Finite Group Databasebeta

← C3×C5×#1874 #14274908

Subgroups — C3×C5×#1874 #14274908

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C212yesmaximal, complemented
4C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×C5×#340C212yesmaximal, complemented
6C5×#1874C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—21no—
8C22×C3×C5×D4C2211yescharacteristic
9C23×C3×C4×C5—21no—
10C23×C3×C4×C5C2211yescharacteristic
11C22×C3×C5×C8C2212yes—
12C3×C5×#121—22no—
13C3×C5×#121C414yescomplemented
14C2×C3×C5×C4⋊C4—21no—
15C2×C3×C5×C4⋊C4—24no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C22⋊C4—21no—
19C3×C5×#102—24no—
20C3×C5×C22⋊C8—22no—
21C3×#1874C511yesmaximal, characteristic, direct product factor, Hall
22C2×C5×#121C2×C311yescharacteristic
23C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
24C2×C5×#102C2×C312yescomplemented
25C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
26C5×#340C2×C312yescomplemented
27C24×C3×C5—21no—
28C24×C3×C5D411yescharacteristic
29C2×C3×C5×D4—24no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4—42no—
34C2×C3×C5×D4—42no—
35C2×C3×C5×D4C2×C412yescomplemented
36C22×C3×C4×C5—22no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—24no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—42no—
42C22×C3×C4×C5—42no—
43C22×C3×C4×C5C2×C412yes—
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D412yes—
46C22×C3×C4×C5C2311yescharacteristic
47C2×C3×C5×C8—22no—
48C2×C3×C5×C8—22no—
49C2×C3×C5×C8—22no—
50C3×C5×C4⋊C4—24no—
51C3×C5×C4⋊C4—22no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4C2×C412yescomplemented
54C3×C5×C4⋊C4D414yescomplemented
55C3×C5×C22⋊C4—24no—
56C2×C3×#121C2×C511yescharacteristic
57C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
58C2×C3×#102C2×C512yescomplemented
59C2×C3×C22⋊C8C2×C511yescharacteristic, complemented
60C3×#340C2×C512yescomplemented
61C22×C5×D4—21no—
62C22×C5×D4C22×C311yescharacteristic
63C23×C4×C5—21no—
64C23×C4×C5C22×C311yescharacteristic
65C22×C5×C8C22×C312yes—
66C5×#121—22no—
67C5×#121C3×C414yescomplemented
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4C22×C311yescharacteristic
71C2×C5×C4⋊C4C22×C312yes—
72C2×C5×C22⋊C4—21no—
73C5×#102—24no—
74C5×C22⋊C8—22no—
75#1874C3×C511yescharacteristic, direct product factor, Sylow
76C23×C3×C5—21no—
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—21no—
80C23×C3×C5—22no—
81C23×C3×C5—41no—
82C23×C3×C5—41no—
83C23×C3×C5—41no—
84C23×C3×C5—41no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5C22⋊C412yes—
88C23×C3×C5D812yes—
89C23×C3×C5SD1612yes—
90C23×C3×C5C2×D411yescharacteristic
91C3×C5×D4—24no—
92C3×C5×D4—48no—
93C3×C5×D4—42no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—24no—
97C2×C3×C4×C5—24no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—24no—
100C2×C3×C4×C5—48no—
101C2×C3×C4×C5—42no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5C22⋊C412yes—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D412yes—
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4112yes—
110C3×C5×C8—42no—
111C22×C3×D4—21no—
112C22×C3×D4C22×C511yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4C22×C511yescharacteristic
115C22×C3×C8C22×C512yes—
116C3×#121—22no—
117C3×#121C4×C514yescomplemented
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—24no—
120C2×C3×C4⋊C4C22×C511yescharacteristic
121C2×C3×C4⋊C4C22×C512yes—
122C2×C3×C22⋊C4—21no—
123C3×#102—24no—
124C3×C22⋊C8—22no—
125C24×C5—21no—
126C24×C5C3×D411yescharacteristic
127C2×C5×D4—24no—
128C2×C5×D4—22no—
129C2×C5×D4—21no—
130C2×C5×D4—22no—
131C2×C5×D4—42no—
132C2×C5×D4—42no—
133C2×C5×D4C2×C3×C412yescomplemented
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—24no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—42no—
140C22×C4×C5—42no—
141C22×C4×C5C2×C3×C412yes—
142C22×C4×C5C3×D411yescharacteristic
143C22×C4×C5C3×D412yes—
144C22×C4×C5C23×C311yescharacteristic
145C2×C5×C8—22no—
146C2×C5×C8—22no—
147C2×C5×C8—22no—
148C5×C4⋊C4—24no—
149C5×C4⋊C4—22no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4C2×C3×C412yescomplemented
152C5×C4⋊C4C3×D414yescomplemented
153C5×C22⋊C4—24no—
154C2×#121C2×C3×C511yescharacteristic
155C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
156C2×#102C2×C3×C512yescomplemented
157C2×C22⋊C8C2×C3×C511yescharacteristic, complemented
158#340C2×C3×C512yescomplemented
159C22×C3×C5—22no—
160C22×C3×C5—22no—
161C22×C3×C5—22no—
162C22×C3×C5—22no—
163C22×C3×C5—22no—
164C22×C3×C5—22no—
165C22×C3×C5—42no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—81no—
169C22×C3×C5—81no—
170C22×C3×C5—81no—
171C22×C3×C5—81no—
172C22×C3×C5#10214yescomplemented
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C22×C3×C5#12011yescharacteristic
175C22×C3×C5#12311yescharacteristic
176C22×C3×C5C2×D811yescharacteristic
177C22×C3×C5C2×SD1611yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C3×C4×C5—22no—
181C3×C4×C5—42no—
182C3×C4×C5—44no—
183C3×C4×C5C4×D412yes—
184C3×C4×C5#12112yes—
185C24×C3—21no—
186C24×C3C5×D411yescharacteristic
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—42no—
192C2×C3×D4—42no—
193C2×C3×D4C2×C4×C512yescomplemented
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4C2×C4×C512yes—
202C22×C3×C4C5×D411yescharacteristic
203C22×C3×C4C5×D412yes—
204C22×C3×C4C23×C511yescharacteristic
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C3×C4⋊C4—24no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4C2×C4×C512yescomplemented
212C3×C4⋊C4C5×D414yescomplemented
213C3×C22⋊C4—24no—
214C23×C5—21no—
215C23×C5—21no—
216C23×C5—21no—
217C23×C5—21no—
218C23×C5—22no—
219C23×C5—41no—
220C23×C5—41no—
221C23×C5—41no—
222C23×C5—41no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5C3×C22⋊C412yes—
226C23×C5C3×D812yes—
227C23×C5C3×SD1612yes—
228C23×C5C2×C3×D411yescharacteristic
229C5×D4—24no—
230C5×D4—48no—
231C5×D4—42no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—22no—
237C2×C4×C5—24no—
238C2×C4×C5—48no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—42no—
243C2×C4×C5C3×C22⋊C412yes—
244C2×C4×C5C22×C3×C411yescharacteristic
245C2×C4×C5C2×C3×D412yes—
246C2×C4×C5C2×C3×D411yescharacteristic
247C2×C4×C5C3×#4112yes—
248C5×C8—42no—
249C22×D4—21no—
250C22×D4C22×C3×C511yescharacteristic
251C23×C4—21no—
252C23×C4C22×C3×C511yescharacteristic
253C22×C8C22×C3×C512yes—
254#121—22no—
255#121C3×C4×C514yescomplemented
256C2×C4⋊C4—21no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4C22×C3×C511yescharacteristic
259C2×C4⋊C4C22×C3×C512yes—
260C2×C22⋊C4—21no—
261#102—24no—
262C22⋊C8—22no—
263C2×C3×C5—24no—
264C2×C3×C5—82no—
265C2×C3×C5#38611yescharacteristic
266C2×C3×C5C2×#10211yescharacteristic
267C2×C3×C5#41711yescharacteristic
268C2×C3×C5#44711yescharacteristic
269C2×C3×C5#44811yescharacteristic
270C2×C3×C5#48011yescharacteristic
271C2×C3×C5#48111yescharacteristic
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—22no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3C5×C22⋊C412yes—
284C23×C3C5×D812yes—
285C23×C3C5×SD1612yes—
286C23×C3C2×C5×D411yescharacteristic
287C3×D4—24no—
288C3×D4—48no—
289C3×D4—42no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—24no—
296C2×C3×C4—48no—
297C2×C3×C4—42no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—42no—
301C2×C3×C4C5×C22⋊C412yes—
302C2×C3×C4C22×C4×C511yescharacteristic
303C2×C3×C4C2×C5×D412yes—
304C2×C3×C4C2×C5×D411yescharacteristic
305C2×C3×C4C5×#4112yes—
306C3×C8—42no—
307C22×C5—22no—
308C22×C5—22no—
309C22×C5—22no—
310C22×C5—22no—
311C22×C5—22no—
312C22×C5—22no—
313C22×C5—42no—
314C22×C5—42no—
315C22×C5—42no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5—81no—
320C22×C5C3×#10214yescomplemented
321C22×C5C2×C3×C22⋊C411yescharacteristic
322C22×C5C3×#12011yescharacteristic
323C22×C5C3×#12311yescharacteristic
324C22×C5C2×C3×D811yescharacteristic
325C22×C5C2×C3×SD1611yescharacteristic
326C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
327C22×C5C3×#13711yescharacteristic
328C4×C5—22no—
329C4×C5—42no—
330C4×C5—44no—
331C4×C5C3×C4×D412yes—
332C4×C5C3×#12112yes—
333C24—21no—
334C24C3×C5×D411yescharacteristic
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4C2×C3×C4×C512yescomplemented
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4C2×C3×C4×C512yes—
350C22×C4C3×C5×D411yescharacteristic
351C22×C4C3×C5×D412yes—
352C22×C4C23×C3×C511yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4C2×C3×C4×C512yescomplemented
360C4⋊C4C3×C5×D414yescomplemented
361C22⋊C4—24no—
362C3×C5#187411yescharacteristic, direct product factor, Hall
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—81no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3—81no—
376C22×C3C5×#10214yescomplemented
377C22×C3C2×C5×C22⋊C411yescharacteristic
378C22×C3C5×#12011yescharacteristic
379C22×C3C5×#12311yescharacteristic
380C22×C3C2×C5×D811yescharacteristic
381C22×C3C2×C5×SD1611yescharacteristic
382C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
383C22×C3C5×#13711yescharacteristic
384C3×C4—22no—
385C3×C4—42no—
386C3×C4—44no—
387C3×C4C4×C5×D412yes—
388C3×C4C5×#12112yes—
389C2×C5—24no—
390C2×C5—82no—
391C2×C5C3×#38611yescharacteristic
392C2×C5C2×C3×#10211yescharacteristic
393C2×C5C3×#41711yescharacteristic
394C2×C5C3×#44711yescharacteristic
395C2×C5C3×#44811yescharacteristic
396C2×C5C3×#48011yescharacteristic
397C2×C5C3×#48111yescharacteristic
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23C3×C5×C22⋊C412yes—
410C23C3×C5×D812yes—
411C23C3×C5×SD1612yes—
412C23C2×C3×C5×D411yescharacteristic
413D4—24no—
414D4—48no—
415D4—42no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—48no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4C3×C5×C22⋊C412yes—
428C2×C4C22×C3×C4×C511yescharacteristic
429C2×C4C2×C3×C5×D412yes—
430C2×C4C2×C3×C5×D411yescharacteristic
431C2×C4C3×C5×#4112yes—
432C8—42no—
433C2×C3—24no—
434C2×C3—82no—
435C2×C3C5×#38611yescharacteristic
436C2×C3C2×C5×#10211yescharacteristic
437C2×C3C5×#41711yescharacteristic
438C2×C3C5×#44711yescharacteristic
439C2×C3C5×#44811yescharacteristic
440C2×C3C5×#48011yescharacteristic
441C2×C3C5×#48111yescharacteristic
442C5C3×#187411yescharacteristic, direct product factor, Sylow
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22C3×C5×#10214yescomplemented
457C22C2×C3×C5×C22⋊C411yescharacteristic
458C22C3×C5×#12011yescharacteristic
459C22C3×C5×#12311yescharacteristic
460C22C2×C3×C5×D811yescharacteristic
461C22C2×C3×C5×SD1611yescharacteristic
462C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
463C22C3×C5×#13711yescharacteristic
464C4—22no—
465C4—42no—
466C4—44no—
467C4C3×C4×C5×D412yes—
468C4C3×C5×#12112yes—
469C3C5×#187411yescharacteristic, direct product factor, Sylow
470C2—24no—
471C2—82no—
472C2C3×C5×#38611yescharacteristic
473C2C2×C3×C5×#10211yescharacteristic
474C2C3×C5×#41711yescharacteristic
475C2C3×C5×#44711yescharacteristic
476C2C3×C5×#44811yescharacteristic
477C2C3×C5×#48011yescharacteristic
478C2C3×C5×#48111yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C4⋊C4C2semidirect
3. C2×C3×C5×#102C2semidirect
4. C2×C3×C5×C22⋊C8C2semidirect
5. C3×C5×#340C2semidirect
6. C5×#1874C3direct (N × H)
13. C3×C5×#121C4semidirect
21. C3×#1874C5direct (N × H)
23. C22×C5×C4⋊C4C2×C3semidirect
24. C2×C5×#102C2×C3semidirect
25. C2×C5×C22⋊C8C2×C3semidirect
26. C5×#340C2×C3semidirect
35. C2×C3×C5×D4C2×C4semidirect
53. C3×C5×C4⋊C4C2×C4semidirect
54. C3×C5×C4⋊C4D4semidirect
57. C22×C3×C4⋊C4C2×C5semidirect
58. C2×C3×#102C2×C5semidirect
59. C2×C3×C22⋊C8C2×C5semidirect
60. C3×#340C2×C5semidirect
67. C5×#121C3×C4semidirect
75. #1874C3×C5direct (N × H)
117. C3×#121C4×C5semidirect
133. C2×C5×D4C2×C3×C4semidirect
151. C5×C4⋊C4C2×C3×C4semidirect
152. C5×C4⋊C4C3×D4semidirect
155. C22×C4⋊C4C2×C3×C5semidirect
156. C2×#102C2×C3×C5semidirect
157. C2×C22⋊C8C2×C3×C5semidirect
158. #340C2×C3×C5semidirect
172. C22×C3×C5#102semidirect
193. C2×C3×D4C2×C4×C5semidirect
211. C3×C4⋊C4C2×C4×C5semidirect
212. C3×C4⋊C4C5×D4semidirect
255. #121C3×C4×C5semidirect
320. C22×C5C3×#102semidirect
341. C2×D4C2×C3×C4×C5semidirect
359. C4⋊C4C2×C3×C4×C5semidirect
360. C4⋊C4C3×C5×D4semidirect
362. C3×C5#1874direct (N × H)
376. C22×C3C5×#102semidirect
442. C5C3×#1874direct (N × H)
456. C22C3×C5×#102semidirect
469. C3C5×#1874direct (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×#1212
C22×C3×C5×C4⋊C42
C2×C3×C5×#1022
C2×C3×C5×C22⋊C82
C3×C5×#3402
C5×#18743
C3×#18745