Finite Group Databasebeta

← C5×#85461 #14511199

Subgroups — C5×#85461 #14511199

Order 1920.

528 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q8×S4C211yesmaximal, characteristic, complemented
2C5×#5914C211yesmaximal, characteristic
3C5×A4×SD16C211yesmaximal, characteristic, complemented
4C5×#5416C211yesmaximal, characteristic, complemented
5C5×#5414C211yesmaximal, characteristic, complemented
6C5×#5400C211yesmaximal, characteristic, complemented
7C5×#5398C211yesmaximal, characteristic, complemented
8C5×#3266—31nomaximal, Hall
9C5×Q8×A4C2211yescharacteristic
10C5×D4×A4C2211yescharacteristic
11C5×GL(2,ℤ/4)—21no—
12C2×C5×SL(2,ℤ/4)—21no—
13C4×C5×S4—21no—
14C4×C5×S4C2211yescharacteristic
15C5×A4⋊Q8—21no—
16C5×A4⋊Q8C2211yescharacteristic
17C5×A4⋊Q8C2211yescharacteristic
18C5×#915—41nomaximal
19C5×C8×A4C2211yescharacteristic
20C5×A4⋊C8C2211yescharacteristic
21#85461C511yesmaximal, characteristic, direct product factor, Hall
22C2×C5×#137—31no—
23C22×C5×SD16D311yescharacteristic, complemented
24C5×D4×Q8—31no—
25C5×#546—31no—
26C5×#497—31no—
27C5×#468—31no—
28C5×#467—31no—
29C5×#464—31no—
30C5×#461—31no—
31C5×#452—31no—
32C5×#451—31no—
33C5×#450—31no—
34C5×#448—31no—
35C5×#440—31no—
36C5×#435—31no—
37C22×C5×A4—21no—
38C2×C5×S4D411yescharacteristic
39C5×D3×Q8—41no—
40C5×#237—41no—
41C4×C5×A4—21no—
42C4×C5×A4C2311yescharacteristic
43C5×SL(2,ℤ/4)—21no—
44C5×SL(2,ℤ/4)—21no—
45C5×SL(2,ℤ/4)D411yescharacteristic
46C3×C5×SD16—41no—
47C5×#216—41no—
48C5×#214—41no—
49C5×Dic12—41no—
50C5×ΓL(1,𝔽25)—41no—
51Q8×S4C2×C511yescharacteristic, complemented
52#5914C2×C511yescharacteristic
53A4×SD16C2×C511yescharacteristic, complemented
54#5416C2×C511yescharacteristic, complemented
55#5414C2×C511yescharacteristic, complemented
56#5400C2×C511yescharacteristic, complemented
57#5398C2×C511yescharacteristic, complemented
58C2×C5×#41—31no—
59C22×C5×Q8—31no—
60C22×C5×Q8C2×D311yescharacteristic
61C22×C5×D4C2×D311yescharacteristic
62C5×#137—61no—
63C5×#137—61no—
64C5×#137—61no—
65C5×#137—61no—
66C2×C5×Q16—31no—
67C2×C5×Q16—31no—
68C2×C5×Q16—31no—
69C2×C5×SD16—31no—
70C2×C5×SD16—31no—
71C2×C5×SD16—31no—
72C2×C5×SD16—31no—
73C2×C5×SD16—31no—
74C2×C5×SD16—31no—
75C2×C5×M16—31no—
76C22×C5×C8C2×D311yescharacteristic
77C5×C4⋊Q8—31no—
78C5×C4⋊Q8—61no—
79C5×#124—31no—
80C5×#123—61no—
81C5×C22⋊Q8—31no—
82C5×C22⋊Q8—31no—
83C5×C22⋊Q8—31no—
84C5×C22⋊Q8—61no—
85C5×C22⋊Q8—61no—
86C5×#121—31no—
87C5×#121—61no—
88C5×#120—61no—
89C4×C5×Q8—31no—
90C4×C5×D4—31no—
91C4×C5×D4—31no—
92C4×C5×D4—61no—
93C2×C5×C22⋊C4—61no—
94C5×#107—31no—
95C5×C4⋊C8—31no—
96C5×#103—31no—
97C5×#103—31no—
98C5×#103—31no—
99C5×#103—31no—
100C5×#102—31no—
101C5×#102—31no—
102C5×C22⋊C8—31no—
103C5×C22⋊C8—31no—
104C5×#97—31no—
105#3266—31noSylow
106C2×C5×A4—41no—
107C2×C5×A4C2×D411yescharacteristic
108C5×S4—21no—
109C3×C5×Q8—41no—
110C3×C5×D4—41no—
111C5×#67—81no—
112C2×C5×Dic3—81no—
113C4×C5×D3—41no—
114C4×C5×D3—81no—
115C5×Dic6—41no—
116C5×Dic6—41no—
117C5×Dic6—81no—
118C3×C5×C8—41no—
119C5×C3⋊C8—41no—
120Q8×A4C22×C511yescharacteristic
121D4×A4C22×C511yescharacteristic
122GL(2,ℤ/4)—21no—
123C2×SL(2,ℤ/4)—21no—
124C4×S4—21no—
125C4×S4C22×C511yescharacteristic
126A4⋊Q8—21no—
127A4⋊Q8C22×C511yescharacteristic
128A4⋊Q8C22×C511yescharacteristic
129#915—41no—
130C8×A4C22×C511yescharacteristic
131A4⋊C8C22×C511yescharacteristic
132C24×C5—21no—
133C5×#41—61no—
134C5×#41—61no—
135C5×#41—121no—
136C2×C5×Q8—31no—
137C2×C5×Q8—31no—
138C2×C5×Q8—31no—
139C2×C5×Q8—31no—
140C2×C5×Q8—61no—
141C2×C5×Q8—61no—
142C2×C5×Q8—61no—
143C2×C5×Q8—61no—
144C2×C5×Q8—121no—
145C2×C5×D4—31no—
146C2×C5×D4—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C22×C4×C5—21no—
152C22×C4×C5—31no—
153C22×C4×C5—61no—
154C22×C4×C5—61no—
155C22×C4×C5—61no—
156C22×C4×C5C22×D311yescharacteristic
157C5×Q16—61no—
158C5×Q16—61no—
159C5×Q16—61no—
160C5×Q16—61no—
161C5×Q16—121no—
162C5×SD16—31no—
163C5×SD16—31no—
164C5×SD16—31no—
165C5×SD16—61no—
166C5×SD16—61no—
167C5×SD16—61no—
168C5×SD16—121no—
169C5×SD16S411yescharacteristic, complemented
170C5×M16—61no—
171C5×M16—61no—
172C2×C5×C8—31no—
173C2×C5×C8—31no—
174C2×C5×C8—31no—
175C2×C5×C8—31no—
176C5×C4⋊C4—31no—
177C5×C4⋊C4—31no—
178C5×C4⋊C4—31no—
179C5×C4⋊C4—61no—
180C5×C4⋊C4—61no—
181C5×C4⋊C4—61no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4—61no—
185C5×C22⋊C4—31no—
186C5×C22⋊C4—31no—
187C5×C22⋊C4—61no—
188C5×C22⋊C4—61no—
189C5×C22⋊C4—61no—
190C5×C22⋊C4—61no—
191C5×C22⋊C4—61no—
192C5×C22⋊C4—61no—
193C5×C22⋊C4—61no—
194C42×C5—31no—
195C42×C5—61no—
196C2×#137—31no—
197C22×SD16C5×D311yescharacteristic, complemented
198D4×Q8—31no—
199#546—31no—
200#497—31no—
201#468—31no—
202#467—31no—
203#464—31no—
204#461—31no—
205#452—31no—
206#451—31no—
207#450—31no—
208#448—31no—
209#440—31no—
210#435—31no—
211C22×C3×C5—81no—
212C2×C5×D3—41no—
213C5×A4#13711yescharacteristic, complemented
214C3×C4×C5—41no—
215C3×C4×C5—81no—
216C5×Dic3—41no—
217C5×Dic3—81no—
218C5×Dic3—81no—
219C22×A4—21no—
220C2×S4C5×D411yescharacteristic
221D3×Q8—41no—
222#237—41no—
223C4×A4—21no—
224C4×A4C23×C511yescharacteristic
225SL(2,ℤ/4)—21no—
226SL(2,ℤ/4)—21no—
227SL(2,ℤ/4)C5×D411yescharacteristic
228C3×SD16—41no—
229#216—41no—
230#214—41no—
231Dic12—41no—
232ΓL(1,𝔽25)—41no—
233C23×C5—31no—
234C23×C5—41no—
235C23×C5—61no—
236C23×C5—61no—
237C23×C5—121no—
238C23×C5D3×D411yescharacteristic
239C5×Q8—31no—
240C5×Q8—61no—
241C5×Q8—61no—
242C5×Q8—61no—
243C5×Q8—61no—
244C5×Q8—61no—
245C5×Q8—61no—
246C5×Q8—121no—
247C5×Q8—121no—
248C5×Q8C2×S411yescharacteristic
249C5×D4—31no—
250C5×D4—61no—
251C5×D4—61no—
252C5×D4—61no—
253C5×D4—61no—
254C5×D4—121no—
255C5×D4—121no—
256C5×D4—241no—
257C5×D4C2×S411yescharacteristic
258C2×C4×C5—31no—
259C2×C4×C5—31no—
260C2×C4×C5—31no—
261C2×C4×C5—31no—
262C2×C4×C5—31no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—121no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5—121no—
275C2×C4×C5—241no—
276C5×C8—31no—
277C5×C8—61no—
278C5×C8—61no—
279C5×C8C2×S411yescharacteristic
280C2×#41—31no—
281C22×Q8—31no—
282C22×Q8C2×C5×D311yescharacteristic
283C22×D4C2×C5×D311yescharacteristic
284#137—61no—
285#137—61no—
286#137—61no—
287#137—61no—
288C2×Q16—31no—
289C2×Q16—31no—
290C2×Q16—31no—
291C2×SD16—31no—
292C2×SD16—31no—
293C2×SD16—31no—
294C2×SD16—31no—
295C2×SD16—31no—
296C2×SD16—31no—
297C2×M16—31no—
298C22×C8C2×C5×D311yescharacteristic
299C4⋊Q8—31no—
300C4⋊Q8—61no—
301#124—31no—
302#123—61no—
303C22⋊Q8—31no—
304C22⋊Q8—31no—
305C22⋊Q8—31no—
306C22⋊Q8—61no—
307C22⋊Q8—61no—
308#121—31no—
309#121—61no—
310#120—61no—
311C4×Q8—31no—
312C4×D4—31no—
313C4×D4—31no—
314C4×D4—61no—
315C2×C22⋊C4—61no—
316#107—31no—
317C4⋊C8—31no—
318#103—31no—
319#103—31no—
320#103—31no—
321#103—31no—
322#102—31no—
323#102—31no—
324C22⋊C8—31no—
325C22⋊C8—31no—
326#97—31no—
327C2×C3×C5—41no—
328C2×C3×C5—161no—
329C5×D3—81no—
330C2×A4—41no—
331C2×A4C2×C5×D411yescharacteristic
332S4—21no—
333C3×Q8—41no—
334C3×D4—41no—
335#67—81no—
336C2×Dic3—81no—
337C4×D3—41no—
338C4×D3—81no—
339Dic6—41no—
340Dic6—41no—
341Dic6—81no—
342C3×C8—41no—
343C3⋊C8—41no—
344C22×C5—21no—
345C22×C5—31no—
346C22×C5—31no—
347C22×C5—61no—
348C22×C5—61no—
349C22×C5—61no—
350C22×C5—61no—
351C22×C5—121no—
352C22×C5—121no—
353C22×C5—121no—
354C22×C5—121no—
355C22×C5#91511yescharacteristic, complemented
356C4×C5—21no—
357C4×C5—31no—
358C4×C5—61no—
359C4×C5—61no—
360C4×C5—61no—
361C4×C5—61no—
362C4×C5—121no—
363C4×C5—121no—
364C4×C5—121no—
365C4×C5—121no—
366C4×C5C22×S411yescharacteristic
367C24—21no—
368#41—61no—
369#41—61no—
370#41—121no—
371C2×Q8—31no—
372C2×Q8—31no—
373C2×Q8—31no—
374C2×Q8—31no—
375C2×Q8—61no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—61no—
379C2×Q8—121no—
380C2×D4—31no—
381C2×D4—31no—
382C2×D4—31no—
383C2×D4—61no—
384C2×D4—61no—
385C2×D4—61no—
386C22×C4—21no—
387C22×C4—31no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4C22×C5×D311yescharacteristic
392Q16—61no—
393Q16—61no—
394Q16—61no—
395Q16—61no—
396Q16—121no—
397SD16—31no—
398SD16—31no—
399SD16—31no—
400SD16—61no—
401SD16—61no—
402SD16—61no—
403SD16—121no—
404SD16C5×S411yescharacteristic, complemented
405M16—61no—
406M16—61no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—31no—
410C2×C8—31no—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C22⋊C4—31no—
421C22⋊C4—31no—
422C22⋊C4—61no—
423C22⋊C4—61no—
424C22⋊C4—61no—
425C22⋊C4—61no—
426C22⋊C4—61no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C42—31no—
430C42—61no—
431C3×C5—41noHall
432C22×C3—81no—
433C2×D3—41no—
434A4C5×#13711yescharacteristic, complemented
435C3×C4—41no—
436C3×C4—81no—
437Dic3—41no—
438Dic3—81no—
439Dic3—81no—
440C2×C5—31no—
441C2×C5—31no—
442C2×C5—41no—
443C2×C5—121no—
444C2×C5—121no—
445C2×C5D4×S411yescharacteristic
446C23—31no—
447C23—41no—
448C23—61no—
449C23—61no—
450C23—121no—
451C23C5×D3×D411yescharacteristic
452Q8—31no—
453Q8—61no—
454Q8—61no—
455Q8—61no—
456Q8—61no—
457Q8—61no—
458Q8—61no—
459Q8—121no—
460Q8—121no—
461Q8C2×C5×S411yescharacteristic
462D4—31no—
463D4—61no—
464D4—61no—
465D4—61no—
466D4—61no—
467D4—121no—
468D4—121no—
469D4—241no—
470D4C2×C5×S411yescharacteristic
471C2×C4—31no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—241no—
489C8—31no—
490C8—61no—
491C8—61no—
492C8C2×C5×S411yescharacteristic
493C2×C3—41no—
494C2×C3—161no—
495D3—81no—
496C5#8546111yescharacteristic, direct product factor, Sylow
497C22—21no—
498C22—31no—
499C22—31no—
500C22—61no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C5×#91511yescharacteristic, complemented
509C4—21no—
510C4—31no—
511C4—61no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—121no—
516C4—121no—
517C4—121no—
518C4—121no—
519C4C22×C5×S411yescharacteristic
520C3—41noSylow
521C2—31no—
522C2—31no—
523C2—41no—
524C2—121no—
525C2—121no—
526C2C5×D4×S411yescharacteristic
subgroupG/H
centerC2×C5D4×S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×SD16D3
socleC23×C5D3×D4
prime radicalC5×#5914C2
hypercenterC5×SD16S4
hypocenterA4C5×#137
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×SD16

Complements

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

NH ≅ G/Ntype
1. C5×Q8×S4C2semidirect
3. C5×A4×SD16C2semidirect
4. C5×#5416C2semidirect
5. C5×#5414C2semidirect
6. C5×#5400C2semidirect
7. C5×#5398C2semidirect
21. #85461C5direct (N × H)
23. C22×C5×SD16D3semidirect
51. Q8×S4C2×C5semidirect
53. A4×SD16C2×C5semidirect
54. #5416C2×C5semidirect
55. #5414C2×C5semidirect
56. #5400C2×C5semidirect
57. #5398C2×C5semidirect
169. C5×SD16S4semidirect
197. C22×SD16C5×D3semidirect
213. C5×A4#137semidirect
355. C22×C5#915semidirect
404. SD16C5×S4semidirect
434. A4C5×#137semidirect
496. C5#85461direct (N × H)
508. C22C5×#915semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×S42
C5×#59142
C5×A4×SD162
C5×#54162
C5×#54142
C5×#54002
C5×#53982
C5×#32663
C5×#9154
#854615