Finite Group Databasebeta

← #14327748

Subgroups — #14327748

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4023C211yesmaximal, characteristic, complemented
2C2×Dic5×#67C211yesmaximal, characteristic
3C2×#91400C211yesmaximal, characteristic, complemented
4#11751045C211yesmaximal, characteristic, complemented
5C5×#4957C211yesmaximal, characteristic
6#11749506C211yesmaximal, characteristic, complemented
7#11749482C211yesmaximal, characteristic
8#11749481C211yesmaximal, characteristic, complemented
9#11748874C211yesmaximal, characteristic, complemented
10C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
11#11748715C211yesmaximal, characteristic, complemented
12#11748714C211yesmaximal, characteristic, complemented
13#11748641C211yesmaximal, characteristic, complemented
14Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10608033—31nomaximal, Hall
17C22×C5×#67C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4023—24no—
36Dic5×#67C418yescomplemented
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6668C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48#91400—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82241—51nomaximal, Hall
56C2×D4×Dic5—31no—
57C2×#4023—31no—
58C2×#4023D311yescharacteristic, complemented
59C5×#390—31no—
60#65510—31no—
61#65265—31no—
62C4⋊C4×Dic5—31no—
63#65234—31no—
64#65234—31no—
65#65233—31no—
66#65233—31no—
67#65231—31no—
68#65231—31no—
69C4×C4⋊Dic5—31no—
70C4×#683—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C5×#67—22no—
80C2×C5×#67—22no—
81C2×C5×#67C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C3×Dic5—22no—
86C22×C3×Dic5—22no—
87C22×C3×Dic5C2×C414yes—
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C2×D3×Dic5—22no—
93C2×D3×Dic5—22no—
94C2×D3×Dic5C2×C414yes—
95C3×C5×C22⋊C4—22no—
96#6719—41no—
97#6719C2×C414yes—
98#6712—41no—
99C4×Dic15—22no—
100C5×#217—41no—
101C5×(C2×D3)⋊C4—22no—
102C5×(C2×D3)⋊C4—41no—
103C5×Dic3⋊C4—22no—
104C4×C5×Dic3—22no—
105C3×C22⋊Dic5—22no—
106C3×#683—22no—
107C3×#683D414yescomplemented
108C3×C4×Dic5—22no—
109C3×C4×Dic5—22no—
110Dic3⋊Dic5—22no—
111Dic3⋊Dic5C2×C414yes—
112#6669—41no—
113#6668—22no—
114#6668—22no—
115(C2×D3)⋊Dic5—22no—
116(C2×D3)⋊Dic5—41no—
117(C2×D3)⋊Dic5C2×C414yes—
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5C2×C414yes—
121C2×C3×#117—51no—
122C2×C4×#67—51no—
123C2×#892—51no—
124#5212—51no—
125#4987—51no—
126#4975—51no—
127Dic3×C4⋊C4—51no—
128#4957—51no—
129#4957D511yescharacteristic
130#4944—51no—
131#4944—51no—
132#4940—51no—
133#4940—51no—
134C4×Dic3⋊C4—51no—
135C4×Dic3⋊C4—51no—
136C22×C5×D4—31no—
137C23×Dic5—31no—
138C23×Dic5C2×D311yescharacteristic
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4C2×D311yescharacteristic
144C2×C42×C5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5C2×D311yescharacteristic
151D4×Dic5—38no—
152C2×C4⋊Dic5—31no—
153C2×C4⋊Dic5—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683—31no—
157C2×#683—31no—
158C2×#683C2×D311yescharacteristic
159C2×#683C2×D311yescharacteristic
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5C2×D311yescharacteristic
165C2×C4×Dic5C2×D311yescharacteristic
166#4023—24no—
167#4023—64no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#2354—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5C22×C412yes—
182C23×C3×C5C2411yescharacteristic
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5C2×D412yes—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15C22×C412yes—
207C2×Dic15C22×C412yes—
208C5×#67—28no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3C22×C412yes—
216C2×C5×Dic3#4112yes—
217C2×C5×Dic3#4112yes—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—28no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5C2×D412yes—
230C2×C3×Dic5#4112yes—
231D3×Dic5—28no—
232C23×C3×C4—51no—
233C22×#67C2×D511yescharacteristic
234C22×C4×D3—51no—
235C3×#117—104no—
236C2×C3×C4⋊C4—51no—
237C2×C3×C4⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4C2×D511yescharacteristic
240C2×C3×C42—51no—
241C2×C3×C42—51no—
242C2×#217—51no—
243C2×#217—51no—
244C2×#217C2×D511yescharacteristic
245C4×#67—58no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×(C2×D3)⋊C4C2×D511yescharacteristic
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4—51no—
256C2×Dic3⋊C4—51no—
257C2×Dic3⋊C4C2×D511yescharacteristic
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3—51no—
261C2×C4×Dic3—51no—
262C2×C4×Dic3C2×D511yescharacteristic
263#892—104no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C24×C5—31no—
271C24×C5C22×D311yescharacteristic
272C2×C5×D4—34no—
273C2×C5×D4—62no—
274C2×C5×D4—62no—
275C22×C4×C5—31no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×Dic5—22no—
281C22×Dic5—22no—
282C22×Dic5—31no—
283C22×Dic5—31no—
284C22×Dic5—34no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5—62no—
288C22×Dic5—62no—
289C22×Dic5C4×D314yes—
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C22×Dic5C22×D311yescharacteristic
293C22×Dic5C22×D311yescharacteristic
294C5×C4⋊C4—62no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—62no—
297C5×C22⋊C4—121no—
298C5×C22⋊C4—121no—
299C42×C5—62no—
300C22⋊Dic5—22no—
301C22⋊Dic5—34no—
302C22⋊Dic5—34no—
303C22⋊Dic5—62no—
304C22⋊Dic5—121no—
305C22⋊Dic5—121no—
306C4⋊Dic5—34no—
307C4⋊Dic5—62no—
308#683—22no—
309#683—62no—
310#683—62no—
311#683—121no—
312#683—121no—
313#683#6714yescomplemented
314C4×Dic5—22no—
315C4×Dic5—22no—
316C4×Dic5—34no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C2×C4×D4—151no—
321C2×#117—51no—
322C2×#117—151no—
323#390—31no—
324#390—151no—
325#388—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#384—151no—
330#380—151no—
331#380—151no—
332C4×C4⋊C4—151no—
333C4×C4⋊C4—151no—
334C4×C4⋊C4—151no—
335C22×C3×C5—22no—
336C22×C3×C5—22no—
337C22×C3×C5—22no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5C23×C411yescharacteristic
343C22×C3×C5C22×D411yescharacteristic
344C22×C3×C5C2×#4111yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5H(5,𝔽2)11yescharacteristic
348C22×C3×C52−1+411yescharacteristic
349C2×C5×D3—22no—
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C3×C4×C5—22no—
357C3×C4×C5—41no—
358Dic15—22no—
359Dic15—22no—
360Dic15—41no—
361Dic15—41no—
362C3×Dic5—22no—
363C3×Dic5—22no—
364C3×Dic5—41no—
365C3×Dic5C4×D414yes—
366C5×Dic3—41no—
367C5×Dic3—41no—
368C5×Dic3#11714yescomplemented
369C24×C3C22×D511yescharacteristic
370C23×D3C22×D511yescharacteristic
371C22×C3×C4—51no—
372C22×C3×C4—54no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—102no—
377C22×C3×C4—102no—
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C2×#67—22no—
381C2×#67—22no—
382C2×#67C4×D514yes—
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3C22×D511yescharacteristic
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D511yescharacteristic
390C2×C4×D3—54no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C3×C4⋊C4—54no—
394C3×C4⋊C4—102no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—102no—
397C3×C42—102no—
398C3×C42—102no—
399#217—41no—
400#217—54no—
401#217—201no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—41no—
404(C2×D3)⋊C4—54no—
405(C2×D3)⋊C4—102no—
406(C2×D3)⋊C4—201no—
407C4⋊Dic3—102no—
408C4⋊Dic3—102no—
409Dic3⋊C4—22no—
410Dic3⋊C4—54no—
411Dic3⋊C4—102no—
412Dic3⋊C4—201no—
413Dic3⋊C4—201no—
414C4×Dic3—22no—
415C4×Dic3—54no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C23×C5—21no—
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—32no—
426C23×C5—61no—
427C23×C5—61no—
428C23×C5—61no—
429C23×C5—61no—
430C23×C5—61no—
431C23×C5—61no—
432C23×C5C2×C4×D312yes—
433C23×C5C23×D311yescharacteristic
434C5×D4—68no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—32no—
441C2×C4×C5—32no—
442C2×C4×C5—32no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5C2×#6712yes—
450C2×Dic5—21no—
451C2×Dic5—21no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—28no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—61no—
461C2×Dic5—61no—
462C2×Dic5—61no—
463C2×Dic5—61no—
464C2×Dic5—68no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5C2×C4×D312yes—
473C2×Dic5#23512yes—
474C2×Dic5C2×#6712yes—
475C2×Dic5C2×#6712yes—
476C22×D4—31no—
477C23×C4—51no—
478C23×C4—151no—
479C4×D4—158no—
480#117—104no—
481#117—304no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—151no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—151no—
500C2×C22⋊C4D3×D511yescharacteristic
501C2×C42—31no—
502C2×C42—51no—
503C2×C42—51no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—151no—
509#95—151no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514C2×C3×C5—42no—
515C2×C3×C5C2×#11711yescharacteristic
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5#52011yescharacteristic
518C2×C3×C5#54711yescharacteristic
519C2×C3×C5#55011yescharacteristic
520C2×C3×C5#55511yescharacteristic
521C2×C3×C5#55611yescharacteristic
522C5×D3—42no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3C2×C4×D512yes—
530C23×C3C23×D511yescharacteristic
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3C2×C4×D512yes—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—52no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—108no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4D4×D512yes—
557#67—28no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—101no—
567C2×Dic3—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3C2×C4×D512yes—
577C2×Dic3#71112yes—
578C2×Dic3#71112yes—
579C4×D3—108no—
580C22×C5—22no—
581C22×C5—22no—
582C22×C5—22no—
583C22×C5—41no—
584C22×C5—41no—
585C22×C5—41no—
586C22×C5—41no—
587C22×C5—62no—
588C22×C5—62no—
589C22×C5—62no—
590C22×C5—121no—
591C22×C5—121no—
592C22×C5—121no—
593C22×C5—121no—
594C22×C5C22×C4×D311yescharacteristic
595C22×C5C2×#23511yescharacteristic
596C22×C5D3×#4111yescharacteristic
597C22×C5D3×#4111yescharacteristic
598C22×C5#100911yescharacteristic
599C22×C5#101011yescharacteristic
600C22×C5C22×#6711yescharacteristic
601C4×C5—22no—
602C4×C5—34no—
603C4×C5—41no—
604C4×C5—121no—
605C4×C5—121no—
606Dic5—22no—
607Dic5—22no—
608Dic5—41no—
609Dic5—62no—
610Dic5—62no—
611Dic5—121no—
612Dic5—121no—
613Dic5C4×#6714yes—
614C24—31no—
615C24C2×D3×D511yescharacteristic
616C2×D4—34no—
617C2×D4—62no—
618C2×D4—62no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—51no—
623C22×C4—54no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—51no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—154no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—151no—
634C22×C4—302no—
635C22×C4—302no—
636C22×C4C2×D3×D511yescharacteristic
637C22×C4C2×D3×D511yescharacteristic
638C4⋊C4—54no—
639C4⋊C4—62no—
640C4⋊C4—102no—
641C4⋊C4—154no—
642C4⋊C4—302no—
643C4⋊C4—302no—
644C4⋊C4—302no—
645C4⋊C4—601no—
646C4⋊C4—601no—
647C22⋊C4—22no—
648C22⋊C4—62no—
649C22⋊C4—102no—
650C22⋊C4—121no—
651C22⋊C4—121no—
652C22⋊C4—154no—
653C22⋊C4—154no—
654C22⋊C4—302no—
655C22⋊C4—601no—
656C22⋊C4—601no—
657C42—62no—
658C42—102no—
659C42—102no—
660C42—154no—
661C42—302no—
662C42—302no—
663C42—302no—
664C3×C5#235411yescharacteristic, complemented, Hall
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3C22×C4×D511yescharacteristic
673C22×C3C2×D4×D511yescharacteristic
674C22×C3C2×#71111yescharacteristic
675C22×C3C2×#71111yescharacteristic
676C22×C3#414411yescharacteristic
677C22×C3D5×#4111yescharacteristic
678C22×C3#415011yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—22no—
687C3×C4—41no—
688C3×C4—54no—
689C3×C4—102no—
690C3×C4—102no—
691C3×C4—201no—
692Dic3—41no—
693Dic3—41no—
694Dic3—102no—
695Dic3—102no—
696Dic3—201no—
697Dic3—201no—
698Dic3#402314yescomplemented
699C2×C5—42no—
700C2×C5—122no—
701C2×C5D3×#11711yescharacteristic
702C2×C5#552311yescharacteristic
703C2×C5#553211yescharacteristic
704C2×C5#553311yescharacteristic
705C2×C5C2×C4×#6711yescharacteristic
706C2×C5#582411yescharacteristic
707C2×C5#583411yescharacteristic
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—32no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23C4×D3×D512yes—
722C23C22×D3×D511yescharacteristic
723D4—68no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—52no—
733C2×C4—52no—
734C2×C4—52no—
735C2×C4—52no—
736C2×C4—52no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—108no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—152no—
752C2×C4—152no—
753C2×C4—308no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4D5×#6712yes—
765C2×C3—42no—
766C2×C3C2×#402311yescharacteristic
767C2×C3C4×D4×D511yescharacteristic
768C2×C3#6588011yescharacteristic
769C2×C3#6594511yescharacteristic
770C2×C3#6595011yescharacteristic
771C2×C3#6600511yescharacteristic
772C2×C3#6605211yescharacteristic
773D3—42no—
774C5#8224111yescharacteristic, complemented, Sylow
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22C2×C4×D3×D511yescharacteristic
790C22D5×#23511yescharacteristic
791C22#9202011yescharacteristic
792C22D3×#71111yescharacteristic
793C22D3×#71111yescharacteristic
794C22#9202711yescharacteristic
795C22C2×D5×#6711yescharacteristic
796C4—22no—
797C4—34no—
798C4—41no—
799C4—54no—
800C4—102no—
801C4—102no—
802C4—121no—
803C4—121no—
804C4—201no—
805C4—302no—
806C4—302no—
807C4—601no—
808C4—601no—
809C3#1060803311yescharacteristic, complemented, Sylow
810C2—42no—
811C2—122no—
812C2D3×#402311yescharacteristic
813C2#1175282411yescharacteristic
814C2#1175290211yescharacteristic
815C2#1175290311yescharacteristic
816C2C4×D5×#6711yescharacteristic
817C2#1175479211yescharacteristic
818C2#1175479911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2354
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
1. C2×C3×#4023C2semidirect
3. C2×#91400C2semidirect
4. #11751045C2semidirect
6. #11749506C2semidirect
8. #11749481C2semidirect
9. #11748874C2semidirect
10. C4×Dic3⋊Dic5C2semidirect
11. #11748715C2semidirect
12. #11748714C2semidirect
13. #11748641C2semidirect
14. Dic5×Dic3⋊C4C2semidirect
15. Dic3×#683C2semidirect
36. Dic5×#67C4semidirect
58. C2×#4023D3semidirect
107. C3×#683D4semidirect
313. #683#67semidirect
368. C5×Dic3#117semidirect
664. C3×C5#2354semidirect
698. Dic3#4023semidirect
774. C5#82241semidirect
809. C3#10608033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40232
C2×Dic5×#672
C2×#914002
#117510452
C5×#49572
#117495062
#117494822
#117494812
#117488742
C4×Dic3⋊Dic52
#117487152
#117487142
#117486412
Dic5×Dic3⋊C42
Dic3×#6832
#106080333
#822415