Finite Group Databasebeta

← C5×#69143 #14313197

Subgroups — C5×#69143 #14313197

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5653C211yesmaximal, characteristic
2C5×D3×#100C211yesmaximal, characteristic, complemented
3C5×D3×#99C211yesmaximal, characteristic, complemented
4C3×C5×#352C211yesmaximal, characteristic, complemented
5C5×#4539C211yesmaximal, characteristic, complemented
6C5×#4475C211yesmaximal, characteristic, complemented
7C5×#4471C211yesmaximal, characteristic, complemented
8C5×#2121—31nomaximal, Hall
9C2×C5×D3×D4C2211yescharacteristic
10C22×C5×D12C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C5×#937C2211yescharacteristic
13C5×#929C411yescharacteristic, complemented
14C5×D3×M16—21no—
15C5×#895—21no—
16C5×#894—21no—
17C5×#884—21no—
18C5×#882—21no—
19C5×#882C411yescharacteristic, complemented
20C5×D3×C22⋊C4—21no—
21C5×D3×C22⋊C4C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#833C2211yescharacteristic
26C5×#823—21no—
27C5×#806—21no—
28#69143C511yesmaximal, characteristic, direct product factor, Hall
29C5×#534—31no—
30C2×C5×#100—31no—
31C2×C5×#99—31no—
32C5×#352—31no—
33C5×#352D311yescharacteristic, complemented
34C5×AΣL(1,𝔽16)—31no—
35C5×AΣL(1,𝔽16)—31no—
36C23×C5×D3C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic, complemented
38C23×C5×D3D411yescharacteristic
39C2×C3×C5×D4C2311yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic, complemented
41C2×C5×#67—21no—
42C2×C5×#67C2×C411yescharacteristic
43C2×C5×#67D411yescharacteristic
44C5×D3×D4—41no—
45C5×D3×D4—41no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—41no—
50C2×C5×D12—41no—
51C2×C5×D12D411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—41no—
54C2×C4×C5×D3D411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
60C5×#217—21no—
61C5×#217C2×C411yescharacteristic, complemented
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×(C2×D3)⋊C4—21no—
65C5×(C2×D3)⋊C4—21no—
66C5×(C2×D3)⋊C4—41no—
67C5×Dic3⋊C4—21no—
68C5×#208—21no—
69C5×ΓL(1,𝔽25)—41no—
70C5×D3×C8—41no—
71#5653C2×C511yescharacteristic
72D3×#100C2×C511yescharacteristic, complemented
73D3×#99C2×C511yescharacteristic, complemented
74C3×#352C2×C511yescharacteristic, complemented
75#4539C2×C511yescharacteristic, complemented
76#4475C2×C511yescharacteristic, complemented
77#4471C2×C511yescharacteristic, complemented
78C22×C5×D4—31no—
79C22×C5×D4—31no—
80C2×C5×M16—61no—
81C5×#123—31no—
82C5×#123—61no—
83C5×#123C2×D311yescharacteristic
84C5×#121—61no—
85C5×#121—61no—
86C5×#120—31no—
87C5×#120—31no—
88C5×#120—61no—
89C2×C5×C22⋊C4—31no—
90C2×C5×C22⋊C4—61no—
91C5×#100—31no—
92C5×#100—61no—
93C5×#100C2×D311yescharacteristic
94C5×#99—31no—
95C5×#99—61no—
96C5×#99C2×D311yescharacteristic
97#2121—31noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3—21no—
101C22×C5×D3—21no—
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—41no—
106C22×C5×D3—81no—
107C22×C5×D3—81no—
108C22×C5×D3—81no—
109C22×C5×D3C22⋊C411yescharacteristic
110C22×C5×D3C22⋊C411yescharacteristic
111C22×C5×D3C22⋊C411yescharacteristic
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C5×#67—41no—
119C5×#67—41no—
120C5×#67—81no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3C22⋊C411yescharacteristic
124C5×D12—41no—
125C5×D12—42no—
126C5×D12—41no—
127C5×D12—41no—
128C5×D12—81no—
129C4×C5×D3—21no—
130C4×C5×D3—21no—
131C4×C5×D3—81no—
132C4×C5×D3—82no—
133C3×C5×C8—41no—
134C5×C3⋊C8—41no—
135C2×D3×D4C22×C511yescharacteristic
136C22×D12C4×C511yescharacteristic, complemented
137C3×#123C22×C511yescharacteristic
138#937C22×C511yescharacteristic
139#929C4×C511yescharacteristic, complemented
140D3×M16—21no—
141#895—21no—
142#894—21no—
143#884—21no—
144#882—21no—
145#882C4×C511yescharacteristic, complemented
146D3×C22⋊C4—21no—
147D3×C22⋊C4C4×C511yescharacteristic, complemented
148C3×#100C22×C511yescharacteristic
149C3×#99C22×C511yescharacteristic
150#834C22×C511yescharacteristic
151#833C22×C511yescharacteristic
152#823—21no—
153#806—21no—
154C24×C5—31no—
155C24×C5—31no—
156C24×C5—31no—
157C2×C5×D4—31no—
158C2×C5×D4—31no—
159C2×C5×D4—31no—
160C2×C5×D4—61no—
161C2×C5×D4—61no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—121no—
165C2×C5×D4—121no—
166C2×C5×D4—121no—
167C2×C5×D4—121no—
168C2×C5×D4C22×D311yescharacteristic
169C22×C4×C5—31no—
170C22×C4×C5—61no—
171C22×C4×C5—121no—
172C22×C4×C5C4×D311yescharacteristic, complemented
173C5×M16—21no—
174C5×M16—61no—
175C5×M16—121no—
176C2×C5×C8—121no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—61no—
179C5×C22⋊C4—21no—
180C5×C22⋊C4—21no—
181C5×C22⋊C4—31no—
182C5×C22⋊C4—61no—
183C5×C22⋊C4—61no—
184C5×C22⋊C4—61no—
185C5×C22⋊C4—61no—
186C5×C22⋊C4—61no—
187C5×C22⋊C4—121no—
188C5×C22⋊C4C4×D311yescharacteristic, complemented
189#534—31no—
190C2×#100—31no—
191C2×#99—31no—
192#352—31no—
193#352C5×D311yescharacteristic, complemented
194AΣL(1,𝔽16)—31no—
195AΣL(1,𝔽16)—31no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C2×C5×D3—42no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C2×C5×D3—81no—
211C2×C5×D3—81no—
212C2×C5×D3—81no—
213C2×C5×D3—82no—
214C2×C5×D3#9911yescharacteristic
215C2×C5×D3#9911yescharacteristic
216C3×C4×C5—21no—
217C3×C4×C5—41no—
218C3×C4×C5—41no—
219C3×C4×C5—81no—
220C5×Dic3—21no—
221C5×Dic3—41no—
222C5×Dic3—81no—
223C23×D3C2×C4×C511yescharacteristic
224C23×D3C2×C4×C511yescharacteristic, complemented
225C23×D3C5×D411yescharacteristic
226C2×C3×D4C23×C511yescharacteristic
227C22×C3×C4C2×C4×C511yescharacteristic, complemented
228C2×#67—21no—
229C2×#67C2×C4×C511yescharacteristic
230C2×#67C5×D411yescharacteristic
231D3×D4—41no—
232D3×D4—41no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—41no—
237C2×D12—41no—
238C2×D12C5×D411yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—41no—
241C2×C4×D3C5×D411yescharacteristic
242C3×M16—21no—
243C3×C4⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4C2×C4×C511yescharacteristic, complemented
247#217—21no—
248#217C2×C4×C511yescharacteristic, complemented
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—41no—
254Dic3⋊C4—21no—
255#208—21no—
256ΓL(1,𝔽25)—41no—
257D3×C8—41no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—31no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—61no—
264C23×C5—61no—
265C23×C5—61no—
266C23×C5—121no—
267C23×C5—241no—
268C23×C5—241no—
269C23×C5—241no—
270C23×C5C2×C4×D311yescharacteristic
271C23×C5D3×D411yescharacteristic
272C5×D4—41no—
273C5×D4—121no—
274C5×D4—121no—
275C5×D4—121no—
276C5×D4—122no—
277C5×D4—121no—
278C5×D4—121no—
279C5×D4—241no—
280C5×D4—241no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—31no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—121no—
290C2×C4×C5—241no—
291C2×C4×C5—242no—
292C2×C4×C5D3×D411yescharacteristic
293C5×C8—41no—
294C5×C8—121no—
295C22×D4—31no—
296C22×D4—31no—
297C2×M16—61no—
298#123—31no—
299#123—61no—
300#123C2×C5×D311yescharacteristic
301#121—61no—
302#121—61no—
303#120—31no—
304#120—31no—
305#120—61no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—61no—
308#100—31no—
309#100—61no—
310#100C2×C5×D311yescharacteristic
311#99—31no—
312#99—61no—
313#99C2×C5×D311yescharacteristic
314C2×C3×C5—21no—
315C2×C3×C5—41no—
316C2×C3×C5—41no—
317C2×C3×C5C2×#9911yescharacteristic
318C5×D3—21no—
319C5×D3—21no—
320C5×D3—41no—
321C5×D3—41no—
322C5×D3—81no—
323C23×C3C22×C4×C511yescharacteristic
324C23×C3C2×C5×D411yescharacteristic
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3—21no—
330C22×D3—41no—
331C22×D3—81no—
332C22×D3—81no—
333C22×D3—81no—
334C22×D3C5×C22⋊C411yescharacteristic
335C22×D3C5×C22⋊C411yescharacteristic
336C22×D3C5×C22⋊C411yescharacteristic
337C3×D4—41no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4C2×C5×D411yescharacteristic
343#67—41no—
344#67—41no—
345#67—81no—
346C2×Dic3—21no—
347C2×Dic3—41no—
348C2×Dic3C5×C22⋊C411yescharacteristic
349D12—41no—
350D12—42no—
351D12—41no—
352D12—41no—
353D12—81no—
354C4×D3—21no—
355C4×D3—21no—
356C4×D3—81no—
357C4×D3—82no—
358C3×C8—41no—
359C3⋊C8—41no—
360C22×C5—21no—
361C22×C5—21no—
362C22×C5—31no—
363C22×C5—31no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—61no—
367C22×C5—61no—
368C22×C5—121no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5—121no—
372C22×C5—121no—
373C22×C5—122no—
374C22×C5—121no—
375C22×C5—241no—
376C22×C5—241no—
377C22×C5—241no—
378C22×C5—242no—
379C22×C5D3×C22⋊C411yescharacteristic
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—61no—
384C4×C5—81no—
385C4×C5—121no—
386C4×C5—241no—
387C24—31no—
388C24—31no—
389C24—31no—
390C2×D4—31no—
391C2×D4—31no—
392C2×D4—31no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—121no—
398C2×D4—121no—
399C2×D4—121no—
400C2×D4—121no—
401C2×D4C22×C5×D311yescharacteristic
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—121no—
405C22×C4C4×C5×D311yescharacteristic, complemented
406M16—21no—
407M16—61no—
408M16—121no—
409C2×C8—121no—
410C4⋊C4—21no—
411C4⋊C4—61no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—31no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—61no—
419C22⋊C4—61no—
420C22⋊C4—121no—
421C22⋊C4C4×C5×D311yescharacteristic, complemented
422C3×C5#212111yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3C2×C5×C22⋊C411yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—41no—
431C2×D3—42no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—81no—
438C2×D3—81no—
439C2×D3—81no—
440C2×D3—82no—
441C2×D3C5×#9911yescharacteristic
442C2×D3C5×#9911yescharacteristic
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—81no—
447Dic3—21no—
448Dic3—41no—
449Dic3—81no—
450C2×C5—21no—
451C2×C5—41no—
452C2×C5—41no—
453C2×C5—61no—
454C2×C5—61no—
455C2×C5—121no—
456C2×C5—121no—
457C2×C5—241no—
458C2×C5D3×#9911yescharacteristic
459C23—31no—
460C23—31no—
461C23—31no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23—121no—
468C23—241no—
469C23—241no—
470C23—241no—
471C23C2×C4×C5×D311yescharacteristic
472C23C5×D3×D411yescharacteristic
473D4—41no—
474D4—121no—
475D4—121no—
476D4—121no—
477D4—122no—
478D4—121no—
479D4—121no—
480D4—241no—
481D4—241no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—31no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—121no—
491C2×C4—241no—
492C2×C4—242no—
493C2×C4C5×D3×D411yescharacteristic
494C8—41no—
495C8—121no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3C2×C5×#9911yescharacteristic
500D3—21no—
501D3—21no—
502D3—41no—
503D3—41no—
504D3—81no—
505C5#6914311yescharacteristic, direct product factor, Sylow
506C22—21no—
507C22—21no—
508C22—31no—
509C22—31no—
510C22—41no—
511C22—41no—
512C22—61no—
513C22—61no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—122no—
520C22—121no—
521C22—241no—
522C22—241no—
523C22—241no—
524C22—242no—
525C22C5×D3×C22⋊C411yescharacteristic
526C4—21no—
527C4—41no—
528C4—41no—
529C4—61no—
530C4—81no—
531C4—121no—
532C4—241no—
533C3C5×#212111yescharacteristic, complemented, Sylow
534C2—21no—
535C2—41no—
536C2—41no—
537C2—61no—
538C2—61no—
539C2—121no—
540C2—121no—
541C2—241no—
542C2C5×D3×#9911yescharacteristic
subgroupG/H
centerC2×C5D3×#99
commutatorC23×C3C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×#352C2
socleC2×C3×C5C2×#99
prime radicalC5×#5653C2
cosocleC2×C3×D4C23×C5
hypercenterC5×#352D3
hypocenterC3C5×#2121
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×#352

Complements

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

NH ≅ G/Ntype
2. C5×D3×#100C2semidirect
3. C5×D3×#99C2semidirect
4. C3×C5×#352C2semidirect
5. C5×#4539C2semidirect
6. C5×#4475C2semidirect
7. C5×#4471C2semidirect
10. C22×C5×D12C4semidirect
13. C5×#929C4semidirect
19. C5×#882C4semidirect
21. C5×D3×C22⋊C4C4semidirect
28. #69143C5direct (N × H)
33. C5×#352D3semidirect
37. C23×C5×D3C2×C4semidirect
40. C22×C3×C4×C5C2×C4semidirect
59. C3×C5×C22⋊C4C2×C4semidirect
61. C5×#217C2×C4semidirect
72. D3×#100C2×C5semidirect
73. D3×#99C2×C5semidirect
74. C3×#352C2×C5semidirect
75. #4539C2×C5semidirect
76. #4475C2×C5semidirect
77. #4471C2×C5semidirect
136. C22×D12C4×C5semidirect
139. #929C4×C5semidirect
145. #882C4×C5semidirect
147. D3×C22⋊C4C4×C5semidirect
172. C22×C4×C5C4×D3semidirect
188. C5×C22⋊C4C4×D3semidirect
193. #352C5×D3semidirect
224. C23×D3C2×C4×C5semidirect
227. C22×C3×C4C2×C4×C5semidirect
246. C3×C22⋊C4C2×C4×C5semidirect
248. #217C2×C4×C5semidirect
405. C22×C4C4×C5×D3semidirect
421. C22⋊C4C4×C5×D3semidirect
422. C3×C5#2121semidirect
505. C5#69143direct (N × H)
533. C3C5×#2121semidirect

Maximal subgroups

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

subgroupindex
C5×#56532
C5×D3×#1002
C5×D3×#992
C3×C5×#3522
C5×#45392
C5×#44752
C5×#44712
C5×#21213
#691435