Finite Group Databasebeta

← C5×#85443 #14511181

Subgroups — C5×#85443 #14511181

Order 1920.

598 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×#5912C211yesmaximal, characteristic, complemented
2C2×C5×C4⋊S4C211yesmaximal, characteristic, complemented
3C5×A4×M16C211yesmaximal, characteristic, complemented
4C5×#5402C212yesmaximal, complemented
5C5×#5401C212yesmaximal, complemented
6C5×#3055—31nomaximal, Hall
7C22×C5×S4—21no—
8C2×C4×C5×A4C2211yescharacteristic
9C5×GL(2,ℤ/4)—21no—
10C5×C4⋊S4—21no—
11C5×C4⋊S4C2212yes—
12C5×C4⋊S4C2211yescharacteristic, complemented
13C4×C5×S4—21no—
14C5×A4⋊Q8C2211yescharacteristic, complemented
15C5×#908—41nomaximal
16C5×C8×A4C2212yescomplemented
17#85443C511yesmaximal, characteristic, direct product factor, Hall
18C2×C5×AGL(1,ℤ/8)—31no—
19C22×C5×M16D311yescharacteristic, complemented
20C5×#525—31no—
21C2×C5×#121—31no—
22C5×#469—32no—
23C5×#468—32no—
24C5×#466—32no—
25C5×#465—32no—
26C5×#428—31no—
27C5×#418—31no—
28C5×#417—31no—
29C22×C5×A4D411yescharacteristic
30C2×C5×S4—21no—
31C2×C5×S4—22no—
32C2×C5×S4—42no—
33C5×#235—41no—
34C2×C5×D12—41no—
35C4×C5×A4D411yescharacteristic
36C4×C5×A4C2311yescharacteristic
37C5×SL(2,ℤ/4)—21no—
38C3×C5×M16—41no—
39C5×D24—42no—
40C5×#204—42no—
41#5912C2×C511yescharacteristic, complemented
42C2×C4⋊S4C2×C511yescharacteristic, complemented
43A4×M16C2×C511yescharacteristic, complemented
44#5402C2×C512yescomplemented
45#5401C2×C512yescomplemented
46C2×C5×#41—31no—
47C22×C5×D4—31no—
48C22×C5×D4—61no—
49C23×C4×C5C2×D311yescharacteristic
50C5×AGL(1,ℤ/8)—61no—
51C5×AGL(1,ℤ/8)—62no—
52C5×AGL(1,ℤ/8)—61no—
53C2×C5×SD16—32no—
54C2×C5×D8—32no—
55C2×C5×M16—31no—
56C2×C5×M16—31no—
57C2×C5×M16—32no—
58C22×C5×C8C2×D312yescomplemented
59C5×#123—61no—
60C5×C22⋊Q8—31no—
61C5×C22⋊Q8—31no—
62C5×#121—32no—
63C5×#121—31no—
64C5×#121—32no—
65C5×#121—31no—
66C5×#121—61no—
67C5×#121—61no—
68C5×#120—61no—
69C4×C5×D4—61no—
70C4×C5×D4—61no—
71C5×#117—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C22⋊C4—61no—
74C5×#107—32no—
75C5×#106—32no—
76C5×#103—32no—
77C5×#102—32no—
78C5×#102—32no—
79C5×#102—32no—
80#3055—31noSylow
81C22×C5×D3—81no—
82C2×C5×A4—21no—
83C2×C5×A4C2×D411yescharacteristic
84C5×S4—41no—
85C5×S4—42no—
86C2×C3×C4×C5—41no—
87C5×#67—81no—
88C5×D12—42no—
89C5×D12—41no—
90C5×D12—81no—
91C4×C5×D3—81no—
92C5×Dic6—41no—
93C3×C5×C8—42no—
94C22×S4—21no—
95C2×C4×A4C22×C511yescharacteristic
96GL(2,ℤ/4)—21no—
97C4⋊S4—21no—
98C4⋊S4C22×C512yes—
99C4⋊S4C22×C511yescharacteristic, complemented
100C4×S4—21no—
101A4⋊Q8C22×C511yescharacteristic, complemented
102#908—41no—
103C8×A4C22×C512yescomplemented
104C24×C5—61no—
105C24×C5D1211yescharacteristic
106C5×#41—61no—
107C5×#41—61no—
108C5×#41—61no—
109C5×#41—61no—
110C2×C5×Q8—31no—
111C2×C5×D4—31no—
112C2×C5×D4—32no—
113C2×C5×D4—61no—
114C2×C5×D4—61no—
115C2×C5×D4—61no—
116C2×C5×D4—61no—
117C2×C5×D4—61no—
118C2×C5×D4—61no—
119C2×C5×D4—62no—
120C2×C5×D4—61no—
121C2×C5×D4—62no—
122C2×C5×D4—61no—
123C2×C5×D4—122no—
124C2×C5×D4—122no—
125C22×C4×C5—31no—
126C22×C4×C5—31no—
127C22×C4×C5—31no—
128C22×C4×C5—31no—
129C22×C4×C5—61no—
130C22×C4×C5—61no—
131C22×C4×C5D1211yescharacteristic
132C22×C4×C5C22×D311yescharacteristic
133C5×SD16—62no—
134C5×SD16—62no—
135C5×D8—62no—
136C5×D8—62no—
137C5×M16—31no—
138C5×M16—32no—
139C5×M16—61no—
140C5×M16S411yescharacteristic, complemented
141C2×C5×C8—32no—
142C2×C5×C8—32no—
143C5×C4⋊C4—32no—
144C5×C4⋊C4—31no—
145C5×C4⋊C4—31no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C22⋊C4—62no—
150C5×C22⋊C4—62no—
151C5×C22⋊C4—61no—
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C42×C5—61no—
157C2×AGL(1,ℤ/8)—31no—
158C22×M16C5×D311yescharacteristic, complemented
159#525—31no—
160C2×#121—31no—
161#469—32no—
162#468—32no—
163#466—32no—
164#465—32no—
165#428—31no—
166#418—31no—
167#417—31no—
168C22×C3×C5—41no—
169C2×C5×D3—81no—
170C2×C5×D3—82no—
171C2×C5×D3—162no—
172C5×A4AGL(1,ℤ/8)11yescharacteristic, complemented
173C3×C4×C5—41no—
174C3×C4×C5—41no—
175C5×Dic3—81no—
176C22×A4C5×D411yescharacteristic
177C2×S4—21no—
178C2×S4—22no—
179C2×S4—42no—
180#235—41no—
181C2×D12—41no—
182C4×A4C5×D411yescharacteristic
183C4×A4C23×C511yescharacteristic
184SL(2,ℤ/4)—21no—
185C3×M16—41no—
186D24—42no—
187#204—42no—
188C23×C5—21no—
189C23×C5—31no—
190C23×C5—31no—
191C23×C5—61no—
192C23×C5—61no—
193C23×C5—62no—
194C23×C5—121no—
195C23×C5—122no—
196C23×C5—122no—
197C23×C5—121no—
198C23×C5C2×D1211yescharacteristic
199C5×Q8—61no—
200C5×Q8—61no—
201C5×D4—62no—
202C5×D4—61no—
203C5×D4—61no—
204C5×D4—62no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—122no—
208C5×D4—121no—
209C5×D4—122no—
210C5×D4—124no—
211C5×D4—121no—
212C5×D4—122no—
213C5×D4—121no—
214C5×D4—121no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5—62no—
226C2×C4×C5—61no—
227C2×C4×C5—121no—
228C2×C4×C5—122no—
229C2×C4×C5—121no—
230C2×C4×C5C2×S411yescharacteristic
231C5×C8—32no—
232C5×C8C2×S412yescomplemented
233C2×#41—31no—
234C22×D4—31no—
235C22×D4—61no—
236C23×C4C2×C5×D311yescharacteristic
237AGL(1,ℤ/8)—61no—
238AGL(1,ℤ/8)—62no—
239AGL(1,ℤ/8)—61no—
240C2×SD16—32no—
241C2×D8—32no—
242C2×M16—31no—
243C2×M16—31no—
244C2×M16—32no—
245C22×C8C2×C5×D312yescomplemented
246#123—61no—
247C22⋊Q8—31no—
248C22⋊Q8—31no—
249#121—32no—
250#121—31no—
251#121—32no—
252#121—31no—
253#121—61no—
254#121—61no—
255#120—61no—
256C4×D4—61no—
257C4×D4—61no—
258#117—31no—
259C2×C4⋊C4—31no—
260C2×C22⋊C4—61no—
261#107—32no—
262#106—32no—
263#103—32no—
264#102—32no—
265#102—32no—
266#102—32no—
267C2×C3×C5—41no—
268C2×C3×C5—81no—
269C5×D3—162no—
270C5×D3—161no—
271C22×D3—81no—
272C2×A4—21no—
273C2×A4C2×C5×D411yescharacteristic
274S4—41no—
275S4—42no—
276C2×C3×C4—41no—
277#67—81no—
278D12—42no—
279D12—41no—
280D12—81no—
281C4×D3—81no—
282Dic6—41no—
283C3×C8—42no—
284C22×C5—31no—
285C22×C5—31no—
286C22×C5—31no—
287C22×C5—61no—
288C22×C5—61no—
289C22×C5—61no—
290C22×C5—61no—
291C22×C5—122no—
292C22×C5—121no—
293C22×C5—121no—
294C22×C5—122no—
295C22×C5—121no—
296C22×C5—122no—
297C22×C5—242no—
298C22×C5—242no—
299C22×C5#90811yescharacteristic, complemented
300C22×C5C4⋊S411yescharacteristic
301C4×C5—31no—
302C4×C5—31no—
303C4×C5—122no—
304C4×C5—121no—
305C4×C5—121no—
306C4×C5—121no—
307C4×C5C4⋊S411yescharacteristic
308C4×C5C22×S411yescharacteristic
309C24—61no—
310C24C5×D1211yescharacteristic
311#41—61no—
312#41—61no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×D4—31no—
317C2×D4—32no—
318C2×D4—61no—
319C2×D4—61no—
320C2×D4—61no—
321C2×D4—61no—
322C2×D4—61no—
323C2×D4—61no—
324C2×D4—62no—
325C2×D4—61no—
326C2×D4—62no—
327C2×D4—61no—
328C2×D4—122no—
329C2×D4—122no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—61no—
335C22×C4—61no—
336C22×C4C5×D1211yescharacteristic
337C22×C4C22×C5×D311yescharacteristic
338SD16—62no—
339SD16—62no—
340D8—62no—
341D8—62no—
342M16—31no—
343M16—32no—
344M16—61no—
345M16C5×S411yescharacteristic, complemented
346C2×C8—32no—
347C2×C8—32no—
348C4⋊C4—31no—
349C4⋊C4—31no—
350C4⋊C4—32no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C22⋊C4—62no—
355C22⋊C4—62no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C42—61no—
362C3×C5—41noHall
363C22×C3—41no—
364C2×D3—81no—
365C2×D3—82no—
366C2×D3—162no—
367A4C5×AGL(1,ℤ/8)11yescharacteristic, complemented
368C3×C4—41no—
369C3×C4—41no—
370Dic3—81no—
371C2×C5—21no—
372C2×C5—31no—
373C2×C5—31no—
374C2×C5—61no—
375C2×C5—242no—
376C2×C5—241no—
377C2×C5C2×C4⋊S411yescharacteristic
378C23—21no—
379C23—31no—
380C23—31no—
381C23—61no—
382C23—61no—
383C23—62no—
384C23—121no—
385C23—122no—
386C23—122no—
387C23—121no—
388C23C2×C5×D1211yescharacteristic
389Q8—61no—
390Q8—61no—
391D4—62no—
392D4—61no—
393D4—61no—
394D4—62no—
395D4—121no—
396D4—122no—
397D4—121no—
398D4—121no—
399D4—124no—
400D4—122no—
401D4—121no—
402D4—122no—
403D4—121no—
404D4—121no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—62no—
416C2×C4—61no—
417C2×C4—121no—
418C2×C4—122no—
419C2×C4—121no—
420C2×C4C2×C5×S411yescharacteristic
421C8—32no—
422C8C2×C5×S412yescomplemented
423C2×C3—41no—
424C2×C3—81no—
425D3—162no—
426D3—161no—
427C5#8544311yescharacteristic, direct product factor, Sylow
428C22—31no—
429C22—31no—
430C22—31no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—61no—
435C22—122no—
436C22—121no—
437C22—121no—
438C22—122no—
439C22—121no—
440C22—122no—
441C22—242no—
442C22—242no—
443C22C5×#90811yescharacteristic, complemented
444C22C5×C4⋊S411yescharacteristic
445C4—31no—
446C4—31no—
447C4—122no—
448C4—121no—
449C4—121no—
450C4—121no—
451C4C5×C4⋊S411yescharacteristic
452C4C22×C5×S411yescharacteristic
453C3—41noSylow
454C2—21no—
455C2—31no—
456C2—31no—
457C2—61no—
458C2—242no—
459C2—241no—
460C2C2×C5×C4⋊S411yescharacteristic
subgroupG/H
centerC2×C5C2×C4⋊S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×M16D3
socleC23×C5C2×D12
hypercenterC5×M16S4
hypocenterA4C5×AGL(1,ℤ/8)
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×M16

Complements

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

NH ≅ G/Ntype
1. C5×#5912C2semidirect
2. C2×C5×C4⋊S4C2semidirect
3. C5×A4×M16C2semidirect
4. C5×#5402C2semidirect
5. C5×#5401C2semidirect
12. C5×C4⋊S4C22semidirect
14. C5×A4⋊Q8C22semidirect
16. C5×C8×A4C22semidirect
17. #85443C5direct (N × H)
19. C22×C5×M16D3semidirect
41. #5912C2×C5semidirect
42. C2×C4⋊S4C2×C5semidirect
43. A4×M16C2×C5semidirect
44. #5402C2×C5semidirect
45. #5401C2×C5semidirect
58. C22×C5×C8C2×D3semidirect
99. C4⋊S4C22×C5semidirect
101. A4⋊Q8C22×C5semidirect
103. C8×A4C22×C5semidirect
140. C5×M16S4semidirect
158. C22×M16C5×D3semidirect
172. C5×A4AGL(1,ℤ/8)semidirect
232. C5×C8C2×S4semidirect
245. C22×C8C2×C5×D3semidirect
299. C22×C5#908semidirect
345. M16C5×S4semidirect
367. A4C5×AGL(1,ℤ/8)semidirect
422. C8C2×C5×S4semidirect
427. C5#85443direct (N × H)
443. C22C5×#908semidirect

Maximal subgroups

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

subgroupindex
C5×#59122
C2×C5×C4⋊S42
C5×A4×M162
C5×#54022
C5×#54012
C5×#30553
C5×#9084
#854435