Finite Group Databasebeta

← #14328130

Subgroups — #14328130

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×#91474C211yesmaximal, characteristic
2C2×#91473C211yesmaximal, characteristic, complemented
3C2×D3×#685C211yesmaximal, characteristic, complemented
4C2×C4×#1202C211yesmaximal, characteristic, complemented
5C2×#91440C211yesmaximal, characteristic, complemented
6#11750769C211yesmaximal, characteristic, complemented
7C5×#4666C211yesmaximal, characteristic, complemented
8C3×#64954C211yesmaximal, characteristic, complemented
9#11748910C211yesmaximal, characteristic, complemented
10#11748903C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12#11748785C211yesmaximal, characteristic, complemented
13#11748712C211yesmaximal, characteristic, complemented
14#11748706C211yesmaximal, characteristic, complemented
15#11748700C211yesmaximal, characteristic, complemented
16#10605308—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic, complemented
22C22×#1202C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic, complemented
37C2×Dic3⋊Dic5C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91474C418yescomplemented
47#91473—24no—
48D3×#685—24no—
49C4×#1202—24no—
50#91440—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74880—51nomaximal, Hall
58C22×#685—31no—
59C2×#4028—31no—
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#64954D311yescharacteristic, complemented
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
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—41no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×C3×D20—41no—
102C2×C3×D20—41no—
103C2×C3×D20C2×C414yescomplemented
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×#1202—22no—
108C2×#1202—22no—
109C2×#1202C2×C414yescomplemented
110C2×#1201—22no—
111C2×#1201—22no—
112C2×#1201C2×C414yescomplemented
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—41no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—41no—
119#6714—22no—
120#6714C2×C414yescomplemented
121C4⋊Dic15—41no—
122#6712—22no—
123C5×(C2×D3)⋊C4C2×C414yescomplemented
124C5×(C2×D3)⋊C4D414yescomplemented
125C4×C5×Dic3—22no—
126C4×C5×Dic3—41no—
127C3×#685—22no—
128C3×#685—22no—
129C3×#685—41no—
130Dic3⋊Dic5—22no—
131#6667D414yescomplemented
132(C2×D3)⋊Dic5—22no—
133#6665—22no—
134#6665—22no—
135#6665—22no—
136#6665—22no—
137#6665C2×C414yescomplemented
138Dic3×Dic5—22no—
139C2×#937—51no—
140C2×C4×#67—51no—
141C2×C4×#67—51no—
142C2×D3×C22⋊C4—51no—
143C2×D3×C22⋊C4—51no—
144C3×#386—51no—
145#5221—51no—
146#4956—51no—
147#4956—51no—
148#4945—51no—
149#4945—51no—
150#4668—51no—
151#4668—51no—
152#4666—51no—
153#4666D511yescharacteristic, complemented
154C24×D5—31no—
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C23×Dic5—31no—
158C22×D20—31no—
159C22×D20C2×D311yescharacteristic
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic, complemented
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
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—64no—
177C2×#685C2×D311yescharacteristic
178C2×#685C2×D311yescharacteristic
179C2×#685C2×D311yescharacteristic, complemented
180C2×C4⋊Dic5—31no—
181C2×C4⋊Dic5—31no—
182C2×#683—31no—
183C2×C4×Dic5—31no—
184#4028—38no—
185#4027—64no—
186D5×C22⋊C4—64no—
187C4×D20—64no—
188C5×#95—31no—
189C5×#95C2×D311yescharacteristic, complemented
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963C2×D311yescharacteristic, complemented
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×D3C22×C412yes—
208C22×C5×D3C2×D412yes—
209C22×C5×D3#4112yes—
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—21no—
221C22×C3×D5—21no—
222C22×C3×D5C22×C412yes—
223C22×C3×D5C22×C412yes—
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×Dic3C22×C412yes—
257C2×C5×Dic3C2×D412yes—
258C2×C5×Dic3C2×D412yes—
259C4×C5×D3—44no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5C2×D412yes—
266C3×D20—44no—
267C3×C4×D5—44no—
268#1202—28no—
269#1201—28no—
270#1200—44no—
271D3×Dic5—44no—
272C24×D3—51no—
273C22×C3×D4—51no—
274C23×C3×C4—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×C4×D3—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×#217—51no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289#937—58no—
290C4×#67—104no—
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)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3C2×D511yescharacteristic, complemented
303C2×C4×Dic3C2×D511yescharacteristic, complemented
304D3×C22⋊C4—104no—
305D3×C22⋊C4—104no—
306C3×#95—51no—
307C3×#95C2×D511yescharacteristic, complemented
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
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×C5—62no—
327C22×C4×C5—62no—
328C22×C4×C5—121no—
329C22×C4×C5C22×D311yescharacteristic
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—41no—
345C2×D20—41no—
346C2×D20—62no—
347C2×D20—62no—
348C2×D20C4×D314yescomplemented
349C2×C4×D5—22no—
350C2×C4×D5—22no—
351C2×C4×D5—41no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C22⋊C4—34no—
359C5×C22⋊C4—34no—
360C42×C5—62no—
361C42×C5—121no—
362C22⋊Dic5—62no—
363#685—22no—
364#685—22no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—41no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374C4⋊Dic5—62no—
375C4⋊Dic5—121no—
376#683—62no—
377C4×Dic5—62no—
378C2×#120—151no—
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—51no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—31no—
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—22no—
411C2×C5×D3—22no—
412C2×C5×D3—22no—
413C2×C5×D3C4×D414yescomplemented
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—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—
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—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
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—201no—
453C2×C3×D4—201no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—102no—
457C22×C3×C4—102no—
458C22×C3×C4—201no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—102no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—102no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3C22×D511yescharacteristic
472C22×Dic3C22×D511yescharacteristic
473C22×Dic3C22×D511yescharacteristic
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—41no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—201no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C22⋊C4—102no—
487C3×C22⋊C4—102no—
488C3×C22⋊C4—201no—
489#217—54no—
490#217—102no—
491#217—102no—
492#217—102no—
493#217—102no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—102no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4C4×D514yescomplemented
499(C2×D3)⋊C4D2014yescomplemented
500C4⋊Dic3—201no—
501Dic3⋊C4—102no—
502Dic3⋊C4—102no—
503C4×Dic3—22no—
504C4×Dic3—41no—
505C4×Dic3—102no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—32no—
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—21no—
525C22×D5—21no—
526C22×D5—32no—
527C22×D5—32no—
528C22×D5—32no—
529C22×D5—68no—
530C22×D5—68no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—124no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5C2×C4×D312yes—
541C22×D5C2×C4×D312yes—
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—32no—
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×C5C2×C4×D312yes—
560C2×C4×C5D3×D412yes—
561C22⋊D5—68no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
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—61no—
576C2×Dic5—124no—
577C2×Dic5D3×D412yes—
578D20—44no—
579D20—68no—
580C4×D5—44no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—51no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—51no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
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—31no—
600C2×C22⋊C4—51no—
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—31no—
616C2×C42—151no—
617#95—31no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95D3×D511yescharacteristic, complemented
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—42no—
632C3×D5—42no—
633C5×D3—24no—
634C23×C3—52no—
635C23×C3—52no—
636C23×C3—101no—
637C23×C3—101no—
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—52no—
654C22×D3—52no—
655C22×D3—52no—
656C22×D3—108no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—108no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3C2×C4×D512yes—
668C22×D3C2×D2012yes—
669C22×D3#70912yes—
670C3×D4—204no—
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—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—204no—
685C2×C3×C4C2×C4×D512yes—
686C2×C3×C4C2×D2012yes—
687#67—108no—
688#67—108no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—52no—
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×Dic3C2×C4×D512yes—
705C2×Dic3C2×D2012yes—
706C2×Dic3D4×D512yes—
707C4×D3—44no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—34no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5#100411yescharacteristic
722C22×C5#100411yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5D3×#4111yescharacteristic
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—34no—
732C2×D5—41no—
733C2×D5—41no—
734C2×D5—41no—
735C2×D5—41no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5—41no—
739C2×D5—41no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—62no—
746C2×D5—1216no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—62no—
751C4×C5—62no—
752C4×C5—62no—
753Dic5—22no—
754Dic5—41no—
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—154no—
771C2×D4—154no—
772C2×D4—201no—
773C2×D4—201no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—302no—
777C2×D4—302no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—121no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—151no—
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—302no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—34no—
809C22⋊C4—102no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—201no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—302no—
821C42—62no—
822C42—121no—
823C42—302no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—201no—
832C22×C3—201no—
833C22×C3—201no—
834C22×C3—201no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3C22×C4×D511yescharacteristic
840C22×C3C22×D2011yescharacteristic
841C22×C3C2×#70911yescharacteristic
842C22×C3C2×D4×D511yescharacteristic
843C22×C3#414411yescharacteristic
844C22×C3D5×#4111yescharacteristic
845C22×C3#414911yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—54no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—102no—
858C2×D3—102no—
859C2×D3—2016no—
860C2×D3C4×D2014yescomplemented
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—102no—
865C3×C4—201no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—64no—
873C2×C5#548611yescharacteristic
874C2×C5C4×D3×D411yescharacteristic
875C2×C5C4×D3×D411yescharacteristic
876C2×C5#559011yescharacteristic
877C2×C5#561211yescharacteristic
878C2×C5#561211yescharacteristic
879C2×C5#565911yescharacteristic
880D5—42no—
881D5—42no—
882D5—64no—
883C23—32no—
884C23—32no—
885C23—32no—
886C23—52no—
887C23—52no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—101no—
893C23—101no—
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—204no—
920D4—308no—
921D4—308no—
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—32no—
932C2×C4—52no—
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—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—124no—
945C2×C4—152no—
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×C4D3×D2012yes—
960C2×C3—202no—
961C2×C3—202no—
962C2×C3C2×C4×D2011yescharacteristic
963C2×C3#6582411yescharacteristic
964C2×C3#6586111yescharacteristic
965C2×C3C4×D4×D511yescharacteristic
966C2×C3#6587911yescharacteristic
967C2×C3D4×D2011yescharacteristic
968C2×C3#6588811yescharacteristic
969D3—24no—
970D3—104no—
971C5#7488011yescharacteristic, complemented, Sylow
972C22—34no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—102no—
980C22—102no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—154no—
986C22—201no—
987C22—201no—
988C22—201no—
989C22—201no—
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
1002C22C2×D3×D2011yescharacteristic
1003C22D3×#70911yescharacteristic
1004C22D3×D4×D511yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202611yescharacteristic
1007C22#9203411yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—62no—
1013C4—62no—
1014C4—102no—
1015C4—201no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1060530811yescharacteristic, complemented, Sylow
1020C2—64no—
1021C2—202no—
1022C2—202no—
1023C2—304no—
1024C2C4×D3×D2011yescharacteristic
1025C2#1175320011yescharacteristic
1026C2#1175323511yescharacteristic
1027C2#1175325511yescharacteristic
1028C2#1175384011yescharacteristic
1029C2#1175388311yescharacteristic
1030C2#1175392111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91474C2
hypercenter#95D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91473C2semidirect
3. C2×D3×#685C2semidirect
4. C2×C4×#1202C2semidirect
5. C2×#91440C2semidirect
6. #11750769C2semidirect
7. C5×#4666C2semidirect
8. C3×#64954C2semidirect
9. #11748910C2semidirect
10. #11748903C2semidirect
11. #11748881C2semidirect
12. #11748785C2semidirect
13. #11748712C2semidirect
14. #11748706C2semidirect
15. #11748700C2semidirect
21. C22×C3×C4×D5C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×#6712C22semidirect
32. C2×C4×C5×Dic3C22semidirect
33. C2×C4×C5×Dic3C22semidirect
36. C2×C3×#685C22semidirect
37. C2×Dic3⋊Dic5C22semidirect
43. C2×#6665C22semidirect
44. C2×#6665C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91474C4semidirect
51. C3×C5×#95C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. #64954D3semidirect
83. C22×D3×D5C2×C4semidirect
103. C2×C3×D20C2×C4semidirect
109. C2×#1202C2×C4semidirect
112. C2×#1201C2×C4semidirect
120. #6714C2×C4semidirect
123. C5×(C2×D3)⋊C4C2×C4semidirect
124. C5×(C2×D3)⋊C4D4semidirect
131. #6667D4semidirect
137. #6665C2×C4semidirect
153. #4666D5semidirect
162. C22×C4×D5C2×D3semidirect
179. C2×#685C2×D3semidirect
189. C5×#95C2×D3semidirect
193. #3963C2×D3semidirect
302. C2×C4×Dic3C2×D5semidirect
303. C2×C4×Dic3C2×D5semidirect
307. C3×#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
348. C2×D20C4×D3semidirect
406. C2×D15C4×D4semidirect
413. C2×C5×D3C4×D4semidirect
498. (C2×D3)⋊C4C4×D5semidirect
499. (C2×D3)⋊C4D20semidirect
622. #95D3×D5semidirect
824. C3×C5#2358semidirect
860. C2×D3C4×D20semidirect
971. C5#74880semidirect
1019. C3#10605308semidirect

Maximal subgroups

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

subgroupindex
C2×#914742
C2×#914732
C2×D3×#6852
C2×C4×#12022
C2×#914402
#117507692
C5×#46662
C3×#649542
#117489102
#117489032
#117488812
#117487852
#117487122
#117487062
#117487002
#106053083
#748805