Finite Group Databasebeta

← C3×C5×#2661 #14275695

Subgroups — C3×C5×#2661 #14275695

Order 1920.

1196 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic, complemented
3C3×C5×#398C211yesmaximal, characteristic, complemented
4C3×C5×#397C211yesmaximal, characteristic, complemented
5C3×C5×#394C212yesmaximal, complemented
6C3×C5×#394C211yesmaximal, characteristic, complemented
7C3×C5×#392C211yesmaximal, characteristic, complemented
8C3×C5×#392C212yesmaximal, complemented
9C3×C5×#390C212yesmaximal, complemented
10C3×C5×#388C212yesmaximal, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2661C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2211yescharacteristic
16C22×C3×C5×D4C2212yes—
17C23×C3×C4×C5C2211yescharacteristic
18C3×C5×#123—24no—
19C3×C5×#121—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C5×C22⋊C4C2212yes—
32C2×C3×C5×C22⋊C4C2212yes—
33C2×C3×C42×C5C2212yes—
34C3×C5×#95C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2661C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×#123C2×C311yescharacteristic, complemented
40C2×C5×#121C2×C311yescharacteristic, complemented
41C5×#398C2×C311yescharacteristic, complemented
42C5×#397C2×C311yescharacteristic, complemented
43C5×#394C2×C312yescomplemented
44C5×#394C2×C311yescharacteristic, complemented
45C5×#392C2×C312yescomplemented
46C5×#392C2×C311yescharacteristic, complemented
47C5×#390C2×C312yescomplemented
48C5×#388C2×C312yescomplemented
49C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
50C24×C3×C5C2311yescharacteristic
51C24×C3×C5C2312yes—
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—24no—
57C2×C3×C5×D4—42no—
58C2×C3×C5×D4—42no—
59C2×C3×C5×D4—42no—
60C2×C3×C5×D4—42no—
61C2×C3×C5×D4—42no—
62C2×C3×C5×D4—42no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5D414yescomplemented
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2312yes—
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—42no—
77C3×C5×C22⋊C4—22no—
78C3×C5×C22⋊C4—24no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4—24no—
83C3×C5×C22⋊C4—42no—
84C3×C5×C22⋊C4—42no—
85C3×C5×C22⋊C4—42no—
86C3×C42×C5—42no—
87C2×C3×#123C2×C511yescharacteristic, complemented
88C2×C3×#121C2×C511yescharacteristic, complemented
89C3×#398C2×C511yescharacteristic, complemented
90C3×#397C2×C511yescharacteristic, complemented
91C3×#394C2×C511yescharacteristic, complemented
92C3×#394C2×C512yescomplemented
93C3×#392C2×C511yescharacteristic, complemented
94C3×#392C2×C512yescomplemented
95C3×#390C2×C512yescomplemented
96C3×#388C2×C512yescomplemented
97C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
98C22×C5×D4C22×C312yes—
99C22×C5×D4C22×C311yescharacteristic
100C22×C5×D4C22×C312yes—
101C22×C5×D4C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C5×#123—24no—
104C5×#121—24no—
105C2×C5×C4⋊C4C22×C311yescharacteristic
106C2×C5×C4⋊C4C22×C311yescharacteristic
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C4⋊C4C22×C312yes—
109C2×C5×C22⋊C4C22×C312yes—
110C2×C5×C22⋊C4C22×C312yes—
111C2×C5×C22⋊C4C22×C312yes—
112C2×C5×C22⋊C4C22×C311yescharacteristic
113C2×C5×C22⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C311yescharacteristic
115C2×C5×C22⋊C4C22×C312yes—
116C2×C5×C22⋊C4C22×C312yes—
117C2×C5×C22⋊C4C22×C312yes—
118C2×C42×C5C22×C312yes—
119C5×#95C22×C311yescharacteristic
120C5×#95C22×C311yescharacteristic
121C5×#95C22×C312yes—
122C5×#95C22×C312yes—
123#2661C3×C511yescharacteristic, direct product factor, Sylow
124C23×C3×C5—22no—
125C23×C3×C5—22no—
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—21no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—21no—
140C23×C3×C5C2×D412yes—
141C23×C3×C5C2411yescharacteristic
142C3×C5×D4—44no—
143C3×C5×D4—48no—
144C3×C5×D4—44no—
145C3×C5×D4—48no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—22no—
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—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5#4114yes—
167C22×C3×D4C22×C512yes—
168C22×C3×D4C22×C511yescharacteristic
169C22×C3×D4C22×C512yes—
170C22×C3×D4C22×C511yescharacteristic
171C23×C3×C4C22×C511yescharacteristic
172C3×#123—24no—
173C3×#121—24no—
174C2×C3×C4⋊C4C22×C511yescharacteristic
175C2×C3×C4⋊C4C22×C511yescharacteristic
176C2×C3×C4⋊C4C22×C511yescharacteristic
177C2×C3×C4⋊C4C22×C512yes—
178C2×C3×C22⋊C4C22×C512yes—
179C2×C3×C22⋊C4C22×C512yes—
180C2×C3×C22⋊C4C22×C512yes—
181C2×C3×C22⋊C4C22×C511yescharacteristic
182C2×C3×C22⋊C4C22×C511yescharacteristic
183C2×C3×C22⋊C4C22×C511yescharacteristic
184C2×C3×C22⋊C4C22×C512yes—
185C2×C3×C22⋊C4C22×C512yes—
186C2×C3×C22⋊C4C22×C512yes—
187C2×C3×C42C22×C512yes—
188C3×#95C22×C511yescharacteristic
189C3×#95C22×C511yescharacteristic
190C3×#95C22×C512yes—
191C3×#95C22×C512yes—
192C24×C5C23×C311yescharacteristic
193C24×C5C23×C312yes—
194C24×C5C23×C311yescharacteristic
195C2×C5×D4—24no—
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4—24no—
199C2×C5×D4—42no—
200C2×C5×D4—42no—
201C2×C5×D4—42no—
202C2×C5×D4—42no—
203C2×C5×D4—42no—
204C2×C5×D4—42no—
205C22×C4×C5—42no—
206C22×C4×C5C3×D414yescomplemented
207C22×C4×C5C23×C312yes—
208C22×C4×C5C23×C311yescharacteristic
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C312yes—
211C22×C4×C5C23×C311yescharacteristic
212C22×C4×C5C23×C311yescharacteristic
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C312yes—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—42no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—24no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—24no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C42×C5—42no—
229C2×#123C2×C3×C511yescharacteristic, complemented
230C2×#121C2×C3×C511yescharacteristic, complemented
231#398C2×C3×C511yescharacteristic, complemented
232#397C2×C3×C511yescharacteristic, complemented
233#394C2×C3×C511yescharacteristic, complemented
234#394C2×C3×C512yescomplemented
235#392C2×C3×C511yescharacteristic, complemented
236#392C2×C3×C512yescomplemented
237#390C2×C3×C512yescomplemented
238#388C2×C3×C512yescomplemented
239C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—42no—
244C22×C3×C5—42no—
245C22×C3×C5—41no—
246C22×C3×C5—42no—
247C22×C3×C5—42no—
248C22×C3×C5—41no—
249C22×C3×C5—42no—
250C22×C3×C5—41no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5—42no—
254C22×C3×C5—42no—
255C22×C3×C5—42no—
256C22×C3×C5—42no—
257C22×C3×C5C22×D411yescharacteristic
258C22×C3×C5C2×#4112yes—
259C22×C3×C5H(5,𝔽2)12yes—
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C3×C4×C5—22no—
263C3×C4×C5—22no—
264C3×C4×C5—24no—
265C3×C4×C5—41no—
266C3×C4×C5—41no—
267C3×C4×C5—41no—
268C3×C4×C5—42no—
269C3×C4×C5—42no—
270C24×C3C23×C511yescharacteristic
271C24×C3C23×C512yes—
272C24×C3C23×C511yescharacteristic
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4—24no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C22×C3×C4—42no—
284C22×C3×C4C5×D414yescomplemented
285C22×C3×C4C23×C512yes—
286C22×C3×C4C23×C511yescharacteristic
287C22×C3×C4C23×C512yes—
288C22×C3×C4C23×C511yescharacteristic
289C22×C3×C4C23×C511yescharacteristic
290C22×C3×C4C23×C511yescharacteristic
291C22×C3×C4C23×C511yescharacteristic
292C22×C3×C4C23×C512yes—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—42no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C42—42no—
307C23×C5—22no—
308C23×C5—22no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—21no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—21no—
323C23×C5C2×C3×D412yes—
324C23×C5C24×C311yescharacteristic
325C5×D4—44no—
326C5×D4—48no—
327C5×D4—44no—
328C5×D4—48no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—21no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—21no—
345C2×C4×C5—22no—
346C2×C4×C5—44no—
347C2×C4×C5C2×C3×D412yes—
348C2×C4×C5C2×C3×D412yes—
349C2×C4×C5C3×#4114yes—
350C22×D4C22×C3×C512yes—
351C22×D4C22×C3×C511yescharacteristic
352C22×D4C22×C3×C511yescharacteristic
353C22×D4C22×C3×C512yes—
354C23×C4C22×C3×C511yescharacteristic
355#123—24no—
356#121—24no—
357C2×C4⋊C4C22×C3×C511yescharacteristic
358C2×C4⋊C4C22×C3×C511yescharacteristic
359C2×C4⋊C4C22×C3×C511yescharacteristic
360C2×C4⋊C4C22×C3×C512yes—
361C2×C22⋊C4C22×C3×C512yes—
362C2×C22⋊C4C22×C3×C511yescharacteristic
363C2×C22⋊C4C22×C3×C511yescharacteristic
364C2×C22⋊C4C22×C3×C511yescharacteristic
365C2×C22⋊C4C22×C3×C512yes—
366C2×C22⋊C4C22×C3×C512yes—
367C2×C22⋊C4C22×C3×C512yes—
368C2×C22⋊C4C22×C3×C512yes—
369C2×C22⋊C4C22×C3×C512yes—
370C2×C42C22×C3×C512yes—
371#95C22×C3×C511yescharacteristic
372#95C22×C3×C511yescharacteristic
373#95C22×C3×C512yes—
374#95C22×C3×C512yes—
375C2×C3×C5—42no—
376C2×C3×C5—82no—
377C2×C3×C5—81no—
378C2×C3×C5#53211yescharacteristic
379C2×C3×C5#53411yescharacteristic
380C2×C3×C5#53511yescharacteristic
381C2×C3×C5#53812yes—
382C2×C3×C5#54012yes—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3C2×C5×D412yes—
400C23×C3C24×C511yescharacteristic
401C3×D4—44no—
402C3×D4—48no—
403C3×D4—44no—
404C3×D4—48no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—44no—
423C2×C3×C4C2×C5×D412yes—
424C2×C3×C4C2×C5×D412yes—
425C2×C3×C4C5×#4114yes—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5—41no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5—41no—
435C22×C5—42no—
436C22×C5—41no—
437C22×C5—42no—
438C22×C5—42no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5C22×C3×D411yescharacteristic
444C22×C5C2×C3×#4112yes—
445C22×C5C3×H(5,𝔽2)12yes—
446C22×C5C3×H(5,𝔽2)11yescharacteristic
447C22×C5C3×H(5,𝔽2)11yescharacteristic
448C4×C5—22no—
449C4×C5—22no—
450C4×C5—24no—
451C4×C5—41no—
452C4×C5—41no—
453C4×C5—41no—
454C4×C5—42no—
455C4×C5—42no—
456C24C23×C3×C511yescharacteristic
457C24C23×C3×C512yes—
458C24C23×C3×C511yescharacteristic
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—24no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C22×C4—42no—
470C22×C4C3×C5×D414yescomplemented
471C22×C4C23×C3×C512yes—
472C22×C4C23×C3×C511yescharacteristic
473C22×C4C23×C3×C512yes—
474C22×C4C23×C3×C511yescharacteristic
475C22×C4C23×C3×C511yescharacteristic
476C22×C4C23×C3×C511yescharacteristic
477C22×C4C23×C3×C511yescharacteristic
478C22×C4C23×C3×C512yes—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—42no—
483C22⋊C4—22no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C42—42no—
493C3×C5#266111yescharacteristic, direct product factor, Hall
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—41no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—41no—
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×#4112yes—
513C22×C3C5×H(5,𝔽2)12yes—
514C22×C3C5×H(5,𝔽2)11yescharacteristic
515C22×C3C5×H(5,𝔽2)11yescharacteristic
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—24no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—42no—
523C3×C4—42no—
524C2×C5—42no—
525C2×C5—82no—
526C2×C5—81no—
527C2×C5C3×#53211yescharacteristic
528C2×C5C3×#53411yescharacteristic
529C2×C5C3×#53511yescharacteristic
530C2×C5C3×#53812yes—
531C2×C5C3×#54012yes—
532C23—22no—
533C23—22no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—21no—
548C23C2×C3×C5×D412yes—
549C23C24×C3×C511yescharacteristic
550D4—44no—
551D4—48no—
552D4—44no—
553D4—48no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4C2×C3×C5×D412yes—
573C2×C4C2×C3×C5×D412yes—
574C2×C4C3×C5×#4114yes—
575C2×C3—42no—
576C2×C3—82no—
577C2×C3—81no—
578C2×C3C5×#53211yescharacteristic
579C2×C3C5×#53411yescharacteristic
580C2×C3C5×#53511yescharacteristic
581C2×C3C5×#53812yes—
582C2×C3C5×#54012yes—
583C5C3×#266111yescharacteristic, direct product factor, Sylow
584C22—22no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—42no—
592C22—41no—
593C22—42no—
594C22—41no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22C22×C3×C5×D411yescharacteristic
602C22C2×C3×C5×#4112yes—
603C22C3×C5×H(5,𝔽2)12yes—
604C22C3×C5×H(5,𝔽2)11yescharacteristic
605C22C3×C5×H(5,𝔽2)11yescharacteristic
606C4—22no—
607C4—22no—
608C4—24no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—42no—
614C3C5×#266111yescharacteristic, direct product factor, Sylow
615C2—42no—
616C2—82no—
617C2—81no—
618C2C3×C5×#53211yescharacteristic
619C2C3×C5×#53411yescharacteristic
620C2C3×C5×#53511yescharacteristic
621C2C3×C5×#53812yes—
622C2C3×C5×#54012yes—
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×#123C2semidirect
2. C2×C3×C5×#121C2semidirect
3. C3×C5×#398C2semidirect
4. C3×C5×#397C2semidirect
5. C3×C5×#394C2semidirect
6. C3×C5×#394C2semidirect
7. C3×C5×#392C2semidirect
8. C3×C5×#392C2semidirect
9. C3×C5×#390C2semidirect
10. C3×C5×#388C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2661C3direct (N × H)
38. C3×#2661C5direct (N × H)
39. C2×C5×#123C2×C3semidirect
40. C2×C5×#121C2×C3semidirect
41. C5×#398C2×C3semidirect
42. C5×#397C2×C3semidirect
43. C5×#394C2×C3semidirect
44. C5×#394C2×C3semidirect
45. C5×#392C2×C3semidirect
46. C5×#392C2×C3semidirect
47. C5×#390C2×C3semidirect
48. C5×#388C2×C3semidirect
49. C4×C5×C22⋊C4C2×C3semidirect
64. C22×C3×C4×C5D4semidirect
87. C2×C3×#123C2×C5semidirect
88. C2×C3×#121C2×C5semidirect
89. C3×#398C2×C5semidirect
90. C3×#397C2×C5semidirect
91. C3×#394C2×C5semidirect
92. C3×#394C2×C5semidirect
93. C3×#392C2×C5semidirect
94. C3×#392C2×C5semidirect
95. C3×#390C2×C5semidirect
96. C3×#388C2×C5semidirect
97. C3×C4×C22⋊C4C2×C5semidirect
123. #2661C3×C5direct (N × H)
206. C22×C4×C5C3×D4semidirect
229. C2×#123C2×C3×C5semidirect
230. C2×#121C2×C3×C5semidirect
231. #398C2×C3×C5semidirect
232. #397C2×C3×C5semidirect
233. #394C2×C3×C5semidirect
234. #394C2×C3×C5semidirect
235. #392C2×C3×C5semidirect
236. #392C2×C3×C5semidirect
237. #390C2×C3×C5semidirect
238. #388C2×C3×C5semidirect
239. C4×C22⋊C4C2×C3×C5semidirect
284. C22×C3×C4C5×D4semidirect
470. C22×C4C3×C5×D4semidirect
493. C3×C5#2661direct (N × H)
583. C5C3×#2661direct (N × H)
614. C3C5×#2661direct (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×#1232
C2×C3×C5×#1212
C3×C5×#3982
C3×C5×#3972
C3×C5×#3942
C3×C5×#3922
C3×C5×#3902
C3×C5×#3882
C3×C4×C5×C22⋊C42
C5×#26613
C3×#26615