Finite Group Databasebeta

← #67×C4⋊Dic5 #14327039

Subgroups — #67×C4⋊Dic5 #14327039

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#67C211yesmaximal, characteristic
2C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C212yesmaximal
4C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
5#11751313C211yesmaximal, characteristic, complemented
6#11749509C212yesmaximal, complemented
7#11748897C212yesmaximal, complemented
8#11748861C211yesmaximal, characteristic, complemented
9#11748786C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
11#11748677C212yesmaximal, complemented
12D4×C4⋊Dic5—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C22×D3×Dic5C2212yes—
18C2×#6719C2212yes—
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C5×#217C2211yescharacteristic
22C4×C5×#67C418yescomplemented
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic5—24no—
27C2×C3×C4⋊Dic5C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30Dic5×#67—28no—
31C2×Dic3⋊Dic5C2212yes—
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×Dic3×Dic5C2212yes—
36D3×C4⋊Dic5—24no—
37#91115C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40C4⋊C4×#67—51nomaximal, Hall
41C2×C4×C5×D4—31no—
42C2×D4×Dic5—32no—
43C22×C4⋊Dic5—31no—
44C22×C4⋊Dic5D311yescharacteristic, complemented
45#65501—31no—
46#65501—31no—
47#65274—32no—
48#65239—32no—
49#65239—32no—
50#65224—31no—
51C4×C4⋊Dic5—31no—
52C24×C3×C5C2311yescharacteristic
53C23×C5×D3C2311yescharacteristic
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5C2×C414yescomplemented
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C2×C5×#67C2×C414yes—
62C2×C5×#67D414yes—
63C2×C5×#67Q814yes—
64C22×C5×Dic3C2311yescharacteristic
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C2×C4×C5×D3—22no—
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3C2×C414yescomplemented
70C22×C3×Dic5—24no—
71C22×C3×Dic5—24no—
72C22×C3×Dic5—42no—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2312yes—
75C2×D3×Dic5—24no—
76C2×D3×Dic5—24no—
77C2×D3×Dic5—42no—
78#6719—24no—
79C4⋊Dic15—22no—
80C4⋊Dic15—22no—
81C5×#217C2×C414yescomplemented
82C5×(C2×D3)⋊C4C2×C414yescomplemented
83C5×Dic3⋊C4C2×C414yescomplemented
84C4×C5×Dic3C2×C414yescomplemented
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5—24no—
87C3×C4⋊Dic5D414yescomplemented
88Dic3⋊Dic5—24no—
89Dic3⋊Dic5—24no—
90Dic3⋊Dic5—42no—
91(C2×D3)⋊Dic5—24no—
92Dic3×Dic5—24no—
93C22×C3×C4⋊C4—51no—
94C2×C4×#67—52no—
95C2×C4×#67D511yescharacteristic
96C2×D3×C4⋊C4—51no—
97#5212—51no—
98#5210—52no—
99#4989—52no—
100#4987—51no—
101#4976—52no—
102#4975—51no—
103Dic3×C4⋊C4—51no—
104C22×C5×D4—31no—
105C23×C4×C5—31no—
106C23×C4×C5C2×D311yescharacteristic
107C23×Dic5—32no—
108C23×Dic5C2×D312yes—
109C4×C5×D4—38no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C22⋊C4—31no—
112C2×C5×C22⋊C4—31no—
113C2×C42×C5—31no—
114C2×C22⋊Dic5—32no—
115C2×C22⋊Dic5—32no—
116D4×Dic5—68no—
117C2×C4⋊Dic5—24no—
118C2×C4⋊Dic5—31no—
119C2×C4⋊Dic5—31no—
120C2×C4⋊Dic5—32no—
121C2×C4⋊Dic5—32no—
122C2×C4⋊Dic5—32no—
123C2×C4⋊Dic5—64no—
124C2×C4⋊Dic5C2×D311yescharacteristic
125C2×C4⋊Dic5C2×D312yes—
126C2×C4⋊Dic5C2×D311yescharacteristic
127C2×C4×Dic5—32no—
128#3963—32no—
129#3963—32no—
130#3963—32no—
131D4×C4⋊C4—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5C22×C412yes—
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×Q812yes—
139C23×C3×C5C2411yescharacteristic
140C22×C5×D3—21no—
141C22×C5×D3—21no—
142C22×C5×D3—21no—
143C22×C5×D3—21no—
144C22×C5×D3C22×C412yes—
145C22×C5×D3C2×D412yes—
146C22×C5×D3C2×Q812yes—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5#4112yes—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C5×#67C4⋊C4116yescomplemented
161C2×C5×Dic3—21no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3C22×C412yes—
166C2×C5×Dic3C22×C412yes—
167C2×C5×Dic3C22×C412yes—
168C2×C5×Dic3C2×D412yes—
169C2×C5×Dic3C2×Q812yes—
170C4×C5×D3—28no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—48no—
177C2×C3×Dic5C2×D414yes—
178D3×Dic5—48no—
179C23×C3×C4—52no—
180C23×C3×C4C2×D511yescharacteristic
181C22×#67C2×D511yescharacteristic
182C22×C4×D3—52no—
183C22×C4×D3C2×D511yescharacteristic
184C2×C3×C4⋊C4—51no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—52no—
187C2×C3×C4⋊C4—104no—
188C2×#217—52no—
189C2×#217C2×D511yescharacteristic
190C4×#67—108no—
191C4×#67Dic518yescomplemented
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D511yescharacteristic
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4C2×D511yescharacteristic
200C2×C4×Dic3—52no—
201C2×C4×Dic3C2×D511yescharacteristic
202D3×C4⋊C4—104no—
203C3⋊#95—52no—
204C3⋊#95—52no—
205C3⋊#95—52no—
206C24×C5—31no—
207C24×C5C22×D311yescharacteristic
208C2×C5×D4—34no—
209C2×C5×D4—34no—
210C2×C5×D4—34no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—31no—
214C22×C4×C5—31no—
215C22×C4×C5—31no—
216C22×C4×C5—34no—
217C22×C4×C5—62no—
218C22×C4×C5—62no—
219C22×C4×C5C4×D314yescomplemented
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—24no—
223C22×Dic5—24no—
224C22×Dic5—32no—
225C22×Dic5—32no—
226C22×Dic5—42no—
227C22×Dic5—64no—
228C22×Dic5—64no—
229C22×Dic5—122no—
230C22×Dic5C22×D312yes—
231C22×Dic5C22×D312yes—
232C5×C4⋊C4—34no—
233C5×C22⋊C4—34no—
234C5×C22⋊C4—34no—
235C42×C5—34no—
236C22⋊Dic5—64no—
237C22⋊Dic5—64no—
238C4⋊Dic5—22no—
239C4⋊Dic5—24no—
240C4⋊Dic5—64no—
241C4⋊Dic5—62no—
242C4⋊Dic5—62no—
243C4⋊Dic5—64no—
244C4⋊Dic5—122no—
245C4⋊Dic5#6714yesdirect product factor
246C4×Dic5—64no—
247C2×C4×D4—31no—
248C2×C4×D4—152no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—151no—
251#389—152no—
252#385—152no—
253#385—152no—
254#384—151no—
255#380—151no—
256#380—151no—
257C4×C4⋊C4—151no—
258C22×C3×C5—22no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—22no—
262C22×C3×C5—22no—
263C22×C3×C5—22no—
264C22×C3×C5C2×C4⋊C414yescomplemented
265C22×C3×C5C23×C411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×Q811yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C22×C3×C5H(5,𝔽2)11yescharacteristic
271C22×C3×C52−1+411yescharacteristic
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3—22no—
276C2×C5×D3—22no—
277C2×C5×D3—22no—
278C2×C5×D3C2×C4⋊C414yescomplemented
279C3×C4×C5—22no—
280C3×C4×C5C4×D414yescomplemented
281Dic15—42no—
282Dic15—42no—
283C3×Dic5—24no—
284C3×Dic5—42no—
285C5×Dic3—22no—
286C5×Dic3—22no—
287C5×Dic3C2×C4⋊C414yescomplemented
288C24×C3C22×D511yescharacteristic
289C23×D3C22×D511yescharacteristic
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—52no—
293C22×C3×C4—52no—
294C22×C3×C4—104no—
295C22×C3×C4—104no—
296C22×C3×C4—202no—
297C22×C3×C4C2×Dic514yescomplemented
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D511yescharacteristic
300C2×#67Dic1014yes—
301C2×#67D2014yes—
302C2×#67C2×Dic514yes—
303C22×Dic3—52no—
304C22×Dic3—52no—
305C22×Dic3C22×D511yescharacteristic
306C22×Dic3C22×D511yescharacteristic
307C22×Dic3C22×D511yescharacteristic
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—104no—
311C2×C4×D3—104no—
312C2×C4×D3—202no—
313C2×C4×D3C2×Dic514yescomplemented
314C3×C4⋊C4—54no—
315C3×C4⋊C4—104no—
316C3×C4⋊C4—102no—
317#217—104no—
318#217C2×Dic514yescomplemented
319(C2×D3)⋊C4—104no—
320(C2×D3)⋊C4C2×Dic514yescomplemented
321C4⋊Dic3—102no—
322C4⋊Dic3—102no—
323Dic3⋊C4—104no—
324Dic3⋊C4—104no—
325Dic3⋊C4—202no—
326Dic3⋊C4C2×Dic514yescomplemented
327C4×Dic3—104no—
328C4×Dic3C2×Dic514yescomplemented
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—32no—
334C23×C5—32no—
335C23×C5—32no—
336C23×C5—61no—
337C23×C5—61no—
338C23×C5—61no—
339C23×C5—61no—
340C23×C5C2×C4×D312yes—
341C23×C5D3×D412yes—
342C23×C5D3×Q812yes—
343C23×C5C23×D311yescharacteristic
344C5×D4—316no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—28no—
348C2×C4×C5—32no—
349C2×C4×C5—32no—
350C2×C4×C5—32no—
351C2×C4×C5—32no—
352C2×C4×C5—32no—
353C2×C4×C5—61no—
354C2×C4×C5—61no—
355C2×C4×C5—61no—
356C2×C4×C5—61no—
357C2×C4×C5—68no—
358C2×C4×C5C2×C4×D312yes—
359C2×C4×C5C2×C4×D312yes—
360C2×C4×C5#23512yes—
361C2×C4×C5C2×#6712yes—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—48no—
368C2×Dic5—62no—
369C2×Dic5—62no—
370C2×Dic5—62no—
371C2×Dic5—62no—
372C2×Dic5—62no—
373C2×Dic5—62no—
374C2×Dic5—128no—
375C2×Dic5C2×#6714yes—
376C22×D4—31no—
377C23×C4—31no—
378C23×C4—52no—
379C23×C4—152no—
380C23×C4D3×D511yescharacteristic
381C4×D4—38no—
382C4×D4—308no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—51no—
386C2×C4⋊C4—52no—
387C2×C4⋊C4—104no—
388C2×C4⋊C4—152no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—151no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—152no—
393C2×C4⋊C4—304no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—152no—
397C2×C22⋊C4—152no—
398C2×C42—31no—
399C2×C42—152no—
400#95—152no—
401#95—152no—
402#95—152no—
403C2×C3×C5—24no—
404C2×C3×C5C22×C4⋊C411yescharacteristic
405C2×C3×C5C2×C4×D411yescharacteristic
406C2×C3×C5#52011yescharacteristic
407C2×C3×C5D4211yescharacteristic
408C2×C3×C5#54711yescharacteristic
409C2×C3×C5D4×Q811yescharacteristic
410C2×C3×C5#55411yescharacteristic
411C5×D3—24no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3C2×Dic1012yes—
417C23×C3C2×D2012yes—
418C23×C3C22×Dic512yes—
419C23×C3C23×D511yescharacteristic
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3C2×Dic1012yes—
425C22×D3C2×D2012yes—
426C22×D3C22×Dic512yes—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—28no—
430C2×C3×C4—54no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—208no—
437C2×C3×C4D4×D512yes—
438C2×C3×C4#71112yes—
439C2×C3×C4C22×Dic512yes—
440C2×C3×C4C22×Dic512yes—
441#67C4⋊Dic5116yesdirect product factor
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—102no—
447C2×Dic3—102no—
448C2×Dic3—102no—
449C2×Dic3—102no—
450C2×Dic3—102no—
451C2×Dic3—102no—
452C2×Dic3C2×Dic1012yes—
453C2×Dic3C2×D2012yes—
454C2×Dic3C22×Dic512yes—
455C2×Dic3C22×Dic512yes—
456C2×Dic3C22×Dic512yes—
457C4×D3—28no—
458C4×D3—208no—
459C22×C5—22no—
460C22×C5—22no—
461C22×C5—22no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—34no—
466C22×C5—62no—
467C22×C5—62no—
468C22×C5—62no—
469C22×C5—62no—
470C22×C5—62no—
471C22×C5—62no—
472C22×C5D3×C4⋊C414yescomplemented
473C22×C5C22×C4×D311yescharacteristic
474C22×C5C2×#23511yescharacteristic
475C22×C5C2×D3×D411yescharacteristic
476C22×C5#100411yescharacteristic
477C22×C5C2×D3×Q811yescharacteristic
478C22×C5#100711yescharacteristic
479C22×C5C22×#6711yescharacteristic
480C4×C5—22no—
481C4×C5—34no—
482C4×C5—62no—
483C4×C5—62no—
484C4×C5C4×#6714yescomplemented
485Dic5—24no—
486Dic5—42no—
487Dic5—122no—
488Dic5—122no—
489C24—31no—
490C24C2×D3×D511yescharacteristic
491C2×D4—34no—
492C2×D4—34no—
493C2×D4—34no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—34no—
500C22×C4—52no—
501C22×C4—52no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—104no—
505C22×C4—104no—
506C22×C4—152no—
507C22×C4—152no—
508C22×C4—202no—
509C22×C4—304no—
510C22×C4—304no—
511C22×C4—602no—
512C22×C4D3×Dic514yescomplemented
513C22×C4C2×D3×D511yescharacteristic
514C22×C4C2×D3×D511yescharacteristic
515C4⋊C4—34no—
516C4⋊C4—54no—
517C4⋊C4—104no—
518C4⋊C4—102no—
519C4⋊C4—304no—
520C4⋊C4—304no—
521C4⋊C4—302no—
522C4⋊C4—302no—
523C4⋊C4—602no—
524C22⋊C4—34no—
525C22⋊C4—34no—
526C22⋊C4—304no—
527C22⋊C4—304no—
528C42—34no—
529C42—304no—
530C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3C2×C4⋊Dic514yescomplemented
538C22×C3C22×Dic1011yescharacteristic
539C22×C3C22×D2011yescharacteristic
540C22×C3C2×D4×D511yescharacteristic
541C22×C3C2×#71111yescharacteristic
542C22×C3#414911yescharacteristic
543C22×C3#415011yescharacteristic
544C22×C3C23×Dic511yescharacteristic
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—22no—
551C2×D3C2×C4⋊Dic514yescomplemented
552C3×C4—22no—
553C3×C4—104no—
554C3×C4—202no—
555C3×C4D4×Dic514yescomplemented
556Dic3—22no—
557Dic3—22no—
558Dic3—202no—
559Dic3—202no—
560Dic3C2×C4⋊Dic514yescomplemented
561C2×C5—24no—
562C2×C5—64no—
563C2×C5C2×D3×C4⋊C411yescharacteristic
564C2×C5#550411yescharacteristic
565C2×C5#550711yescharacteristic
566C2×C5#551111yescharacteristic
567C2×C5C2×C4×#6711yescharacteristic
568C2×C5D4×#6711yescharacteristic
569C2×C5Q8×#6711yescharacteristic
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—32no—
575C23—32no—
576C23—32no—
577C23—61no—
578C23—61no—
579C23—61no—
580C23—61no—
581C23D3×Dic1012yes—
582C23D3×D2012yes—
583C23C2×D3×Dic512yes—
584C23C22×D3×D511yescharacteristic
585D4—316no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—28no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—32no—
592C2×C4—32no—
593C2×C4—32no—
594C2×C4—54no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—68no—
600C2×C4—102no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—208no—
606C2×C4—302no—
607C2×C4—302no—
608C2×C4—302no—
609C2×C4—302no—
610C2×C4—302no—
611C2×C4—302no—
612C2×C4—608no—
613C2×C4C2×D3×Dic512yes—
614C2×C4C2×D3×Dic512yes—
615C2×C4#678212yes—
616C2×C4D5×#6712yes—
617C2×C3—24no—
618C2×C3D4×Dic1011yescharacteristic
619C2×C3#6587711yescharacteristic
620C2×C3D4×D2011yescharacteristic
621C2×C3#6588911yescharacteristic
622C2×C3C22×C4⋊Dic511yescharacteristic
623C2×C3C2×D4×Dic511yescharacteristic
624C2×C3#6616111yescharacteristic
625D3—24no—
626C5C4⋊C4×#6711yescharacteristic, complemented, Sylow
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—34no—
634C22—62no—
635C22—62no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22D3×C4⋊Dic514yescomplemented
641C22C2×D3×Dic1011yescharacteristic
642C22#9200411yescharacteristic
643C22C2×D3×D2011yescharacteristic
644C22#9201711yescharacteristic
645C22C22×D3×Dic511yescharacteristic
646C22C2×#678211yescharacteristic
647C22C2×D5×#6711yescharacteristic
648C4—22no—
649C4—34no—
650C4—62no—
651C4—62no—
652C4—104no—
653C4—202no—
654C4—602no—
655C4—602no—
656C4Dic5×#6714yescomplemented
657C3D4×C4⋊Dic511yescharacteristic, complemented, Sylow
658C2—24no—
659C2—64no—
660C2#67×Dic1011yescharacteristic
661C2C2×D3×C4⋊Dic511yescharacteristic
662C2#1175436111yescharacteristic
663C2#1175449211yescharacteristic
664C2#1175449411yescharacteristic
665C2#67×D2011yescharacteristic
666C2C2×Dic5×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic5C2semidirect
4. C2×D3×C4⋊Dic5C2semidirect
5. #11751313C2semidirect
6. #11749509C2semidirect
7. #11748897C2semidirect
8. #11748861C2semidirect
9. #11748786C2semidirect
10. Dic3×C4⋊Dic5C2semidirect
11. #11748677C2semidirect
22. C4×C5×#67C4semidirect
44. C22×C4⋊Dic5D3semidirect
56. C22×C3×C4×C5C2×C4semidirect
69. C2×C4×C5×D3C2×C4semidirect
81. C5×#217C2×C4semidirect
82. C5×(C2×D3)⋊C4C2×C4semidirect
83. C5×Dic3⋊C4C2×C4semidirect
84. C4×C5×Dic3C2×C4semidirect
87. C3×C4⋊Dic5D4semidirect
160. C5×#67C4⋊C4semidirect
191. C4×#67Dic5semidirect
219. C22×C4×C5C4×D3semidirect
245. C4⋊Dic5#67direct (N × H)
264. C22×C3×C5C2×C4⋊C4semidirect
278. C2×C5×D3C2×C4⋊C4semidirect
280. C3×C4×C5C4×D4semidirect
287. C5×Dic3C2×C4⋊C4semidirect
297. C22×C3×C4C2×Dic5semidirect
313. C2×C4×D3C2×Dic5semidirect
318. #217C2×Dic5semidirect
320. (C2×D3)⋊C4C2×Dic5semidirect
326. Dic3⋊C4C2×Dic5semidirect
328. C4×Dic3C2×Dic5semidirect
441. #67C4⋊Dic5direct (N × H)
472. C22×C5D3×C4⋊C4semidirect
484. C4×C5C4×#67semidirect
512. C22×C4D3×Dic5semidirect
530. C3×C5D4×C4⋊C4semidirect
537. C22×C3C2×C4⋊Dic5semidirect
551. C2×D3C2×C4⋊Dic5semidirect
555. C3×C4D4×Dic5semidirect
560. Dic3C2×C4⋊Dic5semidirect
626. C5C4⋊C4×#67semidirect
640. C22D3×C4⋊Dic5semidirect
656. C4Dic5×#67semidirect
657. C3D4×C4⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#672
C22×C3×C4⋊Dic52
C2×Dic5×#672
C2×D3×C4⋊Dic52
#117513132
#117495092
#117488972
#117488612
#117487862
Dic3×C4⋊Dic52
#117486772
D4×C4⋊Dic53
C4⋊C4×#675