Finite Group Databasebeta

← C3×C5×#1959 #14274993

Subgroups — C3×C5×#1959 #14274993

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#124C211yesmaximal, characteristic
2C2×C3×C5×#103C212yesmaximal, complemented
3C2×C3×C5×#102C212yesmaximal
4C2×C3×C5×#97C211yesmaximal, characteristic, complemented
5C3×C5×#384C211yesmaximal, characteristic, complemented
6C5×#1959C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C3×C5×D4C2211yescharacteristic
9C22×C3×C5×C8C2212yes—
10C3×C5×#124—22no—
11C3×C5×#124C414yescomplemented
12C2×C3×C5×C4⋊C4—22no—
13C2×C3×C5×C4⋊C4C2212yes—
14C2×C3×C5×C22⋊C4—22no—
15C2×C3×C42×C5C2211yescharacteristic
16C3×C5×#103—24no—
17C3×C5×#102—24no—
18C3×C5×#97—22no—
19C3×#1959C511yesmaximal, characteristic, direct product factor, Hall
20C2×C5×#124C2×C311yescharacteristic
21C2×C5×#103C2×C312yescomplemented
22C2×C5×#102C2×C312yes—
23C2×C5×#97C2×C311yescharacteristic, complemented
24C5×#384C2×C311yescharacteristic, complemented
25C24×C3×C5—21no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8—22no—
28C2×C3×C5×Q8—22no—
29C2×C3×C5×Q8C2×C412yes—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5D412yes—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C5×C8—22no—
39C2×C3×C5×C8—22no—
40C2×C3×C5×C8D414yes—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—44no—
44C3×C5×C22⋊C4—28no—
45C3×C42×C5C2×C412yes—
46C3×C42×C5D412yes—
47C2×C3×#124C2×C511yescharacteristic
48C2×C3×#103C2×C512yescomplemented
49C2×C3×#102C2×C512yes—
50C2×C3×#97C2×C511yescharacteristic, complemented
51C3×#384C2×C511yescharacteristic, complemented
52C22×C5×Q8C22×C311yescharacteristic
53C22×C5×D4C22×C311yescharacteristic
54C22×C5×C8C22×C312yes—
55C5×#124—22no—
56C5×#124C3×C414yescomplemented
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4C22×C312yes—
59C2×C5×C22⋊C4—22no—
60C2×C42×C5C22×C311yescharacteristic
61C5×#103—24no—
62C5×#102—24no—
63C5×#97—22no—
64#1959C3×C511yescharacteristic, direct product factor, Sylow
65C23×C3×C5—22no—
66C23×C3×C5—41no—
67C23×C3×C5—41no—
68C23×C3×C5—42no—
69C23×C3×C5—42no—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×Q8—24no—
72C3×C5×Q8—42no—
73C3×C5×D4—24no—
74C3×C5×D4—42no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—42no—
81C2×C3×C4×C5—44no—
82C2×C3×C4×C5C22⋊C414yes—
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D412yes—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4112yes—
87C3×C5×C8—24no—
88C22×C3×Q8C22×C511yescharacteristic
89C22×C3×D4C22×C511yescharacteristic
90C22×C3×C8C22×C512yes—
91C3×#124—22no—
92C3×#124C4×C514yescomplemented
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4C22×C512yes—
95C2×C3×C22⋊C4—22no—
96C2×C3×C42C22×C511yescharacteristic
97C3×#103—24no—
98C3×#102—24no—
99C3×#97—22no—
100C24×C5—21no—
101C2×C5×Q8—21no—
102C2×C5×Q8—22no—
103C2×C5×Q8—22no—
104C2×C5×Q8C2×C3×C412yes—
105C2×C5×D4—22no—
106C2×C5×D4—21no—
107C2×C5×D4—22no—
108C2×C5×D4C2×C3×C412yes—
109C22×C4×C5—21no—
110C22×C4×C5—22no—
111C22×C4×C5C3×D412yes—
112C22×C4×C5C23×C311yescharacteristic
113C2×C5×C8—22no—
114C2×C5×C8—22no—
115C2×C5×C8C3×D414yes—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—44no—
119C5×C22⋊C4—28no—
120C42×C5C2×C3×C412yes—
121C42×C5C3×D412yes—
122C2×#124C2×C3×C511yescharacteristic
123C2×#103C2×C3×C512yescomplemented
124C2×#102C2×C3×C512yes—
125C2×#97C2×C3×C511yescharacteristic, complemented
126#384C2×C3×C511yescharacteristic, complemented
127C22×C3×C5—42no—
128C22×C3×C5—44no—
129C22×C3×C5—82no—
130C22×C3×C5—81no—
131C22×C3×C5—81no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12411yescharacteristic
134C22×C3×C5#12711yescharacteristic
135C22×C3×C5AGL(1,ℤ/8)12yes—
136C22×C3×C5#13712yes—
137C3×C4×C5—24no—
138C3×C4×C5—42no—
139C3×C4×C5—82no—
140C3×C4×C5C4×D412yes—
141C3×C4×C5#12112yes—
142C24×C3—21no—
143C2×C3×Q8—21no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8C2×C4×C512yes—
147C2×C3×D4—22no—
148C2×C3×D4—21no—
149C2×C3×D4—22no—
150C2×C3×D4C2×C4×C512yes—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4C5×D412yes—
154C22×C3×C4C23×C511yescharacteristic
155C2×C3×C8—22no—
156C2×C3×C8—22no—
157C2×C3×C8C5×D414yes—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—44no—
161C3×C22⋊C4—28no—
162C3×C42C2×C4×C512yes—
163C3×C42C5×D412yes—
164C23×C5—22no—
165C23×C5—41no—
166C23×C5—41no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5C2×C3×D411yescharacteristic
170C5×Q8—24no—
171C5×Q8—42no—
172C5×D4—24no—
173C5×D4—42no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—44no—
181C2×C4×C5C3×C22⋊C414yes—
182C2×C4×C5C22×C3×C411yescharacteristic
183C2×C4×C5C2×C3×D412yes—
184C2×C4×C5C2×C3×D411yescharacteristic
185C2×C4×C5C3×#4112yes—
186C5×C8—24no—
187C22×Q8C22×C3×C511yescharacteristic
188C22×D4C22×C3×C511yescharacteristic
189C22×C8C22×C3×C512yes—
190#124—22no—
191#124C3×C4×C514yescomplemented
192C2×C4⋊C4—22no—
193C2×C4⋊C4C22×C3×C512yes—
194C2×C22⋊C4—22no—
195C2×C42C22×C3×C511yescharacteristic
196#103—24no—
197#102—24no—
198#97—22no—
199C2×C3×C5—82no—
200C2×C3×C5#39011yescharacteristic
201C2×C3×C5#41712yes—
202C2×C3×C5#48912yes—
203C2×C3×C5#49611yescharacteristic
204C2×C3×C5#49711yescharacteristic
205C23×C3—22no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3C2×C5×D411yescharacteristic
211C3×Q8—24no—
212C3×Q8—42no—
213C3×D4—24no—
214C3×D4—42no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—42no—
221C2×C3×C4—44no—
222C2×C3×C4C5×C22⋊C414yes—
223C2×C3×C4C22×C4×C511yescharacteristic
224C2×C3×C4C2×C5×D412yes—
225C2×C3×C4C2×C5×D411yescharacteristic
226C2×C3×C4C5×#4112yes—
227C3×C8—24no—
228C22×C5—42no—
229C22×C5—44no—
230C22×C5—82no—
231C22×C5—81no—
232C22×C5—81no—
233C22×C5C2×C3×C22⋊C411yescharacteristic
234C22×C5C3×#12411yescharacteristic
235C22×C5C3×#12711yescharacteristic
236C22×C5C3×AGL(1,ℤ/8)12yes—
237C22×C5C3×#13712yes—
238C4×C5—24no—
239C4×C5—42no—
240C4×C5—82no—
241C4×C5C3×C4×D412yes—
242C4×C5C3×#12112yes—
243C24—21no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8C2×C3×C4×C512yes—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—22no—
251C2×D4C2×C3×C4×C512yes—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4C3×C5×D412yes—
255C22×C4C23×C3×C511yescharacteristic
256C2×C8—22no—
257C2×C8—22no—
258C2×C8C3×C5×D414yes—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—44no—
262C22⋊C4—28no—
263C42C2×C3×C4×C512yes—
264C42C3×C5×D412yes—
265C3×C5#195911yescharacteristic, direct product factor, Hall
266C22×C3—42no—
267C22×C3—44no—
268C22×C3—82no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3C2×C5×C22⋊C411yescharacteristic
272C22×C3C5×#12411yescharacteristic
273C22×C3C5×#12711yescharacteristic
274C22×C3C5×AGL(1,ℤ/8)12yes—
275C22×C3C5×#13712yes—
276C3×C4—24no—
277C3×C4—42no—
278C3×C4—82no—
279C3×C4C4×C5×D412yes—
280C3×C4C5×#12112yes—
281C2×C5—82no—
282C2×C5C3×#39011yescharacteristic
283C2×C5C3×#41712yes—
284C2×C5C3×#48912yes—
285C2×C5C3×#49611yescharacteristic
286C2×C5C3×#49711yescharacteristic
287C23—22no—
288C23—41no—
289C23—41no—
290C23—42no—
291C23—42no—
292C23C2×C3×C5×D411yescharacteristic
293Q8—24no—
294Q8—42no—
295D4—24no—
296D4—42no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4C3×C5×C22⋊C414yes—
305C2×C4C22×C3×C4×C511yescharacteristic
306C2×C4C2×C3×C5×D412yes—
307C2×C4C2×C3×C5×D411yescharacteristic
308C2×C4C3×C5×#4112yes—
309C8—24no—
310C2×C3—82no—
311C2×C3C5×#39011yescharacteristic
312C2×C3C5×#41712yes—
313C2×C3C5×#48912yes—
314C2×C3C5×#49611yescharacteristic
315C2×C3C5×#49711yescharacteristic
316C5C3×#195911yescharacteristic, direct product factor, Sylow
317C22—42no—
318C22—44no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22C2×C3×C5×C22⋊C411yescharacteristic
323C22C3×C5×#12411yescharacteristic
324C22C3×C5×#12711yescharacteristic
325C22C3×C5×AGL(1,ℤ/8)12yes—
326C22C3×C5×#13712yes—
327C4—24no—
328C4—42no—
329C4—82no—
330C4C3×C4×C5×D412yes—
331C4C3×C5×#12112yes—
332C3C5×#195911yescharacteristic, direct product factor, Sylow
333C2—82no—
334C2C3×C5×#39011yescharacteristic
335C2C3×C5×#41712yes—
336C2C3×C5×#48912yes—
337C2C3×C5×#49611yescharacteristic
338C2C3×C5×#49711yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#103C2semidirect
4. C2×C3×C5×#97C2semidirect
5. C3×C5×#384C2semidirect
6. C5×#1959C3direct (N × H)
11. C3×C5×#124C4semidirect
19. C3×#1959C5direct (N × H)
21. C2×C5×#103C2×C3semidirect
23. C2×C5×#97C2×C3semidirect
24. C5×#384C2×C3semidirect
48. C2×C3×#103C2×C5semidirect
50. C2×C3×#97C2×C5semidirect
51. C3×#384C2×C5semidirect
56. C5×#124C3×C4semidirect
64. #1959C3×C5direct (N × H)
92. C3×#124C4×C5semidirect
123. C2×#103C2×C3×C5semidirect
125. C2×#97C2×C3×C5semidirect
126. #384C2×C3×C5semidirect
191. #124C3×C4×C5semidirect
265. C3×C5#1959direct (N × H)
316. C5C3×#1959direct (N × H)
332. C3C5×#1959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1242
C2×C3×C5×#1032
C2×C3×C5×#1022
C2×C3×C5×#972
C3×C5×#3842
C5×#19593
C3×#19595