Finite Group Databasebeta

← D3×#65234 #14320520

Subgroups — D3×#65234 #14320520

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C211yesmaximal, characteristic
3C2×D3×C22⋊Dic5C211yesmaximal, characteristic
4C2×D3×#683C211yesmaximal, characteristic, complemented
5C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
6#11751046C211yesmaximal, characteristic, complemented
7C3×#65234C211yesmaximal, characteristic, complemented
8#11749486C211yesmaximal, characteristic, complemented
9#11749481C211yesmaximal, characteristic, complemented
10D3×#3963C211yesmaximal, characteristic, complemented
11D3×#3963C211yesmaximal, characteristic, complemented
12#11748723C211yesmaximal, characteristic, complemented
13#11748721C211yesmaximal, characteristic, complemented
14#11748717C211yesmaximal, characteristic, complemented
15#11748715C211yesmaximal, characteristic, complemented
16C2×#65234—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6712C2211yescharacteristic, complemented
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C5×#217C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×D3×C22⋊C4—24no—
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37D3×C22⋊Dic5—24no—
38D3×C22⋊Dic5C418yescomplemented
39C2×#6669C2211yescharacteristic, complemented
40C2×#6668C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47D3×#683—24no—
48C4×D3×Dic5—24no—
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57D3×#388—51nomaximal, Hall
58C22×C5×C22⋊C4—31no—
59C22×C22⋊Dic5—31no—
60C22×C22⋊Dic5—31no—
61C22×#683—31no—
62C22×C4×Dic5—31no—
63C2×#3963—31no—
64C2×#3963—31no—
65#65234—31no—
66#65234—31no—
67#65234—31no—
68#65234—31no—
69#65234—31no—
70#65234—31no—
71#65234—31no—
72#65234D311yescharacteristic, direct product factor
73C24×C3×C5C2311yescharacteristic
74C23×C5×D3—22no—
75C23×C5×D3—22no—
76C23×C5×D3—22no—
77C23×C5×D3—22no—
78C23×C5×D3—22no—
79C23×C5×D3—22no—
80C23×C5×D3C2×C414yes—
81C23×C5×D3C2311yescharacteristic
82C23×C5×D3C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—22no—
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3D414yes—
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5—22no—
104C2×D3×Dic5—22no—
105C2×D3×Dic5—22no—
106C2×D3×Dic5—22no—
107C2×D3×Dic5—22no—
108C2×D3×Dic5—22no—
109C2×D3×Dic5—22no—
110C2×D3×Dic5C2×C414yes—
111C2×D3×Dic5C2×C414yes—
112C2×D3×Dic5D414yes—
113C3×C5×C22⋊C4—22no—
114#6719—22no—
115#6719C2×C414yescomplemented
116#6712—22no—
117C4×Dic15—22no—
118C5×#217—22no—
119C5×(C2×D3)⋊C4—22no—
120C5×(C2×D3)⋊C4—22no—
121C3×C22⋊Dic5—22no—
122C3×C22⋊Dic5C2×C414yescomplemented
123C3×#683—22no—
124C3×C4×Dic5—22no—
125#6669—22no—
126#6668—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5C2×C414yescomplemented
130(C2×D3)⋊Dic5C2×C414yescomplemented
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133C2×D3×C4⋊C4—51no—
134C2×D3×C22⋊C4—51no—
135C2×D3×C22⋊C4—51no—
136C2×D3×C22⋊C4D511yescharacteristic
137C2×C42×D3—51no—
138C3×#388—51no—
139#4990—51no—
140#4951—51no—
141#4945—51no—
142#4944—51no—
143#4940—51no—
144#4670—51no—
145#4669—51no—
146D3×#95—51no—
147D3×#95—51no—
148C25×C5—31no—
149C23×C4×C5—31no—
150C23×C4×C5—31no—
151C23×Dic5—31no—
152C23×Dic5—31no—
153C23×Dic5—31no—
154C23×Dic5—31no—
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—64no—
159C2×C5×C22⋊C4C2×D311yescharacteristic
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—38no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—64no—
168C2×C22⋊Dic5C2×D311yescharacteristic
169C2×C22⋊Dic5C2×D311yescharacteristic
170C2×#683—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×#683—64no—
174C2×#683C2×D311yescharacteristic, complemented
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—64no—
179C2×C4×Dic5C2×D311yescharacteristic, complemented
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic, complemented
187#3963C2×D311yescharacteristic, complemented
188C2×#388—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×C5C22×C412yes—
196C23×C3×C5C2411yescharacteristic
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C5×D3—28no—
204C22×C5×D3—28no—
205C22×C5×D3—28no—
206C22×C5×D3—44no—
207C22×C5×D3—44no—
208C22×C5×D3—44no—
209C22×C5×D3—44no—
210C22×C5×D3C22×C412yes—
211C22×C5×D3C22×C412yes—
212C22×C5×D3C2×D412yes—
213C22×C5×D3C2×D412yes—
214C22×C5×D3#4112yes—
215C22×C5×D3#4112yes—
216C22×C5×D3#4112yes—
217C22×C5×D3#4112yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15C22×C412yes—
234C2×Dic15C22×C412yes—
235C2×Dic15C2×D412yes—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3C2×D412yes—
242C4×C5×D3—28no—
243C4×C5×D3—44no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5C22×C412yes—
254C2×C3×Dic5C22×C412yes—
255C2×C3×Dic5C2×D412yes—
256D3×Dic5—28no—
257D3×Dic5—28no—
258D3×Dic5—28no—
259D3×Dic5—44no—
260C24×D3C2×D511yescharacteristic
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×C4×D3—51no—
265C22×C4×D3C2×D511yescharacteristic
266C22×C4×D3C2×D511yescharacteristic
267C2×C3×C4⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C42—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217C2×D511yescharacteristic
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×C4⋊Dic3—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287D3×C4⋊C4—104no—
288D3×C22⋊C4—24no—
289D3×C22⋊C4—58no—
290D3×C22⋊C4—104no—
291C42×D3—104no—
292C3×#95—51no—
293C3×#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95—51no—
300C24×C5—31no—
301C24×C5—34no—
302C24×C5—31no—
303C24×C5—62no—
304C24×C5—62no—
305C24×C5—62no—
306C24×C5—62no—
307C24×C5—62no—
308C24×C5—62no—
309C24×C5C22×D311yescharacteristic
310C22×C4×C5—31no—
311C22×C4×C5—34no—
312C22×C4×C5—31no—
313C22×C4×C5—62no—
314C22×C4×C5—62no—
315C22×C4×C5—62no—
316C22×C4×C5—62no—
317C22×C4×C5—62no—
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D311yescharacteristic
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—34no—
324C22×Dic5—34no—
325C22×Dic5—34no—
326C22×Dic5—31no—
327C22×Dic5—62no—
328C22×Dic5—62no—
329C22×Dic5—62no—
330C22×Dic5—62no—
331C22×Dic5—62no—
332C22×Dic5—62no—
333C22×Dic5—62no—
334C22×Dic5—62no—
335C22×Dic5—62no—
336C22×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C5×C22⋊C4—22no—
341C5×C22⋊C4—62no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—62no—
344C22⋊Dic5—22no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—62no—
349C22⋊Dic5—62no—
350C22⋊Dic5—62no—
351C22⋊Dic5C4×D314yescomplemented
352#683—22no—
353#683—62no—
354#683—62no—
355#683—62no—
356C4×Dic5—22no—
357C4×Dic5—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×C4⋊C4—151no—
361C22×C22⋊C4—31no—
362C22×C22⋊C4—151no—
363C22×C22⋊C4—151no—
364C22×C42—151no—
365#388—51no—
366#388—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#388—151no—
372#388—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5C23×C411yescharacteristic
383C22×C3×C5C22×D411yescharacteristic
384C22×C3×C5C22×D411yescharacteristic
385C22×C3×C5C2×#4111yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C2×C5×D3—22no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—416no—
397C2×C5×D3#11714yes—
398C2×C5×D3C4×D414yes—
399C2×C5×D3C4×D414yes—
400C2×C5×D3#12114yes—
401C2×C5×D3#12314yes—
402C2×C5×D3#12414yes—
403C2×C5×D3#12614yes—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—22no—
408Dic15—22no—
409Dic15—41no—
410C3×Dic5—22no—
411C3×Dic5—22no—
412C3×Dic5—22no—
413C3×Dic5—41no—
414C5×Dic3—22no—
415C5×Dic3—41no—
416C24×C3C22×D511yescharacteristic
417C23×D3—22no—
418C23×D3—22no—
419C23×D3—22no—
420C23×D3—22no—
421C23×D3—22no—
422C23×D3—22no—
423C23×D3C4×D514yes—
424C23×D3C22×D511yescharacteristic
425C23×D3C22×D511yescharacteristic
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—22no—
441C2×C4×D3—22no—
442C2×C4×D3—22no—
443C2×C4×D3—54no—
444C2×C4×D3—54no—
445C2×C4×D3—54no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C2×C4×D3—102no—
450C2×C4×D3—102no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3C22⋊D514yes—
456C3×C4⋊C4—102no—
457C3×C22⋊C4—22no—
458C3×C22⋊C4—54no—
459C3×C22⋊C4—102no—
460C3×C42—102no—
461#217—22no—
462#217—54no—
463#217—102no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—54no—
467(C2×D3)⋊C4—54no—
468(C2×D3)⋊C4—102no—
469(C2×D3)⋊C4—102no—
470C4⋊Dic3—102no—
471Dic3⋊C4—102no—
472Dic3⋊C4—102no—
473C4×Dic3—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—32no—
483C23×C5—32no—
484C23×C5—32no—
485C23×C5—32no—
486C23×C5—32no—
487C23×C5—32no—
488C23×C5—32no—
489C23×C5—32no—
490C23×C5—68no—
491C23×C5—68no—
492C23×C5—68no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5—61no—
496C23×C5—61no—
497C23×C5—61no—
498C23×C5—61no—
499C23×C5—124no—
500C23×C5—124no—
501C23×C5—124no—
502C23×C5—124no—
503C23×C5C2×C4×D312yes—
504C23×C5C23×D311yescharacteristic
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—32no—
511C2×C4×C5—68no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—124no—
518C2×C4×C5D3×D412yes—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—32no—
529C2×Dic5—32no—
530C2×Dic5—32no—
531C2×Dic5—68no—
532C2×Dic5—68no—
533C2×Dic5—68no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—124no—
544C2×Dic5C2×C4×D312yes—
545C2×Dic5C2×C4×D312yes—
546C2×Dic5D3×D412yes—
547C25—31no—
548C23×C4—31no—
549C23×C4—31no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553C23×C4—151no—
554C2×C4⋊C4—51no—
555C2×C4⋊C4—151no—
556C2×C4⋊C4—151no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—304no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—31no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—64no—
565C2×C22⋊C4—158no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C22⋊C4—151no—
572C2×C22⋊C4—304no—
573C2×C22⋊C4D3×D511yescharacteristic
574C2×C42—51no—
575C2×C42—151no—
576C2×C42—151no—
577C2×C42—151no—
578C2×C42—304no—
579#95—51no—
580#95—51no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95—151no—
585#95—151no—
586#95—151no—
587C2×C3×C5—42no—
588C2×C3×C5C2×#11711yescharacteristic
589C2×C3×C5C2×C4×D411yescharacteristic
590C2×C3×C5C2×C4×D411yescharacteristic
591C2×C3×C5C2×#12111yescharacteristic
592C2×C3×C5C2×#12311yescharacteristic
593C2×C3×C5C2×#12411yescharacteristic
594C2×C3×C5C2×#12611yescharacteristic
595C5×D3—42no—
596C5×D3#38818yescomplemented
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3C2×C4×D512yes—
604C23×C3C23×D511yescharacteristic
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—28no—
612C22×D3—28no—
613C22×D3—28no—
614C22×D3—44no—
615C22×D3—44no—
616C22×D3—44no—
617C22×D3—44no—
618C22×D3C2×C4×D512yes—
619C22×D3C2×C4×D512yes—
620C22×D3#70912yes—
621C22×D3D4×D512yes—
622C22×D3#71112yes—
623C22×D3#71112yes—
624C22×D3#71112yes—
625C22×D3C2×C22⋊D512yes—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—52no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4C2×C22⋊D512yes—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—52no—
650C2×Dic3—52no—
651C2×Dic3—52no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3C2×C22⋊D512yes—
662C4×D3—28no—
663C4×D3—44no—
664C4×D3—108no—
665C4×D3—108no—
666C4×D3—108no—
667C4×D3—204no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—34no—
672C22×C5—34no—
673C22×C5—34no—
674C22×C5—34no—
675C22×C5—34no—
676C22×C5—34no—
677C22×C5—34no—
678C22×C5—41no—
679C22×C5—41no—
680C22×C5—41no—
681C22×C5—41no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—1216no—
686C22×C5—121no—
687C22×C5—121no—
688C22×C5—121no—
689C22×C5—121no—
690C22×C5C22×C4×D311yescharacteristic
691C22×C5C2×D3×D411yescharacteristic
692C22×C5C2×D3×D411yescharacteristic
693C22×C5D3×#4111yescharacteristic
694C22×C5D3×#4111yescharacteristic
695C22×C5D3×#4111yescharacteristic
696C22×C5D3×#4111yescharacteristic
697C4×C5—22no—
698C4×C5—41no—
699C4×C5—62no—
700C4×C5—121no—
701Dic5—22no—
702Dic5—22no—
703Dic5—22no—
704Dic5—41no—
705Dic5—62no—
706Dic5—62no—
707Dic5—62no—
708Dic5—121no—
709C24—31no—
710C24—34no—
711C24—31no—
712C24—62no—
713C24—62no—
714C24—62no—
715C24—62no—
716C24—62no—
717C24—62no—
718C24C2×D3×D511yescharacteristic
719C22×C4—31no—
720C22×C4—34no—
721C22×C4—31no—
722C22×C4—51no—
723C22×C4—51no—
724C22×C4—51no—
725C22×C4—51no—
726C22×C4—62no—
727C22×C4—62no—
728C22×C4—62no—
729C22×C4—62no—
730C22×C4—62no—
731C22×C4—154no—
732C22×C4—154no—
733C22×C4—154no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4C2×D3×D511yescharacteristic
748C22×C4C2×D3×D511yescharacteristic
749C4⋊C4—102no—
750C4⋊C4—302no—
751C4⋊C4—302no—
752C4⋊C4—302no—
753C22⋊C4—22no—
754C22⋊C4—54no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—102no—
759C22⋊C4—154no—
760C22⋊C4—154no—
761C22⋊C4—154no—
762C22⋊C4—302no—
763C22⋊C4—302no—
764C22⋊C4—302no—
765C42—102no—
766C42—302no—
767C42—302no—
768C42—302no—
769C3×C5C2×#38811yescharacteristic, complemented, Hall
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3C22×C4×D511yescharacteristic
778C22×C3C2×#70911yescharacteristic
779C22×C3C2×D4×D511yescharacteristic
780C22×C3C2×#71111yescharacteristic
781C22×C3C2×#71111yescharacteristic
782C22×C3C2×#71111yescharacteristic
783C22×C3C22×C22⋊D511yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—416no—
792C2×D3#402314yes—
793C2×D3#402514yes—
794C2×D3#402714yes—
795C2×D3#402914yes—
796C2×D3C4×C22⋊D514yes—
797C2×D3#408214yes—
798C2×D3#408514yes—
799C3×C4—22no—
800C3×C4—41no—
801C3×C4—102no—
802C3×C4—102no—
803C3×C4—102no—
804C3×C4—201no—
805Dic3—22no—
806Dic3—41no—
807Dic3—102no—
808Dic3—102no—
809Dic3—102no—
810Dic3—201no—
811C2×C5—38no—
812C2×C5—42no—
813C2×C5—122no—
814C2×C5D3×#11711yescharacteristic
815C2×C5C4×D3×D411yescharacteristic
816C2×C5C4×D3×D411yescharacteristic
817C2×C5D3×#12111yescharacteristic
818C2×C5D3×#12311yescharacteristic
819C2×C5D3×#12411yescharacteristic
820C2×C5D3×#12611yescharacteristic
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—32no—
828C23—32no—
829C23—32no—
830C23—32no—
831C23—32no—
832C23—32no—
833C23—32no—
834C23—32no—
835C23—68no—
836C23—68no—
837C23—68no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—124no—
845C23—124no—
846C23—124no—
847C23—124no—
848C23C4×D3×D512yes—
849C23C22×D3×D511yescharacteristic
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—32no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—52no—
859C2×C4—68no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—124no—
875C2×C4—152no—
876C2×C4—152no—
877C2×C4—152no—
878C2×C4—308no—
879C2×C4—308no—
880C2×C4—308no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—604no—
891C2×C4D3×C22⋊D512yes—
892C2×C3—42no—
893C2×C3C2×#402311yescharacteristic
894C2×C3C2×#402511yescharacteristic
895C2×C3C2×#402711yescharacteristic
896C2×C3C2×#402911yescharacteristic
897C2×C3C2×C4×C22⋊D511yescharacteristic
898C2×C3C2×#408211yescharacteristic
899C2×C3C2×#408511yescharacteristic
900D3—42no—
901D3#6523418yesdirect product factor
902C5D3×#38811yescharacteristic, complemented, Sylow
903C22—22no—
904C22—22no—
905C22—22no—
906C22—34no—
907C22—34no—
908C22—34no—
909C22—34no—
910C22—34no—
911C22—34no—
912C22—34no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—1216no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22C2×C4×D3×D511yescharacteristic
926C22D3×#70911yescharacteristic
927C22D3×D4×D511yescharacteristic
928C22D3×#71111yescharacteristic
929C22D3×#71111yescharacteristic
930C22D3×#71111yescharacteristic
931C22C2×D3×C22⋊D511yescharacteristic
932C4—22no—
933C4—41no—
934C4—62no—
935C4—102no—
936C4—102no—
937C4—102no—
938C4—121no—
939C4—201no—
940C4—302no—
941C4—302no—
942C4—302no—
943C4—601no—
944C3C2×#6523411yescharacteristic, complemented, Sylow
945C2—38no—
946C2—42no—
947C2—122no—
948C2D3×#402311yescharacteristic
949C2D3×#402511yescharacteristic
950C2D3×#402711yescharacteristic
951C2D3×#402911yescharacteristic
952C2C4×D3×C22⋊D511yescharacteristic
953C2D3×#408211yescharacteristic
954C2D3×#408511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×D3×#683C2semidirect
5. C2×C4×D3×Dic5C2semidirect
6. #11751046C2semidirect
7. C3×#65234C2semidirect
8. #11749486C2semidirect
9. #11749481C2semidirect
10. D3×#3963C2semidirect
11. D3×#3963C2semidirect
12. #11748723C2semidirect
13. #11748721C2semidirect
14. #11748717C2semidirect
15. #11748715C2semidirect
27. C2×#6712C22semidirect
28. C2×C4×Dic15C22semidirect
35. C2×C3×#683C22semidirect
36. C2×C3×C4×Dic5C22semidirect
38. D3×C22⋊Dic5C4semidirect
39. C2×#6669C22semidirect
40. C2×#6668C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. #65234D3direct (N × H)
115. #6719C2×C4semidirect
122. C3×C22⋊Dic5C2×C4semidirect
129. (C2×D3)⋊Dic5C2×C4semidirect
130. (C2×D3)⋊Dic5C2×C4semidirect
174. C2×#683C2×D3semidirect
179. C2×C4×Dic5C2×D3semidirect
186. #3963C2×D3semidirect
187. #3963C2×D3semidirect
351. C22⋊Dic5C4×D3semidirect
596. C5×D3#388semidirect
769. C3×C5C2×#388semidirect
901. D3#65234direct (N × H)
902. C5D3×#388semidirect
944. C3C2×#65234semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C22⋊C42
C2×D3×C22⋊Dic52
C2×D3×#6832
C2×C4×D3×Dic52
#117510462
C3×#652342
#117494862
#117494812
D3×#39632
#117487232
#117487212
#117487172
#117487152
C2×#652343
D3×#3885