Finite Group Databasebeta

← C2×#11753374 #14495351

Subgroups — C2×#11753374 #14495351

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91784C211yesmaximal, characteristic, complemented
2C2×C5×#896C211yesmaximal, characteristic, complemented
3C2×C3×#4035C211yesmaximal, characteristic, complemented
4C2×#91460C211yesmaximal, characteristic, complemented
5C2×#91433C211yesmaximal, characteristic, complemented
6C2×#91433C211yesmaximal, characteristic, complemented
7C2×#91429C211yesmaximal, characteristic, complemented
8C2×#91424C211yesmaximal, characteristic, complemented
9C2×#91420C211yesmaximal, characteristic, complemented
10C2×#91420C211yesmaximal, characteristic, complemented
11C2×#91377C211yesmaximal, characteristic, complemented
12C2×#91375C211yesmaximal, characteristic, complemented
13C2×#91355C211yesmaximal, characteristic, complemented
14C2×#91351C211yesmaximal, characteristic, complemented
15C2×#91350C211yesmaximal, characteristic, complemented
16#11753374C2116yesmaximal, direct product factor
17C2×#65981—31nomaximal, Hall
18C22×D60C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C22×#1200C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33#91784C2218yescomplemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C5×#896C2218yescomplemented
39C2×C3×C4⋊Dic5C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C3×#4035C2218yescomplemented
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6667C2211yescharacteristic
49C2×#6667C2211yescharacteristic
50C2×#6667C2211yescharacteristic
51C2×#6667C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56#91460C2218yescomplemented
57#91433C2218yescomplemented
58#91433C2218yescomplemented
59#91429C2218yescomplemented
60#91424C2218yescomplemented
61#91420C2218yescomplemented
62#91420C2218yescomplemented
63#91377C2218yescomplemented
64#91375C2218yescomplemented
65#91355C2218yescomplemented
66#91351C2218yescomplemented
67#91350C2218yescomplemented
68C2×#5700—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4093—31no—
71C2×#4092—31no—
72C2×#4076—31no—
73C2×#4075—31no—
74#65981—316no—
75C2×#4043—31no—
76C2×#4042—31no—
77C2×#4041—31no—
78C2×#4040—31no—
79C2×#4040—31no—
80C2×#4035D311yescharacteristic, complemented
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4030—31no—
84C2×#4029—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×D60—42no—
94C2×D60—42no—
95C2×D60—42no—
96C2×D60C2314yes—
97C2×D60C2314yes—
98C2×D60C2314yes—
99C2×C4×D15—42no—
100C2×C4×D15C2314yes—
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C2×C4×C5×D3—42no—
105C2×C4×C5×D3C2314yes—
106C2×C5×Dic6—42no—
107C2×C5×Dic6C2314yes—
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×#1204—42no—
113C2×#1204C2314yes—
114C2×#1203—42no—
115C2×#1203—42no—
116C2×#1203—42no—
117C2×#1203C2314yes—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1200—42no—
121C2×#1200—42no—
122C2×#1200C2314yes—
123C2×#1200C2314yes—
124C3×C5×C4⋊C4C2314yes—
125#6714C2314yes—
126#6714C2314yes—
127C5×(C2×D3)⋊C4C2314yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×Dic3⋊C4C2314yes—
130C5×Dic3⋊C4C2314yes—
131C3×C4⋊Dic5C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135C3×#683C2314yes—
136C3×C4×Dic5C2314yes—
137Dic3⋊Dic5C2314yes—
138#6669C2314yes—
139#6667C2314yes—
140#6667C2314yes—
141#6667C2314yes—
142#6667C2314yes—
143#6667C2314yes—
144#6667C2314yes—
145#6667C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147C2×C3×#125—51no—
148#5700—516no—
149C2×#896—51no—
150C2×#896—51no—
151C2×#896—51no—
152C2×#896D511yescharacteristic, complemented
153C2×#895—51no—
154C2×#895—51no—
155C2×#895—51no—
156C2×#895—51no—
157C2×#894—51no—
158C2×#894—51no—
159C2×#894—51no—
160C2×#894—51no—
161C2×#875—51no—
162C2×#875—51no—
163C22×C5×Q8—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×D20—31no—
169C22×D20—31no—
170C22×D20—31no—
171C22×C4×D5—31no—
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×Dic10—31no—
175C5×C22⋊Q8—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4—31no—
178C2×C5×C4⋊C4C2×D311yescharacteristic
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C22⋊Dic5—31no—
182#4093—38no—
183#4092—38no—
184#4076—38no—
185#4075—38no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5C2×D311yescharacteristic
197C2×#683—31no—
198C2×#683C2×D311yescharacteristic
199C2×#683C2×D311yescharacteristic
200C2×#683C2×D311yescharacteristic
201C2×#683C2×D311yescharacteristic
202C2×C4×Dic5C2×D311yescharacteristic
203#4043—38no—
204#4042—38no—
205#4041—38no—
206#4040—38no—
207#4040—38no—
208#4035C2×D318yescomplemented
209#4031—38no—
210#4030—38no—
211#4030—38no—
212#4029—38no—
213C2×#562—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×D15—22no—
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15C2412yes—
225C22×D15C2412yes—
226C22×D15C2412yes—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2412yes—
237C2×Dic15—22no—
238C2×Dic15C2412yes—
239D60—44no—
240D60—44no—
241D60—44no—
242C4×D15—44no—
243C2×C5×Dic3—22no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3C2412yes—
247C2×C5×Dic3C2412yes—
248C2×C5×Dic3C2412yes—
249C4×C5×D3—44no—
250C5×Dic6—44no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259#1204—44no—
260#1203—44no—
261#1203—44no—
262#1203—44no—
263#1200—44no—
264#1200—44no—
265C22×D12—51no—
266C22×D12—51no—
267C22×D12—51no—
268C22×D12—51no—
269C22×D12—51no—
270C22×D12—51no—
271C22×C4×D3—51no—
272C22×C4×D3—51no—
273C22×C4×D3—51no—
274C22×C4×D3C2×D511yescharacteristic
275C22×Dic6—51no—
276C22×Dic6C2×D511yescharacteristic
277C3×#125—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C4⋊C4C2×D511yescharacteristic
284C2×C3×C42—51no—
285C2×(C2×D3)⋊C4—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)⋊C4C2×D511yescharacteristic
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4C2×D511yescharacteristic
300C2×Dic3⋊C4C2×D511yescharacteristic
301#896—58no—
302#896—58no—
303#896—58no—
304#896C2×D518yescomplemented
305#895—58no—
306#895—58no—
307#895—58no—
308#895—58no—
309#894—58no—
310#894—58no—
311#894—58no—
312#894—58no—
313#875—58no—
314#875—58no—
315C24×C5—31no—
316C23×D5—31no—
317C23×D5—31no—
318C23×D5—31no—
319C2×C5×Q8—34no—
320C2×C5×Q8—122no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
325C22×C4×C5—122no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C2×C22⋊D5—34no—
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—122no—
333C2×C22⋊D5—122no—
334C2×C22⋊D5—122no—
335C22×Dic5—31no—
336C22×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C2×D20—34no—
341C2×D20—34no—
342C2×D20—34no—
343C2×D20—122no—
344C2×D20—122no—
345C2×D20—122no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—122no—
350C2×C4×D5—122no—
351C2×C4×D5—122no—
352C2×Dic10—34no—
353C2×Dic10—122no—
354C5×C4⋊C4—34no—
355C5×C4⋊C4—34no—
356C5×C4⋊C4C22×D314yes—
357C5×C22⋊C4—34no—
358C5×C22⋊C4—34no—
359C22⋊Dic5—34no—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369C4⋊Dic5—34no—
370C4⋊Dic5C22×D314yes—
371#683—34no—
372#683C22×D314yes—
373#683C22×D314yes—
374#683C22×D314yes—
375#683C22×D314yes—
376C4×Dic5C22×D314yes—
377#562—1516no—
378C2×#125—51no—
379C2×#124—151no—
380C2×#124—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—31no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8—151no—
389C2×#121—151no—
390C2×#121—151no—
391C2×#121—151no—
392C2×#121—151no—
393C22×C3×C5H(5,𝔽2)12yes—
394C22×C3×C5H(5,𝔽2)12yes—
395C22×C3×C52−1+412yes—
396C22×C3×C5C2511yescharacteristic
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—44no—
407C2×D15—44no—
408C2×D15—44no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417C3×Dic5—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C23×D3—51no—
425C23×D3—51no—
426C23×D3—51no—
427C23×D3C22×D511yescharacteristic
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C22×Dic3—51no—
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C22×Dic3C22×D511yescharacteristic
439C2×D12—54no—
440C2×D12—54no—
441C2×D12—54no—
442C2×D12—54no—
443C2×D12—54no—
444C2×D12—54no—
445C2×D12—202no—
446C2×D12—202no—
447C2×D12—202no—
448C2×D12—202no—
449C2×D12—202no—
450C2×D12—202no—
451C2×C4×D3—42no—
452C2×C4×D3—54no—
453C2×C4×D3—54no—
454C2×C4×D3—54no—
455C2×C4×D3—202no—
456C2×C4×D3—202no—
457C2×C4×D3—202no—
458C2×C4×D3C22×D514yes—
459C2×Dic6—42no—
460C2×Dic6—54no—
461C2×Dic6—202no—
462C2×Dic6C22×D514yes—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C4⋊C4—54no—
467C3×C4⋊C4—54no—
468C3×C4⋊C4C22×D514yes—
469C3×C42—54no—
470(C2×D3)⋊C4—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478(C2×D3)⋊C4—54no—
479(C2×D3)⋊C4—54no—
480(C2×D3)⋊C4C22×D514yes—
481(C2×D3)⋊C4C22×D514yes—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4C22×D514yes—
485Dic3⋊C4C22×D514yes—
486C23×C5—32no—
487C23×C5—62no—
488C23×C5—62no—
489C23×C5—62no—
490C23×C5C23×D311yescharacteristic
491C22×D5—32no—
492C22×D5—32no—
493C22×D5—32no—
494C22×D5—62no—
495C22×D5—62no—
496C22×D5—62no—
497C22×D5—62no—
498C22×D5—62no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C5×Q8—124no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—124no—
514C2×C4×C5C23×D312yes—
515C2×C4×C5C23×D312yes—
516C2×C4×C5C23×D312yes—
517C22⋊D5—124no—
518C22⋊D5—124no—
519C22⋊D5—124no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—22no—
523C2×Dic5—22no—
524C2×Dic5—32no—
525C2×Dic5—62no—
526C2×Dic5C23×D312yes—
527C2×Dic5C23×D312yes—
528C2×Dic5C23×D312yes—
529C2×Dic5C23×D312yes—
530D20—124no—
531D20—124no—
532D20—124no—
533C4×D5—124no—
534C4×D5—124no—
535C4×D5—124no—
536Dic10—124no—
537C22×Q8—31no—
538C22×Q8—151no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—31no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#125—58no—
550#124—158no—
551#124—158no—
552#123—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—38no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8—158no—
560#121—158no—
561#121—158no—
562#121—158no—
563#121—158no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C4⋊C4—51no—
570C2×C4⋊C4—51no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C4⋊C4D3×D511yescharacteristic
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C42—51no—
587C2×C3×C5#56214yescomplemented
588C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
589C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
590C2×C3×C5C2×2−1+411yescharacteristic
591D15—42no—
592D15—42no—
593D15—42no—
594C5×D3—42no—
595C23×C3C23×D511yescharacteristic
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—52no—
600C22×D3—52no—
601C22×D3—52no—
602C22×D3—102no—
603C22×D3—102no—
604C22×D3—102no—
605C22×D3—102no—
606C22×D3—102no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3C23×D512yes—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—102no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4—102no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625C2×C3×C4C23×D512yes—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—52no—
630C2×Dic3—102no—
631C2×Dic3C23×D512yes—
632C2×Dic3C23×D512yes—
633C2×Dic3C23×D512yes—
634D12—204no—
635D12—204no—
636D12—204no—
637D12—204no—
638D12—204no—
639D12—204no—
640C4×D3—44no—
641C4×D3—204no—
642C4×D3—204no—
643C4×D3—204no—
644Dic6—44no—
645Dic6—204no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—124no—
650C22×C5#100712yes—
651C22×C5#100912yes—
652C22×C5#100912yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—62no—
655C2×D5—62no—
656C2×D5—62no—
657C2×D5—62no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—124no—
664C2×D5—124no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671C4×C5—62no—
672Dic5—22no—
673Dic5—22no—
674Dic5—22no—
675Dic5—22no—
676Dic5—62no—
677C24—31no—
678C24—151no—
679C24—151no—
680C24—151no—
681C2×Q8—34no—
682C2×Q8—122no—
683C2×Q8—154no—
684C2×Q8—602no—
685C2×D4—154no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—602no—
692C2×D4—602no—
693C2×D4—602no—
694C2×D4—602no—
695C2×D4—602no—
696C2×D4—602no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—34no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—122no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—151no—
709C22×C4—154no—
710C22×C4—602no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—54no—
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4C2×D3×D514yes—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C42—54no—
739C3×C5C2×#56211yescharacteristic, complemented, Hall
740C22×C3#414412yes—
741C22×C3#414712yes—
742C22×C3#414912yes—
743C22×C3C24×D511yescharacteristic
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—44no—
748C2×D3—102no—
749C2×D3—102no—
750C2×D3—102no—
751C2×D3—102no—
752C2×D3—102no—
753C2×D3—102no—
754C2×D3—102no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—204no—
758C2×D3—204no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—102no—
764C3×C4—102no—
765C3×C4—102no—
766C3×C4—102no—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—102no—
771C2×C5—122no—
772C2×C5#570014yescomplemented
773C2×C5C2×#100711yescharacteristic
774C2×C5C2×#100911yescharacteristic
775C2×C5C2×#100911yescharacteristic
776D5—122no—
777D5—122no—
778D5—122no—
779C23—32no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—152no—
784C23—152no—
785C23—152no—
786C23—302no—
787C23—302no—
788C23—302no—
789C23—302no—
790C23—302no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23—302no—
795C23C22×D3×D511yescharacteristic
796Q8—124no—
797Q8—604no—
798D4—604no—
799D4—604no—
800D4—604no—
801D4—604no—
802D4—604no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—52no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—124no—
822C2×C4—152no—
823C2×C4—302no—
824C2×C4—604no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4C22×D3×D512yes—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3#6598114yescomplemented
831C2×C3C2×#414411yescharacteristic
832C2×C3C2×#414711yescharacteristic
833C2×C3C2×#414911yescharacteristic
834D3—42no—
835D3—202no—
836D3—202no—
837D3—202no—
838C5C2×#570011yescharacteristic, complemented, Sylow
839C22—62no—
840C22—62no—
841C22—62no—
842C22—124no—
843C22—302no—
844C22—302no—
845C22—302no—
846C22—302no—
847C22—302no—
848C22—302no—
849C22—302no—
850C22—302no—
851C22—302no—
852C22—604no—
853C22—604no—
854C22—604no—
855C22#9201912yes—
856C22#9202712yes—
857C22#9202912yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—102no—
867C4—102no—
868C4—102no—
869C4—302no—
870C3C2×#6598111yescharacteristic, complemented, Sylow
871C2—122no—
872C2—602no—
873C2—602no—
874C2—602no—
875C2#1175337414yesdirect product factor
876C2C2×#9201911yescharacteristic
877C2C2×#9202711yescharacteristic
878C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91784C2semidirect
2. C2×C5×#896C2semidirect
3. C2×C3×#4035C2semidirect
4. C2×#91460C2semidirect
5. C2×#91433C2semidirect
6. C2×#91433C2semidirect
7. C2×#91429C2semidirect
8. C2×#91424C2semidirect
9. C2×#91420C2semidirect
10. C2×#91420C2semidirect
11. C2×#91377C2semidirect
12. C2×#91375C2semidirect
13. C2×#91355C2semidirect
14. C2×#91351C2semidirect
15. C2×#91350C2semidirect
16. #11753374C2direct (N × H)
33. #91784C22semidirect
38. C5×#896C22semidirect
45. C3×#4035C22semidirect
56. #91460C22semidirect
57. #91433C22semidirect
58. #91433C22semidirect
59. #91429C22semidirect
60. #91424C22semidirect
61. #91420C22semidirect
62. #91420C22semidirect
63. #91377C22semidirect
64. #91375C22semidirect
65. #91355C22semidirect
66. #91351C22semidirect
67. #91350C22semidirect
80. C2×#4035D3semidirect
152. C2×#896D5semidirect
208. #4035C2×D3semidirect
304. #896C2×D5semidirect
587. C2×C3×C5#562semidirect
739. C3×C5C2×#562semidirect
772. C2×C5#5700semidirect
830. C2×C3#65981semidirect
838. C5C2×#5700semidirect
870. C3C2×#65981semidirect
875. C2#11753374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917842
C2×C5×#8962
C2×C3×#40352
C2×#914602
C2×#914332
C2×#914292
C2×#914242
C2×#914202
C2×#913772
C2×#913752
C2×#913552
C2×#913512
C2×#913502
#117533742
C2×#659813
C2×#57005