Finite Group Databasebeta

← C3×C5×#1638 #14274672

Subgroups — C3×C5×#1638 #14274672

Order 1920.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3C3×C5×#477C211yesmaximal, characteristic, complemented
4C3×C5×#476C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
7C3×C5×D4⋊C8C211yesmaximal, characteristic
8C5×#1638C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#126—22no—
12C3×C5×#124—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C4×C5×Q8—21no—
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×D4C2211yescharacteristic
17C3×C5×#117—21no—
18C3×C5×#107—21no—
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#103—21no—
23C3×C5×#103—22no—
24C3×C5×#102—21no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1638C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic, complemented
29C5×#477C2×C311yescharacteristic, complemented
30C5×#476C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic, complemented
32C5×Q8⋊C8C2×C311yescharacteristic, complemented
33C5×D4⋊C8C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D412yes—
50C3×C5×C22⋊C4—22no—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5—22no—
54C3×C42×C5—21no—
55C3×C42×C5C2311yescharacteristic
56C3×#556C2×C511yescharacteristic
57C3×#487C2×C511yescharacteristic, complemented
58C3×#477C2×C511yescharacteristic, complemented
59C3×#476C2×C511yescharacteristic
60C3×#332C2×C511yescharacteristic, complemented
61C3×Q8⋊C8C2×C511yescharacteristic, complemented
62C3×D4⋊C8C2×C511yescharacteristic
63C5×C4⋊Q8C22×C311yescharacteristic
64C5×C4⋊Q8C22×C311yescharacteristic
65C5×#126—22no—
66C5×#124—21no—
67C5×C22⋊Q8—21no—
68C4×C5×Q8—21no—
69C4×C5×Q8C22×C311yescharacteristic
70C4×C5×D4C22×C311yescharacteristic
71C5×#117—21no—
72C5×#107—21no—
73C5×#106—21no—
74C5×C4⋊C8C22×C311yescharacteristic
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#103—21no—
77C5×#103—22no—
78C5×#102—21no—
79C4×C5×C8C22×C311yescharacteristic
80#1638C3×C511yescharacteristic, direct product factor, Sylow
81C23×C3×C5—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—42no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
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—
102C3×C4⋊Q8C22×C511yescharacteristic
103C3×C4⋊Q8C22×C511yescharacteristic
104C3×#126—22no—
105C3×#124—21no—
106C3×C22⋊Q8—21no—
107C3×C4×Q8—21no—
108C3×C4×Q8C22×C511yescharacteristic
109C3×C4×D4C22×C511yescharacteristic
110C3×#117—21no—
111C3×#107—21no—
112C3×#106—21no—
113C3×C4⋊C8C22×C511yescharacteristic
114C3×C4⋊C8C22×C511yescharacteristic
115C3×#103—21no—
116C3×#103—22no—
117C3×#102—21no—
118C3×C4×C8C22×C511yescharacteristic
119C2×C5×Q8—21no—
120C2×C5×Q8—21no—
121C2×C5×Q8C3×D411yescharacteristic
122C2×C5×D4C3×D411yescharacteristic
123C22×C4×C5—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C3×D411yescharacteristic
133C5×C4⋊C4C3×D411yescharacteristic
134C5×C4⋊C4C3×D412yes—
135C5×C22⋊C4—22no—
136C5×C22⋊C4—22no—
137C5×C22⋊C4—21no—
138C42×C5—22no—
139C42×C5—21no—
140C42×C5C23×C311yescharacteristic
141#556C2×C3×C511yescharacteristic
142#487C2×C3×C511yescharacteristic, complemented
143#477C2×C3×C511yescharacteristic, complemented
144#476C2×C3×C511yescharacteristic
145#332C2×C3×C511yescharacteristic, complemented
146Q8⋊C8C2×C3×C511yescharacteristic, complemented
147D4⋊C8C2×C3×C511yescharacteristic
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5—42no—
156C3×C4×C5—41no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8C5×D411yescharacteristic
165C2×C3×D4C5×D411yescharacteristic
166C22×C3×C4—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4C5×D412yes—
176C3×C4⋊C4C5×D411yescharacteristic
177C3×C4⋊C4C5×D411yescharacteristic
178C3×C22⋊C4—22no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—21no—
181C3×C42—22no—
182C3×C42—21no—
183C3×C42C23×C511yescharacteristic
184C23×C5—21no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—42no—
188C5×Q8—41no—
189C5×Q8—41no—
190C5×D4—21no—
191C5×D4—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—22no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C2×C4×C5C2×C3×D411yescharacteristic
202C5×C8—41no—
203C5×C8—41no—
204C5×C8—41no—
205C4⋊Q8C22×C3×C511yescharacteristic
206C4⋊Q8C22×C3×C511yescharacteristic
207#126—22no—
208#124—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8C22×C3×C511yescharacteristic
212C4×D4C22×C3×C511yescharacteristic
213#117—21no—
214#107—21no—
215#106—21no—
216C4⋊C8C22×C3×C511yescharacteristic
217C4⋊C8C22×C3×C511yescharacteristic
218#103—21no—
219#103—22no—
220#102—21no—
221C4×C8C22×C3×C511yescharacteristic
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—42no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×D4—21no—
233C3×D4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4C2×C5×D411yescharacteristic
242C2×C3×C4C2×C5×D411yescharacteristic
243C2×C3×C4C2×C5×D411yescharacteristic
244C3×C8—41no—
245C3×C8—41no—
246C3×C8—41no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5C3×#12011yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—42no—
255C4×C5—41no—
256C4×C5—81no—
257C4×C5C3×#13511yescharacteristic
258C4×C5C3×#13511yescharacteristic
259C4×C5C3×#13711yescharacteristic
260C4×C5C3×#13711yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8C3×C5×D411yescharacteristic
264C2×D4C3×C5×D411yescharacteristic
265C22×C4—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4C3×C5×D412yes—
275C4⋊C4C3×C5×D411yescharacteristic
276C4⋊C4C3×C5×D411yescharacteristic
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—21no—
280C42—22no—
281C42—21no—
282C42C23×C3×C511yescharacteristic
283C3×C5#163811yescharacteristic, direct product factor, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C5×#12011yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—81no—
294C3×C4C5×#13511yescharacteristic
295C3×C4C5×#13511yescharacteristic
296C3×C4C5×#13711yescharacteristic
297C3×C4C5×#13711yescharacteristic
298C2×C5—81no—
299C2×C5C3×#45211yescharacteristic
300C2×C5C3×#45211yescharacteristic
301C2×C5C3×#45411yescharacteristic
302C23—21no—
303Q8—21no—
304Q8—21no—
305Q8—42no—
306Q8—41no—
307Q8—41no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4C2×C3×C5×D411yescharacteristic
318C2×C4C2×C3×C5×D411yescharacteristic
319C2×C4C2×C3×C5×D411yescharacteristic
320C8—41no—
321C8—41no—
322C8—41no—
323C2×C3—81no—
324C2×C3C5×#45211yescharacteristic
325C2×C3C5×#45211yescharacteristic
326C2×C3C5×#45411yescharacteristic
327C5C3×#163811yescharacteristic, direct product factor, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22C3×C5×#12011yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—42no—
336C4—41no—
337C4—81no—
338C4C3×C5×#13511yescharacteristic
339C4C3×C5×#13511yescharacteristic
340C4C3×C5×#13711yescharacteristic
341C4C3×C5×#13711yescharacteristic
342C3C5×#163811yescharacteristic, direct product factor, Sylow
343C2—81no—
344C2C3×C5×#45211yescharacteristic
345C2C3×C5×#45211yescharacteristic
346C2C3×C5×#45411yescharacteristic
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×#487C2semidirect
3. C3×C5×#477C2semidirect
5. C3×C5×#332C2semidirect
6. C3×C5×Q8⋊C8C2semidirect
8. C5×#1638C3direct (N × H)
26. C3×#1638C5direct (N × H)
28. C5×#487C2×C3semidirect
29. C5×#477C2×C3semidirect
31. C5×#332C2×C3semidirect
32. C5×Q8⋊C8C2×C3semidirect
57. C3×#487C2×C5semidirect
58. C3×#477C2×C5semidirect
60. C3×#332C2×C5semidirect
61. C3×Q8⋊C8C2×C5semidirect
80. #1638C3×C5direct (N × H)
142. #487C2×C3×C5semidirect
143. #477C2×C3×C5semidirect
145. #332C2×C3×C5semidirect
146. Q8⋊C8C2×C3×C5semidirect
283. C3×C5#1638direct (N × H)
327. C5C3×#1638direct (N × H)
342. C3C5×#1638direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5562
C3×C5×#4872
C3×C5×#4772
C3×C5×#4762
C3×C5×#3322
C3×C5×Q8⋊C82
C3×C5×D4⋊C82
C5×#16383
C3×#16385