Finite Group Databasebeta

← C5×#82395 #14323348

Subgroups — C5×#82395 #14323348

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C5×#937C211yesmaximal, characteristic
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C5×#5220C211yesmaximal, characteristic, complemented
5C5×#5213C212yesmaximal, complemented
6C4×C5×#217C211yesmaximal, characteristic, complemented
7C5×#4990C212yesmaximal, complemented
8C5×#4957C212yesmaximal, complemented
9C5×#4955C211yesmaximal, characteristic, complemented
10C5×#4946C211yesmaximal, characteristic, complemented
11C5×#4940C212yesmaximal, complemented
12C5×#2321—31nomaximal, Hall
13C24×C5×D3C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic, complemented
17C22×C5×#67C2212yes—
18C23×C5×Dic3C2211yescharacteristic
19C3×C4×C5×D4—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
23C2×C3×C42×C5C2211yescharacteristic, complemented
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2212yescomplemented
27C5×#937C418yescomplemented
28C2×C5×(C2×D3)⋊C4—24no—
29C2×C5×(C2×D3)⋊C4C2212yes—
30C2×C5×(C2×D3)⋊C4C2212yes—
31C2×C5×(C2×D3)⋊C4C2212yes—
32C2×C5×(C2×D3)⋊C4C2212yes—
33C2×C5×(C2×D3)⋊C4C2212yes—
34C2×C5×Dic3⋊C4C2212yescomplemented
35C2×C4×C5×Dic3C2212yescomplemented
36C5×C3⋊#95C2212yescomplemented
37C5×C3⋊#95C2212yescomplemented
38C5×C3⋊#95C2212yescomplemented
39#82395C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#120—31no—
41C2×C4×C5×D4D311yescharacteristic, complemented
42C22×C5×C22⋊C4—31no—
43C5×#390—32no—
44C5×#388—32no—
45C5×#388—32no—
46C5×#386—31no—
47C5×#386—32no—
48C5×#385—31no—
49C5×#379—31no—
50C4×C5×C22⋊C4—31no—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3—42no—
56C23×C5×D3—42no—
57C23×C5×D3C2×C414yescomplemented
58C23×C5×D3C2312yes—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4C2×C414yes—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5—42no—
65C22×C3×C4×C5D414yescomplemented
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C2×C5×#67—42no—
72C2×C5×#67—42no—
73C2×C5×#67C2×C418yescomplemented
74C22×C5×Dic3—22no—
75C22×C5×Dic3—42no—
76C22×C5×Dic3C2312yes—
77C22×C5×Dic3C2312yes—
78C22×C5×Dic3C2312yes—
79C3×C5×C4⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—22no—
82C3×C42×C5—22no—
83C5×#217—22no—
84C5×#217—42no—
85C5×#217C2×C414yescomplemented
86C5×(C2×D3)⋊C4—24no—
87C5×(C2×D3)⋊C4—24no—
88C5×(C2×D3)⋊C4—42no—
89C5×(C2×D3)⋊C4—42no—
90C5×(C2×D3)⋊C4C2×C418yescomplemented
91C5×Dic3⋊C4—42no—
92C4×C5×Dic3—42no—
93C2×C3×C4×D4C2×C511yescharacteristic, complemented
94C2×#937C2×C511yescharacteristic
95C22×(C2×D3)⋊C4C2×C511yescharacteristic, complemented
96#5220C2×C511yescharacteristic, complemented
97#5213C2×C512yescomplemented
98C4×#217C2×C511yescharacteristic, complemented
99#4990C2×C512yescomplemented
100#4957C2×C512yescomplemented
101#4955C2×C511yescharacteristic, complemented
102#4946C2×C511yescharacteristic, complemented
103#4940C2×C512yescomplemented
104C25×C5—31no—
105C22×C5×D4—32no—
106C22×C5×D4C2×D311yescharacteristic
107C23×C4×C5—31no—
108C23×C4×C5C2×D311yescharacteristic
109C23×C4×C5C2×D311yescharacteristic, complemented
110C5×#120—38no—
111C4×C5×D4—24no—
112C2×C5×C4⋊C4—32no—
113C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
114C2×C5×C22⋊C4—31no—
115C2×C5×C22⋊C4—32no—
116C2×C5×C22⋊C4—31no—
117C2×C5×C22⋊C4—32no—
118C2×C5×C22⋊C4—32no—
119C2×C5×C22⋊C4—32no—
120C2×C5×C22⋊C4—32no—
121C2×C5×C22⋊C4—32no—
122C2×C5×C22⋊C4—64no—
123C2×C5×C22⋊C4C2×D311yescharacteristic
124C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
125C2×C42×C5—32no—
126C2×C42×C5C2×D311yescharacteristic, complemented
127C5×#95—32no—
128C5×#95—32no—
129C5×#95—32no—
130#2321—31noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5C22×C412yes—
138C23×C3×C5C22×C412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5C2411yescharacteristic
142C22×C5×D3—28no—
143C22×C5×D3—22no—
144C22×C5×D3—22no—
145C22×C5×D3—22no—
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—48no—
150C22×C5×D3—44no—
151C22×C5×D3—44no—
152C22×C5×D3—48no—
153C22×C5×D3C22×C414yes—
154C3×C5×D4—28no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5—44no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2×D412yes—
168C5×#67—48no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3—22no—
176C2×C5×Dic3—22no—
177C2×C5×Dic3—44no—
178C2×C5×Dic3C22×C414yes—
179C24×D3C22×C511yescharacteristic
180C22×C3×D4C22×C511yescharacteristic
181C23×C3×C4C22×C511yescharacteristic
182C23×C3×C4C22×C511yescharacteristic, complemented
183C22×#67C22×C512yes—
184C23×Dic3C22×C511yescharacteristic
185C3×C4×D4—24no—
186C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
187C2×C3×C22⋊C4C22×C511yescharacteristic
188C2×C3×C22⋊C4C22×C511yescharacteristic, complemented
189C2×C3×C42C22×C511yescharacteristic, complemented
190C2×#217C22×C511yescharacteristic
191C2×#217C22×C511yescharacteristic
192C2×#217C22×C512yescomplemented
193#937C4×C518yescomplemented
194C2×(C2×D3)⋊C4—24no—
195C2×(C2×D3)⋊C4C22×C512yes—
196C2×(C2×D3)⋊C4C22×C512yes—
197C2×(C2×D3)⋊C4C22×C512yes—
198C2×(C2×D3)⋊C4C22×C512yes—
199C2×(C2×D3)⋊C4C22×C512yes—
200C2×Dic3⋊C4C22×C512yescomplemented
201C2×C4×Dic3C22×C512yescomplemented
202C3⋊#95C22×C512yescomplemented
203C3⋊#95C22×C512yescomplemented
204C3⋊#95C22×C512yescomplemented
205C24×C5—32no—
206C24×C5—34no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5—122no—
210C24×C5—122no—
211C24×C5C22×D311yescharacteristic
212C24×C5C22×D311yescharacteristic
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4—38no—
216C2×C5×D4—122no—
217C2×C5×D4—122no—
218C2×C5×D4C4×D314yes—
219C22×C4×C5—22no—
220C22×C4×C5—32no—
221C22×C4×C5—32no—
222C22×C4×C5—32no—
223C22×C4×C5—42no—
224C22×C4×C5—42no—
225C22×C4×C5—62no—
226C22×C4×C5—122no—
227C22×C4×C5#6714yescomplemented
228C22×C4×C5C22×D311yescharacteristic
229C22×C4×C5C22×D311yescharacteristic
230C22×C4×C5C22×D311yescharacteristic
231C22×C4×C5C22×D311yescharacteristic
232C22×C4×C5C22×D311yescharacteristic
233C5×C4⋊C4—22no—
234C5×C4⋊C4—122no—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—22no—
237C5×C22⋊C4—34no—
238C5×C22⋊C4—38no—
239C5×C22⋊C4—62no—
240C5×C22⋊C4—64no—
241C5×C22⋊C4—64no—
242C5×C22⋊C4—122no—
243C5×C22⋊C4—122no—
244C5×C22⋊C4—122no—
245C42×C5—22no—
246C42×C5—122no—
247C2×#120—31no—
248C2×C4×D4C5×D311yescharacteristic, complemented
249C22×C22⋊C4—31no—
250#390—32no—
251#388—32no—
252#388—32no—
253#386—31no—
254#386—32no—
255#385—31no—
256#379—31no—
257C4×C22⋊C4—31no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5—22no—
263C22×C3×C5—24no—
264C22×C3×C5—41no—
265C22×C3×C5—41no—
266C22×C3×C5—42no—
267C22×C3×C5C4×D414yes—
268C22×C3×C5C23×C411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5H(5,𝔽2)12yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C2×C5×D3—24no—
274C2×C5×D3—24no—
275C2×C5×D3—24no—
276C2×C5×D3—416no—
277C2×C5×D3—42no—
278C2×C5×D3—42no—
279C2×C5×D3—42no—
280C2×C5×D3—42no—
281C3×C4×C5—22no—
282C3×C4×C5—22no—
283C3×C4×C5—22no—
284C3×C4×C5—41no—
285C3×C4×C5—41no—
286C5×Dic3—24no—
287C5×Dic3—42no—
288C5×Dic3—42no—
289C24×C3C23×C511yescharacteristic
290C24×C3C23×C511yescharacteristic
291C23×D3—22no—
292C23×D3—22no—
293C23×D3—42no—
294C23×D3—42no—
295C23×D3C2×C4×C514yescomplemented
296C23×D3C23×C512yes—
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4C2×C4×C514yes—
300C22×C3×C4—22no—
301C22×C3×C4—42no—
302C22×C3×C4—42no—
303C22×C3×C4C5×D414yescomplemented
304C22×C3×C4C23×C511yescharacteristic
305C22×C3×C4C23×C511yescharacteristic
306C22×C3×C4C23×C511yescharacteristic
307C22×C3×C4C23×C511yescharacteristic
308C22×C3×C4C23×C511yescharacteristic
309C2×#67—42no—
310C2×#67—42no—
311C2×#67C2×C4×C518yescomplemented
312C22×Dic3—22no—
313C22×Dic3—42no—
314C22×Dic3C23×C512yes—
315C22×Dic3C23×C512yes—
316C22×Dic3C23×C512yes—
317C3×C4⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—22no—
320C3×C42—22no—
321#217—22no—
322#217—42no—
323#217C2×C4×C514yescomplemented
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4C2×C4×C518yescomplemented
329Dic3⋊C4—42no—
330C4×Dic3—42no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—21no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—21no—
337C23×C5—34no—
338C23×C5—68no—
339C23×C5—62no—
340C23×C5—62no—
341C23×C5—62no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5—128no—
346C23×C5—124no—
347C23×C5—128no—
348C23×C5—124no—
349C23×C5C2×C4×D312yes—
350C23×C5C2×C4×D312yes—
351C23×C5#23512yes—
352C23×C5C2×#6712yes—
353C23×C5C23×D311yescharacteristic
354C5×D4—28no—
355C5×D4—128no—
356C2×C4×C5—21no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—21no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—34no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—62no—
368C2×C4×C5—62no—
369C2×C4×C5—62no—
370C2×C4×C5—62no—
371C2×C4×C5—62no—
372C2×C4×C5—62no—
373C2×C4×C5—62no—
374C2×C4×C5—62no—
375C2×C4×C5—124no—
376C2×C4×C5C2×C4×D312yes—
377C2×C4×C5C2×#6712yes—
378C2×C4×C5C2×#6712yes—
379C25—31no—
380C22×D4—32no—
381C22×D4C2×C5×D311yescharacteristic
382C23×C4—31no—
383C23×C4C2×C5×D311yescharacteristic
384C23×C4C2×C5×D311yescharacteristic, complemented
385#120—38no—
386C4×D4—24no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4C2×C5×D311yescharacteristic, complemented
389C2×C22⋊C4—31no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—64no—
398C2×C22⋊C4C2×C5×D311yescharacteristic
399C2×C22⋊C4C2×C5×D311yescharacteristic, complemented
400C2×C42—32no—
401C2×C42C2×C5×D311yescharacteristic, complemented
402#95—32no—
403#95—32no—
404#95—32no—
405C2×C3×C5—24no—
406C2×C3×C5—42no—
407C2×C3×C5C2×C4×D411yescharacteristic
408C2×C3×C5#51812yes—
409C2×C3×C5#53411yescharacteristic
410C2×C3×C5#53511yescharacteristic
411C2×C3×C5#53812yes—
412C5×D3—44no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3C22×C4×C512yes—
420C23×C3C22×C4×C512yes—
421C23×C3C2×C5×D412yes—
422C23×C3C5×#4112yes—
423C23×C3C24×C511yescharacteristic
424C22×D3—28no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—48no—
432C22×D3—44no—
433C22×D3—44no—
434C22×D3—48no—
435C22×D3C22×C4×C514yes—
436C3×D4—28no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—44no—
446C2×C3×C4—44no—
447C2×C3×C4C22×C4×C512yes—
448C2×C3×C4C2×C5×D412yes—
449C2×C3×C4C2×C5×D412yes—
450#67—48no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—44no—
460C2×Dic3C22×C4×C514yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—24no—
464C22×C5—22no—
465C22×C5—22no—
466C22×C5—24no—
467C22×C5—41no—
468C22×C5—42no—
469C22×C5—41no—
470C22×C5—64no—
471C22×C5—64no—
472C22×C5—64no—
473C22×C5—1216no—
474C22×C5—122no—
475C22×C5—122no—
476C22×C5—122no—
477C22×C5—122no—
478C22×C5C4×#6714yes—
479C22×C5C22×C4×D311yescharacteristic
480C22×C5C2×#23511yescharacteristic
481C22×C5#100412yes—
482C22×C5#100912yes—
483C22×C5C22×#6711yescharacteristic
484C4×C5—22no—
485C4×C5—22no—
486C4×C5—22no—
487C4×C5—41no—
488C4×C5—41no—
489C4×C5—64no—
490C4×C5—122no—
491C4×C5—122no—
492C24—32no—
493C24—34no—
494C24—62no—
495C24—62no—
496C24—122no—
497C24—122no—
498C24C22×C5×D311yescharacteristic
499C24C22×C5×D311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—38no—
503C2×D4—122no—
504C2×D4—122no—
505C2×D4C4×C5×D314yes—
506C22×C4—22no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—62no—
513C22×C4—122no—
514C22×C4C5×#6714yescomplemented
515C22×C4C22×C5×D311yescharacteristic
516C22×C4C22×C5×D311yescharacteristic
517C22×C4C22×C5×D311yescharacteristic
518C22×C4C22×C5×D311yescharacteristic
519C22×C4C22×C5×D311yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—122no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—34no—
525C22⋊C4—38no—
526C22⋊C4—62no—
527C22⋊C4—64no—
528C22⋊C4—64no—
529C22⋊C4—122no—
530C22⋊C4—122no—
531C22⋊C4—122no—
532C42—22no—
533C42—122no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—22no—
540C22×C3—24no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—42no—
544C22×C3C4×C5×D414yes—
545C22×C3C23×C4×C511yescharacteristic
546C22×C3C22×C5×D411yescharacteristic
547C22×C3C2×C5×#4111yescharacteristic
548C22×C3C5×H(5,𝔽2)12yes—
549C22×C3C5×H(5,𝔽2)12yes—
550C2×D3—24no—
551C2×D3—24no—
552C2×D3—24no—
553C2×D3—416no—
554C2×D3—42no—
555C2×D3—42no—
556C2×D3—42no—
557C2×D3—42no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—41no—
562C3×C4—41no—
563Dic3—24no—
564Dic3—42no—
565Dic3—42no—
566C2×C5—24no—
567C2×C5—42no—
568C2×C5—124no—
569C2×C5#554512yes—
570C2×C5#556012yes—
571C2×C5C2×C4×#6711yescharacteristic
572C2×C5#580411yescharacteristic
573C2×C5#583011yescharacteristic
574C23—22no—
575C23—22no—
576C23—21no—
577C23—22no—
578C23—22no—
579C23—21no—
580C23—34no—
581C23—68no—
582C23—62no—
583C23—62no—
584C23—62no—
585C23—62no—
586C23—62no—
587C23—62no—
588C23—128no—
589C23—124no—
590C23—128no—
591C23—124no—
592C23C2×C4×C5×D312yes—
593C23C2×C4×C5×D312yes—
594C23C5×#23512yes—
595C23C2×C5×#6712yes—
596C23C23×C5×D311yescharacteristic
597D4—28no—
598D4—128no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—34no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—124no—
619C2×C4C2×C4×C5×D312yes—
620C2×C4C2×C5×#6712yes—
621C2×C4C2×C5×#6712yes—
622C2×C3—24no—
623C2×C3—42no—
624C2×C3C2×C4×C5×D411yescharacteristic
625C2×C3C5×#51812yes—
626C2×C3C5×#53411yescharacteristic
627C2×C3C5×#53511yescharacteristic
628C2×C3C5×#53812yes—
629D3—44no—
630C5#8239511yescharacteristic, direct product factor, Sylow
631C22—24no—
632C22—22no—
633C22—24no—
634C22—22no—
635C22—22no—
636C22—24no—
637C22—41no—
638C22—42no—
639C22—41no—
640C22—64no—
641C22—64no—
642C22—64no—
643C22—1216no—
644C22—122no—
645C22—122no—
646C22—122no—
647C22—122no—
648C22C4×C5×#6714yes—
649C22C22×C4×C5×D311yescharacteristic
650C22C2×C5×#23511yescharacteristic
651C22C5×#100412yes—
652C22C5×#100912yes—
653C22C22×C5×#6711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—64no—
660C4—122no—
661C4—122no—
662C3C5×#232111yescharacteristic, complemented, Sylow
663C2—24no—
664C2—42no—
665C2—124no—
666C2C5×#554512yes—
667C2C5×#556012yes—
668C2C2×C4×C5×#6711yescharacteristic
669C2C5×#580411yescharacteristic
670C2C5×#583011yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C5×#937C2
cosocleC23×C3C24×C5
hypercenterC2×C4×C5×D4D3
hypocenterC3C5×#2321
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C22×C5×(C2×D3)⋊C4C2semidirect
4. C5×#5220C2semidirect
5. C5×#5213C2semidirect
6. C4×C5×#217C2semidirect
7. C5×#4990C2semidirect
8. C5×#4957C2semidirect
9. C5×#4955C2semidirect
10. C5×#4946C2semidirect
11. C5×#4940C2semidirect
16. C23×C3×C4×C5C22semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
23. C2×C3×C42×C5C22semidirect
26. C2×C5×#217C22semidirect
27. C5×#937C4semidirect
34. C2×C5×Dic3⋊C4C22semidirect
35. C2×C4×C5×Dic3C22semidirect
36. C5×C3⋊#95C22semidirect
37. C5×C3⋊#95C22semidirect
38. C5×C3⋊#95C22semidirect
39. #82395C5direct (N × H)
41. C2×C4×C5×D4D3semidirect
57. C23×C5×D3C2×C4semidirect
65. C22×C3×C4×C5D4semidirect
73. C2×C5×#67C2×C4semidirect
85. C5×#217C2×C4semidirect
90. C5×(C2×D3)⋊C4C2×C4semidirect
93. C2×C3×C4×D4C2×C5semidirect
95. C22×(C2×D3)⋊C4C2×C5semidirect
96. #5220C2×C5semidirect
97. #5213C2×C5semidirect
98. C4×#217C2×C5semidirect
99. #4990C2×C5semidirect
100. #4957C2×C5semidirect
101. #4955C2×C5semidirect
102. #4946C2×C5semidirect
103. #4940C2×C5semidirect
109. C23×C4×C5C2×D3semidirect
113. C2×C5×C4⋊C4C2×D3semidirect
124. C2×C5×C22⋊C4C2×D3semidirect
126. C2×C42×C5C2×D3semidirect
182. C23×C3×C4C22×C5semidirect
186. C2×C3×C4⋊C4C22×C5semidirect
188. C2×C3×C22⋊C4C22×C5semidirect
189. C2×C3×C42C22×C5semidirect
192. C2×#217C22×C5semidirect
193. #937C4×C5semidirect
200. C2×Dic3⋊C4C22×C5semidirect
201. C2×C4×Dic3C22×C5semidirect
202. C3⋊#95C22×C5semidirect
203. C3⋊#95C22×C5semidirect
204. C3⋊#95C22×C5semidirect
227. C22×C4×C5#67semidirect
248. C2×C4×D4C5×D3semidirect
295. C23×D3C2×C4×C5semidirect
303. C22×C3×C4C5×D4semidirect
311. C2×#67C2×C4×C5semidirect
323. #217C2×C4×C5semidirect
328. (C2×D3)⋊C4C2×C4×C5semidirect
384. C23×C4C2×C5×D3semidirect
388. C2×C4⋊C4C2×C5×D3semidirect
399. C2×C22⋊C4C2×C5×D3semidirect
401. C2×C42C2×C5×D3semidirect
514. C22×C4C5×#67semidirect
534. C3×C5#2321semidirect
630. C5#82395direct (N × H)
662. C3C5×#2321semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C5×#9372
C22×C5×(C2×D3)⋊C42
C5×#52202
C5×#52132
C4×C5×#2172
C5×#49902
C5×#49572
C5×#49552
C5×#49462
C5×#49402
C5×#23213
#823955