Finite Group Databasebeta

← C3×C5×#1646 #14274680

Subgroups — C3×C5×#1646 #14274680

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#555C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3C3×C5×#474C211yesmaximal, characteristic, complemented
4C3×C5×#461C211yesmaximal, characteristic, complemented
5C3×C5×#333C211yesmaximal, characteristic, complemented
6C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
7C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
8C5×#1646C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#124—22no—
13C3×C5×#121—21no—
14C3×C5×#121—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C3×C4×C5×D4C2211yescharacteristic
17C3×C5×#117—21no—
18C3×C5×#117—21no—
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#103—22no—
23C3×C5×#103—21no—
24C3×C5×#102—21no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1646C511yesmaximal, characteristic, direct product factor, Hall
27C5×#555C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic, complemented
29C5×#474C2×C311yescharacteristic, complemented
30C5×#461C2×C311yescharacteristic, complemented
31C5×#333C2×C311yescharacteristic, complemented
32C5×D4⋊C8C2×C311yescharacteristic, complemented
33C5×D4⋊C8C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D412yes—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4D411yescharacteristic
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C3×C5×SD16—42no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—22no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—22no—
56C3×C42×C5C2311yescharacteristic
57C3×#555C2×C511yescharacteristic
58C3×#487C2×C511yescharacteristic, complemented
59C3×#474C2×C511yescharacteristic, complemented
60C3×#461C2×C511yescharacteristic, complemented
61C3×#333C2×C511yescharacteristic, complemented
62C3×D4⋊C8C2×C511yescharacteristic, complemented
63C3×D4⋊C8C2×C511yescharacteristic, complemented
64C2×C5×SD16—21no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×C4⋊Q8C22×C311yescharacteristic
67C5×#124—22no—
68C5×#121—21no—
69C5×#121—21no—
70C4×C5×D4C22×C311yescharacteristic
71C4×C5×D4C22×C311yescharacteristic
72C5×#117—21no—
73C5×#117—21no—
74C5×#107—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×C4⋊C8C22×C311yescharacteristic
77C5×#103—22no—
78C5×#103—21no—
79C5×#102—21no—
80C4×C5×C8C22×C311yescharacteristic
81#1646C3×C511yescharacteristic, direct product factor, Sylow
82C23×C3×C5—21no—
83C23×C3×C5—21no—
84C3×C5×Q8—42no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
91C3×C5×D4—82no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3×C5×C8—41no—
106C2×C3×SD16—21no—
107C3×C4⋊Q8C22×C511yescharacteristic
108C3×C4⋊Q8C22×C511yescharacteristic
109C3×#124—22no—
110C3×#121—21no—
111C3×#121—21no—
112C3×C4×D4C22×C511yescharacteristic
113C3×C4×D4C22×C511yescharacteristic
114C3×#117—21no—
115C3×#117—21no—
116C3×#107—21no—
117C3×C4⋊C8C22×C511yescharacteristic
118C3×C4⋊C8C22×C511yescharacteristic
119C3×#103—22no—
120C3×#103—21no—
121C3×#102—21no—
122C3×C4×C8C22×C511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×Q8C3×D412yes—
125C2×C5×D4—22no—
126C2×C5×D4C3×D411yescharacteristic
127C2×C5×D4C3×D411yescharacteristic
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C5×SD16—42no—
131C2×C5×C8—21no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4C3×D411yescharacteristic
139C5×C4⋊C4C3×D411yescharacteristic
140C5×C22⋊C4—22no—
141C5×C22⋊C4—22no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5—22no—
145C42×C5C23×C311yescharacteristic
146#555C2×C3×C511yescharacteristic
147#487C2×C3×C511yescharacteristic, complemented
148#474C2×C3×C511yescharacteristic, complemented
149#461C2×C3×C511yescharacteristic, complemented
150#333C2×C3×C511yescharacteristic, complemented
151D4⋊C8C2×C3×C511yescharacteristic, complemented
152D4⋊C8C2×C3×C511yescharacteristic, complemented
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5—41no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×C4×C5—42no—
164C3×C4×C5—81no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169C2×C3×Q8—21no—
170C2×C3×Q8C5×D412yes—
171C2×C3×D4—22no—
172C2×C3×D4C5×D411yescharacteristic
173C2×C3×D4C5×D411yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C3×SD16—42no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C5×D411yescharacteristic
185C3×C4⋊C4C5×D411yescharacteristic
186C3×C22⋊C4—22no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C42—22no—
191C3×C42C23×C511yescharacteristic
192C23×C5—21no—
193C23×C5—21no—
194C5×Q8—42no—
195C5×Q8—41no—
196C5×Q8—41no—
197C5×D4—21no—
198C5×D4—21no—
199C5×D4—21no—
200C5×D4—21no—
201C5×D4—82no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5C2×C3×D411yescharacteristic
211C2×C4×C5C2×C3×D411yescharacteristic
212C2×C4×C5C2×C3×D411yescharacteristic
213C5×C8—41no—
214C5×C8—41no—
215C5×C8—41no—
216C2×SD16—21no—
217C4⋊Q8C22×C3×C511yescharacteristic
218C4⋊Q8C22×C3×C511yescharacteristic
219#124—22no—
220#121—21no—
221#121—21no—
222C4×D4C22×C3×C511yescharacteristic
223C4×D4C22×C3×C511yescharacteristic
224#117—21no—
225#117—21no—
226#107—21no—
227C4⋊C8C22×C3×C511yescharacteristic
228C4⋊C8C22×C3×C511yescharacteristic
229#103—22no—
230#103—21no—
231#102—21no—
232C4×C8C22×C3×C511yescharacteristic
233C2×C3×C5—81no—
234C2×C3×C5—81no—
235C2×C3×C5#44911yescharacteristic
236C2×C3×C5#45211yescharacteristic
237C2×C3×C5#45511yescharacteristic
238C23×C3—21no—
239C23×C3—21no—
240C3×Q8—42no—
241C3×Q8—41no—
242C3×Q8—41no—
243C3×D4—21no—
244C3×D4—21no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—82no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—22no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4C2×C5×D411yescharacteristic
257C2×C3×C4C2×C5×D411yescharacteristic
258C2×C3×C4C2×C5×D411yescharacteristic
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5C3×#12011yescharacteristic
269C4×C5—21no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5—42no—
273C4×C5—81no—
274C4×C5C3×#13511yescharacteristic
275C4×C5C3×#13511yescharacteristic
276C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
277C4×C5C3×#13711yescharacteristic
278C2×Q8—21no—
279C2×Q8C3×C5×D412yes—
280C2×D4—22no—
281C2×D4C3×C5×D411yescharacteristic
282C2×D4C3×C5×D411yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285SD16—42no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C3×C5×D411yescharacteristic
294C4⋊C4C3×C5×D411yescharacteristic
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C42—22no—
300C42C23×C3×C511yescharacteristic
301C3×C5#164611yescharacteristic, direct product factor, Hall
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3C5×#12011yescharacteristic
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—81no—
314C3×C4C5×#13511yescharacteristic
315C3×C4C5×#13511yescharacteristic
316C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
317C3×C4C5×#13711yescharacteristic
318C2×C5—81no—
319C2×C5—81no—
320C2×C5C3×#44911yescharacteristic
321C2×C5C3×#45211yescharacteristic
322C2×C5C3×#45511yescharacteristic
323C23—21no—
324C23—21no—
325Q8—42no—
326Q8—41no—
327Q8—41no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—82no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4C2×C3×C5×D411yescharacteristic
342C2×C4C2×C3×C5×D411yescharacteristic
343C2×C4C2×C3×C5×D411yescharacteristic
344C8—41no—
345C8—41no—
346C8—41no—
347C2×C3—81no—
348C2×C3—81no—
349C2×C3C5×#44911yescharacteristic
350C2×C3C5×#45211yescharacteristic
351C2×C3C5×#45511yescharacteristic
352C5C3×#164611yescharacteristic, direct product factor, Sylow
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C3×C5×#12011yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—42no—
364C4—81no—
365C4C3×C5×#13511yescharacteristic
366C4C3×C5×#13511yescharacteristic
367C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
368C4C3×C5×#13711yescharacteristic
369C3C5×#164611yescharacteristic, direct product factor, Sylow
370C2—81no—
371C2—81no—
372C2C3×C5×#44911yescharacteristic
373C2C3×C5×#45211yescharacteristic
374C2C3×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#555C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#487C2semidirect
3. C3×C5×#474C2semidirect
4. C3×C5×#461C2semidirect
5. C3×C5×#333C2semidirect
6. C3×C5×D4⋊C8C2semidirect
7. C3×C5×D4⋊C8C2semidirect
8. C5×#1646C3direct (N × H)
26. C3×#1646C5direct (N × H)
28. C5×#487C2×C3semidirect
29. C5×#474C2×C3semidirect
30. C5×#461C2×C3semidirect
31. C5×#333C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. C5×D4⋊C8C2×C3semidirect
58. C3×#487C2×C5semidirect
59. C3×#474C2×C5semidirect
60. C3×#461C2×C5semidirect
61. C3×#333C2×C5semidirect
62. C3×D4⋊C8C2×C5semidirect
63. C3×D4⋊C8C2×C5semidirect
81. #1646C3×C5direct (N × H)
147. #487C2×C3×C5semidirect
148. #474C2×C3×C5semidirect
149. #461C2×C3×C5semidirect
150. #333C2×C3×C5semidirect
151. D4⋊C8C2×C3×C5semidirect
152. D4⋊C8C2×C3×C5semidirect
301. C3×C5#1646direct (N × H)
352. C5C3×#1646direct (N × H)
369. C3C5×#1646direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5552
C3×C5×#4872
C3×C5×#4742
C3×C5×#4612
C3×C5×#3332
C3×C5×D4⋊C82
C5×#16463
C3×#16465