Finite Group Databasebeta

← #14322286

Subgroups — #14322286

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×C5×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#91567C211yesmaximal, characteristic
3C2×#91556C211yesmaximal, characteristic, complemented
4C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×#91446C211yesmaximal, characteristic, complemented
6C2×#91441C211yesmaximal, characteristic, complemented
7C2×#91395C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic, complemented
10#11749482C211yesmaximal, characteristic, complemented
11#11748915C211yesmaximal, characteristic, complemented
12#11748913C211yesmaximal, characteristic, complemented
13#11748908C211yesmaximal, characteristic, complemented
14#11748641C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16C4×#4086—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C4×C5×Dic3C2211yescharacteristic
36C5×#67⋊C4—24no—
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42#91567C418yescomplemented
43#91556—24no—
44Dic3×C22⋊D5—24no—
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×#6667C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×Dic3×Dic5C2211yescharacteristic
53C2×Dic3×Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91446—24no—
57#91441—24no—
58#91395—24no—
59#76293—51nomaximal, Hall
60C2×C4×C5×D4—31no—
61C2×#4086—31no—
62C2×C4×C22⋊D5—31no—
63C2×C4×C22⋊D5—31no—
64C2×C4×C22⋊D5—31no—
65C2×C4×C22⋊D5—31no—
66C2×C4×D20—31no—
67#65510—31no—
68#65277—31no—
69#65265—31no—
70#65246—31no—
71#65246—31no—
72#65246—31no—
73#65246D311yescharacteristic, complemented
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×Dic3—22no—
91C22×C5×Dic3—22no—
92C22×C5×Dic3—22no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C2×C3×C22⋊D5—22no—
100C2×C3×C22⋊D5—22no—
101C2×C3×C22⋊D5C2×C414yescomplemented
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
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×D5×Dic3—22no—
118C2×D5×Dic3—22no—
119C2×D5×Dic3—22no—
120C3×C5×C22⋊C4—22no—
121#6719—22no—
122#6714—22no—
123#6714—22no—
124#6712—22no—
125C4×Dic15—22no—
126C5×(C2×D3)⋊C4—22no—
127C5×Dic3⋊C4—22no—
128C4×C5×Dic3D414yescomplemented
129C3×C22⋊Dic5—22no—
130C3×#685—22no—
131C3×#685—22no—
132C3×#683—22no—
133C3×C4×Dic5—22no—
134Dic3⋊Dic5—22no—
135#6669—22no—
136#6668—22no—
137#6667—22no—
138(C2×D3)⋊Dic5—22no—
139(C2×D3)⋊Dic5—22no—
140#6665—22no—
141Dic3×Dic5—22no—
142Dic3×Dic5C2×C414yescomplemented
143Dic3×Dic5D414yescomplemented
144Dic3×Dic5D414yescomplemented
145C2×#940—51no—
146C2×D4×Dic3—51no—
147C2×#893—51no—
148C2×#67⋊C4—51no—
149C2×#67⋊C4—51no—
150C2×#67⋊C4—51no—
151C2×#67⋊C4D511yescharacteristic, complemented
152C3×#390—51no—
153#4975—51no—
154#4957—51no—
155#4957—51no—
156#4957—51no—
157#4957—51no—
158#4939—51no—
159C42×Dic3—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5C2×D311yescharacteristic
167C22×D20—31no—
168C22×C4×D5—31no—
169C22×C4×D5—31no—
170C4×C5×D4—64no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4C2×D311yescharacteristic
174C2×C42×C5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179#4086—38no—
180C4×C22⋊D5—64no—
181C4×C22⋊D5—64no—
182C4×C22⋊D5—64no—
183C4×C22⋊D5—64no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685C2×D311yescharacteristic
189C2×#685C2×D311yescharacteristic
190C2×C4⋊Dic5—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683C2×D311yescharacteristic
195C2×C4×Dic5—31no—
196C2×C4×Dic5—31no—
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200C2×C4×Dic5C2×D311yescharacteristic
201C4×D20—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—44no—
253C2×C5×Dic3C22×C412yes—
254C2×C5×Dic3C2×D412yes—
255C2×C5×Dic3C2×D412yes—
256C2×C5×Dic3C2×D412yes—
257C2×C5×Dic3C2×D412yes—
258C2×C5×Dic3#4112yes—
259C4×C5×D3—44no—
260C3×C22⋊D5—28no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5C22×C412yes—
267C2×C3×Dic5C2×D412yes—
268C2×C3×Dic5C2×D412yes—
269C2×C3×Dic5#4112yes—
270#1203—28no—
271#1202—28no—
272#1201—28no—
273#1200—44no—
274D5×Dic3—44no—
275C22×C3×D4—51no—
276C22×#67—51no—
277C22×#67—51no—
278C22×#67—51no—
279C22×#67C2×D511yescharacteristic
280C23×Dic3—51no—
281C23×Dic3C2×D511yescharacteristic
282C22×D12—51no—
283C22×C4×D3—51no—
284C22×C4×D3C2×D511yescharacteristic
285C2×C3×C4⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4C2×D511yescharacteristic
290C2×C3×C42—51no—
291C2×#217—51no—
292C2×#217—51no—
293#940—58no—
294D4×Dic3—104no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×C4⋊Dic3—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4C2×D511yescharacteristic
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308C2×C4×Dic3—51no—
309C2×C4×Dic3—51no—
310C2×C4×Dic3—51no—
311C2×C4×Dic3C2×D511yescharacteristic
312#893—104no—
313#67⋊C4—24no—
314#67⋊C4—104no—
315#67⋊C4—104no—
316#67⋊C4—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×C5—62no—
328C22×C4×C5—62no—
329C22×C4×C5—62no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5—62no—
333C22×C4×C5C22×D311yescharacteristic
334C22×C4×C5C22×D311yescharacteristic
335C2×C22⋊D5—22no—
336C2×C22⋊D5—22no—
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—34no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—62no—
342C2×C22⋊D5—62no—
343C2×C22⋊D5—62no—
344C2×C22⋊D5—62no—
345C2×C22⋊D5—62no—
346C2×C22⋊D5C4×D314yescomplemented
347C22×Dic5—31no—
348C22×Dic5—31no—
349C22×Dic5—31no—
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C22×Dic5C22×D311yescharacteristic
353C2×D20—34no—
354C2×D20—62no—
355C2×D20—62no—
356C2×C4×D5—62no—
357C2×C4×D5—62no—
358C2×C4×D5—62no—
359C2×C4×D5—62no—
360C2×C4×D5—62no—
361C2×C4×D5—62no—
362C5×C4⋊C4—62no—
363C5×C22⋊C4—22no—
364C5×C22⋊C4—62no—
365C42×C5—34no—
366C22⋊Dic5—22no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369C22⋊Dic5—62no—
370#685—22no—
371#685—22no—
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—22no—
382C4×Dic5—34no—
383C4×Dic5—34no—
384C4×Dic5—34no—
385C4×Dic5—62no—
386C4×Dic5—62no—
387C2×#127—151no—
388C2×C4×D4—31no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C2×C4×D4—151no—
394#390—51no—
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—22no—
443C3×Dic5—41no—
444C3×Dic5C4×D414yescomplemented
445C5×Dic3—41no—
446C5×Dic3C4×D414yescomplemented
447C5×Dic3#12714yescomplemented
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×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—22no—
461C2×#67—22no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—102no—
468C2×#67—102no—
469C2×#67—102no—
470C2×#67—102no—
471C2×#67C4×D514yescomplemented
472C22×Dic3—22no—
473C22×Dic3—22no—
474C22×Dic3—22no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—51no—
478C22×Dic3—102no—
479C22×Dic3—102no—
480C22×Dic3—102no—
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C2×D12—54no—
485C2×D12—102no—
486C2×D12—102no—
487C2×C4×D3—22no—
488C2×C4×D3—22no—
489C2×C4×D3—22no—
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×C22⋊C4—102no—
497C3×C22⋊C4—102no—
498C3×C42—102no—
499#217—102no—
500#217—102no—
501(C2×D3)⋊C4—22no—
502(C2×D3)⋊C4—102no—
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—54no—
513C4×Dic3—54no—
514C4×Dic3—54no—
515C4×Dic3—102no—
516C4×Dic3—102no—
517C4×Dic3C22⋊D514yescomplemented
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—32no—
558C2×C4×C5—32no—
559C2×C4×C5—61no—
560C2×C4×C5—61no—
561C2×C4×C5—61no—
562C2×C4×C5—124no—
563C2×C4×C5—124no—
564C2×C4×C5D3×D412yes—
565C22⋊D5—28no—
566C22⋊D5—68no—
567C22⋊D5—68no—
568C22⋊D5—68no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—21no—
572C2×Dic5—21no—
573C2×Dic5—21no—
574C2×Dic5—32no—
575C2×Dic5—32no—
576C2×Dic5—32no—
577C2×Dic5—32no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—61no—
581C2×Dic5—61no—
582C2×Dic5—61no—
583C2×Dic5C2×C4×D312yes—
584C2×Dic5D3×D412yes—
585C2×Dic5D3×D412yes—
586C2×Dic5#23712yes—
587D20—68no—
588C4×D5—124no—
589C4×D5—124no—
590C22×D4—31no—
591C22×D4—51no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601C4×D4—64no—
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—51no—
615C2×C22⋊C4—51no—
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—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—101no—
687C2×C3×C4C2×C22⋊D512yes—
688#67—28no—
689#67—108no—
690#67—108no—
691#67—108no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—44no—
696C2×Dic3—52no—
697C2×Dic3—52no—
698C2×Dic3—52no—
699C2×Dic3—52no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—204no—
706C2×Dic3C2×C4×D512yes—
707C2×Dic3#70912yes—
708C2×Dic3D4×D512yes—
709C2×Dic3D4×D512yes—
710C2×Dic3C2×C22⋊D512yes—
711C2×Dic3C2×C22⋊D512yes—
712D12—108no—
713C4×D3—44no—
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×D3×D411yescharacteristic
731C22×C5C2×D3×D411yescharacteristic
732C22×C5C2×D3×D411yescharacteristic
733C22×C5C2×#23711yescharacteristic
734C22×C5D3×#4111yescharacteristic
735C22×C5D3×#4111yescharacteristic
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—34no—
753C4×C5—41no—
754C4×C5—121no—
755Dic5—22no—
756Dic5—34no—
757Dic5—41no—
758Dic5—62no—
759Dic5—121no—
760Dic5#67⋊C414yescomplemented
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—62no—
790C22×C4—62no—
791C22×C4—62no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—62no—
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—102no—
815C22⋊C4—102no—
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—34no—
825C42—102no—
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×#70911yescharacteristic
848C22×C3C2×D4×D511yescharacteristic
849C22×C3C2×D4×D511yescharacteristic
850C22×C3D5×#4111yescharacteristic
851C22×C3D5×#4111yescharacteristic
852C22×C3C22×C22⋊D511yescharacteristic
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—102no—
871C3×C4—201no—
872Dic3—41no—
873Dic3—54no—
874Dic3—102no—
875Dic3—201no—
876Dic3C4×C22⋊D514yescomplemented
877Dic3#408614yescomplemented
878C2×C5—42no—
879C2×C5—122no—
880C2×C5C2×#67⋊C411yescharacteristic
881C2×C5C4×D3×D411yescharacteristic
882C2×C5C4×D3×D411yescharacteristic
883C2×C5#559611yescharacteristic
884C2×C5#559611yescharacteristic
885C2×C5#566811yescharacteristic
886C2×C5D3×#12711yescharacteristic
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—32no—
934C2×C4—32no—
935C2×C4—52no—
936C2×C4—52no—
937C2×C4—52no—
938C2×C4—52no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—124no—
948C2×C4—124no—
949C2×C4—152no—
950C2×C4—152no—
951C2×C4—152no—
952C2×C4—152no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—301no—
958C2×C4—604no—
959C2×C4—604no—
960C2×C4D3×C22⋊D512yes—
961C2×C3—42no—
962C2×C3—202no—
963C2×C3C4×D4×D511yescharacteristic
964C2×C3C4×D4×D511yescharacteristic
965C2×C3#6588211yescharacteristic
966C2×C3#6588211yescharacteristic
967C2×C3C2×C4×C22⋊D511yescharacteristic
968C2×C3C2×#408611yescharacteristic
969C2×C3#6616611yescharacteristic
970D3—42no—
971D3—202no—
972C5#7629311yescharacteristic, 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
1002C22D3×#70911yescharacteristic
1003C22D3×D4×D511yescharacteristic
1004C22D3×D4×D511yescharacteristic
1005C22D5×#23711yescharacteristic
1006C22#9202411yescharacteristic
1007C22C2×D3×C22⋊D511yescharacteristic
1008C4—22no—
1009C4—34no—
1010C4—34no—
1011C4—41no—
1012C4—54no—
1013C4—102no—
1014C4—121no—
1015C4—154no—
1016C4—201no—
1017C4—302no—
1018C4—601no—
1019C3C4×#408611yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—122no—
1022C2—202no—
1023C2—602no—
1024C2#1175283111yescharacteristic
1025C2#1175285511yescharacteristic
1026C2D5×#67⋊C411yescharacteristic
1027C2#1175320311yescharacteristic
1028C2C4×D3×C22⋊D511yescharacteristic
1029C2#1175480311yescharacteristic
1030C2D3×#408611yescharacteristic
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×C5×#67⋊C4C2semidirect
3. C2×#91556C2semidirect
4. C2×Dic3×C22⋊D5C2semidirect
5. C2×#91446C2semidirect
6. C2×#91441C2semidirect
7. C2×#91395C2semidirect
8. #11751058C2semidirect
9. C3×#65246C2semidirect
10. #11749482C2semidirect
11. #11748915C2semidirect
12. #11748913C2semidirect
13. #11748908C2semidirect
14. #11748641C2semidirect
15. C4×Dic3×Dic5C2semidirect
42. #91567C4semidirect
73. #65246D3semidirect
83. C2×#1220C2×C4semidirect
89. C2×C5×#67C2×C4semidirect
101. C2×C3×C22⋊D5C2×C4semidirect
107. C2×#1203C2×C4semidirect
110. C2×#1202C2×C4semidirect
113. C2×#1201C2×C4semidirect
128. C4×C5×Dic3D4semidirect
142. Dic3×Dic5C2×C4semidirect
143. Dic3×Dic5D4semidirect
144. Dic3×Dic5D4semidirect
151. C2×#67⋊C4D5semidirect
346. C2×C22⋊D5C4×D3semidirect
441. Dic15C4×D4semidirect
444. C3×Dic5C4×D4semidirect
446. C5×Dic3C4×D4semidirect
447. C5×Dic3#127semidirect
471. C2×#67C4×D5semidirect
517. C4×Dic3C22⋊D5semidirect
760. Dic5#67⋊C4semidirect
831. C3×C5C4×#127semidirect
876. Dic3C4×C22⋊D5semidirect
877. Dic3#4086semidirect
972. C5#76293semidirect
1019. C3C4×#4086semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#67⋊C42
C2×#915672
C2×#915562
C2×Dic3×C22⋊D52
C2×#914462
C2×#914412
C2×#913952
#117510582
C3×#652462
#117494822
#117489152
#117489132
#117489082
#117486412
C4×Dic3×Dic52
C4×#40863
#762935