Finite Group Databasebeta

← #14328100

Subgroups — #14328100

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91782C211yesmaximal, characteristic, complemented
2C2×#91771C211yesmaximal, characteristic
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
5C2×C4×D60C211yesmaximal, characteristic, complemented
6C3×C5×#388C211yesmaximal, characteristic, complemented
7#11751090C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9#11751057C211yesmaximal, characteristic, complemented
10#11751052C211yesmaximal, characteristic, complemented
11C4×#6714C211yesmaximal, characteristic, complemented
12#11750769C211yesmaximal, characteristic, complemented
13#11750767C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750766C211yesmaximal, characteristic, complemented
16#10607567—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic, complemented
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C42×C5C2211yescharacteristic, complemented
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic, complemented
40C2×#6714C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46#91782—24no—
47#91771C418yescomplemented
48C22⋊C4×D15—24no—
49C22⋊C4×D15—24no—
50C4×D60—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52C3×C5×#95C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57#75836—51nomaximal, Hall
58C2×#4039—31no—
59C2×#4028—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4—31no—
62C2×C4×D20—31no—
63C5×#388D311yescharacteristic, complemented
64#65278—31no—
65#65246—31no—
66#65245—31no—
67#65240—31no—
68C4×#685—31no—
69#64957—31no—
70#64955—31no—
71#64954—31no—
72#64954—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—22no—
77C23×D15—22no—
78C23×D15—41no—
79C23×D15—41no—
80C23×D15C2×C414yescomplemented
81C23×D15C2311yescharacteristic
82C23×D15C2311yescharacteristic
83C23×D15C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—41no—
91C2×#1220—41no—
92C2×#1220C2×C414yescomplemented
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×D60—22no—
99C2×D60—22no—
100C2×D60—22no—
101C2×D60—22no—
102C2×D60C2×C414yescomplemented
103C2×D60C2×C414yescomplemented
104C2×C4×D15—22no—
105C2×C4×D15—22no—
106C2×C4×D15—22no—
107C2×C4×D15—22no—
108C2×C4×D15—22no—
109C2×C4×D15—22no—
110C2×C4×D15—22no—
111C2×C4×D15—22no—
112C2×C4×D15—22no—
113C2×C4×D15—22no—
114C2×C4×D15—41no—
115C2×C4×D15—41no—
116C2×C4×D15—41no—
117C2×C4×D15—41no—
118C2×C4×D15—41no—
119C3×C5×C4⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4C2×C414yescomplemented
123C3×C42×C5—22no—
124#6719—22no—
125#6719—22no—
126#6714—22no—
127#6714—22no—
128#6714—22no—
129#6714—22no—
130#6714—41no—
131#6714C2×C414yescomplemented
132#6714C2×C414yescomplemented
133#6714D414yescomplemented
134#6714D414yescomplemented
135C4⋊Dic15—22no—
136#6712—41no—
137C4×Dic15—22no—
138C4×Dic15—41no—
139C2×#893—51no—
140C2×#882—51no—
141C2×D3×C22⋊C4—51no—
142C2×D3×C22⋊C4—51no—
143C2×C4×D12—51no—
144C3×#388D511yescharacteristic, complemented
145#4989—51no—
146#4957—51no—
147#4956—51no—
148#4951—51no—
149C4×(C2×D3)⋊C4—51no—
150#4668—51no—
151#4666—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C22×C22⋊D5—31no—
156C22×D20—31no—
157C22×D20—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
164C2×C5×C22⋊C4C2×D311yescharacteristic
165C2×C5×C22⋊C4C2×D311yescharacteristic
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C42×C5C2×D311yescharacteristic, complemented
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×C4⋊Dic5—31no—
180C2×#683—31no—
181C2×C4×Dic5—31no—
182C2×C4×Dic5—31no—
183#4039—64no—
184#4028—38no—
185D5×C22⋊C4—64no—
186D5×C22⋊C4—64no—
187C4×D20—64no—
188C5×#95C2×D311yescharacteristic, complemented
189C5×#95C2×D311yescharacteristic, complemented
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5C22×C412yes—
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—28no—
218C22×D15—28no—
219C22×D15—44no—
220C22×D15—44no—
221C22×D15—44no—
222C22×D15—44no—
223C22×D15—44no—
224C22×D15C22×C412yes—
225C22×D15C22×C412yes—
226C22×D15C22×C412yes—
227C22×D15C2×D412yes—
228C22×D15C2×D412yes—
229C22×D15#4112yes—
230C22×D15#4112yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—21no—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5C22×C412yes—
246C2×C3×C4×C5C22×C412yes—
247C2×C3×C4×C5C2×D412yes—
248C2×C3×C4×C5C2×D412yes—
249#1220—44no—
250C2×Dic15—21no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15—21no—
256C2×Dic15—21no—
257C2×Dic15—21no—
258C2×Dic15—21no—
259C2×Dic15—21no—
260C2×Dic15—21no—
261C2×Dic15—21no—
262C2×Dic15C22×C412yes—
263C2×Dic15C2×D412yes—
264C2×Dic15C2×D412yes—
265D60—28no—
266D60—28no—
267C4×D15—44no—
268C4×D15—44no—
269C4×D15—44no—
270C4×D15—44no—
271C4×D15—44no—
272C24×D3—51no—
273C22×#67—51no—
274C22×D12—51no—
275C22×D12—51no—
276C22×C4×D3—51no—
277C22×C4×D3—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
282C2×C3×C22⋊C4C2×D511yescharacteristic
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×C3×C42C2×D511yescharacteristic, complemented
286C2×#217—51no—
287C2×#217—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×C4⋊Dic3—51no—
298C2×Dic3⋊C4—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3—51no—
301#893—104no—
302#882—58no—
303D3×C22⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—104no—
306C3×#95C2×D511yescharacteristic, complemented
307C3×#95C2×D511yescharacteristic, complemented
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5C22×D311yescharacteristic
313C23×D5—31no—
314C23×D5—31no—
315C23×D5—31no—
316C23×D5—34no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—62no—
321C23×D5—121no—
322C23×D5—121no—
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C22×C4×C5C22×D311yescharacteristic
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—34no—
330C2×C22⋊D5—121no—
331C2×C22⋊D5—121no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C2×D20—34no—
338C2×D20—34no—
339C2×D20—62no—
340C2×D20—62no—
341C2×D20—62no—
342C2×D20—62no—
343C2×C4×D5—62no—
344C2×C4×D5—62no—
345C2×C4×D5—62no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—121no—
354C2×C4×D5—121no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4C4×D314yescomplemented
362C42×C5—22no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—121no—
374C4⋊Dic5—62no—
375#683—121no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C22⋊C4—151no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—151no—
385#388D1511yescharacteristic, complemented
386#386—151no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—41no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—416no—
423C2×D15—41no—
424C2×D15—41no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15C4×D414yescomplemented
428C2×D15C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—41no—
434C3×C4×C5—41no—
435Dic15—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—41no—
439Dic15—41no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3—51no—
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—102no—
449C23×D3—201no—
450C23×D3—201no—
451C22×C3×C4C22×D511yescharacteristic
452C22×C3×C4C22×D511yescharacteristic
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C2×#67—54no—
458C2×#67—201no—
459C2×#67—201no—
460C22×Dic3—51no—
461C22×Dic3—51no—
462C22×Dic3—51no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C2×D12—54no—
466C2×D12—54no—
467C2×D12—102no—
468C2×D12—102no—
469C2×D12—102no—
470C2×D12—102no—
471C2×C4×D3—102no—
472C2×C4×D3—102no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3—102no—
476C2×C4×D3—102no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3—201no—
482C2×C4×D3—201no—
483C2×C4×D3—201no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C4⋊C4—22no—
487C3×C22⋊C4—22no—
488C3×C22⋊C4—22no—
489C3×C22⋊C4C4×D514yescomplemented
490C3×C42—22no—
491#217—102no—
492#217—102no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—201no—
502C4⋊Dic3—102no—
503Dic3⋊C4—201no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5C2×C4×D312yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—32no—
515C22×D5—32no—
516C22×D5—32no—
517C22×D5—32no—
518C22×D5—32no—
519C22×D5—32no—
520C22×D5—32no—
521C22×D5—68no—
522C22×D5—68no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5—124no—
541C22×D5—124no—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—21no—
555C2×C4×C5—21no—
556C2×C4×C5C2×C4×D312yes—
557C2×C4×C5C2×C4×D312yes—
558C2×C4×C5D3×D412yes—
559C2×C4×C5D3×D412yes—
560C22⋊D5—124no—
561C2×Dic5—32no—
562C2×Dic5—32no—
563C2×Dic5—32no—
564C2×Dic5—61no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576D20—68no—
577D20—68no—
578C4×D5—124no—
579C4×D5—124no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—151no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—151no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4C2×D1511yescharacteristic, complemented
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—304no—
610C2×C22⋊C4—304no—
611C2×C22⋊C4C2×D1511yescharacteristic
612C2×C22⋊C4C2×D1511yescharacteristic
613C2×C22⋊C4C2×D1511yescharacteristic
614C2×C42—151no—
615C2×C42—151no—
616C2×C42C2×D1511yescharacteristic, complemented
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95C2×D1511yescharacteristic, complemented
622#95C2×D1511yescharacteristic, complemented
623C2×C3×C5—42no—
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5#51811yescharacteristic
627C2×C3×C5D4211yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#55111yescharacteristic
631D15—24no—
632D15—24no—
633D15—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3C2×C4×D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—52no—
643C22×D3—52no—
644C22×D3—52no—
645C22×D3—52no—
646C22×D3—52no—
647C22×D3—52no—
648C22×D3—52no—
649C22×D3—108no—
650C22×D3—108no—
651C22×D3—101no—
652C22×D3—101no—
653C22×D3—101no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—101no—
662C22×D3—101no—
663C22×D3—101no—
664C22×D3—101no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4C2×C4×D512yes—
685C2×C3×C4C2×C4×D512yes—
686C2×C3×C4D4×D512yes—
687C2×C3×C4D4×D512yes—
688#67—204no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704D12—108no—
705D12—108no—
706C4×D3—204no—
707C4×D3—204no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—41no—
715C22×C5—41no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5D3×#4111yescharacteristic
722C22×C5D3×#4111yescharacteristic
723C22×C5#100911yescharacteristic
724C22×C5#100911yescharacteristic
725C2×D5—34no—
726C2×D5—34no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—1216no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—22no—
751C4×C5—41no—
752C4×C5—41no—
753Dic5—62no—
754Dic5—62no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—151no—
759C24—151no—
760C24—151no—
761C24—154no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
768C24C22×D1511yescharacteristic
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—154no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—151no—
779C22×C4—151no—
780C22×C4—151no—
781C22×C4—151no—
782C22×C4—151no—
783C22×C4—302no—
784C22×C4—302no—
785C22×C4—302no—
786C22×C4—302no—
787C22×C4—302no—
788C22×C4—302no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—601no—
794C22×C4—601no—
795C22×C4—601no—
796C22×C4—601no—
797C22×C4—601no—
798C22×C4C22×D1511yescharacteristic
799C22×C4C22×D1511yescharacteristic
800C22×C4C22×D1511yescharacteristic
801C22×C4C22×D1511yescharacteristic
802C22×C4C22×D1511yescharacteristic
803C22×C4C22×D1511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4C4×D1514yescomplemented
821C42—22no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3D5×#4111yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3#414911yescharacteristic
839C2×D3—54no—
840C2×D3—54no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—102no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—102no—
852C2×D3—102no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—2016no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—41no—
866C3×C4—41no—
867Dic3—102no—
868Dic3—102no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—42no—
873C2×C5#552111yescharacteristic
874C2×C5C4×D3×D411yescharacteristic
875C2×C5C4×D3×D411yescharacteristic
876C2×C5#560911yescharacteristic
877C2×C5#565411yescharacteristic
878C2×C5#567611yescharacteristic
879C2×C5#570511yescharacteristic
880D5—64no—
881D5—64no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—152no—
890C23—152no—
891C23—152no—
892C23—152no—
893C23—152no—
894C23—152no—
895C23—152no—
896C23—308no—
897C23—308no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23C2×C4×D1512yes—
918C23C23×D1511yescharacteristic
919D4—308no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—152no—
937C2×C4—152no—
938C2×C4—152no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—604no—
952C2×C4—604no—
953C2×C4—604no—
954C2×C4—604no—
955C2×C4—604no—
956C2×C4C2×C4×D1512yes—
957C2×C4C2×C4×D1512yes—
958C2×C4D4×D1512yes—
959C2×C4D4×D1512yes—
960C2×C3—42no—
961C2×C3#6585511yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3C4×D4×D511yescharacteristic
964C2×C3#6594311yescharacteristic
965C2×C3#6598811yescharacteristic
966C2×C3#6601011yescharacteristic
967C2×C3#6603911yescharacteristic
968D3—104no—
969D3—104no—
970D3—202no—
971C5#7583611yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—154no—
980C22—154no—
981C22—302no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—302no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—302no—
996C22—6016no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C22×C4×D1511yescharacteristic
1002C22C2×D4×D1511yescharacteristic
1003C22C2×D4×D1511yescharacteristic
1004C22#41×D1511yescharacteristic
1005C22#41×D1511yescharacteristic
1006C22#9210011yescharacteristic
1007C22#9210011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—41no—
1014C4—302no—
1015C4—302no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1060756711yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—304no—
1022C2—304no—
1023C2—602no—
1024C2#1175628011yescharacteristic
1025C2C4×D4×D1511yescharacteristic
1026C2C4×D4×D1511yescharacteristic
1027C2#1175636811yescharacteristic
1028C2#1175641311yescharacteristic
1029C2#1175643511yescharacteristic
1030C2#1175646411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#388C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91771C2
hypercenter#388D15
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#91782C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C2×C22⋊C4×D15C2semidirect
5. C2×C4×D60C2semidirect
6. C3×C5×#388C2semidirect
7. #11751090C2semidirect
8. #11751058C2semidirect
9. #11751057C2semidirect
10. #11751052C2semidirect
11. C4×#6714C2semidirect
12. #11750769C2semidirect
13. #11750767C2semidirect
14. #11750766C2semidirect
15. #11750766C2semidirect
25. C22×C4×D15C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
30. C2×C3×C42×C5C22semidirect
39. C2×#6714C22semidirect
40. C2×#6714C22semidirect
41. C2×#6714C22semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. C2×C4×Dic15C22semidirect
45. C2×C4×Dic15C22semidirect
47. #91771C4semidirect
51. C3×C5×#95C22semidirect
52. C3×C5×#95C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
63. C5×#388D3semidirect
80. C23×D15C2×C4semidirect
92. C2×#1220C2×C4semidirect
102. C2×D60C2×C4semidirect
103. C2×D60C2×C4semidirect
122. C3×C5×C22⋊C4C2×C4semidirect
131. #6714C2×C4semidirect
132. #6714C2×C4semidirect
133. #6714D4semidirect
134. #6714D4semidirect
144. C3×#388D5semidirect
163. C2×C5×C4⋊C4C2×D3semidirect
167. C2×C42×C5C2×D3semidirect
188. C5×#95C2×D3semidirect
189. C5×#95C2×D3semidirect
281. C2×C3×C4⋊C4C2×D5semidirect
285. C2×C3×C42C2×D5semidirect
306. C3×#95C2×D5semidirect
307. C3×#95C2×D5semidirect
361. C5×C22⋊C4C4×D3semidirect
385. #388D15semidirect
427. C2×D15C4×D4semidirect
428. C2×D15C4×D4semidirect
489. C3×C22⋊C4C4×D5semidirect
597. C2×C4⋊C4C2×D15semidirect
616. C2×C42C2×D15semidirect
621. #95C2×D15semidirect
622. #95C2×D15semidirect
820. C22⋊C4C4×D15semidirect
824. C3×C5#2358semidirect
971. C5#75836semidirect
1019. C3#10607567semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#917712
C2×C22⋊C4×D152
C2×C4×D602
C3×C5×#3882
#117510902
#117510582
#117510572
#117510522
C4×#67142
#117507692
#117507672
#117507662
#106075673
#758365