Finite Group Databasebeta

← C3×C5×#2490 #14275524

Subgroups — C3×C5×#2490 #14275524

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic
3C3×C5×#397C212yesmaximal, complemented
4C3×C5×#394C212yesmaximal, complemented
5C3×C5×#390C211yesmaximal, characteristic, complemented
6C3×C5×#390C211yesmaximal, characteristic, complemented
7C3×C5×#390C212yesmaximal, complemented
8C3×C5×#388C212yesmaximal, complemented
9C3×C5×#380C211yesmaximal, characteristic, complemented
10C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2490C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×C3×C5×D4C2212yes—
15C23×C3×C4×C5C2211yescharacteristic
16C3×C5×#125—24no—
17C3×C5×#121—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2212yes—
20C2×C3×C5×C4⋊C4C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C42×C5C2211yescharacteristic
32C2×C3×C42×C5C2211yescharacteristic
33C2×C3×C42×C5C2212yes—
34C3×C5×#95C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2490C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×#125C2×C311yescharacteristic, complemented
40C2×C5×#121C2×C311yescharacteristic
41C5×#397C2×C312yescomplemented
42C5×#394C2×C312yescomplemented
43C5×#390C2×C311yescharacteristic, complemented
44C5×#390C2×C311yescharacteristic, complemented
45C5×#390C2×C312yescomplemented
46C5×#388C2×C312yescomplemented
47C5×#380C2×C311yescharacteristic, complemented
48C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
49C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
50C24×C3×C5C2312yes—
51C24×C3×C5C2311yescharacteristic
52C2×C3×C5×D4—24no—
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—42no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C3×C5×C4⋊C4—24no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4D414yes—
75C3×C5×C22⋊C4—22no—
76C3×C5×C22⋊C4—24no—
77C3×C5×C22⋊C4—22no—
78C3×C5×C22⋊C4—24no—
79C3×C5×C22⋊C4—42no—
80C3×C5×C22⋊C4—42no—
81C3×C5×C22⋊C4—42no—
82C3×C5×C22⋊C4—42no—
83C3×C42×C5—22no—
84C3×C42×C5—22no—
85C3×C42×C5—42no—
86C2×C3×#125C2×C511yescharacteristic, complemented
87C2×C3×#121C2×C511yescharacteristic
88C3×#397C2×C512yescomplemented
89C3×#394C2×C512yescomplemented
90C3×#390C2×C511yescharacteristic, complemented
91C3×#390C2×C511yescharacteristic, complemented
92C3×#390C2×C512yescomplemented
93C3×#388C2×C512yescomplemented
94C3×#380C2×C511yescharacteristic, complemented
95C3×C4×C4⋊C4C2×C511yescharacteristic, complemented
96C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
97C22×C5×D4C22×C311yescharacteristic
98C22×C5×D4C22×C312yes—
99C23×C4×C5C22×C311yescharacteristic
100C5×#125—24no—
101C5×#121—24no—
102C2×C5×C4⋊C4C22×C311yescharacteristic
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C312yes—
105C2×C5×C4⋊C4C22×C312yes—
106C2×C5×C4⋊C4C22×C311yescharacteristic
107C2×C5×C22⋊C4C22×C311yescharacteristic
108C2×C5×C22⋊C4C22×C311yescharacteristic
109C2×C5×C22⋊C4C22×C312yes—
110C2×C5×C22⋊C4C22×C312yes—
111C2×C5×C22⋊C4C22×C312yes—
112C2×C5×C22⋊C4C22×C312yes—
113C2×C5×C22⋊C4C22×C312yes—
114C2×C5×C22⋊C4C22×C312yes—
115C2×C42×C5C22×C311yescharacteristic
116C2×C42×C5C22×C311yescharacteristic
117C2×C42×C5C22×C312yes—
118C5×#95C22×C311yescharacteristic
119C5×#95C22×C311yescharacteristic
120C5×#95C22×C312yes—
121C5×#95C22×C312yes—
122#2490C3×C511yescharacteristic, direct product factor, Sylow
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—22no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5#4112yes—
137C23×C3×C5C2411yescharacteristic
138C3×C5×D4—48no—
139C3×C5×D4—44no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—44no—
163C2×C3×C4×C5C2×D414yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5#4112yes—
166C2×C3×C4×C5#4112yes—
167C2×C3×C4×C5#4112yes—
168C22×C3×D4C22×C511yescharacteristic
169C22×C3×D4C22×C512yes—
170C23×C3×C4C22×C511yescharacteristic
171C3×#125—24no—
172C3×#121—24no—
173C2×C3×C4⋊C4C22×C511yescharacteristic
174C2×C3×C4⋊C4C22×C511yescharacteristic
175C2×C3×C4⋊C4C22×C512yes—
176C2×C3×C4⋊C4C22×C512yes—
177C2×C3×C4⋊C4C22×C511yescharacteristic
178C2×C3×C22⋊C4C22×C511yescharacteristic
179C2×C3×C22⋊C4C22×C511yescharacteristic
180C2×C3×C22⋊C4C22×C512yes—
181C2×C3×C22⋊C4C22×C512yes—
182C2×C3×C22⋊C4C22×C512yes—
183C2×C3×C22⋊C4C22×C512yes—
184C2×C3×C22⋊C4C22×C512yes—
185C2×C3×C22⋊C4C22×C512yes—
186C2×C3×C42C22×C511yescharacteristic
187C2×C3×C42C22×C511yescharacteristic
188C2×C3×C42C22×C512yes—
189C3×#95C22×C511yescharacteristic
190C3×#95C22×C511yescharacteristic
191C3×#95C22×C512yes—
192C3×#95C22×C512yes—
193C24×C5C23×C312yes—
194C24×C5C23×C311yescharacteristic
195C2×C5×D4—24no—
196C2×C5×D4—24no—
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—42no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5C23×C311yescharacteristic
205C22×C4×C5C23×C311yescharacteristic
206C22×C4×C5C23×C312yes—
207C22×C4×C5C23×C311yescharacteristic
208C22×C4×C5C23×C312yes—
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C312yes—
211C22×C4×C5C23×C311yescharacteristic
212C22×C4×C5C23×C311yescharacteristic
213C5×C4⋊C4—24no—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4C3×D414yes—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—24no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—24no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C42×C5—22no—
227C42×C5—22no—
228C42×C5—42no—
229C2×#125C2×C3×C511yescharacteristic, complemented
230C2×#121C2×C3×C511yescharacteristic
231#397C2×C3×C512yescomplemented
232#394C2×C3×C512yescomplemented
233#390C2×C3×C511yescharacteristic, complemented
234#390C2×C3×C511yescharacteristic, complemented
235#390C2×C3×C512yescomplemented
236#388C2×C3×C512yescomplemented
237#380C2×C3×C511yescharacteristic, complemented
238C4×C4⋊C4C2×C3×C511yescharacteristic, complemented
239C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5—42no—
248C22×C3×C5—42no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5—42no—
254C22×C3×C5C22×D411yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5H(5,𝔽2)11yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C3×C4×C5—24no—
262C3×C4×C5—22no—
263C3×C4×C5—41no—
264C3×C4×C5—42no—
265C3×C4×C5—41no—
266C3×C4×C5—41no—
267C3×C4×C5—42no—
268C3×C4×C5—41no—
269C3×C4×C5#12414yes—
270C24×C3C23×C512yes—
271C24×C3C23×C511yescharacteristic
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4—42no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4C23×C511yescharacteristic
282C22×C3×C4C23×C511yescharacteristic
283C22×C3×C4C23×C512yes—
284C22×C3×C4C23×C511yescharacteristic
285C22×C3×C4C23×C511yescharacteristic
286C22×C3×C4C23×C512yes—
287C22×C3×C4C23×C512yes—
288C22×C3×C4C23×C511yescharacteristic
289C22×C3×C4C23×C511yescharacteristic
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4C5×D414yes—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C42—22no—
304C3×C42—22no—
305C3×C42—42no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5C3×#4112yes—
320C23×C5C24×C311yescharacteristic
321C5×D4—48no—
322C5×D4—44no—
323C2×C4×C5—21no—
324C2×C4×C5—22no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—22no—
335C2×C4×C5—21no—
336C2×C4×C5—22no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—22no—
344C2×C4×C5—21no—
345C2×C4×C5—44no—
346C2×C4×C5C2×C3×D414yes—
347C2×C4×C5C2×C3×D412yes—
348C2×C4×C5C3×#4112yes—
349C2×C4×C5C3×#4112yes—
350C2×C4×C5C3×#4112yes—
351C22×D4C22×C3×C511yescharacteristic
352C22×D4C22×C3×C512yes—
353C23×C4C22×C3×C511yescharacteristic
354#125—24no—
355#121—24no—
356C2×C4⋊C4C22×C3×C511yescharacteristic
357C2×C4⋊C4C22×C3×C512yes—
358C2×C4⋊C4C22×C3×C512yes—
359C2×C4⋊C4C22×C3×C511yescharacteristic
360C2×C4⋊C4C22×C3×C511yescharacteristic
361C2×C22⋊C4C22×C3×C512yes—
362C2×C22⋊C4C22×C3×C511yescharacteristic
363C2×C22⋊C4C22×C3×C511yescharacteristic
364C2×C22⋊C4C22×C3×C512yes—
365C2×C22⋊C4C22×C3×C512yes—
366C2×C22⋊C4C22×C3×C512yes—
367C2×C22⋊C4C22×C3×C512yes—
368C2×C22⋊C4C22×C3×C512yes—
369C2×C42C22×C3×C511yescharacteristic
370C2×C42C22×C3×C511yescharacteristic
371C2×C42C22×C3×C512yes—
372#95C22×C3×C511yescharacteristic
373#95C22×C3×C511yescharacteristic
374#95C22×C3×C512yes—
375#95C22×C3×C512yes—
376C2×C3×C5—42no—
377C2×C3×C5—82no—
378C2×C3×C5C2×#12411yescharacteristic
379C2×C3×C5#52911yescharacteristic
380C2×C3×C5#54011yescharacteristic
381C2×C3×C5#54611yescharacteristic
382C2×C3×C5#55011yescharacteristic
383C2×C3×C5#55311yescharacteristic
384C2×C3×C5#55311yescharacteristic
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3C5×#4112yes—
399C23×C3C24×C511yescharacteristic
400C3×D4—48no—
401C3×D4—44no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—44no—
425C2×C3×C4C2×C5×D414yes—
426C2×C3×C4C2×C5×D412yes—
427C2×C3×C4C5×#4112yes—
428C2×C3×C4C5×#4112yes—
429C2×C3×C4C5×#4112yes—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—42no—
438C22×C5—42no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5C22×C3×D411yescharacteristic
445C22×C5C2×C3×#4111yescharacteristic
446C22×C5C2×C3×#4111yescharacteristic
447C22×C5C2×C3×#4111yescharacteristic
448C22×C5C2×C3×#4111yescharacteristic
449C22×C5C3×H(5,𝔽2)11yescharacteristic
450C22×C5C3×H(5,𝔽2)11yescharacteristic
451C4×C5—24no—
452C4×C5—22no—
453C4×C5—41no—
454C4×C5—42no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5C3×#12414yes—
460C24C23×C3×C512yes—
461C24C23×C3×C511yescharacteristic
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—42no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4C23×C3×C511yescharacteristic
472C22×C4C23×C3×C511yescharacteristic
473C22×C4C23×C3×C512yes—
474C22×C4C23×C3×C511yescharacteristic
475C22×C4C23×C3×C511yescharacteristic
476C22×C4C23×C3×C512yes—
477C22×C4C23×C3×C512yes—
478C22×C4C23×C3×C511yescharacteristic
479C22×C4C23×C3×C511yescharacteristic
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4C3×C5×D414yes—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—24no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C42—22no—
494C42—22no—
495C42—42no—
496C3×C5#249011yescharacteristic, direct product factor, Hall
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3C22×C5×D411yescharacteristic
512C22×C3C2×C5×#4111yescharacteristic
513C22×C3C2×C5×#4111yescharacteristic
514C22×C3C2×C5×#4111yescharacteristic
515C22×C3C2×C5×#4111yescharacteristic
516C22×C3C5×H(5,𝔽2)11yescharacteristic
517C22×C3C5×H(5,𝔽2)11yescharacteristic
518C3×C4—24no—
519C3×C4—22no—
520C3×C4—41no—
521C3×C4—42no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4—42no—
525C3×C4—41no—
526C3×C4C5×#12414yes—
527C2×C5—42no—
528C2×C5—82no—
529C2×C5C2×C3×#12411yescharacteristic
530C2×C5C3×#52911yescharacteristic
531C2×C5C3×#54011yescharacteristic
532C2×C5C3×#54611yescharacteristic
533C2×C5C3×#55011yescharacteristic
534C2×C5C3×#55311yescharacteristic
535C2×C5C3×#55311yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23C3×C5×#4112yes—
550C23C24×C3×C511yescharacteristic
551D4—48no—
552D4—44no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4C2×C3×C5×D414yes—
577C2×C4C2×C3×C5×D412yes—
578C2×C4C3×C5×#4112yes—
579C2×C4C3×C5×#4112yes—
580C2×C4C3×C5×#4112yes—
581C2×C3—42no—
582C2×C3—82no—
583C2×C3C2×C5×#12411yescharacteristic
584C2×C3C5×#52911yescharacteristic
585C2×C3C5×#54011yescharacteristic
586C2×C3C5×#54611yescharacteristic
587C2×C3C5×#55011yescharacteristic
588C2×C3C5×#55311yescharacteristic
589C2×C3C5×#55311yescharacteristic
590C5C3×#249011yescharacteristic, direct product factor, Sylow
591C22—22no—
592C22—22no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22C22×C3×C5×D411yescharacteristic
606C22C2×C3×C5×#4111yescharacteristic
607C22C2×C3×C5×#4111yescharacteristic
608C22C2×C3×C5×#4111yescharacteristic
609C22C2×C3×C5×#4111yescharacteristic
610C22C3×C5×H(5,𝔽2)11yescharacteristic
611C22C3×C5×H(5,𝔽2)11yescharacteristic
612C4—24no—
613C4—22no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4C3×C5×#12414yes—
621C3C5×#249011yescharacteristic, direct product factor, Sylow
622C2—42no—
623C2—82no—
624C2C2×C3×C5×#12411yescharacteristic
625C2C3×C5×#52911yescharacteristic
626C2C3×C5×#54011yescharacteristic
627C2C3×C5×#54611yescharacteristic
628C2C3×C5×#55011yescharacteristic
629C2C3×C5×#55311yescharacteristic
630C2C3×C5×#55311yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
3. C3×C5×#397C2semidirect
4. C3×C5×#394C2semidirect
5. C3×C5×#390C2semidirect
6. C3×C5×#390C2semidirect
7. C3×C5×#390C2semidirect
8. C3×C5×#388C2semidirect
9. C3×C5×#380C2semidirect
10. C3×C4×C5×C4⋊C4C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2490C3direct (N × H)
38. C3×#2490C5direct (N × H)
39. C2×C5×#125C2×C3semidirect
41. C5×#397C2×C3semidirect
42. C5×#394C2×C3semidirect
43. C5×#390C2×C3semidirect
44. C5×#390C2×C3semidirect
45. C5×#390C2×C3semidirect
46. C5×#388C2×C3semidirect
47. C5×#380C2×C3semidirect
48. C4×C5×C4⋊C4C2×C3semidirect
49. C4×C5×C22⋊C4C2×C3semidirect
86. C2×C3×#125C2×C5semidirect
88. C3×#397C2×C5semidirect
89. C3×#394C2×C5semidirect
90. C3×#390C2×C5semidirect
91. C3×#390C2×C5semidirect
92. C3×#390C2×C5semidirect
93. C3×#388C2×C5semidirect
94. C3×#380C2×C5semidirect
95. C3×C4×C4⋊C4C2×C5semidirect
96. C3×C4×C22⋊C4C2×C5semidirect
122. #2490C3×C5direct (N × H)
229. C2×#125C2×C3×C5semidirect
231. #397C2×C3×C5semidirect
232. #394C2×C3×C5semidirect
233. #390C2×C3×C5semidirect
234. #390C2×C3×C5semidirect
235. #390C2×C3×C5semidirect
236. #388C2×C3×C5semidirect
237. #380C2×C3×C5semidirect
238. C4×C4⋊C4C2×C3×C5semidirect
239. C4×C22⋊C4C2×C3×C5semidirect
496. C3×C5#2490direct (N × H)
590. C5C3×#2490direct (N × H)
621. C3C5×#2490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1252
C2×C3×C5×#1212
C3×C5×#3972
C3×C5×#3942
C3×C5×#3902
C3×C5×#3882
C3×C5×#3802
C3×C4×C5×C4⋊C42
C3×C4×C5×C22⋊C42
C5×#24903
C3×#24905