Finite Group Databasebeta

← C3×C5×#1664 #14274698

Subgroups — C3×C5×#1664 #14274698

Order 1920.

368 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#563C211yesmaximal, characteristic
2C3×C5×#501C211yesmaximal, characteristic, complemented
3C3×C5×#491C211yesmaximal, characteristic, complemented
4C3×C5×#489C211yesmaximal, characteristic
5C3×C5×#330C211yesmaximal, characteristic, complemented
6C3×C5×#330C211yesmaximal, characteristic, complemented
7C3×C5×#329C211yesmaximal, characteristic
8C5×#1664C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#126—21no—
12C3×C5×#126—21no—
13C3×C5×#125C2211yescharacteristic
14C3×C5×#125C2211yescharacteristic
15C3×C5×#124C2211yescharacteristic
16C3×C5×#123—21no—
17C3×C5×C22⋊Q8—21no—
18C3×C5×C22⋊Q8—21no—
19C3×C5×#107—21no—
20C3×C5×#106—21no—
21C3×C5×#103—21no—
22C3×C5×#103—21no—
23C3×C5×#103—21no—
24C3×C5×#102—21no—
25C3×C5×#97C2211yescharacteristic
26C3×C5×#97C2211yescharacteristic
27C3×C5×#97C2211yescharacteristic
28C3×#1664C511yesmaximal, characteristic, direct product factor, Hall
29C5×#563C2×C311yescharacteristic
30C5×#501C2×C311yescharacteristic, complemented
31C5×#491C2×C311yescharacteristic, complemented
32C5×#489C2×C311yescharacteristic
33C5×#330C2×C311yescharacteristic, complemented
34C5×#330C2×C311yescharacteristic, complemented
35C5×#329C2×C311yescharacteristic
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
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⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62C3×C42×C5C2311yescharacteristic
63C3×#563C2×C511yescharacteristic
64C3×#501C2×C511yescharacteristic, complemented
65C3×#491C2×C511yescharacteristic, complemented
66C3×#489C2×C511yescharacteristic
67C3×#330C2×C511yescharacteristic, complemented
68C3×#330C2×C511yescharacteristic, complemented
69C3×#329C2×C511yescharacteristic
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8C22×C311yescharacteristic
72C5×#126—21no—
73C5×#126—21no—
74C5×#125C22×C311yescharacteristic
75C5×#125C22×C311yescharacteristic
76C5×#124C22×C311yescharacteristic
77C5×#123—21no—
78C5×C22⋊Q8—21no—
79C5×C22⋊Q8—21no—
80C5×#107—21no—
81C5×#106—21no—
82C5×#103—21no—
83C5×#103—21no—
84C5×#103—21no—
85C5×#102—21no—
86C5×#97C22×C311yescharacteristic
87C5×#97C22×C311yescharacteristic
88C5×#97C22×C311yescharacteristic
89#1664C3×C511yescharacteristic, direct product factor, Sylow
90C23×C3×C5—21no—
91C3×C5×Q8—41no—
92C3×C5×Q8—42no—
93C3×C5×Q8—81no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—81no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C5×C8—22no—
106C3×C5×C8—41no—
107C3×C5×C8—41no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8C22×C511yescharacteristic
110C3×#126—21no—
111C3×#126—21no—
112C3×#125C22×C511yescharacteristic
113C3×#125C22×C511yescharacteristic
114C3×#124C22×C511yescharacteristic
115C3×#123—21no—
116C3×C22⋊Q8—21no—
117C3×C22⋊Q8—21no—
118C3×#107—21no—
119C3×#106—21no—
120C3×#103—21no—
121C3×#103—21no—
122C3×#103—21no—
123C3×#102—21no—
124C3×#97C22×C511yescharacteristic
125C3×#97C22×C511yescharacteristic
126C3×#97C22×C511yescharacteristic
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×Q8C3×D411yescharacteristic
130C2×C5×D4C3×D411yescharacteristic
131C22×C4×C5—21no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C2×C5×C8—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4C3×D411yescharacteristic
144C5×C4⋊C4C3×D411yescharacteristic
145C5×C4⋊C4C3×D411yescharacteristic
146C5×C4⋊C4C3×D411yescharacteristic
147C5×C22⋊C4—21no—
148C5×C22⋊C4—21no—
149C5×C22⋊C4—21no—
150C5×C22⋊C4—21no—
151C5×C22⋊C4—21no—
152C42×C5—21no—
153C42×C5C23×C311yescharacteristic
154#563C2×C3×C511yescharacteristic
155#501C2×C3×C511yescharacteristic, complemented
156#491C2×C3×C511yescharacteristic, complemented
157#489C2×C3×C511yescharacteristic
158#330C2×C3×C511yescharacteristic, complemented
159#330C2×C3×C511yescharacteristic, complemented
160#329C2×C3×C511yescharacteristic
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×C4×C5—41no—
171C3×C4×C5—41no—
172C3×C4×C5—41no—
173C3×C4×C5—81no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8C5×D411yescharacteristic
177C2×C3×D4C5×D411yescharacteristic
178C22×C3×C4—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4C5×D411yescharacteristic
191C3×C4⋊C4C5×D411yescharacteristic
192C3×C4⋊C4C5×D411yescharacteristic
193C3×C4⋊C4C5×D411yescharacteristic
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C42—21no—
200C3×C42C23×C511yescharacteristic
201C23×C5—21no—
202C5×Q8—41no—
203C5×Q8—42no—
204C5×Q8—81no—
205C5×D4—41no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—41no—
212C2×C4×C5—81no—
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×C4×C5C2×C3×D411yescharacteristic
215C2×C4×C5C2×C3×D411yescharacteristic
216C5×C8—22no—
217C5×C8—41no—
218C5×C8—41no—
219C4⋊Q8—21no—
220C4⋊Q8C22×C3×C511yescharacteristic
221#126—21no—
222#126—21no—
223#125C22×C3×C511yescharacteristic
224#125C22×C3×C511yescharacteristic
225#124C22×C3×C511yescharacteristic
226#123—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229#107—21no—
230#106—21no—
231#103—21no—
232#103—21no—
233#103—21no—
234#102—21no—
235#97C22×C3×C511yescharacteristic
236#97C22×C3×C511yescharacteristic
237#97C22×C3×C511yescharacteristic
238C2×C3×C5—81no—
239C2×C3×C5#45411yescharacteristic
240C2×C3×C5#45511yescharacteristic
241C2×C3×C5#45611yescharacteristic
242C23×C3—21no—
243C3×Q8—41no—
244C3×Q8—42no—
245C3×Q8—81no—
246C3×D4—41no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—41no—
253C2×C3×C4—81no—
254C2×C3×C4C2×C5×D411yescharacteristic
255C2×C3×C4C2×C5×D411yescharacteristic
256C2×C3×C4C2×C5×D411yescharacteristic
257C3×C8—22no—
258C3×C8—41no—
259C3×C8—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5C3×#12011yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—41no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5—81no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8C3×C5×D411yescharacteristic
276C2×D4C3×C5×D411yescharacteristic
277C22×C4—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4C3×C5×D411yescharacteristic
290C4⋊C4C3×C5×D411yescharacteristic
291C4⋊C4C3×C5×D411yescharacteristic
292C4⋊C4C3×C5×D411yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C42—21no—
299C42C23×C3×C511yescharacteristic
300C3×C5#166411yescharacteristic, direct product factor, Hall
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3C5×#12011yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—81no—
314C2×C5—81no—
315C2×C5C3×#45411yescharacteristic
316C2×C5C3×#45511yescharacteristic
317C2×C5C3×#45611yescharacteristic
318C23—21no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322D4—41no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4C2×C3×C5×D411yescharacteristic
331C2×C4C2×C3×C5×D411yescharacteristic
332C2×C4C2×C3×C5×D411yescharacteristic
333C8—22no—
334C8—41no—
335C8—41no—
336C2×C3—81no—
337C2×C3C5×#45411yescharacteristic
338C2×C3C5×#45511yescharacteristic
339C2×C3C5×#45611yescharacteristic
340C5C3×#166411yescharacteristic, direct product factor, Sylow
341C22—41no—
342C22—41no—
343C22—41no—
344C22C3×C5×#12011yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—81no—
354C3C5×#166411yescharacteristic, direct product factor, Sylow
355C2—81no—
356C2C3×C5×#45411yescharacteristic
357C2C3×C5×#45511yescharacteristic
358C2C3×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC2×C3×C5×D4D4
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×#501C2semidirect
3. C3×C5×#491C2semidirect
5. C3×C5×#330C2semidirect
6. C3×C5×#330C2semidirect
8. C5×#1664C3direct (N × H)
28. C3×#1664C5direct (N × H)
30. C5×#501C2×C3semidirect
31. C5×#491C2×C3semidirect
33. C5×#330C2×C3semidirect
34. C5×#330C2×C3semidirect
64. C3×#501C2×C5semidirect
65. C3×#491C2×C5semidirect
67. C3×#330C2×C5semidirect
68. C3×#330C2×C5semidirect
89. #1664C3×C5direct (N × H)
155. #501C2×C3×C5semidirect
156. #491C2×C3×C5semidirect
158. #330C2×C3×C5semidirect
159. #330C2×C3×C5semidirect
300. C3×C5#1664direct (N × H)
340. C5C3×#1664direct (N × H)
354. C3C5×#1664direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5632
C3×C5×#5012
C3×C5×#4912
C3×C5×#4892
C3×C5×#3302
C3×C5×#3292
C5×#16643
C3×#16645