Finite Group Databasebeta

← C4×#91567 #14322280

Subgroups — C4×#91567 #14322280

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×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×#91567C211yesmaximal, characteristic
5C2×C4×#1203C211yesmaximal, characteristic, complemented
6C2×C4×#1202C211yesmaximal, characteristic, complemented
7C2×C4×#1201C211yesmaximal, characteristic, complemented
8#11749489C211yesmaximal, characteristic, complemented
9#11749483C211yesmaximal, characteristic, complemented
10#11749482C211yesmaximal, characteristic, complemented
11#11748916C211yesmaximal, characteristic, complemented
12#11748913C211yesmaximal, characteristic, complemented
13#11748909C211yesmaximal, characteristic, complemented
14#11748641C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16C4×#4086—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C2×#6719C2211yescharacteristic
28C4×#1220—24no—
29C2×#6714C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic
33C4×C5×#67—24no—
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C3×C4×C22⋊D5—24no—
39C2×C3×#685C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42#91567C418yesdirect product factor
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×#6669C2211yescharacteristic
45C2×#6668C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×Dic3×Dic5C2211yescharacteristic
53C2×Dic3×Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56C4×#1203—24no—
57C4×#1202—24no—
58C4×#1201—24no—
59C4×#940—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⋊D5D311yescharacteristic, complemented
66C2×C4×D20—31no—
67#65510—31no—
68#65277—31no—
69#65265—31no—
70#65246—31no—
71#65246—31no—
72#65246—31no—
73#65246—31no—
74C42×Dic5—31no—
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5—22no—
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—22no—
85C2×#1220—22no—
86C2×#1220C2×C414yescomplemented
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C4×D15—22no—
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C2×C5×#67C2×C414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3—22no—
101C2×C4×C5×D3—22no—
102C2×C3×C22⋊D5—22no—
103C2×C3×C22⋊D5—22no—
104C2×C3×C22⋊D5C2×C414yescomplemented
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×#1203—22no—
112C2×#1203—22no—
113C2×#1203C2×C414yescomplemented
114C2×#1202—22no—
115C2×#1202—22no—
116C2×#1202C2×C414yescomplemented
117C2×#1201—22no—
118C2×#1201—22no—
119C2×#1201C2×C414yescomplemented
120#6719—22no—
121#6714—22no—
122#6712—22no—
123C4×Dic15D414yescomplemented
124C5×#217—22no—
125C5×(C2×D3)⋊C4—22no—
126C5×Dic3⋊C4—22no—
127C4×C5×Dic3D414yescomplemented
128C3×C22⋊Dic5—22no—
129C3×#685—22no—
130C3×#683—22no—
131C3×C4×Dic5D414yescomplemented
132Dic3⋊Dic5—22no—
133#6669—22no—
134#6668—22no—
135#6667—22no—
136#6667—22no—
137(C2×D3)⋊Dic5—22no—
138(C2×D3)⋊Dic5—22no—
139#6665—22no—
140#6665—22no—
141Dic3×Dic5—22no—
142Dic3×Dic5—22no—
143Dic3×Dic5—22no—
144Dic3×Dic5C2×C414yescomplemented
145C2×C3×C4×D4—51no—
146C2×#940—51no—
147C2×C4×#67—51no—
148C2×C4×#67—51no—
149C2×C4×#67—51no—
150C2×C4×#67D511yescharacteristic, complemented
151C2×C4×D12—51no—
152#5221—51no—
153#4988—51no—
154#4975—51no—
155#4957—51no—
156#4957—51no—
157#4957—51no—
158#4957—51no—
159C42×Dic3—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C23×C4×C5C2×D311yescharacteristic
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×D5C2×D311yescharacteristic
170C4×C5×D4—64no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
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—24no—
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×#685—31no—
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—44no—
236C2×C3×C4×C5C2×D412yes—
237C2×C3×C4×C5C2×D412yes—
238C2×C3×C4×C5C2×D412yes—
239#1220—28no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15C22×C412yes—
246C2×Dic15C2×D412yes—
247C2×Dic15C2×D412yes—
248C2×Dic15#4112yes—
249C4×D15—44no—
250C5×#67—28no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3C22×C412yes—
257C2×C5×Dic3C2×D412yes—
258C2×C5×Dic3C2×D412yes—
259C2×C5×Dic3#4112yes—
260C4×C5×D3—44no—
261C3×C22⋊D5—28no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5C22×C412yes—
268C2×C3×Dic5C2×D412yes—
269C2×C3×Dic5C2×D412yes—
270C2×C3×Dic5#4112yes—
271C3×C4×D5—44no—
272#1203—28no—
273#1202—28no—
274#1201—28no—
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C23×C3×C4C2×D511yescharacteristic
278C22×#67—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67C2×D511yescharacteristic
282C22×D12—51no—
283C22×C4×D3—51no—
284C22×C4×D3C2×D511yescharacteristic
285C3×C4×D4—104no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C42—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
294#940—58no—
295C4×#67—24no—
296C4×#67—104no—
297C4×#67—104no—
298C4×#67—104no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4C2×D511yescharacteristic
305C2×C4⋊Dic3—51no—
306C2×Dic3⋊C4—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4C2×D511yescharacteristic
310C2×C4×Dic3—51no—
311C2×C4×Dic3—51no—
312C2×C4×Dic3—51no—
313C2×C4×Dic3—51no—
314C2×C4×Dic3—51no—
315C2×C4×Dic3C2×D511yescharacteristic
316C4×D12—104no—
317C24×C5—31no—
318C24×C5C22×D311yescharacteristic
319C23×D5—31no—
320C23×D5C22×D311yescharacteristic
321C2×C5×D4—34no—
322C2×C5×D4—62no—
323C2×C5×D4—62no—
324C22×C4×C5—22no—
325C22×C4×C5—22no—
326C22×C4×C5—22no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
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—22no—
357C2×C4×D5—22no—
358C2×C4×D5—22no—
359C2×C4×D5—62no—
360C2×C4×D5—62no—
361C2×C4×D5—62no—
362C5×C4⋊C4—62no—
363C5×C22⋊C4—62no—
364C5×C22⋊C4—62no—
365C42×C5—34no—
366C22⋊Dic5—22no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369C22⋊Dic5—62no—
370#685—22no—
371#685—62no—
372#685—62no—
373#685—62no—
374#685—62no—
375#685—62no—
376C4⋊Dic5—62no—
377#683—22no—
378#683—62no—
379#683—62no—
380#683—62no—
381C4×Dic5—34no—
382C4×Dic5—34no—
383C4×Dic5—62no—
384C4×Dic5—62no—
385C4×Dic5—62no—
386C4×Dic5#6714yescomplemented
387C2×#127—151no—
388C2×C4×D4—31no—
389C2×C4×D4—51no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C2×C4×D4—151no—
394#390—151no—
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—41no—
438C3×C4×C5#12714yescomplemented
439Dic15—22no—
440Dic15—41no—
441Dic15C4×D414yescomplemented
442C3×Dic5—22no—
443C3×Dic5—41no—
444C3×Dic5C4×D414yescomplemented
445C5×Dic3—22no—
446C5×Dic3—41no—
447C5×Dic3C4×D414yescomplemented
448C24×C3—51no—
449C24×C3C22×D511yescharacteristic
450C23×D3—51no—
451C23×D3C22×D511yescharacteristic
452C2×C3×D4—54no—
453C2×C3×D4—102no—
454C2×C3×D4—102no—
455C22×C3×C4—22no—
456C22×C3×C4—22no—
457C22×C3×C4—22no—
458C22×C3×C4—51no—
459C22×C3×C4—51no—
460C22×C3×C4—51no—
461C22×C3×C4—102no—
462C22×C3×C4—102no—
463C22×C3×C4—102no—
464C22×C3×C4C22×D511yescharacteristic
465C22×C3×C4C22×D511yescharacteristic
466C2×#67—22no—
467C2×#67—22no—
468C2×#67—54no—
469C2×#67—54no—
470C2×#67—54no—
471C2×#67—102no—
472C2×#67—102no—
473C2×#67—102no—
474C2×#67—102no—
475C2×#67—102no—
476C2×#67—102no—
477C2×#67C4×D514yescomplemented
478C22×Dic3—51no—
479C22×Dic3—51no—
480C22×Dic3—51no—
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C2×D12—54no—
485C2×D12—102no—
486C2×D12—102no—
487C2×C4×D3—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—102no—
495C3×C22⋊C4—102no—
496C3×C42—54no—
497#217—22no—
498#217—102no—
499#217—102no—
500#217—102no—
501(C2×D3)⋊C4—22no—
502(C2×D3)⋊C4—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—102no—
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—32no—
552C2×C4×C5—32no—
553C2×C4×C5—32no—
554C2×C4×C5—32no—
555C2×C4×C5—44no—
556C2×C4×C5—61no—
557C2×C4×C5—61no—
558C2×C4×C5—61no—
559C2×C4×C5—61no—
560C2×C4×C5—61no—
561C2×C4×C5—124no—
562C2×C4×C5D3×D412yes—
563C2×C4×C5D3×D412yes—
564C2×C4×C5C2×#6712yes—
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×Dic5#23512yes—
585C2×Dic5C2×#6712yes—
586C2×Dic5C2×#6712yes—
587D20—68no—
588C4×D5—44no—
589C4×D5—124no—
590C22×D4—31no—
591C22×D4—51no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C23×C4—31no—
597C23×C4—51no—
598C23×C4—151no—
599C23×C4D3×D511yescharacteristic
600#127—158no—
601C4×D4—64no—
602C4×D4—104no—
603C4×D4—304no—
604C4×D4—304no—
605C4×D4—304no—
606C4×D4—304no—
607C2×C4⋊C4—31no—
608C2×C4⋊C4—51no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C4⋊C4—151no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—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⋊C4—151no—
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—44no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—52no—
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×C4D4×D512yes—
688C2×C3×C4D4×D512yes—
689C2×C3×C4C2×C22⋊D512yes—
690#67—28no—
691#67—108no—
692#67—108no—
693#67—108no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—52no—
700C2×Dic3—52no—
701C2×Dic3—52no—
702C2×Dic3—52no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3C2×C4×D512yes—
709C2×Dic3#70912yes—
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×#23511yescharacteristic
731C22×C5C2×D3×D411yescharacteristic
732C22×C5C2×D3×D411yescharacteristic
733C22×C5D3×#4111yescharacteristic
734C22×C5D3×#4111yescharacteristic
735C22×C5C22×#6711yescharacteristic
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—41no—
740C2×D5—41no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—62no—
744C2×D5—62no—
745C2×D5—62no—
746C2×D5—121no—
747C2×D5—121no—
748C2×D5—121no—
749C2×D5—121no—
750C4×C5—34no—
751C4×C5—41no—
752C4×C5—62no—
753C4×C5—121no—
754C4×C5#94014yescomplemented
755Dic5—22no—
756Dic5—34no—
757Dic5—41no—
758Dic5—62no—
759Dic5—121no—
760Dic5C4×#6714yescomplemented
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—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—51no—
790C22×C4—51no—
791C22×C4—51no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—62no—
795C22×C4—102no—
796C22×C4—102no—
797C22×C4—102no—
798C22×C4—151no—
799C22×C4—151no—
800C22×C4—151no—
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—62no—
813C22⋊C4—62no—
814C22⋊C4—102no—
815C22⋊C4—102no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—302no—
821C22⋊C4—302no—
822C22⋊C4—302no—
823C22⋊C4—302no—
824C42—34no—
825C42—54no—
826C42—154no—
827C42—154no—
828C42—302no—
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—41no—
868C3×C4—54no—
869C3×C4—102no—
870C3×C4—201no—
871C3×C4#408614yescomplemented
872Dic3—22no—
873Dic3—41no—
874Dic3—54no—
875Dic3—102no—
876Dic3—201no—
877Dic3C4×C22⋊D514yescomplemented
878C2×C5—42no—
879C2×C5—122no—
880C2×C5C4×D3×D411yescharacteristic
881C2×C5C4×D3×D411yescharacteristic
882C2×C5#554811yescharacteristic
883C2×C5#554811yescharacteristic
884C2×C5C2×C4×#6711yescharacteristic
885C2×C5C2×#94011yescharacteristic
886C2×C5#583211yescharacteristic
887D5—42no—
888D5—122no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—32no—
896C23—52no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—152no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—301no—
914C23—301no—
915C23—301no—
916C23C4×D3×D512yes—
917C23C22×D3×D511yescharacteristic
918D4—68no—
919D4—108no—
920D4—308no—
921D4—308no—
922D4—308no—
923D4—308no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—44no—
932C2×C4—52no—
933C2×C4—52no—
934C2×C4—52no—
935C2×C4—52no—
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—124no—
947C2×C4—152no—
948C2×C4—152no—
949C2×C4—152no—
950C2×C4—152no—
951C2×C4—204no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—604no—
958C2×C4D5×#6712yes—
959C2×C4D3×C22⋊D512yes—
960C2×C4#679012yes—
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—
972C5C4×#94011yescharacteristic, complemented, Sylow
973C22—22no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—201no—
991C22—201no—
992C22—201no—
993C22—201no—
994C22—302no—
995C22—302no—
996C22—302no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22D5×#23511yescharacteristic
1003C22D3×#70911yescharacteristic
1004C22#9201611yescharacteristic
1005C22C2×D5×#6711yescharacteristic
1006C22C2×D3×C22⋊D511yescharacteristic
1007C22C2×#679011yescharacteristic
1008C4—34no—
1009C4—41no—
1010C4—54no—
1011C4—62no—
1012C4—102no—
1013C4—121no—
1014C4—154no—
1015C4—201no—
1016C4—302no—
1017C4—601no—
1018C4#9156714yesdirect product factor
1019C3C4×#408611yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—122no—
1022C2—202no—
1023C2—602no—
1024C2#1175431111yescharacteristic
1025C2#1175453911yescharacteristic
1026C2#1175455511yescharacteristic
1027C2C4×D5×#6711yescharacteristic
1028C2C4×D3×C22⋊D511yescharacteristic
1029C2C4×#679011yescharacteristic
1030C2C2×#9156711yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#127
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C2×C4×C5×#67C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
5. C2×C4×#1203C2semidirect
6. C2×C4×#1202C2semidirect
7. C2×C4×#1201C2semidirect
8. #11749489C2semidirect
9. #11749483C2semidirect
10. #11749482C2semidirect
11. #11748916C2semidirect
12. #11748913C2semidirect
13. #11748909C2semidirect
14. #11748641C2semidirect
15. C4×Dic3×Dic5C2semidirect
42. #91567C4direct (N × H)
65. C2×C4×C22⋊D5D3semidirect
86. C2×#1220C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
104. C2×C3×C22⋊D5C2×C4semidirect
113. C2×#1203C2×C4semidirect
116. C2×#1202C2×C4semidirect
119. C2×#1201C2×C4semidirect
123. C4×Dic15D4semidirect
127. C4×C5×Dic3D4semidirect
131. C3×C4×Dic5D4semidirect
144. Dic3×Dic5C2×C4semidirect
150. C2×C4×#67D5semidirect
346. C2×C22⋊D5C4×D3semidirect
386. C4×Dic5#67semidirect
438. C3×C4×C5#127semidirect
441. Dic15C4×D4semidirect
444. C3×Dic5C4×D4semidirect
447. C5×Dic3C4×D4semidirect
477. C2×#67C4×D5semidirect
517. C4×Dic3C22⋊D5semidirect
754. C4×C5#940semidirect
760. Dic5C4×#67semidirect
831. C3×C5C4×#127semidirect
871. C3×C4#4086semidirect
877. Dic3C4×C22⋊D5semidirect
972. C5C4×#940semidirect
1018. C4#91567direct (N × H)
1019. C3C4×#4086semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C4×C5×#672
C2×C3×C4×C22⋊D52
C2×#915672
C2×C4×#12032
C2×C4×#12022
C2×C4×#12012
#117494892
#117494832
#117494822
#117489162
#117489132
#117489092
#117486412
C4×Dic3×Dic52
C4×#40863
C4×#9405