Finite Group Databasebeta

← C3×C5×#1606 #14274640

Subgroups — C3×C5×#1606 #14274640

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#538C211yesmaximal, characteristic
2C3×C5×#451C211yesmaximal, characteristic, complemented
3C3×C5×#448C211yesmaximal, characteristic, complemented
4C3×C5×#393C211yesmaximal, characteristic, complemented
5C3×C5×#328C211yesmaximal, characteristic, complemented
6C3×C5×#327C211yesmaximal, characteristic, complemented
7C3×C5×#323C211yesmaximal, characteristic, complemented
8C5×#1606C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×Q16—21no—
11C2×C3×C5×SD16—21no—
12C3×C5×#126—21no—
13C3×C5×#124—21no—
14C3×C5×#123—21no—
15C3×C5×C22⋊Q8C2211yescharacteristic
16C3×C5×#121—21no—
17C3×C5×#121C2211yescharacteristic
18C3×C5×#120—21no—
19C3×C4×C5×D4—21no—
20C2×C3×C5×C22⋊C4—21no—
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C3×C5×#103—21no—
23C3×C5×#103—21no—
24C3×C5×C22⋊C8C2211yescharacteristic
25C3×C5×C22⋊C8C2211yescharacteristic
26C3×C5×#95—21no—
27C3×C5×#95C2211yescharacteristic
28C3×#1606C511yesmaximal, characteristic, direct product factor, Hall
29C5×#538C2×C311yescharacteristic
30C5×#451C2×C311yescharacteristic, complemented
31C5×#448C2×C311yescharacteristic, complemented
32C5×#393C2×C311yescharacteristic, complemented
33C5×#328C2×C311yescharacteristic, complemented
34C5×#327C2×C311yescharacteristic, complemented
35C5×#323C2×C311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C2×C3×C5×Q8D411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4D411yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5C2311yescharacteristic
50C3×C5×Q16—42no—
51C3×C5×SD16—42no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4D411yescharacteristic
57C3×C5×C4⋊C4D411yescharacteristic
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4—21no—
65C3×C5×C22⋊C4—42no—
66C3×C42×C5—21no—
67C3×#538C2×C511yescharacteristic
68C3×#451C2×C511yescharacteristic, complemented
69C3×#448C2×C511yescharacteristic, complemented
70C3×#393C2×C511yescharacteristic, complemented
71C3×#328C2×C511yescharacteristic, complemented
72C3×#327C2×C511yescharacteristic, complemented
73C3×#323C2×C511yescharacteristic, complemented
74C22×C5×Q8C22×C311yescharacteristic
75C2×C5×Q16—21no—
76C2×C5×SD16—21no—
77C5×#126—21no—
78C5×#124—21no—
79C5×#123—21no—
80C5×C22⋊Q8C22×C311yescharacteristic
81C5×#121—21no—
82C5×#121C22×C311yescharacteristic
83C5×#120—21no—
84C4×C5×D4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4C22×C311yescharacteristic
87C5×#103—21no—
88C5×#103—21no—
89C5×C22⋊C8C22×C311yescharacteristic
90C5×C22⋊C8C22×C311yescharacteristic
91C5×#95—21no—
92C5×#95C22×C311yescharacteristic
93#1606C3×C511yescharacteristic, direct product factor, Sylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—21no—
97C23×C3×C5—21no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C2×D411yescharacteristic
101C3×C5×Q8—22no—
102C3×C5×Q8—22no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C3×C5×Q8—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C3×C5×D4—81no—
110C3×C5×D4—81no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—81no—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C3×C5×C8—41no—
127C3×C5×C8—41no—
128C22×C3×Q8C22×C511yescharacteristic
129C2×C3×Q16—21no—
130C2×C3×SD16—21no—
131C3×#126—21no—
132C3×#124—21no—
133C3×#123—21no—
134C3×C22⋊Q8C22×C511yescharacteristic
135C3×#121—21no—
136C3×#121C22×C511yescharacteristic
137C3×#120—21no—
138C3×C4×D4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4C22×C511yescharacteristic
141C3×#103—21no—
142C3×#103—21no—
143C3×C22⋊C8C22×C511yescharacteristic
144C3×C22⋊C8C22×C511yescharacteristic
145C3×#95—21no—
146C3×#95C22×C511yescharacteristic
147C24×C5C3×D411yescharacteristic
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—42no—
151C2×C5×Q8C3×D411yescharacteristic
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4C3×D411yescharacteristic
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5C3×D411yescharacteristic
160C22×C4×C5C23×C311yescharacteristic
161C5×Q16—42no—
162C5×SD16—42no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4C3×D411yescharacteristic
168C5×C4⋊C4C3×D411yescharacteristic
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—42no—
177C42×C5—21no—
178#538C2×C3×C511yescharacteristic
179#451C2×C3×C511yescharacteristic, complemented
180#448C2×C3×C511yescharacteristic, complemented
181#393C2×C3×C511yescharacteristic, complemented
182#328C2×C3×C511yescharacteristic, complemented
183#327C2×C3×C511yescharacteristic, complemented
184#323C2×C3×C511yescharacteristic, complemented
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5—42no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5—81no—
195C22×C3×C5#12011yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C22×C3×C5#13711yescharacteristic
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—41no—
202C3×C4×C5—41no—
203C3×C4×C5—42no—
204C3×C4×C5—41no—
205C3×C4×C5—81no—
206C24×C3C5×D411yescharacteristic
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—42no—
210C2×C3×Q8C5×D411yescharacteristic
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4C5×D411yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4C5×D411yescharacteristic
219C22×C3×C4C23×C511yescharacteristic
220C3×Q16—42no—
221C3×SD16—42no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4C5×D411yescharacteristic
227C3×C4⋊C4C5×D411yescharacteristic
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—42no—
236C3×C42—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—21no—
241C23×C5—41no—
242C23×C5—41no—
243C23×C5C2×C3×D411yescharacteristic
244C5×Q8—22no—
245C5×Q8—22no—
246C5×Q8—41no—
247C5×Q8—41no—
248C5×Q8—41no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—81no—
253C5×D4—81no—
254C2×C4×C5—22no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5—81no—
267C2×C4×C5C2×C3×D411yescharacteristic
268C2×C4×C5C2×C3×D411yescharacteristic
269C5×C8—41no—
270C5×C8—41no—
271C22×Q8C22×C3×C511yescharacteristic
272C2×Q16—21no—
273C2×SD16—21no—
274#126—21no—
275#124—21no—
276#123—21no—
277C22⋊Q8C22×C3×C511yescharacteristic
278#121—21no—
279#121C22×C3×C511yescharacteristic
280#120—21no—
281C4×D4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4C22×C3×C511yescharacteristic
284#103—21no—
285#103—21no—
286C22⋊C8C22×C3×C511yescharacteristic
287C22⋊C8C22×C3×C511yescharacteristic
288#95—21no—
289#95C22×C3×C511yescharacteristic
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—81no—
293C2×C3×C5—81no—
294C2×C3×C5#45211yescharacteristic
295C2×C3×C5#45511yescharacteristic
296C2×C3×C5B(4,𝔽2)11yescharacteristic
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3C2×C5×D411yescharacteristic
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—41no—
307C3×Q8—41no—
308C3×Q8—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—81no—
313C3×D4—81no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—81no—
327C2×C3×C4C2×C5×D411yescharacteristic
328C2×C3×C4C2×C5×D411yescharacteristic
329C3×C8—41no—
330C3×C8—41no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—42no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—81no—
341C22×C5C3×#12011yescharacteristic
342C22×C5C3×#13511yescharacteristic
343C22×C5C3×#13711yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—41no—
347C4×C5—41no—
348C4×C5—41no—
349C4×C5—42no—
350C4×C5—41no—
351C4×C5—81no—
352C24C3×C5×D411yescharacteristic
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—42no—
356C2×Q8C3×C5×D411yescharacteristic
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C3×C5×D411yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4C3×C5×D411yescharacteristic
365C22×C4C23×C3×C511yescharacteristic
366Q16—42no—
367SD16—42no—
368C2×C8—21no—
369C2×C8—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4C3×C5×D411yescharacteristic
373C4⋊C4C3×C5×D411yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—42no—
382C42—21no—
383C3×C5#160611yescharacteristic, direct product factor, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—42no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3C5×#12011yescharacteristic
395C22×C3C5×#13511yescharacteristic
396C22×C3C5×#13711yescharacteristic
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—42no—
403C3×C4—41no—
404C3×C4—81no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—81no—
408C2×C5—81no—
409C2×C5C3×#45211yescharacteristic
410C2×C5C3×#45511yescharacteristic
411C2×C5C3×B(4,𝔽2)11yescharacteristic
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—41no—
417C23—41no—
418C23C2×C3×C5×D411yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—81no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—81no—
442C2×C4C2×C3×C5×D411yescharacteristic
443C2×C4C2×C3×C5×D411yescharacteristic
444C8—41no—
445C8—41no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—81no—
449C2×C3—81no—
450C2×C3C5×#45211yescharacteristic
451C2×C3C5×#45511yescharacteristic
452C2×C3C5×B(4,𝔽2)11yescharacteristic
453C5C3×#160611yescharacteristic, direct product factor, Sylow
454C22—21no—
455C22—21no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22C3×C5×#12011yescharacteristic
465C22C3×C5×#13511yescharacteristic
466C22C3×C5×#13711yescharacteristic
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—42no—
473C4—41no—
474C4—81no—
475C3C5×#160611yescharacteristic, direct product factor, Sylow
476C2—21no—
477C2—21no—
478C2—81no—
479C2—81no—
480C2C3×C5×#45211yescharacteristic
481C2C3×C5×#45511yescharacteristic
482C2C3×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC3×C5×#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#451C2semidirect
3. C3×C5×#448C2semidirect
4. C3×C5×#393C2semidirect
5. C3×C5×#328C2semidirect
6. C3×C5×#327C2semidirect
7. C3×C5×#323C2semidirect
8. C5×#1606C3direct (N × H)
28. C3×#1606C5direct (N × H)
30. C5×#451C2×C3semidirect
31. C5×#448C2×C3semidirect
32. C5×#393C2×C3semidirect
33. C5×#328C2×C3semidirect
34. C5×#327C2×C3semidirect
35. C5×#323C2×C3semidirect
68. C3×#451C2×C5semidirect
69. C3×#448C2×C5semidirect
70. C3×#393C2×C5semidirect
71. C3×#328C2×C5semidirect
72. C3×#327C2×C5semidirect
73. C3×#323C2×C5semidirect
93. #1606C3×C5direct (N × H)
179. #451C2×C3×C5semidirect
180. #448C2×C3×C5semidirect
181. #393C2×C3×C5semidirect
182. #328C2×C3×C5semidirect
183. #327C2×C3×C5semidirect
184. #323C2×C3×C5semidirect
383. C3×C5#1606direct (N × H)
453. C5C3×#1606direct (N × H)
475. C3C5×#1606direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5382
C3×C5×#4512
C3×C5×#4482
C3×C5×#3932
C3×C5×#3282
C3×C5×#3272
C3×C5×#3232
C5×#16063
C3×#16065