Finite Group Databasebeta

← #14326355

Subgroups — #14326355

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2C2×D5×#217C211yesmaximal, characteristic
3C2×#91357C211yesmaximal, characteristic, complemented
4#11751052C211yesmaximal, characteristic, complemented
5C5×#4951C211yesmaximal, characteristic, complemented
6#11749488C211yesmaximal, characteristic
7#11749486C211yesmaximal, characteristic, complemented
8#11749485C211yesmaximal, characteristic, complemented
9#11748900C211yesmaximal, characteristic, complemented
10#11748899C211yesmaximal, characteristic, complemented
11#11748884C211yesmaximal, characteristic, complemented
12Dic3×#685C211yesmaximal, characteristic, complemented
13#11748759C211yesmaximal, characteristic, complemented
14#11748737C211yesmaximal, characteristic, complemented
15#11748702C211yesmaximal, characteristic, complemented
16#10607563—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C3×D5×C22⋊C4C418yescomplemented
35D5×#217—24no—
36C2×#6668C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91357—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#82097—51nomaximal, Hall
56C2×D5×C22⋊C4—31no—
57C2×D5×C22⋊C4D311yescharacteristic
58C2×#4018—31no—
59C5×#388—31no—
60#65278—31no—
61#65276—31no—
62#65244—31no—
63#65240—31no—
64#65234—31no—
65#65233—31no—
66C4×#685—31no—
67#64957—31no—
68#64955—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5—22no—
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5C2×C414yes—
79C23×C3×D5C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×C4×D5—22no—
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—41no—
96C2×C3×C4×D5—41no—
97C2×C3×C4×D5C2×C414yescomplemented
98C2×C3×C4×D5C2×C414yescomplemented
99C2×D5×Dic3—22no—
100C2×D5×Dic3—22no—
101C2×D5×Dic3—22no—
102C2×D5×Dic3—22no—
103C2×D5×Dic3—41no—
104C2×D5×Dic3—41no—
105C3×C5×C22⋊C4C2×C414yescomplemented
106#6719—22no—
107#6719—41no—
108C4⋊Dic15—41no—
109C4×Dic15—22no—
110C5×#217—22no—
111C5×#217—41no—
112C5×C4⋊Dic3—41no—
113C4×C5×Dic3—22no—
114C3×C22⋊Dic5C2×C414yescomplemented
115C3×#685C2×C414yes—
116C3×#685C2×C414yes—
117#6668—22no—
118#6668—22no—
119#6665—22no—
120#6665—22no—
121#6665—22no—
122#6665—22no—
123#6665—22no—
124#6665D414yes—
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C22×C3×C22⋊C4—51no—
128C22×#217—51no—
129C2×#926—51no—
130#5247—51no—
131#5212—51no—
132#5211—51no—
133C4×#217—51no—
134#4951—51no—
135#4951—51no—
136#4951—51no—
137#4951D511yescharacteristic, complemented
138#4950—51no—
139#4950—51no—
140Dic3×C22⋊C4—51no—
141Dic3×C22⋊C4—51no—
142C24×D5C2×D311yescharacteristic
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5C2×D311yescharacteristic
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5C2×D311yescharacteristic
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685C2×D311yescharacteristic
162C2×#685C2×D311yescharacteristic
163C2×C4⋊Dic5—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169D5×C22⋊C4—64no—
170D5×C22⋊C4Dic318yescomplemented
171#4018—64no—
172C5×#95—31no—
173C5×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2342—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×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—28no—
198C22×C3×D5—28no—
199C22×C3×D5—44no—
200C22×C3×D5—44no—
201C22×C3×D5—44no—
202C22×C3×D5—44no—
203C22×C3×D5—44no—
204C22×C3×D5C22×C412yes—
205C22×C3×D5C22×C412yes—
206C22×C3×D5C2×D412yes—
207C22×C3×D5#4112yes—
208C22×C3×D5#4112yes—
209C22×C3×D5#4112yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C22×C412yes—
215C2×C3×C4×C5C22×C412yes—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C2×D412yes—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3C2×D412yes—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C22×C412yes—
246C3×C4×D5—28no—
247C3×C4×D5—44no—
248D5×Dic3—44no—
249D5×Dic3—44no—
250C25×C3—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×Dic3—51no—
254C23×Dic3—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—58no—
259C2×C3×C22⋊C4C2×D511yescharacteristic
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—51no—
266C2×#217—51no—
267C2×#217—51no—
268C2×#217—104no—
269C2×#217C2×D511yescharacteristic
270C2×#217C2×D511yescharacteristic
271#926—104no—
272C2×C4⋊Dic3—51no—
273C2×C4⋊Dic3—51no—
274C2×C4⋊Dic3—51no—
275C2×C4⋊Dic3C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279C2×C4×Dic3C2×D511yescharacteristic, complemented
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5C22×D311yescharacteristic
289C23×D5—22no—
290C23×D5—22no—
291C23×D5—22no—
292C23×D5—22no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C2×Dic314yes—
296C23×D5C22×D311yescharacteristic
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—31no—
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×C4×D5—22no—
311C2×C4×D5—22no—
312C2×C4×D5—41no—
313C2×C4×D5—41no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5C2×Dic314yescomplemented
321C2×C4×D5C2×Dic314yescomplemented
322C5×C4⋊C4—121no—
323C5×C22⋊C4—62no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4C2×Dic314yescomplemented
326C42×C5—62no—
327C22⋊Dic5—62no—
328C22⋊Dic5—121no—
329C22⋊Dic5C2×Dic314yescomplemented
330#685—34no—
331#685—62no—
332#685—62no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685C2×Dic314yes—
337#685C2×Dic314yes—
338C4⋊Dic5—121no—
339#683—62no—
340#683—62no—
341C4×Dic5—62no—
342C4×Dic5—121no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—51no—
346C22×C22⋊C4—151no—
347#388—31no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×C3×D5—22no—
374C2×C3×D5—22no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—22no—
385C2×C3×D5—416no—
386C2×C3×D5#11714yescomplemented
387C2×C3×D5C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390Dic15—22no—
391Dic15—41no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—22no—
396C5×Dic3—22no—
397C5×Dic3—41no—
398C5×Dic3—41no—
399C5×Dic3—41no—
400C24×C3—51no—
401C24×C3—51no—
402C24×C3—54no—
403C24×C3—102no—
404C24×C3—102no—
405C24×C3—102no—
406C24×C3—102no—
407C24×C3—201no—
408C24×C3—201no—
409C24×C3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—54no—
413C22×C3×C4—54no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—201no—
417C22×C3×C4—201no—
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×Dic3—51no—
421C22×Dic3—51no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3—102no—
425C22×Dic3—102no—
426C22×Dic3—102no—
427C22×Dic3—102no—
428C22×Dic3—201no—
429C22×Dic3—201no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C3×C22⋊C4—54no—
435C3×C22⋊C4—54no—
436C3×C22⋊C4—54no—
437C3×C22⋊C4C4×D514yescomplemented
438#217—22no—
439#217—41no—
440#217—54no—
441#217—102no—
442#217—102no—
443#217—102no—
444#217—102no—
445#217—102no—
446#217—102no—
447#217—201no—
448C4⋊Dic3—41no—
449C4⋊Dic3—102no—
450C4⋊Dic3—102no—
451C4⋊Dic3—201no—
452C4×Dic3—22no—
453C4×Dic3—102no—
454C4×Dic3—201no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C22×Dic312yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—28no—
473C22×D5—28no—
474C22×D5—44no—
475C22×D5—44no—
476C22×D5—44no—
477C22×D5—44no—
478C22×D5—44no—
479C22×D5#23512yes—
480C22×D5#23512yes—
481C22×D5D3×D412yes—
482C22×D5#23712yes—
483C22×D5C22×Dic312yes—
484C22×D5C22×Dic312yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—32no—
490C2×C4×C5—61no—
491C2×C4×C5—61no—
492C2×C4×C5—61no—
493C2×C4×C5—61no—
494C2×C4×C5—61no—
495C2×C4×C5—61no—
496C2×C4×C5—61no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5C22×Dic312yes—
502C2×C4×C5C22×Dic312yes—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—32no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5C22×Dic312yes—
520C2×Dic5C22×Dic312yes—
521C4×D5—28no—
522C4×D5—44no—
523C4×D5—124no—
524C4×D5—124no—
525C25—51no—
526C23×C4—51no—
527C23×C4—51no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—58no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4—151no—
545C2×C22⋊C4—151no—
546C2×C22⋊C4—151no—
547C2×C22⋊C4—151no—
548C2×C22⋊C4—151no—
549C2×C22⋊C4—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—31no—
552C2×C42—151no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—31no—
557#95—151no—
558#95—151no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5—42no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571C3×D5—24no—
572C3×D5—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—52no—
580C23×C3—52no—
581C23×C3—52no—
582C23×C3—52no—
583C23×C3—52no—
584C23×C3—52no—
585C23×C3—108no—
586C23×C3—108no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—204no—
596C23×C3—204no—
597C23×C3—204no—
598C23×C3—204no—
599C23×C3—204no—
600C23×C3C2×C4×D512yes—
601C23×C3C23×D511yescharacteristic
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—52no—
607C2×C3×C4—52no—
608C2×C3×C4—108no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—204no—
614C2×C3×C4C2×C4×D512yes—
615C2×C3×C4C2×C4×D512yes—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—52no—
628C2×Dic3—101no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—204no—
640C2×Dic3—204no—
641C2×Dic3D4×D512yes—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5C2×#23511yescharacteristic
650C22×C5C2×#23511yescharacteristic
651C22×C5C2×D3×D411yescharacteristic
652C22×C5C2×#23711yescharacteristic
653C22×C5#100411yescharacteristic
654C22×C5#100411yescharacteristic
655C22×C5C23×Dic311yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—416no—
669C2×D5#92614yescomplemented
670C2×D5D4×Dic314yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—121no—
675C4×C5—121no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—22no—
679Dic5—62no—
680Dic5—121no—
681Dic5—121no—
682Dic5—121no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—102no—
687C24—102no—
688C24—102no—
689C24—102no—
690C24—201no—
691C24—201no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—54no—
700C22×C4—54no—
701C22×C4—102no—
702C22×C4—102no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—201no—
708C22×C4—201no—
709C22×C4—302no—
710C22×C4—302no—
711C22×C4—302no—
712C22×C4—302no—
713C22×C4—601no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—121no—
718C4⋊C4—302no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—54no—
722C22⋊C4—54no—
723C22⋊C4—54no—
724C22⋊C4—62no—
725C22⋊C4—121no—
726C22⋊C4—154no—
727C22⋊C4—302no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—601no—
734C22⋊C4D5×Dic314yescomplemented
735C42—62no—
736C42—302no—
737C42—601no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—54no—
748C22×C3—54no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—102no—
760C22×C3—102no—
761C22×C3—2016no—
762C22×C3C22×C4×D511yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3#414411yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C22×C3D5×#4111yescharacteristic
768C22×C3#414911yescharacteristic
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—102no—
772C3×C4—102no—
773Dic3—22no—
774Dic3—41no—
775Dic3—41no—
776Dic3—41no—
777Dic3—102no—
778Dic3—201no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—42no—
782C2×C5#549011yescharacteristic
783C2×C5#549011yescharacteristic
784C2×C5#549511yescharacteristic
785C2×C5#549511yescharacteristic
786C2×C5C2×#92611yescharacteristic
787C2×C5C2×D4×Dic311yescharacteristic
788C2×C5#579811yescharacteristic
789D5—24no—
790D5—24no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—52no—
798C23—52no—
799C23—52no—
800C23—52no—
801C23—52no—
802C23—52no—
803C23—108no—
804C23—108no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—101no—
811C23—101no—
812C23—101no—
813C23—204no—
814C23—204no—
815C23—204no—
816C23—204no—
817C23—204no—
818C23C2×D5×Dic312yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—32no—
825C2×C4—52no—
826C2×C4—52no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—108no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—152no—
844C2×C4—204no—
845C2×C4—301no—
846C2×C4—301no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—604no—
857C2×C4—604no—
858C2×C4C2×D5×Dic312yes—
859C2×C4C2×D5×Dic312yes—
860C2×C3—42no—
861C2×C3—104no—
862C2×C3—104no—
863C2×C3D5×#11711yescharacteristic
864C2×C3C4×D4×D511yescharacteristic
865C2×C3#6587911yescharacteristic
866C2×C3#6594611yescharacteristic
867C2×C3#6598811yescharacteristic
868C2×C3#6601311yescharacteristic
869C2×C3#6603911yescharacteristic
870C5#8209711yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—54no—
879C22—54no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—102no—
888C22—102no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—2016no—
893C22D5×#23511yescharacteristic
894C22D5×#23511yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22D5×#23711yescharacteristic
897C22#9202511yescharacteristic
898C22#9202611yescharacteristic
899C22C22×D5×Dic311yescharacteristic
900C4—22no—
901C4—22no—
902C4—62no—
903C4—102no—
904C4—102no—
905C4—121no—
906C4—121no—
907C4—121no—
908C4—302no—
909C4—601no—
910C4—601no—
911C4—601no—
912C3#1060756311yescharacteristic, complemented, Sylow
913C2—42no—
914C2—104no—
915C2—104no—
916C2#1175288911yescharacteristic
917C2#1175289111yescharacteristic
918C2#1175322611yescharacteristic
919C2#1175323611yescharacteristic
920C2D5×#92611yescharacteristic
921C2D4×D5×Dic311yescharacteristic
922C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
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
3. C2×#91357C2semidirect
4. #11751052C2semidirect
5. C5×#4951C2semidirect
7. #11749486C2semidirect
8. #11749485C2semidirect
9. #11748900C2semidirect
10. #11748899C2semidirect
11. #11748884C2semidirect
12. Dic3×#685C2semidirect
13. #11748759C2semidirect
14. #11748737C2semidirect
15. #11748702C2semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
34. C3×D5×C22⋊C4C4semidirect
36. C2×#6668C22semidirect
37. C2×#6668C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
97. C2×C3×C4×D5C2×C4semidirect
98. C2×C3×C4×D5C2×C4semidirect
105. C3×C5×C22⋊C4C2×C4semidirect
114. C3×C22⋊Dic5C2×C4semidirect
137. #4951D5semidirect
170. D5×C22⋊C4Dic3semidirect
275. C2×C4⋊Dic3C2×D5semidirect
279. C2×C4×Dic3C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
320. C2×C4×D5C2×Dic3semidirect
321. C2×C4×D5C2×Dic3semidirect
325. C5×C22⋊C4C2×Dic3semidirect
329. C22⋊Dic5C2×Dic3semidirect
386. C2×C3×D5#117semidirect
437. C3×C22⋊C4C4×D5semidirect
669. C2×D5#926semidirect
734. C22⋊C4D5×Dic3semidirect
739. C3×C5#2342semidirect
870. C5#82097semidirect
912. C3#10607563semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C2×D5×#2172
C2×#913572
#117510522
C5×#49512
#117494882
#117494862
#117494852
#117489002
#117488992
#117488842
Dic3×#6852
#117487592
#117487372
#117487022
#106075633
#820975