Finite Group Databasebeta

← C5×#85310 #14511048

Subgroups — C5×#85310 #14511048

Order 1920.

854 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 92 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×C5×C4⋊S4C212yesmaximal, complemented
2C2×C5×C4⋊S4C211yesmaximal, characteristic, complemented
3C2×C4×C5×S4C211yesmaximal, characteristic, complemented
4C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×(C2×S4)⋊C4C212yesmaximal, complemented
6C5×#2416—31nomaximal, Hall
7C22×C5×S4C2212yes—
8C22×C5×S4C2211yescharacteristic
9C2×C4×C5×A4C2212yes—
10C2×C4×C5×A4C2211yescharacteristic
11C2×C5×SL(2,ℤ/4)C2211yescharacteristic
12C5×C4⋊S4—24no—
13C5×C4⋊S4—22no—
14C4×C5×S4—22no—
15C5×#895—41nomaximal
16#85310C511yesmaximal, characteristic, direct product factor, Hall
17C2×C5×#121—31no—
18C2×C5×#121—32no—
19C2×C5×#121—31no—
20C2×C4×C5×D4—31no—
21C22×C5×C4⋊C4D311yescharacteristic, complemented
22C5×#396—32no—
23C5×#394—32no—
24C5×#390—31no—
25C5×#389—31no—
26C5×#386—32no—
27C5×#380—31no—
28C22×C5×A4C2311yescharacteristic
29C2×C5×S4—21no—
30C2×C5×S4—21no—
31C2×C5×S4—22no—
32C2×C5×S4—22no—
33C2×C5×S4—22no—
34C2×C5×S4D412yescomplemented
35C2×C5×D12—41no—
36C2×C5×D12—42no—
37C2×C4×C5×D3—41no—
38C4×C5×A4—22no—
39C4×C5×A4D412yescomplemented
40C5×SL(2,ℤ/4)—21no—
41C3×C5×C4⋊C4—41no—
42C5×(C2×D3)⋊C4—42no—
43C2×C4⋊S4C2×C512yescomplemented
44C2×C4⋊S4C2×C511yescharacteristic, complemented
45C2×C4×S4C2×C511yescharacteristic, complemented
46A4×C4⋊C4C2×C511yescharacteristic, complemented
47(C2×S4)⋊C4C2×C512yescomplemented
48C22×C5×D4—31no—
49C22×C5×D4—31no—
50C22×C5×D4—32no—
51C22×C5×D4—32no—
52C23×C4×C5—31no—
53C23×C4×C5C2×D312yes—
54C23×C4×C5C2×D311yescharacteristic
55C5×#121—61no—
56C5×#121—62no—
57C5×#121—64no—
58C5×#121—62no—
59C5×#121—64no—
60C5×#121—62no—
61C5×#121—61no—
62C4×C5×D4—62no—
63C4×C5×D4—62no—
64C2×C5×C4⋊C4—31no—
65C2×C5×C4⋊C4—31no—
66C2×C5×C4⋊C4—32no—
67C2×C5×C4⋊C4—31no—
68C2×C5×C4⋊C4—32no—
69C2×C5×C4⋊C4—31no—
70C2×C5×C22⋊C4—32no—
71C2×C5×C22⋊C4—32no—
72C2×C5×C22⋊C4—32no—
73C2×C5×C22⋊C4—31no—
74C2×C5×C22⋊C4—32no—
75C2×C5×C22⋊C4—31no—
76C2×C5×C22⋊C4—32no—
77C2×C42×C5—31no—
78C5×#95—32no—
79C5×#95—32no—
80#2416—31noSylow
81C22×C5×D3—41no—
82C22×C5×D3—42no—
83C2×C5×A4C2×D411yescharacteristic
84C2×C5×A4C2×D411yescharacteristic
85C2×C5×A4#4111yescharacteristic
86C5×S4—22no—
87C5×S4—42no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—42no—
90C2×C5×Dic3—41no—
91C5×D12—82no—
92C5×D12—84no—
93C4×C5×D3—82no—
94C22×S4C22×C512yes—
95C22×S4C22×C511yescharacteristic
96C2×C4×A4C22×C512yes—
97C2×C4×A4C22×C511yescharacteristic
98C2×SL(2,ℤ/4)C22×C511yescharacteristic
99C4⋊S4—24no—
100C4⋊S4—22no—
101C4×S4—22no—
102#895—41no—
103C24×C5—31no—
104C24×C5—32no—
105C24×C5C22×D311yescharacteristic
106C2×C5×D4—32no—
107C2×C5×D4—32no—
108C2×C5×D4—61no—
109C2×C5×D4—62no—
110C2×C5×D4—62no—
111C2×C5×D4—62no—
112C2×C5×D4—61no—
113C2×C5×D4—61no—
114C2×C5×D4—61no—
115C2×C5×D4—61no—
116C2×C5×D4—64no—
117C2×C5×D4—62no—
118C2×C5×D4—62no—
119C2×C5×D4—62no—
120C2×C5×D4—62no—
121C2×C5×D4—62no—
122C2×C5×D4—62no—
123C2×C5×D4—62no—
124C2×C5×D4—61no—
125C2×C5×D4—122no—
126C22×C4×C5—22no—
127C22×C4×C5—31no—
128C22×C4×C5—31no—
129C22×C4×C5—32no—
130C22×C4×C5—31no—
131C22×C4×C5—32no—
132C22×C4×C5—32no—
133C22×C4×C5—31no—
134C22×C4×C5—31no—
135C22×C4×C5—32no—
136C22×C4×C5—62no—
137C22×C4×C5—61no—
138C22×C4×C5—62no—
139C22×C4×C5—62no—
140C22×C4×C5—61no—
141C22×C4×C5D1212yescomplemented
142C5×C4⋊C4—32no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—62no—
146C5×C4⋊C4—62no—
147C5×C4⋊C4—64no—
148C5×C4⋊C4S411yescharacteristic, complemented
149C5×C22⋊C4—62no—
150C5×C22⋊C4—64no—
151C5×C22⋊C4—64no—
152C5×C22⋊C4—62no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—64no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—62no—
157C5×C22⋊C4—122no—
158C42×C5—62no—
159C2×#121—31no—
160C2×#121—32no—
161C2×#121—31no—
162C2×C4×D4—31no—
163C22×C4⋊C4C5×D311yescharacteristic, complemented
164#396—32no—
165#394—32no—
166#390—31no—
167#389—31no—
168#386—32no—
169#380—31no—
170C22×C3×C5—41no—
171C2×C5×D3—42no—
172C2×C5×D3—81no—
173C2×C5×D3—81no—
174C2×C5×D3—82no—
175C2×C5×D3—82no—
176C2×C5×D3—82no—
177C5×A4#12111yescharacteristic, complemented
178C3×C4×C5—42no—
179C3×C4×C5—82no—
180C5×Dic3—81no—
181C22×A4C23×C511yescharacteristic
182C2×S4—21no—
183C2×S4—21no—
184C2×S4—22no—
185C2×S4—22no—
186C2×S4—22no—
187C2×S4C5×D412yescomplemented
188C2×D12—41no—
189C2×D12—42no—
190C2×C4×D3—41no—
191C4×A4—22no—
192C4×A4C5×D412yescomplemented
193SL(2,ℤ/4)—21no—
194C3×C4⋊C4—41no—
195(C2×D3)⋊C4—42no—
196C23×C5—31no—
197C23×C5—31no—
198C23×C5—31no—
199C23×C5—31no—
200C23×C5—32no—
201C23×C5—61no—
202C23×C5—61no—
203C23×C5—61no—
204C23×C5—61no—
205C23×C5—61no—
206C23×C5—62no—
207C23×C5—62no—
208C23×C5—62no—
209C23×C5—62no—
210C23×C5—62no—
211C23×C5—62no—
212C23×C5—61no—
213C23×C5—62no—
214C23×C5C2×D1211yescharacteristic
215C23×C5D3×D411yescharacteristic
216C23×C5#23911yescharacteristic
217C5×D4—62no—
218C5×D4—62no—
219C5×D4—62no—
220C5×D4—62no—
221C5×D4—124no—
222C5×D4—122no—
223C5×D4—124no—
224C5×D4—122no—
225C5×D4—122no—
226C5×D4—122no—
227C5×D4—122no—
228C5×D4—122no—
229C2×C4×C5—31no—
230C2×C4×C5—32no—
231C2×C4×C5—32no—
232C2×C4×C5—32no—
233C2×C4×C5—32no—
234C2×C4×C5—32no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5—61no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5—62no—
250C2×C4×C5—61no—
251C2×C4×C5—122no—
252C2×C4×C5—122no—
253C2×C4×C5C2×S412yes—
254C2×C4×C5C2×S411yescharacteristic
255C22×D4—31no—
256C22×D4—31no—
257C22×D4—32no—
258C22×D4—32no—
259C23×C4—31no—
260C23×C4C2×C5×D312yes—
261C23×C4C2×C5×D311yescharacteristic
262#121—61no—
263#121—62no—
264#121—64no—
265#121—62no—
266#121—64no—
267#121—62no—
268#121—61no—
269C4×D4—62no—
270C4×D4—62no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—32no—
277C2×C22⋊C4—31no—
278C2×C22⋊C4—32no—
279C2×C22⋊C4—32no—
280C2×C22⋊C4—32no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—31no—
283C2×C22⋊C4—32no—
284C2×C42—31no—
285#95—32no—
286#95—32no—
287C2×C3×C5—41no—
288C2×C3×C5—41no—
289C2×C3×C5—41no—
290C5×D3—82no—
291C5×D3—162no—
292C22×D3—41no—
293C22×D3—42no—
294C2×A4C2×C5×D411yescharacteristic
295C2×A4C2×C5×D411yescharacteristic
296C2×A4C5×#4111yescharacteristic
297S4—22no—
298S4—42no—
299C2×C3×C4—41no—
300C2×C3×C4—42no—
301C2×Dic3—41no—
302D12—82no—
303D12—84no—
304C4×D3—82no—
305C22×C5—31no—
306C22×C5—31no—
307C22×C5—31no—
308C22×C5—31no—
309C22×C5—31no—
310C22×C5—31no—
311C22×C5—31no—
312C22×C5—31no—
313C22×C5—31no—
314C22×C5—61no—
315C22×C5—62no—
316C22×C5—62no—
317C22×C5—62no—
318C22×C5—121no—
319C22×C5—121no—
320C22×C5—122no—
321C22×C5—122no—
322C22×C5—122no—
323C22×C5—122no—
324C22×C5—121no—
325C22×C5—121no—
326C22×C5—122no—
327C22×C5—122no—
328C22×C5—122no—
329C22×C5#89511yescharacteristic, complemented
330C22×C5C22×S411yescharacteristic
331C4×C5—22no—
332C4×C5—32no—
333C4×C5—62no—
334C4×C5—62no—
335C4×C5—121no—
336C4×C5—122no—
337C4×C5—121no—
338C4×C5C4⋊S412yescomplemented
339C24—31no—
340C24—32no—
341C24C22×C5×D311yescharacteristic
342C2×D4—32no—
343C2×D4—32no—
344C2×D4—61no—
345C2×D4—62no—
346C2×D4—62no—
347C2×D4—62no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—64no—
353C2×D4—62no—
354C2×D4—62no—
355C2×D4—62no—
356C2×D4—62no—
357C2×D4—62no—
358C2×D4—62no—
359C2×D4—62no—
360C2×D4—61no—
361C2×D4—122no—
362C22×C4—22no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—32no—
366C22×C4—31no—
367C22×C4—32no—
368C22×C4—32no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—32no—
372C22×C4—62no—
373C22×C4—61no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—61no—
377C22×C4C5×D1212yescomplemented
378C4⋊C4—32no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4—62no—
382C4⋊C4—62no—
383C4⋊C4—64no—
384C4⋊C4C5×S411yescharacteristic, complemented
385C22⋊C4—62no—
386C22⋊C4—64no—
387C22⋊C4—64no—
388C22⋊C4—62no—
389C22⋊C4—61no—
390C22⋊C4—64no—
391C22⋊C4—61no—
392C22⋊C4—62no—
393C22⋊C4—122no—
394C42—62no—
395C3×C5—41noHall
396C22×C3—41no—
397C2×D3—42no—
398C2×D3—81no—
399C2×D3—81no—
400C2×D3—82no—
401C2×D3—82no—
402C2×D3—82no—
403A4C5×#12111yescharacteristic, complemented
404C3×C4—42no—
405C3×C4—82no—
406Dic3—81no—
407C2×C5—31no—
408C2×C5—31no—
409C2×C5—31no—
410C2×C5—31no—
411C2×C5—122no—
412C2×C5—242no—
413C2×C5C2×C4⋊S411yescharacteristic
414C2×C5D4×S411yescharacteristic
415C2×C5#591911yescharacteristic
416C23—31no—
417C23—31no—
418C23—31no—
419C23—31no—
420C23—32no—
421C23—61no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—61no—
426C23—62no—
427C23—62no—
428C23—62no—
429C23—62no—
430C23—62no—
431C23—62no—
432C23—61no—
433C23—62no—
434C23C2×C5×D1211yescharacteristic
435C23C5×D3×D411yescharacteristic
436C23C5×#23911yescharacteristic
437D4—62no—
438D4—62no—
439D4—62no—
440D4—62no—
441D4—124no—
442D4—122no—
443D4—124no—
444D4—122no—
445D4—122no—
446D4—122no—
447D4—122no—
448D4—122no—
449C2×C4—31no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4C2×C5×S412yes—
474C2×C4C2×C5×S411yescharacteristic
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—41no—
478D3—82no—
479D3—162no—
480C5#8531011yescharacteristic, direct product factor, Sylow
481C22—31no—
482C22—31no—
483C22—31no—
484C22—31no—
485C22—31no—
486C22—31no—
487C22—31no—
488C22—31no—
489C22—31no—
490C22—61no—
491C22—62no—
492C22—62no—
493C22—62no—
494C22—121no—
495C22—121no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22—122no—
500C22—121no—
501C22—121no—
502C22—122no—
503C22—122no—
504C22—122no—
505C22C5×#89511yescharacteristic, complemented
506C22C22×C5×S411yescharacteristic
507C4—22no—
508C4—32no—
509C4—62no—
510C4—62no—
511C4—122no—
512C4—121no—
513C4—121no—
514C4C5×C4⋊S412yescomplemented
515C3—41noSylow
516C2—31no—
517C2—31no—
518C2—31no—
519C2—31no—
520C2—122no—
521C2—242no—
522C2C2×C5×C4⋊S411yescharacteristic
523C2C5×D4×S411yescharacteristic
524C2C5×#591911yescharacteristic
subgroupG/H
centerC22×C5C22×S4
commutator, cosocleC22×A4C23×C5
FrattiniC22C22×C5×S4
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
hypercenterC5×C4⋊C4S4
hypocenterA4C5×#121
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×C4⋊S4C2semidirect
2. C2×C5×C4⋊S4C2semidirect
3. C2×C4×C5×S4C2semidirect
4. C5×A4×C4⋊C4C2semidirect
5. C5×(C2×S4)⋊C4C2semidirect
16. #85310C5direct (N × H)
21. C22×C5×C4⋊C4D3semidirect
34. C2×C5×S4D4semidirect
39. C4×C5×A4D4semidirect
43. C2×C4⋊S4C2×C5semidirect
44. C2×C4⋊S4C2×C5semidirect
45. C2×C4×S4C2×C5semidirect
46. A4×C4⋊C4C2×C5semidirect
47. (C2×S4)⋊C4C2×C5semidirect
141. C22×C4×C5D12semidirect
148. C5×C4⋊C4S4semidirect
163. C22×C4⋊C4C5×D3semidirect
177. C5×A4#121semidirect
187. C2×S4C5×D4semidirect
192. C4×A4C5×D4semidirect
329. C22×C5#895semidirect
338. C4×C5C4⋊S4semidirect
377. C22×C4C5×D12semidirect
384. C4⋊C4C5×S4semidirect
403. A4C5×#121semidirect
480. C5#85310direct (N × H)
505. C22C5×#895semidirect
514. C4C5×C4⋊S4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊S42
C2×C4×C5×S42
C5×A4×C4⋊C42
C5×(C2×S4)⋊C42
C5×#24163
C5×#8954
#853105