Finite Group Databasebeta

← C3×C5×#1635 #14274669

Subgroups — C3×C5×#1635 #14274669

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3C3×C5×#476C211yesmaximal, characteristic, complemented
4C3×C5×#476C211yesmaximal, characteristic, complemented
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
7C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
8C5×#1635C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#123—22no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×#121—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C3×C4×C5×D4C2211yescharacteristic
17C2×C3×C5×C4⋊C4—21no—
18C3×C5×#106—21no—
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#103—22no—
23C3×C5×#102—21no—
24C3×C5×#102—21no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1635C511yesmaximal, characteristic, direct product factor, Hall
27C5×#547C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic, complemented
29C5×#476C2×C311yescharacteristic, complemented
30C5×#476C2×C311yescharacteristic, complemented
31C5×#332C2×C311yescharacteristic, complemented
32C5×D4⋊C8C2×C311yescharacteristic, complemented
33C5×D4⋊C8C2×C311yescharacteristic, complemented
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4D411yescharacteristic
40C2×C3×C5×D4D411yescharacteristic
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—22no—
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×C4⋊C4D412yes—
54C3×C5×C22⋊C4—22no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C42×C5C2311yescharacteristic
58C3×#547C2×C511yescharacteristic
59C3×#487C2×C511yescharacteristic, complemented
60C3×#476C2×C511yescharacteristic, complemented
61C3×#476C2×C511yescharacteristic, complemented
62C3×#332C2×C511yescharacteristic, complemented
63C3×D4⋊C8C2×C511yescharacteristic, complemented
64C3×D4⋊C8C2×C511yescharacteristic, complemented
65C2×C5×#41—21no—
66C5×C4⋊Q8C22×C311yescharacteristic
67C5×C4⋊Q8C22×C311yescharacteristic
68C5×#123—22no—
69C5×C22⋊Q8—21no—
70C5×#121—21no—
71C4×C5×D4C22×C311yescharacteristic
72C4×C5×D4C22×C311yescharacteristic
73C2×C5×C4⋊C4—21no—
74C5×#106—21no—
75C5×#106—21no—
76C5×C4⋊C8C22×C311yescharacteristic
77C5×C4⋊C8C22×C311yescharacteristic
78C5×#103—22no—
79C5×#102—21no—
80C5×#102—21no—
81C4×C5×C8C22×C311yescharacteristic
82#1635C3×C511yescharacteristic, direct product factor, Sylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C3×C5×Q8—42no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
91C3×C5×D4—44no—
92C3×C5×D4SD1612yes—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—44no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C5×C8—41no—
106C3×C5×C8—41no—
107C3×C5×C8—41no—
108C2×C3×#41—21no—
109C3×C4⋊Q8C22×C511yescharacteristic
110C3×C4⋊Q8C22×C511yescharacteristic
111C3×#123—22no—
112C3×C22⋊Q8—21no—
113C3×#121—21no—
114C3×C4×D4C22×C511yescharacteristic
115C3×C4×D4C22×C511yescharacteristic
116C2×C3×C4⋊C4—21no—
117C3×#106—21no—
118C3×#106—21no—
119C3×C4⋊C8C22×C511yescharacteristic
120C3×C4⋊C8C22×C511yescharacteristic
121C3×#103—22no—
122C3×#102—21no—
123C3×#102—21no—
124C3×C4×C8C22×C511yescharacteristic
125C5×#41—42no—
126C5×#41—42no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×D4—22no—
130C2×C5×D4C3×D411yescharacteristic
131C2×C5×D4C3×D411yescharacteristic
132C22×C4×C5—22no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C2×C5×C8—21no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4C3×D411yescharacteristic
143C5×C4⋊C4C3×D411yescharacteristic
144C5×C4⋊C4C3×D412yes—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—21no—
147C5×C22⋊C4—21no—
148C42×C5C23×C311yescharacteristic
149#547C2×C3×C511yescharacteristic
150#487C2×C3×C511yescharacteristic, complemented
151#476C2×C3×C511yescharacteristic, complemented
152#476C2×C3×C511yescharacteristic, complemented
153#332C2×C3×C511yescharacteristic, complemented
154D4⋊C8C2×C3×C511yescharacteristic, complemented
155D4⋊C8C2×C3×C511yescharacteristic, complemented
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—42no—
166C3×C4×C5—41no—
167C3×C4×C5—81no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172C3×#41—42no—
173C3×#41—42no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×D4—22no—
177C2×C3×D4C5×D411yescharacteristic
178C2×C3×D4C5×D411yescharacteristic
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4C5×D412yes—
190C3×C4⋊C4C5×D411yescharacteristic
191C3×C4⋊C4C5×D411yescharacteristic
192C3×C22⋊C4—22no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C42C23×C511yescharacteristic
196C23×C5—21no—
197C23×C5—21no—
198C5×Q8—42no—
199C5×Q8—41no—
200C5×Q8—41no—
201C5×D4—21no—
202C5×D4—21no—
203C5×D4—21no—
204C5×D4—44no—
205C5×D4C3×SD1612yes—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—22no—
209C2×C4×C5—44no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C2×C3×D411yescharacteristic
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×C4×C5C2×C3×D411yescharacteristic
218C5×C8—41no—
219C5×C8—41no—
220C5×C8—41no—
221C2×#41—21no—
222C4⋊Q8C22×C3×C511yescharacteristic
223C4⋊Q8C22×C3×C511yescharacteristic
224#123—22no—
225C22⋊Q8—21no—
226#121—21no—
227C4×D4C22×C3×C511yescharacteristic
228C4×D4C22×C3×C511yescharacteristic
229C2×C4⋊C4—21no—
230#106—21no—
231#106—21no—
232C4⋊C8C22×C3×C511yescharacteristic
233C4⋊C8C22×C3×C511yescharacteristic
234#103—22no—
235#102—21no—
236#102—21no—
237C4×C8C22×C3×C511yescharacteristic
238C2×C3×C5—42no—
239C2×C3×C5—81no—
240C2×C3×C5#45011yescharacteristic
241C2×C3×C5#45211yescharacteristic
242C2×C3×C5#45411yescharacteristic
243C23×C3—21no—
244C23×C3—21no—
245C3×Q8—42no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—44no—
252C3×D4C5×SD1612yes—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—22no—
256C2×C3×C4—44no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4C2×C5×D411yescharacteristic
263C2×C3×C4C2×C5×D411yescharacteristic
264C2×C3×C4C2×C5×D411yescharacteristic
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—41no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5C3×#12011yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—42no—
278C4×C5—41no—
279C4×C5—81no—
280C4×C5C2×C3×SD1611yescharacteristic
281C4×C5C3×#13511yescharacteristic
282C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
283C4×C5C3×#13711yescharacteristic
284#41—42no—
285#41—42no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×D4—22no—
289C2×D4C3×C5×D411yescharacteristic
290C2×D4C3×C5×D411yescharacteristic
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4C3×C5×D412yes—
302C4⋊C4C3×C5×D411yescharacteristic
303C4⋊C4C3×C5×D411yescharacteristic
304C22⋊C4—22no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C42C23×C3×C511yescharacteristic
308C3×C5#163511yescharacteristic, direct product factor, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3C5×#12011yescharacteristic
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4—81no—
321C3×C4C2×C5×SD1611yescharacteristic
322C3×C4C5×#13511yescharacteristic
323C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
324C3×C4C5×#13711yescharacteristic
325C2×C5—42no—
326C2×C5—81no—
327C2×C5C3×#45011yescharacteristic
328C2×C5C3×#45211yescharacteristic
329C2×C5C3×#45411yescharacteristic
330C23—21no—
331C23—21no—
332Q8—42no—
333Q8—41no—
334Q8—41no—
335D4—21no—
336D4—21no—
337D4—21no—
338D4—44no—
339D4C3×C5×SD1612yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4C2×C3×C5×D411yescharacteristic
350C2×C4C2×C3×C5×D411yescharacteristic
351C2×C4C2×C3×C5×D411yescharacteristic
352C8—41no—
353C8—41no—
354C8—41no—
355C2×C3—42no—
356C2×C3—81no—
357C2×C3C5×#45011yescharacteristic
358C2×C3C5×#45211yescharacteristic
359C2×C3C5×#45411yescharacteristic
360C5C3×#163511yescharacteristic, direct product factor, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22C3×C5×#12011yescharacteristic
368C4—21no—
369C4—41no—
370C4—42no—
371C4—41no—
372C4—81no—
373C4C2×C3×C5×SD1611yescharacteristic
374C4C3×C5×#13511yescharacteristic
375C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
376C4C3×C5×#13711yescharacteristic
377C3C5×#163511yescharacteristic, direct product factor, Sylow
378C2—42no—
379C2—81no—
380C2C3×C5×#45011yescharacteristic
381C2C3×C5×#45211yescharacteristic
382C2C3×C5×#45411yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#547C2
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×#476C2semidirect
4. C3×C5×#476C2semidirect
5. C3×C5×#332C2semidirect
6. C3×C5×D4⋊C8C2semidirect
7. C3×C5×D4⋊C8C2semidirect
8. C5×#1635C3direct (N × H)
26. C3×#1635C5direct (N × H)
28. C5×#487C2×C3semidirect
29. C5×#476C2×C3semidirect
30. C5×#476C2×C3semidirect
31. C5×#332C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. C5×D4⋊C8C2×C3semidirect
59. C3×#487C2×C5semidirect
60. C3×#476C2×C5semidirect
61. C3×#476C2×C5semidirect
62. C3×#332C2×C5semidirect
63. C3×D4⋊C8C2×C5semidirect
64. C3×D4⋊C8C2×C5semidirect
82. #1635C3×C5direct (N × H)
150. #487C2×C3×C5semidirect
151. #476C2×C3×C5semidirect
152. #476C2×C3×C5semidirect
153. #332C2×C3×C5semidirect
154. D4⋊C8C2×C3×C5semidirect
155. D4⋊C8C2×C3×C5semidirect
308. C3×C5#1635direct (N × H)
360. C5C3×#1635direct (N × H)
377. C3C5×#1635direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5472
C3×C5×#4872
C3×C5×#4762
C3×C5×#3322
C3×C5×D4⋊C82
C5×#16353
C3×#16355