Finite Group Databasebeta

← C3×C5×#1603 #14274637

Subgroups — C3×C5×#1603 #14274637

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic
2C3×C5×#451C211yesmaximal, characteristic, complemented
3C3×C5×#448C211yesmaximal, characteristic
4C3×C5×#395C211yesmaximal, characteristic, complemented
5C3×C5×#328C211yesmaximal, characteristic, complemented
6C3×C5×#327C211yesmaximal, characteristic
7C3×C5×#324C211yesmaximal, characteristic, complemented
8C5×#1603C311yesmaximal, 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×#125—21no—
14C3×C5×#123—21no—
15C3×C5×#123—21no—
16C3×C5×C22⋊Q8—21no—
17C3×C5×C22⋊Q8C2211yescharacteristic
18C3×C5×#121C2211yescharacteristic
19C3×C4×C5×D4—21no—
20C2×C3×C5×C4⋊C4—21no—
21C2×C3×C5×C4⋊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×#1603C511yesmaximal, characteristic, direct product factor, Hall
29C5×#539C2×C311yescharacteristic
30C5×#451C2×C311yescharacteristic, complemented
31C5×#448C2×C311yescharacteristic
32C5×#395C2×C311yescharacteristic, complemented
33C5×#328C2×C311yescharacteristic, complemented
34C5×#327C2×C311yescharacteristic
35C5×#324C2×C311yescharacteristic, complemented
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—42no—
39C2×C3×C5×Q8D411yescharacteristic
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×C5D411yescharacteristic
47C22×C3×C4×C5C2311yescharacteristic
48C3×C5×Q16—42no—
49C3×C5×SD16—42no—
50C2×C3×C5×C8—21no—
51C2×C3×C5×C8—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—42no—
59C3×C5×C4⋊C4D411yescharacteristic
60C3×C5×C4⋊C4D411yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4—21no—
65C3×C5×C22⋊C4—21no—
66C3×C42×C5—21no—
67C3×#539C2×C511yescharacteristic
68C3×#451C2×C511yescharacteristic, complemented
69C3×#448C2×C511yescharacteristic
70C3×#395C2×C511yescharacteristic, complemented
71C3×#328C2×C511yescharacteristic, complemented
72C3×#327C2×C511yescharacteristic
73C3×#324C2×C511yescharacteristic, complemented
74C22×C5×Q8C22×C311yescharacteristic
75C2×C5×Q16—21no—
76C2×C5×SD16—21no—
77C5×#126—21no—
78C5×#125—21no—
79C5×#123—21no—
80C5×#123—21no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8C22×C311yescharacteristic
83C5×#121C22×C311yescharacteristic
84C4×C5×D4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C5×#103—21no—
88C5×#103—21no—
89C5×C22⋊C8C22×C311yescharacteristic
90C5×C22⋊C8C22×C311yescharacteristic
91C5×#95—21no—
92C5×#95C22×C311yescharacteristic
93#1603C3×C511yescharacteristic, direct product factor, Sylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—22no—
97C3×C5×Q8—22no—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C3×C5×Q8—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—22no—
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—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—81no—
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C3×C5×C8—41no—
123C3×C5×C8—41no—
124C22×C3×Q8C22×C511yescharacteristic
125C2×C3×Q16—21no—
126C2×C3×SD16—21no—
127C3×#126—21no—
128C3×#125—21no—
129C3×#123—21no—
130C3×#123—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8C22×C511yescharacteristic
133C3×#121C22×C511yescharacteristic
134C3×C4×D4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C22×C511yescharacteristic
137C3×#103—21no—
138C3×#103—21no—
139C3×C22⋊C8C22×C511yescharacteristic
140C3×C22⋊C8C22×C511yescharacteristic
141C3×#95—21no—
142C3×#95C22×C511yescharacteristic
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—42no—
146C2×C5×Q8C3×D411yescharacteristic
147C2×C5×D4—21no—
148C2×C5×D4C3×D411yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5C3×D411yescharacteristic
153C22×C4×C5C3×D411yescharacteristic
154C22×C4×C5C23×C311yescharacteristic
155C5×Q16—42no—
156C5×SD16—42no—
157C2×C5×C8—21no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—42no—
166C5×C4⋊C4C3×D411yescharacteristic
167C5×C4⋊C4C3×D411yescharacteristic
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C42×C5—21no—
174#539C2×C3×C511yescharacteristic
175#451C2×C3×C511yescharacteristic, complemented
176#448C2×C3×C511yescharacteristic
177#395C2×C3×C511yescharacteristic, complemented
178#328C2×C3×C511yescharacteristic, complemented
179#327C2×C3×C511yescharacteristic
180#324C2×C3×C511yescharacteristic, complemented
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#13511yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—42no—
192C3×C4×C5—41no—
193C3×C4×C5—41no—
194C3×C4×C5—41no—
195C3×C4×C5—42no—
196C3×C4×C5—41no—
197C3×C4×C5—41no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—42no—
201C2×C3×Q8C5×D411yescharacteristic
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×C4C5×D411yescharacteristic
209C22×C3×C4C23×C511yescharacteristic
210C3×Q16—42no—
211C3×SD16—42no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—42no—
221C3×C4⋊C4C5×D411yescharacteristic
222C3×C4⋊C4C5×D411yescharacteristic
223C3×C22⋊C4—21no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C42—21no—
229C23×C5—21no—
230C23×C5C2×C3×D411yescharacteristic
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—41no—
234C5×Q8—41no—
235C5×Q8—41no—
236C5×D4—41no—
237C5×D4—41no—
238C5×D4—41no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
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—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—81no—
255C2×C4×C5C2×C3×D411yescharacteristic
256C2×C4×C5C2×C3×D411yescharacteristic
257C5×C8—41no—
258C5×C8—41no—
259C22×Q8C22×C3×C511yescharacteristic
260C2×Q16—21no—
261C2×SD16—21no—
262#126—21no—
263#125—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8C22×C3×C511yescharacteristic
268#121C22×C3×C511yescharacteristic
269C4×D4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C22×C3×C511yescharacteristic
272#103—21no—
273#103—21no—
274C22⋊C8C22×C3×C511yescharacteristic
275C22⋊C8C22×C3×C511yescharacteristic
276#95—21no—
277#95C22×C3×C511yescharacteristic
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—81no—
281C2×C3×C5#45211yescharacteristic
282C2×C3×C5#45611yescharacteristic
283C2×C3×C5B(4,𝔽2)11yescharacteristic
284C23×C3—21no—
285C23×C3C2×C5×D411yescharacteristic
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—41no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—81no—
310C2×C3×C4C2×C5×D411yescharacteristic
311C2×C3×C4C2×C5×D411yescharacteristic
312C3×C8—41no—
313C3×C8—41no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—41no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5C3×#12011yescharacteristic
320C22×C5C3×#13511yescharacteristic
321C22×C5C3×#13711yescharacteristic
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—42no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—41no—
328C4×C5—42no—
329C4×C5—41no—
330C4×C5—41no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C2×Q8C3×C5×D411yescharacteristic
335C2×D4—21no—
336C2×D4C3×C5×D411yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4C3×C5×D411yescharacteristic
341C22×C4C3×C5×D411yescharacteristic
342C22×C4C23×C3×C511yescharacteristic
343Q16—42no—
344SD16—42no—
345C2×C8—21no—
346C2×C8—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—42no—
354C4⋊C4C3×C5×D411yescharacteristic
355C4⋊C4C3×C5×D411yescharacteristic
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C42—21no—
362C3×C5#160311yescharacteristic, direct product factor, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3C5×#12011yescharacteristic
369C22×C3C5×#13511yescharacteristic
370C22×C3C5×#13711yescharacteristic
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—42no—
378C3×C4—41no—
379C3×C4—41no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—81no—
383C2×C5C3×#45211yescharacteristic
384C2×C5C3×#45611yescharacteristic
385C2×C5C3×B(4,𝔽2)11yescharacteristic
386C23—21no—
387C23C2×C3×C5×D411yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—41no—
391Q8—41no—
392Q8—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4C2×C3×C5×D411yescharacteristic
413C2×C4C2×C3×C5×D411yescharacteristic
414C8—41no—
415C8—41no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—81no—
419C2×C3C5×#45211yescharacteristic
420C2×C3C5×#45611yescharacteristic
421C2×C3C5×B(4,𝔽2)11yescharacteristic
422C5C3×#160311yescharacteristic, direct product factor, Sylow
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22C3×C5×#12011yescharacteristic
429C22C3×C5×#13511yescharacteristic
430C22C3×C5×#13711yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—42no—
438C4—41no—
439C4—41no—
440C3C5×#160311yescharacteristic, direct product factor, Sylow
441C2—21no—
442C2—21no—
443C2—81no—
444C2C3×C5×#45211yescharacteristic
445C2C3×C5×#45611yescharacteristic
446C2C3×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC3×C5×#121C22
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
4. C3×C5×#395C2semidirect
5. C3×C5×#328C2semidirect
7. C3×C5×#324C2semidirect
8. C5×#1603C3direct (N × H)
28. C3×#1603C5direct (N × H)
30. C5×#451C2×C3semidirect
32. C5×#395C2×C3semidirect
33. C5×#328C2×C3semidirect
35. C5×#324C2×C3semidirect
68. C3×#451C2×C5semidirect
70. C3×#395C2×C5semidirect
71. C3×#328C2×C5semidirect
73. C3×#324C2×C5semidirect
93. #1603C3×C5direct (N × H)
175. #451C2×C3×C5semidirect
177. #395C2×C3×C5semidirect
178. #328C2×C3×C5semidirect
180. #324C2×C3×C5semidirect
362. C3×C5#1603direct (N × H)
422. C5C3×#1603direct (N × H)
440. C3C5×#1603direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5392
C3×C5×#4512
C3×C5×#4482
C3×C5×#3952
C3×C5×#3282
C3×C5×#3272
C3×C5×#3242
C5×#16033
C3×#16035