Finite Group Databasebeta

← #14322284

Subgroups — #14322284

Order 1920.

1848 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×C3×#4027C211yesmaximal, characteristic, complemented
2C2×#91567C211yesmaximal, characteristic
3C2×#91552C211yesmaximal, characteristic, complemented
4C2×Dic5×#67C211yesmaximal, characteristic, complemented
5C2×#91444C211yesmaximal, characteristic, complemented
6C2×#91440C211yesmaximal, characteristic, complemented
7C2×#91405C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9C5×#4957C211yesmaximal, characteristic, complemented
10#11749489C211yesmaximal, characteristic, complemented
11#11748915C211yesmaximal, characteristic, complemented
12#11748912C211yesmaximal, characteristic, complemented
13#11748909C211yesmaximal, characteristic, complemented
14#11748641C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16#10608024—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C3×#4027—24no—
42#91567C418yescomplemented
43#91552—24no—
44Dic5×#67—24no—
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×#6667C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×Dic3×Dic5C2211yescharacteristic
53C2×Dic3×Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91444—24no—
57#91440—24no—
58#91405—24no—
59C4×#940—51nomaximal, Hall
60C2×#4086—31no—
61C2×D4×Dic5—31no—
62C2×#4039—31no—
63C2×#4027—31no—
64C2×#4027—31no—
65C2×#4027—31no—
66C2×#4027D311yescharacteristic, complemented
67C5×#390—31no—
68#65265—31no—
69#65246—31no—
70#65246—31no—
71#65246—31no—
72#65246—31no—
73#65228—31no—
74C42×Dic5—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—22no—
82C2×#1220—22no—
83C2×#1220C2×C414yescomplemented
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C2×C5×#67C2×C414yescomplemented
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5C2×C414yescomplemented
96C22×C3×Dic5—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—22no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—22no—
105C2×#1203—22no—
106C2×#1203—22no—
107C2×#1203C2×C414yescomplemented
108C2×#1202—22no—
109C2×#1202—22no—
110C2×#1202C2×C414yescomplemented
111C2×#1201—22no—
112C2×#1201—22no—
113C2×#1201C2×C414yescomplemented
114C2×#1200—22no—
115C2×#1200—22no—
116C2×#1200—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—22no—
120C3×C5×C22⋊C4—22no—
121#6719—22no—
122#6714—22no—
123#6714—22no—
124#6712—22no—
125C4×Dic15—22no—
126C5×#217—22no—
127C5×(C2×D3)⋊C4—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×Dic3⋊C4—22no—
130C4×C5×Dic3—22no—
131C3×#685—22no—
132C3×#683—22no—
133C3×C4×Dic5D414yescomplemented
134Dic3⋊Dic5—22no—
135#6669—22no—
136#6668—22no—
137#6667—22no—
138(C2×D3)⋊Dic5—22no—
139#6665—22no—
140#6665—22no—
141Dic3×Dic5—22no—
142Dic3×Dic5C2×C414yescomplemented
143Dic3×Dic5D414yescomplemented
144Dic3×Dic5D414yescomplemented
145C2×C3×C4×D4—51no—
146C2×#940—51no—
147C2×C4×#67—51no—
148C2×C4×#67—51no—
149C2×C4×#67—51no—
150C2×C4×#67—51no—
151C2×C4×D12—51no—
152#5221—51no—
153#4988—51no—
154#4975—51no—
155#4957—51no—
156#4957—51no—
157#4957—51no—
158#4957D511yescharacteristic, complemented
159C42×Dic3—51no—
160C22×C5×D4—31no—
161C22×C22⋊D5—31no—
162C22×C22⋊D5—31no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5C2×D311yescharacteristic
165C23×Dic5—31no—
166C23×Dic5C2×D311yescharacteristic
167C22×D20—31no—
168C22×C4×D5—31no—
169C22×C4×D5C2×D311yescharacteristic
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4C2×D311yescharacteristic
175C2×C42×C5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178#4086—38no—
179D4×Dic5—64no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685C2×D311yescharacteristic
186C2×C4⋊Dic5—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—31no—
190C2×#683C2×D311yescharacteristic
191C2×C4×Dic5—31no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196C2×C4×Dic5C2×D311yescharacteristic
197#4039—64no—
198#4027—24no—
199#4027—64no—
200#4027—64no—
201#4027—64no—
202C4×#127—151noSylow
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—21no—
206C23×C3×C5—21no—
207C23×C3×C5—21no—
208C23×C3×C5—21no—
209C23×C3×C5C22×C412yes—
210C23×C3×C5C2411yescharacteristic
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15C22×C412yes—
218C22×C5×D3—21no—
219C22×C5×D3—21no—
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3—21no—
223C22×C5×D3—21no—
224C22×C5×D3C22×C412yes—
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5—21no—
230C22×C3×D5—21no—
231C22×C3×D5C22×C412yes—
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×C5C2×D412yes—
238#1220—28no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15C22×C412yes—
245C2×Dic15C2×D412yes—
246C2×Dic15C2×D412yes—
247C2×Dic15#4112yes—
248C5×#67—28no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3C22×C412yes—
255C2×C5×Dic3C2×D412yes—
256C2×C5×Dic3C2×D412yes—
257C2×C5×Dic3#4112yes—
258C3×C22⋊D5—28no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—44no—
263C2×C3×Dic5C22×C412yes—
264C2×C3×Dic5C2×D412yes—
265C2×C3×Dic5C2×D412yes—
266C2×C3×Dic5C2×D412yes—
267C2×C3×Dic5C2×D412yes—
268C2×C3×Dic5#4112yes—
269C3×C4×D5—44no—
270#1203—28no—
271#1202—28no—
272#1201—28no—
273#1200—44no—
274D3×Dic5—44no—
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67C2×D511yescharacteristic
282C22×D12—51no—
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C3×C4×D4—104no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4C2×D511yescharacteristic
289C2×C3×C42—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
294#940—58no—
295C4×#67—104no—
296C4×#67—104no—
297C4×#67—104no—
298C4×#67—104no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4C2×D511yescharacteristic
304C2×(C2×D3)⋊C4C2×D511yescharacteristic
305C2×C4⋊Dic3—51no—
306C2×Dic3⋊C4—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4C2×D511yescharacteristic
310C2×C4×Dic3—51no—
311C2×C4×Dic3—51no—
312C2×C4×Dic3—51no—
313C2×C4×Dic3—51no—
314C2×C4×Dic3—51no—
315C2×C4×Dic3C2×D511yescharacteristic
316C4×D12—104no—
317C24×C5—31no—
318C24×C5C22×D311yescharacteristic
319C23×D5—31no—
320C23×D5C22×D311yescharacteristic
321C2×C5×D4—34no—
322C2×C5×D4—62no—
323C2×C5×D4—62no—
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—22no—
330C2×C22⋊D5—22no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—62no—
335C2×C22⋊D5—62no—
336C2×C22⋊D5—62no—
337C2×C22⋊D5—62no—
338C2×C22⋊D5—62no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5C4×D314yescomplemented
341C22×Dic5—22no—
342C22×Dic5—22no—
343C22×Dic5—22no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—31no—
347C22×Dic5—62no—
348C22×Dic5—62no—
349C22×Dic5—62no—
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C22×Dic5C22×D311yescharacteristic
353C2×D20—34no—
354C2×D20—62no—
355C2×D20—62no—
356C2×C4×D5—22no—
357C2×C4×D5—22no—
358C2×C4×D5—22no—
359C2×C4×D5—62no—
360C2×C4×D5—62no—
361C2×C4×D5—62no—
362C5×C4⋊C4—62no—
363C5×C22⋊C4—22no—
364C5×C22⋊C4—62no—
365C5×C22⋊C4—62no—
366C5×C22⋊C4—62no—
367C42×C5—62no—
368C22⋊Dic5—62no—
369C22⋊Dic5—62no—
370#685—22no—
371#685—62no—
372#685—62no—
373#685—62no—
374#685—62no—
375#685—62no—
376C4⋊Dic5—62no—
377#683—22no—
378#683—62no—
379#683—62no—
380#683—62no—
381C4×Dic5—34no—
382C4×Dic5—34no—
383C4×Dic5—34no—
384C4×Dic5—62no—
385C4×Dic5—62no—
386C4×Dic5#6714yescomplemented
387C2×#127—151no—
388C2×C4×D4—51no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C2×C4×D4—151no—
394#390—31no—
395#390—151no—
396#390—151no—
397#390—151no—
398#390—151no—
399#390—151no—
400#384—151no—
401C43—151no—
402C22×C3×C5—22no—
403C22×C3×C5—22no—
404C22×C3×C5—22no—
405C22×C3×C5—41no—
406C22×C3×C5—41no—
407C22×C3×C5—41no—
408C22×C3×C5—41no—
409C22×C3×C5C23×C411yescharacteristic
410C22×C3×C5C22×D411yescharacteristic
411C22×C3×C5C22×D411yescharacteristic
412C22×C3×C5C22×D411yescharacteristic
413C22×C3×C5C2×#4111yescharacteristic
414C22×C3×C5C2×#4111yescharacteristic
415C22×C3×C5C2×#4111yescharacteristic
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—41no—
420C2×D15—41no—
421C2×D15—41no—
422C2×D15—41no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3—41no—
429C2×C5×D3—41no—
430C2×C3×D5—22no—
431C2×C3×D5—22no—
432C2×C3×D5—22no—
433C2×C3×D5—41no—
434C2×C3×D5—41no—
435C2×C3×D5—41no—
436C2×C3×D5—41no—
437C3×C4×C5—22no—
438C3×C4×C5—41no—
439Dic15—22no—
440Dic15—41no—
441Dic15C4×D414yescomplemented
442C3×Dic5—41no—
443C3×Dic5C4×D414yescomplemented
444C3×Dic5#12714yescomplemented
445C5×Dic3—22no—
446C5×Dic3—41no—
447C5×Dic3C4×D414yescomplemented
448C24×C3—51no—
449C24×C3C22×D511yescharacteristic
450C23×D3—51no—
451C23×D3C22×D511yescharacteristic
452C2×C3×D4—54no—
453C2×C3×D4—102no—
454C2×C3×D4—102no—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—102no—
459C22×C3×C4—102no—
460C22×C3×C4—102no—
461C22×C3×C4—102no—
462C22×C3×C4—102no—
463C22×C3×C4—102no—
464C22×C3×C4C22×D511yescharacteristic
465C22×C3×C4C22×D511yescharacteristic
466C2×#67—22no—
467C2×#67—22no—
468C2×#67—54no—
469C2×#67—54no—
470C2×#67—54no—
471C2×#67—102no—
472C2×#67—102no—
473C2×#67—102no—
474C2×#67—102no—
475C2×#67—102no—
476C2×#67—102no—
477C2×#67C4×D514yescomplemented
478C22×Dic3—51no—
479C22×Dic3—51no—
480C22×Dic3—51no—
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C2×D12—54no—
485C2×D12—102no—
486C2×D12—102no—
487C2×C4×D3—102no—
488C2×C4×D3—102no—
489C2×C4×D3—102no—
490C2×C4×D3—102no—
491C2×C4×D3—102no—
492C2×C4×D3—102no—
493C3×C4⋊C4—102no—
494C3×C22⋊C4—22no—
495C3×C22⋊C4—102no—
496C3×C42—54no—
497#217—22no—
498#217—102no—
499#217—102no—
500#217—102no—
501(C2×D3)⋊C4—22no—
502(C2×D3)⋊C4—22no—
503(C2×D3)⋊C4—102no—
504(C2×D3)⋊C4—102no—
505(C2×D3)⋊C4—102no—
506(C2×D3)⋊C4—102no—
507C4⋊Dic3—102no—
508Dic3⋊C4—22no—
509Dic3⋊C4—102no—
510Dic3⋊C4—102no—
511Dic3⋊C4—102no—
512C4×Dic3—22no—
513C4×Dic3—54no—
514C4×Dic3—54no—
515C4×Dic3—54no—
516C4×Dic3—102no—
517C4×Dic3—102no—
518C23×C5—21no—
519C23×C5—21no—
520C23×C5—21no—
521C23×C5—21no—
522C23×C5—21no—
523C23×C5—21no—
524C23×C5—32no—
525C23×C5—61no—
526C23×C5—61no—
527C23×C5—61no—
528C23×C5—61no—
529C23×C5—61no—
530C23×C5—61no—
531C23×C5C2×C4×D312yes—
532C23×C5C23×D311yescharacteristic
533C22×D5—21no—
534C22×D5—21no—
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—32no—
540C22×D5—61no—
541C22×D5—61no—
542C22×D5—61no—
543C22×D5—61no—
544C22×D5—61no—
545C22×D5—61no—
546C22×D5C2×C4×D312yes—
547C5×D4—68no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—32no—
554C2×C4×C5—32no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—61no—
558C2×C4×C5—61no—
559C2×C4×C5—61no—
560C2×C4×C5—61no—
561C2×C4×C5—61no—
562C2×C4×C5C2×#6712yes—
563C22⋊D5—28no—
564C22⋊D5—68no—
565C22⋊D5—68no—
566C22⋊D5—68no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—44no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—124no—
581C2×Dic5C2×C4×D312yes—
582C2×Dic5#23512yes—
583C2×Dic5D3×D412yes—
584C2×Dic5D3×D412yes—
585C2×Dic5C2×#6712yes—
586C2×Dic5C2×#6712yes—
587D20—68no—
588C4×D5—44no—
589C4×D5—124no—
590C22×D4—31no—
591C22×D4—51no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C23×C4—51no—
597C23×C4—51no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601C4×D4—104no—
602C4×D4—304no—
603C4×D4—304no—
604C4×D4—304no—
605C4×D4—304no—
606C4×D4—304no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—51no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C4⋊C4—151no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—51no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C22⋊C4—151no—
621C2×C22⋊C4—151no—
622C2×C22⋊C4—151no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4D3×D511yescharacteristic
625C2×C42—31no—
626C2×C42—51no—
627C2×C42—151no—
628C2×C42—151no—
629C2×C42—151no—
630C2×C42—151no—
631C2×C42—151no—
632C2×C3×C5—42no—
633C2×C3×C5C2×C4×D411yescharacteristic
634C2×C3×C5C2×C4×D411yescharacteristic
635C2×C3×C5C2×C4×D411yescharacteristic
636C2×C3×C5C2×#12711yescharacteristic
637C2×C3×C5#53211yescharacteristic
638C2×C3×C5#53211yescharacteristic
639C2×C3×C5#53211yescharacteristic
640D15—42no—
641C3×D5—42no—
642C5×D3—42no—
643C23×C3—21no—
644C23×C3—21no—
645C23×C3—21no—
646C23×C3—21no—
647C23×C3—21no—
648C23×C3—21no—
649C23×C3—52no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—101no—
654C23×C3—101no—
655C23×C3—101no—
656C23×C3C2×C4×D512yes—
657C23×C3C23×D511yescharacteristic
658C22×D3—21no—
659C22×D3—21no—
660C22×D3—21no—
661C22×D3—21no—
662C22×D3—21no—
663C22×D3—21no—
664C22×D3—52no—
665C22×D3—101no—
666C22×D3—101no—
667C22×D3—101no—
668C22×D3—101no—
669C22×D3—101no—
670C22×D3—101no—
671C22×D3C2×C4×D512yes—
672C3×D4—108no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—52no—
681C2×C3×C4—52no—
682C2×C3×C4—52no—
683C2×C3×C4—52no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—101no—
687C2×C3×C4—204no—
688C2×C3×C4—204no—
689C2×C3×C4D4×D512yes—
690#67—28no—
691#67—108no—
692#67—108no—
693#67—108no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—52no—
700C2×Dic3—52no—
701C2×Dic3—52no—
702C2×Dic3—52no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3C2×C4×D512yes—
709C2×Dic3D4×D512yes—
710C2×Dic3D4×D512yes—
711C2×Dic3#71112yes—
712D12—108no—
713C4×D3—204no—
714C4×D3—204no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—41no—
719C22×C5—41no—
720C22×C5—41no—
721C22×C5—41no—
722C22×C5—62no—
723C22×C5—62no—
724C22×C5—62no—
725C22×C5—121no—
726C22×C5—121no—
727C22×C5—121no—
728C22×C5—121no—
729C22×C5C22×C4×D311yescharacteristic
730C22×C5C2×#23511yescharacteristic
731C22×C5C2×D3×D411yescharacteristic
732C22×C5C2×D3×D411yescharacteristic
733C22×C5D3×#4111yescharacteristic
734C22×C5D3×#4111yescharacteristic
735C22×C5C22×#6711yescharacteristic
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—41no—
740C2×D5—41no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—62no—
746C2×D5—121no—
747C2×D5—121no—
748C2×D5—121no—
749C2×D5—121no—
750C4×C5—22no—
751C4×C5—34no—
752C4×C5—41no—
753C4×C5—62no—
754C4×C5—121no—
755Dic5—34no—
756Dic5—41no—
757Dic5—62no—
758Dic5—121no—
759Dic5C4×#6714yescomplemented
760Dic5#94014yescomplemented
761C24—31no—
762C24—51no—
763C24—151no—
764C24C2×D3×D511yescharacteristic
765C2×D4—34no—
766C2×D4—54no—
767C2×D4—62no—
768C2×D4—62no—
769C2×D4—102no—
770C2×D4—102no—
771C2×D4—154no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—154no—
775C2×D4—302no—
776C2×D4—302no—
777C2×D4—302no—
778C2×D4—302no—
779C2×D4—302no—
780C2×D4—302no—
781C2×D4—302no—
782C2×D4—302no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—102no—
794C22×C4—102no—
795C22×C4—151no—
796C22×C4—151no—
797C22×C4—151no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—302no—
801C22×C4—302no—
802C22×C4—302no—
803C22×C4—302no—
804C22×C4C2×D3×D511yescharacteristic
805C22×C4C2×D3×D511yescharacteristic
806C4⋊C4—62no—
807C4⋊C4—102no—
808C4⋊C4—302no—
809C4⋊C4—302no—
810C4⋊C4—302no—
811C4⋊C4—302no—
812C22⋊C4—22no—
813C22⋊C4—62no—
814C22⋊C4—62no—
815C22⋊C4—62no—
816C22⋊C4—102no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—302no—
821C22⋊C4—302no—
822C22⋊C4—302no—
823C22⋊C4—302no—
824C42—54no—
825C42—62no—
826C42—154no—
827C42—154no—
828C42—154no—
829C42—302no—
830C42—302no—
831C3×C5C4×#12711yescharacteristic, complemented, Hall
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—102no—
840C22×C3—102no—
841C22×C3—102no—
842C22×C3—201no—
843C22×C3—201no—
844C22×C3—201no—
845C22×C3—201no—
846C22×C3C22×C4×D511yescharacteristic
847C22×C3C2×D4×D511yescharacteristic
848C22×C3C2×D4×D511yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3C2×#71111yescharacteristic
851C22×C3D5×#4111yescharacteristic
852C22×C3D5×#4111yescharacteristic
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—102no—
861C2×D3—102no—
862C2×D3—102no—
863C2×D3—201no—
864C2×D3—201no—
865C2×D3—201no—
866C2×D3—201no—
867C3×C4—22no—
868C3×C4—41no—
869C3×C4—54no—
870C3×C4—54no—
871C3×C4—201no—
872Dic3—22no—
873Dic3—41no—
874Dic3—54no—
875Dic3—102no—
876Dic3—201no—
877Dic3#402714yescomplemented
878C2×C5—42no—
879C2×C5—122no—
880C2×C5C4×D3×D411yescharacteristic
881C2×C5C4×D3×D411yescharacteristic
882C2×C5#554811yescharacteristic
883C2×C5#554811yescharacteristic
884C2×C5C2×C4×#6711yescharacteristic
885C2×C5C2×#94011yescharacteristic
886C2×C5#583211yescharacteristic
887D5—42no—
888D5—122no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—32no—
896C23—52no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—152no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—301no—
914C23—301no—
915C23—301no—
916C23C4×D3×D512yes—
917C23C22×D3×D511yescharacteristic
918D4—68no—
919D4—108no—
920D4—308no—
921D4—308no—
922D4—308no—
923D4—308no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—52no—
934C2×C4—52no—
935C2×C4—52no—
936C2×C4—52no—
937C2×C4—52no—
938C2×C4—52no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—152no—
948C2×C4—152no—
949C2×C4—152no—
950C2×C4—152no—
951C2×C4—204no—
952C2×C4—204no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—301no—
958C2×C4—604no—
959C2×C4—604no—
960C2×C4D5×#6712yes—
961C2×C3—42no—
962C2×C3—202no—
963C2×C3C2×#402711yescharacteristic
964C2×C3C4×D4×D511yescharacteristic
965C2×C3C4×D4×D511yescharacteristic
966C2×C3#6593011yescharacteristic
967C2×C3#6593011yescharacteristic
968C2×C3#6600211yescharacteristic
969C2×C3D5×#12711yescharacteristic
970D3—42no—
971D3—202no—
972C5C4×#94011yescharacteristic, complemented, Sylow
973C22—22no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—201no—
991C22—201no—
992C22—201no—
993C22—201no—
994C22—302no—
995C22—302no—
996C22—302no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22D5×#23511yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D3×D4×D511yescharacteristic
1005C22D3×#71111yescharacteristic
1006C22#9202411yescharacteristic
1007C22C2×D5×#6711yescharacteristic
1008C4—22no—
1009C4—34no—
1010C4—41no—
1011C4—54no—
1012C4—54no—
1013C4—62no—
1014C4—121no—
1015C4—154no—
1016C4—201no—
1017C4—302no—
1018C4—601no—
1019C3#1060802411yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—122no—
1022C2—202no—
1023C2—602no—
1024C2#1175284311yescharacteristic
1025C2#1175285111yescharacteristic
1026C2D3×#402711yescharacteristic
1027C2#1175320311yescharacteristic
1028C2C4×D5×#6711yescharacteristic
1029C2#1175479611yescharacteristic
1030C2D5×#94011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×#127
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
1. C2×C3×#4027C2semidirect
3. C2×#91552C2semidirect
4. C2×Dic5×#67C2semidirect
5. C2×#91444C2semidirect
6. C2×#91440C2semidirect
7. C2×#91405C2semidirect
8. #11751058C2semidirect
9. C5×#4957C2semidirect
10. #11749489C2semidirect
11. #11748915C2semidirect
12. #11748912C2semidirect
13. #11748909C2semidirect
14. #11748641C2semidirect
15. C4×Dic3×Dic5C2semidirect
42. #91567C4semidirect
66. C2×#4027D3semidirect
83. C2×#1220C2×C4semidirect
89. C2×C5×#67C2×C4semidirect
95. C2×C3×C22⋊D5C2×C4semidirect
107. C2×#1203C2×C4semidirect
110. C2×#1202C2×C4semidirect
113. C2×#1201C2×C4semidirect
133. C3×C4×Dic5D4semidirect
142. Dic3×Dic5C2×C4semidirect
143. Dic3×Dic5D4semidirect
144. Dic3×Dic5D4semidirect
158. #4957D5semidirect
340. C2×C22⋊D5C4×D3semidirect
386. C4×Dic5#67semidirect
441. Dic15C4×D4semidirect
443. C3×Dic5C4×D4semidirect
444. C3×Dic5#127semidirect
447. C5×Dic3C4×D4semidirect
477. C2×#67C4×D5semidirect
759. Dic5C4×#67semidirect
760. Dic5#940semidirect
831. C3×C5C4×#127semidirect
877. Dic3#4027semidirect
972. C5C4×#940semidirect
1019. C3#10608024semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C2×#915672
C2×#915522
C2×Dic5×#672
C2×#914442
C2×#914402
C2×#914052
#117510582
C5×#49572
#117494892
#117489152
#117489122
#117489092
#117486412
C4×Dic3×Dic52
#106080243
C4×#9405