Finite Group Databasebeta

← #14328155

Subgroups — #14328155

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×#91771C211yesmaximal, characteristic
2C2×#91561C211yesmaximal, characteristic, complemented
3C2×#91556C211yesmaximal, characteristic, complemented
4C22×#6667C211yesmaximal, characteristic, complemented
5C2×#91418C211yesmaximal, characteristic, complemented
6C5×#4950C211yesmaximal, characteristic, complemented
7C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#11749494C211yesmaximal, characteristic, complemented
9#11748904C211yesmaximal, characteristic, complemented
10#11748904C211yesmaximal, characteristic, complemented
11#11748902C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13#11748829C211yesmaximal, characteristic, complemented
14#11748768C211yesmaximal, characteristic, complemented
15#11748685C211yesmaximal, characteristic, complemented
16#10606327—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×#1200C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29#91771C418yescomplemented
30C2×C5×#217C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36#91561—24no—
37#91556—24no—
38C2×#6669C2211yescharacteristic, complemented
39C2×#6667—24no—
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic, complemented
47C2×#6667C2211yescharacteristic, complemented
48C2×#6667C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91418—24no—
51C5×C3⋊#95C2211yescharacteristic, complemented
52C5×C3⋊#95C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#73577—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×#685—31no—
60C2×#4039—31no—
61C2×#4028—31no—
62C2×D5×C22⋊C4—31no—
63C5×#385—31no—
64#65279—31no—
65#65278—31no—
66#65277—31no—
67#65247—31no—
68C22⋊C4×Dic5D311yescharacteristic, complemented
69#64958—31no—
70#64955—31no—
71#64954—31no—
72#64954—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—22no—
77C23×D15—22no—
78C23×D15—41no—
79C23×D15—41no—
80C23×D15C2×C414yescomplemented
81C23×D15C2311yescharacteristic
82C23×D15C2311yescharacteristic
83C23×D15C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—22no—
87C2×#1220—22no—
88C2×#1220C2×C414yescomplemented
89C22×Dic15C2311yescharacteristic
90C2×D60—22no—
91C2×D60—22no—
92C2×D60—41no—
93C2×D60—41no—
94C2×D60C2×C414yescomplemented
95C2×D60C2×C414yescomplemented
96C22×C5×Dic3—22no—
97C22×C5×Dic3—22no—
98C22×C5×Dic3—41no—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C3×Dic5—22no—
104C22×C3×Dic5—22no—
105C22×C3×Dic5—41no—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×#1200—22no—
111C2×#1200—22no—
112C2×#1200—22no—
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—22no—
116C2×#1200—41no—
117C2×#1200—41no—
118C2×#1200—41no—
119C3×C5×C22⋊C4C2×C414yescomplemented
120#6714C2×C414yescomplemented
121#6714C2×C414yescomplemented
122C5×#217—22no—
123C5×C4⋊Dic3—22no—
124C5×C4⋊Dic3—41no—
125C3×C22⋊Dic5D414yescomplemented
126C3×C4×Dic5—22no—
127C3×C4×Dic5—41no—
128#6669—22no—
129#6667—22no—
130#6667—22no—
131#6667—22no—
132#6667—22no—
133#6667—22no—
134#6667—22no—
135#6667—22no—
136#6667—41no—
137#6667D414yescomplemented
138Dic3×Dic5—22no—
139C22×(C2×D3)⋊C4—51no—
140C2×#882—51no—
141C2×#67⋊C4—51no—
142C2×D3×C22⋊C4—51no—
143C2×C4×D12—51no—
144C3×C4×C22⋊C4—51no—
145#5213—51no—
146#4950D511yescharacteristic, complemented
147#4940—51no—
148#4939—51no—
149C4×(C2×D3)⋊C4—51no—
150#4670—51no—
151#4668—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C23×Dic5C2×D311yescharacteristic
158C22×D20—31no—
159C22×D20—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
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—31no—
179C2×#685—31no—
180C2×#685—64no—
181C2×#683—31no—
182C2×C4×Dic5—31no—
183C2×C4×Dic5C2×D311yescharacteristic, complemented
184C2×C4×Dic5C2×D311yescharacteristic, complemented
185#4039—64no—
186#4028—38no—
187D5×C22⋊C4—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×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—28no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—28no—
221C22×D15—44no—
222C22×D15—44no—
223C22×D15—44no—
224C22×D15—44no—
225C22×D15—44no—
226C22×D15C22×C412yes—
227C22×D15C22×C412yes—
228C22×D15C22×C412yes—
229C22×D15C2×D412yes—
230C22×D15#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—
237#1220—28no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15C22×C412yes—
241D60—28no—
242D60—44no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
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—44no—
255C2×C5×Dic3C2×D412yes—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
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—44no—
266C2×C3×Dic5C2×D412yes—
267C2×C3×Dic5C2×D412yes—
268C2×C3×Dic5C2×D412yes—
269#1200—44no—
270#1200—44no—
271#1200—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C23×Dic3C2×D511yescharacteristic
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4C2×D511yescharacteristic
283C2×C3×C42—51no—
284C2×C3×C42—51no—
285C2×#217C2×D511yescharacteristic
286C2×(C2×D3)⋊C4—51no—
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—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—104no—
298C2×C4⋊Dic3C2×D511yescharacteristic, complemented
299C2×C4⋊Dic3C2×D511yescharacteristic, complemented
300C2×Dic3⋊C4—51no—
301C2×C4×Dic3—51no—
302#882—58no—
303#67⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—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—31no—
314C23×D5—31no—
315C23×D5—31no—
316C23×D5—34no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—62no—
321C23×D5—121no—
322C23×D5—121no—
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—22no—
336C22×Dic5—22no—
337C22×Dic5—31no—
338C22×Dic5—41no—
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
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—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C4⋊C4—121no—
360C5×C22⋊C4—62no—
361C5×C22⋊C4C4×D314yescomplemented
362C22⋊Dic5D1214yescomplemented
363#685—34no—
364#685—34no—
365#685—34no—
366#685—62no—
367#685—62no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—121no—
374#683—62no—
375C4×Dic5—22no—
376C4×Dic5—41no—
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—151no—
387#386—151no—
388#386—151no—
389#385—31no—
390#385—151no—
391C4×C22⋊C4—51no—
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—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—416no—
420C2×D15—41no—
421C2×D15—41no—
422C2×D15—41no—
423C2×D15—41no—
424C2×D15—41no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432C3×Dic5—22no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C5×Dic3—22no—
437C5×Dic3—41no—
438C5×Dic3—41no—
439C5×Dic3—41no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3—51no—
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—102no—
449C23×D3—201no—
450C23×D3—201no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—102no—
456C22×C3×C4—102no—
457C22×C3×C4—201no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—102no—
462C2×#67—102no—
463C22×Dic3—22no—
464C22×Dic3—22no—
465C22×Dic3—41no—
466C22×Dic3—51no—
467C22×Dic3C22×D511yescharacteristic
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×C22⋊C4—54no—
487C3×C22⋊C4C4×D514yescomplemented
488C3×C42—102no—
489C3×C42—201no—
490#217—22no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—102no—
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—102no—
501(C2×D3)⋊C4—201no—
502C4⋊Dic3—22no—
503C4⋊Dic3—41no—
504Dic3⋊C4—102no—
505C4×Dic3—102no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5C2×C4×D312yes—
511C23×C5C2×D1212yes—
512C23×C5#23512yes—
513C23×C5C23×D311yescharacteristic
514C22×D5—32no—
515C22×D5—32no—
516C22×D5—32no—
517C22×D5—32no—
518C22×D5—32no—
519C22×D5—68no—
520C22×D5—61no—
521C22×D5—61no—
522C22×D5—61no—
523C22×D5—61no—
524C22×D5—68no—
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—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5—124no—
541C22×D5—124no—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—32no—
547C2×C4×C5—61no—
548C2×C4×C5—61no—
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×C5C2×C4×D312yes—
560C2×C4×C5C2×C4×D312yes—
561C22⋊D5—68no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—32no—
572C2×Dic5—44no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5C2×D1212yes—
576C2×Dic5C2×D1212yes—
577C2×Dic5D3×D412yes—
578D20—68no—
579D20—124no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—151no—
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—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—151no—
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—51no—
615C2×C42—51no—
616C2×C42—151no—
617#95—31no—
618#95—31no—
619#95—51no—
620#95—51no—
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—24no—
632D15—42no—
633D15—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3C2×C4×D512yes—
639C23×C3D4×D512yes—
640C23×C3#71312yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—52no—
643C22×D3—52no—
644C22×D3—52no—
645C22×D3—52no—
646C22×D3—52no—
647C22×D3—108no—
648C22×D3—101no—
649C22×D3—101no—
650C22×D3—101no—
651C22×D3—101no—
652C22×D3—101no—
653C22×D3—101no—
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—108no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—52no—
675C2×C3×C4—52no—
676C2×C3×C4—52no—
677C2×C3×C4—101no—
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×C4C2×C4×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—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—44no—
702C2×Dic3—52no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3D4×D512yes—
706D12—108no—
707D12—204no—
708C4×D3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5C4×D1214yescomplemented
718C22×C5C22×C4×D311yescharacteristic
719C22×C5C22×D1211yescharacteristic
720C22×C5C2×#23511yescharacteristic
721C22×C5C2×D3×D411yescharacteristic
722C22×C5#100411yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5#100911yescharacteristic
725C2×D5—34no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—1216no—
739C2×D5—121no—
740C2×D5—121no—
741C2×D5—121no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—121no—
751C4×C5—121no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—22no—
755Dic5—22no—
756Dic5—41no—
757Dic5—62no—
758C24—151no—
759C24—151no—
760C24—151no—
761C24—154no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
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—51no—
785C22×C4—51no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—201no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—601no—
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—54no—
808C22⋊C4—62no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
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⋊C4#120014yescomplemented
821C42—102no—
822C42—201no—
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#403914yescomplemented
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3C2×#71311yescharacteristic
837C22×C3D5×#4111yescharacteristic
838C22×C3#414911yescharacteristic
839C2×D3—54no—
840C2×D3—102no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—102no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—102no—
852C2×D3—2016no—
853C2×D3—201no—
854C2×D3—201no—
855C2×D3—201no—
856C2×D3—201no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—41no—
869Dic3—41no—
870Dic3—41no—
871Dic3—102no—
872C2×C5—24no—
873C2×C5C2×C4×D1211yescharacteristic
874C2×C5#549011yescharacteristic
875C2×C5#552711yescharacteristic
876C2×C5C4×D3×D411yescharacteristic
877C2×C5#554511yescharacteristic
878C2×C5D4×D1211yescharacteristic
879C2×C5#555411yescharacteristic
880D5—64no—
881D5—122no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—152no—
888C23—152no—
889C23—152no—
890C23—152no—
891C23—152no—
892C23—308no—
893C23—301no—
894C23—301no—
895C23—301no—
896C23—301no—
897C23—308no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—604no—
911C23—604no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23#677312yes—
916C23D5×D1212yes—
917C23C2×#120012yes—
918C23C22×D3×D511yescharacteristic
919D4—308no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—52no—
928C2×C4—52no—
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—61no—
940C2×C4—61no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—101no—
948C2×C4—101no—
949C2×C4—101no—
950C2×C4—124no—
951C2×C4—152no—
952C2×C4—204no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C2×#120012yes—
959C2×C4C2×#120012yes—
960C2×C3—24no—
961C2×C3C2×#403911yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3#6587911yescharacteristic
964C2×C3#6592411yescharacteristic
965C2×C3#6596411yescharacteristic
966C2×C3#6597111yescharacteristic
967C2×C3#6598811yescharacteristic
968D3—104no—
969D3—202no—
970D3—202no—
971C5#7357711yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—154no—
979C22—302no—
980C22—302no—
981C22—302no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—302no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—6016no—
992C22—601no—
993C22—601no—
994C22—601no—
995C22—601no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22#9141814yescomplemented
1001C22C2×#677311yescharacteristic
1002C22C2×D5×D1211yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22#9202411yescharacteristic
1005C22#9202611yescharacteristic
1006C22#9202711yescharacteristic
1007C22C22×#120011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—102no—
1012C4—102no—
1013C4—102no—
1014C4—121no—
1015C4—121no—
1016C4—121no—
1017C4—201no—
1018C4—302no—
1019C3#1060632711yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—304no—
1022C2—602no—
1023C2—602no—
1024C2#1175303411yescharacteristic
1025C2#1175307311yescharacteristic
1026C2#1175325411yescharacteristic
1027C2#1175326611yescharacteristic
1028C2C2×#9141811yescharacteristic
1029C2D4×#120011yescharacteristic
1030C2#1175492211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91771C2
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×#91561C2semidirect
3. C2×#91556C2semidirect
4. C22×#6667C2semidirect
5. C2×#91418C2semidirect
6. C5×#4950C2semidirect
7. C3×C22⋊C4×Dic5C2semidirect
8. #11749494C2semidirect
9. #11748904C2semidirect
10. #11748904C2semidirect
11. #11748902C2semidirect
12. #11748875C2semidirect
13. #11748829C2semidirect
14. #11748768C2semidirect
15. #11748685C2semidirect
25. C22×#1200C22semidirect
29. #91771C4semidirect
31. C2×C5×C4⋊Dic3C22semidirect
32. C2×C5×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C2×C3×C4×Dic5C22semidirect
38. C2×#6669C22semidirect
46. C2×#6667C22semidirect
47. C2×#6667C22semidirect
48. C2×#6667C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. C5×C3⋊#95C22semidirect
52. C5×C3⋊#95C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
68. C22⋊C4×Dic5D3semidirect
80. C23×D15C2×C4semidirect
88. C2×#1220C2×C4semidirect
94. C2×D60C2×C4semidirect
95. C2×D60C2×C4semidirect
119. C3×C5×C22⋊C4C2×C4semidirect
120. #6714C2×C4semidirect
121. #6714C2×C4semidirect
125. C3×C22⋊Dic5D4semidirect
137. #6667D4semidirect
146. #4950D5semidirect
183. C2×C4×Dic5C2×D3semidirect
184. C2×C4×Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
298. C2×C4⋊Dic3C2×D5semidirect
299. C2×C4⋊Dic3C2×D5semidirect
310. C3⋊#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
361. C5×C22⋊C4C4×D3semidirect
362. C22⋊Dic5D12semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×D15C4×D4semidirect
487. C3×C22⋊C4C4×D5semidirect
717. C22×C5C4×D12semidirect
820. C22⋊C4#1200semidirect
824. C3×C5#2358semidirect
831. C22×C3#4039semidirect
971. C5#73577semidirect
1000. C22#91418semidirect
1019. C3#10606327semidirect

Maximal subgroups

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

subgroupindex
C2×#917712
C2×#915612
C2×#915562
C22×#66672
C2×#914182
C5×#49502
C3×C22⋊C4×Dic52
#117494942
#117489042
#117489022
#117488752
#117488292
#117487682
#117486852
#106063273
#735775