Finite Group Databasebeta

← #14328156

Subgroups — #14328156

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×C5×#882C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#91435C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
7C3×#65239C211yesmaximal, characteristic, complemented
8#11749501C211yesmaximal, characteristic, complemented
9#11748901C211yesmaximal, characteristic, complemented
10#11748901C211yesmaximal, characteristic, complemented
11#11748897C211yesmaximal, characteristic, complemented
12#11748886C211yesmaximal, characteristic, complemented
13#11748797C211yesmaximal, characteristic, complemented
14#11748794C211yesmaximal, characteristic, complemented
15#11748675C211yesmaximal, characteristic, complemented
16#10614310—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C4×Dic15C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×#882C418yescomplemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
36D3×C22⋊Dic5—24no—
37Dic5×#67—24no—
38C2×Dic3⋊Dic5C2211yescharacteristic, complemented
39C2×(C2×D3)⋊Dic5—24no—
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×Dic3×Dic5C2211yescharacteristic, complemented
50#91435—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#74596—51nomaximal, Hall
58C2×C5×#120—31no—
59C22×C22⋊Dic5—31no—
60C22×C22⋊Dic5—31no—
61C2×D4×Dic5—31no—
62C2×D4×Dic5—31no—
63#65510—31no—
64#65509—31no—
65#65509—31no—
66#65509—31no—
67#65240—31no—
68#65240—31no—
69#65239—31no—
70#65239D311yescharacteristic, complemented
71C22⋊C4×Dic5—31no—
72C22⋊C4×Dic5—31no—
73C24×C3×C5C2311yescharacteristic
74C23×C5×D3—22no—
75C23×C5×D3—22no—
76C23×C5×D3—22no—
77C23×C5×D3—22no—
78C23×C5×D3—41no—
79C23×C5×D3—41no—
80C23×C5×D3C2×C414yescomplemented
81C23×C5×D3C2311yescharacteristic
82C23×C5×D3C2311yescharacteristic
83C23×C5×D3C2311yescharacteristic
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
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C2×C5×#67C2×C414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C2×C5×D12—22no—
98C2×C5×D12—22no—
99C2×C5×D12—41no—
100C2×C5×D12—41no—
101C2×C5×D12C2×C414yescomplemented
102C2×C5×D12C2×C414yescomplemented
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×D3×Dic5—22no—
111C2×D3×Dic5—22no—
112C2×D3×Dic5—22no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—22no—
116C2×D3×Dic5—41no—
117C2×D3×Dic5—41no—
118C2×D3×Dic5—41no—
119C3×C5×C22⋊C4C2×C414yescomplemented
120#6719D414yescomplemented
121C4×Dic15—22no—
122C4×Dic15—41no—
123C5×(C2×D3)⋊C4C2×C414yescomplemented
124C5×(C2×D3)⋊C4C2×C414yescomplemented
125C3×C22⋊Dic5—22no—
126C3×C4⋊Dic5—22no—
127C3×C4⋊Dic5—41no—
128Dic3⋊Dic5—22no—
129(C2×D3)⋊Dic5—22no—
130(C2×D3)⋊Dic5—22no—
131(C2×D3)⋊Dic5—22no—
132(C2×D3)⋊Dic5—22no—
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5—22no—
135(C2×D3)⋊Dic5—22no—
136(C2×D3)⋊Dic5—41no—
137(C2×D3)⋊Dic5D414yescomplemented
138Dic3×Dic5—22no—
139C2×C4×#67—51no—
140C22×(C2×D3)⋊C4—51no—
141C2×#893—51no—
142C2×#882D511yescharacteristic
143C2×D3×C22⋊C4—51no—
144C3×#385—51no—
145#4990—51no—
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—
154C25×C5—31no—
155C22×C5×D4—31no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C23×Dic5—31no—
159C23×Dic5—31no—
160C23×Dic5—31no—
161C23×Dic5—31no—
162C23×Dic5C2×D311yescharacteristic
163C5×#120—38no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5—31no—
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—64no—
178C2×C22⋊Dic5—64no—
179C2×C22⋊Dic5C2×D311yescharacteristic
180D4×Dic5—64no—
181D4×Dic5—64no—
182C2×C4⋊Dic5—31no—
183C2×C4⋊Dic5C2×D311yescharacteristic, complemented
184C2×C4⋊Dic5C2×D311yescharacteristic, complemented
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188#3963—31no—
189#3963—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×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—28no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
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×D3—21no—
217C22×C5×D3—21no—
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3—28no—
221C22×C5×D3—44no—
222C22×C5×D3—44no—
223C22×C5×D3—44no—
224C22×C5×D3—44no—
225C22×C5×D3—44no—
226C22×C5×D3C22×C412yes—
227C22×C5×D3C22×C412yes—
228C22×C5×D3C22×C412yes—
229C22×C5×D3C2×D412yes—
230C22×C5×D3#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—44no—
247C2×Dic15C2×D412yes—
248C2×Dic15C2×D412yes—
249C2×Dic15C2×D412yes—
250C5×#67—28no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3C22×C412yes—
254C5×D12—28no—
255C5×D12—44no—
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—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5—44no—
268C2×C3×Dic5C2×D412yes—
269D3×Dic5—44no—
270D3×Dic5—44no—
271D3×Dic5—44no—
272C24×D3C2×D511yescharacteristic
273C23×C3×C4—51no—
274C22×#67C2×D511yescharacteristic
275C23×Dic3—51no—
276C22×D12C2×D511yescharacteristic
277C22×D12C2×D511yescharacteristic
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4C2×D511yescharacteristic
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—51no—
296C2×(C2×D3)⋊C4—104no—
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×(C2×D3)⋊C4C2×D511yescharacteristic
299C2×Dic3⋊C4—51no—
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303#893—104no—
304#882Dic518yescomplemented
305D3×C22⋊C4—104no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5—31no—
314C24×C5—31no—
315C24×C5—34no—
316C24×C5—62no—
317C24×C5—62no—
318C24×C5—62no—
319C24×C5—62no—
320C24×C5—121no—
321C24×C5—121no—
322C24×C5C22×D311yescharacteristic
323C2×C5×D4—34no—
324C2×C5×D4—34no—
325C2×C5×D4—34no—
326C2×C5×D4—62no—
327C2×C5×D4—62no—
328C2×C5×D4—62no—
329C2×C5×D4—62no—
330C2×C5×D4—121no—
331C2×C5×D4—121no—
332C22×C4×C5—31no—
333C22×C4×C5C22×D311yescharacteristic
334C22×C4×C5C22×D311yescharacteristic
335C22×Dic5—22no—
336C22×Dic5—22no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—41no—
342C22×Dic5—62no—
343C22×Dic5—62no—
344C22×Dic5—62no—
345C22×Dic5—62no—
346C22×Dic5—62no—
347C22×Dic5—62no—
348C22×Dic5—62no—
349C22×Dic5—62no—
350C22×Dic5—121no—
351C22×Dic5—121no—
352C22×Dic5—121no—
353C22×Dic5—121no—
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D311yescharacteristic
357C22×Dic5C22×D311yescharacteristic
358C5×C22⋊C4—34no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4C4×D314yescomplemented
361C22⋊Dic5—22no—
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364C22⋊Dic5—62no—
365C22⋊Dic5—62no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369C22⋊Dic5—62no—
370C22⋊Dic5—62no—
371C22⋊Dic5—121no—
372C4⋊Dic5—22no—
373C4⋊Dic5—41no—
374C4⋊Dic5—62no—
375C4×Dic5—62no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—31no—
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—51no—
390#385—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5C4×D414yescomplemented
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×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×D3—22no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—416no—
420C2×C5×D3—41no—
421C2×C5×D3—41no—
422C2×C5×D3—41no—
423C2×C5×D3—41no—
424C2×C5×D3—41no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—22no—
433Dic15—22no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C3×Dic5—41no—
438C3×Dic5—41no—
439C5×Dic3—22no—
440C24×C3C22×D511yescharacteristic
441C23×D3—22no—
442C23×D3—22no—
443C23×D3—22no—
444C23×D3—22no—
445C23×D3—41no—
446C23×D3—41no—
447C23×D3C2×Dic514yescomplemented
448C23×D3C22×D511yescharacteristic
449C23×D3C22×D511yescharacteristic
450C23×D3C22×D511yescharacteristic
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—22no—
461C2×#67—22no—
462C2×#67C2×Dic514yescomplemented
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—102no—
468C22×Dic3—102no—
469C22×Dic3—201no—
470C22×Dic3C22×D511yescharacteristic
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—41no—
474C2×D12—41no—
475C2×D12C2×Dic514yescomplemented
476C2×D12C2×Dic514yescomplemented
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—102no—
487C3×C4⋊C4—201no—
488C3×C22⋊C4—102no—
489C3×C22⋊C4C2×Dic514yescomplemented
490#217—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—102no—
493(C2×D3)⋊C4—102no—
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—201no—
500(C2×D3)⋊C4C2×Dic514yescomplemented
501(C2×D3)⋊C4C2×Dic514yescomplemented
502Dic3⋊C4—102no—
503C4×Dic3—102no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—32no—
511C23×C5—32no—
512C23×C5—32no—
513C23×C5—32no—
514C23×C5—32no—
515C23×C5—68no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5—68no—
521C23×C5—61no—
522C23×C5—61no—
523C23×C5—61no—
524C23×C5—61no—
525C23×C5—61no—
526C23×C5—61no—
527C23×C5—61no—
528C23×C5—61no—
529C23×C5—61no—
530C23×C5—61no—
531C23×C5—61no—
532C23×C5—61no—
533C23×C5—124no—
534C23×C5—124no—
535C23×C5—124no—
536C23×C5—124no—
537C23×C5—124no—
538C23×C5C2×C4×D312yes—
539C23×C5D3×D412yes—
540C23×C5#23912yes—
541C23×C5C23×D311yescharacteristic
542C5×D4—68no—
543C5×D4—68no—
544C5×D4—124no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—32no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5C2×C4×D312yes—
553C2×C4×C5C2×C4×D312yes—
554C2×Dic5—21no—
555C2×Dic5—21no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—32no—
566C2×Dic5—32no—
567C2×Dic5—32no—
568C2×Dic5—44no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—124no—
579C2×Dic5—124no—
580C2×Dic5—124no—
581C2×Dic5—124no—
582C2×Dic5D3×D412yes—
583C25—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C23×C4—51no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592#120—38no—
593C4×D4—304no—
594C4×D4—304no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
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—151no—
615C2×C42—151no—
616C2×C42—151no—
617#95—51no—
618#95—51no—
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
631C5×D3—24no—
632C5×D3—42no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3D4×D512yes—
639C23×C3#71112yes—
640C23×C3C22×Dic512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—21no—
654C22×D3—21no—
655C22×D3—21no—
656C22×D3—21no—
657C22×D3—21no—
658C22×D3—28no—
659C22×D3—28no—
660C22×D3—44no—
661C22×D3—44no—
662C22×D3—44no—
663C22×D3—44no—
664C22×D3—44no—
665C22×D3D4×D512yes—
666C22×D3#71112yes—
667C22×D3C22×Dic512yes—
668C22×D3C22×Dic512yes—
669C22×D3C22×Dic512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—52no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
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×C4C22×Dic512yes—
688C2×C3×C4C22×Dic512yes—
689#67—28no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—52no—
693C2×Dic3—52no—
694C2×Dic3—52no—
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×Dic3C22×Dic512yes—
706D12—28no—
707D12—44no—
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×C5—34no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—62no—
724C22×C5—62no—
725C22×C5—62no—
726C22×C5—62no—
727C22×C5—62no—
728C22×C5—62no—
729C22×C5—62no—
730C22×C5—1216no—
731C22×C5—121no—
732C22×C5—121no—
733C22×C5—121no—
734C22×C5—121no—
735C22×C5—121no—
736C22×C5—121no—
737C22×C5—121no—
738C22×C5—121no—
739C22×C5#89314yescomplemented
740C22×C5C22×C4×D311yescharacteristic
741C22×C5C2×D3×D411yescharacteristic
742C22×C5C2×D3×D411yescharacteristic
743C22×C5#100411yescharacteristic
744C22×C5C2×#23911yescharacteristic
745C22×C5D3×#4111yescharacteristic
746C22×C5#100911yescharacteristic
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750Dic5—22no—
751Dic5—41no—
752Dic5—41no—
753Dic5—41no—
754Dic5—62no—
755Dic5—62no—
756Dic5—62no—
757Dic5—121no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—34no—
762C24—62no—
763C24—62no—
764C24—62no—
765C24—62no—
766C24—121no—
767C24—121no—
768C24C2×D3×D511yescharacteristic
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—121no—
777C2×D4—121no—
778C22×C4—31no—
779C22×C4—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—102no—
784C22×C4—102no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—201no—
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—102no—
805C4⋊C4—201no—
806C4⋊C4—302no—
807C22⋊C4—34no—
808C22⋊C4—34no—
809C22⋊C4—102no—
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⋊C4D3×Dic514yescomplemented
821C42—302no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3D4×Dic514yescomplemented
832C22×C3C2×D4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×#71111yescharacteristic
835C22×C3C2×#71111yescharacteristic
836C22×C3#414411yescharacteristic
837C22×C3#414411yescharacteristic
838C22×C3C23×Dic511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—416no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3D4×Dic514yescomplemented
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864C3×C4—201no—
865C3×C4—201no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—102no—
869Dic3—102no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—64no—
874C2×C5—122no—
875C2×C5—122no—
876C2×C5C2×#89311yescharacteristic
877C2×C5C4×D3×D411yescharacteristic
878C2×C5#554511yescharacteristic
879C2×C5#559011yescharacteristic
880C2×C5#563011yescharacteristic
881C2×C5#563711yescharacteristic
882C2×C5#565411yescharacteristic
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—32no—
889C23—32no—
890C23—32no—
891C23—32no—
892C23—68no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—68no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—124no—
911C23—124no—
912C23—124no—
913C23—124no—
914C23—124no—
915C23#676812yes—
916C23#677712yes—
917C23C2×D3×Dic512yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—68no—
921D4—124no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—52no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—152no—
942C2×C4—152no—
943C2×C4—152no—
944C2×C4—204no—
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×D3×Dic512yes—
959C2×C4C2×D3×Dic512yes—
960C2×C3—24no—
961C2×C3#6592111yescharacteristic
962C2×C3#6592411yescharacteristic
963C2×C3#6592511yescharacteristic
964C2×C3#6592511yescharacteristic
965C2×C3C2×D4×Dic511yescharacteristic
966C2×C3C2×D4×Dic511yescharacteristic
967C2×C3#6613211yescharacteristic
968D3—24no—
969D3—42no—
970D3—42no—
971C5#7459611yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—34no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—1216no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—121no—
997C22—121no—
998C22—121no—
999C22—121no—
1000C22#9143514yescomplemented
1001C22C2×#676811yescharacteristic
1002C22C2×#677711yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D3×#71111yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202711yescharacteristic
1007C22C22×D3×Dic511yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—102no—
1012C4—201no—
1013C4—201no—
1014C4—201no—
1015C4—302no—
1016C4—302no—
1017C4—302no—
1018C4—601no—
1019C3#1061431011yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—64no—
1022C2—122no—
1023C2—122no—
1024C2#1175285711yescharacteristic
1025C2#1175299511yescharacteristic
1026C2#1175322511yescharacteristic
1027C2#1175327311yescharacteristic
1028C2C2×#9143511yescharacteristic
1029C2D3×D4×Dic511yescharacteristic
1030C2#1175491411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#882C2
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×D3×C22⋊Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. C22×(C2×D3)⋊Dic5C2semidirect
5. C2×#91435C2semidirect
6. C22⋊C4×Dic15C2semidirect
7. C3×#65239C2semidirect
8. #11749501C2semidirect
9. #11748901C2semidirect
10. #11748901C2semidirect
11. #11748897C2semidirect
12. #11748886C2semidirect
13. #11748797C2semidirect
14. #11748794C2semidirect
15. #11748675C2semidirect
25. C22×D3×Dic5C22semidirect
28. C2×C4×Dic15C22semidirect
29. C2×C4×Dic15C22semidirect
32. C5×#882C4semidirect
34. C2×C3×C4⋊Dic5C22semidirect
35. C2×C3×C4⋊Dic5C22semidirect
38. C2×Dic3⋊Dic5C22semidirect
46. C2×(C2×D3)⋊Dic5C22semidirect
47. C2×(C2×D3)⋊Dic5C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
49. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
70. #65239D3semidirect
80. C23×C5×D3C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
101. C2×C5×D12C2×C4semidirect
102. C2×C5×D12C2×C4semidirect
119. C3×C5×C22⋊C4C2×C4semidirect
120. #6719D4semidirect
123. C5×(C2×D3)⋊C4C2×C4semidirect
124. C5×(C2×D3)⋊C4C2×C4semidirect
137. (C2×D3)⋊Dic5D4semidirect
183. C2×C4⋊Dic5C2×D3semidirect
184. C2×C4⋊Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
304. #882Dic5semidirect
360. C5×C22⋊C4C4×D3semidirect
399. C22×C3×C5C4×D4semidirect
428. C2×C5×D3C4×D4semidirect
447. C23×D3C2×Dic5semidirect
462. C2×#67C2×Dic5semidirect
475. C2×D12C2×Dic5semidirect
476. C2×D12C2×Dic5semidirect
489. C3×C22⋊C4C2×Dic5semidirect
500. (C2×D3)⋊C4C2×Dic5semidirect
501. (C2×D3)⋊C4C2×Dic5semidirect
739. C22×C5#893semidirect
820. C22⋊C4D3×Dic5semidirect
824. C3×C5#2358semidirect
831. C22×C3D4×Dic5semidirect
860. C2×D3D4×Dic5semidirect
971. C5#74596semidirect
1000. C22#91435semidirect
1019. C3#10614310semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8822
C2×D3×C22⋊Dic52
C2×Dic5×#672
C22×(C2×D3)⋊Dic52
C2×#914352
C22⋊C4×Dic152
C3×#652392
#117495012
#117489012
#117488972
#117488862
#117487972
#117487942
#117486752
#106143103
#745965