Finite Group Databasebeta

← C3×C5×#2000 #14275034

Subgroups — C3×C5×#2000 #14275034

Order 1920.

888 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
1C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#121C211yesmaximal, characteristic
4C2×C3×C5×#103C211yesmaximal, characteristic, complemented
5C2×C3×C5×#102C211yesmaximal, characteristic, complemented
6C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
7C3×C5×#340C211yesmaximal, characteristic, complemented
8C5×#2000C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×D4—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C2×C3×C5×SD16—22no—
14C2×C3×C5×SD16—22no—
15C2×C3×C5×SD16—22no—
16C22×C3×C5×C8C2211yescharacteristic
17C22×C3×C5×C8C2211yescharacteristic
18C3×C5×C22⋊Q8—22no—
19C3×C5×C22⋊Q8—22no—
20C3×C5×#121—22no—
21C3×C5×#121—22no—
22C2×C3×C5×C4⋊C4—21no—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4—21no—
26C2×C3×C5×C22⋊C4—21no—
27C3×C5×#103—22no—
28C3×C5×#102—22no—
29C3×C5×C22⋊C8—22no—
30C3×#2000C511yesmaximal, characteristic, direct product factor, Hall
31C22×C5×SD16C2×C311yescharacteristic, complemented
32C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
33C2×C5×#121C2×C311yescharacteristic
34C2×C5×#103C2×C311yescharacteristic, complemented
35C2×C5×#102C2×C311yescharacteristic, complemented
36C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
37C5×#340C2×C311yescharacteristic, complemented
38C24×C3×C5—21no—
39C24×C3×C5D411yescharacteristic
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—21no—
45C2×C3×C5×Q8D412yescomplemented
46C2×C3×C5×D4—24no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—42no—
53C2×C3×C5×D4—42no—
54C2×C3×C5×D4D412yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5D411yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C3×C5×SD16—28no—
67C2×C3×C5×C8—21no—
68C2×C3×C5×C8—21no—
69C2×C3×C5×C8—21no—
70C2×C3×C5×C8—21no—
71C2×C3×C5×C8—21no—
72C2×C3×C5×C8D412yescomplemented
73C3×C5×C4⋊C4—24no—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4D412yes—
77C3×C5×C4⋊C4D412yescomplemented
78C3×C5×C22⋊C4—24no—
79C3×C5×C22⋊C4—24no—
80C22×C3×SD16C2×C511yescharacteristic, complemented
81C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
82C2×C3×#121C2×C511yescharacteristic
83C2×C3×#103C2×C511yescharacteristic, complemented
84C2×C3×#102C2×C511yescharacteristic, complemented
85C2×C3×C22⋊C8C2×C511yescharacteristic, complemented
86C3×#340C2×C511yescharacteristic, complemented
87C22×C5×Q8C22×C311yescharacteristic
88C22×C5×D4—21no—
89C22×C5×D4C22×C311yescharacteristic
90C23×C4×C5C22×C311yescharacteristic
91C2×C5×SD16—22no—
92C2×C5×SD16—22no—
93C2×C5×SD16—22no—
94C22×C5×C8C22×C311yescharacteristic
95C22×C5×C8C22×C311yescharacteristic
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—22no—
98C5×#121—22no—
99C5×#121—22no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C22×C311yescharacteristic
102C2×C5×C4⋊C4C22×C311yescharacteristic
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C5×#103—22no—
106C5×#102—22no—
107C5×C22⋊C8—22no—
108#2000C3×C511yescharacteristic, direct product factor, Sylow
109C23×C3×C5—21no—
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—21no—
113C23×C3×C5—21no—
114C23×C3×C5—21no—
115C23×C3×C5—22no—
116C23×C3×C5—41no—
117C23×C3×C5—41no—
118C23×C3×C5—41no—
119C23×C3×C5—41no—
120C23×C3×C5—41no—
121C23×C3×C5—41no—
122C23×C3×C5SD1612yescomplemented
123C23×C3×C5C2×D411yescharacteristic
124C3×C5×Q8—22no—
125C3×C5×Q8—22no—
126C3×C5×Q8—41no—
127C3×C5×Q8—41no—
128C3×C5×D4—22no—
129C3×C5×D4—22no—
130C3×C5×D4—48no—
131C3×C5×D4—41no—
132C3×C5×D4—41no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5—41no—
143C2×C3×C4×C5—41no—
144C2×C3×C4×C5—41no—
145C2×C3×C4×C5—41no—
146C2×C3×C4×C5—41no—
147C2×C3×C4×C5—41no—
148C2×C3×C4×C5—41no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5#4111yescharacteristic
155C3×C5×C8—22no—
156C3×C5×C8—41no—
157C22×C3×Q8C22×C511yescharacteristic
158C22×C3×D4—21no—
159C22×C3×D4C22×C511yescharacteristic
160C23×C3×C4C22×C511yescharacteristic
161C2×C3×SD16—22no—
162C2×C3×SD16—22no—
163C2×C3×SD16—22no—
164C22×C3×C8C22×C511yescharacteristic
165C22×C3×C8C22×C511yescharacteristic
166C3×C22⋊Q8—22no—
167C3×C22⋊Q8—22no—
168C3×#121—22no—
169C3×#121—22no—
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4C22×C511yescharacteristic
172C2×C3×C4⋊C4C22×C511yescharacteristic
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—21no—
175C3×#103—22no—
176C3×#102—22no—
177C3×C22⋊C8—22no—
178C24×C5—21no—
179C24×C5C3×D411yescharacteristic
180C2×C5×Q8—21no—
181C2×C5×Q8—21no—
182C2×C5×Q8—21no—
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8C3×D412yescomplemented
186C2×C5×D4—24no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—42no—
193C2×C5×D4—42no—
194C2×C5×D4C3×D412yes—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5C3×D411yescharacteristic
205C22×C4×C5C23×C311yescharacteristic
206C5×SD16—28no—
207C2×C5×C8—21no—
208C2×C5×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8C3×D412yescomplemented
213C5×C4⋊C4—24no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C3×D412yes—
217C5×C4⋊C4C3×D412yescomplemented
218C5×C22⋊C4—24no—
219C5×C22⋊C4—24no—
220C22×SD16C2×C3×C511yescharacteristic, complemented
221C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
222C2×#121C2×C3×C511yescharacteristic
223C2×#103C2×C3×C511yescharacteristic, complemented
224C2×#102C2×C3×C511yescharacteristic, complemented
225C2×C22⋊C8C2×C3×C511yescharacteristic, complemented
226#340C2×C3×C511yescharacteristic, complemented
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—22no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5—41no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—81no—
238C22×C3×C5—81no—
239C22×C3×C5—81no—
240C22×C3×C5—81no—
241C22×C3×C5#12011yescharacteristic
242C22×C3×C5#12011yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5C2×SD1611yescharacteristic
245C22×C3×C5#13511yescharacteristic
246C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
247C22×C3×C5#13711yescharacteristic
248C3×C4×C5—41no—
249C3×C4×C5—42no—
250C3×C4×C5—42no—
251C3×C4×C5—42no—
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12111yescharacteristic
254C3×C4×C5#12111yescharacteristic
255C3×C4×C5#12711yescharacteristic
256C24×C3—21no—
257C24×C3C5×D411yescharacteristic
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8C5×D412yescomplemented
264C2×C3×D4—24no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4C5×D412yes—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4C5×D411yescharacteristic
283C22×C3×C4C23×C511yescharacteristic
284C3×SD16—28no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8C5×D412yescomplemented
291C3×C4⋊C4—24no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C5×D412yes—
295C3×C4⋊C4C5×D412yescomplemented
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—22no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5C3×SD1612yescomplemented
312C23×C5C2×C3×D411yescharacteristic
313C5×Q8—22no—
314C5×Q8—22no—
315C5×Q8—41no—
316C5×Q8—41no—
317C5×D4—22no—
318C5×D4—22no—
319C5×D4—48no—
320C5×D4—41no—
321C5×D4—41no—
322C2×C4×C5—21no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5C2×C3×D411yescharacteristic
339C2×C4×C5C2×C3×D411yescharacteristic
340C2×C4×C5C2×C3×D411yescharacteristic
341C2×C4×C5C2×C3×D411yescharacteristic
342C2×C4×C5C2×C3×D411yescharacteristic
343C2×C4×C5C3×#4111yescharacteristic
344C5×C8—22no—
345C5×C8—41no—
346C22×Q8C22×C3×C511yescharacteristic
347C22×D4—21no—
348C22×D4C22×C3×C511yescharacteristic
349C23×C4C22×C3×C511yescharacteristic
350C2×SD16—22no—
351C2×SD16—22no—
352C2×SD16—22no—
353C22×C8C22×C3×C511yescharacteristic
354C22×C8C22×C3×C511yescharacteristic
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357#121—22no—
358#121—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C22×C3×C511yescharacteristic
361C2×C4⋊C4C22×C3×C511yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364#103—22no—
365#102—22no—
366C22⋊C8—22no—
367C2×C3×C5—42no—
368C2×C3×C5—82no—
369C2×C3×C5#39211yescharacteristic
370C2×C3×C5#44811yescharacteristic
371C2×C3×C5#44911yescharacteristic
372C2×C3×C5#45011yescharacteristic
373C2×C3×C5#45211yescharacteristic
374C2×C3×C5#46511yescharacteristic
375C2×C3×C5#46811yescharacteristic
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3C5×SD1612yescomplemented
390C23×C3C2×C5×D411yescharacteristic
391C3×Q8—22no—
392C3×Q8—22no—
393C3×Q8—41no—
394C3×Q8—41no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—48no—
398C3×D4—41no—
399C3×D4—41no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4C2×C5×D411yescharacteristic
417C2×C3×C4C2×C5×D411yescharacteristic
418C2×C3×C4C2×C5×D411yescharacteristic
419C2×C3×C4C2×C5×D411yescharacteristic
420C2×C3×C4C2×C5×D411yescharacteristic
421C2×C3×C4C5×#4111yescharacteristic
422C3×C8—22no—
423C3×C8—41no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5—81no—
435C22×C5—81no—
436C22×C5—81no—
437C22×C5—81no—
438C22×C5C3×#12011yescharacteristic
439C22×C5C3×#12011yescharacteristic
440C22×C5C3×#12111yescharacteristic
441C22×C5C2×C3×SD1611yescharacteristic
442C22×C5C3×#13511yescharacteristic
443C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
444C22×C5C3×#13711yescharacteristic
445C4×C5—41no—
446C4×C5—42no—
447C4×C5—42no—
448C4×C5—42no—
449C4×C5C3×#12011yescharacteristic
450C4×C5C3×#12111yescharacteristic
451C4×C5C3×#12111yescharacteristic
452C4×C5C3×#12711yescharacteristic
453C24—21no—
454C24C3×C5×D411yescharacteristic
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C3×C5×D412yescomplemented
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4C3×C5×D412yes—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4C3×C5×D411yescharacteristic
480C22×C4C23×C3×C511yescharacteristic
481SD16—28no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C3×C5×D412yescomplemented
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4C3×C5×D412yes—
492C4⋊C4C3×C5×D412yescomplemented
493C22⋊C4—24no—
494C22⋊C4—24no—
495C3×C5#200011yescharacteristic, direct product factor, Hall
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3C5×#12011yescharacteristic
511C22×C3C5×#12011yescharacteristic
512C22×C3C5×#12111yescharacteristic
513C22×C3C2×C5×SD1611yescharacteristic
514C22×C3C5×#13511yescharacteristic
515C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
516C22×C3C5×#13711yescharacteristic
517C3×C4—41no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—42no—
521C3×C4C5×#12011yescharacteristic
522C3×C4C5×#12111yescharacteristic
523C3×C4C5×#12111yescharacteristic
524C3×C4C5×#12711yescharacteristic
525C2×C5—42no—
526C2×C5—82no—
527C2×C5C3×#39211yescharacteristic
528C2×C5C3×#44811yescharacteristic
529C2×C5C3×#44911yescharacteristic
530C2×C5C3×#45011yescharacteristic
531C2×C5C3×#45211yescharacteristic
532C2×C5C3×#46511yescharacteristic
533C2×C5C3×#46811yescharacteristic
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C3×C5×SD1612yescomplemented
548C23C2×C3×C5×D411yescharacteristic
549Q8—22no—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553D4—22no—
554D4—22no—
555D4—48no—
556D4—41no—
557D4—41no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4C2×C3×C5×D411yescharacteristic
575C2×C4C2×C3×C5×D411yescharacteristic
576C2×C4C2×C3×C5×D411yescharacteristic
577C2×C4C2×C3×C5×D411yescharacteristic
578C2×C4C2×C3×C5×D411yescharacteristic
579C2×C4C3×C5×#4111yescharacteristic
580C8—22no—
581C8—41no—
582C2×C3—42no—
583C2×C3—82no—
584C2×C3C5×#39211yescharacteristic
585C2×C3C5×#44811yescharacteristic
586C2×C3C5×#44911yescharacteristic
587C2×C3C5×#45011yescharacteristic
588C2×C3C5×#45211yescharacteristic
589C2×C3C5×#46511yescharacteristic
590C2×C3C5×#46811yescharacteristic
591C5C3×#200011yescharacteristic, direct product factor, Sylow
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C3×C5×#12011yescharacteristic
607C22C3×C5×#12011yescharacteristic
608C22C3×C5×#12111yescharacteristic
609C22C2×C3×C5×SD1611yescharacteristic
610C22C3×C5×#13511yescharacteristic
611C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
612C22C3×C5×#13711yescharacteristic
613C4—42no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4C3×C5×#12011yescharacteristic
618C4C3×C5×#12111yescharacteristic
619C4C3×C5×#12111yescharacteristic
620C4C3×C5×#12711yescharacteristic
621C3C5×#200011yescharacteristic, direct product factor, Sylow
622C2—42no—
623C2—82no—
624C2C3×C5×#39211yescharacteristic
625C2C3×C5×#44811yescharacteristic
626C2C3×C5×#44911yescharacteristic
627C2C3×C5×#45011yescharacteristic
628C2C3×C5×#45211yescharacteristic
629C2C3×C5×#46511yescharacteristic
630C2C3×C5×#46811yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×SD16C2semidirect
2. C2×C3×C5×C22⋊Q8C2semidirect
4. C2×C3×C5×#103C2semidirect
5. C2×C3×C5×#102C2semidirect
6. C2×C3×C5×C22⋊C8C2semidirect
7. C3×C5×#340C2semidirect
8. C5×#2000C3direct (N × H)
30. C3×#2000C5direct (N × H)
31. C22×C5×SD16C2×C3semidirect
32. C2×C5×C22⋊Q8C2×C3semidirect
34. C2×C5×#103C2×C3semidirect
35. C2×C5×#102C2×C3semidirect
36. C2×C5×C22⋊C8C2×C3semidirect
37. C5×#340C2×C3semidirect
45. C2×C3×C5×Q8D4semidirect
72. C2×C3×C5×C8D4semidirect
77. C3×C5×C4⋊C4D4semidirect
80. C22×C3×SD16C2×C5semidirect
81. C2×C3×C22⋊Q8C2×C5semidirect
83. C2×C3×#103C2×C5semidirect
84. C2×C3×#102C2×C5semidirect
85. C2×C3×C22⋊C8C2×C5semidirect
86. C3×#340C2×C5semidirect
108. #2000C3×C5direct (N × H)
122. C23×C3×C5SD16semidirect
185. C2×C5×Q8C3×D4semidirect
212. C2×C5×C8C3×D4semidirect
217. C5×C4⋊C4C3×D4semidirect
220. C22×SD16C2×C3×C5semidirect
221. C2×C22⋊Q8C2×C3×C5semidirect
223. C2×#103C2×C3×C5semidirect
224. C2×#102C2×C3×C5semidirect
225. C2×C22⋊C8C2×C3×C5semidirect
226. #340C2×C3×C5semidirect
263. C2×C3×Q8C5×D4semidirect
290. C2×C3×C8C5×D4semidirect
295. C3×C4⋊C4C5×D4semidirect
311. C23×C5C3×SD16semidirect
389. C23×C3C5×SD16semidirect
460. C2×Q8C3×C5×D4semidirect
487. C2×C8C3×C5×D4semidirect
492. C4⋊C4C3×C5×D4semidirect
495. C3×C5#2000direct (N × H)
547. C23C3×C5×SD16semidirect
591. C5C3×#2000direct (N × H)
621. C3C5×#2000direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C5×SD162
C2×C3×C5×C22⋊Q82
C2×C3×C5×#1212
C2×C3×C5×#1032
C2×C3×C5×#1022
C2×C3×C5×C22⋊C82
C3×C5×#3402
C5×#20003
C3×#20005