Finite Group Databasebeta

← C3×C5×#1924 #14274958

Subgroups — C3×C5×#1924 #14274958

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C4⋊C8C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊C8C211yesmaximal, characteristic
3C2×C3×C5×C22⋊C8C211yesmaximal, characteristic
4C2×C3×C5×#97C211yesmaximal, characteristic, complemented
5C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
6C3×C5×#336C211yesmaximal, characteristic, complemented
7C3×C5×#336C211yesmaximal, characteristic, complemented
8C5×#1924C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C2×C3×C5×C22⋊C4C411yescharacteristic
15C2×C3×C5×C22⋊C4C411yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C3×C5×C4⋊C8—22no—
19C3×C5×C22⋊C8—22no—
20C3×C5×C22⋊C8—22no—
21C3×C5×#97—22no—
22C3×C5×#95C411yescharacteristic
23C3×C5×#95C411yescharacteristic
24C3×#1924C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×C4⋊C8C2×C311yescharacteristic, complemented
26C2×C5×C22⋊C8C2×C311yescharacteristic
27C2×C5×C22⋊C8C2×C311yescharacteristic
28C2×C5×#97C2×C311yescharacteristic, complemented
29C4×C5×C22⋊C4C2×C311yescharacteristic
30C5×#336C2×C311yescharacteristic, complemented
31C5×#336C2×C311yescharacteristic, complemented
32C24×C3×C5C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×C4×C5C2×C411yescharacteristic
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
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×C8—21no—
55C2×C3×C5×C8D412yes—
56C2×C3×C5×C8D412yes—
57C3×C5×C22⋊C4—22no—
58C3×C5×C22⋊C4—22no—
59C3×C42×C5—21no—
60C3×C42×C5—21no—
61C3×C42×C5—21no—
62C3×C42×C5—21no—
63C2×C3×C4⋊C8C2×C511yescharacteristic, complemented
64C2×C3×C22⋊C8C2×C511yescharacteristic
65C2×C3×C22⋊C8C2×C511yescharacteristic
66C2×C3×#97C2×C511yescharacteristic, complemented
67C3×C4×C22⋊C4C2×C511yescharacteristic
68C3×#336C2×C511yescharacteristic, complemented
69C3×#336C2×C511yescharacteristic, complemented
70C23×C4×C5C22×C311yescharacteristic
71C22×C5×C8C22×C311yescharacteristic
72C22×C5×C8C22×C311yescharacteristic
73C22×C5×C8C22×C311yescharacteristic
74C22×C5×C8C22×C311yescharacteristic
75C2×C5×C22⋊C4C3×C411yescharacteristic
76C2×C5×C22⋊C4C3×C411yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78C2×C42×C5C22×C311yescharacteristic
79C5×C4⋊C8—22no—
80C5×C22⋊C8—22no—
81C5×C22⋊C8—22no—
82C5×#97—22no—
83C5×#95C3×C411yescharacteristic
84C5×#95C3×C411yescharacteristic
85#1924C3×C511yescharacteristic, direct product factor, Sylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—21no—
91C23×C3×C5—21no—
92C23×C3×C5M1612yes—
93C23×C3×C5C22×C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5M1612yes—
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C3×C5×C8—22no—
120C3×C5×C8—22no—
121C3×C5×C8—41no—
122C3×C5×C8—41no—
123C23×C3×C4C22×C511yescharacteristic
124C22×C3×C8C22×C511yescharacteristic
125C22×C3×C8C22×C511yescharacteristic
126C22×C3×C8C22×C511yescharacteristic
127C22×C3×C8C22×C511yescharacteristic
128C2×C3×C22⋊C4C4×C511yescharacteristic
129C2×C3×C22⋊C4C4×C511yescharacteristic
130C2×C3×C42C22×C511yescharacteristic
131C2×C3×C42C22×C511yescharacteristic
132C3×C4⋊C8—22no—
133C3×C22⋊C8—22no—
134C3×C22⋊C8—22no—
135C3×#97—22no—
136C3×#95C4×C511yescharacteristic
137C3×#95C4×C511yescharacteristic
138C24×C5C2×C3×C411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×C3×C411yescharacteristic
146C22×C4×C5C2×C3×C411yescharacteristic
147C22×C4×C5C2×C3×C411yescharacteristic
148C22×C4×C5C2×C3×C411yescharacteristic
149C22×C4×C5C2×C3×C411yescharacteristic
150C22×C4×C5C23×C311yescharacteristic
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C2×C5×C8—21no—
156C2×C5×C8—21no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8C3×D412yes—
162C2×C5×C8C3×D412yes—
163C5×C22⋊C4—22no—
164C5×C22⋊C4—22no—
165C42×C5—21no—
166C42×C5—21no—
167C42×C5—21no—
168C42×C5—21no—
169C2×C4⋊C8C2×C3×C511yescharacteristic, complemented
170C2×C22⋊C8C2×C3×C511yescharacteristic
171C2×C22⋊C8C2×C3×C511yescharacteristic
172C2×#97C2×C3×C511yescharacteristic, complemented
173C4×C22⋊C4C2×C3×C511yescharacteristic
174#336C2×C3×C511yescharacteristic, complemented
175#336C2×C3×C511yescharacteristic, complemented
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—22no—
179C22×C3×C5—41no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5#11711yescharacteristic
184C22×C3×C5C4×D411yescharacteristic
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5C2×M1611yescharacteristic
187C22×C3×C5C2×M1611yescharacteristic
188C22×C3×C5#13111yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C3×C4×C5—22no—
191C3×C4×C5—41no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5—41no—
195C3×C4×C5#12111yescharacteristic
196C3×C4×C5#12311yescharacteristic
197C3×C4×C5#12411yescharacteristic
198C3×C4×C5#12611yescharacteristic
199C24×C3C2×C4×C511yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C2×C4×C511yescharacteristic
207C22×C3×C4C2×C4×C511yescharacteristic
208C22×C3×C4C2×C4×C511yescharacteristic
209C22×C3×C4C2×C4×C511yescharacteristic
210C22×C3×C4C2×C4×C511yescharacteristic
211C22×C3×C4C23×C511yescharacteristic
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8C5×D412yes—
223C2×C3×C8C5×D412yes—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—22no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—21no—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5C3×M1612yes—
237C23×C5C22×C3×C411yescharacteristic
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—21no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—21no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5C3×M1612yes—
257C2×C4×C5C2×C3×D411yescharacteristic
258C2×C4×C5C2×C3×D411yescharacteristic
259C2×C4×C5C3×#4111yescharacteristic
260C2×C4×C5C3×#4111yescharacteristic
261C2×C4×C5C3×#4111yescharacteristic
262C2×C4×C5C3×#4111yescharacteristic
263C5×C8—22no—
264C5×C8—22no—
265C5×C8—41no—
266C5×C8—41no—
267C23×C4C22×C3×C511yescharacteristic
268C22×C8C22×C3×C511yescharacteristic
269C22×C8C22×C3×C511yescharacteristic
270C22×C8C22×C3×C511yescharacteristic
271C22×C8C22×C3×C511yescharacteristic
272C2×C22⋊C4C3×C4×C511yescharacteristic
273C2×C22⋊C4C3×C4×C511yescharacteristic
274C2×C42C22×C3×C511yescharacteristic
275C2×C42C22×C3×C511yescharacteristic
276C4⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279#97—22no—
280#95C3×C4×C511yescharacteristic
281#95C3×C4×C511yescharacteristic
282C2×C3×C5—42no—
283C2×C3×C5#38811yescharacteristic
284C2×C3×C5#43211yescharacteristic
285C2×C3×C5#43311yescharacteristic
286C2×C3×C5#43511yescharacteristic
287C2×C3×C5#43511yescharacteristic
288C2×C3×C5#43511yescharacteristic
289C2×C3×C5#43611yescharacteristic
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3C5×M1612yes—
297C23×C3C22×C4×C511yescharacteristic
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4C5×M1612yes—
317C2×C3×C4C2×C5×D411yescharacteristic
318C2×C3×C4C2×C5×D411yescharacteristic
319C2×C3×C4C5×#4111yescharacteristic
320C2×C3×C4C5×#4111yescharacteristic
321C2×C3×C4C5×#4111yescharacteristic
322C2×C3×C4C5×#4111yescharacteristic
323C3×C8—22no—
324C3×C8—22no—
325C3×C8—41no—
326C3×C8—41no—
327C22×C5—22no—
328C22×C5—22no—
329C22×C5—22no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5—41no—
334C22×C5C3×#11711yescharacteristic
335C22×C5C3×C4×D411yescharacteristic
336C22×C5C3×C4×D411yescharacteristic
337C22×C5C2×C3×M1611yescharacteristic
338C22×C5C2×C3×M1611yescharacteristic
339C22×C5C3×#13111yescharacteristic
340C22×C5C3×#13111yescharacteristic
341C4×C5—22no—
342C4×C5—41no—
343C4×C5—41no—
344C4×C5—41no—
345C4×C5—41no—
346C4×C5C3×#12111yescharacteristic
347C4×C5C3×#12311yescharacteristic
348C4×C5C3×#12411yescharacteristic
349C4×C5C3×#12611yescharacteristic
350C24C2×C3×C4×C511yescharacteristic
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4C2×C3×C4×C511yescharacteristic
358C22×C4C2×C3×C4×C511yescharacteristic
359C22×C4C2×C3×C4×C511yescharacteristic
360C22×C4C2×C3×C4×C511yescharacteristic
361C22×C4C2×C3×C4×C511yescharacteristic
362C22×C4C23×C3×C511yescharacteristic
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C3×C5×D412yes—
374C2×C8C3×C5×D412yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C42—21no—
378C42—21no—
379C42—21no—
380C42—21no—
381C3×C5#192411yescharacteristic, direct product factor, Hall
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3C5×#11711yescharacteristic
390C22×C3C4×C5×D411yescharacteristic
391C22×C3C4×C5×D411yescharacteristic
392C22×C3C2×C5×M1611yescharacteristic
393C22×C3C2×C5×M1611yescharacteristic
394C22×C3C5×#13111yescharacteristic
395C22×C3C5×#13111yescharacteristic
396C3×C4—22no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4C5×#12111yescharacteristic
402C3×C4C5×#12311yescharacteristic
403C3×C4C5×#12411yescharacteristic
404C3×C4C5×#12611yescharacteristic
405C2×C5—42no—
406C2×C5C3×#38811yescharacteristic
407C2×C5C3×#43211yescharacteristic
408C2×C5C3×#43311yescharacteristic
409C2×C5C3×#43511yescharacteristic
410C2×C5C3×#43511yescharacteristic
411C2×C5C3×#43511yescharacteristic
412C2×C5C3×#43611yescharacteristic
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23C3×C5×M1612yes—
420C23C22×C3×C4×C511yescharacteristic
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4C3×C5×M1612yes—
440C2×C4C2×C3×C5×D411yescharacteristic
441C2×C4C2×C3×C5×D411yescharacteristic
442C2×C4C3×C5×#4111yescharacteristic
443C2×C4C3×C5×#4111yescharacteristic
444C2×C4C3×C5×#4111yescharacteristic
445C2×C4C3×C5×#4111yescharacteristic
446C8—22no—
447C8—22no—
448C8—41no—
449C8—41no—
450C2×C3—42no—
451C2×C3C5×#38811yescharacteristic
452C2×C3C5×#43211yescharacteristic
453C2×C3C5×#43311yescharacteristic
454C2×C3C5×#43511yescharacteristic
455C2×C3C5×#43511yescharacteristic
456C2×C3C5×#43511yescharacteristic
457C2×C3C5×#43611yescharacteristic
458C5C3×#192411yescharacteristic, direct product factor, Sylow
459C22—22no—
460C22—22no—
461C22—22no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22C3×C5×#11711yescharacteristic
467C22C3×C4×C5×D411yescharacteristic
468C22C3×C4×C5×D411yescharacteristic
469C22C2×C3×C5×M1611yescharacteristic
470C22C2×C3×C5×M1611yescharacteristic
471C22C3×C5×#13111yescharacteristic
472C22C3×C5×#13111yescharacteristic
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—41no—
478C4C3×C5×#12111yescharacteristic
479C4C3×C5×#12311yescharacteristic
480C4C3×C5×#12411yescharacteristic
481C4C3×C5×#12611yescharacteristic
482C3C5×#192411yescharacteristic, direct product factor, Sylow
483C2—42no—
484C2C3×C5×#38811yescharacteristic
485C2C3×C5×#43211yescharacteristic
486C2C3×C5×#43311yescharacteristic
487C2C3×C5×#43511yescharacteristic
488C2C3×C5×#43511yescharacteristic
489C2C3×C5×#43511yescharacteristic
490C2C3×C5×#43611yescharacteristic
subgroupG/H
centerC22×C3×C4×C5C23
commutatorC23C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C4⋊C8C2semidirect
4. C2×C3×C5×#97C2semidirect
6. C3×C5×#336C2semidirect
7. C3×C5×#336C2semidirect
8. C5×#1924C3direct (N × H)
24. C3×#1924C5direct (N × H)
25. C2×C5×C4⋊C8C2×C3semidirect
28. C2×C5×#97C2×C3semidirect
30. C5×#336C2×C3semidirect
31. C5×#336C2×C3semidirect
63. C2×C3×C4⋊C8C2×C5semidirect
66. C2×C3×#97C2×C5semidirect
68. C3×#336C2×C5semidirect
69. C3×#336C2×C5semidirect
85. #1924C3×C5direct (N × H)
169. C2×C4⋊C8C2×C3×C5semidirect
172. C2×#97C2×C3×C5semidirect
174. #336C2×C3×C5semidirect
175. #336C2×C3×C5semidirect
381. C3×C5#1924direct (N × H)
458. C5C3×#1924direct (N × H)
482. C3C5×#1924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C4⋊C82
C2×C3×C5×C22⋊C82
C2×C3×C5×#972
C3×C4×C5×C22⋊C42
C3×C5×#3362
C5×#19243
C3×#19245