Finite Group Databasebeta

← C3×C5×#2352 #14275386

Subgroups — C3×C5×#2352 #14275386

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic, complemented
3C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#388C212yesmaximal, complemented
5C3×C5×#387C212yesmaximal, complemented
6C3×C5×#386C212yesmaximal
7C3×C5×#382C211yesmaximal, characteristic, complemented
8C3×C5×#380C211yesmaximal, characteristic, complemented
9C3×C5×#380C211yesmaximal, characteristic, complemented
10C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C212yesmaximal, complemented
12C5×#2352C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C3×C4×C5×D4C418yescomplemented
18C3×C5×#117—24no—
19C2×C3×C5×C4⋊C4—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2212yes—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C42×C5C2212yes—
32C2×C3×C42×C5C2212yes—
33C2×C3×C42×C5C2211yescharacteristic
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×#2352C511yesmaximal, characteristic, direct product factor, Hall
40C2×C4×C5×D4C2×C311yescharacteristic
41C2×C5×#117C2×C311yescharacteristic, complemented
42C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
43C5×#388C2×C312yescomplemented
44C5×#387C2×C312yescomplemented
45C5×#386C2×C312yes—
46C5×#382C2×C311yescharacteristic, complemented
47C5×#380C2×C311yescharacteristic, complemented
48C5×#380C2×C311yescharacteristic, complemented
49C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
50C4×C5×C22⋊C4C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—42no—
63C22×C3×C4×C5C2×C414yes—
64C22×C3×C4×C5C2×C414yescomplemented
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C3×C5×C4⋊C4—24no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—22no—
77C3×C5×C4⋊C4—22no—
78C3×C5×C4⋊C4C2×C414yescomplemented
79C3×C5×C4⋊C4D414yescomplemented
80C3×C5×C22⋊C4—24no—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4—42no—
83C3×C5×C22⋊C4C2×C414yes—
84C3×C5×C22⋊C4C2×C414yescomplemented
85C3×C42×C5—24no—
86C3×C42×C5—42no—
87C3×C42×C5C2×C414yescomplemented
88C2×C3×C4×D4C2×C511yescharacteristic
89C2×C3×#117C2×C511yescharacteristic, complemented
90C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
91C3×#388C2×C512yescomplemented
92C3×#387C2×C512yescomplemented
93C3×#386C2×C512yes—
94C3×#382C2×C511yescharacteristic, complemented
95C3×#380C2×C511yescharacteristic, complemented
96C3×#380C2×C511yescharacteristic, complemented
97C3×C4×C4⋊C4C2×C511yescharacteristic, complemented
98C3×C4×C22⋊C4C2×C512yescomplemented
99C22×C5×D4C22×C311yescharacteristic
100C23×C4×C5C22×C312yes—
101C23×C4×C5C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C4×C5×D4C3×C418yescomplemented
104C5×#117—24no—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4C22×C311yescharacteristic
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C2×C5×C4⋊C4C22×C312yes—
110C2×C5×C4⋊C4C22×C311yescharacteristic
111C2×C5×C4⋊C4C22×C311yescharacteristic
112C2×C5×C22⋊C4C22×C312yes—
113C2×C5×C22⋊C4C22×C312yes—
114C2×C5×C22⋊C4C22×C312yes—
115C2×C5×C22⋊C4C22×C311yescharacteristic
116C2×C5×C22⋊C4C22×C311yescharacteristic
117C2×C42×C5C22×C312yes—
118C2×C42×C5C22×C312yes—
119C2×C42×C5C22×C311yescharacteristic
120C5×#95C22×C312yes—
121C5×#95C22×C312yes—
122C5×#95C22×C312yes—
123C5×#95C22×C312yes—
124C5×#95C22×C312yes—
125#2352C3×C511yescharacteristic, direct product factor, Sylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
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×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5C22×C412yes—
137C23×C3×C5C22×C412yes—
138C23×C3×C5#4112yes—
139C23×C3×C5#4112yes—
140C23×C3×C5C2411yescharacteristic
141C3×C5×D4—28no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—28no—
153C2×C3×C4×C5—28no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—48no—
164C2×C3×C4×C5C22×C412yes—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C22×C412yes—
167C2×C3×C4×C5C22×C412yes—
168C2×C3×C4×C5C22×C412yes—
169C2×C3×C4×C5C2×D414yes—
170C2×C3×C4×C5C2×D412yes—
171C2×C3×C4×C5#4112yes—
172C22×C3×D4C22×C511yescharacteristic
173C23×C3×C4C22×C512yes—
174C23×C3×C4C22×C511yescharacteristic
175C23×C3×C4C22×C511yescharacteristic
176C3×C4×D4C4×C518yescomplemented
177C3×#117—24no—
178C2×C3×C4⋊C4—24no—
179C2×C3×C4⋊C4C22×C511yescharacteristic
180C2×C3×C4⋊C4C22×C511yescharacteristic
181C2×C3×C4⋊C4C22×C511yescharacteristic
182C2×C3×C4⋊C4C22×C512yes—
183C2×C3×C4⋊C4C22×C511yescharacteristic
184C2×C3×C4⋊C4C22×C511yescharacteristic
185C2×C3×C22⋊C4C22×C512yes—
186C2×C3×C22⋊C4C22×C512yes—
187C2×C3×C22⋊C4C22×C512yes—
188C2×C3×C22⋊C4C22×C511yescharacteristic
189C2×C3×C22⋊C4C22×C511yescharacteristic
190C2×C3×C42C22×C512yes—
191C2×C3×C42C22×C512yes—
192C2×C3×C42C22×C511yescharacteristic
193C3×#95C22×C512yes—
194C3×#95C22×C512yes—
195C3×#95C22×C512yes—
196C3×#95C22×C512yes—
197C3×#95C22×C512yes—
198C24×C5C23×C311yescharacteristic
199C24×C5C23×C311yescharacteristic
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4C2×C3×C414yes—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—24no—
208C22×C4×C5—24no—
209C22×C4×C5—42no—
210C22×C4×C5C2×C3×C414yes—
211C22×C4×C5C2×C3×C414yescomplemented
212C22×C4×C5C23×C312yes—
213C22×C4×C5C23×C312yes—
214C22×C4×C5C23×C312yes—
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C311yescharacteristic
217C22×C4×C5C23×C311yescharacteristic
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C312yes—
220C22×C4×C5C23×C311yescharacteristic
221C5×C4⋊C4—24no—
222C5×C4⋊C4—22no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C4⋊C4C2×C3×C414yescomplemented
226C5×C4⋊C4C3×D414yescomplemented
227C5×C22⋊C4—24no—
228C5×C22⋊C4—24no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4C2×C3×C414yes—
231C5×C22⋊C4C2×C3×C414yescomplemented
232C42×C5—24no—
233C42×C5—42no—
234C42×C5C2×C3×C414yescomplemented
235C2×C4×D4C2×C3×C511yescharacteristic
236C2×#117C2×C3×C511yescharacteristic, complemented
237C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
238#388C2×C3×C512yescomplemented
239#387C2×C3×C512yescomplemented
240#386C2×C3×C512yes—
241#382C2×C3×C511yescharacteristic, complemented
242#380C2×C3×C511yescharacteristic, complemented
243#380C2×C3×C511yescharacteristic, complemented
244C4×C4⋊C4C2×C3×C511yescharacteristic, complemented
245C4×C22⋊C4C2×C3×C512yescomplemented
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—22no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5—41no—
258C22×C3×C5—41no—
259C22×C3×C5#11714yescomplemented
260C22×C3×C5C23×C411yescharacteristic
261C22×C3×C5C22×D411yescharacteristic
262C22×C3×C5C2×#4111yescharacteristic
263C22×C3×C5C2×#4111yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5H(5,𝔽2)11yescharacteristic
266C22×C3×C52−1+411yescharacteristic
267C3×C4×C5—22no—
268C3×C4×C5—22no—
269C3×C4×C5—22no—
270C3×C4×C5—22no—
271C3×C4×C5—24no—
272C3×C4×C5—42no—
273C3×C4×C5—42no—
274C3×C4×C5—42no—
275C3×C4×C5C4×D414yes—
276C24×C3C23×C511yescharacteristic
277C24×C3C23×C511yescharacteristic
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4C2×C4×C514yes—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—42no—
288C22×C3×C4C2×C4×C514yes—
289C22×C3×C4C2×C4×C514yescomplemented
290C22×C3×C4C23×C512yes—
291C22×C3×C4C23×C512yes—
292C22×C3×C4C23×C512yes—
293C22×C3×C4C23×C511yescharacteristic
294C22×C3×C4C23×C511yescharacteristic
295C22×C3×C4C23×C511yescharacteristic
296C22×C3×C4C23×C511yescharacteristic
297C22×C3×C4C23×C512yes—
298C22×C3×C4C23×C511yescharacteristic
299C3×C4⋊C4—24no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4C2×C4×C514yescomplemented
304C3×C4⋊C4C5×D414yescomplemented
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4C2×C4×C514yes—
309C3×C22⋊C4C2×C4×C514yescomplemented
310C3×C42—24no—
311C3×C42—42no—
312C3×C42C2×C4×C514yescomplemented
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5C22×C3×C412yes—
324C23×C5C22×C3×C412yes—
325C23×C5C3×#4112yes—
326C23×C5C3×#4112yes—
327C23×C5C24×C311yescharacteristic
328C5×D4—28no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—21no—
339C2×C4×C5—28no—
340C2×C4×C5—28no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—48no—
351C2×C4×C5C22×C3×C412yes—
352C2×C4×C5C22×C3×C412yes—
353C2×C4×C5C22×C3×C412yes—
354C2×C4×C5C22×C3×C412yes—
355C2×C4×C5C22×C3×C412yes—
356C2×C4×C5C2×C3×D414yes—
357C2×C4×C5C2×C3×D412yes—
358C2×C4×C5C3×#4112yes—
359C22×D4C22×C3×C511yescharacteristic
360C23×C4C22×C3×C512yes—
361C23×C4C22×C3×C511yescharacteristic
362C23×C4C22×C3×C511yescharacteristic
363C4×D4C3×C4×C518yescomplemented
364#117—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4C22×C3×C511yescharacteristic
367C2×C4⋊C4C22×C3×C512yes—
368C2×C4⋊C4C22×C3×C511yescharacteristic
369C2×C4⋊C4C22×C3×C511yescharacteristic
370C2×C4⋊C4C22×C3×C511yescharacteristic
371C2×C4⋊C4C22×C3×C511yescharacteristic
372C2×C22⋊C4C22×C3×C512yes—
373C2×C22⋊C4C22×C3×C512yes—
374C2×C22⋊C4C22×C3×C512yes—
375C2×C22⋊C4C22×C3×C511yescharacteristic
376C2×C22⋊C4C22×C3×C511yescharacteristic
377C2×C42C22×C3×C512yes—
378C2×C42C22×C3×C512yes—
379C2×C42C22×C3×C511yescharacteristic
380#95C22×C3×C512yes—
381#95C22×C3×C512yes—
382#95C22×C3×C512yes—
383#95C22×C3×C512yes—
384#95C22×C3×C512yes—
385C2×C3×C5—24no—
386C2×C3×C5—42no—
387C2×C3×C5C2×#11711yescharacteristic
388C2×C3×C5C2×C4×D411yescharacteristic
389C2×C3×C5#52011yescharacteristic
390C2×C3×C5#54611yescharacteristic
391C2×C3×C5#54811yescharacteristic
392C2×C3×C5#55211yescharacteristic
393C2×C3×C5#55311yescharacteristic
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3C22×C4×C512yes—
405C23×C3C22×C4×C512yes—
406C23×C3C5×#4112yes—
407C23×C3C5×#4112yes—
408C23×C3C24×C511yescharacteristic
409C3×D4—28no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—28no—
421C2×C3×C4—28no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—48no—
432C2×C3×C4C22×C4×C512yes—
433C2×C3×C4C22×C4×C512yes—
434C2×C3×C4C22×C4×C512yes—
435C2×C3×C4C22×C4×C512yes—
436C2×C3×C4C22×C4×C512yes—
437C2×C3×C4C2×C5×D414yes—
438C2×C3×C4C2×C5×D412yes—
439C2×C3×C4C5×#4112yes—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5C3×#11714yescomplemented
454C22×C5C23×C3×C411yescharacteristic
455C22×C5C22×C3×D411yescharacteristic
456C22×C5C2×C3×#4111yescharacteristic
457C22×C5C2×C3×#4111yescharacteristic
458C22×C5C2×C3×#4111yescharacteristic
459C22×C5C3×H(5,𝔽2)11yescharacteristic
460C22×C5C3×2−1+411yescharacteristic
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—22no—
464C4×C5—22no—
465C4×C5—24no—
466C4×C5—42no—
467C4×C5—42no—
468C4×C5—42no—
469C4×C5C3×C4×D414yes—
470C24C23×C3×C511yescharacteristic
471C24C23×C3×C511yescharacteristic
472C2×D4—22no—
473C2×D4—22no—
474C2×D4C2×C3×C4×C514yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—42no—
482C22×C4C2×C3×C4×C514yes—
483C22×C4C2×C3×C4×C514yescomplemented
484C22×C4C23×C3×C512yes—
485C22×C4C23×C3×C512yes—
486C22×C4C23×C3×C512yes—
487C22×C4C23×C3×C511yescharacteristic
488C22×C4C23×C3×C511yescharacteristic
489C22×C4C23×C3×C511yescharacteristic
490C22×C4C23×C3×C511yescharacteristic
491C22×C4C23×C3×C512yes—
492C22×C4C23×C3×C511yescharacteristic
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4C2×C3×C4×C514yescomplemented
498C4⋊C4C3×C5×D414yescomplemented
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—42no—
502C22⋊C4C2×C3×C4×C514yes—
503C22⋊C4C2×C3×C4×C514yescomplemented
504C42—24no—
505C42—42no—
506C42C2×C3×C4×C514yescomplemented
507C3×C5#235211yescharacteristic, direct product factor, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3C5×#11714yescomplemented
522C22×C3C23×C4×C511yescharacteristic
523C22×C3C22×C5×D411yescharacteristic
524C22×C3C2×C5×#4111yescharacteristic
525C22×C3C2×C5×#4111yescharacteristic
526C22×C3C2×C5×#4111yescharacteristic
527C22×C3C5×H(5,𝔽2)11yescharacteristic
528C22×C3C5×2−1+411yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—24no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4C4×C5×D414yes—
538C2×C5—24no—
539C2×C5—42no—
540C2×C5C2×C3×#11711yescharacteristic
541C2×C5C2×C3×C4×D411yescharacteristic
542C2×C5C3×#52011yescharacteristic
543C2×C5C3×#54611yescharacteristic
544C2×C5C3×#54811yescharacteristic
545C2×C5C3×#55211yescharacteristic
546C2×C5C3×#55311yescharacteristic
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23C22×C3×C4×C512yes—
558C23C22×C3×C4×C512yes—
559C23C3×C5×#4112yes—
560C23C3×C5×#4112yes—
561C23C24×C3×C511yescharacteristic
562D4—28no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—28no—
574C2×C4—28no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—48no—
585C2×C4C22×C3×C4×C512yes—
586C2×C4C22×C3×C4×C512yes—
587C2×C4C22×C3×C4×C512yes—
588C2×C4C22×C3×C4×C512yes—
589C2×C4C22×C3×C4×C512yes—
590C2×C4C2×C3×C5×D414yes—
591C2×C4C2×C3×C5×D412yes—
592C2×C4C3×C5×#4112yes—
593C2×C3—24no—
594C2×C3—42no—
595C2×C3C2×C5×#11711yescharacteristic
596C2×C3C2×C4×C5×D411yescharacteristic
597C2×C3C5×#52011yescharacteristic
598C2×C3C5×#54611yescharacteristic
599C2×C3C5×#54811yescharacteristic
600C2×C3C5×#55211yescharacteristic
601C2×C3C5×#55311yescharacteristic
602C5C3×#235211yescharacteristic, direct product factor, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C3×C5×#11714yescomplemented
617C22C23×C3×C4×C511yescharacteristic
618C22C22×C3×C5×D411yescharacteristic
619C22C2×C3×C5×#4111yescharacteristic
620C22C2×C3×C5×#4111yescharacteristic
621C22C2×C3×C5×#4111yescharacteristic
622C22C3×C5×H(5,𝔽2)11yescharacteristic
623C22C3×C5×2−1+411yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—24no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4C3×C4×C5×D414yes—
633C3C5×#235211yescharacteristic, direct product factor, Sylow
634C2—24no—
635C2—42no—
636C2C2×C3×C5×#11711yescharacteristic
637C2C2×C3×C4×C5×D411yescharacteristic
638C2C3×C5×#52011yescharacteristic
639C2C3×C5×#54611yescharacteristic
640C2C3×C5×#54811yescharacteristic
641C2C3×C5×#55211yescharacteristic
642C2C3×C5×#55311yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#117C2semidirect
3. C22×C3×C5×C4⋊C4C2semidirect
4. C3×C5×#388C2semidirect
5. C3×C5×#387C2semidirect
7. C3×C5×#382C2semidirect
8. C3×C5×#380C2semidirect
9. C3×C5×#380C2semidirect
10. C3×C4×C5×C4⋊C4C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2352C3direct (N × H)
17. C3×C4×C5×D4C4semidirect
39. C3×#2352C5direct (N × H)
41. C2×C5×#117C2×C3semidirect
42. C22×C5×C4⋊C4C2×C3semidirect
43. C5×#388C2×C3semidirect
44. C5×#387C2×C3semidirect
46. C5×#382C2×C3semidirect
47. C5×#380C2×C3semidirect
48. C5×#380C2×C3semidirect
49. C4×C5×C4⋊C4C2×C3semidirect
50. C4×C5×C22⋊C4C2×C3semidirect
64. C22×C3×C4×C5C2×C4semidirect
78. C3×C5×C4⋊C4C2×C4semidirect
79. C3×C5×C4⋊C4D4semidirect
84. C3×C5×C22⋊C4C2×C4semidirect
87. C3×C42×C5C2×C4semidirect
89. C2×C3×#117C2×C5semidirect
90. C22×C3×C4⋊C4C2×C5semidirect
91. C3×#388C2×C5semidirect
92. C3×#387C2×C5semidirect
94. C3×#382C2×C5semidirect
95. C3×#380C2×C5semidirect
96. C3×#380C2×C5semidirect
97. C3×C4×C4⋊C4C2×C5semidirect
98. C3×C4×C22⋊C4C2×C5semidirect
103. C4×C5×D4C3×C4semidirect
125. #2352C3×C5direct (N × H)
176. C3×C4×D4C4×C5semidirect
211. C22×C4×C5C2×C3×C4semidirect
225. C5×C4⋊C4C2×C3×C4semidirect
226. C5×C4⋊C4C3×D4semidirect
231. C5×C22⋊C4C2×C3×C4semidirect
234. C42×C5C2×C3×C4semidirect
236. C2×#117C2×C3×C5semidirect
237. C22×C4⋊C4C2×C3×C5semidirect
238. #388C2×C3×C5semidirect
239. #387C2×C3×C5semidirect
241. #382C2×C3×C5semidirect
242. #380C2×C3×C5semidirect
243. #380C2×C3×C5semidirect
244. C4×C4⋊C4C2×C3×C5semidirect
245. C4×C22⋊C4C2×C3×C5semidirect
259. C22×C3×C5#117semidirect
289. C22×C3×C4C2×C4×C5semidirect
303. C3×C4⋊C4C2×C4×C5semidirect
304. C3×C4⋊C4C5×D4semidirect
309. C3×C22⋊C4C2×C4×C5semidirect
312. C3×C42C2×C4×C5semidirect
363. C4×D4C3×C4×C5semidirect
453. C22×C5C3×#117semidirect
483. C22×C4C2×C3×C4×C5semidirect
497. C4⋊C4C2×C3×C4×C5semidirect
498. C4⋊C4C3×C5×D4semidirect
503. C22⋊C4C2×C3×C4×C5semidirect
506. C42C2×C3×C4×C5semidirect
507. C3×C5#2352direct (N × H)
521. C22×C3C5×#117semidirect
602. C5C3×#2352direct (N × H)
616. C22C3×C5×#117semidirect
633. C3C5×#2352direct (N × H)

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×C3×C5×#1172
C22×C3×C5×C4⋊C42
C3×C5×#3882
C3×C5×#3872
C3×C5×#3862
C3×C5×#3822
C3×C5×#3802
C3×C4×C5×C4⋊C42
C3×C4×C5×C22⋊C42
C5×#23523
C3×#23525