Finite Group Databasebeta

← C5×#73821 #14323351

Subgroups — C5×#73821 #14323351

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#953C211yesmaximal, characteristic
2C22×C5×#217C211yesmaximal, characteristic, complemented
3C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#379C211yesmaximal, characteristic, complemented
5C5×#4958C211yesmaximal, characteristic, complemented
6C5×#4957C212yesmaximal, complemented
7C5×#4956C212yesmaximal, complemented
8C5×#4946C211yesmaximal, characteristic, complemented
9C5×#4945C212yesmaximal, complemented
10C5×#4944C212yesmaximal, complemented
11C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2321—31nomaximal, Hall
13C25×C3×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C5×#67C2212yes—
16C23×C5×Dic3C2211yescharacteristic
17C23×C5×Dic3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic, complemented
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C5×C22⋊C4C2212yes—
23C5×#953C418yescomplemented
24C2×C5×#217—24no—
25C2×C5×#217C2212yes—
26C2×C5×#217C2212yes—
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2212yes—
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2212yescomplemented
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C5×Dic3⋊C4C2212yescomplemented
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C2×C4×C5×Dic3C2212yescomplemented
35C5×#67⋊C4—24no—
36C5×C3⋊#95C2212yescomplemented
37C5×C3⋊#95C2212yescomplemented
38C5×C3⋊#95C2212yescomplemented
39#73821C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#120—31no—
41C2×C4×C5×D4—31no—
42C22×C5×C22⋊C4—31no—
43C5×#390—32no—
44C5×#388—32no—
45C5×#388—32no—
46C5×#386—32no—
47C5×#386—31no—
48C5×#385—31no—
49C5×#379D311yescharacteristic, complemented
50C4×C5×C22⋊C4—31no—
51C24×C3×C5—22no—
52C24×C3×C5—22no—
53C24×C3×C5—42no—
54C24×C3×C5—42no—
55C24×C3×C5C2×C414yescomplemented
56C24×C3×C5C2312yes—
57C24×C3×C5C2311yescharacteristic
58C23×C5×D3C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C2×C5×#67—22no—
63C2×C5×#67—22no—
64C2×C5×#67—42no—
65C2×C5×#67—42no—
66C2×C5×#67C2×C414yes—
67C2×C5×#67C2×C418yescomplemented
68C22×C5×Dic3—22no—
69C22×C5×Dic3—42no—
70C22×C5×Dic3—42no—
71C22×C5×Dic3D414yescomplemented
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C2×C4×C5×D3—22no—
78C2×C4×C5×D3—42no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—42no—
82C3×C5×C22⋊C4—42no—
83C5×#217—24no—
84C5×#217—24no—
85C5×#217C2×C418yescomplemented
86C5×#217C2×C414yescomplemented
87C5×(C2×D3)⋊C4—22no—
88C5×(C2×D3)⋊C4—42no—
89C5×Dic3⋊C4—22no—
90C5×Dic3⋊C4—42no—
91C4×C5×Dic3—22no—
92C4×C5×Dic3—42no—
93C2×#953C2×C511yescharacteristic
94C22×#217C2×C511yescharacteristic, complemented
95C2×#67⋊C4C2×C511yescharacteristic, complemented
96C3×#379C2×C511yescharacteristic, complemented
97#4958C2×C511yescharacteristic, complemented
98#4957C2×C512yescomplemented
99#4956C2×C512yescomplemented
100#4946C2×C511yescharacteristic, complemented
101#4945C2×C512yescomplemented
102#4944C2×C512yescomplemented
103Dic3×C22⋊C4C2×C511yescharacteristic, complemented
104C25×C5C2×D311yescharacteristic
105C22×C5×D4—31no—
106C22×C5×D4—32no—
107C23×C4×C5—31no—
108C23×C4×C5—31no—
109C23×C4×C5—31no—
110C5×#120—38no—
111C4×C5×D4—64no—
112C2×C5×C4⋊C4—31no—
113C2×C5×C4⋊C4—32no—
114C2×C5×C22⋊C4—31no—
115C2×C5×C22⋊C4—32no—
116C2×C5×C22⋊C4—32no—
117C2×C5×C22⋊C4—32no—
118C2×C5×C22⋊C4—31no—
119C2×C5×C22⋊C4—32no—
120C2×C5×C22⋊C4—64no—
121C2×C5×C22⋊C4C2×D311yescharacteristic
122C2×C5×C22⋊C4C2×D311yescharacteristic
123C2×C5×C22⋊C4C2×D312yes—
124C2×C5×C22⋊C4C2×D312yes—
125C2×C42×C5—31no—
126C2×C42×C5—32no—
127C5×#95—32no—
128C5×#95—32no—
129C5×#95—32no—
130#2321—31noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—28no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—48no—
141C23×C3×C5—44no—
142C23×C3×C5—44no—
143C23×C3×C5—48no—
144C23×C3×C5C22×C414yes—
145C23×C3×C5C22×C412yes—
146C23×C3×C5C2×D412yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
149C22×C5×D3—21no—
150C22×C5×D3—21no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3C22×C412yes—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C5×#67—28no—
162C5×#67—48no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—44no—
173C2×C5×Dic3—44no—
174C2×C5×Dic3C22×C412yes—
175C2×C5×Dic3C22×C414yes—
176C2×C5×Dic3C2×D412yes—
177C2×C5×Dic3C2×D412yes—
178C4×C5×D3—44no—
179C25×C3C22×C511yescharacteristic
180C22×#67C22×C511yescharacteristic
181C22×#67C22×C512yes—
182C23×Dic3C22×C511yescharacteristic
183C23×Dic3C22×C511yescharacteristic
184C22×C4×D3C22×C511yescharacteristic, complemented
185C2×C3×C22⋊C4C22×C511yescharacteristic
186C2×C3×C22⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C512yes—
188C2×C3×C22⋊C4C22×C512yes—
189#953C4×C518yescomplemented
190C2×#217—24no—
191C2×#217C22×C512yes—
192C2×#217C22×C512yes—
193C2×#217C22×C511yescharacteristic
194C2×#217C22×C512yes—
195C2×(C2×D3)⋊C4C22×C511yescharacteristic, complemented
196C2×(C2×D3)⋊C4C22×C512yescomplemented
197C2×Dic3⋊C4C22×C511yescharacteristic, complemented
198C2×Dic3⋊C4C22×C512yescomplemented
199C2×C4×Dic3C22×C511yescharacteristic, complemented
200C2×C4×Dic3C22×C512yescomplemented
201#67⋊C4—24no—
202C3⋊#95C22×C512yescomplemented
203C3⋊#95C22×C512yescomplemented
204C3⋊#95C22×C512yescomplemented
205C24×C5—22no—
206C24×C5—22no—
207C24×C5—31no—
208C24×C5—42no—
209C24×C5—42no—
210C24×C5C4×D314yescomplemented
211C24×C5C22×D312yes—
212C24×C5C22×D311yescharacteristic
213C2×C5×D4—34no—
214C2×C5×D4—38no—
215C2×C5×D4—62no—
216C2×C5×D4—62no—
217C2×C5×D4—122no—
218C2×C5×D4—122no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—32no—
222C22×C4×C5—31no—
223C22×C4×C5—34no—
224C22×C4×C5—32no—
225C22×C4×C5—62no—
226C22×C4×C5—62no—
227C22×C4×C5—122no—
228C22×C4×C5—122no—
229C22×C4×C5—122no—
230C22×C4×C5C22×D311yescharacteristic
231C22×C4×C5C22×D312yes—
232C22×C4×C5C22×D311yescharacteristic
233C5×C4⋊C4—62no—
234C5×C4⋊C4—122no—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—22no—
237C5×C22⋊C4—38no—
238C5×C22⋊C4—34no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—62no—
242C5×C22⋊C4—64no—
243C5×C22⋊C4—64no—
244C5×C22⋊C4—122no—
245C42×C5—62no—
246C42×C5—122no—
247C2×#120—31no—
248C2×C4×D4—31no—
249C22×C22⋊C4—31no—
250#390—32no—
251#388—32no—
252#388—32no—
253#386—32no—
254#386—31no—
255#385—31no—
256#379C5×D311yescharacteristic, complemented
257C4×C22⋊C4—31no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5—24no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—416no—
266C22×C3×C5—42no—
267C22×C3×C5—42no—
268C22×C3×C5—42no—
269C22×C3×C5—42no—
270C22×C3×C5C4×D414yes—
271C22×C3×C5C23×C411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5H(5,𝔽2)12yes—
275C22×C3×C5H(5,𝔽2)12yes—
276C2×C5×D3—22no—
277C2×C5×D3—24no—
278C2×C5×D3—41no—
279C2×C5×D3—41no—
280C2×C5×D3—42no—
281C3×C4×C5—41no—
282C3×C4×C5—41no—
283C3×C4×C5—42no—
284C5×Dic3—22no—
285C5×Dic3—24no—
286C5×Dic3—22no—
287C5×Dic3—22no—
288C5×Dic3—42no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—42no—
292C24×C3—42no—
293C24×C3C2×C4×C514yescomplemented
294C24×C3C23×C512yes—
295C24×C3C23×C511yescharacteristic
296C23×D3C23×C511yescharacteristic
297C22×C3×C4C23×C512yes—
298C22×C3×C4C23×C511yescharacteristic
299C22×C3×C4C23×C511yescharacteristic
300C2×#67—22no—
301C2×#67—22no—
302C2×#67—42no—
303C2×#67—42no—
304C2×#67C2×C4×C514yes—
305C2×#67C2×C4×C518yescomplemented
306C22×Dic3—22no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C22×Dic3C5×D414yescomplemented
310C22×Dic3C23×C512yes—
311C22×Dic3C23×C511yescharacteristic
312C22×Dic3C23×C512yes—
313C22×Dic3C23×C511yescharacteristic
314C22×Dic3C23×C511yescharacteristic
315C2×C4×D3—22no—
316C2×C4×D3—42no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321#217—24no—
322#217—24no—
323#217C2×C4×C518yescomplemented
324#217C2×C4×C514yescomplemented
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—42no—
327Dic3⋊C4—22no—
328Dic3⋊C4—42no—
329C4×Dic3—22no—
330C4×Dic3—42no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—28no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—32no—
341C23×C5—48no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—48no—
345C23×C5—61no—
346C23×C5—61no—
347C23×C5—62no—
348C23×C5—62no—
349C23×C5C2×C4×D314yes—
350C23×C5C2×C4×D312yes—
351C23×C5D3×D412yes—
352C23×C5#23712yes—
353C23×C5C23×D311yescharacteristic
354C5×D4—68no—
355C5×D4—128no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—32no—
364C2×C4×C5—34no—
365C2×C4×C5—32no—
366C2×C4×C5—32no—
367C2×C4×C5—61no—
368C2×C4×C5—61no—
369C2×C4×C5—62no—
370C2×C4×C5—62no—
371C2×C4×C5—62no—
372C2×C4×C5—62no—
373C2×C4×C5—62no—
374C2×C4×C5—62no—
375C2×C4×C5—62no—
376C2×C4×C5—124no—
377C2×C4×C5—124no—
378C2×C4×C5—124no—
379C25C2×C5×D311yescharacteristic
380C22×D4—31no—
381C22×D4—32no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385#120—38no—
386C4×D4—64no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—32no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4C2×C5×D311yescharacteristic
397C2×C22⋊C4C2×C5×D311yescharacteristic
398C2×C22⋊C4C2×C5×D312yes—
399C2×C22⋊C4C2×C5×D312yes—
400C2×C42—31no—
401C2×C42—32no—
402#95—32no—
403#95—32no—
404#95—32no—
405C2×C3×C5—24no—
406C2×C3×C5—44no—
407C2×C3×C5C2×C4×D411yescharacteristic
408C2×C3×C5#51812yes—
409C2×C3×C5#53411yescharacteristic
410C2×C3×C5#53511yescharacteristic
411C2×C3×C5#53812yes—
412C5×D3—42no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—28no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—48no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—48no—
426C23×C3C22×C4×C514yes—
427C23×C3C22×C4×C512yes—
428C23×C3C2×C5×D412yes—
429C23×C3C5×#4112yes—
430C23×C3C24×C511yescharacteristic
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3C22×C4×C512yes—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443#67—28no—
444#67—48no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—44no—
455C2×Dic3—44no—
456C2×Dic3C22×C4×C512yes—
457C2×Dic3C22×C4×C514yes—
458C2×Dic3C2×C5×D412yes—
459C2×Dic3C2×C5×D412yes—
460C4×D3—44no—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—24no—
468C22×C5—416no—
469C22×C5—42no—
470C22×C5—42no—
471C22×C5—42no—
472C22×C5—42no—
473C22×C5—62no—
474C22×C5—64no—
475C22×C5—121no—
476C22×C5—121no—
477C22×C5—122no—
478C22×C5#67⋊C414yes—
479C22×C5C22×C4×D311yescharacteristic
480C22×C5C2×D3×D411yescharacteristic
481C22×C5C2×#23711yescharacteristic
482C22×C5#100412yes—
483C22×C5#100412yes—
484C4×C5—41no—
485C4×C5—41no—
486C4×C5—42no—
487C4×C5—62no—
488C4×C5—64no—
489C4×C5—62no—
490C4×C5—62no—
491C4×C5—122no—
492C24—22no—
493C24—22no—
494C24—31no—
495C24—42no—
496C24—42no—
497C24C4×C5×D314yescomplemented
498C24C22×C5×D312yes—
499C24C22×C5×D311yescharacteristic
500C2×D4—34no—
501C2×D4—38no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—122no—
505C2×D4—122no—
506C22×C4—31no—
507C22×C4—32no—
508C22×C4—31no—
509C22×C4—31no—
510C22×C4—34no—
511C22×C4—32no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—122no—
515C22×C4—122no—
516C22×C4—122no—
517C22×C4C22×C5×D312yes—
518C22×C4C22×C5×D311yescharacteristic
519C22×C4C22×C5×D311yescharacteristic
520C4⋊C4—62no—
521C4⋊C4—122no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—38no—
525C22⋊C4—34no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—62no—
529C22⋊C4—64no—
530C22⋊C4—64no—
531C22⋊C4—122no—
532C42—62no—
533C42—122no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—416no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3C4×C5×D414yes—
548C22×C3C23×C4×C511yescharacteristic
549C22×C3C22×C5×D411yescharacteristic
550C22×C3C2×C5×#4111yescharacteristic
551C22×C3C5×H(5,𝔽2)12yes—
552C22×C3C5×H(5,𝔽2)12yes—
553C2×D3—22no—
554C2×D3—24no—
555C2×D3—41no—
556C2×D3—41no—
557C2×D3—42no—
558C3×C4—41no—
559C3×C4—41no—
560C3×C4—42no—
561Dic3—22no—
562Dic3—24no—
563Dic3—22no—
564Dic3—22no—
565Dic3—42no—
566C2×C5—24no—
567C2×C5—44no—
568C2×C5—122no—
569C2×C5C2×#67⋊C411yescharacteristic
570C2×C5#548612yes—
571C2×C5#558911yescharacteristic
572C2×C5#559211yescharacteristic
573C2×C5#559312yes—
574C23—22no—
575C23—22no—
576C23—28no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—32no—
584C23—48no—
585C23—44no—
586C23—44no—
587C23—48no—
588C23—61no—
589C23—61no—
590C23—62no—
591C23—62no—
592C23C2×C4×C5×D314yes—
593C23C2×C4×C5×D312yes—
594C23C5×D3×D412yes—
595C23C5×#23712yes—
596C23C23×C5×D311yescharacteristic
597D4—68no—
598D4—128no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—32no—
607C2×C4—34no—
608C2×C4—32no—
609C2×C4—32no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—124no—
620C2×C4—124no—
621C2×C4—124no—
622C2×C3—24no—
623C2×C3—44no—
624C2×C3C2×C4×C5×D411yescharacteristic
625C2×C3C5×#51812yes—
626C2×C3C5×#53411yescharacteristic
627C2×C3C5×#53511yescharacteristic
628C2×C3C5×#53812yes—
629D3—42no—
630C5#7382111yescharacteristic, direct product factor, Sylow
631C22—24no—
632C22—22no—
633C22—22no—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—416no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—62no—
644C22—64no—
645C22—121no—
646C22—121no—
647C22—122no—
648C22C5×#67⋊C414yes—
649C22C22×C4×C5×D311yescharacteristic
650C22C2×C5×D3×D411yescharacteristic
651C22C2×C5×#23711yescharacteristic
652C22C5×#100412yes—
653C22C5×#100412yes—
654C4—41no—
655C4—41no—
656C4—42no—
657C4—62no—
658C4—64no—
659C4—62no—
660C4—62no—
661C4—122no—
662C3C5×#232111yescharacteristic, complemented, Sylow
663C2—24no—
664C2—44no—
665C2—122no—
666C2C2×C5×#67⋊C411yescharacteristic
667C2C5×#548612yes—
668C2C5×#558911yescharacteristic
669C2C5×#559211yescharacteristic
670C2C5×#559312yes—
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#379C2
socleC23×C3×C5C24
prime radicalC2×C5×#953C2
cosocleC23×C3C24×C5
hypercenterC5×#379D3
hypocenterC3C5×#2321
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#379

Complements

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

NH ≅ G/Ntype
2. C22×C5×#217C2semidirect
3. C2×C5×#67⋊C4C2semidirect
4. C3×C5×#379C2semidirect
5. C5×#4958C2semidirect
6. C5×#4957C2semidirect
7. C5×#4956C2semidirect
8. C5×#4946C2semidirect
9. C5×#4945C2semidirect
10. C5×#4944C2semidirect
11. C5×Dic3×C22⋊C4C2semidirect
18. C22×C4×C5×D3C22semidirect
23. C5×#953C4semidirect
29. C2×C5×(C2×D3)⋊C4C22semidirect
30. C2×C5×(C2×D3)⋊C4C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
32. C2×C5×Dic3⋊C4C22semidirect
33. C2×C4×C5×Dic3C22semidirect
34. C2×C4×C5×Dic3C22semidirect
36. C5×C3⋊#95C22semidirect
37. C5×C3⋊#95C22semidirect
38. C5×C3⋊#95C22semidirect
39. #73821C5direct (N × H)
49. C5×#379D3semidirect
55. C24×C3×C5C2×C4semidirect
67. C2×C5×#67C2×C4semidirect
71. C22×C5×Dic3D4semidirect
85. C5×#217C2×C4semidirect
86. C5×#217C2×C4semidirect
94. C22×#217C2×C5semidirect
95. C2×#67⋊C4C2×C5semidirect
96. C3×#379C2×C5semidirect
97. #4958C2×C5semidirect
98. #4957C2×C5semidirect
99. #4956C2×C5semidirect
100. #4946C2×C5semidirect
101. #4945C2×C5semidirect
102. #4944C2×C5semidirect
103. Dic3×C22⋊C4C2×C5semidirect
184. C22×C4×D3C22×C5semidirect
189. #953C4×C5semidirect
195. C2×(C2×D3)⋊C4C22×C5semidirect
196. C2×(C2×D3)⋊C4C22×C5semidirect
197. C2×Dic3⋊C4C22×C5semidirect
198. C2×Dic3⋊C4C22×C5semidirect
199. C2×C4×Dic3C22×C5semidirect
200. C2×C4×Dic3C22×C5semidirect
202. C3⋊#95C22×C5semidirect
203. C3⋊#95C22×C5semidirect
204. C3⋊#95C22×C5semidirect
210. C24×C5C4×D3semidirect
256. #379C5×D3semidirect
293. C24×C3C2×C4×C5semidirect
305. C2×#67C2×C4×C5semidirect
309. C22×Dic3C5×D4semidirect
323. #217C2×C4×C5semidirect
324. #217C2×C4×C5semidirect
497. C24C4×C5×D3semidirect
534. C3×C5#2321semidirect
630. C5#73821direct (N × H)
662. C3C5×#2321semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9532
C22×C5×#2172
C2×C5×#67⋊C42
C3×C5×#3792
C5×#49582
C5×#49572
C5×#49562
C5×#49462
C5×#49452
C5×#49442
C5×Dic3×C22⋊C42
C5×#23213
#738215