Finite Group Databasebeta

← #14328126

Subgroups — #14328126

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×C3×#4039C211yesmaximal, characteristic, complemented
2C2×#91474C211yesmaximal, characteristic
3C2×#91473C211yesmaximal, characteristic, complemented
4C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#1202C211yesmaximal, characteristic, complemented
6#11751090C211yesmaximal, characteristic, complemented
7C5×#4990C211yesmaximal, characteristic, complemented
8#11748916C211yesmaximal, characteristic, complemented
9#11748905C211yesmaximal, characteristic, complemented
10#11748896C211yesmaximal, characteristic, complemented
11Dic3×#685C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13#11748747C211yesmaximal, characteristic, complemented
14#11748704C211yesmaximal, characteristic, complemented
15#11748700C211yesmaximal, characteristic, complemented
16#10607567—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic, complemented
22C22×#1202C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C3×#4039—24no—
38C2×Dic3⋊Dic5C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic, complemented
45C2×#6665C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91474C418yescomplemented
48#91473—24no—
49D5×(C2×D3)⋊C4—24no—
50C4×#1202—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C5×C3⋊#95C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82398—51nomaximal, Hall
58C2×#4039D311yescharacteristic, complemented
59C2×#4028—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4—31no—
62C2×C4×D20—31no—
63C5×#388—31no—
64#65278—31no—
65#65246—31no—
66#65245—31no—
67#65240—31no—
68C4×#685—31no—
69#64957—31no—
70#64955—31no—
71#64954—31no—
72#64954—31no—
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×D3×D5—22no—
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—41no—
82C22×D3×D5—41no—
83C22×D3×D5C2×C414yescomplemented
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×C3×D20—22no—
99C2×C3×D20—22no—
100C2×C3×D20C2×C414yescomplemented
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—41no—
106C2×C3×C4×D5—41no—
107C2×#1202—22no—
108C2×#1202—22no—
109C2×#1202C2×C414yescomplemented
110C2×#1201—41no—
111C2×#1201—41no—
112C2×#1201C2×C414yescomplemented
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—41no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—41no—
119C3×C5×C4⋊C4—22no—
120#6714—22no—
121#6714C2×C414yescomplemented
122#6712—41no—
123C5×(C2×D3)⋊C4—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4C2×C414yescomplemented
126C4×C5×Dic3—22no—
127C3×#685—22no—
128C3×#685D414yescomplemented
129C3×C4×Dic5—22no—
130Dic3⋊Dic5—22no—
131#6667D414yescomplemented
132(C2×D3)⋊Dic5—22no—
133(C2×D3)⋊Dic5—22no—
134#6665—22no—
135#6665—22no—
136#6665—41no—
137#6665C2×C414yescomplemented
138Dic3×Dic5—41no—
139C2×C3×C4×D4—51no—
140C2×#937—51no—
141C2×C4×#67—51no—
142C22×(C2×D3)⋊C4—51no—
143C2×D3×C22⋊C4—51no—
144#5220—51no—
145#5213—51no—
146#5210—51no—
147#4990D511yescharacteristic, complemented
148#4989—51no—
149#4957—51no—
150#4956—51no—
151Dic3×C22⋊C4—51no—
152#4940—51no—
153C4×(C2×D3)⋊C4—51no—
154C24×D5—31no—
155C22×C22⋊D5—31no—
156C22×D20—31no—
157C22×D20C2×D311yescharacteristic
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5C2×D311yescharacteristic
162C22×C4×D5C2×D311yescharacteristic, complemented
163C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
164C2×C5×C22⋊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×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685C2×D311yescharacteristic
178C2×#685C2×D311yescharacteristic, complemented
179C2×C4⋊Dic5—31no—
180C2×#683—31no—
181C2×C4×Dic5—31no—
182C2×C4×Dic5C2×D311yescharacteristic, complemented
183#4039—24no—
184#4028—38no—
185D5×C22⋊C4—64no—
186D5×C22⋊C4—64no—
187C4×D20—64no—
188C5×#95—31no—
189C5×#95—31no—
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#2358—151noSylow
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15C22×C412yes—
201C22×D15C2×D412yes—
202C22×D15#4112yes—
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—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5C22×C412yes—
221C22×C3×D5C22×C412yes—
222C22×C3×D5C2×D412yes—
223C22×C3×D5#4112yes—
224C2×D3×D5—28no—
225C2×D3×D5—28no—
226C2×D3×D5—44no—
227C2×D3×D5—44no—
228C2×D3×D5—44no—
229C2×D3×D5—44no—
230C2×D3×D5—44no—
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—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C2×D412yes—
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—
249C4×D15—44no—
250C2×C5×Dic3—21no—
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×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5C2×D412yes—
264C2×C3×Dic5C2×D412yes—
265C3×D20—28no—
266C3×C4×D5—44no—
267C3×C4×D5—44no—
268#1202—28no—
269#1201—44no—
270#1200—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C22×C3×D4—51no—
274C23×C3×C4—51no—
275C23×C3×C4—51no—
276C22×#67—51no—
277C22×#67—51no—
278C23×Dic3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C3×C4×D4—104no—
282C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C42—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290#937—58no—
291C4×#67—104no—
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
299C2×(C2×D3)⋊C4C2×D511yescharacteristic
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305D3×C22⋊C4—104no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95C2×D511yescharacteristic, complemented
311C3⋊#95C2×D511yescharacteristic, complemented
312C24×C5—31no—
313C23×D5—31no—
314C23×D5—34no—
315C23×D5—62no—
316C23×D5—62no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—121no—
320C23×D5—121no—
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D311yescharacteristic
323C22×C4×C5—31no—
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—34no—
330C2×C22⋊D5—121no—
331C2×C22⋊D5—121no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5C22×D311yescharacteristic
336C22×Dic5C22×D311yescharacteristic
337C2×D20—22no—
338C2×D20—22no—
339C2×D20—34no—
340C2×D20—62no—
341C2×D20—62no—
342C2×D20C4×D314yescomplemented
343C2×C4×D5—22no—
344C2×C4×D5—22no—
345C2×C4×D5—22no—
346C2×C4×D5—22no—
347C2×C4×D5—41no—
348C2×C4×D5—41no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—22no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4—62no—
361C5×C22⋊C4—62no—
362C42×C5—62no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365#685—22no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—121no—
373#685#6714yescomplemented
374C4⋊Dic5—62no—
375#683—121no—
376C4×Dic5—22no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—51no—
380C2×C4×D4—151no—
381C22×C22⋊C4—151no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—31no—
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×C5C23×C411yescharacteristic
394C22×C3×C5C22×D411yescharacteristic
395C22×C3×C5C22×D411yescharacteristic
396C22×C3×C5C2×#4111yescharacteristic
397C22×C3×C5C2×#4111yescharacteristic
398C22×C3×C5H(5,𝔽2)11yescharacteristic
399C22×C3×C5H(5,𝔽2)11yescharacteristic
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15C4×D414yescomplemented
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—41no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5C4×D414yescomplemented
428D3×D5—416no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—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
451C2×C3×D4—54no—
452C2×C3×D4—102no—
453C2×C3×D4—102no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—102no—
457C22×C3×C4—102no—
458C22×C3×C4—102no—
459C22×C3×C4—102no—
460C22×C3×C4—201no—
461C22×C3×C4—201no—
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D511yescharacteristic
464C22×C3×C4C22×D511yescharacteristic
465C2×#67—54no—
466C2×#67—54no—
467C2×#67—102no—
468C2×#67—102no—
469C2×#67—201no—
470C2×#67—201no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—201no—
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
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—22no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4—102no—
489C3×C42—102no—
490#217—54no—
491#217—102no—
492#217—102no—
493#217—201no—
494(C2×D3)⋊C4—22no—
495(C2×D3)⋊C4—22no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—54no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4C4×D514yescomplemented
502Dic3⋊C4—102no—
503Dic3⋊C4—201no—
504C4×Dic3—22no—
505C4×Dic3—201no—
506C23×C5—32no—
507C23×C5—61no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5C23×D311yescharacteristic
514C22×D5—21no—
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—21no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—32no—
525C22×D5—32no—
526C22×D5—32no—
527C22×D5—68no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—68no—
533C22×D5—124no—
534C22×D5—124no—
535C22×D5—124no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5C2×C4×D312yes—
539C22×D5C2×C4×D312yes—
540C22×D5#23512yes—
541C22×D5C2×#6712yes—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—32no—
550C2×C4×C5—32no—
551C2×C4×C5—61no—
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×C5C2×C4×D312yes—
559C2×C4×C5C2×#6712yes—
560C22⋊D5—124no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—32no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5D3×D412yes—
575C2×Dic5C2×#6712yes—
576D20—28no—
577D20—68no—
578C4×D5—44no—
579C4×D5—44no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—51no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—51no—
588C23×C4—51no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—104no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4D3×D511yescharacteristic, complemented
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
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—51no—
616C2×C42—151no—
617#95—31no—
618#95—31no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5C2×C4×D411yescharacteristic
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5#51811yescharacteristic
626C2×C3×C5D4211yescharacteristic
627C2×C3×C5#54611yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#55111yescharacteristic
630D15—24no—
631C3×D5—24no—
632C3×D5—42no—
633C5×D3—42no—
634C23×C3—52no—
635C23×C3—52no—
636C23×C3—52no—
637C23×C3—52no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3C23×D511yescharacteristic
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—21no—
654C22×D3—21no—
655C22×D3—52no—
656C22×D3—52no—
657C22×D3—52no—
658C22×D3—108no—
659C22×D3—108no—
660C22×D3—101no—
661C22×D3—101no—
662C22×D3—101no—
663C22×D3—101no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3C2×C4×D512yes—
670C3×D4—108no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—204no—
685C2×C3×C4—204no—
686C2×C3×C4C2×C4×D512yes—
687C2×C3×C4D4×D512yes—
688#67—108no—
689#67—204no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—52no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—204no—
707C2×Dic3C2×C4×D512yes—
708C2×Dic3D4×D512yes—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—121no—
715C22×C5—121no—
716C22×C5—121no—
717C22×C5—121no—
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C2×#23511yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5#100411yescharacteristic
722C22×C5D3×#4111yescharacteristic
723C22×C5#100911yescharacteristic
724C22×C5C22×#6711yescharacteristic
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—22no—
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—34no—
735C2×D5—41no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5—41no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—1216no—
746C2×D5C4×#6714yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—62no—
751C4×C5—62no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—22no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—51no—
761C24—154no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
769C2×D4—54no—
770C2×D4—102no—
771C2×D4—102no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—102no—
784C22×C4—102no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—201no—
791C22×C4—201no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—601no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4C2×D3×D511yescharacteristic
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—62no—
811C22⋊C4—102no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—62no—
822C42—102no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—54no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3—102no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3C22×C4×D511yescharacteristic
840C22×C3C2×D4×D511yescharacteristic
841C22×C3C2×D4×D511yescharacteristic
842C22×C3D5×#4111yescharacteristic
843C22×C3D5×#4111yescharacteristic
844C22×C3#414911yescharacteristic
845C22×C3#414911yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—54no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—102no—
858C2×D3—102no—
859C2×D3—102no—
860C2×D3—2016no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—102no—
865C3×C4—102no—
866Dic3—22no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—122no—
873C2×C5C4×D3×D411yescharacteristic
874C2×C5#554511yescharacteristic
875C2×C5#555011yescharacteristic
876C2×C5#555611yescharacteristic
877C2×C5C2×C4×#6711yescharacteristic
878C2×C5D4×#6711yescharacteristic
879C2×C5#582911yescharacteristic
880D5—24no—
881D5—42no—
882D5—64no—
883C23—32no—
884C23—52no—
885C23—52no—
886C23—52no—
887C23—52no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—101no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—152no—
905C23—152no—
906C23—152no—
907C23—308no—
908C23—308no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
918C23C22×D3×D511yescharacteristic
919D4—108no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—32no—
930C2×C4—32no—
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—61no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—152no—
945C2×C4—204no—
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—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C4×D3×D512yes—
959C2×C4D5×#6712yes—
960C2×C3—104no—
961C2×C3—202no—
962C2×C3#6585511yescharacteristic
963C2×C3C4×D4×D511yescharacteristic
964C2×C3C4×D4×D511yescharacteristic
965C2×C3#6594311yescharacteristic
966C2×C3#6598811yescharacteristic
967C2×C3#6601011yescharacteristic
968C2×C3#6603911yescharacteristic
969D3—42no—
970D3—104no—
971C5#8239811yescharacteristic, complemented, Sylow
972C22—54no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—102no—
977C22—102no—
978C22—102no—
979C22—102no—
980C22—102no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—154no—
990C22—201no—
991C22—201no—
992C22—201no—
993C22—201no—
994C22—302no—
995C22—302no—
996C22—302no—
997C22—302no—
998C22—302no—
999C22—302no—
1000C22—6016no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22D5×#23511yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22#9202611yescharacteristic
1005C22#9203411yescharacteristic
1006C22#9203511yescharacteristic
1007C22C2×D5×#6711yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—102no—
1015C4—121no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1060756711yescharacteristic, complemented, Sylow
1020C2—104no—
1021C2—122no—
1022C2—202no—
1023C2—304no—
1024C2#1175383911yescharacteristic
1025C2#1175384011yescharacteristic
1026C2#1175386811yescharacteristic
1027C2#1175390111yescharacteristic
1028C2C4×D5×#6711yescharacteristic
1029C2#1175503811yescharacteristic
1030C2#1175527411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91474C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4039C2semidirect
3. C2×#91473C2semidirect
4. C2×D5×(C2×D3)⋊C4C2semidirect
5. C2×C4×#1202C2semidirect
6. #11751090C2semidirect
7. C5×#4990C2semidirect
8. #11748916C2semidirect
9. #11748905C2semidirect
10. #11748896C2semidirect
11. Dic3×#685C2semidirect
12. #11748875C2semidirect
13. #11748747C2semidirect
14. #11748704C2semidirect
15. #11748700C2semidirect
21. C22×C3×C4×D5C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
29. C2×#6712C22semidirect
33. C2×C4×C5×Dic3C22semidirect
35. C2×C3×#685C22semidirect
36. C2×C3×C4×Dic5C22semidirect
38. C2×Dic3⋊Dic5C22semidirect
44. C2×#6665C22semidirect
45. C2×#6665C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91474C4semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C5×C3⋊#95C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
58. C2×#4039D3semidirect
83. C22×D3×D5C2×C4semidirect
100. C2×C3×D20C2×C4semidirect
109. C2×#1202C2×C4semidirect
112. C2×#1201C2×C4semidirect
121. #6714C2×C4semidirect
125. C5×(C2×D3)⋊C4C2×C4semidirect
128. C3×#685D4semidirect
131. #6667D4semidirect
137. #6665C2×C4semidirect
147. #4990D5semidirect
162. C22×C4×D5C2×D3semidirect
163. C2×C5×C4⋊C4C2×D3semidirect
178. C2×#685C2×D3semidirect
182. C2×C4×Dic5C2×D3semidirect
282. C2×C3×C4⋊C4C2×D5semidirect
304. C2×C4×Dic3C2×D5semidirect
310. C3⋊#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
342. C2×D20C4×D3semidirect
373. #685#67semidirect
406. C2×D15C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
501. (C2×D3)⋊C4C4×D5semidirect
597. C2×C4⋊C4D3×D5semidirect
746. C2×D5C4×#67semidirect
824. C3×C5#2358semidirect
971. C5#82398semidirect
1019. C3#10607567semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×#914742
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×C4×#12022
#117510902
C5×#49902
#117489162
#117489052
#117488962
Dic3×#6852
#117488752
#117487472
#117487042
#117487002
#106075673
#823985