Finite Group Databasebeta

← C3×C5×#1862 #14274896

Subgroups — C3×C5×#1862 #14274896

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×C5×#107C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic
4C2×C3×C5×#102C211yesmaximal, characteristic
5C3×C5×#389C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×C5×#336C211yesmaximal, characteristic, complemented
8C5×#1862C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C23×C3×C4×C5—21no—
11C22×C3×C5×C8C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C3×C4×C5×D4—22no—
14C3×C4×C5×D4—22no—
15C2×C3×C5×C4⋊C4—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4—21no—
20C2×C3×C42×C5C2211yescharacteristic
21C3×C5×#107—22no—
22C3×C5×#102—22no—
23C3×C5×#102C414yescomplemented
24C3×C5×#95—21no—
25C3×#1862C511yesmaximal, characteristic, direct product factor, Hall
26C2×C4×C5×D4C2×C311yescharacteristic
27C2×C5×#107C2×C311yescharacteristic, complemented
28C2×C5×#102C2×C311yescharacteristic
29C2×C5×#102C2×C311yescharacteristic
30C5×#389C2×C311yescharacteristic, complemented
31C5×#340C2×C311yescharacteristic, complemented
32C5×#336C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C2×C3×C5×D4Q812yes—
40C22×C3×C4×C5—24no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—42no—
45C22×C3×C4×C5—42no—
46C22×C3×C4×C5D411yescharacteristic
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C2×C3×C5×C8C2×C412yescomplemented
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C4⋊C4—42no—
60C3×C5×C4⋊C4C2×C412yescomplemented
61C3×C5×C4⋊C4D412yes—
62C3×C5×C22⋊C4—24no—
63C3×C42×C5—21no—
64C3×C42×C5—21no—
65C2×C3×C4×D4C2×C511yescharacteristic
66C2×C3×#107C2×C511yescharacteristic, complemented
67C2×C3×#102C2×C511yescharacteristic
68C2×C3×#102C2×C511yescharacteristic
69C3×#389C2×C511yescharacteristic, complemented
70C3×#340C2×C511yescharacteristic, complemented
71C3×#336C2×C511yescharacteristic, complemented
72C22×C5×D4C22×C311yescharacteristic
73C23×C4×C5—21no—
74C22×C5×C8C22×C311yescharacteristic
75C22×C5×C8C22×C311yescharacteristic
76C4×C5×D4—22no—
77C4×C5×D4—22no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4C22×C311yescharacteristic
80C2×C5×C4⋊C4C22×C311yescharacteristic
81C2×C5×C4⋊C4C22×C311yescharacteristic
82C2×C5×C22⋊C4—21no—
83C2×C42×C5C22×C311yescharacteristic
84C5×#107—22no—
85C5×#102—22no—
86C5×#102C3×C414yescomplemented
87C5×#95—21no—
88#1862C3×C511yescharacteristic, direct product factor, Sylow
89C23×C3×C5—22no—
90C23×C3×C5—22no—
91C23×C3×C5—22no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—41no—
95C23×C3×C5—41no—
96C23×C3×C5C2×D411yescharacteristic
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4C4⋊C414yescomplemented
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—48no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5D812yes—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×Q811yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122C2×C3×C4×C5#4111yescharacteristic
123C3×C5×C8—22no—
124C3×C5×C8—41no—
125C22×C3×D4C22×C511yescharacteristic
126C23×C3×C4—21no—
127C22×C3×C8C22×C511yescharacteristic
128C22×C3×C8C22×C511yescharacteristic
129C3×C4×D4—22no—
130C3×C4×D4—22no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4C22×C511yescharacteristic
133C2×C3×C4⋊C4C22×C511yescharacteristic
134C2×C3×C4⋊C4C22×C511yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C42C22×C511yescharacteristic
137C3×#107—22no—
138C3×#102—22no—
139C3×#102C4×C514yescomplemented
140C3×#95—21no—
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4C2×C3×C412yes—
146C2×C5×D4C3×D412yes—
147C2×C5×D4C3×Q812yes—
148C22×C4×C5—24no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5C3×D411yescharacteristic
155C22×C4×C5C3×D411yescharacteristic
156C22×C4×C5C23×C311yescharacteristic
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8C2×C3×C412yescomplemented
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—42no—
168C5×C4⋊C4C2×C3×C412yescomplemented
169C5×C4⋊C4C3×D412yes—
170C5×C22⋊C4—24no—
171C42×C5—21no—
172C42×C5—21no—
173C2×C4×D4C2×C3×C511yescharacteristic
174C2×#107C2×C3×C511yescharacteristic, complemented
175C2×#102C2×C3×C511yescharacteristic
176C2×#102C2×C3×C511yescharacteristic
177#389C2×C3×C511yescharacteristic, complemented
178#340C2×C3×C511yescharacteristic, complemented
179#336C2×C3×C511yescharacteristic, complemented
180C22×C3×C5—24no—
181C22×C3×C5—42no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—42no—
185C22×C3×C5—42no—
186C22×C3×C5—42no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5C22⋊Q811yescharacteristic
190C22×C3×C5C2×D811yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5#13711yescharacteristic
194C3×C4×C5—22no—
195C3×C4×C5—42no—
196C3×C4×C5—42no—
197C3×C4×C5—41no—
198C3×C4×C5—81no—
199C3×C4×C5C2×C4⋊C411yescharacteristic
200C3×C4×C5C4×D411yescharacteristic
201C3×C4×C5C22⋊Q811yescharacteristic
202C3×C4×C5#12311yescharacteristic
203C24×C3—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4C2×C4×C512yes—
208C2×C3×D4C5×D412yes—
209C2×C3×D4C5×Q812yes—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4C5×D411yescharacteristic
217C22×C3×C4C5×D411yescharacteristic
218C22×C3×C4C23×C511yescharacteristic
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8C2×C4×C512yescomplemented
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—42no—
230C3×C4⋊C4C2×C4×C512yescomplemented
231C3×C4⋊C4C5×D412yes—
232C3×C22⋊C4—24no—
233C3×C42—21no—
234C3×C42—21no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5C2×C3×D411yescharacteristic
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—22no—
246C5×D4C3×C4⋊C414yescomplemented
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—22no—
250C2×C4×C5—21no—
251C2×C4×C5—22no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—48no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5C3×D812yes—
263C2×C4×C5C22×C3×C411yescharacteristic
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C2×C3×D411yescharacteristic
266C2×C4×C5C2×C3×Q811yescharacteristic
267C2×C4×C5C3×#4111yescharacteristic
268C2×C4×C5C3×#4111yescharacteristic
269C5×C8—22no—
270C5×C8—41no—
271C22×D4C22×C3×C511yescharacteristic
272C23×C4—21no—
273C22×C8C22×C3×C511yescharacteristic
274C22×C8C22×C3×C511yescharacteristic
275C4×D4—22no—
276C4×D4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C22×C3×C511yescharacteristic
279C2×C4⋊C4C22×C3×C511yescharacteristic
280C2×C4⋊C4C22×C3×C511yescharacteristic
281C2×C22⋊C4—21no—
282C2×C42C22×C3×C511yescharacteristic
283#107—22no—
284#102—22no—
285#102C3×C4×C514yescomplemented
286#95—21no—
287C2×C3×C5—44no—
288C2×C3×C5#38511yescharacteristic
289C2×C3×C5C4×D811yescharacteristic
290C2×C3×C5#44011yescharacteristic
291C2×C3×C5#44711yescharacteristic
292C2×C3×C5#45211yescharacteristic
293C2×C3×C5#47411yescharacteristic
294C2×C3×C5#47811yescharacteristic
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3C2×C5×D411yescharacteristic
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4C5×C4⋊C414yescomplemented
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—48no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4C5×D812yes—
323C2×C3×C4C22×C4×C511yescharacteristic
324C2×C3×C4C2×C5×D411yescharacteristic
325C2×C3×C4C2×C5×D411yescharacteristic
326C2×C3×C4C2×C5×Q811yescharacteristic
327C2×C3×C4C5×#4111yescharacteristic
328C2×C3×C4C5×#4111yescharacteristic
329C3×C8—22no—
330C3×C8—41no—
331C22×C5—24no—
332C22×C5—42no—
333C22×C5—42no—
334C22×C5—42no—
335C22×C5—42no—
336C22×C5—42no—
337C22×C5—42no—
338C22×C5C3×C4×D411yescharacteristic
339C22×C5C3×#12011yescharacteristic
340C22×C5C3×C22⋊Q811yescharacteristic
341C22×C5C2×C3×D811yescharacteristic
342C22×C5C3×#13511yescharacteristic
343C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
344C22×C5C3×#13711yescharacteristic
345C4×C5—22no—
346C4×C5—42no—
347C4×C5—42no—
348C4×C5—41no—
349C4×C5—81no—
350C4×C5C2×C3×C4⋊C411yescharacteristic
351C4×C5C3×C4×D411yescharacteristic
352C4×C5C3×C22⋊Q811yescharacteristic
353C4×C5C3×#12311yescharacteristic
354C24—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4C2×C3×C4×C512yes—
359C2×D4C3×C5×D412yes—
360C2×D4C3×C5×Q812yes—
361C22×C4—24no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4C3×C5×D411yescharacteristic
368C22×C4C3×C5×D411yescharacteristic
369C22×C4C23×C3×C511yescharacteristic
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8C2×C3×C4×C512yescomplemented
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—42no—
381C4⋊C4C2×C3×C4×C512yescomplemented
382C4⋊C4C3×C5×D412yes—
383C22⋊C4—24no—
384C42—21no—
385C42—21no—
386C3×C5#186211yescharacteristic, direct product factor, Hall
387C22×C3—24no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3C4×C5×D411yescharacteristic
395C22×C3C5×#12011yescharacteristic
396C22×C3C5×C22⋊Q811yescharacteristic
397C22×C3C2×C5×D811yescharacteristic
398C22×C3C5×#13511yescharacteristic
399C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
400C22×C3C5×#13711yescharacteristic
401C3×C4—22no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—41no—
405C3×C4—81no—
406C3×C4C2×C5×C4⋊C411yescharacteristic
407C3×C4C4×C5×D411yescharacteristic
408C3×C4C5×C22⋊Q811yescharacteristic
409C3×C4C5×#12311yescharacteristic
410C2×C5—44no—
411C2×C5C3×#38511yescharacteristic
412C2×C5C3×C4×D811yescharacteristic
413C2×C5C3×#44011yescharacteristic
414C2×C5C3×#44711yescharacteristic
415C2×C5C3×#45211yescharacteristic
416C2×C5C3×#47411yescharacteristic
417C2×C5C3×#47811yescharacteristic
418C23—22no—
419C23—22no—
420C23—22no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C2×C3×C5×D411yescharacteristic
426D4—22no—
427D4—22no—
428D4—22no—
429D4C3×C5×C4⋊C414yescomplemented
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—48no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4C3×C5×D812yes—
446C2×C4C22×C3×C4×C511yescharacteristic
447C2×C4C2×C3×C5×D411yescharacteristic
448C2×C4C2×C3×C5×D411yescharacteristic
449C2×C4C2×C3×C5×Q811yescharacteristic
450C2×C4C3×C5×#4111yescharacteristic
451C2×C4C3×C5×#4111yescharacteristic
452C8—22no—
453C8—41no—
454C2×C3—44no—
455C2×C3C5×#38511yescharacteristic
456C2×C3C4×C5×D811yescharacteristic
457C2×C3C5×#44011yescharacteristic
458C2×C3C5×#44711yescharacteristic
459C2×C3C5×#45211yescharacteristic
460C2×C3C5×#47411yescharacteristic
461C2×C3C5×#47811yescharacteristic
462C5C3×#186211yescharacteristic, direct product factor, Sylow
463C22—24no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C3×C4×C5×D411yescharacteristic
471C22C3×C5×#12011yescharacteristic
472C22C3×C5×C22⋊Q811yescharacteristic
473C22C2×C3×C5×D811yescharacteristic
474C22C3×C5×#13511yescharacteristic
475C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
476C22C3×C5×#13711yescharacteristic
477C4—22no—
478C4—41no—
479C4—42no—
480C4—42no—
481C4—81no—
482C4C2×C3×C5×C4⋊C411yescharacteristic
483C4C3×C4×C5×D411yescharacteristic
484C4C3×C5×C22⋊Q811yescharacteristic
485C4C3×C5×#12311yescharacteristic
486C3C5×#186211yescharacteristic, direct product factor, Sylow
487C2—44no—
488C2C3×C5×#38511yescharacteristic
489C2C3×C4×C5×D811yescharacteristic
490C2C3×C5×#44011yescharacteristic
491C2C3×C5×#44711yescharacteristic
492C2C3×C5×#45211yescharacteristic
493C2C3×C5×#47411yescharacteristic
494C2C3×C5×#47811yescharacteristic
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
2. C2×C3×C5×#107C2semidirect
5. C3×C5×#389C2semidirect
6. C3×C5×#340C2semidirect
7. C3×C5×#336C2semidirect
8. C5×#1862C3direct (N × H)
23. C3×C5×#102C4semidirect
25. C3×#1862C5direct (N × H)
27. C2×C5×#107C2×C3semidirect
30. C5×#389C2×C3semidirect
31. C5×#340C2×C3semidirect
32. C5×#336C2×C3semidirect
54. C2×C3×C5×C8C2×C4semidirect
60. C3×C5×C4⋊C4C2×C4semidirect
66. C2×C3×#107C2×C5semidirect
69. C3×#389C2×C5semidirect
70. C3×#340C2×C5semidirect
71. C3×#336C2×C5semidirect
86. C5×#102C3×C4semidirect
88. #1862C3×C5direct (N × H)
100. C3×C5×D4C4⋊C4semidirect
139. C3×#102C4×C5semidirect
162. C2×C5×C8C2×C3×C4semidirect
168. C5×C4⋊C4C2×C3×C4semidirect
174. C2×#107C2×C3×C5semidirect
177. #389C2×C3×C5semidirect
178. #340C2×C3×C5semidirect
179. #336C2×C3×C5semidirect
224. C2×C3×C8C2×C4×C5semidirect
230. C3×C4⋊C4C2×C4×C5semidirect
246. C5×D4C3×C4⋊C4semidirect
285. #102C3×C4×C5semidirect
306. C3×D4C5×C4⋊C4semidirect
375. C2×C8C2×C3×C4×C5semidirect
381. C4⋊C4C2×C3×C4×C5semidirect
386. C3×C5#1862direct (N × H)
429. D4C3×C5×C4⋊C4semidirect
462. C5C3×#1862direct (N × H)
486. C3C5×#1862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×C5×#1072
C2×C3×C5×#1022
C3×C5×#3892
C3×C5×#3402
C3×C5×#3362
C5×#18623
C3×#18625