Finite Group Databasebeta

← #14328132

Subgroups — #14328132

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×#91475C211yesmaximal, characteristic
2C2×#91473C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#1203C211yesmaximal, characteristic, complemented
5C2×#91441C211yesmaximal, characteristic, complemented
6#11750769C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64955C211yesmaximal, characteristic, complemented
9#11748919C211yesmaximal, characteristic, complemented
10#11748905C211yesmaximal, characteristic, complemented
11#11748900C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13#11748764C211yesmaximal, characteristic, complemented
14#11748723C211yesmaximal, characteristic, complemented
15#11748715C211yesmaximal, characteristic, complemented
16#10606611—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic, complemented
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×#6712C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46#91475C418yescomplemented
47#91473—24no—
48D5×(C2×D3)⋊C4—24no—
49C4×#1203—24no—
50#91441—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×#4083—31no—
59C2×C4×C22⋊D5—31no—
60C2×C4×C22⋊D5—31no—
61C2×D5×C22⋊C4—31no—
62C2×D5×C22⋊C4—31no—
63C5×#386—31no—
64#65510—31no—
65#65245—31no—
66#65245—31no—
67#65234—31no—
68#65234—31no—
69#64957—31no—
70#64957—31no—
71#64955—31no—
72#64955D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
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
89C22×Dic15C2311yescharacteristic
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C2×C5×D12—41no—
96C2×C5×D12—41no—
97C2×C5×D12C2×C414yescomplemented
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×#1201—22no—
111C2×#1201—22no—
112C2×#1201C2×C414yescomplemented
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200—41no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—41no—
119#6714—22no—
120#6714C2×C414yescomplemented
121C4⋊Dic15—41no—
122#6712—22no—
123C5×(C2×D3)⋊C4—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4—41no—
126C3×#685C2×C414yescomplemented
127C3×#685D414yescomplemented
128C3×C4×Dic5—22no—
129C3×C4×Dic5—41no—
130#6668—22no—
131#6667D414yescomplemented
132(C2×D3)⋊Dic5—22no—
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5—22no—
135(C2×D3)⋊Dic5—22no—
136(C2×D3)⋊Dic5C2×C414yescomplemented
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#4668—51no—
152#4665—51no—
153#4665D511yescharacteristic, complemented
154C24×D5—31no—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171#4083—38no—
172C4×C22⋊D5—64no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685C2×D311yescharacteristic
179C2×#685C2×D311yescharacteristic
180C2×C4⋊Dic5—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×C4×Dic5—31no—
184C2×C4×Dic5C2×D311yescharacteristic, complemented
185C2×C4×Dic5C2×D311yescharacteristic, complemented
186D5×C22⋊C4—64no—
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×D15C22×C412yes—
201C22×D15C2×D412yes—
202C22×D15#4112yes—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
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×D3C22×C412yes—
216C22×C5×D3C22×C412yes—
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×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15C22×C412yes—
249C4×D15—44no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3C2×D412yes—
256C5×D12—44no—
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#1201—28no—
270#1200—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12C2×D511yescharacteristic
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic, complemented
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—104no—
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×Dic3⋊C4—51no—
301C2×C4×Dic3—51no—
302#882—58no—
303#67⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—104no—
306C3×#95—51no—
307C3×#95C2×D511yescharacteristic, complemented
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95C2×D511yescharacteristic, complemented
312C24×C5—31no—
313C24×C5—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
323C2×C5×D4—34no—
324C2×C5×D4—121no—
325C2×C5×D4—121no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—62no—
329C22×C4×C5—62no—
330C22×C4×C5—121no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×C4×C5C22×D311yescharacteristic
334C2×C22⋊D5—34no—
335C2×C22⋊D5—34no—
336C2×C22⋊D5—62no—
337C2×C22⋊D5—62no—
338C2×C22⋊D5—62no—
339C2×C22⋊D5—62no—
340C22×Dic5—31no—
341C22×Dic5—31no—
342C22×Dic5—31no—
343C22×Dic5C22×D311yescharacteristic
344C22×Dic5C22×D311yescharacteristic
345C22×Dic5C22×D311yescharacteristic
346C2×C4×D5—22no—
347C2×C4×D5—22no—
348C2×C4×D5—41no—
349C2×C4×D5—62no—
350C2×C4×D5—62no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C22⋊C4—62no—
359C5×C22⋊C4—62no—
360C5×C22⋊C4—121no—
361C22⋊Dic5—34no—
362C22⋊Dic5—62no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365C22⋊Dic5—62no—
366#685—34no—
367#685—34no—
368#685—62no—
369#685—62no—
370#685C4×D314yescomplemented
371#685D1214yescomplemented
372C4⋊Dic5—121no—
373#683—62no—
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—31no—
387#386—151no—
388#386—151no—
389#385—151no—
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×D15C4×D414yescomplemented
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—41no—
414C2×C5×D3—41no—
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×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—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C23×D3—51no—
442C23×D3—54no—
443C23×D3—102no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—201no—
448C23×D3—201no—
449C23×D3C22×D511yescharacteristic
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—51no—
466C22×Dic3—102no—
467C22×Dic3—102no—
468C22×Dic3—201no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—41no—
472C2×D12—41no—
473C2×D12—54no—
474C2×D12—102no—
475C2×D12—102no—
476C2×D12C4×D514yescomplemented
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—22no—
493(C2×D3)⋊C4—41no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—102no—
502C4⋊Dic3—102no—
503C4⋊Dic3—201no—
504Dic3⋊C4—102no—
505C4×Dic3—102no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—32no—
526C22×D5—32no—
527C22×D5—32no—
528C22×D5—68no—
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—
542C5×D4—124no—
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—21no—
550C2×C4×C5—32no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—124no—
557C2×C4×C5C2×C4×D312yes—
558C2×C4×C5C2×D1212yes—
559C22⋊D5—68no—
560C22⋊D5—68no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—32no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5C2×C4×D312yes—
577C2×Dic5C2×D1212yes—
578C2×Dic5D3×D412yes—
579C4×D5—44no—
580C4×D5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
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—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
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—24no—
631C3×D5—24no—
632C5×D3—42no—
633C5×D3—42no—
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—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—21no—
654C22×D3—52no—
655C22×D3—52no—
656C22×D3—52no—
657C22×D3—108no—
658C22×D3—108no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—101no—
662C22×D3—101no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3C2×C4×D512yes—
669C22×D3C2×C4×D512yes—
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—52no—
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×Dic3D4×D512yes—
706D12—44no—
707D12—108no—
708C4×D3—44no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—121no—
718C22×C5—121no—
719C22×C5—121no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C22×D1211yescharacteristic
727C22×C5C2×#23511yescharacteristic
728C22×C5C2×D3×D411yescharacteristic
729C22×C5#100411yescharacteristic
730C22×C5D3×#4111yescharacteristic
731C22×C5#100911yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—34no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—1216no—
746C2×D5C4×D1214yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—22no—
753Dic5—22no—
754Dic5—22no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—31no—
760C24—51no—
761C24—154no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
769C2×D4—34no—
770C2×D4—121no—
771C2×D4—121no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—302no—
777C2×D4—302no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—121no—
788C22×C4—151no—
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—302no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—54no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—62no—
811C22⋊C4—121no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—302no—
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×C3#414411yescharacteristic
837C22×C3D5×#4111yescharacteristic
838C22×C3D5×#4111yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—54no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—102no—
857C2×D3—102no—
858C2×D3—102no—
859C2×D3—102no—
860C2×D3—2016no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—102no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—122no—
873C2×C5—122no—
874C2×C5C2×C4×D1211yescharacteristic
875C2×C5#549011yescharacteristic
876C2×C5#552711yescharacteristic
877C2×C5C4×D3×D411yescharacteristic
878C2×C5#554511yescharacteristic
879C2×C5D4×D1211yescharacteristic
880C2×C5#555411yescharacteristic
881D5—24no—
882D5—64no—
883C23—32no—
884C23—32no—
885C23—52no—
886C23—52no—
887C23—52no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—152no—
905C23—152no—
906C23—152no—
907C23—308no—
908C23—308no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
918C23C22×D3×D511yescharacteristic
919D4—124no—
920D4—308no—
921D4—308no—
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—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—124no—
945C2×C4—152no—
946C2×C4—204no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
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×C3#6582011yescharacteristic
962C2×C3C4×D4×D511yescharacteristic
963C2×C3C4×D4×D511yescharacteristic
964C2×C3#6592411yescharacteristic
965C2×C3#6594611yescharacteristic
966C2×C3#6594611yescharacteristic
967C2×C3#6599311yescharacteristic
968D3—42no—
969D3—42no—
970D3—104no—
971C5#7357711yescharacteristic, complemented, Sylow
972C22—54no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—102no—
980C22—102no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—154no—
994C22—302no—
995C22—302no—
996C22—302no—
997C22—302no—
998C22—302no—
999C22—302no—
1000C22—6016no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22C2×D5×D1211yescharacteristic
1003C22D5×#23511yescharacteristic
1004C22D3×D4×D511yescharacteristic
1005C22#9202511yescharacteristic
1006C22#9202711yescharacteristic
1007C22#9203411yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—62no—
1012C4—102no—
1013C4—102no—
1014C4—102no—
1015C4—121no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1060661111yescharacteristic, complemented, Sylow
1020C2—104no—
1021C2—122no—
1022C2—122no—
1023C2—304no—
1024C2C4×D5×D1211yescharacteristic
1025C2#1175320211yescharacteristic
1026C2#1175323611yescharacteristic
1027C2#1175325411yescharacteristic
1028C2#1175384011yescharacteristic
1029C2#1175387711yescharacteristic
1030C2#1175390011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
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×#91473C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. C2×C4×#1203C2semidirect
5. C2×#91441C2semidirect
6. #11750769C2semidirect
7. C5×#4665C2semidirect
8. C3×#64955C2semidirect
9. #11748919C2semidirect
10. #11748905C2semidirect
11. #11748900C2semidirect
12. #11748875C2semidirect
13. #11748764C2semidirect
14. #11748723C2semidirect
15. #11748715C2semidirect
20. C22×C4×C5×D3C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×#6712C22semidirect
32. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. C2×#6668C22semidirect
42. C2×(C2×D3)⋊Dic5C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. #91475C4semidirect
51. C3×C5×#95C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. #64955D3semidirect
83. C22×D3×D5C2×C4semidirect
97. C2×C5×D12C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1201C2×C4semidirect
120. #6714C2×C4semidirect
126. C3×#685C2×C4semidirect
127. C3×#685D4semidirect
131. #6667D4semidirect
136. (C2×D3)⋊Dic5C2×C4semidirect
153. #4665D5semidirect
184. C2×C4×Dic5C2×D3semidirect
185. C2×C4×Dic5C2×D3semidirect
189. C5×#95C2×D3semidirect
193. #3963C2×D3semidirect
280. C22×C4×D3C2×D5semidirect
297. C2×(C2×D3)⋊C4C2×D5semidirect
307. C3×#95C2×D5semidirect
311. C3⋊#95C2×D5semidirect
370. #685C4×D3semidirect
371. #685D12semidirect
406. C2×D15C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
476. C2×D12C4×D5semidirect
622. #95D3×D5semidirect
746. C2×D5C4×D12semidirect
824. C3×C5#2358semidirect
971. C5#73577semidirect
1019. C3#10606611semidirect

Maximal subgroups

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

subgroupindex
C2×#914752
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×C4×#12032
C2×#914412
#117507692
C5×#46652
C3×#649552
#117489192
#117489052
#117489002
#117488752
#117487642
#117487232
#117487152
#106066113
#735775