Finite Group Databasebeta

← C3×C5×#1878 #14274912

Subgroups — C3×C5×#1878 #14274912

Order 1920.

676 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
1C22×C3×C5×Q16C211yesmaximal, characteristic
2C2×C3×C4×C5×Q8C211yesmaximal, characteristic
3C2×C3×C5×#103C211yesmaximal, characteristic
4C2×C3×C5×#103C211yesmaximal, characteristic
5C3×C5×#391C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic
7C3×C5×#336C211yesmaximal, characteristic
8C5×#1878C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C3×C5×Q16—22no—
12C2×C3×C5×Q16—22no—
13C2×C3×C5×Q16C414yescomplemented
14C22×C3×C5×C8C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×C4×C5×Q8—22no—
17C3×C4×C5×Q8—22no—
18C2×C3×C5×C4⋊C4—21no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5—21no—
22C2×C3×C42×C5C2211yescharacteristic
23C3×C5×#103—22no—
24C3×C5×#103—22no—
25C3×C5×#95—21no—
26C3×C5×#95—21no—
27C3×#1878C511yesmaximal, characteristic, direct product factor, Hall
28C22×C5×Q16C2×C311yescharacteristic
29C2×C4×C5×Q8C2×C311yescharacteristic
30C2×C5×#103C2×C311yescharacteristic
31C2×C5×#103C2×C311yescharacteristic
32C5×#391C2×C311yescharacteristic
33C5×#340C2×C311yescharacteristic
34C5×#336C2×C311yescharacteristic
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8C2×C412yes—
44C2×C3×C5×Q8C2×C412yes—
45C2×C3×C5×Q8D412yes—
46C2×C3×C5×Q8D412yes—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5D411yescharacteristic
52C22×C3×C4×C5D411yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C3×C5×Q16—28no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8C2×C412yes—
61C3×C5×C4⋊C4—24no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4D412yes—
66C3×C42×C5—24no—
67C3×C42×C5—21no—
68C3×C42×C5—21no—
69C22×C3×Q16C2×C511yescharacteristic
70C2×C3×C4×Q8C2×C511yescharacteristic
71C2×C3×#103C2×C511yescharacteristic
72C2×C3×#103C2×C511yescharacteristic
73C3×#391C2×C511yescharacteristic
74C3×#340C2×C511yescharacteristic
75C3×#336C2×C511yescharacteristic
76C22×C5×Q8C22×C311yescharacteristic
77C22×C5×Q8C22×C311yescharacteristic
78C2×C5×Q16—22no—
79C2×C5×Q16—22no—
80C2×C5×Q16C3×C414yescomplemented
81C22×C5×C8C22×C311yescharacteristic
82C22×C5×C8C22×C311yescharacteristic
83C4×C5×Q8—22no—
84C4×C5×Q8—22no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C5×C4⋊C4C22×C311yescharacteristic
88C2×C42×C5—21no—
89C2×C42×C5C22×C311yescharacteristic
90C5×#103—22no—
91C5×#103—22no—
92C5×#95—21no—
93C5×#95—21no—
94#1878C3×C511yescharacteristic, direct product factor, Sylow
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—22no—
97C3×C5×Q8—22no—
98C3×C5×Q8—22no—
99C3×C5×Q8—22no—
100C3×C5×Q8—22no—
101C3×C5×Q8—41no—
102C3×C5×Q8—41no—
103C3×C5×Q8C22⋊C414yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5Q1612yescomplemented
122C2×C3×C4×C5C22×C411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C3×C5×C8—22no—
129C3×C5×C8—41no—
130C22×C3×Q8C22×C511yescharacteristic
131C22×C3×Q8C22×C511yescharacteristic
132C2×C3×Q16—22no—
133C2×C3×Q16—22no—
134C2×C3×Q16C4×C514yescomplemented
135C22×C3×C8C22×C511yescharacteristic
136C22×C3×C8C22×C511yescharacteristic
137C3×C4×Q8—22no—
138C3×C4×Q8—22no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C22×C511yescharacteristic
141C2×C3×C4⋊C4C22×C511yescharacteristic
142C2×C3×C42—21no—
143C2×C3×C42C22×C511yescharacteristic
144C3×#103—22no—
145C3×#103—22no—
146C3×#95—21no—
147C3×#95—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8C2×C3×C412yes—
157C2×C5×Q8C2×C3×C412yes—
158C2×C5×Q8C3×D412yes—
159C2×C5×Q8C3×D412yes—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5C3×D411yescharacteristic
165C22×C4×C5C3×D411yescharacteristic
166C22×C4×C5C23×C311yescharacteristic
167C5×Q16—28no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8C2×C3×C412yes—
174C5×C4⋊C4—24no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4C3×D412yes—
179C42×C5—24no—
180C42×C5—21no—
181C42×C5—21no—
182C22×Q16C2×C3×C511yescharacteristic
183C2×C4×Q8C2×C3×C511yescharacteristic
184C2×#103C2×C3×C511yescharacteristic
185C2×#103C2×C3×C511yescharacteristic
186#391C2×C3×C511yescharacteristic
187#340C2×C3×C511yescharacteristic
188#336C2×C3×C511yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5#12011yescharacteristic
191C22×C3×C5#12111yescharacteristic
192C22×C3×C5C2×Q1611yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C22×C3×C5#13711yescharacteristic
195C22×C3×C5#13711yescharacteristic
196C3×C4×C5—24no—
197C3×C4×C5—22no—
198C3×C4×C5—42no—
199C3×C4×C5—41no—
200C3×C4×C5—42no—
201C3×C4×C5—81no—
202C3×C4×C5C2×C22⋊C411yescharacteristic
203C3×C4×C5C4×D411yescharacteristic
204C3×C4×C5#12111yescharacteristic
205C3×C4×C5#12311yescharacteristic
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8C2×C4×C512yes—
215C2×C3×Q8C2×C4×C512yes—
216C2×C3×Q8C5×D412yes—
217C2×C3×Q8C5×D412yes—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4C5×D411yescharacteristic
223C22×C3×C4C5×D411yescharacteristic
224C22×C3×C4C23×C511yescharacteristic
225C3×Q16—28no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8C2×C4×C512yes—
232C3×C4⋊C4—24no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4C5×D412yes—
237C3×C42—24no—
238C3×C42—21no—
239C3×C42—21no—
240C23×C5C2×C3×D411yescharacteristic
241C5×Q8—22no—
242C5×Q8—22no—
243C5×Q8—22no—
244C5×Q8—22no—
245C5×Q8—22no—
246C5×Q8—41no—
247C5×Q8—41no—
248C5×Q8C3×C22⋊C414yes—
249C2×C4×C5—22no—
250C2×C4×C5—21no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—21no—
254C2×C4×C5—22no—
255C2×C4×C5—21no—
256C2×C4×C5—22no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5C3×Q1612yescomplemented
267C2×C4×C5C22×C3×C411yescharacteristic
268C2×C4×C5C2×C3×D411yescharacteristic
269C2×C4×C5C2×C3×D411yescharacteristic
270C2×C4×C5C2×C3×D411yescharacteristic
271C2×C4×C5C3×#4111yescharacteristic
272C2×C4×C5C3×#4111yescharacteristic
273C5×C8—22no—
274C5×C8—41no—
275C22×Q8C22×C3×C511yescharacteristic
276C22×Q8C22×C3×C511yescharacteristic
277C2×Q16—22no—
278C2×Q16—22no—
279C2×Q16C3×C4×C514yescomplemented
280C22×C8C22×C3×C511yescharacteristic
281C22×C8C22×C3×C511yescharacteristic
282C4×Q8—22no—
283C4×Q8—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4C22×C3×C511yescharacteristic
286C2×C4⋊C4C22×C3×C511yescharacteristic
287C2×C42—21no—
288C2×C42C22×C3×C511yescharacteristic
289#103—22no—
290#103—22no—
291#95—21no—
292#95—21no—
293C2×C3×C5#38611yescharacteristic
294C2×C3×C5C4×Q1611yescharacteristic
295C2×C3×C5#44111yescharacteristic
296C2×C3×C5#45111yescharacteristic
297C2×C3×C5#45211yescharacteristic
298C2×C3×C5#46211yescharacteristic
299C2×C3×C5#46411yescharacteristic
300C23×C3C2×C5×D411yescharacteristic
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—41no—
307C3×Q8—41no—
308C3×Q8C5×C22⋊C414yes—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4C5×Q1612yescomplemented
327C2×C3×C4C22×C4×C511yescharacteristic
328C2×C3×C4C2×C5×D411yescharacteristic
329C2×C3×C4C2×C5×D411yescharacteristic
330C2×C3×C4C2×C5×D411yescharacteristic
331C2×C3×C4C5×#4111yescharacteristic
332C2×C3×C4C5×#4111yescharacteristic
333C3×C8—22no—
334C3×C8—41no—
335C22×C5C3×C4×D411yescharacteristic
336C22×C5C3×#12011yescharacteristic
337C22×C5C3×#12111yescharacteristic
338C22×C5C2×C3×Q1611yescharacteristic
339C22×C5C3×#13511yescharacteristic
340C22×C5C3×#13711yescharacteristic
341C22×C5C3×#13711yescharacteristic
342C4×C5—24no—
343C4×C5—22no—
344C4×C5—42no—
345C4×C5—41no—
346C4×C5—42no—
347C4×C5—81no—
348C4×C5C2×C3×C22⋊C411yescharacteristic
349C4×C5C3×C4×D411yescharacteristic
350C4×C5C3×#12111yescharacteristic
351C4×C5C3×#12311yescharacteristic
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8C2×C3×C4×C512yes—
361C2×Q8C2×C3×C4×C512yes—
362C2×Q8C3×C5×D412yes—
363C2×Q8C3×C5×D412yes—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4C3×C5×D411yescharacteristic
369C22×C4C3×C5×D411yescharacteristic
370C22×C4C23×C3×C511yescharacteristic
371Q16—28no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8C2×C3×C4×C512yes—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4C3×C5×D412yes—
383C42—24no—
384C42—21no—
385C42—21no—
386C3×C5#187811yescharacteristic, direct product factor, Hall
387C22×C3C4×C5×D411yescharacteristic
388C22×C3C5×#12011yescharacteristic
389C22×C3C5×#12111yescharacteristic
390C22×C3C2×C5×Q1611yescharacteristic
391C22×C3C5×#13511yescharacteristic
392C22×C3C5×#13711yescharacteristic
393C22×C3C5×#13711yescharacteristic
394C3×C4—24no—
395C3×C4—22no—
396C3×C4—42no—
397C3×C4—41no—
398C3×C4—42no—
399C3×C4—81no—
400C3×C4C2×C5×C22⋊C411yescharacteristic
401C3×C4C4×C5×D411yescharacteristic
402C3×C4C5×#12111yescharacteristic
403C3×C4C5×#12311yescharacteristic
404C2×C5C3×#38611yescharacteristic
405C2×C5C3×C4×Q1611yescharacteristic
406C2×C5C3×#44111yescharacteristic
407C2×C5C3×#45111yescharacteristic
408C2×C5C3×#45211yescharacteristic
409C2×C5C3×#46211yescharacteristic
410C2×C5C3×#46411yescharacteristic
411C23C2×C3×C5×D411yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—41no—
418Q8—41no—
419Q8C3×C5×C22⋊C414yes—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4C3×C5×Q1612yescomplemented
438C2×C4C22×C3×C4×C511yescharacteristic
439C2×C4C2×C3×C5×D411yescharacteristic
440C2×C4C2×C3×C5×D411yescharacteristic
441C2×C4C2×C3×C5×D411yescharacteristic
442C2×C4C3×C5×#4111yescharacteristic
443C2×C4C3×C5×#4111yescharacteristic
444C8—22no—
445C8—41no—
446C2×C3C5×#38611yescharacteristic
447C2×C3C4×C5×Q1611yescharacteristic
448C2×C3C5×#44111yescharacteristic
449C2×C3C5×#45111yescharacteristic
450C2×C3C5×#45211yescharacteristic
451C2×C3C5×#46211yescharacteristic
452C2×C3C5×#46411yescharacteristic
453C5C3×#187811yescharacteristic, direct product factor, Sylow
454C22C3×C4×C5×D411yescharacteristic
455C22C3×C5×#12011yescharacteristic
456C22C3×C5×#12111yescharacteristic
457C22C2×C3×C5×Q1611yescharacteristic
458C22C3×C5×#13511yescharacteristic
459C22C3×C5×#13711yescharacteristic
460C22C3×C5×#13711yescharacteristic
461C4—22no—
462C4—24no—
463C4—41no—
464C4—42no—
465C4—42no—
466C4—81no—
467C4C2×C3×C5×C22⋊C411yescharacteristic
468C4C3×C4×C5×D411yescharacteristic
469C4C3×C5×#12111yescharacteristic
470C4C3×C5×#12311yescharacteristic
471C3C5×#187811yescharacteristic, direct product factor, Sylow
472C2C3×C5×#38611yescharacteristic
473C2C3×C4×C5×Q1611yescharacteristic
474C2C3×C5×#44111yescharacteristic
475C2C3×C5×#45111yescharacteristic
476C2C3×C5×#45211yescharacteristic
477C2C3×C5×#46211yescharacteristic
478C2C3×C5×#46411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
LCSG ▷ C2×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
8. C5×#1878C3direct (N × H)
13. C2×C3×C5×Q16C4semidirect
27. C3×#1878C5direct (N × H)
80. C2×C5×Q16C3×C4semidirect
94. #1878C3×C5direct (N × H)
121. C2×C3×C4×C5Q16semidirect
134. C2×C3×Q16C4×C5semidirect
266. C2×C4×C5C3×Q16semidirect
279. C2×Q16C3×C4×C5semidirect
326. C2×C3×C4C5×Q16semidirect
386. C3×C5#1878direct (N × H)
437. C2×C4C3×C5×Q16semidirect
453. C5C3×#1878direct (N × H)
471. C3C5×#1878direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C5×Q162
C2×C3×C4×C5×Q82
C2×C3×C5×#1032
C3×C5×#3912
C3×C5×#3402
C3×C5×#3362
C5×#18783
C3×#18785