Finite Group Databasebeta

← #14328127

Subgroups — #14328127

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×#91476C211yesmaximal, characteristic
2C2×D3×#685C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#1203C211yesmaximal, characteristic, complemented
5C2×#91396C211yesmaximal, characteristic, complemented
6#11750766C211yesmaximal, characteristic, complemented
7C5×#4668C211yesmaximal, characteristic, complemented
8C3×#64955C211yesmaximal, characteristic, complemented
9#11748907C211yesmaximal, characteristic, complemented
10#11748899C211yesmaximal, characteristic, complemented
11#11748883C211yesmaximal, characteristic, complemented
12Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11748768C211yesmaximal, characteristic, complemented
14#11748727C211yesmaximal, characteristic, complemented
15#11748671C211yesmaximal, characteristic, complemented
16#10606327—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic, complemented
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic, complemented
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic, complemented
42C2×#6667C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91476C418yescomplemented
47D3×#685—24no—
48D5×(C2×D3)⋊C4—24no—
49C4×#1203—24no—
50#91396—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, 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×Dic5—31no—
69#64958—31no—
70#64955D311yescharacteristic, complemented
71#64954—31no—
72#64954—31no—
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×D3×D5—22no—
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—41no—
82C22×D3×D5—41no—
83C22×D3×D5C2×C414yescomplemented
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C2×D60—41no—
90C2×D60—41no—
91C2×D60C2×C414yescomplemented
92C2×C4×D15—22no—
93C2×C4×D15—22no—
94C2×C4×D15—41no—
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3—41no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×#1203—22no—
108C2×#1203—22no—
109C2×#1203C2×C414yescomplemented
110C2×#1202—22no—
111C2×#1202—22no—
112C2×#1202C2×C414yescomplemented
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—41no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—41no—
119#6714—22no—
120#6714—22no—
121#6714—41no—
122C5×(C2×D3)⋊C4—22no—
123C5×(C2×D3)⋊C4C2×C414yescomplemented
124C5×C4⋊Dic3—41no—
125C5×Dic3⋊C4—22no—
126C3×#685C2×C414yescomplemented
127C3×#685D414yescomplemented
128C3×C4×Dic5—22no—
129C3×C4×Dic5—41no—
130#6668—22no—
131#6667—22no—
132#6667—22no—
133#6667—22no—
134#6667—22no—
135#6667C2×C414yescomplemented
136(C2×D3)⋊Dic5D414yescomplemented
137#6665—22no—
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#4950—51no—
147#4940—51no—
148#4939—51no—
149C4×(C2×D3)⋊C4—51no—
150#4670—51no—
151#4668D511yescharacteristic, complemented
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C23×C4×C5—31no—
156C22×C22⋊D5—31no—
157C23×Dic5—31no—
158C22×D20—31no—
159C22×D20—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
163C2×C5×C4⋊C4—31no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C22⋊Dic5—31no—
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—64no—
179C2×#685C2×D311yescharacteristic
180C2×#685C2×D311yescharacteristic
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×#95C2×D311yescharacteristic, complemented
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963C2×D311yescharacteristic, complemented
194#2358—151noSylow
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×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×D3C22×C412yes—
215C22×C5×D3C2×D412yes—
216C22×C5×D3#4112yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5C22×C412yes—
222C22×C3×D5C2×D412yes—
223C22×C3×D5#4112yes—
224C2×D3×D5—28no—
225C2×D3×D5—28no—
226C2×D3×D5—44no—
227C2×D3×D5—44no—
228C2×D3×D5—44no—
229C2×D3×D5—44no—
230C2×D3×D5—44no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C2×D412yes—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15C2×D412yes—
246D60—44no—
247C4×D15—44no—
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—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3C22×C412yes—
257C4×C5×D3—44no—
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×Dic5C22×C412yes—
265C2×C3×Dic5C2×D412yes—
266C2×C3×Dic5C2×D412yes—
267C3×C4×D5—44no—
268#1203—28no—
269#1202—28no—
270D3×Dic5—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C42—51no—
284C2×C3×C42—51no—
285C2×#217—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)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—104no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3C2×D511yescharacteristic, complemented
300C2×Dic3⋊C4C2×D511yescharacteristic, complemented
301C2×C4×Dic3—51no—
302#882—58no—
303#67⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—104no—
306C3×#95—51no—
307C3×#95C2×D511yescharacteristic, complemented
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95C2×D511yescharacteristic, complemented
312C24×C5—31no—
313C23×D5—31no—
314C23×D5—31no—
315C23×D5—34no—
316C23×D5—62no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—121no—
321C23×D5—121no—
322C23×D5C22×D311yescharacteristic
323C22×C4×C5—31no—
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5—62no—
327C22×C4×C5—62no—
328C22×C4×C5—121no—
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C2×C22⋊D5—34no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—62no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—62no—
338C22×Dic5—62no—
339C22×Dic5—121no—
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—22no—
350C2×C4×D5—22no—
351C2×C4×D5—41no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C4⋊C4—121no—
360C5×C22⋊C4—34no—
361C5×C22⋊C4—62no—
362C22⋊Dic5—34no—
363#685—34no—
364#685—62no—
365#685—62no—
366#685—62no—
367#685—62no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—121no—
372#685C4×D314yescomplemented
373#685D1214yescomplemented
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×C5C23×C411yescharacteristic
394C22×C3×C5C22×D411yescharacteristic
395C22×C3×C5C22×D411yescharacteristic
396C22×C3×C5C2×#4111yescharacteristic
397C22×C3×C5C2×#4111yescharacteristic
398C22×C3×C5H(5,𝔽2)11yescharacteristic
399C22×C3×C5H(5,𝔽2)11yescharacteristic
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—41no—
407C2×D15—41no—
408C2×D15—41no—
409C2×D15—41no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15—41no—
413C2×D15—41no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3C4×D414yescomplemented
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5C4×D414yescomplemented
428D3×D5—416no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432Dic15—22no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—41no—
439C5×Dic3—41no—
440C24×C3—51no—
441C23×D3—51no—
442C23×D3—51no—
443C23×D3—54no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—201no—
449C23×D3—201no—
450C23×D3C22×D511yescharacteristic
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—201no—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—102no—
462C2×#67—102no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—102no—
466C22×Dic3—102no—
467C22×Dic3—201no—
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—54no—
472C2×D12—54no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—201no—
476C2×D12—201no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—41no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C22⋊C4—54no—
487C3×C22⋊C4—54no—
488C3×C42—102no—
489C3×C42—201no—
490#217—102no—
491(C2×D3)⋊C4—22no—
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—201no—
501(C2×D3)⋊C4C4×D514yescomplemented
502C4⋊Dic3—41no—
503C4⋊Dic3—102no—
504Dic3⋊C4—22no—
505C4×Dic3—102no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—32no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5C23×D311yescharacteristic
514C22×D5—21no—
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—32no—
519C22×D5—32no—
520C22×D5—68no—
521C22×D5—61no—
522C22×D5—61no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—68no—
534C22×D5—124no—
535C22×D5—124no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5C2×C4×D312yes—
540C22×D5C2×D1212yes—
541C22×D5#23512yes—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—32no—
550C2×C4×C5—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×D1212yes—
561C22⋊D5—68no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—32no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—124no—
575C2×Dic5C2×C4×D312yes—
576C2×Dic5C2×D1212yes—
577C2×Dic5D3×D412yes—
578D20—68no—
579D20—124no—
580C4×D5—44no—
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—31no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
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—151no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4—304no—
614C2×C42—51no—
615C2×C42—51no—
616C2×C42—151no—
617#95—31no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95D3×D511yescharacteristic, complemented
623C2×C3×C5C2×C4×D411yescharacteristic
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5#51811yescharacteristic
626C2×C3×C5D4211yescharacteristic
627C2×C3×C5#54611yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#55111yescharacteristic
630D15—42no—
631D15—42no—
632C3×D5—24no—
633C5×D3—24no—
634C23×C3—52no—
635C23×C3—52no—
636C23×C3—52no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—52no—
647C22×D3—52no—
648C22×D3—108no—
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—108no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3C2×C4×D512yes—
668C22×D3D4×D512yes—
669C22×D3#71312yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—204no—
687C2×C3×C4C2×C4×D512yes—
688C2×C3×C4D4×D512yes—
689#67—108no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—52no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—204no—
705C2×Dic3C2×C4×D512yes—
706D12—108no—
707D12—204no—
708C4×D3—44no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—34no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
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—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—1216no—
738C2×D5—121no—
739C2×D5—121no—
740C2×D5—121no—
741C2×D5—121no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5C4×D1214yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—62no—
751C4×C5—121no—
752C4×C5—121no—
753Dic5—22no—
754Dic5—22no—
755Dic5—22no—
756Dic5—62no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—154no—
761C24—151no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—154no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—102no—
787C22×C4—102no—
788C22×C4—121no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—201no—
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×C4C2×D3×D511yescharacteristic
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—121no—
806C4⋊C4—302no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—54no—
810C22⋊C4—62no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—102no—
822C42—201no—
823C42—302no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—54no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3C2×#71311yescharacteristic
837C22×C3D5×#4111yescharacteristic
838C22×C3#414911yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—102no—
846C2×D3—102no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—2016no—
852C2×D3—201no—
853C2×D3—201no—
854C2×D3—201no—
855C2×D3—201no—
856C2×D3—201no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3#403914yescomplemented
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—102no—
867Dic3—22no—
868Dic3—41no—
869Dic3—41no—
870Dic3—102no—
871Dic3—201no—
872C2×C5—64no—
873C2×C5C2×C4×D1211yescharacteristic
874C2×C5#549011yescharacteristic
875C2×C5#552711yescharacteristic
876C2×C5C4×D3×D411yescharacteristic
877C2×C5#554511yescharacteristic
878C2×C5D4×D1211yescharacteristic
879C2×C5#555411yescharacteristic
880D5—24no—
881D5—122no—
882D5—122no—
883C23—32no—
884C23—32no—
885C23—32no—
886C23—52no—
887C23—52no—
888C23—52no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—152no—
898C23—152no—
899C23—308no—
900C23—308no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
918C23C22×D3×D511yescharacteristic
919D4—308no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—32no—
930C2×C4—52no—
931C2×C4—52no—
932C2×C4—52no—
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—124no—
948C2×C4—152no—
949C2×C4—204no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C4×D3×D512yes—
959C2×C4D5×D1212yes—
960C2×C3—104no—
961C2×C3C2×#403911yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3#6587911yescharacteristic
964C2×C3#6592411yescharacteristic
965C2×C3#6596411yescharacteristic
966C2×C3#6597111yescharacteristic
967C2×C3#6598811yescharacteristic
968D3—24no—
969D3—202no—
970D3—202no—
971C5#7357711yescharacteristic, complemented, Sylow
972C22—34no—
973C22—54no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—102no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—6016no—
993C22—601no—
994C22—601no—
995C22—601no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22C2×D5×D1211yescharacteristic
1003C22D5×#23511yescharacteristic
1004C22D3×D4×D511yescharacteristic
1005C22#9202611yescharacteristic
1006C22#9202711yescharacteristic
1007C22D3×#71311yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—102no—
1013C4—102no—
1014C4—102no—
1015C4—121no—
1016C4—121no—
1017C4—302no—
1018C4—601no—
1019C3#1060632711yescharacteristic, complemented, Sylow
1020C2—64no—
1021C2—104no—
1022C2—602no—
1023C2—602no—
1024C2C4×D5×D1211yescharacteristic
1025C2#1175320411yescharacteristic
1026C2#1175322611yescharacteristic
1027C2#1175325411yescharacteristic
1028C2D3×#403911yescharacteristic
1029C2#1175387611yescharacteristic
1030C2#1175389711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91476C2
hypercenter#95D3×D5
hypocenterC3×C5#2358
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×D3×#685C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. C2×C4×#1203C2semidirect
5. C2×#91396C2semidirect
6. #11750766C2semidirect
7. C5×#4668C2semidirect
8. C3×#64955C2semidirect
9. #11748907C2semidirect
10. #11748899C2semidirect
11. #11748883C2semidirect
12. Dic5×(C2×D3)⋊C4C2semidirect
13. #11748768C2semidirect
14. #11748727C2semidirect
15. #11748671C2semidirect
19. C22×C4×D15C22semidirect
28. C2×#6714C22semidirect
31. C2×C5×C4⋊Dic3C22semidirect
32. C2×C5×Dic3⋊C4C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. C2×#6668C22semidirect
41. C2×#6667C22semidirect
42. C2×#6667C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91476C4semidirect
51. C3×C5×#95C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
70. #64955D3semidirect
83. C22×D3×D5C2×C4semidirect
91. C2×D60C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1202C2×C4semidirect
123. C5×(C2×D3)⋊C4C2×C4semidirect
126. C3×#685C2×C4semidirect
127. C3×#685D4semidirect
135. #6667C2×C4semidirect
136. (C2×D3)⋊Dic5D4semidirect
151. #4668D5semidirect
183. C2×C4×Dic5C2×D3semidirect
184. C2×C4×Dic5C2×D3semidirect
189. C5×#95C2×D3semidirect
193. #3963C2×D3semidirect
299. C2×C4⋊Dic3C2×D5semidirect
300. C2×Dic3⋊C4C2×D5semidirect
307. C3×#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
372. #685C4×D3semidirect
373. #685D12semidirect
420. C2×C5×D3C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
501. (C2×D3)⋊C4C4×D5semidirect
622. #95D3×D5semidirect
746. C2×D5C4×D12semidirect
824. C3×C5#2358semidirect
860. C2×D3#4039semidirect
971. C5#73577semidirect
1019. C3#10606327semidirect

Maximal subgroups

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

subgroupindex
C2×#914762
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×C4×#12032
C2×#913962
#117507662
C5×#46682
C3×#649552
#117489072
#117488992
#117488832
Dic5×(C2×D3)⋊C42
#117487682
#117487272
#117486712
#106063273
#735775