Finite Group Databasebeta

← #14320296

Subgroups — #14320296

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6777C211yesmaximal, characteristic
2C22×C4×D3×D5C211yesmaximal, characteristic, complemented
3C2×#91473C211yesmaximal, characteristic, complemented
4C2×#91473C211yesmaximal, characteristic, complemented
5C2×#91473C211yesmaximal, characteristic, complemented
6D15×#95C211yesmaximal, characteristic, complemented
7C5×#4665C211yesmaximal, characteristic, complemented
8C3×#64954C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748910C211yesmaximal, characteristic, complemented
11#11748906C211yesmaximal, characteristic, complemented
12#11748905C211yesmaximal, characteristic, complemented
13#11748901C211yesmaximal, characteristic, complemented
14#11748896C211yesmaximal, characteristic, complemented
15#11748888C211yesmaximal, characteristic, complemented
16D5×#386—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×D3×D5C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic, complemented
24C22×C3×D20C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic, complemented
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C22×#1200C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic, complemented
31C22×D5×Dic3C2211yescharacteristic, complemented
32C2×#6777—24no—
33C2×#6777—24no—
34C2×#6777C418yescomplemented
35C2×C4×D3×D5—24no—
36C2×C4×D3×D5—24no—
37C2×C4×D3×D5—24no—
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
47C2×#6665C2211yescharacteristic, complemented
48C2×#6665C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic, complemented
50#91473—24no—
51#91473—24no—
52#91473—24no—
53C3×C5×#95C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57C5×C3⋊#95C2211yescharacteristic, complemented
58C3×#3963C2211yescharacteristic, complemented
59#90994C2211yescharacteristic, complemented
60#90994C2211yescharacteristic, complemented
61D3×#386—51nomaximal, Hall
62C22×D4×D5—31no—
63C23×C4×D5—31no—
64C2×D5×C22⋊C4—31no—
65C2×D5×C22⋊C4—31no—
66C2×D5×C22⋊C4—31no—
67C5×#386—31no—
68#65509—31no—
69#65502—31no—
70#65247—31no—
71#65245—31no—
72#65245—31no—
73#64954—31no—
74#64954D311yescharacteristic, complemented
75D5×#95—31no—
76D5×#95—31no—
77C23×D15C2311yescharacteristic
78C23×C5×D3C2311yescharacteristic
79C23×C5×D3C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C23×C3×D5C2311yescharacteristic
82C22×D3×D5—22no—
83C22×D3×D5—22no—
84C22×D3×D5—22no—
85C22×D3×D5—22no—
86C22×D3×D5—22no—
87C22×D3×D5—22no—
88C22×D3×D5—22no—
89C22×D3×D5—22no—
90C22×D3×D5—22no—
91C22×D3×D5—22no—
92C22×D3×D5C2×C414yes—
93C22×D3×D5C2×C414yescomplemented
94C22×D3×D5D414yes—
95C22×D3×D5D414yes—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×C4×D15—22no—
103C2×C4×D15—22no—
104C2×C4×D15—22no—
105C2×C4×D15—22no—
106C2×C4×D15—22no—
107C2×C4×D15—22no—
108C2×C4×D15—22no—
109C2×C4×D15C2×C414yescomplemented
110C2×C4×D15D414yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—22no—
114C2×C5×D12—22no—
115C2×C5×D12C2×C414yescomplemented
116C2×C4×C5×D3—22no—
117C2×C4×C5×D3—22no—
118C2×C4×C5×D3—22no—
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C2×C3×D20—22no—
122C2×C3×D20—22no—
123C2×C3×D20C2×C414yescomplemented
124C2×C3×C4×D5—22no—
125C2×C3×C4×D5—22no—
126C2×C3×C4×D5—22no—
127C2×#1201—22no—
128C2×#1201—22no—
129C2×#1201—22no—
130C2×#1201—22no—
131C2×#1201C2×C414yescomplemented
132C2×#1201C2×C414yescomplemented
133C2×#1200—22no—
134C2×#1200—22no—
135C2×#1200—22no—
136C2×#1200—22no—
137C2×#1200—22no—
138C2×#1200D414yescomplemented
139C2×D3×Dic5—22no—
140C2×D3×Dic5—22no—
141C2×D3×Dic5—22no—
142C2×D5×Dic3—22no—
143C2×D5×Dic3—22no—
144C2×D5×Dic3—22no—
145#6777—232no—
146C4×D3×D5—232no—
147C5×(C2×D3)⋊C4—22no—
148C5×(C2×D3)⋊C4—22no—
149C5×(C2×D3)⋊C4—22no—
150C3×#685—22no—
151C3×#685—22no—
152C3×#685—22no—
153(C2×D3)⋊Dic5—22no—
154(C2×D3)⋊Dic5—22no—
155(C2×D3)⋊Dic5—22no—
156#6665—22no—
157#6665—22no—
158#6665—22no—
159C22×D3×D4—51no—
160C23×C4×D3—51no—
161C2×D3×C22⋊C4—51no—
162C2×D3×C22⋊C4—51no—
163C2×D3×C22⋊C4—51no—
164C3×#386—51no—
165#5220—51no—
166#5213—51no—
167#4958—51no—
168#4956—51no—
169#4956—51no—
170#4665—51no—
171#4665D511yescharacteristic, complemented
172D3×#95—51no—
173D3×#95—51no—
174C24×D5—31no—
175C24×D5—31no—
176C22×C5×D4—31no—
177C23×C4×C5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C23×Dic5—31no—
181C2×D4×D5—38no—
182C2×D4×D5—64no—
183C2×D4×D5—64no—
184C22×D20C2×D311yescharacteristic
185C22×C4×D5—31no—
186C22×C4×D5—31no—
187C22×C4×D5—31no—
188C22×C4×D5—31no—
189C22×C4×D5—31no—
190C22×C4×D5—31no—
191C22×C4×D5—64no—
192C22×C4×D5—64no—
193C22×C4×D5—64no—
194C22×C4×D5C2×D311yescharacteristic, complemented
195C2×C5×C22⋊C4—31no—
196C2×C5×C22⋊C4—31no—
197C2×C5×C22⋊C4—31no—
198C2×C22⋊Dic5—31no—
199C2×C22⋊Dic5—31no—
200C2×C22⋊Dic5—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685C2×D311yescharacteristic, complemented
205C2×#685C2×D311yescharacteristic, complemented
206C2×#685C2×D311yescharacteristic, complemented
207D5×C22⋊C4—64no—
208D5×C22⋊C4—64no—
209D5×C22⋊C4—64no—
210C5×#95—31no—
211C5×#95C2×D311yescharacteristic, complemented
212#3963—31no—
213#3963—31no—
214#3963—31no—
215#3963—31no—
216#3963—31no—
217#3963C2×D311yescharacteristic, complemented
218C2×#386—151noSylow
219C23×C3×C5C2411yescharacteristic
220C22×D15C22×C412yes—
221C22×D15C2×D412yes—
222C22×D15C2×D412yes—
223C22×D15C2×D412yes—
224C22×D15C2×D412yes—
225C22×D15#4112yes—
226C22×D15#4112yes—
227C22×C5×D3—21no—
228C22×C5×D3—21no—
229C22×C5×D3—21no—
230C22×C5×D3—21no—
231C22×C5×D3—21no—
232C22×C5×D3—21no—
233C22×C5×D3—21no—
234C22×C5×D3—21no—
235C22×C5×D3—21no—
236C22×C5×D3—21no—
237C22×C5×D3C22×C412yes—
238C22×C5×D3C22×C412yescomplemented
239C22×C5×D3C2×D412yes—
240C22×C5×D3C2×D412yes—
241C22×C3×D5—21no—
242C22×C3×D5—21no—
243C22×C3×D5—21no—
244C22×C3×D5—21no—
245C22×C3×D5—21no—
246C22×C3×D5—21no—
247C22×C3×D5—21no—
248C22×C3×D5—21no—
249C22×C3×D5—21no—
250C22×C3×D5—21no—
251C22×C3×D5C22×C412yes—
252C22×C3×D5C22×C412yescomplemented
253C22×C3×D5C2×D412yes—
254C22×C3×D5C2×D412yes—
255C2×D3×D5—28no—
256C2×D3×D5—28no—
257C2×D3×D5—28no—
258C2×D3×D5—28no—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—28no—
262C2×D3×D5—28no—
263C2×D3×D5—28no—
264C2×D3×D5—44no—
265C2×D3×D5—44no—
266C2×D3×D5—44no—
267C2×D3×D5—44no—
268C2×D3×D5C22⋊C4116yescomplemented
269C2×C3×C4×C5—21no—
270C2×C3×C4×C5—21no—
271C2×C3×C4×C5—21no—
272C2×C3×C4×C5—21no—
273C2×C3×C4×C5—21no—
274C2×C3×C4×C5—21no—
275C2×C3×C4×C5—21no—
276C2×C3×C4×C5C22×C412yescomplemented
277C2×C3×C4×C5C2×D412yescomplemented
278C2×Dic15—21no—
279C2×Dic15—21no—
280C2×Dic15—21no—
281C2×Dic15—21no—
282C2×Dic15—21no—
283C2×Dic15—21no—
284C2×Dic15—21no—
285C2×Dic15C22×C412yescomplemented
286C2×Dic15C2×D412yescomplemented
287C4×D15—28no—
288C4×D15—28no—
289C4×D15—44no—
290C2×C5×Dic3—21no—
291C2×C5×Dic3—21no—
292C2×C5×Dic3—21no—
293C2×C5×Dic3—21no—
294C2×C5×Dic3—21no—
295C2×C5×Dic3C2×D412yescomplemented
296C5×D12—28no—
297C4×C5×D3—28no—
298C2×C3×Dic5—21no—
299C2×C3×Dic5—21no—
300C2×C3×Dic5—21no—
301C2×C3×Dic5—21no—
302C2×C3×Dic5—21no—
303C2×C3×Dic5C2×D412yescomplemented
304C3×D20—28no—
305C3×C4×D5—28no—
306#1201—28no—
307#1201—28no—
308#1200—28no—
309#1200—44no—
310D3×Dic5—28no—
311D5×Dic3—28no—
312C24×D3—51no—
313C24×D3—51no—
314C22×C3×D4—51no—
315C23×C3×C4—51no—
316C22×#67—51no—
317C22×#67—51no—
318C23×Dic3—51no—
319C2×D3×D4—58no—
320C2×D3×D4—104no—
321C2×D3×D4—104no—
322C22×D12C2×D511yescharacteristic
323C22×C4×D3—51no—
324C22×C4×D3—51no—
325C22×C4×D3—51no—
326C22×C4×D3—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C22×C4×D3—104no—
330C22×C4×D3—104no—
331C22×C4×D3—104no—
332C22×C4×D3C2×D511yescharacteristic, complemented
333C2×C3×C22⋊C4—51no—
334C2×C3×C22⋊C4—51no—
335C2×C3×C22⋊C4—51no—
336C2×#217—51no—
337C2×#217—51no—
338C2×#217—51no—
339C2×(C2×D3)⋊C4—51no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
343C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
344C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
345D3×C22⋊C4—104no—
346D3×C22⋊C4—104no—
347D3×C22⋊C4—104no—
348C3×#95—51no—
349C3×#95C2×D511yescharacteristic, complemented
350C3⋊#95—51no—
351C3⋊#95—51no—
352C3⋊#95—51no—
353C3⋊#95—51no—
354C3⋊#95—51no—
355C3⋊#95C2×D511yescharacteristic, complemented
356C24×C5—31no—
357C24×C5—31no—
358C23×D5—31no—
359C23×D5—34no—
360C23×D5—34no—
361C23×D5—34no—
362C23×D5—34no—
363C23×D5—62no—
364C23×D5—62no—
365C23×D5—62no—
366C23×D5—62no—
367C23×D5—62no—
368C23×D5—62no—
369C23×D5—62no—
370C23×D5—62no—
371C23×D5—62no—
372C23×D5—62no—
373C23×D5C22×D311yescharacteristic
374C23×D5C22×D311yescharacteristic
375C2×C5×D4—34no—
376C2×C5×D4—62no—
377C2×C5×D4—62no—
378C22×C4×C5—31no—
379C22×C4×C5—31no—
380C22×C4×C5—62no—
381C22×C4×C5—62no—
382C22×C4×C5—62no—
383C22×C4×C5C22×D311yescharacteristic
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—62no—
389C2×C22⋊D5—62no—
390C2×C22⋊D5—62no—
391C2×C22⋊D5—62no—
392C22×Dic5—31no—
393C22×Dic5—31no—
394C22×Dic5—31no—
395C22×Dic5—62no—
396C22×Dic5—62no—
397C22×Dic5—62no—
398C22×Dic5C22×D311yescharacteristic
399C22×Dic5C22×D311yescharacteristic
400D4×D5—632no—
401C2×D20—22no—
402C2×D20—22no—
403C2×D20C4×D314yescomplemented
404C2×C4×D5—22no—
405C2×C4×D5—22no—
406C2×C4×D5—22no—
407C2×C4×D5—34no—
408C2×C4×D5—34no—
409C2×C4×D5—34no—
410C2×C4×D5—632no—
411C2×C4×D5—62no—
412C2×C4×D5—62no—
413C2×C4×D5—62no—
414C2×C4×D5—62no—
415C2×C4×D5—62no—
416C2×C4×D5—62no—
417C2×C4×D5—62no—
418C2×C4×D5—62no—
419C2×C4×D5—62no—
420C2×C4×D5—62no—
421C2×C4×D5—62no—
422C2×C4×D5—62no—
423C2×C4×D5—62no—
424C2×C4×D5—62no—
425C2×C4×D5—62no—
426C5×C22⋊C4—62no—
427C5×C22⋊C4—62no—
428C5×C22⋊C4—62no—
429C22⋊Dic5—62no—
430C22⋊Dic5—62no—
431C22⋊Dic5—62no—
432#685—22no—
433#685—22no—
434#685—22no—
435#685—62no—
436#685—62no—
437#685—62no—
438C23×D4—151no—
439C24×C4—151no—
440C22×C22⋊C4—151no—
441C22×C22⋊C4—151no—
442C22×C22⋊C4—151no—
443#386—31no—
444#386—51no—
445#386—151no—
446#386—151no—
447#386—151no—
448#386—151no—
449#386—151no—
450#386—151no—
451C2×#95—151no—
452C2×#95—151no—
453C22×C3×C5C23×C411yescharacteristic
454C22×C3×C5C22×D411yescharacteristic
455C22×C3×C5C22×D411yescharacteristic
456C22×C3×C5C22×D411yescharacteristic
457C22×C3×C5C22×D411yescharacteristic
458C22×C3×C5C2×#4111yescharacteristic
459C22×C3×C5C2×#4111yescharacteristic
460C2×D15C2×C22⋊C414yes—
461C2×D15C4×D414yes—
462C2×D15C4×D414yes—
463C2×D15#12014yes—
464C2×D15#12114yes—
465C2×D15#12114yes—
466C2×D15#12314yes—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3—22no—
476C2×C5×D3—41no—
477C2×C5×D3—41no—
478C2×C5×D3—41no—
479C2×C5×D3—41no—
480C2×C5×D3C2×C22⋊C414yescomplemented
481C2×C3×D5—22no—
482C2×C3×D5—22no—
483C2×C3×D5—22no—
484C2×C3×D5—22no—
485C2×C3×D5—22no—
486C2×C3×D5—22no—
487C2×C3×D5—22no—
488C2×C3×D5—22no—
489C2×C3×D5—22no—
490C2×C3×D5—41no—
491C2×C3×D5—41no—
492C2×C3×D5—41no—
493C2×C3×D5—41no—
494C2×C3×D5C2×C22⋊C414yescomplemented
495D3×D5—232no—
496D3×D5—416no—
497C3×C4×C5—22no—
498C3×C4×C5—22no—
499C3×C4×C5—41no—
500Dic15—22no—
501Dic15—22no—
502Dic15—41no—
503C3×Dic5—22no—
504C3×Dic5—41no—
505C5×Dic3—22no—
506C5×Dic3—41no—
507C24×C3—51no—
508C24×C3—51no—
509C23×D3—51no—
510C23×D3—54no—
511C23×D3—54no—
512C23×D3—54no—
513C23×D3—54no—
514C23×D3—102no—
515C23×D3—102no—
516C23×D3—102no—
517C23×D3—102no—
518C23×D3—102no—
519C23×D3—102no—
520C23×D3—102no—
521C23×D3—102no—
522C23×D3—102no—
523C23×D3—102no—
524C23×D3C22×D511yescharacteristic
525C23×D3C22×D511yescharacteristic
526C2×C3×D4—54no—
527C2×C3×D4—102no—
528C2×C3×D4—102no—
529C22×C3×C4—51no—
530C22×C3×C4—51no—
531C22×C3×C4—102no—
532C22×C3×C4—102no—
533C22×C3×C4—102no—
534C22×C3×C4C22×D511yescharacteristic
535C22×C3×C4C22×D511yescharacteristic
536C22×C3×C4C22×D511yescharacteristic
537C2×#67—54no—
538C2×#67—54no—
539C2×#67—102no—
540C2×#67—102no—
541C2×#67—102no—
542C2×#67—102no—
543C22×Dic3—51no—
544C22×Dic3—51no—
545C22×Dic3—51no—
546C22×Dic3—102no—
547C22×Dic3—102no—
548C22×Dic3—102no—
549C22×Dic3C22×D511yescharacteristic
550C22×Dic3C22×D511yescharacteristic
551D3×D4—1032no—
552C2×D12—22no—
553C2×D12—22no—
554C2×D12C4×D514yescomplemented
555C2×C4×D3—22no—
556C2×C4×D3—22no—
557C2×C4×D3—22no—
558C2×C4×D3—54no—
559C2×C4×D3—54no—
560C2×C4×D3—54no—
561C2×C4×D3—1032no—
562C2×C4×D3—102no—
563C2×C4×D3—102no—
564C2×C4×D3—102no—
565C2×C4×D3—102no—
566C2×C4×D3—102no—
567C2×C4×D3—102no—
568C2×C4×D3—102no—
569C2×C4×D3—102no—
570C2×C4×D3—102no—
571C2×C4×D3—102no—
572C2×C4×D3—102no—
573C2×C4×D3—102no—
574C2×C4×D3—102no—
575C2×C4×D3—102no—
576C2×C4×D3—102no—
577C3×C22⋊C4—102no—
578C3×C22⋊C4—102no—
579C3×C22⋊C4—102no—
580#217—102no—
581#217—102no—
582#217—102no—
583(C2×D3)⋊C4—22no—
584(C2×D3)⋊C4—22no—
585(C2×D3)⋊C4—22no—
586(C2×D3)⋊C4—102no—
587(C2×D3)⋊C4—102no—
588(C2×D3)⋊C4—102no—
589C23×C5—32no—
590C23×C5—32no—
591C23×C5—32no—
592C23×C5—32no—
593C23×C5—61no—
594C23×C5—61no—
595C23×C5—61no—
596C23×C5—61no—
597C23×C5—61no—
598C23×C5—61no—
599C23×C5—61no—
600C23×C5—61no—
601C23×C5—61no—
602C23×C5—61no—
603C23×C5C23×D311yescharacteristic
604C22×D5—21no—
605C22×D5—21no—
606C22×D5—21no—
607C22×D5—21no—
608C22×D5—21no—
609C22×D5—21no—
610C22×D5—21no—
611C22×D5—21no—
612C22×D5—21no—
613C22×D5—21no—
614C22×D5—32no—
615C22×D5—32no—
616C22×D5—32no—
617C22×D5—32no—
618C22×D5—32no—
619C22×D5—32no—
620C22×D5—32no—
621C22×D5—316no—
622C22×D5—68no—
623C22×D5—68no—
624C22×D5—68no—
625C22×D5—68no—
626C22×D5—68no—
627C22×D5—68no—
628C22×D5—68no—
629C22×D5—68no—
630C22×D5—68no—
631C22×D5—124no—
632C22×D5—124no—
633C22×D5—124no—
634C22×D5—124no—
635C22×D5C2×C4×D312yes—
636C22×D5C2×C4×D312yescomplemented
637C22×D5D3×D412yes—
638C22×D5D3×D412yes—
639C5×D4—68no—
640C2×C4×C5—21no—
641C2×C4×C5—21no—
642C2×C4×C5—21no—
643C2×C4×C5—21no—
644C2×C4×C5—21no—
645C2×C4×C5—21no—
646C2×C4×C5—21no—
647C2×C4×C5—32no—
648C2×C4×C5—68no—
649C2×C4×C5—61no—
650C2×C4×C5—61no—
651C2×C4×C5—61no—
652C2×C4×C5—61no—
653C2×C4×C5—61no—
654C2×C4×C5C2×C4×D312yescomplemented
655C2×C4×C5D3×D412yescomplemented
656C22⋊D5—68no—
657C22⋊D5—68no—
658C2×Dic5—21no—
659C2×Dic5—21no—
660C2×Dic5—21no—
661C2×Dic5—21no—
662C2×Dic5—21no—
663C2×Dic5—32no—
664C2×Dic5—32no—
665C2×Dic5—68no—
666C2×Dic5—61no—
667C2×Dic5—61no—
668C2×Dic5—61no—
669C2×Dic5—61no—
670C2×Dic5—61no—
671C2×Dic5—61no—
672C2×Dic5—61no—
673C2×Dic5D3×D412yescomplemented
674D20—28no—
675C4×D5—28no—
676C4×D5—68no—
677C4×D5—68no—
678C4×D5—68no—
679C4×D5—68no—
680C4×D5—124no—
681C4×D5—124no—
682C25—151no—
683C25—151no—
684C22×D4—31no—
685C22×D4—51no—
686C22×D4—158no—
687C22×D4—151no—
688C22×D4—151no—
689C22×D4—304no—
690C22×D4—304no—
691C23×C4—31no—
692C23×C4—51no—
693C23×C4—151no—
694C23×C4—151no—
695C23×C4—151no—
696C23×C4—151no—
697C23×C4—151no—
698C23×C4—151no—
699C23×C4—151no—
700C23×C4—304no—
701C23×C4—304no—
702C23×C4—304no—
703C2×C22⋊C4—31no—
704C2×C22⋊C4—31no—
705C2×C22⋊C4—31no—
706C2×C22⋊C4—51no—
707C2×C22⋊C4—51no—
708C2×C22⋊C4—51no—
709C2×C22⋊C4—151no—
710C2×C22⋊C4—151no—
711C2×C22⋊C4—151no—
712C2×C22⋊C4—151no—
713C2×C22⋊C4—151no—
714C2×C22⋊C4—151no—
715C2×C22⋊C4—304no—
716C2×C22⋊C4—304no—
717C2×C22⋊C4—304no—
718#95—31no—
719#95—51no—
720#95—151no—
721#95—151no—
722#95—151no—
723#95—151no—
724#95—151no—
725#95D3×D511yescharacteristic, complemented
726C2×C3×C5C22×C22⋊C411yescharacteristic
727C2×C3×C5C2×C4×D411yescharacteristic
728C2×C3×C5C2×C4×D411yescharacteristic
729C2×C3×C5C2×#12011yescharacteristic
730C2×C3×C5C2×#12111yescharacteristic
731C2×C3×C5C2×#12111yescharacteristic
732C2×C3×C5C2×#12311yescharacteristic
733D15#38618yescomplemented
734C3×D5—24no—
735C3×D5—42no—
736C5×D3—24no—
737C5×D3—42no—
738C23×C3—52no—
739C23×C3—52no—
740C23×C3—52no—
741C23×C3—52no—
742C23×C3—101no—
743C23×C3—101no—
744C23×C3—101no—
745C23×C3—101no—
746C23×C3—101no—
747C23×C3—101no—
748C23×C3—101no—
749C23×C3—101no—
750C23×C3—101no—
751C23×C3—101no—
752C23×C3C23×D511yescharacteristic
753C22×D3—21no—
754C22×D3—21no—
755C22×D3—21no—
756C22×D3—21no—
757C22×D3—21no—
758C22×D3—21no—
759C22×D3—21no—
760C22×D3—21no—
761C22×D3—21no—
762C22×D3—21no—
763C22×D3—52no—
764C22×D3—52no—
765C22×D3—52no—
766C22×D3—52no—
767C22×D3—52no—
768C22×D3—52no—
769C22×D3—52no—
770C22×D3—516no—
771C22×D3—108no—
772C22×D3—108no—
773C22×D3—108no—
774C22×D3—108no—
775C22×D3—108no—
776C22×D3—108no—
777C22×D3—108no—
778C22×D3—108no—
779C22×D3—108no—
780C22×D3—204no—
781C22×D3—204no—
782C22×D3—204no—
783C22×D3—204no—
784C22×D3C2×C4×D512yes—
785C22×D3C2×C4×D512yescomplemented
786C22×D3D4×D512yes—
787C22×D3D4×D512yes—
788C3×D4—108no—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—21no—
793C2×C3×C4—21no—
794C2×C3×C4—21no—
795C2×C3×C4—21no—
796C2×C3×C4—52no—
797C2×C3×C4—108no—
798C2×C3×C4—101no—
799C2×C3×C4—101no—
800C2×C3×C4—101no—
801C2×C3×C4—101no—
802C2×C3×C4—101no—
803C2×C3×C4C2×C4×D512yescomplemented
804C2×C3×C4D4×D512yescomplemented
805#67—108no—
806#67—108no—
807C2×Dic3—21no—
808C2×Dic3—21no—
809C2×Dic3—21no—
810C2×Dic3—21no—
811C2×Dic3—21no—
812C2×Dic3—52no—
813C2×Dic3—52no—
814C2×Dic3—108no—
815C2×Dic3—101no—
816C2×Dic3—101no—
817C2×Dic3—101no—
818C2×Dic3—101no—
819C2×Dic3—101no—
820C2×Dic3—101no—
821C2×Dic3—101no—
822C2×Dic3D4×D512yescomplemented
823D12—28no—
824C4×D3—28no—
825C4×D3—108no—
826C4×D3—108no—
827C4×D3—108no—
828C4×D3—108no—
829C4×D3—204no—
830C4×D3—204no—
831C22×C5—34no—
832C22×C5—62no—
833C22×C5—62no—
834C22×C5—62no—
835C22×C5—62no—
836C22×C5—62no—
837C22×C5—62no—
838C22×C5—62no—
839C22×C5—62no—
840C22×C5—62no—
841C22×C5—121no—
842C22×C5—121no—
843C22×C5—121no—
844C22×C5—121no—
845C22×C5C22×C4×D311yescharacteristic
846C22×C5C2×D3×D411yescharacteristic
847C22×C5C2×D3×D411yescharacteristic
848C22×C5C2×D3×D411yescharacteristic
849C22×C5C2×D3×D411yescharacteristic
850C22×C5D3×#4111yescharacteristic
851C22×C5D3×#4111yescharacteristic
852C2×D5—22no—
853C2×D5—22no—
854C2×D5—22no—
855C2×D5—22no—
856C2×D5—22no—
857C2×D5—22no—
858C2×D5—22no—
859C2×D5—22no—
860C2×D5—22no—
861C2×D5—34no—
862C2×D5—34no—
863C2×D5—34no—
864C2×D5—34no—
865C2×D5—34no—
866C2×D5—34no—
867C2×D5—34no—
868C2×D5—41no—
869C2×D5—41no—
870C2×D5—41no—
871C2×D5—41no—
872C2×D5—632no—
873C2×D5—1216no—
874C2×D5D3×C22⋊C414yescomplemented
875C4×C5—22no—
876C4×C5—22no—
877C4×C5—41no—
878C4×C5—62no—
879C4×C5—121no—
880Dic5—22no—
881Dic5—41no—
882Dic5—62no—
883Dic5—62no—
884Dic5—121no—
885C24—31no—
886C24—31no—
887C24—51no—
888C24—51no—
889C24—154no—
890C24—154no—
891C24—154no—
892C24—154no—
893C24—151no—
894C24—302no—
895C24—302no—
896C24—302no—
897C24—302no—
898C24—302no—
899C24—302no—
900C24—302no—
901C24—302no—
902C24—302no—
903C24—302no—
904C2×D4—34no—
905C2×D4—54no—
906C2×D4—62no—
907C2×D4—62no—
908C2×D4—102no—
909C2×D4—102no—
910C2×D4—154no—
911C2×D4—154no—
912C2×D4—3032no—
913C2×D4—302no—
914C2×D4—302no—
915C2×D4—302no—
916C2×D4—302no—
917C22×C4—31no—
918C22×C4—31no—
919C22×C4—51no—
920C22×C4—51no—
921C22×C4—62no—
922C22×C4—62no—
923C22×C4—62no—
924C22×C4—102no—
925C22×C4—102no—
926C22×C4—102no—
927C22×C4—154no—
928C22×C4—151no—
929C22×C4—151no—
930C22×C4—154no—
931C22×C4—154no—
932C22×C4—151no—
933C22×C4—302no—
934C22×C4—302no—
935C22×C4—302no—
936C22×C4—302no—
937C22×C4—302no—
938C22×C4—302no—
939C22×C4—302no—
940C22×C4—302no—
941C22×C4—302no—
942C22×C4—302no—
943C22×C4—302no—
944C22×C4—3032no—
945C22×C4—302no—
946C22×C4—302no—
947C22×C4—302no—
948C22×C4—302no—
949C22×C4—302no—
950C22×C4—302no—
951C22×C4—302no—
952C22×C4C2×D3×D511yescharacteristic
953C22×C4C2×D3×D511yescharacteristic
954C22×C4C2×D3×D511yescharacteristic
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—102no—
959C22⋊C4—102no—
960C22⋊C4—102no—
961C22⋊C4—302no—
962C22⋊C4—302no—
963C22⋊C4—302no—
964C22⋊C4—302no—
965C22⋊C4—302no—
966C22⋊C4—302no—
967C3×C5C2×#38611yescharacteristic, complemented, Hall
968C22×C3—54no—
969C22×C3—102no—
970C22×C3—102no—
971C22×C3—102no—
972C22×C3—102no—
973C22×C3—102no—
974C22×C3—102no—
975C22×C3—102no—
976C22×C3—102no—
977C22×C3—102no—
978C22×C3—201no—
979C22×C3—201no—
980C22×C3—201no—
981C22×C3—201no—
982C22×C3C22×C4×D511yescharacteristic
983C22×C3C2×D4×D511yescharacteristic
984C22×C3C2×D4×D511yescharacteristic
985C22×C3C2×D4×D511yescharacteristic
986C22×C3C2×D4×D511yescharacteristic
987C22×C3D5×#4111yescharacteristic
988C22×C3D5×#4111yescharacteristic
989C2×D3—22no—
990C2×D3—22no—
991C2×D3—22no—
992C2×D3—22no—
993C2×D3—22no—
994C2×D3—22no—
995C2×D3—22no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—41no—
999C2×D3—41no—
1000C2×D3—41no—
1001C2×D3—41no—
1002C2×D3—54no—
1003C2×D3—54no—
1004C2×D3—54no—
1005C2×D3—54no—
1006C2×D3—54no—
1007C2×D3—54no—
1008C2×D3—54no—
1009C2×D3—1032no—
1010C2×D3—2016no—
1011C2×D3D5×C22⋊C414yescomplemented
1012C3×C4—22no—
1013C3×C4—22no—
1014C3×C4—41no—
1015C3×C4—102no—
1016C3×C4—201no—
1017Dic3—22no—
1018Dic3—41no—
1019Dic3—102no—
1020Dic3—102no—
1021Dic3—201no—
1022C2×C5—64no—
1023C2×C5—122no—
1024C2×C5C2×D3×C22⋊C411yescharacteristic
1025C2×C5C4×D3×D411yescharacteristic
1026C2×C5C4×D3×D411yescharacteristic
1027C2×C5D3×#12011yescharacteristic
1028C2×C5D3×#12111yescharacteristic
1029C2×C5D3×#12111yescharacteristic
1030C2×C5D3×#12311yescharacteristic
1031D5—24no—
1032D5—38no—
1033D5—42no—
1034C23—32no—
1035C23—32no—
1036C23—32no—
1037C23—32no—
1038C23—52no—
1039C23—52no—
1040C23—52no—
1041C23—52no—
1042C23—61no—
1043C23—61no—
1044C23—61no—
1045C23—61no—
1046C23—61no—
1047C23—61no—
1048C23—61no—
1049C23—61no—
1050C23—61no—
1051C23—61no—
1052C23—101no—
1053C23—101no—
1054C23—101no—
1055C23—101no—
1056C23—101no—
1057C23—101no—
1058C23—101no—
1059C23—101no—
1060C23—101no—
1061C23—101no—
1062C23—1516no—
1063C23—152no—
1064C23—152no—
1065C23—152no—
1066C23—152no—
1067C23—152no—
1068C23—152no—
1069C23—152no—
1070C23—308no—
1071C23—308no—
1072C23—308no—
1073C23—308no—
1074C23—308no—
1075C23—308no—
1076C23—308no—
1077C23—308no—
1078C23—308no—
1079C23—604no—
1080C23—604no—
1081C23—604no—
1082C23—604no—
1083C23C22×D3×D511yescharacteristic
1084D4—68no—
1085D4—108no—
1086D4—308no—
1087D4—308no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—32no—
1096C2×C4—52no—
1097C2×C4—68no—
1098C2×C4—61no—
1099C2×C4—61no—
1100C2×C4—61no—
1101C2×C4—61no—
1102C2×C4—61no—
1103C2×C4—108no—
1104C2×C4—101no—
1105C2×C4—101no—
1106C2×C4—101no—
1107C2×C4—101no—
1108C2×C4—101no—
1109C2×C4—152no—
1110C2×C4—152no—
1111C2×C4—308no—
1112C2×C4—308no—
1113C2×C4—308no—
1114C2×C4—308no—
1115C2×C4—308no—
1116C2×C4—301no—
1117C2×C4—301no—
1118C2×C4—301no—
1119C2×C4—301no—
1120C2×C4—301no—
1121C2×C4—301no—
1122C2×C4—301no—
1123C2×C4—604no—
1124C2×C4—604no—
1125C2×C4C4×D3×D512yescomplemented
1126C2×C4#677712yescomplemented
1127C2×C3—104no—
1128C2×C3—202no—
1129C2×C3C2×D5×C22⋊C411yescharacteristic
1130C2×C3C4×D4×D511yescharacteristic
1131C2×C3C4×D4×D511yescharacteristic
1132C2×C3D5×#12011yescharacteristic
1133C2×C3D5×#12111yescharacteristic
1134C2×C3D5×#12111yescharacteristic
1135C2×C3D5×#12311yescharacteristic
1136D3—24no—
1137D3—42no—
1138D3—58no—
1139C5D3×#38611yescharacteristic, complemented, Sylow
1140C22—34no—
1141C22—54no—
1142C22—62no—
1143C22—62no—
1144C22—62no—
1145C22—62no—
1146C22—62no—
1147C22—62no—
1148C22—62no—
1149C22—62no—
1150C22—62no—
1151C22—102no—
1152C22—102no—
1153C22—102no—
1154C22—102no—
1155C22—102no—
1156C22—102no—
1157C22—102no—
1158C22—102no—
1159C22—102no—
1160C22—121no—
1161C22—121no—
1162C22—121no—
1163C22—121no—
1164C22—154no—
1165C22—154no—
1166C22—154no—
1167C22—154no—
1168C22—154no—
1169C22—154no—
1170C22—154no—
1171C22—201no—
1172C22—201no—
1173C22—201no—
1174C22—201no—
1175C22—3032no—
1176C22—6016no—
1177C22C2×C4×D3×D511yescharacteristic
1178C22C2×#677711yescharacteristic
1179C22#9201611yescharacteristic
1180C22D3×D4×D511yescharacteristic
1181C22D3×D4×D511yescharacteristic
1182C22D3×D4×D511yescharacteristic
1183C22#9203411yescharacteristic
1184C4—22no—
1185C4—22no—
1186C4—41no—
1187C4—62no—
1188C4—102no—
1189C4—121no—
1190C4—201no—
1191C4—302no—
1192C4—302no—
1193C4—601no—
1194C3D5×#38611yescharacteristic, complemented, Sylow
1195C2—64no—
1196C2—104no—
1197C2—122no—
1198C2—158no—
1199C2—202no—
1200C2C4×#677711yescharacteristic
1201C2D3×D5×C22⋊C411yescharacteristic
1202C2#1175320711yescharacteristic
1203C2#1175321911yescharacteristic
1204C2#1175384011yescharacteristic
1205C2#1175384411yescharacteristic
1206C2#1175385011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6777C2
hypercenter#95D3×D5
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C22×C4×D3×D5C2semidirect
3. C2×#91473C2semidirect
4. C2×#91473C2semidirect
5. C2×#91473C2semidirect
6. D15×#95C2semidirect
7. C5×#4665C2semidirect
8. C3×#64954C2semidirect
9. #11748911C2semidirect
10. #11748910C2semidirect
11. #11748906C2semidirect
12. #11748905C2semidirect
13. #11748901C2semidirect
14. #11748896C2semidirect
15. #11748888C2semidirect
23. C22×C4×C5×D3C22semidirect
25. C22×C3×C4×D5C22semidirect
30. C22×D3×Dic5C22semidirect
31. C22×D5×Dic3C22semidirect
34. C2×#6777C4semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C5×(C2×D3)⋊C4C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
44. C2×(C2×D3)⋊Dic5C22semidirect
45. C2×(C2×D3)⋊Dic5C22semidirect
46. C2×(C2×D3)⋊Dic5C22semidirect
47. C2×#6665C22semidirect
48. C2×#6665C22semidirect
49. C2×#6665C22semidirect
53. C3×C5×#95C22semidirect
54. #91115C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
57. C5×C3⋊#95C22semidirect
58. C3×#3963C22semidirect
59. #90994C22semidirect
60. #90994C22semidirect
74. #64954D3semidirect
93. C22×D3×D5C2×C4semidirect
109. C2×C4×D15C2×C4semidirect
110. C2×C4×D15D4semidirect
115. C2×C5×D12C2×C4semidirect
123. C2×C3×D20C2×C4semidirect
131. C2×#1201C2×C4semidirect
132. C2×#1201C2×C4semidirect
138. C2×#1200D4semidirect
171. #4665D5semidirect
194. C22×C4×D5C2×D3semidirect
204. C2×#685C2×D3semidirect
205. C2×#685C2×D3semidirect
206. C2×#685C2×D3semidirect
211. C5×#95C2×D3semidirect
217. #3963C2×D3semidirect
238. C22×C5×D3C22×C4semidirect
252. C22×C3×D5C22×C4semidirect
268. C2×D3×D5C22⋊C4semidirect
276. C2×C3×C4×C5C22×C4semidirect
277. C2×C3×C4×C5C2×D4semidirect
285. C2×Dic15C22×C4semidirect
286. C2×Dic15C2×D4semidirect
295. C2×C5×Dic3C2×D4semidirect
303. C2×C3×Dic5C2×D4semidirect
332. C22×C4×D3C2×D5semidirect
342. C2×(C2×D3)⋊C4C2×D5semidirect
343. C2×(C2×D3)⋊C4C2×D5semidirect
344. C2×(C2×D3)⋊C4C2×D5semidirect
349. C3×#95C2×D5semidirect
355. C3⋊#95C2×D5semidirect
403. C2×D20C4×D3semidirect
480. C2×C5×D3C2×C22⋊C4semidirect
494. C2×C3×D5C2×C22⋊C4semidirect
554. C2×D12C4×D5semidirect
636. C22×D5C2×C4×D3semidirect
654. C2×C4×C5C2×C4×D3semidirect
655. C2×C4×C5D3×D4semidirect
673. C2×Dic5D3×D4semidirect
725. #95D3×D5semidirect
733. D15#386semidirect
785. C22×D3C2×C4×D5semidirect
803. C2×C3×C4C2×C4×D5semidirect
804. C2×C3×C4D4×D5semidirect
822. C2×Dic3D4×D5semidirect
874. C2×D5D3×C22⋊C4semidirect
967. C3×C5C2×#386semidirect
1011. C2×D3D5×C22⋊C4semidirect
1125. C2×C4C4×D3×D5semidirect
1126. C2×C4#6777semidirect
1139. C5D3×#386semidirect
1194. C3D5×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#67772
C22×C4×D3×D52
C2×#914732
D15×#952
C5×#46652
C3×#649542
#117489112
#117489102
#117489062
#117489052
#117489012
#117488962
#117488882
D5×#3863
D3×#3865