Finite Group Databasebeta

← #14329467

Subgroups — #14329467

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×#91552C211yesmaximal, characteristic, complemented
4C2×#91446C211yesmaximal, characteristic, complemented
5C2×C4×#1201C211yesmaximal, characteristic, complemented
6#11751058C211yesmaximal, characteristic, complemented
7C5×#4956C211yesmaximal, characteristic, complemented
8#11749492C211yesmaximal, characteristic, complemented
9#11749489C211yesmaximal, characteristic, complemented
10#11748916C211yesmaximal, characteristic, complemented
11#11748908C211yesmaximal, characteristic, complemented
12#11748907C211yesmaximal, characteristic, complemented
13#11748700C211yesmaximal, characteristic, complemented
14#11748640C211yesmaximal, characteristic, complemented
15#11748637C211yesmaximal, characteristic, complemented
16#10606410—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4027—24no—
39#91567C418yescomplemented
40#91552—24no—
41C2×#6669C2211yescharacteristic
42C2×#6668C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51#91446—24no—
52C4×#1201—24no—
53C5×C3⋊#95C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#82343—51nomaximal, Hall
58C2×#4086—31no—
59C2×C4×C22⋊D5—31no—
60C2×C4×C22⋊D5—31no—
61C2×#4027—31no—
62C2×#4027D311yescharacteristic, complemented
63C5×#386—31no—
64#65509—31no—
65#65246—31no—
66#65246—31no—
67#65246—31no—
68#65246—31no—
69#64954—31no—
70#64954—31no—
71#64938—31no—
72#64938—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—22no—
80C2×#1220—22no—
81C2×#1220C2×C414yescomplemented
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C5×#67—41no—
86C2×C5×#67—41no—
87C2×C5×#67C2×C414yescomplemented
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3—41no—
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—41no—
110C2×#1202—41no—
111C2×#1202C2×C414yescomplemented
112C2×#1201—22no—
113C2×#1201—22no—
114C2×#1201C2×C414yescomplemented
115C2×#1200—22no—
116C2×#1200—22no—
117C2×#1200—41no—
118C3×C5×C22⋊C4—22no—
119#6719—41no—
120#6714—22no—
121#6714—41no—
122#6712—22no—
123C4×Dic15—22no—
124C5×#217—22no—
125C5×(C2×D3)⋊C4—41no—
126C3×#685—22no—
127C3×#683D414yescomplemented
128C3×C4×Dic5—22no—
129#6669D414yescomplemented
130#6668—22no—
131#6667—22no—
132(C2×D3)⋊Dic5—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#4957—51no—
150#4956—51no—
151#4956D511yescharacteristic, complemented
152#4939—51no—
153C4×Dic3⋊C4—51no—
154C22×C5×D4—31no—
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C23×Dic5C2×D311yescharacteristic
161C22×D20—31no—
162C22×C4×D5—31no—
163C22×C4×D5C2×D311yescharacteristic
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170#4086—38no—
171C4×C22⋊D5—64no—
172C4×C22⋊D5—64no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685C2×D311yescharacteristic
179C2×#683—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683C2×D311yescharacteristic
183C2×C4×Dic5—31no—
184C2×C4×Dic5—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5C2×D311yescharacteristic
188#4027—24no—
189#4027—64no—
190C5×#95—31no—
191C5×#95—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—28no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15C22×C412yes—
238C2×Dic15C2×D412yes—
239C2×Dic15#4112yes—
240C5×#67—44no—
241C2×C5×Dic3—21no—
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—
250C4×C5×D3—44no—
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—44no—
265#1201—28no—
266#1200—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×D3C2×D511yescharacteristic
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)⋊C4—51no—
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302#893—104no—
303C3⋊#95—51no—
304C3⋊#95—51no—
305C3⋊#95C2×D511yescharacteristic
306C3⋊#95C2×D511yescharacteristic
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C23×D5—31no—
310C23×D5C22×D311yescharacteristic
311C2×C5×D4—34no—
312C2×C5×D4—121no—
313C2×C5×D4—121no—
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—31no—
317C22×C4×C5—62no—
318C22×C4×C5—62no—
319C22×C4×C5—121no—
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—22no—
323C2×C22⋊D5—22no—
324C2×C22⋊D5—34no—
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—62no—
328C2×C22⋊D5—62no—
329C2×C22⋊D5—62no—
330C2×C22⋊D5—62no—
331C2×C22⋊D5—62no—
332C2×C22⋊D5—62no—
333C2×C22⋊D5C4×D314yescomplemented
334C22×Dic5—22no—
335C22×Dic5—22no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—41no—
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C2×D20—34no—
344C2×D20—121no—
345C2×D20—121no—
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×C22⋊C4—22no—
353C5×C22⋊C4—62no—
354C5×C22⋊C4—121no—
355C22⋊Dic5—62no—
356C22⋊Dic5—62no—
357C22⋊Dic5—121no—
358#685—22no—
359#685—62no—
360#685—62no—
361#685—62no—
362#685—121no—
363#685—121no—
364#683—34no—
365#683—62no—
366#683—62no—
367#683#6714yescomplemented
368C4×Dic5—22no—
369C4×Dic5—34no—
370C4×Dic5—62no—
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—151no—
379#390—151no—
380#390—151no—
381#390—151no—
382#386—31no—
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—41no—
426Dic15—41no—
427Dic15C4×D414yescomplemented
428C3×Dic5—22no—
429C3×Dic5—22no—
430C3×Dic5C4×D414yescomplemented
431C5×Dic3—22no—
432C5×Dic3—22no—
433C5×Dic3—41no—
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—41no—
453C2×#67—41no—
454C2×#67—54no—
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—102no—
460C2×#67—102no—
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—22no—
474C2×C4×D3—22no—
475C2×C4×D3—41no—
476C2×C4×D3—102no—
477C2×C4×D3—102no—
478C2×C4×D3—201no—
479C3×C4⋊C4—54no—
480C3×C22⋊C4—22no—
481C3×C22⋊C4—102no—
482C3×C42—102no—
483#217—22no—
484#217—102no—
485#217—201no—
486#217—201no—
487(C2×D3)⋊C4—41no—
488(C2×D3)⋊C4—102no—
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—54no—
495Dic3⋊C4—102no—
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—124no—
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—61no—
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×C5—124no—
545C2×C4×C5C2×#6712yes—
546C22⋊D5—28no—
547C22⋊D5—68no—
548C22⋊D5—68no—
549C22⋊D5—68no—
550C2×Dic5—21no—
551C2×Dic5—21no—
552C2×Dic5—21no—
553C2×Dic5—21no—
554C2×Dic5—32no—
555C2×Dic5—32no—
556C2×Dic5—32no—
557C2×Dic5—44no—
558C2×Dic5—61no—
559C2×Dic5—61no—
560C2×Dic5—61no—
561C2×Dic5—61no—
562C2×Dic5—61no—
563C2×Dic5—61no—
564C2×Dic5C2×C4×D312yes—
565C2×Dic5#23512yes—
566C2×Dic5D3×D412yes—
567C2×Dic5C2×#6712yes—
568C2×Dic5C2×#6712yes—
569D20—124no—
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—31no—
579C23×C4—51no—
580C23×C4—51no—
581C23×C4—151no—
582#127—158no—
583C4×D4—104no—
584C4×D4—304no—
585C4×D4—304no—
586C4×D4—304no—
587C2×C4⋊C4—51no—
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—151no—
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—51no—
604C2×C42—151no—
605C2×C42—151no—
606C2×C42—151no—
607C2×C42—151no—
608#95—31no—
609#95—31no—
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—44no—
671#67—108no—
672#67—108no—
673#67—204no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—52no—
682C2×Dic3—52no—
683C2×Dic3—52no—
684C2×Dic3—101no—
685C2×Dic3—101no—
686C2×Dic3—101no—
687C2×Dic3—101no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3C2×C4×D512yes—
691C2×Dic3D4×D512yes—
692D12—108no—
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×#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—41no—
732C4×C5—62no—
733C4×C5—62no—
734C4×C5—121no—
735Dic5—22no—
736Dic5—22no—
737Dic5—34no—
738Dic5—121no—
739Dic5—121no—
740Dic5C4×#6714yescomplemented
741C24—31no—
742C24—51no—
743C24—151no—
744C24C2×D3×D511yescharacteristic
745C2×D4—34no—
746C2×D4—54no—
747C2×D4—102no—
748C2×D4—102no—
749C2×D4—121no—
750C2×D4—121no—
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—302no—
760C2×D4—302no—
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—62no—
770C22×C4—62no—
771C22×C4—102no—
772C22×C4—102no—
773C22×C4—102no—
774C22×C4—102no—
775C22×C4—121no—
776C22×C4—151no—
777C22×C4—151no—
778C22×C4—151no—
779C22×C4—201no—
780C22×C4—201no—
781C22×C4—302no—
782C22×C4—302no—
783C22×C4—601no—
784C22×C4C2×D3×D511yescharacteristic
785C22×C4C2×D3×D511yescharacteristic
786C4⋊C4—54no—
787C4⋊C4—154no—
788C4⋊C4—302no—
789C4⋊C4—302no—
790C22⋊C4—22no—
791C22⋊C4—62no—
792C22⋊C4—102no—
793C22⋊C4—121no—
794C22⋊C4—302no—
795C22⋊C4—302no—
796C22⋊C4—302no—
797C22⋊C4—302no—
798C22⋊C4—302no—
799C22⋊C4—601no—
800C22⋊C4—601no—
801C22⋊C4—601no—
802C42—102no—
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×D4×D511yescharacteristic
824C22×C3C2×D4×D511yescharacteristic
825C22×C3#414411yescharacteristic
826C22×C3#414411yescharacteristic
827C22×C3D5×#4111yescharacteristic
828C22×C3D5×#4111yescharacteristic
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—22no—
849Dic3—22no—
850Dic3—41no—
851Dic3—54no—
852Dic3—201no—
853Dic3—201no—
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—108no—
895D4—124no—
896D4—308no—
897D4—308no—
898D4—308no—
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—52no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—52no—
911C2×C4—52no—
912C2×C4—61no—
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—124no—
924C2×C4—152no—
925C2×C4—152no—
926C2×C4—152no—
927C2×C4—204no—
928C2×C4—204no—
929C2×C4—301no—
930C2×C4—301no—
931C2×C4—301no—
932C2×C4—301no—
933C2×C4—301no—
934C2×C4—301no—
935C2×C4—604no—
936C2×C4D5×#6712yes—
937C2×C3—42no—
938C2×C3—202no—
939C2×C3#6582011yescharacteristic
940C2×C3C4×D4×D511yescharacteristic
941C2×C3C4×D4×D511yescharacteristic
942C2×C3#6592411yescharacteristic
943C2×C3#6593311yescharacteristic
944C2×C3#6593311yescharacteristic
945C2×C3#6599811yescharacteristic
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
980C22#9202411yescharacteristic
981C22#9202511yescharacteristic
982C22#9202711yescharacteristic
983C22C2×D5×#6711yescharacteristic
984C4—22no—
985C4—41no—
986C4—54no—
987C4—62no—
988C4—62no—
989C4—102no—
990C4—102no—
991C4—121no—
992C4—154no—
993C4—601no—
994C4—601no—
995C3#1060641011yescharacteristic, complemented, Sylow
996C2—42no—
997C2—122no—
998C2—202no—
999C2—602no—
1000C2#1175309911yescharacteristic
1001C2#1175318811yescharacteristic
1002C2#1175320211yescharacteristic
1003C2#1175320311yescharacteristic
1004C2C4×D5×#6711yescharacteristic
1005C2#1175493811yescharacteristic
1006C2#1175503111yescharacteristic
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×#91552C2semidirect
4. C2×#91446C2semidirect
5. C2×C4×#1201C2semidirect
6. #11751058C2semidirect
7. C5×#4956C2semidirect
8. #11749492C2semidirect
9. #11749489C2semidirect
10. #11748916C2semidirect
11. #11748908C2semidirect
12. #11748907C2semidirect
13. #11748700C2semidirect
14. #11748640C2semidirect
15. #11748637C2semidirect
39. #91567C4semidirect
62. C2×#4027D3semidirect
81. C2×#1220C2×C4semidirect
87. 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. #6669D4semidirect
138. Dic3×Dic5C2×C4semidirect
151. #4956D5semidirect
333. C2×C22⋊D5C4×D3semidirect
367. #683#67semidirect
427. Dic15C4×D4semidirect
430. C3×Dic5C4×D4semidirect
463. C2×#67C4×D5semidirect
740. Dic5C4×#67semidirect
807. C3×C5#2366semidirect
948. C5#82343semidirect
995. C3#10606410semidirect

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×#915522
C2×#914462
C2×C4×#12012
#117510582
C5×#49562
#117494922
#117494892
#117489162
#117489082
#117489072
#117487002
#117486402
#117486372
#106064103
#823435