Finite Group Databasebeta

← C3×C5×#1869 #14274903

Subgroups — C3×C5×#1869 #14274903

Order 1920.

864 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×C8C211yesmaximal, characteristic, complemented
2C2×C3×C4×C5×D4C211yesmaximal, characteristic
3C2×C3×C5×C22⋊C8C212yesmaximal, complemented
4C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×C5×#336C212yesmaximal, complemented
6C5×#1869C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C411yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C23×C3×C4×C5C2211yescharacteristic
10C22×C3×C5×C8—22no—
11C22×C3×C5×C8—24no—
12C22×C3×C5×C8C2212yes—
13C22×C3×C5×C8C2212yes—
14C3×C4×C5×D4—22no—
15C3×C4×C5×D4—22no—
16C2×C3×C5×C4⋊C4C411yescharacteristic
17C2×C3×C5×C22⋊C4C411yescharacteristic
18C2×C3×C5×C22⋊C4C411yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C3×C5×C22⋊C8—22no—
21C3×C5×C22⋊C8—24no—
22C3×#1869C511yesmaximal, characteristic, direct product factor, Hall
23C23×C5×C8C2×C311yescharacteristic, complemented
24C2×C4×C5×D4C2×C311yescharacteristic
25C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
26C2×C5×C22⋊C8C2×C312yescomplemented
27C5×#336C2×C312yescomplemented
28C24×C3×C5C2×C411yescharacteristic
29C24×C3×C5C2×C411yescharacteristic
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4C814yescomplemented
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×C4×C5C2×C411yescharacteristic
43C22×C3×C4×C5D412yes—
44C22×C3×C4×C5D412yes—
45C22×C3×C4×C5C2311yescharacteristic
46C2×C3×C5×C8—28no—
47C2×C3×C5×C8—22no—
48C2×C3×C5×C8—22no—
49C2×C3×C5×C8—22no—
50C2×C3×C5×C8—22no—
51C2×C3×C5×C8—22no—
52C2×C3×C5×C8D414yescomplemented
53C3×C5×C4⋊C4—22no—
54C3×C5×C22⋊C4—22no—
55C3×C5×C22⋊C4—22no—
56C3×C42×C5—21no—
57C3×C42×C5—21no—
58C23×C3×C8C2×C511yescharacteristic, complemented
59C2×C3×C4×D4C2×C511yescharacteristic
60C2×C3×C22⋊C8C2×C511yescharacteristic, complemented
61C2×C3×C22⋊C8C2×C512yescomplemented
62C3×#336C2×C512yescomplemented
63C22×C5×D4C3×C411yescharacteristic
64C23×C4×C5C22×C311yescharacteristic
65C23×C4×C5C22×C311yescharacteristic
66C22×C5×C8—22no—
67C22×C5×C8—24no—
68C22×C5×C8C22×C312yes—
69C22×C5×C8C22×C312yes—
70C4×C5×D4—22no—
71C4×C5×D4—22no—
72C2×C5×C4⋊C4C3×C411yescharacteristic
73C2×C5×C22⋊C4C3×C411yescharacteristic
74C2×C5×C22⋊C4C3×C411yescharacteristic
75C2×C42×C5C22×C311yescharacteristic
76C5×C22⋊C8—22no—
77C5×C22⋊C8—24no—
78#1869C3×C511yescharacteristic, direct product factor, Sylow
79C23×C3×C5—22no—
80C23×C3×C5—22no—
81C23×C3×C5—21no—
82C23×C3×C5—22no—
83C23×C3×C5—21no—
84C23×C3×C5—22no—
85C23×C3×C5C22⋊C412yes—
86C23×C3×C5C2×C812yes—
87C23×C3×C5C2×C812yescomplemented
88C23×C3×C5M1612yes—
89C23×C3×C5C22×C411yescharacteristic
90C3×C5×D4—28no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—24no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—42no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22⋊C412yes—
105C2×C3×C4×C5C2×C812yescomplemented
106C2×C3×C4×C5C2×D412yes—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4112yes—
110C3×C5×C8—24no—
111C3×C5×C8—42no—
112C22×C3×D4C4×C511yescharacteristic
113C23×C3×C4C22×C511yescharacteristic
114C23×C3×C4C22×C511yescharacteristic
115C22×C3×C8—22no—
116C22×C3×C8—24no—
117C22×C3×C8C22×C512yes—
118C22×C3×C8C22×C512yes—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C2×C3×C4⋊C4C4×C511yescharacteristic
122C2×C3×C22⋊C4C4×C511yescharacteristic
123C2×C3×C22⋊C4C4×C511yescharacteristic
124C2×C3×C42C22×C511yescharacteristic
125C3×C22⋊C8—22no—
126C3×C22⋊C8—24no—
127C24×C5C2×C3×C411yescharacteristic
128C24×C5C2×C3×C411yescharacteristic
129C2×C5×D4—22no—
130C2×C5×D4—22no—
131C2×C5×D4C3×C814yescomplemented
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5C2×C3×C411yescharacteristic
139C22×C4×C5C2×C3×C411yescharacteristic
140C22×C4×C5C2×C3×C411yescharacteristic
141C22×C4×C5C2×C3×C411yescharacteristic
142C22×C4×C5C3×D412yes—
143C22×C4×C5C3×D412yes—
144C22×C4×C5C23×C311yescharacteristic
145C2×C5×C8—28no—
146C2×C5×C8—22no—
147C2×C5×C8—22no—
148C2×C5×C8—22no—
149C2×C5×C8—22no—
150C2×C5×C8—22no—
151C2×C5×C8C3×D414yescomplemented
152C5×C4⋊C4—22no—
153C5×C22⋊C4—22no—
154C5×C22⋊C4—22no—
155C42×C5—21no—
156C42×C5—21no—
157C23×C8C2×C3×C511yescharacteristic, complemented
158C2×C4×D4C2×C3×C511yescharacteristic
159C2×C22⋊C8C2×C3×C511yescharacteristic, complemented
160C2×C22⋊C8C2×C3×C512yescomplemented
161#336C2×C3×C512yescomplemented
162C22×C3×C5—22no—
163C22×C3×C5—22no—
164C22×C3×C5—24no—
165C22×C3×C5—24no—
166C22×C3×C5—22no—
167C22×C3×C5—24no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—42no—
171C22×C3×C5C22⋊C814yescomplemented
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C22×C3×C5C4×D412yes—
174C22×C3×C5C22×C811yescharacteristic
175C22×C3×C5C2×M1611yescharacteristic
176C22×C3×C5#13112yes—
177C3×C4×C5—22no—
178C3×C4×C5—22no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×C4×C5#12011yescharacteristic
182C3×C4×C5#12112yes—
183C3×C4×C5#12311yescharacteristic
184C24×C3C2×C4×C511yescharacteristic
185C24×C3C2×C4×C511yescharacteristic
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4C5×C814yescomplemented
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4C2×C4×C511yescharacteristic
196C22×C3×C4C2×C4×C511yescharacteristic
197C22×C3×C4C2×C4×C511yescharacteristic
198C22×C3×C4C2×C4×C511yescharacteristic
199C22×C3×C4C5×D412yes—
200C22×C3×C4C5×D412yes—
201C22×C3×C4C23×C511yescharacteristic
202C2×C3×C8—28no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8C5×D414yescomplemented
209C3×C4⋊C4—22no—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—22no—
212C3×C42—21no—
213C3×C42—21no—
214C23×C5—22no—
215C23×C5—22no—
216C23×C5—21no—
217C23×C5—22no—
218C23×C5—21no—
219C23×C5—22no—
220C23×C5C3×C22⋊C412yes—
221C23×C5C2×C3×C812yes—
222C23×C5C2×C3×C812yescomplemented
223C23×C5C3×M1612yes—
224C23×C5C22×C3×C411yescharacteristic
225C5×D4—28no—
226C2×C4×C5—21no—
227C2×C4×C5—22no—
228C2×C4×C5—21no—
229C2×C4×C5—22no—
230C2×C4×C5—24no—
231C2×C4×C5—22no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—41no—
237C2×C4×C5—42no—
238C2×C4×C5—41no—
239C2×C4×C5C3×C22⋊C412yes—
240C2×C4×C5C2×C3×C812yescomplemented
241C2×C4×C5C2×C3×D412yes—
242C2×C4×C5C2×C3×D411yescharacteristic
243C2×C4×C5C2×C3×D411yescharacteristic
244C2×C4×C5C3×#4112yes—
245C5×C8—24no—
246C5×C8—42no—
247C22×D4C3×C4×C511yescharacteristic
248C23×C4C22×C3×C511yescharacteristic
249C23×C4C22×C3×C511yescharacteristic
250C22×C8—22no—
251C22×C8—24no—
252C22×C8C22×C3×C512yes—
253C22×C8C22×C3×C512yes—
254C4×D4—22no—
255C4×D4—22no—
256C2×C4⋊C4C3×C4×C511yescharacteristic
257C2×C22⋊C4C3×C4×C511yescharacteristic
258C2×C22⋊C4C3×C4×C511yescharacteristic
259C2×C42C22×C3×C511yescharacteristic
260C22⋊C8—22no—
261C22⋊C8—24no—
262C2×C3×C5—24no—
263C2×C3×C5—42no—
264C2×C3×C5#38611yescharacteristic
265C2×C3×C5C2×C22⋊C811yescharacteristic
266C2×C3×C5#40811yescharacteristic
267C2×C3×C5C8×D412yes—
268C2×C3×C5#43512yes—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—22no—
275C23×C3C5×C22⋊C412yes—
276C23×C3C2×C5×C812yes—
277C23×C3C2×C5×C812yescomplemented
278C23×C3C5×M1612yes—
279C23×C3C22×C4×C511yescharacteristic
280C3×D4—28no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—22no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—41no—
294C2×C3×C4C5×C22⋊C412yes—
295C2×C3×C4C2×C5×C812yescomplemented
296C2×C3×C4C2×C5×D412yes—
297C2×C3×C4C2×C5×D411yescharacteristic
298C2×C3×C4C2×C5×D411yescharacteristic
299C2×C3×C4C5×#4112yes—
300C3×C8—24no—
301C3×C8—42no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—24no—
305C22×C5—24no—
306C22×C5—22no—
307C22×C5—24no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5—42no—
311C22×C5C3×C22⋊C814yescomplemented
312C22×C5C2×C3×C22⋊C411yescharacteristic
313C22×C5C3×C4×D412yes—
314C22×C5C22×C3×C811yescharacteristic
315C22×C5C2×C3×M1611yescharacteristic
316C22×C5C3×#13112yes—
317C4×C5—22no—
318C4×C5—22no—
319C4×C5—41no—
320C4×C5—41no—
321C4×C5C3×#12011yescharacteristic
322C4×C5C3×#12112yes—
323C4×C5C3×#12311yescharacteristic
324C24C2×C3×C4×C511yescharacteristic
325C24C2×C3×C4×C511yescharacteristic
326C2×D4—22no—
327C2×D4—22no—
328C2×D4C3×C5×C814yescomplemented
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4C2×C3×C4×C511yescharacteristic
336C22×C4C2×C3×C4×C511yescharacteristic
337C22×C4C2×C3×C4×C511yescharacteristic
338C22×C4C2×C3×C4×C511yescharacteristic
339C22×C4C3×C5×D412yes—
340C22×C4C3×C5×D412yes—
341C22×C4C23×C3×C511yescharacteristic
342C2×C8—28no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8C3×C5×D414yescomplemented
349C4⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C42—21no—
353C42—21no—
354C3×C5#186911yescharacteristic, direct product factor, Hall
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—24no—
358C22×C3—24no—
359C22×C3—22no—
360C22×C3—24no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—42no—
364C22×C3C5×C22⋊C814yescomplemented
365C22×C3C2×C5×C22⋊C411yescharacteristic
366C22×C3C4×C5×D412yes—
367C22×C3C22×C5×C811yescharacteristic
368C22×C3C2×C5×M1611yescharacteristic
369C22×C3C5×#13112yes—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4C5×#12011yescharacteristic
375C3×C4C5×#12112yes—
376C3×C4C5×#12311yescharacteristic
377C2×C5—24no—
378C2×C5—42no—
379C2×C5C3×#38611yescharacteristic
380C2×C5C2×C3×C22⋊C811yescharacteristic
381C2×C5C3×#40811yescharacteristic
382C2×C5C3×C8×D412yes—
383C2×C5C3×#43512yes—
384C23—22no—
385C23—22no—
386C23—21no—
387C23—22no—
388C23—21no—
389C23—22no—
390C23C3×C5×C22⋊C412yes—
391C23C2×C3×C5×C812yes—
392C23C2×C3×C5×C812yescomplemented
393C23C3×C5×M1612yes—
394C23C22×C3×C4×C511yescharacteristic
395D4—28no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4C3×C5×C22⋊C412yes—
410C2×C4C2×C3×C5×C812yescomplemented
411C2×C4C2×C3×C5×D412yes—
412C2×C4C2×C3×C5×D411yescharacteristic
413C2×C4C2×C3×C5×D411yescharacteristic
414C2×C4C3×C5×#4112yes—
415C8—24no—
416C8—42no—
417C2×C3—24no—
418C2×C3—42no—
419C2×C3C5×#38611yescharacteristic
420C2×C3C2×C5×C22⋊C811yescharacteristic
421C2×C3C5×#40811yescharacteristic
422C2×C3C5×C8×D412yes—
423C2×C3C5×#43512yes—
424C5C3×#186911yescharacteristic, direct product factor, Sylow
425C22—22no—
426C22—22no—
427C22—24no—
428C22—24no—
429C22—22no—
430C22—24no—
431C22—41no—
432C22—41no—
433C22—42no—
434C22C3×C5×C22⋊C814yescomplemented
435C22C2×C3×C5×C22⋊C411yescharacteristic
436C22C3×C4×C5×D412yes—
437C22C22×C3×C5×C811yescharacteristic
438C22C2×C3×C5×M1611yescharacteristic
439C22C3×C5×#13112yes—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4C3×C5×#12011yescharacteristic
445C4C3×C5×#12112yes—
446C4C3×C5×#12311yescharacteristic
447C3C5×#186911yescharacteristic, direct product factor, Sylow
448C2—24no—
449C2—42no—
450C2C3×C5×#38611yescharacteristic
451C2C2×C3×C5×C22⋊C811yescharacteristic
452C2C3×C5×#40811yescharacteristic
453C2C3×C5×C8×D412yes—
454C2C3×C5×#43512yes—
subgroupG/H
centerC22×C3×C4×C5C23
commutatorC22C22×C3×C5×C8
Frattini, cosocleC22×C4C23×C3×C5
socleC23×C3×C5C22×C4
prime radicalC22×C3×C5×D4C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×C8C2semidirect
3. C2×C3×C5×C22⋊C8C2semidirect
4. C2×C3×C5×C22⋊C8C2semidirect
5. C3×C5×#336C2semidirect
6. C5×#1869C3direct (N × H)
22. C3×#1869C5direct (N × H)
23. C23×C5×C8C2×C3semidirect
25. C2×C5×C22⋊C8C2×C3semidirect
26. C2×C5×C22⋊C8C2×C3semidirect
27. C5×#336C2×C3semidirect
32. C2×C3×C5×D4C8semidirect
52. C2×C3×C5×C8D4semidirect
58. C23×C3×C8C2×C5semidirect
60. C2×C3×C22⋊C8C2×C5semidirect
61. C2×C3×C22⋊C8C2×C5semidirect
62. C3×#336C2×C5semidirect
78. #1869C3×C5direct (N × H)
87. C23×C3×C5C2×C8semidirect
105. C2×C3×C4×C5C2×C8semidirect
131. C2×C5×D4C3×C8semidirect
151. C2×C5×C8C3×D4semidirect
157. C23×C8C2×C3×C5semidirect
159. C2×C22⋊C8C2×C3×C5semidirect
160. C2×C22⋊C8C2×C3×C5semidirect
161. #336C2×C3×C5semidirect
171. C22×C3×C5C22⋊C8semidirect
188. C2×C3×D4C5×C8semidirect
208. C2×C3×C8C5×D4semidirect
222. C23×C5C2×C3×C8semidirect
240. C2×C4×C5C2×C3×C8semidirect
277. C23×C3C2×C5×C8semidirect
295. C2×C3×C4C2×C5×C8semidirect
311. C22×C5C3×C22⋊C8semidirect
328. C2×D4C3×C5×C8semidirect
348. C2×C8C3×C5×D4semidirect
354. C3×C5#1869direct (N × H)
364. C22×C3C5×C22⋊C8semidirect
392. C23C2×C3×C5×C8semidirect
410. C2×C4C2×C3×C5×C8semidirect
424. C5C3×#1869direct (N × H)
434. C22C3×C5×C22⋊C8semidirect
447. C3C5×#1869direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×C82
C2×C3×C4×C5×D42
C2×C3×C5×C22⋊C82
C3×C5×#3362
C5×#18693
C3×#18695