Finite Group Databasebeta

← C3×C5×#1799 #14274833

Subgroups — C3×C5×#1799 #14274833

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×C5×#99C212yesmaximal
3C3×C5×#380C212yesmaximal, complemented
4C3×C5×#342C212yesmaximal, complemented
5C5×#1799C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4C2211yescharacteristic
7C23×C3×C4×C5C411yescharacteristic, complemented
8C23×C3×C4×C5C2211yescharacteristic
9C3×C4×C5×D4—22no—
10C3×C4×C5×D4—22no—
11C2×C3×C5×C4⋊C4—22no—
12C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
13C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
14C2×C3×C5×C22⋊C4C2214yes—
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×C3×C42×C5C411yescharacteristic, complemented
17C3×C5×#99—24no—
18C3×C5×#95—22no—
19C3×#1799C511yesmaximal, characteristic, direct product factor, Hall
20C2×C4×C5×D4C2×C311yescharacteristic
21C2×C5×#99C2×C312yes—
22C5×#380C2×C312yescomplemented
23C5×#342C2×C312yescomplemented
24C24×C3×C5C2×C411yescharacteristic
25C24×C3×C5C2311yescharacteristic
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4D412yes—
29C2×C3×C5×D4Q812yes—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—24no—
33C22×C3×C4×C5—42no—
34C22×C3×C4×C5—42no—
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5D412yes—
41C22×C3×C4×C5D412yes—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—44no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—24no—
47C3×C5×C22⋊C4—24no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C2×C3×C4×D4C2×C511yescharacteristic
51C2×C3×#99C2×C512yes—
52C3×#380C2×C512yescomplemented
53C3×#342C2×C512yescomplemented
54C22×C5×D4C22×C311yescharacteristic
55C23×C4×C5C3×C411yescharacteristic, complemented
56C23×C4×C5C22×C311yescharacteristic
57C4×C5×D4—22no—
58C4×C5×D4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
61C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
62C2×C5×C22⋊C4C22×C314yes—
63C2×C5×C22⋊C4C22×C311yescharacteristic
64C2×C42×C5C3×C411yescharacteristic, complemented
65C5×#99—24no—
66C5×#95—22no—
67#1799C3×C511yescharacteristic, direct product factor, Sylow
68C23×C3×C5—21no—
69C23×C3×C5—21no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5—41no—
74C23×C3×C5C4⋊C412yescomplemented
75C23×C3×C5C22×C411yescharacteristic
76C23×C3×C5C2×D412yes—
77C23×C3×C5C2×D411yescharacteristic
78C23×C3×C5C2×Q811yescharacteristic
79C23×C3×C5#4112yes—
80C3×C5×D4—24no—
81C3×C5×D4—24no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—24no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—44no—
95C2×C3×C4×C5—44no—
96C2×C3×C4×C5—44no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C412yes—
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C4⋊C412yescomplemented
101C22×C3×D4C22×C511yescharacteristic
102C23×C3×C4C4×C511yescharacteristic, complemented
103C23×C3×C4C22×C511yescharacteristic
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4C4×C511yescharacteristic, complemented
108C2×C3×C22⋊C4C4×C511yescharacteristic, complemented
109C2×C3×C22⋊C4C22×C514yes—
110C2×C3×C22⋊C4C22×C511yescharacteristic
111C2×C3×C42C4×C511yescharacteristic, complemented
112C3×#99—24no—
113C3×#95—22no—
114C24×C5C2×C3×C411yescharacteristic
115C24×C5C23×C311yescharacteristic
116C2×C5×D4—22no—
117C2×C5×D4—22no—
118C2×C5×D4C3×D412yes—
119C2×C5×D4C3×Q812yes—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—24no—
123C22×C4×C5—42no—
124C22×C4×C5—42no—
125C22×C4×C5C2×C3×C411yescharacteristic
126C22×C4×C5C2×C3×C411yescharacteristic
127C22×C4×C5C2×C3×C411yescharacteristic
128C22×C4×C5C2×C3×C411yescharacteristic
129C22×C4×C5C2×C3×C411yescharacteristic
130C22×C4×C5C3×D412yes—
131C22×C4×C5C3×D412yes—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—44no—
134C5×C22⋊C4—22no—
135C5×C22⋊C4—22no—
136C5×C22⋊C4—24no—
137C5×C22⋊C4—24no—
138C42×C5—21no—
139C42×C5—21no—
140C2×C4×D4C2×C3×C511yescharacteristic
141C2×#99C2×C3×C512yes—
142#380C2×C3×C512yescomplemented
143#342C2×C3×C512yescomplemented
144C22×C3×C5—22no—
145C22×C3×C5—21no—
146C22×C3×C5—22no—
147C22×C3×C5—21no—
148C22×C3×C5—22no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5—42no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5—41no—
155C22×C3×C5—41no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C2×C4⋊C411yescharacteristic
158C22×C3×C5#11711yescharacteristic
159C22×C3×C5#12112yes—
160C22×C3×C5C22⋊Q812yes—
161C3×C4×C5—22no—
162C3×C4×C5—21no—
163C3×C4×C5—22no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5—84no—
167C3×C4×C5#9912yescomplemented
168C24×C3C2×C4×C511yescharacteristic
169C24×C3C23×C511yescharacteristic
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4C5×D412yes—
173C2×C3×D4C5×Q812yes—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—24no—
177C22×C3×C4—42no—
178C22×C3×C4—42no—
179C22×C3×C4C2×C4×C511yescharacteristic
180C22×C3×C4C2×C4×C511yescharacteristic
181C22×C3×C4C2×C4×C511yescharacteristic
182C22×C3×C4C2×C4×C511yescharacteristic
183C22×C3×C4C2×C4×C511yescharacteristic
184C22×C3×C4C5×D412yes—
185C22×C3×C4C5×D412yes—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—44no—
188C3×C22⋊C4—22no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—24no—
191C3×C22⋊C4—24no—
192C3×C42—21no—
193C3×C42—21no—
194C23×C5—21no—
195C23×C5—21no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5—41no—
199C23×C5—41no—
200C23×C5C3×C4⋊C412yescomplemented
201C23×C5C22×C3×C411yescharacteristic
202C23×C5C2×C3×D412yes—
203C23×C5C2×C3×D411yescharacteristic
204C23×C5C2×C3×Q811yescharacteristic
205C23×C5C3×#4112yes—
206C5×D4—24no—
207C5×D4—24no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—24no—
211C2×C4×C5—22no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—41no—
215C2×C4×C5—42no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—44no—
221C2×C4×C5—44no—
222C2×C4×C5—44no—
223C2×C4×C5C3×C22⋊C411yescharacteristic
224C2×C4×C5C3×C22⋊C412yes—
225C2×C4×C5C3×C22⋊C411yescharacteristic
226C2×C4×C5C3×C4⋊C412yescomplemented
227C22×D4C22×C3×C511yescharacteristic
228C23×C4C3×C4×C511yescharacteristic, complemented
229C23×C4C22×C3×C511yescharacteristic
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C3×C4×C511yescharacteristic, complemented
234C2×C22⋊C4C3×C4×C511yescharacteristic, complemented
235C2×C22⋊C4C22×C3×C514yes—
236C2×C22⋊C4C22×C3×C511yescharacteristic
237C2×C42C3×C4×C511yescharacteristic, complemented
238#99—24no—
239#95—22no—
240C2×C3×C5—22no—
241C2×C3×C5—21no—
242C2×C3×C5—21no—
243C2×C3×C5—22no—
244C2×C3×C5—42no—
245C2×C3×C5#38011yescharacteristic
246C2×C3×C5C2×#9911yescharacteristic
247C2×C3×C5#41011yescharacteristic
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—41no—
254C23×C3C5×C4⋊C412yescomplemented
255C23×C3C22×C4×C511yescharacteristic
256C23×C3C2×C5×D412yes—
257C23×C3C2×C5×D411yescharacteristic
258C23×C3C2×C5×Q811yescharacteristic
259C23×C3C5×#4112yes—
260C3×D4—24no—
261C3×D4—24no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—24no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—44no—
275C2×C3×C4—44no—
276C2×C3×C4—44no—
277C2×C3×C4C5×C22⋊C411yescharacteristic
278C2×C3×C4C5×C22⋊C412yes—
279C2×C3×C4C5×C22⋊C411yescharacteristic
280C2×C3×C4C5×C4⋊C412yescomplemented
281C22×C5—22no—
282C22×C5—21no—
283C22×C5—22no—
284C22×C5—21no—
285C22×C5—22no—
286C22×C5—41no—
287C22×C5—41no—
288C22×C5—42no—
289C22×C5—42no—
290C22×C5—42no—
291C22×C5—41no—
292C22×C5—41no—
293C22×C5C2×C3×C22⋊C411yescharacteristic
294C22×C5C2×C3×C4⋊C411yescharacteristic
295C22×C5C3×#11711yescharacteristic
296C22×C5C3×#12112yes—
297C22×C5C3×C22⋊Q812yes—
298C4×C5—22no—
299C4×C5—21no—
300C4×C5—22no—
301C4×C5—41no—
302C4×C5—41no—
303C4×C5—84no—
304C4×C5C3×#9912yescomplemented
305C24C2×C3×C4×C511yescharacteristic
306C24C23×C3×C511yescharacteristic
307C2×D4—22no—
308C2×D4—22no—
309C2×D4C3×C5×D412yes—
310C2×D4C3×C5×Q812yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4C2×C3×C4×C511yescharacteristic
317C22×C4C2×C3×C4×C511yescharacteristic
318C22×C4C2×C3×C4×C511yescharacteristic
319C22×C4C2×C3×C4×C511yescharacteristic
320C22×C4C2×C3×C4×C511yescharacteristic
321C22×C4C3×C5×D412yes—
322C22×C4C3×C5×D412yes—
323C4⋊C4—22no—
324C4⋊C4—44no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C42—21no—
330C42—21no—
331C3×C5#179911yescharacteristic, direct product factor, Hall
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3C2×C5×C22⋊C411yescharacteristic
345C22×C3C2×C5×C4⋊C411yescharacteristic
346C22×C3C5×#11711yescharacteristic
347C22×C3C5×#12112yes—
348C22×C3C5×C22⋊Q812yes—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—22no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—84no—
355C3×C4C5×#9912yescomplemented
356C2×C5—22no—
357C2×C5—21no—
358C2×C5—21no—
359C2×C5—22no—
360C2×C5—42no—
361C2×C5C3×#38011yescharacteristic
362C2×C5C2×C3×#9911yescharacteristic
363C2×C5C3×#41011yescharacteristic
364C23—21no—
365C23—21no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23C3×C5×C4⋊C412yescomplemented
371C23C22×C3×C4×C511yescharacteristic
372C23C2×C3×C5×D412yes—
373C23C2×C3×C5×D411yescharacteristic
374C23C2×C3×C5×Q811yescharacteristic
375C23C3×C5×#4112yes—
376D4—24no—
377D4—24no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4C3×C5×C22⋊C411yescharacteristic
394C2×C4C3×C5×C22⋊C412yes—
395C2×C4C3×C5×C22⋊C411yescharacteristic
396C2×C4C3×C5×C4⋊C412yescomplemented
397C2×C3—22no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—22no—
401C2×C3—42no—
402C2×C3C5×#38011yescharacteristic
403C2×C3C2×C5×#9911yescharacteristic
404C2×C3C5×#41011yescharacteristic
405C5C3×#179911yescharacteristic, direct product factor, Sylow
406C22—22no—
407C22—21no—
408C22—22no—
409C22—21no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—41no—
417C22—41no—
418C22C2×C3×C5×C22⋊C411yescharacteristic
419C22C2×C3×C5×C4⋊C411yescharacteristic
420C22C3×C5×#11711yescharacteristic
421C22C3×C5×#12112yes—
422C22C3×C5×C22⋊Q812yes—
423C4—22no—
424C4—21no—
425C4—22no—
426C4—41no—
427C4—41no—
428C4—84no—
429C4C3×C5×#9912yescomplemented
430C3C5×#179911yescharacteristic, direct product factor, Sylow
431C2—22no—
432C2—21no—
433C2—21no—
434C2—22no—
435C2—42no—
436C2C3×C5×#38011yescharacteristic
437C2C2×C3×C5×#9911yescharacteristic
438C2C3×C5×#41011yescharacteristic
subgroupG/H
center, socleC22×C3×C5C2×C22⋊C4
commutatorC23C22×C3×C4×C5
Frattini, cosocleC24C23×C3×C5
prime radicalC22×C3×C5×D4C22
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
3. C3×C5×#380C2semidirect
4. C3×C5×#342C2semidirect
5. C5×#1799C3direct (N × H)
7. C23×C3×C4×C5C4semidirect
12. C2×C3×C5×C4⋊C4C4semidirect
13. C2×C3×C5×C22⋊C4C4semidirect
16. C2×C3×C42×C5C4semidirect
19. C3×#1799C5direct (N × H)
22. C5×#380C2×C3semidirect
23. C5×#342C2×C3semidirect
52. C3×#380C2×C5semidirect
53. C3×#342C2×C5semidirect
55. C23×C4×C5C3×C4semidirect
60. C2×C5×C4⋊C4C3×C4semidirect
61. C2×C5×C22⋊C4C3×C4semidirect
64. C2×C42×C5C3×C4semidirect
67. #1799C3×C5direct (N × H)
74. C23×C3×C5C4⋊C4semidirect
100. C2×C3×C4×C5C4⋊C4semidirect
102. C23×C3×C4C4×C5semidirect
107. C2×C3×C4⋊C4C4×C5semidirect
108. C2×C3×C22⋊C4C4×C5semidirect
111. C2×C3×C42C4×C5semidirect
142. #380C2×C3×C5semidirect
143. #342C2×C3×C5semidirect
167. C3×C4×C5#99semidirect
200. C23×C5C3×C4⋊C4semidirect
226. C2×C4×C5C3×C4⋊C4semidirect
228. C23×C4C3×C4×C5semidirect
233. C2×C4⋊C4C3×C4×C5semidirect
234. C2×C22⋊C4C3×C4×C5semidirect
237. C2×C42C3×C4×C5semidirect
254. C23×C3C5×C4⋊C4semidirect
280. C2×C3×C4C5×C4⋊C4semidirect
304. C4×C5C3×#99semidirect
331. C3×C5#1799direct (N × H)
355. C3×C4C5×#99semidirect
370. C23C3×C5×C4⋊C4semidirect
396. C2×C4C3×C5×C4⋊C4semidirect
405. C5C3×#1799direct (N × H)
429. C4C3×C5×#99semidirect
430. C3C5×#1799direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×C5×#992
C3×C5×#3802
C3×C5×#3422
C5×#17993
C3×#17995