Finite Group Databasebeta

← C2×C3×#65490 #14425072

Subgroups — C2×C3×#65490 #14425072

Order 1920.

1456 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C3×#4082C211yesmaximal, characteristic, complemented
4C2×C3×#4078C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6C3×#65490C218yesmaximal, direct product factor
7C2×C3×#3957C211yesmaximal, characteristic, complemented
8C2×C3×#3956C211yesmaximal, characteristic, complemented
9C2×#65490C311yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C3×#4150—22no—
13C3×#4150—22no—
14C3×#4150—22no—
15C3×#4150C2214yescomplemented
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×AGL(1,ℤ/8)—22no—
24C3×C5×AGL(1,ℤ/8)C2214yescomplemented
25C2×C3×C5×SD16—21no—
26C2×C3×C5×D8—21no—
27C2×C3×C5×M16C2211yescharacteristic
28C2×C3×C22⋊Dic5—22no—
29C3×#4082—22no—
30C3×#4082C2214yescomplemented
31C2×C3×#687—21no—
32C3×#4078—22no—
33C3×#4078C2214yescomplemented
34C2×C3×#686—21no—
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×#681C2211yescharacteristic
37C3×#3969C2214yescomplemented
38C3×#3957C2214yescomplemented
39C3×#3956C2214yescomplemented
40C2×C3×#454—51nomaximal, Hall
41C2×#4150C2×C311yescharacteristic, complemented
42C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
43C2×#4082C2×C311yescharacteristic, complemented
44C2×#4078C2×C311yescharacteristic, complemented
45C2×#3969C2×C311yescharacteristic, complemented
46#65490C2×C318yesdirect product factor
47C2×#3957C2×C311yescharacteristic, complemented
48C2×#3956C2×C311yescharacteristic, complemented
49C24×C3×C5—21no—
50C3×C5×#41—21no—
51C3×C5×#41—21no—
52C3×C5×#41D412yes—
53C3×C5×#41C2312yes—
54C2×C3×C5×Q8D411yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4—21no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4D411yescharacteristic
62C2×C3×C5×D4C2312yes—
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×SD16—24no—
96C3×C5×D8—24no—
97C3×C5×M16—21no—
98C3×C5×M16C2312yes—
99C2×C3×C5×C8—21no—
100C3×C22⋊Dic5—28no—
101C3×#687—24no—
102C3×#686—24no—
103C3×C4×Dic5—21no—
104C3×C4×Dic5C2312yes—
105C3×#681—21no—
106C3×#681C2312yes—
107C2×C3×#168—21no—
108C2×C3×2−1+4—51no—
109C2×C3×AGL(1,ℤ/8)—51no—
110C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
111C2×C3×#124—51no—
112C3×#454—58no—
113C2×C3×#104—51no—
114C2×C3×#104—51no—
115C2×C3×#101—51no—
116C2×C5×#41C22×C311yescharacteristic
117C22×C5×D4C22×C311yescharacteristic
118#4150—22no—
119#4150—22no—
120#4150—22no—
121#4150C22×C314yescomplemented
122C2×Q8×D5—21no—
123C2×#711—21no—
124C2×#711—22no—
125C2×#709—21no—
126C2×#709C22×C311yescharacteristic
127C22×Dic10—21no—
128C22×Dic10C22×C311yescharacteristic
129C5×AGL(1,ℤ/8)—22no—
130C5×AGL(1,ℤ/8)C22×C314yescomplemented
131C2×C5×SD16—21no—
132C2×C5×D8—21no—
133C2×C5×M16C22×C311yescharacteristic
134C2×C22⋊Dic5—22no—
135#4082—22no—
136#4082C22×C314yescomplemented
137C2×#687—21no—
138#4078—22no—
139#4078C22×C314yescomplemented
140C2×#686—21no—
141C2×C4×Dic5C22×C311yescharacteristic
142C2×#681C22×C311yescharacteristic
143#3969C22×C314yescomplemented
144#3957C22×C314yescomplemented
145#3956C22×C314yescomplemented
146C2×#454—51noSylow
147C23×C3×C5—21no—
148C23×C3×C5—22no—
149C23×C3×C5—44no—
150C23×C3×C5—41no—
151C23×C3×C5—41no—
152C23×C3×C5C2×D411yescharacteristic
153C22×C3×D5—21no—
154C3×C5×Q8—21no—
155C3×C5×Q8C2×D412yes—
156C3×C5×D4—22no—
157C3×C5×D4—22no—
158C3×C5×D4—21no—
159C3×C5×D4—22no—
160C3×C5×D4—22no—
161C3×C5×D4—41no—
162C3×C5×D4—41no—
163C3×C5×D4C2×D412yes—
164C2×C3×C4×C5—21no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2×D411yescharacteristic
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2×D411yescharacteristic
171C2×C3×C4×C5C2×D411yescharacteristic
172C2×C3×C4×C5C2411yescharacteristic
173C3×C22⋊D5—28no—
174C3×C22⋊D5—22no—
175C3×C22⋊D5—22no—
176C2×C3×Dic5—28no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—42no—
182C2×C3×Dic5C2×D414yes—
183C3×D20—21no—
184C3×D20C2×D412yes—
185C3×C4×D5—28no—
186C3×C4×D5—22no—
187C3×C4×D5—22no—
188C3×Dic10—28no—
189C3×Dic10—22no—
190C3×Dic10—21no—
191C3×Dic10—22no—
192C3×Dic10—22no—
193C3×Dic10—22no—
194C3×Dic10C2×D412yes—
195C3×C5×C8—22no—
196C3×#168—22no—
197C3×2−1+4—54no—
198C3×2−1+4—102no—
199C3×2−1+4—102no—
200C3×2−1+4—102no—
201C2×C3×#41—51no—
202C2×C3×#41—101no—
203C2×C3×#41—102no—
204C2×C3×#41—101no—
205C2×C3×#41C2×D511yescharacteristic
206C22×C3×Q8—51no—
207C22×C3×Q8—101no—
208C22×C3×Q8—101no—
209C22×C3×D4C2×D511yescharacteristic
210C3×AGL(1,ℤ/8)—22no—
211C3×AGL(1,ℤ/8)—54no—
212C3×AGL(1,ℤ/8)—102no—
213C3×AGL(1,ℤ/8)C2×D514yescomplemented
214C2×C3×SD16—21no—
215C2×C3×SD16—101no—
216C2×C3×D8—21no—
217C2×C3×D8—101no—
218C2×C3×M16—51no—
219C2×C3×M16C2×D511yescharacteristic
220C3×#124—54no—
221C3×#124—102no—
222C2×C3×C22⋊C4—102no—
223C2×C3×C42—51no—
224C3×#104—54no—
225C3×#104—54no—
226C3×#101—54no—
227C24×C5—21no—
228C5×#41—21no—
229C5×#41—21no—
230C5×#41C3×D412yes—
231C5×#41C23×C312yes—
232C2×C5×Q8C3×D411yescharacteristic
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4—21no—
237C2×C5×D4—21no—
238C2×C5×D4—21no—
239C2×C5×D4C3×D411yescharacteristic
240C2×C5×D4C23×C312yes—
241C22×C4×C5—21no—
242C22×C4×C5C23×C311yescharacteristic
243C2×C22⋊D5—22no—
244C2×C22⋊D5—21no—
245C22×Dic5—22no—
246C22×Dic5—21no—
247C22×Dic5C3×D412yes—
248Q8×D5—24no—
249Q8×D5—24no—
250#711—28no—
251#711—24no—
252#711—24no—
253#711—28no—
254#709—24no—
255#709—21no—
256#709—21no—
257#709—24no—
258#709C3×D412yes—
259#709C23×C312yes—
260C2×D20C3×D411yescharacteristic
261C2×C4×D5—22no—
262C2×C4×D5—21no—
263C2×Dic10—22no—
264C2×Dic10—24no—
265C2×Dic10—21no—
266C2×Dic10—21no—
267C2×Dic10—21no—
268C2×Dic10—21no—
269C2×Dic10—24no—
270C2×Dic10C3×D412yes—
271C2×Dic10C3×D411yescharacteristic
272C2×Dic10C23×C312yes—
273C5×SD16—24no—
274C5×D8—24no—
275C5×M16—21no—
276C5×M16C23×C312yes—
277C2×C5×C8—21no—
278C22⋊Dic5—28no—
279#687—24no—
280#686—24no—
281C4×Dic5—21no—
282C4×Dic5C23×C312yes—
283#681—21no—
284#681C23×C312yes—
285C2×#168—21no—
286C2×2−1+4—51no—
287C2×AGL(1,ℤ/8)—51no—
288C2×AGL(1,ℤ/8)C3×D511yescharacteristic, complemented
289C2×#124—51no—
290#454—58no—
291C2×#104—51no—
292C2×#104—51no—
293C2×#101—51no—
294C22×C3×C5—22no—
295C22×C3×C5—22no—
296C22×C3×C5—44no—
297C22×C3×C5—42no—
298C22×C3×C5—42no—
299C22×C3×C5—82no—
300C22×C3×C5—82no—
301C22×C3×C5#12011yescharacteristic
302C22×C3×C5#12011yescharacteristic
303C22×C3×C5C22×D411yescharacteristic
304C2×C3×D5—22no—
305C2×C3×D5—42no—
306C3×C4×C5—22no—
307C3×C4×C5#12011yescharacteristic
308C3×C4×C5#12011yescharacteristic
309C3×C4×C5C22×D411yescharacteristic
310C3×C4×C5C22×D411yescharacteristic
311C3×Dic5—24no—
312C3×Dic5—22no—
313C3×Dic5—42no—
314C24×C3—21no—
315C3×#41—21no—
316C3×#41—21no—
317C3×#41—52no—
318C3×#41—52no—
319C3×#41—104no—
320C3×#41—104no—
321C3×#41—108no—
322C3×#41—108no—
323C3×#41—104no—
324C3×#41—104no—
325C3×#41—101no—
326C3×#41—101no—
327C3×#41C22⋊D512yes—
328C3×#41C22×D512yes—
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×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—51no—
349C2×C3×D4—102no—
350C2×C3×D4—101no—
351C2×C3×D4C22⋊D511yescharacteristic
352C2×C3×D4C22×D512yes—
353C22×C3×C4—21no—
354C22×C3×C4—52no—
355C22×C3×C4—102no—
356C22×C3×C4—102no—
357C22×C3×C4—101no—
358C22×C3×C4—101no—
359C22×C3×C4C22×D511yescharacteristic
360C3×SD16—24no—
361C3×SD16—104no—
362C3×D8—24no—
363C3×D8—104no—
364C3×M16—21no—
365C3×M16—52no—
366C3×M16—101no—
367C3×M16C22×D512yes—
368C2×C3×C8—21no—
369C2×C3×C8—101no—
370C3×C22⋊C4—108no—
371C3×C42—52no—
372C3×C42—101no—
373C23×C5—21no—
374C23×C5—22no—
375C23×C5—44no—
376C23×C5—41no—
377C23×C5—41no—
378C23×C5C2×C3×D411yescharacteristic
379C22×D5—21no—
380C5×Q8—21no—
381C5×Q8C2×C3×D412yes—
382C5×D4—22no—
383C5×D4—22no—
384C5×D4—21no—
385C5×D4—22no—
386C5×D4—22no—
387C5×D4—41no—
388C5×D4—41no—
389C5×D4C2×C3×D412yes—
390C2×C4×C5—21no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5C2×C3×D411yescharacteristic
394C2×C4×C5C2×C3×D411yescharacteristic
395C2×C4×C5C2×C3×D411yescharacteristic
396C2×C4×C5C2×C3×D411yescharacteristic
397C2×C4×C5C2×C3×D411yescharacteristic
398C2×C4×C5C24×C311yescharacteristic
399C22⋊D5—28no—
400C22⋊D5—22no—
401C22⋊D5—22no—
402C2×Dic5—28no—
403C2×Dic5—22no—
404C2×Dic5—21no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—42no—
408C2×Dic5C2×C3×D414yes—
409D20—21no—
410D20C2×C3×D412yes—
411C4×D5—28no—
412C4×D5—22no—
413C4×D5—22no—
414Dic10—28no—
415Dic10—22no—
416Dic10—21no—
417Dic10—22no—
418Dic10—22no—
419Dic10—22no—
420Dic10C2×C3×D412yes—
421C5×C8—22no—
422#168—22no—
4232−1+4—54no—
4242−1+4—102no—
4252−1+4—102no—
4262−1+4—102no—
427C2×#41—51no—
428C2×#41—101no—
429C2×#41—102no—
430C2×#41—101no—
431C2×#41C2×C3×D511yescharacteristic
432C22×Q8—51no—
433C22×Q8—101no—
434C22×Q8—101no—
435C22×D4C2×C3×D511yescharacteristic
436AGL(1,ℤ/8)—22no—
437AGL(1,ℤ/8)—54no—
438AGL(1,ℤ/8)—102no—
439AGL(1,ℤ/8)C2×C3×D514yescomplemented
440C2×SD16—21no—
441C2×SD16—101no—
442C2×D8—21no—
443C2×D8—101no—
444C2×M16—51no—
445C2×M16C2×C3×D511yescharacteristic
446#124—54no—
447#124—102no—
448C2×C22⋊C4—102no—
449C2×C42—51no—
450#104—54no—
451#104—54no—
452#101—54no—
453C2×C3×C5—21no—
454C2×C3×C5—21no—
455C2×C3×C5—42no—
456C2×C3×C5—82no—
457C2×C3×C5#45412yescomplemented
458C2×C3×C5C2×#12011yescharacteristic
459C3×D5—42no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—44no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—101no—
466C23×C3D4×D511yescharacteristic
467C3×Q8—21no—
468C3×Q8—52no—
469C3×Q8—108no—
470C3×Q8—102no—
471C3×Q8—102no—
472C3×Q8—102no—
473C3×Q8—102no—
474C3×Q8—101no—
475C3×Q8C2×C22⋊D512yes—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—21no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—52no—
484C3×D4—108no—
485C3×D4—102no—
486C3×D4—102no—
487C3×D4—101no—
488C3×D4C2×C22⋊D512yes—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—54no—
493C2×C3×C4—108no—
494C2×C3×C4—108no—
495C2×C3×C4—102no—
496C2×C3×C4—102no—
497C2×C3×C4—101no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—202no—
502C2×C3×C4D4×D511yescharacteristic
503C2×C3×C4D4×D511yescharacteristic
504C2×C3×C4D4×D511yescharacteristic
505C2×C3×C4C2×C22⋊D511yescharacteristic
506C2×C3×C4C2×C22⋊D511yescharacteristic
507C2×C3×C4C23×D511yescharacteristic
508C3×C8—22no—
509C3×C8—102no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—44no—
513C22×C5—42no—
514C22×C5—42no—
515C22×C5—82no—
516C22×C5—82no—
517C22×C5C3×#12011yescharacteristic
518C22×C5C3×#12011yescharacteristic
519C22×C5C22×C3×D411yescharacteristic
520C2×D5—22no—
521C2×D5—42no—
522C4×C5—22no—
523C4×C5C3×#12011yescharacteristic
524C4×C5C3×#12011yescharacteristic
525C4×C5C22×C3×D411yescharacteristic
526C4×C5C22×C3×D411yescharacteristic
527Dic5—24no—
528Dic5—22no—
529Dic5—42no—
530C24—21no—
531#41—21no—
532#41—21no—
533#41—52no—
534#41—52no—
535#41—104no—
536#41—104no—
537#41—108no—
538#41—108no—
539#41—104no—
540#41—104no—
541#41—101no—
542#41—101no—
543#41C3×C22⋊D512yes—
544#41C22×C3×D512yes—
545C2×Q8—52no—
546C2×Q8—52no—
547C2×Q8—51no—
548C2×Q8—104no—
549C2×Q8—102no—
550C2×Q8—104no—
551C2×Q8—104no—
552C2×Q8—104no—
553C2×Q8—101no—
554C2×Q8—101no—
555C2×Q8—101no—
556C2×Q8—101no—
557C2×Q8C3×C22⋊D511yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—51no—
565C2×D4—102no—
566C2×D4—101no—
567C2×D4C3×C22⋊D511yescharacteristic
568C2×D4C22×C3×D512yes—
569C22×C4—21no—
570C22×C4—52no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4C22×C3×D511yescharacteristic
576SD16—24no—
577SD16—104no—
578D8—24no—
579D8—104no—
580M16—21no—
581M16—52no—
582M16—101no—
583M16C22×C3×D512yes—
584C2×C8—21no—
585C2×C8—101no—
586C22⋊C4—108no—
587C42—52no—
588C42—101no—
589C3×C5C2×#45411yescharacteristic, complemented, Hall
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—82no—
596C22×C3—82no—
597C22×C3—102no—
598C22×C3—202no—
599C22×C3#408311yescharacteristic
600C22×C3#408311yescharacteristic
601C22×C3C2×D4×D511yescharacteristic
602C3×C4—22no—
603C3×C4—104no—
604C3×C4—102no—
605C3×C4—202no—
606C3×C4#408311yescharacteristic
607C3×C4#408311yescharacteristic
608C3×C4C2×D4×D511yescharacteristic
609C3×C4C22×C22⋊D511yescharacteristic
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—42no—
613C2×C5—82no—
614C2×C5C3×#45412yescomplemented
615C2×C5C2×C3×#12011yescharacteristic
616D5—42no—
617C23—21no—
618C23—22no—
619C23—44no—
620C23—41no—
621C23—41no—
622C23—101no—
623C23C3×D4×D511yescharacteristic
624Q8—21no—
625Q8—52no—
626Q8—108no—
627Q8—102no—
628Q8—102no—
629Q8—101no—
630Q8—102no—
631Q8—102no—
632Q8C2×C3×C22⋊D512yes—
633D4—22no—
634D4—22no—
635D4—21no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—52no—
641D4—108no—
642D4—102no—
643D4—102no—
644D4—101no—
645D4C2×C3×C22⋊D512yes—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—54no—
650C2×C4—108no—
651C2×C4—108no—
652C2×C4—102no—
653C2×C4—102no—
654C2×C4—101no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—202no—
659C2×C4C3×D4×D511yescharacteristic
660C2×C4C3×D4×D511yescharacteristic
661C2×C4C3×D4×D511yescharacteristic
662C2×C4C2×C3×C22⋊D511yescharacteristic
663C2×C4C2×C3×C22⋊D511yescharacteristic
664C2×C4C23×C3×D511yescharacteristic
665C8—22no—
666C8—102no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—42no—
670C2×C3—82no—
671C2×C3—202no—
672C2×C3#6549012yesdirect product factor
673C2×C3C2×#408311yescharacteristic
674C5C2×C3×#45411yescharacteristic, complemented, Sylow
675C22—22no—
676C22—22no—
677C22—44no—
678C22—42no—
679C22—42no—
680C22—82no—
681C22—82no—
682C22—102no—
683C22—202no—
684C22C3×#408311yescharacteristic
685C22C3×#408311yescharacteristic
686C22C2×C3×D4×D511yescharacteristic
687C4—22no—
688C4—104no—
689C4—102no—
690C4—202no—
691C4C3×#408311yescharacteristic
692C4C3×#408311yescharacteristic
693C4C2×C3×D4×D511yescharacteristic
694C4C22×C3×C22⋊D511yescharacteristic
695C3C2×#6549011yescharacteristic, direct product factor, Sylow
696C2—21no—
697C2—21no—
698C2—42no—
699C2—82no—
700C2—202no—
701C2C3×#6549012yesdirect product factor
702C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5#120
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C2×C3×#454
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4150C2semidirect
2. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
3. C2×C3×#4082C2semidirect
4. C2×C3×#4078C2semidirect
5. C2×C3×#3969C2semidirect
6. C3×#65490C2direct (N × H)
7. C2×C3×#3957C2semidirect
8. C2×C3×#3956C2semidirect
9. C2×#65490C3direct (N × H)
15. C3×#4150C22semidirect
24. C3×C5×AGL(1,ℤ/8)C22semidirect
30. C3×#4082C22semidirect
33. C3×#4078C22semidirect
37. C3×#3969C22semidirect
38. C3×#3957C22semidirect
39. C3×#3956C22semidirect
41. C2×#4150C2×C3semidirect
42. C2×C5×AGL(1,ℤ/8)C2×C3semidirect
43. C2×#4082C2×C3semidirect
44. C2×#4078C2×C3semidirect
45. C2×#3969C2×C3semidirect
46. #65490C2×C3direct (N × H)
47. C2×#3957C2×C3semidirect
48. C2×#3956C2×C3semidirect
110. C2×C3×AGL(1,ℤ/8)D5semidirect
121. #4150C22×C3semidirect
130. C5×AGL(1,ℤ/8)C22×C3semidirect
136. #4082C22×C3semidirect
139. #4078C22×C3semidirect
143. #3969C22×C3semidirect
144. #3957C22×C3semidirect
145. #3956C22×C3semidirect
213. C3×AGL(1,ℤ/8)C2×D5semidirect
288. C2×AGL(1,ℤ/8)C3×D5semidirect
439. AGL(1,ℤ/8)C2×C3×D5semidirect
457. C2×C3×C5#454semidirect
589. C3×C5C2×#454semidirect
614. C2×C5C3×#454semidirect
672. C2×C3#65490direct (N × H)
674. C5C2×C3×#454semidirect
695. C3C2×#65490direct (N × H)
701. C2C3×#65490direct (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×AGL(1,ℤ/8)2
C2×C3×#40822
C2×C3×#40782
C2×C3×#39692
C3×#654902
C2×C3×#39572
C2×C3×#39562
C2×#654903
C2×C3×#4545