Finite Group Databasebeta

← #14328159

Subgroups — #14328159

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×#4028C211yesmaximal, characteristic
2C2×#91559C211yesmaximal, characteristic, complemented
3C2×D5×#217C211yesmaximal, characteristic, complemented
4C22×#6665C211yesmaximal, characteristic, complemented
5C2×Dic3×D20C211yesmaximal, characteristic, complemented
6#11751051C211yesmaximal, characteristic, complemented
7C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#11749495C211yesmaximal, characteristic, complemented
9#11748900C211yesmaximal, characteristic, complemented
10#11748896C211yesmaximal, characteristic, complemented
11#11748896C211yesmaximal, characteristic, complemented
12Dic3×#685C211yesmaximal, characteristic, complemented
13#11748785C211yesmaximal, characteristic, complemented
14#11748772C211yesmaximal, characteristic, complemented
15#11748770C211yesmaximal, characteristic, complemented
16#10605308—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×C4⋊Dic15C2211yescharacteristic, complemented
30C2×C5×#217C2211yescharacteristic
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C3×#4028C418yescomplemented
36#91559—24no—
37D5×#217—24no—
38C2×#6668C2211yescharacteristic, complemented
39C2×#6665—24no—
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic, complemented
47C2×#6665C2211yescharacteristic, complemented
48C2×#6665C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50Dic3×D20—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C5×C3⋊#95C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82579—51nomaximal, Hall
58C22×#685—31no—
59C2×#4028D311yescharacteristic
60C2×#4027—31no—
61C2×D5×C22⋊C4—31no—
62C2×C4×D20—31no—
63C4×C5×C22⋊C4—31no—
64#65502—31no—
65#65239—31no—
66#65229—31no—
67#65228—31no—
68C4×#685—31no—
69#64959—31no—
70#64957—31no—
71#64954—31no—
72#64954—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—41no—
79C23×C3×D5—41no—
80C23×C3×D5C2×C414yescomplemented
81C23×C3×D5C2311yescharacteristic
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15—22no—
87C22×Dic15—22no—
88C22×Dic15—41no—
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3—41no—
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C3×C22⋊D5—22no—
101C2×C3×C22⋊D5—22no—
102C2×C3×C22⋊D5C2×C414yescomplemented
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×D20—22no—
105C2×C3×D20—22no—
106C2×C3×D20—41no—
107C2×C3×D20—41no—
108C2×C3×D20C2×C414yescomplemented
109C2×C3×D20C2×C414yescomplemented
110C2×D5×Dic3—22no—
111C2×D5×Dic3—22no—
112C2×D5×Dic3—22no—
113C2×D5×Dic3—22no—
114C2×D5×Dic3—22no—
115C2×D5×Dic3—22no—
116C2×D5×Dic3—41no—
117C2×D5×Dic3—41no—
118C2×D5×Dic3—41no—
119C3×C5×C22⋊C4C2×C414yescomplemented
120#6719—22no—
121C4⋊Dic15—22no—
122C4⋊Dic15—41no—
123C5×#217D414yescomplemented
124C4×C5×Dic3—22no—
125C4×C5×Dic3—41no—
126C3×#685C2×C414yescomplemented
127C3×#685C2×C414yescomplemented
128#6668—22no—
129#6665—22no—
130#6665—22no—
131#6665—22no—
132#6665—22no—
133#6665—22no—
134#6665—22no—
135#6665—22no—
136#6665—41no—
137#6665D414yescomplemented
138Dic3×Dic5—22no—
139C2×C3×#120—51no—
140C22×#217—51no—
141C22×#217—51no—
142C2×D4×Dic3—51no—
143C2×D4×Dic3—51no—
144#5221—51no—
145#5220—51no—
146#5220—51no—
147#5220—51no—
148#4951—51no—
149#4951—51no—
150#4950—51no—
151#4950—51no—
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4D511yescharacteristic, complemented
154C24×D5C2×D311yescharacteristic
155C23×C4×C5—31no—
156C22×C22⋊D5C2×D311yescharacteristic
157C23×Dic5—31no—
158C22×D20C2×D311yescharacteristic
159C22×D20C2×D311yescharacteristic
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4C2×D311yescharacteristic
165C2×C42×C5—31no—
166C2×C42×C5—31no—
167C2×C22⋊Dic5—31no—
168C2×#685—31no—
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—64no—
178C2×#685C2×D311yescharacteristic
179C2×#685C2×D311yescharacteristic
180C2×C4⋊Dic5—31no—
181C2×C4⋊Dic5—31no—
182C2×#683—31no—
183C2×C4×Dic5—31no—
184#4028Dic318yescomplemented
185#4027—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×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×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—28no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
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×D5—28no—
221C22×C3×D5—44no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5—44no—
225C22×C3×D5—44no—
226C22×C3×D5C22×C412yes—
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×C5C22×C412yes—
236C2×C3×C4×C5C22×C412yes—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
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×Dic15—44no—
249C2×Dic15C2×D412yes—
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—21no—
258C2×C5×Dic3—21no—
259C2×C5×Dic3—44no—
260C2×C5×Dic3C2×D412yes—
261C2×C5×Dic3C2×D412yes—
262C2×C5×Dic3C2×D412yes—
263C3×C22⋊D5—28no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5C22×C412yes—
267C3×D20—28no—
268C3×D20—44no—
269D5×Dic3—44no—
270D5×Dic3—44no—
271D5×Dic3—44no—
272C25×C3—51no—
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4—51no—
276C23×Dic3—51no—
277C23×Dic3—51no—
278C23×Dic3—51no—
279C23×Dic3—51no—
280C23×Dic3C2×D511yescharacteristic
281C3×#120—58no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217—104no—
296C2×#217—104no—
297C2×#217C2×D511yescharacteristic
298D4×Dic3—104no—
299D4×Dic3—104no—
300C2×C4⋊Dic3—51no—
301C2×C4⋊Dic3—51no—
302C2×C4⋊Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305C2×C4×Dic3C2×D511yescharacteristic, complemented
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—41no—
318C23×D5—41no—
319C23×D5C2×Dic314yescomplemented
320C23×D5C22×D311yescharacteristic
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—22no—
333C2×C22⋊D5—22no—
334C2×C22⋊D5C2×Dic314yescomplemented
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—62no—
340C22×Dic5—62no—
341C22×Dic5—121no—
342C22×Dic5C22×D311yescharacteristic
343C2×D20—22no—
344C2×D20—22no—
345C2×D20—41no—
346C2×D20—41no—
347C2×D20C2×Dic314yescomplemented
348C2×D20C2×Dic314yescomplemented
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×C22⋊C4—34no—
359C5×C22⋊C4C2×Dic314yescomplemented
360C42×C5—62no—
361C42×C5—121no—
362C22⋊Dic5—62no—
363#685—34no—
364#685—62no—
365#685—62no—
366#685—62no—
367#685—62no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—121no—
372#685C2×Dic314yescomplemented
373#685C2×Dic314yescomplemented
374C4⋊Dic5—62no—
375C4⋊Dic5—121no—
376#683—62no—
377C4×Dic5—62no—
378C2×#120—51no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C22⋊C4—151no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—151no—
385#388—151no—
386#386—151no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—31no—
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×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—416no—
420C2×C3×D5—41no—
421C2×C3×D5—41no—
422C2×C3×D5—41no—
423C2×C3×D5—41no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—41no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—51no—
443C24×C3—54no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—102no—
448C24×C3—201no—
449C24×C3—201no—
450C24×C3C22×D511yescharacteristic
451C2×C3×D4—54no—
452C2×C3×D4—54no—
453C2×C3×D4—54no—
454C2×C3×D4—102no—
455C2×C3×D4—102no—
456C2×C3×D4—102no—
457C2×C3×D4—102no—
458C2×C3×D4—201no—
459C2×C3×D4—201no—
460C22×C3×C4—51no—
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×Dic3—22no—
464C22×Dic3—22no—
465C22×Dic3—41no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—102no—
471C22×Dic3—102no—
472C22×Dic3—102no—
473C22×Dic3—102no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—102no—
477C22×Dic3—102no—
478C22×Dic3—201no—
479C22×Dic3—201no—
480C22×Dic3—201no—
481C22×Dic3—201no—
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C22×Dic3C22×D511yescharacteristic
485C22×Dic3C22×D511yescharacteristic
486C3×C22⋊C4—54no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4C4×D514yescomplemented
489#217—54no—
490#217—102no—
491#217—102no—
492#217—102no—
493#217—102no—
494#217—102no—
495#217—102no—
496#217—102no—
497#217—102no—
498#217—201no—
499#217D2014yescomplemented
500C4⋊Dic3—102no—
501C4⋊Dic3—102no—
502C4⋊Dic3—201no—
503C4×Dic3—22no—
504C4×Dic3—41no—
505C4×Dic3—102no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5D3×D412yes—
511C23×C5#23712yes—
512C23×C5C22×Dic312yes—
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—21no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—28no—
532C22×D5—44no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5—44no—
536C22×D5—44no—
537C22×D5D3×D412yes—
538C22×D5#23712yes—
539C22×D5C22×Dic312yes—
540C22×D5C22×Dic312yes—
541C22×D5C22×Dic312yes—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—32no—
547C2×C4×C5—32no—
548C2×C4×C5—32no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
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—124no—
559C2×C4×C5C22×Dic312yes—
560C2×C4×C5C22×Dic312yes—
561C22⋊D5—28no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—32no—
565C2×Dic5—61no—
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×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—124no—
577C2×Dic5C22×Dic312yes—
578D20—28no—
579D20—44no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—51no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4—51no—
587C23×C4—31no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—58no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
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—304no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4D3×D511yescharacteristic
614C2×C42—31no—
615C2×C42—31no—
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
631C3×D5—24no—
632C3×D5—42no—
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—52no—
643C23×C3—108no—
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—101no—
654C23×C3—101no—
655C23×C3—101no—
656C23×C3—101no—
657C23×C3—101no—
658C23×C3—101no—
659C23×C3—101no—
660C23×C3—108no—
661C23×C3—204no—
662C23×C3—204no—
663C23×C3—204no—
664C23×C3—204no—
665C23×C3—204no—
666C23×C3C2×C4×D512yes—
667C23×C3C2×D2012yes—
668C23×C3#70912yes—
669C23×C3C23×D511yescharacteristic
670C3×D4—108no—
671C3×D4—108no—
672C3×D4—204no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—52no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4C2×C4×D512yes—
681C2×C3×C4C2×C4×D512yes—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—44no—
692C2×Dic3—52no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—204no—
705C2×Dic3—204no—
706C2×Dic3—204no—
707C2×Dic3—204no—
708C2×Dic3C2×D2012yes—
709C2×Dic3C2×D2012yes—
710C2×Dic3D4×D512yes—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5D4×Dic314yescomplemented
718C22×C5C2×D3×D411yescharacteristic
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×#23711yescharacteristic
721C22×C5C2×#23711yescharacteristic
722C22×C5#100411yescharacteristic
723C22×C5#100411yescharacteristic
724C22×C5C23×Dic311yescharacteristic
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—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—416no—
738C2×D5—41no—
739C2×D5—41no—
740C2×D5—41no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5D4×Dic314yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—62no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—62no—
755Dic5—121no—
756Dic5—121no—
757Dic5—121no—
758C24—51no—
759C24—51no—
760C24—51no—
761C24—54no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—102no—
766C24—201no—
767C24—201no—
768C24C2×D3×D511yescharacteristic
769C2×D4—54no—
770C2×D4—54no—
771C2×D4—54no—
772C2×D4—102no—
773C2×D4—102no—
774C2×D4—102no—
775C2×D4—102no—
776C2×D4—201no—
777C2×D4—201no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—121no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—302no—
791C22×C4—302no—
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×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—302no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—54no—
810C22⋊C4—154no—
811C22⋊C4—302no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4D5×Dic314yescomplemented
821C42—62no—
822C42—121no—
823C42—302no—
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—102no—
842C22×C3—102no—
843C22×C3—102no—
844C22×C3—2016no—
845C22×C3—201no—
846C22×C3—201no—
847C22×C3—201no—
848C22×C3—201no—
849C22×C3—201no—
850C22×C3—201no—
851C22×C3—201no—
852C22×C3—201no—
853C22×C3C4×D2014yescomplemented
854C22×C3C22×C4×D511yescharacteristic
855C22×C3C22×D2011yescharacteristic
856C22×C3C2×#70911yescharacteristic
857C22×C3C2×D4×D511yescharacteristic
858C22×C3#414411yescharacteristic
859C22×C3D5×#4111yescharacteristic
860C22×C3#414911yescharacteristic
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864Dic3—22no—
865Dic3—22no—
866Dic3—22no—
867Dic3—41no—
868Dic3—102no—
869Dic3—201no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5#558711yescharacteristic
874C2×C5#559011yescharacteristic
875C2×C5#559111yescharacteristic
876C2×C5#559111yescharacteristic
877C2×C5C2×D4×Dic311yescharacteristic
878C2×C5C2×D4×Dic311yescharacteristic
879C2×C5#579811yescharacteristic
880D5—24no—
881D5—42no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—52no—
888C23—52no—
889C23—52no—
890C23—52no—
891C23—52no—
892C23—108no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—108no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—204no—
911C23—204no—
912C23—204no—
913C23—204no—
914C23—204no—
915C23#676512yes—
916C23D3×D2012yes—
917C23C2×D5×Dic312yes—
918C23C22×D3×D511yescharacteristic
919D4—108no—
920D4—108no—
921D4—204no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—52no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—124no—
942C2×C4—152no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—604no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C2×D5×Dic312yes—
959C2×C4C2×D5×Dic312yes—
960C2×C3—24no—
961C2×C3—104no—
962C2×C3—202no—
963C2×C3—202no—
964C2×C3C2×C4×D2011yescharacteristic
965C2×C3#6582411yescharacteristic
966C2×C3#6586111yescharacteristic
967C2×C3C4×D4×D511yescharacteristic
968C2×C3#6587911yescharacteristic
969C2×C3D4×D2011yescharacteristic
970C2×C3#6588811yescharacteristic
971C5#8257911yescharacteristic, 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—102no—
989C22—102no—
990C22—102no—
991C22—2016no—
992C22—201no—
993C22—201no—
994C22—201no—
995C22—201no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22Dic3×D2014yescomplemented
1001C22C2×#676511yescharacteristic
1002C22C2×D3×D2011yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D5×#23711yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202611yescharacteristic
1007C22C22×D5×Dic311yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—121no—
1015C4—302no—
1016C4—601no—
1017C4—601no—
1018C4—601no—
1019C3#1060530811yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—104no—
1022C2—202no—
1023C2—202no—
1024C2#1175291611yescharacteristic
1025C2#1175307011yescharacteristic
1026C2#1175323511yescharacteristic
1027C2#1175326711yescharacteristic
1028C2C2×Dic3×D2011yescharacteristic
1029C2D4×D5×Dic311yescharacteristic
1030C2#1175491011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4028C2
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
2. C2×#91559C2semidirect
3. C2×D5×#217C2semidirect
4. C22×#6665C2semidirect
5. C2×Dic3×D20C2semidirect
6. #11751051C2semidirect
7. C5×Dic3×C22⋊C4C2semidirect
8. #11749495C2semidirect
9. #11748900C2semidirect
10. #11748896C2semidirect
11. #11748896C2semidirect
12. Dic3×#685C2semidirect
13. #11748785C2semidirect
14. #11748772C2semidirect
15. #11748770C2semidirect
25. C22×D5×Dic3C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×C4⋊Dic15C22semidirect
31. C2×C4×C5×Dic3C22semidirect
32. C2×C4×C5×Dic3C22semidirect
35. C3×#4028C4semidirect
38. C2×#6668C22semidirect
46. C2×#6665C22semidirect
47. C2×#6665C22semidirect
48. C2×#6665C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C5×C3⋊#95C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
80. C23×C3×D5C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
108. C2×C3×D20C2×C4semidirect
109. C2×C3×D20C2×C4semidirect
119. C3×C5×C22⋊C4C2×C4semidirect
123. C5×#217D4semidirect
126. C3×#685C2×C4semidirect
127. C3×#685C2×C4semidirect
137. #6665D4semidirect
153. Dic3×C22⋊C4D5semidirect
184. #4028Dic3semidirect
304. C2×C4×Dic3C2×D5semidirect
305. C2×C4×Dic3C2×D5semidirect
310. C3⋊#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
319. C23×D5C2×Dic3semidirect
334. C2×C22⋊D5C2×Dic3semidirect
347. C2×D20C2×Dic3semidirect
348. C2×D20C2×Dic3semidirect
359. C5×C22⋊C4C2×Dic3semidirect
372. #685C2×Dic3semidirect
373. #685C2×Dic3semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
488. C3×C22⋊C4C4×D5semidirect
499. #217D20semidirect
717. C22×C5D4×Dic3semidirect
746. C2×D5D4×Dic3semidirect
820. C22⋊C4D5×Dic3semidirect
824. C3×C5#2358semidirect
853. C22×C3C4×D20semidirect
971. C5#82579semidirect
1000. C22Dic3×D20semidirect
1019. C3#10605308semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40282
C2×#915592
C2×D5×#2172
C22×#66652
C2×Dic3×D202
#117510512
C5×Dic3×C22⋊C42
#117494952
#117489002
#117488962
Dic3×#6852
#117487852
#117487722
#117487702
#106053083
#825795