacteristic
258C2×D5—32no—
259C2×D5—61no—
260C2×D5—61no—
261C2×D5—68no—
262C2×D5C2×C4×A412yes—
263C2×D5#99412yes—
264C2×D52−1+4⋊C312yes—
265C4×C5—22no—
266C4×C5—31no—
267C4×C5—31no—
268C4×C5—62no—
269C4×C5C2×C4×A412yes—
270Dic5—22no—
271Dic5—32no—
272Dic5—62no—
273Dic5C2×C4×A412yes—
274C24—151no—
275#41—32no—
276#41—52no—
277#41—154no—
278#41—154no—
279#41—154no—
280#41—154no—
281#41—152no—
282#41C3×C4×D512yescomplemented
283C2×Q8—52no—
284C2×Q8—151no—
285C2×Q8—152no—
286C2×Q8C22×C3×D511yescharacteristic
287C2×D4—31no—
288C2×D4—151no—
289C2×D4—154no—
290C2×D4—154no—
291C2×D4—152no—
292C22×C4—31no—
293C22×C4—32no—
294C22×C4—51no—
295C22×C4—52no—
296C22×C4—151no—
297C22×C4—154no—
298C22×C4—154no—
299C22×C4—151no—
300C22×C4—152no—
301C22×C4—154no—
302C22×C4—151no—
303C22×C4—151no—
304C22×C4—152no—
305C22×C4—604no—
306C4⋊C4—32no—
307C4⋊C4—31no—
308C4⋊C4—52no—
309C4⋊C4—51no—
310C4⋊C4—152no—
311C4⋊C4—152no—
312C4⋊C4—154no—
313C4⋊C4—151no—
314C4⋊C4D5×A411yescharacteristic
315C22⋊C4—32no—
316C22⋊C4—152no—
317C22⋊C4—152no—
318C22⋊C4—152no—
319C42—32no—
320C42—152no—
321C42—152no—
322C42—152no—
323C3×C5—41noHall
324C22×C3—41no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—202no—
328C3×C4—42no—
329C3×C4—82no—
330C3×C4—202no—
331C3×C4—402no—
332C2×C5—62no—
333C2×C5C22×C4×A411yescharacteristic
334C2×C5C2×#99411yescharacteristic
335C2×C5C2×2−1+4⋊C311yescharacteristic
336D5—62no—
337D5#520⋊C314yesdirect product factor
338C23—31no—
339C23—51no—
340C23—154no—
341C23—151no—
342C23—302no—
343C23—302no—
344Q8—31no—
345Q8—152no—
346Q8—152no—
347Q8C2×C3×C4×D511yescharacteristic
348D4—32no—
349D4—32no—
350D4—152no—
351D4—152no—
352D4—158no—
353C2×C4—31no—
354C2×C4—32no—
355C2×C4—32no—
356C2×C4—32no—
357C2×C4—51no—
358C2×C4—54no—
359C2×C4—52no—
360C2×C4—104no—
361C2×C4—122no—
362C2×C4—152no—
363C2×C4—152no—
364C2×C4—152no—
365C2×C4—152no—
366C2×C4—154no—
367C2×C4—151no—
368C2×C4—154no—
369C2×C4—152no—
370C2×C4—304no—
371C2×C4—604no—
372C2×C4—602no—
373C2×C4C2×D5×A412yes—
374C2×C4C2×D5×A411yescharacteristic
375C2×C3—41no—
376C2×C3—41no—
377C2×C3—41no—
378C2×C3—204no—
379C5C2×#520⋊C311yescharacteristic, complemented, Sylow
380C22—32no—
381C22—52no—
382C22—52no—
383C22—52no—
384C22—61no—
385C22—61no—
386C22—152no—
387C22—308no—
388C22—301no—
389C22—301no—
390C22C22×D5×A411yescharacteristic
391C4—22no—
392C4—31no—
393C4—31no—
394C4—52no—
395C4—62no—
396C4—102no—
397C4—152no—
398C4—302no—
399C4C4×D5×A412yes—
400C3—41noSylow
401C2—54no—
402C2—62no—
403C2—302no—
404C2C2×C4×D5×A411yescharacteristic
405C2D5×#99411yescharacteristic
406C2D5×2−1+4⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, hypocenterC5×Q8C22×C3×C4
FittingC5×#520C2×C3
socleC22×C5C23×A4
prime radicalC2×D5×#41⋊C3C2
cosocleC2×C5×Q8C23×C3
hypercenterC4⋊C4D5×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#520⋊C3C2semidirect
3. #66161⋊C3C2semidirect
4. C4×D5×SL(2,𝔽3)C2semidirect
5. #65908⋊C3C2semidirect
6. D5×#520C3semidirect
8. D5×#41⋊C3C4semidirect
12. C4×C5×SL(2,𝔽3)C22semidirect
13. Dic5×SL(2,𝔽3)C22semidirect
16. C5×#520C2×C3semidirect
17. #66161C2×C3semidirect
18. #65908C2×C3semidirect
28. C5×#41⋊C3C2×C4semidirect
30. D5×SL(2,𝔽3)C2×C4semidirect
31. C5⋊(#41⋊C3)C2×C4semidirect
38. #520⋊C3D5direct (N × H)
42. D5×#41C3×C4semidirect
84. C5×SL(2,𝔽3)C22×C4semidirect
91. C4×SL(2,𝔽3)C2×D5semidirect
94. C5×#41C2×C3×C4semidirect
103. #713C2×C3×C4semidirect
147. #520C3×D5semidirect
163. #41⋊C3C4×D5semidirect
253. SL(2,𝔽3)C2×C4×D5semidirect
282. #41C3×C4×D5semidirect
337. D5#520⋊C3direct (N × H)
379. C5C2×#520⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C5×#520⋊C32
#66161⋊C32
C4×D5×SL(2,𝔽3)2
#65908⋊C32
D5×#5203
C3×D5×C4⋊C44
C2×#520⋊C35