Finite Group Databasebeta

← C3×C5×#1614 #14274648

Subgroups — C3×C5×#1614 #14274648

Order 1920.

472 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
1C3×C5×#543C211yesmaximal, characteristic
2C3×C5×#484C212yesmaximal, complemented
3C3×C5×#399C211yesmaximal, characteristic
4C3×C5×#328C212yesmaximal, complemented
5C3×C5×#323C211yesmaximal, characteristic
6C5×#1614C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C22⋊Q8—22no—
8C3×C5×C22⋊Q8—21no—
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8C2212yes—
11C2×C3×C5×C4⋊C4—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C3×C5×#107—22no—
17C3×C5×#103—22no—
18C3×C5×C22⋊C8C2212yes—
19C3×C5×#95C2211yescharacteristic
20C3×#1614C511yesmaximal, characteristic, direct product factor, Hall
21C5×#543C2×C311yescharacteristic
22C5×#484C2×C312yescomplemented
23C5×#399C2×C311yescharacteristic
24C5×#328C2×C312yescomplemented
25C5×#323C2×C311yescharacteristic
26C24×C3×C5D411yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—42no—
41C3×C5×C4⋊C4D412yes—
42C3×C5×C22⋊C4—22no—
43C3×C5×C22⋊C4—22no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—42no—
46C3×#543C2×C511yescharacteristic
47C3×#484C2×C512yescomplemented
48C3×#399C2×C511yescharacteristic
49C3×#328C2×C512yescomplemented
50C3×#323C2×C511yescharacteristic
51C5×C22⋊Q8—22no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8—22no—
54C5×C22⋊Q8C22×C312yes—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4C22×C311yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4C22×C311yescharacteristic
60C5×#107—22no—
61C5×#103—22no—
62C5×C22⋊C8C22×C312yes—
63C5×#95C22×C311yescharacteristic
64#1614C3×C511yescharacteristic, direct product factor, Sylow
65C23×C3×C5—21no—
66C23×C3×C5—21no—
67C23×C3×C5—41no—
68C23×C3×C5—41no—
69C23×C3×C5Q1612yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×Q8—42no—
72C3×C5×Q8—81no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—81no—
85C2×C3×C4×C5—81no—
86C2×C3×C4×C5C2×D412yes—
87C3×C5×C8—42no—
88C3×C22⋊Q8—22no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8C22×C512yes—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C22×C511yescharacteristic
94C2×C3×C22⋊C4—21no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4C22×C511yescharacteristic
97C3×#107—22no—
98C3×#103—22no—
99C3×C22⋊C8C22×C512yes—
100C3×#95C22×C511yescharacteristic
101C24×C5C3×D411yescharacteristic
102C2×C5×Q8—21no—
103C2×C5×Q8C3×D412yes—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5C3×D411yescharacteristic
109C22×C4×C5C23×C311yescharacteristic
110C2×C5×C8—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—42no—
116C5×C4⋊C4C3×D412yes—
117C5×C22⋊C4—22no—
118C5×C22⋊C4—22no—
119C5×C22⋊C4—22no—
120C5×C22⋊C4—42no—
121#543C2×C3×C511yescharacteristic
122#484C2×C3×C512yescomplemented
123#399C2×C3×C511yescharacteristic
124#328C2×C3×C512yescomplemented
125#323C2×C3×C511yescharacteristic
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—22no—
129C22×C3×C5—42no—
130C22×C3×C5—41no—
131C22×C3×C5—41no—
132C22×C3×C5—81no—
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5C2×Q1611yescharacteristic
135C22×C3×C5#13711yescharacteristic
136C3×C4×C5—22no—
137C3×C4×C5—42no—
138C3×C4×C5—41no—
139C3×C4×C5—42no—
140C3×C4×C5—42no—
141C3×C4×C5—81no—
142C24×C3C5×D411yescharacteristic
143C2×C3×Q8—21no—
144C2×C3×Q8C5×D412yes—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4C5×D411yescharacteristic
150C22×C3×C4C23×C511yescharacteristic
151C2×C3×C8—22no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—42no—
157C3×C4⋊C4C5×D412yes—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—42no—
162C23×C5—21no—
163C23×C5—21no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5C3×Q1612yes—
167C23×C5C2×C3×D411yescharacteristic
168C5×Q8—42no—
169C5×Q8—81no—
170C2×C4×C5—22no—
171C2×C4×C5—22no—
172C2×C4×C5—21no—
173C2×C4×C5—22no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—81no—
182C2×C4×C5—81no—
183C2×C4×C5C2×C3×D412yes—
184C5×C8—42no—
185C22⋊Q8—22no—
186C22⋊Q8—21no—
187C22⋊Q8—22no—
188C22⋊Q8C22×C3×C512yes—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C22×C3×C511yescharacteristic
191C2×C22⋊C4—21no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4C22×C3×C511yescharacteristic
194#107—22no—
195#103—22no—
196C22⋊C8C22×C3×C512yes—
197#95C22×C3×C511yescharacteristic
198C2×C3×C5—21no—
199C2×C3×C5—21no—
200C2×C3×C5—42no—
201C2×C3×C5#45111yescharacteristic
202C2×C3×C5#45311yescharacteristic
203C2×C3×C5#45811yescharacteristic
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3C5×Q1612yes—
209C23×C3C2×C5×D411yescharacteristic
210C3×Q8—42no—
211C3×Q8—81no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—22no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—81no—
224C2×C3×C4—81no—
225C2×C3×C4C2×C5×D412yes—
226C3×C8—42no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—81no—
234C22×C5C3×#12011yescharacteristic
235C22×C5C2×C3×Q1611yescharacteristic
236C22×C5C3×#13711yescharacteristic
237C4×C5—22no—
238C4×C5—42no—
239C4×C5—41no—
240C4×C5—42no—
241C4×C5—42no—
242C4×C5—81no—
243C24C3×C5×D411yescharacteristic
244C2×Q8—21no—
245C2×Q8C3×C5×D412yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4C3×C5×D411yescharacteristic
251C22×C4C23×C3×C511yescharacteristic
252C2×C8—22no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4C3×C5×D412yes—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—42no—
263C3×C5#161411yescharacteristic, direct product factor, Hall
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—22no—
267C22×C3—42no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—81no—
271C22×C3C5×#12011yescharacteristic
272C22×C3C2×C5×Q1611yescharacteristic
273C22×C3C5×#13711yescharacteristic
274C3×C4—22no—
275C3×C4—42no—
276C3×C4—41no—
277C3×C4—42no—
278C3×C4—42no—
279C3×C4—81no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—42no—
283C2×C5C3×#45111yescharacteristic
284C2×C5C3×#45311yescharacteristic
285C2×C5C3×#45811yescharacteristic
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23C3×C5×Q1612yes—
291C23C2×C3×C5×D411yescharacteristic
292Q8—42no—
293Q8—81no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×C3×C5×D412yes—
308C8—42no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3C5×#45111yescharacteristic
313C2×C3C5×#45311yescharacteristic
314C2×C3C5×#45811yescharacteristic
315C5C3×#161411yescharacteristic, direct product factor, Sylow
316C22—21no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22C3×C5×#12011yescharacteristic
324C22C2×C3×C5×Q1611yescharacteristic
325C22C3×C5×#13711yescharacteristic
326C4—22no—
327C4—42no—
328C4—41no—
329C4—42no—
330C4—42no—
331C4—81no—
332C3C5×#161411yescharacteristic, direct product factor, Sylow
333C2—21no—
334C2—21no—
335C2—42no—
336C2C3×C5×#45111yescharacteristic
337C2C3×C5×#45311yescharacteristic
338C2C3×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC24×C3×C5D4
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×#484C2semidirect
4. C3×C5×#328C2semidirect
6. C5×#1614C3direct (N × H)
20. C3×#1614C5direct (N × H)
22. C5×#484C2×C3semidirect
24. C5×#328C2×C3semidirect
47. C3×#484C2×C5semidirect
49. C3×#328C2×C5semidirect
64. #1614C3×C5direct (N × H)
122. #484C2×C3×C5semidirect
124. #328C2×C3×C5semidirect
263. C3×C5#1614direct (N × H)
315. C5C3×#1614direct (N × H)
332. C3C5×#1614direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5432
C3×C5×#4842
C3×C5×#3992
C3×C5×#3282
C3×C5×#3232
C5×#16143
C3×#16145