Finite Group Databasebeta

← C3×C5×#1877 #14274911

Subgroups — C3×C5×#1877 #14274911

Order 1920.

804 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C211yesmaximal, characteristic
3C2×C3×C5×#103C211yesmaximal, characteristic, complemented
4C2×C3×C5×#102C211yesmaximal, characteristic
5C3×C5×#391C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×C5×#336C211yesmaximal, characteristic, complemented
8C5×#1877C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C23×C3×C4×C5—21no—
12C2×C3×C5×SD16—22no—
13C2×C3×C5×SD16—22no—
14C2×C3×C5×SD16C414yescomplemented
15C22×C3×C5×C8C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C3×C4×C5×D4—22no—
18C3×C4×C5×D4—22no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4—21no—
22C2×C3×C42×C5C2211yescharacteristic
23C3×C5×#103—22no—
24C3×C5×#102—22no—
25C3×C5×#95—21no—
26C3×C5×#95—21no—
27C3×#1877C511yesmaximal, characteristic, direct product factor, Hall
28C22×C5×SD16C2×C311yescharacteristic
29C2×C4×C5×D4C2×C311yescharacteristic
30C2×C5×#103C2×C311yescharacteristic, complemented
31C2×C5×#102C2×C311yescharacteristic
32C5×#391C2×C311yescharacteristic, complemented
33C5×#340C2×C311yescharacteristic, complemented
34C5×#336C2×C311yescharacteristic, complemented
35C24×C3×C5—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8C2×C412yescomplemented
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4C2×C412yes—
46C2×C3×C5×D4D412yes—
47C2×C3×C5×D4D412yes—
48C22×C3×C4×C5—24no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5—42no—
54C22×C3×C4×C5D411yescharacteristic
55C22×C3×C4×C5D411yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C3×C5×SD16—28no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8—21no—
61C2×C3×C5×C8—21no—
62C2×C3×C5×C8—21no—
63C2×C3×C5×C8C2×C412yescomplemented
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4D412yes—
68C3×C5×C22⋊C4—24no—
69C3×C42×C5—21no—
70C3×C42×C5—21no—
71C22×C3×SD16C2×C511yescharacteristic
72C2×C3×C4×D4C2×C511yescharacteristic
73C2×C3×#103C2×C511yescharacteristic, complemented
74C2×C3×#102C2×C511yescharacteristic
75C3×#391C2×C511yescharacteristic, complemented
76C3×#340C2×C511yescharacteristic, complemented
77C3×#336C2×C511yescharacteristic, complemented
78C22×C5×Q8C22×C311yescharacteristic
79C22×C5×D4C22×C311yescharacteristic
80C23×C4×C5—21no—
81C2×C5×SD16—22no—
82C2×C5×SD16—22no—
83C2×C5×SD16C3×C414yescomplemented
84C22×C5×C8C22×C311yescharacteristic
85C22×C5×C8C22×C311yescharacteristic
86C4×C5×D4—22no—
87C4×C5×D4—22no—
88C2×C5×C4⋊C4C22×C311yescharacteristic
89C2×C5×C4⋊C4C22×C311yescharacteristic
90C2×C5×C22⋊C4—21no—
91C2×C42×C5C22×C311yescharacteristic
92C5×#103—22no—
93C5×#102—22no—
94C5×#95—21no—
95C5×#95—21no—
96#1877C3×C511yescharacteristic, direct product factor, Sylow
97C23×C3×C5—22no—
98C23×C3×C5—22no—
99C23×C3×C5—22no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×Q8—22no—
106C3×C5×Q8—22no—
107C3×C5×Q8—41no—
108C3×C5×Q8—41no—
109C3×C5×D4—22no—
110C3×C5×D4—22no—
111C3×C5×D4—22no—
112C3×C5×D4C22⋊C414yes—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—48no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5SD1612yescomplemented
129C2×C3×C4×C5C22×C411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5#4111yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C3×C5×C8—22no—
136C3×C5×C8—41no—
137C22×C3×Q8C22×C511yescharacteristic
138C22×C3×D4C22×C511yescharacteristic
139C23×C3×C4—21no—
140C2×C3×SD16—22no—
141C2×C3×SD16—22no—
142C2×C3×SD16C4×C514yescomplemented
143C22×C3×C8C22×C511yescharacteristic
144C22×C3×C8C22×C511yescharacteristic
145C3×C4×D4—22no—
146C3×C4×D4—22no—
147C2×C3×C4⋊C4C22×C511yescharacteristic
148C2×C3×C4⋊C4C22×C511yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C42C22×C511yescharacteristic
151C3×#103—22no—
152C3×#102—22no—
153C3×#95—21no—
154C3×#95—21no—
155C24×C5—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8C2×C3×C412yescomplemented
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4C2×C3×C412yes—
166C2×C5×D4C3×D412yes—
167C2×C5×D4C3×D412yes—
168C22×C4×C5—24no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—42no—
173C22×C4×C5—42no—
174C22×C4×C5C3×D411yescharacteristic
175C22×C4×C5C3×D411yescharacteristic
176C22×C4×C5C23×C311yescharacteristic
177C5×SD16—28no—
178C2×C5×C8—21no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8C2×C3×C412yescomplemented
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4C3×D412yes—
188C5×C22⋊C4—24no—
189C42×C5—21no—
190C42×C5—21no—
191C22×SD16C2×C3×C511yescharacteristic
192C2×C4×D4C2×C3×C511yescharacteristic
193C2×#103C2×C3×C511yescharacteristic, complemented
194C2×#102C2×C3×C511yescharacteristic
195#391C2×C3×C511yescharacteristic, complemented
196#340C2×C3×C511yescharacteristic, complemented
197#336C2×C3×C511yescharacteristic, complemented
198C22×C3×C5—24no—
199C22×C3×C5—42no—
200C22×C3×C5—42no—
201C22×C3×C5—42no—
202C22×C3×C5—42no—
203C22×C3×C5—42no—
204C22×C3×C5—42no—
205C22×C3×C5C4×D411yescharacteristic
206C22×C3×C5#12011yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C22×C3×C5C2×SD1611yescharacteristic
209C22×C3×C5#13511yescharacteristic
210C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
211C22×C3×C5#13711yescharacteristic
212C3×C4×C5—22no—
213C3×C4×C5—42no—
214C3×C4×C5—42no—
215C3×C4×C5—41no—
216C3×C4×C5—81no—
217C3×C4×C5C2×C22⋊C411yescharacteristic
218C3×C4×C5C4×D411yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12311yescharacteristic
221C24×C3—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×C4×C512yescomplemented
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C2×C4×C512yes—
232C2×C3×D4C5×D412yes—
233C2×C3×D4C5×D412yes—
234C22×C3×C4—24no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—42no—
239C22×C3×C4—42no—
240C22×C3×C4C5×D411yescharacteristic
241C22×C3×C4C5×D411yescharacteristic
242C22×C3×C4C23×C511yescharacteristic
243C3×SD16—28no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8C2×C4×C512yescomplemented
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4C5×D412yes—
254C3×C22⋊C4—24no—
255C3×C42—21no—
256C3×C42—21no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—22no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5C2×C3×D411yescharacteristic
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8—41no—
268C5×Q8—41no—
269C5×D4—22no—
270C5×D4—22no—
271C5×D4—22no—
272C5×D4C3×C22⋊C414yes—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5—22no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—48no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5C3×SD1612yescomplemented
289C2×C4×C5C22×C3×C411yescharacteristic
290C2×C4×C5C2×C3×D411yescharacteristic
291C2×C4×C5C2×C3×D411yescharacteristic
292C2×C4×C5C2×C3×D411yescharacteristic
293C2×C4×C5C3×#4111yescharacteristic
294C2×C4×C5C3×#4111yescharacteristic
295C5×C8—22no—
296C5×C8—41no—
297C22×Q8C22×C3×C511yescharacteristic
298C22×D4C22×C3×C511yescharacteristic
299C23×C4—21no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×SD16C3×C4×C514yescomplemented
303C22×C8C22×C3×C511yescharacteristic
304C22×C8C22×C3×C511yescharacteristic
305C4×D4—22no—
306C4×D4—22no—
307C2×C4⋊C4C22×C3×C511yescharacteristic
308C2×C4⋊C4C22×C3×C511yescharacteristic
309C2×C22⋊C4—21no—
310C2×C42C22×C3×C511yescharacteristic
311#103—22no—
312#102—22no—
313#95—21no—
314#95—21no—
315C2×C3×C5—44no—
316C2×C3×C5#38611yescharacteristic
317C2×C3×C5C4×SD1611yescharacteristic
318C2×C3×C5#44011yescharacteristic
319C2×C3×C5#45011yescharacteristic
320C2×C3×C5#45211yescharacteristic
321C2×C3×C5#46111yescharacteristic
322C2×C3×C5#46311yescharacteristic
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3C2×C5×D411yescharacteristic
331C3×Q8—22no—
332C3×Q8—22no—
333C3×Q8—41no—
334C3×Q8—41no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4C5×C22⋊C414yes—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—48no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4C5×SD1612yescomplemented
355C2×C3×C4C22×C4×C511yescharacteristic
356C2×C3×C4C2×C5×D411yescharacteristic
357C2×C3×C4C2×C5×D411yescharacteristic
358C2×C3×C4C2×C5×D411yescharacteristic
359C2×C3×C4C5×#4111yescharacteristic
360C2×C3×C4C5×#4111yescharacteristic
361C3×C8—22no—
362C3×C8—41no—
363C22×C5—24no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—42no—
368C22×C5—42no—
369C22×C5—42no—
370C22×C5C3×C4×D411yescharacteristic
371C22×C5C3×#12011yescharacteristic
372C22×C5C3×#12111yescharacteristic
373C22×C5C2×C3×SD1611yescharacteristic
374C22×C5C3×#13511yescharacteristic
375C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
376C22×C5C3×#13711yescharacteristic
377C4×C5—22no—
378C4×C5—42no—
379C4×C5—42no—
380C4×C5—41no—
381C4×C5—81no—
382C4×C5C2×C3×C22⋊C411yescharacteristic
383C4×C5C3×C4×D411yescharacteristic
384C4×C5C3×#12111yescharacteristic
385C4×C5C3×#12311yescharacteristic
386C24—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C2×C3×C4×C512yescomplemented
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4C2×C3×C4×C512yes—
397C2×D4C3×C5×D412yes—
398C2×D4C3×C5×D412yes—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4C3×C5×D411yescharacteristic
406C22×C4C3×C5×D411yescharacteristic
407C22×C4C23×C3×C511yescharacteristic
408SD16—28no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8C2×C3×C4×C512yescomplemented
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4C3×C5×D412yes—
419C22⋊C4—24no—
420C42—21no—
421C42—21no—
422C3×C5#187711yescharacteristic, direct product factor, Hall
423C22×C3—24no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3C4×C5×D411yescharacteristic
431C22×C3C5×#12011yescharacteristic
432C22×C3C5×#12111yescharacteristic
433C22×C3C2×C5×SD1611yescharacteristic
434C22×C3C5×#13511yescharacteristic
435C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
436C22×C3C5×#13711yescharacteristic
437C3×C4—22no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—41no—
441C3×C4—81no—
442C3×C4C2×C5×C22⋊C411yescharacteristic
443C3×C4C4×C5×D411yescharacteristic
444C3×C4C5×#12111yescharacteristic
445C3×C4C5×#12311yescharacteristic
446C2×C5—44no—
447C2×C5C3×#38611yescharacteristic
448C2×C5C3×C4×SD1611yescharacteristic
449C2×C5C3×#44011yescharacteristic
450C2×C5C3×#45011yescharacteristic
451C2×C5C3×#45211yescharacteristic
452C2×C5C3×#46111yescharacteristic
453C2×C5C3×#46311yescharacteristic
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23C2×C3×C5×D411yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—41no—
465Q8—41no—
466D4—22no—
467D4—22no—
468D4—22no—
469D4C3×C5×C22⋊C414yes—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—48no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4C3×C5×SD1612yescomplemented
486C2×C4C22×C3×C4×C511yescharacteristic
487C2×C4C2×C3×C5×D411yescharacteristic
488C2×C4C2×C3×C5×D411yescharacteristic
489C2×C4C2×C3×C5×D411yescharacteristic
490C2×C4C3×C5×#4111yescharacteristic
491C2×C4C3×C5×#4111yescharacteristic
492C8—22no—
493C8—41no—
494C2×C3—44no—
495C2×C3C5×#38611yescharacteristic
496C2×C3C4×C5×SD1611yescharacteristic
497C2×C3C5×#44011yescharacteristic
498C2×C3C5×#45011yescharacteristic
499C2×C3C5×#45211yescharacteristic
500C2×C3C5×#46111yescharacteristic
501C2×C3C5×#46311yescharacteristic
502C5C3×#187711yescharacteristic, direct product factor, Sylow
503C22—24no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22C3×C4×C5×D411yescharacteristic
511C22C3×C5×#12011yescharacteristic
512C22C3×C5×#12111yescharacteristic
513C22C2×C3×C5×SD1611yescharacteristic
514C22C3×C5×#13511yescharacteristic
515C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
516C22C3×C5×#13711yescharacteristic
517C4—22no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—81no—
522C4C2×C3×C5×C22⋊C411yescharacteristic
523C4C3×C4×C5×D411yescharacteristic
524C4C3×C5×#12111yescharacteristic
525C4C3×C5×#12311yescharacteristic
526C3C5×#187711yescharacteristic, direct product factor, Sylow
527C2—44no—
528C2C3×C5×#38611yescharacteristic
529C2C3×C4×C5×SD1611yescharacteristic
530C2C3×C5×#44011yescharacteristic
531C2C3×C5×#45011yescharacteristic
532C2C3×C5×#45211yescharacteristic
533C2C3×C5×#46111yescharacteristic
534C2C3×C5×#46311yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C5×#103C2semidirect
5. C3×C5×#391C2semidirect
6. C3×C5×#340C2semidirect
7. C3×C5×#336C2semidirect
8. C5×#1877C3direct (N × H)
14. C2×C3×C5×SD16C4semidirect
27. C3×#1877C5direct (N × H)
30. C2×C5×#103C2×C3semidirect
32. C5×#391C2×C3semidirect
33. C5×#340C2×C3semidirect
34. C5×#336C2×C3semidirect
41. C2×C3×C5×Q8C2×C4semidirect
63. C2×C3×C5×C8C2×C4semidirect
73. C2×C3×#103C2×C5semidirect
75. C3×#391C2×C5semidirect
76. C3×#340C2×C5semidirect
77. C3×#336C2×C5semidirect
83. C2×C5×SD16C3×C4semidirect
96. #1877C3×C5direct (N × H)
128. C2×C3×C4×C5SD16semidirect
142. C2×C3×SD16C4×C5semidirect
161. C2×C5×Q8C2×C3×C4semidirect
183. C2×C5×C8C2×C3×C4semidirect
193. C2×#103C2×C3×C5semidirect
195. #391C2×C3×C5semidirect
196. #340C2×C3×C5semidirect
197. #336C2×C3×C5semidirect
227. C2×C3×Q8C2×C4×C5semidirect
249. C2×C3×C8C2×C4×C5semidirect
288. C2×C4×C5C3×SD16semidirect
302. C2×SD16C3×C4×C5semidirect
354. C2×C3×C4C5×SD16semidirect
392. C2×Q8C2×C3×C4×C5semidirect
414. C2×C8C2×C3×C4×C5semidirect
422. C3×C5#1877direct (N × H)
485. C2×C4C3×C5×SD16semidirect
502. C5C3×#1877direct (N × H)
526. C3C5×#1877direct (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×C4×C5×D42
C2×C3×C5×#1032
C2×C3×C5×#1022
C3×C5×#3912
C3×C5×#3402
C3×C5×#3362
C5×#18773
C3×#18775