Finite Group Databasebeta

← Dic5×#895 #14321463

Subgroups — Dic5×#895 #14321463

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#895C211yesmaximal, characteristic
2C2×Dic5×D12C212yesmaximal, complemented
3C2×Dic5×D12C211yesmaximal, characteristic, complemented
4C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
5#11751085C211yesmaximal, characteristic, complemented
6C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
7#11748901C212yesmaximal, complemented
8Dic5×(C2×D3)⋊C4C212yesmaximal, complemented
9#11748797C211yesmaximal, characteristic, complemented
10#11748786C211yesmaximal, characteristic, complemented
11#11748686C212yesmaximal, complemented
12Dic5×#121—31nomaximal, Hall
13C22×C5×D12C2212yes—
14C22×C5×D12C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C22×D3×Dic5C2211yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C4⋊Dic15C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2212yes—
24C5×#895C418yescomplemented
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×Dic3×Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2211yescharacteristic
34Dic5×D12—28no—
35Dic5×D12—24no—
36C4×D3×Dic5—24no—
37#91115C2212yes—
38C3×#3963C2212yes—
39#90994C2212yes—
40C4×#895—51nomaximal, Hall
41C2×C5×#121—31no—
42C2×D4×Dic5—31no—
43C2×D4×Dic5—32no—
44C22×C4×Dic5—31no—
45#65510—31no—
46#65509—32no—
47#65501—31no—
48#65274—31no—
49C4⋊C4×Dic5D311yescharacteristic, complemented
50#65240—32no—
51C22⋊C4×Dic5—32no—
52C23×C5×D3C2312yes—
53C23×C5×D3C2311yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C2×C5×D12—24no—
61C2×C5×D12—24no—
62C2×C5×D12—22no—
63C2×C5×D12—22no—
64C2×C5×D12C2×C418yescomplemented
65C2×C5×D12C2×C414yescomplemented
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3—22no—
68C2×C4×C5×D3C2×C414yescomplemented
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×D3×Dic5—22no—
73C2×D3×Dic5—22no—
74C2×D3×Dic5—22no—
75C2×D3×Dic5—22no—
76C2×D3×Dic5—22no—
77C2×D3×Dic5—24no—
78C2×D3×Dic5—24no—
79C2×D3×Dic5—24no—
80C2×D3×Dic5D414yescomplemented
81C3×C5×C4⋊C4C2×C414yescomplemented
82C4⋊Dic15—22no—
83C4⋊Dic15—24no—
84C4×Dic15—22no—
85C5×(C2×D3)⋊C4C2×C418yescomplemented
86C3×C4⋊Dic5—22no—
87C3×C4×Dic5—24no—
88C3×C4×Dic5D414yescomplemented
89(C2×D3)⋊Dic5—24no—
90(C2×D3)⋊Dic5—24no—
91(C2×D3)⋊Dic5—24no—
92(C2×D3)⋊Dic5—24no—
93Dic3×Dic5—22no—
94Dic3×Dic5—22no—
95C2×#895D511yescharacteristic
96C2×C4×D12—51no—
97C2×C4×D12—52no—
98C2×C42×D3—51no—
99C3×C4×C4⋊C4—51no—
100#4988—51no—
101#4987—51no—
102#4984—51no—
103C4×(C2×D3)⋊C4—52no—
104#4670—52no—
105#4665—52no—
106C22×C5×D4—32no—
107C22×C5×D4—31no—
108C23×C4×C5—31no—
109C23×Dic5—31no—
110C23×Dic5—31no—
111C23×Dic5—32no—
112C5×#121—38no—
113C2×C5×C4⋊C4C2×D311yescharacteristic
114C2×C5×C22⋊C4—32no—
115C2×C22⋊Dic5—32no—
116C2×C22⋊Dic5—32no—
117C2×C22⋊Dic5—32no—
118C2×C22⋊Dic5—32no—
119D4×Dic5—68no—
120D4×Dic5—64no—
121C2×C4⋊Dic5—32no—
122C2×C4⋊Dic5—31no—
123C2×C4⋊Dic5C2×D311yescharacteristic
124C2×C4×Dic5—31no—
125C2×C4×Dic5—31no—
126C2×C4×Dic5—31no—
127C2×C4×Dic5—64no—
128C2×C4×Dic5C2×D312yes—
129C2×C4×Dic5C2×D311yescharacteristic
130#3963—32no—
131#3963—32no—
132#3963C2×D312yes—
133C4×#121—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×C5×D3—21no—
136C22×C5×D3—21no—
137C22×C5×D3—21no—
138C22×C5×D3—21no—
139C22×C5×D3—22no—
140C22×C5×D3—22no—
141C22×C5×D3—22no—
142C22×C5×D3—22no—
143C22×C5×D3—22no—
144C22×C5×D3—22no—
145C22×C5×D3C22×C414yes—
146C22×C5×D3C22×C412yes—
147C22×C5×D3C2×D412yes—
148C22×C5×D3#4112yes—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5C22×C414yes—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5#4112yes—
155C2×Dic15—21no—
156C2×Dic15—21no—
157C2×Dic15—21no—
158C2×Dic15—21no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15C2×D412yes—
163C2×Dic15#4112yes—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3C22×C412yes—
167C5×D12—216no—
168C5×D12—28no—
169C4×C5×D3—28no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5C2×D412yes—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5#4112yes—
179D3×Dic5—28no—
180D3×Dic5—28no—
181D3×Dic5—48no—
182C22×D12C2×D512yes—
183C22×D12C2×D511yescharacteristic
184C22×C4×D3—51no—
185C22×C4×D3—51no—
186C22×C4×D3—52no—
187C22×C4×D3C2×D511yescharacteristic
188C2×C3×C4⋊C4—51no—
189C2×C3×C4⋊C4C2×D511yescharacteristic
190C2×C3×C42—51no—
191C2×C3×C42—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4C2×D512yes—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3—51no—
199C2×C4×Dic3—51no—
200C2×C4×Dic3—51no—
201C2×C4×Dic3—51no—
202#895Dic518yesdirect product factor
203C4×D12—104no—
204C4×D12—108no—
205C42×D3—104no—
206C3×#95—52no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C24×C5—31no—
210C24×C5—32no—
211C2×C5×D4—38no—
212C2×C5×D4—34no—
213C2×C5×D4—64no—
214C2×C5×D4—64no—
215C2×C5×D4—62no—
216C2×C5×D4—62no—
217C22×C4×C5—31no—
218C22×C4×C5—34no—
219C22×C4×C5—62no—
220C22×C4×C5—62no—
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—31no—
224C22×Dic5—31no—
225C22×Dic5—34no—
226C22×Dic5—32no—
227C22×Dic5—62no—
228C22×Dic5—62no—
229C22×Dic5—62no—
230C22×Dic5—62no—
231C22×Dic5—62no—
232C22×Dic5—64no—
233C22×Dic5—64no—
234C22×Dic5—64no—
235C22×Dic5C22×D312yes—
236C22×Dic5C22×D311yescharacteristic
237C22×Dic5C22×D311yescharacteristic
238C5×C4⋊C4C4×D314yescomplemented
239C5×C22⋊C4—38no—
240C22⋊Dic5—64no—
241C22⋊Dic5—64no—
242C22⋊Dic5—64no—
243C22⋊Dic5—64no—
244C4⋊Dic5—22no—
245C4⋊Dic5—64no—
246C4⋊Dic5—62no—
247C4×Dic5—24no—
248C4×Dic5—62no—
249C4×Dic5—62no—
250C4×Dic5—62no—
251C4×Dic5D1214yescomplemented
252C2×#121—31no—
253C2×C4×D4—151no—
254C2×C4×D4—152no—
255C22×C42—151no—
256#390—151no—
257#389—151no—
258#388—152no—
259#386—152no—
260#380—151no—
261C4×C4⋊C4—51no—
262C4×C22⋊C4—152no—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C2×#4111yescharacteristic
267C22×C3×C5C2×#4111yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×C5×D3—22no—
271C2×C5×D3—22no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3—22no—
276C2×C5×D3—24no—
277C2×C5×D3—24no—
278C2×C5×D3—24no—
279C2×C5×D3—42no—
280C2×C5×D3—42no—
281C2×C5×D3—42no—
282C2×C5×D3—42no—
283C2×C5×D3C4×D414yescomplemented
284C3×C4×C5—24no—
285C3×C4×C5C4×D414yescomplemented
286Dic15—22no—
287Dic15—22no—
288Dic15—42no—
289C3×Dic5—22no—
290C3×Dic5—42no—
291C3×Dic5#12114yescomplemented
292C5×Dic3—22no—
293C23×D3C22×D512yes—
294C23×D3C22×D511yescharacteristic
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—52no—
298C22×C3×C4C22×D512yes—
299C22×C3×C4C22×D511yescharacteristic
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—52no—
303C22×Dic3C22×D511yescharacteristic
304C2×D12—24no—
305C2×D12—24no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12C2×Dic518yescomplemented
309C2×D12C2×Dic514yescomplemented
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—54no—
313C2×C4×D3—102no—
314C2×C4×D3—102no—
315C2×C4×D3—102no—
316C2×C4×D3—102no—
317C2×C4×D3—102no—
318C2×C4×D3—104no—
319C2×C4×D3—104no—
320C2×C4×D3—104no—
321C2×C4×D3C2×Dic514yescomplemented
322C3×C4⋊C4—102no—
323C3×C4⋊C4C2×Dic514yescomplemented
324C3×C42—54no—
325C3×C42—104no—
326(C2×D3)⋊C4—104no—
327(C2×D3)⋊C4—104no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—104no—
330(C2×D3)⋊C4C2×Dic518yescomplemented
331C4⋊Dic3—104no—
332C4⋊Dic3—102no—
333C4×Dic3—102no—
334C4×Dic3—102no—
335C4×Dic3—102no—
336C23×C5—32no—
337C23×C5—32no—
338C23×C5—32no—
339C23×C5—34no—
340C23×C5—61no—
341C23×C5—61no—
342C23×C5—61no—
343C23×C5—61no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—62no—
349C23×C5—62no—
350C23×C5C23×D311yescharacteristic
351C5×D4—616no—
352C5×D4—68no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—32no—
356C2×C4×C5—61no—
357C2×C4×C5—61no—
358C2×C4×C5—68no—
359C2×C4×C5C2×C4×D314yes—
360C2×C4×C5C2×C4×D312yes—
361C2×C4×C5C2×D1212yes—
362C2×C4×C5#23512yes—
363C2×Dic5—21no—
364C2×Dic5—21no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—32no—
369C2×Dic5—32no—
370C2×Dic5—68no—
371C2×Dic5—61no—
372C2×Dic5—61no—
373C2×Dic5—61no—
374C2×Dic5—61no—
375C2×Dic5—68no—
376C2×Dic5—62no—
377C2×Dic5—62no—
378C2×Dic5—62no—
379C2×Dic5—128no—
380C2×Dic5C2×D1212yes—
381C2×Dic5C2×D1212yes—
382C2×Dic5D3×D412yes—
383C2×Dic5#23912yes—
384C22×D4—32no—
385C22×D4—31no—
386C23×C4—31no—
387C23×C4—151no—
388C23×C4—152no—
389C23×C4—151no—
390#121—38no—
391C4×D4—304no—
392C4×D4—308no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—151no—
395C2×C4⋊C4—152no—
396C2×C4⋊C4D3×D511yescharacteristic
397C2×C22⋊C4—32no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—51no—
403C2×C42—52no—
404C2×C42—151no—
405C2×C42—151no—
406C2×C42—151no—
407C2×C42—304no—
408#95—52no—
409#95—152no—
410#95—152no—
411C2×C3×C5C2×C4×D411yescharacteristic
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C4×#4111yescharacteristic
414C2×C3×C5C2×#12111yescharacteristic
415C2×C3×C5#52511yescharacteristic
416C2×C3×C5#52911yescharacteristic
417C2×C3×C5#53211yescharacteristic
418C5×D3—24no—
419C5×D3—44no—
420C23×C3C23×D511yescharacteristic
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3D4×D512yes—
432C22×D3#71112yes—
433C22×D3C22×Dic514yes—
434C22×D3C22×Dic512yes—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—52no—
438C2×C3×C4—52no—
439C2×C3×C4—52no—
440C2×C3×C4—52no—
441C2×C3×C4—101no—
442C2×C3×C4—101no—
443C2×C3×C4—102no—
444C2×C3×C4—102no—
445C2×C3×C4—102no—
446C2×C3×C4D4×D512yes—
447C2×C3×C4#71112yes—
448C2×C3×C4C22×Dic514yes—
449C2×C3×C4C22×Dic512yes—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—52no—
453C2×Dic3—52no—
454C2×Dic3—101no—
455C2×Dic3—101no—
456C2×Dic3—101no—
457C2×Dic3—101no—
458C2×Dic3—102no—
459C2×Dic3—102no—
460C2×Dic3—102no—
461C2×Dic3C22×Dic512yes—
462D12—216no—
463D12—28no—
464C4×D3—28no—
465C4×D3—108no—
466C4×D3—108no—
467C4×D3—208no—
468C22×C5—34no—
469C22×C5—62no—
470C22×C5—62no—
471C22×C5—62no—
472C22×C5—62no—
473C22×C5—62no—
474C22×C5—62no—
475C22×C5—64no—
476C22×C5—64no—
477C22×C5—64no—
478C22×C5—122no—
479C22×C5—122no—
480C22×C5—122no—
481C22×C5—122no—
482C22×C5C22×C4×D311yescharacteristic
483C22×C5C22×D1211yescharacteristic
484C22×C5C2×#23511yescharacteristic
485C22×C5C2×D3×D411yescharacteristic
486C22×C5C2×#23911yescharacteristic
487C22×C5D3×#4111yescharacteristic
488C22×C5D3×#4111yescharacteristic
489C4×C5—24no—
490C4×C5—62no—
491C4×C5C4×D1214yescomplemented
492Dic5—22no—
493Dic5—42no—
494Dic5—62no—
495Dic5—62no—
496Dic5—122no—
497Dic5#89514yesdirect product factor
498C24—31no—
499C24—32no—
500C2×D4—38no—
501C2×D4—34no—
502C2×D4—64no—
503C2×D4—64no—
504C2×D4—62no—
505C2×D4—62no—
506C22×C4—31no—
507C22×C4—34no—
508C22×C4—51no—
509C22×C4—51no—
510C22×C4—52no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—154no—
514C22×C4—151no—
515C22×C4—151no—
516C22×C4—152no—
517C22×C4—302no—
518C22×C4—302no—
519C22×C4—302no—
520C22×C4—304no—
521C22×C4—304no—
522C22×C4—304no—
523C22×C4—302no—
524C22×C4—302no—
525C22×C4C2×D3×D512yes—
526C22×C4C2×D3×D511yescharacteristic
527C4⋊C4—102no—
528C4⋊C4—304no—
529C4⋊C4—302no—
530C4⋊C4D3×Dic514yescomplemented
531C22⋊C4—38no—
532C22⋊C4—304no—
533C22⋊C4—304no—
534C22⋊C4—304no—
535C22⋊C4—304no—
536C42—54no—
537C42—104no—
538C42—302no—
539C42—302no—
540C42—302no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3C2×D4×D511yescharacteristic
543C22×C3C2×D4×D511yescharacteristic
544C22×C3C2×#71111yescharacteristic
545C22×C3C2×#71111yescharacteristic
546C22×C3D5×#4111yescharacteristic
547C22×C3D5×#4111yescharacteristic
548C22×C3C23×Dic511yescharacteristic
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—22no—
554C2×D3—22no—
555C2×D3—24no—
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—42no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—42no—
562C2×D3D4×Dic514yescomplemented
563C3×C4—24no—
564C3×C4—54no—
565C3×C4—102no—
566C3×C4—202no—
567C3×C4D4×Dic514yescomplemented
568Dic3—22no—
569Dic3—102no—
570Dic3—102no—
571Dic3—202no—
572C2×C5—64no—
573C2×C5—124no—
574C2×C5C2×C4×D1211yescharacteristic
575C2×C5C2×#89511yescharacteristic
576C2×C5#552411yescharacteristic
577C2×C5C4×D3×D411yescharacteristic
578C2×C5#554811yescharacteristic
579C2×C5C4×#23911yescharacteristic
580C2×C5#558011yescharacteristic
581C23—32no—
582C23—32no—
583C23—32no—
584C23—34no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23—61no—
589C23—62no—
590C23—62no—
591C23—62no—
592C23—62no—
593C23—62no—
594C23—62no—
595C23C22×D3×D511yescharacteristic
596D4—616no—
597D4—68no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—32no—
601C2×C4—52no—
602C2×C4—52no—
603C2×C4—52no—
604C2×C4—52no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—68no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—102no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—152no—
614C2×C4—152no—
615C2×C4—308no—
616C2×C4—308no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—302no—
622C2×C4—302no—
623C2×C4—302no—
624C2×C4—608no—
625C2×C4#677212yes—
626C2×C4D5×D1212yes—
627C2×C4C2×D3×Dic514yes—
628C2×C4C2×D3×Dic512yes—
629C2×C3#6593011yescharacteristic
630C2×C3#6593411yescharacteristic
631C2×C3D5×#12111yescharacteristic
632C2×C3#6594011yescharacteristic
633C2×C3C2×D4×Dic511yescharacteristic
634C2×C3C2×D4×Dic511yescharacteristic
635C2×C3#41×Dic511yescharacteristic
636D3—24no—
637D3—44no—
638C5C4×#89511yescharacteristic, complemented, Sylow
639C22—34no—
640C22—62no—
641C22—62no—
642C22—62no—
643C22—62no—
644C22—62no—
645C22—62no—
646C22—64no—
647C22—64no—
648C22—64no—
649C22—122no—
650C22—122no—
651C22—122no—
652C22—122no—
653C22C2×#677211yescharacteristic
654C22C2×D5×D1211yescharacteristic
655C22D3×D4×D511yescharacteristic
656C22D3×#71111yescharacteristic
657C22D5×#23911yescharacteristic
658C22#9203411yescharacteristic
659C22C22×D3×Dic511yescharacteristic
660C4—24no—
661C4—54no—
662C4—62no—
663C4—102no—
664C4—202no—
665C4—302no—
666C4—302no—
667C4—602no—
668C4Dic5×D1214yescomplemented
669C3Dic5×#12111yescharacteristic, complemented, Sylow
670C2—64no—
671C2—124no—
672C2#1175353511yescharacteristic
673C2#1175368011yescharacteristic
674C2D5×#89511yescharacteristic
675C2#1175387311yescharacteristic
676C2C2×Dic5×D1211yescharacteristic
677C2D3×D4×Dic511yescharacteristic
678C2Dic5×#23911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#895C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic5×D12C2semidirect
3. C2×Dic5×D12C2semidirect
4. C2×C4×D3×Dic5C2semidirect
5. #11751085C2semidirect
6. C3×C4⋊C4×Dic5C2semidirect
7. #11748901C2semidirect
8. Dic5×(C2×D3)⋊C4C2semidirect
9. #11748797C2semidirect
10. #11748786C2semidirect
11. #11748686C2semidirect
24. C5×#895C4semidirect
49. C4⋊C4×Dic5D3semidirect
64. C2×C5×D12C2×C4semidirect
65. C2×C5×D12C2×C4semidirect
68. C2×C4×C5×D3C2×C4semidirect
80. C2×D3×Dic5D4semidirect
81. C3×C5×C4⋊C4C2×C4semidirect
85. C5×(C2×D3)⋊C4C2×C4semidirect
88. C3×C4×Dic5D4semidirect
202. #895Dic5direct (N × H)
238. C5×C4⋊C4C4×D3semidirect
251. C4×Dic5D12semidirect
283. C2×C5×D3C4×D4semidirect
285. C3×C4×C5C4×D4semidirect
291. C3×Dic5#121semidirect
308. C2×D12C2×Dic5semidirect
309. C2×D12C2×Dic5semidirect
321. C2×C4×D3C2×Dic5semidirect
323. C3×C4⋊C4C2×Dic5semidirect
330. (C2×D3)⋊C4C2×Dic5semidirect
491. C4×C5C4×D12semidirect
497. Dic5#895direct (N × H)
530. C4⋊C4D3×Dic5semidirect
541. C3×C5C4×#121semidirect
562. C2×D3D4×Dic5semidirect
567. C3×C4D4×Dic5semidirect
638. C5C4×#895semidirect
668. C4Dic5×D12semidirect
669. C3Dic5×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8952
C2×Dic5×D122
C2×C4×D3×Dic52
#117510852
C3×C4⋊C4×Dic52
#117489012
Dic5×(C2×D3)⋊C42
#117487972
#117487862
#117486862
Dic5×#1213
C4×#8955