Finite Group Databasebeta

← #14326366

Subgroups — #14326366

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×C5×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C211yesmaximal, characteristic
3C2×#91338C211yesmaximal, characteristic, complemented
4#11751052C211yesmaximal, characteristic, complemented
5C3×#65240C211yesmaximal, characteristic, complemented
6#11749496C211yesmaximal, characteristic
7#11749479C211yesmaximal, characteristic, complemented
8#11749478C211yesmaximal, characteristic, complemented
9#11748903C211yesmaximal, characteristic, complemented
10#11748897C211yesmaximal, characteristic, complemented
11#11748886C211yesmaximal, characteristic, complemented
12Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11748782C211yesmaximal, characteristic, complemented
14#11748777C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
16#10613828—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C5×D3×C22⋊C4C418yescomplemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35D3×C22⋊Dic5—24no—
36C2×Dic3⋊Dic5C2211yescharacteristic, complemented
37C2×Dic3⋊Dic5C2211yescharacteristic, complemented
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91338—24no—
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75833—51nomaximal, Hall
56C22×C5×C22⋊C4—31no—
57C22×C22⋊Dic5—31no—
58C2×#4072—31no—
59#65536—31no—
60#65501—31no—
61#65500—31no—
62C4×C22⋊Dic5—31no—
63#65240—31no—
64#65240—31no—
65#65240—31no—
66#65240D311yescharacteristic, complemented
67#65239—31no—
68#65239—31no—
69C22⋊C4×Dic5—31no—
70C22⋊C4×Dic5—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3—22no—
73C23×C5×D3—22no—
74C23×C5×D3—22no—
75C23×C5×D3—22no—
76C23×C5×D3—41no—
77C23×C5×D3—41no—
78C23×C5×D3C2×C414yes—
79C23×C5×D3C2311yescharacteristic
80C23×C5×D3C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—41no—
92C2×C4×C5×D3—41no—
93C2×C4×C5×D3C2×C414yescomplemented
94C2×C4×C5×D3C2×C414yescomplemented
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×D3×Dic5—22no—
100C2×D3×Dic5—22no—
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5—41no—
104C2×D3×Dic5—41no—
105C3×C5×C22⋊C4C2×C414yescomplemented
106#6719—22no—
107#6719—41no—
108C4⋊Dic15—22no—
109C4×Dic15—41no—
110C5×#217C2×C414yescomplemented
111C5×(C2×D3)⋊C4C2×C414yes—
112C5×(C2×D3)⋊C4C2×C414yes—
113C3×C22⋊Dic5—22no—
114C3×C22⋊Dic5—41no—
115C3×C4⋊Dic5—22no—
116C3×C4×Dic5—41no—
117Dic3⋊Dic5—41no—
118Dic3⋊Dic5—41no—
119(C2×D3)⋊Dic5—22no—
120(C2×D3)⋊Dic5—22no—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—22no—
123(C2×D3)⋊Dic5—22no—
124(C2×D3)⋊Dic5D414yes—
125Dic3×Dic5—22no—
126Dic3×Dic5—22no—
127C2×#892—51no—
128C2×D3×C22⋊C4—51no—
129C2×D3×C22⋊C4D511yescharacteristic
130C3×#388—51no—
131#4989—51no—
132#4955—51no—
133#4951—51no—
134#4945—51no—
135#4944—51no—
136C4×(C2×D3)⋊C4—51no—
137C4×(C2×D3)⋊C4—51no—
138#4668—51no—
139#4667—51no—
140#4666—51no—
141#4664—51no—
142C25×C5—31no—
143C23×C4×C5—31no—
144C23×C4×C5—31no—
145C23×Dic5—31no—
146C23×Dic5—31no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—38no—
151C2×C5×C22⋊C4C2×D311yescharacteristic
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5—31no—
157C2×C22⋊Dic5—31no—
158C2×C22⋊Dic5—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—64no—
161C2×C22⋊Dic5C2×D311yescharacteristic
162C2×C22⋊Dic5C2×D311yescharacteristic
163#4072—64no—
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4⋊Dic5—31no—
167C2×C4⋊Dic5C2×D311yescharacteristic, complemented
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic, complemented
172#3963—31no—
173#3963—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×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
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×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—28no—
198C22×C5×D3—28no—
199C22×C5×D3—44no—
200C22×C5×D3—44no—
201C22×C5×D3—44no—
202C22×C5×D3—44no—
203C22×C5×D3—44no—
204C22×C5×D3C22×C412yes—
205C22×C5×D3C22×C412yes—
206C22×C5×D3C2×D412yes—
207C22×C5×D3#4112yes—
208C22×C5×D3#4112yes—
209C22×C5×D3#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×Dic3C22×C412yes—
233C2×C5×Dic3C22×C412yes—
234C4×C5×D3—28no—
235C4×C5×D3—44no—
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—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C2×D412yes—
248D3×Dic5—44no—
249D3×Dic5—44no—
250C24×D3C2×D511yescharacteristic
251C22×C4×D3—51no—
252C22×C4×D3—51no—
253C22×C4×D3C2×D511yescharacteristic
254C22×C4×D3C2×D511yescharacteristic
255C2×C3×C4⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42—51no—
260C2×#217—51no—
261C2×#217—51no—
262C2×#217C2×D511yescharacteristic
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)⋊C4C2×D511yescharacteristic
270C2×(C2×D3)⋊C4C2×D511yescharacteristic
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277#892—104no—
278D3×C22⋊C4—104no—
279D3×C22⋊C4Dic518yescomplemented
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C24×C5—31no—
290C24×C5—34no—
291C24×C5—62no—
292C24×C5—62no—
293C24×C5—62no—
294C24×C5—62no—
295C24×C5—121no—
296C24×C5—121no—
297C24×C5C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—34no—
301C22×C4×C5—34no—
302C22×C4×C5—62no—
303C22×C4×C5—62no—
304C22×C4×C5—121no—
305C22×C4×C5—121no—
306C22×C4×C5C22×D311yescharacteristic
307C22×C4×C5C22×D311yescharacteristic
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—62no—
313C22×Dic5—62no—
314C22×Dic5—62no—
315C22×Dic5—62no—
316C22×Dic5—121no—
317C22×Dic5—121no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C22⋊C4—34no—
323C5×C22⋊C4—34no—
324C5×C22⋊C4—34no—
325C5×C22⋊C4C4×D314yescomplemented
326C22⋊Dic5—22no—
327C22⋊Dic5—34no—
328C22⋊Dic5—41no—
329C22⋊Dic5—62no—
330C22⋊Dic5—62no—
331C22⋊Dic5—62no—
332C22⋊Dic5—62no—
333C22⋊Dic5—62no—
334C22⋊Dic5—62no—
335C22⋊Dic5—121no—
336C4⋊Dic5—22no—
337C4⋊Dic5—62no—
338C4⋊Dic5—121no—
339C4⋊Dic5—121no—
340C4×Dic5—41no—
341C4×Dic5—62no—
342C4×Dic5—62no—
343C4×Dic5—121no—
344C2×#117—151no—
345C22×C22⋊C4—31no—
346C22×C22⋊C4—151no—
347#388—51no—
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×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—22no—
380C2×C5×D3—22no—
381C2×C5×D3—22no—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—416no—
386C2×C5×D3#11714yescomplemented
387C2×C5×D3C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390Dic15—22no—
391Dic15—41no—
392Dic15—41no—
393Dic15—41no—
394C3×Dic5—22no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C3×Dic5—41no—
398C5×Dic3—22no—
399C5×Dic3—22no—
400C24×C3C22×D511yescharacteristic
401C23×D3—22no—
402C23×D3—22no—
403C23×D3—22no—
404C23×D3—22no—
405C23×D3—41no—
406C23×D3—41no—
407C23×D3C2×Dic514yes—
408C23×D3C22×D511yescharacteristic
409C23×D3C22×D511yescharacteristic
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—41no—
425C2×C4×D3—41no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—102no—
430C2×C4×D3—201no—
431C2×C4×D3—201no—
432C2×C4×D3C2×Dic514yescomplemented
433C2×C4×D3C2×Dic514yescomplemented
434C3×C4⋊C4—102no—
435C3×C22⋊C4—102no—
436C3×C22⋊C4—201no—
437C3×C22⋊C4C2×Dic514yescomplemented
438C3×C42—201no—
439#217—102no—
440#217—201no—
441#217C2×Dic514yescomplemented
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)⋊C4C2×Dic514yes—
449(C2×D3)⋊C4C2×Dic514yes—
450C4⋊Dic3—102no—
451Dic3⋊C4—201no—
452Dic3⋊C4—201no—
453C4×Dic3—102no—
454C4×Dic3—102no—
455C4×Dic3—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5—32no—
463C23×C5—32no—
464C23×C5—32no—
465C23×C5—32no—
466C23×C5—32no—
467C23×C5—32no—
468C23×C5—68no—
469C23×C5—68no—
470C23×C5—61no—
471C23×C5—61no—
472C23×C5—61no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—124no—
479C23×C5—124no—
480C23×C5—124no—
481C23×C5—124no—
482C23×C5—124no—
483C23×C5C2×C4×D312yes—
484C23×C5C23×D311yescharacteristic
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—32no—
490C2×C4×C5—32no—
491C2×C4×C5—68no—
492C2×C4×C5—61no—
493C2×C4×C5—61no—
494C2×C4×C5—61no—
495C2×C4×C5—61no—
496C2×C4×C5—124no—
497C2×C4×C5C2×C4×D312yes—
498C2×C4×C5C2×C4×D312yes—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—32no—
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×Dic5—61no—
520C2×Dic5—61no—
521C2×Dic5—61no—
522C2×Dic5—124no—
523C2×Dic5—124no—
524C2×Dic5D3×D412yes—
525C25—31no—
526C23×C4—31no—
527C23×C4—31no—
528C23×C4—151no—
529C23×C4—151no—
530#117—304no—
531C2×C4⋊C4—51no—
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—38no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
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—151no—
553C2×C42—151no—
554C2×C42—151no—
555#95—51no—
556#95—51no—
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
571C5×D3—24no—
572C5×D3—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3C22×Dic512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—28no—
590C22×D3—28no—
591C22×D3—44no—
592C22×D3—44no—
593C22×D3—44no—
594C22×D3—44no—
595C22×D3—44no—
596C22×D3#70912yes—
597C22×D3#70912yes—
598C22×D3D4×D512yes—
599C22×D3#71112yes—
600C22×D3C22×Dic512yes—
601C22×D3C22×Dic512yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—52no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
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×C4C22×Dic512yes—
619C2×C3×C4C22×Dic512yes—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—52no—
625C2×Dic3—101no—
626C2×Dic3—101no—
627C2×Dic3—101no—
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×Dic3C22×Dic512yes—
637C2×Dic3C22×Dic512yes—
638C4×D3—28no—
639C4×D3—44no—
640C4×D3—204no—
641C4×D3—204no—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—34no—
646C22×C5—34no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—62no—
656C22×C5—62no—
657C22×C5—62no—
658C22×C5—62no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—1216no—
664C22×C5C22×C4×D311yescharacteristic
665C22×C5C2×D3×D411yescharacteristic
666C22×C5#100411yescharacteristic
667C22×C5D3×#4111yescharacteristic
668C22×C5D3×#4111yescharacteristic
669C22×C5D3×#4111yescharacteristic
670C22×C5#100911yescharacteristic
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—62no—
675Dic5—22no—
676Dic5—41no—
677Dic5—41no—
678Dic5—41no—
679Dic5—62no—
680Dic5—121no—
681Dic5—121no—
682Dic5—121no—
683C24—31no—
684C24—31no—
685C24—34no—
686C24—62no—
687C24—62no—
688C24—62no—
689C24—62no—
690C24—121no—
691C24—121no—
692C24C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—34no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—121no—
704C22×C4—121no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
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—102no—
718C4⋊C4—302no—
719C4⋊C4—601no—
720C4⋊C4—601no—
721C22⋊C4—34no—
722C22⋊C4—34no—
723C22⋊C4—34no—
724C22⋊C4—102no—
725C22⋊C4—154no—
726C22⋊C4—201no—
727C22⋊C4—302no—
728C22⋊C4—302no—
729C22⋊C4—302no—
730C22⋊C4—302no—
731C22⋊C4—302no—
732C22⋊C4—302no—
733C22⋊C4—601no—
734C22⋊C4D3×Dic514yescomplemented
735C42—201no—
736C42—302no—
737C42—302no—
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×C3C2×#70911yescharacteristic
748C22×C3C2×#70911yescharacteristic
749C22×C3C2×D4×D511yescharacteristic
750C22×C3C2×#71111yescharacteristic
751C22×C3#414411yescharacteristic
752C22×C3#414411yescharacteristic
753C22×C3C23×Dic511yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—416no—
767C2×D3#407214yescomplemented
768C2×D3D4×Dic514yes—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—102no—
772C3×C4—201no—
773C3×C4—201no—
774C3×C4—201no—
775Dic3—22no—
776Dic3—22no—
777Dic3—102no—
778Dic3—201no—
779Dic3—201no—
780Dic3—201no—
781C2×C5—42no—
782C2×C5—64no—
783C2×C5—64no—
784C2×C5D3×#11711yescharacteristic
785C2×C5C4×D3×D411yescharacteristic
786C2×C5#554511yescharacteristic
787C2×C5#561011yescharacteristic
788C2×C5#565911yescharacteristic
789C2×C5#567611yescharacteristic
790C2×C5#570511yescharacteristic
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—32no—
798C23—32no—
799C23—32no—
800C23—32no—
801C23—32no—
802C23—32no—
803C23—68no—
804C23—68no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—124no—
814C23—124no—
815C23—124no—
816C23—124no—
817C23—124no—
818C23C2×D3×Dic512yes—
819C23C22×D3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—52no—
827C2×C4—68no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—124no—
844C2×C4—152no—
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×D3×Dic512yes—
859C2×C4C2×D3×Dic512yes—
860C2×C3—42no—
861C2×C3#6582411yescharacteristic
862C2×C3#6582411yescharacteristic
863C2×C3#6582911yescharacteristic
864C2×C3#6582911yescharacteristic
865C2×C3C2×#407211yescharacteristic
866C2×C3C2×D4×Dic511yescharacteristic
867C2×C3#6613211yescharacteristic
868D3—24no—
869D3—24no—
870C5#7583311yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—34no—
875C22—34no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—62no—
881C22—62no—
882C22—62no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—1216no—
893C22D3×#70911yescharacteristic
894C22D3×#70911yescharacteristic
895C22D3×D4×D511yescharacteristic
896C22D3×#71111yescharacteristic
897C22#9202511yescharacteristic
898C22#9202711yescharacteristic
899C22C22×D3×Dic511yescharacteristic
900C4—22no—
901C4—22no—
902C4—62no—
903C4—62no—
904C4—102no—
905C4—201no—
906C4—201no—
907C4—201no—
908C4—302no—
909C4—601no—
910C4—601no—
911C4—601no—
912C3#1061382811yescharacteristic, complemented, Sylow
913C2—42no—
914C2—64no—
915C2—64no—
916C2#1175297211yescharacteristic
917C2#1175311811yescharacteristic
918C2#1175323211yescharacteristic
919C2#1175325811yescharacteristic
920C2D3×#407211yescharacteristic
921C2D3×D4×Dic511yescharacteristic
922C2#1175491411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C5×D3C22
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×#91338C2semidirect
4. #11751052C2semidirect
5. C3×#65240C2semidirect
7. #11749479C2semidirect
8. #11749478C2semidirect
9. #11748903C2semidirect
10. #11748897C2semidirect
11. #11748886C2semidirect
12. Dic5×(C2×D3)⋊C4C2semidirect
13. #11748782C2semidirect
14. #11748777C2semidirect
15. C4×(C2×D3)⋊Dic5C2semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
30. C5×D3×C22⋊C4C4semidirect
33. C2×C3×C4⋊Dic5C22semidirect
34. C2×C3×C4×Dic5C22semidirect
36. C2×Dic3⋊Dic5C22semidirect
37. C2×Dic3⋊Dic5C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
66. #65240D3semidirect
93. C2×C4×C5×D3C2×C4semidirect
94. C2×C4×C5×D3C2×C4semidirect
105. C3×C5×C22⋊C4C2×C4semidirect
110. C5×#217C2×C4semidirect
167. C2×C4⋊Dic5C2×D3semidirect
171. C2×C4×Dic5C2×D3semidirect
178. #3963C2×D3semidirect
179. #3963C2×D3semidirect
279. D3×C22⋊C4Dic5semidirect
325. C5×C22⋊C4C4×D3semidirect
386. C2×C5×D3#117semidirect
432. C2×C4×D3C2×Dic5semidirect
433. C2×C4×D3C2×Dic5semidirect
437. C3×C22⋊C4C2×Dic5semidirect
441. #217C2×Dic5semidirect
734. C22⋊C4D3×Dic5semidirect
739. C3×C5#2342semidirect
767. C2×D3#4072semidirect
870. C5#75833semidirect
912. C3#10613828semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C22⋊C42
C2×D3×C22⋊Dic52
C2×#913382
#117510522
C3×#652402
#117494962
#117494792
#117494782
#117489032
#117488972
#117488862
Dic5×(C2×D3)⋊C42
#117487822
#117487772
C4×(C2×D3)⋊Dic52
#106138283
#758335