Finite Group Databasebeta

← C4×D5×#41⋊C3 #14514030

Subgroups — C4×D5×#41⋊C3 #14514030

Order 1920.

846 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 139 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
2C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
3Dic5×#41⋊C3C211yesmaximal, characteristic, complemented
4C4×D5×SL(2,𝔽3)C212yesmaximal, complemented
5C4×C5⋊(#41⋊C3)C212yesmaximal, complemented
6C4×D5×#41C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8D5×#41⋊C3C414yesdirect product factor
9C2×D5×SL(2,𝔽3)C2211yescharacteristic
10C2×C5⋊(#41⋊C3)C2211yescharacteristic
11C3×C42×D5—41nomaximal
12C4×C5×SL(2,𝔽3)C2212yescomplemented
13Dic5×SL(2,𝔽3)C2212yescomplemented
14C2×C4×#41⋊C3—51nomaximal, Hall
15C2×D5×#41C2×C311yescharacteristic
16C4×C5×#41C2×C311yescharacteristic, complemented
17#41×Dic5C2×C311yescharacteristic, complemented
18C4×#713C2×C312yescomplemented
19C4×Q8×D5C2×C312yes—
20C4×D4×D5—32no—
21C4×#711—32no—
22#65856—31no—
23D5×#117—31no—
24C4×#709—31no—
25C2×C42×D5—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×C42×C5—41no—
33C3×C4×Dic5—41no—
34C3×C4×Dic5—42no—
35C22×#41⋊C3—51no—
36C4×#41⋊C3—51no—
37C4×#41⋊C3—52no—
38C4×#41⋊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×C42×C5—31no—
54Q8×Dic5C22×C312yes—
55D4×Dic5—32no—
56C4×C22⋊D5—34no—
57#4072—31no—
58C2×C4×Dic5—31no—
59C2×C4×Dic5—32no—
60#4039—32no—
61#4038—32no—
62D5×C4⋊C4—32no—
63#4033—32no—
64#4027—34no—
65D5×C22⋊C4—32no—
66#4023—32no—
67C4×D20—32no—
68#4018—32no—
69C42×D5—31no—
70C42×D5—32no—
71C42×D5—31no—
72C42×D5—31no—
73C42×D5—32no—
74C42×D5A411yescharacteristic
75C4×Dic10—32no—
76C2×C4×#41—51noSylow
77C22×C3×D5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—42no—
80C2×C3×Dic5—42no—
81C2×C3×Dic5—41no—
82C3×C4×D5—44no—
83C3×C4×D5—48no—
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×C42—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—32no—
120C2×C4×D5—32no—
121C2×C4×D5—68no—
122C2×C4×D5C2×A411yescharacteristic
123C2×C4×D5C2×A412yes—
124C2×Dic10—31no—
125C5×C4⋊C4—32no—
126C5×C22⋊C4—32no—
127C42×C5—31no—
128C42×C5—32no—
129C42×C5C2×A411yescharacteristic
130C22⋊Dic5—32no—
131#685—34no—
132C4⋊Dic5—32no—
133#683—34no—
134C4×Dic5—32no—
135C4×Dic5—31no—
136C4×Dic5—32no—
137C4×Dic5—32no—
138C4×Dic5—32no—
139C4×Dic5C2×A412yes—
140C4×Dic5C2×A411yescharacteristic
141C22×#41—51no—
142C4×#41—51no—
143C4×#41—52no—
144C4×#41—151no—
145C4×#41—151no—
146C4×#41—152no—
147C4×#41C3×D511yescharacteristic, complemented
148C2×C4×Q8—52no—
149C2×C4×D4—152no—
150C2×#117—151no—
151C22×C42—151no—
152C22×C3×C5—41no—
153C2×C3×D5—42no—
154C2×C3×D5—44no—
155C3×C4×C5—42no—
156C3×C4×C5—44no—
157C3×Dic5—42no—
158C3×Dic5—44no—
159C22×C3×C4—201no—
160C22×C3×C4—202no—
161#41⋊C3—52no—
162#41⋊C3C4×D512yesdirect product factor
163C2×SL(2,𝔽3)—52no—
164C2×SL(2,𝔽3)C22×D511yescharacteristic
165C3×C42—41no—
166C3×C42—202no—
167C3×C42—201no—
168C23×C5—31no—
169C22×D5—31no—
170C22×D5—34no—
171C22×D5—64no—
172C22×D5C22×A411yescharacteristic
173C5×Q8—31no—
174C5×Q8C22×C3×C411yescharacteristic
175C5×D4—32no—
176C5×D4—32no—
177C2×C4×C5—31no—
178C2×C4×C5—32no—
179C2×C4×C5—32no—
180C2×C4×C5—32no—
181C2×C4×C5—64no—
182C2×C4×C5C22×A411yescharacteristic
183C2×C4×C5C22×A412yes—
184C22⋊D5—38no—
185C2×Dic5—31no—
186C2×Dic5—34no—
187C2×Dic5—32no—
188C2×Dic5—64no—
189C2×Dic5C22×A411yescharacteristic
190C2×Dic5C22×A412yes—
191D20—32no—
192D20—32no—
193C4×D5—32no—
194C4×D5—32no—
195C4×D5—34no—
196C4×D5—32no—
197C4×D5—32no—
198C4×D5—64no—
199C4×D5—64no—
200C4×D5—64no—
201C4×D5C4×A414yes—
202C4×D5#41⋊C318yesdirect product factor
203Dic10—32no—
204Dic10—32no—
205C2×#41—54no—
206C2×#41—51no—
207C2×#41—151no—
208C2×#41—151no—
209C2×#41—154no—
210C2×#41C2×C3×D511yescharacteristic
211C22×Q8—51no—
212C22×D4—151no—
213C23×C4—151no—
214C23×C4—152no—
215C4×Q8—52no—
216C4×Q8—152no—
217C4×Q8—152no—
218C4×Q8C2×C3×D512yes—
219C4×D4—32no—
220C4×D4—152no—
221C4×D4—154no—
222C4×D4—152no—
223C4×D4—154no—
224C4×D4—152no—
225#117—31no—
226#117—152no—
227#117—152no—
228#117—152no—
229#117—151no—
230C2×C4⋊C4—152no—
231C2×C22⋊C4—152no—
232C2×C42—31no—
233C2×C42—51no—
234C2×C42—152no—
235C2×C42—151no—
236C2×C42—151no—
237C2×C42—152no—
238C2×C42—151no—
239C2×C42—152no—
240C2×C42—151no—
241C2×C3×C5—41no—
242C2×C3×C5—42no—
243C3×D5—44no—
244C23×C3—201no—
245C2×C3×C4—42no—
246C2×C3×C4—41no—
247C2×C3×C4—204no—
248C2×C3×C4—208no—
249C2×C3×C4—202no—
250C2×C3×C4—201no—
251SL(2,𝔽3)C2×C4×D511yescharacteristic, complemented
252C22×C5—32no—
253C22×C5—62no—
254C22×C5C23×A411yescharacteristic
255C2×D5—32no—
256C2×D5—62no—
257C2×D5—68no—
258C2×D5C2×C4×A412yes—
259C2×D5C2×#41⋊C314yes—
260C4×C5—31no—
261C4×C5—31no—
262C4×C5—62no—
263C4×C5C2×C4×A412yes—
264C4×C5C2×#41⋊C314yescomplemented
265Dic5—32no—
266Dic5—62no—
267Dic5C2×C4×A412yes—
268Dic5C2×#41⋊C314yescomplemented
269C24—151no—
270#41—32no—
271#41—52no—
272#41—154no—
273#41—154no—
274#41—154no—
275#41—154no—
276#41—152no—
277#41C3×C4×D512yescomplemented
278C2×Q8—52no—
279C2×Q8—151no—
280C2×Q8—152no—
281C2×Q8C22×C3×D511yescharacteristic
282C2×D4—31no—
283C2×D4—151no—
284C2×D4—154no—
285C2×D4—154no—
286C2×D4—152no—
287C22×C4—31no—
288C22×C4—32no—
289C22×C4—51no—
290C22×C4—52no—
291C22×C4—151no—
292C22×C4—154no—
293C22×C4—154no—
294C22×C4—152no—
295C22×C4—151no—
296C22×C4—152no—
297C22×C4—151no—
298C22×C4—152no—
299C22×C4—151no—
300C22×C4—152no—
301C22×C4—308no—
302C4⋊C4—32no—
303C4⋊C4—152no—
304C4⋊C4—154no—
305C22⋊C4—32no—
306C22⋊C4—154no—
307C22⋊C4—152no—
308C42—31no—
309C42—32no—
310C42—51no—
311C42—52no—
312C42—152no—
313C42—152no—
314C42—152no—
315C42—151no—
316C42—152no—
317C42D5×A411yescharacteristic
318C3×C5—41noHall
319C22×C3—41no—
320C22×C3—204no—
321C22×C3—202no—
322C3×C4—42no—
323C3×C4—44no—
324C3×C4—204no—
325C3×C4—202no—
326C2×C5—62no—
327C2×C5C22×C4×A411yescharacteristic
328C2×C5C22×#41⋊C312yes—
329D5—62no—
330D5C4×#41⋊C314yesdirect product factor
331C23—31no—
332C23—51no—
333C23—154no—
334C23—151no—
335C23—304no—
336Q8—31no—
337Q8—152no—
338Q8—152no—
339Q8C2×C3×C4×D511yescharacteristic
340D4—32no—
341D4—32no—
342D4—152no—
343D4—152no—
344D4—158no—
345C2×C4—31no—
346C2×C4—32no—
347C2×C4—32no—
348C2×C4—32no—
349C2×C4—51no—
350C2×C4—52no—
351C2×C4—54no—
352C2×C4—58no—
353C2×C4—64no—
354C2×C4—152no—
355C2×C4—152no—
356C2×C4—152no—
357C2×C4—152no—
358C2×C4—154no—
359C2×C4—151no—
360C2×C4—154no—
361C2×C4—152no—
362C2×C4—304no—
363C2×C4—304no—
364C2×C4—304no—
365C2×C4—304no—
366C2×C4C2×D5×A411yescharacteristic
367C2×C4C2×D5×A412yes—
368C2×C3—41no—
369C2×C3—42no—
370C2×C3—204no—
371C5C2×C4×#41⋊C311yescharacteristic, complemented, Sylow
372C22—32no—
373C22—52no—
374C22—54no—
375C22—62no—
376C22—152no—
377C22—308no—
378C22—302no—
379C22C22×D5×A411yescharacteristic
380C4—31no—
381C4—31no—
382C4—52no—
383C4—54no—
384C4—62no—
385C4—152no—
386C4—302no—
387C4C4×D5×A412yes—
388C4D5×#41⋊C314yesdirect product factor
389C3—41noSylow
390C2—54no—
391C2—62no—
392C2—302no—
393C2C2×C4×D5×A411yescharacteristic
394C2C2×D5×#41⋊C312yes—
subgroupG/H
center, hypercenterC42D5×A4
commutator, hypocenterC5×Q8C22×C3×C4
FrattiniC22C22×D5×A4
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
prime radicalC2×D5×#41⋊C3C2
cosocleC2×C5×Q8C23×C3
LCSG ▷ C5×Q8
UCSC1 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C5×#41⋊C3C2semidirect
3. Dic5×#41⋊C3C2semidirect
4. C4×D5×SL(2,𝔽3)C2semidirect
5. C4×C5⋊(#41⋊C3)C2semidirect
6. C4×D5×#41C3semidirect
8. D5×#41⋊C3C4direct (N × H)
12. C4×C5×SL(2,𝔽3)C22semidirect
13. Dic5×SL(2,𝔽3)C22semidirect
16. C4×C5×#41C2×C3semidirect
17. #41×Dic5C2×C3semidirect
18. C4×#713C2×C3semidirect
28. C5×#41⋊C3C2×C4semidirect
30. D5×SL(2,𝔽3)C2×C4semidirect
31. C5⋊(#41⋊C3)C2×C4semidirect
38. C4×#41⋊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. C4×#41C3×D5semidirect
162. #41⋊C3C4×D5direct (N × H)
202. C4×D5#41⋊C3direct (N × H)
251. SL(2,𝔽3)C2×C4×D5semidirect
264. C4×C5C2×#41⋊C3semidirect
268. Dic5C2×#41⋊C3semidirect
277. #41C3×C4×D5semidirect
330. D5C4×#41⋊C3direct (N × H)
371. C5C2×C4×#41⋊C3semidirect
388. C4D5×#41⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C4×C5×#41⋊C32
Dic5×#41⋊C32
C4×D5×SL(2,𝔽3)2
C4×C5⋊(#41⋊C3)2
C4×D5×#413
C3×C42×D54
C2×C4×#41⋊C35