Finite Group Databasebeta

← #14326375

Subgroups — #14326375

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×D3×#685C211yesmaximal, characteristic
2C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#91394C211yesmaximal, characteristic, complemented
4#11750771C211yesmaximal, characteristic, complemented
5C5×#4668C211yesmaximal, characteristic, complemented
6C3×#64955C211yesmaximal, characteristic, complemented
7#11748940C211yesmaximal, characteristic
8#11748903C211yesmaximal, characteristic, complemented
9Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11748871C211yesmaximal, characteristic, complemented
11#11748759C211yesmaximal, characteristic, complemented
12#11748727C211yesmaximal, characteristic, complemented
13#11748726C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
15#11748685C211yesmaximal, characteristic, complemented
16#10606326—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C2×Dic3⋊Dic5C2211yescharacteristic, complemented
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44D3×#685—24no—
45D5×(C2×D3)⋊C4C418yescomplemented
46#91394—24no—
47C3×C5×#95C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#73575—51nomaximal, Hall
56C22×#685—31no—
57C2×#4038—31no—
58C2×D5×C22⋊C4—31no—
59C5×#385—31no—
60C4×C22⋊Dic5—31no—
61#65279—31no—
62#65279—31no—
63#65276—31no—
64#65244—31no—
65#65239—31no—
66C22⋊C4×Dic5—31no—
67#64959—31no—
68#64959—31no—
69#64955D311yescharacteristic, complemented
70#64953—31no—
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
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—41no—
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×C3×C4×D5—41no—
97C2×C3×C4×D5—41no—
98C2×C3×C4×D5C2×C414yescomplemented
99C2×D3×Dic5—22no—
100C2×D3×Dic5—22no—
101C2×D3×Dic5—41no—
102C2×D5×Dic3—22no—
103C2×D5×Dic3—22no—
104C2×D5×Dic3C2×C414yescomplemented
105#6714—22no—
106#6714—41no—
107#6714C2×C414yescomplemented
108C4⋊Dic15—41no—
109C4×Dic15—22no—
110C5×(C2×D3)⋊C4—22no—
111C5×(C2×D3)⋊C4C2×C414yes—
112C5×C4⋊Dic3—41no—
113C5×Dic3⋊C4—22no—
114C3×#685—22no—
115C3×#685D414yes—
116C3×C4×Dic5—41no—
117C3×C4×Dic5—41no—
118Dic3⋊Dic5—22no—
119#6667—22no—
120#6667—41no—
121#6667C2×C414yescomplemented
122(C2×D3)⋊Dic5—22no—
123(C2×D3)⋊Dic5C2×C414yes—
124#6665—22no—
125#6665—22no—
126Dic3×Dic5—22no—
127C22×(C2×D3)⋊C4—51no—
128C2×D3×C22⋊C4—51no—
129C2×#877—51no—
130C3×C4×C22⋊C4—51no—
131#5212—51no—
132#4955—51no—
133#4943—51no—
134#4940—51no—
135#4940—51no—
136C4×(C2×D3)⋊C4—51no—
137C4×(C2×D3)⋊C4—51no—
138#4670—51no—
139#4670—51no—
140#4668—51no—
141#4668D511yescharacteristic, complemented
142C24×D5—31no—
143C23×C4×C5—31no—
144C23×Dic5—31no—
145C22×C4×D5—31no—
146C22×C4×D5C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×#685—31no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—64no—
162C2×#685C2×D311yescharacteristic
163C2×#685C2×D311yescharacteristic
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168C2×C4×Dic5C2×D311yescharacteristic, complemented
169C2×C4×Dic5C2×D311yescharacteristic, complemented
170#4038—64no—
171D5×C22⋊C4—38no—
172C5×#95—31no—
173C5×#95C2×D311yescharacteristic, complemented
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5C2411yescharacteristic
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15—21no—
187C22×D15—21no—
188C22×D15C22×C412yes—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3C22×C412yes—
194C22×C5×D3#4112yes—
195C22×C5×D3#4112yes—
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×C5C22×C412yes—
218C2×C3×C4×C5C2×D412yes—
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×Dic15C22×C412yes—
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×Dic3C22×C412yes—
237C4×C5×D3—44no—
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×Dic5C22×C412yes—
246C2×C3×Dic5C2×D412yes—
247C3×C4×D5—44no—
248D3×Dic5—44no—
249D5×Dic3—28no—
250C24×D3—51no—
251C23×C3×C4—51no—
252C23×Dic3—51no—
253C22×C4×D3—51no—
254C22×C4×D3C2×D511yescharacteristic
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×#217—51no—
260C2×#217—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—58no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4C2×D511yescharacteristic
271C2×(C2×D3)⋊C4C2×D511yescharacteristic
272C2×C4⋊Dic3—51no—
273C2×C4⋊Dic3C2×D511yescharacteristic, complemented
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278D3×C22⋊C4—104no—
279#877—104no—
280C3×#95—51no—
281C3×#95C2×D511yescharacteristic, complemented
282C3⋊#95—51no—
283C3⋊#95—51no—
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×C5—62no—
302C22×C4×C5—62no—
303C22×C4×C5—121no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—31no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—62no—
311C22×Dic5—62no—
312C22×Dic5—121no—
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—34no—
317C2×C4×D5—41no—
318C2×C4×D5—41no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5C4×D314yescomplemented
322C5×C4⋊C4—62no—
323C5×C4⋊C4—121no—
324C5×C22⋊C4—34no—
325C5×C22⋊C4—62no—
326C22⋊Dic5—34no—
327C22⋊Dic5—62no—
328#685—22no—
329#685—34no—
330#685—34no—
331#685—62no—
332#685—62no—
333#685—62no—
334#685—62no—
335#685—121no—
336#685—121no—
337#685D1214yes—
338C4⋊Dic5—62no—
339C4⋊Dic5—121no—
340C4×Dic5—41no—
341C4×Dic5—41no—
342C4×Dic5—62no—
343C4×Dic5—62no—
344C2×#117—151no—
345C22×C22⋊C4—151no—
346C22×C22⋊C4—151no—
347#388—151no—
348#388—151no—
349#388—151no—
350#388—151no—
351#385—31no—
352#385—151no—
353#381—151no—
354#380—151no—
355#379—151no—
356C4×C22⋊C4—51no—
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—41no—
370C2×D15—41no—
371C2×D15—41no—
372C2×D15—41no—
373C2×C5×D3—22no—
374C2×C5×D3—22no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3#11714yescomplemented
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—22no—
390C3×C4×C5—41no—
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—22no—
396C3×Dic5—41no—
397C5×Dic3—22no—
398C5×Dic3—41no—
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—51no—
412C22×C3×C4—54no—
413C22×C3×C4—51no—
414C22×C3×C4—201no—
415C22×C3×C4—201no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×Dic3—51no—
420C22×Dic3—54no—
421C22×Dic3—51no—
422C22×Dic3—51no—
423C22×Dic3—102no—
424C22×Dic3—102no—
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C22×Dic3C22×D511yescharacteristic
428C2×C4×D3—22no—
429C2×C4×D3—22no—
430C2×C4×D3—41no—
431C2×C4×D3—102no—
432C2×C4×D3—102no—
433C2×C4×D3—201no—
434C3×C22⋊C4—54no—
435C3×C22⋊C4—102no—
436C3×C42—201no—
437C3×C42—201no—
438#217—102no—
439#217—102no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—54no—
442(C2×D3)⋊C4—54no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—102no—
445(C2×D3)⋊C4—102no—
446(C2×D3)⋊C4—102no—
447(C2×D3)⋊C4—201no—
448(C2×D3)⋊C4—201no—
449(C2×D3)⋊C4C4×D514yes—
450C4⋊Dic3—41no—
451C4⋊Dic3—201no—
452Dic3⋊C4—22no—
453Dic3⋊C4—102no—
454C4×Dic3—102no—
455C4×Dic3—102no—
456C23×C5—32no—
457C23×C5—32no—
458C23×C5—32no—
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—68no—
470C22×D5—61no—
471C22×D5—61no—
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×D5C2×D1212yes—
484C22×D5#23512yes—
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—32no—
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×C5—124no—
502C2×C4×C5C2×C4×D312yes—
503C2×C4×C5C2×D1212yes—
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—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5—124no—
521C2×Dic5C2×C4×D312yes—
522C2×Dic5C2×D1212yes—
523C4×D5—44no—
524C4×D5—68no—
525C25—151no—
526C23×C4—31no—
527C23×C4—51no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
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—158no—
540C2×C22⋊C4—151no—
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—51no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—51no—
557#95—151no—
558#95—151no—
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—42no—
571C3×D5—24no—
572C5×D3—24no—
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—52no—
586C22×D3—108no—
587C22×D3—101no—
588C22×D3—101no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—108no—
594C22×D3—204no—
595C22×D3—204no—
596C22×D3—204no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3C2×C4×D512yes—
600C22×D3#71112yes—
601C22×D3#71312yes—
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—52no—
610C2×C3×C4—52no—
611C2×C3×C4—101no—
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—204no—
619C2×C3×C4C2×C4×D512yes—
620C2×C3×C4D4×D512yes—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—52no—
630C2×Dic3—108no—
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×Dic3C2×C4×D512yes—
640C4×D3—44no—
641C4×D3—204no—
642C22×C5—34no—
643C22×C5—62no—
644C22×C5—62no—
645C22×C5—62no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C22×D1211yescharacteristic
651C22×C5C2×#23511yescharacteristic
652C22×C5#100411yescharacteristic
653C22×C5#100411yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5D3×#4111yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—1216no—
666C2×D5—121no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5C4×D1214yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—41no—
674C4×C5—62no—
675C4×C5—121no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—22no—
679Dic5—41no—
680Dic5—62no—
681Dic5—121no—
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—51no—
698C22×C4—54no—
699C22×C4—51no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—121no—
703C22×C4—154no—
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×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—121no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—54no—
723C22⋊C4—62no—
724C22⋊C4—102no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—601no—
734C22⋊C4—601no—
735C42—201no—
736C42—201no—
737C42—302no—
738C42—302no—
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×C3C2×#71111yescharacteristic
750C22×C3#414411yescharacteristic
751C22×C3C2×#71311yescharacteristic
752C22×C3D5×#4111yescharacteristic
753C22×C3#414911yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—2016no—
764C2×D3—201no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3#403814yescomplemented
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—41no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—41no—
777Dic3—41no—
778Dic3—102no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—64no—
782C2×C5C2×C4×D1211yescharacteristic
783C2×C5#548611yescharacteristic
784C2×C5D3×#11711yescharacteristic
785C2×C5#555411yescharacteristic
786C2×C5#555411yescharacteristic
787C2×C5#555611yescharacteristic
788C2×C5#555611yescharacteristic
789D5—24no—
790D5—122no—
791C23—32no—
792C23—32no—
793C23—32no—
794C23—52no—
795C23—52no—
796C23—52no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—152no—
806C23—308no—
807C23—308no—
808C23—301no—
809C23—301no—
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—32no—
828C2×C4—52no—
829C2×C4—52no—
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—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—124no—
846C2×C4—152no—
847C2×C4—204no—
848C2×C4—308no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—604no—
858C2×C4C4×D3×D512yes—
859C2×C4D5×D1212yes—
860C2×C3—104no—
861C2×C3C2×#403811yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6592511yescharacteristic
865C2×C3#6596411yescharacteristic
866C2×C3#6597111yescharacteristic
867C2×C3#6599211yescharacteristic
868D3—24no—
869D3—202no—
870C5#7357511yescharacteristic, complemented, Sylow
871C22—34no—
872C22—54no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—102no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—302no—
886C22—302no—
887C22—302no—
888C22—6016no—
889C22—601no—
890C22—601no—
891C22—601no—
892C22—601no—
893C22C2×C4×D3×D511yescharacteristic
894C22C2×D5×D1211yescharacteristic
895C22D5×#23511yescharacteristic
896C22D3×#71111yescharacteristic
897C22#9202511yescharacteristic
898C22#9202611yescharacteristic
899C22D3×#71311yescharacteristic
900C4—22no—
901C4—22no—
902C4—41no—
903C4—62no—
904C4—102no—
905C4—102no—
906C4—121no—
907C4—121no—
908C4—201no—
909C4—302no—
910C4—601no—
911C4—601no—
912C3#1060632611yescharacteristic, complemented, Sylow
913C2—64no—
914C2—104no—
915C2—602no—
916C2C4×D5×D1211yescharacteristic
917C2#1175320011yescharacteristic
918C2#1175326511yescharacteristic
919C2#1175327911yescharacteristic
920C2D3×#403811yescharacteristic
921C2#1175387611yescharacteristic
922C2#1175389811yescharacteristic
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×#91394C2semidirect
4. #11750771C2semidirect
5. C5×#4668C2semidirect
6. C3×#64955C2semidirect
8. #11748903C2semidirect
9. Dic5×(C2×D3)⋊C4C2semidirect
10. #11748871C2semidirect
11. #11748759C2semidirect
12. #11748727C2semidirect
13. #11748726C2semidirect
14. C4×(C2×D3)⋊Dic5C2semidirect
15. #11748685C2semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C2×Dic3⋊Dic5C22semidirect
43. C2×Dic3×Dic5C22semidirect
45. D5×(C2×D3)⋊C4C4semidirect
47. C3×C5×#95C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
69. #64955D3semidirect
98. C2×C3×C4×D5C2×C4semidirect
104. C2×D5×Dic3C2×C4semidirect
107. #6714C2×C4semidirect
121. #6667C2×C4semidirect
141. #4668D5semidirect
168. C2×C4×Dic5C2×D3semidirect
169. C2×C4×Dic5C2×D3semidirect
173. C5×#95C2×D3semidirect
179. #3963C2×D3semidirect
273. C2×C4⋊Dic3C2×D5semidirect
275. C2×Dic3⋊C4C2×D5semidirect
281. C3×#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
321. C2×C4×D5C4×D3semidirect
379. C2×C5×D3#117semidirect
562. #95D3×D5semidirect
739. C3×C5#2342semidirect
768. C2×D3#4038semidirect
870. C5#73575semidirect
912. C3#10606326semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#913942
#117507712
C5×#46682
C3×#649552
#117489402
#117489032
Dic5×(C2×D3)⋊C42
#117488712
#117487592
#117487272
#117487262
C4×(C2×D3)⋊Dic52
#117486852
#106063263
#735755