Finite Group Databasebeta

← C3×C5×#1996 #14275030

Subgroups — C3×C5×#1996 #14275030

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic
3C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
4C3×C5×#342C214yesmaximal
5C5×#1996C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×Q8C411yescharacteristic, complemented
7C23×C3×C4×C5C2211yescharacteristic
8C3×C5×C22⋊Q8—21no—
9C3×C5×C22⋊Q8—21no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8—21no—
12C2×C3×C5×C4⋊C4—21no—
13C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
14C2×C3×C5×C4⋊C4C412yescomplemented
15C2×C3×C5×C22⋊C4C2212yes—
16C2×C3×C5×C22⋊C4C2212yes—
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C3×C42×C5—21no—
19C3×C5×#95—21no—
20C3×C5×#95—21no—
21C3×#1996C511yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C22⋊Q8C2×C311yescharacteristic
23C5×#380C2×C311yescharacteristic
24C4×C5×C22⋊C4C2×C311yescharacteristic
25C5×#342C2×C314yes—
26C24×C3×C5C2311yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8—21no—
29C2×C3×C5×Q8—42no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C412yes—
35C22×C3×C4×C5C2×C412yes—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—42no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4—22no—
49C3×C5×C22⋊C4—24no—
50C3×C5×C22⋊C4Q814yescomplemented
51C3×C42×C5—42no—
52C2×C3×C22⋊Q8C2×C511yescharacteristic
53C3×#380C2×C511yescharacteristic
54C3×C4×C22⋊C4C2×C511yescharacteristic
55C3×#342C2×C514yes—
56C22×C5×Q8C3×C411yescharacteristic, complemented
57C23×C4×C5C22×C311yescharacteristic
58C5×C22⋊Q8—21no—
59C5×C22⋊Q8—21no—
60C5×C22⋊Q8—21no—
61C5×C22⋊Q8—21no—
62C2×C5×C4⋊C4—21no—
63C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
64C2×C5×C4⋊C4C3×C412yescomplemented
65C2×C5×C22⋊C4C22×C312yes—
66C2×C5×C22⋊C4C22×C312yes—
67C2×C5×C22⋊C4C22×C312yes—
68C2×C42×C5—21no—
69C5×#95—21no—
70C5×#95—21no—
71#1996C3×C511yescharacteristic, direct product factor, Sylow
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C23×C3×C5C2×D411yescharacteristic
77C23×C3×C5C2×Q812yes—
78C23×C3×C5#4112yes—
79C3×C5×Q8—42no—
80C3×C5×Q8—42no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5—42no—
95C2×C3×C4×C5—42no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C22×C3×Q8C4×C511yescharacteristic, complemented
102C23×C3×C4C22×C511yescharacteristic
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—21no—
105C3×C22⋊Q8—21no—
106C3×C22⋊Q8—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C4×C511yescharacteristic, complemented
109C2×C3×C4⋊C4C4×C512yescomplemented
110C2×C3×C22⋊C4C22×C512yes—
111C2×C3×C22⋊C4C22×C512yes—
112C2×C3×C22⋊C4C22×C512yes—
113C2×C3×C42—21no—
114C3×#95—21no—
115C3×#95—21no—
116C24×C5C23×C311yescharacteristic
117C2×C5×Q8—21no—
118C2×C5×Q8—21no—
119C2×C5×Q8—42no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—42no—
123C22×C4×C5C2×C3×C411yescharacteristic
124C22×C4×C5C2×C3×C412yes—
125C22×C4×C5C2×C3×C412yes—
126C22×C4×C5C2×C3×C411yescharacteristic
127C22×C4×C5C3×D411yescharacteristic
128C22×C4×C5C3×D411yescharacteristic
129C22×C4×C5C3×D411yescharacteristic
130C22×C4×C5C3×D411yescharacteristic
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—22no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—42no—
136C5×C22⋊C4—22no—
137C5×C22⋊C4—22no—
138C5×C22⋊C4—22no—
139C5×C22⋊C4—24no—
140C5×C22⋊C4C3×Q814yescomplemented
141C42×C5—42no—
142C2×C22⋊Q8C2×C3×C511yescharacteristic
143#380C2×C3×C511yescharacteristic
144C4×C22⋊C4C2×C3×C511yescharacteristic
145#342C2×C3×C514yes—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C22×C3×C5C4×Q812yes—
156C22×C3×C5C22⋊Q812yes—
157C22×C3×C5#12411yescharacteristic
158C22×C3×C5C4⋊Q811yescharacteristic
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—44no—
163C3×C4×C5—42no—
164C3×C4×C5—42no—
165C3×C4×C5—82no—
166C3×C4×C5#9912yes—
167C24×C3C23×C511yescharacteristic
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—42no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—42no—
174C22×C3×C4C2×C4×C511yescharacteristic
175C22×C3×C4C2×C4×C512yes—
176C22×C3×C4C2×C4×C512yes—
177C22×C3×C4C2×C4×C511yescharacteristic
178C22×C3×C4C5×D411yescharacteristic
179C22×C3×C4C5×D411yescharacteristic
180C22×C3×C4C5×D411yescharacteristic
181C22×C3×C4C5×D411yescharacteristic
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—42no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—22no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—24no—
191C3×C22⋊C4C5×Q814yescomplemented
192C3×C42—42no—
193C23×C5—41no—
194C23×C5—41no—
195C23×C5C22×C3×C411yescharacteristic
196C23×C5C2×C3×D411yescharacteristic
197C23×C5C2×C3×D411yescharacteristic
198C23×C5C2×C3×Q812yes—
199C23×C5C3×#4112yes—
200C5×Q8—42no—
201C5×Q8—42no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—22no—
206C2×C4×C5—22no—
207C2×C4×C5—24no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5—42no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5C3×C22⋊C411yescharacteristic
219C2×C4×C5C3×C22⋊C411yescharacteristic
220C2×C4×C5C3×C22⋊C411yescharacteristic
221C2×C4×C5C3×C22⋊C411yescharacteristic
222C22×Q8C3×C4×C511yescharacteristic, complemented
223C23×C4C22×C3×C511yescharacteristic
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C3×C4×C511yescharacteristic, complemented
230C2×C4⋊C4C3×C4×C512yescomplemented
231C2×C22⋊C4C22×C3×C512yes—
232C2×C22⋊C4C22×C3×C512yes—
233C2×C22⋊C4C22×C3×C512yes—
234C2×C42—21no—
235#95—21no—
236#95—21no—
237C2×C3×C5—22no—
238C2×C3×C5—21no—
239C2×C3×C5—22no—
240C2×C3×C5—21no—
241C2×C3×C5#39111yescharacteristic
242C2×C3×C5C2×#9911yescharacteristic
243C2×C3×C5#41011yescharacteristic
244C23×C3—41no—
245C23×C3—41no—
246C23×C3C22×C4×C511yescharacteristic
247C23×C3C2×C5×D411yescharacteristic
248C23×C3C2×C5×D411yescharacteristic
249C23×C3C2×C5×Q812yes—
250C23×C3C5×#4112yes—
251C3×Q8—42no—
252C3×Q8—42no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—24no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4C5×C22⋊C411yescharacteristic
270C2×C3×C4C5×C22⋊C411yescharacteristic
271C2×C3×C4C5×C22⋊C411yescharacteristic
272C2×C3×C4C5×C22⋊C411yescharacteristic
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—42no—
280C22×C5—42no—
281C22×C5C2×C3×C22⋊C411yescharacteristic
282C22×C5C3×C4×Q812yes—
283C22×C5C3×C22⋊Q812yes—
284C22×C5C3×#12411yescharacteristic
285C22×C5C3×C4⋊Q811yescharacteristic
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—44no—
290C4×C5—42no—
291C4×C5—42no—
292C4×C5—82no—
293C4×C5C3×#9912yes—
294C24C23×C3×C511yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4C2×C3×C4×C511yescharacteristic
302C22×C4C2×C3×C4×C512yes—
303C22×C4C2×C3×C4×C512yes—
304C22×C4C2×C3×C4×C511yescharacteristic
305C22×C4C3×C5×D411yescharacteristic
306C22×C4C3×C5×D411yescharacteristic
307C22×C4C3×C5×D411yescharacteristic
308C22×C4C3×C5×D411yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—42no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—24no—
318C22⋊C4C3×C5×Q814yescomplemented
319C42—42no—
320C3×C5#199611yescharacteristic, direct product factor, Hall
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3C2×C5×C22⋊C411yescharacteristic
330C22×C3C4×C5×Q812yes—
331C22×C3C5×C22⋊Q812yes—
332C22×C3C5×#12411yescharacteristic
333C22×C3C5×C4⋊Q811yescharacteristic
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—44no—
338C3×C4—42no—
339C3×C4—42no—
340C3×C4—82no—
341C3×C4C5×#9912yes—
342C2×C5—22no—
343C2×C5—21no—
344C2×C5—22no—
345C2×C5—21no—
346C2×C5C3×#39111yescharacteristic
347C2×C5C2×C3×#9911yescharacteristic
348C2×C5C3×#41011yescharacteristic
349C23—41no—
350C23—41no—
351C23C22×C3×C4×C511yescharacteristic
352C23C2×C3×C5×D411yescharacteristic
353C23C2×C3×C5×D411yescharacteristic
354C23C2×C3×C5×Q812yes—
355C23C3×C5×#4112yes—
356Q8—42no—
357Q8—42no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4C3×C5×C22⋊C411yescharacteristic
375C2×C4C3×C5×C22⋊C411yescharacteristic
376C2×C4C3×C5×C22⋊C411yescharacteristic
377C2×C4C3×C5×C22⋊C411yescharacteristic
378C2×C3—22no—
379C2×C3—21no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3C5×#39111yescharacteristic
383C2×C3C2×C5×#9911yescharacteristic
384C2×C3C5×#41011yescharacteristic
385C5C3×#199611yescharacteristic, direct product factor, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22C2×C3×C5×C22⋊C411yescharacteristic
395C22C3×C4×C5×Q812yes—
396C22C3×C5×C22⋊Q812yes—
397C22C3×C5×#12411yescharacteristic
398C22C3×C5×C4⋊Q811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—44no—
403C4—42no—
404C4—42no—
405C4—82no—
406C4C3×C5×#9912yes—
407C3C5×#199611yescharacteristic, direct product factor, Sylow
408C2—22no—
409C2—21no—
410C2—22no—
411C2—21no—
412C2C3×C5×#39111yescharacteristic
413C2C2×C3×C5×#9911yescharacteristic
414C2C3×C5×#41011yescharacteristic
subgroupG/H
center, socleC22×C3×C5C2×C22⋊C4
commutatorC23C22×C3×C4×C5
Frattini, cosocleC24C23×C3×C5
prime radicalC24×C3×C5C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. C5×#1996C3direct (N × H)
6. C22×C3×C5×Q8C4semidirect
13. C2×C3×C5×C4⋊C4C4semidirect
14. C2×C3×C5×C4⋊C4C4semidirect
21. C3×#1996C5direct (N × H)
50. C3×C5×C22⋊C4Q8semidirect
56. C22×C5×Q8C3×C4semidirect
63. C2×C5×C4⋊C4C3×C4semidirect
64. C2×C5×C4⋊C4C3×C4semidirect
71. #1996C3×C5direct (N × H)
101. C22×C3×Q8C4×C5semidirect
108. C2×C3×C4⋊C4C4×C5semidirect
109. C2×C3×C4⋊C4C4×C5semidirect
140. C5×C22⋊C4C3×Q8semidirect
191. C3×C22⋊C4C5×Q8semidirect
222. C22×Q8C3×C4×C5semidirect
229. C2×C4⋊C4C3×C4×C5semidirect
230. C2×C4⋊C4C3×C4×C5semidirect
318. C22⋊C4C3×C5×Q8semidirect
320. C3×C5#1996direct (N × H)
385. C5C3×#1996direct (N × H)
407. C3C5×#1996direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C3×C5×#3802
C3×C4×C5×C22⋊C42
C3×C5×#3422
C5×#19963
C3×#19965