Finite Group Databasebeta

← C3×C5×#1618 #14274652

Subgroups — C3×C5×#1618 #14274652

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#538C211yesmaximal, characteristic
2C3×C5×#484C211yesmaximal, characteristic, complemented
3C3×C5×#481C211yesmaximal, characteristic, complemented
4C3×C5×#399C211yesmaximal, characteristic, complemented
5C3×C5×#328C211yesmaximal, characteristic, complemented
6C3×C5×#327C211yesmaximal, characteristic, complemented
7C3×C5×#323C211yesmaximal, characteristic, complemented
8C5×#1618C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#126—21no—
10C3×C5×#124—21no—
11C3×C5×#123—21no—
12C3×C5×C22⋊Q8C2211yescharacteristic
13C3×C5×#121—21no—
14C3×C5×#121C2211yescharacteristic
15C3×C5×#120—21no—
16C3×C4×C5×D4—21no—
17C2×C3×C5×C4⋊C4—21no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4—21no—
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C3×C5×#107—21no—
22C3×C5×#106—21no—
23C3×C5×#103—21no—
24C3×C5×#102—21no—
25C3×C5×C22⋊C8C2211yescharacteristic
26C3×C5×C22⋊C8C2211yescharacteristic
27C3×C5×#95C2211yescharacteristic
28C3×#1618C511yesmaximal, characteristic, direct product factor, Hall
29C5×#538C2×C311yescharacteristic
30C5×#484C2×C311yescharacteristic, complemented
31C5×#481C2×C311yescharacteristic, complemented
32C5×#399C2×C311yescharacteristic, complemented
33C5×#328C2×C311yescharacteristic, complemented
34C5×#327C2×C311yescharacteristic, complemented
35C5×#323C2×C311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—42no—
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
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—42no—
64C3×C42×C5—21no—
65C3×#538C2×C511yescharacteristic
66C3×#484C2×C511yescharacteristic, complemented
67C3×#481C2×C511yescharacteristic, complemented
68C3×#399C2×C511yescharacteristic, complemented
69C3×#328C2×C511yescharacteristic, complemented
70C3×#327C2×C511yescharacteristic, complemented
71C3×#323C2×C511yescharacteristic, complemented
72C5×#126—21no—
73C5×#124—21no—
74C5×#123—21no—
75C5×C22⋊Q8C22×C311yescharacteristic
76C5×#121—21no—
77C5×#121C22×C311yescharacteristic
78C5×#120—21no—
79C4×C5×D4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4C22×C311yescharacteristic
82C2×C5×C22⋊C4—21no—
83C2×C5×C22⋊C4C22×C311yescharacteristic
84C5×#107—21no—
85C5×#106—21no—
86C5×#103—21no—
87C5×#102—21no—
88C5×C22⋊C8C22×C311yescharacteristic
89C5×C22⋊C8C22×C311yescharacteristic
90C5×#95C22×C311yescharacteristic
91#1618C3×C511yescharacteristic, direct product factor, Sylow
92C23×C3×C5—21no—
93C23×C3×C5—21no—
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5C2×D411yescharacteristic
99C3×C5×Q8—41no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—81no—
104C3×C5×D4—81no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
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×C5—41no—
117C2×C3×C4×C5—81no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C3×C5×C8—41no—
121C3×C5×C8—41no—
122C3×#126—21no—
123C3×#124—21no—
124C3×#123—21no—
125C3×C22⋊Q8C22×C511yescharacteristic
126C3×#121—21no—
127C3×#121C22×C511yescharacteristic
128C3×#120—21no—
129C3×C4×D4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4C22×C511yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4C22×C511yescharacteristic
134C3×#107—21no—
135C3×#106—21no—
136C3×#103—21no—
137C3×#102—21no—
138C3×C22⋊C8C22×C511yescharacteristic
139C3×C22⋊C8C22×C511yescharacteristic
140C3×#95C22×C511yescharacteristic
141C24×C5C3×D411yescharacteristic
142C2×C5×Q8C3×D411yescharacteristic
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4C3×D411yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5C3×D411yescharacteristic
151C22×C4×C5C23×C311yescharacteristic
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—42no—
159C5×C4⋊C4C3×D411yescharacteristic
160C5×C4⋊C4C3×D411yescharacteristic
161C5×C22⋊C4—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4—21no—
167C5×C22⋊C4—21no—
168C5×C22⋊C4—42no—
169C42×C5—21no—
170#538C2×C3×C511yescharacteristic
171#484C2×C3×C511yescharacteristic, complemented
172#481C2×C3×C511yescharacteristic, complemented
173#399C2×C3×C511yescharacteristic, complemented
174#328C2×C3×C511yescharacteristic, complemented
175#327C2×C3×C511yescharacteristic, complemented
176#323C2×C3×C511yescharacteristic, complemented
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—42no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—81no—
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5#13511yescharacteristic
189C22×C3×C5#13711yescharacteristic
190C3×C4×C5—21no—
191C3×C4×C5—21no—
192C3×C4×C5—42no—
193C3×C4×C5—41no—
194C3×C4×C5—41no—
195C3×C4×C5—41no—
196C3×C4×C5—41no—
197C3×C4×C5—81no—
198C24×C3C5×D411yescharacteristic
199C2×C3×Q8C5×D411yescharacteristic
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4C5×D411yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4C5×D411yescharacteristic
208C22×C3×C4C23×C511yescharacteristic
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—42no—
216C3×C4⋊C4C5×D411yescharacteristic
217C3×C4⋊C4C5×D411yescharacteristic
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—21no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—42no—
226C3×C42—21no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—41no—
232C23×C5—41no—
233C23×C5C2×C3×D411yescharacteristic
234C5×Q8—41no—
235C5×D4—41no—
236C5×D4—41no—
237C5×D4—41no—
238C5×D4—81no—
239C5×D4—81no—
240C2×C4×C5—22no—
241C2×C4×C5—21no—
242C2×C4×C5—21no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—81no—
253C2×C4×C5C2×C3×D411yescharacteristic
254C2×C4×C5C2×C3×D411yescharacteristic
255C5×C8—41no—
256C5×C8—41no—
257#126—21no—
258#124—21no—
259#123—21no—
260C22⋊Q8C22×C3×C511yescharacteristic
261#121—21no—
262#121C22×C3×C511yescharacteristic
263#120—21no—
264C4×D4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C22×C3×C511yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4C22×C3×C511yescharacteristic
269#107—21no—
270#106—21no—
271#103—21no—
272#102—21no—
273C22⋊C8C22×C3×C511yescharacteristic
274C22⋊C8C22×C3×C511yescharacteristic
275#95C22×C3×C511yescharacteristic
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—81no—
279C2×C3×C5—81no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45311yescharacteristic
282C2×C3×C5#45811yescharacteristic
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3C2×C5×D411yescharacteristic
290C3×Q8—41no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—81no—
295C3×D4—81no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—81no—
309C2×C3×C4C2×C5×D411yescharacteristic
310C2×C3×C4C2×C5×D411yescharacteristic
311C3×C8—41no—
312C3×C8—41no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—42no—
316C22×C5—41no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5—41no—
320C22×C5—41no—
321C22×C5—41no—
322C22×C5—81no—
323C22×C5C3×#12011yescharacteristic
324C22×C5C3×#13511yescharacteristic
325C22×C5C3×#13711yescharacteristic
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—42no—
329C4×C5—41no—
330C4×C5—41no—
331C4×C5—41no—
332C4×C5—41no—
333C4×C5—81no—
334C24C3×C5×D411yescharacteristic
335C2×Q8C3×C5×D411yescharacteristic
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4C3×C5×D411yescharacteristic
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4C3×C5×D411yescharacteristic
344C22×C4C23×C3×C511yescharacteristic
345C2×C8—21no—
346C2×C8—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—42no—
352C4⋊C4C3×C5×D411yescharacteristic
353C4⋊C4C3×C5×D411yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—42no—
362C42—21no—
363C3×C5#161811yescharacteristic, direct product factor, Hall
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—42no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—81no—
374C22×C3C5×#12011yescharacteristic
375C22×C3C5×#13511yescharacteristic
376C22×C3C5×#13711yescharacteristic
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—42no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—81no—
385C2×C5—21no—
386C2×C5—21no—
387C2×C5—81no—
388C2×C5—81no—
389C2×C5C3×#45211yescharacteristic
390C2×C5C3×#45311yescharacteristic
391C2×C5C3×#45811yescharacteristic
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23C2×C3×C5×D411yescharacteristic
399Q8—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—81no—
404D4—81no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—81no—
418C2×C4C2×C3×C5×D411yescharacteristic
419C2×C4C2×C3×C5×D411yescharacteristic
420C8—41no—
421C8—41no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3C5×#45211yescharacteristic
427C2×C3C5×#45311yescharacteristic
428C2×C3C5×#45811yescharacteristic
429C5C3×#161811yescharacteristic, direct product factor, Sylow
430C22—21no—
431C22—21no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22C3×C5×#12011yescharacteristic
441C22C3×C5×#13511yescharacteristic
442C22C3×C5×#13711yescharacteristic
443C4—21no—
444C4—21no—
445C4—42no—
446C4—41no—
447C4—41no—
448C4—41no—
449C4—41no—
450C4—81no—
451C3C5×#161811yescharacteristic, direct product factor, Sylow
452C2—21no—
453C2—21no—
454C2—81no—
455C2—81no—
456C2C3×C5×#45211yescharacteristic
457C2C3×C5×#45311yescharacteristic
458C2C3×C5×#45811yescharacteristic
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×#484C2semidirect
3. C3×C5×#481C2semidirect
4. C3×C5×#399C2semidirect
5. C3×C5×#328C2semidirect
6. C3×C5×#327C2semidirect
7. C3×C5×#323C2semidirect
8. C5×#1618C3direct (N × H)
28. C3×#1618C5direct (N × H)
30. C5×#484C2×C3semidirect
31. C5×#481C2×C3semidirect
32. C5×#399C2×C3semidirect
33. C5×#328C2×C3semidirect
34. C5×#327C2×C3semidirect
35. C5×#323C2×C3semidirect
66. C3×#484C2×C5semidirect
67. C3×#481C2×C5semidirect
68. C3×#399C2×C5semidirect
69. C3×#328C2×C5semidirect
70. C3×#327C2×C5semidirect
71. C3×#323C2×C5semidirect
91. #1618C3×C5direct (N × H)
171. #484C2×C3×C5semidirect
172. #481C2×C3×C5semidirect
173. #399C2×C3×C5semidirect
174. #328C2×C3×C5semidirect
175. #327C2×C3×C5semidirect
176. #323C2×C3×C5semidirect
363. C3×C5#1618direct (N × H)
429. C5C3×#1618direct (N × H)
451. C3C5×#1618direct (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×#4842
C3×C5×#4812
C3×C5×#3992
C3×C5×#3282
C3×C5×#3272
C3×C5×#3232
C5×#16183
C3×#16185