Finite Group Databasebeta

← #14329469

Subgroups — #14329469

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×#91567C211yesmaximal, characteristic
4C2×#91441C211yesmaximal, characteristic, complemented
5C2×#91396C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7#11749518C211yesmaximal, characteristic, complemented
8#11749483C211yesmaximal, characteristic, complemented
9#11749482C211yesmaximal, characteristic, complemented
10#11748918C211yesmaximal, characteristic, complemented
11#11748915C211yesmaximal, characteristic, complemented
12#11748914C211yesmaximal, characteristic, complemented
13#11748912C211yesmaximal, characteristic, complemented
14#11748651C211yesmaximal, characteristic, complemented
15#11748645C211yesmaximal, characteristic, complemented
16#10614074—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C4×#1220—24no—
29C2×#6714C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic
33C4×C5×#67—24no—
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40#91567C418yescomplemented
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6669C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51#91441—24no—
52#91396—24no—
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74679—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4086—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×C22⋊D5—31no—
62C2×#4039—31no—
63#65510—31no—
64#65502—31no—
65#65502D311yescharacteristic, complemented
66C4⋊C4×Dic5—31no—
67#65246—31no—
68#65246—31no—
69#65245—31no—
70#65245—31no—
71#65228—31no—
72C4×#683—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5—41no—
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220C2×C414yescomplemented
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C2×C4×D15—22no—
89C2×C4×D15—22no—
90C2×C4×D15—41no—
91C2×C5×#67—22no—
92C2×C5×#67—22no—
93C2×C5×#67C2×C414yescomplemented
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—41no—
100C2×C3×C22⋊D5—41no—
101C2×C3×C22⋊D5—41no—
102C2×C3×C22⋊D5C2×C414yescomplemented
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1203—41no—
107C2×#1203—41no—
108C2×#1203C2×C414yescomplemented
109C2×#1202—22no—
110C2×#1202—22no—
111C2×#1202C2×C414yescomplemented
112C2×#1201—22no—
113C2×#1201—22no—
114C2×#1201C2×C414yescomplemented
115C2×D5×Dic3—22no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—41no—
118#6719—22no—
119#6714—22no—
120#6712D414yescomplemented
121C4×Dic15—22no—
122C5×#217—22no—
123C5×(C2×D3)⋊C4—22no—
124C5×Dic3⋊C4D414yescomplemented
125C4×C5×Dic3—22no—
126C3×C22⋊Dic5—41no—
127C3×#685—22no—
128C3×#685—22no—
129Dic3⋊Dic5—22no—
130#6669—22no—
131#6667—22no—
132#6667—41no—
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5—41no—
135#6665—41no—
136Dic3×Dic5—22no—
137Dic3×Dic5—22no—
138Dic3×Dic5C2×C414yescomplemented
139C2×#940—51no—
140C2×C4×#67—51no—
141C2×C4×#67D511yescharacteristic, complemented
142C2×#67⋊C4—51no—
143C2×#67⋊C4—51no—
144C3×#386—51no—
145#5220—51no—
146#4957—51no—
147#4957—51no—
148#4957—51no—
149#4957—51no—
150#4665—51no—
151#4665—51no—
152#4649—51no—
153#4649—51no—
154C22×C5×D4—31no—
155C23×C4×C5—31no—
156C23×C4×C5C2×D311yescharacteristic
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C22×C22⋊D5C2×D311yescharacteristic
161C22×D20—31no—
162C22×C4×D5—31no—
163C22×C4×D5—31no—
164C4×C5×D4—64no—
165C2×C5×C4⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C5×C22⋊C4—31no—
168C2×C42×C5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5C2×D311yescharacteristic
173#4086—38no—
174C4×C22⋊D5—64no—
175C4×C22⋊D5—64no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685C2×D311yescharacteristic
181C2×#685C2×D311yescharacteristic
182C2×C4⋊Dic5—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188C2×C4×Dic5—31no—
189#4039—64no—
190#3963—31no—
191#3963—31no—
192#3963C2×D311yescharacteristic
193#3963C2×D311yescharacteristic
194#2366—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×D15C22×C412yes—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3—21no—
215C22×C5×D3—21no—
216C22×C5×D3C22×C412yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5C22×C412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—44no—
229C2×C3×C4×C5C2×D412yes—
230C2×C3×C4×C5C2×D412yes—
231#1220—28no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15C22×C412yes—
238C2×Dic15C2×D412yes—
239C2×Dic15C2×D412yes—
240C2×Dic15#4112yes—
241C4×D15—44no—
242C5×#67—28no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3C22×C412yes—
249C2×C5×Dic3C2×D412yes—
250C2×C5×Dic3C2×D412yes—
251C2×C5×Dic3#4112yes—
252C4×C5×D3—44no—
253C3×C22⋊D5—44no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
263#1203—44no—
264#1202—28no—
265#1201—28no—
266D5×Dic3—44no—
267C22×C3×D4—51no—
268C23×C3×C4C2×D511yescharacteristic
269C22×#67—51no—
270C22×#67—51no—
271C22×#67—51no—
272C22×#67C2×D511yescharacteristic
273C23×Dic3—51no—
274C22×D12—51no—
275C22×C4×D3—51no—
276C22×C4×D3C2×D511yescharacteristic
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×#217—51no—
281C2×#217—51no—
282C2×#217C2×D511yescharacteristic
283#940—58no—
284C4×#67—24no—
285C4×#67—104no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4C2×D511yescharacteristic
292C2×Dic3⋊C4—51no—
293C2×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4C2×D511yescharacteristic
296C2×C4×Dic3—51no—
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3C2×D511yescharacteristic
301#67⋊C4—104no—
302#67⋊C4—104no—
303C3×#95—51no—
304C3×#95—51no—
305C3⋊#95—51no—
306C3⋊#95—51no—
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C23×D5—31no—
310C23×D5C22×D311yescharacteristic
311C2×C5×D4—34no—
312C2×C5×D4—62no—
313C2×C5×D4—62no—
314C22×C4×C5—22no—
315C22×C4×C5—22no—
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5—31no—
319C22×C4×C5—41no—
320C22×C4×C5—62no—
321C22×C4×C5—62no—
322C22×C4×C5—121no—
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—34no—
328C2×C22⋊D5—41no—
329C2×C22⋊D5—41no—
330C2×C22⋊D5—62no—
331C2×C22⋊D5—62no—
332C2×C22⋊D5—62no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—121no—
335C2×C22⋊D5—121no—
336C2×C22⋊D5C4×D314yescomplemented
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C2×D20—34no—
344C2×D20—62no—
345C2×D20—62no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—62no—
350C2×C4×D5—121no—
351C2×C4×D5—121no—
352C5×C4⋊C4—34no—
353C5×C22⋊C4—62no—
354C5×C22⋊C4—62no—
355C42×C5—62no—
356C22⋊Dic5—41no—
357C22⋊Dic5—62no—
358C22⋊Dic5—62no—
359C22⋊Dic5—121no—
360#685—22no—
361#685—22no—
362#685—62no—
363#685—62no—
364#685—121no—
365#685—121no—
366C4⋊Dic5—62no—
367#683—34no—
368#683—62no—
369C4×Dic5—34no—
370C4×Dic5—62no—
371C4×Dic5—62no—
372C4×Dic5—62no—
373C2×#127—151no—
374C2×C4×D4—31no—
375C2×C4×D4—151no—
376C2×C4×D4—151no—
377C2×C4×D4—151no—
378#390—151no—
379#390—151no—
380#390—151no—
381#390—151no—
382#386—51no—
383#386—151no—
384#386—151no—
385#386—151no—
386C4×C4⋊C4—151no—
387C4×C4⋊C4—151no—
388C22×C3×C5—22no—
389C22×C3×C5—22no—
390C22×C3×C5—22no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—41no—
394C22×C3×C5—41no—
395C22×C3×C5C23×C411yescharacteristic
396C22×C3×C5C22×D411yescharacteristic
397C22×C3×C5C22×D411yescharacteristic
398C22×C3×C5C2×#4111yescharacteristic
399C22×C3×C5C2×#4111yescharacteristic
400C22×C3×C5H(5,𝔽2)11yescharacteristic
401C22×C3×C5H(5,𝔽2)11yescharacteristic
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—41no—
406C2×D15—41no—
407C2×D15—41no—
408C2×D15—41no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—41no—
413C2×C5×D3—41no—
414C2×C5×D3—41no—
415C2×C5×D3—41no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—41no—
420C2×C3×D5—41no—
421C2×C3×D5—41no—
422C2×C3×D5—41no—
423C3×C4×C5—22no—
424C3×C4×C5—22no—
425Dic15—22no—
426Dic15—41no—
427Dic15C4×D414yescomplemented
428C3×Dic5—22no—
429C3×Dic5—41no—
430C3×Dic5—41no—
431C5×Dic3—22no—
432C5×Dic3—41no—
433C5×Dic3C4×D414yescomplemented
434C24×C3—51no—
435C24×C3C22×D511yescharacteristic
436C23×D3—51no—
437C23×D3C22×D511yescharacteristic
438C2×C3×D4—54no—
439C2×C3×D4—201no—
440C2×C3×D4—201no—
441C22×C3×C4—22no—
442C22×C3×C4—22no—
443C22×C3×C4—41no—
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C2×#67—22no—
450C2×#67—22no—
451C2×#67—54no—
452C2×#67—54no—
453C2×#67—54no—
454C2×#67—102no—
455C2×#67—102no—
456C2×#67—102no—
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—102no—
460C2×#67C4×D514yescomplemented
461C22×Dic3—51no—
462C22×Dic3—51no—
463C22×Dic3—51no—
464C22×Dic3—102no—
465C22×Dic3—102no—
466C22×Dic3—201no—
467C22×Dic3C22×D511yescharacteristic
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C2×D12—54no—
471C2×D12—201no—
472C2×D12—201no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—41no—
476C2×C4×D3—102no—
477C2×C4×D3—102no—
478C2×C4×D3—201no—
479C3×C22⋊C4—102no—
480C3×C22⋊C4—102no—
481C3×C22⋊C4—201no—
482#217—22no—
483#217—102no—
484#217—201no—
485(C2×D3)⋊C4—22no—
486(C2×D3)⋊C4—102no—
487(C2×D3)⋊C4—102no—
488(C2×D3)⋊C4—102no—
489(C2×D3)⋊C4—201no—
490(C2×D3)⋊C4—201no—
491Dic3⋊C4—54no—
492Dic3⋊C4—102no—
493Dic3⋊C4—102no—
494Dic3⋊C4C22⋊D514yescomplemented
495C4×Dic3—22no—
496C4×Dic3—54no—
497C4×Dic3—102no—
498C4×Dic3—102no—
499C4×Dic3—102no—
500C23×C5—21no—
501C23×C5—21no—
502C23×C5—21no—
503C23×C5—21no—
504C23×C5—21no—
505C23×C5—21no—
506C23×C5—32no—
507C23×C5—61no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5C2×C4×D312yes—
514C23×C5C23×D311yescharacteristic
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—21no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—32no—
522C22×D5—61no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5C2×C4×D312yes—
529C5×D4—68no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—44no—
539C2×C4×C5—61no—
540C2×C4×C5—61no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5—124no—
545C2×C4×C5D3×D412yes—
546C2×C4×C5D3×D412yes—
547C22⋊D5—44no—
548C22⋊D5—68no—
549C22⋊D5—68no—
550C22⋊D5—124no—
551C2×Dic5—21no—
552C2×Dic5—21no—
553C2×Dic5—21no—
554C2×Dic5—21no—
555C2×Dic5—21no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—21no—
559C2×Dic5—32no—
560C2×Dic5—32no—
561C2×Dic5—32no—
562C2×Dic5—32no—
563C2×Dic5—61no—
564C2×Dic5—61no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5C2×C4×D312yes—
569D20—68no—
570C4×D5—124no—
571C4×D5—124no—
572C22×D4—31no—
573C22×D4—51no—
574C22×D4—151no—
575C22×D4—151no—
576C22×D4—151no—
577C22×D4—151no—
578C23×C4—31no—
579C23×C4—151no—
580C23×C4—151no—
581C23×C4D3×D511yescharacteristic
582#127—158no—
583C4×D4—64no—
584C4×D4—304no—
585C4×D4—304no—
586C4×D4—304no—
587C2×C4⋊C4—31no—
588C2×C4⋊C4—151no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—31no—
593C2×C22⋊C4—51no—
594C2×C22⋊C4—51no—
595C2×C22⋊C4—51no—
596C2×C22⋊C4—151no—
597C2×C22⋊C4—151no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C42—31no—
604C2×C42—151no—
605C2×C42—151no—
606C2×C42—151no—
607C2×C42—151no—
608#95—51no—
609#95—51no—
610#95—151no—
611#95—151no—
612C2×C3×C5—42no—
613C2×C3×C5C2×C4×D411yescharacteristic
614C2×C3×C5C2×C4×D411yescharacteristic
615C2×C3×C5#51811yescharacteristic
616C2×C3×C5D4211yescharacteristic
617C2×C3×C5#55011yescharacteristic
618C2×C3×C5#55011yescharacteristic
619C2×C3×C5#55911yescharacteristic
620D15—42no—
621C3×D5—42no—
622C5×D3—42no—
623C23×C3—21no—
624C23×C3—21no—
625C23×C3—21no—
626C23×C3—21no—
627C23×C3—21no—
628C23×C3—21no—
629C23×C3—52no—
630C23×C3—101no—
631C23×C3—101no—
632C23×C3—101no—
633C23×C3—101no—
634C23×C3—101no—
635C23×C3—101no—
636C23×C3C2×C4×D512yes—
637C23×C3C23×D511yescharacteristic
638C22×D3—21no—
639C22×D3—21no—
640C22×D3—21no—
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—52no—
645C22×D3—101no—
646C22×D3—101no—
647C22×D3—101no—
648C22×D3—101no—
649C22×D3—101no—
650C22×D3—101no—
651C22×D3C2×C4×D512yes—
652C3×D4—204no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—44no—
658C2×C3×C4—52no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—101no—
662C2×C3×C4—101no—
663C2×C3×C4—101no—
664C2×C3×C4—101no—
665C2×C3×C4—101no—
666C2×C3×C4—101no—
667C2×C3×C4D4×D512yes—
668C2×C3×C4C2×C22⋊D512yes—
669#67—28no—
670#67—108no—
671#67—108no—
672#67—108no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—52no—
679C2×Dic3—52no—
680C2×Dic3—52no—
681C2×Dic3—52no—
682C2×Dic3—101no—
683C2×Dic3—101no—
684C2×Dic3—101no—
685C2×Dic3—101no—
686C2×Dic3—101no—
687C2×Dic3—204no—
688C2×Dic3C2×C4×D512yes—
689C2×Dic3#70912yes—
690C2×Dic3C2×C22⋊D512yes—
691C2×Dic3C2×C22⋊D512yes—
692D12—204no—
693C4×D3—44no—
694C4×D3—204no—
695C22×C5—22no—
696C22×C5—22no—
697C22×C5—22no—
698C22×C5—41no—
699C22×C5—41no—
700C22×C5—41no—
701C22×C5—41no—
702C22×C5—62no—
703C22×C5—62no—
704C22×C5—62no—
705C22×C5—121no—
706C22×C5—121no—
707C22×C5—121no—
708C22×C5—121no—
709C22×C5C22×C4×D311yescharacteristic
710C22×C5C2×D3×D411yescharacteristic
711C22×C5C2×D3×D411yescharacteristic
712C22×C5#100411yescharacteristic
713C22×C5#100411yescharacteristic
714C22×C5D3×#4111yescharacteristic
715C22×C5D3×#4111yescharacteristic
716C2×D5—22no—
717C2×D5—22no—
718C2×D5—22no—
719C2×D5—41no—
720C2×D5—41no—
721C2×D5—41no—
722C2×D5—41no—
723C2×D5—62no—
724C2×D5—62no—
725C2×D5—62no—
726C2×D5—121no—
727C2×D5—121no—
728C2×D5—121no—
729C2×D5—121no—
730C4×C5—22no—
731C4×C5—22no—
732C4×C5—34no—
733C4×C5—62no—
734C4×C5—121no—
735Dic5—22no—
736Dic5—34no—
737Dic5—41no—
738Dic5—41no—
739Dic5—62no—
740Dic5—121no—
741C24—31no—
742C24—51no—
743C24—151no—
744C24C2×D3×D511yescharacteristic
745C2×D4—34no—
746C2×D4—54no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—154no—
750C2×D4—154no—
751C2×D4—154no—
752C2×D4—154no—
753C2×D4—201no—
754C2×D4—201no—
755C2×D4—302no—
756C2×D4—302no—
757C2×D4—302no—
758C2×D4—302no—
759C2×D4—302no—
760C2×D4—302no—
761C2×D4—601no—
762C2×D4—601no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—41no—
769C22×C4—51no—
770C22×C4—51no—
771C22×C4—51no—
772C22×C4—62no—
773C22×C4—62no—
774C22×C4—121no—
775C22×C4—151no—
776C22×C4—151no—
777C22×C4—151no—
778C22×C4—302no—
779C22×C4—302no—
780C22×C4—302no—
781C22×C4—302no—
782C22×C4—601no—
783C22×C4—601no—
784C22×C4C2×D3×D511yescharacteristic
785C22×C4C2×D3×D511yescharacteristic
786C4⋊C4—34no—
787C4⋊C4—154no—
788C4⋊C4—302no—
789C4⋊C4—302no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—102no—
793C22⋊C4—102no—
794C22⋊C4—201no—
795C22⋊C4—302no—
796C22⋊C4—302no—
797C22⋊C4—302no—
798C22⋊C4—302no—
799C22⋊C4—601no—
800C22⋊C4—601no—
801C22⋊C4—601no—
802C42—62no—
803C42—154no—
804C42—302no—
805C42—302no—
806C42—302no—
807C3×C5#236611yescharacteristic, complemented, Hall
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—201no—
819C22×C3—201no—
820C22×C3—201no—
821C22×C3—201no—
822C22×C3C22×C4×D511yescharacteristic
823C22×C3C2×#70911yescharacteristic
824C22×C3C2×D4×D511yescharacteristic
825C22×C3#414411yescharacteristic
826C22×C3D5×#4111yescharacteristic
827C22×C3#414911yescharacteristic
828C22×C3C22×C22⋊D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—201no—
840C2×D3—201no—
841C2×D3—201no—
842C2×D3—201no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—102no—
846C3×C4—201no—
847C3×C4—201no—
848Dic3—22no—
849Dic3—41no—
850Dic3—54no—
851Dic3—102no—
852Dic3—201no—
853Dic3C4×C22⋊D514yescomplemented
854C2×C5—42no—
855C2×C5—122no—
856C2×C5#548611yescharacteristic
857C2×C5C4×D3×D411yescharacteristic
858C2×C5C4×D3×D411yescharacteristic
859C2×C5#559011yescharacteristic
860C2×C5#559911yescharacteristic
861C2×C5#559911yescharacteristic
862C2×C5#566411yescharacteristic
863D5—42no—
864D5—122no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—32no—
872C23—52no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—101no—
880C23—101no—
881C23—101no—
882C23—101no—
883C23—101no—
884C23—101no—
885C23—152no—
886C23—301no—
887C23—301no—
888C23—301no—
889C23—301no—
890C23—301no—
891C23—301no—
892C23C4×D3×D512yes—
893C23C22×D3×D511yescharacteristic
894D4—68no—
895D4—204no—
896D4—308no—
897D4—308no—
898D4—308no—
899D4—604no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—44no—
909C2×C4—52no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—101no—
916C2×C4—101no—
917C2×C4—101no—
918C2×C4—101no—
919C2×C4—101no—
920C2×C4—101no—
921C2×C4—101no—
922C2×C4—101no—
923C2×C4—124no—
924C2×C4—152no—
925C2×C4—152no—
926C2×C4—152no—
927C2×C4—152no—
928C2×C4—301no—
929C2×C4—301no—
930C2×C4—301no—
931C2×C4—301no—
932C2×C4—301no—
933C2×C4—604no—
934C2×C4—604no—
935C2×C4D3×C22⋊D512yes—
936C2×C4#679012yes—
937C2×C3—42no—
938C2×C3—202no—
939C2×C3C4×D4×D511yescharacteristic
940C2×C3#6587911yescharacteristic
941C2×C3#6588711yescharacteristic
942C2×C3#6589311yescharacteristic
943C2×C3C2×C4×C22⋊D511yescharacteristic
944C2×C3D4×C22⋊D511yescharacteristic
945C2×C3#6616811yescharacteristic
946D3—42no—
947D3—202no—
948C5#7467911yescharacteristic, complemented, Sylow
949C22—22no—
950C22—22no—
951C22—22no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—102no—
960C22—102no—
961C22—102no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—201no—
967C22—201no—
968C22—201no—
969C22—201no—
970C22—302no—
971C22—302no—
972C22—302no—
973C22—601no—
974C22—601no—
975C22—601no—
976C22—601no—
977C22C2×C4×D3×D511yescharacteristic
978C22D3×#70911yescharacteristic
979C22#9201611yescharacteristic
980C22#9201711yescharacteristic
981C22C2×D3×C22⋊D511yescharacteristic
982C22C2×#679011yescharacteristic
983C22#9204911yescharacteristic
984C4—22no—
985C4—22no—
986C4—34no—
987C4—62no—
988C4—102no—
989C4—121no—
990C4—154no—
991C4—201no—
992C4—201no—
993C4—302no—
994C4—601no—
995C3#1061407411yescharacteristic, complemented, Sylow
996C2—42no—
997C2—122no—
998C2—202no—
999C2—602no—
1000C2#1175437011yescharacteristic
1001C2#1175442811yescharacteristic
1002C2#1175453511yescharacteristic
1003C2#1175462511yescharacteristic
1004C2C4×D3×C22⋊D511yescharacteristic
1005C2C4×#679011yescharacteristic
1006C2#1175544011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2366
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×#1220C2semidirect
2. C2×C4×C5×#67C2semidirect
4. C2×#91441C2semidirect
5. C2×#91396C2semidirect
6. C3×#65502C2semidirect
7. #11749518C2semidirect
8. #11749483C2semidirect
9. #11749482C2semidirect
10. #11748918C2semidirect
11. #11748915C2semidirect
12. #11748914C2semidirect
13. #11748912C2semidirect
14. #11748651C2semidirect
15. #11748645C2semidirect
40. #91567C4semidirect
65. #65502D3semidirect
84. C2×#1220C2×C4semidirect
93. C2×C5×#67C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
108. C2×#1203C2×C4semidirect
111. C2×#1202C2×C4semidirect
114. C2×#1201C2×C4semidirect
120. #6712D4semidirect
124. C5×Dic3⋊C4D4semidirect
138. Dic3×Dic5C2×C4semidirect
141. C2×C4×#67D5semidirect
336. C2×C22⋊D5C4×D3semidirect
427. Dic15C4×D4semidirect
433. C5×Dic3C4×D4semidirect
460. C2×#67C4×D5semidirect
494. Dic3⋊C4C22⋊D5semidirect
807. C3×C5#2366semidirect
853. Dic3C4×C22⋊D5semidirect
948. C5#74679semidirect
995. C3#10614074semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C4×C5×#672
C2×#915672
C2×#914412
C2×#913962
C3×#655022
#117495182
#117494832
#117494822
#117489182
#117489152
#117489142
#117489122
#117486512
#117486452
#106140743
#746795