Finite Group Databasebeta

← C3×C5×#1599 #14274633

Subgroups — C3×C5×#1599 #14274633

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#544C211yesmaximal, characteristic, complemented
2C3×C5×#450C212yesmaximal
3C3×C5×#394C211yesmaximal, characteristic
4C3×C5×#328C212yesmaximal, complemented
5C3×C5×#324C211yesmaximal, characteristic, complemented
6C5×#1599C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×C5×SD16—22no—
9C3×C5×C4⋊Q8—22no—
10C3×C5×#125—22no—
11C3×C5×C22⋊Q8—21no—
12C3×C5×C22⋊Q8C2212yes—
13C3×C5×#117—21no—
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C22⋊C4—21no—
16C2×C3×C5×C22⋊C4—21no—
17C3×C5×#102—22no—
18C3×C5×C22⋊C8C2212yes—
19C3×C5×#95C2211yescharacteristic
20C3×#1599C511yesmaximal, characteristic, direct product factor, Hall
21C5×#544C2×C311yescharacteristic, complemented
22C5×#450C2×C312yes—
23C5×#394C2×C311yescharacteristic
24C5×#328C2×C312yescomplemented
25C5×#324C2×C311yescharacteristic, complemented
26C24×C3×C5—21no—
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—42no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C3×C5×SD16—44no—
36C2×C3×C5×C8—22no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4D412yes—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—42no—
46C3×C5×C22⋊C4—42no—
47C3×C42×C5—22no—
48C3×#544C2×C511yescharacteristic, complemented
49C3×#450C2×C512yes—
50C3×#394C2×C511yescharacteristic
51C3×#328C2×C512yescomplemented
52C3×#324C2×C511yescharacteristic, complemented
53C22×C5×D4C22×C311yescharacteristic
54C2×C5×SD16—22no—
55C5×C4⋊Q8—22no—
56C5×#125—22no—
57C5×C22⋊Q8—21no—
58C5×C22⋊Q8C22×C312yes—
59C5×#117—21no—
60C2×C5×C4⋊C4C22×C311yescharacteristic
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C5×#102—22no—
64C5×C22⋊C8C22×C312yes—
65C5×#95C22×C311yescharacteristic
66#1599C3×C511yescharacteristic, direct product factor, Sylow
67C23×C3×C5—22no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5C2×D411yescharacteristic
75C3×C5×Q8—42no—
76C3×C5×Q8—81no—
77C3×C5×D4—24no—
78C3×C5×D4—42no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5SD1612yescomplemented
90C2×C3×C4×C5C2×D412yes—
91C3×C5×C8—42no—
92C22×C3×D4C22×C511yescharacteristic
93C2×C3×SD16—22no—
94C3×C4⋊Q8—22no—
95C3×#125—22no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8C22×C512yes—
98C3×#117—21no—
99C2×C3×C4⋊C4C22×C511yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C3×#102—22no—
103C3×C22⋊C8C22×C512yes—
104C3×#95C22×C511yescharacteristic
105C24×C5—21no—
106C2×C5×Q8—21no—
107C2×C5×Q8C3×D412yes—
108C2×C5×D4—22no—
109C2×C5×D4—42no—
110C22×C4×C5—21no—
111C22×C4×C5C3×D411yescharacteristic
112C22×C4×C5C3×D411yescharacteristic
113C22×C4×C5C23×C311yescharacteristic
114C5×SD16—44no—
115C2×C5×C8—22no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4—22no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4C3×D412yes—
123C5×C22⋊C4—22no—
124C5×C22⋊C4—42no—
125C5×C22⋊C4—42no—
126C42×C5—22no—
127#544C2×C3×C511yescharacteristic, complemented
128#450C2×C3×C512yes—
129#394C2×C3×C511yescharacteristic
130#328C2×C3×C512yescomplemented
131#324C2×C3×C511yescharacteristic, complemented
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—42no—
137C22×C3×C5—81no—
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12011yescharacteristic
142C22×C3×C5C2×SD1611yescharacteristic
143C22×C3×C5#13711yescharacteristic
144C3×C4×C5—22no—
145C3×C4×C5—22no—
146C3×C4×C5—42no—
147C3×C4×C5—41no—
148C3×C4×C5—42no—
149C3×C4×C5—81no—
150C24×C3—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8C5×D412yes—
153C2×C3×D4—22no—
154C2×C3×D4—42no—
155C22×C3×C4—21no—
156C22×C3×C4C5×D411yescharacteristic
157C22×C3×C4C5×D411yescharacteristic
158C22×C3×C4C23×C511yescharacteristic
159C3×SD16—44no—
160C2×C3×C8—22no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4C5×D412yes—
168C3×C22⋊C4—22no—
169C3×C22⋊C4—42no—
170C3×C22⋊C4—42no—
171C3×C42—22no—
172C23×C5—22no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5C2×C3×D411yescharacteristic
180C5×Q8—42no—
181C5×Q8—81no—
182C5×D4—24no—
183C5×D4—42no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—21no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5C3×SD1612yescomplemented
195C2×C4×C5C2×C3×D412yes—
196C5×C8—42no—
197C22×D4C22×C3×C511yescharacteristic
198C2×SD16—22no—
199C4⋊Q8—22no—
200#125—22no—
201C22⋊Q8—21no—
202C22⋊Q8C22×C3×C512yes—
203#117—21no—
204C2×C4⋊C4C22×C3×C511yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207#102—22no—
208C22⋊C8C22×C3×C512yes—
209#95C22×C3×C511yescharacteristic
210C2×C3×C5—21no—
211C2×C3×C5—21no—
212C2×C3×C5—82no—
213C2×C3×C5#44811yescharacteristic
214C2×C3×C5#45411yescharacteristic
215C2×C3×C5B(4,𝔽2)11yescharacteristic
216C23×C3—22no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3C2×C5×D411yescharacteristic
224C3×Q8—42no—
225C3×Q8—81no—
226C3×D4—24no—
227C3×D4—42no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4C5×SD1612yescomplemented
239C2×C3×C4C2×C5×D412yes—
240C3×C8—42no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5—42no—
246C22×C5—81no—
247C22×C5—81no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5C3×#12011yescharacteristic
251C22×C5C2×C3×SD1611yescharacteristic
252C22×C5C3×#13711yescharacteristic
253C4×C5—22no—
254C4×C5—22no—
255C4×C5—42no—
256C4×C5—41no—
257C4×C5—42no—
258C4×C5—81no—
259C24—21no—
260C2×Q8—21no—
261C2×Q8C3×C5×D412yes—
262C2×D4—22no—
263C2×D4—42no—
264C22×C4—21no—
265C22×C4C3×C5×D411yescharacteristic
266C22×C4C3×C5×D411yescharacteristic
267C22×C4C23×C3×C511yescharacteristic
268SD16—44no—
269C2×C8—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4C3×C5×D412yes—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C42—22no—
281C3×C5#159911yescharacteristic, direct product factor, Hall
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—81no—
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3C5×#12011yescharacteristic
292C22×C3C2×C5×SD1611yescharacteristic
293C22×C3C5×#13711yescharacteristic
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—42no—
299C3×C4—81no—
300C2×C5—21no—
301C2×C5—21no—
302C2×C5—82no—
303C2×C5C3×#44811yescharacteristic
304C2×C5C3×#45411yescharacteristic
305C2×C5C3×B(4,𝔽2)11yescharacteristic
306C23—22no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C2×C3×C5×D411yescharacteristic
314Q8—42no—
315Q8—81no—
316D4—24no—
317D4—42no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4C3×C5×SD1612yescomplemented
329C2×C4C2×C3×C5×D412yes—
330C8—42no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—82no—
334C2×C3C5×#44811yescharacteristic
335C2×C3C5×#45411yescharacteristic
336C2×C3C5×B(4,𝔽2)11yescharacteristic
337C5C3×#159911yescharacteristic, direct product factor, Sylow
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22C3×C5×#12011yescharacteristic
348C22C2×C3×C5×SD1611yescharacteristic
349C22C3×C5×#13711yescharacteristic
350C4—22no—
351C4—22no—
352C4—42no—
353C4—41no—
354C4—42no—
355C4—81no—
356C3C5×#159911yescharacteristic, direct product factor, Sylow
357C2—21no—
358C2—21no—
359C2—82no—
360C2C3×C5×#44811yescharacteristic
361C2C3×C5×#45411yescharacteristic
362C2C3×C5×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
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
1. C3×C5×#544C2semidirect
4. C3×C5×#328C2semidirect
5. C3×C5×#324C2semidirect
6. C5×#1599C3direct (N × H)
20. C3×#1599C5direct (N × H)
21. C5×#544C2×C3semidirect
24. C5×#328C2×C3semidirect
25. C5×#324C2×C3semidirect
48. C3×#544C2×C5semidirect
51. C3×#328C2×C5semidirect
52. C3×#324C2×C5semidirect
66. #1599C3×C5direct (N × H)
89. C2×C3×C4×C5SD16semidirect
127. #544C2×C3×C5semidirect
130. #328C2×C3×C5semidirect
131. #324C2×C3×C5semidirect
194. C2×C4×C5C3×SD16semidirect
238. C2×C3×C4C5×SD16semidirect
281. C3×C5#1599direct (N × H)
328. C2×C4C3×C5×SD16semidirect
337. C5C3×#1599direct (N × H)
356. C3C5×#1599direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5442
C3×C5×#4502
C3×C5×#3942
C3×C5×#3282
C3×C5×#3242
C5×#15993
C3×#15995