Finite Group Databasebeta

← C5×#3524⋊C3 #14511359

Subgroups — C5×#3524⋊C3 #14511359

Order 1920.

510 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#557⋊C3C211yesmaximal, characteristic, complemented
2C5×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3C5×#548⋊C3C211yesmaximal, characteristic, complemented
4C5×#548⋊C3C211yesmaximal, characteristic, complemented
5C5×#520⋊C3C211yesmaximal, characteristic, complemented
6C5×#519⋊C3C211yesmaximal, characteristic, complemented
7C4×C5×#41⋊C3C211yesmaximal, characteristic, complemented
8C5×#3524C311yesmaximal, characteristic, complemented, Hall
9C2×C5×#41⋊C3C2211yescharacteristic
10C2×C5×#41⋊C3C2211yescharacteristic
11C22×C5×SL(2,𝔽3)C2211yescharacteristic
12C3×C5×#126—41nomaximal
13C4×C5×SL(2,𝔽3)C2211yescharacteristic
14C4×C5×SL(2,𝔽3)C2211yescharacteristic
15C4×C5×SL(2,𝔽3)C2211yescharacteristic
16C4×C5×SL(2,𝔽3)C2211yescharacteristic
17#3524⋊C3C511yesmaximal, characteristic, direct product factor, Hall
18C5×#559—31no—
19C5×#557C2×C311yescharacteristic, complemented
20C5×#555—31no—
21C5×#553—31no—
22C5×#552—31no—
23C5×#550C2×C311yescharacteristic, complemented
24C5×#548C2×C311yescharacteristic
25C5×#548C2×C311yescharacteristic
26C5×#542—31no—
27C5×#540—31no—
28C5×#529—31no—
29C5×#529—31no—
30C5×#520C2×C311yescharacteristic, complemented
31C5×#519C2×C311yescharacteristic
32C4×C5×#41C2×C311yescharacteristic, complemented
33C5×#41⋊C3—21no—
34C5×#41⋊C3—21no—
35C2×C5×SL(2,𝔽3)—21no—
36C2×C5×SL(2,𝔽3)C2311yescharacteristic
37C3×C5×C4⋊C4—41no—
38C3×C5×C4⋊C4—41no—
39C3×C5×C4⋊C4—41no—
40C3×C5×C22⋊C4—41no—
41C3×C5×C22⋊C4—41no—
42C3×C5×C22⋊C4—41no—
43C3×C42×C5—41no—
44#557⋊C3C2×C511yescharacteristic, complemented
45C4⋊(#41⋊C3)C2×C511yescharacteristic, complemented
46#548⋊C3C2×C511yescharacteristic, complemented
47#548⋊C3C2×C511yescharacteristic, complemented
48#520⋊C3C2×C511yescharacteristic, complemented
49#519⋊C3C2×C511yescharacteristic, complemented
50C4×#41⋊C3C2×C511yescharacteristic, complemented
51C2×C5×#41C22×C311yescharacteristic
52C2×C5×#41C22×C311yescharacteristic
53C22×C5×Q8C22×C311yescharacteristic
54C5×C4⋊Q8—31no—
55C5×#127—31no—
56C5×#126—32no—
57C5×#126—31no—
58C5×#126A411yescharacteristic
59C5×#125—31no—
60C5×#125—31no—
61C5×#125—31no—
62C5×#124—32no—
63C5×#124—31no—
64C5×#124—31no—
65C5×#124—31no—
66C5×#123—32no—
67C5×#123—32no—
68C5×#123—31no—
69C5×#123—31no—
70C5×C22⋊Q8—31no—
71C5×C22⋊Q8—31no—
72C5×C22⋊Q8—31no—
73C5×#121—31no—
74C5×#121—31no—
75C5×#121—32no—
76C5×#121—31no—
77C5×#121—31no—
78C5×#121—31no—
79C4×C5×Q8—31no—
80C4×C5×Q8—31no—
81C4×C5×Q8—31no—
82C4×C5×Q8C22×C311yescharacteristic
83C4×C5×Q8C22×C311yescharacteristic
84C4×C5×Q8C22×C311yescharacteristic
85C4×C5×Q8C22×C311yescharacteristic
86C4×C5×D4—32no—
87C4×C5×D4—31no—
88C4×C5×D4—31no—
89C4×C5×D4—31no—
90C4×C5×D4—31no—
91C4×C5×D4—31no—
92C4×C5×D4—31no—
93C4×C5×D4—31no—
94C5×#117—32no—
95C5×#117—31no—
96C5×#117—31no—
97C5×#117—31no—
98C5×#117—31no—
99C2×C5×C4⋊C4—31no—
100C2×C42×C5—31no—
101#3524C3×C511yescharacteristic, complemented, Sylow
102C23×C3×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C5×SL(2,𝔽3)#4111yescharacteristic
110C2×#41⋊C3C22×C511yescharacteristic
111C2×#41⋊C3C22×C511yescharacteristic
112C22×SL(2,𝔽3)C22×C511yescharacteristic
113C3×#126—41no—
114C4×SL(2,𝔽3)C22×C511yescharacteristic
115C4×SL(2,𝔽3)C22×C511yescharacteristic
116C4×SL(2,𝔽3)C22×C511yescharacteristic
117C4×SL(2,𝔽3)C22×C511yescharacteristic
118C5×#41—21no—
119C5×#41—21no—
120C5×#41—61no—
121C5×#41—61no—
122C2×C5×Q8—21no—
123C2×C5×Q8—31no—
124C2×C5×Q8—31no—
125C2×C5×Q8—61no—
126C2×C5×Q8C23×C311yescharacteristic
127C2×C5×D4—31no—
128C2×C5×D4—31no—
129C2×C5×D4—32no—
130C2×C5×D4—31no—
131C2×C5×D4—31no—
132C2×C5×D4—31no—
133C22×C4×C5—31no—
134C22×C4×C5—32no—
135C22×C4×C5—31no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—32no—
144C5×C4⋊C4—31no—
145C5×C4⋊C4—31no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—31no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4C2×A411yescharacteristic
152C5×C4⋊C4C2×A411yescharacteristic
153C5×C4⋊C4C2×A411yescharacteristic
154C5×C22⋊C4—32no—
155C5×C22⋊C4—32no—
156C5×C22⋊C4—32no—
157C5×C22⋊C4—31no—
158C5×C22⋊C4—31no—
159C5×C22⋊C4—31no—
160C5×C22⋊C4—31no—
161C5×C22⋊C4—31no—
162C5×C22⋊C4—31no—
163C5×C22⋊C4—31no—
164C5×C22⋊C4C2×A411yescharacteristic
165C5×C22⋊C4C2×A411yescharacteristic
166C5×C22⋊C4C2×A411yescharacteristic
167C42×C5—32no—
168C42×C5—31no—
169C42×C5—31no—
170C42×C5—31no—
171C42×C5—31no—
172C42×C5—31no—
173C42×C5C2×A411yescharacteristic
174#559—31no—
175#557C2×C3×C511yescharacteristic, complemented
176#555—31no—
177#553—31no—
178#552—31no—
179#550C2×C3×C511yescharacteristic, complemented
180#548C2×C3×C511yescharacteristic
181#548C2×C3×C511yescharacteristic
182#542—31no—
183#540—31no—
184#529—31no—
185#529—31no—
186#520C2×C3×C511yescharacteristic, complemented
187#519C2×C3×C511yescharacteristic
188C4×#41C2×C3×C511yescharacteristic, complemented
189C22×C3×C5—41no—
190C22×C3×C5—81no—
191C22×C3×C5—81no—
192C22×C3×C5—81no—
193C3×C4×C5—81no—
194C3×C4×C5—81no—
195C3×C4×C5—81no—
196C3×C4×C5—81no—
197C3×C4×C5—81no—
198C3×C4×C5—81no—
199#41⋊C3—21no—
200#41⋊C3—21no—
201C2×SL(2,𝔽3)—21no—
202C2×SL(2,𝔽3)C23×C511yescharacteristic
203C3×C4⋊C4—41no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—41no—
206C3×C22⋊C4—41no—
207C3×C22⋊C4—41no—
208C3×C22⋊C4—41no—
209C3×C42—41no—
210C23×C5—31no—
211C23×C5—31no—
212C23×C5C22×A411yescharacteristic
213C5×Q8—31no—
214C5×Q8—61no—
215C5×Q8—61no—
216C5×Q8—121no—
217C5×Q8C3×#4111yescharacteristic
218C5×D4—61no—
219C5×D4—61no—
220C5×D4—61no—
221C5×D4—61no—
222C5×D4—121no—
223C5×D4—121no—
224C5×D4—121no—
225C5×D4—122no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—31no—
230C2×C4×C5—31no—
231C2×C4×C5—31no—
232C2×C4×C5—61no—
233C2×C4×C5—61no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—61no—
238C2×C4×C5—121no—
239C2×C4×C5—121no—
240C2×C4×C5—122no—
241C2×C4×C5C22×A411yescharacteristic
242C2×C4×C5C22×A411yescharacteristic
243C2×C4×C5C22×A411yescharacteristic
244C2×C4×C5C22×A411yescharacteristic
245C2×C4×C5C22×A411yescharacteristic
246C2×C4×C5C22×A411yescharacteristic
247C2×#41C22×C3×C511yescharacteristic
248C2×#41C22×C3×C511yescharacteristic
249C22×Q8C22×C3×C511yescharacteristic
250C4⋊Q8—31no—
251#127—31no—
252#126—32no—
253#126—31no—
254#126C5×A411yescharacteristic
255#125—31no—
256#125—31no—
257#125—31no—
258#124—32no—
259#124—31no—
260#124—31no—
261#124—31no—
262#123—32no—
263#123—32no—
264#123—31no—
265#123—31no—
266C22⋊Q8—31no—
267C22⋊Q8—31no—
268C22⋊Q8—31no—
269#121—31no—
270#121—31no—
271#121—32no—
272#121—31no—
273#121—31no—
274#121—31no—
275C4×Q8—31no—
276C4×Q8—31no—
277C4×Q8—31no—
278C4×Q8C22×C3×C511yescharacteristic
279C4×Q8C22×C3×C511yescharacteristic
280C4×Q8C22×C3×C511yescharacteristic
281C4×Q8C22×C3×C511yescharacteristic
282C4×D4—32no—
283C4×D4—31no—
284C4×D4—31no—
285C4×D4—31no—
286C4×D4—31no—
287C4×D4—31no—
288C4×D4—31no—
289C4×D4—31no—
290#117—32no—
291#117—31no—
292#117—31no—
293#117—31no—
294#117—31no—
295C2×C4⋊C4—31no—
296C2×C42—31no—
297C2×C3×C5—41no—
298C2×C3×C5—41no—
299C2×C3×C5—41no—
300C2×C3×C5—161no—
301C23×C3—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308SL(2,𝔽3)C5×#4111yescharacteristic
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5—61no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5—61no—
318C22×C5C23×A411yescharacteristic
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—31no—
326C4×C5—31no—
327C4×C5—61no—
328C4×C5—61no—
329C4×C5—61no—
330C4×C5—61no—
331C4×C5—61no—
332#41—21no—
333#41—21no—
334#41—61no—
335#41—61no—
336C2×Q8—21no—
337C2×Q8—31no—
338C2×Q8—31no—
339C2×Q8—61no—
340C2×Q8C23×C3×C511yescharacteristic
341C2×D4—31no—
342C2×D4—31no—
343C2×D4—32no—
344C2×D4—31no—
345C2×D4—31no—
346C2×D4—31no—
347C22×C4—31no—
348C22×C4—32no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—31no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—31no—
357C4⋊C4—32no—
358C4⋊C4—31no—
359C4⋊C4—31no—
360C4⋊C4—31no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4C2×C5×A411yescharacteristic
366C4⋊C4C2×C5×A411yescharacteristic
367C4⋊C4C2×C5×A411yescharacteristic
368C22⋊C4—32no—
369C22⋊C4—32no—
370C22⋊C4—32no—
371C22⋊C4—31no—
372C22⋊C4—31no—
373C22⋊C4—31no—
374C22⋊C4—31no—
375C22⋊C4—31no—
376C22⋊C4—31no—
377C22⋊C4—31no—
378C22⋊C4C2×C5×A411yescharacteristic
379C22⋊C4C2×C5×A411yescharacteristic
380C22⋊C4C2×C5×A411yescharacteristic
381C42—32no—
382C42—31no—
383C42—31no—
384C42—31no—
385C42—31no—
386C42—31no—
387C42C2×C5×A411yescharacteristic
388C3×C5—41noHall
389C22×C3—41no—
390C22×C3—81no—
391C22×C3—81no—
392C22×C3—81no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—81no—
397C3×C4—81no—
398C3×C4—81no—
399C2×C5—41no—
400C2×C5—121no—
401C2×C5—121no—
402C2×C5A4×#4111yescharacteristic
403C2×C5#594511yescharacteristic
404C2×C5#594511yescharacteristic
405C23—31no—
406C23—31no—
407C23C22×C5×A411yescharacteristic
408Q8—31no—
409Q8—61no—
410Q8—61no—
411Q8—121no—
412Q8C3×C5×#4111yescharacteristic
413D4—61no—
414D4—61no—
415D4—61no—
416D4—61no—
417D4—121no—
418D4—121no—
419D4—121no—
420D4—122no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—31no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—122no—
436C2×C4C22×C5×A411yescharacteristic
437C2×C4C22×C5×A411yescharacteristic
438C2×C4C22×C5×A411yescharacteristic
439C2×C4C22×C5×A411yescharacteristic
440C2×C4C22×C5×A411yescharacteristic
441C2×C4C22×C5×A411yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—161no—
446C5#3524⋊C311yescharacteristic, direct product factor, Sylow
447C22—21no—
448C22—21no—
449C22—21no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—61no—
454C22—61no—
455C22—61no—
456C22C23×C5×A411yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—31no—
464C4—31no—
465C4—61no—
466C4—61no—
467C4—61no—
468C4—61no—
469C4—61no—
470C3—41noSylow
471C2—41no—
472C2—121no—
473C2—121no—
474C2C5×A4×#4111yescharacteristic
475C2C5×#594511yescharacteristic
476C2C5×#594511yescharacteristic
subgroupG/H
center, socleC22×C5C23×A4
commutator, cosocleC2×Q8C23×C3×C5
FrattiniC22C23×C5×A4
FittingC5×#3524C3
hypercenterC5×#126A4
hypocenterQ8C3×C5×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C5 ◁ C5×#126

Complements

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

NH ≅ G/Ntype
1. C5×#557⋊C3C2semidirect
2. C5×C4⋊(#41⋊C3)C2semidirect
3. C5×#548⋊C3C2semidirect
4. C5×#548⋊C3C2semidirect
5. C5×#520⋊C3C2semidirect
6. C5×#519⋊C3C2semidirect
7. C4×C5×#41⋊C3C2semidirect
8. C5×#3524C3semidirect
17. #3524⋊C3C5direct (N × H)
19. C5×#557C2×C3semidirect
23. C5×#550C2×C3semidirect
30. C5×#520C2×C3semidirect
32. C4×C5×#41C2×C3semidirect
44. #557⋊C3C2×C5semidirect
45. C4⋊(#41⋊C3)C2×C5semidirect
46. #548⋊C3C2×C5semidirect
47. #548⋊C3C2×C5semidirect
48. #520⋊C3C2×C5semidirect
49. #519⋊C3C2×C5semidirect
50. C4×#41⋊C3C2×C5semidirect
101. #3524C3×C5semidirect
175. #557C2×C3×C5semidirect
179. #550C2×C3×C5semidirect
186. #520C2×C3×C5semidirect
188. C4×#41C2×C3×C5semidirect
446. C5#3524⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#557⋊C32
C5×C4⋊(#41⋊C3)2
C5×#548⋊C32
C5×#520⋊C32
C5×#519⋊C32
C4×C5×#41⋊C32
C5×#35243
C3×C5×#1264
#3524⋊C35