Finite Group Databasebeta

← D3×#64942 #14320367

Subgroups — D3×#64942 #14320367

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic5C211yesmaximal, characteristic
2C2×D3×#683C211yesmaximal, characteristic
3C2×C4×D3×Dic5C211yesmaximal, characteristic
4#11750754C211yesmaximal, characteristic, complemented
5C5×D3×#95C211yesmaximal, characteristic
6C3×#64942C211yesmaximal, characteristic, complemented
7D3×#3963C211yesmaximal, characteristic
8D3×#3963C211yesmaximal, characteristic
9D3×#3963C211yesmaximal, characteristic
10#11748821C211yesmaximal, characteristic, complemented
11#11748814C211yesmaximal, characteristic, complemented
12#11748697C211yesmaximal, characteristic, complemented
13#11748688C211yesmaximal, characteristic, complemented
14#11748659C211yesmaximal, characteristic, complemented
15#11748656C211yesmaximal, characteristic, complemented
16C2×#64942—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×Dic3×Dic5C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36D3×C4⋊Dic5C418yescomplemented
37D3×#683—24no—
38C4×D3×Dic5—24no—
39C3×C5×#95C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55D3×#387—51nomaximal, Hall
56C22×C4⋊Dic5—31no—
57C22×#683—31no—
58C22×C4×Dic5—31no—
59C2×C5×#95—31no—
60C2×#3963—31no—
61C2×#3963—31no—
62C2×#3963—31no—
63#64942—31no—
64#64942—31no—
65#64942—31no—
66#64942—31no—
67#64942—31no—
68#64942—31no—
69#64942—31no—
70#64942D311yescharacteristic, direct product factor
71C23×C5×D3C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3—22no—
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3—22no—
89C2×C4×C5×D3C2×C414yes—
90C2×C4×C5×D3D414yes—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×D3×Dic5—22no—
96C2×D3×Dic5—22no—
97C2×D3×Dic5—22no—
98C2×D3×Dic5—22no—
99C2×D3×Dic5—22no—
100C2×D3×Dic5—22no—
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5—22no—
104C2×D3×Dic5C2×C414yes—
105C2×D3×Dic5C2×C414yes—
106C2×D3×Dic5Q814yes—
107C4⋊Dic15C2×C414yescomplemented
108#6712—22no—
109C4×Dic15—22no—
110C3×C4⋊Dic5C2×C414yescomplemented
111C3×#683—22no—
112C3×C4×Dic5—22no—
113Dic3⋊Dic5C2×C414yescomplemented
114Dic3⋊Dic5C2×C414yescomplemented
115#6669—22no—
116#6668—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119C2×D3×C4⋊C4—51no—
120C2×D3×C4⋊C4—51no—
121C2×C42×D3—51no—
122C3×#387—51no—
123#4980—51no—
124#4978—51no—
125#4933—51no—
126D3×#95—51no—
127D3×#95—51no—
128D3×#95—51no—
129D3×#95D511yescharacteristic
130#4655—51no—
131#4654—51no—
132#4653—51no—
133#4652—51no—
134C23×C4×C5—31no—
135C23×C4×C5—31no—
136C23×C4×C5—31no—
137C23×Dic5—31no—
138C23×Dic5—31no—
139C23×Dic5—31no—
140C23×Dic5—31no—
141C2×C4⋊Dic5—31no—
142C2×C4⋊Dic5—31no—
143C2×C4⋊Dic5—31no—
144C2×C4⋊Dic5—38no—
145C2×C4⋊Dic5C2×D311yescharacteristic
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683—64no—
150C2×#683C2×D311yescharacteristic
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—64no—
155C2×C4×Dic5C2×D311yescharacteristic
156C5×#95—31no—
157C5×#95—31no—
158C5×#95—31no—
159C5×#95C2×D311yescharacteristic
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963C2×D311yescharacteristic
170#3963C2×D311yescharacteristic
171#3963C2×D311yescharacteristic
172C2×#387—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×C5×D3C22×C412yes—
175C22×C5×D3C2×D412yes—
176C22×C5×D3C2×Q812yes—
177C22×C5×D3#4112yes—
178C22×C5×D3#4112yes—
179C22×C5×D3#4112yes—
180C22×C5×D3#4112yes—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C2×D412yes—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15C22×C412yes—
200C2×Dic15C22×C412yes—
201C2×Dic15C2×Q812yes—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C2×D412yes—
211C4×C5×D3—28no—
212C4×C5×D3—28no—
213C4×C5×D3—44no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5C22×C412yes—
224C2×C3×Dic5C22×C412yes—
225C2×C3×Dic5C2×Q812yes—
226D3×Dic5—28no—
227D3×Dic5—28no—
228D3×Dic5—28no—
229D3×Dic5—44no—
230C22×C4×D3—51no—
231C22×C4×D3—51no—
232C22×C4×D3—51no—
233C22×C4×D3—51no—
234C22×C4×D3C2×D511yescharacteristic
235C22×C4×D3C2×D511yescharacteristic
236C22×C4×D3C2×D511yescharacteristic
237C2×C3×C4⋊C4—51no—
238C2×C3×C4⋊C4—51no—
239C2×C3×C42—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3—51no—
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249D3×C4⋊C4—58no—
250D3×C4⋊C4—104no—
251C42×D3—104no—
252C3×#95—51no—
253C3×#95—51no—
254C3×#95—51no—
255C3×#95C2×D511yescharacteristic
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95—51no—
263C3⋊#95—51no—
264C3⋊#95—51no—
265C3⋊#95C2×D511yescharacteristic
266C3⋊#95C2×D511yescharacteristic
267C3⋊#95C2×D511yescharacteristic
268C24×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—34no—
272C22×C4×C5—34no—
273C22×C4×C5—31no—
274C22×C4×C5—62no—
275C22×C4×C5—62no—
276C22×C4×C5—62no—
277C22×C4×C5—62no—
278C22×C4×C5—62no—
279C22×C4×C5—62no—
280C22×C4×C5—62no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C22×C4×C5C22×D311yescharacteristic
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5—34no—
288C22×Dic5—34no—
289C22×Dic5—34no—
290C22×Dic5—31no—
291C22×Dic5—62no—
292C22×Dic5—62no—
293C22×Dic5—62no—
294C22×Dic5—62no—
295C22×Dic5—62no—
296C22×Dic5—62no—
297C22×Dic5—62no—
298C22×Dic5—62no—
299C22×Dic5—62no—
300C22×Dic5C22×D311yescharacteristic
301C22×Dic5C22×D311yescharacteristic
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304C4⋊Dic5—34no—
305C4⋊Dic5—34no—
306C4⋊Dic5—34no—
307C4⋊Dic5C4×D314yescomplemented
308#683—22no—
309#683—62no—
310#683—62no—
311#683—62no—
312C4×Dic5—22no—
313C4×Dic5—62no—
314C4×Dic5—62no—
315C4×Dic5—62no—
316C22×C4⋊C4—151no—
317C22×C4⋊C4—151no—
318C22×C42—151no—
319#387—51no—
320#387—151no—
321#387—151no—
322#387—151no—
323#387—151no—
324#387—151no—
325#387—151no—
326#387—151no—
327C2×#95—31no—
328C2×#95—151no—
329C2×#95—151no—
330C2×#95—151no—
331C22×C3×C5C23×C411yescharacteristic
332C22×C3×C5C22×D411yescharacteristic
333C22×C3×C5C22×Q811yescharacteristic
334C22×C3×C5C2×#4111yescharacteristic
335C22×C3×C5C2×#4111yescharacteristic
336C22×C3×C5C2×#4111yescharacteristic
337C22×C3×C5C2×#4111yescharacteristic
338C2×C5×D3#11714yes—
339C2×C5×D3C4×D414yes—
340C2×C5×D3C4×Q814yes—
341C2×C5×D3C22⋊Q814yes—
342C2×C5×D3#12314yes—
343C2×C5×D3#12514yes—
344C2×C5×D3#12614yes—
345C3×C4×C5—22no—
346C3×C4×C5—22no—
347C3×C4×C5—41no—
348Dic15—22no—
349Dic15—22no—
350Dic15—22no—
351Dic15—41no—
352C3×Dic5—22no—
353C3×Dic5—22no—
354C3×Dic5—22no—
355C3×Dic5—41no—
356C5×Dic3—22no—
357C5×Dic3—22no—
358C5×Dic3—41no—
359C23×D3C22×D511yescharacteristic
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×Dic3—51no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3C22×D511yescharacteristic
372C22×Dic3C22×D511yescharacteristic
373C22×Dic3C22×D511yescharacteristic
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—54no—
382C2×C4×D3—54no—
383C2×C4×D3—54no—
384C2×C4×D3—102no—
385C2×C4×D3—102no—
386C2×C4×D3—102no—
387C2×C4×D3—102no—
388C2×C4×D3—102no—
389C2×C4×D3—102no—
390C2×C4×D3—102no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3C4×D514yes—
394C2×C4×D3D2014yes—
395C3×C4⋊C4—54no—
396C3×C4⋊C4—102no—
397C3×C42—102no—
398C4⋊Dic3—54no—
399C4⋊Dic3—102no—
400Dic3⋊C4—54no—
401Dic3⋊C4—54no—
402Dic3⋊C4—102no—
403Dic3⋊C4—102no—
404C4×Dic3—102no—
405C4×Dic3—102no—
406C4×Dic3—102no—
407C23×C5—32no—
408C23×C5—32no—
409C23×C5—32no—
410C23×C5—32no—
411C23×C5—32no—
412C23×C5—32no—
413C23×C5—32no—
414C23×C5C23×D311yescharacteristic
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—32no—
423C2×C4×C5—32no—
424C2×C4×C5—68no—
425C2×C4×C5—68no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—124no—
434C2×C4×C5C2×C4×D312yes—
435C2×C4×C5D3×D412yes—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—32no—
446C2×Dic5—32no—
447C2×Dic5—32no—
448C2×Dic5—68no—
449C2×Dic5—68no—
450C2×Dic5—68no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—61no—
459C2×Dic5—61no—
460C2×Dic5—124no—
461C2×Dic5C2×C4×D312yes—
462C2×Dic5C2×C4×D312yes—
463C2×Dic5D3×Q812yes—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—151no—
468C23×C4—151no—
469C23×C4—151no—
470C23×C4—151no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—158no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—151no—
476C2×C4⋊C4—151no—
477C2×C4⋊C4—151no—
478C2×C4⋊C4—151no—
479C2×C4⋊C4—151no—
480C2×C4⋊C4—304no—
481C2×C42—51no—
482C2×C42—151no—
483C2×C42—151no—
484C2×C42—151no—
485C2×C42—304no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—51no—
490#95—51no—
491#95—51no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498#95—151no—
499#95—151no—
500#95—151no—
501#95D3×D511yescharacteristic
502C2×C3×C5C2×#11711yescharacteristic
503C2×C3×C5C2×C4×D411yescharacteristic
504C2×C3×C5C2×C4×Q811yescharacteristic
505C2×C3×C5C2×C22⋊Q811yescharacteristic
506C2×C3×C5C2×#12311yescharacteristic
507C2×C3×C5C2×#12511yescharacteristic
508C2×C3×C5C2×#12611yescharacteristic
509C5×D3#38718yescomplemented
510C23×C3C23×D511yescharacteristic
511C22×D3C2×C4×D512yes—
512C22×D3C2×D2012yes—
513C22×D3#70912yes—
514C22×D3#71112yes—
515C22×D3#71112yes—
516C22×D3#71112yes—
517C22×D3Q8×D512yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—52no—
526C2×C3×C4—52no—
527C2×C3×C4—52no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4C2×C4×D512yes—
538C2×C3×C4C2×D2012yes—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—52no—
547C2×Dic3—52no—
548C2×Dic3—52no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3C2×C4×D512yes—
559C2×Dic3C2×D2012yes—
560C4×D3—28no—
561C4×D3—28no—
562C4×D3—44no—
563C4×D3—108no—
564C4×D3—108no—
565C4×D3—108no—
566C4×D3—204no—
567C22×C5—34no—
568C22×C5—34no—
569C22×C5—34no—
570C22×C5—34no—
571C22×C5—34no—
572C22×C5—34no—
573C22×C5—34no—
574C22×C5C22×C4×D311yescharacteristic
575C22×C5C2×D3×D411yescharacteristic
576C22×C5C2×D3×Q811yescharacteristic
577C22×C5D3×#4111yescharacteristic
578C22×C5D3×#4111yescharacteristic
579C22×C5D3×#4111yescharacteristic
580C22×C5D3×#4111yescharacteristic
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—41no—
584C4×C5—62no—
585C4×C5—62no—
586C4×C5—121no—
587Dic5—22no—
588Dic5—22no—
589Dic5—22no—
590Dic5—41no—
591Dic5—62no—
592Dic5—62no—
593Dic5—62no—
594Dic5—121no—
595C24—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—34no—
599C22×C4—34no—
600C22×C4—31no—
601C22×C4—51no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—154no—
613C22×C4—154no—
614C22×C4—154no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—151no—
619C22×C4—302no—
620C22×C4—302no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—302no—
624C22×C4—302no—
625C22×C4—302no—
626C22×C4—302no—
627C22×C4—302no—
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C22×C4C2×D3×D511yescharacteristic
631C4⋊C4—54no—
632C4⋊C4—102no—
633C4⋊C4—154no—
634C4⋊C4—154no—
635C4⋊C4—154no—
636C4⋊C4—302no—
637C4⋊C4—302no—
638C4⋊C4—302no—
639C42—102no—
640C42—302no—
641C42—302no—
642C42—302no—
643C3×C5C2×#38711yescharacteristic, complemented, Hall
644C22×C3C22×C4×D511yescharacteristic
645C22×C3C22×D2011yescharacteristic
646C22×C3C2×#70911yescharacteristic
647C22×C3C2×#71111yescharacteristic
648C22×C3C2×#71111yescharacteristic
649C22×C3C2×#71111yescharacteristic
650C22×C3C2×Q8×D511yescharacteristic
651C2×D3C4×D2014yes—
652C2×D3#402314yes—
653C2×D3#402514yes—
654C2×D3#403214yes—
655C2×D3#403314yes—
656C2×D3#403514yes—
657C2×D3#404314yes—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—41no—
661C3×C4—102no—
662C3×C4—102no—
663C3×C4—102no—
664C3×C4—201no—
665Dic3—22no—
666Dic3—22no—
667Dic3—41no—
668Dic3—102no—
669Dic3—102no—
670Dic3—102no—
671Dic3—201no—
672C2×C5—38no—
673C2×C5D3×#11711yescharacteristic
674C2×C5C4×D3×D411yescharacteristic
675C2×C5C4×D3×Q811yescharacteristic
676C2×C5D3×C22⋊Q811yescharacteristic
677C2×C5D3×#12311yescharacteristic
678C2×C5D3×#12511yescharacteristic
679C2×C5D3×#12611yescharacteristic
680C23—32no—
681C23—32no—
682C23—32no—
683C23—32no—
684C23—32no—
685C23—32no—
686C23—32no—
687C23C22×D3×D511yescharacteristic
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—52no—
698C2×C4—52no—
699C2×C4—52no—
700C2×C4—68no—
701C2×C4—68no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—101no—
713C2×C4—101no—
714C2×C4—101no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—124no—
719C2×C4—152no—
720C2×C4—152no—
721C2×C4—152no—
722C2×C4—308no—
723C2×C4—308no—
724C2×C4—308no—
725C2×C4—301no—
726C2×C4—301no—
727C2×C4—301no—
728C2×C4—301no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—604no—
735C2×C4C4×D3×D512yes—
736C2×C4D3×D2012yes—
737C2×C3C2×C4×D2011yescharacteristic
738C2×C3C2×#402311yescharacteristic
739C2×C3C2×#402511yescharacteristic
740C2×C3C2×#403211yescharacteristic
741C2×C3C2×#403311yescharacteristic
742C2×C3C2×#403511yescharacteristic
743C2×C3C2×#404311yescharacteristic
744D3#6494218yesdirect product factor
745C5D3×#38711yescharacteristic, complemented, Sylow
746C22—34no—
747C22—34no—
748C22—34no—
749C22—34no—
750C22—34no—
751C22—34no—
752C22—34no—
753C22C2×C4×D3×D511yescharacteristic
754C22C2×D3×D2011yescharacteristic
755C22D3×#70911yescharacteristic
756C22D3×#71111yescharacteristic
757C22D3×#71111yescharacteristic
758C22D3×#71111yescharacteristic
759C22D3×Q8×D511yescharacteristic
760C4—22no—
761C4—22no—
762C4—41no—
763C4—62no—
764C4—62no—
765C4—102no—
766C4—102no—
767C4—102no—
768C4—121no—
769C4—201no—
770C4—302no—
771C4—302no—
772C4—302no—
773C4—601no—
774C3C2×#6494211yescharacteristic, complemented, Sylow
775C2—38no—
776C2C4×D3×D2011yescharacteristic
777C2D3×#402311yescharacteristic
778C2D3×#402511yescharacteristic
779C2D3×#403211yescharacteristic
780C2D3×#403311yescharacteristic
781C2D3×#403511yescharacteristic
782C2D3×#404311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5C2×#387
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #11750754C2semidirect
6. C3×#64942C2semidirect
10. #11748821C2semidirect
11. #11748814C2semidirect
12. #11748697C2semidirect
13. #11748688C2semidirect
14. #11748659C2semidirect
15. #11748656C2semidirect
36. D3×C4⋊Dic5C4semidirect
70. #64942D3direct (N × H)
107. C4⋊Dic15C2×C4semidirect
110. C3×C4⋊Dic5C2×C4semidirect
113. Dic3⋊Dic5C2×C4semidirect
114. Dic3⋊Dic5C2×C4semidirect
307. C4⋊Dic5C4×D3semidirect
509. C5×D3#387semidirect
643. C3×C5C2×#387semidirect
744. D3#64942direct (N × H)
745. C5D3×#387semidirect
774. C3C2×#64942semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic52
C2×D3×#6832
C2×C4×D3×Dic52
#117507542
C5×D3×#952
C3×#649422
D3×#39632
#117488212
#117488142
#117486972
#117486882
#117486592
#117486562
C2×#649423
D3×#3875