Finite Group Databasebeta

← C3×C5×#1876 #14274910

Subgroups — C3×C5×#1876 #14274910

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic
2C2×C3×C5×#131C211yesmaximal, characteristic, complemented
3C2×C3×C5×#104C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic, complemented
5C3×C5×#408C211yesmaximal, characteristic, complemented
6C3×C5×#341C211yesmaximal, characteristic, complemented
7C3×C5×#336C211yesmaximal, characteristic, complemented
8C5×#1876C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×#41C2211yescharacteristic
11C3×C5×#135—22no—
12C3×C5×#135—22no—
13C2×C3×C5×Q16C411yescharacteristic, complemented
14C2×C3×C5×SD16C411yescharacteristic, complemented
15C2×C3×C5×SD16C411yescharacteristic, complemented
16C2×C3×C5×D8C411yescharacteristic, complemented
17C3×C5×#131—22no—
18C3×C5×#131—22no—
19C2×C3×C5×M16—21no—
20C2×C3×C5×M16C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C22×C3×C5×C8—21no—
23C22×C3×C5×C8C2211yescharacteristic
24C22×C3×C5×C8C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C3×C5×#104—22no—
27C3×C5×#104—22no—
28C3×C5×C22⋊C8—21no—
29C3×C5×C22⋊C8—21no—
30C3×#1876C511yesmaximal, characteristic, direct product factor, Hall
31C2×C5×#135C2×C311yescharacteristic
32C2×C5×#131C2×C311yescharacteristic, complemented
33C2×C5×#104C2×C311yescharacteristic, complemented
34C2×C5×#104C2×C311yescharacteristic, complemented
35C5×#408C2×C311yescharacteristic, complemented
36C5×#341C2×C311yescharacteristic, complemented
37C5×#336C2×C311yescharacteristic, complemented
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41D412yes—
45C3×C5×#41D412yes—
46C2×C3×C5×Q8C2×C411yescharacteristic
47C2×C3×C5×Q8C2×C411yescharacteristic
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4C2×C411yescharacteristic
51C2×C3×C5×D4C2×C411yescharacteristic
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C3×C5×Q16—22no—
57C3×C5×SD16—22no—
58C3×C5×SD16—22no—
59C3×C5×D8—22no—
60C3×C5×M16—24no—
61C3×C5×M16—21no—
62C3×C5×M16—21no—
63C3×C5×M16—21no—
64C3×C5×M16D412yes—
65C2×C3×C5×C8—24no—
66C2×C3×C5×C8—21no—
67C2×C3×C5×C8—21no—
68C2×C3×C5×C8—21no—
69C2×C3×C5×C8—21no—
70C2×C3×C5×C8—21no—
71C2×C3×C5×C8—21no—
72C2×C3×C5×C8C2×C411yescharacteristic
73C2×C3×C5×C8C2×C411yescharacteristic
74C2×C3×C5×C8D411yescharacteristic
75C2×C3×C5×C8D411yescharacteristic
76C3×C42×C5—21no—
77C3×C42×C5—21no—
78C2×C3×#135C2×C511yescharacteristic
79C2×C3×#131C2×C511yescharacteristic, complemented
80C2×C3×#104C2×C511yescharacteristic, complemented
81C2×C3×#104C2×C511yescharacteristic, complemented
82C3×#408C2×C511yescharacteristic, complemented
83C3×#341C2×C511yescharacteristic, complemented
84C3×#336C2×C511yescharacteristic, complemented
85C2×C5×#41C22×C311yescharacteristic
86C2×C5×#41C22×C311yescharacteristic
87C5×#135—22no—
88C5×#135—22no—
89C2×C5×Q16C3×C411yescharacteristic, complemented
90C2×C5×SD16C3×C411yescharacteristic, complemented
91C2×C5×SD16C3×C411yescharacteristic, complemented
92C2×C5×D8C3×C411yescharacteristic, complemented
93C5×#131—22no—
94C5×#131—22no—
95C2×C5×M16—21no—
96C2×C5×M16C22×C311yescharacteristic
97C2×C5×M16C22×C311yescharacteristic
98C22×C5×C8—21no—
99C22×C5×C8C22×C311yescharacteristic
100C22×C5×C8C22×C311yescharacteristic
101C2×C42×C5C22×C311yescharacteristic
102C5×#104—22no—
103C5×#104—22no—
104C5×C22⋊C8—21no—
105C5×C22⋊C8—21no—
106#1876C3×C511yescharacteristic, direct product factor, Sylow
107C23×C3×C5—21no—
108C23×C3×C5—21no—
109C23×C3×C5#4111yescharacteristic
110C3×C5×Q8—21no—
111C3×C5×Q8—21no—
112C3×C5×Q8—21no—
113C3×C5×Q8C22⋊C412yes—
114C3×C5×D4—22no—
115C3×C5×D4—22no—
116C3×C5×D4—21no—
117C3×C5×D4—21no—
118C3×C5×D4—21no—
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4C22⋊C412yes—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5—41no—
129C2×C3×C4×C5—41no—
130C2×C3×C4×C5—41no—
131C2×C3×C4×C5C22×C411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5#4111yescharacteristic
137C3×C5×C8—21no—
138C3×C5×C8—21no—
139C3×C5×C8—21no—
140C3×C5×C8—22no—
141C3×C5×C8—21no—
142C3×C5×C8—41no—
143C2×C3×#41C22×C511yescharacteristic
144C2×C3×#41C22×C511yescharacteristic
145C3×#135—22no—
146C3×#135—22no—
147C2×C3×Q16C4×C511yescharacteristic, complemented
148C2×C3×SD16C4×C511yescharacteristic, complemented
149C2×C3×SD16C4×C511yescharacteristic, complemented
150C2×C3×D8C4×C511yescharacteristic, complemented
151C3×#131—22no—
152C3×#131—22no—
153C2×C3×M16—21no—
154C2×C3×M16C22×C511yescharacteristic
155C2×C3×M16C22×C511yescharacteristic
156C22×C3×C8—21no—
157C22×C3×C8C22×C511yescharacteristic
158C22×C3×C8C22×C511yescharacteristic
159C2×C3×C42C22×C511yescharacteristic
160C3×#104—22no—
161C3×#104—22no—
162C3×C22⋊C8—21no—
163C3×C22⋊C8—21no—
164C5×#41—21no—
165C5×#41—21no—
166C5×#41—21no—
167C5×#41—21no—
168C5×#41—21no—
169C5×#41—21no—
170C5×#41C3×D412yes—
171C5×#41C3×D412yes—
172C2×C5×Q8C2×C3×C411yescharacteristic
173C2×C5×Q8C2×C3×C411yescharacteristic
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4C2×C3×C411yescharacteristic
177C2×C5×D4C2×C3×C411yescharacteristic
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5C23×C311yescharacteristic
182C5×Q16—22no—
183C5×SD16—22no—
184C5×SD16—22no—
185C5×D8—22no—
186C5×M16—24no—
187C5×M16—21no—
188C5×M16—21no—
189C5×M16—21no—
190C5×M16C3×D412yes—
191C2×C5×C8—24no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8C2×C3×C411yescharacteristic
199C2×C5×C8C2×C3×C411yescharacteristic
200C2×C5×C8C3×D411yescharacteristic
201C2×C5×C8C3×D411yescharacteristic
202C42×C5—21no—
203C42×C5—21no—
204C2×#135C2×C3×C511yescharacteristic
205C2×#131C2×C3×C511yescharacteristic, complemented
206C2×#104C2×C3×C511yescharacteristic, complemented
207C2×#104C2×C3×C511yescharacteristic, complemented
208#408C2×C3×C511yescharacteristic, complemented
209#341C2×C3×C511yescharacteristic, complemented
210#336C2×C3×C511yescharacteristic, complemented
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—22no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5—41no—
219C22×C3×C5C4×D411yescharacteristic
220C22×C3×C5#12111yescharacteristic
221C22×C3×C5#12311yescharacteristic
222C3×C4×C5—22no—
223C3×C4×C5—42no—
224C3×C4×C5—41no—
225C3×C4×C5C2×C22⋊C411yescharacteristic
226C3×C4×C5C4×D411yescharacteristic
227C3×C4×C5#12011yescharacteristic
228C3×C4×C5#12111yescharacteristic
229C3×#41—21no—
230C3×#41—21no—
231C3×#41—21no—
232C3×#41—21no—
233C3×#41—21no—
234C3×#41—21no—
235C3×#41C5×D412yes—
236C3×#41C5×D412yes—
237C2×C3×Q8C2×C4×C511yescharacteristic
238C2×C3×Q8C2×C4×C511yescharacteristic
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4C2×C4×C511yescharacteristic
242C2×C3×D4C2×C4×C511yescharacteristic
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C23×C511yescharacteristic
247C3×Q16—22no—
248C3×SD16—22no—
249C3×SD16—22no—
250C3×D8—22no—
251C3×M16—24no—
252C3×M16—21no—
253C3×M16—21no—
254C3×M16—21no—
255C3×M16C5×D412yes—
256C2×C3×C8—24no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8C2×C4×C511yescharacteristic
264C2×C3×C8C2×C4×C511yescharacteristic
265C2×C3×C8C5×D411yescharacteristic
266C2×C3×C8C5×D411yescharacteristic
267C3×C42—21no—
268C3×C42—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5C3×#4111yescharacteristic
272C5×Q8—21no—
273C5×Q8—21no—
274C5×Q8—21no—
275C5×Q8C3×C22⋊C412yes—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—21no—
279C5×D4—21no—
280C5×D4—21no—
281C5×D4—41no—
282C5×D4—41no—
283C5×D4C3×C22⋊C412yes—
284C2×C4×C5—21no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5C22×C3×C411yescharacteristic
294C2×C4×C5C2×C3×D411yescharacteristic
295C2×C4×C5C2×C3×D411yescharacteristic
296C2×C4×C5C2×C3×D411yescharacteristic
297C2×C4×C5C2×C3×D411yescharacteristic
298C2×C4×C5C3×#4111yescharacteristic
299C5×C8—21no—
300C5×C8—21no—
301C5×C8—21no—
302C5×C8—22no—
303C5×C8—21no—
304C5×C8—41no—
305C2×#41C22×C3×C511yescharacteristic
306C2×#41C22×C3×C511yescharacteristic
307#135—22no—
308#135—22no—
309C2×Q16C3×C4×C511yescharacteristic, complemented
310C2×SD16C3×C4×C511yescharacteristic, complemented
311C2×SD16C3×C4×C511yescharacteristic, complemented
312C2×D8C3×C4×C511yescharacteristic, complemented
313#131—22no—
314#131—22no—
315C2×M16—21no—
316C2×M16C22×C3×C511yescharacteristic
317C2×M16C22×C3×C511yescharacteristic
318C22×C8—21no—
319C22×C8C22×C3×C511yescharacteristic
320C22×C8C22×C3×C511yescharacteristic
321C2×C42C22×C3×C511yescharacteristic
322#104—22no—
323#104—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C2×C3×C5—21no—
327C2×C3×C5—21no—
328C2×C3×C5—42no—
329C2×C3×C5—81no—
330C2×C3×C5#38611yescharacteristic
331C2×C3×C5#44311yescharacteristic
332C2×C3×C5#44411yescharacteristic
333C23×C3—21no—
334C23×C3—21no—
335C23×C3C5×#4111yescharacteristic
336C3×Q8—21no—
337C3×Q8—21no—
338C3×Q8—21no—
339C3×Q8C5×C22⋊C412yes—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4C5×C22⋊C412yes—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4C22×C4×C511yescharacteristic
358C2×C3×C4C2×C5×D411yescharacteristic
359C2×C3×C4C2×C5×D411yescharacteristic
360C2×C3×C4C2×C5×D411yescharacteristic
361C2×C3×C4C2×C5×D411yescharacteristic
362C2×C3×C4C5×#4111yescharacteristic
363C3×C8—21no—
364C3×C8—21no—
365C3×C8—21no—
366C3×C8—22no—
367C3×C8—21no—
368C3×C8—41no—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—22no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5C3×C4×D411yescharacteristic
378C22×C5C3×#12111yescharacteristic
379C22×C5C3×#12311yescharacteristic
380C4×C5—22no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5C2×C3×C22⋊C411yescharacteristic
384C4×C5C3×C4×D411yescharacteristic
385C4×C5C3×#12011yescharacteristic
386C4×C5C3×#12111yescharacteristic
387#41—21no—
388#41—21no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41C3×C5×D412yes—
394#41C3×C5×D412yes—
395C2×Q8C2×C3×C4×C511yescharacteristic
396C2×Q8C2×C3×C4×C511yescharacteristic
397C2×D4—21no—
398C2×D4—21no—
399C2×D4C2×C3×C4×C511yescharacteristic
400C2×D4C2×C3×C4×C511yescharacteristic
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C23×C3×C511yescharacteristic
405Q16—22no—
406SD16—22no—
407SD16—22no—
408D8—22no—
409M16—24no—
410M16—21no—
411M16—21no—
412M16—21no—
413M16C3×C5×D412yes—
414C2×C8—24no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×C3×C4×C511yescharacteristic
422C2×C8C2×C3×C4×C511yescharacteristic
423C2×C8C3×C5×D411yescharacteristic
424C2×C8C3×C5×D411yescharacteristic
425C42—21no—
426C42—21no—
427C3×C5#187611yescharacteristic, direct product factor, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3C4×C5×D411yescharacteristic
437C22×C3C5×#12111yescharacteristic
438C22×C3C5×#12311yescharacteristic
439C3×C4—22no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4C2×C5×C22⋊C411yescharacteristic
443C3×C4C4×C5×D411yescharacteristic
444C3×C4C5×#12011yescharacteristic
445C3×C4C5×#12111yescharacteristic
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—42no—
449C2×C5—81no—
450C2×C5C3×#38611yescharacteristic
451C2×C5C3×#44311yescharacteristic
452C2×C5C3×#44411yescharacteristic
453C23—21no—
454C23—21no—
455C23C3×C5×#4111yescharacteristic
456Q8—21no—
457Q8—21no—
458Q8—21no—
459Q8C3×C5×C22⋊C412yes—
460D4—22no—
461D4—22no—
462D4—21no—
463D4—21no—
464D4—21no—
465D4—41no—
466D4—41no—
467D4C3×C5×C22⋊C412yes—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4C22×C3×C4×C511yescharacteristic
478C2×C4C2×C3×C5×D411yescharacteristic
479C2×C4C2×C3×C5×D411yescharacteristic
480C2×C4C2×C3×C5×D411yescharacteristic
481C2×C4C2×C3×C5×D411yescharacteristic
482C2×C4C3×C5×#4111yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8—22no—
487C8—21no—
488C8—41no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—42no—
492C2×C3—81no—
493C2×C3C5×#38611yescharacteristic
494C2×C3C5×#44311yescharacteristic
495C2×C3C5×#44411yescharacteristic
496C5C3×#187611yescharacteristic, direct product factor, Sylow
497C22—21no—
498C22—21no—
499C22—22no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22C3×C4×C5×D411yescharacteristic
506C22C3×C5×#12111yescharacteristic
507C22C3×C5×#12311yescharacteristic
508C4—22no—
509C4—42no—
510C4—41no—
511C4C2×C3×C5×C22⋊C411yescharacteristic
512C4C3×C4×C5×D411yescharacteristic
513C4C3×C5×#12011yescharacteristic
514C4C3×C5×#12111yescharacteristic
515C3C5×#187611yescharacteristic, direct product factor, Sylow
516C2—21no—
517C2—21no—
518C2—42no—
519C2—81no—
520C2C3×C5×#38611yescharacteristic
521C2C3×C5×#44311yescharacteristic
522C2C3×C5×#44411yescharacteristic
subgroupG/H
centerC2×C3×C4×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#135C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#131C2semidirect
3. C2×C3×C5×#104C2semidirect
4. C2×C3×C5×#104C2semidirect
5. C3×C5×#408C2semidirect
6. C3×C5×#341C2semidirect
7. C3×C5×#336C2semidirect
8. C5×#1876C3direct (N × H)
13. C2×C3×C5×Q16C4semidirect
14. C2×C3×C5×SD16C4semidirect
15. C2×C3×C5×SD16C4semidirect
16. C2×C3×C5×D8C4semidirect
30. C3×#1876C5direct (N × H)
32. C2×C5×#131C2×C3semidirect
33. C2×C5×#104C2×C3semidirect
34. C2×C5×#104C2×C3semidirect
35. C5×#408C2×C3semidirect
36. C5×#341C2×C3semidirect
37. C5×#336C2×C3semidirect
79. C2×C3×#131C2×C5semidirect
80. C2×C3×#104C2×C5semidirect
81. C2×C3×#104C2×C5semidirect
82. C3×#408C2×C5semidirect
83. C3×#341C2×C5semidirect
84. C3×#336C2×C5semidirect
89. C2×C5×Q16C3×C4semidirect
90. C2×C5×SD16C3×C4semidirect
91. C2×C5×SD16C3×C4semidirect
92. C2×C5×D8C3×C4semidirect
106. #1876C3×C5direct (N × H)
147. C2×C3×Q16C4×C5semidirect
148. C2×C3×SD16C4×C5semidirect
149. C2×C3×SD16C4×C5semidirect
150. C2×C3×D8C4×C5semidirect
205. C2×#131C2×C3×C5semidirect
206. C2×#104C2×C3×C5semidirect
207. C2×#104C2×C3×C5semidirect
208. #408C2×C3×C5semidirect
209. #341C2×C3×C5semidirect
210. #336C2×C3×C5semidirect
309. C2×Q16C3×C4×C5semidirect
310. C2×SD16C3×C4×C5semidirect
311. C2×SD16C3×C4×C5semidirect
312. C2×D8C3×C4×C5semidirect
427. C3×C5#1876direct (N × H)
496. C5C3×#1876direct (N × H)
515. C3C5×#1876direct (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×#1352
C2×C3×C5×#1312
C2×C3×C5×#1042
C3×C5×#4082
C3×C5×#3412
C3×C5×#3362
C5×#18763
C3×#18765