Finite Group Databasebeta

← #14328152

Subgroups — #14328152

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
1C22×#6714C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×#91573C211yesmaximal, characteristic
4C2×#91561C211yesmaximal, characteristic, complemented
5C2×#91446C211yesmaximal, characteristic, complemented
6C3×#65499C211yesmaximal, characteristic, complemented
7#11749501C211yesmaximal, characteristic, complemented
8#11749487C211yesmaximal, characteristic, complemented
9#11748919C211yesmaximal, characteristic, complemented
10#11748914C211yesmaximal, characteristic, complemented
11#11748909C211yesmaximal, characteristic, complemented
12#11748894C211yesmaximal, characteristic, complemented
13#11748881C211yesmaximal, characteristic, complemented
14#11748728C211yesmaximal, characteristic, complemented
15#11748669C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic, complemented
22C22×#1203C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C2×#6714—24no—
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×C5×#217C2211yescharacteristic
32C4×C5×#67—24no—
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C4×C5×Dic3C2211yescharacteristic, complemented
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic, complemented
39C2×C3×#683C2211yescharacteristic, complemented
40#91573C418yescomplemented
41#91561—24no—
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91446—24no—
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74596—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685—31no—
62C2×D5×C22⋊C4—31no—
63#65509—31no—
64#65502—31no—
65#65499D311yescharacteristic, complemented
66#65279—31no—
67#65278—31no—
68#65246—31no—
69#65245—31no—
70C22⋊C4×Dic5—31no—
71#65229—31no—
72C4×#685—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×C5×D3C2311yescharacteristic
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15—22no—
90C22×Dic15—22no—
91C22×Dic15—41no—
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×C5×#67—22no—
95C2×C5×#67—22no—
96C2×C5×#67C2×C414yescomplemented
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C4×C5×D3—22no—
101C2×C4×C5×D3—22no—
102C2×C4×C5×D3—41no—
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×#1203—22no—
108C2×#1203—22no—
109C2×#1203—41no—
110C2×#1203—41no—
111C2×#1203C2×C414yescomplemented
112C2×#1203C2×C414yescomplemented
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—22no—
116C2×#1200—22no—
117C2×#1200—41no—
118C2×#1200—41no—
119#6714—22no—
120#6714—22no—
121#6714—22no—
122#6714D414yescomplemented
123C5×#217D414yescomplemented
124C5×(C2×D3)⋊C4—22no—
125C5×Dic3⋊C4—22no—
126C4×C5×Dic3—22no—
127C3×C22⋊Dic5—22no—
128C3×C22⋊Dic5C2×C414yescomplemented
129C3×#683—22no—
130C3×#683—41no—
131#6667—22no—
132#6667—22no—
133#6667C2×C414yescomplemented
134#6667C2×C414yescomplemented
135(C2×D3)⋊Dic5—22no—
136(C2×D3)⋊Dic5—41no—
137Dic3×Dic5—22no—
138Dic3×Dic5—41no—
139C2×C4×#67D511yescharacteristic, complemented
140C22×(C2×D3)⋊C4—51no—
141C2×#893—51no—
142C2×#882—51no—
143C2×D3×C22⋊C4—51no—
144C3×#385—51no—
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—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5C2×D311yescharacteristic
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5C2×D311yescharacteristic
171C2×C22⋊Dic5C2×D311yescharacteristic
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—64no—
183C2×#683C2×D311yescharacteristic, complemented
184C2×#683C2×D311yescharacteristic, complemented
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187D5×C22⋊C4—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963C2×D311yescharacteristic, complemented
193#3963C2×D311yescharacteristic, complemented
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—28no—
215C22×D15—44no—
216C22×D15—44no—
217C22×D15—44no—
218C22×D15—44no—
219C22×D15—44no—
220C22×D15C22×C412yes—
221C22×D15C22×C412yes—
222C22×D15C2×D412yes—
223C22×D15#4112yes—
224C22×C5×D3—21no—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3—21no—
230C22×C5×D3C22×C412yes—
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—44no—
237C2×C3×C4×C5C2×D412yes—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—44no—
244C2×Dic15C2×D412yes—
245C5×#67—28no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3C22×C412yes—
253C2×C5×Dic3C2×D412yes—
254C2×C5×Dic3C2×D412yes—
255C4×C5×D3—44no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5C22×C412yes—
267C2×C3×Dic5C22×C412yes—
268#1203—28no—
269#1203—44no—
270#1200—44no—
271#1200—44no—
272C24×D3—51no—
273C23×C3×C4C2×D511yescharacteristic
274C22×#67C2×D511yescharacteristic
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×#217C2×D511yescharacteristic
286C4×#67—24no—
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—104no—
298C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
299C2×Dic3⋊C4C2×D511yescharacteristic, complemented
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3C2×D511yescharacteristic, complemented
303#893—104no—
304#882—58no—
305D3×C22⋊C4—104no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
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—
323C2×C5×D4—34no—
324C2×C5×D4—62no—
325C2×C5×D4—62no—
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—41no—
332C22×C4×C5—62no—
333C22×C4×C5—62no—
334C22×C4×C5—121no—
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—121no—
342C2×C22⋊D5—121no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—62no—
346C22×Dic5—62no—
347C22×Dic5—121no—
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D311yescharacteristic
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4—62no—
361C42×C5—62no—
362C22⋊Dic5—22no—
363C22⋊Dic5—62no—
364C22⋊Dic5—121no—
365C22⋊Dic5C4×D314yescomplemented
366#685—34no—
367#685—34no—
368#685—34no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—22no—
375#683—41no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—31no—
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—51no—
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—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—416no—
417C2×D15—41no—
418C2×D15—41no—
419C2×D15—41no—
420C2×D15—41no—
421C2×D15C4×D414yescomplemented
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3—41no—
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—41no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3—51no—
443C23×D3—54no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—201no—
449C23×D3—201no—
450C23×D3C22×D511yescharacteristic
451C22×C3×C4—22no—
452C22×C3×C4—22no—
453C22×C3×C4—41no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—22no—
461C2×#67—22no—
462C2×#67C4×D514yescomplemented
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—102no—
466C22×Dic3—102no—
467C22×Dic3—201no—
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—201no—
476C2×D12—201no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—41no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C4⋊C4—102no—
487C3×C4⋊C4—201no—
488C3×C22⋊C4—54no—
489C3×C22⋊C4—102no—
490#217C22⋊D514yescomplemented
491(C2×D3)⋊C4—22no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
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—22no—
503C4×Dic3—22no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—32no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5C2×C4×D312yes—
518C23×C5D3×D412yes—
519C23×C5#23912yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—32no—
522C22×D5—32no—
523C22×D5—32no—
524C22×D5—32no—
525C22×D5—68no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—68no—
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—
542C5×D4—68no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—32no—
549C2×C4×C5—32no—
550C2×C4×C5—32no—
551C2×C4×C5—44no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—61no—
557C2×C4×C5—61no—
558C2×C4×C5—124no—
559C2×C4×C5D3×D412yes—
560C22⋊D5—68no—
561C22⋊D5—124no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—21no—
572C2×Dic5—32no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—124no—
579C2×Dic5C2×C4×D312yes—
580C2×Dic5C2×C4×D312yes—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4D3×D511yescharacteristic
592#120—158no—
593C4×D4—64no—
594C4×D4—304no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4—51no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
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—151no—
611C2×C22⋊C4—151no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4—304no—
614C2×C42—31no—
615C2×C42—151no—
616C2×C42—151no—
617#95—51no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
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—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3C2×C4×D512yes—
639C23×C3#70912yes—
640C23×C3C2×C22⋊D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—52no—
649C22×D3—52no—
650C22×D3—52no—
651C22×D3—52no—
652C22×D3—108no—
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—108no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3C2×C4×D512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—44no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—101no—
687C2×C3×C4—101no—
688C2×C3×C4D4×D512yes—
689#67—28no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—52no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—204no—
703C2×Dic3C2×C4×D512yes—
704C2×Dic3C2×C22⋊D512yes—
705C2×Dic3C2×C22⋊D512yes—
706D12—108no—
707D12—204no—
708C4×D3—44no—
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—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5#89314yescomplemented
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×D3×D411yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5#100411yescharacteristic
729C22×C5C2×#23911yescharacteristic
730C22×C5D3×#4111yescharacteristic
731C22×C5#100911yescharacteristic
732C2×D5—34no—
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—41no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—62no—
752Dic5—22no—
753Dic5—22no—
754Dic5—41no—
755Dic5—41no—
756Dic5—62no—
757Dic5—121no—
758C24—31no—
759C24—151no—
760C24—151no—
761C24—154no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
768C24C2×D3×D511yescharacteristic
769C2×D4—34no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—41no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—102no—
806C4⋊C4—201no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—62no—
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×C3C4×C22⋊D514yescomplemented
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×#70911yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3C22×C22⋊D511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—54no—
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—41no—
863C3×C4—102no—
864C3×C4—102no—
865C3×C4—201no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—122no—
874C2×C5C2×#89311yescharacteristic
875C2×C5C4×D3×D411yescharacteristic
876C2×C5#554511yescharacteristic
877C2×C5#559011yescharacteristic
878C2×C5#563011yescharacteristic
879C2×C5#563711yescharacteristic
880C2×C5#565411yescharacteristic
881D5—64no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—152no—
895C23—152no—
896C23—152no—
897C23—152no—
898C23—308no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—308no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—604no—
911C23—604no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23#676912yes—
916C23C4×D3×D512yes—
917C23D3×C22⋊D512yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—32no—
930C2×C4—44no—
931C2×C4—52no—
932C2×C4—52no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—101no—
948C2×C4—101no—
949C2×C4—124no—
950C2×C4—152no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4—604no—
959C2×C4#679012yes—
960C2×C3—24no—
961C2×C3C4×D4×D511yescharacteristic
962C2×C3#6587911yescharacteristic
963C2×C3#6588411yescharacteristic
964C2×C3#6589011yescharacteristic
965C2×C3C2×C4×C22⋊D511yescharacteristic
966C2×C3D4×C22⋊D511yescharacteristic
967C2×C3#6616311yescharacteristic
968D3—42no—
969D3—104no—
970D3—202no—
971C5#7459611yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—154no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—6016no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22#9144614yescomplemented
1001C22C2×#676911yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22#9201611yescharacteristic
1004C22#9201911yescharacteristic
1005C22C2×D3×C22⋊D511yescharacteristic
1006C22C2×#679011yescharacteristic
1007C22#9204911yescharacteristic
1008C4—22no—
1009C4—41no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—102no—
1015C4—201no—
1016C4—201no—
1017C4—302no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—122no—
1022C2—304no—
1023C2—602no—
1024C2#1175438211yescharacteristic
1025C2#1175446511yescharacteristic
1026C2C2×#9144611yescharacteristic
1027C2C4×#679011yescharacteristic
1028C2#1175462911yescharacteristic
1029C2#1175465611yescharacteristic
1030C2#1175544011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91573C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6714C2semidirect
2. C2×C4×C5×#67C2semidirect
4. C2×#91561C2semidirect
5. C2×#91446C2semidirect
6. C3×#65499C2semidirect
7. #11749501C2semidirect
8. #11749487C2semidirect
9. #11748919C2semidirect
10. #11748914C2semidirect
11. #11748909C2semidirect
12. #11748894C2semidirect
13. #11748881C2semidirect
14. #11748728C2semidirect
15. #11748669C2semidirect
21. C22×C4×C5×D3C22semidirect
33. C2×C5×(C2×D3)⋊C4C22semidirect
34. C2×C5×Dic3⋊C4C22semidirect
35. C2×C4×C5×Dic3C22semidirect
38. C2×C3×#683C22semidirect
39. C2×C3×#683C22semidirect
40. #91573C4semidirect
46. C2×(C2×D3)⋊Dic5C22semidirect
47. C2×(C2×D3)⋊Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
65. #65499D3semidirect
80. C23×D15C2×C4semidirect
96. C2×C5×#67C2×C4semidirect
111. C2×#1203C2×C4semidirect
112. C2×#1203C2×C4semidirect
122. #6714D4semidirect
123. C5×#217D4semidirect
128. C3×C22⋊Dic5C2×C4semidirect
133. #6667C2×C4semidirect
134. #6667C2×C4semidirect
139. C2×C4×#67D5semidirect
183. C2×#683C2×D3semidirect
184. C2×#683C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
280. C22×C4×D3C2×D5semidirect
298. C2×(C2×D3)⋊C4C2×D5semidirect
299. C2×Dic3⋊C4C2×D5semidirect
302. C2×C4×Dic3C2×D5semidirect
365. C22⋊Dic5C4×D3semidirect
399. C22×C3×C5C4×D4semidirect
421. C2×D15C4×D4semidirect
462. C2×#67C4×D5semidirect
490. #217C22⋊D5semidirect
724. C22×C5#893semidirect
824. C3×C5#2358semidirect
831. C22×C3C4×C22⋊D5semidirect
971. C5#74596semidirect
1000. C22#91446semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C22×#67142
C2×C4×C5×#672
C2×#915732
C2×#915612
C2×#914462
C3×#654992
#117495012
#117494872
#117489192
#117489142
#117489092
#117488942
#117488812
#117487282
#117486692
#106141293
#745965