Finite Group Databasebeta

← C2×C3×#65494 #14425129

Subgroups — C2×C3×#65494 #14425129

Order 1920.

1416 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic
2C2×C3×C5×#137C211yesmaximal, characteristic, complemented
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4C2×C3×#4088C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6C3×#65494C218yesmaximal, direct product factor
7C2×C3×#3957C211yesmaximal, characteristic, complemented
8C2×C3×#3956C211yesmaximal, characteristic, complemented
9C2×#65494C311yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×C3×C5×Q8C2211yescharacteristic
12C3×#4150—22no—
13C3×#4150—22no—
14C3×#4150—22no—
15C3×#4150C2214yes—
16C2×C3×Q8×D5—21no—
17C2×C3×#711—21no—
18C2×C3×#711—22no—
19C2×C3×#709—21no—
20C2×C3×#709C2211yescharacteristic
21C22×C3×Dic10—21no—
22C22×C3×Dic10C2211yescharacteristic
23C3×C5×#137—22no—
24C3×C5×#137C2214yescomplemented
25C2×C3×C5×Q16—21no—
26C2×C3×C5×SD16—21no—
27C2×C3×C5×M16C2211yescharacteristic
28C3×#4090—22no—
29C3×#4090C2214yescomplemented
30C2×C3×#689—21no—
31C3×#4088—22no—
32C3×#4088C2214yescomplemented
33C2×C3×#688—21no—
34C2×C3×#683—22no—
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×#681C2211yescharacteristic
37C3×#3969C2214yescomplemented
38C3×#3957C2214yescomplemented
39C3×#3956C2214yescomplemented
40C2×C3×#456—51nomaximal, Hall
41C2×#4150C2×C311yescharacteristic
42C2×C5×#137C2×C311yescharacteristic, complemented
43C2×#4090C2×C311yescharacteristic, complemented
44C2×#4088C2×C311yescharacteristic, complemented
45C2×#3969C2×C311yescharacteristic, complemented
46#65494C2×C318yesdirect product factor
47C2×#3957C2×C311yescharacteristic, complemented
48C2×#3956C2×C311yescharacteristic, complemented
49C3×C5×#41—21no—
50C3×C5×#41—21no—
51C3×C5×#41D412yes—
52C3×C5×#41C2312yes—
53C2×C3×C5×Q8—21no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8D411yescharacteristic
59C2×C3×C5×Q8C2312yes—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4D411yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—21no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—21no—
69C22×C3×Dic5D412yes—
70C3×Q8×D5—24no—
71C3×Q8×D5—24no—
72C3×#711—28no—
73C3×#711—24no—
74C3×#711—24no—
75C3×#711—28no—
76C3×#709—24no—
77C3×#709—21no—
78C3×#709—21no—
79C3×#709—24no—
80C3×#709D412yes—
81C3×#709C2312yes—
82C2×C3×D20D411yescharacteristic
83C2×C3×C4×D5—22no—
84C2×C3×C4×D5—21no—
85C2×C3×Dic10—22no—
86C2×C3×Dic10—24no—
87C2×C3×Dic10—21no—
88C2×C3×Dic10—21no—
89C2×C3×Dic10—21no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10—24no—
92C2×C3×Dic10D412yes—
93C2×C3×Dic10D411yescharacteristic
94C2×C3×Dic10C2312yes—
95C3×C5×Q16—24no—
96C3×C5×SD16—24no—
97C3×C5×M16—21no—
98C3×C5×M16C2312yes—
99C2×C3×C5×C8—21no—
100C3×#689—24no—
101C3×#688—24no—
102C3×#683—28no—
103C3×C4×Dic5—21no—
104C3×C4×Dic5C2312yes—
105C3×#681—21no—
106C3×#681C2312yes—
107C2×C3×#168—21no—
108C2×C3×2−1+4—51no—
109C2×C3×#137—51no—
110C2×C3×#137D511yescharacteristic, complemented
111C2×C3×C4⋊Q8—51no—
112C3×#456—58no—
113C2×C3×#104—51no—
114C2×C3×#104—51no—
115C2×C3×#101—51no—
116C2×C5×#41C22×C311yescharacteristic
117C22×C5×Q8C22×C311yescharacteristic
118#4150—22no—
119#4150—22no—
120#4150—22no—
121#4150C22×C314yes—
122C2×Q8×D5—21no—
123C2×#711—21no—
124C2×#711—22no—
125C2×#709—21no—
126C2×#709C22×C311yescharacteristic
127C22×Dic10—21no—
128C22×Dic10C22×C311yescharacteristic
129C5×#137—22no—
130C5×#137C22×C314yescomplemented
131C2×C5×Q16—21no—
132C2×C5×SD16—21no—
133C2×C5×M16C22×C311yescharacteristic
134#4090—22no—
135#4090C22×C314yescomplemented
136C2×#689—21no—
137#4088—22no—
138#4088C22×C314yescomplemented
139C2×#688—21no—
140C2×#683—22no—
141C2×C4×Dic5C22×C311yescharacteristic
142C2×#681C22×C311yescharacteristic
143#3969C22×C314yescomplemented
144#3957C22×C314yescomplemented
145#3956C22×C314yescomplemented
146C2×#456—51noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×C3×D5—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8—22no—
152C3×C5×Q8—22no—
153C3×C5×Q8—41no—
154C3×C5×Q8—41no—
155C3×C5×Q8C2×D412yes—
156C3×C5×D4—22no—
157C3×C5×D4—22no—
158C3×C5×D4—21no—
159C3×C5×D4C2×D412yes—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—41no—
165C2×C3×C4×C5—41no—
166C2×C3×C4×C5C2×D411yescharacteristic
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2×D411yescharacteristic
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2×D411yescharacteristic
171C2×C3×C4×C5C2411yescharacteristic
172C3×C22⋊D5—28no—
173C3×C22⋊D5—22no—
174C3×C22⋊D5—22no—
175C2×C3×Dic5—28no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C2×D414yes—
182C3×D20—21no—
183C3×D20C2×D412yes—
184C3×C4×D5—28no—
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×Dic10—28no—
188C3×Dic10—22no—
189C3×Dic10—21no—
190C3×Dic10—22no—
191C3×Dic10—22no—
192C3×Dic10—22no—
193C3×Dic10C2×D412yes—
194C3×C5×C8—22no—
195C3×#168—22no—
196C3×2−1+4—54no—
197C3×2−1+4—102no—
198C3×2−1+4—102no—
199C3×2−1+4—102no—
200C2×C3×#41—51no—
201C2×C3×#41—101no—
202C2×C3×#41—102no—
203C2×C3×#41—101no—
204C2×C3×#41C2×D511yescharacteristic
205C22×C3×Q8—51no—
206C22×C3×Q8—101no—
207C22×C3×Q8—101no—
208C22×C3×Q8C2×D511yescharacteristic
209C3×#137—22no—
210C3×#137—54no—
211C3×#137—102no—
212C3×#137C2×D514yescomplemented
213C2×C3×Q16—21no—
214C2×C3×Q16—101no—
215C2×C3×SD16—21no—
216C2×C3×SD16—101no—
217C2×C3×M16—51no—
218C2×C3×M16C2×D511yescharacteristic
219C3×C4⋊Q8—54no—
220C3×C4⋊Q8—102no—
221C2×C3×C4⋊C4—102no—
222C2×C3×C42—51no—
223C3×#104—54no—
224C3×#104—54no—
225C3×#101—54no—
226C5×#41—21no—
227C5×#41—21no—
228C5×#41C3×D412yes—
229C5×#41C23×C312yes—
230C2×C5×Q8—21no—
231C2×C5×Q8—21no—
232C2×C5×Q8—21no—
233C2×C5×Q8—21no—
234C2×C5×Q8—21no—
235C2×C5×Q8C3×D411yescharacteristic
236C2×C5×Q8C23×C312yes—
237C2×C5×D4—21no—
238C2×C5×D4C3×D411yescharacteristic
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5C23×C311yescharacteristic
242C2×C22⋊D5—22no—
243C2×C22⋊D5—21no—
244C22×Dic5—22no—
245C22×Dic5—21no—
246C22×Dic5C3×D412yes—
247Q8×D5—24no—
248Q8×D5—24no—
249#711—28no—
250#711—24no—
251#711—24no—
252#711—28no—
253#709—24no—
254#709—21no—
255#709—21no—
256#709—24no—
257#709C3×D412yes—
258#709C23×C312yes—
259C2×D20C3×D411yescharacteristic
260C2×C4×D5—22no—
261C2×C4×D5—21no—
262C2×Dic10—22no—
263C2×Dic10—24no—
264C2×Dic10—21no—
265C2×Dic10—21no—
266C2×Dic10—21no—
267C2×Dic10—21no—
268C2×Dic10—24no—
269C2×Dic10C3×D412yes—
270C2×Dic10C3×D411yescharacteristic
271C2×Dic10C23×C312yes—
272C5×Q16—24no—
273C5×SD16—24no—
274C5×M16—21no—
275C5×M16C23×C312yes—
276C2×C5×C8—21no—
277#689—24no—
278#688—24no—
279#683—28no—
280C4×Dic5—21no—
281C4×Dic5C23×C312yes—
282#681—21no—
283#681C23×C312yes—
284C2×#168—21no—
285C2×2−1+4—51no—
286C2×#137—51no—
287C2×#137C3×D511yescharacteristic, complemented
288C2×C4⋊Q8—51no—
289#456—58no—
290C2×#104—51no—
291C2×#104—51no—
292C2×#101—51no—
293C22×C3×C5—22no—
294C22×C3×C5—22no—
295C22×C3×C5—42no—
296C22×C3×C5#12011yescharacteristic
297C22×C3×C5#12011yescharacteristic
298C22×C3×C5C22×D411yescharacteristic
299C2×C3×D5—22no—
300C2×C3×D5—42no—
301C3×C4×C5—22no—
302C3×C4×C5—42no—
303C3×C4×C5#12011yescharacteristic
304C3×C4×C5#12011yescharacteristic
305C3×C4×C5C22×D411yescharacteristic
306C3×C4×C5C22×D411yescharacteristic
307C3×Dic5—24no—
308C3×Dic5—24no—
309C3×Dic5—22no—
310C3×#41—21no—
311C3×#41—21no—
312C3×#41—52no—
313C3×#41—52no—
314C3×#41—104no—
315C3×#41—104no—
316C3×#41—108no—
317C3×#41—108no—
318C3×#41—104no—
319C3×#41—104no—
320C3×#41—101no—
321C3×#41—101no—
322C3×#41C22⋊D512yes—
323C3×#41C22×D512yes—
324C2×C3×Q8—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—21no—
329C2×C3×Q8—52no—
330C2×C3×Q8—52no—
331C2×C3×Q8—51no—
332C2×C3×Q8—104no—
333C2×C3×Q8—102no—
334C2×C3×Q8—104no—
335C2×C3×Q8—104no—
336C2×C3×Q8—104no—
337C2×C3×Q8—101no—
338C2×C3×Q8—101no—
339C2×C3×Q8—101no—
340C2×C3×Q8—101no—
341C2×C3×Q8C22⋊D511yescharacteristic
342C2×C3×Q8C22×D512yes—
343C2×C3×D4—21no—
344C2×C3×D4—51no—
345C2×C3×D4—102no—
346C2×C3×D4—101no—
347C2×C3×D4C22⋊D511yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—52no—
351C22×C3×C4—102no—
352C22×C3×C4—102no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4C22×D511yescharacteristic
356C3×Q16—24no—
357C3×Q16—104no—
358C3×SD16—24no—
359C3×SD16—104no—
360C3×M16—21no—
361C3×M16—52no—
362C3×M16—101no—
363C3×M16C22×D512yes—
364C2×C3×C8—21no—
365C2×C3×C8—101no—
366C3×C4⋊C4—108no—
367C3×C42—52no—
368C3×C42—101no—
369C23×C5—21no—
370C23×C5C2×C3×D411yescharacteristic
371C22×D5—21no—
372C5×Q8—21no—
373C5×Q8—22no—
374C5×Q8—22no—
375C5×Q8—41no—
376C5×Q8—41no—
377C5×Q8C2×C3×D412yes—
378C5×D4—22no—
379C5×D4—22no—
380C5×D4—21no—
381C5×D4C2×C3×D412yes—
382C2×C4×C5—21no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5C2×C3×D411yescharacteristic
389C2×C4×C5C2×C3×D411yescharacteristic
390C2×C4×C5C2×C3×D411yescharacteristic
391C2×C4×C5C2×C3×D411yescharacteristic
392C2×C4×C5C2×C3×D411yescharacteristic
393C2×C4×C5C24×C311yescharacteristic
394C22⋊D5—28no—
395C22⋊D5—22no—
396C22⋊D5—22no—
397C2×Dic5—28no—
398C2×Dic5—24no—
399C2×Dic5—22no—
400C2×Dic5—21no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5C2×C3×D414yes—
404D20—21no—
405D20C2×C3×D412yes—
406C4×D5—28no—
407C4×D5—22no—
408C4×D5—22no—
409Dic10—28no—
410Dic10—22no—
411Dic10—21no—
412Dic10—22no—
413Dic10—22no—
414Dic10—22no—
415Dic10C2×C3×D412yes—
416C5×C8—22no—
417#168—22no—
4182−1+4—54no—
4192−1+4—102no—
4202−1+4—102no—
4212−1+4—102no—
422C2×#41—51no—
423C2×#41—101no—
424C2×#41—102no—
425C2×#41—101no—
426C2×#41C2×C3×D511yescharacteristic
427C22×Q8—51no—
428C22×Q8—101no—
429C22×Q8—101no—
430C22×Q8C2×C3×D511yescharacteristic
431#137—22no—
432#137—54no—
433#137—102no—
434#137C2×C3×D514yescomplemented
435C2×Q16—21no—
436C2×Q16—101no—
437C2×SD16—21no—
438C2×SD16—101no—
439C2×M16—51no—
440C2×M16C2×C3×D511yescharacteristic
441C4⋊Q8—54no—
442C4⋊Q8—102no—
443C2×C4⋊C4—102no—
444C2×C42—51no—
445#104—54no—
446#104—54no—
447#101—54no—
448C2×C3×C5—21no—
449C2×C3×C5—21no—
450C2×C3×C5—42no—
451C2×C3×C5#45612yescomplemented
452C2×C3×C5C2×#12011yescharacteristic
453C3×D5—42no—
454C23×C3—21no—
455C23×C3—101no—
456C23×C3D4×D511yescharacteristic
457C3×Q8—21no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—52no—
463C3×Q8—108no—
464C3×Q8—102no—
465C3×Q8—102no—
466C3×Q8—102no—
467C3×Q8—102no—
468C3×Q8—101no—
469C3×Q8C2×C22⋊D512yes—
470C3×D4—22no—
471C3×D4—22no—
472C3×D4—21no—
473C3×D4—52no—
474C3×D4—108no—
475C3×D4—102no—
476C3×D4—102no—
477C3×D4—101no—
478C3×D4C2×C22⋊D512yes—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—54no—
486C2×C3×C4—108no—
487C2×C3×C4—104no—
488C2×C3×C4—108no—
489C2×C3×C4—102no—
490C2×C3×C4—102no—
491C2×C3×C4—102no—
492C2×C3×C4—101no—
493C2×C3×C4—102no—
494C2×C3×C4—102no—
495C2×C3×C4D4×D511yescharacteristic
496C2×C3×C4D4×D511yescharacteristic
497C2×C3×C4D4×D511yescharacteristic
498C2×C3×C4C2×C22⋊D511yescharacteristic
499C2×C3×C4C2×C22⋊D511yescharacteristic
500C2×C3×C4C23×D511yescharacteristic
501C3×C8—22no—
502C3×C8—102no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—42no—
506C22×C5C3×#12011yescharacteristic
507C22×C5C3×#12011yescharacteristic
508C22×C5C22×C3×D411yescharacteristic
509C2×D5—22no—
510C2×D5—42no—
511C4×C5—22no—
512C4×C5—42no—
513C4×C5C3×#12011yescharacteristic
514C4×C5C3×#12011yescharacteristic
515C4×C5C22×C3×D411yescharacteristic
516C4×C5C22×C3×D411yescharacteristic
517Dic5—24no—
518Dic5—24no—
519Dic5—22no—
520#41—21no—
521#41—21no—
522#41—52no—
523#41—52no—
524#41—104no—
525#41—104no—
526#41—108no—
527#41—108no—
528#41—104no—
529#41—104no—
530#41—101no—
531#41—101no—
532#41C3×C22⋊D512yes—
533#41C22×C3×D512yes—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—52no—
540C2×Q8—52no—
541C2×Q8—51no—
542C2×Q8—104no—
543C2×Q8—102no—
544C2×Q8—104no—
545C2×Q8—104no—
546C2×Q8—104no—
547C2×Q8—101no—
548C2×Q8—101no—
549C2×Q8—101no—
550C2×Q8—101no—
551C2×Q8C3×C22⋊D511yescharacteristic
552C2×Q8C22×C3×D512yes—
553C2×D4—21no—
554C2×D4—51no—
555C2×D4—102no—
556C2×D4—101no—
557C2×D4C3×C22⋊D511yescharacteristic
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—52no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—101no—
564C22×C4—101no—
565C22×C4C22×C3×D511yescharacteristic
566Q16—24no—
567Q16—104no—
568SD16—24no—
569SD16—104no—
570M16—21no—
571M16—52no—
572M16—101no—
573M16C22×C3×D512yes—
574C2×C8—21no—
575C2×C8—101no—
576C4⋊C4—108no—
577C42—52no—
578C42—101no—
579C3×C5C2×#45611yescharacteristic, complemented, Hall
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—42no—
583C22×C3—102no—
584C22×C3—202no—
585C22×C3#408311yescharacteristic
586C22×C3#408311yescharacteristic
587C22×C3C2×D4×D511yescharacteristic
588C3×C4—22no—
589C3×C4—42no—
590C3×C4—104no—
591C3×C4—104no—
592C3×C4—102no—
593C3×C4#408311yescharacteristic
594C3×C4#408311yescharacteristic
595C3×C4C2×D4×D511yescharacteristic
596C3×C4C22×C22⋊D511yescharacteristic
597C2×C5—21no—
598C2×C5—21no—
599C2×C5—42no—
600C2×C5C3×#45612yescomplemented
601C2×C5C2×C3×#12011yescharacteristic
602D5—42no—
603C23—21no—
604C23—101no—
605C23C3×D4×D511yescharacteristic
606Q8—21no—
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—52no—
612Q8—108no—
613Q8—102no—
614Q8—102no—
615Q8—101no—
616Q8—102no—
617Q8—102no—
618Q8C2×C3×C22⋊D512yes—
619D4—22no—
620D4—22no—
621D4—21no—
622D4—52no—
623D4—108no—
624D4—102no—
625D4—102no—
626D4—101no—
627D4C2×C3×C22⋊D512yes—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—54no—
635C2×C4—108no—
636C2×C4—108no—
637C2×C4—104no—
638C2×C4—102no—
639C2×C4—102no—
640C2×C4—101no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—102no—
644C2×C4C3×D4×D511yescharacteristic
645C2×C4C3×D4×D511yescharacteristic
646C2×C4C3×D4×D511yescharacteristic
647C2×C4C2×C3×C22⋊D511yescharacteristic
648C2×C4C2×C3×C22⋊D511yescharacteristic
649C2×C4C23×C3×D511yescharacteristic
650C8—22no—
651C8—102no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—42no—
655C2×C3—202no—
656C2×C3#6549412yesdirect product factor
657C2×C3C2×#408311yescharacteristic
658C5C2×C3×#45611yescharacteristic, complemented, Sylow
659C22—22no—
660C22—22no—
661C22—42no—
662C22—102no—
663C22—202no—
664C22C3×#408311yescharacteristic
665C22C3×#408311yescharacteristic
666C22C2×C3×D4×D511yescharacteristic
667C4—22no—
668C4—42no—
669C4—104no—
670C4—104no—
671C4—102no—
672C4C3×#408311yescharacteristic
673C4C3×#408311yescharacteristic
674C4C2×C3×D4×D511yescharacteristic
675C4C22×C3×C22⋊D511yescharacteristic
676C3C2×#6549411yescharacteristic, direct product factor, Sylow
677C2—21no—
678C2—21no—
679C2—42no—
680C2—202no—
681C2C3×#6549412yesdirect product factor
682C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#137C2
socleC22×C3×C5#120
prime radicalC2×C3×#4150C2
hypercenterC2×C3×#137D5
hypocenterC5C2×C3×#456
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#137C2semidirect
3. C2×C3×#4090C2semidirect
4. C2×C3×#4088C2semidirect
5. C2×C3×#3969C2semidirect
6. C3×#65494C2direct (N × H)
7. C2×C3×#3957C2semidirect
8. C2×C3×#3956C2semidirect
9. C2×#65494C3direct (N × H)
24. C3×C5×#137C22semidirect
29. C3×#4090C22semidirect
32. C3×#4088C22semidirect
37. C3×#3969C22semidirect
38. C3×#3957C22semidirect
39. C3×#3956C22semidirect
42. C2×C5×#137C2×C3semidirect
43. C2×#4090C2×C3semidirect
44. C2×#4088C2×C3semidirect
45. C2×#3969C2×C3semidirect
46. #65494C2×C3direct (N × H)
47. C2×#3957C2×C3semidirect
48. C2×#3956C2×C3semidirect
110. C2×C3×#137D5semidirect
130. C5×#137C22×C3semidirect
135. #4090C22×C3semidirect
138. #4088C22×C3semidirect
143. #3969C22×C3semidirect
144. #3957C22×C3semidirect
145. #3956C22×C3semidirect
212. C3×#137C2×D5semidirect
287. C2×#137C3×D5semidirect
434. #137C2×C3×D5semidirect
451. C2×C3×C5#456semidirect
579. C3×C5C2×#456semidirect
600. C2×C5C3×#456semidirect
656. C2×C3#65494direct (N × H)
658. C5C2×C3×#456semidirect
676. C3C2×#65494direct (N × H)
681. C2C3×#65494direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×C3×C5×#1372
C2×C3×#40902
C2×C3×#40882
C2×C3×#39692
C3×#654942
C2×C3×#39572
C2×C3×#39562
C2×#654943
C2×C3×#4565