Finite Group Databasebeta

← #14326320

Subgroups — #14326320

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×#91561C211yesmaximal, characteristic
2C22×#6667C211yesmaximal, characteristic
3C2×#91402C211yesmaximal, characteristic, complemented
4#11751056C211yesmaximal, characteristic
5C5×#4946C211yesmaximal, characteristic, complemented
6C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
7#11749509C211yesmaximal, characteristic, complemented
8Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#11748889C211yesmaximal, characteristic, complemented
10#11748882C211yesmaximal, characteristic, complemented
11#11748875C211yesmaximal, characteristic, complemented
12#11748727C211yesmaximal, characteristic, complemented
13#11748726C211yesmaximal, characteristic, complemented
14#11748669C211yesmaximal, characteristic, complemented
15#11748668C211yesmaximal, characteristic, complemented
16#10606326—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic, complemented
33C2×C3×C4×Dic5C2211yescharacteristic, complemented
34#91561C418yescomplemented
35C2×Dic3⋊Dic5C2211yescharacteristic, complemented
36C2×Dic3⋊Dic5C2211yescharacteristic, complemented
37C2×#6667—24no—
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91402—24no—
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#73574—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×Dic5D311yescharacteristic, complemented
67#64959—31no—
68#64959—31no—
69#64955—31no—
70#64953—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15—22no—
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15C2×C414yes—
79C23×D15C2311yescharacteristic
80C23×D15C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×C5×Dic3—22no—
86C22×C5×Dic3—22no—
87C22×C5×Dic3—41no—
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C3×Dic5—22no—
93C22×C3×Dic5—22no—
94C22×C3×Dic5—41no—
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—41no—
102C2×#1200—41no—
103C2×#1200C2×C414yescomplemented
104C2×#1200C2×C414yescomplemented
105C3×C5×C22⋊C4—22no—
106#6719—22no—
107#6714—22no—
108#6714—22no—
109#6714—41no—
110#6714—41no—
111C5×#217C2×C414yes—
112C5×Dic3⋊C4—22no—
113C5×Dic3⋊C4—41no—
114C3×C22⋊Dic5C2×C414yes—
115C3×C4×Dic5—22no—
116C3×C4×Dic5—41no—
117Dic3⋊Dic5—22no—
118Dic3⋊Dic5—41no—
119#6667—22no—
120#6667—22no—
121#6667—22no—
122#6667C2×C414yescomplemented
123#6667C2×C414yescomplemented
124#6667D414yes—
125Dic3×Dic5—22no—
126Dic3×Dic5—41no—
127C22×(C2×D3)⋊C4—51no—
128C2×D3×C22⋊C4—51no—
129C2×#872—51no—
130C3×C4×C22⋊C4—51no—
131#5210—51no—
132#4955—51no—
133#4946D511yescharacteristic, complemented
134Dic3×C22⋊C4—51no—
135#4940—51no—
136#4940—51no—
137C4×(C2×D3)⋊C4—51no—
138#4669—51no—
139#4669—51no—
140#4667—51no—
141#4664—51no—
142C24×D5—31no—
143C23×C4×C5—31no—
144C23×Dic5C2×D311yescharacteristic
145C22×C4×D5—31no—
146C22×C4×D5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5C2×D311yescharacteristic
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—31no—
162C2×#685—31no—
163C2×#685—64no—
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×#95—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic, complemented
179#3963C2×D311yescharacteristic, complemented
180#2342—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5#4112yes—
187C23×C3×C5#4112yes—
188C23×C3×C5C2411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—28no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—28no—
201C22×D15—44no—
202C22×D15—44no—
203C22×D15—44no—
204C22×D15—44no—
205C22×D15—44no—
206C22×D15C22×C412yes—
207C22×D15C22×C412yes—
208C22×D15C2×D412yes—
209C22×D15#4112yes—
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×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—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—21no—
231C2×C5×Dic3—44no—
232C2×C5×Dic3C22×C412yes—
233C2×C5×Dic3C22×C412yes—
234C2×C5×Dic3C2×D412yes—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
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—44no—
245C2×C3×Dic5C22×C412yes—
246C2×C3×Dic5C22×C412yes—
247C2×C3×Dic5C2×D412yes—
248#1200—28no—
249#1200—44no—
250C24×D3—51no—
251C23×C3×C4—51no—
252C23×Dic3C2×D511yescharacteristic
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4C2×D511yescharacteristic
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×#217—51no—
260C2×#217C2×D511yescharacteristic
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
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)⋊C4—51no—
271C2×(C2×D3)⋊C4—104no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4C2×D511yescharacteristic, complemented
275C2×Dic3⋊C4C2×D511yescharacteristic, complemented
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278D3×C22⋊C4—58no—
279#872—104no—
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—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—62no—
293C23×D5—62no—
294C23×D5—62no—
295C23×D5—62no—
296C23×D5—121no—
297C23×D5—121no—
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5—121no—
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C22×Dic5—22no—
308C22×Dic5—22no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—41no—
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C2×C4×D5—34no—
317C2×C4×D5—34no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—121no—
321C2×C4×D5—121no—
322C5×C4⋊C4—62no—
323C5×C4⋊C4—121no—
324C5×C22⋊C4—22no—
325C5×C22⋊C4—34no—
326C22⋊Dic5—62no—
327C22⋊Dic5C4×D314yes—
328#685—34no—
329#685—34no—
330#685—34no—
331#685—62no—
332#685—62no—
333#685—62no—
334#685—62no—
335#685—62no—
336#685—121no—
337#685—121no—
338C4⋊Dic5—62no—
339C4⋊Dic5—121no—
340C4×Dic5—22no—
341C4×Dic5—41no—
342C4×Dic5—62no—
343C4×Dic5—121no—
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×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5#11714yescomplemented
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×D15—22no—
374C2×D15—22no—
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—416no—
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15C4×D414yes—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390Dic15—41no—
391Dic15—41no—
392C3×Dic5—22no—
393C3×Dic5—22no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C5×Dic3—22no—
397C5×Dic3—22no—
398C5×Dic3—22no—
399C5×Dic3—41no—
400C24×C3C22×D511yescharacteristic
401C23×D3—51no—
402C23×D3—51no—
403C23×D3—54no—
404C23×D3—102no—
405C23×D3—102no—
406C23×D3—102no—
407C23×D3—102no—
408C23×D3—201no—
409C23×D3—201no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—201no—
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×Dic3—22no—
420C22×Dic3—22no—
421C22×Dic3—41no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3C22×D511yescharacteristic
425C22×Dic3C22×D511yescharacteristic
426C22×Dic3C22×D511yescharacteristic
427C22×Dic3C22×D511yescharacteristic
428C2×C4×D3—54no—
429C2×C4×D3—54no—
430C2×C4×D3—102no—
431C2×C4×D3—102no—
432C2×C4×D3—201no—
433C2×C4×D3—201no—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—54no—
436C3×C42—102no—
437C3×C42—201no—
438#217—102no—
439#217C4×D514yes—
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—102no—
447(C2×D3)⋊C4—102no—
448(C2×D3)⋊C4—201no—
449(C2×D3)⋊C4—201no—
450Dic3⋊C4—22no—
451Dic3⋊C4—41no—
452Dic3⋊C4—102no—
453Dic3⋊C4—201no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5C2×C4×D312yes—
461C23×C5#23512yes—
462C23×C5#23512yes—
463C23×C5C23×D311yescharacteristic
464C22×D5—32no—
465C22×D5—32no—
466C22×D5—32no—
467C22×D5—32no—
468C22×D5—68no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C22×D5—61no—
473C22×D5—68no—
474C22×D5—61no—
475C22×D5—61no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—61no—
480C22×D5—124no—
481C22×D5—124no—
482C22×D5—124no—
483C22×D5—124no—
484C22×D5—124no—
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—32no—
492C2×C4×C5—32no—
493C2×C4×C5—32no—
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—61no—
502C2×C4×C5—61no—
503C2×C4×C5—124no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—44no—
514C2×Dic5—61no—
515C2×Dic5—61no—
516C2×Dic5—61no—
517C2×Dic5—61no—
518C2×Dic5—61no—
519C2×Dic5—61no—
520C2×Dic5C2×C4×D312yes—
521C2×Dic5C2×C4×D312yes—
522C2×Dic5D3×D412yes—
523C4×D5—68no—
524C4×D5—124no—
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—51no—
537C2×C22⋊C4—158no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
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—304no—
550C2×C22⋊C4D3×D511yescharacteristic
551C2×C42—51no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42—151no—
555#95—31no—
556#95—31no—
557#95—51no—
558#95—51no—
559#95—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563C2×C3×C5—24no—
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
571D15—24no—
572D15—42no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3C2×C4×D512yes—
578C23×C3#71112yes—
579C23×C3#71312yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—52no—
583C22×D3—52no—
584C22×D3—52no—
585C22×D3—108no—
586C22×D3—101no—
587C22×D3—101no—
588C22×D3—101no—
589C22×D3—101no—
590C22×D3—101no—
591C22×D3—101no—
592C22×D3—101no—
593C22×D3—101no—
594C22×D3—101no—
595C22×D3—101no—
596C22×D3—108no—
597C22×D3—204no—
598C22×D3—204no—
599C22×D3—204no—
600C22×D3—204no—
601C22×D3—204no—
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—52no—
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—101no—
619C2×C3×C4—101no—
620C2×C3×C4—204no—
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—21no—
630C2×Dic3—44no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3C2×C4×D512yes—
638C2×Dic3C2×C4×D512yes—
639C2×Dic3D4×D512yes—
640C4×D3—108no—
641C4×D3—204no—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5#87214yescomplemented
649C22×C5C22×C4×D311yescharacteristic
650C22×C5C2×#23511yescharacteristic
651C22×C5C2×#23511yescharacteristic
652C22×C5C2×D3×D411yescharacteristic
653C22×C5#100411yescharacteristic
654C22×C5D3×#4111yescharacteristic
655C22×C5#100911yescharacteristic
656C2×D5—34no—
657C2×D5—62no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—1216no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C4×C5—41no—
672C4×C5—41no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—121no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—41no—
681Dic5—121no—
682Dic5—121no—
683C24—151no—
684C24—151no—
685C24—154no—
686C24—302no—
687C24—302no—
688C24—302no—
689C24—302no—
690C24—601no—
691C24—601no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—102no—
704C22×C4—102no—
705C22×C4—121no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—201no—
711C22×C4—302no—
712C22×C4—302no—
713C22×C4—601no—
714C22×C4—601no—
715C22×C4C2×D3×D511yescharacteristic
716C22×C4C2×D3×D511yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—121no—
719C4⋊C4—302no—
720C4⋊C4—601no—
721C22⋊C4—22no—
722C22⋊C4—34no—
723C22⋊C4—54no—
724C22⋊C4—154no—
725C22⋊C4—154no—
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⋊C4—601no—
735C42—102no—
736C42—201no—
737C42—302no—
738C42—601no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3#403814yescomplemented
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—54no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—2016no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—102no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—41no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—24no—
782C2×C5C2×#87211yescharacteristic
783C2×C5#549011yescharacteristic
784C2×C5#552711yescharacteristic
785C2×C5C4×D3×D411yescharacteristic
786C2×C5#554511yescharacteristic
787C2×C5#555011yescharacteristic
788C2×C5#555611yescharacteristic
789D5—64no—
790D5—122no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—152no—
796C23—152no—
797C23—152no—
798C23—152no—
799C23—308no—
800C23—301no—
801C23—301no—
802C23—301no—
803C23—301no—
804C23—308no—
805C23—301no—
806C23—301no—
807C23—301no—
808C23—301no—
809C23—301no—
810C23—301no—
811C23—604no—
812C23—604no—
813C23—604no—
814C23—604no—
815C23—604no—
816C23#677312yes—
817C23C4×D3×D512yes—
818C23#678212yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—52no—
830C2×C4—52no—
831C2×C4—52no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—124no—
851C2×C4—204no—
852C2×C4—308no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—604no—
860C2×C3—24no—
861C2×C3C2×#403811yescharacteristic
862C2×C3C4×D4×D511yescharacteristic
863C2×C3#6587911yescharacteristic
864C2×C3#6592511yescharacteristic
865C2×C3#6596411yescharacteristic
866C2×C3#6597111yescharacteristic
867C2×C3#6599211yescharacteristic
868D3—104no—
869D3—202no—
870C5#7357411yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—154no—
878C22—302no—
879C22—302no—
880C22—302no—
881C22—302no—
882C22—302no—
883C22—302no—
884C22—302no—
885C22—302no—
886C22—302no—
887C22—6016no—
888C22—601no—
889C22—601no—
890C22—601no—
891C22—601no—
892C22#9140214yescomplemented
893C22C2×#677311yescharacteristic
894C22C2×C4×D3×D511yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22#9202411yescharacteristic
897C22#9202611yescharacteristic
898C22#9202711yescharacteristic
899C22C2×#678211yescharacteristic
900C4—41no—
901C4—41no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—102no—
907C4—102no—
908C4—121no—
909C4—201no—
910C4—601no—
911C4—601no—
912C3#1060632611yescharacteristic, complemented, Sylow
913C2—24no—
914C2—304no—
915C2—602no—
916C2#1175303411yescharacteristic
917C2#1175307311yescharacteristic
918C2#1175320311yescharacteristic
919C2#1175320411yescharacteristic
920C2C2×#9140211yescharacteristic
921C2#1175473611yescharacteristic
922C2#1175477811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
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×#91402C2semidirect
5. C5×#4946C2semidirect
6. C3×C22⋊C4×Dic5C2semidirect
7. #11749509C2semidirect
8. Dic3×C22⋊Dic5C2semidirect
9. #11748889C2semidirect
10. #11748882C2semidirect
11. #11748875C2semidirect
12. #11748727C2semidirect
13. #11748726C2semidirect
14. #11748669C2semidirect
15. #11748668C2semidirect
29. C2×C5×Dic3⋊C4C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
32. C2×C3×C4×Dic5C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. #91561C4semidirect
35. C2×Dic3⋊Dic5C22semidirect
36. C2×Dic3⋊Dic5C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
66. C22⋊C4×Dic5D3semidirect
103. C2×#1200C2×C4semidirect
104. C2×#1200C2×C4semidirect
122. #6667C2×C4semidirect
123. #6667C2×C4semidirect
133. #4946D5semidirect
168. C2×C4×Dic5C2×D3semidirect
169. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
274. C2×Dic3⋊C4C2×D5semidirect
275. C2×Dic3⋊C4C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
365. C22×C3×C5#117semidirect
648. C22×C5#872semidirect
739. C3×C5#2342semidirect
746. C22×C3#4038semidirect
870. C5#73574semidirect
892. C22#91402semidirect
912. C3#10606326semidirect

Maximal subgroups

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

subgroupindex
C2×#915612
C22×#66672
C2×#914022
#117510562
C5×#49462
C3×C22⋊C4×Dic52
#117495092
Dic3×C22⋊Dic52
#117488892
#117488822
#117488752
#117487272
#117487262
#117486692
#117486682
#106063263
#735745