Finite Group Databasebeta

← C5×#68955 #14307474

Subgroups — C5×#68955 #14307474

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#878C211yesmaximal, characteristic
2C5×#4942C211yesmaximal, characteristic
3C5×Dic3×C22⋊C4C211yesmaximal, characteristic
4C3×C5×#342C211yesmaximal, characteristic
5C5×#4527C211yesmaximal, characteristic
6C5×#4527C211yesmaximal, characteristic
7C5×#4526C211yesmaximal, characteristic
8C5×#1996—31nomaximal, Hall
9C23×C5×Dic3C2211yescharacteristic
10C22×C5×Dic6C411yescharacteristic, complemented
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×#217C2211yescharacteristic
17C2×C5×C4⋊Dic3C411yescharacteristic, complemented
18C2×C5×Dic3⋊C4—21no—
19C2×C5×Dic3⋊C4C411yescharacteristic, complemented
20C2×C5×Dic3⋊C4C411yescharacteristic, complemented
21C2×C4×C5×Dic3—21no—
22C5×#878—21no—
23C5×#878—21no—
24C5×#878—21no—
25C5×#878—21no—
26C5×C3⋊#95—21no—
27C5×C3⋊#95—21no—
28#68955C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×C22⋊Q8—31no—
30C5×#380—31no—
31C4×C5×C22⋊C4—31no—
32C5×#342—31no—
33C5×#342—31no—
34C5×#342—31no—
35C5×#342D311yescharacteristic
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C5×Dic3—21no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3—42no—
44C22×C5×Dic3C2×C411yescharacteristic
45C22×C5×Dic3C2×C411yescharacteristic
46C22×C5×Dic3C2×C411yescharacteristic
47C22×C5×Dic3C2×C411yescharacteristic
48C22×C5×Dic3D411yescharacteristic
49C22×C5×Dic3D411yescharacteristic
50C22×C5×Dic3D411yescharacteristic
51C22×C5×Dic3D411yescharacteristic
52C2×C5×Dic6—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6—42no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4Q812yescomplemented
61C5×#217—21no—
62C5×#217—21no—
63C5×#217—21no—
64C5×#217—21no—
65C5×#217—21no—
66C5×#217Q812yescomplemented
67C5×C4⋊Dic3—21no—
68C5×C4⋊Dic3—21no—
69C5×Dic3⋊C4—21no—
70C5×Dic3⋊C4—21no—
71C5×Dic3⋊C4—21no—
72C5×Dic3⋊C4—21no—
73C5×Dic3⋊C4—42no—
74C4×C5×Dic3—42no—
75C2×#878C2×C511yescharacteristic
76#4942C2×C511yescharacteristic
77Dic3×C22⋊C4C2×C511yescharacteristic
78C3×#342C2×C511yescharacteristic
79#4527C2×C511yescharacteristic
80#4527C2×C511yescharacteristic
81#4526C2×C511yescharacteristic
82C22×C5×Q8—31no—
83C23×C4×C5—31no—
84C5×C22⋊Q8—61no—
85C5×C22⋊Q8—61no—
86C5×C22⋊Q8—61no—
87C5×C22⋊Q8—61no—
88C2×C5×C4⋊C4—31no—
89C2×C5×C4⋊C4—31no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4—61no—
92C2×C5×C22⋊C4—31no—
93C2×C5×C22⋊C4—31no—
94C2×C5×C22⋊C4—31no—
95C2×C5×C22⋊C4C2×D311yescharacteristic
96C2×C5×C22⋊C4C2×D311yescharacteristic
97C2×C5×C22⋊C4C2×D311yescharacteristic
98C2×C42×C5—61no—
99C5×#95—61no—
100C5×#95—61no—
101#1996—31noSylow
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5C2×Q811yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—22no—
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×C5×Dic3—22no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3—41no—
130C2×C5×Dic3—41no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3—41no—
134C2×C5×Dic3—41no—
135C2×C5×Dic3—41no—
136C2×C5×Dic3—41no—
137C2×C5×Dic3C22⋊C411yescharacteristic
138C2×C5×Dic3C22⋊C411yescharacteristic
139C2×C5×Dic3C22⋊C411yescharacteristic
140C2×C5×Dic3C22⋊C411yescharacteristic
141C5×Dic6—42no—
142C5×Dic6—42no—
143C23×Dic3C22×C511yescharacteristic
144C22×Dic6C4×C511yescharacteristic, complemented
145C2×C3×C22⋊C4C22×C511yescharacteristic
146C2×C3×C22⋊C4C22×C511yescharacteristic
147C2×C3×C22⋊C4C22×C511yescharacteristic
148C2×#217C22×C511yescharacteristic
149C2×#217C22×C511yescharacteristic
150C2×#217C22×C511yescharacteristic
151C2×C4⋊Dic3C4×C511yescharacteristic, complemented
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4C4×C511yescharacteristic, complemented
154C2×Dic3⋊C4C4×C511yescharacteristic, complemented
155C2×C4×Dic3—21no—
156#878—21no—
157#878—21no—
158#878—21no—
159#878—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C24×C5C22×D311yescharacteristic
163C2×C5×Q8—61no—
164C2×C5×Q8—61no—
165C2×C5×Q8—122no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—31no—
173C22×C4×C5—31no—
174C22×C4×C5—31no—
175C22×C4×C5—31no—
176C22×C4×C5—61no—
177C22×C4×C5—61no—
178C22×C4×C5—122no—
179C22×C4×C5C4×D311yescharacteristic
180C22×C4×C5C4×D311yescharacteristic
181C5×C4⋊C4—61no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4—61no—
184C5×C4⋊C4—61no—
185C5×C4⋊C4—61no—
186C5×C4⋊C4—61no—
187C5×C4⋊C4—122no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C5×C22⋊C4—32no—
194C5×C22⋊C4—61no—
195C5×C22⋊C4—61no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—61no—
198C5×C22⋊C4—61no—
199C5×C22⋊C4Dic612yescomplemented
200C42×C5—122no—
201C2×C22⋊Q8—31no—
202#380—31no—
203C4×C22⋊C4—31no—
204#342—31no—
205#342—31no—
206#342—31no—
207#342C5×D311yescharacteristic
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—21no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×Q811yescharacteristic
220C22×C3×C5C4×Q811yescharacteristic
221C22×C3×C5C22⋊Q811yescharacteristic
222C22×C3×C5C22⋊Q811yescharacteristic
223C22×C3×C5#12411yescharacteristic
224C22×C3×C5C4⋊Q811yescharacteristic
225C3×C4×C5—42no—
226C3×C4×C5—41no—
227C3×C4×C5—41no—
228C3×C4×C5—81no—
229C5×Dic3—21no—
230C5×Dic3—21no—
231C5×Dic3—21no—
232C5×Dic3—42no—
233C5×Dic3—41no—
234C5×Dic3—41no—
235C5×Dic3—81no—
236C5×Dic3#9912yes—
237C24×C3C23×C511yescharacteristic
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×C4×C511yescharacteristic
241C22×C3×C4C2×C4×C511yescharacteristic
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—42no—
245C22×Dic3C2×C4×C511yescharacteristic
246C22×Dic3C2×C4×C511yescharacteristic
247C22×Dic3C2×C4×C511yescharacteristic
248C22×Dic3C2×C4×C511yescharacteristic
249C22×Dic3C5×D411yescharacteristic
250C22×Dic3C5×D411yescharacteristic
251C22×Dic3C5×D411yescharacteristic
252C22×Dic3C5×D411yescharacteristic
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—42no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—21no—
261C3×C22⋊C4C5×Q812yescomplemented
262#217—21no—
263#217—21no—
264#217—21no—
265#217—21no—
266#217—21no—
267#217C5×Q812yescomplemented
268C4⋊Dic3—21no—
269C4⋊Dic3—21no—
270Dic3⋊C4—21no—
271Dic3⋊C4—21no—
272Dic3⋊C4—21no—
273Dic3⋊C4—21no—
274Dic3⋊C4—42no—
275C4×Dic3—42no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5C2×Dic611yescharacteristic
279C23×C5C2×C4×D311yescharacteristic
280C23×C5#23511yescharacteristic
281C23×C5D3×D411yescharacteristic
282C23×C5D3×D411yescharacteristic
283C23×C5#23711yescharacteristic
284C23×C5D3×Q811yescharacteristic
285C5×Q8—122no—
286C5×Q8—122no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—31no—
291C2×C4×C5—31no—
292C2×C4×C5—31no—
293C2×C4×C5—31no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—62no—
302C2×C4×C5—62no—
303C2×C4×C5—62no—
304C2×C4×C5—61no—
305C2×C4×C5—61no—
306C2×C4×C5—62no—
307C2×C4×C5—121no—
308C2×C4×C5—121no—
309C2×C4×C5—121no—
310C2×C4×C5—121no—
311C2×C4×C5—121no—
312C2×C4×C5—121no—
313C2×C4×C5—121no—
314C2×C4×C5—121no—
315C2×C4×C5—121no—
316C2×C4×C5—121no—
317C22×Q8—31no—
318C23×C4—31no—
319C22⋊Q8—61no—
320C22⋊Q8—61no—
321C22⋊Q8—61no—
322C22⋊Q8—61no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—61no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4C2×C5×D311yescharacteristic
331C2×C22⋊C4C2×C5×D311yescharacteristic
332C2×C22⋊C4C2×C5×D311yescharacteristic
333C2×C42—61no—
334#95—61no—
335#95—61no—
336C2×C3×C5—21no—
337C2×C3×C5—21no—
338C2×C3×C5—21no—
339C2×C3×C5—21no—
340C2×C3×C5—21no—
341C2×C3×C5—21no—
342C2×C3×C5#39111yescharacteristic
343C2×C3×C5C2×#9911yescharacteristic
344C2×C3×C5#41011yescharacteristic
345C23×C3—41no—
346C23×C3—41no—
347C23×C3C22×C4×C511yescharacteristic
348C23×C3C2×C5×D411yescharacteristic
349C23×C3C2×C5×D411yescharacteristic
350C23×C3C2×C5×Q811yescharacteristic
351C23×C3C2×C5×Q811yescharacteristic
352C23×C3C5×#4111yescharacteristic
353C23×C3C5×#4111yescharacteristic
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3C5×C22⋊C411yescharacteristic
381C2×Dic3C5×C22⋊C411yescharacteristic
382C2×Dic3C5×C22⋊C411yescharacteristic
383C2×Dic3C5×C22⋊C411yescharacteristic
384Dic6—42no—
385Dic6—42no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5C4×Dic611yescharacteristic
397C22×C5#87811yescharacteristic
398C22×C5D3×C22⋊C411yescharacteristic
399C22×C5#88511yescharacteristic
400C22×C5#88711yescharacteristic
401C22×C5#88811yescharacteristic
402C22×C5#89611yescharacteristic
403C4×C5—32no—
404C4×C5—42no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—61no—
408C4×C5—61no—
409C4×C5—61no—
410C4×C5—81no—
411C4×C5—122no—
412C4×C5—121no—
413C4×C5—121no—
414C4×C5—241no—
415C24C22×C5×D311yescharacteristic
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—122no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—122no—
432C22×C4C4×C5×D311yescharacteristic
433C22×C4C4×C5×D311yescharacteristic
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—122no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—32no—
447C22⋊C4—61no—
448C22⋊C4—61no—
449C22⋊C4—61no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4C5×Dic612yescomplemented
453C42—122no—
454C3×C5#199611yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3C2×C5×C22⋊C411yescharacteristic
466C22×C3C4×C5×Q811yescharacteristic
467C22×C3C4×C5×Q811yescharacteristic
468C22×C3C5×C22⋊Q811yescharacteristic
469C22×C3C5×C22⋊Q811yescharacteristic
470C22×C3C5×#12411yescharacteristic
471C22×C3C5×C4⋊Q811yescharacteristic
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—81no—
476Dic3—21no—
477Dic3—21no—
478Dic3—21no—
479Dic3—42no—
480Dic3—41no—
481Dic3—41no—
482Dic3—81no—
483Dic3C5×#9912yes—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5#464611yescharacteristic
491C2×C5#474011yescharacteristic
492C2×C5D3×#9911yescharacteristic
493C23—41no—
494C23—41no—
495C23C2×C5×Dic611yescharacteristic
496C23C2×C4×C5×D311yescharacteristic
497C23C5×#23511yescharacteristic
498C23C5×D3×D411yescharacteristic
499C23C5×D3×D411yescharacteristic
500C23C5×#23711yescharacteristic
501C23C5×D3×Q811yescharacteristic
502Q8—122no—
503Q8—122no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—31no—
508C2×C4—31no—
509C2×C4—31no—
510C2×C4—31no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3C5×#39111yescharacteristic
541C2×C3C2×C5×#9911yescharacteristic
542C2×C3C5×#41011yescharacteristic
543C5#6895511yescharacteristic, direct product factor, Sylow
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22C4×C5×Dic611yescharacteristic
555C22C5×#87811yescharacteristic
556C22C5×D3×C22⋊C411yescharacteristic
557C22C5×#88511yescharacteristic
558C22C5×#88711yescharacteristic
559C22C5×#88811yescharacteristic
560C22C5×#89611yescharacteristic
561C4—32no—
562C4—42no—
563C4—41no—
564C4—41no—
565C4—61no—
566C4—61no—
567C4—61no—
568C4—81no—
569C4—122no—
570C4—121no—
571C4—121no—
572C4—241no—
573C3C5×#199611yescharacteristic, complemented, Sylow
574C2—21no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2C5×#464611yescharacteristic
581C2C5×#474011yescharacteristic
582C2C5×D3×#9911yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#342C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C23
cosocleC24×C3C23×C5
hypercenterC5×#342D3
hypocenterC3C5×#1996
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C5×#342

Complements

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

NH ≅ G/Ntype
10. C22×C5×Dic6C4semidirect
17. C2×C5×C4⋊Dic3C4semidirect
19. C2×C5×Dic3⋊C4C4semidirect
20. C2×C5×Dic3⋊C4C4semidirect
28. #68955C5direct (N × H)
60. C3×C5×C22⋊C4Q8semidirect
66. C5×#217Q8semidirect
144. C22×Dic6C4×C5semidirect
151. C2×C4⋊Dic3C4×C5semidirect
153. C2×Dic3⋊C4C4×C5semidirect
154. C2×Dic3⋊C4C4×C5semidirect
199. C5×C22⋊C4Dic6semidirect
261. C3×C22⋊C4C5×Q8semidirect
267. #217C5×Q8semidirect
452. C22⋊C4C5×Dic6semidirect
454. C3×C5#1996semidirect
543. C5#68955direct (N × H)
573. C3C5×#1996semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8782
C5×#49422
C5×Dic3×C22⋊C42
C3×C5×#3422
C5×#45272
C5×#45262
C5×#19963
#689555