Finite Group Databasebeta

← C3×C5×#2067 #14275101

Subgroups — C3×C5×#2067 #14275101

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#107C211yesmaximal, characteristic, complemented
2C2×C3×C5×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic
4C2×C3×C5×#102C211yesmaximal, characteristic
5C3×C5×#390C211yesmaximal, characteristic
6C3×C5×#389C211yesmaximal, characteristic, complemented
7C3×C5×#340C211yesmaximal, characteristic, complemented
8C5×#2067C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4—21no—
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—
18C2×C3×C42×C5C2211yescharacteristic
19C3×C5×#107—22no—
20C3×C5×C4⋊C8—22no—
21C3×C5×#102—22no—
22C3×C5×#102—22no—
23C3×C5×#95—21no—
24C3×#2067C511yesmaximal, characteristic, direct product factor, Hall
25C2×C5×#107C2×C311yescharacteristic, complemented
26C2×C5×C4⋊C8C2×C311yescharacteristic, complemented
27C2×C5×#102C2×C311yescharacteristic
28C2×C5×#102C2×C311yescharacteristic
29C5×#390C2×C311yescharacteristic
30C5×#389C2×C311yescharacteristic, complemented
31C5×#340C2×C311yescharacteristic, complemented
32C24×C3×C5—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4Q812yes—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8D412yes—
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—42no—
57C3×C5×C4⋊C4D412yes—
58C3×C5×C22⋊C4—42no—
59C3×C5×C22⋊C4—42no—
60C3×C42×C5—21no—
61C3×C42×C5—21no—
62C2×C3×#107C2×C511yescharacteristic, complemented
63C2×C3×C4⋊C8C2×C511yescharacteristic, complemented
64C2×C3×#102C2×C511yescharacteristic
65C2×C3×#102C2×C511yescharacteristic
66C3×#390C2×C511yescharacteristic
67C3×#389C2×C511yescharacteristic, complemented
68C3×#340C2×C511yescharacteristic, complemented
69C22×C5×D4C22×C311yescharacteristic
70C22×C5×C8C22×C311yescharacteristic
71C22×C5×C8C22×C311yescharacteristic
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4C22×C311yescharacteristic
74C2×C5×C4⋊C4C22×C311yescharacteristic
75C2×C5×C4⋊C4C22×C311yescharacteristic
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C42×C5C22×C311yescharacteristic
79C5×#107—22no—
80C5×C4⋊C8—22no—
81C5×#102—22no—
82C5×#102—22no—
83C5×#95—21no—
84#2067C3×C511yescharacteristic, direct product factor, Sylow
85C23×C3×C5—22no—
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C23×C3×C5—41no—
89C23×C3×C5—41no—
90C23×C3×C5—41no—
91C23×C3×C5—41no—
92C23×C3×C5C2×D411yescharacteristic
93C3×C5×D4—22no—
94C3×C5×D4—22no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5D812yes—
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×Q811yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C3×C5×C8—22no—
119C3×C5×C8—41no—
120C22×C3×D4C22×C511yescharacteristic
121C22×C3×C8C22×C511yescharacteristic
122C22×C3×C8C22×C511yescharacteristic
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4C22×C511yescharacteristic
125C2×C3×C4⋊C4C22×C511yescharacteristic
126C2×C3×C4⋊C4C22×C511yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C42C22×C511yescharacteristic
130C3×#107—22no—
131C3×C4⋊C8—22no—
132C3×#102—22no—
133C3×#102—22no—
134C3×#95—21no—
135C24×C5—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4C3×Q812yes—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C3×D411yescharacteristic
146C22×C4×C5C3×D411yescharacteristic
147C22×C4×C5C23×C311yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C2×C5×C8—21no—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8C3×D412yes—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—42no—
160C5×C4⋊C4C3×D412yes—
161C5×C22⋊C4—42no—
162C5×C22⋊C4—42no—
163C42×C5—21no—
164C42×C5—21no—
165C2×#107C2×C3×C511yescharacteristic, complemented
166C2×C4⋊C8C2×C3×C511yescharacteristic, complemented
167C2×#102C2×C3×C511yescharacteristic
168C2×#102C2×C3×C511yescharacteristic
169#390C2×C3×C511yescharacteristic
170#389C2×C3×C511yescharacteristic, complemented
171#340C2×C3×C511yescharacteristic, complemented
172C22×C3×C5—42no—
173C22×C3×C5—42no—
174C22×C3×C5—42no—
175C22×C3×C5—81no—
176C22×C3×C5—81no—
177C22×C3×C5—81no—
178C22×C3×C5—81no—
179C22×C3×C5#12111yescharacteristic
180C22×C3×C5#12111yescharacteristic
181C22×C3×C5C22⋊Q811yescharacteristic
182C22×C3×C5C2×D811yescharacteristic
183C22×C3×C5#13511yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
185C22×C3×C5#13711yescharacteristic
186C3×C4×C5—22no—
187C3×C4×C5—42no—
188C3×C4×C5—41no—
189C3×C4×C5—81no—
190C3×C4×C5—81no—
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5#12611yescharacteristic
195C24×C3—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4C5×Q812yes—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4C5×D411yescharacteristic
206C22×C3×C4C5×D411yescharacteristic
207C22×C3×C4C23×C511yescharacteristic
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8C5×D412yes—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—42no—
220C3×C4⋊C4C5×D412yes—
221C3×C22⋊C4—42no—
222C3×C22⋊C4—42no—
223C3×C42—21no—
224C3×C42—21no—
225C23×C5—22no—
226C23×C5—41no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5—41no—
230C23×C5—41no—
231C23×C5—41no—
232C23×C5C2×C3×D411yescharacteristic
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—41no—
236C5×D4—41no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—22no—
241C2×C4×C5—21no—
242C2×C4×C5—21no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5C3×D812yes—
252C2×C4×C5C2×C3×D411yescharacteristic
253C2×C4×C5C2×C3×D411yescharacteristic
254C2×C4×C5C2×C3×Q811yescharacteristic
255C2×C4×C5C3×#4111yescharacteristic
256C2×C4×C5C3×#4111yescharacteristic
257C2×C4×C5C3×#4111yescharacteristic
258C5×C8—22no—
259C5×C8—41no—
260C22×D4C22×C3×C511yescharacteristic
261C22×C8C22×C3×C511yescharacteristic
262C22×C8C22×C3×C511yescharacteristic
263C2×C4⋊C4—21no—
264C2×C4⋊C4C22×C3×C511yescharacteristic
265C2×C4⋊C4C22×C3×C511yescharacteristic
266C2×C4⋊C4C22×C3×C511yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C42C22×C3×C511yescharacteristic
270#107—22no—
271C4⋊C8—22no—
272#102—22no—
273#102—22no—
274#95—21no—
275C2×C3×C5—82no—
276C2×C3×C5#39611yescharacteristic
277C2×C3×C5#45911yescharacteristic
278C2×C3×C5#46411yescharacteristic
279C2×C3×C5#46611yescharacteristic
280C2×C3×C5#46811yescharacteristic
281C2×C3×C5#47411yescharacteristic
282C2×C3×C5#47811yescharacteristic
283C23×C3—22no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—41no—
290C23×C3C2×C5×D411yescharacteristic
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4C5×D812yes—
310C2×C3×C4C2×C5×D411yescharacteristic
311C2×C3×C4C2×C5×D411yescharacteristic
312C2×C3×C4C2×C5×Q811yescharacteristic
313C2×C3×C4C5×#4111yescharacteristic
314C2×C3×C4C5×#4111yescharacteristic
315C2×C3×C4C5×#4111yescharacteristic
316C3×C8—22no—
317C3×C8—41no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5—42no—
321C22×C5—81no—
322C22×C5—81no—
323C22×C5—81no—
324C22×C5—81no—
325C22×C5C3×#12111yescharacteristic
326C22×C5C3×#12111yescharacteristic
327C22×C5C3×C22⋊Q811yescharacteristic
328C22×C5C2×C3×D811yescharacteristic
329C22×C5C3×#13511yescharacteristic
330C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
331C22×C5C3×#13711yescharacteristic
332C4×C5—22no—
333C4×C5—42no—
334C4×C5—41no—
335C4×C5—81no—
336C4×C5—81no—
337C4×C5C3×#12111yescharacteristic
338C4×C5C3×C22⋊Q811yescharacteristic
339C4×C5C3×C22⋊Q811yescharacteristic
340C4×C5C3×#12611yescharacteristic
341C24—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4C3×C5×Q812yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4C3×C5×D411yescharacteristic
352C22×C4C3×C5×D411yescharacteristic
353C22×C4C23×C3×C511yescharacteristic
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8C3×C5×D412yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—42no—
366C4⋊C4C3×C5×D412yes—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C42—21no—
370C42—21no—
371C3×C5#206711yescharacteristic, direct product factor, Hall
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—81no—
376C22×C3—81no—
377C22×C3—81no—
378C22×C3—81no—
379C22×C3C5×#12111yescharacteristic
380C22×C3C5×#12111yescharacteristic
381C22×C3C5×C22⋊Q811yescharacteristic
382C22×C3C2×C5×D811yescharacteristic
383C22×C3C5×#13511yescharacteristic
384C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
385C22×C3C5×#13711yescharacteristic
386C3×C4—22no—
387C3×C4—42no—
388C3×C4—41no—
389C3×C4—81no—
390C3×C4—81no—
391C3×C4C5×#12111yescharacteristic
392C3×C4C5×C22⋊Q811yescharacteristic
393C3×C4C5×C22⋊Q811yescharacteristic
394C3×C4C5×#12611yescharacteristic
395C2×C5—82no—
396C2×C5C3×#39611yescharacteristic
397C2×C5C3×#45911yescharacteristic
398C2×C5C3×#46411yescharacteristic
399C2×C5C3×#46611yescharacteristic
400C2×C5C3×#46811yescharacteristic
401C2×C5C3×#47411yescharacteristic
402C2×C5C3×#47811yescharacteristic
403C23—22no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23C2×C3×C5×D411yescharacteristic
411D4—22no—
412D4—22no—
413D4—41no—
414D4—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4C3×C5×D812yes—
430C2×C4C2×C3×C5×D411yescharacteristic
431C2×C4C2×C3×C5×D411yescharacteristic
432C2×C4C2×C3×C5×Q811yescharacteristic
433C2×C4C3×C5×#4111yescharacteristic
434C2×C4C3×C5×#4111yescharacteristic
435C2×C4C3×C5×#4111yescharacteristic
436C8—22no—
437C8—41no—
438C2×C3—82no—
439C2×C3C5×#39611yescharacteristic
440C2×C3C5×#45911yescharacteristic
441C2×C3C5×#46411yescharacteristic
442C2×C3C5×#46611yescharacteristic
443C2×C3C5×#46811yescharacteristic
444C2×C3C5×#47411yescharacteristic
445C2×C3C5×#47811yescharacteristic
446C5C3×#206711yescharacteristic, direct product factor, Sylow
447C22—42no—
448C22—42no—
449C22—42no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22C3×C5×#12111yescharacteristic
455C22C3×C5×#12111yescharacteristic
456C22C3×C5×C22⋊Q811yescharacteristic
457C22C2×C3×C5×D811yescharacteristic
458C22C3×C5×#13511yescharacteristic
459C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
460C22C3×C5×#13711yescharacteristic
461C4—22no—
462C4—42no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4C3×C5×#12111yescharacteristic
467C4C3×C5×C22⋊Q811yescharacteristic
468C4C3×C5×C22⋊Q811yescharacteristic
469C4C3×C5×#12611yescharacteristic
470C3C5×#206711yescharacteristic, direct product factor, Sylow
471C2—82no—
472C2C3×C5×#39611yescharacteristic
473C2C3×C5×#45911yescharacteristic
474C2C3×C5×#46411yescharacteristic
475C2C3×C5×#46611yescharacteristic
476C2C3×C5×#46811yescharacteristic
477C2C3×C5×#47411yescharacteristic
478C2C3×C5×#47811yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#107C2semidirect
2. C2×C3×C5×C4⋊C8C2semidirect
6. C3×C5×#389C2semidirect
7. C3×C5×#340C2semidirect
8. C5×#2067C3direct (N × H)
24. C3×#2067C5direct (N × H)
25. C2×C5×#107C2×C3semidirect
26. C2×C5×C4⋊C8C2×C3semidirect
30. C5×#389C2×C3semidirect
31. C5×#340C2×C3semidirect
62. C2×C3×#107C2×C5semidirect
63. C2×C3×C4⋊C8C2×C5semidirect
67. C3×#389C2×C5semidirect
68. C3×#340C2×C5semidirect
84. #2067C3×C5direct (N × H)
165. C2×#107C2×C3×C5semidirect
166. C2×C4⋊C8C2×C3×C5semidirect
170. #389C2×C3×C5semidirect
171. #340C2×C3×C5semidirect
371. C3×C5#2067direct (N × H)
446. C5C3×#2067direct (N × H)
470. C3C5×#2067direct (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×#1072
C2×C3×C5×C4⋊C82
C2×C3×C5×#1022
C3×C5×#3902
C3×C5×#3892
C3×C5×#3402
C5×#20673
C3×#20675