Finite Group Databasebeta

← #14323917

Subgroups — #14323917

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#939C211yesmaximal, characteristic
2C2×Dic5×#67C211yesmaximal, characteristic, complemented
3C2×#91529C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6#11749519C211yesmaximal, characteristic, complemented
7#11749513C211yesmaximal, characteristic, complemented
8#11749509C211yesmaximal, characteristic, complemented
9#11749482C211yesmaximal, characteristic, complemented
10#11749482C211yesmaximal, characteristic, complemented
11#11749478C211yesmaximal, characteristic, complemented
12#11748903C211yesmaximal, characteristic, complemented
13#11748794C211yesmaximal, characteristic, complemented
14#11748693C211yesmaximal, characteristic, complemented
15#11748651C211yesmaximal, characteristic, complemented
16#10614364—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C5×#939C418yescomplemented
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36Dic5×#67—24no—
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45#91529—24no—
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74665—51nomaximal, Hall
56C2×C5×#121—31no—
57C2×D4×Dic5—31no—
58C2×#4072—31no—
59#65510—31no—
60#65510—31no—
61#65510—31no—
62#65509—31no—
63#65509D311yescharacteristic, complemented
64#65501—31no—
65#65274—31no—
66C4⋊C4×Dic5—31no—
67#65240—31no—
68#65240—31no—
69#65239—31no—
70#65239—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C2×C3×C5×D4—41no—
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4C2×C414yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C2×C5×#67—22no—
83C2×C5×#67—22no—
84C2×C5×#67—41no—
85C2×C5×#67—41no—
86C2×C5×#67C2×C414yes—
87C2×C5×#67C2×C414yescomplemented
88C22×C5×Dic3—22no—
89C22×C5×Dic3—22no—
90C22×C5×Dic3C2×C414yescomplemented
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C3×Dic5—22no—
95C22×C3×Dic5—41no—
96C22×C3×Dic5—41no—
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×D3×Dic5—22no—
102C2×D3×Dic5—41no—
103C2×D3×Dic5—41no—
104#6719—22no—
105#6719—22no—
106#6719—41no—
107#6719—41no—
108C4⋊Dic15—41no—
109C4×Dic15—41no—
110C5×#217C2×C414yescomplemented
111C5×(C2×D3)⋊C4C2×C414yescomplemented
112C5×Dic3⋊C4C2×C414yescomplemented
113C3×C22⋊Dic5—22no—
114C3×C22⋊Dic5—41no—
115C3×C22⋊Dic5—41no—
116Dic3⋊Dic5—22no—
117Dic3⋊Dic5—22no—
118Dic3⋊Dic5—22no—
119Dic3⋊Dic5—22no—
120Dic3⋊Dic5—41no—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—41no—
123(C2×D3)⋊Dic5—41no—
124Dic3×Dic5—22no—
125Dic3×Dic5—41no—
126Dic3×Dic5D414yescomplemented
127C2×#939D511yescharacteristic
128C2×C4×#67—51no—
129C2×#877—51no—
130C3×#386—51no—
131#5221—51no—
132#5210—51no—
133#4957—51no—
134#4957—51no—
135#4956—51no—
136#4944—51no—
137#4942—51no—
138#4669—51no—
139#4668—51no—
140#4649—51no—
141#4647—51no—
142C22×C5×D4—31no—
143C22×C5×D4—31no—
144C22×C5×D4C2×D311yescharacteristic
145C23×C4×C5—31no—
146C23×Dic5—31no—
147C23×Dic5C2×D311yescharacteristic
148C5×#121—38no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
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⋊Dic5C2×D311yescharacteristic
160C2×C22⋊Dic5C2×D311yescharacteristic
161C2×C22⋊Dic5C2×D311yescharacteristic
162D4×Dic5—64no—
163#4072—64no—
164C2×C4⋊Dic5—31no—
165C2×C4⋊Dic5—31no—
166C2×C4⋊Dic5—31no—
167C2×C4⋊Dic5—31no—
168C2×C4⋊Dic5—31no—
169C2×C4⋊Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
172C2×C4×Dic5—31no—
173C2×C4×Dic5—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic
179#3963C2×D311yescharacteristic
180#2324—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×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C22×C412yes—
195C23×C3×C5C2411yescharacteristic
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3C22×C412yes—
203C3×C5×D4—44no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5C22×C412yes—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15C2×D412yes—
219C5×#67—28no—
220C5×#67—44no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—28no—
226C2×C5×Dic3C22×C412yes—
227C2×C5×Dic3C22×C412yes—
228C2×C5×Dic3C22×C412yes—
229C2×C5×Dic3C2×D412yes—
230C2×C5×Dic3#4112yes—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
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—44no—
243C2×C3×Dic5C2×D412yes—
244D3×Dic5—44no—
245C22×C3×D4C2×D511yescharacteristic
246C23×C3×C4—51no—
247C22×#67C2×D511yescharacteristic
248C22×#67C2×D511yescharacteristic
249C23×Dic3C2×D511yescharacteristic
250C22×C4×D3—51no—
251C2×C3×C22⋊C4—51no—
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×#217—51no—
255C2×#217—51no—
256C2×#217—51no—
257C2×#217—51no—
258C2×#217C2×D511yescharacteristic
259#939Dic518yescomplemented
260C4×#67—104no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4C2×D511yescharacteristic
265C2×C4⋊Dic3—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4C2×D511yescharacteristic
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276#877—104no—
277C3×#95—51no—
278C3×#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C24×C5—31no—
284C24×C5C22×D311yescharacteristic
285C24×C5C22×D311yescharacteristic
286C2×C5×D4—34no—
287C2×C5×D4—34no—
288C2×C5×D4—41no—
289C2×C5×D4—41no—
290C2×C5×D4—62no—
291C2×C5×D4—62no—
292C2×C5×D4—121no—
293C2×C5×D4—121no—
294C2×C5×D4C4×D314yescomplemented
295C22×C4×C5—31no—
296C22×C4×C5—34no—
297C22×C4×C5—31no—
298C22×C4×C5—31no—
299C22×C4×C5—62no—
300C22×C4×C5—62no—
301C22×C4×C5C22×D311yescharacteristic
302C22×Dic5—22no—
303C22×Dic5—31no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—41no—
308C22×Dic5—41no—
309C22×Dic5—62no—
310C22×Dic5—121no—
311C22×Dic5—121no—
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C5×C4⋊C4—34no—
317C5×C22⋊C4—34no—
318C5×C22⋊C4—34no—
319C22⋊Dic5—22no—
320C22⋊Dic5—41no—
321C22⋊Dic5—41no—
322C22⋊Dic5—62no—
323C22⋊Dic5—62no—
324C22⋊Dic5—62no—
325C22⋊Dic5—121no—
326C22⋊Dic5—121no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329C4⋊Dic5—62no—
330C4⋊Dic5—62no—
331C4⋊Dic5—62no—
332C4⋊Dic5—62no—
333C4⋊Dic5—121no—
334C4⋊Dic5—121no—
335C4×Dic5—34no—
336C4×Dic5—62no—
337C4×Dic5—121no—
338C4×Dic5—121no—
339C2×#121—31no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—151no—
343#390—151no—
344#390—151no—
345#389—151no—
346#388—151no—
347#388—151no—
348#386—51no—
349#386—151no—
350#385—151no—
351#385—151no—
352#380—151no—
353C4×C4⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C52−1+411yescharacteristic
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C3×C4×C5—22no—
383Dic15—22no—
384Dic15—41no—
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—22no—
388C3×Dic5—41no—
389C3×Dic5—41no—
390C3×Dic5—41no—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3C4×D414yes—
394C24×C3C22×D511yescharacteristic
395C24×C3C22×D511yescharacteristic
396C23×D3C22×D511yescharacteristic
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4C2×Dic514yescomplemented
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×C3×C4—51no—
404C22×C3×C4—102no—
405C22×C3×C4—201no—
406C22×C3×C4—201no—
407C22×C3×C4C22×D511yescharacteristic
408C2×#67—22no—
409C2×#67—22no—
410C2×#67—41no—
411C2×#67—41no—
412C2×#67C2×Dic514yes—
413C2×#67C2×Dic514yescomplemented
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3C2×Dic514yescomplemented
421C22×Dic3C22×D511yescharacteristic
422C22×Dic3C22×D511yescharacteristic
423C22×Dic3C22×D511yescharacteristic
424C2×C4×D3—102no—
425C2×C4×D3—201no—
426C2×C4×D3—201no—
427C3×C22⋊C4—102no—
428C3×C22⋊C4—201no—
429C3×C22⋊C4—201no—
430#217—102no—
431#217—102no—
432#217—201no—
433#217—201no—
434#217C2×Dic514yescomplemented
435(C2×D3)⋊C4—102no—
436(C2×D3)⋊C4—201no—
437(C2×D3)⋊C4—201no—
438(C2×D3)⋊C4C2×Dic514yescomplemented
439C4⋊Dic3—201no—
440Dic3⋊C4—102no—
441Dic3⋊C4—102no—
442Dic3⋊C4—102no—
443Dic3⋊C4—102no—
444Dic3⋊C4—201no—
445Dic3⋊C4C2×Dic514yescomplemented
446C4×Dic3—54no—
447C4×Dic3—102no—
448C4×Dic3—201no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5—32no—
463C23×C5—61no—
464C23×C5—61no—
465C23×C5—61no—
466C23×C5—61no—
467C23×C5—61no—
468C23×C5—61no—
469C23×C5C2×C4×D312yes—
470C23×C5C2×C4×D312yes—
471C23×C5C23×D311yescharacteristic
472C5×D4—44no—
473C5×D4—68no—
474C5×D4—124no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—32no—
478C2×C4×C5—32no—
479C2×C4×C5—32no—
480C2×C4×C5—32no—
481C2×C4×C5—32no—
482C2×C4×C5—68no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5C2×C4×D312yes—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—32no—
500C2×Dic5—44no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—124no—
513C2×Dic5D3×D412yes—
514C22×D4—31no—
515C22×D4—31no—
516C22×D4D3×D511yescharacteristic
517C23×C4—31no—
518C23×C4—51no—
519C23×C4—151no—
520#121—38no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—51no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546#95—51no—
547#95—51no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5—42no—
553C2×C3×C5—42no—
554C2×C3×C5C2×C4×D411yescharacteristic
555C2×C3×C5#51811yescharacteristic
556C2×C3×C5#52011yescharacteristic
557C2×C3×C5#53511yescharacteristic
558C2×C3×C5#53711yescharacteristic
559C2×C3×C5#54011yescharacteristic
560C2×C3×C5#54211yescharacteristic
561C5×D3—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3C22×Dic512yes—
575C23×C3C22×Dic512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3C22×Dic512yes—
584C3×D4—44no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—52no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—204no—
600C2×C3×C4C22×Dic512yes—
601#67—28no—
602#67—44no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—28no—
608C2×Dic3—52no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3D4×D512yes—
621C2×Dic3#71112yes—
622C2×Dic3C22×Dic512yes—
623C2×Dic3C22×Dic512yes—
624C2×Dic3C22×Dic512yes—
625C4×D3—204no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5—22no—
631C22×C5—22no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—62no—
641C22×C5—62no—
642C22×C5—62no—
643C22×C5—121no—
644C22×C5—121no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5C22×C4×D311yescharacteristic
648C22×C5C2×D3×D411yescharacteristic
649C22×C5#100411yescharacteristic
650C22×C5#100411yescharacteristic
651C22×C5#100411yescharacteristic
652C22×C5D3×#4111yescharacteristic
653C22×C5#101011yescharacteristic
654C4×C5—22no—
655C4×C5—34no—
656C4×C5—62no—
657C4×C5—62no—
658Dic5—22no—
659Dic5—41no—
660Dic5—41no—
661Dic5—41no—
662Dic5—62no—
663Dic5—121no—
664Dic5—121no—
665Dic5—121no—
666C24—31no—
667C24C2×D3×D511yescharacteristic
668C24C2×D3×D511yescharacteristic
669C2×D4—34no—
670C2×D4—34no—
671C2×D4—41no—
672C2×D4—41no—
673C2×D4—62no—
674C2×D4—62no—
675C2×D4—121no—
676C2×D4—121no—
677C2×D4D3×Dic514yescomplemented
678C22×C4—31no—
679C22×C4—34no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—51no—
685C22×C4—51no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—102no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—151no—
692C22×C4—151no—
693C22×C4—201no—
694C22×C4—201no—
695C22×C4—302no—
696C22×C4—601no—
697C22×C4—601no—
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—302no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—601no—
705C4⋊C4—601no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—102no—
709C22⋊C4—201no—
710C22⋊C4—201no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C22⋊C4—601no—
717C22⋊C4—601no—
718C42—154no—
719C42—302no—
720C42—601no—
721C42—601no—
722C3×C5#232411yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3C2×D4×D511yescharacteristic
738C22×C3C2×#71111yescharacteristic
739C22×C3#414411yescharacteristic
740C22×C3#414411yescharacteristic
741C22×C3#414911yescharacteristic
742C22×C3#415011yescharacteristic
743C22×C3C23×Dic511yescharacteristic
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C3×C4—22no—
752C3×C4—102no—
753C3×C4—201no—
754C3×C4—201no—
755C3×C4—201no—
756Dic3—22no—
757Dic3—22no—
758Dic3—102no—
759Dic3—201no—
760Dic3—201no—
761Dic3—201no—
762Dic3D4×Dic514yes—
763C2×C5—42no—
764C2×C5—42no—
765C2×C5—122no—
766C2×C5#548611yescharacteristic
767C2×C5C4×D3×D411yescharacteristic
768C2×C5#554611yescharacteristic
769C2×C5#559211yescharacteristic
770C2×C5#560811yescharacteristic
771C2×C5#561511yescharacteristic
772C2×C5#566211yescharacteristic
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—32no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23C2×D3×Dic512yes—
793C23C2×D3×Dic512yes—
794C23C22×D3×D511yescharacteristic
795D4—44no—
796D4—68no—
797D4—124no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—52no—
806C2×C4—68no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—101no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—152no—
823C2×C4—204no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—604no—
836C2×C4C2×D3×Dic512yes—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3#6593711yescharacteristic
840C2×C3#6594111yescharacteristic
841C2×C3#6594211yescharacteristic
842C2×C3#6595311yescharacteristic
843C2×C3C2×D4×Dic511yescharacteristic
844C2×C3#6613211yescharacteristic
845C2×C3#6616111yescharacteristic
846D3—42no—
847C5#7466511yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—62no—
863C22—62no—
864C22—62no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22#9202011yescharacteristic
870C22D3×D4×D511yescharacteristic
871C22D3×#71111yescharacteristic
872C22#9202611yescharacteristic
873C22C22×D3×Dic511yescharacteristic
874C22#9204911yescharacteristic
875C22#9204911yescharacteristic
876C4—22no—
877C4—34no—
878C4—62no—
879C4—62no—
880C4—102no—
881C4—201no—
882C4—201no—
883C4—201no—
884C4—302no—
885C4—601no—
886C4—601no—
887C4—601no—
888C3#1061436411yescharacteristic, complemented, Sylow
889C2—42no—
890C2—42no—
891C2—122no—
892C2D3×D4×Dic511yescharacteristic
893C2#1175477611yescharacteristic
894C2#1175487211yescharacteristic
895C2#1175489011yescharacteristic
896C2#1175492011yescharacteristic
897C2#1175502911yescharacteristic
898C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#939C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic5×#67C2semidirect
3. C2×#91529C2semidirect
4. #11751322C2semidirect
5. C3×#65509C2semidirect
6. #11749519C2semidirect
7. #11749513C2semidirect
8. #11749509C2semidirect
9. #11749482C2semidirect
10. #11749482C2semidirect
11. #11749478C2semidirect
12. #11748903C2semidirect
13. #11748794C2semidirect
14. #11748693C2semidirect
15. #11748651C2semidirect
30. C5×#939C4semidirect
63. #65509D3semidirect
76. C2×C3×C5×D4C2×C4semidirect
87. C2×C5×#67C2×C4semidirect
90. C22×C5×Dic3C2×C4semidirect
110. C5×#217C2×C4semidirect
111. C5×(C2×D3)⋊C4C2×C4semidirect
112. C5×Dic3⋊C4C2×C4semidirect
126. Dic3×Dic5D4semidirect
259. #939Dic5semidirect
294. C2×C5×D4C4×D3semidirect
399. C2×C3×D4C2×Dic5semidirect
413. C2×#67C2×Dic5semidirect
420. C22×Dic3C2×Dic5semidirect
434. #217C2×Dic5semidirect
438. (C2×D3)⋊C4C2×Dic5semidirect
445. Dic3⋊C4C2×Dic5semidirect
677. C2×D4D3×Dic5semidirect
722. C3×C5#2324semidirect
847. C5#74665semidirect
888. C3#10614364semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9392
C2×Dic5×#672
C2×#915292
#117513222
C3×#655092
#117495192
#117495132
#117495092
#117494822
#117494782
#117489032
#117487942
#117486932
#117486512
#106143643
#746655