Finite Group Databasebeta

← C3×C5×#2635 #14275669

Subgroups — C3×C5×#2635 #14275669

Order 1920.

1240 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×#121C211yesmaximal, characteristic, complemented
2C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
3C3×C5×#400C211yesmaximal, characteristic, complemented
4C3×C5×#399C211yesmaximal, characteristic, complemented
5C3×C5×#394C212yesmaximal, complemented
6C3×C5×#394C211yesmaximal, characteristic, complemented
7C3×C5×#392C211yesmaximal, characteristic, complemented
8C3×C5×#392C212yesmaximal, complemented
9C3×C5×#388C212yesmaximal, complemented
10C3×C5×#386C212yesmaximal, complemented
11C3×C5×#381C211yesmaximal, characteristic, complemented
12C5×#2635C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×C3×C5×D4C2212yes—
15C22×C3×C5×D4C2211yescharacteristic
16C22×C3×C5×D4C2212yes—
17C23×C3×C4×C5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C3×C5×#121—24no—
20C3×C4×C5×D4—24no—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊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×C5×C22⋊C4C2212yes—
32C2×C3×C42×C5C2211yescharacteristic
33C3×C5×#95C2212yes—
34C3×C5×#95C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2635C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×#121C2×C311yescharacteristic, complemented
40C2×C4×C5×D4C2×C311yescharacteristic, complemented
41C5×#400C2×C311yescharacteristic, complemented
42C5×#399C2×C311yescharacteristic, complemented
43C5×#394C2×C311yescharacteristic, complemented
44C5×#394C2×C312yescomplemented
45C5×#392C2×C312yescomplemented
46C5×#392C2×C311yescharacteristic, complemented
47C5×#388C2×C312yescomplemented
48C5×#386C2×C312yescomplemented
49C5×#381C2×C311yescharacteristic, complemented
50C24×C3×C5C2312yes—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—24no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—42no—
60C2×C3×C5×D4—42no—
61C2×C3×C5×D4—42no—
62C2×C3×C5×D4—42no—
63C2×C3×C5×D4—42no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—42no—
66C22×C3×C4×C5—42no—
67C22×C3×C4×C5D414yescomplemented
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C3×C5×C4⋊C4—22no—
77C3×C5×C4⋊C4—22no—
78C3×C5×C4⋊C4—42no—
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×C5×C22⋊C4—42no—
87C3×C42×C5—22no—
88C2×C3×#121C2×C511yescharacteristic, complemented
89C2×C3×C4×D4C2×C511yescharacteristic, complemented
90C3×#400C2×C511yescharacteristic, complemented
91C3×#399C2×C511yescharacteristic, complemented
92C3×#394C2×C511yescharacteristic, complemented
93C3×#394C2×C512yescomplemented
94C3×#392C2×C511yescharacteristic, complemented
95C3×#392C2×C512yescomplemented
96C3×#388C2×C512yescomplemented
97C3×#386C2×C512yescomplemented
98C3×#381C2×C511yescharacteristic, complemented
99C22×C5×D4C22×C311yescharacteristic
100C22×C5×D4C22×C312yes—
101C22×C5×D4C22×C312yes—
102C22×C5×D4C22×C311yescharacteristic
103C23×C4×C5C22×C311yescharacteristic
104C23×C4×C5C22×C311yescharacteristic
105C5×#121—24no—
106C4×C5×D4—24no—
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C2×C5×C4⋊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×C312yes—
115C2×C5×C22⋊C4C22×C312yes—
116C2×C5×C22⋊C4C22×C312yes—
117C2×C5×C22⋊C4C22×C312yes—
118C2×C42×C5C22×C311yescharacteristic
119C5×#95C22×C312yes—
120C5×#95C22×C311yescharacteristic
121C5×#95C22×C311yescharacteristic
122C5×#95C22×C312yes—
123C5×#95C22×C312yes—
124#2635C3×C511yescharacteristic, direct product factor, Sylow
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—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5C2×D412yes—
141C23×C3×C5#4112yes—
142C23×C3×C5C2411yescharacteristic
143C3×C5×D4—28no—
144C3×C5×D4—44no—
145C3×C5×D4—48no—
146C3×C5×D4—48no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—22no—
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—22no—
164C2×C3×C4×C5—44no—
165C2×C3×C4×C5—44no—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2×D412yes—
168C2×C3×C4×C5#4112yes—
169C22×C3×D4C22×C511yescharacteristic
170C22×C3×D4C22×C512yes—
171C22×C3×D4C22×C512yes—
172C22×C3×D4C22×C511yescharacteristic
173C23×C3×C4C22×C511yescharacteristic
174C23×C3×C4C22×C511yescharacteristic
175C3×#121—24no—
176C3×C4×D4—24no—
177C2×C3×C4⋊C4C22×C511yescharacteristic
178C2×C3×C4⋊C4C22×C511yescharacteristic
179C2×C3×C4⋊C4C22×C512yes—
180C2×C3×C22⋊C4C22×C512yes—
181C2×C3×C22⋊C4C22×C512yes—
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×C22⋊C4C22×C512yes—
188C2×C3×C42C22×C511yescharacteristic
189C3×#95C22×C512yes—
190C3×#95C22×C511yescharacteristic
191C3×#95C22×C511yescharacteristic
192C3×#95C22×C512yes—
193C3×#95C22×C512yes—
194C24×C5C23×C312yes—
195C24×C5C23×C311yescharacteristic
196C24×C5C23×C311yescharacteristic
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—24no—
200C2×C5×D4—24no—
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4—42no—
204C2×C5×D4—42no—
205C2×C5×D4—42no—
206C2×C5×D4—42no—
207C2×C5×D4—42no—
208C22×C4×C5—22no—
209C22×C4×C5—42no—
210C22×C4×C5—42no—
211C22×C4×C5C3×D414yescomplemented
212C22×C4×C5C23×C311yescharacteristic
213C22×C4×C5C23×C312yes—
214C22×C4×C5C23×C311yescharacteristic
215C22×C4×C5C23×C312yes—
216C22×C4×C5C23×C312yes—
217C22×C4×C5C23×C311yescharacteristic
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C311yescharacteristic
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—42no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—24no—
226C5×C22⋊C4—24no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C42×C5—22no—
232C2×#121C2×C3×C511yescharacteristic, complemented
233C2×C4×D4C2×C3×C511yescharacteristic, complemented
234#400C2×C3×C511yescharacteristic, complemented
235#399C2×C3×C511yescharacteristic, complemented
236#394C2×C3×C511yescharacteristic, complemented
237#394C2×C3×C512yescomplemented
238#392C2×C3×C511yescharacteristic, complemented
239#392C2×C3×C512yescomplemented
240#388C2×C3×C512yescomplemented
241#386C2×C3×C512yescomplemented
242#381C2×C3×C511yescharacteristic, complemented
243C22×C3×C5—22no—
244C22×C3×C5—22no—
245C22×C3×C5—22no—
246C22×C3×C5—22no—
247C22×C3×C5—24no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
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×C5—42no—
258C22×C3×C5—42no—
259C22×C3×C5—42no—
260C22×C3×C5C22×D411yescharacteristic
261C22×C3×C5C2×#4111yescharacteristic
262C22×C3×C5C2×#4111yescharacteristic
263C22×C3×C5H(5,𝔽2)12yes—
264C22×C3×C5H(5,𝔽2)12yes—
265C3×C4×C5—22no—
266C3×C4×C5—22no—
267C3×C4×C5—22no—
268C3×C4×C5—41no—
269C3×C4×C5—41no—
270C3×C4×C5—42no—
271C3×C4×C5—42no—
272C3×C4×C5—42no—
273C24×C3C23×C512yes—
274C24×C3C23×C511yescharacteristic
275C24×C3C23×C511yescharacteristic
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—24no—
279C2×C3×D4—24no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C22×C3×C4—22no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4C5×D414yescomplemented
291C22×C3×C4C23×C512yes—
292C22×C3×C4C23×C512yes—
293C22×C3×C4C23×C511yescharacteristic
294C22×C3×C4C23×C512yes—
295C22×C3×C4C23×C511yescharacteristic
296C22×C3×C4C23×C511yescharacteristic
297C22×C3×C4C23×C511yescharacteristic
298C22×C3×C4C23×C511yescharacteristic
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—42no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C42—22no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5C2×C3×D412yes—
327C23×C5C3×#4112yes—
328C23×C5C24×C311yescharacteristic
329C5×D4—28no—
330C5×D4—44no—
331C5×D4—48no—
332C5×D4—48no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
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—44no—
351C2×C4×C5—44no—
352C2×C4×C5C2×C3×D412yes—
353C2×C4×C5C2×C3×D412yes—
354C2×C4×C5C3×#4112yes—
355C22×D4C22×C3×C511yescharacteristic
356C22×D4C22×C3×C512yes—
357C22×D4C22×C3×C511yescharacteristic
358C22×D4C22×C3×C512yes—
359C23×C4C22×C3×C511yescharacteristic
360C23×C4C22×C3×C511yescharacteristic
361#121—24no—
362C4×D4—24no—
363C2×C4⋊C4C22×C3×C511yescharacteristic
364C2×C4⋊C4C22×C3×C511yescharacteristic
365C2×C4⋊C4C22×C3×C512yes—
366C2×C22⋊C4C22×C3×C511yescharacteristic
367C2×C22⋊C4C22×C3×C511yescharacteristic
368C2×C22⋊C4C22×C3×C512yes—
369C2×C22⋊C4C22×C3×C512yes—
370C2×C22⋊C4C22×C3×C512yes—
371C2×C22⋊C4C22×C3×C512yes—
372C2×C22⋊C4C22×C3×C512yes—
373C2×C22⋊C4C22×C3×C512yes—
374C2×C42C22×C3×C511yescharacteristic
375#95C22×C3×C512yes—
376#95C22×C3×C511yescharacteristic
377#95C22×C3×C511yescharacteristic
378#95C22×C3×C512yes—
379#95C22×C3×C512yes—
380C2×C3×C5—42no—
381C2×C3×C5—42no—
382C2×C3×C5—82no—
383C2×C3×C5#52511yescharacteristic
384C2×C3×C5#53411yescharacteristic
385C2×C3×C5#53511yescharacteristic
386C2×C3×C5#53812yes—
387C2×C3×C5#54012yes—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3C2×C5×D412yes—
404C23×C3C5×#4112yes—
405C23×C3C24×C511yescharacteristic
406C3×D4—28no—
407C3×D4—44no—
408C3×D4—48no—
409C3×D4—48no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—44no—
428C2×C3×C4—44no—
429C2×C3×C4C2×C5×D412yes—
430C2×C3×C4C2×C5×D412yes—
431C2×C3×C4C5×#4112yes—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—24no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5C22×C3×D411yescharacteristic
450C22×C5C2×C3×#4111yescharacteristic
451C22×C5C2×C3×#4111yescharacteristic
452C22×C5C3×H(5,𝔽2)12yes—
453C22×C5C3×H(5,𝔽2)12yes—
454C4×C5—22no—
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—41no—
458C4×C5—41no—
459C4×C5—42no—
460C4×C5—42no—
461C4×C5—42no—
462C24C23×C3×C512yes—
463C24C23×C3×C511yescharacteristic
464C24C23×C3×C511yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C22×C4—22no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4C3×C5×D414yescomplemented
480C22×C4C23×C3×C512yes—
481C22×C4C23×C3×C512yes—
482C22×C4C23×C3×C511yescharacteristic
483C22×C4C23×C3×C512yes—
484C22×C4C23×C3×C511yescharacteristic
485C22×C4C23×C3×C511yescharacteristic
486C22×C4C23×C3×C511yescharacteristic
487C22×C4C23×C3×C511yescharacteristic
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—42no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C42—22no—
500C3×C5#263511yescharacteristic, direct product factor, Hall
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—24no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3C22×C5×D411yescharacteristic
519C22×C3C2×C5×#4111yescharacteristic
520C22×C3C2×C5×#4111yescharacteristic
521C22×C3C5×H(5,𝔽2)12yes—
522C22×C3C5×H(5,𝔽2)12yes—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—41no—
527C3×C4—41no—
528C3×C4—42no—
529C3×C4—42no—
530C3×C4—42no—
531C2×C5—42no—
532C2×C5—42no—
533C2×C5—82no—
534C2×C5C3×#52511yescharacteristic
535C2×C5C3×#53411yescharacteristic
536C2×C5C3×#53511yescharacteristic
537C2×C5C3×#53812yes—
538C2×C5C3×#54012yes—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23C2×C3×C5×D412yes—
555C23C3×C5×#4112yes—
556C23C24×C3×C511yescharacteristic
557D4—28no—
558D4—44no—
559D4—48no—
560D4—48no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4C2×C3×C5×D412yes—
581C2×C4C2×C3×C5×D412yes—
582C2×C4C3×C5×#4112yes—
583C2×C3—42no—
584C2×C3—42no—
585C2×C3—82no—
586C2×C3C5×#52511yescharacteristic
587C2×C3C5×#53411yescharacteristic
588C2×C3C5×#53511yescharacteristic
589C2×C3C5×#53812yes—
590C2×C3C5×#54012yes—
591C5C3×#263511yescharacteristic, direct product factor, Sylow
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—24no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22C22×C3×C5×D411yescharacteristic
610C22C2×C3×C5×#4111yescharacteristic
611C22C2×C3×C5×#4111yescharacteristic
612C22C3×C5×H(5,𝔽2)12yes—
613C22C3×C5×H(5,𝔽2)12yes—
614C4—22no—
615C4—22no—
616C4—22no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—42no—
622C3C5×#263511yescharacteristic, direct product factor, Sylow
623C2—42no—
624C2—42no—
625C2—82no—
626C2C3×C5×#52511yescharacteristic
627C2C3×C5×#53411yescharacteristic
628C2C3×C5×#53511yescharacteristic
629C2C3×C5×#53812yes—
630C2C3×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×#121C2semidirect
2. C2×C3×C4×C5×D4C2semidirect
3. C3×C5×#400C2semidirect
4. C3×C5×#399C2semidirect
5. C3×C5×#394C2semidirect
6. C3×C5×#394C2semidirect
7. C3×C5×#392C2semidirect
8. C3×C5×#392C2semidirect
9. C3×C5×#388C2semidirect
10. C3×C5×#386C2semidirect
11. C3×C5×#381C2semidirect
12. C5×#2635C3direct (N × H)
38. C3×#2635C5direct (N × H)
39. C2×C5×#121C2×C3semidirect
40. C2×C4×C5×D4C2×C3semidirect
41. C5×#400C2×C3semidirect
42. C5×#399C2×C3semidirect
43. C5×#394C2×C3semidirect
44. C5×#394C2×C3semidirect
45. C5×#392C2×C3semidirect
46. C5×#392C2×C3semidirect
47. C5×#388C2×C3semidirect
48. C5×#386C2×C3semidirect
49. C5×#381C2×C3semidirect
67. C22×C3×C4×C5D4semidirect
88. C2×C3×#121C2×C5semidirect
89. C2×C3×C4×D4C2×C5semidirect
90. C3×#400C2×C5semidirect
91. C3×#399C2×C5semidirect
92. C3×#394C2×C5semidirect
93. C3×#394C2×C5semidirect
94. C3×#392C2×C5semidirect
95. C3×#392C2×C5semidirect
96. C3×#388C2×C5semidirect
97. C3×#386C2×C5semidirect
98. C3×#381C2×C5semidirect
124. #2635C3×C5direct (N × H)
211. C22×C4×C5C3×D4semidirect
232. C2×#121C2×C3×C5semidirect
233. C2×C4×D4C2×C3×C5semidirect
234. #400C2×C3×C5semidirect
235. #399C2×C3×C5semidirect
236. #394C2×C3×C5semidirect
237. #394C2×C3×C5semidirect
238. #392C2×C3×C5semidirect
239. #392C2×C3×C5semidirect
240. #388C2×C3×C5semidirect
241. #386C2×C3×C5semidirect
242. #381C2×C3×C5semidirect
290. C22×C3×C4C5×D4semidirect
479. C22×C4C3×C5×D4semidirect
500. C3×C5#2635direct (N × H)
591. C5C3×#2635direct (N × H)
622. C3C5×#2635direct (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×#4002
C3×C5×#3992
C3×C5×#3942
C3×C5×#3922
C3×C5×#3882
C3×C5×#3862
C3×C5×#3812
C5×#26353
C3×#26355