Finite Group Databasebeta

← #14320600

Subgroups — #14320600

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
3C2×#91347C211yesmaximal, characteristic, complemented
4C5×#4950C211yesmaximal, characteristic, complemented
5C3×#65239C211yesmaximal, characteristic, complemented
6#11749498C211yesmaximal, characteristic
7#11749494C211yesmaximal, characteristic
8#11749487C211yesmaximal, characteristic, complemented
9#11748699C211yesmaximal, characteristic, complemented
10#11748687C211yesmaximal, characteristic, complemented
11#11748685C211yesmaximal, characteristic, complemented
12#11748678C211yesmaximal, characteristic, complemented
13#11748674C211yesmaximal, characteristic, complemented
14#11748670C211yesmaximal, characteristic, complemented
15#11748653C211yesmaximal, characteristic, complemented
16#10606108—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26#91770C418yescomplemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×#6667C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×Dic3×Dic5—24no—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91347—24no—
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74377—51nomaximal, Hall
56C22×C4×Dic5—31no—
57C2×#4038—31no—
58C2×#4027—31no—
59C5×#385—31no—
60#65502—31no—
61#65279—31no—
62#65267—31no—
63C4⋊C4×Dic5—31no—
64#65247—31no—
65#65239D311yescharacteristic, complemented
66C22⋊C4×Dic5—31no—
67#64959—31no—
68#64955—31no—
69#64944—31no—
70#64937—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C2×#1220—22no—
76C2×#1220—22no—
77C2×#1220C2×C414yes—
78C22×Dic15—22no—
79C22×Dic15—22no—
80C22×Dic15C2×C414yes—
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15C2×C414yescomplemented
87C22×C5×Dic3—22no—
88C22×C5×Dic3—22no—
89C22×C5×Dic3—22no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C3×Dic5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5—22no—
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C3×C5×C22⋊C4C2×C414yes—
102#6714C2×C414yescomplemented
103#6712C2×C414yescomplemented
104C4×Dic15C2×C414yescomplemented
105C5×#217—22no—
106C5×C4⋊Dic3—22no—
107C5×C4⋊Dic3—22no—
108C3×C22⋊Dic5—22no—
109C3×C4⋊Dic5—22no—
110C3×C4⋊Dic5—22no—
111#6667—22no—
112#6667—22no—
113#6667—22no—
114#6667—22no—
115Dic3×Dic5—22no—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5D414yescomplemented
121C22×C4×Dic3—51no—
122C2×#892—51no—
123C2×#67⋊C4—51no—
124C3×#385—51no—
125#5213—51no—
126#4990—51no—
127#4978—51no—
128Dic3×C4⋊C4—51no—
129#4958—51no—
130#4950D511yescharacteristic, complemented
131Dic3×C22⋊C4—51no—
132#4670—51no—
133#4666—51no—
134#4655—51no—
135#4648—51no—
136C23×C4×C5—31no—
137C22×C22⋊D5—31no—
138C23×Dic5—31no—
139C23×Dic5C2×D311yescharacteristic
140C22×C4×D5—31no—
141C2×C5×C4⋊C4—31no—
142C2×C5×C4⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4C2×D311yescharacteristic
145C2×C22⋊Dic5C2×D311yescharacteristic
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×C4⋊Dic5C2×D311yescharacteristic
152C2×C4⋊Dic5C2×D311yescharacteristic
153C2×#683—31no—
154C2×C4×Dic5—31no—
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—64no—
162#4038—64no—
163#4027—38no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174#2290—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5#4112yes—
181C23×C3×C5#4112yes—
182C23×C3×C5C2411yescharacteristic
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15—21no—
189C22×D15C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×C3×C4×C5C22×C412yes—
196#1220—28no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—28no—
202C2×Dic15C22×C412yes—
203C2×Dic15C22×C412yes—
204C2×Dic15C22×C412yes—
205C2×Dic15C2×D412yes—
206C2×Dic15#4112yes—
207C4×D15—28no—
208C2×C5×Dic3—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×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3C2×D412yes—
220C2×C5×Dic3#4112yes—
221C2×C3×Dic5—28no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5C2×D412yes—
233C2×C3×Dic5#4112yes—
234C23×C3×C4—51no—
235C22×#67—51no—
236C23×Dic3—51no—
237C23×Dic3C2×D511yescharacteristic
238C22×C4×D3—51no—
239C2×C3×C4⋊C4—51no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×C3×C22⋊C4C2×D511yescharacteristic
243C2×#217C2×D511yescharacteristic
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×C4⋊Dic3C2×D511yescharacteristic
250C2×C4⋊Dic3C2×D511yescharacteristic
251C2×Dic3⋊C4—51no—
252C2×C4×Dic3—51no—
253C2×C4×Dic3—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—104no—
260#892—104no—
261#67⋊C4—58no—
262C3×#95—51no—
263C3×#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95C2×D511yescharacteristic
271C3⋊#95C2×D511yescharacteristic
272C24×C5C22×D311yescharacteristic
273C23×D5—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5—62no—
279C22×C4×C5—62no—
280C22×C4×C5—62no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—34no—
284C2×C22⋊D5—62no—
285C2×C22⋊D5—62no—
286C22×Dic5—22no—
287C22×Dic5—22no—
288C22×Dic5—22no—
289C22×Dic5—31no—
290C22×Dic5—34no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—62no—
294C22×Dic5—62no—
295C22×Dic5C22×D311yescharacteristic
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C22×Dic5C22×D311yescharacteristic
299C2×C4×D5—34no—
300C2×C4×D5—62no—
301C2×C4×D5—62no—
302C5×C4⋊C4—62no—
303C5×C4⋊C4—62no—
304C5×C22⋊C4—62no—
305C5×C22⋊C4C4×D314yes—
306C22⋊Dic5—22no—
307#685—34no—
308#685—62no—
309#685—62no—
310#685—62no—
311#685—62no—
312C4⋊Dic5—22no—
313C4⋊Dic5—22no—
314#683—34no—
315C4×Dic5—34no—
316C4×Dic5—34no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C4×Dic5—62no—
322C2×C4×D4—151no—
323C2×#117—151no—
324C22×C42—151no—
325#388—151no—
326#388—151no—
327#387—151no—
328#387—151no—
329#386—151no—
330#386—151no—
331#385—31no—
332#385—51no—
333C4×C4⋊C4—151no—
334C4×C22⋊C4—151no—
335C4×C22⋊C4—151no—
336#376—151no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5#11714yescomplemented
344C22×C3×C5C23×C411yescharacteristic
345C22×C3×C5C22×D411yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5C2×#4111yescharacteristic
349C22×C3×C5C2×#4111yescharacteristic
350C22×C3×C5C2×#4111yescharacteristic
351C2×D15—22no—
352C2×D15—22no—
353C2×D15—22no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—41no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360Dic15—22no—
361Dic15—22no—
362Dic15C4×D414yes—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C5×Dic3—22no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3—41no—
371C24×C3C22×D511yescharacteristic
372C23×D3—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4—102no—
378C22×C3×C4—102no—
379C22×C3×C4—102no—
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—54no—
383C2×#67—102no—
384C2×#67—102no—
385C22×Dic3—22no—
386C22×Dic3—22no—
387C22×Dic3—22no—
388C22×Dic3—51no—
389C22×Dic3—54no—
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—102no—
393C22×Dic3—102no—
394C22×Dic3C22×D511yescharacteristic
395C22×Dic3C22×D511yescharacteristic
396C22×Dic3C22×D511yescharacteristic
397C22×Dic3C22×D511yescharacteristic
398C2×C4×D3—54no—
399C2×C4×D3—102no—
400C2×C4×D3—102no—
401C3×C4⋊C4—102no—
402C3×C4⋊C4—102no—
403C3×C22⋊C4—102no—
404C3×C22⋊C4C4×D514yes—
405#217—22no—
406(C2×D3)⋊C4—54no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4—102no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4—102no—
411C4⋊Dic3—22no—
412C4⋊Dic3—22no—
413Dic3⋊C4—54no—
414C4×Dic3—54no—
415C4×Dic3—54no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—102no—
420C4×Dic3—102no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5C2×C4×D312yes—
426C23×C5#23712yes—
427C23×C5#23912yes—
428C23×C5C23×D311yescharacteristic
429C22×D5—32no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
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—68no—
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×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5C2×C4×D312yes—
454C2×C4×C5C2×C4×D312yes—
455C22⋊D5—68no—
456C2×Dic5—28no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—21no—
467C2×Dic5—32no—
468C2×Dic5—32no—
469C2×Dic5—32no—
470C2×Dic5—32no—
471C2×Dic5—32no—
472C2×Dic5—68no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5D3×D412yes—
478C2×Dic5#23712yes—
479C4×D5—68no—
480C22×D4—151no—
481C23×C4—31no—
482C23×C4—51no—
483C23×C4—151no—
484C23×C4—151no—
485C4×D4—158no—
486#117—304no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—151no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4D3×D511yescharacteristic
500C2×C42—151no—
501C2×C42—151no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—304no—
508#95—31no—
509#95—31no—
510#95—51no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95—151no—
518C2×C3×C5—24no—
519C2×C3×C5C2×#11711yescharacteristic
520C2×C3×C5C2×C4×D411yescharacteristic
521C2×C3×C5C4×#4111yescharacteristic
522C2×C3×C5#52511yescharacteristic
523C2×C3×C5#52511yescharacteristic
524C2×C3×C5#52911yescharacteristic
525C2×C3×C5#52911yescharacteristic
526D15—42no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3C2×C4×D512yes—
532C23×C3#71112yes—
533C23×C3#71312yes—
534C23×C3C23×D511yescharacteristic
535C22×D3—52no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C22×D3—101no—
541C22×D3—101no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
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×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4C2×C4×D512yes—
560C2×C3×C4C2×C4×D512yes—
561#67—108no—
562C2×Dic3—28no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—52no—
574C2×Dic3—52no—
575C2×Dic3—52no—
576C2×Dic3—52no—
577C2×Dic3—52no—
578C2×Dic3—108no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3D4×D512yes—
584C2×Dic3#71112yes—
585C4×D3—108no—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5#89214yescomplemented
593C22×C5C22×C4×D311yescharacteristic
594C22×C5C2×D3×D411yescharacteristic
595C22×C5C2×#23711yescharacteristic
596C22×C5C2×#23711yescharacteristic
597C22×C5C2×#23911yescharacteristic
598C22×C5D3×#4111yescharacteristic
599C22×C5D3×#4111yescharacteristic
600C2×D5—62no—
601C2×D5—62no—
602C2×D5—62no—
603C2×D5—121no—
604C2×D5—121no—
605C2×D5—121no—
606C2×D5—121no—
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—62no—
610C4×C5—62no—
611C4×C5—121no—
612C4×C5—121no—
613Dic5—22no—
614Dic5—22no—
615Dic5—34no—
616Dic5—41no—
617Dic5—41no—
618Dic5—62no—
619Dic5—62no—
620C24—151no—
621C24C2×D3×D511yescharacteristic
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—151no—
640C22×C4—154no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—154no—
644C22×C4—302no—
645C22×C4—302no—
646C22×C4—302no—
647C22×C4—302no—
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—62no—
651C4⋊C4—62no—
652C4⋊C4—102no—
653C4⋊C4—102no—
654C4⋊C4—154no—
655C22⋊C4—62no—
656C22⋊C4—102no—
657C22⋊C4—154no—
658C22⋊C4—302no—
659C22⋊C4—302no—
660C22⋊C4—302no—
661C22⋊C4—302no—
662C22⋊C4#120014yes—
663C42—154no—
664C42—154no—
665C42—302no—
666C42—302no—
667C42—302no—
668C42—302no—
669C42—302no—
670C3×C5#229011yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3#403814yescomplemented
678C22×C3C22×C4×D511yescharacteristic
679C22×C3C2×D4×D511yescharacteristic
680C22×C3C2×#71111yescharacteristic
681C22×C3C2×#71111yescharacteristic
682C22×C3C2×#71311yescharacteristic
683C22×C3D5×#4111yescharacteristic
684C22×C3D5×#4111yescharacteristic
685C2×D3—102no—
686C2×D3—102no—
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—201no—
691C2×D3—201no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—102no—
695C3×C4—102no—
696C3×C4—201no—
697C3×C4—201no—
698Dic3—22no—
699Dic3—22no—
700Dic3—41no—
701Dic3—41no—
702Dic3—54no—
703Dic3—102no—
704Dic3—102no—
705C2×C5—24no—
706C2×C5C2×#89211yescharacteristic
707C2×C5C4×#23711yescharacteristic
708C2×C5C4×D3×D411yescharacteristic
709C2×C5#558611yescharacteristic
710C2×C5#562411yescharacteristic
711C2×C5#562711yescharacteristic
712C2×C5#564911yescharacteristic
713D5—122no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—152no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23—301no—
725C23#676612yes—
726C23#676812yes—
727C23C2×#120012yes—
728C23C22×D3×D511yescharacteristic
729D4—308no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—52no—
737C2×C4—52no—
738C2×C4—68no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—108no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—152no—
761C2×C4—152no—
762C2×C4—152no—
763C2×C4—152no—
764C2×C4—152no—
765C2×C4—308no—
766C2×C4—308no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—301no—
771C2×C4C2×#120012yes—
772C2×C4C2×#120012yes—
773C2×C3—24no—
774C2×C3C2×#403811yescharacteristic
775C2×C3C4×#71111yescharacteristic
776C2×C3C4×D4×D511yescharacteristic
777C2×C3#6592011yescharacteristic
778C2×C3#6595811yescharacteristic
779C2×C3#6596111yescharacteristic
780C2×C3#6598311yescharacteristic
781D3—202no—
782C5#7437711yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—302no—
790C22—302no—
791C22—302no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22#9134714yescomplemented
797C22C2×#676611yescharacteristic
798C22C2×#676811yescharacteristic
799C22D3×D4×D511yescharacteristic
800C22D5×#23711yescharacteristic
801C22D3×#71111yescharacteristic
802C22#9202411yescharacteristic
803C22C22×#120011yescharacteristic
804C4—22no—
805C4—22no—
806C4—62no—
807C4—62no—
808C4—102no—
809C4—102no—
810C4—121no—
811C4—121no—
812C4—154no—
813C4—201no—
814C4—201no—
815C4—302no—
816C4—302no—
817C3#1060610811yescharacteristic, complemented, Sylow
818C2—24no—
819C2—602no—
820C2#1175282811yescharacteristic
821C2#1175284211yescharacteristic
822C2#1175295911yescharacteristic
823C2#1175298811yescharacteristic
824C2C2×#9134711yescharacteristic
825C2D4×#120011yescharacteristic
826C2#1175485311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2290
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
2. C22×Dic3×Dic5C2semidirect
3. C2×#91347C2semidirect
4. C5×#4950C2semidirect
5. C3×#65239C2semidirect
8. #11749487C2semidirect
9. #11748699C2semidirect
10. #11748687C2semidirect
11. #11748685C2semidirect
12. #11748678C2semidirect
13. #11748674C2semidirect
14. #11748670C2semidirect
15. #11748653C2semidirect
26. #91770C4semidirect
65. #65239D3semidirect
86. C2×C4×D15C2×C4semidirect
102. #6714C2×C4semidirect
103. #6712C2×C4semidirect
104. C4×Dic15C2×C4semidirect
120. Dic3×Dic5D4semidirect
130. #4950D5semidirect
343. C22×C3×C5#117semidirect
592. C22×C5#892semidirect
670. C3×C5#2290semidirect
677. C22×C3#4038semidirect
782. C5#74377semidirect
796. C22#91347semidirect
817. C3#10606108semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C22×Dic3×Dic52
C2×#913472
C5×#49502
C3×#652392
#117494982
#117494942
#117494872
#117486992
#117486872
#117486852
#117486782
#117486742
#117486702
#117486532
#106061083
#743775