Finite Group Databasebeta

← C3×C5×#3094 #14276128

Subgroups — C3×C5×#3094 #14276128

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic, complemented
3C3×C5×#482C214yesmaximal, complemented
4C3×C5×#481C212yesmaximal, complemented
5C3×C5×#480C212yesmaximal, complemented
6C3×C5×#428C212yesmaximal, complemented
7C3×C5×#418C212yesmaximal, complemented
8C3×C5×#407C211yesmaximal, characteristic, complemented
9C5×#3094C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×D4—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C2×C3×C5×M16C2212yes—
14C3×C5×#121—21no—
15C3×C5×#121—21no—
16C3×C5×#121C2212yes—
17C3×C5×#121C2212yes—
18C3×C5×#117—21no—
19C3×C5×#117—21no—
20C3×C5×#117C2212yes—
21C3×C5×#117C2212yescomplemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
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×#102C2214yescomplemented
31C3×C5×#102C2214yescomplemented
32C3×C5×C22⋊C8C2212yescomplemented
33C3×C5×C22⋊C8C2212yescomplemented
34C3×#3094C511yesmaximal, characteristic, direct product factor, Hall
35C2×C5×#121C2×C311yescharacteristic
36C2×C5×#117C2×C311yescharacteristic, complemented
37C5×#482C2×C314yescomplemented
38C5×#481C2×C312yescomplemented
39C5×#480C2×C312yescomplemented
40C5×#428C2×C312yescomplemented
41C5×#418C2×C312yescomplemented
42C5×#407C2×C311yescharacteristic, complemented
43C24×C3×C5—21no—
44C24×C3×C5D411yescharacteristic
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—24no—
49C2×C3×C5×D4—44no—
50C2×C3×C5×D4C2312yes—
51C22×C3×C4×C5—24no—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5D411yescharacteristic
56C22×C3×C4×C5D411yescharacteristic
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C3×C5×M16—24no—
62C2×C3×C5×C8C2314yes—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2312yes—
67C3×C5×C4⋊C4C2312yes—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—22no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4—22no—
72C3×C5×C22⋊C4—22no—
73C3×C42×C5—22no—
74C3×C42×C5—22no—
75C2×C3×#121C2×C511yescharacteristic
76C2×C3×#117C2×C511yescharacteristic, complemented
77C3×#482C2×C514yescomplemented
78C3×#481C2×C512yescomplemented
79C3×#480C2×C512yescomplemented
80C3×#428C2×C512yescomplemented
81C3×#418C2×C512yescomplemented
82C3×#407C2×C511yescharacteristic, complemented
83C22×C5×D4—21no—
84C22×C5×D4C22×C311yescharacteristic
85C23×C4×C5C22×C311yescharacteristic
86C2×C5×M16C22×C312yes—
87C5×#121—21no—
88C5×#121—21no—
89C5×#121C22×C312yes—
90C5×#121C22×C312yes—
91C5×#117—21no—
92C5×#117—21no—
93C5×#117C22×C312yes—
94C5×#117C22×C312yescomplemented
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
97C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C42×C5—21no—
101C5×#107C22×C314yescomplemented
102C5×#106C22×C314yescomplemented
103C5×#102C22×C314yescomplemented
104C5×#102C22×C314yescomplemented
105C5×C22⋊C8C22×C312yescomplemented
106C5×C22⋊C8C22×C312yescomplemented
107#3094C3×C511yescharacteristic, direct product factor, Sylow
108C23×C3×C5—22no—
109C23×C3×C5—22no—
110C23×C3×C5—22no—
111C23×C3×C5—41no—
112C23×C3×C5—42no—
113C23×C3×C5—42no—
114C23×C3×C5—42no—
115C23×C3×C5C2×D411yescharacteristic
116C23×C3×C5C2×D411yescharacteristic
117C23×C3×C5C2×D411yescharacteristic
118C3×C5×D4—24no—
119C3×C5×D4—44no—
120C3×C5×D4—44no—
121C3×C5×D4—42no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—42no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5#4114yes—
137C2×C3×C4×C5C2411yescharacteristic
138C3×C5×C8—24no—
139C22×C3×D4—21no—
140C22×C3×D4C22×C511yescharacteristic
141C23×C3×C4C22×C511yescharacteristic
142C2×C3×M16C22×C512yes—
143C3×#121—21no—
144C3×#121—21no—
145C3×#121C22×C512yes—
146C3×#121C22×C512yes—
147C3×#117—21no—
148C3×#117—21no—
149C3×#117C22×C512yes—
150C3×#117C22×C512yescomplemented
151C2×C3×C4⋊C4C22×C511yescharacteristic
152C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
153C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C42—21no—
157C3×#107C22×C514yescomplemented
158C3×#106C22×C514yescomplemented
159C3×#102C22×C514yescomplemented
160C3×#102C22×C514yescomplemented
161C3×C22⋊C8C22×C512yescomplemented
162C3×C22⋊C8C22×C512yescomplemented
163C24×C5—21no—
164C24×C5C3×D411yescharacteristic
165C2×C5×D4—22no—
166C2×C5×D4—22no—
167C2×C5×D4—21no—
168C2×C5×D4—24no—
169C2×C5×D4—44no—
170C2×C5×D4C23×C312yes—
171C22×C4×C5—24no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5C3×D411yescharacteristic
176C22×C4×C5C3×D411yescharacteristic
177C22×C4×C5C3×D411yescharacteristic
178C22×C4×C5C23×C311yescharacteristic
179C22×C4×C5C23×C311yescharacteristic
180C22×C4×C5C23×C311yescharacteristic
181C5×M16—24no—
182C2×C5×C8C23×C314yes—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4C23×C312yes—
187C5×C4⋊C4C23×C312yes—
188C5×C4⋊C4C23×C312yes—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—22no—
193C42×C5—22no—
194C42×C5—22no—
195C2×#121C2×C3×C511yescharacteristic
196C2×#117C2×C3×C511yescharacteristic, complemented
197#482C2×C3×C514yescomplemented
198#481C2×C3×C512yescomplemented
199#480C2×C3×C512yescomplemented
200#428C2×C3×C512yescomplemented
201#418C2×C3×C512yescomplemented
202#407C2×C3×C511yescharacteristic, complemented
203C22×C3×C5—21no—
204C22×C3×C5—21no—
205C22×C3×C5—21no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5—44no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—42no—
214C22×C3×C5—84no—
215C22×C3×C5#12312yes—
216C22×C3×C5AGL(1,ℤ/8)12yes—
217C22×C3×C5C22×D411yescharacteristic
218C3×C4×C5—21no—
219C3×C4×C5—21no—
220C3×C4×C5—42no—
221C3×C4×C5—42no—
222C3×C4×C5—42no—
223C3×C4×C5#12312yes—
224C3×C4×C5C2×#4112yes—
225C24×C3—21no—
226C24×C3C5×D411yescharacteristic
227C2×C3×D4—22no—
228C2×C3×D4—22no—
229C2×C3×D4—21no—
230C2×C3×D4—24no—
231C2×C3×D4—44no—
232C2×C3×D4C23×C512yes—
233C22×C3×C4—24no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C5×D411yescharacteristic
238C22×C3×C4C5×D411yescharacteristic
239C22×C3×C4C5×D411yescharacteristic
240C22×C3×C4C23×C511yescharacteristic
241C22×C3×C4C23×C511yescharacteristic
242C22×C3×C4C23×C511yescharacteristic
243C3×M16—24no—
244C2×C3×C8C23×C514yes—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4C23×C512yes—
249C3×C4⋊C4C23×C512yes—
250C3×C4⋊C4C23×C512yes—
251C3×C22⋊C4—22no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—22no—
255C3×C42—22no—
256C3×C42—22no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—22no—
260C23×C5—41no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5C2×C3×D411yescharacteristic
265C23×C5C2×C3×D411yescharacteristic
266C23×C5C2×C3×D411yescharacteristic
267C5×D4—24no—
268C5×D4—44no—
269C5×D4—44no—
270C5×D4—42no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5C2×C3×D411yescharacteristic
283C2×C4×C5C2×C3×D411yescharacteristic
284C2×C4×C5C2×C3×D411yescharacteristic
285C2×C4×C5C3×#4114yes—
286C2×C4×C5C24×C311yescharacteristic
287C5×C8—24no—
288C22×D4—21no—
289C22×D4C22×C3×C511yescharacteristic
290C23×C4C22×C3×C511yescharacteristic
291C2×M16C22×C3×C512yes—
292#121—21no—
293#121—21no—
294#121C22×C3×C512yes—
295#121C22×C3×C512yes—
296#117—21no—
297#117—21no—
298#117C22×C3×C512yes—
299#117C22×C3×C512yescomplemented
300C2×C4⋊C4C22×C3×C511yescharacteristic
301C2×C4⋊C4C22×C3×C511yescharacteristic, complemented
302C2×C4⋊C4C22×C3×C511yescharacteristic, complemented
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C42—21no—
306#107C22×C3×C514yescomplemented
307#106C22×C3×C514yescomplemented
308#102C22×C3×C514yescomplemented
309#102C22×C3×C514yescomplemented
310C22⋊C8C22×C3×C512yescomplemented
311C22⋊C8C22×C3×C512yescomplemented
312C2×C3×C5—22no—
313C2×C3×C5—22no—
314C2×C3×C5—41no—
315C2×C3×C5—82no—
316C2×C3×C5C2×#12311yescharacteristic
317C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
318C2×C3×C5#57511yescharacteristic
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3C2×C5×D411yescharacteristic
327C23×C3C2×C5×D411yescharacteristic
328C23×C3C2×C5×D411yescharacteristic
329C3×D4—24no—
330C3×D4—44no—
331C3×D4—44no—
332C3×D4—42no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4C2×C5×D411yescharacteristic
345C2×C3×C4C2×C5×D411yescharacteristic
346C2×C3×C4C2×C5×D411yescharacteristic
347C2×C3×C4C5×#4114yes—
348C2×C3×C4C24×C511yescharacteristic
349C3×C8—24no—
350C22×C5—21no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—21no—
355C22×C5—21no—
356C22×C5—21no—
357C22×C5—44no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5—84no—
362C22×C5C3×#12312yes—
363C22×C5C3×AGL(1,ℤ/8)12yes—
364C22×C5C22×C3×D411yescharacteristic
365C4×C5—21no—
366C4×C5—21no—
367C4×C5—42no—
368C4×C5—42no—
369C4×C5—42no—
370C4×C5C3×#12312yes—
371C4×C5C2×C3×#4112yes—
372C24—21no—
373C24C3×C5×D411yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—24no—
378C2×D4—44no—
379C2×D4C23×C3×C512yes—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C3×C5×D411yescharacteristic
385C22×C4C3×C5×D411yescharacteristic
386C22×C4C3×C5×D411yescharacteristic
387C22×C4C23×C3×C511yescharacteristic
388C22×C4C23×C3×C511yescharacteristic
389C22×C4C23×C3×C511yescharacteristic
390M16—24no—
391C2×C8C23×C3×C514yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4C23×C3×C512yes—
396C4⋊C4C23×C3×C512yes—
397C4⋊C4C23×C3×C512yes—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C42—22no—
403C42—22no—
404C3×C5#309411yescharacteristic, direct product factor, Hall
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—44no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—84no—
417C22×C3C5×#12312yes—
418C22×C3C5×AGL(1,ℤ/8)12yes—
419C22×C3C22×C5×D411yescharacteristic
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4C5×#12312yes—
426C3×C4C2×C5×#4112yes—
427C2×C5—22no—
428C2×C5—22no—
429C2×C5—41no—
430C2×C5—82no—
431C2×C5C2×C3×#12311yescharacteristic
432C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
433C2×C5C3×#57511yescharacteristic
434C23—22no—
435C23—22no—
436C23—22no—
437C23—41no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23C2×C3×C5×D411yescharacteristic
442C23C2×C3×C5×D411yescharacteristic
443C23C2×C3×C5×D411yescharacteristic
444D4—24no—
445D4—44no—
446D4—44no—
447D4—42no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4C2×C3×C5×D411yescharacteristic
460C2×C4C2×C3×C5×D411yescharacteristic
461C2×C4C2×C3×C5×D411yescharacteristic
462C2×C4C3×C5×#4114yes—
463C2×C4C24×C3×C511yescharacteristic
464C8—24no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—41no—
468C2×C3—82no—
469C2×C3C2×C5×#12311yescharacteristic
470C2×C3C2×C5×AGL(1,ℤ/8)11yescharacteristic
471C2×C3C5×#57511yescharacteristic
472C5C3×#309411yescharacteristic, direct product factor, Sylow
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—44no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—84no—
485C22C3×C5×#12312yes—
486C22C3×C5×AGL(1,ℤ/8)12yes—
487C22C22×C3×C5×D411yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4C3×C5×#12312yes—
494C4C2×C3×C5×#4112yes—
495C3C5×#309411yescharacteristic, direct product factor, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—82no—
500C2C2×C3×C5×#12311yescharacteristic
501C2C2×C3×C5×AGL(1,ℤ/8)11yescharacteristic
502C2C3×C5×#57511yescharacteristic
subgroupG/H
center, socleC22×C3×C5C22×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC2×C3×C5×#121C2
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
2. C2×C3×C5×#117C2semidirect
3. C3×C5×#482C2semidirect
4. C3×C5×#481C2semidirect
5. C3×C5×#480C2semidirect
6. C3×C5×#428C2semidirect
7. C3×C5×#418C2semidirect
8. C3×C5×#407C2semidirect
9. C5×#3094C3direct (N × H)
21. C3×C5×#117C22semidirect
23. C2×C3×C5×C4⋊C4C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
28. C3×C5×#107C22semidirect
29. C3×C5×#106C22semidirect
30. C3×C5×#102C22semidirect
31. C3×C5×#102C22semidirect
32. C3×C5×C22⋊C8C22semidirect
33. C3×C5×C22⋊C8C22semidirect
34. C3×#3094C5direct (N × H)
36. C2×C5×#117C2×C3semidirect
37. C5×#482C2×C3semidirect
38. C5×#481C2×C3semidirect
39. C5×#480C2×C3semidirect
40. C5×#428C2×C3semidirect
41. C5×#418C2×C3semidirect
42. C5×#407C2×C3semidirect
76. C2×C3×#117C2×C5semidirect
77. C3×#482C2×C5semidirect
78. C3×#481C2×C5semidirect
79. C3×#480C2×C5semidirect
80. C3×#428C2×C5semidirect
81. C3×#418C2×C5semidirect
82. C3×#407C2×C5semidirect
94. C5×#117C22×C3semidirect
96. C2×C5×C4⋊C4C22×C3semidirect
97. C2×C5×C4⋊C4C22×C3semidirect
101. C5×#107C22×C3semidirect
102. C5×#106C22×C3semidirect
103. C5×#102C22×C3semidirect
104. C5×#102C22×C3semidirect
105. C5×C22⋊C8C22×C3semidirect
106. C5×C22⋊C8C22×C3semidirect
107. #3094C3×C5direct (N × H)
150. C3×#117C22×C5semidirect
152. C2×C3×C4⋊C4C22×C5semidirect
153. C2×C3×C4⋊C4C22×C5semidirect
157. C3×#107C22×C5semidirect
158. C3×#106C22×C5semidirect
159. C3×#102C22×C5semidirect
160. C3×#102C22×C5semidirect
161. C3×C22⋊C8C22×C5semidirect
162. C3×C22⋊C8C22×C5semidirect
196. C2×#117C2×C3×C5semidirect
197. #482C2×C3×C5semidirect
198. #481C2×C3×C5semidirect
199. #480C2×C3×C5semidirect
200. #428C2×C3×C5semidirect
201. #418C2×C3×C5semidirect
202. #407C2×C3×C5semidirect
299. #117C22×C3×C5semidirect
301. C2×C4⋊C4C22×C3×C5semidirect
302. C2×C4⋊C4C22×C3×C5semidirect
306. #107C22×C3×C5semidirect
307. #106C22×C3×C5semidirect
308. #102C22×C3×C5semidirect
309. #102C22×C3×C5semidirect
310. C22⋊C8C22×C3×C5semidirect
311. C22⋊C8C22×C3×C5semidirect
404. C3×C5#3094direct (N × H)
472. C5C3×#3094direct (N × H)
495. C3C5×#3094direct (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×#1212
C2×C3×C5×#1172
C3×C5×#4822
C3×C5×#4812
C3×C5×#4802
C3×C5×#4282
C3×C5×#4182
C3×C5×#4072
C5×#30943
C3×#30945