Finite Group Databasebeta

← C5×#68304 #14283256

Subgroups — C5×#68304 #14283256

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×#121C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3C5×#4664C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C5×#4537C211yesmaximal, characteristic, complemented
6C5×#4470C211yesmaximal, characteristic, complemented
7C5×#4451C211yesmaximal, characteristic, complemented
8C5×#1510—31nomaximal, Hall
9C2×C5×D3×D4—21no—
10C2×C5×D3×D4C411yescharacteristic, complemented
11C22×C4×C5×D3C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C5×#939—21no—
14C5×#938C411yescharacteristic, complemented
15C5×#930C2211yescharacteristic
16C2×C5×(C2×D3)⋊C4—21no—
17C2×C5×ΓL(1,𝔽25)—21no—
18C5×#895C411yescharacteristic, complemented
19C5×D3×C4⋊C4C411yescharacteristic, complemented
20C5×#884—21no—
21C5×D3×C22⋊C4—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23C3×C5×#95C2211yescharacteristic, complemented
24C5×C3⋊#95—21no—
25C5×C3⋊#95C2211yescharacteristic, complemented
26C5×#830C2211yescharacteristic, complemented
27C5×(C2×D3)⋊C8—21no—
28#68304C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×#121—31no—
30C5×#407—31no—
31C5×#381—31no—
32C5×#327—31no—
33C5×#327—31no—
34C5×#327—31no—
35C5×#327D311yescharacteristic, complemented
36C23×C5×D3—21no—
37C23×C5×D3D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C22×C5×Dic3—21no—
46C22×C5×Dic3D411yescharacteristic
47C5×D3×D4—42no—
48C5×D3×D4—42no—
49C5×D3×D4—42no—
50C2×C5×D12—21no—
51C2×C5×D12C2×C411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—42no—
54C2×C4×C5×D3C2×C411yescharacteristic
55C2×C4×C5×D3C2×C411yescharacteristic
56C2×C4×C5×D3D411yescharacteristic
57C2×C4×C5×D3D411yescharacteristic
58C2×C3×C5×C8—21no—
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C3×C5×C22⋊C4—21no—
61C5×#217—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×(C2×D3)⋊C4—42no—
65C5×C4⋊Dic3C2×C411yescharacteristic
66C5×Dic3⋊C4—21no—
67C2×C5×C3⋊C8—21no—
68C5×ΓL(1,𝔽25)—42no—
69D3×#121C2×C511yescharacteristic
70#4726C2×C511yescharacteristic, complemented
71#4664C2×C511yescharacteristic, complemented
72C3×#327C2×C511yescharacteristic, complemented
73#4537C2×C511yescharacteristic, complemented
74#4470C2×C511yescharacteristic, complemented
75#4451C2×C511yescharacteristic, complemented
76C22×C5×D4—31no—
77C22×C5×D4—61no—
78C23×C4×C5—31no—
79C2×C5×M16—61no—
80C5×#121—31no—
81C5×#121—31no—
82C5×#121—31no—
83C5×#121—61no—
84C5×#121—61no—
85C5×#121C2×D311yescharacteristic
86C2×C5×C4⋊C4—31no—
87C2×C5×C22⋊C4—61no—
88C2×C5×C22⋊C4—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic, complemented
92C5×#95—31no—
93C5×#95—61no—
94C5×#95C2×D311yescharacteristic, complemented
95#1510—31noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×C5×D3—21no—
99C22×C5×D3—21no—
100C22×C5×D3—22no—
101C22×C5×D3—21no—
102C22×C5×D3—41no—
103C22×C5×D3—42no—
104C22×C5×D3—42no—
105C22×C5×D3—42no—
106C22×C5×D3C22⋊C411yescharacteristic
107C22×C5×D3C22⋊C411yescharacteristic
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C5×#67—42no—
119C5×#67—42no—
120C5×#67—41no—
121C5×#67—41no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3—41no—
127C2×C5×Dic3C22⋊C411yescharacteristic
128C2×C5×Dic3C22⋊C411yescharacteristic
129C5×D12—41no—
130C5×D12—42no—
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—41no—
134C4×C5×D3—41no—
135C4×C5×D3—42no—
136C3×C5×C8—41no—
137C5×C3⋊C8—41no—
138C2×D3×D4—21no—
139C2×D3×D4C4×C511yescharacteristic, complemented
140C22×C4×D3C22×C511yescharacteristic
141C3×#121C22×C511yescharacteristic
142#939—21no—
143#938C4×C511yescharacteristic, complemented
144#930C22×C511yescharacteristic
145C2×(C2×D3)⋊C4—21no—
146C2×ΓL(1,𝔽25)—21no—
147#895C4×C511yescharacteristic, complemented
148D3×C4⋊C4C4×C511yescharacteristic, complemented
149#884—21no—
150D3×C22⋊C4—21no—
151C3×C22⋊C8C22×C511yescharacteristic, complemented
152C3×#95C22×C511yescharacteristic, complemented
153C3⋊#95—21no—
154C3⋊#95C22×C511yescharacteristic, complemented
155#830C22×C511yescharacteristic, complemented
156(C2×D3)⋊C8—21no—
157C24×C5—31no—
158C24×C5—61no—
159C2×C5×D4—21no—
160C2×C5×D4—31no—
161C2×C5×D4—61no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—122no—
166C2×C5×D4—122no—
167C2×C5×D4—122no—
168C2×C5×D4C4×D311yescharacteristic
169C22×C4×C5—21no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—61no—
176C22×C4×C5—61no—
177C22×C4×C5—122no—
178C22×C4×C5C22×D311yescharacteristic
179C5×M16—122no—
180C2×C5×C8—21no—
181C2×C5×C8—61no—
182C5×C4⋊C4—31no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4C4×D311yescharacteristic
185C5×C22⋊C4—21no—
186C5×C22⋊C4—61no—
187C5×C22⋊C4—61no—
188C5×C22⋊C4—61no—
189C5×C22⋊C4—122no—
190C2×#121—31no—
191#407—31no—
192#381—31no—
193#327—31no—
194#327—31no—
195#327—31no—
196#327C5×D311yescharacteristic, complemented
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
205C2×C5×D3—21no—
206C2×C5×D3—21no—
207C2×C5×D3—21no—
208C2×C5×D3—21no—
209C2×C5×D3—21no—
210C2×C5×D3—42no—
211C2×C5×D3—42no—
212C2×C5×D3—41no—
213C2×C5×D3—41no—
214C2×C5×D3—41no—
215C2×C5×D3—84no—
216C2×C5×D3#9912yes—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219C3×C4×C5—41no—
220C3×C4×C5—81no—
221C5×Dic3—21no—
222C5×Dic3—21no—
223C5×Dic3—41no—
224C5×Dic3—81no—
225C23×D3—21no—
226C23×D3C5×D411yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4C2×C4×C511yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4C23×C511yescharacteristic
231C2×#67—21no—
232C2×#67—21no—
233C2×#67—21no—
234C22×Dic3—21no—
235C22×Dic3C5×D411yescharacteristic
236D3×D4—42no—
237D3×D4—42no—
238D3×D4—42no—
239C2×D12—21no—
240C2×D12C2×C4×C511yescharacteristic
241C2×C4×D3—21no—
242C2×C4×D3—42no—
243C2×C4×D3C2×C4×C511yescharacteristic
244C2×C4×D3C2×C4×C511yescharacteristic
245C2×C4×D3C5×D411yescharacteristic
246C2×C4×D3C5×D411yescharacteristic
247C2×C3×C8—21no—
248C3×C4⋊C4C2×C4×C511yescharacteristic
249C3×C22⋊C4—21no—
250#217—21no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—42no—
254C4⋊Dic3C2×C4×C511yescharacteristic
255Dic3⋊C4—21no—
256C2×C3⋊C8—21no—
257ΓL(1,𝔽25)—42no—
258C23×C5—21no—
259C23×C5—31no—
260C23×C5—31no—
261C23×C5—62no—
262C23×C5—61no—
263C23×C5—61no—
264C23×C5—61no—
265C23×C5—121no—
266C23×C5—122no—
267C23×C5—122no—
268C23×C5—122no—
269C23×C5D3×D411yescharacteristic
270C5×D4—41no—
271C5×D4—41no—
272C5×D4—41no—
273C5×D4—121no—
274C5×D4—122no—
275C5×D4—122no—
276C5×D4—122no—
277C5×D4—121no—
278C5×D4—121no—
279C2×C4×C5—21no—
280C2×C4×C5—31no—
281C2×C4×C5—31no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—61no—
289C2×C4×C5—121no—
290C2×C4×C5—121no—
291C2×C4×C5—122no—
292C2×C4×C5—121no—
293C2×C4×C5—121no—
294C2×C4×C5—121no—
295C2×C4×C5—121no—
296C2×C4×C5C2×C4×D311yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C5×C8—41no—
299C5×C8—121no—
300C22×D4—31no—
301C22×D4—61no—
302C23×C4—31no—
303C2×M16—61no—
304#121—31no—
305#121—31no—
306#121—31no—
307#121—61no—
308#121—61no—
309#121C2×C5×D311yescharacteristic
310C2×C4⋊C4—31no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—61no—
313C22⋊C8—31no—
314C22⋊C8—61no—
315C22⋊C8C2×C5×D311yescharacteristic, complemented
316#95—31no—
317#95—61no—
318#95C2×C5×D311yescharacteristic, complemented
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5—81no—
322C2×C3×C5C2×#9911yescharacteristic
323C2×C3×C5#41811yescharacteristic
324C2×C3×C5#42111yescharacteristic
325C5×D3—22no—
326C5×D3—41no—
327C5×D3—81no—
328C23×C3—21no—
329C23×C3C2×C5×D411yescharacteristic
330C22×D3—21no—
331C22×D3—21no—
332C22×D3—22no—
333C22×D3—21no—
334C22×D3—41no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—42no—
338C22×D3C5×C22⋊C411yescharacteristic
339C22×D3C5×C22⋊C411yescharacteristic
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C2×C3×C4—21no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4C22×C4×C511yescharacteristic
349C2×C3×C4C2×C5×D411yescharacteristic
350#67—42no—
351#67—42no—
352#67—41no—
353#67—41no—
354C2×Dic3—21no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3C5×C22⋊C411yescharacteristic
360C2×Dic3C5×C22⋊C411yescharacteristic
361D12—41no—
362D12—42no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—41no—
366C4×D3—41no—
367C4×D3—42no—
368C3×C8—41no—
369C3⋊C8—41no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—32no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5—41no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5—61no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—122no—
382C22×C5—122no—
383C22×C5—121no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—244no—
387C22×C5D3×C22⋊C411yescharacteristic
388C22×C5#91111yescharacteristic
389C22×C5#91411yescharacteristic
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—61no—
394C4×C5—61no—
395C4×C5—81no—
396C4×C5—121no—
397C4×C5—241no—
398C24—31no—
399C24—61no—
400C2×D4—21no—
401C2×D4—31no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—122no—
407C2×D4—122no—
408C2×D4—122no—
409C2×D4C4×C5×D311yescharacteristic
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—122no—
419C22×C4C22×C5×D311yescharacteristic
420M16—122no—
421C2×C8—21no—
422C2×C8—61no—
423C4⋊C4—31no—
424C4⋊C4—61no—
425C4⋊C4C4×C5×D311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—61no—
430C22⋊C4—122no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3C2×C5×C22⋊C411yescharacteristic
438C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
439C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
440C2×D3—21no—
441C2×D3—21no—
442C2×D3—21no—
443C2×D3—21no—
444C2×D3—21no—
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—84no—
451C2×D3C5×#9912yes—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—81no—
456Dic3—21no—
457Dic3—21no—
458Dic3—41no—
459Dic3—81no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—62no—
463C2×C5—81no—
464C2×C5—121no—
465C2×C5—241no—
466C2×C5D3×#9911yescharacteristic
467C2×C5#477011yescharacteristic
468C2×C5#482111yescharacteristic
469C23—21no—
470C23—31no—
471C23—31no—
472C23—62no—
473C23—61no—
474C23—61no—
475C23—61no—
476C23—121no—
477C23—122no—
478C23—122no—
479C23—122no—
480C23C5×D3×D411yescharacteristic
481D4—41no—
482D4—41no—
483D4—41no—
484D4—121no—
485D4—122no—
486D4—122no—
487D4—122no—
488D4—121no—
489D4—121no—
490C2×C4—21no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—122no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4C2×C4×C5×D311yescharacteristic
508C2×C4C5×D3×D411yescharacteristic
509C8—41no—
510C8—121no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—81no—
514C2×C3C2×C5×#9911yescharacteristic
515C2×C3C5×#41811yescharacteristic
516C2×C3C5×#42111yescharacteristic
517D3—22no—
518D3—41no—
519D3—81no—
520C5#6830411yescharacteristic, direct product factor, Sylow
521C22—21no—
522C22—21no—
523C22—32no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—61no—
528C22—61no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—122no—
533C22—122no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—244no—
538C22C5×D3×C22⋊C411yescharacteristic
539C22C5×#91111yescharacteristic
540C22C5×#91411yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—61no—
545C4—61no—
546C4—81no—
547C4—121no—
548C4—241no—
549C3C5×#151011yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—62no—
553C2—81no—
554C2—121no—
555C2—241no—
556C2C5×D3×#9911yescharacteristic
557C2C5×#477011yescharacteristic
558C2C5×#482111yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×D3×#121C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#327D3
hypocenterC3C5×#1510
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

Complements

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

NH ≅ G/Ntype
2. C5×#4726C2semidirect
3. C5×#4664C2semidirect
4. C3×C5×#327C2semidirect
5. C5×#4537C2semidirect
6. C5×#4470C2semidirect
7. C5×#4451C2semidirect
10. C2×C5×D3×D4C4semidirect
14. C5×#938C4semidirect
18. C5×#895C4semidirect
19. C5×D3×C4⋊C4C4semidirect
22. C3×C5×C22⋊C8C22semidirect
23. C3×C5×#95C22semidirect
25. C5×C3⋊#95C22semidirect
26. C5×#830C22semidirect
28. #68304C5direct (N × H)
35. C5×#327D3semidirect
70. #4726C2×C5semidirect
71. #4664C2×C5semidirect
72. C3×#327C2×C5semidirect
73. #4537C2×C5semidirect
74. #4470C2×C5semidirect
75. #4451C2×C5semidirect
91. C5×C22⋊C8C2×D3semidirect
94. C5×#95C2×D3semidirect
139. C2×D3×D4C4×C5semidirect
143. #938C4×C5semidirect
147. #895C4×C5semidirect
148. D3×C4⋊C4C4×C5semidirect
151. C3×C22⋊C8C22×C5semidirect
152. C3×#95C22×C5semidirect
154. C3⋊#95C22×C5semidirect
155. #830C22×C5semidirect
196. #327C5×D3semidirect
315. C22⋊C8C2×C5×D3semidirect
318. #95C2×C5×D3semidirect
431. C3×C5#1510semidirect
520. C5#68304direct (N × H)
549. C3C5×#1510semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1212
C5×#47262
C5×#46642
C3×C5×#3272
C5×#45372
C5×#44702
C5×#44512
C5×#15103
#683045