Finite Group Databasebeta

← C5×#82236 #14323879

Subgroups — C5×#82236 #14323879

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic
3C2×C4×C5×D12C211yesmaximal, characteristic, complemented
4C5×#5212C211yesmaximal, characteristic, complemented
5C5×#4990C212yesmaximal, complemented
6C5×#4989C212yesmaximal, complemented
7C5×#4957C212yesmaximal, complemented
8C5×#4956C212yesmaximal, complemented
9C5×#4939C211yesmaximal, characteristic, complemented
10C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11C5×#4928C211yesmaximal, characteristic, complemented
12C5×#2324—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2212yes—
15C22×C5×D12C2211yescharacteristic
16C22×C4×C5×D3C2212yes—
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C5×#217C2212yes—
25C5×#930C418yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C5×(C2×D3)⋊C4C2212yes—
29C2×C5×(C2×D3)⋊C4C2212yes—
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C5×C4⋊Dic3C2211yescharacteristic
33C2×C5×Dic3⋊C4C2212yes—
34C2×C4×C5×Dic3C2212yes—
35C4×C5×D12—24no—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#82236C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#121—31no—
41C2×C4×C5×D4—31no—
42C2×C5×#117D311yescharacteristic, complemented
43C5×#390—32no—
44C5×#390—31no—
45C5×#389—31no—
46C5×#388—32no—
47C5×#386—32no—
48C5×#385—32no—
49C5×#380—31no—
50C4×C5×C4⋊C4—31no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2312yes—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C2×C5×#67—42no—
63C2×C5×#67—42no—
64C2×C5×#67C2×C418yescomplemented
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2312yes—
68C2×C5×D12—22no—
69C2×C5×D12—22no—
70C2×C5×D12C2×C414yes—
71C2×C4×C5×D3—24no—
72C2×C4×C5×D3—42no—
73C2×C4×C5×D3—42no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4—22no—
78C3×C42×C5—22no—
79C3×C42×C5D414yescomplemented
80C5×#217—42no—
81C5×(C2×D3)⋊C4—24no—
82C5×(C2×D3)⋊C4—42no—
83C5×(C2×D3)⋊C4—42no—
84C5×(C2×D3)⋊C4C2×C418yescomplemented
85C5×C4⋊Dic3—22no—
86C5×C4⋊Dic3—22no—
87C5×C4⋊Dic3C2×C414yescomplemented
88C5×Dic3⋊C4—42no—
89C4×C5×Dic3—42no—
90C2×C3×#117C2×C511yescharacteristic, complemented
91C2×#930C2×C511yescharacteristic
92C2×C4×D12C2×C511yescharacteristic, complemented
93#5212C2×C511yescharacteristic, complemented
94#4990C2×C512yescomplemented
95#4989C2×C512yescomplemented
96#4957C2×C512yescomplemented
97#4956C2×C512yescomplemented
98#4939C2×C511yescharacteristic, complemented
99C4×C4⋊Dic3C2×C511yescharacteristic, complemented
100#4928C2×C511yescharacteristic, complemented
101C22×C5×D4—32no—
102C22×C5×D4—31no—
103C23×C4×C5—32no—
104C23×C4×C5C2×D311yescharacteristic
105C5×#121—38no—
106C4×C5×D4—64no—
107C5×#117—24no—
108C2×C5×C4⋊C4—31no—
109C2×C5×C4⋊C4—31no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C4⋊C4—32no—
112C2×C5×C4⋊C4C2×D311yescharacteristic
113C2×C5×C4⋊C4C2×D311yescharacteristic
114C2×C5×C22⋊C4—32no—
115C2×C5×C22⋊C4—32no—
116C2×C5×C22⋊C4—32no—
117C2×C5×C22⋊C4—32no—
118C2×C5×C22⋊C4—32no—
119C2×C5×C22⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4C2×D311yescharacteristic
121C2×C42×C5—32no—
122C2×C42×C5C2×D311yescharacteristic
123C2×C42×C5C2×D311yescharacteristic
124C5×#95—32no—
125C5×#95—32no—
126C5×#95—32no—
127#2324—31noSylow
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5C22×C412yes—
135C23×C3×C5C2411yescharacteristic
136C22×C5×D3—22no—
137C22×C5×D3—22no—
138C22×C5×D3—22no—
139C22×C5×D3—22no—
140C22×C5×D3—22no—
141C22×C5×D3—22no—
142C22×C5×D3C22×C414yes—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C22×C412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5#4112yes—
162C5×#67—48no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3C22×C414yes—
172C5×D12—28no—
173C4×C5×D3—48no—
174C23×C3×C4C22×C511yescharacteristic
175C22×#67C22×C512yes—
176C22×D12C22×C511yescharacteristic
177C22×C4×D3C22×C512yes—
178C3×#117—24no—
179C2×C3×C4⋊C4C22×C511yescharacteristic
180C2×C3×C4⋊C4C22×C511yescharacteristic
181C2×C3×C22⋊C4C22×C511yescharacteristic
182C2×C3×C22⋊C4C22×C511yescharacteristic
183C2×C3×C42C22×C511yescharacteristic
184C2×C3×C42C22×C511yescharacteristic
185C2×#217C22×C512yes—
186#930C4×C518yescomplemented
187C2×(C2×D3)⋊C4C22×C512yes—
188C2×(C2×D3)⋊C4C22×C512yes—
189C2×(C2×D3)⋊C4C22×C512yes—
190C2×(C2×D3)⋊C4C22×C512yes—
191C2×C4⋊Dic3C22×C511yescharacteristic
192C2×C4⋊Dic3C22×C511yescharacteristic
193C2×C4⋊Dic3C22×C511yescharacteristic
194C2×Dic3⋊C4C22×C512yes—
195C2×C4×Dic3C22×C512yes—
196C4×D12—24no—
197C3⋊#95C22×C512yes—
198C3⋊#95C22×C512yes—
199C3⋊#95C22×C512yes—
200C24×C5—32no—
201C24×C5C22×D311yescharacteristic
202C2×C5×D4—38no—
203C2×C5×D4—34no—
204C2×C5×D4—62no—
205C2×C5×D4—62no—
206C2×C5×D4—122no—
207C2×C5×D4—122no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5—32no—
213C22×C4×C5—64no—
214C22×C4×C5—122no—
215C22×C4×C5—122no—
216C22×C4×C5C4×D314yescomplemented
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C4⋊C4—34no—
226C5×C4⋊C4—62no—
227C5×C4⋊C4—62no—
228C5×C4⋊C4—122no—
229C5×C22⋊C4—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—38no—
232C5×C22⋊C4—64no—
233C5×C22⋊C4—122no—
234C5×C22⋊C4—122no—
235C5×C22⋊C4—122no—
236C42×C5—22no—
237C42×C5—122no—
238C42×C5#6714yescomplemented
239C2×#121—31no—
240C2×C4×D4—31no—
241C2×#117C5×D311yescharacteristic, complemented
242#390—32no—
243#390—31no—
244#389—31no—
245#388—32no—
246#386—32no—
247#385—32no—
248#380—31no—
249C4×C4⋊C4—31no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5C23×C411yescharacteristic
258C22×C3×C5C22×D411yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C22×C3×C5H(5,𝔽2)11yescharacteristic
263C22×C3×C52−1+411yescharacteristic
264C2×C5×D3—24no—
265C2×C5×D3—24no—
266C2×C5×D3—24no—
267C2×C5×D3—42no—
268C2×C5×D3—42no—
269C2×C5×D3—42no—
270C2×C5×D3—42no—
271C3×C4×C5—22no—
272C3×C4×C5—22no—
273C3×C4×C5—22no—
274C3×C4×C5—41no—
275C3×C4×C5—41no—
276C3×C4×C5C4×D414yes—
277C5×Dic3—24no—
278C5×Dic3—42no—
279C5×Dic3—42no—
280C24×C3C23×C511yescharacteristic
281C23×D3C23×C512yes—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4C2×C4×C514yescomplemented
285C22×C3×C4C23×C511yescharacteristic
286C22×C3×C4C23×C511yescharacteristic
287C22×C3×C4C23×C511yescharacteristic
288C22×C3×C4C23×C511yescharacteristic
289C22×C3×C4C23×C511yescharacteristic
290C22×C3×C4C23×C511yescharacteristic
291C2×#67—42no—
292C2×#67—42no—
293C2×#67C2×C4×C518yescomplemented
294C22×Dic3C23×C512yes—
295C22×Dic3C23×C512yes—
296C22×Dic3C23×C512yes—
297C2×D12—22no—
298C2×D12—22no—
299C2×D12C2×C4×C514yes—
300C2×C4×D3—24no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C42—22no—
308C3×C42C5×D414yescomplemented
309#217—42no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4C2×C4×C518yescomplemented
314C4⋊Dic3—22no—
315C4⋊Dic3—22no—
316C4⋊Dic3C2×C4×C514yescomplemented
317Dic3⋊C4—42no—
318C4×Dic3—42no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—34no—
326C23×C5—62no—
327C23×C5—62no—
328C23×C5—62no—
329C23×C5—62no—
330C23×C5—62no—
331C23×C5—62no—
332C23×C5C2×C4×D312yes—
333C23×C5C23×D311yescharacteristic
334C5×D4—68no—
335C5×D4—128no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—28no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—34no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5—62no—
354C2×C4×C5—62no—
355C2×C4×C5—62no—
356C2×C4×C5—62no—
357C2×C4×C5—62no—
358C2×C4×C5—128no—
359C2×C4×C5C2×C4×D312yes—
360C2×C4×C5C2×C4×D312yes—
361C2×C4×C5#23512yes—
362C2×C4×C5C2×#6712yes—
363C2×C4×C5C2×#6712yes—
364C2×C4×C5C2×#6712yes—
365C22×D4—32no—
366C22×D4—31no—
367C23×C4—32no—
368C23×C4C2×C5×D311yescharacteristic
369#121—38no—
370C4×D4—64no—
371#117—24no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4C2×C5×D311yescharacteristic
377C2×C4⋊C4C2×C5×D311yescharacteristic
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4C2×C5×D311yescharacteristic
384C2×C22⋊C4C2×C5×D311yescharacteristic
385C2×C42—32no—
386C2×C42C2×C5×D311yescharacteristic
387C2×C42C2×C5×D311yescharacteristic
388#95—32no—
389#95—32no—
390#95—32no—
391C2×C3×C5—42no—
392C2×C3×C5C2×C4×D411yescharacteristic
393C2×C3×C5#51811yescharacteristic
394C2×C3×C5#52011yescharacteristic
395C2×C3×C5#53511yescharacteristic
396C2×C3×C5#53711yescharacteristic
397C2×C3×C5#54011yescharacteristic
398C2×C3×C5#54211yescharacteristic
399C5×D3—44no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3C22×C4×C512yes—
407C23×C3C24×C511yescharacteristic
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3C22×C4×C514yes—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—28no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4C22×C4×C512yes—
429C2×C3×C4C22×C4×C512yes—
430C2×C3×C4C2×C5×D412yes—
431C2×C3×C4C2×C5×D412yes—
432C2×C3×C4C2×C5×D412yes—
433C2×C3×C4C5×#4112yes—
434#67—48no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3C22×C4×C514yes—
444D12—28no—
445C4×D3—48no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—64no—
454C22×C5—64no—
455C22×C5—64no—
456C22×C5—122no—
457C22×C5—122no—
458C22×C5—122no—
459C22×C5—122no—
460C22×C5C22×C4×D311yescharacteristic
461C22×C5C2×#23511yescharacteristic
462C22×C5#100911yescharacteristic
463C22×C5#100911yescharacteristic
464C22×C5#100911yescharacteristic
465C22×C5#101011yescharacteristic
466C22×C5C22×#6711yescharacteristic
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—22no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—64no—
473C4×C5—122no—
474C4×C5—122no—
475C4×C5C4×#6714yes—
476C24—32no—
477C24C22×C5×D311yescharacteristic
478C2×D4—38no—
479C2×D4—34no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—122no—
483C2×D4—122no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—64no—
490C22×C4—122no—
491C22×C4—122no—
492C22×C4C4×C5×D314yescomplemented
493C22×C4C22×C5×D311yescharacteristic
494C22×C4C22×C5×D311yescharacteristic
495C22×C4C22×C5×D311yescharacteristic
496C22×C4C22×C5×D311yescharacteristic
497C22×C4C22×C5×D311yescharacteristic
498C22×C4C22×C5×D311yescharacteristic
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—34no—
502C4⋊C4—62no—
503C4⋊C4—62no—
504C4⋊C4—122no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—38no—
508C22⋊C4—64no—
509C22⋊C4—122no—
510C22⋊C4—122no—
511C22⋊C4—122no—
512C42—22no—
513C42—122no—
514C42C5×#6714yescomplemented
515C3×C5#232411yescharacteristic, complemented, Hall
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3C23×C4×C511yescharacteristic
524C22×C3C22×C5×D411yescharacteristic
525C22×C3C2×C5×#4111yescharacteristic
526C22×C3C5×H(5,𝔽2)11yescharacteristic
527C22×C3C5×H(5,𝔽2)11yescharacteristic
528C22×C3C5×H(5,𝔽2)11yescharacteristic
529C22×C3C5×2−1+411yescharacteristic
530C2×D3—24no—
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3—42no—
536C2×D3—42no—
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—22no—
540C3×C4—41no—
541C3×C4—41no—
542C3×C4C4×C5×D414yes—
543Dic3—24no—
544Dic3—42no—
545Dic3—42no—
546C2×C5—42no—
547C2×C5—124no—
548C2×C5#552111yescharacteristic
549C2×C5#552311yescharacteristic
550C2×C5#553411yescharacteristic
551C2×C5#553511yescharacteristic
552C2×C5C2×C4×#6711yescharacteristic
553C2×C5#583011yescharacteristic
554C2×C5#583311yescharacteristic
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—34no—
562C23—62no—
563C23—62no—
564C23—62no—
565C23—62no—
566C23—62no—
567C23—62no—
568C23C2×C4×C5×D312yes—
569C23C23×C5×D311yescharacteristic
570D4—68no—
571D4—128no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—28no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—34no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—128no—
595C2×C4C2×C4×C5×D312yes—
596C2×C4C2×C4×C5×D312yes—
597C2×C4C5×#23512yes—
598C2×C4C2×C5×#6712yes—
599C2×C4C2×C5×#6712yes—
600C2×C4C2×C5×#6712yes—
601C2×C3—42no—
602C2×C3C2×C4×C5×D411yescharacteristic
603C2×C3C5×#51811yescharacteristic
604C2×C3C5×#52011yescharacteristic
605C2×C3C5×#53511yescharacteristic
606C2×C3C5×#53711yescharacteristic
607C2×C3C5×#54011yescharacteristic
608C2×C3C5×#54211yescharacteristic
609D3—44no—
610C5#8223611yescharacteristic, direct product factor, Sylow
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—64no—
619C22—64no—
620C22—64no—
621C22—122no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22C22×C4×C5×D311yescharacteristic
626C22C2×C5×#23511yescharacteristic
627C22C5×#100911yescharacteristic
628C22C5×#100911yescharacteristic
629C22C5×#100911yescharacteristic
630C22C5×#101011yescharacteristic
631C22C22×C5×#6711yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—41no—
636C4—41no—
637C4—64no—
638C4—122no—
639C4—122no—
640C4C4×C5×#6714yes—
641C3C5×#232411yescharacteristic, complemented, Sylow
642C2—42no—
643C2—124no—
644C2C5×#552111yescharacteristic
645C2C5×#552311yescharacteristic
646C2C5×#553411yescharacteristic
647C2C5×#553511yescharacteristic
648C2C2×C4×C5×#6711yescharacteristic
649C2C5×#583011yescharacteristic
650C2C5×#583311yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC2×C5×#930C2
cosocleC23×C3C24×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C2×C4×C5×D12C2semidirect
4. C5×#5212C2semidirect
5. C5×#4990C2semidirect
6. C5×#4989C2semidirect
7. C5×#4957C2semidirect
8. C5×#4956C2semidirect
9. C5×#4939C2semidirect
10. C4×C5×C4⋊Dic3C2semidirect
11. C5×#4928C2semidirect
25. C5×#930C4semidirect
39. #82236C5direct (N × H)
42. C2×C5×#117D3semidirect
55. C22×C3×C4×C5C2×C4semidirect
64. C2×C5×#67C2×C4semidirect
79. C3×C42×C5D4semidirect
84. C5×(C2×D3)⋊C4C2×C4semidirect
87. C5×C4⋊Dic3C2×C4semidirect
90. C2×C3×#117C2×C5semidirect
92. C2×C4×D12C2×C5semidirect
93. #5212C2×C5semidirect
94. #4990C2×C5semidirect
95. #4989C2×C5semidirect
96. #4957C2×C5semidirect
97. #4956C2×C5semidirect
98. #4939C2×C5semidirect
99. C4×C4⋊Dic3C2×C5semidirect
100. #4928C2×C5semidirect
186. #930C4×C5semidirect
216. C22×C4×C5C4×D3semidirect
238. C42×C5#67semidirect
241. C2×#117C5×D3semidirect
284. C22×C3×C4C2×C4×C5semidirect
293. C2×#67C2×C4×C5semidirect
308. C3×C42C5×D4semidirect
313. (C2×D3)⋊C4C2×C4×C5semidirect
316. C4⋊Dic3C2×C4×C5semidirect
492. C22×C4C4×C5×D3semidirect
514. C42C5×#67semidirect
515. C3×C5#2324semidirect
610. C5#82236direct (N × H)
641. C3C5×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×C5×#9302
C2×C4×C5×D122
C5×#52122
C5×#49902
C5×#49892
C5×#49572
C5×#49562
C5×#49392
C4×C5×C4⋊Dic32
C5×#49282
C5×#23243
#822365