Finite Group Databasebeta

← #14323919

Subgroups — #14323919

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4085C211yesmaximal, characteristic
2C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#91528C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C5×#5220C211yesmaximal, characteristic, complemented
6#11749518C211yesmaximal, characteristic, complemented
7#11749511C211yesmaximal, characteristic, complemented
8#11749506C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11749489C211yesmaximal, characteristic, complemented
11#11749485C211yesmaximal, characteristic, complemented
12#11748900C211yesmaximal, characteristic, complemented
13#11748791C211yesmaximal, characteristic, complemented
14#11748680C211yesmaximal, characteristic, complemented
15#11748637C211yesmaximal, characteristic, complemented
16#10606396—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C2×C5×#217C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C3×#4085C418yescomplemented
34C2×C3×#685C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36Dic3×C22⋊D5—24no—
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6668C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45#91528—24no—
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82633—51nomaximal, Hall
56C2×#4085D311yescharacteristic
57C2×C4×C22⋊D5—31no—
58C2×#4023—31no—
59C5×#386—31no—
60#65510—31no—
61#65499—31no—
62#65246—31no—
63#65246—31no—
64#65245—31no—
65#65233—31no—
66#65231—31no—
67#64958—31no—
68#64957—31no—
69#64938—31no—
70#64936—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C2×C3×C5×D4—41no—
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4C2×C414yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×C5×Dic3—22no—
83C22×C5×Dic3—41no—
84C22×C5×Dic3—41no—
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C2×C3×C22⋊D5—22no—
90C2×C3×C22⋊D5—22no—
91C2×C3×C22⋊D5—41no—
92C2×C3×C22⋊D5—41no—
93C2×C3×C22⋊D5C2×C414yes—
94C2×C3×C22⋊D5C2×C414yescomplemented
95C22×C3×Dic5—22no—
96C22×C3×Dic5—22no—
97C22×C3×Dic5C2×C414yescomplemented
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×D5×Dic3—22no—
102C2×D5×Dic3—41no—
103C2×D5×Dic3—41no—
104#6719—22no—
105#6719—22no—
106#6719—41no—
107#6719—41no—
108C4⋊Dic15—41no—
109C4×Dic15—41no—
110C5×#217—22no—
111C5×#217—41no—
112C5×#217—41no—
113C3×C22⋊Dic5C2×C414yescomplemented
114C3×#685C2×C414yescomplemented
115C3×#683C2×C414yescomplemented
116#6668—22no—
117#6668—22no—
118#6668—22no—
119#6668—22no—
120#6668—41no—
121#6665—22no—
122#6665—41no—
123#6665—41no—
124Dic3×Dic5—22no—
125Dic3×Dic5—41no—
126Dic3×Dic5D414yescomplemented
127C2×C3×#121—51no—
128C2×D4×Dic3—51no—
129C2×#926—51no—
130#5221—51no—
131#5221—51no—
132#5221—51no—
133#5220—51no—
134#5220D511yescharacteristic, complemented
135#5212—51no—
136#4984—51no—
137Dic3×C4⋊C4—51no—
138#4951—51no—
139#4951—51no—
140#4950—51no—
141#4950—51no—
142C22×C5×D4C2×D311yescharacteristic
143C23×C4×C5—31no—
144C22×C22⋊D5C2×D311yescharacteristic
145C22×C22⋊D5C2×D311yescharacteristic
146C23×Dic5C2×D311yescharacteristic
147C22×C4×D5—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5C2×D311yescharacteristic
156#4085Dic318yescomplemented
157C4×C22⋊D5—64no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685C2×D311yescharacteristic
162C2×C4⋊Dic5—31no—
163C2×#683—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×#683C2×D311yescharacteristic
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
172C2×C4×Dic5—31no—
173#4023—64no—
174C5×#95—31no—
175C5×#95—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2324—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C22×C412yes—
195C23×C3×C5C2411yescharacteristic
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5C22×C412yes—
203C3×C5×D4—44no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5C22×C412yes—
207C2×Dic15—21no—
208C2×Dic15—21no—
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×Dic15C2×D412yes—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—44no—
231C2×C5×Dic3C2×D412yes—
232C3×C22⋊D5—28no—
233C3×C22⋊D5—44no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—28no—
239C2×C3×Dic5C22×C412yes—
240C2×C3×Dic5C22×C412yes—
241C2×C3×Dic5C22×C412yes—
242C2×C3×Dic5C2×D412yes—
243C2×C3×Dic5#4112yes—
244D5×Dic3—44no—
245C22×C3×D4—51no—
246C22×C3×D4—51no—
247C22×C3×D4C2×D511yescharacteristic
248C23×C3×C4—51no—
249C23×Dic3—51no—
250C23×Dic3C2×D511yescharacteristic
251C3×#121—58no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4—51no—
255C2×#217—51no—
256C2×#217—51no—
257C2×#217—51no—
258C2×#217—51no—
259C2×#217—51no—
260C2×#217—51no—
261C2×#217—51no—
262C2×#217C2×D511yescharacteristic
263C2×#217C2×D511yescharacteristic
264C2×#217C2×D511yescharacteristic
265D4×Dic3—104no—
266#926—104no—
267C2×C4⋊Dic3—51no—
268C2×C4⋊Dic3—51no—
269C2×C4⋊Dic3—51no—
270C2×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×C4⋊Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C3⋊#95—51no—
278C3⋊#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95C2×D511yescharacteristic
282C3⋊#95C2×D511yescharacteristic
283C24×C5C22×D311yescharacteristic
284C24×C5C22×D311yescharacteristic
285C23×D5C22×D311yescharacteristic
286C2×C5×D4—41no—
287C2×C5×D4—41no—
288C2×C5×D4C2×Dic314yescomplemented
289C22×C4×C5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—31no—
293C22×C4×C5—62no—
294C22×C4×C5—121no—
295C22×C4×C5—121no—
296C22×C4×C5C22×D311yescharacteristic
297C2×C22⋊D5—22no—
298C2×C22⋊D5—22no—
299C2×C22⋊D5—41no—
300C2×C22⋊D5—41no—
301C2×C22⋊D5C2×Dic314yes—
302C2×C22⋊D5C2×Dic314yescomplemented
303C22×Dic5—22no—
304C22×Dic5—22no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5C2×Dic314yescomplemented
310C22×Dic5C22×D311yescharacteristic
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C2×C4×D5—62no—
314C2×C4×D5—121no—
315C2×C4×D5—121no—
316C5×C22⋊C4—62no—
317C5×C22⋊C4—121no—
318C5×C22⋊C4—121no—
319C22⋊Dic5—62no—
320C22⋊Dic5—62no—
321C22⋊Dic5—121no—
322C22⋊Dic5—121no—
323C22⋊Dic5C2×Dic314yescomplemented
324#685—62no—
325#685—121no—
326#685—121no—
327#685C2×Dic314yescomplemented
328C4⋊Dic5—121no—
329#683—62no—
330#683—62no—
331#683—62no—
332#683—62no—
333#683—121no—
334#683C2×Dic314yescomplemented
335C4×Dic5—34no—
336C4×Dic5—62no—
337C4×Dic5—121no—
338C4×Dic5—121no—
339C2×#121—51no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—151no—
343#390—151no—
344#390—151no—
345#389—151no—
346#388—151no—
347#388—151no—
348#386—31no—
349#386—151no—
350#385—151no—
351#385—151no—
352#380—151no—
353C4×C4⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C52−1+411yescharacteristic
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C3×C4×C5—22no—
383Dic15—22no—
384Dic15—41no—
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5C4×D414yes—
390C5×Dic3—22no—
391C5×Dic3—41no—
392C5×Dic3—41no—
393C5×Dic3—41no—
394C24×C3—51no—
395C24×C3C22×D511yescharacteristic
396C24×C3C22×D511yescharacteristic
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4—54no—
400C2×C3×D4—54no—
401C2×C3×D4—102no—
402C2×C3×D4—102no—
403C2×C3×D4—201no—
404C2×C3×D4—201no—
405C2×C3×D4C4×D514yescomplemented
406C22×C3×C4—51no—
407C22×C3×C4—54no—
408C22×C3×C4—51no—
409C22×C3×C4—51no—
410C22×C3×C4—102no—
411C22×C3×C4—102no—
412C22×C3×C4C22×D511yescharacteristic
413C22×Dic3—22no—
414C22×Dic3—41no—
415C22×Dic3—41no—
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3—102no—
421C22×Dic3—201no—
422C22×Dic3—201no—
423C22×Dic3C22×D511yescharacteristic
424C22×Dic3C22×D511yescharacteristic
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C3×C4⋊C4—54no—
428C3×C22⋊C4—54no—
429C3×C22⋊C4—54no—
430#217—22no—
431#217—41no—
432#217—41no—
433#217—102no—
434#217—102no—
435#217—102no—
436#217—201no—
437#217—201no—
438#217—201no—
439#217—201no—
440C4⋊Dic3—102no—
441C4⋊Dic3—102no—
442C4⋊Dic3—102no—
443C4⋊Dic3—102no—
444C4⋊Dic3—201no—
445C4⋊Dic3—201no—
446C4×Dic3—54no—
447C4×Dic3—102no—
448C4×Dic3—201no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C22×Dic312yes—
463C23×C5C22×Dic312yes—
464C23×C5C23×D311yescharacteristic
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5C22×Dic312yes—
472C5×D4—44no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—32no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5—124no—
488C2×C4×C5C22×Dic312yes—
489C22⋊D5—28no—
490C22⋊D5—44no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—28no—
496C2×Dic5—32no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5D3×D412yes—
509C2×Dic5#23712yes—
510C2×Dic5C22×Dic312yes—
511C2×Dic5C22×Dic312yes—
512C2×Dic5C22×Dic312yes—
513C4×D5—124no—
514C22×D4—51no—
515C22×D4—51no—
516C22×D4D3×D511yescharacteristic
517C23×C4—31no—
518C23×C4—51no—
519C23×C4—151no—
520#121—58no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—51no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546#95—31no—
547#95—31no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5—42no—
553C2×C3×C5—42no—
554C2×C3×C5C2×C4×D411yescharacteristic
555C2×C3×C5#51811yescharacteristic
556C2×C3×C5#52011yescharacteristic
557C2×C3×C5#53511yescharacteristic
558C2×C3×C5#53711yescharacteristic
559C2×C3×C5#54011yescharacteristic
560C2×C3×C5#54211yescharacteristic
561C3×D5—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—52no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3—101no—
581C23×C3C2×C4×D512yes—
582C23×C3C2×C4×D512yes—
583C23×C3C23×D511yescharacteristic
584C3×D4—44no—
585C3×D4—108no—
586C3×D4—204no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—52no—
594C2×C3×C4—108no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4C2×C4×D512yes—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—44no—
612C2×Dic3—52no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—101no—
624C2×Dic3—204no—
625C2×Dic3D4×D512yes—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5—22no—
631C22×C5—22no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5C2×D3×D411yescharacteristic
641C22×C5C2×#23711yescharacteristic
642C22×C5#100411yescharacteristic
643C22×C5#100411yescharacteristic
644C22×C5#100911yescharacteristic
645C22×C5#101011yescharacteristic
646C22×C5C23×Dic311yescharacteristic
647C2×D5—22no—
648C2×D5—22no—
649C2×D5—22no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C4×C5—22no—
655C4×C5—62no—
656C4×C5—121no—
657C4×C5—121no—
658C4×C5—121no—
659Dic5—22no—
660Dic5—22no—
661Dic5—62no—
662Dic5—121no—
663Dic5—121no—
664Dic5—121no—
665Dic5D4×Dic314yes—
666C24—51no—
667C24C2×D3×D511yescharacteristic
668C24C2×D3×D511yescharacteristic
669C2×D4—41no—
670C2×D4—41no—
671C2×D4—54no—
672C2×D4—54no—
673C2×D4—102no—
674C2×D4—102no—
675C2×D4—201no—
676C2×D4—201no—
677C2×D4D5×Dic314yescomplemented
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—51no—
683C22×C4—54no—
684C22×C4—51no—
685C22×C4—51no—
686C22×C4—62no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—121no—
690C22×C4—121no—
691C22×C4—151no—
692C22×C4—151no—
693C22×C4—151no—
694C22×C4—151no—
695C22×C4—302no—
696C22×C4—601no—
697C22×C4—601no—
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—54no—
700C4⋊C4—302no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—601no—
705C4⋊C4—601no—
706C22⋊C4—54no—
707C22⋊C4—54no—
708C22⋊C4—62no—
709C22⋊C4—121no—
710C22⋊C4—121no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C22⋊C4—601no—
717C22⋊C4—601no—
718C42—154no—
719C42—302no—
720C42—601no—
721C42—601no—
722C3×C5#232411yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—102no—
738C22×C3—102no—
739C22×C3—102no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3C22×C4×D511yescharacteristic
745C22×C3C2×D4×D511yescharacteristic
746C22×C3#414411yescharacteristic
747C22×C3#414411yescharacteristic
748C22×C3#414411yescharacteristic
749C22×C3D5×#4111yescharacteristic
750C22×C3#415011yescharacteristic
751C3×C4—22no—
752C3×C4—54no—
753C3×C4—102no—
754C3×C4—102no—
755Dic3—22no—
756Dic3—41no—
757Dic3—41no—
758Dic3—41no—
759Dic3—102no—
760Dic3—201no—
761Dic3—201no—
762Dic3—201no—
763C2×C5—42no—
764C2×C5—42no—
765C2×C5#560311yescharacteristic
766C2×C5#560711yescharacteristic
767C2×C5#560811yescharacteristic
768C2×C5#561911yescharacteristic
769C2×C5C2×D4×Dic311yescharacteristic
770C2×C5#579811yescharacteristic
771C2×C5#582711yescharacteristic
772D5—42no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—52no—
786C23—101no—
787C23—101no—
788C23—101no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23C2×D5×Dic312yes—
793C23C2×D5×Dic312yes—
794C23C22×D3×D511yescharacteristic
795D4—44no—
796D4—108no—
797D4—204no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—52no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—52no—
805C2×C4—52no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—108no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—124no—
823C2×C4—152no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—604no—
836C2×C4C2×D5×Dic312yes—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3—202no—
840C2×C3#6582011yescharacteristic
841C2×C3C4×D4×D511yescharacteristic
842C2×C3#6588011yescharacteristic
843C2×C3#6592611yescharacteristic
844C2×C3#6594211yescharacteristic
845C2×C3#6594911yescharacteristic
846C2×C3#6599611yescharacteristic
847C5#8263311yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—102no—
863C22—102no—
864C22—102no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22—201no—
869C22#9202011yescharacteristic
870C22D3×D4×D511yescharacteristic
871C22D5×#23711yescharacteristic
872C22#9202711yescharacteristic
873C22C22×D5×Dic311yescharacteristic
874C22#9204911yescharacteristic
875C22#9204911yescharacteristic
876C4—22no—
877C4—54no—
878C4—62no—
879C4—102no—
880C4—102no—
881C4—121no—
882C4—121no—
883C4—121no—
884C4—302no—
885C4—601no—
886C4—601no—
887C4—601no—
888C3#1060639611yescharacteristic, complemented, Sylow
889C2—42no—
890C2—42no—
891C2—202no—
892C2D4×D5×Dic311yescharacteristic
893C2#1175477611yescharacteristic
894C2#1175486011yescharacteristic
895C2#1175486711yescharacteristic
896C2#1175492311yescharacteristic
897C2#1175504611yescharacteristic
898C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4085C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×C22⋊D5C2semidirect
3. C2×#91528C2semidirect
4. #11751322C2semidirect
5. C5×#5220C2semidirect
6. #11749518C2semidirect
7. #11749511C2semidirect
8. #11749506C2semidirect
9. #11749489C2semidirect
10. #11749489C2semidirect
11. #11749485C2semidirect
12. #11748900C2semidirect
13. #11748791C2semidirect
14. #11748680C2semidirect
15. #11748637C2semidirect
33. C3×#4085C4semidirect
76. C2×C3×C5×D4C2×C4semidirect
94. C2×C3×C22⋊D5C2×C4semidirect
97. C22×C3×Dic5C2×C4semidirect
113. C3×C22⋊Dic5C2×C4semidirect
114. C3×#685C2×C4semidirect
115. C3×#683C2×C4semidirect
126. Dic3×Dic5D4semidirect
134. #5220D5semidirect
156. #4085Dic3semidirect
288. C2×C5×D4C2×Dic3semidirect
302. C2×C22⋊D5C2×Dic3semidirect
309. C22×Dic5C2×Dic3semidirect
323. C22⋊Dic5C2×Dic3semidirect
327. #685C2×Dic3semidirect
334. #683C2×Dic3semidirect
405. C2×C3×D4C4×D5semidirect
677. C2×D4D5×Dic3semidirect
722. C3×C5#2324semidirect
847. C5#82633semidirect
888. C3#10606396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40852
C2×Dic3×C22⋊D52
C2×#915282
#117513222
C5×#52202
#117495182
#117495112
#117495062
#117494892
#117494852
#117489002
#117487912
#117486802
#117486372
#106063963
#826335