Finite Group Databasebeta

← Dic5×#939 #14321481

Subgroups — Dic5×#939 #14321481

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#939C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4C2×Dic5×#67C211yesmaximal, characteristic, complemented
5C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
6#11751321C211yesmaximal, characteristic, complemented
7#11749513C211yesmaximal, characteristic, complemented
8#11749501C211yesmaximal, characteristic, complemented
9#11749482C211yesmaximal, characteristic, complemented
10#11749479C211yesmaximal, characteristic, complemented
11Dic5×#217C211yesmaximal, characteristic, complemented
12Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11748677C211yesmaximal, characteristic, complemented
14#11748675C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16Dic5×#121—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C5×#939C418yescomplemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×D4×Dic5—24no—
35C2×C3×C4⋊Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37Dic5×#67—24no—
38Dic5×#67—24no—
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5—24no—
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57C4×#939—51nomaximal, Hall
58C2×C5×#121—31no—
59C2×D4×Dic5—31no—
60C2×D4×Dic5—31no—
61C2×D4×Dic5D311yescharacteristic, complemented
62C22×C4×Dic5—31no—
63#65510—31no—
64#65509—31no—
65#65509—31no—
66#65501—31no—
67#65274—31no—
68C4⋊C4×Dic5—31no—
69#65240—31no—
70#65240—31no—
71C22⋊C4×Dic5—31no—
72C22⋊C4×Dic5—31no—
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4C2×C414yescomplemented
79C22×C3×C4×C5C2311yescharacteristic
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15—22no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C2×C5×#67—22no—
90C2×C5×#67—22no—
91C2×C5×#67C2×C414yescomplemented
92C2×C5×#67C2×C414yescomplemented
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3C2×C414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C3×Dic5—22no—
100C22×C3×Dic5—22no—
101C22×C3×Dic5—22no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5—22no—
104C22×C3×Dic5D414yescomplemented
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C2×D3×Dic5—22no—
110C2×D3×Dic5—22no—
111C2×D3×Dic5—22no—
112#6719—22no—
113#6719—22no—
114#6719—22no—
115C5×#217C2×C414yescomplemented
116C5×(C2×D3)⋊C4C2×C414yescomplemented
117C5×Dic3⋊C4C2×C414yescomplemented
118C3×C22⋊Dic5—22no—
119C3×C22⋊Dic5—22no—
120C3×C4⋊Dic5—22no—
121C3×C4×Dic5—22no—
122Dic3⋊Dic5—22no—
123Dic3⋊Dic5—22no—
124Dic3⋊Dic5—22no—
125(C2×D3)⋊Dic5—22no—
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5—22no—
128Dic3×Dic5—22no—
129Dic3×Dic5—22no—
130Dic3×Dic5—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5D414yescomplemented
133C2×C3×C4×D4—51no—
134C2×#939D511yescharacteristic
135C2×C4×#67—51no—
136C2×C4×#67—51no—
137C22×C4×Dic3—51no—
138#5220—51no—
139C4×#217—51no—
140#4990—51no—
141#4976—51no—
142#4958—51no—
143#4957—51no—
144#4945—51no—
145#4942—51no—
146C4×(C2×D3)⋊C4—51no—
147C4×Dic3⋊C4—51no—
148C22×C5×D4—31no—
149C22×C5×D4—31no—
150C22×C5×D4C2×D311yescharacteristic
151C23×C4×C5—31no—
152C23×Dic5—31no—
153C23×Dic5—31no—
154C23×Dic5C2×D311yescharacteristic
155C23×Dic5C2×D311yescharacteristic
156C5×#121—38no—
157C2×C5×C4⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5C2×D311yescharacteristic
167C2×C22⋊Dic5C2×D311yescharacteristic
168D4×Dic5—24no—
169D4×Dic5—64no—
170D4×Dic5—64no—
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5C2×D311yescharacteristic
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179C2×C4×Dic5—31no—
180C2×C4×Dic5—64no—
181C2×C4×Dic5C2×D311yescharacteristic
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188C4×#121—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2×D412yes—
202C23×C3×C5#4112yes—
203C23×C3×C5C2411yescharacteristic
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3C22×C412yes—
211C3×C5×D4—28no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C22×C412yes—
215C2×Dic15—28no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15C2×D412yes—
227C2×Dic15#4112yes—
228C5×#67—28no—
229C5×#67—28no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—28no—
235C2×C5×Dic3C22×C412yes—
236C2×C5×Dic3C22×C412yes—
237C2×C5×Dic3C22×C412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3#4112yes—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—28no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—44no—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5C2×D412yes—
253C2×C3×Dic5#4112yes—
254D3×Dic5—44no—
255C22×C3×D4C2×D511yescharacteristic
256C23×C3×C4—51no—
257C23×C3×C4—51no—
258C22×#67C2×D511yescharacteristic
259C22×#67C2×D511yescharacteristic
260C23×Dic3—51no—
261C23×Dic3C2×D511yescharacteristic
262C22×C4×D3—51no—
263C3×C4×D4—104no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C42—51no—
268C2×#217—51no—
269C2×#217—51no—
270C2×#217—51no—
271C2×#217C2×D511yescharacteristic
272#939Dic518yesdirect product factor
273C4×#67—104no—
274C4×#67—104no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4C2×D511yescharacteristic
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288C2×C4×Dic3—104no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C24×C5—31no—
296C24×C5C22×D311yescharacteristic
297C24×C5C22×D311yescharacteristic
298C2×C5×D4—22no—
299C2×C5×D4—22no—
300C2×C5×D4—34no—
301C2×C5×D4—34no—
302C2×C5×D4—62no—
303C2×C5×D4—62no—
304C2×C5×D4—62no—
305C2×C5×D4—62no—
306C2×C5×D4C4×D314yescomplemented
307C22×C4×C5—31no—
308C22×C4×C5—34no—
309C22×C4×C5—31no—
310C22×C4×C5—31no—
311C22×C4×C5—62no—
312C22×C4×C5—62no—
313C22×C4×C5C22×D311yescharacteristic
314C22×Dic5—22no—
315C22×Dic5—22no—
316C22×Dic5—22no—
317C22×Dic5—22no—
318C22×Dic5—22no—
319C22×Dic5—31no—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—62no—
324C22×Dic5—62no—
325C22×Dic5—62no—
326C22×Dic5—62no—
327C22×Dic5—62no—
328C22×Dic5—62no—
329C22×Dic5#6714yescomplemented
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D311yescharacteristic
334C5×C4⋊C4—34no—
335C5×C22⋊C4—34no—
336C5×C22⋊C4—34no—
337C22⋊Dic5—22no—
338C22⋊Dic5—22no—
339C22⋊Dic5—62no—
340C22⋊Dic5—62no—
341C22⋊Dic5—62no—
342C22⋊Dic5—62no—
343C22⋊Dic5—62no—
344C22⋊Dic5—62no—
345C4⋊Dic5—22no—
346C4⋊Dic5—62no—
347C4⋊Dic5—62no—
348C4⋊Dic5—62no—
349C4×Dic5—22no—
350C4×Dic5—34no—
351C4×Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C2×#121—31no—
356C2×C4×D4—51no—
357C2×C4×D4—151no—
358C2×C4×D4—151no—
359C22×C42—151no—
360#390—151no—
361#389—151no—
362#388—151no—
363#388—151no—
364#386—151no—
365#386—151no—
366#380—151no—
367C4×C4⋊C4—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5C4×D414yescomplemented
384C22×C3×C5C23×C411yescharacteristic
385C22×C3×C5C22×D411yescharacteristic
386C22×C3×C5C22×D411yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C22×C3×C5C2×#4111yescharacteristic
390C22×C3×C5C2×#4111yescharacteristic
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C3×C4×C5—22no—
399Dic15—22no—
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—22no—
404C3×Dic5—41no—
405C3×Dic5—41no—
406C3×Dic5#12114yescomplemented
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3C4×D414yescomplemented
410C24×C3C22×D511yescharacteristic
411C24×C3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C2×C3×D4—22no—
414C2×C3×D4—22no—
415C2×C3×D4C2×Dic514yescomplemented
416C22×C3×C4—51no—
417C22×C3×C4—54no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4—102no—
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—22no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—22no—
431C2×#67C2×Dic514yescomplemented
432C2×#67C2×Dic514yescomplemented
433C22×Dic3—22no—
434C22×Dic3—22no—
435C22×Dic3—51no—
436C22×Dic3—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3—102no—
440C22×Dic3—102no—
441C22×Dic3—102no—
442C22×Dic3C2×Dic514yescomplemented
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445C22×Dic3C22×D511yescharacteristic
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C3×C4⋊C4—102no—
450C3×C22⋊C4—102no—
451C3×C22⋊C4—102no—
452C3×C42—102no—
453#217—102no—
454#217—102no—
455#217—102no—
456#217C2×Dic514yescomplemented
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—102no—
460(C2×D3)⋊C4C2×Dic514yescomplemented
461Dic3⋊C4—102no—
462Dic3⋊C4—102no—
463Dic3⋊C4—102no—
464Dic3⋊C4C2×Dic514yescomplemented
465C4×Dic3—54no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—32no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—61no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5C2×C4×D312yes—
488C23×C5C2×C4×D312yes—
489C23×C5#23512yes—
490C23×C5C2×#6712yes—
491C23×C5C23×D311yescharacteristic
492C5×D4—28no—
493C5×D4—68no—
494C5×D4—68no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—32no—
498C2×C4×C5—32no—
499C2×C4×C5—32no—
500C2×C4×C5—32no—
501C2×C4×C5—32no—
502C2×C4×C5—68no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5C2×C4×D312yes—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—28no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—32no—
518C2×Dic5—32no—
519C2×Dic5—44no—
520C2×Dic5—68no—
521C2×Dic5—61no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—124no—
532C2×Dic5D3×D412yes—
533C2×Dic5#23712yes—
534C2×Dic5C2×#6712yes—
535C2×Dic5C2×#6712yes—
536C22×D4—31no—
537C22×D4—31no—
538C22×D4D3×D511yescharacteristic
539C23×C4—31no—
540C23×C4—51no—
541C23×C4—51no—
542C23×C4—151no—
543C23×C4—151no—
544#121—38no—
545C4×D4—104no—
546C4×D4—304no—
547C4×D4—304no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C42—51no—
564C2×C42—151no—
565C2×C42—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569C2×C42—304no—
570#95—151no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95—151no—
576C2×C3×C5—24no—
577C2×C3×C5—42no—
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C2×C4×D411yescharacteristic
580C2×C3×C5C4×#4111yescharacteristic
581C2×C3×C5C2×#12111yescharacteristic
582C2×C3×C5#52511yescharacteristic
583C2×C3×C5#52911yescharacteristic
584C2×C3×C5#53211yescharacteristic
585C5×D3—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3D4×D512yes—
597C23×C3#71112yes—
598C23×C3C22×Dic512yes—
599C23×C3C22×Dic512yes—
600C23×C3C23×D511yescharacteristic
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3C22×Dic512yes—
608C3×D4—28no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—52no—
612C2×C3×C4—52no—
613C2×C3×C4—52no—
614C2×C3×C4—52no—
615C2×C3×C4—108no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—204no—
625C2×C3×C4C22×Dic512yes—
626#67—28no—
627#67—28no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—28no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—108no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—101no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3D4×D512yes—
647C2×Dic3#71112yes—
648C2×Dic3C22×Dic512yes—
649C2×Dic3C22×Dic512yes—
650C2×Dic3C22×Dic512yes—
651C4×D3—204no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—22no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—41no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—62no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—121no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5C4×#6714yescomplemented
673C22×C5C22×C4×D311yescharacteristic
674C22×C5C2×#23511yescharacteristic
675C22×C5C2×D3×D411yescharacteristic
676C22×C5C2×#23711yescharacteristic
677C22×C5D3×#4111yescharacteristic
678C22×C5D3×#4111yescharacteristic
679C22×C5C22×#6711yescharacteristic
680C4×C5—22no—
681C4×C5—34no—
682C4×C5—62no—
683C4×C5—62no—
684Dic5—22no—
685Dic5—41no—
686Dic5—41no—
687Dic5—62no—
688Dic5—62no—
689Dic5—121no—
690Dic5—121no—
691Dic5#93914yesdirect product factor
692C24—31no—
693C24C2×D3×D511yescharacteristic
694C24C2×D3×D511yescharacteristic
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—34no—
698C2×D4—34no—
699C2×D4—62no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4D3×Dic514yescomplemented
704C22×C4—31no—
705C22×C4—34no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—51no—
709C22×C4—54no—
710C22×C4—51no—
711C22×C4—51no—
712C22×C4—51no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—151no—
721C22×C4—151no—
722C22×C4—151no—
723C22×C4—151no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4—302no—
728C22×C4—302no—
729C22×C4—302no—
730C22×C4C2×D3×D511yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—102no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C4⋊C4—302no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—102no—
739C22⋊C4—102no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—302no—
745C22⋊C4—302no—
746C42—102no—
747C42—154no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3D4×Dic514yescomplemented
767C22×C3C2×D4×D511yescharacteristic
768C22×C3C2×D4×D511yescharacteristic
769C22×C3C2×#71111yescharacteristic
770C22×C3C2×#71111yescharacteristic
771C22×C3D5×#4111yescharacteristic
772C22×C3D5×#4111yescharacteristic
773C22×C3C23×Dic511yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C3×C4—22no—
782C3×C4—54no—
783C3×C4—102no—
784C3×C4—201no—
785C3×C4—201no—
786Dic3—22no—
787Dic3—22no—
788Dic3—102no—
789Dic3—102no—
790Dic3—201no—
791Dic3—201no—
792Dic3D4×Dic514yescomplemented
793C2×C5—24no—
794C2×C5—42no—
795C2×C5—122no—
796C2×C5C4×#23711yescharacteristic
797C2×C5#553811yescharacteristic
798C2×C5C4×D3×D411yescharacteristic
799C2×C5#554711yescharacteristic
800C2×C5C2×C4×#6711yescharacteristic
801C2×C5C2×#93911yescharacteristic
802C2×C5#583211yescharacteristic
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—32no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23C2×D3×Dic512yes—
821C23C2×D3×Dic512yes—
822C23#678212yes—
823C23D5×#6712yes—
824C23C22×D3×D511yescharacteristic
825D4—28no—
826D4—68no—
827D4—68no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—52no—
836C2×C4—52no—
837C2×C4—52no—
838C2×C4—52no—
839C2×C4—68no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—108no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—152no—
854C2×C4—152no—
855C2×C4—204no—
856C2×C4—308no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—301no—
862C2×C4—301no—
863C2×C4—301no—
864C2×C4—301no—
865C2×C4—301no—
866C2×C4—301no—
867C2×C4—604no—
868C2×C4C2×D3×Dic512yes—
869C2×C3—24no—
870C2×C3—42no—
871C2×C3#6593011yescharacteristic
872C2×C3#6593411yescharacteristic
873C2×C3D5×#12111yescharacteristic
874C2×C3#6594011yescharacteristic
875C2×C3C2×D4×Dic511yescharacteristic
876C2×C3C2×D4×Dic511yescharacteristic
877C2×C3#41×Dic511yescharacteristic
878D3—42no—
879C5C4×#93911yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22Dic5×#6714yescomplemented
901C22D3×D4×D511yescharacteristic
902C22D5×#23711yescharacteristic
903C22D3×#71111yescharacteristic
904C22#9202411yescharacteristic
905C22C22×D3×Dic511yescharacteristic
906C22C2×#678211yescharacteristic
907C22C2×D5×#6711yescharacteristic
908C4—22no—
909C4—34no—
910C4—54no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—201no—
915C4—201no—
916C4—302no—
917C4—302no—
918C4—601no—
919C4—601no—
920C3Dic5×#12111yescharacteristic, complemented, Sylow
921C2—24no—
922C2—42no—
923C2—122no—
924C2D3×D4×Dic511yescharacteristic
925C2#1175477311yescharacteristic
926C2#1175479611yescharacteristic
927C2Dic5×#23711yescharacteristic
928C2#1175484911yescharacteristic
929C2D5×#93911yescharacteristic
930C2C2×Dic5×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#939C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C4×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. C2×Dic5×#67C2semidirect
5. C22×Dic3×Dic5C2semidirect
6. #11751321C2semidirect
7. #11749513C2semidirect
8. #11749501C2semidirect
9. #11749482C2semidirect
10. #11749479C2semidirect
11. Dic5×#217C2semidirect
12. Dic5×(C2×D3)⋊C4C2semidirect
13. #11748677C2semidirect
14. #11748675C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
29. C5×#939C4semidirect
61. C2×D4×Dic5D3semidirect
78. C2×C3×C5×D4C2×C4semidirect
91. C2×C5×#67C2×C4semidirect
92. C2×C5×#67C2×C4semidirect
95. C22×C5×Dic3C2×C4semidirect
104. C22×C3×Dic5D4semidirect
115. C5×#217C2×C4semidirect
116. C5×(C2×D3)⋊C4C2×C4semidirect
117. C5×Dic3⋊C4C2×C4semidirect
132. Dic3×Dic5D4semidirect
272. #939Dic5direct (N × H)
306. C2×C5×D4C4×D3semidirect
329. C22×Dic5#67semidirect
383. C22×C3×C5C4×D4semidirect
406. C3×Dic5#121semidirect
409. C5×Dic3C4×D4semidirect
415. C2×C3×D4C2×Dic5semidirect
431. C2×#67C2×Dic5semidirect
432. C2×#67C2×Dic5semidirect
442. C22×Dic3C2×Dic5semidirect
456. #217C2×Dic5semidirect
460. (C2×D3)⋊C4C2×Dic5semidirect
464. Dic3⋊C4C2×Dic5semidirect
672. C22×C5C4×#67semidirect
691. Dic5#939direct (N × H)
703. C2×D4D3×Dic5semidirect
752. C3×C5C4×#121semidirect
766. C22×C3D4×Dic5semidirect
792. Dic3D4×Dic5semidirect
879. C5C4×#939semidirect
900. C22Dic5×#67semidirect
920. C3Dic5×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9392
C2×C3×D4×Dic52
C2×Dic5×#672
C22×Dic3×Dic52
#117513212
#117495132
#117495012
#117494822
#117494792
Dic5×#2172
Dic5×(C2×D3)⋊C42
#117486772
#117486752
Dic5×Dic3⋊C42
Dic5×#1213
C4×#9395