Finite Group Databasebeta

← #14328142

Subgroups — #14328142

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×D5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#91564C211yesmaximal, characteristic
3C2×#91556C211yesmaximal, characteristic, complemented
4C22×#6665C211yesmaximal, characteristic, complemented
5C2×#91444C211yesmaximal, characteristic, complemented
6#11751059C211yesmaximal, characteristic, complemented
7C5×#4946C211yesmaximal, characteristic, complemented
8#11749487C211yesmaximal, characteristic, complemented
9#11748913C211yesmaximal, characteristic, complemented
10#11748907C211yesmaximal, characteristic, complemented
11#11748711C211yesmaximal, characteristic, complemented
12#11748708C211yesmaximal, characteristic, complemented
13#11748703C211yesmaximal, characteristic, complemented
14#11748702C211yesmaximal, characteristic, complemented
15#11748700C211yesmaximal, characteristic, complemented
16#10606327—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1200C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6714C2211yescharacteristic, complemented
28C2×#6714C2211yescharacteristic, complemented
29C2×C5×#217C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C3×D5×C22⋊C4—24no—
36#91564C418yescomplemented
37#91556—24no—
38C2×#6669C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic, complemented
40C2×#6665—24no—
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91444—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C5×C3⋊#95C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82099—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×#685—31no—
60C2×#4039—31no—
61C2×#4028—31no—
62C2×D5×C22⋊C4D311yescharacteristic, complemented
63C5×#385—31no—
64#65279—31no—
65#65278—31no—
66#65277—31no—
67#65247—31no—
68C22⋊C4×Dic5—31no—
69#64958—31no—
70#64955—31no—
71#64954—31no—
72#64954—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
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×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—22no—
87C2×#1220—22no—
88C2×#1220C2×C414yescomplemented
89C22×Dic15—22no—
90C22×Dic15—22no—
91C22×Dic15—41no—
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×C5×Dic3—22no—
96C22×C5×Dic3—22no—
97C22×C5×Dic3—41no—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—22no—
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—41no—
109C2×C3×C4×D5—41no—
110C2×#1202—22no—
111C2×#1202—22no—
112C2×#1202—41no—
113C2×#1202—41no—
114C2×#1202C2×C414yescomplemented
115C2×#1202C2×C414yescomplemented
116C2×#1200—22no—
117C2×#1200—22no—
118C2×#1200—41no—
119C3×C5×C22⋊C4—22no—
120#6714—22no—
121#6714—41no—
122C5×#217C2×C414yescomplemented
123C5×Dic3⋊C4—22no—
124C5×Dic3⋊C4—41no—
125C3×C22⋊Dic5D414yescomplemented
126C3×#685—22no—
127C3×#685—22no—
128#6669—22no—
129#6667—22no—
130#6665—22no—
131#6665—22no—
132#6665—22no—
133#6665C2×C414yescomplemented
134#6665C2×C414yescomplemented
135#6665D414yescomplemented
136Dic3×Dic5—22no—
137Dic3×Dic5—22no—
138Dic3×Dic5—41no—
139C22×C3×C22⋊C4—51no—
140C2×#953—51no—
141C22×#217—51no—
142C2×C4×#67—51no—
143C2×#67⋊C4—51no—
144#5213—51no—
145#5210—51no—
146C4×#217—51no—
147#4958—51no—
148#4957—51no—
149#4956—51no—
150#4946D511yescharacteristic, complemented
151#4945—51no—
152#4944—51no—
153Dic3×C22⋊C4—51no—
154C24×D5C2×D311yescharacteristic
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C23×Dic5—31no—
158C22×D20—31no—
159C22×D20—31no—
160C22×C4×D5—31no—
161C22×C4×D5C2×D311yescharacteristic
162C22×C4×D5C2×D311yescharacteristic
163C2×C5×C4⋊C4—31no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C22⋊Dic5C2×D311yescharacteristic
168C4×C22⋊D5—64no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—64no—
179C2×#685C2×D311yescharacteristic
180C2×#685C2×D311yescharacteristic
181C2×#683—31no—
182C2×C4×Dic5—31no—
183C2×C4×Dic5—31no—
184C2×C4×Dic5—31no—
185#4039—64no—
186#4028—38no—
187D5×C22⋊C4—24no—
188C5×#95—31no—
189C5×#95—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×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15C22×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—21no—
237#1220—28no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—44no—
246C2×Dic15C22×C412yes—
247C2×Dic15C2×D412yes—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
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×Dic3—44no—
258C2×C5×Dic3C22×C412yes—
259C2×C5×Dic3C22×C412yes—
260C2×C5×Dic3C2×D412yes—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5C2×D412yes—
266C2×C3×Dic5C2×D412yes—
267C3×C4×D5—44no—
268C3×C4×D5—44no—
269#1202—28no—
270#1202—44no—
271#1200—44no—
272C25×C3—51no—
273C23×C3×C4—51no—
274C23×C3×C4—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×#67—51no—
278C23×Dic3—51no—
279C23×Dic3C2×D511yescharacteristic
280C22×C4×D3—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—104no—
285C2×C3×C22⋊C4C2×D511yescharacteristic
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—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4C2×D511yescharacteristic, complemented
301C2×Dic3⋊C4C2×D511yescharacteristic, complemented
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305#67⋊C4—104no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95C2×D511yescharacteristic, complemented
311C3⋊#95C2×D511yescharacteristic, complemented
312C24×C5C22×D311yescharacteristic
313C23×D5—22no—
314C23×D5—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—31no—
318C23×D5—41no—
319C23×D5—41no—
320C23×D5C4×D314yescomplemented
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D311yescharacteristic
323C22×C4×C5—31no—
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—62no—
328C22×C4×C5—62no—
329C22×C4×C5—121no—
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C2×C22⋊D5—34no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—62no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—62no—
339C22×Dic5—62no—
340C22×Dic5—121no—
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C2×D20—34no—
344C2×D20—34no—
345C2×D20—62no—
346C2×D20—62no—
347C2×D20—121no—
348C2×D20—121no—
349C2×C4×D5—22no—
350C2×C4×D5—22no—
351C2×C4×D5—22no—
352C2×C4×D5—22no—
353C2×C4×D5—41no—
354C2×C4×D5—41no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C4⋊C4—121no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4—34no—
362C22⋊Dic5#6714yescomplemented
363#685—22no—
364#685—22no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—121no—
374#683—62no—
375C4×Dic5—62no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—151no—
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—31no—
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×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15—41no—
413C2×D15—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—41no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
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×D3—51no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—102no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—102no—
457C22×C3×C4—201no—
458C22×C3×C4—201no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—102no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—102no—
468C2×#67—201no—
469C2×#67—201no—
470C22×Dic3—22no—
471C22×Dic3—22no—
472C22×Dic3—41no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—102no—
477C22×Dic3—102no—
478C22×Dic3—201no—
479C22×Dic3C22×D511yescharacteristic
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—201no—
486C3×C22⋊C4—22no—
487C3×C22⋊C4—54no—
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#217C4×D514yescomplemented
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—201no—
500Dic3⋊C4—22no—
501Dic3⋊C4—41no—
502Dic3⋊C4—102no—
503C4×Dic3—102no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5C2×C4×D312yes—
511C23×C5#23512yes—
512C23×C5C2×#6712yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—21no—
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—28no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—28no—
526C22×D5—32no—
527C22×D5—44no—
528C22×D5—44no—
529C22×D5—44no—
530C22×D5—44no—
531C22×D5—44no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—61no—
538C22×D5C2×C4×D312yes—
539C22×D5C2×C4×D312yes—
540C22×D5D3×D412yes—
541C22×D5#23712yes—
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—32no—
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×C5—61no—
559C2×C4×C5—61no—
560C2×C4×C5—124no—
561C22⋊D5—68no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—32no—
567C2×Dic5—32no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—124no—
576C2×Dic5C2×#6712yes—
577C2×Dic5C2×#6712yes—
578D20—68no—
579D20—124no—
580C4×D5—44no—
581C4×D5—44no—
582C4×D5—124no—
583C25—51no—
584C22×D4—151no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—51no—
589C23×C4—51no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—104no—
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⋊C4D3×D511yescharacteristic
614C2×C42—151no—
615C2×C42—151no—
616C2×C42—151no—
617#95—31no—
618#95—31no—
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
631D15—42no—
632C3×D5—24no—
633C3×D5—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×C3D4×D512yes—
661C23×C3#71312yes—
662C23×C3C23×D511yescharacteristic
663C22×D3—52no—
664C22×D3—101no—
665C22×D3—101no—
666C22×D3—101no—
667C22×D3—101no—
668C22×D3—101no—
669C22×D3—101no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—204no—
683C2×C3×C4—204no—
684#67—108no—
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—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—44no—
697C2×Dic3—52no—
698C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
709C2×Dic3D4×D512yes—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5C4×#6714yescomplemented
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C2×#23511yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5C2×#23711yescharacteristic
722C22×C5#100411yescharacteristic
723C22×C5#100411yescharacteristic
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—416no—
735C2×D5—41no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5—41no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5#67⋊C414yescomplemented
747C4×C5—41no—
748C4×C5—41no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—62no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—22no—
755Dic5—62no—
756Dic5—62no—
757Dic5—121no—
758C24—51no—
759C24—51no—
760C24—54no—
761C24—102no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—151no—
766C24—201no—
767C24—201no—
768C24C2×D3×D511yescharacteristic
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—154no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—102no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—201no—
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—121no—
806C4⋊C4—302no—
807C22⋊C4—22no—
808C22⋊C4—34no—
809C22⋊C4—54no—
810C22⋊C4—102no—
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—302no—
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×C3#403914yescomplemented
847C22×C3C22×C4×D511yescharacteristic
848C22×C3C2×D4×D511yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3#414411yescharacteristic
851C22×C3C2×#71311yescharacteristic
852C22×C3D5×#4111yescharacteristic
853C22×C3#414911yescharacteristic
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—102no—
864C3×C4—102no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5C2×#67⋊C411yescharacteristic
874C2×C5#548611yescharacteristic
875C2×C5#549011yescharacteristic
876C2×C5#549511yescharacteristic
877C2×C5C2×C4×#6711yescharacteristic
878C2×C5D4×#6711yescharacteristic
879C2×C5#580611yescharacteristic
880D5—24no—
881D5—42no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—52no—
888C23—52no—
889C23—52no—
890C23—52no—
891C23—108no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—108no—
897C23—101no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—152no—
904C23—204no—
905C23—204no—
906C23—204no—
907C23—204no—
908C23—204no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—301no—
914C23—301no—
915C23#677312yes—
916C23C4×D3×D512yes—
917C23D5×#6712yes—
918C23C22×D3×D511yescharacteristic
919D4—308no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—32no—
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—61no—
941C2×C4—61no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—124no—
947C2×C4—152no—
948C2×C4—152no—
949C2×C4—204no—
950C2×C4—204no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—301no—
958C2×C4—604no—
959C2×C4—604no—
960C2×C3—24no—
961C2×C3—104no—
962C2×C3—202no—
963C2×C3C2×#403911yescharacteristic
964C2×C3C4×D4×D511yescharacteristic
965C2×C3#6587911yescharacteristic
966C2×C3#6592411yescharacteristic
967C2×C3#6596411yescharacteristic
968C2×C3#6597111yescharacteristic
969C2×C3#6598811yescharacteristic
970D3—202no—
971C5#8209911yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—54no—
979C22—102no—
980C22—102no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—2016no—
989C22—201no—
990C22—201no—
991C22—201no—
992C22—201no—
993C22—302no—
994C22—302no—
995C22—302no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22#9144414yescomplemented
1001C22C2×#677311yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D5×#23711yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202611yescharacteristic
1007C22C2×D5×#6711yescharacteristic
1008C4—41no—
1009C4—41no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—102no—
1015C4—121no—
1016C4—302no—
1017C4—302no—
1018C4—601no—
1019C3#1060632711yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—104no—
1022C2—202no—
1023C2—602no—
1024C2#1175307311yescharacteristic
1025C2#1175310511yescharacteristic
1026C2D5×#67⋊C411yescharacteristic
1027C2#1175320011yescharacteristic
1028C2C2×#9144411yescharacteristic
1029C2#1175478911yescharacteristic
1030C2#1175503111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91564C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2358
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×D5×C22⋊C4C2semidirect
3. C2×#91556C2semidirect
4. C22×#6665C2semidirect
5. C2×#91444C2semidirect
6. #11751059C2semidirect
7. C5×#4946C2semidirect
8. #11749487C2semidirect
9. #11748913C2semidirect
10. #11748907C2semidirect
11. #11748711C2semidirect
12. #11748708C2semidirect
13. #11748703C2semidirect
14. #11748702C2semidirect
15. #11748700C2semidirect
25. C22×#1200C22semidirect
27. C2×#6714C22semidirect
28. C2×#6714C22semidirect
30. C2×C5×Dic3⋊C4C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
36. #91564C4semidirect
38. C2×#6669C22semidirect
39. C2×#6667C22semidirect
47. C2×Dic3×Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C5×C3⋊#95C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
62. C2×D5×C22⋊C4D3semidirect
81. C23×C3×D5C2×C4semidirect
88. C2×#1220C2×C4semidirect
114. C2×#1202C2×C4semidirect
115. C2×#1202C2×C4semidirect
122. C5×#217C2×C4semidirect
125. C3×C22⋊Dic5D4semidirect
133. #6665C2×C4semidirect
134. #6665C2×C4semidirect
135. #6665D4semidirect
150. #4946D5semidirect
300. C2×Dic3⋊C4C2×D5semidirect
301. C2×Dic3⋊C4C2×D5semidirect
310. C3⋊#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
320. C23×D5C4×D3semidirect
362. C22⋊Dic5#67semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
496. #217C4×D5semidirect
717. C22×C5C4×#67semidirect
746. C2×D5#67⋊C4semidirect
824. C3×C5#2358semidirect
846. C22×C3#4039semidirect
971. C5#82099semidirect
1000. C22#91444semidirect
1019. C3#10606327semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C2×#915642
C2×#915562
C22×#66652
C2×#914442
#117510592
C5×#49462
#117494872
#117489132
#117489072
#117487112
#117487082
#117487032
#117487022
#117487002
#106063273
#820995