Finite Group Databasebeta

← #14329462

Subgroups — #14329462

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×C3×#4027C211yesmaximal, characteristic, complemented
2C2×#91567C211yesmaximal, characteristic
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4C2×C4×#1202C211yesmaximal, characteristic, complemented
5C2×#91406C211yesmaximal, characteristic, complemented
6#11751057C211yesmaximal, characteristic, complemented
7C5×#4957C211yesmaximal, characteristic, complemented
8#11749494C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11748913C211yesmaximal, characteristic, complemented
11#11748911C211yesmaximal, characteristic, complemented
12#11748908C211yesmaximal, characteristic, complemented
13#11748905C211yesmaximal, characteristic, complemented
14Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10608037—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4027—24no—
39#91567C418yescomplemented
40Dic5×#67—24no—
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6668C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51C4×#1202—24no—
52#91406—24no—
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#82343—51nomaximal, Hall
58C2×#4086—31no—
59C2×D4×Dic5—31no—
60C2×#4027—31no—
61C2×#4027D311yescharacteristic, complemented
62C2×C4×D20—31no—
63C5×#390—31no—
64#65277—31no—
65C4⋊C4×Dic5—31no—
66#65247—31no—
67#65247—31no—
68#65246—31no—
69#65246—31no—
70#65245—31no—
71#65245—31no—
72C4×#683—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—41no—
80C2×#1220—41no—
81C2×#1220C2×C414yescomplemented
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C4×D15—22no—
86C2×C4×D15—22no—
87C2×C4×D15—41no—
88C2×C5×#67—22no—
89C2×C5×#67—22no—
90C2×C5×#67C2×C414yescomplemented
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5C2×C414yescomplemented
97C22×C3×Dic5—22no—
98C22×C3×Dic5—22no—
99C22×C3×Dic5—41no—
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—41no—
106C2×#1203—22no—
107C2×#1203—22no—
108C2×#1203C2×C414yescomplemented
109C2×#1202—22no—
110C2×#1202—22no—
111C2×#1202C2×C414yescomplemented
112C2×#1201—41no—
113C2×#1201—41no—
114C2×#1201C2×C414yescomplemented
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—41no—
118C3×C5×C22⋊C4—22no—
119#6719—22no—
120#6714—41no—
121C5×#217—41no—
122C5×(C2×D3)⋊C4—22no—
123C5×(C2×D3)⋊C4—41no—
124C5×Dic3⋊C4—22no—
125C4×C5×Dic3—22no—
126C3×#685—22no—
127C3×#683D414yescomplemented
128C3×C4×Dic5—22no—
129Dic3⋊Dic5D414yescomplemented
130#6668—22no—
131#6667—22no—
132#6667—22no—
133(C2×D3)⋊Dic5—22no—
134#6665—22no—
135#6665—41no—
136Dic3×Dic5—22no—
137Dic3×Dic5—22no—
138Dic3×Dic5C2×C414yescomplemented
139C2×C3×C4×D4—51no—
140C2×#940—51no—
141C2×C4×#67—51no—
142C2×C4×#67—51no—
143C2×#893—51no—
144#5221—51no—
145#5213—51no—
146#5213—51no—
147Dic3×C4⋊C4—51no—
148#4957—51no—
149#4957D511yescharacteristic, complemented
150#4956—51no—
151#4956—51no—
152#4939—51no—
153C4×Dic3⋊C4—51no—
154C22×C5×D4—31no—
155C22×C22⋊D5—31no—
156C22×C22⋊D5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5C2×D311yescharacteristic
159C23×Dic5—31no—
160C23×Dic5C2×D311yescharacteristic
161C22×D20—31no—
162C22×C4×D5—31no—
163C22×C4×D5C2×D311yescharacteristic
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C5×C22⋊C4—31no—
168C2×C5×C22⋊C4C2×D311yescharacteristic
169C2×C42×C5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172#4086—38no—
173D4×Dic5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685C2×D311yescharacteristic
180C2×C4⋊Dic5—31no—
181C2×#683—31no—
182C2×#683C2×D311yescharacteristic
183C2×C4×Dic5—31no—
184C2×C4×Dic5—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5C2×D311yescharacteristic
187#4027—24no—
188#4027—64no—
189C4×D20—64no—
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
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—21no—
229C2×C3×C4×C5C2×D412yes—
230#1220—44no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15C22×C412yes—
239C2×Dic15C2×D412yes—
240C4×D15—44no—
241C5×#67—28no—
242C2×C5×Dic3—21no—
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×Dic3#4112yes—
251C3×C22⋊D5—28no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—44no—
257C2×C3×Dic5C22×C412yes—
258C2×C3×Dic5C2×D412yes—
259C2×C3×Dic5C2×D412yes—
260C2×C3×Dic5C2×D412yes—
261C2×C3×Dic5#4112yes—
262C3×C4×D5—44no—
263#1203—28no—
264#1202—28no—
265#1201—44no—
266D3×Dic5—44no—
267C22×C3×D4—51no—
268C23×C3×C4—51no—
269C23×C3×C4—51no—
270C22×#67—51no—
271C22×#67—51no—
272C22×#67—51no—
273C22×#67C2×D511yescharacteristic
274C22×D12—51no—
275C22×C4×D3—51no—
276C22×C4×D3—51no—
277C3×C4×D4—104no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×C3×C42—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217C2×D511yescharacteristic
286#940—58no—
287C4×#67—104no—
288C4×#67—104no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4C2×D511yescharacteristic
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3C2×D511yescharacteristic
302#893—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—31no—
315C22×C4×C5—31no—
316C22×C4×C5—31no—
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—22no—
320C2×C22⋊D5—22no—
321C2×C22⋊D5—34no—
322C2×C22⋊D5—34no—
323C2×C22⋊D5—34no—
324C2×C22⋊D5—62no—
325C2×C22⋊D5—62no—
326C2×C22⋊D5—121no—
327C2×C22⋊D5—121no—
328C2×C22⋊D5—121no—
329C2×C22⋊D5—121no—
330C2×C22⋊D5C4×D314yescomplemented
331C22×Dic5—22no—
332C22×Dic5—22no—
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—41no—
337C22×Dic5—62no—
338C22×Dic5—62no—
339C22×Dic5—121no—
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C2×D20—34no—
344C2×D20—62no—
345C2×D20—62no—
346C2×C4×D5—22no—
347C2×C4×D5—22no—
348C2×C4×D5—41no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—121no—
352C5×C4⋊C4—62no—
353C5×C22⋊C4—22no—
354C5×C22⋊C4—62no—
355C5×C22⋊C4—121no—
356C5×C22⋊C4—121no—
357C42×C5—62no—
358C22⋊Dic5—62no—
359C22⋊Dic5—62no—
360#685—22no—
361#685—62no—
362#685—62no—
363#685—62no—
364#685—121no—
365#685—121no—
366C4⋊Dic5—34no—
367#683—62no—
368#683#6714yescomplemented
369C4×Dic5—22no—
370C4×Dic5—34no—
371C4×Dic5—62no—
372C4×Dic5—62no—
373C2×#127—151no—
374C2×C4×D4—51no—
375C2×C4×D4—151no—
376C2×C4×D4—151no—
377C2×C4×D4—151no—
378#390—31no—
379#390—151no—
380#390—151no—
381#390—151no—
382#386—151no—
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—41no—
425Dic15—22no—
426Dic15—22no—
427Dic15—41no—
428C3×Dic5—22no—
429C3×Dic5—22no—
430C3×Dic5C4×D414yescomplemented
431C5×Dic3—41no—
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—102no—
440C2×C3×D4—102no—
441C22×C3×C4—51no—
442C22×C3×C4—51no—
443C22×C3×C4—51no—
444C22×C3×C4—102no—
445C22×C3×C4—102no—
446C22×C3×C4—102no—
447C22×C3×C4—102no—
448C22×C3×C4—201no—
449C22×C3×C4—201no—
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D511yescharacteristic
452C2×#67—22no—
453C2×#67—22no—
454C2×#67—54no—
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—201no—
460C2×#67—201no—
461C2×#67—201no—
462C2×#67—201no—
463C2×#67C4×D514yescomplemented
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3C22×D511yescharacteristic
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C2×D12—54no—
471C2×D12—102no—
472C2×D12—102no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3—102no—
476C2×C4×D3—102no—
477C2×C4×D3—201no—
478C2×C4×D3—201no—
479C3×C4⋊C4—54no—
480C3×C22⋊C4—22no—
481C3×C22⋊C4—102no—
482C3×C42—102no—
483#217—41no—
484#217—102no—
485#217—102no—
486#217—201no—
487(C2×D3)⋊C4—22no—
488(C2×D3)⋊C4—41no—
489(C2×D3)⋊C4—102no—
490(C2×D3)⋊C4—102no—
491(C2×D3)⋊C4—102no—
492(C2×D3)⋊C4—201no—
493C4⋊Dic3—102no—
494Dic3⋊C4—22no—
495Dic3⋊C4—54no—
496C4×Dic3—22no—
497C4×Dic3—54no—
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—21no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—61no—
539C2×C4×C5—61no—
540C2×C4×C5—61no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5C2×#6712yes—
545C22⋊D5—28no—
546C22⋊D5—68no—
547C22⋊D5—124no—
548C22⋊D5—124no—
549C2×Dic5—21no—
550C2×Dic5—21no—
551C2×Dic5—21no—
552C2×Dic5—21no—
553C2×Dic5—32no—
554C2×Dic5—32no—
555C2×Dic5—44no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—61no—
559C2×Dic5—61no—
560C2×Dic5—61no—
561C2×Dic5—61no—
562C2×Dic5—61no—
563C2×Dic5—124no—
564C2×Dic5C2×C4×D312yes—
565C2×Dic5#23512yes—
566C2×Dic5D3×D412yes—
567C2×Dic5C2×#6712yes—
568C2×Dic5C2×#6712yes—
569D20—68no—
570C4×D5—44no—
571C4×D5—124no—
572C22×D4—31no—
573C22×D4—51no—
574C22×D4—151no—
575C22×D4—151no—
576C22×D4—151no—
577C22×D4—151no—
578C23×C4—51no—
579C23×C4—51no—
580C23×C4—151no—
581C23×C4—151no—
582#127—158no—
583C4×D4—104no—
584C4×D4—304no—
585C4×D4—304no—
586C4×D4—304no—
587C2×C4⋊C4—31no—
588C2×C4⋊C4—51no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—31no—
593C2×C22⋊C4—31no—
594C2×C22⋊C4—51no—
595C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
603C2×C42—31no—
604C2×C42—51no—
605C2×C42—151no—
606C2×C42—151no—
607C2×C42—151no—
608#95—151no—
609#95—151no—
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—108no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—52no—
659C2×C3×C4—52no—
660C2×C3×C4—52no—
661C2×C3×C4—52no—
662C2×C3×C4—52no—
663C2×C3×C4—101no—
664C2×C3×C4—101no—
665C2×C3×C4—101no—
666C2×C3×C4—101no—
667C2×C3×C4—204no—
668C2×C3×C4—204no—
669C2×C3×C4D4×D512yes—
670#67—28no—
671#67—108no—
672#67—204no—
673#67—204no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—52no—
681C2×Dic3—52no—
682C2×Dic3—101no—
683C2×Dic3—101no—
684C2×Dic3—101no—
685C2×Dic3—101no—
686C2×Dic3—101no—
687C2×Dic3—101no—
688C2×Dic3—101no—
689C2×Dic3C2×C4×D512yes—
690C2×Dic3D4×D512yes—
691C2×Dic3#71112yes—
692D12—108no—
693C4×D3—204no—
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×#23511yescharacteristic
711C22×C5C2×D3×D411yescharacteristic
712C22×C5#100411yescharacteristic
713C22×C5D3×#4111yescharacteristic
714C22×C5#100911yescharacteristic
715C22×C5C22×#6711yescharacteristic
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—34no—
732C4×C5—41no—
733C4×C5—121no—
734C4×C5—121no—
735Dic5—22no—
736Dic5—22no—
737Dic5—62no—
738Dic5—62no—
739Dic5—121no—
740Dic5C4×#6714yescomplemented
741C24—31no—
742C24—51no—
743C24—151no—
744C24C2×D3×D511yescharacteristic
745C2×D4—34no—
746C2×D4—54no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—102no—
750C2×D4—102no—
751C2×D4—154no—
752C2×D4—154no—
753C2×D4—154no—
754C2×D4—154no—
755C2×D4—302no—
756C2×D4—302no—
757C2×D4—302no—
758C2×D4—302no—
759C2×D4—601no—
760C2×D4—601no—
761C2×D4—601no—
762C2×D4—601no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—51no—
767C22×C4—51no—
768C22×C4—51no—
769C22×C4—102no—
770C22×C4—102no—
771C22×C4—102no—
772C22×C4—102no—
773C22×C4—151no—
774C22×C4—151no—
775C22×C4—151no—
776C22×C4—201no—
777C22×C4—201no—
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—54no—
787C4⋊C4—62no—
788C4⋊C4—154no—
789C4⋊C4—302no—
790C22⋊C4—22no—
791C22⋊C4—62no—
792C22⋊C4—102no—
793C22⋊C4—121no—
794C22⋊C4—121no—
795C22⋊C4—302no—
796C22⋊C4—302no—
797C22⋊C4—302no—
798C22⋊C4—302no—
799C22⋊C4—302no—
800C22⋊C4—601no—
801C22⋊C4—601no—
802C42—62no—
803C42—102no—
804C42—154no—
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×D4×D511yescharacteristic
824C22×C3C2×D4×D511yescharacteristic
825C22×C3C2×#71111yescharacteristic
826C22×C3#414411yescharacteristic
827C22×C3D5×#4111yescharacteristic
828C22×C3#414911yescharacteristic
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—41no—
845C3×C4—54no—
846C3×C4—102no—
847C3×C4—102no—
848Dic3—41no—
849Dic3—41no—
850Dic3—102no—
851Dic3—102no—
852Dic3—201no—
853Dic3#402714yescomplemented
854C2×C5—42no—
855C2×C5—122no—
856C2×C5C4×D3×D411yescharacteristic
857C2×C5#554511yescharacteristic
858C2×C5#555311yescharacteristic
859C2×C5#555911yescharacteristic
860C2×C5C2×C4×#6711yescharacteristic
861C2×C5D4×#6711yescharacteristic
862C2×C5#583411yescharacteristic
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—108no—
896D4—308no—
897D4—308no—
898D4—604no—
899D4—604no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—52no—
911C2×C4—52no—
912C2×C4—52no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—101no—
920C2×C4—101no—
921C2×C4—101no—
922C2×C4—101no—
923C2×C4—152no—
924C2×C4—152no—
925C2×C4—204no—
926C2×C4—204no—
927C2×C4—301no—
928C2×C4—301no—
929C2×C4—301no—
930C2×C4—301no—
931C2×C4—301no—
932C2×C4—301no—
933C2×C4—301no—
934C2×C4—604no—
935C2×C4—604no—
936C2×C4D5×#6712yes—
937C2×C3—42no—
938C2×C3—202no—
939C2×C3C2×#402711yescharacteristic
940C2×C3C4×D4×D511yescharacteristic
941C2×C3#6587911yescharacteristic
942C2×C3#6593311yescharacteristic
943C2×C3#6594311yescharacteristic
944C2×C3#6601511yescharacteristic
945C2×C3#6605211yescharacteristic
946D3—42no—
947D3—202no—
948C5#8234311yescharacteristic, 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
978C22D5×#23511yescharacteristic
979C22D3×D4×D511yescharacteristic
980C22D3×#71111yescharacteristic
981C22#9202611yescharacteristic
982C22#9202711yescharacteristic
983C22C2×D5×#6711yescharacteristic
984C4—22no—
985C4—34no—
986C4—41no—
987C4—54no—
988C4—102no—
989C4—102no—
990C4—121no—
991C4—121no—
992C4—302no—
993C4—302no—
994C4—601no—
995C3#1060803711yescharacteristic, complemented, Sylow
996C2—42no—
997C2—122no—
998C2—202no—
999C2—602no—
1000C2#1175310011yescharacteristic
1001C2#1175318811yescharacteristic
1002C2D3×#402711yescharacteristic
1003C2#1175320411yescharacteristic
1004C2C4×D5×#6711yescharacteristic
1005C2#1175479911yescharacteristic
1006C2#1175503811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2366
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4027C2semidirect
3. C2×Dic5×#67C2semidirect
4. C2×C4×#1202C2semidirect
5. C2×#91406C2semidirect
6. #11751057C2semidirect
7. C5×#4957C2semidirect
8. #11749494C2semidirect
9. #11749489C2semidirect
10. #11748913C2semidirect
11. #11748911C2semidirect
12. #11748908C2semidirect
13. #11748905C2semidirect
14. Dic5×Dic3⋊C4C2semidirect
15. Dic3×#683C2semidirect
39. #91567C4semidirect
61. C2×#4027D3semidirect
81. C2×#1220C2×C4semidirect
90. C2×C5×#67C2×C4semidirect
96. C2×C3×C22⋊D5C2×C4semidirect
108. C2×#1203C2×C4semidirect
111. C2×#1202C2×C4semidirect
114. C2×#1201C2×C4semidirect
127. C3×#683D4semidirect
129. Dic3⋊Dic5D4semidirect
138. Dic3×Dic5C2×C4semidirect
149. #4957D5semidirect
330. C2×C22⋊D5C4×D3semidirect
368. #683#67semidirect
430. C3×Dic5C4×D4semidirect
433. C5×Dic3C4×D4semidirect
463. C2×#67C4×D5semidirect
740. Dic5C4×#67semidirect
807. C3×C5#2366semidirect
853. Dic3#4027semidirect
948. C5#82343semidirect
995. C3#10608037semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C2×#915672
C2×Dic5×#672
C2×C4×#12022
C2×#914062
#117510572
C5×#49572
#117494942
#117494892
#117489132
#117489112
#117489082
#117489052
Dic5×Dic3⋊C42
Dic3×#6832
#106080373
#823435