Finite Group Databasebeta

← #14328094

Subgroups — #14328094

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×C4×#1220C211yesmaximal, characteristic, complemented
2C22×#6714C211yesmaximal, characteristic, complemented
3C2×#91782C211yesmaximal, characteristic, complemented
4C2×#91771C211yesmaximal, characteristic
5C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
6C3×C5×#385C211yesmaximal, characteristic, complemented
7#11751091C211yesmaximal, characteristic, complemented
8#11751090C211yesmaximal, characteristic, complemented
9#11751089C211yesmaximal, characteristic, complemented
10#11751059C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
12#11750770C211yesmaximal, characteristic, complemented
13#11750767C211yesmaximal, characteristic, complemented
14#11750766C211yesmaximal, characteristic, complemented
15#11750766C211yesmaximal, characteristic, complemented
16#10606327—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C22×D60C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic, complemented
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C4×#1220—24no—
32C2×#6714—24no—
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45C2×C4×Dic15C2211yescharacteristic, complemented
46C2×C4×Dic15C2211yescharacteristic, complemented
47C2×C4×Dic15C2211yescharacteristic, complemented
48#91782—24no—
49#91771C418yescomplemented
50C22⋊C4×D15—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52C3×C5×#95C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57#74596—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×#685—31no—
60C2×#4039—31no—
61C2×#4028—31no—
62C2×D5×C22⋊C4—31no—
63C5×#385D311yescharacteristic, complemented
64#65279—31no—
65#65278—31no—
66#65277—31no—
67#65247—31no—
68C22⋊C4×Dic5—31no—
69#64958—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×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—22no—
94C2×#1220—22no—
95C2×#1220C2×C414yescomplemented
96C22×Dic15—22no—
97C22×Dic15—22no—
98C22×Dic15—41no—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C2×D60—22no—
105C2×D60—22no—
106C2×D60—41no—
107C2×D60—41no—
108C2×D60C2×C414yescomplemented
109C2×D60C2×C414yescomplemented
110C2×C4×D15—22no—
111C2×C4×D15—22no—
112C2×C4×D15—22no—
113C2×C4×D15—22no—
114C2×C4×D15—22no—
115C2×C4×D15—22no—
116C2×C4×D15—41no—
117C2×C4×D15—41no—
118C2×C4×D15—41no—
119C3×C5×C4⋊C4—22no—
120C3×C5×C4⋊C4—41no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4C2×C414yescomplemented
123#6719D414yescomplemented
124#6714—22no—
125#6714—22no—
126#6714—22no—
127#6714—22no—
128#6714—22no—
129#6714—22no—
130#6714—22no—
131#6714—41no—
132#6714C2×C414yescomplemented
133#6714C2×C414yescomplemented
134#6714D414yescomplemented
135#6712—22no—
136C4×Dic15—22no—
137C4×Dic15—22no—
138C4×Dic15—41no—
139C2×C4×#67—51no—
140C22×(C2×D3)⋊C4—51no—
141C2×#893—51no—
142C2×#882—51no—
143C2×D3×C22⋊C4—51no—
144C3×#385D511yescharacteristic, complemented
145#4990—51no—
146#4989—51no—
147#4988—51no—
148#4958—51no—
149Dic3×C22⋊C4—51no—
150#4669—51no—
151#4666—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C23×C4×C5C2×D311yescharacteristic
156C22×C22⋊D5—31no—
157C23×Dic5—31no—
158C22×D20—31no—
159C22×D20—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
164C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C5×C22⋊C4C2×D311yescharacteristic
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C22⋊Dic5—31no—
168C4×C22⋊D5—64no—
169C2×#685—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×#685—31no—
180C2×#685—64no—
181C2×#683—31no—
182C2×C4×Dic5—31no—
183C2×C4×Dic5—31no—
184C2×C4×Dic5—31no—
185#4039—64no—
186#4028—38no—
187D5×C22⋊C4—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×C5C22×C412yes—
200C23×C3×C5C2×D412yes—
201C23×C3×C5#4112yes—
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—28no—
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—21no—
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—28no—
221C22×D15—44no—
222C22×D15—44no—
223C22×D15—44no—
224C22×D15—44no—
225C22×D15—44no—
226C22×D15C22×C412yes—
227C22×D15C22×C412yes—
228C22×D15C22×C412yes—
229C22×D15C2×D412yes—
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×C5—21no—
246C2×C3×C4×C5—44no—
247C2×C3×C4×C5C22×C412yes—
248C2×C3×C4×C5C22×C412yes—
249C2×C3×C4×C5C2×D412yes—
250#1220—28no—
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×Dic15—44no—
263C2×Dic15C22×C412yes—
264C2×Dic15C2×D412yes—
265C2×Dic15C2×D412yes—
266C2×Dic15C2×D412yes—
267D60—28no—
268D60—44no—
269C4×D15—44no—
270C4×D15—44no—
271C4×D15—44no—
272C24×D3—51no—
273C23×C3×C4C2×D511yescharacteristic
274C22×#67—51no—
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
282C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×#217—51no—
286C4×#67—104no—
287C2×(C2×D3)⋊C4—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×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—104no—
299C2×Dic3⋊C4—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303#893—104no—
304#882—58no—
305D3×C22⋊C4—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×C5—22no—
324C22×C4×C5—22no—
325C22×C4×C5—41no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C2×C22⋊D5—34no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—62no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—62no—
341C22×Dic5—62no—
342C22×Dic5—121no—
343C2×D20—34no—
344C2×D20—34no—
345C2×D20—62no—
346C2×D20—62no—
347C2×D20—121no—
348C2×D20—121no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—22no—
359C5×C4⋊C4—41no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4C4×D314yescomplemented
362C22⋊Dic5—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—62no—
367#685—62no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—121no—
374#683—62no—
375C4×Dic5—62no—
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#388—151no—
386#386—151no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385D1511yescharacteristic, complemented
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5C4×D414yescomplemented
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—416no—
420C2×D15—41no—
421C2×D15—41no—
422C2×D15—41no—
423C2×D15—41no—
424C2×D15—41no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—41no—
433C3×C4×C5—41no—
434C3×C4×C5—41no—
435Dic15—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
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×C4—22no—
452C22×C3×C4—22no—
453C22×C3×C4—41no—
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—102no—
462C2×#67—102no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—102no—
469C22×Dic3—102no—
470C22×Dic3—201no—
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—201no—
476C2×D12—201no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—201no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—41no—
488C3×C22⋊C4—22no—
489C3×C22⋊C4C4×D514yescomplemented
490#217—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—102no—
495(C2×D3)⋊C4—102no—
496(C2×D3)⋊C4—102no—
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—
502Dic3⋊C4—102no—
503C4×Dic3—102no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5C2×C4×D312yes—
511C23×C5D3×D412yes—
512C23×C5#23912yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—32no—
515C22×D5—32no—
516C22×D5—32no—
517C22×D5—32no—
518C22×D5—32no—
519C22×D5—68no—
520C22×D5—61no—
521C22×D5—61no—
522C22×D5—61no—
523C22×D5—61no—
524C22×D5—68no—
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×C5—21no—
557C2×C4×C5—44no—
558C2×C4×C5C2×C4×D312yes—
559C2×C4×C5C2×C4×D312yes—
560C2×C4×C5D3×D412yes—
561C22⋊D5—68no—
562C2×Dic5—32no—
563C2×Dic5—32no—
564C2×Dic5—32no—
565C2×Dic5—32no—
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—
576C2×Dic5—61no—
577C2×Dic5—124no—
578D20—68no—
579D20—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×C4C2×D1511yescharacteristic
592#120—158no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4C2×D1511yescharacteristic, complemented
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—151no—
610C2×C22⋊C4—304no—
611C2×C22⋊C4—304no—
612C2×C22⋊C4C2×D1511yescharacteristic
613C2×C22⋊C4C2×D1511yescharacteristic
614C2×C42—151no—
615C2×C42—151no—
616C2×C42—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95C2×D1511yescharacteristic, complemented
622#95C2×D1511yescharacteristic, complemented
623C2×C3×C5—24no—
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—42no—
633D15—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3C2×C4×D512yes—
639C23×C3D4×D512yes—
640C23×C3#71312yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—52no—
643C22×D3—52no—
644C22×D3—52no—
645C22×D3—52no—
646C22×D3—52no—
647C22×D3—108no—
648C22×D3—101no—
649C22×D3—101no—
650C22×D3—101no—
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—108no—
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×C4—21no—
685C2×C3×C4—44no—
686C2×C3×C4C2×C4×D512yes—
687C2×C3×C4C2×C4×D512yes—
688C2×C3×C4D4×D512yes—
689#67—108no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—52no—
693C2×Dic3—52no—
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—
704C2×Dic3—101no—
705C2×Dic3—204no—
706D12—108no—
707D12—204no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5#89314yescomplemented
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5#100411yescharacteristic
722C22×C5C2×#23911yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5#100911yescharacteristic
725C2×D5—34no—
726C2×D5—62no—
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—1216no—
739C2×D5—121no—
740C2×D5—121no—
741C2×D5—121no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—41no—
751C4×C5—41no—
752C4×C5—41no—
753Dic5—62no—
754Dic5—62no—
755Dic5—62no—
756Dic5—62no—
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—22no—
779C22×C4—22no—
780C22×C4—41no—
781C22×C4—151no—
782C22×C4—151no—
783C22×C4—151no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—302no—
787C22×C4—302no—
788C22×C4—302no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
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—41no—
806C4⋊C4—302no—
807C22⋊C4—22no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—302no—
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—302no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3#403914yescomplemented
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3C2×#71311yescharacteristic
837C22×C3D5×#4111yescharacteristic
838C22×C3#414911yescharacteristic
839C2×D3—54no—
840C2×D3—102no—
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—2016no—
853C2×D3—201no—
854C2×D3—201no—
855C2×D3—201no—
856C2×D3—201no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867Dic3—102no—
868Dic3—102no—
869Dic3—102no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5C2×#89311yescharacteristic
874C2×C5C4×D3×D411yescharacteristic
875C2×C5#554511yescharacteristic
876C2×C5#559011yescharacteristic
877C2×C5#563011yescharacteristic
878C2×C5#563711yescharacteristic
879C2×C5#565411yescharacteristic
880D5—64no—
881D5—122no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—152no—
888C23—152no—
889C23—152no—
890C23—152no—
891C23—152no—
892C23—308no—
893C23—301no—
894C23—301no—
895C23—301no—
896C23—301no—
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—604no—
911C23—604no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23C2×C4×D1512yes—
916C23D4×D1512yes—
917C23#682112yes—
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—21no—
937C2×C4—44no—
938C2×C4—152no—
939C2×C4—152no—
940C2×C4—152no—
941C2×C4—152no—
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—301no—
952C2×C4—301no—
953C2×C4—604no—
954C2×C4—604no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4C2×C4×D1512yes—
958C2×C4C2×C4×D1512yes—
959C2×C4D4×D1512yes—
960C2×C3—24no—
961C2×C3C2×#403911yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3#6587911yescharacteristic
964C2×C3#6592411yescharacteristic
965C2×C3#6596411yescharacteristic
966C2×C3#6597111yescharacteristic
967C2×C3#6598811yescharacteristic
968D3—104no—
969D3—202no—
970D3—202no—
971C5#7459611yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—154no—
979C22—302no—
980C22—302no—
981C22—302no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—302no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—6016no—
992C22—601no—
993C22—601no—
994C22—601no—
995C22—601no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22#9178214yescomplemented
1001C22C22×C4×D1511yescharacteristic
1002C22C2×D4×D1511yescharacteristic
1003C22C2×D4×D1511yescharacteristic
1004C22#9209511yescharacteristic
1005C22C2×#682111yescharacteristic
1006C22#41×D1511yescharacteristic
1007C22#9210011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—41no—
1012C4—41no—
1013C4—41no—
1014C4—302no—
1015C4—302no—
1016C4—302no—
1017C4—302no—
1018C4—601no—
1019C3#1060632711yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—304no—
1022C2—602no—
1023C2—602no—
1024C2C2×#9178211yescharacteristic
1025C2C4×D4×D1511yescharacteristic
1026C2#1175630411yescharacteristic
1027C2#1175634911yescharacteristic
1028C2#1175638911yescharacteristic
1029C2#1175639611yescharacteristic
1030C2#1175641311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#385C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91771C2
hypercenter#385D15
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C22×#6714C2semidirect
3. C2×#91782C2semidirect
5. C2×C22⋊C4×D15C2semidirect
6. C3×C5×#385C2semidirect
7. #11751091C2semidirect
8. #11751090C2semidirect
9. #11751089C2semidirect
10. #11751059C2semidirect
11. C22⋊C4×Dic15C2semidirect
12. #11750770C2semidirect
13. #11750767C2semidirect
14. #11750766C2semidirect
15. #11750766C2semidirect
25. C22×C4×D15C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
27. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. C2×C4×Dic15C22semidirect
46. C2×C4×Dic15C22semidirect
47. C2×C4×Dic15C22semidirect
49. #91771C4semidirect
51. C3×C5×#95C22semidirect
52. C3×C5×#95C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
63. C5×#385D3semidirect
80. C23×D15C2×C4semidirect
95. C2×#1220C2×C4semidirect
108. C2×D60C2×C4semidirect
109. C2×D60C2×C4semidirect
122. C3×C5×C22⋊C4C2×C4semidirect
123. #6719D4semidirect
132. #6714C2×C4semidirect
133. #6714C2×C4semidirect
134. #6714D4semidirect
144. C3×#385D5semidirect
163. C2×C5×C4⋊C4C2×D3semidirect
164. C2×C5×C4⋊C4C2×D3semidirect
188. C5×#95C2×D3semidirect
189. C5×#95C2×D3semidirect
281. C2×C3×C4⋊C4C2×D5semidirect
282. C2×C3×C4⋊C4C2×D5semidirect
306. C3×#95C2×D5semidirect
307. C3×#95C2×D5semidirect
361. C5×C22⋊C4C4×D3semidirect
390. #385D15semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×D15C4×D4semidirect
489. C3×C22⋊C4C4×D5semidirect
596. C2×C4⋊C4C2×D15semidirect
597. C2×C4⋊C4C2×D15semidirect
621. #95C2×D15semidirect
622. #95C2×D15semidirect
717. C22×C5#893semidirect
820. C22⋊C4C4×D15semidirect
824. C3×C5#2358semidirect
831. C22×C3#4039semidirect
971. C5#74596semidirect
1000. C22#91782semidirect
1019. C3#10606327semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C22×#67142
C2×#917822
C2×#917712
C2×C22⋊C4×D152
C3×C5×#3852
#117510912
#117510902
#117510892
#117510592
C22⋊C4×Dic152
#117507702
#117507672
#117507662
#106063273
#745965