Finite Group Databasebeta

← #14329507

Subgroups — #14329507

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×#91774C211yesmaximal, characteristic
3C2×#91770C211yesmaximal, characteristic
4C3×C5×#388C211yesmaximal, characteristic, complemented
5#11751090C211yesmaximal, characteristic, complemented
6#11751058C211yesmaximal, characteristic
7#11751047C211yesmaximal, characteristic, complemented
8#11751045C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
10C4×#6714C211yesmaximal, characteristic, complemented
11C4×#6712C211yesmaximal, characteristic, complemented
12#11750770C211yesmaximal, characteristic, complemented
13#11750770C211yesmaximal, characteristic, complemented
14#11750750C211yesmaximal, characteristic, complemented
15#11750747C211yesmaximal, characteristic, complemented
16#10607212—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×#6712C2211yescharacteristic
38C2×C4×Dic15C2211yescharacteristic
39C2×C4×Dic15C2211yescharacteristic
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42C2×C4×Dic15C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44#91776—24no—
45#91774C418yescomplemented
46#91770—24no—
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#75481—51nomaximal, Hall
56C2×#4033—31no—
57C2×#4031—31no—
58C2×#4027—31no—
59C5×#388D311yescharacteristic, complemented
60#65278—31no—
61#65246—31no—
62#65235—31no—
63#65233—31no—
64C22⋊C4×Dic5—31no—
65C4×#685—31no—
66C4×#683—31no—
67#64958—31no—
68#64958—31no—
69#64938—31no—
70#64935—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—22no—
80C2×#1220—22no—
81C2×#1220C2×C414yes—
82C22×Dic15—22no—
83C22×Dic15—22no—
84C22×Dic15—41no—
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C2×C4×D15—22no—
93C2×C4×D15—22no—
94C2×C4×D15—41no—
95C2×Dic30—22no—
96C2×Dic30—22no—
97C2×Dic30C2×C414yescomplemented
98C3×C5×C4⋊C4—22no—
99C3×C5×C22⋊C4—22no—
100C3×C5×C22⋊C4—41no—
101C3×C5×C22⋊C4C2×C414yescomplemented
102C3×C42×C5—41no—
103#6719—22no—
104#6719C2×C414yescomplemented
105#6714—22no—
106#6714—22no—
107#6714—41no—
108#6714C2×C414yescomplemented
109#6714C2×C414yescomplemented
110#6712—22no—
111#6712—22no—
112#6712—22no—
113#6712—22no—
114#6712D414yes—
115C4×Dic15—22no—
116C4×Dic15—22no—
117C4×Dic15—22no—
118C4×Dic15—22no—
119C4×Dic15—41no—
120C4×Dic15C2×C414yescomplemented
121C2×#887—51no—
122C2×#885—51no—
123C2×#67⋊C4—51no—
124C3×#388D511yescharacteristic, complemented
125#4989—51no—
126#4957—51no—
127#4946—51no—
128#4944—51no—
129Dic3×C22⋊C4—51no—
130C4×(C2×D3)⋊C4—51no—
131C4×Dic3⋊C4—51no—
132#4669—51no—
133#4669—51no—
134#4649—51no—
135#4646—51no—
136C22×C22⋊D5—31no—
137C23×Dic5—31no—
138C22×C4×D5—31no—
139C22×Dic10—31no—
140C2×C5×C4⋊C4C2×D311yescharacteristic
141C2×C5×C22⋊C4C2×D311yescharacteristic
142C2×C5×C22⋊C4C2×D311yescharacteristic
143C2×C5×C22⋊C4C2×D311yescharacteristic
144C2×C42×C5C2×D311yescharacteristic
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163#4033—64no—
164#4031—38no—
165#4027—64no—
166C5×#95C2×D311yescharacteristic
167C5×#95C2×D311yescharacteristic
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#2367—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×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×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5C22×C412yes—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C2×D412yes—
208#1220—28no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—44no—
223C2×Dic15C22×C412yes—
224C2×Dic15C22×C412yes—
225C2×Dic15C22×C412yes—
226C2×Dic15C2×D412yes—
227C2×Dic15C2×D412yes—
228C2×Dic15#4112yes—
229C2×Dic15#4112yes—
230C2×Dic15#4112yes—
231C4×D15—44no—
232Dic30—28no—
233C22×#67—51no—
234C23×Dic3—51no—
235C22×C4×D3—51no—
236C22×Dic6—51no—
237C2×C3×C4⋊C4C2×D511yescharacteristic
238C2×C3×C22⋊C4C2×D511yescharacteristic
239C2×C3×C22⋊C4C2×D511yescharacteristic
240C2×C3×C22⋊C4C2×D511yescharacteristic
241C2×C3×C42C2×D511yescharacteristic
242C2×#217—51no—
243C2×#217—51no—
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×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260#887—104no—
261#885—58no—
262#67⋊C4—104no—
263C3×#95C2×D511yescharacteristic
264C3×#95C2×D511yescharacteristic
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C24×C5C22×D311yescharacteristic
272C23×D5—31no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×C4×C5C22×D311yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C2×C22⋊D5—34no—
280C2×C22⋊D5—62no—
281C2×C22⋊D5—62no—
282C22×Dic5—31no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5—31no—
288C22×Dic5—31no—
289C22×Dic5—62no—
290C22×Dic5—62no—
291C22×Dic5—121no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—121no—
295C2×Dic10—34no—
296C2×Dic10—62no—
297C2×Dic10—62no—
298C5×C4⋊C4—22no—
299C5×C22⋊C4—22no—
300C5×C22⋊C4—41no—
301C5×C22⋊C4C4×D314yescomplemented
302C42×C5—41no—
303C22⋊Dic5—34no—
304C22⋊Dic5—62no—
305#685—34no—
306#685—34no—
307#685—62no—
308#685—62no—
309#685—121no—
310#683—34no—
311#683—62no—
312#683—62no—
313#683—62no—
314#683—62no—
315C4×Dic5—34no—
316C4×Dic5—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—121no—
321C2×#124—151no—
322C2×C4×Q8—151no—
323C2×C4×D4—151no—
324#391—151no—
325#390—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#388D1511yescharacteristic, complemented
330#385—151no—
331#385—151no—
332C4×C4⋊C4—151no—
333C4×C4⋊C4—151no—
334C4×C22⋊C4—151no—
335C4×C22⋊C4—151no—
336C22×C3×C5—22no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5C23×C411yescharacteristic
344C22×C3×C5C22×D411yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C52−1+411yescharacteristic
350C2×D15—22no—
351C2×D15—22no—
352C2×D15—22no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—41no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363Dic15—22no—
364Dic15—22no—
365Dic15—22no—
366Dic15—22no—
367Dic15—22no—
368Dic15—41no—
369Dic15C4×D414yes—
370C24×C3C22×D511yescharacteristic
371C23×D3—51no—
372C22×C3×C4C22×D511yescharacteristic
373C22×C3×C4C22×D511yescharacteristic
374C22×C3×C4C22×D511yescharacteristic
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—54no—
379C2×#67—102no—
380C2×#67—102no—
381C22×Dic3—51no—
382C22×Dic3—51no—
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—51no—
388C22×Dic3—102no—
389C22×Dic3—102no—
390C22×Dic3—201no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—201no—
394C2×Dic6—54no—
395C2×Dic6—102no—
396C2×Dic6—102no—
397C3×C4⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—41no—
400C3×C22⋊C4C4×D514yescomplemented
401C3×C42—41no—
402#217—54no—
403#217—102no—
404(C2×D3)⋊C4—54no—
405(C2×D3)⋊C4—54no—
406(C2×D3)⋊C4—102no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4—201no—
409Dic3⋊C4—54no—
410Dic3⋊C4—102no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413Dic3⋊C4—102no—
414C4×Dic3—54no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—201no—
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5C2×C4×D312yes—
427C23×C5C23×D311yescharacteristic
428C22×D5—32no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5C2×C4×D312yes—
451C2×C4×C5C2×C4×D312yes—
452C2×C4×C5D3×D412yes—
453C22⋊D5—68no—
454C2×Dic5—32no—
455C2×Dic5—32no—
456C2×Dic5—32no—
457C2×Dic5—32no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—61no—
463C2×Dic5—61no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—124no—
476C4×D5—124no—
477Dic10—68no—
478C22×Q8—151no—
479C22×D4—151no—
480C23×C4—151no—
481C23×C4—151no—
482#124—158no—
483C4×Q8—304no—
484C4×D4—304no—
485C2×C4⋊C4—151no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4C2×D1511yescharacteristic
491C2×C22⋊C4—151no—
492C2×C22⋊C4—151no—
493C2×C22⋊C4—151no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4C2×D1511yescharacteristic
499C2×C22⋊C4C2×D1511yescharacteristic
500C2×C22⋊C4C2×D1511yescharacteristic
501C2×C42—151no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42C2×D1511yescharacteristic
508#95—151no—
509#95—151no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514#95C2×D1511yescharacteristic
515#95C2×D1511yescharacteristic
516C2×C3×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5#52011yescharacteristic
520C2×C3×C5#54611yescharacteristic
521C2×C3×C5#54811yescharacteristic
522C2×C3×C5#55611yescharacteristic
523C2×C3×C5#55911yescharacteristic
524D15—42no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3C2×C4×D512yes—
532C23×C3C23×D511yescharacteristic
533C22×D3—52no—
534C22×D3—101no—
535C22×D3—101no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4C2×C4×D512yes—
556C2×C3×C4C2×C4×D512yes—
557C2×C3×C4D4×D512yes—
558#67—108no—
559C2×Dic3—52no—
560C2×Dic3—52no—
561C2×Dic3—52no—
562C2×Dic3—52no—
563C2×Dic3—52no—
564C2×Dic3—52no—
565C2×Dic3—52no—
566C2×Dic3—52no—
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×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—204no—
581C4×D3—204no—
582Dic6—108no—
583C22×C5—22no—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—41no—
590C22×C5C22×C4×D311yescharacteristic
591C22×C5C2×D3×D411yescharacteristic
592C22×C5#100411yescharacteristic
593C22×C5D3×#4111yescharacteristic
594C22×C5D3×#4111yescharacteristic
595C22×C5D3×#4111yescharacteristic
596C22×C5#101011yescharacteristic
597C2×D5—62no—
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—121no—
601C2×D5—121no—
602C2×D5—121no—
603C2×D5—121no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—41no—
608C4×C5—41no—
609C4×C5—41no—
610Dic5—34no—
611Dic5—62no—
612Dic5—62no—
613Dic5—62no—
614Dic5—62no—
615Dic5—62no—
616Dic5—121no—
617C24—151no—
618C24C22×D1511yescharacteristic
619C2×Q8—154no—
620C2×Q8—302no—
621C2×Q8—302no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—151no—
626C22×C4—151no—
627C22×C4—151no—
628C22×C4—151no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—302no—
633C22×C4—302no—
634C22×C4—302no—
635C22×C4—302no—
636C22×C4—601no—
637C22×C4—601no—
638C22×C4C22×D1511yescharacteristic
639C22×C4C22×D1511yescharacteristic
640C22×C4C22×D1511yescharacteristic
641C22×C4C22×D1511yescharacteristic
642C22×C4C22×D1511yescharacteristic
643C22×C4C22×D1511yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—154no—
646C4⋊C4—302no—
647C4⋊C4—302no—
648C4⋊C4—302no—
649C4⋊C4—302no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—154no—
653C22⋊C4—154no—
654C22⋊C4—154no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C22⋊C4—601no—
659C22⋊C4C4×D1514yescomplemented
660C42—41no—
661C42—154no—
662C42—302no—
663C42—302no—
664C42—302no—
665C42—302no—
666C42—601no—
667C3×C5#236711yescharacteristic, complemented, Hall
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3C22×C4×D511yescharacteristic
676C22×C3C2×D4×D511yescharacteristic
677C22×C3#414411yescharacteristic
678C22×C3D5×#4111yescharacteristic
679C22×C3D5×#4111yescharacteristic
680C22×C3D5×#4111yescharacteristic
681C22×C3#415011yescharacteristic
682C2×D3—102no—
683C2×D3—102no—
684C2×D3—102no—
685C2×D3—201no—
686C2×D3—201no—
687C2×D3—201no—
688C2×D3—201no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695Dic3—54no—
696Dic3—102no—
697Dic3—102no—
698Dic3—102no—
699Dic3—102no—
700Dic3—102no—
701Dic3—201no—
702C2×C5—42no—
703C2×C5#552211yescharacteristic
704C2×C5C4×D3×D411yescharacteristic
705C2×C5#554611yescharacteristic
706C2×C5#561011yescharacteristic
707C2×C5#566411yescharacteristic
708C2×C5#567711yescharacteristic
709C2×C5#570211yescharacteristic
710D5—122no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—152no—
718C23—301no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23C2×C4×D1512yes—
725C23C23×D1511yescharacteristic
726Q8—308no—
727D4—308no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—152no—
744C2×C4—152no—
745C2×C4—152no—
746C2×C4—152no—
747C2×C4—152no—
748C2×C4—152no—
749C2×C4—152no—
750C2×C4—152no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—301no—
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×C4—604no—
765C2×C4—604no—
766C2×C4C2×C4×D1512yes—
767C2×C4C2×C4×D1512yes—
768C2×C4D4×D1512yes—
769C2×C3—42no—
770C2×C3#6585611yescharacteristic
771C2×C3C4×D4×D511yescharacteristic
772C2×C3#6588011yescharacteristic
773C2×C3#6594411yescharacteristic
774C2×C3#6599811yescharacteristic
775C2×C3#6601111yescharacteristic
776C2×C3#6603611yescharacteristic
777D3—202no—
778C5#7548111yescharacteristic, complemented, Sylow
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—302no—
787C22—302no—
788C22—302no—
789C22—601no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22C22×C4×D1511yescharacteristic
794C22C2×D4×D1511yescharacteristic
795C22#9209511yescharacteristic
796C22#41×D1511yescharacteristic
797C22#41×D1511yescharacteristic
798C22#41×D1511yescharacteristic
799C22#9210111yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—154no—
807C4—302no—
808C4—302no—
809C4—302no—
810C4—302no—
811C4—302no—
812C4—601no—
813C3#1060721211yescharacteristic, complemented, Sylow
814C2—42no—
815C2—602no—
816C2#1175628111yescharacteristic
817C2C4×D4×D1511yescharacteristic
818C2#1175630511yescharacteristic
819C2#1175636911yescharacteristic
820C2#1175642311yescharacteristic
821C2#1175643611yescharacteristic
822C2#1175646111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#388D15
hypocenterC3×C5#2367
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91776C2semidirect
4. C3×C5×#388C2semidirect
5. #11751090C2semidirect
7. #11751047C2semidirect
8. #11751045C2semidirect
9. C22⋊C4×Dic15C2semidirect
10. C4×#6714C2semidirect
11. C4×#6712C2semidirect
12. #11750770C2semidirect
13. #11750770C2semidirect
14. #11750750C2semidirect
15. #11750747C2semidirect
45. #91774C4semidirect
59. C5×#388D3semidirect
97. C2×Dic30C2×C4semidirect
101. C3×C5×C22⋊C4C2×C4semidirect
104. #6719C2×C4semidirect
108. #6714C2×C4semidirect
109. #6714C2×C4semidirect
120. C4×Dic15C2×C4semidirect
124. C3×#388D5semidirect
301. C5×C22⋊C4C4×D3semidirect
329. #388D15semidirect
400. C3×C22⋊C4C4×D5semidirect
659. C22⋊C4C4×D15semidirect
667. C3×C5#2367semidirect
778. C5#75481semidirect
813. C3#10607212semidirect

Maximal subgroups

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

subgroupindex
C2×#917762
C2×#917742
C2×#917702
C3×C5×#3882
#117510902
#117510582
#117510472
#117510452
C22⋊C4×Dic152
C4×#67142
C4×#67122
#117507702
#117507502
#117507472
#106072123
#754815