Finite Group Databasebeta

← C5×#74378 #14321075

Subgroups — C5×#74378 #14321075

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Dic3C211yesmaximal, characteristic
2C2×C5×#877C211yesmaximal, characteristic
3C2×C5×#877C211yesmaximal, characteristic
4C3×C5×#385C211yesmaximal, characteristic
5C5×#5210C211yesmaximal, characteristic
6C5×#4976C212yesmaximal, complemented
7C5×Dic3×C4⋊C4C212yesmaximal, complemented
8C5×#4950C211yesmaximal, characteristic
9C5×#4946C211yesmaximal, characteristic
10C5×#4649C212yesmaximal, complemented
11C5×#4647C212yesmaximal, complemented
12C5×#2296—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2212yes—
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C5×#217C2211yescharacteristic
20C2×C5×#217C2211yescharacteristic
21C2×C5×C4⋊Dic3C2212yes—
22C2×C5×Dic3⋊C4C2211yescharacteristic
23C2×C5×Dic3⋊C4C2212yes—
24C2×C5×Dic3⋊C4C2212yes—
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2212yes—
27C2×C4×C5×Dic3—24no—
28C2×C4×C5×Dic3C2212yes—
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C4×C5×Dic3C2212yes—
31C2×C4×C5×Dic3C2211yescharacteristic
32C2×C4×C5×Dic3C2212yes—
33C5×#877—24no—
34C5×#877C418yescomplemented
35C3×C5×#95C2212yes—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#74378C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#117—31no—
41C2×C5×#117—31no—
42C22×C42×C5—31no—
43C5×#389—32no—
44C5×#389—32no—
45C5×#385—31no—
46C5×#385—31no—
47C5×#385—31no—
48C5×#385D311yescharacteristic
49C4×C5×C4⋊C4—32no—
50C4×C5×C4⋊C4—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—24no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C5×Dic3—22no—
59C22×C5×Dic3—24no—
60C22×C5×Dic3C2×C414yes—
61C22×C5×Dic3D414yes—
62C22×C5×Dic3Q814yes—
63C22×C5×Dic3C2311yescharacteristic
64C22×C5×Dic3C2311yescharacteristic
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C3×C5×C4⋊C4—24no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4C2×C414yes—
72C5×#217—22no—
73C5×#217C2×C414yes—
74C5×C4⋊Dic3—24no—
75C5×Dic3⋊C4—24no—
76C5×Dic3⋊C4—22no—
77C5×Dic3⋊C4—22no—
78C5×Dic3⋊C4—24no—
79C5×Dic3⋊C4C2×C418yescomplemented
80C4×C5×Dic3—22no—
81C4×C5×Dic3—22no—
82C4×C5×Dic3—24no—
83C4×C5×Dic3—24no—
84C4×C5×Dic3C2×C418yescomplemented
85C22×C4×Dic3C2×C511yescharacteristic
86C2×#877C2×C511yescharacteristic
87C2×#877C2×C511yescharacteristic
88C3×#385C2×C511yescharacteristic
89#5210C2×C511yescharacteristic
90#4976C2×C512yescomplemented
91Dic3×C4⋊C4C2×C512yescomplemented
92#4950C2×C511yescharacteristic
93#4946C2×C511yescharacteristic
94#4649C2×C512yescomplemented
95#4647C2×C512yescomplemented
96C23×C4×C5—31no—
97C23×C4×C5—31no—
98C23×C4×C5C2×D311yescharacteristic
99C5×#117—38no—
100C5×#117—64no—
101C2×C5×C4⋊C4—32no—
102C2×C5×C4⋊C4—32no—
103C2×C5×C4⋊C4—32no—
104C2×C5×C4⋊C4—32no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4—31no—
107C2×C5×C4⋊C4C2×D312yes—
108C2×C5×C22⋊C4—31no—
109C2×C5×C22⋊C4—31no—
110C2×C5×C22⋊C4C2×D311yescharacteristic
111C2×C5×C22⋊C4C2×D311yescharacteristic
112C2×C42×C5—32no—
113C2×C42×C5—32no—
114C2×C42×C5—31no—
115C2×C42×C5—31no—
116C2×C42×C5—32no—
117C2×C42×C5—64no—
118C5×#95—32no—
119C5×#95—32no—
120C5×#95—32no—
121C5×#95C2×D312yes—
122#2296—31noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×Q812yes—
128C23×C3×C5C2411yescharacteristic
129C2×C3×C4×C5—28no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C414yes—
139C2×C3×C4×C5#4114yes—
140C2×C5×Dic3—28no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C4⋊C4116yescomplemented
150C2×C5×Dic3C22×C414yes—
151C2×C5×Dic3C22×C412yes—
152C2×C5×Dic3C22×C412yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3C2×Q812yes—
156C2×C5×Dic3C2×Q812yes—
157C2×C5×Dic3#4114yes—
158C23×C3×C4C22×C511yescharacteristic
159C23×Dic3C22×C511yescharacteristic
160C23×Dic3C22×C511yescharacteristic
161C2×C3×C4⋊C4C22×C512yes—
162C2×C3×C22⋊C4C22×C511yescharacteristic
163C2×C3×C22⋊C4C22×C511yescharacteristic
164C2×#217C22×C511yescharacteristic
165C2×#217C22×C511yescharacteristic
166C2×C4⋊Dic3C22×C512yes—
167C2×Dic3⋊C4C22×C511yescharacteristic
168C2×Dic3⋊C4C22×C512yes—
169C2×Dic3⋊C4C22×C512yes—
170C2×Dic3⋊C4C22×C511yescharacteristic
171C2×Dic3⋊C4C22×C512yes—
172C2×C4×Dic3—24no—
173C2×C4×Dic3C22×C512yes—
174C2×C4×Dic3C22×C511yescharacteristic
175C2×C4×Dic3C22×C512yes—
176C2×C4×Dic3C22×C511yescharacteristic
177C2×C4×Dic3C22×C512yes—
178#877—24no—
179#877C4×C518yescomplemented
180C3×#95C22×C512yes—
181C3⋊#95C22×C512yes—
182C3⋊#95C22×C512yes—
183C3⋊#95C22×C512yes—
184C24×C5C22×D311yescharacteristic
185C22×C4×C5—22no—
186C22×C4×C5—24no—
187C22×C4×C5—34no—
188C22×C4×C5—34no—
189C22×C4×C5—34no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—32no—
193C22×C4×C5—32no—
194C22×C4×C5—31no—
195C22×C4×C5—31no—
196C22×C4×C5—64no—
197C22×C4×C5—62no—
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×C4×C5C22×D312yes—
201C22×C4×C5C22×D312yes—
202C5×C4⋊C4—24no—
203C5×C4⋊C4—38no—
204C5×C4⋊C4—62no—
205C5×C4⋊C4—62no—
206C5×C4⋊C4—64no—
207C5×C4⋊C4—64no—
208C5×C4⋊C4—64no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—34no—
211C5×C22⋊C4—62no—
212C5×C22⋊C4C4×D314yes—
213C42×C5—38no—
214C42×C5—64no—
215C42×C5—64no—
216C42×C5—62no—
217C42×C5—62no—
218C2×#117—31no—
219C2×#117—31no—
220C22×C42—31no—
221#389—32no—
222#389—32no—
223#385—31no—
224#385—31no—
225#385—31no—
226#385C5×D311yescharacteristic
227C4×C4⋊C4—32no—
228C4×C4⋊C4—32no—
229C22×C3×C5—24no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—24no—
233C22×C3×C5C2×C4⋊C414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C22×Q811yescharacteristic
237C22×C3×C5C2×#4112yes—
238C22×C3×C5C2×#4112yes—
239C3×C4×C5—24no—
240C3×C4×C5—24no—
241C3×C4×C5—41no—
242C3×C4×C5—41no—
243C5×Dic3—24no—
244C5×Dic3—24no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C5×Dic3C2×C4⋊C414yes—
248C5×Dic3C2×C4⋊C414yes—
249C24×C3C23×C511yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—24no—
252C22×C3×C4C23×C511yescharacteristic
253C22×C3×C4C23×C511yescharacteristic
254C22×C3×C4C23×C512yes—
255C22×C3×C4C23×C512yes—
256C22×Dic3—22no—
257C22×Dic3—24no—
258C22×Dic3C2×C4×C514yes—
259C22×Dic3C5×D414yes—
260C22×Dic3C5×Q814yes—
261C22×Dic3C23×C511yescharacteristic
262C22×Dic3C23×C511yescharacteristic
263C22×Dic3C23×C512yes—
264C22×Dic3C23×C512yes—
265C22×Dic3C23×C511yescharacteristic
266C22×Dic3C23×C511yescharacteristic
267C3×C4⋊C4—24no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4C2×C4×C514yes—
270#217—22no—
271#217C2×C4×C514yes—
272C4⋊Dic3—24no—
273Dic3⋊C4—24no—
274Dic3⋊C4—22no—
275Dic3⋊C4—22no—
276Dic3⋊C4—24no—
277Dic3⋊C4C2×C4×C518yescomplemented
278C4×Dic3—22no—
279C4×Dic3—22no—
280C4×Dic3—24no—
281C4×Dic3—24no—
282C4×Dic3C2×C4×C518yescomplemented
283C23×C5—22no—
284C23×C5—22no—
285C23×C5C2×C4×D312yes—
286C23×C5D3×D412yes—
287C23×C5D3×Q812yes—
288C23×C5C23×D311yescharacteristic
289C2×C4×C5—28no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—316no—
299C2×C4×C5—32no—
300C2×C4×C5—32no—
301C2×C4×C5—32no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—32no—
305C2×C4×C5—34no—
306C2×C4×C5—34no—
307C2×C4×C5—68no—
308C2×C4×C5—62no—
309C2×C4×C5—62no—
310C2×C4×C5—62no—
311C2×C4×C5—62no—
312C2×C4×C5—61no—
313C2×C4×C5—61no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D314yes—
317C2×C4×C5#23714yes—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4C2×C5×D311yescharacteristic
321#117—38no—
322#117—64no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—32no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4C2×C5×D312yes—
330C2×C22⋊C4—31no—
331C2×C22⋊C4—31no—
332C2×C22⋊C4C2×C5×D311yescharacteristic
333C2×C22⋊C4C2×C5×D311yescharacteristic
334C2×C42—32no—
335C2×C42—31no—
336C2×C42—31no—
337C2×C42—32no—
338C2×C42—32no—
339C2×C42—64no—
340#95—32no—
341#95—32no—
342#95—32no—
343#95C2×C5×D312yes—
344C2×C3×C5—24no—
345C2×C3×C5C22×C4⋊C411yescharacteristic
346C2×C3×C5C4×#4112yes—
347C2×C3×C5#52511yescharacteristic
348C2×C3×C5#52511yescharacteristic
349C2×C3×C5#53312yes—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3C22×C4×C512yes—
353C23×C3C2×C5×D412yes—
354C23×C3C2×C5×Q812yes—
355C23×C3C24×C511yescharacteristic
356C2×C3×C4—28no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4C22×C4×C514yes—
366C2×C3×C4C5×#4114yes—
367C2×Dic3—28no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3C5×C4⋊C4116yescomplemented
377C2×Dic3C22×C4×C514yes—
378C2×Dic3C22×C4×C512yes—
379C2×Dic3C22×C4×C512yes—
380C2×Dic3C2×C5×D412yes—
381C2×Dic3C2×C5×D412yes—
382C2×Dic3C2×C5×Q812yes—
383C2×Dic3C2×C5×Q812yes—
384C2×Dic3C5×#4114yes—
385C22×C5—22no—
386C22×C5—24no—
387C22×C5—22no—
388C22×C5—24no—
389C22×C5D3×C4⋊C414yes—
390C22×C5C22×C4×D311yescharacteristic
391C22×C5C2×D3×D411yescharacteristic
392C22×C5C2×#23712yes—
393C22×C5C2×D3×Q811yescharacteristic
394C22×C5D3×#4112yes—
395C4×C5—24no—
396C4×C5—24no—
397C4×C5—34no—
398C4×C5—34no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5—64no—
402C4×C5—64no—
403C4×C5—121no—
404C4×C5—121no—
405C24C22×C5×D311yescharacteristic
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—34no—
409C22×C4—34no—
410C22×C4—34no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—64no—
418C22×C4—62no—
419C22×C4C22×C5×D311yescharacteristic
420C22×C4C22×C5×D311yescharacteristic
421C22×C4C22×C5×D312yes—
422C22×C4C22×C5×D312yes—
423C4⋊C4—24no—
424C4⋊C4—38no—
425C4⋊C4—62no—
426C4⋊C4—62no—
427C4⋊C4—64no—
428C4⋊C4—64no—
429C4⋊C4—64no—
430C22⋊C4—22no—
431C22⋊C4—34no—
432C22⋊C4—62no—
433C22⋊C4C4×C5×D314yes—
434C42—38no—
435C42—64no—
436C42—64no—
437C42—62no—
438C42—62no—
439C3×C5#229611yescharacteristic, complemented, Hall
440C22×C3—24no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—24no—
444C22×C3C2×C5×C4⋊C414yes—
445C22×C3C23×C4×C511yescharacteristic
446C22×C3C22×C5×D411yescharacteristic
447C22×C3C22×C5×Q811yescharacteristic
448C22×C3C2×C5×#4112yes—
449C22×C3C2×C5×#4112yes—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—41no—
453C3×C4—41no—
454Dic3—24no—
455Dic3—24no—
456Dic3—41no—
457Dic3—41no—
458Dic3C2×C5×C4⋊C414yes—
459Dic3C2×C5×C4⋊C414yes—
460C2×C5—24no—
461C2×C5C2×D3×C4⋊C411yescharacteristic
462C2×C5C4×#23712yes—
463C2×C5#558611yescharacteristic
464C2×C5#562212yes—
465C2×C5#565611yescharacteristic
466C23—22no—
467C23—22no—
468C23C2×C4×C5×D312yes—
469C23C5×D3×D412yes—
470C23C5×D3×Q812yes—
471C23C23×C5×D311yescharacteristic
472C2×C4—28no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—316no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—34no—
489C2×C4—34no—
490C2×C4—68no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4C2×C4×C5×D314yes—
500C2×C4C5×#23714yes—
501C2×C3—24no—
502C2×C3C22×C5×C4⋊C411yescharacteristic
503C2×C3C4×C5×#4112yes—
504C2×C3C5×#52511yescharacteristic
505C2×C3C5×#52511yescharacteristic
506C2×C3C5×#53312yes—
507C5#7437811yescharacteristic, direct product factor, Sylow
508C22—22no—
509C22—24no—
510C22—22no—
511C22—24no—
512C22C5×D3×C4⋊C414yes—
513C22C22×C4×C5×D311yescharacteristic
514C22C2×C5×D3×D411yescharacteristic
515C22C2×C5×#23712yes—
516C22C2×C5×D3×Q811yescharacteristic
517C22C5×D3×#4112yes—
518C4—24no—
519C4—24no—
520C4—34no—
521C4—34no—
522C4—41no—
523C4—41no—
524C4—64no—
525C4—64no—
526C4—121no—
527C4—121no—
528C3C5×#229611yescharacteristic, complemented, Sylow
529C2—24no—
530C2C2×C5×D3×C4⋊C411yescharacteristic
531C2C4×C5×#23712yes—
532C2C5×#558611yescharacteristic
533C2C5×#562212yes—
534C2C5×#565611yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC5×#385D3
hypocenterC3C5×#2296
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#385

Complements

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

NH ≅ G/Ntype
6. C5×#4976C2semidirect
7. C5×Dic3×C4⋊C4C2semidirect
10. C5×#4649C2semidirect
11. C5×#4647C2semidirect
34. C5×#877C4semidirect
39. #74378C5direct (N × H)
79. C5×Dic3⋊C4C2×C4semidirect
84. C4×C5×Dic3C2×C4semidirect
90. #4976C2×C5semidirect
91. Dic3×C4⋊C4C2×C5semidirect
94. #4649C2×C5semidirect
95. #4647C2×C5semidirect
149. C2×C5×Dic3C4⋊C4semidirect
179. #877C4×C5semidirect
277. Dic3⋊C4C2×C4×C5semidirect
282. C4×Dic3C2×C4×C5semidirect
376. C2×Dic3C5×C4⋊C4semidirect
439. C3×C5#2296semidirect
507. C5#74378direct (N × H)
528. C3C5×#2296semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×Dic32
C2×C5×#8772
C3×C5×#3852
C5×#52102
C5×#49762
C5×Dic3×C4⋊C42
C5×#49502
C5×#49462
C5×#46492
C5×#46472
C5×#22963
#743785