Finite Group Databasebeta

← #14326257

Subgroups — #14326257

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×#91473C211yesmaximal, characteristic
2C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#91357C211yesmaximal, characteristic, complemented
4#11750767C211yesmaximal, characteristic, complemented
5C5×#4669C211yesmaximal, characteristic, complemented
6C3×#64953C211yesmaximal, characteristic, complemented
7#11748940C211yesmaximal, characteristic
8#11748895C211yesmaximal, characteristic, complemented
9#11748884C211yesmaximal, characteristic, complemented
10#11748881C211yesmaximal, characteristic, complemented
11#11748878C211yesmaximal, characteristic, complemented
12#11748794C211yesmaximal, characteristic, complemented
13#11748731C211yesmaximal, characteristic, complemented
14#11748724C211yesmaximal, characteristic, complemented
15#11748723C211yesmaximal, characteristic, complemented
16#10607563—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic, complemented
25C2×C4×Dic15C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic, complemented
34C2×#6668C2211yescharacteristic, complemented
35C2×#6668C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44#91473—24no—
45D5×(C2×D3)⋊C4C418yescomplemented
46#91357—24no—
47C3×C5×#95C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#74122—51nomaximal, Hall
56C2×D5×C22⋊C4—31no—
57C2×D5×C22⋊C4—31no—
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#64953D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×D3×D5—22no—
75C22×D3×D5—22no—
76C22×D3×D5—22no—
77C22×D3×D5—22no—
78C22×D3×D5—41no—
79C22×D3×D5—41no—
80C22×D3×D5C2×C414yes—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C4×D15—22no—
88C2×C4×D15—22no—
89C2×C4×D15—41no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5C2×C414yescomplemented
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—41no—
102C2×D5×Dic3—41no—
103C2×D5×Dic3—41no—
104C2×D5×Dic3C2×C414yescomplemented
105#6714—22no—
106#6714C2×C414yes—
107C4×Dic15—22no—
108C4×Dic15—41no—
109C5×(C2×D3)⋊C4—22no—
110C5×(C2×D3)⋊C4—41no—
111C5×(C2×D3)⋊C4C2×C414yescomplemented
112C5×Dic3⋊C4—41no—
113C4×C5×Dic3—22no—
114C3×#685—22no—
115C3×#685—22no—
116Dic3⋊Dic5—41no—
117#6668—22no—
118#6668—22no—
119#6667—22no—
120#6667C2×C414yes—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—41no—
123(C2×D3)⋊Dic5C2×C414yescomplemented
124#6665—22no—
125#6665D414yes—
126Dic3×Dic5—41no—
127C22×(C2×D3)⋊C4—51no—
128C2×#926—51no—
129C2×D3×C22⋊C4—51no—
130C3×#381—51no—
131#4955—51no—
132#4942—51no—
133Dic3×C22⋊C4—51no—
134#4670—51no—
135#4670—51no—
136#4669—51no—
137#4669D511yescharacteristic, complemented
138#4668—51no—
139#4668—51no—
140#4666—51no—
141#4666—51no—
142C24×D5—31no—
143C22×C4×D5—31no—
144C22×C4×D5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
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—38no—
170D5×C22⋊C4—64no—
171#4018—64no—
172C5×#95—31no—
173C5×#95C2×D311yescharacteristic, complemented
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963C2×D311yescharacteristic, complemented
178#3963C2×D311yescharacteristic, complemented
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×D15#4112yes—
188C22×D15#4112yes—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3C22×C412yes—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5C22×C412yes—
201C22×C3×D5C2×D412yes—
202C22×C3×D5#4112yes—
203C2×D3×D5—28no—
204C2×D3×D5—28no—
205C2×D3×D5—44no—
206C2×D3×D5—44no—
207C2×D3×D5—44no—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5C22×C412yes—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15C22×C412yes—
227C2×Dic15C2×D412yes—
228C4×D15—44no—
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×Dic3C22×C412yes—
237C2×C5×Dic3C2×D412yes—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5C22×C412yes—
247C3×C4×D5—28no—
248#1200—44no—
249D5×Dic3—44no—
250C24×D3—51no—
251C23×C3×C4—51no—
252C23×Dic3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×#217—51no—
258C2×#217—51no—
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—58no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4C2×D511yescharacteristic
268C2×(C2×D3)⋊C4C2×D511yescharacteristic
269C2×(C2×D3)⋊C4C2×D511yescharacteristic
270#926—104no—
271C2×C4⋊Dic3—51no—
272C2×C4⋊Dic3—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4C2×D511yescharacteristic, complemented
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3C2×D511yescharacteristic, complemented
279D3×C22⋊C4—104no—
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C3×#95C2×D511yescharacteristic, complemented
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95C2×D511yescharacteristic, complemented
288C24×C5—31no—
289C23×D5—31no—
290C23×D5—34no—
291C23×D5—62no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5C22×D311yescharacteristic
302C22×C4×C5C22×D311yescharacteristic
303C22×C4×C5C22×D311yescharacteristic
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×C4×D5—22no—
311C2×C4×D5—22no—
312C2×C4×D5—34no—
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—62no—
316C2×C4×D5—62no—
317C2×C4×D5—121no—
318C2×C4×D5—121no—
319C2×C4×D5—121no—
320C2×C4×D5—121no—
321C2×C4×D5C4×D314yescomplemented
322C5×C4⋊C4—121no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—62no—
325C5×C22⋊C4—121no—
326C42×C5—62no—
327C22⋊Dic5—34no—
328C22⋊Dic5—62no—
329C22⋊Dic5—121no—
330#685—22no—
331#685—22no—
332#685—34no—
333#685—34no—
334#685—34no—
335#685—62no—
336#685—62no—
337#685—62no—
338C4⋊Dic5—121no—
339#683—62no—
340#683—62no—
341C4×Dic5—62no—
342C4×Dic5—121no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—31no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—151no—
352#385—151no—
353#381—51no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—151no—
357C4×C22⋊C4—151no—
358C4×C22⋊C4—151no—
359C22×C3×C5C23×C411yescharacteristic
360C22×C3×C5C22×D411yescharacteristic
361C22×C3×C5C2×#4111yescharacteristic
362C22×C3×C5C2×#4111yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C2×D15—22no—
367C2×D15—22no—
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—22no—
372C2×D15#11714yescomplemented
373C2×C5×D3—22no—
374C2×C5×D3—22no—
375C2×C5×D3—22no—
376C2×C5×D3—41no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5C4×D414yes—
387D3×D5—416no—
388C3×C4×C5—22no—
389C3×C4×C5—41no—
390C3×C4×C5—41no—
391Dic15—22no—
392Dic15—22no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3—51no—
401C23×D3—51no—
402C23×D3—54no—
403C23×D3—102no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—201no—
408C23×D3—201no—
409C23×D3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—54no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3—54no—
422C22×Dic3—51no—
423C22×Dic3—201no—
424C22×Dic3—201no—
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C22×Dic3C22×D511yescharacteristic
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—102no—
431C2×C4×D3—102no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C22⋊C4—102no—
435C3×C22⋊C4—102no—
436#217—54no—
437#217—102no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—54no—
441(C2×D3)⋊C4—54no—
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—102no—
444(C2×D3)⋊C4—102no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—201no—
447(C2×D3)⋊C4C4×D514yescomplemented
448C4⋊Dic3—102no—
449C4⋊Dic3—102no—
450Dic3⋊C4—41no—
451Dic3⋊C4—201no—
452C4×Dic3—22no—
453C4×Dic3—102no—
454C4×Dic3—201no—
455C4×Dic3—201no—
456C23×C5—32no—
457C23×C5—61no—
458C23×C5—61no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—61no—
462C23×C5—61no—
463C23×C5C23×D311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—32no—
469C22×D5—32no—
470C22×D5—32no—
471C22×D5—68no—
472C22×D5—61no—
473C22×D5—61no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—68no—
477C22×D5—124no—
478C22×D5—124no—
479C22×D5—124no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5C2×C4×D312yes—
483C22×D5D3×D412yes—
484C22×D5#23712yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—32no—
494C2×C4×C5—32no—
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×C5—61no—
502C2×C4×C5C2×C4×D312yes—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—32no—
512C2×Dic5—32no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5C2×C4×D312yes—
521C4×D5—28no—
522C4×D5—124no—
523C4×D5—124no—
524C4×D5—124no—
525C25—151no—
526C23×C4—51no—
527C23×C4—151no—
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—31no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—158no—
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—151no—
550C2×C22⋊C4—304no—
551C2×C42—31no—
552C2×C42—151no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—51no—
557#95—51no—
558#95—51no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95D3×D511yescharacteristic, complemented
563C2×C3×C5C2×#11711yescharacteristic
564C2×C3×C5C2×C4×D411yescharacteristic
565C2×C3×C5#51811yescharacteristic
566C2×C3×C5#54611yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#55111yescharacteristic
569C2×C3×C5#55111yescharacteristic
570D15—24no—
571C3×D5—24no—
572C5×D3—42no—
573C23×C3—52no—
574C23×C3—52no—
575C23×C3—52no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3C23×D511yescharacteristic
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—52no—
588C22×D3—52no—
589C22×D3—52no—
590C22×D3—108no—
591C22×D3—108no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—204no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3C2×C4×D512yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—52no—
611C2×C3×C4—108no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4C2×C4×D512yes—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—52no—
629C2×Dic3—52no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—204no—
638C2×Dic3C2×C4×D512yes—
639C2×Dic3D4×D512yes—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—62no—
643C22×C5—62no—
644C22×C5—62no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×D3×D411yescharacteristic
651C22×C5C2×#23711yescharacteristic
652C22×C5D3×#4111yescharacteristic
653C22×C5D3×#4111yescharacteristic
654C22×C5#100911yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—34no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—1216no—
670C2×D5#67⋊C414yes—
671C4×C5—22no—
672C4×C5—41no—
673C4×C5—41no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—41no—
679Dic5—41no—
680Dic5—62no—
681Dic5—62no—
682Dic5—121no—
683C24—31no—
684C24—51no—
685C24—154no—
686C24—151no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—302no—
691C24—601no—
692C24—601no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—51no—
697C22×C4—54no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—102no—
701C22×C4—102no—
702C22×C4—154no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—302no—
707C22×C4—302no—
708C22×C4—302no—
709C22×C4—302no—
710C22×C4—601no—
711C22×C4—601no—
712C22×C4—601no—
713C22×C4—601no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—121no—
718C4⋊C4—302no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—62no—
723C22⋊C4—102no—
724C22⋊C4—102no—
725C22⋊C4—121no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—302no—
734C22⋊C4—601no—
735C42—62no—
736C42—302no—
737C42—601no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—54no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3C22×C4×D511yescharacteristic
748C22×C3C2×D4×D511yescharacteristic
749C22×C3#414411yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C22×C3D5×#4111yescharacteristic
752C22×C3D5×#4111yescharacteristic
753C22×C3#414911yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—54no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—102no—
766C2×D3—102no—
767C2×D3—102no—
768C2×D3—2016no—
769C3×C4—22no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—102no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—41no—
778Dic3—102no—
779Dic3—102no—
780Dic3—201no—
781C2×C5—122no—
782C2×C5C2×#67⋊C411yescharacteristic
783C2×C5D3×#11711yescharacteristic
784C2×C5#552111yescharacteristic
785C2×C5#565411yescharacteristic
786C2×C5#565411yescharacteristic
787C2×C5#565811yescharacteristic
788C2×C5#565811yescharacteristic
789D5—24no—
790D5—64no—
791C23—32no—
792C23—52no—
793C23—52no—
794C23—52no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—152no—
806C23—152no—
807C23—152no—
808C23—308no—
809C23—308no—
810C23—301no—
811C23—301no—
812C23—301no—
813C23—301no—
814C23—604no—
815C23—604no—
816C23—604no—
817C23—604no—
818C23—604no—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—52no—
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—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—152no—
848C2×C4—152no—
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×C4—604no—
859C2×C4C4×D3×D512yes—
860C2×C3—104no—
861C2×C3D5×#11711yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6594611yescharacteristic
865C2×C3#6598811yescharacteristic
866C2×C3#6601311yescharacteristic
867C2×C3#6603911yescharacteristic
868D3—42no—
869D3—104no—
870C5#7412211yescharacteristic, complemented, Sylow
871C22—54no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—102no—
876C22—102no—
877C22—102no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—154no—
886C22—302no—
887C22—302no—
888C22—302no—
889C22—302no—
890C22—302no—
891C22—302no—
892C22—6016no—
893C22C2×C4×D3×D511yescharacteristic
894C22#9201611yescharacteristic
895C22#9201611yescharacteristic
896C22D3×D4×D511yescharacteristic
897C22D5×#23711yescharacteristic
898C22#9202711yescharacteristic
899C22#9203511yescharacteristic
900C4—22no—
901C4—41no—
902C4—41no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—121no—
907C4—201no—
908C4—201no—
909C4—302no—
910C4—302no—
911C4—601no—
912C3#1060756311yescharacteristic, complemented, Sylow
913C2—104no—
914C2—122no—
915C2—304no—
916C2#1175272311yescharacteristic
917C2D5×#67⋊C411yescharacteristic
918C2#1175323711yescharacteristic
919C2#1175328611yescharacteristic
920C2#1175383711yescharacteristic
921C2#1175385411yescharacteristic
922C2#1175390511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C2×#91357C2semidirect
4. #11750767C2semidirect
5. C5×#4669C2semidirect
6. C3×#64953C2semidirect
8. #11748895C2semidirect
9. #11748884C2semidirect
10. #11748881C2semidirect
11. #11748878C2semidirect
12. #11748794C2semidirect
13. #11748731C2semidirect
14. #11748724C2semidirect
15. #11748723C2semidirect
24. C2×C4×Dic15C22semidirect
25. C2×C4×Dic15C22semidirect
29. C2×C5×Dic3⋊C4C22semidirect
30. C2×C4×C5×Dic3C22semidirect
33. C2×Dic3⋊Dic5C22semidirect
34. C2×#6668C22semidirect
35. C2×#6668C22semidirect
43. C2×Dic3×Dic5C22semidirect
45. D5×(C2×D3)⋊C4C4semidirect
47. C3×C5×#95C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C3×#3963C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
70. #64953D3semidirect
98. C2×C3×C4×D5C2×C4semidirect
104. C2×D5×Dic3C2×C4semidirect
111. C5×(C2×D3)⋊C4C2×C4semidirect
123. (C2×D3)⋊Dic5C2×C4semidirect
137. #4669D5semidirect
173. C5×#95C2×D3semidirect
177. #3963C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
274. C2×Dic3⋊C4C2×D5semidirect
278. C2×C4×Dic3C2×D5semidirect
283. C3×#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
321. C2×C4×D5C4×D3semidirect
372. C2×D15#117semidirect
447. (C2×D3)⋊C4C4×D5semidirect
562. #95D3×D5semidirect
739. C3×C5#2342semidirect
870. C5#74122semidirect
912. C3#10607563semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#913572
#117507672
C5×#46692
C3×#649532
#117489402
#117488952
#117488842
#117488812
#117488782
#117487942
#117487312
#117487242
#117487232
#106075633
#741225