Finite Group Databasebeta

← C3×C5×#1632 #14274666

Subgroups — C3×C5×#1632 #14274666

Order 1920.

428 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#554C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic, complemented
3C3×C5×#477C211yesmaximal, characteristic, complemented
4C3×C5×#476C211yesmaximal, characteristic
5C3×C5×#333C211yesmaximal, characteristic, complemented
6C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
7C3×C5×D4⋊C8C211yesmaximal, characteristic
8C5×#1632C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#125—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8—22no—
15C3×C4×C5×Q8C2211yescharacteristic
16C3×C4×C5×D4—21no—
17C3×C4×C5×D4C2211yescharacteristic
18C2×C3×C5×C4⋊C4—21no—
19C3×C5×#107—21no—
20C3×C5×#106—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×C4⋊C8C2211yescharacteristic
23C3×C5×#103—21no—
24C3×C5×#102—21no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1632C511yesmaximal, characteristic, direct product factor, Hall
27C5×#554C2×C311yescharacteristic
28C5×#494C2×C311yescharacteristic, complemented
29C5×#477C2×C311yescharacteristic, complemented
30C5×#476C2×C311yescharacteristic
31C5×#333C2×C311yescharacteristic, complemented
32C5×Q8⋊C8C2×C311yescharacteristic, complemented
33C5×D4⋊C8C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×Q8D412yes—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5—21no—
40C3×C5×Q16—44no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—22no—
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×C5×C22⋊C4—22no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—21no—
56C3×C42×C5C2311yescharacteristic
57C3×#554C2×C511yescharacteristic
58C3×#494C2×C511yescharacteristic, complemented
59C3×#477C2×C511yescharacteristic, complemented
60C3×#476C2×C511yescharacteristic
61C3×#333C2×C511yescharacteristic, complemented
62C3×Q8⋊C8C2×C511yescharacteristic, complemented
63C3×D4⋊C8C2×C511yescharacteristic
64C2×C5×Q16—22no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×C4⋊Q8C22×C311yescharacteristic
67C5×#125—21no—
68C5×C22⋊Q8—21no—
69C5×C22⋊Q8—22no—
70C4×C5×Q8C22×C311yescharacteristic
71C4×C5×D4—21no—
72C4×C5×D4C22×C311yescharacteristic
73C2×C5×C4⋊C4—21no—
74C5×#107—21no—
75C5×#106—21no—
76C5×C4⋊C8C22×C311yescharacteristic
77C5×C4⋊C8C22×C311yescharacteristic
78C5×#103—21no—
79C5×#102—21no—
80C4×C5×C8C22×C311yescharacteristic
81#1632C3×C511yescharacteristic, direct product factor, Sylow
82C23×C3×C5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C3×C5×Q8—42no—
87C3×C5×D4—21no—
88C3×C5×D4Q1612yescomplemented
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×C5—82no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C5×C8—22no—
101C3×C5×C8—41no—
102C3×C5×C8—41no—
103C2×C3×Q16—22no—
104C3×C4⋊Q8C22×C511yescharacteristic
105C3×C4⋊Q8C22×C511yescharacteristic
106C3×#125—21no—
107C3×C22⋊Q8—21no—
108C3×C22⋊Q8—22no—
109C3×C4×Q8C22×C511yescharacteristic
110C3×C4×D4—21no—
111C3×C4×D4C22×C511yescharacteristic
112C2×C3×C4⋊C4—21no—
113C3×#107—21no—
114C3×#106—21no—
115C3×C4⋊C8C22×C511yescharacteristic
116C3×C4⋊C8C22×C511yescharacteristic
117C3×#103—21no—
118C3×#102—21no—
119C3×C4×C8C22×C511yescharacteristic
120C2×C5×Q8—21no—
121C2×C5×Q8C3×D411yescharacteristic
122C2×C5×Q8C3×D412yes—
123C2×C5×D4C3×D411yescharacteristic
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C5×Q16—44no—
127C2×C5×C8—21no—
128C2×C5×C8—21no—
129C2×C5×C8—21no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—22no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4C3×D411yescharacteristic
138C5×C4⋊C4C3×D411yescharacteristic
139C5×C22⋊C4—22no—
140C5×C22⋊C4—21no—
141C42×C5—21no—
142C42×C5C23×C311yescharacteristic
143#554C2×C3×C511yescharacteristic
144#494C2×C3×C511yescharacteristic, complemented
145#477C2×C3×C511yescharacteristic, complemented
146#476C2×C3×C511yescharacteristic
147#333C2×C3×C511yescharacteristic, complemented
148Q8⋊C8C2×C3×C511yescharacteristic, complemented
149D4⋊C8C2×C3×C511yescharacteristic
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5—42no—
159C3×C4×C5—81no—
160C3×C4×C5C2×Q1611yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C2×C3×Q8—21no—
165C2×C3×Q8C5×D411yescharacteristic
166C2×C3×Q8C5×D412yes—
167C2×C3×D4C5×D411yescharacteristic
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C3×Q16—44no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4C5×D411yescharacteristic
182C3×C4⋊C4C5×D411yescharacteristic
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
185C3×C42—21no—
186C3×C42C23×C511yescharacteristic
187C23×C5—21no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—42no—
191C5×Q8—42no—
192C5×D4—21no—
193C5×D4C3×Q1612yescomplemented
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—22no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—82no—
202C2×C4×C5C2×C3×D411yescharacteristic
203C2×C4×C5C2×C3×D411yescharacteristic
204C2×C4×C5C2×C3×D411yescharacteristic
205C5×C8—22no—
206C5×C8—41no—
207C5×C8—41no—
208C2×Q16—22no—
209C4⋊Q8C22×C3×C511yescharacteristic
210C4⋊Q8C22×C3×C511yescharacteristic
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—22no—
214C4×Q8C22×C3×C511yescharacteristic
215C4×D4—21no—
216C4×D4C22×C3×C511yescharacteristic
217C2×C4⋊C4—21no—
218#107—21no—
219#106—21no—
220C4⋊C8C22×C3×C511yescharacteristic
221C4⋊C8C22×C3×C511yescharacteristic
222#103—21no—
223#102—21no—
224C4×C8C22×C3×C511yescharacteristic
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—42no—
233C3×Q8—42no—
234C3×D4—21no—
235C3×D4C5×Q1612yescomplemented
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—22no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—82no—
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246C2×C3×C4C2×C5×D411yescharacteristic
247C3×C8—22no—
248C3×C8—41no—
249C3×C8—41no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5C3×#12011yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—42no—
259C4×C5—81no—
260C4×C5C2×C3×Q1611yescharacteristic
261C4×C5C3×#13511yescharacteristic
262C4×C5C3×#13711yescharacteristic
263C4×C5C3×#13711yescharacteristic
264C2×Q8—21no—
265C2×Q8C3×C5×D411yescharacteristic
266C2×Q8C3×C5×D412yes—
267C2×D4C3×C5×D411yescharacteristic
268C22×C4—22no—
269C22×C4—21no—
270Q16—44no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C3×C5×D411yescharacteristic
282C4⋊C4C3×C5×D411yescharacteristic
283C22⋊C4—22no—
284C22⋊C4—21no—
285C42—21no—
286C42C23×C3×C511yescharacteristic
287C3×C5#163211yescharacteristic, direct product factor, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3C5×#12011yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4—81no—
298C3×C4C2×C5×Q1611yescharacteristic
299C3×C4C5×#13511yescharacteristic
300C3×C4C5×#13711yescharacteristic
301C3×C4C5×#13711yescharacteristic
302C2×C5—42no—
303C2×C5C3×#45111yescharacteristic
304C2×C5C3×#45211yescharacteristic
305C2×C5C3×#45311yescharacteristic
306C23—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—42no—
311D4—21no—
312D4C3×C5×Q1612yescomplemented
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4C2×C3×C5×D411yescharacteristic
322C2×C4C2×C3×C5×D411yescharacteristic
323C2×C4C2×C3×C5×D411yescharacteristic
324C8—22no—
325C8—41no—
326C8—41no—
327C2×C3—42no—
328C2×C3C5×#45111yescharacteristic
329C2×C3C5×#45211yescharacteristic
330C2×C3C5×#45311yescharacteristic
331C5C3×#163211yescharacteristic, direct product factor, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22C3×C5×#12011yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—42no—
341C4—81no—
342C4C2×C3×C5×Q1611yescharacteristic
343C4C3×C5×#13511yescharacteristic
344C4C3×C5×#13711yescharacteristic
345C4C3×C5×#13711yescharacteristic
346C3C5×#163211yescharacteristic, direct product factor, Sylow
347C2—42no—
348C2C3×C5×#45111yescharacteristic
349C2C3×C5×#45211yescharacteristic
350C2C3×C5×#45311yescharacteristic
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×#494C2semidirect
3. C3×C5×#477C2semidirect
5. C3×C5×#333C2semidirect
6. C3×C5×Q8⋊C8C2semidirect
8. C5×#1632C3direct (N × H)
26. C3×#1632C5direct (N × H)
28. C5×#494C2×C3semidirect
29. C5×#477C2×C3semidirect
31. C5×#333C2×C3semidirect
32. C5×Q8⋊C8C2×C3semidirect
58. C3×#494C2×C5semidirect
59. C3×#477C2×C5semidirect
61. C3×#333C2×C5semidirect
62. C3×Q8⋊C8C2×C5semidirect
81. #1632C3×C5direct (N × H)
88. C3×C5×D4Q16semidirect
144. #494C2×C3×C5semidirect
145. #477C2×C3×C5semidirect
147. #333C2×C3×C5semidirect
148. Q8⋊C8C2×C3×C5semidirect
193. C5×D4C3×Q16semidirect
235. C3×D4C5×Q16semidirect
287. C3×C5#1632direct (N × H)
312. D4C3×C5×Q16semidirect
331. C5C3×#1632direct (N × H)
346. C3C5×#1632direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5542
C3×C5×#4942
C3×C5×#4772
C3×C5×#4762
C3×C5×#3332
C3×C5×Q8⋊C82
C3×C5×D4⋊C82
C5×#16323
C3×#16325