Finite Group Databasebeta

← C3×C5×#2420 #14275454

Subgroups — C3×C5×#2420 #14275454

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
3C3×C5×#397C212yesmaximal, complemented
4C3×C5×#394C212yesmaximal, complemented
5C3×C5×#390C211yesmaximal, characteristic, complemented
6C3×C5×#389C211yesmaximal, characteristic, complemented
7C3×C5×#386C212yesmaximal, complemented
8C3×C5×#382C211yesmaximal, characteristic, complemented
9C3×C5×#381C212yesmaximal, complemented
10C3×C5×#380C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2420C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2212yes—
17C3×C5×#121—24no—
18C3×C4×C5×D4—24no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C42×C5C2211yescharacteristic
31C2×C3×C42×C5C2211yescharacteristic
32C3×C5×#95C2211yescharacteristic
33C3×C5×#95C2211yescharacteristic
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2420C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×#121C2×C311yescharacteristic
40C2×C4×C5×D4C2×C311yescharacteristic, complemented
41C5×#397C2×C312yescomplemented
42C5×#394C2×C312yescomplemented
43C5×#390C2×C311yescharacteristic, complemented
44C5×#389C2×C311yescharacteristic, complemented
45C5×#386C2×C312yescomplemented
46C5×#382C2×C311yescharacteristic, complemented
47C5×#381C2×C312yescomplemented
48C5×#380C2×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—42no—
57C2×C3×C5×D4D414yes—
58C22×C3×C4×C5—24no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—42no—
77C3×C5×C22⋊C4—24no—
78C3×C5×C22⋊C4—24no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—42no—
82C3×C5×C22⋊C4—42no—
83C3×C5×C22⋊C4—42no—
84C3×C42×C5—22no—
85C3×C42×C5—22no—
86C2×C3×#121C2×C511yescharacteristic
87C2×C3×C4×D4C2×C511yescharacteristic, complemented
88C3×#397C2×C512yescomplemented
89C3×#394C2×C512yescomplemented
90C3×#390C2×C511yescharacteristic, complemented
91C3×#389C2×C511yescharacteristic, complemented
92C3×#386C2×C512yescomplemented
93C3×#382C2×C511yescharacteristic, complemented
94C3×#381C2×C512yescomplemented
95C3×#380C2×C511yescharacteristic, complemented
96C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
97C22×C5×D4C22×C312yes—
98C22×C5×D4C22×C311yescharacteristic
99C23×C4×C5C22×C311yescharacteristic
100C23×C4×C5C22×C312yes—
101C5×#121—24no—
102C4×C5×D4—24no—
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C4⋊C4C22×C311yescharacteristic
106C2×C5×C4⋊C4C22×C312yes—
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×C42×C5C22×C311yescharacteristic
115C2×C42×C5C22×C311yescharacteristic
116C5×#95C22×C311yescharacteristic
117C5×#95C22×C311yescharacteristic
118C5×#95C22×C312yes—
119C5×#95C22×C312yes—
120C5×#95C22×C312yes—
121C5×#95C22×C312yes—
122#2420C3×C511yescharacteristic, direct product factor, Sylow
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—21no—
132C23×C3×C5—22no—
133C23×C3×C5—22no—
134C23×C3×C5—21no—
135C23×C3×C5C2×D414yes—
136C23×C3×C5#4112yes—
137C23×C3×C5C2411yescharacteristic
138C3×C5×D4—28no—
139C3×C5×D4—48no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
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—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—48no—
164C2×C3×C4×C5—44no—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5#4112yes—
167C2×C3×C4×C5#4112yes—
168C2×C3×C4×C5#4112yes—
169C22×C3×D4C22×C512yes—
170C22×C3×D4C22×C511yescharacteristic
171C23×C3×C4C22×C511yescharacteristic
172C23×C3×C4C22×C512yes—
173C3×#121—24no—
174C3×C4×D4—24no—
175C2×C3×C4⋊C4C22×C511yescharacteristic
176C2×C3×C4⋊C4C22×C511yescharacteristic
177C2×C3×C4⋊C4C22×C511yescharacteristic
178C2×C3×C4⋊C4C22×C512yes—
179C2×C3×C22⋊C4C22×C511yescharacteristic
180C2×C3×C22⋊C4C22×C511yescharacteristic
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
188C3×#95C22×C511yescharacteristic
189C3×#95C22×C511yescharacteristic
190C3×#95C22×C512yes—
191C3×#95C22×C512yes—
192C3×#95C22×C512yes—
193C3×#95C22×C512yes—
194C24×C5C23×C312yes—
195C24×C5C23×C311yescharacteristic
196C2×C5×D4—24no—
197C2×C5×D4—24no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—42no—
201C2×C5×D4C3×D414yes—
202C22×C4×C5—24no—
203C22×C4×C5—22no—
204C22×C4×C5—24no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—42no—
208C22×C4×C5C23×C311yescharacteristic
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C22×C4×C5C23×C312yes—
212C22×C4×C5C23×C312yes—
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C312yes—
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C311yescharacteristic
217C5×C4⋊C4—22no—
218C5×C4⋊C4—22no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—42no—
221C5×C22⋊C4—24no—
222C5×C22⋊C4—24no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C42×C5—22no—
229C42×C5—22no—
230C2×#121C2×C3×C511yescharacteristic
231C2×C4×D4C2×C3×C511yescharacteristic, complemented
232#397C2×C3×C512yescomplemented
233#394C2×C3×C512yescomplemented
234#390C2×C3×C511yescharacteristic, complemented
235#389C2×C3×C511yescharacteristic, complemented
236#386C2×C3×C512yescomplemented
237#382C2×C3×C511yescharacteristic, complemented
238#381C2×C3×C512yescomplemented
239#380C2×C3×C511yescharacteristic, complemented
240C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
241C22×C3×C5—24no—
242C22×C3×C5—22no—
243C22×C3×C5—24no—
244C22×C3×C5—22no—
245C22×C3×C5—24no—
246C22×C3×C5—22no—
247C22×C3×C5—41no—
248C22×C3×C5—42no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
251C22×C3×C5—41no—
252C22×C3×C5—42no—
253C22×C3×C5—41no—
254C22×C3×C5—42no—
255C22×C3×C5C22×D411yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C3×C4×C5—22no—
263C3×C4×C5—41no—
264C3×C4×C5—42no—
265C3×C4×C5—41no—
266C3×C4×C5—42no—
267C3×C4×C5—42no—
268C3×C4×C5—41no—
269C3×C4×C5—41no—
270C3×C4×C5#12314yes—
271C24×C3C23×C512yes—
272C24×C3C23×C511yescharacteristic
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4—42no—
278C2×C3×D4C5×D414yes—
279C22×C3×C4—24no—
280C22×C3×C4—22no—
281C22×C3×C4—24no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—42no—
285C22×C3×C4C23×C511yescharacteristic
286C22×C3×C4C23×C511yescharacteristic
287C22×C3×C4C23×C511yescharacteristic
288C22×C3×C4C23×C512yes—
289C22×C3×C4C23×C512yes—
290C22×C3×C4C23×C512yes—
291C22×C3×C4C23×C511yescharacteristic
292C22×C3×C4C23×C511yescharacteristic
293C22×C3×C4C23×C511yescharacteristic
294C3×C4⋊C4—22no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—42no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C42—22no—
306C3×C42—22no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—22no—
311C23×C5—21no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—21no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—21no—
319C23×C5C2×C3×D414yes—
320C23×C5C3×#4112yes—
321C23×C5C24×C311yescharacteristic
322C5×D4—28no—
323C5×D4—48no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—21no—
346C2×C4×C5—22no—
347C2×C4×C5—48no—
348C2×C4×C5—44no—
349C2×C4×C5C2×C3×D412yes—
350C2×C4×C5C3×#4112yes—
351C2×C4×C5C3×#4112yes—
352C2×C4×C5C3×#4112yes—
353C22×D4C22×C3×C512yes—
354C22×D4C22×C3×C511yescharacteristic
355C23×C4C22×C3×C511yescharacteristic
356C23×C4C22×C3×C512yes—
357#121—24no—
358C4×D4—24no—
359C2×C4⋊C4C22×C3×C511yescharacteristic
360C2×C4⋊C4C22×C3×C511yescharacteristic
361C2×C4⋊C4C22×C3×C511yescharacteristic
362C2×C4⋊C4C22×C3×C512yes—
363C2×C22⋊C4C22×C3×C512yes—
364C2×C22⋊C4C22×C3×C512yes—
365C2×C22⋊C4C22×C3×C511yescharacteristic
366C2×C22⋊C4C22×C3×C511yescharacteristic
367C2×C22⋊C4C22×C3×C512yes—
368C2×C22⋊C4C22×C3×C512yes—
369C2×C22⋊C4C22×C3×C512yes—
370C2×C42C22×C3×C511yescharacteristic
371C2×C42C22×C3×C511yescharacteristic
372#95C22×C3×C511yescharacteristic
373#95C22×C3×C511yescharacteristic
374#95C22×C3×C512yes—
375#95C22×C3×C512yes—
376#95C22×C3×C512yes—
377#95C22×C3×C512yes—
378C2×C3×C5—44no—
379C2×C3×C5—42no—
380C2×C3×C5C2×#12311yescharacteristic
381C2×C3×C5#52911yescharacteristic
382C2×C3×C5#54011yescharacteristic
383C2×C3×C5#54611yescharacteristic
384C2×C3×C5#54611yescharacteristic
385C2×C3×C5#55311yescharacteristic
386C2×C3×C5#55511yescharacteristic
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—22no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—21no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3C2×C5×D414yes—
400C23×C3C5×#4112yes—
401C23×C3C24×C511yescharacteristic
402C3×D4—28no—
403C3×D4—48no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
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—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—48no—
428C2×C3×C4—44no—
429C2×C3×C4C2×C5×D412yes—
430C2×C3×C4C5×#4112yes—
431C2×C3×C4C5×#4112yes—
432C2×C3×C4C5×#4112yes—
433C22×C5—24no—
434C22×C5—22no—
435C22×C5—24no—
436C22×C5—22no—
437C22×C5—24no—
438C22×C5—22no—
439C22×C5—41no—
440C22×C5—42no—
441C22×C5—41no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5—42no—
445C22×C5—41no—
446C22×C5—42no—
447C22×C5C22×C3×D411yescharacteristic
448C22×C5C2×C3×#4111yescharacteristic
449C22×C5C2×C3×#4111yescharacteristic
450C22×C5C2×C3×#4111yescharacteristic
451C22×C5C2×C3×#4111yescharacteristic
452C22×C5C3×H(5,𝔽2)11yescharacteristic
453C22×C5C3×H(5,𝔽2)11yescharacteristic
454C4×C5—22no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5—41no—
458C4×C5—42no—
459C4×C5—42no—
460C4×C5—41no—
461C4×C5—41no—
462C4×C5C3×#12314yes—
463C24C23×C3×C512yes—
464C24C23×C3×C511yescharacteristic
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—42no—
470C2×D4C3×C5×D414yes—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—42no—
477C22×C4C23×C3×C511yescharacteristic
478C22×C4C23×C3×C511yescharacteristic
479C22×C4C23×C3×C511yescharacteristic
480C22×C4C23×C3×C512yes—
481C22×C4C23×C3×C512yes—
482C22×C4C23×C3×C512yes—
483C22×C4C23×C3×C511yescharacteristic
484C22×C4C23×C3×C511yescharacteristic
485C22×C4C23×C3×C511yescharacteristic
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C42—22no—
498C42—22no—
499C3×C5#242011yescharacteristic, direct product factor, Hall
500C22×C3—24no—
501C22×C3—22no—
502C22×C3—24no—
503C22×C3—22no—
504C22×C3—24no—
505C22×C3—22no—
506C22×C3—41no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—42no—
510C22×C3—41no—
511C22×C3—42no—
512C22×C3—41no—
513C22×C3—42no—
514C22×C3C22×C5×D411yescharacteristic
515C22×C3C2×C5×#4111yescharacteristic
516C22×C3C2×C5×#4111yescharacteristic
517C22×C3C2×C5×#4111yescharacteristic
518C22×C3C2×C5×#4111yescharacteristic
519C22×C3C5×H(5,𝔽2)11yescharacteristic
520C22×C3C5×H(5,𝔽2)11yescharacteristic
521C3×C4—22no—
522C3×C4—41no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—41no—
528C3×C4—41no—
529C3×C4C5×#12314yes—
530C2×C5—44no—
531C2×C5—42no—
532C2×C5C2×C3×#12311yescharacteristic
533C2×C5C3×#52911yescharacteristic
534C2×C5C3×#54011yescharacteristic
535C2×C5C3×#54611yescharacteristic
536C2×C5C3×#54611yescharacteristic
537C2×C5C3×#55311yescharacteristic
538C2×C5C3×#55511yescharacteristic
539C23—21no—
540C23—21no—
541C23—21no—
542C23—22no—
543C23—21no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—21no—
551C23C2×C3×C5×D414yes—
552C23C3×C5×#4112yes—
553C23C24×C3×C511yescharacteristic
554D4—28no—
555D4—48no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—48no—
580C2×C4—44no—
581C2×C4C2×C3×C5×D412yes—
582C2×C4C3×C5×#4112yes—
583C2×C4C3×C5×#4112yes—
584C2×C4C3×C5×#4112yes—
585C2×C3—44no—
586C2×C3—42no—
587C2×C3C2×C5×#12311yescharacteristic
588C2×C3C5×#52911yescharacteristic
589C2×C3C5×#54011yescharacteristic
590C2×C3C5×#54611yescharacteristic
591C2×C3C5×#54611yescharacteristic
592C2×C3C5×#55311yescharacteristic
593C2×C3C5×#55511yescharacteristic
594C5C3×#242011yescharacteristic, direct product factor, Sylow
595C22—24no—
596C22—22no—
597C22—24no—
598C22—22no—
599C22—24no—
600C22—22no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—42no—
609C22C22×C3×C5×D411yescharacteristic
610C22C2×C3×C5×#4111yescharacteristic
611C22C2×C3×C5×#4111yescharacteristic
612C22C2×C3×C5×#4111yescharacteristic
613C22C2×C3×C5×#4111yescharacteristic
614C22C3×C5×H(5,𝔽2)11yescharacteristic
615C22C3×C5×H(5,𝔽2)11yescharacteristic
616C4—22no—
617C4—41no—
618C4—42no—
619C4—42no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4C3×C5×#12314yes—
625C3C5×#242011yescharacteristic, direct product factor, Sylow
626C2—44no—
627C2—42no—
628C2C2×C3×C5×#12311yescharacteristic
629C2C3×C5×#52911yescharacteristic
630C2C3×C5×#54011yescharacteristic
631C2C3×C5×#54611yescharacteristic
632C2C3×C5×#54611yescharacteristic
633C2C3×C5×#55311yescharacteristic
634C2C3×C5×#55511yescharacteristic
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
2. C2×C3×C4×C5×D4C2semidirect
3. C3×C5×#397C2semidirect
4. C3×C5×#394C2semidirect
5. C3×C5×#390C2semidirect
6. C3×C5×#389C2semidirect
7. C3×C5×#386C2semidirect
8. C3×C5×#382C2semidirect
9. C3×C5×#381C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2420C3direct (N × H)
38. C3×#2420C5direct (N × H)
40. C2×C4×C5×D4C2×C3semidirect
41. C5×#397C2×C3semidirect
42. C5×#394C2×C3semidirect
43. C5×#390C2×C3semidirect
44. C5×#389C2×C3semidirect
45. C5×#386C2×C3semidirect
46. C5×#382C2×C3semidirect
47. C5×#381C2×C3semidirect
48. C5×#380C2×C3semidirect
49. C4×C5×C22⋊C4C2×C3semidirect
87. C2×C3×C4×D4C2×C5semidirect
88. C3×#397C2×C5semidirect
89. C3×#394C2×C5semidirect
90. C3×#390C2×C5semidirect
91. C3×#389C2×C5semidirect
92. C3×#386C2×C5semidirect
93. C3×#382C2×C5semidirect
94. C3×#381C2×C5semidirect
95. C3×#380C2×C5semidirect
96. C3×C4×C22⋊C4C2×C5semidirect
122. #2420C3×C5direct (N × H)
231. C2×C4×D4C2×C3×C5semidirect
232. #397C2×C3×C5semidirect
233. #394C2×C3×C5semidirect
234. #390C2×C3×C5semidirect
235. #389C2×C3×C5semidirect
236. #386C2×C3×C5semidirect
237. #382C2×C3×C5semidirect
238. #381C2×C3×C5semidirect
239. #380C2×C3×C5semidirect
240. C4×C22⋊C4C2×C3×C5semidirect
499. C3×C5#2420direct (N × H)
594. C5C3×#2420direct (N × H)
625. C3C5×#2420direct (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×#1212
C2×C3×C4×C5×D42
C3×C5×#3972
C3×C5×#3942
C3×C5×#3902
C3×C5×#3892
C3×C5×#3862
C3×C5×#3822
C3×C5×#3812
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#24203
C3×#24205