Finite Group Databasebeta

← C3×C5×#1907 #14274941

Subgroups — C3×C5×#1907 #14274941

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C3×C5×#131C211yesmaximal, characteristic, complemented
3C3×C5×#417C211yesmaximal, characteristic, complemented
4C2×C3×C5×#102C211yesmaximal, characteristic, complemented
5C2×C3×C5×#100C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7C3×C5×#341C211yesmaximal, characteristic, complemented
8C5×#1907C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C3×C5×AGL(1,ℤ/8)—22no—
12C3×C5×AGL(1,ℤ/8)C414yescomplemented
13C2×C3×C5×SD16—21no—
14C2×C3×C5×D8—21no—
15C3×C5×#131—22no—
16C3×C5×#131—22no—
17C2×C3×C5×M16—21no—
18C2×C3×C5×M16C2211yescharacteristic
19C2×C3×C5×M16C2211yescharacteristic
20C2×C3×C5×M16C2211yescharacteristic
21C22×C3×C5×C8—21no—
22C22×C3×C5×C8C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C3×C5×#103—21no—
25C3×C5×#102—21no—
26C3×C5×#102—21no—
27C3×C5×#102—21no—
28C3×C5×#100—22no—
29C3×#1907C511yesmaximal, characteristic, direct product factor, Hall
30C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic
31C2×C5×#131C2×C311yescharacteristic, complemented
32C5×#417C2×C311yescharacteristic, complemented
33C2×C5×#102C2×C311yescharacteristic, complemented
34C2×C5×#100C2×C311yescharacteristic, complemented
35C5×#343C2×C311yescharacteristic, complemented
36C5×#341C2×C311yescharacteristic, complemented
37C24×C3×C5—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41C2×C412yes—
41C3×C5×#41D412yes—
42C2×C3×C5×Q8D411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4C2×C412yes—
50C2×C3×C5×D4D411yescharacteristic
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C3×C5×SD16—24no—
55C3×C5×D8—24no—
56C3×C5×M16—24no—
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C3×C5×M16—21no—
60C3×C5×M16—21no—
61C3×C5×M16C2×C412yes—
62C3×C5×M16D412yes—
63C2×C3×C5×C8—24no—
64C2×C3×C5×C8—21no—
65C2×C3×C5×C8—21no—
66C2×C3×C5×C8—21no—
67C2×C3×C5×C8—21no—
68C2×C3×C5×C8—21no—
69C2×C3×C5×C8D411yescharacteristic
70C2×C3×C5×C8D411yescharacteristic
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4—21no—
73C2×C3×AGL(1,ℤ/8)C2×C511yescharacteristic
74C2×C3×#131C2×C511yescharacteristic, complemented
75C3×#417C2×C511yescharacteristic, complemented
76C2×C3×#102C2×C511yescharacteristic, complemented
77C2×C3×#100C2×C511yescharacteristic, complemented
78C3×#343C2×C511yescharacteristic, complemented
79C3×#341C2×C511yescharacteristic, complemented
80C2×C5×#41C22×C311yescharacteristic
81C22×C5×D4C22×C311yescharacteristic
82C5×AGL(1,ℤ/8)—22no—
83C5×AGL(1,ℤ/8)C3×C414yescomplemented
84C2×C5×SD16—21no—
85C2×C5×D8—21no—
86C5×#131—22no—
87C5×#131—22no—
88C2×C5×M16—21no—
89C2×C5×M16C22×C311yescharacteristic
90C2×C5×M16C22×C311yescharacteristic
91C2×C5×M16C22×C311yescharacteristic
92C22×C5×C8—21no—
93C22×C5×C8C22×C311yescharacteristic
94C2×C5×C4⋊C4C22×C311yescharacteristic
95C5×#103—21no—
96C5×#102—21no—
97C5×#102—21no—
98C5×#102—21no—
99C5×#100—22no—
100#1907C3×C511yescharacteristic, direct product factor, Sylow
101C23×C3×C5—21no—
102C23×C3×C5—22no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—81no—
106C23×C3×C5—81no—
107C23×C3×C5#4111yescharacteristic
108C3×C5×Q8—21no—
109C3×C5×Q8C22⋊C412yes—
110C3×C5×D4—22no—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—22no—
114C3×C5×D4—21no—
115C3×C5×D4—41no—
116C3×C5×D4—41no—
117C3×C5×D4C22⋊C412yes—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—81no—
123C2×C3×C4×C5C22×C411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5#4111yescharacteristic
129C3×C5×C8—22no—
130C3×C5×C8—21no—
131C3×C5×C8—22no—
132C3×C5×C8—21no—
133C3×C5×C8—41no—
134C2×C3×#41C22×C511yescharacteristic
135C22×C3×D4C22×C511yescharacteristic
136C3×AGL(1,ℤ/8)—22no—
137C3×AGL(1,ℤ/8)C4×C514yescomplemented
138C2×C3×SD16—21no—
139C2×C3×D8—21no—
140C3×#131—22no—
141C3×#131—22no—
142C2×C3×M16—21no—
143C2×C3×M16C22×C511yescharacteristic
144C2×C3×M16C22×C511yescharacteristic
145C2×C3×M16C22×C511yescharacteristic
146C22×C3×C8—21no—
147C22×C3×C8C22×C511yescharacteristic
148C2×C3×C4⋊C4C22×C511yescharacteristic
149C3×#103—21no—
150C3×#102—21no—
151C3×#102—21no—
152C3×#102—21no—
153C3×#100—22no—
154C24×C5—21no—
155C5×#41—21no—
156C5×#41—21no—
157C5×#41C2×C3×C412yes—
158C5×#41C3×D412yes—
159C2×C5×Q8C3×D411yescharacteristic
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C2×C3×C412yes—
167C2×C5×D4C3×D411yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5C23×C311yescharacteristic
171C5×SD16—24no—
172C5×D8—24no—
173C5×M16—24no—
174C5×M16—21no—
175C5×M16—21no—
176C5×M16—21no—
177C5×M16—21no—
178C5×M16C2×C3×C412yes—
179C5×M16C3×D412yes—
180C2×C5×C8—24no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8C3×D411yescharacteristic
187C2×C5×C8C3×D411yescharacteristic
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C2×AGL(1,ℤ/8)C2×C3×C511yescharacteristic
191C2×#131C2×C3×C511yescharacteristic, complemented
192#417C2×C3×C511yescharacteristic, complemented
193C2×#102C2×C3×C511yescharacteristic, complemented
194C2×#100C2×C3×C511yescharacteristic, complemented
195#343C2×C3×C511yescharacteristic, complemented
196#341C2×C3×C511yescharacteristic, complemented
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5—22no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5—42no—
203C22×C3×C5—82no—
204C22×C3×C5—82no—
205C22×C3×C5—81no—
206C22×C3×C5—81no—
207C22×C3×C5C4×D411yescharacteristic
208C22×C3×C5#12111yescharacteristic
209C22×C3×C5#12311yescharacteristic
210C3×C4×C5—22no—
211C3×C4×C5—81no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C24×C3—21no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41C2×C4×C512yes—
220C3×#41C5×D412yes—
221C2×C3×Q8C5×D411yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4C2×C4×C512yes—
229C2×C3×D4C5×D411yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C23×C511yescharacteristic
233C3×SD16—24no—
234C3×D8—24no—
235C3×M16—24no—
236C3×M16—21no—
237C3×M16—21no—
238C3×M16—21no—
239C3×M16—21no—
240C3×M16C2×C4×C512yes—
241C3×M16C5×D412yes—
242C2×C3×C8—24no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8C5×D411yescharacteristic
249C2×C3×C8C5×D411yescharacteristic
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C23×C5—21no—
253C23×C5—22no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—81no—
257C23×C5—81no—
258C23×C5C3×#4111yescharacteristic
259C5×Q8—21no—
260C5×Q8C3×C22⋊C412yes—
261C5×D4—22no—
262C5×D4—22no—
263C5×D4—22no—
264C5×D4—22no—
265C5×D4—21no—
266C5×D4—41no—
267C5×D4—41no—
268C5×D4C3×C22⋊C412yes—
269C2×C4×C5—21no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—41no—
273C2×C4×C5—81no—
274C2×C4×C5C22×C3×C411yescharacteristic
275C2×C4×C5C2×C3×D411yescharacteristic
276C2×C4×C5C2×C3×D411yescharacteristic
277C2×C4×C5C2×C3×D411yescharacteristic
278C2×C4×C5C2×C3×D411yescharacteristic
279C2×C4×C5C3×#4111yescharacteristic
280C5×C8—22no—
281C5×C8—21no—
282C5×C8—22no—
283C5×C8—21no—
284C5×C8—41no—
285C2×#41C22×C3×C511yescharacteristic
286C22×D4C22×C3×C511yescharacteristic
287AGL(1,ℤ/8)—22no—
288AGL(1,ℤ/8)C3×C4×C514yescomplemented
289C2×SD16—21no—
290C2×D8—21no—
291#131—22no—
292#131—22no—
293C2×M16—21no—
294C2×M16C22×C3×C511yescharacteristic
295C2×M16C22×C3×C511yescharacteristic
296C2×M16C22×C3×C511yescharacteristic
297C22×C8—21no—
298C22×C8C22×C3×C511yescharacteristic
299C2×C4⋊C4C22×C3×C511yescharacteristic
300#103—21no—
301#102—21no—
302#102—21no—
303#102—21no—
304#100—22no—
305C2×C3×C5—21no—
306C2×C3×C5—21no—
307C2×C3×C5—42no—
308C2×C3×C5—82no—
309C2×C3×C5#38611yescharacteristic
310C2×C3×C5#47111yescharacteristic
311C2×C3×C5#47211yescharacteristic
312C23×C3—21no—
313C23×C3—22no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—81no—
317C23×C3—81no—
318C23×C3C5×#4111yescharacteristic
319C3×Q8—21no—
320C3×Q8C5×C22⋊C412yes—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—21no—
326C3×D4—41no—
327C3×D4—41no—
328C3×D4C5×C22⋊C412yes—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—41no—
333C2×C3×C4—81no—
334C2×C3×C4C22×C4×C511yescharacteristic
335C2×C3×C4C2×C5×D411yescharacteristic
336C2×C3×C4C2×C5×D411yescharacteristic
337C2×C3×C4C2×C5×D411yescharacteristic
338C2×C3×C4C2×C5×D411yescharacteristic
339C2×C3×C4C5×#4111yescharacteristic
340C3×C8—22no—
341C3×C8—21no—
342C3×C8—22no—
343C3×C8—21no—
344C3×C8—41no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—22no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—42no—
351C22×C5—82no—
352C22×C5—82no—
353C22×C5—81no—
354C22×C5—81no—
355C22×C5C3×C4×D411yescharacteristic
356C22×C5C3×#12111yescharacteristic
357C22×C5C3×#12311yescharacteristic
358C4×C5—22no—
359C4×C5—81no—
360C4×C5C2×C3×C22⋊C411yescharacteristic
361C4×C5C3×C4×D411yescharacteristic
362C4×C5C3×#12011yescharacteristic
363C4×C5C3×#12111yescharacteristic
364C24—21no—
365#41—21no—
366#41—21no—
367#41C2×C3×C4×C512yes—
368#41C3×C5×D412yes—
369C2×Q8C3×C5×D411yescharacteristic
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4C2×C3×C4×C512yes—
377C2×D4C3×C5×D411yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4C23×C3×C511yescharacteristic
381SD16—24no—
382D8—24no—
383M16—24no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16C2×C3×C4×C512yes—
389M16C3×C5×D412yes—
390C2×C8—24no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8C3×C5×D411yescharacteristic
397C2×C8C3×C5×D411yescharacteristic
398C4⋊C4—21no—
399C4⋊C4—21no—
400C3×C5#190711yescharacteristic, direct product factor, Hall
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—42no—
407C22×C3—82no—
408C22×C3—82no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3C4×C5×D411yescharacteristic
412C22×C3C5×#12111yescharacteristic
413C22×C3C5×#12311yescharacteristic
414C3×C4—22no—
415C3×C4—81no—
416C3×C4C2×C5×C22⋊C411yescharacteristic
417C3×C4C4×C5×D411yescharacteristic
418C3×C4C5×#12011yescharacteristic
419C3×C4C5×#12111yescharacteristic
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—42no—
423C2×C5—82no—
424C2×C5C3×#38611yescharacteristic
425C2×C5C3×#47111yescharacteristic
426C2×C5C3×#47211yescharacteristic
427C23—21no—
428C23—22no—
429C23—41no—
430C23—41no—
431C23—81no—
432C23—81no—
433C23C3×C5×#4111yescharacteristic
434Q8—21no—
435Q8C3×C5×C22⋊C412yes—
436D4—22no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4—21no—
441D4—41no—
442D4—41no—
443D4C3×C5×C22⋊C412yes—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—81no—
449C2×C4C22×C3×C4×C511yescharacteristic
450C2×C4C2×C3×C5×D411yescharacteristic
451C2×C4C2×C3×C5×D411yescharacteristic
452C2×C4C2×C3×C5×D411yescharacteristic
453C2×C4C2×C3×C5×D411yescharacteristic
454C2×C4C3×C5×#4111yescharacteristic
455C8—22no—
456C8—21no—
457C8—22no—
458C8—21no—
459C8—41no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—42no—
463C2×C3—82no—
464C2×C3C5×#38611yescharacteristic
465C2×C3C5×#47111yescharacteristic
466C2×C3C5×#47211yescharacteristic
467C5C3×#190711yescharacteristic, direct product factor, Sylow
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—82no—
475C22—82no—
476C22—81no—
477C22—81no—
478C22C3×C4×C5×D411yescharacteristic
479C22C3×C5×#12111yescharacteristic
480C22C3×C5×#12311yescharacteristic
481C4—22no—
482C4—81no—
483C4C2×C3×C5×C22⋊C411yescharacteristic
484C4C3×C4×C5×D411yescharacteristic
485C4C3×C5×#12011yescharacteristic
486C4C3×C5×#12111yescharacteristic
487C3C5×#190711yescharacteristic, direct product factor, Sylow
488C2—21no—
489C2—21no—
490C2—42no—
491C2—82no—
492C2C3×C5×#38611yescharacteristic
493C2C3×C5×#47111yescharacteristic
494C2C3×C5×#47211yescharacteristic
subgroupG/H
center, socleC22×C3×C5#121
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC2×C3×C5×AGL(1,ℤ/8)C2
LCSG ▷ C2×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
2. C2×C3×C5×#131C2semidirect
3. C3×C5×#417C2semidirect
4. C2×C3×C5×#102C2semidirect
5. C2×C3×C5×#100C2semidirect
6. C3×C5×#343C2semidirect
7. C3×C5×#341C2semidirect
8. C5×#1907C3direct (N × H)
12. C3×C5×AGL(1,ℤ/8)C4semidirect
29. C3×#1907C5direct (N × H)
31. C2×C5×#131C2×C3semidirect
32. C5×#417C2×C3semidirect
33. C2×C5×#102C2×C3semidirect
34. C2×C5×#100C2×C3semidirect
35. C5×#343C2×C3semidirect
36. C5×#341C2×C3semidirect
74. C2×C3×#131C2×C5semidirect
75. C3×#417C2×C5semidirect
76. C2×C3×#102C2×C5semidirect
77. C2×C3×#100C2×C5semidirect
78. C3×#343C2×C5semidirect
79. C3×#341C2×C5semidirect
83. C5×AGL(1,ℤ/8)C3×C4semidirect
100. #1907C3×C5direct (N × H)
137. C3×AGL(1,ℤ/8)C4×C5semidirect
191. C2×#131C2×C3×C5semidirect
192. #417C2×C3×C5semidirect
193. C2×#102C2×C3×C5semidirect
194. C2×#100C2×C3×C5semidirect
195. #343C2×C3×C5semidirect
196. #341C2×C3×C5semidirect
288. AGL(1,ℤ/8)C3×C4×C5semidirect
400. C3×C5#1907direct (N × H)
467. C5C3×#1907direct (N × H)
487. C3C5×#1907direct (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×AGL(1,ℤ/8)2
C2×C3×C5×#1312
C3×C5×#4172
C2×C3×C5×#1022
C2×C3×C5×#1002
C3×C5×#3432
C3×C5×#3412
C5×#19073
C3×#19075