Finite Group Databasebeta

← C3×C5×#3095 #14276129

Subgroups — C3×C5×#3095 #14276129

Order 1920.

820 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic
3C3×C5×#485C214yesmaximal, complemented
4C3×C5×#484C212yesmaximal, complemented
5C3×C5×#483C212yesmaximal, complemented
6C3×C5×#428C212yesmaximal, complemented
7C3×C5×#419C212yesmaximal, complemented
8C3×C5×#407C211yesmaximal, characteristic
9C5×#3095C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C2×C3×C5×M16C2212yes—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8—21no—
15C3×C5×C22⋊Q8C2212yes—
16C3×C5×C22⋊Q8C2212yes—
17C3×C5×#117—21no—
18C3×C5×#117—21no—
19C3×C5×#117C2212yes—
20C3×C5×#117C2212yes—
21C2×C3×C5×C4⋊C4—21no—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4—21no—
26C2×C3×C5×C22⋊C4—21no—
27C2×C3×C42×C5—21no—
28C3×C5×#107C2214yescomplemented
29C3×C5×#106C2214yescomplemented
30C3×C5×#103C2214yescomplemented
31C3×C5×#103C2214yescomplemented
32C3×C5×C22⋊C8C2212yes—
33C3×C5×C22⋊C8C2212yes—
34C3×#3095C511yesmaximal, characteristic, direct product factor, Hall
35C2×C5×C22⋊Q8C2×C311yescharacteristic
36C2×C5×#117C2×C311yescharacteristic
37C5×#485C2×C314yescomplemented
38C5×#484C2×C312yescomplemented
39C5×#483C2×C312yescomplemented
40C5×#428C2×C312yescomplemented
41C5×#419C2×C312yescomplemented
42C5×#407C2×C311yescharacteristic
43C24×C3×C5D411yescharacteristic
44C2×C3×C5×Q8—21no—
45C2×C3×C5×Q8—24no—
46C2×C3×C5×Q8C2312yes—
47C22×C3×C4×C5—24no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5D411yescharacteristic
53C22×C3×C4×C5D411yescharacteristic
54C22×C3×C4×C5D411yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C3×C5×M16—24no—
59C2×C3×C5×C8C2314yes—
60C3×C5×C4⋊C4—22no—
61C3×C5×C4⋊C4—22no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C3×C5×C4⋊C4C2312yes—
67C3×C5×C4⋊C4C2312yes—
68C3×C5×C22⋊C4—22no—
69C3×C5×C22⋊C4—22no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4—22no—
72C3×C42×C5—22no—
73C3×C42×C5—22no—
74C2×C3×C22⋊Q8C2×C511yescharacteristic
75C2×C3×#117C2×C511yescharacteristic
76C3×#485C2×C514yescomplemented
77C3×#484C2×C512yescomplemented
78C3×#483C2×C512yescomplemented
79C3×#428C2×C512yescomplemented
80C3×#419C2×C512yescomplemented
81C3×#407C2×C511yescharacteristic
82C22×C5×Q8C22×C311yescharacteristic
83C23×C4×C5C22×C311yescharacteristic
84C2×C5×M16C22×C312yes—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C5×C22⋊Q8C22×C312yes—
88C5×C22⋊Q8C22×C312yes—
89C5×#117—21no—
90C5×#117—21no—
91C5×#117C22×C312yes—
92C5×#117C22×C312yes—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4C22×C311yescharacteristic
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C5×C4⋊C4C22×C311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C42×C5—21no—
100C5×#107C22×C314yescomplemented
101C5×#106C22×C314yescomplemented
102C5×#103C22×C314yescomplemented
103C5×#103C22×C314yescomplemented
104C5×C22⋊C8C22×C312yes—
105C5×C22⋊C8C22×C312yes—
106#3095C3×C511yescharacteristic, direct product factor, Sylow
107C23×C3×C5—22no—
108C23×C3×C5—22no—
109C23×C3×C5—41no—
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C3×C5×Q8—24no—
114C3×C5×Q8—42no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—42no—
125C2×C3×C4×C5—42no—
126C2×C3×C4×C5—42no—
127C2×C3×C4×C5—42no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5#4114yes—
132C2×C3×C4×C5C2411yescharacteristic
133C3×C5×C8—24no—
134C22×C3×Q8C22×C511yescharacteristic
135C23×C3×C4C22×C511yescharacteristic
136C2×C3×M16C22×C512yes—
137C3×C22⋊Q8—21no—
138C3×C22⋊Q8—21no—
139C3×C22⋊Q8C22×C512yes—
140C3×C22⋊Q8C22×C512yes—
141C3×#117—21no—
142C3×#117—21no—
143C3×#117C22×C512yes—
144C3×#117C22×C512yes—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4C22×C511yescharacteristic
147C2×C3×C4⋊C4C22×C511yescharacteristic
148C2×C3×C4⋊C4C22×C511yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C42—21no—
152C3×#107C22×C514yescomplemented
153C3×#106C22×C514yescomplemented
154C3×#103C22×C514yescomplemented
155C3×#103C22×C514yescomplemented
156C3×C22⋊C8C22×C512yes—
157C3×C22⋊C8C22×C512yes—
158C24×C5C3×D411yescharacteristic
159C2×C5×Q8—21no—
160C2×C5×Q8—24no—
161C2×C5×Q8C23×C312yes—
162C22×C4×C5—24no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5C3×D411yescharacteristic
168C22×C4×C5C3×D411yescharacteristic
169C22×C4×C5C3×D411yescharacteristic
170C22×C4×C5C23×C311yescharacteristic
171C22×C4×C5C23×C311yescharacteristic
172C22×C4×C5C23×C311yescharacteristic
173C5×M16—24no—
174C2×C5×C8C23×C314yes—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4C23×C312yes—
181C5×C4⋊C4C23×C312yes—
182C5×C4⋊C4C23×C312yes—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C42×C5—22no—
188C42×C5—22no—
189C2×C22⋊Q8C2×C3×C511yescharacteristic
190C2×#117C2×C3×C511yescharacteristic
191#485C2×C3×C514yescomplemented
192#484C2×C3×C512yescomplemented
193#483C2×C3×C512yescomplemented
194#428C2×C3×C512yescomplemented
195#419C2×C3×C512yescomplemented
196#407C2×C3×C511yescharacteristic
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5—21no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5—44no—
205C22×C3×C5#12312yes—
206C22×C3×C5#13712yes—
207C22×C3×C5C22×D411yescharacteristic
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—42no—
211C3×C4×C5—42no—
212C3×C4×C5—42no—
213C3×C4×C5—42no—
214C3×C4×C5#12312yes—
215C3×C4×C5C2×#4112yes—
216C24×C3C5×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—24no—
219C2×C3×Q8C23×C512yes—
220C22×C3×C4—24no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4C5×D411yescharacteristic
226C22×C3×C4C5×D411yescharacteristic
227C22×C3×C4C5×D411yescharacteristic
228C22×C3×C4C23×C511yescharacteristic
229C22×C3×C4C23×C511yescharacteristic
230C22×C3×C4C23×C511yescharacteristic
231C3×M16—24no—
232C2×C3×C8C23×C514yes—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4C23×C512yes—
239C3×C4⋊C4C23×C512yes—
240C3×C4⋊C4C23×C512yes—
241C3×C22⋊C4—22no—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—22no—
244C3×C22⋊C4—22no—
245C3×C42—22no—
246C3×C42—22no—
247C23×C5—22no—
248C23×C5—22no—
249C23×C5—41no—
250C23×C5C2×C3×D411yescharacteristic
251C23×C5C2×C3×D411yescharacteristic
252C23×C5C2×C3×D411yescharacteristic
253C5×Q8—24no—
254C5×Q8—42no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5C2×C3×D411yescharacteristic
269C2×C4×C5C2×C3×D411yescharacteristic
270C2×C4×C5C2×C3×D411yescharacteristic
271C2×C4×C5C3×#4114yes—
272C2×C4×C5C24×C311yescharacteristic
273C5×C8—24no—
274C22×Q8C22×C3×C511yescharacteristic
275C23×C4C22×C3×C511yescharacteristic
276C2×M16C22×C3×C512yes—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8C22×C3×C512yes—
280C22⋊Q8C22×C3×C512yes—
281#117—21no—
282#117—21no—
283#117C22×C3×C512yes—
284#117C22×C3×C512yes—
285C2×C4⋊C4—21no—
286C2×C4⋊C4C22×C3×C511yescharacteristic
287C2×C4⋊C4C22×C3×C511yescharacteristic
288C2×C4⋊C4C22×C3×C511yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C42—21no—
292#107C22×C3×C514yescomplemented
293#106C22×C3×C514yescomplemented
294#103C22×C3×C514yescomplemented
295#103C22×C3×C514yescomplemented
296C22⋊C8C22×C3×C512yes—
297C22⋊C8C22×C3×C512yes—
298C2×C3×C5—22no—
299C2×C3×C5—22no—
300C2×C3×C5—41no—
301C2×C3×C5C2×#12311yescharacteristic
302C2×C3×C5C2×#13711yescharacteristic
303C2×C3×C5#57511yescharacteristic
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—41no—
307C23×C3C2×C5×D411yescharacteristic
308C23×C3C2×C5×D411yescharacteristic
309C23×C3C2×C5×D411yescharacteristic
310C3×Q8—24no—
311C3×Q8—42no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4C2×C5×D411yescharacteristic
326C2×C3×C4C2×C5×D411yescharacteristic
327C2×C3×C4C2×C5×D411yescharacteristic
328C2×C3×C4C5×#4114yes—
329C2×C3×C4C24×C511yescharacteristic
330C3×C8—24no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—44no—
339C22×C5C3×#12312yes—
340C22×C5C3×#13712yes—
341C22×C5C22×C3×D411yescharacteristic
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—42no—
345C4×C5—42no—
346C4×C5—42no—
347C4×C5—42no—
348C4×C5C3×#12312yes—
349C4×C5C2×C3×#4112yes—
350C24C3×C5×D411yescharacteristic
351C2×Q8—21no—
352C2×Q8—24no—
353C2×Q8C23×C3×C512yes—
354C22×C4—24no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4C3×C5×D411yescharacteristic
360C22×C4C3×C5×D411yescharacteristic
361C22×C4C3×C5×D411yescharacteristic
362C22×C4C23×C3×C511yescharacteristic
363C22×C4C23×C3×C511yescharacteristic
364C22×C4C23×C3×C511yescharacteristic
365M16—24no—
366C2×C8C23×C3×C514yes—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4C23×C3×C512yes—
373C4⋊C4C23×C3×C512yes—
374C4⋊C4C23×C3×C512yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C42—22no—
380C42—22no—
381C3×C5#309511yescharacteristic, direct product factor, Hall
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—44no—
390C22×C3C5×#12312yes—
391C22×C3C5×#13712yes—
392C22×C3C22×C5×D411yescharacteristic
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4C5×#12312yes—
400C3×C4C2×C5×#4112yes—
401C2×C5—22no—
402C2×C5—22no—
403C2×C5—41no—
404C2×C5C2×C3×#12311yescharacteristic
405C2×C5C2×C3×#13711yescharacteristic
406C2×C5C3×#57511yescharacteristic
407C23—22no—
408C23—22no—
409C23—41no—
410C23C2×C3×C5×D411yescharacteristic
411C23C2×C3×C5×D411yescharacteristic
412C23C2×C3×C5×D411yescharacteristic
413Q8—24no—
414Q8—42no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4C2×C3×C5×D411yescharacteristic
429C2×C4C2×C3×C5×D411yescharacteristic
430C2×C4C2×C3×C5×D411yescharacteristic
431C2×C4C3×C5×#4114yes—
432C2×C4C24×C3×C511yescharacteristic
433C8—24no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—41no—
437C2×C3C2×C5×#12311yescharacteristic
438C2×C3C2×C5×#13711yescharacteristic
439C2×C3C5×#57511yescharacteristic
440C5C3×#309511yescharacteristic, direct product factor, Sylow
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—44no—
449C22C3×C5×#12312yes—
450C22C3×C5×#13712yes—
451C22C22×C3×C5×D411yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4C3×C5×#12312yes—
459C4C2×C3×C5×#4112yes—
460C3C5×#309511yescharacteristic, direct product factor, Sylow
461C2—22no—
462C2—22no—
463C2—41no—
464C2C2×C3×C5×#12311yescharacteristic
465C2C2×C3×C5×#13711yescharacteristic
466C2C3×C5×#57511yescharacteristic
subgroupG/H
center, socleC22×C3×C5C22×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC24×C3×C5D4
LCSG ▷ C2×C4 ▷ 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×#485C2semidirect
4. C3×C5×#484C2semidirect
5. C3×C5×#483C2semidirect
6. C3×C5×#428C2semidirect
7. C3×C5×#419C2semidirect
9. C5×#3095C3direct (N × H)
28. C3×C5×#107C22semidirect
29. C3×C5×#106C22semidirect
30. C3×C5×#103C22semidirect
31. C3×C5×#103C22semidirect
34. C3×#3095C5direct (N × H)
37. C5×#485C2×C3semidirect
38. C5×#484C2×C3semidirect
39. C5×#483C2×C3semidirect
40. C5×#428C2×C3semidirect
41. C5×#419C2×C3semidirect
76. C3×#485C2×C5semidirect
77. C3×#484C2×C5semidirect
78. C3×#483C2×C5semidirect
79. C3×#428C2×C5semidirect
80. C3×#419C2×C5semidirect
100. C5×#107C22×C3semidirect
101. C5×#106C22×C3semidirect
102. C5×#103C22×C3semidirect
103. C5×#103C22×C3semidirect
106. #3095C3×C5direct (N × H)
152. C3×#107C22×C5semidirect
153. C3×#106C22×C5semidirect
154. C3×#103C22×C5semidirect
155. C3×#103C22×C5semidirect
191. #485C2×C3×C5semidirect
192. #484C2×C3×C5semidirect
193. #483C2×C3×C5semidirect
194. #428C2×C3×C5semidirect
195. #419C2×C3×C5semidirect
292. #107C22×C3×C5semidirect
293. #106C22×C3×C5semidirect
294. #103C22×C3×C5semidirect
295. #103C22×C3×C5semidirect
381. C3×C5#3095direct (N × H)
440. C5C3×#3095direct (N × H)
460. C3C5×#3095direct (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
C2×C3×C5×#1172
C3×C5×#4852
C3×C5×#4842
C3×C5×#4832
C3×C5×#4282
C3×C5×#4192
C3×C5×#4072
C5×#30953
C3×#30955