Finite Group Databasebeta

← #14328153

Subgroups — #14328153

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×C5×#67C211yesmaximal, characteristic, complemented
2C22×C3×#685C211yesmaximal, characteristic, complemented
3C2×#91563C211yesmaximal, characteristic
4C2×D5×#217C211yesmaximal, characteristic, complemented
5C2×#91441C211yesmaximal, characteristic, complemented
6#11751311C211yesmaximal, characteristic, complemented
7#11749492C211yesmaximal, characteristic, complemented
8Dic5×#217C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748906C211yesmaximal, characteristic, complemented
12#11748891C211yesmaximal, characteristic, complemented
13Dic3×#685C211yesmaximal, characteristic, complemented
14#11748711C211yesmaximal, characteristic, complemented
15#11748706C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic, complemented
21C23×C3×Dic5C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6712C2211yescharacteristic, complemented
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×#217C2211yescharacteristic
31C4×C5×#67—24no—
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
34C2×C4×C5×Dic3C2211yescharacteristic, complemented
35C2×C3×#685—24no—
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40#91563C418yescomplemented
41D5×#217—24no—
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91441—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82099—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685D311yescharacteristic, complemented
62C2×D5×C22⋊C4—31no—
63#65509—31no—
64#65502—31no—
65#65499—31no—
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×C5×D3C2311yescharacteristic
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—41no—
80C23×C3×D5—41no—
81C23×C3×D5C2×C414yescomplemented
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C2×C5×#67C2×C414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3—22no—
101C2×C4×C5×D3—41no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5—22no—
104C22×C3×Dic5—41no—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×#1201—22no—
108C2×#1201—22no—
109C2×#1201—41no—
110C2×#1201—41no—
111C2×#1201C2×C414yescomplemented
112C2×#1201C2×C414yescomplemented
113C2×D5×Dic3—22no—
114C2×D5×Dic3—22no—
115C2×D5×Dic3—22no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—41no—
118C2×D5×Dic3—41no—
119#6719—22no—
120#6719C2×C414yescomplemented
121#6712—22no—
122#6712—41no—
123C5×#217D414yescomplemented
124C5×(C2×D3)⋊C4—22no—
125C5×Dic3⋊C4—22no—
126C4×C5×Dic3—22no—
127C3×#685—22no—
128C3×#685—22no—
129C3×#685—22no—
130C3×#685D414yescomplemented
131(C2×D3)⋊Dic5—22no—
132(C2×D3)⋊Dic5—41no—
133#6665—22no—
134#6665—22no—
135#6665C2×C414yescomplemented
136#6665C2×C414yescomplemented
137Dic3×Dic5—22no—
138Dic3×Dic5—41no—
139C22×C3×C22⋊C4—51no—
140C2×#953—51no—
141C22×#217—51no—
142C2×C4×#67D511yescharacteristic, complemented
143C2×#67⋊C4—51no—
144#5213—51no—
145#5210—51no—
146C4×#217—51no—
147#4958—51no—
148#4957—51no—
149#4956—51no—
150#4946—51no—
151#4945—51no—
152#4944—51no—
153Dic3×C22⋊C4—51no—
154C24×D5C2×D311yescharacteristic
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5C2×D311yescharacteristic
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5C2×D311yescharacteristic
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⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—24no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685C2×D311yescharacteristic
180C2×#685C2×D311yescharacteristic
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
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#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×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3C22×C412yes—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—28no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—28no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5—44no—
225C22×C3×D5—44no—
226C22×C3×D5—44no—
227C22×C3×D5C22×C412yes—
228C22×C3×D5C22×C412yes—
229C22×C3×D5C2×D412yes—
230C22×C3×D5#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—44no—
237C2×C3×C4×C5C2×D412yes—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15C22×C412yes—
249C2×Dic15C22×C412yes—
250C5×#67—28no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3—21no—
257C2×C5×Dic3C22×C412yes—
258C2×C5×Dic3C2×D412yes—
259C2×C5×Dic3C2×D412yes—
260C4×C5×D3—44no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—44no—
267C2×C3×Dic5C2×D412yes—
268#1201—28no—
269#1201—44no—
270D5×Dic3—44no—
271D5×Dic3—44no—
272C25×C3—51no—
273C23×C3×C4—51no—
274C23×C3×C4C2×D511yescharacteristic
275C22×#67—51no—
276C22×#67—51no—
277C22×#67C2×D511yescharacteristic
278C23×Dic3—51no—
279C23×Dic3—51no—
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C22⋊C4—104no—
286#953—58no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—104no—
294C2×#217C2×D511yescharacteristic
295C4×#67—24no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4C2×D511yescharacteristic, complemented
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305#67⋊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—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—22no—
318C23×D5—41no—
319C23×D5—41no—
320C23×D5C4×D314yescomplemented
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D311yescharacteristic
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—22no—
344C22×Dic5—22no—
345C22×Dic5—31no—
346C22×Dic5—31no—
347C22×Dic5—31no—
348C22×Dic5—31no—
349C22×Dic5—41no—
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—34no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
366#685—22no—
367#685—22no—
368#685—22no—
369#685—34no—
370#685—34no—
371#685—62no—
372#685—62no—
373#685#6714yescomplemented
374#683—62no—
375#683—121no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—31no—
380C2×C4×D4—151no—
381C22×C22⋊C4—51no—
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#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×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—41no—
411C2×C5×D3—41no—
412C2×C5×D3—41no—
413C2×C5×D3—41no—
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—416no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—54no—
443C24×C3—102no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—201no—
448C24×C3—201no—
449C24×C3C22×D511yescharacteristic
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—102no—
457C22×C3×C4—102no—
458C22×C3×C4—201no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—22no—
462C2×#67—22no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—201no—
468C2×#67—201no—
469C2×#67C4×D514yescomplemented
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—102no—
477C22×Dic3—102no—
478C22×Dic3—201no—
479C22×Dic3—201no—
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C2×C4×D3—22no—
484C2×C4×D3—22no—
485C2×C4×D3—41no—
486C3×C22⋊C4—54no—
487C3×C22⋊C4—102no—
488C3×C22⋊C4—102no—
489C3×C22⋊C4—102no—
490#217—54no—
491#217—54no—
492#217—54no—
493#217—102no—
494#217—102no—
495#217—102no—
496#217C22⋊D514yescomplemented
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—201no—
500Dic3⋊C4—22no—
501Dic3⋊C4—102no—
502Dic3⋊C4—201no—
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#23712yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—28no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—21no—
532C22×D5—28no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5—44no—
536C22×D5—44no—
537C22×D5—44no—
538C22×D5C2×C4×D312yes—
539C22×D5C2×C4×D312yes—
540C22×D5#23512yes—
541C22×D5C2×#6712yes—
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×C5C2×#6712yes—
560C22⋊D5—68no—
561C22⋊D5—124no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—32no—
568C2×Dic5—32no—
569C2×Dic5—44no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5C2×#6712yes—
581C4×D5—124no—
582C4×D5—124no—
583C25—51no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—51no—
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—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—104no—
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—151no—
613C2×C22⋊C4—304no—
614C2×C42—31no—
615C2×C42—151no—
616C2×C42—151no—
617#95—151no—
618#95—151no—
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
631C3×D5—24no—
632C3×D5—42no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—52no—
640C23×C3—52no—
641C23×C3—52no—
642C23×C3—108no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—108no—
654C23×C3—204no—
655C23×C3—204no—
656C23×C3—204no—
657C23×C3—204no—
658C23×C3—204no—
659C23×C3C2×C4×D512yes—
660C23×C3#70912yes—
661C23×C3C2×C22⋊D512yes—
662C23×C3C23×D511yescharacteristic
663C22×D3—21no—
664C22×D3—21no—
665C22×D3—21no—
666C22×D3—21no—
667C22×D3—21no—
668C22×D3—21no—
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—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—204no—
683C2×C3×C4D4×D512yes—
684#67—28no—
685#67—108no—
686#67—204no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—52no—
694C2×Dic3—52no—
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—
706C2×Dic3—204no—
707C2×Dic3C2×C4×D512yes—
708C2×Dic3C2×C22⋊D512yes—
709C2×Dic3C2×C22⋊D512yes—
710C4×D3—44no—
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#67⋊C414yescomplemented
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×#23511yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5C2×#23711yescharacteristic
729C22×C5#100411yescharacteristic
730C22×C5#100411yescharacteristic
731C22×C5C22×#6711yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—22no—
740C2×D5—22no—
741C2×D5—416no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5C4×#6714yescomplemented
747C4×C5—22no—
748C4×C5—41no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—62no—
752Dic5—22no—
753Dic5—41no—
754Dic5—62no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—51no—
761C24—54no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—102no—
766C24—201no—
767C24—201no—
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—62no—
787C22×C4—62no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—201no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—102no—
811C22⋊C4—102no—
812C22⋊C4—102no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—154no—
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×C3—54no—
832C22×C3—102no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—102no—
836C22×C3—102no—
837C22×C3—102no—
838C22×C3—102no—
839C22×C3—102no—
840C22×C3—102no—
841C22×C3—2016no—
842C22×C3—201no—
843C22×C3—201no—
844C22×C3—201no—
845C22×C3—201no—
846C22×C3C4×C22⋊D514yescomplemented
847C22×C3C22×C4×D511yescharacteristic
848C22×C3C2×#70911yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3#414411yescharacteristic
851C22×C3D5×#4111yescharacteristic
852C22×C3#414911yescharacteristic
853C22×C3C22×C22⋊D511yescharacteristic
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C3×C4—22no—
862C3×C4—41no—
863C3×C4—102no—
864C3×C4—201no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—102no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—122no—
874C2×C5C2×#67⋊C411yescharacteristic
875C2×C5#548611yescharacteristic
876C2×C5#549011yescharacteristic
877C2×C5#549511yescharacteristic
878C2×C5C2×C4×#6711yescharacteristic
879C2×C5D4×#6711yescharacteristic
880C2×C5#580611yescharacteristic
881D5—24no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—52no—
889C23—52no—
890C23—52no—
891C23—52no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—108no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—108no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—204no—
911C23—204no—
912C23—204no—
913C23—204no—
914C23—204no—
915C23#676512yes—
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—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—124no—
944C2×C4—152no—
945C2×C4—152no—
946C2×C4—204no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—604no—
958C2×C4—604no—
959C2×C4D5×#6712yes—
960C2×C3—24no—
961C2×C3—104no—
962C2×C3—202no—
963C2×C3C4×D4×D511yescharacteristic
964C2×C3#6587911yescharacteristic
965C2×C3#6588411yescharacteristic
966C2×C3#6589011yescharacteristic
967C2×C3C2×C4×C22⋊D511yescharacteristic
968C2×C3D4×C22⋊D511yescharacteristic
969C2×C3#6616311yescharacteristic
970D3—42no—
971C5#8209911yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—54no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—2016no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22#9144114yescomplemented
1001C22C2×#676511yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22D5×#23511yescharacteristic
1004C22#9201711yescharacteristic
1005C22C2×D5×#6711yescharacteristic
1006C22C2×D3×C22⋊D511yescharacteristic
1007C22#9204911yescharacteristic
1008C4—22no—
1009C4—41no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—201no—
1015C4—302no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—104no—
1022C2—122no—
1023C2—202no—
1024C2#1175430511yescharacteristic
1025C2#1175439911yescharacteristic
1026C2C2×#9144111yescharacteristic
1027C2C4×D5×#6711yescharacteristic
1028C2#1175462511yescharacteristic
1029C2#1175465011yescharacteristic
1030C2#67×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91563C2
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. C2×C4×C5×#67C2semidirect
2. C22×C3×#685C2semidirect
4. C2×D5×#217C2semidirect
5. C2×#91441C2semidirect
6. #11751311C2semidirect
7. #11749492C2semidirect
8. Dic5×#217C2semidirect
9. #11748916C2semidirect
10. #11748910C2semidirect
11. #11748906C2semidirect
12. #11748891C2semidirect
13. Dic3×#685C2semidirect
14. #11748711C2semidirect
15. #11748706C2semidirect
20. C22×C4×C5×D3C22semidirect
28. C2×#6712C22semidirect
29. C2×#6712C22semidirect
32. C2×C5×(C2×D3)⋊C4C22semidirect
33. C2×C5×Dic3⋊C4C22semidirect
34. C2×C4×C5×Dic3C22semidirect
40. #91563C4semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
61. C22×#685D3semidirect
81. C23×C3×D5C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
111. C2×#1201C2×C4semidirect
112. C2×#1201C2×C4semidirect
120. #6719C2×C4semidirect
123. C5×#217D4semidirect
130. C3×#685D4semidirect
135. #6665C2×C4semidirect
136. #6665C2×C4semidirect
142. C2×C4×#67D5semidirect
280. C22×C4×D3C2×D5semidirect
298. C2×(C2×D3)⋊C4C2×D5semidirect
301. C2×Dic3⋊C4C2×D5semidirect
304. C2×C4×Dic3C2×D5semidirect
320. C23×D5C4×D3semidirect
373. #685#67semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
469. C2×#67C4×D5semidirect
496. #217C22⋊D5semidirect
724. C22×C5#67⋊C4semidirect
746. C2×D5C4×#67semidirect
824. C3×C5#2358semidirect
846. C22×C3C4×C22⋊D5semidirect
971. C5#82099semidirect
1000. C22#91441semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#672
C22×C3×#6852
C2×#915632
C2×D5×#2172
C2×#914412
#117513112
#117494922
Dic5×#2172
#117489162
#117489102
#117489062
#117488912
Dic3×#6852
#117487112
#117487062
#106141293
#820995