Finite Group Databasebeta

← C3×C5×#1661 #14274695

Subgroups — C3×C5×#1661 #14274695

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#562C211yesmaximal, characteristic
2C3×C5×#501C211yesmaximal, characteristic, complemented
3C3×C5×#497C211yesmaximal, characteristic, complemented
4C3×C5×#489C211yesmaximal, characteristic, complemented
5C3×C5×#330C211yesmaximal, characteristic, complemented
6C3×C5×#329C211yesmaximal, characteristic, complemented
7C3×C5×#329C211yesmaximal, characteristic, complemented
8C5×#1661C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#125C2211yescharacteristic
13C3×C5×#124C2211yescharacteristic
14C3×C5×#124C2211yescharacteristic
15C3×C5×#123—21no—
16C3×C5×#123—21no—
17C3×C5×C22⋊Q8—21no—
18C3×C5×C22⋊Q8—21no—
19C3×C5×#121—21no—
20C3×C5×#121—21no—
21C3×C5×#107—21no—
22C3×C5×#106—21no—
23C3×C5×#103—21no—
24C3×C5×#102—21no—
25C3×C5×#97C2211yescharacteristic
26C3×C5×#97C2211yescharacteristic
27C3×C5×#97C2211yescharacteristic
28C3×#1661C511yesmaximal, characteristic, direct product factor, Hall
29C5×#562C2×C311yescharacteristic
30C5×#501C2×C311yescharacteristic, complemented
31C5×#497C2×C311yescharacteristic, complemented
32C5×#489C2×C311yescharacteristic, complemented
33C5×#330C2×C311yescharacteristic, complemented
34C5×#329C2×C311yescharacteristic, complemented
35C5×#329C2×C311yescharacteristic, complemented
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C2×C3×C5×D4D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C3×C5×Q16—42no—
46C3×C5×SD16—42no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4D411yescharacteristic
57C3×C5×C4⋊C4D411yescharacteristic
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65C3×#562C2×C511yescharacteristic
66C3×#501C2×C511yescharacteristic, complemented
67C3×#497C2×C511yescharacteristic, complemented
68C3×#489C2×C511yescharacteristic, complemented
69C3×#330C2×C511yescharacteristic, complemented
70C3×#329C2×C511yescharacteristic, complemented
71C3×#329C2×C511yescharacteristic, complemented
72C2×C5×Q16—21no—
73C2×C5×SD16—21no—
74C5×C4⋊Q8C22×C311yescharacteristic
75C5×#125C22×C311yescharacteristic
76C5×#124C22×C311yescharacteristic
77C5×#124C22×C311yescharacteristic
78C5×#123—21no—
79C5×#123—21no—
80C5×C22⋊Q8—21no—
81C5×C22⋊Q8—21no—
82C5×#121—21no—
83C5×#121—21no—
84C5×#107—21no—
85C5×#106—21no—
86C5×#103—21no—
87C5×#102—21no—
88C5×#97C22×C311yescharacteristic
89C5×#97C22×C311yescharacteristic
90C5×#97C22×C311yescharacteristic
91#1661C3×C511yescharacteristic, direct product factor, Sylow
92C23×C3×C5—21no—
93C23×C3×C5—21no—
94C3×C5×Q8—41no—
95C3×C5×Q8—41no—
96C3×C5×Q8—41no—
97C3×C5×Q8—41no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C3×C5×D4—81no—
101C3×C5×D4—81no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—81no—
108C2×C3×C4×C5—81no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C3×C5×C8—22no—
113C3×C5×C8—22no—
114C3×C5×C8—41no—
115C2×C3×Q16—21no—
116C2×C3×SD16—21no—
117C3×C4⋊Q8C22×C511yescharacteristic
118C3×#125C22×C511yescharacteristic
119C3×#124C22×C511yescharacteristic
120C3×#124C22×C511yescharacteristic
121C3×#123—21no—
122C3×#123—21no—
123C3×C22⋊Q8—21no—
124C3×C22⋊Q8—21no—
125C3×#121—21no—
126C3×#121—21no—
127C3×#107—21no—
128C3×#106—21no—
129C3×#103—21no—
130C3×#102—21no—
131C3×#97C22×C511yescharacteristic
132C3×#97C22×C511yescharacteristic
133C3×#97C22×C511yescharacteristic
134C2×C5×Q8—21no—
135C2×C5×Q8C3×D411yescharacteristic
136C2×C5×Q8C3×D411yescharacteristic
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4C3×D411yescharacteristic
140C2×C5×D4C3×D411yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C5×Q16—42no—
144C5×SD16—42no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4C3×D411yescharacteristic
155C5×C4⋊C4C3×D411yescharacteristic
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—21no—
159C5×C22⋊C4—21no—
160C5×C22⋊C4—21no—
161C5×C22⋊C4—21no—
162C42×C5C23×C311yescharacteristic
163#562C2×C3×C511yescharacteristic
164#501C2×C3×C511yescharacteristic, complemented
165#497C2×C3×C511yescharacteristic, complemented
166#489C2×C3×C511yescharacteristic, complemented
167#330C2×C3×C511yescharacteristic, complemented
168#329C2×C3×C511yescharacteristic, complemented
169#329C2×C3×C511yescharacteristic, complemented
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5#12011yescharacteristic
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183C3×C4×C5—41no—
184C3×C4×C5—81no—
185C2×C3×Q8—21no—
186C2×C3×Q8C5×D411yescharacteristic
187C2×C3×Q8C5×D411yescharacteristic
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4C5×D411yescharacteristic
191C2×C3×D4C5×D411yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C3×Q16—42no—
195C3×SD16—42no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4C5×D411yescharacteristic
206C3×C4⋊C4C5×D411yescharacteristic
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213C3×C42C23×C511yescharacteristic
214C23×C5—21no—
215C23×C5—21no—
216C5×Q8—41no—
217C5×Q8—41no—
218C5×Q8—41no—
219C5×Q8—41no—
220C5×D4—41no—
221C5×D4—41no—
222C5×D4—81no—
223C5×D4—81no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—41no—
229C2×C4×C5—81no—
230C2×C4×C5—81no—
231C2×C4×C5C2×C3×D411yescharacteristic
232C2×C4×C5C2×C3×D411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C5×C8—22no—
235C5×C8—22no—
236C5×C8—41no—
237C2×Q16—21no—
238C2×SD16—21no—
239C4⋊Q8C22×C3×C511yescharacteristic
240#125C22×C3×C511yescharacteristic
241#124C22×C3×C511yescharacteristic
242#124C22×C3×C511yescharacteristic
243#123—21no—
244#123—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247#121—21no—
248#121—21no—
249#107—21no—
250#106—21no—
251#103—21no—
252#102—21no—
253#97C22×C3×C511yescharacteristic
254#97C22×C3×C511yescharacteristic
255#97C22×C3×C511yescharacteristic
256C2×C3×C5—81no—
257C2×C3×C5—81no—
258C2×C3×C5#45311yescharacteristic
259C2×C3×C5#45511yescharacteristic
260C2×C3×C5#45611yescharacteristic
261C23×C3—21no—
262C23×C3—21no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—81no—
270C3×D4—81no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—81no—
277C2×C3×C4—81no—
278C2×C3×C4C2×C5×D411yescharacteristic
279C2×C3×C4C2×C5×D411yescharacteristic
280C2×C3×C4C2×C5×D411yescharacteristic
281C3×C8—22no—
282C3×C8—22no—
283C3×C8—41no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—41no—
287C22×C5—41no—
288C22×C5—41no—
289C22×C5—41no—
290C22×C5C3×#12011yescharacteristic
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—41no—
295C4×C5—41no—
296C4×C5—41no—
297C4×C5—41no—
298C4×C5—81no—
299C2×Q8—21no—
300C2×Q8C3×C5×D411yescharacteristic
301C2×Q8C3×C5×D411yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C3×C5×D411yescharacteristic
305C2×D4C3×C5×D411yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308Q16—42no—
309SD16—42no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4C3×C5×D411yescharacteristic
320C4⋊C4C3×C5×D411yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C42C23×C3×C511yescharacteristic
328C3×C5#166111yescharacteristic, direct product factor, Hall
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3C5×#12011yescharacteristic
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—81no—
344C2×C5—81no—
345C2×C5—81no—
346C2×C5C3×#45311yescharacteristic
347C2×C5C3×#45511yescharacteristic
348C2×C5C3×#45611yescharacteristic
349C23—21no—
350C23—21no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354Q8—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4C2×C3×C5×D411yescharacteristic
367C2×C4C2×C3×C5×D411yescharacteristic
368C2×C4C2×C3×C5×D411yescharacteristic
369C8—22no—
370C8—22no—
371C8—41no—
372C2×C3—81no—
373C2×C3—81no—
374C2×C3C5×#45311yescharacteristic
375C2×C3C5×#45511yescharacteristic
376C2×C3C5×#45611yescharacteristic
377C5C3×#166111yescharacteristic, direct product factor, Sylow
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22C3×C5×#12011yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—81no—
393C3C5×#166111yescharacteristic, direct product factor, Sylow
394C2—81no—
395C2—81no—
396C2C3×C5×#45311yescharacteristic
397C2C3×C5×#45511yescharacteristic
398C2C3×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#562C2
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×#497C2semidirect
4. C3×C5×#489C2semidirect
5. C3×C5×#330C2semidirect
6. C3×C5×#329C2semidirect
7. C3×C5×#329C2semidirect
8. C5×#1661C3direct (N × H)
28. C3×#1661C5direct (N × H)
30. C5×#501C2×C3semidirect
31. C5×#497C2×C3semidirect
32. C5×#489C2×C3semidirect
33. C5×#330C2×C3semidirect
34. C5×#329C2×C3semidirect
35. C5×#329C2×C3semidirect
66. C3×#501C2×C5semidirect
67. C3×#497C2×C5semidirect
68. C3×#489C2×C5semidirect
69. C3×#330C2×C5semidirect
70. C3×#329C2×C5semidirect
71. C3×#329C2×C5semidirect
91. #1661C3×C5direct (N × H)
164. #501C2×C3×C5semidirect
165. #497C2×C3×C5semidirect
166. #489C2×C3×C5semidirect
167. #330C2×C3×C5semidirect
168. #329C2×C3×C5semidirect
169. #329C2×C3×C5semidirect
328. C3×C5#1661direct (N × H)
377. C5C3×#1661direct (N × H)
393. C3C5×#1661direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5622
C3×C5×#5012
C3×C5×#4972
C3×C5×#4892
C3×C5×#3302
C3×C5×#3292
C5×#16613
C3×#16615