Finite Group Databasebeta

← C3×C5×#1964 #14274998

Subgroups — C3×C5×#1964 #14274998

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C5×#99C214yesmaximal, complemented
3C3×C5×#380C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×#1964C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4C411yescharacteristic, complemented
7C22×C3×C5×D4C2212yes—
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#121—21no—
10C3×C5×#121—21no—
11C3×C5×#121—21no—
12C3×C5×#121—21no—
13C2×C3×C5×C4⋊C4—21no—
14C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
15C2×C3×C5×C22⋊C4C412yescomplemented
16C2×C3×C5×C22⋊C4C2212yes—
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C3×C42×C5—21no—
19C3×C5×#99—28no—
20C3×C5×#95—21no—
21C3×C5×#95—21no—
22C3×#1964C511yesmaximal, characteristic, direct product factor, Hall
23C2×C5×#121C2×C311yescharacteristic
24C2×C5×#99C2×C314yescomplemented
25C5×#380C2×C311yescharacteristic, complemented
26C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
27C24×C3×C5C2×C412yes—
28C24×C3×C5C2311yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—24no—
32C2×C3×C5×D4—24no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—42no—
36C22×C3×C4×C5—22no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—42no—
39C22×C3×C4×C5C2×C412yes—
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—42no—
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—22no—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—24no—
53C3×C5×C22⋊C4D414yescomplemented
54C3×C42×C5—42no—
55C2×C3×#121C2×C511yescharacteristic
56C2×C3×#99C2×C514yescomplemented
57C3×#380C2×C511yescharacteristic, complemented
58C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
59C22×C5×D4C3×C411yescharacteristic, complemented
60C22×C5×D4C22×C312yes—
61C23×C4×C5C22×C311yescharacteristic
62C5×#121—21no—
63C5×#121—21no—
64C5×#121—21no—
65C5×#121—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
68C2×C5×C22⋊C4C3×C412yescomplemented
69C2×C5×C22⋊C4C22×C312yes—
70C2×C5×C22⋊C4C22×C312yes—
71C2×C42×C5—21no—
72C5×#99—28no—
73C5×#95—21no—
74C5×#95—21no—
75#1964C3×C511yescharacteristic, direct product factor, Sylow
76C23×C3×C5—22no—
77C23×C3×C5—24no—
78C23×C3×C5—41no—
79C23×C3×C5—41no—
80C23×C3×C5—42no—
81C23×C3×C5—42no—
82C23×C3×C5C22×C411yescharacteristic
83C23×C3×C5C2×D411yescharacteristic
84C23×C3×C5C2×D411yescharacteristic
85C23×C3×C5C2×D412yes—
86C23×C3×C5#4112yes—
87C3×C5×D4—42no—
88C3×C5×D4—44no—
89C3×C5×D4—42no—
90C3×C5×D4—42no—
91C3×C5×D4—42no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—24no—
97C2×C3×C4×C5—24no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—42no—
102C2×C3×C4×C5—42no—
103C2×C3×C4×C5—42no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—42no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C22⋊C411yescharacteristic
108C2×C3×C4×C5C22⋊C411yescharacteristic
109C2×C3×C4×C5C22⋊C411yescharacteristic
110C22×C3×D4C4×C511yescharacteristic, complemented
111C22×C3×D4C22×C512yes—
112C23×C3×C4C22×C511yescharacteristic
113C3×#121—21no—
114C3×#121—21no—
115C3×#121—21no—
116C3×#121—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4C4×C511yescharacteristic, complemented
119C2×C3×C22⋊C4C4×C512yescomplemented
120C2×C3×C22⋊C4C22×C512yes—
121C2×C3×C22⋊C4C22×C512yes—
122C2×C3×C42—21no—
123C3×#99—28no—
124C3×#95—21no—
125C3×#95—21no—
126C24×C5C2×C3×C412yes—
127C24×C5C23×C311yescharacteristic
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—24no—
131C2×C5×D4—24no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—42no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—42no—
138C22×C4×C5C2×C3×C412yes—
139C22×C4×C5C2×C3×C411yescharacteristic
140C22×C4×C5C2×C3×C411yescharacteristic
141C22×C4×C5C3×D411yescharacteristic
142C22×C4×C5C3×D411yescharacteristic
143C22×C4×C5C3×D411yescharacteristic
144C22×C4×C5C3×D411yescharacteristic
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—42no—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—22no—
150C5×C22⋊C4—22no—
151C5×C22⋊C4—24no—
152C5×C22⋊C4C3×D414yescomplemented
153C42×C5—42no—
154C2×#121C2×C3×C511yescharacteristic
155C2×#99C2×C3×C514yescomplemented
156#380C2×C3×C511yescharacteristic, complemented
157C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5—21no—
164C22×C3×C5—42no—
165C22×C3×C5—42no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—42no—
169C22×C3×C5—84no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C22×C3×C5C4×D412yes—
172C22×C3×C5#12112yes—
173C22×C3×C5#12411yescharacteristic
174C22×C3×C5#12711yescharacteristic
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—44no—
179C3×C4×C5—42no—
180C3×C4×C5—82no—
181C3×C4×C5#9912yescomplemented
182C24×C3C2×C4×C512yes—
183C24×C3C23×C511yescharacteristic
184C2×C3×D4—24no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—24no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—42no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—42no—
194C22×C3×C4C2×C4×C512yes—
195C22×C3×C4C2×C4×C511yescharacteristic
196C22×C3×C4C2×C4×C511yescharacteristic
197C22×C3×C4C5×D411yescharacteristic
198C22×C3×C4C5×D411yescharacteristic
199C22×C3×C4C5×D411yescharacteristic
200C22×C3×C4C5×D411yescharacteristic
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—42no—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—22no—
207C3×C22⋊C4—24no—
208C3×C22⋊C4C5×D414yescomplemented
209C3×C42—42no—
210C23×C5—22no—
211C23×C5—24no—
212C23×C5—41no—
213C23×C5—41no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5C22×C3×C411yescharacteristic
217C23×C5C2×C3×D411yescharacteristic
218C23×C5C2×C3×D411yescharacteristic
219C23×C5C2×C3×D412yes—
220C23×C5C3×#4112yes—
221C5×D4—42no—
222C5×D4—44no—
223C5×D4—42no—
224C5×D4—42no—
225C5×D4—42no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5C3×C22⋊C411yescharacteristic
241C2×C4×C5C3×C22⋊C411yescharacteristic
242C2×C4×C5C3×C22⋊C411yescharacteristic
243C2×C4×C5C3×C22⋊C411yescharacteristic
244C22×D4C3×C4×C511yescharacteristic, complemented
245C22×D4C22×C3×C512yes—
246C23×C4C22×C3×C511yescharacteristic
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C3×C4×C511yescharacteristic, complemented
253C2×C22⋊C4C3×C4×C512yescomplemented
254C2×C22⋊C4C22×C3×C512yes—
255C2×C22⋊C4C22×C3×C512yes—
256C2×C42—21no—
257#99—28no—
258#95—21no—
259#95—21no—
260C2×C3×C5—22no—
261C2×C3×C5—21no—
262C2×C3×C5—22no—
263C2×C3×C5—21no—
264C2×C3×C5—82no—
265C2×C3×C5#39011yescharacteristic
266C2×C3×C5C2×#9911yescharacteristic
267C2×C3×C5#41011yescharacteristic
268C23×C3—22no—
269C23×C3—24no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3C22×C4×C511yescharacteristic
275C23×C3C2×C5×D411yescharacteristic
276C23×C3C2×C5×D411yescharacteristic
277C23×C3C2×C5×D412yes—
278C23×C3C5×#4112yes—
279C3×D4—42no—
280C3×D4—44no—
281C3×D4—42no—
282C3×D4—42no—
283C3×D4—42no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4C5×C22⋊C411yescharacteristic
299C2×C3×C4C5×C22⋊C411yescharacteristic
300C2×C3×C4C5×C22⋊C411yescharacteristic
301C2×C3×C4C5×C22⋊C411yescharacteristic
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—42no—
309C22×C5—42no—
310C22×C5—42no—
311C22×C5—42no—
312C22×C5—42no—
313C22×C5—84no—
314C22×C5C2×C3×C22⋊C411yescharacteristic
315C22×C5C3×C4×D412yes—
316C22×C5C3×#12112yes—
317C22×C5C3×#12411yescharacteristic
318C22×C5C3×#12711yescharacteristic
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—44no—
323C4×C5—42no—
324C4×C5—82no—
325C4×C5C3×#9912yescomplemented
326C24C2×C3×C4×C512yes—
327C24C23×C3×C511yescharacteristic
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—24no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—42no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—42no—
338C22×C4C2×C3×C4×C512yes—
339C22×C4C2×C3×C4×C511yescharacteristic
340C22×C4C2×C3×C4×C511yescharacteristic
341C22×C4C3×C5×D411yescharacteristic
342C22×C4C3×C5×D411yescharacteristic
343C22×C4C3×C5×D411yescharacteristic
344C22×C4C3×C5×D411yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—42no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—24no—
352C22⋊C4C3×C5×D414yescomplemented
353C42—42no—
354C3×C5#196411yescharacteristic, direct product factor, Hall
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—84no—
367C22×C3C2×C5×C22⋊C411yescharacteristic
368C22×C3C4×C5×D412yes—
369C22×C3C5×#12112yes—
370C22×C3C5×#12411yescharacteristic
371C22×C3C5×#12711yescharacteristic
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—44no—
376C3×C4—42no—
377C3×C4—82no—
378C3×C4C5×#9912yescomplemented
379C2×C5—22no—
380C2×C5—21no—
381C2×C5—22no—
382C2×C5—21no—
383C2×C5—82no—
384C2×C5C3×#39011yescharacteristic
385C2×C5C2×C3×#9911yescharacteristic
386C2×C5C3×#41011yescharacteristic
387C23—22no—
388C23—24no—
389C23—41no—
390C23—41no—
391C23—42no—
392C23—42no—
393C23C22×C3×C4×C511yescharacteristic
394C23C2×C3×C5×D411yescharacteristic
395C23C2×C3×C5×D411yescharacteristic
396C23C2×C3×C5×D412yes—
397C23C3×C5×#4112yes—
398D4—42no—
399D4—44no—
400D4—42no—
401D4—42no—
402D4—42no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4C3×C5×C22⋊C411yescharacteristic
418C2×C4C3×C5×C22⋊C411yescharacteristic
419C2×C4C3×C5×C22⋊C411yescharacteristic
420C2×C4C3×C5×C22⋊C411yescharacteristic
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—82no—
426C2×C3C5×#39011yescharacteristic
427C2×C3C2×C5×#9911yescharacteristic
428C2×C3C5×#41011yescharacteristic
429C5C3×#196411yescharacteristic, direct product factor, Sylow
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22C2×C3×C5×C22⋊C411yescharacteristic
443C22C3×C4×C5×D412yes—
444C22C3×C5×#12112yes—
445C22C3×C5×#12411yescharacteristic
446C22C3×C5×#12711yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—44no—
451C4—42no—
452C4—82no—
453C4C3×C5×#9912yescomplemented
454C3C5×#196411yescharacteristic, direct product factor, Sylow
455C2—22no—
456C2—21no—
457C2—22no—
458C2—21no—
459C2—82no—
460C2C3×C5×#39011yescharacteristic
461C2C2×C3×C5×#9911yescharacteristic
462C2C3×C5×#41011yescharacteristic
subgroupG/H
center, socleC22×C3×C5C2×C22⋊C4
commutatorC23C22×C3×C4×C5
Frattini, cosocleC24C23×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#99C2semidirect
3. C3×C5×#380C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
5. C5×#1964C3direct (N × H)
6. C22×C3×C5×D4C4semidirect
14. C2×C3×C5×C4⋊C4C4semidirect
15. C2×C3×C5×C22⋊C4C4semidirect
22. C3×#1964C5direct (N × H)
24. C2×C5×#99C2×C3semidirect
25. C5×#380C2×C3semidirect
26. C4×C5×C22⋊C4C2×C3semidirect
53. C3×C5×C22⋊C4D4semidirect
56. C2×C3×#99C2×C5semidirect
57. C3×#380C2×C5semidirect
58. C3×C4×C22⋊C4C2×C5semidirect
59. C22×C5×D4C3×C4semidirect
67. C2×C5×C4⋊C4C3×C4semidirect
68. C2×C5×C22⋊C4C3×C4semidirect
75. #1964C3×C5direct (N × H)
110. C22×C3×D4C4×C5semidirect
118. C2×C3×C4⋊C4C4×C5semidirect
119. C2×C3×C22⋊C4C4×C5semidirect
152. C5×C22⋊C4C3×D4semidirect
155. C2×#99C2×C3×C5semidirect
156. #380C2×C3×C5semidirect
157. C4×C22⋊C4C2×C3×C5semidirect
181. C3×C4×C5#99semidirect
208. C3×C22⋊C4C5×D4semidirect
244. C22×D4C3×C4×C5semidirect
252. C2×C4⋊C4C3×C4×C5semidirect
253. C2×C22⋊C4C3×C4×C5semidirect
325. C4×C5C3×#99semidirect
352. C22⋊C4C3×C5×D4semidirect
354. C3×C5#1964direct (N × H)
378. C3×C4C5×#99semidirect
429. C5C3×#1964direct (N × H)
453. C4C3×C5×#99semidirect
454. C3C5×#1964direct (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
C2×C3×C5×#992
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#19643
C3×#19645