Finite Group Databasebeta

← C3×C5×#1645 #14274679

Subgroups — C3×C5×#1645 #14274679

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×Q82C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic
3C3×C5×#475C211yesmaximal, characteristic
4C3×C5×#462C211yesmaximal, characteristic
5C3×C5×#333C211yesmaximal, characteristic
6C3×C5×Q8⋊C8C211yesmaximal, characteristic
7C3×C5×Q8⋊C8C211yesmaximal, characteristic
8C5×#1645C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16—21no—
10C3×C5×C4⋊Q8—22no—
11C3×C5×C4⋊Q8—21no—
12C3×C5×C4⋊Q8—21no—
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×Q8—21no—
16C3×C4×C5×Q8—21no—
17C3×C4×C5×Q8C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#103—21no—
23C3×C5×#103—22no—
24C3×C5×#103—21no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1645C511yesmaximal, characteristic, direct product factor, Hall
27C5×Q82C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic
29C5×#475C2×C311yescharacteristic
30C5×#462C2×C311yescharacteristic
31C5×#333C2×C311yescharacteristic
32C5×Q8⋊C8C2×C311yescharacteristic
33C5×Q8⋊C8C2×C311yescharacteristic
34C2×C3×C5×Q8—22no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×Q8D412yes—
39C3×C5×Q16—42no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C42×C5—22no—
54C3×C42×C5—21no—
55C3×C42×C5—21no—
56C3×C42×C5C2311yescharacteristic
57C3×Q82C2×C511yescharacteristic
58C3×#487C2×C511yescharacteristic
59C3×#475C2×C511yescharacteristic
60C3×#462C2×C511yescharacteristic
61C3×#333C2×C511yescharacteristic
62C3×Q8⋊C8C2×C511yescharacteristic
63C3×Q8⋊C8C2×C511yescharacteristic
64C2×C5×Q16—21no—
65C5×C4⋊Q8—22no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C22×C311yescharacteristic
69C5×C4⋊Q8C22×C311yescharacteristic
70C4×C5×Q8—21no—
71C4×C5×Q8—21no—
72C4×C5×Q8C22×C311yescharacteristic
73C4×C5×Q8C22×C311yescharacteristic
74C5×#106—21no—
75C5×C4⋊C8C22×C311yescharacteristic
76C5×C4⋊C8C22×C311yescharacteristic
77C5×#103—21no—
78C5×#103—22no—
79C5×#103—21no—
80C4×C5×C8C22×C311yescharacteristic
81#1645C3×C511yescharacteristic, direct product factor, Sylow
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—42no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×Q8—82no—
88C3×C5×Q8SD1612yes—
89C3×C5×Q8Q1612yescomplemented
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C3×C5×C8—41no—
102C2×C3×Q16—21no—
103C3×C4⋊Q8—22no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8C22×C511yescharacteristic
107C3×C4⋊Q8C22×C511yescharacteristic
108C3×C4×Q8—21no—
109C3×C4×Q8—21no—
110C3×C4×Q8C22×C511yescharacteristic
111C3×C4×Q8C22×C511yescharacteristic
112C3×#106—21no—
113C3×C4⋊C8C22×C511yescharacteristic
114C3×C4⋊C8C22×C511yescharacteristic
115C3×#103—21no—
116C3×#103—22no—
117C3×#103—21no—
118C3×C4×C8C22×C511yescharacteristic
119C2×C5×Q8—22no—
120C2×C5×Q8—21no—
121C2×C5×Q8C3×D411yescharacteristic
122C2×C5×Q8C3×D411yescharacteristic
123C2×C5×Q8C3×D412yes—
124C5×Q16—42no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—22no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4C3×D411yescharacteristic
137C5×C4⋊C4C3×D411yescharacteristic
138C42×C5—22no—
139C42×C5—21no—
140C42×C5—21no—
141C42×C5C23×C311yescharacteristic
142Q82C2×C3×C511yescharacteristic
143#487C2×C3×C511yescharacteristic
144#475C2×C3×C511yescharacteristic
145#462C2×C3×C511yescharacteristic
146#333C2×C3×C511yescharacteristic
147Q8⋊C8C2×C3×C511yescharacteristic
148Q8⋊C8C2×C3×C511yescharacteristic
149C22×C3×C5#12011yescharacteristic
150C3×C4×C5—22no—
151C3×C4×C5—22no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5—41no—
155C3×C4×C5—41no—
156C3×C4×C5—81no—
157C3×C4×C5C2×SD1611yescharacteristic
158C3×C4×C5C2×Q1611yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C2×C3×Q8—22no—
162C2×C3×Q8—21no—
163C2×C3×Q8C5×D411yescharacteristic
164C2×C3×Q8C5×D411yescharacteristic
165C2×C3×Q8C5×D412yes—
166C3×Q16—42no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4C5×D411yescharacteristic
179C3×C4⋊C4C5×D411yescharacteristic
180C3×C42—22no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42C23×C511yescharacteristic
184C5×Q8—21no—
185C5×Q8—21no—
186C5×Q8—42no—
187C5×Q8—41no—
188C5×Q8—41no—
189C5×Q8—82no—
190C5×Q8C3×SD1612yes—
191C5×Q8C3×Q1612yescomplemented
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C5×C8—41no—
202C5×C8—41no—
203C5×C8—41no—
204C2×Q16—21no—
205C4⋊Q8—22no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8C22×C3×C511yescharacteristic
209C4⋊Q8C22×C3×C511yescharacteristic
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8C22×C3×C511yescharacteristic
213C4×Q8C22×C3×C511yescharacteristic
214#106—21no—
215C4⋊C8C22×C3×C511yescharacteristic
216C4⋊C8C22×C3×C511yescharacteristic
217#103—21no—
218#103—22no—
219#103—21no—
220C4×C8C22×C3×C511yescharacteristic
221C2×C3×C5#44811yescharacteristic
222C2×C3×C5#45111yescharacteristic
223C2×C3×C5#45511yescharacteristic
224C3×Q8—21no—
225C3×Q8—21no—
226C3×Q8—42no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—82no—
230C3×Q8C5×SD1612yes—
231C3×Q8C5×Q1612yescomplemented
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4C2×C5×D411yescharacteristic
239C2×C3×C4C2×C5×D411yescharacteristic
240C2×C3×C4C2×C5×D411yescharacteristic
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—41no—
244C22×C5C3×#12011yescharacteristic
245C4×C5—22no—
246C4×C5—22no—
247C4×C5—21no—
248C4×C5—42no—
249C4×C5—41no—
250C4×C5—41no—
251C4×C5—81no—
252C4×C5C2×C3×SD1611yescharacteristic
253C4×C5C2×C3×Q1611yescharacteristic
254C4×C5C3×#13711yescharacteristic
255C4×C5C3×#13711yescharacteristic
256C2×Q8—22no—
257C2×Q8—21no—
258C2×Q8C3×C5×D411yescharacteristic
259C2×Q8C3×C5×D411yescharacteristic
260C2×Q8C3×C5×D412yes—
261Q16—42no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4C3×C5×D411yescharacteristic
274C4⋊C4C3×C5×D411yescharacteristic
275C42—22no—
276C42—21no—
277C42—21no—
278C42C23×C3×C511yescharacteristic
279C3×C5#164511yescharacteristic, direct product factor, Hall
280C22×C3C5×#12011yescharacteristic
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—42no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—81no—
288C3×C4C2×C5×SD1611yescharacteristic
289C3×C4C2×C5×Q1611yescharacteristic
290C3×C4C5×#13711yescharacteristic
291C3×C4C5×#13711yescharacteristic
292C2×C5C3×#44811yescharacteristic
293C2×C5C3×#45111yescharacteristic
294C2×C5C3×#45511yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—42no—
298Q8—41no—
299Q8—41no—
300Q8—82no—
301Q8C3×C5×SD1612yes—
302Q8C3×C5×Q1612yescomplemented
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4C2×C3×C5×D411yescharacteristic
310C2×C4C2×C3×C5×D411yescharacteristic
311C2×C4C2×C3×C5×D411yescharacteristic
312C8—41no—
313C8—41no—
314C8—41no—
315C2×C3C5×#44811yescharacteristic
316C2×C3C5×#45111yescharacteristic
317C2×C3C5×#45511yescharacteristic
318C5C3×#164511yescharacteristic, direct product factor, Sylow
319C22C3×C5×#12011yescharacteristic
320C4—22no—
321C4—21no—
322C4—22no—
323C4—42no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4C2×C3×C5×SD1611yescharacteristic
328C4C2×C3×C5×Q1611yescharacteristic
329C4C3×C5×#13711yescharacteristic
330C4C3×C5×#13711yescharacteristic
331C3C5×#164511yescharacteristic, direct product factor, Sylow
332C2C3×C5×#44811yescharacteristic
333C2C3×C5×#45111yescharacteristic
334C2C3×C5×#45511yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
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
8. C5×#1645C3direct (N × H)
26. C3×#1645C5direct (N × H)
81. #1645C3×C5direct (N × H)
89. C3×C5×Q8Q16semidirect
191. C5×Q8C3×Q16semidirect
231. C3×Q8C5×Q16semidirect
279. C3×C5#1645direct (N × H)
302. Q8C3×C5×Q16semidirect
318. C5C3×#1645direct (N × H)
331. C3C5×#1645direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×Q822
C3×C5×#4872
C3×C5×#4752
C3×C5×#4622
C3×C5×#3332
C3×C5×Q8⋊C82
C5×#16453
C3×#16455