Finite Group Databasebeta

← C3×C5×#2416 #14275450

Subgroups — C3×C5×#2416 #14275450

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C212yesmaximal, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic, complemented
3C2×C3×C5×#121C211yesmaximal, characteristic, complemented
4C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
5C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×C5×#396C212yesmaximal, complemented
7C3×C5×#394C212yesmaximal, complemented
8C3×C5×#390C211yesmaximal, characteristic, complemented
9C3×C5×#389C211yesmaximal, characteristic, complemented
10C3×C5×#386C212yesmaximal, complemented
11C3×C5×#380C211yesmaximal, characteristic, complemented
12C5×#2416C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2212yes—
16C22×C3×C5×D4C2211yescharacteristic
17C23×C3×C4×C5C2211yescharacteristic
18C23×C3×C4×C5C2212yes—
19C23×C3×C4×C5C2211yescharacteristic
20C3×C5×#121—28no—
21C3×C5×#121—24no—
22C3×C5×#121—24no—
23C3×C4×C5×D4—24no—
24C2×C3×C5×C4⋊C4—24no—
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2212yes—
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2212yes—
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2212yes—
34C2×C3×C5×C22⋊C4C2212yes—
35C2×C3×C5×C22⋊C4C2212yes—
36C2×C3×C5×C22⋊C4C2212yes—
37C2×C3×C5×C22⋊C4C2212yes—
38C2×C3×C42×C5C2211yescharacteristic
39C3×C5×#95C2212yes—
40C3×C5×#95C2212yes—
41C3×#2416C511yesmaximal, characteristic, direct product factor, Hall
42C2×C5×#121C2×C312yescomplemented
43C2×C5×#121C2×C311yescharacteristic, complemented
44C2×C5×#121C2×C311yescharacteristic, complemented
45C2×C4×C5×D4C2×C311yescharacteristic, complemented
46C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
47C5×#396C2×C312yescomplemented
48C5×#394C2×C312yescomplemented
49C5×#390C2×C311yescharacteristic, complemented
50C5×#389C2×C311yescharacteristic, complemented
51C5×#386C2×C312yescomplemented
52C5×#380C2×C311yescharacteristic, complemented
53C24×C3×C5C2312yes—
54C24×C3×C5C2311yescharacteristic
55C24×C3×C5C2311yescharacteristic
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—24no—
59C2×C3×C5×D4—24no—
60C2×C3×C5×D4—24no—
61C2×C3×C5×D4—24no—
62C2×C3×C5×D4—24no—
63C2×C3×C5×D4—22no—
64C2×C3×C5×D4—22no—
65C2×C3×C5×D4—22no—
66C2×C3×C5×D4—42no—
67C2×C3×C5×D4D414yescomplemented
68C22×C3×C4×C5—22no—
69C22×C3×C4×C5—22no—
70C22×C3×C4×C5—24no—
71C22×C3×C4×C5—24no—
72C22×C3×C4×C5—22no—
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—42no—
76C22×C3×C4×C5D414yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2312yes—
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2312yes—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2312yes—
84C22×C3×C4×C5C2311yescharacteristic
85C3×C5×C4⋊C4—24no—
86C3×C5×C4⋊C4—22no—
87C3×C5×C4⋊C4—22no—
88C3×C5×C4⋊C4—24no—
89C3×C5×C4⋊C4—22no—
90C3×C5×C4⋊C4D414yescomplemented
91C3×C5×C22⋊C4—22no—
92C3×C5×C22⋊C4—24no—
93C3×C5×C22⋊C4—22no—
94C3×C5×C22⋊C4—24no—
95C3×C5×C22⋊C4—24no—
96C3×C5×C22⋊C4—24no—
97C3×C5×C22⋊C4—42no—
98C3×C42×C5—22no—
99C2×C3×#121C2×C512yescomplemented
100C2×C3×#121C2×C511yescharacteristic, complemented
101C2×C3×#121C2×C511yescharacteristic, complemented
102C2×C3×C4×D4C2×C511yescharacteristic, complemented
103C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
104C3×#396C2×C512yescomplemented
105C3×#394C2×C512yescomplemented
106C3×#390C2×C511yescharacteristic, complemented
107C3×#389C2×C511yescharacteristic, complemented
108C3×#386C2×C512yescomplemented
109C3×#380C2×C511yescharacteristic, complemented
110C22×C5×D4C22×C312yes—
111C22×C5×D4C22×C311yescharacteristic
112C22×C5×D4C22×C312yes—
113C22×C5×D4C22×C311yescharacteristic
114C23×C4×C5C22×C311yescharacteristic
115C23×C4×C5C22×C312yes—
116C23×C4×C5C22×C311yescharacteristic
117C5×#121—28no—
118C5×#121—24no—
119C5×#121—24no—
120C4×C5×D4—24no—
121C2×C5×C4⋊C4—24no—
122C2×C5×C4⋊C4C22×C311yescharacteristic
123C2×C5×C4⋊C4C22×C311yescharacteristic
124C2×C5×C4⋊C4C22×C312yes—
125C2×C5×C4⋊C4C22×C312yes—
126C2×C5×C4⋊C4C22×C311yescharacteristic
127C2×C5×C4⋊C4C22×C311yescharacteristic
128C2×C5×C22⋊C4C22×C312yes—
129C2×C5×C22⋊C4C22×C311yescharacteristic
130C2×C5×C22⋊C4C22×C312yes—
131C2×C5×C22⋊C4C22×C312yes—
132C2×C5×C22⋊C4C22×C311yescharacteristic
133C2×C5×C22⋊C4C22×C312yes—
134C2×C5×C22⋊C4C22×C312yes—
135C2×C42×C5C22×C311yescharacteristic
136C5×#95C22×C312yes—
137C5×#95C22×C312yes—
138#2416C3×C511yescharacteristic, direct product factor, Sylow
139C23×C3×C5—21no—
140C23×C3×C5—21no—
141C23×C3×C5—21no—
142C23×C3×C5—21no—
143C23×C3×C5—21no—
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5—21no—
147C23×C3×C5—21no—
148C23×C3×C5—21no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5—22no—
152C23×C3×C5—22no—
153C23×C3×C5—22no—
154C23×C3×C5—22no—
155C23×C3×C5—22no—
156C23×C3×C5C2×D412yes—
157C23×C3×C5C2×D412yes—
158C23×C3×C5C2×D412yes—
159C23×C3×C5#4112yes—
160C23×C3×C5C2411yescharacteristic
161C3×C5×D4—28no—
162C3×C5×D4—48no—
163C3×C5×D4—48no—
164C3×C5×D4—44no—
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—21no—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5—28no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—22no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5—22no—
178C2×C3×C4×C5—22no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—48no—
185C2×C3×C4×C5—44no—
186C2×C3×C4×C5C2×D412yes—
187C2×C3×C4×C5C2×D412yes—
188C2×C3×C4×C5C2×D414yes—
189C2×C3×C4×C5C2×D412yes—
190C2×C3×C4×C5C2×D412yes—
191C2×C3×C4×C5#4112yes—
192C22×C3×D4C22×C512yes—
193C22×C3×D4C22×C511yescharacteristic
194C22×C3×D4C22×C512yes—
195C22×C3×D4C22×C511yescharacteristic
196C23×C3×C4C22×C511yescharacteristic
197C23×C3×C4C22×C512yes—
198C23×C3×C4C22×C511yescharacteristic
199C3×#121—28no—
200C3×#121—24no—
201C3×#121—24no—
202C3×C4×D4—24no—
203C2×C3×C4⋊C4—24no—
204C2×C3×C4⋊C4C22×C511yescharacteristic
205C2×C3×C4⋊C4C22×C511yescharacteristic
206C2×C3×C4⋊C4C22×C512yes—
207C2×C3×C4⋊C4C22×C512yes—
208C2×C3×C4⋊C4C22×C511yescharacteristic
209C2×C3×C4⋊C4C22×C511yescharacteristic
210C2×C3×C22⋊C4C22×C512yes—
211C2×C3×C22⋊C4C22×C511yescharacteristic
212C2×C3×C22⋊C4C22×C512yes—
213C2×C3×C22⋊C4C22×C512yes—
214C2×C3×C22⋊C4C22×C511yescharacteristic
215C2×C3×C22⋊C4C22×C512yes—
216C2×C3×C22⋊C4C22×C512yes—
217C2×C3×C42C22×C511yescharacteristic
218C3×#95C22×C512yes—
219C3×#95C22×C512yes—
220C24×C5C23×C312yes—
221C24×C5C23×C311yescharacteristic
222C24×C5C23×C311yescharacteristic
223C2×C5×D4—22no—
224C2×C5×D4—22no—
225C2×C5×D4—24no—
226C2×C5×D4—24no—
227C2×C5×D4—24no—
228C2×C5×D4—24no—
229C2×C5×D4—24no—
230C2×C5×D4—22no—
231C2×C5×D4—22no—
232C2×C5×D4—22no—
233C2×C5×D4—42no—
234C2×C5×D4C3×D414yescomplemented
235C22×C4×C5—22no—
236C22×C4×C5—22no—
237C22×C4×C5—24no—
238C22×C4×C5—24no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5—42no—
243C22×C4×C5C3×D414yescomplemented
244C22×C4×C5C23×C311yescharacteristic
245C22×C4×C5C23×C312yes—
246C22×C4×C5C23×C311yescharacteristic
247C22×C4×C5C23×C312yes—
248C22×C4×C5C23×C311yescharacteristic
249C22×C4×C5C23×C311yescharacteristic
250C22×C4×C5C23×C312yes—
251C22×C4×C5C23×C311yescharacteristic
252C5×C4⋊C4—24no—
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—22no—
257C5×C4⋊C4C3×D414yescomplemented
258C5×C22⋊C4—22no—
259C5×C22⋊C4—24no—
260C5×C22⋊C4—22no—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—42no—
265C42×C5—22no—
266C2×#121C2×C3×C512yescomplemented
267C2×#121C2×C3×C511yescharacteristic, complemented
268C2×#121C2×C3×C511yescharacteristic, complemented
269C2×C4×D4C2×C3×C511yescharacteristic, complemented
270C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
271#396C2×C3×C512yescomplemented
272#394C2×C3×C512yescomplemented
273#390C2×C3×C511yescharacteristic, complemented
274#389C2×C3×C511yescharacteristic, complemented
275#386C2×C3×C512yescomplemented
276#380C2×C3×C511yescharacteristic, complemented
277C22×C3×C5—22no—
278C22×C3×C5—22no—
279C22×C3×C5—22no—
280C22×C3×C5—22no—
281C22×C3×C5—22no—
282C22×C3×C5—22no—
283C22×C3×C5—22no—
284C22×C3×C5—22no—
285C22×C3×C5—22no—
286C22×C3×C5—41no—
287C22×C3×C5—41no—
288C22×C3×C5—41no—
289C22×C3×C5—41no—
290C22×C3×C5—42no—
291C22×C3×C5—42no—
292C22×C3×C5—42no—
293C22×C3×C5—42no—
294C22×C3×C5—42no—
295C22×C3×C5—42no—
296C22×C3×C5—42no—
297C22×C3×C5#12114yescomplemented
298C22×C3×C5C22×D411yescharacteristic
299C22×C3×C5C22×D411yescharacteristic
300C22×C3×C5C22×D411yescharacteristic
301C22×C3×C5C2×#4111yescharacteristic
302C22×C3×C5C2×#4111yescharacteristic
303C22×C3×C5H(5,𝔽2)11yescharacteristic
304C22×C3×C52−1+411yescharacteristic
305C3×C4×C5—22no—
306C3×C4×C5—22no—
307C3×C4×C5—24no—
308C3×C4×C5—41no—
309C3×C4×C5—42no—
310C3×C4×C5—41no—
311C3×C4×C5—42no—
312C3×C4×C5#12114yescomplemented
313C24×C3C23×C512yes—
314C24×C3C23×C511yescharacteristic
315C24×C3C23×C511yescharacteristic
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—24no—
319C2×C3×D4—24no—
320C2×C3×D4—24no—
321C2×C3×D4—24no—
322C2×C3×D4—24no—
323C2×C3×D4—22no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—42no—
327C2×C3×D4C5×D414yescomplemented
328C22×C3×C4—22no—
329C22×C3×C4—22no—
330C22×C3×C4—24no—
331C22×C3×C4—24no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—42no—
336C22×C3×C4C5×D414yescomplemented
337C22×C3×C4C23×C511yescharacteristic
338C22×C3×C4C23×C511yescharacteristic
339C22×C3×C4C23×C512yes—
340C22×C3×C4C23×C512yes—
341C22×C3×C4C23×C512yes—
342C22×C3×C4C23×C511yescharacteristic
343C22×C3×C4C23×C511yescharacteristic
344C22×C3×C4C23×C511yescharacteristic
345C3×C4⋊C4—24no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—24no—
349C3×C4⋊C4—22no—
350C3×C4⋊C4C5×D414yescomplemented
351C3×C22⋊C4—22no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—42no—
358C3×C42—22no—
359C23×C5—21no—
360C23×C5—21no—
361C23×C5—21no—
362C23×C5—21no—
363C23×C5—21no—
364C23×C5—21no—
365C23×C5—21no—
366C23×C5—21no—
367C23×C5—21no—
368C23×C5—21no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5C2×C3×D412yes—
377C23×C5C2×C3×D412yes—
378C23×C5C2×C3×D412yes—
379C23×C5C3×#4112yes—
380C23×C5C24×C311yescharacteristic
381C5×D4—28no—
382C5×D4—48no—
383C5×D4—48no—
384C5×D4—44no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—22no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—22no—
391C2×C4×C5—28no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—22no—
395C2×C4×C5—21no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—21no—
400C2×C4×C5—22no—
401C2×C4×C5—21no—
402C2×C4×C5—22no—
403C2×C4×C5—21no—
404C2×C4×C5—48no—
405C2×C4×C5—44no—
406C2×C4×C5C2×C3×D412yes—
407C2×C4×C5C2×C3×D412yes—
408C2×C4×C5C2×C3×D414yes—
409C2×C4×C5C2×C3×D412yes—
410C2×C4×C5C2×C3×D412yes—
411C2×C4×C5C3×#4112yes—
412C22×D4C22×C3×C512yes—
413C22×D4C22×C3×C511yescharacteristic
414C22×D4C22×C3×C512yes—
415C22×D4C22×C3×C511yescharacteristic
416C23×C4C22×C3×C511yescharacteristic
417C23×C4C22×C3×C512yes—
418C23×C4C22×C3×C511yescharacteristic
419#121—28no—
420#121—24no—
421#121—24no—
422C4×D4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4C22×C3×C511yescharacteristic
425C2×C4⋊C4C22×C3×C512yes—
426C2×C4⋊C4C22×C3×C511yescharacteristic
427C2×C4⋊C4C22×C3×C511yescharacteristic
428C2×C4⋊C4C22×C3×C512yes—
429C2×C4⋊C4C22×C3×C511yescharacteristic
430C2×C22⋊C4C22×C3×C511yescharacteristic
431C2×C22⋊C4C22×C3×C511yescharacteristic
432C2×C22⋊C4C22×C3×C512yes—
433C2×C22⋊C4C22×C3×C512yes—
434C2×C22⋊C4C22×C3×C512yes—
435C2×C22⋊C4C22×C3×C512yes—
436C2×C22⋊C4C22×C3×C512yes—
437C2×C42C22×C3×C511yescharacteristic
438#95C22×C3×C512yes—
439#95C22×C3×C512yes—
440C2×C3×C5—24no—
441C2×C3×C5—42no—
442C2×C3×C5—82no—
443C2×C3×C5C2×#12111yescharacteristic
444C2×C3×C5C2×#12111yescharacteristic
445C2×C3×C5#53711yescharacteristic
446C2×C3×C5D4211yescharacteristic
447C2×C3×C5#54711yescharacteristic
448C2×C3×C5#54811yescharacteristic
449C2×C3×C5#55311yescharacteristic
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3C2×C5×D412yes—
468C23×C3C2×C5×D412yes—
469C23×C3C2×C5×D412yes—
470C23×C3C5×#4112yes—
471C23×C3C24×C511yescharacteristic
472C3×D4—28no—
473C3×D4—48no—
474C3×D4—48no—
475C3×D4—44no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—28no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—48no—
496C2×C3×C4—44no—
497C2×C3×C4C2×C5×D412yes—
498C2×C3×C4C2×C5×D412yes—
499C2×C3×C4C2×C5×D414yes—
500C2×C3×C4C2×C5×D412yes—
501C2×C3×C4C2×C5×D412yes—
502C2×C3×C4C5×#4112yes—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—22no—
507C22×C5—22no—
508C22×C5—22no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5—42no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5C3×#12114yescomplemented
524C22×C5C22×C3×D411yescharacteristic
525C22×C5C22×C3×D411yescharacteristic
526C22×C5C22×C3×D411yescharacteristic
527C22×C5C2×C3×#4111yescharacteristic
528C22×C5C2×C3×#4111yescharacteristic
529C22×C5C3×H(5,𝔽2)11yescharacteristic
530C22×C5C3×2−1+411yescharacteristic
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—24no—
534C4×C5—41no—
535C4×C5—42no—
536C4×C5—41no—
537C4×C5—42no—
538C4×C5C3×#12114yescomplemented
539C24C23×C3×C512yes—
540C24C23×C3×C511yescharacteristic
541C24C23×C3×C511yescharacteristic
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—42no—
553C2×D4C3×C5×D414yescomplemented
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—42no—
562C22×C4C3×C5×D414yescomplemented
563C22×C4C23×C3×C511yescharacteristic
564C22×C4C23×C3×C511yescharacteristic
565C22×C4C23×C3×C512yes—
566C22×C4C23×C3×C512yes—
567C22×C4C23×C3×C512yes—
568C22×C4C23×C3×C511yescharacteristic
569C22×C4C23×C3×C511yescharacteristic
570C22×C4C23×C3×C511yescharacteristic
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4C3×C5×D414yescomplemented
577C22⋊C4—22no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C42—22no—
585C3×C5#241611yescharacteristic, direct product factor, Hall
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3C5×#12114yescomplemented
607C22×C3C22×C5×D411yescharacteristic
608C22×C3C22×C5×D411yescharacteristic
609C22×C3C22×C5×D411yescharacteristic
610C22×C3C2×C5×#4111yescharacteristic
611C22×C3C2×C5×#4111yescharacteristic
612C22×C3C5×H(5,𝔽2)11yescharacteristic
613C22×C3C5×2−1+411yescharacteristic
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—24no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4C5×#12114yescomplemented
622C2×C5—24no—
623C2×C5—42no—
624C2×C5—82no—
625C2×C5C2×C3×#12111yescharacteristic
626C2×C5C2×C3×#12111yescharacteristic
627C2×C5C3×#53711yescharacteristic
628C2×C5C3×D4211yescharacteristic
629C2×C5C3×#54711yescharacteristic
630C2×C5C3×#54811yescharacteristic
631C2×C5C3×#55311yescharacteristic
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23C2×C3×C5×D412yes—
650C23C2×C3×C5×D412yes—
651C23C2×C3×C5×D412yes—
652C23C3×C5×#4112yes—
653C23C24×C3×C511yescharacteristic
654D4—28no—
655D4—48no—
656D4—48no—
657D4—44no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—28no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—48no—
678C2×C4—44no—
679C2×C4C2×C3×C5×D412yes—
680C2×C4C2×C3×C5×D412yes—
681C2×C4C2×C3×C5×D414yes—
682C2×C4C2×C3×C5×D412yes—
683C2×C4C2×C3×C5×D412yes—
684C2×C4C3×C5×#4112yes—
685C2×C3—24no—
686C2×C3—42no—
687C2×C3—82no—
688C2×C3C2×C5×#12111yescharacteristic
689C2×C3C2×C5×#12111yescharacteristic
690C2×C3C5×#53711yescharacteristic
691C2×C3C5×D4211yescharacteristic
692C2×C3C5×#54711yescharacteristic
693C2×C3C5×#54811yescharacteristic
694C2×C3C5×#55311yescharacteristic
695C5C3×#241611yescharacteristic, direct product factor, Sylow
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22C3×C5×#12114yescomplemented
717C22C22×C3×C5×D411yescharacteristic
718C22C22×C3×C5×D411yescharacteristic
719C22C22×C3×C5×D411yescharacteristic
720C22C2×C3×C5×#4111yescharacteristic
721C22C2×C3×C5×#4111yescharacteristic
722C22C3×C5×H(5,𝔽2)11yescharacteristic
723C22C3×C5×2−1+411yescharacteristic
724C4—22no—
725C4—22no—
726C4—24no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4C3×C5×#12114yescomplemented
732C3C5×#241611yescharacteristic, direct product factor, Sylow
733C2—24no—
734C2—42no—
735C2—82no—
736C2C2×C3×C5×#12111yescharacteristic
737C2C2×C3×C5×#12111yescharacteristic
738C2C3×C5×#53711yescharacteristic
739C2C3×C5×D4211yescharacteristic
740C2C3×C5×#54711yescharacteristic
741C2C3×C5×#54811yescharacteristic
742C2C3×C5×#55311yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
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×#121C2semidirect
2. C2×C3×C5×#121C2semidirect
3. C2×C3×C5×#121C2semidirect
4. C2×C3×C4×C5×D4C2semidirect
5. C22×C3×C5×C4⋊C4C2semidirect
6. C3×C5×#396C2semidirect
7. C3×C5×#394C2semidirect
8. C3×C5×#390C2semidirect
9. C3×C5×#389C2semidirect
10. C3×C5×#386C2semidirect
11. C3×C5×#380C2semidirect
12. C5×#2416C3direct (N × H)
41. C3×#2416C5direct (N × H)
42. C2×C5×#121C2×C3semidirect
43. C2×C5×#121C2×C3semidirect
44. C2×C5×#121C2×C3semidirect
45. C2×C4×C5×D4C2×C3semidirect
46. C22×C5×C4⋊C4C2×C3semidirect
47. C5×#396C2×C3semidirect
48. C5×#394C2×C3semidirect
49. C5×#390C2×C3semidirect
50. C5×#389C2×C3semidirect
51. C5×#386C2×C3semidirect
52. C5×#380C2×C3semidirect
67. C2×C3×C5×D4D4semidirect
76. C22×C3×C4×C5D4semidirect
90. C3×C5×C4⋊C4D4semidirect
99. C2×C3×#121C2×C5semidirect
100. C2×C3×#121C2×C5semidirect
101. C2×C3×#121C2×C5semidirect
102. C2×C3×C4×D4C2×C5semidirect
103. C22×C3×C4⋊C4C2×C5semidirect
104. C3×#396C2×C5semidirect
105. C3×#394C2×C5semidirect
106. C3×#390C2×C5semidirect
107. C3×#389C2×C5semidirect
108. C3×#386C2×C5semidirect
109. C3×#380C2×C5semidirect
138. #2416C3×C5direct (N × H)
234. C2×C5×D4C3×D4semidirect
243. C22×C4×C5C3×D4semidirect
257. C5×C4⋊C4C3×D4semidirect
266. C2×#121C2×C3×C5semidirect
267. C2×#121C2×C3×C5semidirect
268. C2×#121C2×C3×C5semidirect
269. C2×C4×D4C2×C3×C5semidirect
270. C22×C4⋊C4C2×C3×C5semidirect
271. #396C2×C3×C5semidirect
272. #394C2×C3×C5semidirect
273. #390C2×C3×C5semidirect
274. #389C2×C3×C5semidirect
275. #386C2×C3×C5semidirect
276. #380C2×C3×C5semidirect
297. C22×C3×C5#121semidirect
312. C3×C4×C5#121semidirect
327. C2×C3×D4C5×D4semidirect
336. C22×C3×C4C5×D4semidirect
350. C3×C4⋊C4C5×D4semidirect
523. C22×C5C3×#121semidirect
538. C4×C5C3×#121semidirect
553. C2×D4C3×C5×D4semidirect
562. C22×C4C3×C5×D4semidirect
576. C4⋊C4C3×C5×D4semidirect
585. C3×C5#2416direct (N × H)
606. C22×C3C5×#121semidirect
621. C3×C4C5×#121semidirect
695. C5C3×#2416direct (N × H)
716. C22C3×C5×#121semidirect
731. C4C3×C5×#121semidirect
732. C3C5×#2416direct (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
C22×C3×C5×C4⋊C42
C3×C5×#3962
C3×C5×#3942
C3×C5×#3902
C3×C5×#3892
C3×C5×#3862
C3×C5×#3802
C5×#24163
C3×#24165