Finite Group Databasebeta

← C3×C5×#2005 #14275039

Subgroups — C3×C5×#2005 #14275039

Order 1920.

724 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×#137C211yesmaximal, characteristic
2C3×C5×#536C211yesmaximal, characteristic
3C2×C3×C5×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic
5C3×C5×#419C211yesmaximal, characteristic, complemented
6C2×C3×C5×#101C211yesmaximal, characteristic, complemented
7C3×C5×#339C211yesmaximal, characteristic, complemented
8C5×#2005C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×Q8C2211yescharacteristic
12C3×C5×#137—22no—
13C3×C5×#137—22no—
14C2×C3×C5×Q16—21no—
15C2×C3×C5×SD16—21no—
16C2×C3×C5×M16C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18C3×C5×C4⋊Q8—22no—
19C3×C5×C4⋊Q8—21no—
20C3×C5×C4⋊Q8—22no—
21C3×C5×#124—21no—
22C3×C5×#123—22no—
23C3×C5×C22⋊Q8—22no—
24C3×C5×#117C2211yescharacteristic
25C2×C3×C5×C4⋊C4—22no—
26C2×C3×C42×C5C2211yescharacteristic
27C3×C5×#104—22no—
28C3×C5×#103—22no—
29C3×C5×#101—22no—
30C3×#2005C511yesmaximal, characteristic, direct product factor, Hall
31C2×C5×#137C2×C311yescharacteristic
32C5×#536C2×C311yescharacteristic
33C2×C5×C4⋊Q8C2×C311yescharacteristic, complemented
34C2×C5×#104C2×C311yescharacteristic
35C5×#419C2×C311yescharacteristic, complemented
36C2×C5×#101C2×C311yescharacteristic, complemented
37C5×#339C2×C311yescharacteristic, complemented
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—21no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—21no—
52C2×C3×C5×Q8—21no—
53C2×C3×C5×Q8D412yes—
54C2×C3×C5×Q8D411yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4D411yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5D412yes—
61C22×C3×C4×C5C2311yescharacteristic
62C3×C5×Q16—24no—
63C3×C5×SD16—24no—
64C3×C5×M16—21no—
65C3×C5×M16—21no—
66C3×C5×M16—21no—
67C3×C5×M16D412yes—
68C2×C3×C5×C8—21no—
69C2×C3×C5×C8—21no—
70C3×C5×C4⋊C4—28no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C4⋊C4D412yes—
73C3×C5×C22⋊C4—24no—
74C3×C5×C22⋊C4—21no—
75C3×C42×C5—21no—
76C3×C42×C5—21no—
77C3×C42×C5D412yes—
78C2×C3×#137C2×C511yescharacteristic
79C3×#536C2×C511yescharacteristic
80C2×C3×C4⋊Q8C2×C511yescharacteristic, complemented
81C2×C3×#104C2×C511yescharacteristic
82C3×#419C2×C511yescharacteristic, complemented
83C2×C3×#101C2×C511yescharacteristic, complemented
84C3×#339C2×C511yescharacteristic, complemented
85C2×C5×#41C22×C311yescharacteristic
86C22×C5×Q8C22×C311yescharacteristic
87C22×C5×Q8C22×C311yescharacteristic
88C5×#137—22no—
89C5×#137—22no—
90C2×C5×Q16—21no—
91C2×C5×SD16—21no—
92C2×C5×M16C22×C311yescharacteristic
93C2×C5×M16C22×C311yescharacteristic
94C5×C4⋊Q8—22no—
95C5×C4⋊Q8—21no—
96C5×C4⋊Q8—22no—
97C5×#124—21no—
98C5×#123—22no—
99C5×C22⋊Q8—22no—
100C5×#117C22×C311yescharacteristic
101C2×C5×C4⋊C4—22no—
102C2×C42×C5C22×C311yescharacteristic
103C5×#104—22no—
104C5×#103—22no—
105C5×#101—22no—
106#2005C3×C511yescharacteristic, direct product factor, Sylow
107C23×C3×C5—21no—
108C23×C3×C5C2×D411yescharacteristic
109C3×C5×Q8—22no—
110C3×C5×Q8—21no—
111C3×C5×Q8—22no—
112C3×C5×Q8—21no—
113C3×C5×Q8—41no—
114C3×C5×Q8—41no—
115C3×C5×Q8—41no—
116C3×C5×Q8—41no—
117C3×C5×Q8—41no—
118C3×C5×Q8—41no—
119C3×C5×D4—21no—
120C3×C5×D4—21no—
121C3×C5×D4—41no—
122C3×C5×D4—41no—
123C2×C3×C4×C5—24no—
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—21no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5#4111yescharacteristic
141C3×C5×C8—22no—
142C3×C5×C8—41no—
143C2×C3×#41C22×C511yescharacteristic
144C22×C3×Q8C22×C511yescharacteristic
145C22×C3×Q8C22×C511yescharacteristic
146C3×#137—22no—
147C3×#137—22no—
148C2×C3×Q16—21no—
149C2×C3×SD16—21no—
150C2×C3×M16C22×C511yescharacteristic
151C2×C3×M16C22×C511yescharacteristic
152C3×C4⋊Q8—22no—
153C3×C4⋊Q8—21no—
154C3×C4⋊Q8—22no—
155C3×#124—21no—
156C3×#123—22no—
157C3×C22⋊Q8—22no—
158C3×#117C22×C511yescharacteristic
159C2×C3×C4⋊C4—22no—
160C2×C3×C42C22×C511yescharacteristic
161C3×#104—22no—
162C3×#103—22no—
163C3×#101—22no—
164C5×#41—21no—
165C5×#41—21no—
166C5×#41—21no—
167C5×#41—21no—
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8C3×D411yescharacteristic
180C2×C5×Q8C3×D412yes—
181C2×C5×D4—21no—
182C2×C5×D4C3×D411yescharacteristic
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5C3×D412yes—
187C22×C4×C5C23×C311yescharacteristic
188C5×Q16—24no—
189C5×SD16—24no—
190C5×M16—21no—
191C5×M16—21no—
192C5×M16—21no—
193C5×M16C3×D412yes—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C5×C4⋊C4—28no—
197C5×C4⋊C4—24no—
198C5×C4⋊C4C3×D412yes—
199C5×C22⋊C4—24no—
200C5×C22⋊C4—21no—
201C42×C5—21no—
202C42×C5—21no—
203C42×C5C3×D412yes—
204C2×#137C2×C3×C511yescharacteristic
205#536C2×C3×C511yescharacteristic
206C2×C4⋊Q8C2×C3×C511yescharacteristic, complemented
207C2×#104C2×C3×C511yescharacteristic
208#419C2×C3×C511yescharacteristic, complemented
209C2×#101C2×C3×C511yescharacteristic, complemented
210#339C2×C3×C511yescharacteristic, complemented
211C22×C3×C5—22no—
212C22×C3×C5—41no—
213C22×C3×C5—42no—
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12011yescharacteristic
216C22×C3×C5#12111yescharacteristic
217C3×C4×C5—24no—
218C3×C4×C5—42no—
219C3×C4×C5—41no—
220C3×C4×C5—42no—
221C3×C4×C5—42no—
222C3×C4×C5#12011yescharacteristic
223C3×C4×C5#12111yescharacteristic
224C3×C4×C5#12111yescharacteristic
225C3×C4×C5#12711yescharacteristic
226C3×#41—21no—
227C3×#41—21no—
228C3×#41—21no—
229C3×#41—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8C5×D411yescharacteristic
242C2×C3×Q8C5×D412yes—
243C2×C3×D4—21no—
244C2×C3×D4C5×D411yescharacteristic
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C5×D412yes—
249C22×C3×C4C23×C511yescharacteristic
250C3×Q16—24no—
251C3×SD16—24no—
252C3×M16—21no—
253C3×M16—21no—
254C3×M16—21no—
255C3×M16C5×D412yes—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C3×C4⋊C4—28no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4C5×D412yes—
261C3×C22⋊C4—24no—
262C3×C22⋊C4—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42C5×D412yes—
266C23×C5—21no—
267C23×C5C2×C3×D411yescharacteristic
268C5×Q8—22no—
269C5×Q8—21no—
270C5×Q8—22no—
271C5×Q8—21no—
272C5×Q8—41no—
273C5×Q8—41no—
274C5×Q8—41no—
275C5×Q8—41no—
276C5×Q8—41no—
277C5×Q8—41no—
278C5×D4—21no—
279C5×D4—21no—
280C5×D4—41no—
281C5×D4—41no—
282C2×C4×C5—24no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5C2×C3×D411yescharacteristic
295C2×C4×C5C2×C3×D411yescharacteristic
296C2×C4×C5C2×C3×D411yescharacteristic
297C2×C4×C5C2×C3×D411yescharacteristic
298C2×C4×C5C2×C3×D411yescharacteristic
299C2×C4×C5C3×#4111yescharacteristic
300C5×C8—22no—
301C5×C8—41no—
302C2×#41C22×C3×C511yescharacteristic
303C22×Q8C22×C3×C511yescharacteristic
304C22×Q8C22×C3×C511yescharacteristic
305#137—22no—
306#137—22no—
307C2×Q16—21no—
308C2×SD16—21no—
309C2×M16C22×C3×C511yescharacteristic
310C2×M16C22×C3×C511yescharacteristic
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—22no—
314#124—21no—
315#123—22no—
316C22⋊Q8—22no—
317#117C22×C3×C511yescharacteristic
318C2×C4⋊C4—22no—
319C2×C42C22×C3×C511yescharacteristic
320#104—22no—
321#103—22no—
322#101—22no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5—81no—
326C2×C3×C5#39211yescharacteristic
327C2×C3×C5#45612yes—
328C23×C3—21no—
329C23×C3C2×C5×D411yescharacteristic
330C3×Q8—22no—
331C3×Q8—21no—
332C3×Q8—22no—
333C3×Q8—21no—
334C3×Q8—41no—
335C3×Q8—41no—
336C3×Q8—41no—
337C3×Q8—41no—
338C3×Q8—41no—
339C3×Q8—41no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—41no—
343C3×D4—41no—
344C2×C3×C4—24no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4C2×C5×D411yescharacteristic
357C2×C3×C4C2×C5×D411yescharacteristic
358C2×C3×C4C2×C5×D411yescharacteristic
359C2×C3×C4C2×C5×D411yescharacteristic
360C2×C3×C4C2×C5×D411yescharacteristic
361C2×C3×C4C5×#4111yescharacteristic
362C3×C8—22no—
363C3×C8—41no—
364C22×C5—22no—
365C22×C5—41no—
366C22×C5—42no—
367C22×C5C3×#12011yescharacteristic
368C22×C5C3×#12011yescharacteristic
369C22×C5C3×#12111yescharacteristic
370C4×C5—24no—
371C4×C5—42no—
372C4×C5—41no—
373C4×C5—42no—
374C4×C5—42no—
375C4×C5C3×#12011yescharacteristic
376C4×C5C3×#12111yescharacteristic
377C4×C5C3×#12111yescharacteristic
378C4×C5C3×#12711yescharacteristic
379#41—21no—
380#41—21no—
381#41—21no—
382#41—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8C3×C5×D411yescharacteristic
395C2×Q8C3×C5×D412yes—
396C2×D4—21no—
397C2×D4C3×C5×D411yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4C3×C5×D412yes—
402C22×C4C23×C3×C511yescharacteristic
403Q16—24no—
404SD16—24no—
405M16—21no—
406M16—21no—
407M16—21no—
408M16C3×C5×D412yes—
409C2×C8—21no—
410C2×C8—21no—
411C4⋊C4—28no—
412C4⋊C4—24no—
413C4⋊C4C3×C5×D412yes—
414C22⋊C4—24no—
415C22⋊C4—21no—
416C42—21no—
417C42—21no—
418C42C3×C5×D412yes—
419C3×C5#200511yescharacteristic, direct product factor, Hall
420C22×C3—22no—
421C22×C3—41no—
422C22×C3—42no—
423C22×C3C5×#12011yescharacteristic
424C22×C3C5×#12011yescharacteristic
425C22×C3C5×#12111yescharacteristic
426C3×C4—24no—
427C3×C4—42no—
428C3×C4—41no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4C5×#12011yescharacteristic
432C3×C4C5×#12111yescharacteristic
433C3×C4C5×#12111yescharacteristic
434C3×C4C5×#12711yescharacteristic
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—81no—
438C2×C5C3×#39211yescharacteristic
439C2×C5C3×#45612yes—
440C23—21no—
441C23C2×C3×C5×D411yescharacteristic
442Q8—22no—
443Q8—21no—
444Q8—22no—
445Q8—21no—
446Q8—41no—
447Q8—41no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452D4—21no—
453D4—21no—
454D4—41no—
455D4—41no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4C2×C3×C5×D411yescharacteristic
469C2×C4C2×C3×C5×D411yescharacteristic
470C2×C4C2×C3×C5×D411yescharacteristic
471C2×C4C2×C3×C5×D411yescharacteristic
472C2×C4C2×C3×C5×D411yescharacteristic
473C2×C4C3×C5×#4111yescharacteristic
474C8—22no—
475C8—41no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—81no—
479C2×C3C5×#39211yescharacteristic
480C2×C3C5×#45612yes—
481C5C3×#200511yescharacteristic, direct product factor, Sylow
482C22—22no—
483C22—42no—
484C22—41no—
485C22C3×C5×#12011yescharacteristic
486C22C3×C5×#12011yescharacteristic
487C22C3×C5×#12111yescharacteristic
488C4—24no—
489C4—42no—
490C4—42no—
491C4—41no—
492C4—42no—
493C4C3×C5×#12011yescharacteristic
494C4C3×C5×#12111yescharacteristic
495C4C3×C5×#12111yescharacteristic
496C4C3×C5×#12711yescharacteristic
497C3C5×#200511yescharacteristic, direct product factor, Sylow
498C2—21no—
499C2—21no—
500C2—81no—
501C2C3×C5×#39211yescharacteristic
502C2C3×C5×#45612yes—
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC2×C3×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C5×C4⋊Q8C2semidirect
5. C3×C5×#419C2semidirect
6. C2×C3×C5×#101C2semidirect
7. C3×C5×#339C2semidirect
8. C5×#2005C3direct (N × H)
30. C3×#2005C5direct (N × H)
33. C2×C5×C4⋊Q8C2×C3semidirect
35. C5×#419C2×C3semidirect
36. C2×C5×#101C2×C3semidirect
37. C5×#339C2×C3semidirect
80. C2×C3×C4⋊Q8C2×C5semidirect
82. C3×#419C2×C5semidirect
83. C2×C3×#101C2×C5semidirect
84. C3×#339C2×C5semidirect
106. #2005C3×C5direct (N × H)
206. C2×C4⋊Q8C2×C3×C5semidirect
208. #419C2×C3×C5semidirect
209. C2×#101C2×C3×C5semidirect
210. #339C2×C3×C5semidirect
419. C3×C5#2005direct (N × H)
481. C5C3×#2005direct (N × H)
497. C3C5×#2005direct (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×#1372
C3×C5×#5362
C2×C3×C5×C4⋊Q82
C2×C3×C5×#1042
C3×C5×#4192
C2×C3×C5×#1012
C3×C5×#3392
C5×#20053
C3×#20055