Finite Group Databasebeta

← D5×#3550 #13007104

Subgroups — D5×#3550 #13007104

Order 1280.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3550C211yesmaximal, characteristic, complemented
2D5×#563C214yesmaximal, complemented
3#10619020C214yesmaximal, complemented
4D5×#559C212yesmaximal, complemented
5#10618959C212yesmaximal, complemented
6Q82×D5C212yesmaximal, complemented
7#10618945C212yesmaximal, complemented
8D5×#556C214yesmaximal, complemented
9#10618896C214yesmaximal, complemented
10D4×Q8×D5C214yesmaximal, complemented
11#10618656C214yesmaximal, complemented
12D5×#542C218yesmaximal, complemented
13#10618435C218yesmaximal, complemented
14D5×#536C214yesmaximal, complemented
15#10618250C214yesmaximal, complemented
16D5×#533C212yesmaximal, complemented
17#10618168C212yesmaximal, complemented
18D5×#532C211yesmaximal, characteristic
19#10618132C211yesmaximal, characteristic, complemented
20C2×D5×#41C2212yes—
21C22×Q8×D5C2214yes—
22C5×#563C2214yescomplemented
23C5×#559C2212yescomplemented
24C5×Q82C2212yescomplemented
25C5×#556C2214yescomplemented
26C5×D4×Q8C2214yescomplemented
27C5×#542C2218yescomplemented
28C5×#536C2214yescomplemented
29C5×#533C2212yescomplemented
30C5×#532C2211yescharacteristic
31#66166C2212yes—
32#66159C2214yescomplemented
33#66150C2214yescomplemented
34Q8×C22⋊D5C2218yescomplemented
35#66069C2218yescomplemented
36#66067C2218yescomplemented
37#66066C2214yescomplemented
38#66062C2212yescomplemented
39#66062C2212yescomplemented
40#66061C2214yescomplemented
41#66061C2218yescomplemented
42#66059C2211yescharacteristic
43#66058C2218yescomplemented
44D5×C4⋊Q8C2211yescharacteristic
45D5×C4⋊Q8C2212yes—
46D5×C4⋊Q8C2212yes—
47D5×C4⋊Q8C2218yes—
48D5×C4⋊Q8C2218yes—
49#66056C2212yescomplemented
50#66056C2218yescomplemented
51#66056C2218yescomplemented
52#66050C2211yescharacteristic
53D5×#127C2211yescharacteristic
54#66047C2212yescomplemented
55#66046C22116yescomplemented
56#66044C22116yescomplemented
57D5×#126C22116yes—
58#66036C22116yescomplemented
59#66033C2218yescomplemented
60#66022C2214yescomplemented
61D5×#125C2214yes—
62#66016C2218yescomplemented
63#66015C2218yescomplemented
64#66009C2218yescomplemented
65D5×#124C2212yes—
66D5×#124C2218yes—
67D5×#124C2218yes—
68#66006C2214yescomplemented
69#66005C2218yescomplemented
70#66003C22116yescomplemented
71#66002C2212yes—
72#65998C2218yescomplemented
73#65996C22116yescomplemented
74D5×#123C2218yes—
75D5×#123C2218yes—
76#65985C2218yescomplemented
77#65982C2218yescomplemented
78#65982C2218yescomplemented
79#65980C22116yescomplemented
80#65977C2218yescomplemented
81#65975C2218yescomplemented
82#65974C22116yescomplemented
83#65966C2218yescomplemented
84#65966C22116yescomplemented
85#65962C2218yescomplemented
86#65962C2218yescomplemented
87D5×C22⋊Q8C2218yes—
88D5×C22⋊Q8C22116yes—
89D5×C22⋊Q8C2214yes—
90D5×C22⋊Q8C2214yes—
91#65956C2214yescomplemented
92#65956C2214yescomplemented
93D5×#121C2214yes—
94#65937C2218yescomplemented
95#65930C2214yes—
96#65919C2214yescomplemented
97#65918C2214yescomplemented
98#65916C2218yescomplemented
99#65912C2214yescomplemented
100#65912C2214yescomplemented
101Q8×D20C2214yescomplemented
102C4×Q8×D5C2214yes—
103C4×Q8×D5C2218yes—
104C4×Q8×D5C2214yes—
105#65902C2218yescomplemented
106Q8×Dic10C2218yescomplemented
107Q8×Dic10C2214yescomplemented
108#65895C2218yescomplemented
109#65893C2218yescomplemented
110#65882C2214yes—
111C4×D4×D5C2214yes—
112C4×D4×D5C2218yes—
113#65876C2214yescomplemented
114D4×Dic10C2214yescomplemented
115D4×Dic10C2218yescomplemented
116#65868C2218yescomplemented
117#65867C2218yescomplemented
118#65860C2214yescomplemented
119D5×#117C2214yes—
120D5×#117C2214yes—
121#65851C2214yescomplemented
122#65811C2211yescharacteristic
123C2×C42×D5C2211yescharacteristic
124#65804C2212yescomplemented
125C2×#3550—51nomaximal, Sylow
126C2×C5×#41C2312yes—
127C22×C5×Q8C2314yes—
128D5×#41—48no—
129C2×#713C2312yes—
130C2×Q8×D5—416no—
131C2×Q8×D5C2314yes—
132C2×Q8×D5C2314yes—
133C2×Q8×D5C2312yes—
134C2×Q8×D5C2318yes—
135C2×Q8×D5C2318yes—
136C2×Q8×D5C2318yes—
137C2×#711C2312yes—
138C2×#711C2314yes—
139C2×D4×D5C2314yes—
140C2×D4×D5C2312yes—
141C2×D4×D5C2314yes—
142C2×#709C2312yes—
143C2×#709C2314yes—
144C22×C4×D5C2312yes—
145C22×C4×D5C2311yescharacteristic
146C22×C4×D5C2314yes—
147C22×C4×D5C2318yes—
148C22×Dic10C2314yes—
149C22×Dic10C2318yes—
150C5×C4⋊Q8C2311yescharacteristic
151C5×C4⋊Q8C2318yes—
152C5×C4⋊Q8C2318yes—
153C5×C4⋊Q8C2312yes—
154C5×C4⋊Q8C2312yes—
155C5×#127C2311yescharacteristic
156C5×#126C23116yes—
157C5×#125C2314yes—
158C5×#124C2312yes—
159C5×#124C2318yes—
160C5×#124C2318yes—
161C5×#123C2318yes—
162C5×#123C2318yes—
163C5×C22⋊Q8C2314yes—
164C5×C22⋊Q8C2314yes—
165C5×C22⋊Q8C2318yes—
166C5×C22⋊Q8C23116yes—
167C5×#121C2314yes—
168C4×C5×Q8C2318yes—
169C4×C5×Q8C2314yes—
170C4×C5×Q8C2314yes—
171C4×C5×D4C2314yes—
172C4×C5×D4C2318yes—
173C5×#117C2314yes—
174C5×#117C2314yes—
175C2×C42×C5C2311yescharacteristic
176#4093C2318yes—
177#4093C2312yes—
178#4093C2318yes—
179#4092C23116yes—
180#4092C2318yes—
181#4092C2314yes—
182#4092C2314yes—
183Q8×Dic5C2314yes—
184Q8×Dic5C2314yes—
185Q8×Dic5C2318yes—
186#4090C2312yes—
187#4090C2318yes—
188#4090C23116yes—
189#4090C2318yes—
190#4090C2314yes—
191#4090C2314yes—
192#4086C2314yes—
193#4086C2312yes—
194#4085C2318yes—
195#4084C2314yes—
196#4082C2312yes—
197#4082C2318yes—
198#4082C2318yes—
199#4081C2318yes—
200#4081C2318yes—
201D4×Dic5C2314yes—
202D4×Dic5C2318yes—
203#4076C2314yes—
204#4075C2318yes—
205#4075C2318yes—
206C4×C22⋊D5C2318yes—
207C4×C22⋊D5C23116yes—
208#4072C2314yes—
209#4072C2314yes—
210#4070C2314yes—
211#4070C2314yes—
212#4070C2318yes—
213#4070C23116yes—
214C2×C4×Dic5C2312yes—
215C2×C4×Dic5C2311yescharacteristic
216#4044C23116yes—
217#4044C23116yes—
218#4044C23116yes—
219#4043C2314yes—
220#4043C2314yes—
221#4043C2318yes—
222#4043C23116yes—
223#4042C2318yes—
224#4042C23116yes—
225#4042C23116yes—
226#4042C23116yes—
227#4042C2318yes—
228#4041C2314yes—
229#4040C23116yes—
230#4040C23116yes—
231#4039C2314yes—
232#4039C2318yes—
233#4038C2314yes—
234#4038C2314yes—
235#4038C2318yes—
236D5×C4⋊C4C2314yes—
237D5×C4⋊C4C2314yes—
238D5×C4⋊C4C23116yes—
239D5×C4⋊C4C2318yes—
240D5×C4⋊C4C2314yes—
241D5×C4⋊C4C2314yes—
242D5×C4⋊C4C2314yes—
243D5×C4⋊C4C2318yes—
244#4036C2314yes—
245#4036C2314yes—
246#4035C2318yes—
247#4035C2318yes—
248#4034C2314yes—
249#4034C2318yes—
250#4034C2318yes—
251#4034C23116yes—
252#4034C23116yes—
253#4034C23116yes—
254#4034C2314yes—
255#4034C2314yes—
256#4034C2314yes—
257#4034C2314yes—
258#4033C2314yes—
259#4033C2318yes—
260#4033C2318yes—
261#4033C23116yes—
262#4033C2314yes—
263#4033C2318yes—
264#4032C2318yes—
265#4032C2318yes—
266#4031C23116yes—
267#4031C23116yes—
268#4031C2318yes—
269#4031C23116yes—
270#4031C23116yes—
271#4030C2318yes—
272#4029C23116yes—
273#4029C23116yes—
274#4027C2318yes—
275#4027C23116yes—
276D5×C22⋊C4C2318yes—
277D5×C22⋊C4C2318yes—
278D5×C22⋊C4C2318yes—
279D5×C22⋊C4C23116yes—
280#4025C23116yes—
281#4025C23116yes—
282#4025C23116yes—
283#4024C2318yes—
284#4024C2318yes—
285#4024C23116yes—
286#4024C23116yes—
287#4024C23116yes—
288#4023C2318yes—
289#4023C2318yes—
290#4022C23116yes—
291#4021C2318yes—
292#4021C2312yes—
293#4021C2318yes—
294#4020C2311yescharacteristic
295C4×D20C2314yes—
296C4×D20C2318yes—
297#4018C2318yes—
298#4018C2318yes—
299C42×D5C2311yescharacteristic
300C42×D5C2311yescharacteristic
301C42×D5C2312yes—
302C42×D5C2318yes—
303C42×D5C2318yes—
304C42×D5C2312yes—
305C42×D5C2311yescharacteristic
306C42×D5C2311yescharacteristic
307#4016C2314yes—
308#4015C2311yescharacteristic
309#4015C2312yes—
310#4015C2312yes—
311#4015C2318yes—
312#4015C2318yes—
313C4×Dic10C2314yes—
314C4×Dic10C2318yes—
315C4×Dic10C23116yes—
316C4×Dic10C2318yes—
317C4×Dic10C2314yes—
318C4×Dic10C2318yes—
319#3550—54no—
320#3550—52no—
321#3550—52no—
322#3550—54no—
323#3550—54no—
324#3550—58no—
325#3550—54no—
326#3550—52no—
327#3550—51no—
328#3550D511yescharacteristic, direct product factor
329C2×#563—54no—
330C2×#559—52no—
331C2×Q82—52no—
332C2×#556—54no—
333C2×D4×Q8—54no—
334C2×#542—58no—
335C2×#536—54no—
336C2×#533—52no—
337C2×#532—51no—
338C23×D5C2414yes—
339C23×D5C2411yescharacteristic
340C5×#41—44no—
341C2×C5×Q8—48no—
342C2×C5×Q8C2414yes—
343C2×C5×Q8C2414yes—
344C2×C5×Q8C2418yes—
345C2×C5×Q8C2412yes—
346C2×C5×D4C2414yes—
347C2×C5×D4C2414yes—
348C2×C5×D4C2412yes—
349C22×C4×C5C2412yes—
350C22×C4×C5C2411yescharacteristic
351C22×C4×C5C2414yes—
352C22×C4×C5C2418yes—
353C2×C22⋊D5C2418yes—
354C2×C22⋊D5C2414yes—
355C2×C22⋊D5C2414yes—
356C2×C22⋊D5C2414yes—
357C22×Dic5C2414yes—
358C22×Dic5C2411yescharacteristic
359C22×Dic5C2412yes—
360C22×Dic5C2418yes—
361#713—44no—
362Q8×D5—216no—
363Q8×D5—216no—
364Q8×D5—416no—
365Q8×D5—416no—
366Q8×D5—416no—
367Q8×D5—44no—
368#711—44no—
369#711—48no—
370D4×D5—216no—
371D4×D5—44no—
372D4×D5—48no—
373#709—48no—
374#709—44no—
375C2×D20C2414yes—
376C2×D20C2412yes—
377C2×D20C2414yes—
378C2×C4×D5—216no—
379C2×C4×D5—24no—
380C2×C4×D5—28no—
381C2×C4×D5—416no—
382C2×C4×D5C2418yes—
383C2×C4×D5C2411yescharacteristic
384C2×C4×D5C2414yes—
385C2×C4×D5C2411yescharacteristic
386C2×C4×D5C2414yes—
387C2×C4×D5C2411yescharacteristic
388C2×C4×D5C2414yes—
389C2×C4×D5C2412yes—
390C2×C4×D5C2412yes—
391C2×C4×D5C2412yes—
392C2×C4×D5C2418yes—
393C2×C4×D5C24116yes—
394C2×C4×D5C2411yescharacteristic
395C2×C4×D5C2412yes—
396C2×Dic10—416no—
397C2×Dic10—48no—
398C2×Dic10C2414yes—
399C2×Dic10C2418yes—
400C2×Dic10C2414yes—
401C2×Dic10C2418yes—
402C2×Dic10C2418yes—
403C2×Dic10C24116yes—
404C2×Dic10C2414yes—
405C2×Dic10C2412yes—
406C5×C4⋊C4C2414yes—
407C5×C4⋊C4C2414yes—
408C5×C4⋊C4C2414yes—
409C5×C4⋊C4C2414yes—
410C5×C4⋊C4C2414yes—
411C5×C4⋊C4C2418yes—
412C5×C4⋊C4C24116yes—
413C5×C4⋊C4C2418yes—
414C5×C22⋊C4C2418yes—
415C5×C22⋊C4C2418yes—
416C5×C22⋊C4C2418yes—
417C5×C22⋊C4C24116yes—
418C42×C5C2412yes—
419C42×C5C2411yescharacteristic
420C42×C5C2411yescharacteristic
421C42×C5C2418yes—
422C42×C5C2418yes—
423C22⋊Dic5C2418yes—
424C22⋊Dic5C2418yes—
425C22⋊Dic5C2418yes—
426C22⋊Dic5C24116yes—
427#685C2418yes—
428#685C24116yes—
429#685C2418yes—
430#685C24116yes—
431#685C2418yes—
432#685C24116yes—
433#685C2418yes—
434C4⋊Dic5C2414yes—
435C4⋊Dic5C2414yes—
436C4⋊Dic5C24116yes—
437C4⋊Dic5C2418yes—
438C4⋊Dic5C2414yes—
439C4⋊Dic5C2418yes—
440C4⋊Dic5C2414yes—
441C4⋊Dic5C2414yes—
442#683C2418yes—
443#683C2418yes—
444#683C2418yes—
445#683C2418yes—
446#683C2418yes—
447#683C24116yes—
448#683C24116yes—
449#683C2418yes—
450#683C2418yes—
451#683C2418yes—
452#683C2418yes—
453C4×Dic5C2412yes—
454C4×Dic5C2412yes—
455C4×Dic5C2418yes—
456C4×Dic5C24116yes—
457C4×Dic5C2418yes—
458C4×Dic5C2412yes—
459C4×Dic5C2412yes—
460C4×Dic5C2411yescharacteristic
461C4×Dic5C2412yes—
462C4×Dic5C2411yescharacteristic
463C4×Dic5C2418yes—
464C4×Dic5C2418yes—
465C22×#41—52no—
466C23×Q8—54no—
467#563—58no—
468#563—516no—
469#563—58no—
470#563—54no—
471#563—58no—
472#563—516no—
473#563C2×D514yescomplemented
474#559—52no—
475#559—58no—
476#559—58no—
477#559—54no—
478#559—58no—
479#559C2×D512yescomplemented
480Q82—58no—
481Q82—58no—
482Q82—52no—
483Q82—58no—
484Q82—54no—
485Q82C2×D512yescomplemented
486#556—54no—
487#556—516no—
488#556—58no—
489#556—58no—
490#556—58no—
491#556—54no—
492#556—54no—
493#556—58no—
494#556C2×D514yescomplemented
495D4×Q8—58no—
496D4×Q8—58no—
497D4×Q8—54no—
498D4×Q8—58no—
499D4×Q8—516no—
500D4×Q8—54no—
501D4×Q8—58no—
502D4×Q8—54no—
503D4×Q8C2×D514yescomplemented
504#542—58no—
505#542—516no—
506#542—516no—
507#542—58no—
508#542—516no—
509#542—516no—
510#542—58no—
511#542—58no—
512#542—58no—
513#542—58no—
514#542—58no—
515#542C2×D518yescomplemented
516#536—54no—
517#536—54no—
518#536—58no—
519#536—58no—
520#536—58no—
521#536—58no—
522#536—58no—
523#536—58no—
524#536—54no—
525#536C2×D514yescomplemented
526#533—52no—
527#533—52no—
528#533—54no—
529#533—54no—
530#533—54no—
531#533—54no—
532#533—54no—
533#533—54no—
534#533—52no—
535#533C2×D512yescomplemented
536#532—52no—
537#532—51no—
538#532—51no—
539#532—52no—
540#532—54no—
541#532—54no—
542#532—51no—
543#532C2×D511yescharacteristic
544C2×C4⋊Q8—51no—
545C2×C4⋊Q8—52no—
546C2×C4⋊Q8—52no—
547C2×C4⋊Q8—58no—
548C2×C4⋊Q8—58no—
549C2×#127—51no—
550C2×#126—516no—
551C2×#125—54no—
552C2×#124—52no—
553C2×#124—58no—
554C2×#124—58no—
555C2×#123—58no—
556C2×#123—58no—
557C2×C22⋊Q8—54no—
558C2×C22⋊Q8—54no—
559C2×C22⋊Q8—58no—
560C2×C22⋊Q8—516no—
561C2×#121—54no—
562C2×C4×Q8—54no—
563C2×C4×Q8—54no—
564C2×C4×Q8—58no—
565C2×C4×D4—54no—
566C2×C4×D4—58no—
567C2×#117—54no—
568C2×#117—54no—
569C22×C42—51no—
570C23×C5C2514yes—
571C23×C5C2511yescharacteristic
572C22×D5—28no—
573C22×D5—22no—
574C22×D5—24no—
575C22×D5—216no—
576C22×D5C2514yes—
577C22×D5C2511yescharacteristic
578C22×D5C2511yescharacteristic
579C5×Q8—28no—
580C5×Q8—28no—
581C5×Q8—48no—
582C5×Q8—42no—
583C5×D4—28no—
584C5×D4—44no—
585C5×D4—42no—
586C2×C4×C5—28no—
587C2×C4×C5—22no—
588C2×C4×C5—24no—
589C2×C4×C5—48no—
590C2×C4×C5C2518yes—
591C2×C4×C5C2511yescharacteristic
592C2×C4×C5C2514yes—
593C2×C4×C5C2512yes—
594C2×C4×C5C2518yes—
595C2×C4×C5C2511yescharacteristic
596C2×C4×C5C2512yes—
597C22⋊D5—216no—
598C22⋊D5—44no—
599C22⋊D5—44no—
600C22⋊D5—44no—
601C2×Dic5—28no—
602C2×Dic5—22no—
603C2×Dic5—24no—
604C2×Dic5—48no—
605C2×Dic5C2518yes—
606C2×Dic5C2512yes—
607C2×Dic5C2511yescharacteristic
608C2×Dic5C2514yes—
609C2×Dic5C2518yes—
610C2×Dic5C2511yescharacteristic
611C2×Dic5C2512yes—
612D20—28no—
613D20—44no—
614D20—42no—
615C4×D5—22no—
616C4×D5—28no—
617C4×D5—216no—
618C4×D5—24no—
619C4×D5—216no—
620C4×D5—22no—
621C4×D5—28no—
622C4×D5—24no—
623C4×D5—22no—
624C4×D5—28no—
625C4×D5—24no—
626C4×D5—416no—
627C4×D5H(5,𝔽2)14yes—
628C4×D52−1+418yes—
629Dic10—28no—
630Dic10—28no—
631Dic10—216no—
632Dic10—216no—
633Dic10—48no—
634Dic10—416no—
635Dic10—42no—
636Dic10—44no—
637C2×#41—52no—
638C2×#41—54no—
639C2×#41—52no—
640C2×#41—54no—
641C2×#41—52no—
642C2×#41—208no—
643C2×#41C22×D512yes—
644C22×Q8—54no—
645C22×Q8—54no—
646C22×Q8—58no—
647C22×Q8—52no—
648C22×Q8—58no—
649C22×Q8—58no—
650C22×Q8—58no—
651C22×Q8—54no—
652C22×Q8—2016no—
653C22×Q8C22×D514yes—
654C22×D4—54no—
655C22×D4—54no—
656C22×D4—52no—
657C23×C4—52no—
658C23×C4—54no—
659C23×C4—51no—
660C23×C4—58no—
661C4⋊Q8—52no—
662C4⋊Q8—54no—
663C4⋊Q8—54no—
664C4⋊Q8—58no—
665C4⋊Q8—58no—
666C4⋊Q8—516no—
667C4⋊Q8—54no—
668C4⋊Q8—54no—
669C4⋊Q8—54no—
670C4⋊Q8—54no—
671C4⋊Q8—54no—
672C4⋊Q8—516no—
673C4⋊Q8—516no—
674C4⋊Q8—516no—
675C4⋊Q8—58no—
676C4⋊Q8—58no—
677C4⋊Q8—51no—
678C4⋊Q8—52no—
679C4⋊Q8—52no—
680C4⋊Q8—58no—
681C4⋊Q8—58no—
682C4⋊Q8C22×D511yescharacteristic
683C4⋊Q8C22×D512yes—
684C4⋊Q8C22×D512yes—
685C4⋊Q8C22×D518yes—
686C4⋊Q8C22×D518yes—
687#127—52no—
688#127—54no—
689#127—51no—
690#127C22×D511yescharacteristic
691#126—516no—
692#126—516no—
693#126—516no—
694#126—516no—
695#126—516no—
696#126—516no—
697#126—516no—
698#126C22×D5116yes—
699#125—58no—
700#125—58no—
701#125—54no—
702#125—54no—
703#125—54no—
704#125C22×D514yes—
705#124—52no—
706#124—58no—
707#124—58no—
708#124—52no—
709#124—58no—
710#124—58no—
711#124—58no—
712#124—516no—
713#124—516no—
714#124—516no—
715#124—516no—
716#124—52no—
717#124—58no—
718#124—58no—
719#124C22×D512yes—
720#124C22×D518yes—
721#124C22×D518yes—
722#123—58no—
723#123—58no—
724#123—58no—
725#123—58no—
726#123—516no—
727#123—516no—
728#123—516no—
729#123—58no—
730#123—516no—
731#123—58no—
732#123C22×D518yes—
733#123C22×D518yes—
734C22⋊Q8—54no—
735C22⋊Q8—54no—
736C22⋊Q8—58no—
737C22⋊Q8—516no—
738C22⋊Q8—54no—
739C22⋊Q8—54no—
740C22⋊Q8—58no—
741C22⋊Q8—516no—
742C22⋊Q8—58no—
743C22⋊Q8—54no—
744C22⋊Q8—58no—
745C22⋊Q8—54no—
746C22⋊Q8—516no—
747C22⋊Q8—58no—
748C22⋊Q8—516no—
749C22⋊Q8—516no—
750C22⋊Q8—516no—
751C22⋊Q8—58no—
752C22⋊Q8—58no—
753C22⋊Q8—516no—
754C22⋊Q8—516no—
755C22⋊Q8—516no—
756C22⋊Q8C22×D514yes—
757C22⋊Q8C22×D514yes—
758C22⋊Q8C22×D518yes—
759C22⋊Q8C22×D5116yes—
760#121—54no—
761#121—58no—
762#121—54no—
763#121—54no—
764#121—58no—
765#121C22×D514yes—
766C4×Q8—54no—
767C4×Q8—54no—
768C4×Q8—58no—
769C4×Q8—58no—
770C4×Q8—54no—
771C4×Q8—58no—
772C4×Q8—54no—
773C4×Q8—516no—
774C4×Q8—58no—
775C4×Q8—58no—
776C4×Q8—54no—
777C4×Q8—58no—
778C4×Q8—54no—
779C4×Q8—516no—
780C4×Q8—58no—
781C4×Q8C22×D514yes—
782C4×Q8C22×D514yes—
783C4×Q8C22×D518yes—
784C4×D4—54no—
785C4×D4—58no—
786C4×D4—58no—
787C4×D4—516no—
788C4×D4—54no—
789C4×D4—58no—
790C4×D4—58no—
791C4×D4—516no—
792C4×D4—54no—
793C4×D4—58no—
794C4×D4C22×D514yes—
795C4×D4C22×D518yes—
796#117—54no—
797#117—54no—
798#117—54no—
799#117—54no—
800#117—58no—
801#117—58no—
802#117—58no—
803#117—58no—
804#117—58no—
805#117C22×D514yes—
806#117C22×D514yes—
807C2×C4⋊C4—54no—
808C2×C4⋊C4—54no—
809C2×C4⋊C4—54no—
810C2×C4⋊C4—54no—
811C2×C4⋊C4—54no—
812C2×C4⋊C4—58no—
813C2×C4⋊C4—516no—
814C2×C4⋊C4—58no—
815C2×C22⋊C4—58no—
816C2×C22⋊C4—58no—
817C2×C22⋊C4—58no—
818C2×C22⋊C4—516no—
819C2×C42—51no—
820C2×C42—52no—
821C2×C42—58no—
822C2×C42—58no—
823C2×C42—52no—
824C2×C42—51no—
825C2×C42—51no—
826C2×C42—51no—
827C2×C42—51no—
828C2×C42—52no—
829C2×C42C22×D511yescharacteristic
830C22×C5—24no—
831C22×C5—21no—
832C22×C5—22no—
833C22×C5—28no—
834C22×C5C2611yescharacteristic
835C2×D5—24no—
836C2×D5—21no—
837C2×D5—22no—
838C2×D5—28no—
839C2×D5—416no—
840C2×D5—44no—
841C2×D5C2×H(5,𝔽2)12yes—
842C2×D5C2×2−1+414yes—
843C4×C5—28no—
844C4×C5—24no—
845C4×C5—21no—
846C4×C5—28no—
847C4×C5—22no—
848C4×C5C2×H(5,𝔽2)12yes—
849C4×C5C2×2−1+414yes—
850Dic5—28no—
851Dic5—24no—
852Dic5—21no—
853Dic5—28no—
854Dic5—22no—
855Dic5C2×H(5,𝔽2)12yes—
856Dic5C2×2−1+414yes—
857C24—54no—
858C24—51no—
859#41—44no—
860#41—208no—
861#41—204no—
862#41—208no—
863#41—204no—
864#41—204no—
865C2×Q8—48no—
866C2×Q8—58no—
867C2×Q8—54no—
868C2×Q8—58no—
869C2×Q8—54no—
870C2×Q8—516no—
871C2×Q8—58no—
872C2×Q8—52no—
873C2×Q8—54no—
874C2×Q8—1016no—
875C2×Q8—1016no—
876C2×Q8—208no—
877C2×Q8—2016no—
878C2×Q8—2016no—
879C2×Q8—204no—
880C2×Q8—2016no—
881C2×Q8—2016no—
882C2×Q8C23×D514yes—
883C2×Q8C23×D514yes—
884C2×Q8C23×D518yes—
885C2×Q8C23×D512yes—
886C2×D4—58no—
887C2×D4—54no—
888C2×D4—54no—
889C2×D4—54no—
890C2×D4—54no—
891C2×D4—54no—
892C2×D4—52no—
893C2×D4—1016no—
894C2×D4—204no—
895C2×D4—208no—
896C2×D4C23×D514yes—
897C2×D4C23×D514yes—
898C2×D4C23×D512yes—
899C22×C4—52no—
900C22×C4—51no—
901C22×C4—52no—
902C22×C4—51no—
903C22×C4—54no—
904C22×C4—58no—
905C22×C4—58no—
906C22×C4—52no—
907C22×C4—54no—
908C22×C4—51no—
909C22×C4—52no—
910C22×C4—52no—
911C22×C4—51no—
912C22×C4—51no—
913C22×C4—58no—
914C22×C4—54no—
915C22×C4—54no—
916C22×C4—516no—
917C22×C4—1016no—
918C22×C4—104no—
919C22×C4—108no—
920C22×C4—2016no—
921C22×C4C23×D512yes—
922C22×C4C23×D511yescharacteristic
923C22×C4C23×D514yes—
924C22×C4C23×D518yes—
925C4⋊C4—58no—
926C4⋊C4—54no—
927C4⋊C4—58no—
928C4⋊C4—54no—
929C4⋊C4—58no—
930C4⋊C4—54no—
931C4⋊C4—58no—
932C4⋊C4—54no—
933C4⋊C4—58no—
934C4⋊C4—54no—
935C4⋊C4—58no—
936C4⋊C4—58no—
937C4⋊C4—58no—
938C4⋊C4—516no—
939C4⋊C4—516no—
940C4⋊C4—516no—
941C4⋊C4—58no—
942C4⋊C4—58no—
943C4⋊C4—58no—
944C4⋊C4C23×D514yes—
945C4⋊C4C23×D514yes—
946C4⋊C4C23×D514yes—
947C4⋊C4C23×D514yes—
948C4⋊C4C23×D514yes—
949C4⋊C4C23×D518yes—
950C4⋊C4C23×D5116yes—
951C4⋊C4C23×D518yes—
952C22⋊C4—58no—
953C22⋊C4—58no—
954C22⋊C4—58no—
955C22⋊C4—516no—
956C22⋊C4—58no—
957C22⋊C4—58no—
958C22⋊C4—516no—
959C22⋊C4—58no—
960C22⋊C4—58no—
961C22⋊C4—516no—
962C22⋊C4—516no—
963C22⋊C4C23×D518yes—
964C22⋊C4C23×D518yes—
965C22⋊C4C23×D518yes—
966C22⋊C4C23×D5116yes—
967C42—52no—
968C42—52no—
969C42—52no—
970C42—51no—
971C42—52no—
972C42—51no—
973C42—52no—
974C42—58no—
975C42—58no—
976C42—58no—
977C42—58no—
978C42—516no—
979C42C23×D512yes—
980C42C23×D511yescharacteristic
981C42C23×D511yescharacteristic
982C42C23×D518yes—
983C42C23×D518yes—
984C2×C5—44no—
985C2×C5—41no—
986C2×C5C22×H(5,𝔽2)11yescharacteristic
987C2×C5C22×2−1+412yes—
988D5—44no—
989D5—41no—
990D5#355014yesdirect product factor
991C23—51no—
992C23—54no—
993C23—51no—
994C23—108no—
995C23—102no—
996C23—104no—
997C23—1016no—
998C23C24×D514yes—
999C23C24×D511yescharacteristic
1000Q8—28no—
1001Q8—28no—
1002Q8—48no—
1003Q8—42no—
1004Q8—1016no—
1005Q8—1016no—
1006Q8—108no—
1007Q8—108no—
1008Q8—208no—
1009Q8—2016no—
1010Q8—202no—
1011Q8—204no—
1012D4—28no—
1013D4—42no—
1014D4—44no—
1015D4—1016no—
1016D4—108no—
1017D4—202no—
1018D4—204no—
1019D4—204no—
1020D4—204no—
1021D4—204no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—48no—
1026C2×C4—52no—
1027C2×C4—51no—
1028C2×C4—54no—
1029C2×C4—58no—
1030C2×C4—58no—
1031C2×C4—52no—
1032C2×C4—54no—
1033C2×C4—51no—
1034C2×C4—58no—
1035C2×C4—108no—
1036C2×C4—102no—
1037C2×C4—104no—
1038C2×C4—102no—
1039C2×C4—108no—
1040C2×C4—104no—
1041C2×C4—1016no—
1042C2×C4—1016no—
1043C2×C4—108no—
1044C2×C4—102no—
1045C2×C4—104no—
1046C2×C4—108no—
1047C2×C4—102no—
1048C2×C4—104no—
1049C2×C4—2016no—
1050C2×C4—208no—
1051C2×C4C24×D518yes—
1052C2×C4C24×D512yes—
1053C2×C4C24×D514yes—
1054C2×C4C24×D511yescharacteristic
1055C2×C4C24×D518yes—
1056C2×C4C24×D511yescharacteristic
1057C2×C4C24×D512yes—
1058C5C2×#355011yescharacteristic, complemented, Sylow
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—52no—
1064C22—54no—
1065C22—104no—
1066C22—101no—
1067C22—102no—
1068C22—108no—
1069C22—2016no—
1070C22—204no—
1071C22C25×D511yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—52no—
1078C4—54no—
1079C4—101no—
1080C4—104no—
1081C4—108no—
1082C4—102no—
1083C4—108no—
1084C4D5×H(5,𝔽2)12yes—
1085C4D5×2−1+414yes—
1086C2—44no—
1087C2—41no—
1088C2—54no—
1089C2—204no—
1090C2—201no—
1091C2C2×D5×H(5,𝔽2)11yescharacteristic
1092C2C2×D5×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3550C2
prime radicalD5×#532C2
hypercenter#3550D5
hypocenterC5C2×#3550
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. C5×#3550C2semidirect
2. D5×#563C2semidirect
3. #10619020C2semidirect
4. D5×#559C2semidirect
5. #10618959C2semidirect
6. Q82×D5C2semidirect
7. #10618945C2semidirect
8. D5×#556C2semidirect
9. #10618896C2semidirect
10. D4×Q8×D5C2semidirect
11. #10618656C2semidirect
12. D5×#542C2semidirect
13. #10618435C2semidirect
14. D5×#536C2semidirect
15. #10618250C2semidirect
16. D5×#533C2semidirect
17. #10618168C2semidirect
19. #10618132C2semidirect
22. C5×#563C22semidirect
23. C5×#559C22semidirect
24. C5×Q82C22semidirect
25. C5×#556C22semidirect
26. C5×D4×Q8C22semidirect
27. C5×#542C22semidirect
28. C5×#536C22semidirect
29. C5×#533C22semidirect
32. #66159C22semidirect
33. #66150C22semidirect
34. Q8×C22⋊D5C22semidirect
35. #66069C22semidirect
36. #66067C22semidirect
37. #66066C22semidirect
38. #66062C22semidirect
39. #66062C22semidirect
40. #66061C22semidirect
41. #66061C22semidirect
43. #66058C22semidirect
49. #66056C22semidirect
50. #66056C22semidirect
51. #66056C22semidirect
54. #66047C22semidirect
55. #66046C22semidirect
56. #66044C22semidirect
58. #66036C22semidirect
59. #66033C22semidirect
60. #66022C22semidirect
62. #66016C22semidirect
63. #66015C22semidirect
64. #66009C22semidirect
68. #66006C22semidirect
69. #66005C22semidirect
70. #66003C22semidirect
72. #65998C22semidirect
73. #65996C22semidirect
76. #65985C22semidirect
77. #65982C22semidirect
78. #65982C22semidirect
79. #65980C22semidirect
80. #65977C22semidirect
81. #65975C22semidirect
82. #65974C22semidirect
83. #65966C22semidirect
84. #65966C22semidirect
85. #65962C22semidirect
86. #65962C22semidirect
91. #65956C22semidirect
92. #65956C22semidirect
94. #65937C22semidirect
96. #65919C22semidirect
97. #65918C22semidirect
98. #65916C22semidirect
99. #65912C22semidirect
100. #65912C22semidirect
101. Q8×D20C22semidirect
105. #65902C22semidirect
106. Q8×Dic10C22semidirect
107. Q8×Dic10C22semidirect
108. #65895C22semidirect
109. #65893C22semidirect
113. #65876C22semidirect
114. D4×Dic10C22semidirect
115. D4×Dic10C22semidirect
116. #65868C22semidirect
117. #65867C22semidirect
118. #65860C22semidirect
121. #65851C22semidirect
124. #65804C22semidirect
328. #3550D5direct (N × H)
473. #563C2×D5semidirect
479. #559C2×D5semidirect
485. Q82C2×D5semidirect
494. #556C2×D5semidirect
503. D4×Q8C2×D5semidirect
515. #542C2×D5semidirect
525. #536C2×D5semidirect
535. #533C2×D5semidirect
990. D5#3550direct (N × H)
1058. C5C2×#3550semidirect

Maximal subgroups

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

subgroupindex
C5×#35502
D5×#5632
#106190202
D5×#5592
#106189592
Q82×D52
#106189452
D5×#5562
#106188962
D4×Q8×D52
#106186562
D5×#5422
#106184352
D5×#5362
#106182502
D5×#5332
#106181682
D5×#5322
#106181322
C2×#35505