Finite Group Databasebeta

← #14328125

Subgroups — #14328125

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×#91782C211yesmaximal, characteristic, complemented
2C2×#91476C211yesmaximal, characteristic
3C2×#91473C211yesmaximal, characteristic, complemented
4C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#1202C211yesmaximal, characteristic, complemented
6C5×#4990C211yesmaximal, characteristic, complemented
7C3×#65278C211yesmaximal, characteristic, complemented
8#11748918C211yesmaximal, characteristic, complemented
9#11748909C211yesmaximal, characteristic, complemented
10#11748904C211yesmaximal, characteristic, complemented
11#11748884C211yesmaximal, characteristic, complemented
12#11748881C211yesmaximal, characteristic, complemented
13#11748872C211yesmaximal, characteristic, complemented
14#11748794C211yesmaximal, characteristic, complemented
15#11748729C211yesmaximal, characteristic, complemented
16#10607567—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic, complemented
29C2×C4×Dic15C2211yescharacteristic, complemented
30#91782—24no—
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic, complemented
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic, complemented
38C2×Dic3⋊Dic5C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic, complemented
42C2×#6667C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91476C418yescomplemented
48#91473—24no—
49D5×(C2×D3)⋊C4—24no—
50C4×#1202—24no—
51C5×C3⋊#95C2211yescharacteristic, complemented
52C5×C3⋊#95C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74596—51nomaximal, Hall
58C2×#4039—31no—
59C2×#4028—31no—
60C2×D5×C22⋊C4—31no—
61C2×D5×C22⋊C4—31no—
62C2×C4×D20—31no—
63C5×#388—31no—
64#65278D311yescharacteristic, complemented
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×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
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
89C2×D60—22no—
90C2×D60—22no—
91C2×D60C2×C414yescomplemented
92C2×C4×D15—22no—
93C2×C4×D15—22no—
94C2×C4×D15—22no—
95C2×C4×D15—22no—
96C2×C4×D15—41no—
97C2×C4×D15—41no—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×#1203—41no—
108C2×#1203—41no—
109C2×#1203C2×C414yescomplemented
110C2×#1202—22no—
111C2×#1202—22no—
112C2×#1202C2×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#6714D414yescomplemented
122C4×Dic15—22no—
123C5×(C2×D3)⋊C4—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4C2×C414yescomplemented
126C4×C5×Dic3—22no—
127C3×#685—22no—
128C3×#685C2×C414yescomplemented
129C3×#683—41no—
130Dic3⋊Dic5—22no—
131#6667—22no—
132#6667—22no—
133#6667—41no—
134#6667C2×C414yescomplemented
135(C2×D3)⋊Dic5—22no—
136(C2×D3)⋊Dic5—22no—
137#6665D414yescomplemented
138Dic3×Dic5—41no—
139C2×C4×#67—51no—
140C22×(C2×D3)⋊C4—51no—
141C2×#893—51no—
142C2×#882—51no—
143C2×D3×C22⋊C4—51no—
144C3×#385—51no—
145#4990D511yescharacteristic, complemented
146#4989—51no—
147#4988—51no—
148#4958—51no—
149Dic3×C22⋊C4—51no—
150#4669—51no—
151#4666—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C22×C22⋊D5—31no—
156C22×D20—31no—
157C22×D20—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
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
179C2×C4⋊Dic5—31no—
180C2×#683C2×D311yescharacteristic, complemented
181C2×C4×Dic5—31no—
182C2×C4×Dic5—31no—
183#4039—64no—
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#3963C2×D311yescharacteristic, complemented
193#3963C2×D311yescharacteristic, complemented
194#2358—151noSylow
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15C22×C412yes—
207C22×D15C22×C412yes—
208C22×D15C2×D412yes—
209C22×D15#4112yes—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3—21no—
215C22×C5×D3—21no—
216C22×C5×D3C22×C412yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×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×Dic15C2×D412yes—
245C2×Dic15C2×D412yes—
246D60—28no—
247C4×D15—44no—
248C4×D15—44no—
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×Dic3C22×C412yes—
257C2×C5×Dic3C2×D412yes—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5C22×C412yes—
267C3×C4×D5—44no—
268#1203—44no—
269#1202—28no—
270#1200—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×#217—51no—
286C4×#67—104no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—104no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×(C2×D3)⋊C4C2×D511yescharacteristic
299C2×Dic3⋊C4—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3C2×D511yescharacteristic, complemented
303#893—104no—
304#882—58no—
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—31no—
315C23×D5—34no—
316C23×D5—62no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—121no—
321C23×D5—121no—
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×Dic5C22×D311yescharacteristic
335C22×Dic5C22×D311yescharacteristic
336C22×Dic5C22×D311yescharacteristic
337C2×D20—34no—
338C2×D20—34no—
339C2×D20—62no—
340C2×D20—62no—
341C2×D20—62no—
342C2×D20—62no—
343C2×C4×D5—22no—
344C2×C4×D5—22no—
345C2×C4×D5—41no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—121no—
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#685C4×D314yescomplemented
374C4⋊Dic5—62no—
375#683—41no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—151no—
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—51no—
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×D15—22no—
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—41no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15—41no—
413C2×D15C4×D414yescomplemented
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—41no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
420C2×C5×D3—41no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5C4×D414yescomplemented
428D3×D5—416no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432Dic15—22no—
433Dic15—22no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C23×D3—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
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—201no—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—102no—
462C2×#67—102no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—102no—
466C22×Dic3—102no—
467C22×Dic3—201no—
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—201no—
476C2×D12—201no—
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×C4⋊C4—22no—
487C3×C4⋊C4—201no—
488C3×C22⋊C4—54no—
489C3×C22⋊C4—102no—
490#217—54no—
491(C2×D3)⋊C4—22no—
492(C2×D3)⋊C4—22no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—102no—
496(C2×D3)⋊C4—102no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—201no—
501(C2×D3)⋊C4C4×D514yescomplemented
502Dic3⋊C4—102no—
503C4×Dic3—22no—
504C4×Dic3—102no—
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—32no—
519C22×D5—32no—
520C22×D5—32no—
521C22×D5—32no—
522C22×D5—68no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—68no—
534C22×D5—124no—
535C22×D5—124no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5C2×C4×D312yes—
540C22×D5D3×D412yes—
541C22×D5#23912yes—
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×C5D3×D412yes—
560C22⋊D5—124no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—32no—
570C2×Dic5—32no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5C2×C4×D312yes—
576D20—68no—
577D20—68no—
578C4×D5—44no—
579C4×D5—124no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—151no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—51no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—51no—
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—151no—
616C2×C42—151no—
617#95—31no—
618#95—31no—
619#95—51no—
620#95—51no—
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—
631D15—42no—
632C3×D5—24no—
633C5×D3—42no—
634C23×C3—52no—
635C23×C3—52no—
636C23×C3—52no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—52no—
649C22×D3—52no—
650C22×D3—52no—
651C22×D3—52no—
652C22×D3—108no—
653C22×D3—108no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
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—
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—21no—
677C2×C3×C4—52no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—204no—
687C2×C3×C4C2×C4×D512yes—
688C2×C3×C4D4×D512yes—
689#67—108no—
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—52no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—204no—
704C2×Dic3C2×C4×D512yes—
705C2×Dic3D4×D512yes—
706D12—108no—
707D12—204no—
708C4×D3—204no—
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×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5#100411yescharacteristic
722C22×C5C2×#23911yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5#100911yescharacteristic
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—34no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—1216no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5#89314yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—62no—
751C4×C5—62no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—41no—
755Dic5—41no—
756Dic5—62no—
757Dic5—62no—
758C24—31no—
759C24—51no—
760C24—154no—
761C24—151no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
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—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—102no—
785C22×C4—102no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—201no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—601no—
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—201no—
806C4⋊C4—302no—
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—302no—
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×C3C22×C4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3D5×#4111yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3#414911yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—54no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—102no—
852C2×D3—102no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—2016no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—102no—
865C3×C4—201no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—22no—
869Dic3—41no—
870Dic3—102no—
871Dic3—102no—
872C2×C5—122no—
873C2×C5C2×#89311yescharacteristic
874C2×C5C4×D3×D411yescharacteristic
875C2×C5#554511yescharacteristic
876C2×C5#559011yescharacteristic
877C2×C5#563011yescharacteristic
878C2×C5#563711yescharacteristic
879C2×C5#565411yescharacteristic
880D5—24no—
881D5—64no—
882D5—122no—
883C23—32no—
884C23—52no—
885C23—52no—
886C23—52no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—152no—
898C23—152no—
899C23—152no—
900C23—152no—
901C23—308no—
902C23—308no—
903C23—301no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
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—21no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—52no—
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—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—152no—
948C2×C4—152no—
949C2×C4—204no—
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×C4C4×D3×D512yes—
959C2×C4#679012yes—
960C2×C3—104no—
961C2×C3#6585511yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3C4×D4×D511yescharacteristic
964C2×C3#6594311yescharacteristic
965C2×C3#6598811yescharacteristic
966C2×C3#6601011yescharacteristic
967C2×C3#6603911yescharacteristic
968D3—42no—
969D3—104no—
970D3—202no—
971C5#7459611yescharacteristic, complemented, Sylow
972C22—54no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—102no—
977C22—102no—
978C22—102no—
979C22—102no—
980C22—102no—
981C22—102no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—121no—
986C22—154no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—302no—
996C22—6016no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22#9201611yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22#9202611yescharacteristic
1005C22D5×#23911yescharacteristic
1006C22#9203511yescharacteristic
1007C22C2×#679011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—62no—
1013C4—102no—
1014C4—121no—
1015C4—201no—
1016C4—201no—
1017C4—302no—
1018C4—302no—
1019C3#1060756711yescharacteristic, complemented, Sylow
1020C2—104no—
1021C2—122no—
1022C2—304no—
1023C2—602no—
1024C2D5×#89311yescharacteristic
1025C2#1175383911yescharacteristic
1026C2#1175385411yescharacteristic
1027C2#1175391511yescharacteristic
1028C2C4×#679011yescharacteristic
1029C2#1175503911yescharacteristic
1030C2#1175528311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91476C2
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×#91782C2semidirect
3. C2×#91473C2semidirect
4. C2×D5×(C2×D3)⋊C4C2semidirect
5. C2×C4×#1202C2semidirect
6. C5×#4990C2semidirect
7. C3×#65278C2semidirect
8. #11748918C2semidirect
9. #11748909C2semidirect
10. #11748904C2semidirect
11. #11748884C2semidirect
12. #11748881C2semidirect
13. #11748872C2semidirect
14. #11748794C2semidirect
15. #11748729C2semidirect
20. C22×C4×D15C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
28. C2×#6714C22semidirect
29. C2×C4×Dic15C22semidirect
34. C2×C4×C5×Dic3C22semidirect
37. C2×C3×#683C22semidirect
38. C2×Dic3⋊Dic5C22semidirect
41. C2×#6667C22semidirect
42. C2×#6667C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91476C4semidirect
51. C5×C3⋊#95C22semidirect
52. C5×C3⋊#95C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
64. #65278D3semidirect
83. C22×D3×D5C2×C4semidirect
91. C2×D60C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1202C2×C4semidirect
121. #6714D4semidirect
125. C5×(C2×D3)⋊C4C2×C4semidirect
128. C3×#685C2×C4semidirect
134. #6667C2×C4semidirect
137. #6665D4semidirect
145. #4990D5semidirect
163. C2×C5×C4⋊C4C2×D3semidirect
180. C2×#683C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
282. C2×C3×C4⋊C4C2×D5semidirect
302. C2×C4×Dic3C2×D5semidirect
310. C3⋊#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
373. #685C4×D3semidirect
413. C2×D15C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
501. (C2×D3)⋊C4C4×D5semidirect
597. C2×C4⋊C4D3×D5semidirect
746. C2×D5#893semidirect
824. C3×C5#2358semidirect
971. C5#74596semidirect
1019. C3#10607567semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#914762
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×C4×#12022
C5×#49902
C3×#652782
#117489182
#117489092
#117489042
#117488842
#117488812
#117488722
#117487942
#117487292
#106075673
#745965