Finite Group Databasebeta

← #14329495

Subgroups — #14329495

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91451C211yesmaximal, characteristic
2C2×#91446C211yesmaximal, characteristic, complemented
3C2×C4×#1203C211yesmaximal, characteristic, complemented
4C2×#91406C211yesmaximal, characteristic, complemented
5C2×#91405C211yesmaximal, characteristic, complemented
6#11750766C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64938C211yesmaximal, characteristic, complemented
9#11748909C211yesmaximal, characteristic, complemented
10#11748909C211yesmaximal, characteristic, complemented
11#11748908C211yesmaximal, characteristic, complemented
12#11748908C211yesmaximal, characteristic, complemented
13#11748904C211yesmaximal, characteristic, complemented
14#11748901C211yesmaximal, characteristic, complemented
15#11748638C211yesmaximal, characteristic, complemented
16#10606410—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48#91451C418yescomplemented
49#91446—24no—
50C4×#1203—24no—
51#91406—24no—
52#91405—24no—
53C3×C5×#95C2211yescharacteristic
54#91115C2211yescharacteristic
55C5×C3⋊#95C2211yescharacteristic
56C3×#3963C2211yescharacteristic
57#73653—51nomaximal, Hall
58C2×#4086—31no—
59C2×C4×C22⋊D5—31no—
60C2×C4×C22⋊D5—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#386—31no—
64#65509—31no—
65#65246—31no—
66#65246—31no—
67#65246—31no—
68#65246—31no—
69#64954—31no—
70#64954—31no—
71#64938—31no—
72#64938D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C2×D60—41no—
83C2×D60—41no—
84C2×D60C2×C414yescomplemented
85C2×C4×D15—22no—
86C2×C4×D15—22no—
87C2×C4×D15—41no—
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C5×D12—41no—
91C2×C5×D12—41no—
92C2×C5×D12C2×C414yescomplemented
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—22no—
95C2×C4×C5×D3—41no—
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×#1203—22no—
101C2×#1203—22no—
102C2×#1203—22no—
103C2×#1203—22no—
104C2×#1203—22no—
105C2×#1203—22no—
106C2×#1203—22no—
107C2×#1203—22no—
108C2×#1203C2×C414yescomplemented
109C2×#1203C2×C414yescomplemented
110C2×#1203C2×C414yescomplemented
111C2×#1203C2×C414yescomplemented
112C2×#1200—22no—
113C2×#1200—22no—
114C2×#1200—41no—
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—41no—
118#6714—22no—
119#6714—22no—
120#6714—41no—
121C5×(C2×D3)⋊C4—22no—
122C5×(C2×D3)⋊C4—22no—
123C5×(C2×D3)⋊C4—41no—
124C3×#683—22no—
125C3×#683D414yescomplemented
126C3×C4×Dic5—22no—
127C3×C4×Dic5—22no—
128C3×C4×Dic5C2×C414yescomplemented
129#6668—22no—
130#6668D414yescomplemented
131#6667—22no—
132#6667—22no—
133#6667—41no—
134(C2×D3)⋊Dic5—22no—
135(C2×D3)⋊Dic5—22no—
136(C2×D3)⋊Dic5—41no—
137Dic3×Dic5—22no—
138Dic3×Dic5—22no—
139C2×#893—51no—
140C2×#893—51no—
141C2×#874—51no—
142C2×C4×D12—51no—
143C2×C4×D12—51no—
144C3×C4×C4⋊C4—51no—
145#4988—51no—
146#4988—51no—
147#4939—51no—
148#4939—51no—
149C4×C4⋊Dic3—51no—
150#4665—51no—
151#4665—51no—
152#4665—51no—
153#4665D511yescharacteristic, complemented
154C22×C5×D4—31no—
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5—31no—
161C22×D20—31no—
162C22×C4×D5—31no—
163C22×C4×D5—31no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170#4086—38no—
171C4×C22⋊D5—64no—
172C4×C22⋊D5—64no—
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#683—31no—
180C2×#683—31no—
181C2×#683C2×D311yescharacteristic
182C2×#683C2×D311yescharacteristic
183C2×C4×Dic5—31no—
184C2×C4×Dic5—31no—
185C2×C4×Dic5C2×D311yescharacteristic
186C2×C4×Dic5C2×D311yescharacteristic
187C2×C4×Dic5C2×D311yescharacteristic
188#4027—64no—
189#4027—64no—
190C5×#95—31no—
191C5×#95C2×D311yescharacteristic
192#3963—31no—
193#3963C2×D311yescharacteristic
194#2366—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×D15—21no—
207C22×D15—21no—
208C22×D15C22×C412yes—
209C22×D15C22×C412yes—
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—21no—
221C22×C5×D3—21no—
222C22×C5×D3C22×C412yes—
223C22×C5×D3C22×C412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5C22×C412yes—
232C2×C3×C4×C5C2×D412yes—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15C2×D412yes—
239D60—44no—
240C4×D15—44no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3C2×D412yes—
247C5×D12—44no—
248C4×C5×D3—44no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5C22×C412yes—
255C2×C3×Dic5C22×C412yes—
256C2×C3×Dic5C2×D412yes—
257C2×C3×Dic5C2×D412yes—
258C2×C3×Dic5C2×D412yes—
259C2×C3×Dic5#4112yes—
260C2×C3×Dic5#4112yes—
261#1203—28no—
262#1203—28no—
263#1203—28no—
264#1203—28no—
265#1200—44no—
266D3×Dic5—44no—
267C22×D12—51no—
268C22×D12—51no—
269C22×D12—51no—
270C22×D12—51no—
271C22×D12—51no—
272C22×D12C2×D511yescharacteristic
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C22×C4×D3C2×D511yescharacteristic
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C42—51no—
280C2×C3×C42—51no—
281C2×C3×C42—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
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)⋊C4C2×D511yescharacteristic
292C2×(C2×D3)⋊C4C2×D511yescharacteristic
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×C4⋊Dic3—51no—
295C2×C4⋊Dic3—51no—
296C2×C4×Dic3—51no—
297C2×C4×Dic3—51no—
298#893—104no—
299#893—104no—
300#874—58no—
301C4×D12—104no—
302C4×D12—104no—
303C3×#95—51no—
304C3×#95C2×D511yescharacteristic
305C3⋊#95—51no—
306C3⋊#95C2×D511yescharacteristic
307C24×C5—31no—
308C24×C5—31no—
309C23×D5—31no—
310C23×D5—31no—
311C2×C5×D4—34no—
312C2×C5×D4—121no—
313C2×C5×D4—121no—
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—62no—
317C22×C4×C5—62no—
318C22×C4×C5—121no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—34no—
323C2×C22⋊D5—34no—
324C2×C22⋊D5—34no—
325C2×C22⋊D5—34no—
326C2×C22⋊D5—62no—
327C2×C22⋊D5—62no—
328C2×C22⋊D5—62no—
329C2×C22⋊D5—62no—
330C2×C22⋊D5—62no—
331C2×C22⋊D5—62no—
332C2×C22⋊D5—62no—
333C2×C22⋊D5—62no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—62no—
337C22×Dic5—62no—
338C22×Dic5—121no—
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C2×D20—34no—
344C2×D20—121no—
345C2×D20—121no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—62no—
350C2×C4×D5—121no—
351C2×C4×D5—121no—
352C5×C22⋊C4—62no—
353C5×C22⋊C4—62no—
354C5×C22⋊C4—121no—
355C22⋊Dic5—62no—
356C22⋊Dic5—62no—
357C22⋊Dic5—121no—
358#685—62no—
359#685—62no—
360#685—62no—
361#685—62no—
362#685—121no—
363#685—121no—
364#683—22no—
365#683—34no—
366#683—62no—
367#683D1214yescomplemented
368C4×Dic5—22no—
369C4×Dic5—22no—
370C4×Dic5—62no—
371C4×Dic5—62no—
372C4×Dic5C4×D314yescomplemented
373C2×#127—151no—
374C2×C4×D4—151no—
375C2×C4×D4—151no—
376C2×C4×D4—151no—
377C2×C4×D4—151no—
378#390—151no—
379#390—151no—
380#390—151no—
381#390—151no—
382#386—31no—
383#386—151no—
384#386—151no—
385#386—151no—
386C4×C4⋊C4—51no—
387C4×C4⋊C4—151no—
388C22×C3×C5C23×C411yescharacteristic
389C22×C3×C5C22×D411yescharacteristic
390C22×C3×C5C22×D411yescharacteristic
391C22×C3×C5C2×#4111yescharacteristic
392C22×C3×C5C2×#4111yescharacteristic
393C22×C3×C5H(5,𝔽2)11yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C2×D15—22no—
396C2×D15—22no—
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—41no—
404C2×D15—41no—
405C2×D15—41no—
406C2×D15—41no—
407C2×D15—41no—
408C2×D15—41no—
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—41no—
416C2×C5×D3—41no—
417C2×C5×D3—41no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
420C2×C5×D3—41no—
421C2×C5×D3—41no—
422C2×C5×D3—41no—
423C3×C4×C5—22no—
424C3×C4×C5—22no—
425C3×C4×C5—41no—
426Dic15—22no—
427Dic15—41no—
428C3×Dic5—22no—
429C3×Dic5—41no—
430C3×Dic5C4×D414yescomplemented
431C3×Dic5C4×D414yescomplemented
432C5×Dic3—22no—
433C5×Dic3—41no—
434C23×D3—51no—
435C23×D3—51no—
436C23×D3C22×D511yescharacteristic
437C23×D3C22×D511yescharacteristic
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—51no—
441C22×C3×C4—51no—
442C22×C3×C4C22×D511yescharacteristic
443C22×C3×C4C22×D511yescharacteristic
444C22×C3×C4C22×D511yescharacteristic
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3C22×D511yescharacteristic
448C22×Dic3C22×D511yescharacteristic
449C2×D12—41no—
450C2×D12—41no—
451C2×D12—54no—
452C2×D12—54no—
453C2×D12—54no—
454C2×D12—54no—
455C2×D12—54no—
456C2×D12—102no—
457C2×D12—102no—
458C2×D12—102no—
459C2×D12—102no—
460C2×D12—102no—
461C2×D12—102no—
462C2×D12—102no—
463C2×D12—102no—
464C2×D12—201no—
465C2×D12—201no—
466C2×D12C4×D514yescomplemented
467C2×C4×D3—22no—
468C2×C4×D3—22no—
469C2×C4×D3—41no—
470C2×C4×D3—102no—
471C2×C4×D3—102no—
472C2×C4×D3—102no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3—102no—
476C2×C4×D3—201no—
477C2×C4×D3—201no—
478C2×C4×D3—201no—
479C3×C4⋊C4—54no—
480C3×C4⋊C4—102no—
481C3×C42—54no—
482C3×C42—102no—
483C3×C42—102no—
484(C2×D3)⋊C4—22no—
485(C2×D3)⋊C4—22no—
486(C2×D3)⋊C4—41no—
487(C2×D3)⋊C4—102no—
488(C2×D3)⋊C4—102no—
489(C2×D3)⋊C4—102no—
490(C2×D3)⋊C4—102no—
491(C2×D3)⋊C4—102no—
492(C2×D3)⋊C4—102no—
493(C2×D3)⋊C4—201no—
494(C2×D3)⋊C4—201no—
495(C2×D3)⋊C4—201no—
496C4⋊Dic3—54no—
497C4⋊Dic3—102no—
498C4×Dic3—102no—
499C4×Dic3—102no—
500C23×C5—32no—
501C23×C5—32no—
502C23×C5—61no—
503C23×C5—61no—
504C23×C5—61no—
505C23×C5—61no—
506C23×C5—61no—
507C23×C5—61no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5C23×D311yescharacteristic
515C22×D5—32no—
516C22×D5—32no—
517C22×D5—61no—
518C22×D5—61no—
519C22×D5—61no—
520C22×D5—61no—
521C22×D5—61no—
522C22×D5—61no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C5×D4—124no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—21no—
537C2×C4×C5—32no—
538C2×C4×C5—61no—
539C2×C4×C5—61no—
540C2×C4×C5—61no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—124no—
544C2×C4×C5C2×C4×D312yes—
545C2×C4×C5C2×D1212yes—
546C22⋊D5—68no—
547C22⋊D5—68no—
548C22⋊D5—68no—
549C22⋊D5—68no—
550C2×Dic5—21no—
551C2×Dic5—21no—
552C2×Dic5—21no—
553C2×Dic5—21no—
554C2×Dic5—21no—
555C2×Dic5—32no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—61no—
559C2×Dic5—61no—
560C2×Dic5—61no—
561C2×Dic5—124no—
562C2×Dic5C2×C4×D312yes—
563C2×Dic5C2×C4×D312yes—
564C2×Dic5C2×D1212yes—
565C2×Dic5C2×D1212yes—
566C2×Dic5#23512yes—
567C2×Dic5D3×D412yes—
568C2×Dic5#23912yes—
569D20—124no—
570C4×D5—124no—
571C4×D5—124no—
572C22×D4—31no—
573C22×D4—151no—
574C22×D4—151no—
575C22×D4—151no—
576C22×D4—151no—
577C22×D4—151no—
578C23×C4—31no—
579C23×C4—151no—
580C23×C4—151no—
581C23×C4—151no—
582#127—158no—
583C4×D4—304no—
584C4×D4—304no—
585C4×D4—304no—
586C4×D4—304no—
587C2×C4⋊C4—51no—
588C2×C4⋊C4—51no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—31no—
593C2×C22⋊C4—31no—
594C2×C22⋊C4—151no—
595C2×C22⋊C4—151no—
596C2×C22⋊C4—151no—
597C2×C22⋊C4—151no—
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C42—51no—
604C2×C42—51no—
605C2×C42—51no—
606C2×C42—151no—
607C2×C42—151no—
608#95—31no—
609#95—51no—
610#95—151no—
611#95D3×D511yescharacteristic
612C2×C3×C5C2×C4×D411yescharacteristic
613C2×C3×C5C2×C4×D411yescharacteristic
614C2×C3×C5#51811yescharacteristic
615C2×C3×C5D4211yescharacteristic
616C2×C3×C5#55011yescharacteristic
617C2×C3×C5#55011yescharacteristic
618C2×C3×C5#55911yescharacteristic
619D15—42no—
620D15—42no—
621C5×D3—42no—
622C5×D3—42no—
623C23×C3C23×D511yescharacteristic
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—52no—
637C22×D3—52no—
638C22×D3—101no—
639C22×D3—101no—
640C22×D3—101no—
641C22×D3—101no—
642C22×D3—101no—
643C22×D3—101no—
644C22×D3—101no—
645C22×D3—101no—
646C22×D3—101no—
647C22×D3—101no—
648C22×D3—101no—
649C22×D3—101no—
650C22×D3C2×C4×D512yes—
651C22×D3C2×C4×D512yes—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—52no—
660C2×C3×C4—52no—
661C2×C3×C4—52no—
662C2×C3×C4—52no—
663C2×C3×C4—52no—
664C2×C3×C4—52no—
665C2×C3×C4—52no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4C2×C4×D512yes—
672C2×C3×C4D4×D512yes—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—52no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3—101no—
683C2×Dic3—101no—
684C2×Dic3D4×D512yes—
685D12—44no—
686D12—108no—
687D12—108no—
688D12—108no—
689D12—108no—
690D12—204no—
691C4×D3—44no—
692C4×D3—204no—
693C4×D3—204no—
694C4×D3—204no—
695C22×C5—62no—
696C22×C5—62no—
697C22×C5—62no—
698C22×C5—62no—
699C22×C5—62no—
700C22×C5—62no—
701C22×C5—121no—
702C22×C5—121no—
703C22×C5—121no—
704C22×C5—121no—
705C22×C5—121no—
706C22×C5—121no—
707C22×C5—121no—
708C22×C5—121no—
709C22×C5C22×C4×D311yescharacteristic
710C22×C5C22×D1211yescharacteristic
711C22×C5C2×#23511yescharacteristic
712C22×C5C2×D3×D411yescharacteristic
713C22×C5C2×#23911yescharacteristic
714C22×C5#100911yescharacteristic
715C22×C5#100911yescharacteristic
716C2×D5—62no—
717C2×D5—62no—
718C2×D5—62no—
719C2×D5—62no—
720C2×D5—62no—
721C2×D5—62no—
722C2×D5—121no—
723C2×D5—121no—
724C2×D5—121no—
725C2×D5—121no—
726C2×D5—121no—
727C2×D5—121no—
728C2×D5—121no—
729C2×D5—121no—
730C4×C5—22no—
731C4×C5—22no—
732C4×C5—41no—
733C4×C5—62no—
734C4×C5—121no—
735Dic5—22no—
736Dic5—41no—
737Dic5—62no—
738Dic5—121no—
739Dic5C4×D1214yescomplemented
740Dic5#89314yescomplemented
741C24—31no—
742C24—31no—
743C24—151no—
744C24—151no—
745C2×D4—34no—
746C2×D4—121no—
747C2×D4—121no—
748C2×D4—154no—
749C2×D4—154no—
750C2×D4—154no—
751C2×D4—154no—
752C2×D4—154no—
753C2×D4—302no—
754C2×D4—302no—
755C2×D4—302no—
756C2×D4—302no—
757C2×D4—302no—
758C2×D4—302no—
759C2×D4—302no—
760C2×D4—302no—
761C2×D4—601no—
762C2×D4—601no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—51no—
766C22×C4—51no—
767C22×C4—51no—
768C22×C4—51no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—121no—
772C22×C4—151no—
773C22×C4—151no—
774C22×C4—302no—
775C22×C4—302no—
776C22×C4—302no—
777C22×C4—302no—
778C22×C4—302no—
779C22×C4—302no—
780C22×C4—601no—
781C22×C4—601no—
782C22×C4—601no—
783C22×C4C2×D3×D511yescharacteristic
784C22×C4C2×D3×D511yescharacteristic
785C22×C4C2×D3×D511yescharacteristic
786C4⋊C4—54no—
787C4⋊C4—102no—
788C4⋊C4—154no—
789C4⋊C4—302no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—121no—
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—
802C42—54no—
803C42—102no—
804C42—102no—
805C42—302no—
806C42—302no—
807C3×C5#236611yescharacteristic, complemented, Hall
808C22×C3C22×C4×D511yescharacteristic
809C22×C3C2×D4×D511yescharacteristic
810C22×C3C2×D4×D511yescharacteristic
811C22×C3#414411yescharacteristic
812C22×C3#414411yescharacteristic
813C22×C3D5×#4111yescharacteristic
814C22×C3D5×#4111yescharacteristic
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—102no—
830C2×D3—102no—
831C2×D3—102no—
832C2×D3—102no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—201no—
836C2×D3—201no—
837C2×D3—201no—
838C2×D3—201no—
839C2×D3—201no—
840C2×D3—201no—
841C2×D3—201no—
842C2×D3—201no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—41no—
846C3×C4—54no—
847C3×C4—54no—
848C3×C4—102no—
849C3×C4—201no—
850Dic3—22no—
851Dic3—41no—
852Dic3—102no—
853Dic3—201no—
854C2×C5—122no—
855C2×C5—122no—
856C2×C5C2×C4×D1211yescharacteristic
857C2×C5C2×#89311yescharacteristic
858C2×C5#552111yescharacteristic
859C2×C5D4×D1211yescharacteristic
860C2×C5#555311yescharacteristic
861C2×C5#557711yescharacteristic
862C2×C5#558511yescharacteristic
863D5—122no—
864D5—122no—
865C23—32no—
866C23—32no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—152no—
880C23—152no—
881C23—301no—
882C23—301no—
883C23—301no—
884C23—301no—
885C23—301no—
886C23—301no—
887C23—301no—
888C23—301no—
889C23—301no—
890C23—301no—
891C23—301no—
892C23—301no—
893C23C22×D3×D511yescharacteristic
894D4—124no—
895D4—308no—
896D4—308no—
897D4—308no—
898D4—308no—
899D4—604no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—32no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—52no—
911C2×C4—52no—
912C2×C4—52no—
913C2×C4—52no—
914C2×C4—52no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—101no—
921C2×C4—101no—
922C2×C4—101no—
923C2×C4—101no—
924C2×C4—101no—
925C2×C4—124no—
926C2×C4—152no—
927C2×C4—301no—
928C2×C4—301no—
929C2×C4—301no—
930C2×C4—301no—
931C2×C4—301no—
932C2×C4—604no—
933C2×C4—604no—
934C2×C4—604no—
935C2×C4C4×D3×D512yes—
936C2×C4D5×D1212yes—
937C2×C3#6582011yescharacteristic
938C2×C3C4×D4×D511yescharacteristic
939C2×C3C4×D4×D511yescharacteristic
940C2×C3#6592411yescharacteristic
941C2×C3#6593311yescharacteristic
942C2×C3#6593311yescharacteristic
943C2×C3#6599811yescharacteristic
944D3—42no—
945D3—42no—
946D3—202no—
947D3—202no—
948C5#7365311yescharacteristic, complemented, Sylow
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—121no—
962C22—121no—
963C22—302no—
964C22—302no—
965C22—302no—
966C22—302no—
967C22—302no—
968C22—302no—
969C22—601no—
970C22—601no—
971C22—601no—
972C22—601no—
973C22—601no—
974C22—601no—
975C22—601no—
976C22—601no—
977C22C2×C4×D3×D511yescharacteristic
978C22C2×D5×D1211yescharacteristic
979C22D5×#23511yescharacteristic
980C22D3×D4×D511yescharacteristic
981C22#9202711yescharacteristic
982C22#9202711yescharacteristic
983C22D5×#23911yescharacteristic
984C4—22no—
985C4—22no—
986C4—41no—
987C4—54no—
988C4—54no—
989C4—62no—
990C4—102no—
991C4—121no—
992C4—201no—
993C4—302no—
994C4—601no—
995C3#1060641011yescharacteristic, complemented, Sylow
996C2—122no—
997C2—122no—
998C2—602no—
999C2—602no—
1000C2C4×D5×D1211yescharacteristic
1001C2#1175306711yescharacteristic
1002C2#1175318811yescharacteristic
1003C2#1175325411yescharacteristic
1004C2#1175369211yescharacteristic
1005C2#1175373011yescharacteristic
1006C2D5×#89311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91451C2
hypercenter#95D3×D5
hypocenterC3×C5#2366
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×#91446C2semidirect
3. C2×C4×#1203C2semidirect
4. C2×#91406C2semidirect
5. C2×#91405C2semidirect
6. #11750766C2semidirect
7. C5×#4665C2semidirect
8. C3×#64938C2semidirect
9. #11748909C2semidirect
10. #11748909C2semidirect
11. #11748908C2semidirect
12. #11748908C2semidirect
13. #11748904C2semidirect
14. #11748901C2semidirect
15. #11748638C2semidirect
48. #91451C4semidirect
72. #64938D3semidirect
84. C2×D60C2×C4semidirect
92. C2×C5×D12C2×C4semidirect
108. C2×#1203C2×C4semidirect
109. C2×#1203C2×C4semidirect
110. C2×#1203C2×C4semidirect
111. C2×#1203C2×C4semidirect
125. C3×#683D4semidirect
128. C3×C4×Dic5C2×C4semidirect
130. #6668D4semidirect
153. #4665D5semidirect
367. #683D12semidirect
372. C4×Dic5C4×D3semidirect
430. C3×Dic5C4×D4semidirect
431. C3×Dic5C4×D4semidirect
466. C2×D12C4×D5semidirect
739. Dic5C4×D12semidirect
740. Dic5#893semidirect
807. C3×C5#2366semidirect
948. C5#73653semidirect
995. C3#10606410semidirect

Maximal subgroups

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

subgroupindex
C2×#914512
C2×#914462
C2×C4×#12032
C2×#914062
C2×#914052
#117507662
C5×#46652
C3×#649382
#117489092
#117489082
#117489042
#117489012
#117486382
#106064103
#736535