Finite Group Databasebeta

← C3×C5×#1607 #14274641

Subgroups — C3×C5×#1607 #14274641

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#534C211yesmaximal, characteristic
2C3×C5×#480C212yesmaximal, complemented
3C3×C5×#397C211yesmaximal, characteristic, complemented
4C3×C5×#327C212yesmaximal, complemented
5C3×C5×#323C211yesmaximal, characteristic, complemented
6C5×#1607C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—21no—
8C3×C5×#123—22no—
9C3×C5×#121—21no—
10C3×C5×#121C2212yes—
11C3×C5×#120—22no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C3×C5×#107—22no—
16C3×C5×#102—22no—
17C3×C5×C22⋊C8C2212yescomplemented
18C3×C5×#95—21no—
19C3×C5×#95C2211yescharacteristic, complemented
20C3×#1607C511yesmaximal, characteristic, direct product factor, Hall
21C5×#534C2×C311yescharacteristic
22C5×#480C2×C312yescomplemented
23C5×#397C2×C311yescharacteristic, complemented
24C5×#327C2×C312yescomplemented
25C5×#323C2×C311yescharacteristic, complemented
26C24×C3×C5—21no—
27C24×C3×C5D411yescharacteristic
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—42no—
32C2×C3×C5×D4—42no—
33C2×C3×C5×D4D412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C5×C8—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4D412yes—
43C3×C5×C22⋊C4—22no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—42no—
47C3×#534C2×C511yescharacteristic
48C3×#480C2×C512yescomplemented
49C3×#397C2×C511yescharacteristic, complemented
50C3×#327C2×C512yescomplemented
51C3×#323C2×C511yescharacteristic, complemented
52C22×C5×D4—21no—
53C5×#123—22no—
54C5×#121—21no—
55C5×#121C22×C312yes—
56C5×#120—22no—
57C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4C22×C311yescharacteristic
60C5×#107—22no—
61C5×#102—22no—
62C5×C22⋊C8C22×C312yescomplemented
63C5×#95—21no—
64C5×#95C22×C311yescharacteristic, complemented
65#1607C3×C511yescharacteristic, direct product factor, Sylow
66C23×C3×C5—21no—
67C23×C3×C5—21no—
68C23×C3×C5—22no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5—42no—
72C23×C3×C5—81no—
73C23×C3×C5—81no—
74C23×C3×C5D812yes—
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×D4—42no—
77C3×C5×D4—44no—
78C3×C5×D4—42no—
79C3×C5×D4—42no—
80C3×C5×D4—81no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—42no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D412yes—
93C3×C5×C8—42no—
94C22×C3×D4—21no—
95C3×#123—22no—
96C3×#121—21no—
97C3×#121C22×C512yes—
98C3×#120—22no—
99C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4C22×C511yescharacteristic
102C3×#107—22no—
103C3×#102—22no—
104C3×C22⋊C8C22×C512yescomplemented
105C3×#95—21no—
106C3×#95C22×C511yescharacteristic, complemented
107C24×C5—21no—
108C24×C5C3×D411yescharacteristic
109C2×C5×D4—22no—
110C2×C5×D4—22no—
111C2×C5×D4—21no—
112C2×C5×D4—42no—
113C2×C5×D4—42no—
114C2×C5×D4C3×D412yes—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5C3×D411yescharacteristic
119C22×C4×C5C23×C311yescharacteristic
120C2×C5×C8—22no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4C3×D412yes—
124C5×C22⋊C4—22no—
125C5×C22⋊C4—22no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—42no—
128#534C2×C3×C511yescharacteristic
129#480C2×C3×C512yescomplemented
130#397C2×C3×C511yescharacteristic, complemented
131#327C2×C3×C512yescomplemented
132#323C2×C3×C511yescharacteristic, complemented
133C22×C3×C5—21no—
134C22×C3×C5—21no—
135C22×C3×C5—22no—
136C22×C3×C5—42no—
137C22×C3×C5—41no—
138C22×C3×C5—41no—
139C22×C3×C5—42no—
140C22×C3×C5—42no—
141C22×C3×C5—42no—
142C22×C3×C5—81no—
143C22×C3×C5—84no—
144C22×C3×C5#12011yescharacteristic
145C22×C3×C5C2×D811yescharacteristic
146C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
147C3×C4×C5—22no—
148C3×C4×C5—42no—
149C3×C4×C5—41no—
150C3×C4×C5—81no—
151C3×C4×C5—81no—
152C24×C3—21no—
153C24×C3C5×D411yescharacteristic
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—21no—
157C2×C3×D4—42no—
158C2×C3×D4—42no—
159C2×C3×D4C5×D412yes—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4C5×D411yescharacteristic
164C22×C3×C4C23×C511yescharacteristic
165C2×C3×C8—22no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4C5×D412yes—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—42no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—22no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—42no—
179C23×C5—81no—
180C23×C5—81no—
181C23×C5C3×D812yes—
182C23×C5C2×C3×D411yescharacteristic
183C5×D4—42no—
184C5×D4—44no—
185C5×D4—42no—
186C5×D4—42no—
187C5×D4—81no—
188C2×C4×C5—21no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5—42no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5C2×C3×D412yes—
200C5×C8—42no—
201C22×D4—21no—
202#123—22no—
203#121—21no—
204#121C22×C3×C512yes—
205#120—22no—
206C2×C4⋊C4C22×C3×C511yescharacteristic, complemented
207C2×C22⋊C4—21no—
208C2×C22⋊C4C22×C3×C511yescharacteristic
209#107—22no—
210#102—22no—
211C22⋊C8C22×C3×C512yescomplemented
212#95—21no—
213#95C22×C3×C511yescharacteristic, complemented
214C2×C3×C5—21no—
215C2×C3×C5—21no—
216C2×C3×C5—42no—
217C2×C3×C5—82no—
218C2×C3×C5#44711yescharacteristic
219C2×C3×C5#45511yescharacteristic
220C2×C3×C5#45811yescharacteristic
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—22no—
224C23×C3—41no—
225C23×C3—41no—
226C23×C3—42no—
227C23×C3—81no—
228C23×C3—81no—
229C23×C3C5×D812yes—
230C23×C3C2×C5×D411yescharacteristic
231C3×D4—42no—
232C3×D4—44no—
233C3×D4—42no—
234C3×D4—42no—
235C3×D4—81no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4—42no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4C2×C5×D412yes—
248C3×C8—42no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—22no—
252C22×C5—42no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—42no—
256C22×C5—42no—
257C22×C5—42no—
258C22×C5—81no—
259C22×C5—84no—
260C22×C5C3×#12011yescharacteristic
261C22×C5C2×C3×D811yescharacteristic
262C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
263C4×C5—22no—
264C4×C5—42no—
265C4×C5—41no—
266C4×C5—81no—
267C4×C5—81no—
268C24—21no—
269C24C3×C5×D411yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4C3×C5×D412yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4C3×C5×D411yescharacteristic
280C22×C4C23×C3×C511yescharacteristic
281C2×C8—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4C3×C5×D412yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C3×C5#160711yescharacteristic, direct product factor, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—42no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—81no—
300C22×C3—84no—
301C22×C3C5×#12011yescharacteristic
302C22×C3C2×C5×D811yescharacteristic
303C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
304C3×C4—22no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—81no—
308C3×C4—81no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—42no—
312C2×C5—82no—
313C2×C5C3×#44711yescharacteristic
314C2×C5C3×#45511yescharacteristic
315C2×C5C3×#45811yescharacteristic
316C23—21no—
317C23—21no—
318C23—22no—
319C23—41no—
320C23—41no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23C3×C5×D812yes—
325C23C2×C3×C5×D411yescharacteristic
326D4—42no—
327D4—44no—
328D4—42no—
329D4—42no—
330D4—81no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4C2×C3×C5×D412yes—
343C8—42no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—42no—
347C2×C3—82no—
348C2×C3C5×#44711yescharacteristic
349C2×C3C5×#45511yescharacteristic
350C2×C3C5×#45811yescharacteristic
351C5C3×#160711yescharacteristic, direct product factor, Sylow
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—81no—
362C22—84no—
363C22C3×C5×#12011yescharacteristic
364C22C2×C3×C5×D811yescharacteristic
365C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
366C4—22no—
367C4—41no—
368C4—42no—
369C4—81no—
370C4—81no—
371C3C5×#160711yescharacteristic, direct product factor, Sylow
372C2—21no—
373C2—21no—
374C2—42no—
375C2—82no—
376C2C3×C5×#44711yescharacteristic
377C2C3×C5×#45511yescharacteristic
378C2C3×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC3×C5×#534C2
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×#480C2semidirect
3. C3×C5×#397C2semidirect
4. C3×C5×#327C2semidirect
5. C3×C5×#323C2semidirect
6. C5×#1607C3direct (N × H)
12. C2×C3×C5×C4⋊C4C22semidirect
17. C3×C5×C22⋊C8C22semidirect
19. C3×C5×#95C22semidirect
20. C3×#1607C5direct (N × H)
22. C5×#480C2×C3semidirect
23. C5×#397C2×C3semidirect
24. C5×#327C2×C3semidirect
25. C5×#323C2×C3semidirect
48. C3×#480C2×C5semidirect
49. C3×#397C2×C5semidirect
50. C3×#327C2×C5semidirect
51. C3×#323C2×C5semidirect
57. C2×C5×C4⋊C4C22×C3semidirect
62. C5×C22⋊C8C22×C3semidirect
64. C5×#95C22×C3semidirect
65. #1607C3×C5direct (N × H)
99. C2×C3×C4⋊C4C22×C5semidirect
104. C3×C22⋊C8C22×C5semidirect
106. C3×#95C22×C5semidirect
129. #480C2×C3×C5semidirect
130. #397C2×C3×C5semidirect
131. #327C2×C3×C5semidirect
132. #323C2×C3×C5semidirect
206. C2×C4⋊C4C22×C3×C5semidirect
211. C22⋊C8C22×C3×C5semidirect
213. #95C22×C3×C5semidirect
289. C3×C5#1607direct (N × H)
351. C5C3×#1607direct (N × H)
371. C3C5×#1607direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5342
C3×C5×#4802
C3×C5×#3972
C3×C5×#3272
C3×C5×#3232
C5×#16073
C3×#16075