Finite Group Databasebeta

← #14328161

Subgroups — #14328161

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×C22⋊C4×D15C211yesmaximal, characteristic, complemented
2C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#91573C211yesmaximal, characteristic
4C22×#6667C211yesmaximal, characteristic, complemented
5C2×C4×#1203C211yesmaximal, characteristic, complemented
6C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
7#11749511C211yesmaximal, characteristic, complemented
8#11749492C211yesmaximal, characteristic, complemented
9#11748918C211yesmaximal, characteristic, complemented
10#11748914C211yesmaximal, characteristic, complemented
11#11748908C211yesmaximal, characteristic, complemented
12#11748731C211yesmaximal, characteristic, complemented
13#11748730C211yesmaximal, characteristic, complemented
14#11748727C211yesmaximal, characteristic, complemented
15C4×#6667C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C23×C3×Dic5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C22⋊C4×D15—24no—
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
32C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C5×#67⋊C4—24no—
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C2×C3×C4×Dic5C2211yescharacteristic, complemented
38#91573C418yescomplemented
39C2×#6668C2211yescharacteristic, complemented
40C2×#6668C2211yescharacteristic, complemented
41C2×#6667—24no—
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50C4×#1203—24no—
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#73577—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685—31no—
62C2×D5×C22⋊C4—31no—
63#65509—31no—
64#65502—31no—
65#65499—31no—
66#65279—31no—
67#65278—31no—
68#65246—31no—
69#65245—31no—
70C22⋊C4×Dic5D311yescharacteristic, complemented
71#65229—31no—
72C4×#685—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15—22no—
75C23×D15—22no—
76C23×D15—22no—
77C23×D15—22no—
78C23×D15—41no—
79C23×D15—41no—
80C23×D15C2×C414yescomplemented
81C23×D15C2311yescharacteristic
82C23×D15C2311yescharacteristic
83C23×C5×D3C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C2×C4×D15—22no—
89C2×C4×D15—22no—
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—41no—
93C2×C4×D15—41no—
94C2×C5×#67—22no—
95C2×C5×#67—22no—
96C2×C5×#67C2×C414yescomplemented
97C22×C5×Dic3—22no—
98C22×C5×Dic3—22no—
99C22×C5×Dic3—41no—
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C2×C4×C5×D3—22no—
104C2×C4×C5×D3—22no—
105C2×C4×C5×D3—41no—
106C22×C3×Dic5—22no—
107C22×C3×Dic5—22no—
108C22×C3×Dic5—41no—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×#1203—22no—
114C2×#1203—22no—
115C2×#1203—41no—
116C2×#1203—41no—
117C2×#1203C2×C414yescomplemented
118C2×#1203C2×C414yescomplemented
119C3×C5×C22⋊C4D414yescomplemented
120#6719—22no—
121#6714—22no—
122#6714—22no—
123C5×(C2×D3)⋊C4—22no—
124C5×Dic3⋊C4—22no—
125C4×C5×Dic3—22no—
126C3×C22⋊Dic5C2×C414yescomplemented
127C3×C4×Dic5—22no—
128C3×C4×Dic5—41no—
129#6668—22no—
130#6668—41no—
131#6667—22no—
132#6667—22no—
133#6667—22no—
134#6667C2×C414yescomplemented
135#6667C2×C414yescomplemented
136#6667D414yescomplemented
137(C2×D3)⋊Dic5—22no—
138(C2×D3)⋊Dic5—41no—
139C22×(C2×D3)⋊C4—51no—
140C2×#882—51no—
141C2×#67⋊C4D511yescharacteristic, complemented
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#4665—51no—
154C24×D5—31no—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5C2×D311yescharacteristic
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5C2×D311yescharacteristic
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—64no—
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5C2×D311yescharacteristic, complemented
186C2×C4×Dic5C2×D311yescharacteristic, complemented
187D5×C22⋊C4—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963C2×D311yescharacteristic, complemented
193#3963C2×D311yescharacteristic, complemented
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C2×D412yes—
201C23×C3×C5#4112yes—
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—28no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—28no—
215C22×D15—44no—
216C22×D15—44no—
217C22×D15—44no—
218C22×D15—44no—
219C22×D15—44no—
220C22×D15C22×C412yes—
221C22×D15C22×C412yes—
222C22×D15C2×D412yes—
223C22×D15#4112yes—
224C22×C5×D3—21no—
225C22×C5×D3—21no—
226C22×C5×D3—21no—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3—21no—
230C22×C5×D3C22×C412yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5C2×D412yes—
236C2×C3×C4×C5C2×D412yes—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C4×D15—44no—
244C4×D15—44no—
245C5×#67—28no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—44no—
254C2×C5×Dic3C22×C412yes—
255C2×C5×Dic3C2×D412yes—
256C4×C5×D3—44no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—44no—
267C2×C3×Dic5C22×C412yes—
268C2×C3×Dic5C22×C412yes—
269C2×C3×Dic5C2×D412yes—
270#1203—28no—
271#1203—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67C2×D511yescharacteristic
275C23×Dic3C2×D511yescharacteristic
276C22×D12—51no—
277C22×D12—51no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4C2×D511yescharacteristic
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—51no—
296C2×(C2×D3)⋊C4—104no—
297C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×Dic3⋊C4C2×D511yescharacteristic, complemented
301C2×C4×Dic3C2×D511yescharacteristic, complemented
302#882—58no—
303#67⋊C4—24no—
304D3×C22⋊C4—104no—
305C4×D12—104no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5—31no—
316C23×D5—34no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—62no—
321C23×D5—121no—
322C23×D5—121no—
323C2×C5×D4—34no—
324C2×C5×D4—62no—
325C2×C5×D4—62no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—62no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5—62no—
333C22×C4×C5—121no—
334C22×C4×C5—121no—
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—121no—
342C2×C22⋊D5—121no—
343C22×Dic5—22no—
344C22×Dic5—22no—
345C22×Dic5—31no—
346C22×Dic5—31no—
347C22×Dic5—41no—
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D311yescharacteristic
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
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×C22⋊C4—62no—
360C5×C22⋊C4D1214yescomplemented
361C42×C5—62no—
362C22⋊Dic5—62no—
363C22⋊Dic5—62no—
364C22⋊Dic5—121no—
365C22⋊Dic5C4×D314yescomplemented
366#685—34no—
367#685—34no—
368#685—34no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—62no—
375#683—121no—
376C4×Dic5—22no—
377C4×Dic5—41no—
378C2×#120—151no—
379C2×C4×D4—31no—
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—151no—
390#385—151no—
391C4×C22⋊C4—51no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5C4×D414yescomplemented
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—416no—
417C2×D15—41no—
418C2×D15—41no—
419C2×D15—41no—
420C2×D15—41no—
421C2×D15C4×D414yescomplemented
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3—41no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—41no—
432Dic15—41no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3C22×D511yescharacteristic
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—51no—
455C22×C3×C4—102no—
456C22×C3×C4—102no—
457C22×C3×C4—201no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—22no—
461C2×#67—22no—
462C2×#67C4×D514yescomplemented
463C22×Dic3—22no—
464C22×Dic3—22no—
465C22×Dic3—41no—
466C22×Dic3—51no—
467C22×Dic3—51no—
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⋊C4C22⋊D514yescomplemented
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—54no—
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—102no—
501(C2×D3)⋊C4—201no—
502C4⋊Dic3—102no—
503C4⋊Dic3—201no—
504Dic3⋊C4—22no—
505C4×Dic3—22no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—32no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5C2×C4×D312yes—
518C23×C5C2×D1212yes—
519C23×C5#23512yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—32no—
522C22×D5—32no—
523C22×D5—32no—
524C22×D5—32no—
525C22×D5—68no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—68no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5—124no—
541C22×D5—124no—
542C5×D4—68no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—32no—
548C2×C4×C5—32no—
549C2×C4×C5—61no—
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—124no—
557C2×C4×C5—124no—
558C2×C4×C5C2×D1212yes—
559C2×C4×C5C2×D1212yes—
560C22⋊D5—68no—
561C22⋊D5—124no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—44no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5C2×C4×D312yes—
579C2×Dic5C2×C4×D312yes—
580C2×Dic5D3×D412yes—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—31no—
589C23×C4—51no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—64no—
594C4×D4—304no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—151no—
611C2×C22⋊C4—304no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4D3×D511yescharacteristic
614C2×C42—31no—
615C2×C42—51no—
616C2×C42—51no—
617#95—51no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—24no—
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5#51811yescharacteristic
627C2×C3×C5D4211yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#55111yescharacteristic
631D15—24no—
632D15—42no—
633C5×D3—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3C2×C4×D512yes—
639C23×C3#70912yes—
640C23×C3C2×C22⋊D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—52no—
649C22×D3—52no—
650C22×D3—52no—
651C22×D3—52no—
652C22×D3—108no—
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—101no—
662C22×D3—101no—
663C22×D3—108no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3C2×C4×D512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—52no—
675C2×C3×C4—52no—
676C2×C3×C4—52no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—204no—
687C2×C3×C4C2×C22⋊D512yes—
688C2×C3×C4C2×C22⋊D512yes—
689#67—28no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—44no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3C2×C4×D512yes—
705C2×Dic3D4×D512yes—
706D12—108no—
707D12—204no—
708C4×D3—44no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5C4×D1214yescomplemented
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—34no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—1216no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—22no—
753Dic5—22no—
754Dic5—22no—
755Dic5—41no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—151no—
760C24—151no—
761C24—154no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
768C24C2×D3×D511yescharacteristic
769C2×D4—34no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—154no—
773C2×D4—154no—
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—51no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—121no—
792C22×C4—121no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—201no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—54no—
808C22⋊C4—62no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4#120314yescomplemented
821C42—62no—
822C42—102no—
823C42—201no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3C4×C22⋊D514yescomplemented
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×#70911yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3C22×C22⋊D511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—54no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—102no—
852C2×D3—102no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—2016no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—22no—
869Dic3—41no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
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—64no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—32no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—152no—
895C23—152no—
896C23—152no—
897C23—152no—
898C23—308no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—308no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—604no—
911C23—604no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23#677112yes—
916C23C4×D3×D512yes—
917C23C2×#120312yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—52no—
929C2×C4—52no—
930C2×C4—52no—
931C2×C4—61no—
932C2×C4—61no—
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—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—124no—
948C2×C4—124no—
949C2×C4—204no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4C2×#120312yes—
959C2×C4C2×#120312yes—
960C2×C3—24no—
961C2×C3C4×D4×D511yescharacteristic
962C2×C3#6587911yescharacteristic
963C2×C3#6588411yescharacteristic
964C2×C3#6589011yescharacteristic
965C2×C3C2×C4×C22⋊D511yescharacteristic
966C2×C3D4×C22⋊D511yescharacteristic
967C2×C3#6616311yescharacteristic
968D3—42no—
969D3—104no—
970D3—202no—
971C5#7357711yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—154no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—6016no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22C4×#120314yescomplemented
1001C22C2×#677111yescharacteristic
1002C22C2×C4×D3×D511yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22#9202411yescharacteristic
1005C22#9202611yescharacteristic
1006C22#9202711yescharacteristic
1007C22C22×#120311yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—102no—
1013C4—102no—
1014C4—102no—
1015C4—121no—
1016C4—201no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—122no—
1022C2—304no—
1023C2—602no—
1024C2#1175280911yescharacteristic
1025C2#1175307211yescharacteristic
1026C2#1175320311yescharacteristic
1027C2#1175320411yescharacteristic
1028C2C2×C4×#120311yescharacteristic
1029C2D4×#120311yescharacteristic
1030C2#1175498211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91573C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C22⋊C4×D15C2semidirect
2. C2×C5×#67⋊C4C2semidirect
4. C22×#6667C2semidirect
5. C2×C4×#1203C2semidirect
6. C3×C22⋊C4×Dic5C2semidirect
7. #11749511C2semidirect
8. #11749492C2semidirect
9. #11748918C2semidirect
10. #11748914C2semidirect
11. #11748908C2semidirect
12. #11748731C2semidirect
13. #11748730C2semidirect
14. #11748727C2semidirect
15. C4×#6667C2semidirect
22. C22×C4×C5×D3C22semidirect
31. C2×C5×(C2×D3)⋊C4C22semidirect
32. C2×C5×Dic3⋊C4C22semidirect
33. C2×C4×C5×Dic3C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. C2×C3×C4×Dic5C22semidirect
38. #91573C4semidirect
39. C2×#6668C22semidirect
40. C2×#6668C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
49. C2×(C2×D3)⋊Dic5C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
70. C22⋊C4×Dic5D3semidirect
80. C23×D15C2×C4semidirect
96. C2×C5×#67C2×C4semidirect
117. C2×#1203C2×C4semidirect
118. C2×#1203C2×C4semidirect
119. C3×C5×C22⋊C4D4semidirect
126. C3×C22⋊Dic5C2×C4semidirect
134. #6667C2×C4semidirect
135. #6667C2×C4semidirect
136. #6667D4semidirect
141. C2×#67⋊C4D5semidirect
185. C2×C4×Dic5C2×D3semidirect
186. C2×C4×Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
280. C22×C4×D3C2×D5semidirect
297. C2×(C2×D3)⋊C4C2×D5semidirect
300. C2×Dic3⋊C4C2×D5semidirect
301. C2×C4×Dic3C2×D5semidirect
360. C5×C22⋊C4D12semidirect
365. C22⋊Dic5C4×D3semidirect
399. C22×C3×C5C4×D4semidirect
421. C2×D15C4×D4semidirect
462. C2×#67C4×D5semidirect
487. C3×C22⋊C4C22⋊D5semidirect
724. C22×C5C4×D12semidirect
820. C22⋊C4#1203semidirect
824. C3×C5#2358semidirect
831. C22×C3C4×C22⋊D5semidirect
971. C5#73577semidirect
1000. C22C4×#1203semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D152
C2×C5×#67⋊C42
C2×#915732
C22×#66672
C2×C4×#12032
C3×C22⋊C4×Dic52
#117495112
#117494922
#117489182
#117489142
#117489082
#117487312
#117487302
#117487272
C4×#66672
#106141293
#735775