Finite Group Databasebeta

← C3×C5×#2077 #14275111

Subgroups — C3×C5×#2077 #14275111

Order 1920.

512 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×#106C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊C8C211yesmaximal, characteristic
3C3×C5×#380C211yesmaximal, characteristic
4C3×C5×#380C211yesmaximal, characteristic
5C3×C5×#340C211yesmaximal, characteristic, complemented
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×C5×#340C211yesmaximal, characteristic, complemented
8C5×#2077C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C22⋊C4—21no—
17C2×C3×C5×C22⋊C4—21no—
18C3×C5×#106—22no—
19C3×C5×C22⋊C8—22no—
20C3×C5×#95—21no—
21C3×C5×#95—21no—
22C3×#2077C511yesmaximal, characteristic, direct product factor, Hall
23C2×C5×#106C2×C311yescharacteristic, complemented
24C2×C5×C22⋊C8C2×C311yescharacteristic
25C5×#380C2×C311yescharacteristic
26C5×#380C2×C311yescharacteristic
27C5×#340C2×C311yescharacteristic, complemented
28C5×#340C2×C311yescharacteristic, complemented
29C5×#340C2×C311yescharacteristic, complemented
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8D412yes—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C22⋊C4—42no—
58C3×C5×C22⋊C4—42no—
59C2×C3×#106C2×C511yescharacteristic, complemented
60C2×C3×C22⋊C8C2×C511yescharacteristic
61C3×#380C2×C511yescharacteristic
62C3×#380C2×C511yescharacteristic
63C3×#340C2×C511yescharacteristic, complemented
64C3×#340C2×C511yescharacteristic, complemented
65C3×#340C2×C511yescharacteristic, complemented
66C23×C4×C5C22×C311yescharacteristic
67C22×C5×C8C22×C311yescharacteristic
68C22×C5×C8C22×C311yescharacteristic
69C2×C5×C4⋊C4C22×C311yescharacteristic
70C2×C5×C4⋊C4C22×C311yescharacteristic
71C2×C5×C4⋊C4C22×C311yescharacteristic
72C2×C5×C4⋊C4C22×C311yescharacteristic
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C5×#106—22no—
76C5×C22⋊C8—22no—
77C5×#95—21no—
78C5×#95—21no—
79#2077C3×C511yescharacteristic, direct product factor, Sylow
80C23×C3×C5—21no—
81C23×C3×C5—21no—
82C23×C3×C5—21no—
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—21no—
86C23×C3×C5SD1612yes—
87C23×C3×C5C2×D411yescharacteristic
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C3×C5×C8—22no—
114C3×C5×C8—41no—
115C23×C3×C4C22×C511yescharacteristic
116C22×C3×C8C22×C511yescharacteristic
117C22×C3×C8C22×C511yescharacteristic
118C2×C3×C4⋊C4C22×C511yescharacteristic
119C2×C3×C4⋊C4C22×C511yescharacteristic
120C2×C3×C4⋊C4C22×C511yescharacteristic
121C2×C3×C4⋊C4C22×C511yescharacteristic
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C3×#106—22no—
125C3×C22⋊C8—22no—
126C3×#95—21no—
127C3×#95—21no—
128C24×C5C3×D411yescharacteristic
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C23×C311yescharacteristic
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C2×C5×C8C3×D412yes—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—21no—
155C5×C22⋊C4—42no—
156C5×C22⋊C4—42no—
157C2×#106C2×C3×C511yescharacteristic, complemented
158C2×C22⋊C8C2×C3×C511yescharacteristic
159#380C2×C3×C511yescharacteristic
160#380C2×C3×C511yescharacteristic
161#340C2×C3×C511yescharacteristic, complemented
162#340C2×C3×C511yescharacteristic, complemented
163#340C2×C3×C511yescharacteristic, complemented
164C22×C3×C5—22no—
165C22×C3×C5—22no—
166C22×C3×C5—22no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12111yescharacteristic
172C22×C3×C5#12311yescharacteristic
173C22×C3×C5#12311yescharacteristic
174C22×C3×C5C2×SD1611yescharacteristic
175C22×C3×C5#13511yescharacteristic
176C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C3×C4×C5—41no—
179C3×C4×C5—81no—
180C3×C4×C5—81no—
181C3×C4×C5—81no—
182C3×C4×C5—81no—
183C3×C4×C5#12311yescharacteristic
184C3×C4×C5#12411yescharacteristic
185C3×C4×C5#12611yescharacteristic
186C3×C4×C5#12611yescharacteristic
187C24×C3C5×D411yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4C5×D411yescharacteristic
199C22×C3×C4C23×C511yescharacteristic
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8C5×D412yes—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C22⋊C4—42no—
215C3×C22⋊C4—42no—
216C23×C5—21no—
217C23×C5—21no—
218C23×C5—21no—
219C23×C5—21no—
220C23×C5—21no—
221C23×C5—21no—
222C23×C5C3×SD1612yes—
223C23×C5C2×C3×D411yescharacteristic
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C2×C3×D411yescharacteristic
244C2×C4×C5C3×#4111yescharacteristic
245C2×C4×C5C3×#4111yescharacteristic
246C2×C4×C5C3×#4111yescharacteristic
247C2×C4×C5C3×#4111yescharacteristic
248C2×C4×C5C3×#4111yescharacteristic
249C5×C8—22no—
250C5×C8—41no—
251C23×C4C22×C3×C511yescharacteristic
252C22×C8C22×C3×C511yescharacteristic
253C22×C8C22×C3×C511yescharacteristic
254C2×C4⋊C4C22×C3×C511yescharacteristic
255C2×C4⋊C4C22×C3×C511yescharacteristic
256C2×C4⋊C4C22×C3×C511yescharacteristic
257C2×C4⋊C4C22×C3×C511yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260#106—22no—
261C22⋊C8—22no—
262#95—21no—
263#95—21no—
264C2×C3×C5—42no—
265C2×C3×C5#39711yescharacteristic
266C2×C3×C5#46511yescharacteristic
267C2×C3×C5#46811yescharacteristic
268C2×C3×C5#48111yescharacteristic
269C2×C3×C5#48211yescharacteristic
270C2×C3×C5#48311yescharacteristic
271C2×C3×C5#48511yescharacteristic
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3C5×SD1612yes—
279C23×C3C2×C5×D411yescharacteristic
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4C2×C5×D411yescharacteristic
300C2×C3×C4C5×#4111yescharacteristic
301C2×C3×C4C5×#4111yescharacteristic
302C2×C3×C4C5×#4111yescharacteristic
303C2×C3×C4C5×#4111yescharacteristic
304C2×C3×C4C5×#4111yescharacteristic
305C3×C8—22no—
306C3×C8—41no—
307C22×C5—22no—
308C22×C5—22no—
309C22×C5—22no—
310C22×C5—41no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C3×#12111yescharacteristic
315C22×C5C3×#12311yescharacteristic
316C22×C5C3×#12311yescharacteristic
317C22×C5C2×C3×SD1611yescharacteristic
318C22×C5C3×#13511yescharacteristic
319C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
320C22×C5C3×#13711yescharacteristic
321C4×C5—41no—
322C4×C5—81no—
323C4×C5—81no—
324C4×C5—81no—
325C4×C5—81no—
326C4×C5C3×#12311yescharacteristic
327C4×C5C3×#12411yescharacteristic
328C4×C5C3×#12611yescharacteristic
329C4×C5C3×#12611yescharacteristic
330C24C3×C5×D411yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4C3×C5×D411yescharacteristic
342C22×C4C23×C3×C511yescharacteristic
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8C3×C5×D412yes—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C3×C5#207711yescharacteristic, direct product factor, Hall
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3C5×#12111yescharacteristic
368C22×C3C5×#12311yescharacteristic
369C22×C3C5×#12311yescharacteristic
370C22×C3C2×C5×SD1611yescharacteristic
371C22×C3C5×#13511yescharacteristic
372C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
373C22×C3C5×#13711yescharacteristic
374C3×C4—41no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—81no—
378C3×C4—81no—
379C3×C4C5×#12311yescharacteristic
380C3×C4C5×#12411yescharacteristic
381C3×C4C5×#12611yescharacteristic
382C3×C4C5×#12611yescharacteristic
383C2×C5—42no—
384C2×C5C3×#39711yescharacteristic
385C2×C5C3×#46511yescharacteristic
386C2×C5C3×#46811yescharacteristic
387C2×C5C3×#48111yescharacteristic
388C2×C5C3×#48211yescharacteristic
389C2×C5C3×#48311yescharacteristic
390C2×C5C3×#48511yescharacteristic
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23C3×C5×SD1612yes—
398C23C2×C3×C5×D411yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4C2×C3×C5×D411yescharacteristic
419C2×C4C3×C5×#4111yescharacteristic
420C2×C4C3×C5×#4111yescharacteristic
421C2×C4C3×C5×#4111yescharacteristic
422C2×C4C3×C5×#4111yescharacteristic
423C2×C4C3×C5×#4111yescharacteristic
424C8—22no—
425C8—41no—
426C2×C3—42no—
427C2×C3C5×#39711yescharacteristic
428C2×C3C5×#46511yescharacteristic
429C2×C3C5×#46811yescharacteristic
430C2×C3C5×#48111yescharacteristic
431C2×C3C5×#48211yescharacteristic
432C2×C3C5×#48311yescharacteristic
433C2×C3C5×#48511yescharacteristic
434C5C3×#207711yescharacteristic, direct product factor, Sylow
435C22—22no—
436C22—22no—
437C22—22no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22C3×C5×#12111yescharacteristic
443C22C3×C5×#12311yescharacteristic
444C22C3×C5×#12311yescharacteristic
445C22C2×C3×C5×SD1611yescharacteristic
446C22C3×C5×#13511yescharacteristic
447C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
448C22C3×C5×#13711yescharacteristic
449C4—41no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4C3×C5×#12311yescharacteristic
455C4C3×C5×#12411yescharacteristic
456C4C3×C5×#12611yescharacteristic
457C4C3×C5×#12611yescharacteristic
458C3C5×#207711yescharacteristic, direct product factor, Sylow
459C2—42no—
460C2C3×C5×#39711yescharacteristic
461C2C3×C5×#46511yescharacteristic
462C2C3×C5×#46811yescharacteristic
463C2C3×C5×#48111yescharacteristic
464C2C3×C5×#48211yescharacteristic
465C2C3×C5×#48311yescharacteristic
466C2C3×C5×#48511yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC24×C3×C5D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#106C2semidirect
5. C3×C5×#340C2semidirect
6. C3×C5×#340C2semidirect
7. C3×C5×#340C2semidirect
8. C5×#2077C3direct (N × H)
22. C3×#2077C5direct (N × H)
23. C2×C5×#106C2×C3semidirect
27. C5×#340C2×C3semidirect
28. C5×#340C2×C3semidirect
29. C5×#340C2×C3semidirect
59. C2×C3×#106C2×C5semidirect
63. C3×#340C2×C5semidirect
64. C3×#340C2×C5semidirect
65. C3×#340C2×C5semidirect
79. #2077C3×C5direct (N × H)
157. C2×#106C2×C3×C5semidirect
161. #340C2×C3×C5semidirect
162. #340C2×C3×C5semidirect
163. #340C2×C3×C5semidirect
359. C3×C5#2077direct (N × H)
434. C5C3×#2077direct (N × H)
458. C3C5×#2077direct (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×#1062
C2×C3×C5×C22⋊C82
C3×C5×#3802
C3×C5×#3402
C5×#20773
C3×#20775