Finite Group Databasebeta

← D5×#3501 #13007195

Subgroups — D5×#3501 #13007195

Order 1280.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3501C211yesmaximal, characteristic, complemented
2#10618850C218yesmaximal, complemented
3#10618849C214yesmaximal, complemented
4D5×#554C218yesmaximal, complemented
5D5×#554C214yesmaximal, complemented
6#10618662C214yesmaximal, complemented
7D4×Q8×D5C214yesmaximal, complemented
8#10618500C212yesmaximal, complemented
9D5×#544C212yesmaximal, complemented
10D5×#543C214yesmaximal, complemented
11#10618475C214yesmaximal, complemented
12#10618181C212yesmaximal, complemented
13D5×#533C212yesmaximal, complemented
14#10617887C214yesmaximal, complemented
15C2×D5×C22⋊Q8C214yesmaximal, complemented
16D5×#518C212yesmaximal
17#10617761C212yesmaximal, complemented
18C2×C4×D4×D5C211yesmaximal, characteristic
19#10617667C211yesmaximal, characteristic, complemented
20C22×Q8×D5C2214yescomplemented
21C22×D4×D5C2211yescharacteristic
22C23×C4×D5C2212yes—
23C5×#554C2214yescomplemented
24C5×#554C2218yescomplemented
25C5×D4×Q8C2214yescomplemented
26C5×#544C2212yescomplemented
27C5×#543C2214yescomplemented
28C5×#533C2212yescomplemented
29C2×C5×C22⋊Q8C2214yescomplemented
30C5×#518C2212yes—
31C2×C4×C5×D4C2211yescharacteristic
32Q8×C22⋊D5C2218yescomplemented
33C2×#4092C2214yescomplemented
34#66132C2212yes—
35C2×D4×Dic5C2211yescharacteristic
36C2×C4×C22⋊D5C2212yes—
37C2×#4070C2214yescomplemented
38#66064C2218yescomplemented
39#66064C2214yescomplemented
40#66063C2218yescomplemented
41#66062C2212yescomplemented
42#66062C2212yescomplemented
43#66061C2214yescomplemented
44#66061C2218yescomplemented
45D5×C4⋊Q8C2212yescomplemented
46D5×C4⋊Q8C2218yescomplemented
47D5×C4⋊Q8C2212yescomplemented
48#66024C2218yescomplemented
49#66024C2218yescomplemented
50#66024C2218yescomplemented
51#66023C2218yescomplemented
52#66022C2214yescomplemented
53D5×#125C2214yescomplemented
54D5×#125C2218yescomplemented
55#65970C22116yescomplemented
56#65970C22116yescomplemented
57#65970C22116yescomplemented
58#65969C2218yescomplemented
59#65969C22116yescomplemented
60#65968C2218yescomplemented
61#65968C2218yescomplemented
62#65968C22116yescomplemented
63#65968C22116yescomplemented
64#65966C2218yescomplemented
65#65966C22116yescomplemented
66D5×C22⋊Q8C2214yes—
67D5×C22⋊Q8C2218yes—
68D5×C22⋊Q8C2214yes—
69D5×C22⋊Q8C2218yescomplemented
70D5×C22⋊Q8C2218yescomplemented
71D5×C22⋊Q8C2218yescomplemented
72D5×C22⋊Q8C2218yescomplemented
73D5×C22⋊Q8C22116yescomplemented
74D5×C22⋊Q8C22116yescomplemented
75D5×C22⋊Q8C2218yescomplemented
76D5×C22⋊Q8C2218yescomplemented
77#65957C2218yescomplemented
78#65956C2214yescomplemented
79#65956C2214yescomplemented
80#65913C2214yescomplemented
81#65913C2218yescomplemented
82#65912C2214yescomplemented
83#65912C2214yescomplemented
84Q8×D20C2214yescomplemented
85C4×Q8×D5C2214yescomplemented
86C4×Q8×D5C2214yescomplemented
87#65879C2218yes—
88#65879C2218yes—
89C4×D4×D5C2214yes—
90C4×D4×D5C2218yes—
91C4×D4×D5C2214yes—
92C4×D4×D5C2214yes—
93C4×D4×D5C2214yes—
94C4×D4×D5C2218yes—
95#65877C2214yescomplemented
96#65877C2218yescomplemented
97#65873C2218yescomplemented
98#65873C2218yescomplemented
99#65873C2218yescomplemented
100D4×Dic10C2214yescomplemented
101D4×Dic10C2218yescomplemented
102#65855C2214yes—
103D5×#117C2214yes—
104#65853C2214yescomplemented
105#65851C2214yescomplemented
106#65845C2218yescomplemented
107#65845C22116yescomplemented
108C2×#4043C2214yescomplemented
109C2×#4042C2218yescomplemented
110C2×#4039C2211yescharacteristic
111C2×D5×C4⋊C4C2211yescharacteristic
112C2×D5×C4⋊C4C2218yescomplemented
113C2×D5×C4⋊C4C2214yescomplemented
114#65834C2212yescomplemented
115#65820C2218yes—
116C2×#4027C2212yes—
117C2×D5×C22⋊C4C2218yes—
118C2×D5×C22⋊C4C2212yes—
119#65817C2218yescomplemented
120#65817C2214yescomplemented
121C2×#4024C2218yescomplemented
122C2×C4×D20C2211yescharacteristic
123C2×C42×D5C2211yescharacteristic
124#65804C2212yescomplemented
125C2×#3501—51nomaximal, Sylow
126C24×D5C2312yes—
127C22×C5×Q8C2314yescomplemented
128C22×C5×D4C2311yescharacteristic
129C23×C4×C5C2312yes—
130C22×C22⋊D5C2312yes—
131C23×Dic5C2312yes—
132C2×Q8×D5—416no—
133C2×Q8×D5C2314yes—
134C2×Q8×D5C2318yes—
135C2×Q8×D5C2314yes—
136C2×Q8×D5C2318yescomplemented
137C2×Q8×D5C2318yescomplemented
138C2×D4×D5Q8116yescomplemented
139C2×D4×D5C2314yes—
140C2×D4×D5C2314yes—
141C22×D20C2311yescharacteristic
142C22×C4×D5—48no—
143C22×C4×D5C2311yescharacteristic
144C22×C4×D5C2314yes—
145C22×C4×D5C2311yescharacteristic
146C22×C4×D5C2312yes—
147C22×C4×D5C2312yes—
148C22×C4×D5C2318yes—
149C22×C4×D5C2318yes—
150C22×C4×D5C2312yes—
151C22×C4×D5C2314yes—
152C22×C4×D5C2314yes—
153C22×C4×D5C2314yes—
154C22×C4×D5C2311yescharacteristic
155C22×Dic10C2318yescomplemented
156C22×Dic10C2314yescomplemented
157C5×C4⋊Q8C2312yescomplemented
158C5×C4⋊Q8C2318yescomplemented
159C5×C4⋊Q8C2312yescomplemented
160C5×#125C2314yescomplemented
161C5×#125C2318yescomplemented
162C5×C22⋊Q8C2314yes—
163C5×C22⋊Q8C2318yes—
164C5×C22⋊Q8C2314yes—
165C5×C22⋊Q8C2318yescomplemented
166C5×C22⋊Q8C2318yescomplemented
167C5×C22⋊Q8C23116yescomplemented
168C5×C22⋊Q8C23116yescomplemented
169C4×C5×Q8C2314yescomplemented
170C4×C5×Q8C2314yescomplemented
171C4×C5×D4C2318yes—
172C4×C5×D4C2314yes—
173C4×C5×D4C2314yes—
174C4×C5×D4C2318yes—
175C5×#117C2314yes—
176C2×C5×C4⋊C4C2311yescharacteristic
177C2×C5×C4⋊C4C2318yescomplemented
178C2×C5×C4⋊C4C2314yescomplemented
179C2×C5×C22⋊C4C2318yes—
180C2×C5×C22⋊C4C2312yes—
181C2×C42×C5C2311yescharacteristic
182C2×C22⋊Dic5C2318yes—
183C2×C22⋊Dic5C2312yes—
184#4092C2314yes—
185#4092C2314yes—
186#4092C2318yes—
187#4092C23116yescomplemented
188#4092C2318yescomplemented
189#4092C2318yescomplemented
190#4092C23116yescomplemented
191Q8×Dic5C2314yescomplemented
192Q8×Dic5C2314yescomplemented
193#4090C23116yescomplemented
194#4090C2314yescomplemented
195#4090C2314yescomplemented
196D4×Dic5C2314yes—
197D4×Dic5C2318yes—
198D4×Dic5C2318yes—
199D4×Dic5C2314yes—
200C4×C22⋊D5C23116yes—
201C4×C22⋊D5C23116yes—
202C4×C22⋊D5C2318yes—
203C4×C22⋊D5C2318yes—
204C2×#685C2312yes—
205C2×#685C2312yes—
206C2×#685C2318yes—
207C2×#685C2318yes—
208#4072C2314yes—
209C2×C4⋊Dic5C2311yescharacteristic
210C2×C4⋊Dic5C2318yescomplemented
211C2×C4⋊Dic5C2314yescomplemented
212#4070C2314yes—
213#4070C2314yes—
214#4070C2318yes—
215#4070C23116yescomplemented
216#4070C23116yescomplemented
217#4070C2318yescomplemented
218#4070C2318yescomplemented
219C2×#683C2312yes—
220C2×#683C2318yescomplemented
221C2×#683C2318yescomplemented
222C2×#683C2318yescomplemented
223C2×C4×Dic5C2311yescharacteristic
224C2×C4×Dic5C2311yescharacteristic
225C2×C4×Dic5C2311yescharacteristic
226#4043C2314yes—
227#4043C2314yes—
228#4043C2318yes—
229#4043C2318yescomplemented
230#4043C23116yescomplemented
231#4043C2318yescomplemented
232#4043C23116yescomplemented
233#4042C23116yes—
234#4042C2318yes—
235#4042C2318yes—
236#4042C23116yescomplemented
237#4042C23116yescomplemented
238#4042C23116yescomplemented
239#4042C23116yescomplemented
240#4042C23116yescomplemented
241#4042C23116yescomplemented
242#4039C2318yes—
243#4039C2314yes—
244#4039C2314yes—
245#4039C2318yes—
246#4038C2314yes—
247#4038C2314yes—
248D5×C4⋊C4C2314yes—
249D5×C4⋊C4C2314yes—
250D5×C4⋊C4C2314yes—
251D5×C4⋊C4C23116yes—
252D5×C4⋊C4C2314yes—
253D5×C4⋊C4C2314yes—
254D5×C4⋊C4C2314yes—
255D5×C4⋊C4C2318yes—
256D5×C4⋊C4C2318yes—
257D5×C4⋊C4C2318yes—
258D5×C4⋊C4C2318yescomplemented
259D5×C4⋊C4C23116yescomplemented
260D5×C4⋊C4C23116yescomplemented
261D5×C4⋊C4C2318yescomplemented
262#4036C2314yescomplemented
263#4036C2314yescomplemented
264#4036C2318yescomplemented
265#4036C2318yescomplemented
266#4035C23116yescomplemented
267#4035C2318yescomplemented
268#4035C23116yescomplemented
269#4035C2318yescomplemented
270#4034C2314yescomplemented
271#4034C2318yescomplemented
272#4034C2318yescomplemented
273#4034C2314yescomplemented
274#4034C23116yescomplemented
275#4034C2314yescomplemented
276#4034C2314yescomplemented
277#4033C2314yescomplemented
278#4033C2314yescomplemented
279#4033C2318yescomplemented
280#4033C2318yescomplemented
281#4027C2318yes—
282#4027C2318yes—
283#4027C23116yes—
284#4027C23116yes—
285D5×C22⋊C4C2318yes—
286D5×C22⋊C4C23116yes—
287D5×C22⋊C4C2318yes—
288D5×C22⋊C4C23116yes—
289D5×C22⋊C4C2318yes—
290D5×C22⋊C4C23116yes—
291#4024C2318yes—
292#4024C23116yes—
293#4024C2318yes—
294#4024C23116yescomplemented
295#4024C23116yescomplemented
296#4024C23116yescomplemented
297#4024C23116yescomplemented
298#4024C23116yescomplemented
299#4024C23116yescomplemented
300#4023C2318yes—
301C4×D20C2314yes—
302C4×D20C2318yes—
303C4×D20C2314yes—
304C4×D20C2318yes—
305#4018C2318yes—
306C42×D5C2312yes—
307C42×D5C2318yes—
308C42×D5C2312yes—
309C42×D5C2312yes—
310C42×D5C2312yes—
311#4016C2314yescomplemented
312#4016C2318yescomplemented
313#4015C2312yescomplemented
314#4015C2312yescomplemented
315#4015C2318yescomplemented
316C4×Dic10C2314yescomplemented
317C4×Dic10C2314yescomplemented
318C4×Dic10C2318yescomplemented
319C4×Dic10C2318yescomplemented
320#3501—54no—
321#3501—58no—
322#3501—54no—
323#3501—52no—
324#3501—54no—
325#3501—52no—
326#3501—54no—
327#3501—52no—
328#3501—51no—
329#3501D511yescharacteristic, direct product factor
330C2×#554—54no—
331C2×#554—58no—
332C2×D4×Q8—54no—
333C2×#544—52no—
334C2×#543—54no—
335C2×#533—52no—
336C22×C22⋊Q8—54no—
337C2×#518—52no—
338C22×C4×D4—51no—
339C24×C5C2412yes—
340C23×D5—44no—
341C23×D5—44no—
342C23×D5C2×Q8116yescomplemented
343C23×D5C2414yes—
344C23×D5C2411yescharacteristic
345C23×D5C2412yes—
346C23×D5C2414yes—
347C2×C5×Q8—48no—
348C2×C5×Q8C2414yes—
349C2×C5×Q8C2414yes—
350C2×C5×Q8C2418yes—
351C2×C5×D4C2×Q818yescomplemented
352C2×C5×D4C2414yes—
353C22×C4×C5—44no—
354C22×C4×C5C2411yescharacteristic
355C22×C4×C5C2414yes—
356C22×C4×C5C2411yescharacteristic
357C22×C4×C5C2412yes—
358C22×C4×C5C2418yes—
359C22×C4×C5C2418yes—
360C22×C4×C5C2414yes—
361C22×C4×C5C2411yescharacteristic
362C2×C22⋊D5C2×Q8116yescomplemented
363C2×C22⋊D5C2418yes—
364C22×Dic5—44no—
365C22×Dic5C2414yes—
366C22×Dic5C2411yescharacteristic
367C22×Dic5C2411yescharacteristic
368C22×Dic5C2418yes—
369C22×Dic5C2412yes—
370C22×Dic5C2418yes—
371C22×Dic5C2414yes—
372C22×Dic5C2411yescharacteristic
373Q8×D5—216no—
374Q8×D5—416no—
375Q8×D5—416no—
376Q8×D5—416no—
377Q8×D5—48no—
378D4×D5C2×Q8132yescomplemented
379D4×D5C2×Q8132yescomplemented
380C2×D20C2×Q818yescomplemented
381C2×D20C2414yes—
382C2×C4×D5—24no—
383C2×C4×D5—216no—
384C2×C4×D5—48no—
385C2×C4×D5—44no—
386C2×C4×D5—48no—
387C2×C4×D5—44no—
388C2×C4×D5—48no—
389C2×C4×D5—44no—
390C2×C4×D5—416no—
391C2×C4×D5—42no—
392C2×C4×D5—416no—
393C2×C4×D5C2×Q818yescomplemented
394C2×C4×D5C2411yescharacteristic
395C2×C4×D5C2411yescharacteristic
396C2×C4×D5C2411yescharacteristic
397C2×C4×D5C2414yes—
398C2×C4×D5C2414yes—
399C2×C4×D5C2414yes—
400C2×C4×D5C2418yes—
401C2×C4×D5C2418yes—
402C2×C4×D5C2412yes—
403C2×C4×D5C2414yes—
404C2×C4×D5C2414yes—
405C2×C4×D5C2414yes—
406C2×C4×D5C24116yes—
407C2×C4×D5C2412yes—
408C2×C4×D5C24116yes—
409C2×C4×D5C2412yes—
410C2×C4×D5C2412yes—
411C2×C4×D5C2411yescharacteristic
412C2×Dic10—416no—
413C2×Dic10—48no—
414C2×Dic10C2414yes—
415C2×Dic10C2418yes—
416C2×Dic10C24116yes—
417C2×Dic10C2418yes—
418C2×Dic10C2414yes—
419C2×Dic10C2418yes—
420C5×C4⋊C4C2414yes—
421C5×C4⋊C4C2418yes—
422C5×C4⋊C4C2414yes—
423C5×C4⋊C4C2418yes—
424C5×C4⋊C4C24116yes—
425C5×C4⋊C4C2414yes—
426C5×C4⋊C4C2414yes—
427C5×C4⋊C4C2418yes—
428C5×C4⋊C4C2414yes—
429C5×C22⋊C4C2418yes—
430C5×C22⋊C4C2418yes—
431C5×C22⋊C4C24116yes—
432C42×C5C2412yes—
433C42×C5C2412yes—
434C42×C5C2418yes—
435C22⋊Dic5C2418yes—
436C22⋊Dic5C2418yes—
437C22⋊Dic5C24116yes—
438#685C2418yes—
439#685C2418yes—
440#685C2418yes—
441#685C24116yes—
442#685C24116yes—
443#685C2418yes—
444C4⋊Dic5C2414yes—
445C4⋊Dic5C2414yes—
446C4⋊Dic5C2418yes—
447C4⋊Dic5C2418yes—
448C4⋊Dic5C2414yes—
449C4⋊Dic5C2414yes—
450C4⋊Dic5C2414yes—
451C4⋊Dic5C24116yes—
452C4⋊Dic5C2418yes—
453#683C2418yes—
454#683C2418yes—
455#683C2418yes—
456#683C2418yes—
457#683C2418yes—
458#683C2418yes—
459#683C24116yes—
460#683C24116yes—
461#683C2418yes—
462#683C2418yes—
463#683C24116yes—
464#683C2418yes—
465C4×Dic5C2412yes—
466C4×Dic5C2412yes—
467C4×Dic5C2418yes—
468C4×Dic5C2412yes—
469C4×Dic5C2412yes—
470C4×Dic5C2412yes—
471C4×Dic5C2412yes—
472C4×Dic5C2418yes—
473C4×Dic5C2418yes—
474C23×Q8—54no—
475C23×D4—51no—
476C24×C4—52no—
477#554—58no—
478#554—54no—
479#554—58no—
480#554—58no—
481#554—58no—
482#554—58no—
483#554—516no—
484#554—516no—
485#554—516no—
486#554—516no—
487#554—54no—
488#554—58no—
489#554—58no—
490#554—58no—
491#554—58no—
492#554—58no—
493#554—54no—
494#554—58no—
495#554—516no—
496#554C2×D514yescomplemented
497#554C2×D518yescomplemented
498D4×Q8—58no—
499D4×Q8—58no—
500D4×Q8—54no—
501D4×Q8—58no—
502D4×Q8—516no—
503D4×Q8—54no—
504D4×Q8—58no—
505D4×Q8—54no—
506D4×Q8C2×D514yescomplemented
507#544—58no—
508#544—58no—
509#544—58no—
510#544—54no—
511#544—52no—
512#544C2×D512yescomplemented
513#543—58no—
514#543—58no—
515#543—516no—
516#543—516no—
517#543—58no—
518#543—54no—
519#543C2×D514yescomplemented
520#533—52no—
521#533—52no—
522#533—54no—
523#533—54no—
524#533—54no—
525#533—54no—
526#533—54no—
527#533—54no—
528#533—52no—
529#533C2×D512yescomplemented
530C2×C4⋊Q8—52no—
531C2×C4⋊Q8—52no—
532C2×C4⋊Q8—58no—
533C2×#125—54no—
534C2×#125—58no—
535C2×C22⋊Q8—54no—
536C2×C22⋊Q8—54no—
537C2×C22⋊Q8—54no—
538C2×C22⋊Q8—58no—
539C2×C22⋊Q8—58no—
540C2×C22⋊Q8—58no—
541C2×C22⋊Q8—54no—
542C2×C22⋊Q8—58no—
543C2×C22⋊Q8—58no—
544C2×C22⋊Q8—58no—
545C2×C22⋊Q8—58no—
546C2×C22⋊Q8—516no—
547C2×C22⋊Q8—516no—
548C2×C22⋊Q8—58no—
549C2×C22⋊Q8—54no—
550C2×C22⋊Q8—58no—
551C2×C22⋊Q8C2×D514yescomplemented
552#518—52no—
553#518—58no—
554#518—58no—
555#518—54no—
556#518—58no—
557#518C2×D512yes—
558C2×C4×Q8—54no—
559C2×C4×Q8—54no—
560C2×C4×D4—51no—
561C2×C4×D4—52no—
562C2×C4×D4—54no—
563C2×C4×D4—54no—
564C2×C4×D4—54no—
565C2×C4×D4—54no—
566C2×C4×D4—58no—
567C2×C4×D4—58no—
568C2×C4×D4—51no—
569C2×C4×D4—52no—
570C2×C4×D4—51no—
571C2×C4×D4C2×D511yescharacteristic
572C2×#117—54no—
573C22×C4⋊C4—51no—
574C22×C4⋊C4—58no—
575C22×C4⋊C4—54no—
576C22×C22⋊C4—52no—
577C22×C22⋊C4—58no—
578C22×C42—51no—
579C23×C5—42no—
580C23×C5—42no—
581C23×C5C22×Q818yescomplemented
582C23×C5C2511yescharacteristic
583C23×C5C2514yes—
584C22×D5—28no—
585C22×D5—22no—
586C22×D5—28no—
587C22×D5—22no—
588C22×D5—432no—
589C22×D5—42no—
590C22×D5—44no—
591C22×D5—42no—
592C22×D5—44no—
593C22×D5C22×Q814yes—
594C22×D5C22×Q8116yes—
595C22×D5C22×Q818yescomplemented
596C22×D5C22×Q8116yescomplemented
597C22×D5C2511yescharacteristic
598C22×D5C2514yes—
599C22×D5C2511yescharacteristic
600C5×Q8—28no—
601C5×Q8—48no—
602C5×Q8—44no—
603C5×D4C22×Q8116yescomplemented
604C2×C4×C5—28no—
605C2×C4×C5—22no—
606C2×C4×C5—48no—
607C2×C4×C5—42no—
608C2×C4×C5—44no—
609C2×C4×C5—41no—
610C2×C4×C5—48no—
611C2×C4×C5C22×Q814yescomplemented
612C2×C4×C5C2511yescharacteristic
613C2×C4×C5C2512yes—
614C2×C4×C5C2518yes—
615C2×C4×C5C2518yes—
616C2×C4×C5C2514yes—
617C2×C4×C5C2512yes—
618C2×C4×C5C2511yescharacteristic
619C22⋊D5C22×Q8132yescomplemented
620C2×Dic5—28no—
621C2×Dic5—22no—
622C2×Dic5—48no—
623C2×Dic5—42no—
624C2×Dic5—44no—
625C2×Dic5—41no—
626C2×Dic5—48no—
627C2×Dic5C22×Q814yescomplemented
628C2×Dic5C2511yescharacteristic
629C2×Dic5C2512yes—
630C2×Dic5C2518yes—
631C2×Dic5C2518yes—
632C2×Dic5C2514yes—
633C2×Dic5C2512yes—
634C2×Dic5C2511yescharacteristic
635D20C22×Q8116yescomplemented
636C4×D5—22no—
637C4×D5—28no—
638C4×D5—216no—
639C4×D5—216no—
640C4×D5—24no—
641C4×D5—22no—
642C4×D5—28no—
643C4×D5—22no—
644C4×D5—28no—
645C4×D5—44no—
646C4×D5—44no—
647C4×D5—44no—
648C4×D5—42no—
649C4×D5—416no—
650C4×D5—416no—
651C4×D5C22×Q818yes—
652C4×D5C22×Q818yescomplemented
653C4×D5H(5,𝔽2)14yes—
654Dic10—28no—
655Dic10—216no—
656Dic10—48no—
657Dic10—416no—
658Dic10—48no—
659Dic10—44no—
660C25—52no—
661C22×Q8—54no—
662C22×Q8—54no—
663C22×Q8—58no—
664C22×Q8—58no—
665C22×Q8—58no—
666C22×Q8—58no—
667C22×Q8—54no—
668C22×Q8—2016no—
669C22×Q8C22×D514yescomplemented
670C22×D4—52no—
671C22×D4—516no—
672C22×D4—54no—
673C22×D4—54no—
674C22×D4—51no—
675C22×D4C22×D511yescharacteristic
676C23×C4—51no—
677C23×C4—52no—
678C23×C4—54no—
679C23×C4—51no—
680C23×C4—51no—
681C23×C4—58no—
682C23×C4—58no—
683C23×C4—52no—
684C23×C4—54no—
685C23×C4—52no—
686C23×C4—54no—
687C23×C4—52no—
688C23×C4—54no—
689C23×C4—208no—
690C23×C4C22×D512yes—
691C4⋊Q8—54no—
692C4⋊Q8—54no—
693C4⋊Q8—516no—
694C4⋊Q8—54no—
695C4⋊Q8—54no—
696C4⋊Q8—54no—
697C4⋊Q8—54no—
698C4⋊Q8—516no—
699C4⋊Q8—58no—
700C4⋊Q8—58no—
701C4⋊Q8—52no—
702C4⋊Q8—52no—
703C4⋊Q8—58no—
704C4⋊Q8C22×D512yescomplemented
705C4⋊Q8C22×D512yescomplemented
706C4⋊Q8C22×D518yescomplemented
707#125—58no—
708#125—58no—
709#125—54no—
710#125—54no—
711#125—516no—
712#125—516no—
713#125—58no—
714#125—58no—
715#125—54no—
716#125—58no—
717#125C22×D514yescomplemented
718#125C22×D518yescomplemented
719C22⋊Q8—54no—
720C22⋊Q8—58no—
721C22⋊Q8—58no—
722C22⋊Q8—58no—
723C22⋊Q8—54no—
724C22⋊Q8—516no—
725C22⋊Q8—516no—
726C22⋊Q8—54no—
727C22⋊Q8—58no—
728C22⋊Q8—58no—
729C22⋊Q8—58no—
730C22⋊Q8—54no—
731C22⋊Q8—516no—
732C22⋊Q8—516no—
733C22⋊Q8—58no—
734C22⋊Q8—54no—
735C22⋊Q8—516no—
736C22⋊Q8—58no—
737C22⋊Q8—516no—
738C22⋊Q8—58no—
739C22⋊Q8—516no—
740C22⋊Q8—58no—
741C22⋊Q8—58no—
742C22⋊Q8—54no—
743C22⋊Q8—516no—
744C22⋊Q8—516no—
745C22⋊Q8—516no—
746C22⋊Q8—516no—
747C22⋊Q8—516no—
748C22⋊Q8—516no—
749C22⋊Q8—58no—
750C22⋊Q8—516no—
751C22⋊Q8—516no—
752C22⋊Q8—516no—
753C22⋊Q8—58no—
754C22⋊Q8—516no—
755C22⋊Q8—516no—
756C22⋊Q8—516no—
757C22⋊Q8—516no—
758C22⋊Q8C22×D514yes—
759C22⋊Q8C22×D518yes—
760C22⋊Q8C22×D514yes—
761C22⋊Q8C22×D518yescomplemented
762C22⋊Q8C22×D518yescomplemented
763C22⋊Q8C22×D5116yescomplemented
764C22⋊Q8C22×D5116yescomplemented
765C4×Q8—54no—
766C4×Q8—54no—
767C4×Q8—58no—
768C4×Q8—54no—
769C4×Q8—54no—
770C4×Q8—58no—
771C4×Q8—58no—
772C4×Q8—54no—
773C4×Q8—58no—
774C4×Q8—54no—
775C4×Q8C22×D514yescomplemented
776C4×Q8C22×D514yescomplemented
777C4×D4—54no—
778C4×D4—54no—
779C4×D4—58no—
780C4×D4—58no—
781C4×D4—58no—
782C4×D4—58no—
783C4×D4—516no—
784C4×D4—516no—
785C4×D4—54no—
786C4×D4—54no—
787C4×D4—58no—
788C4×D4—58no—
789C4×D4—58no—
790C4×D4—58no—
791C4×D4—516no—
792C4×D4—516no—
793C4×D4—54no—
794C4×D4—54no—
795C4×D4—58no—
796C4×D4—58no—
797C4×D4C22×D514yes—
798C4×D4C22×D514yes—
799C4×D4C22×D518yes—
800C4×D4C22×D518yes—
801#117—54no—
802#117—54no—
803#117—54no—
804#117—58no—
805#117—58no—
806#117C22×D514yes—
807C2×C4⋊C4—52no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—58no—
810C2×C4⋊C4—58no—
811C2×C4⋊C4—58no—
812C2×C4⋊C4—58no—
813C2×C4⋊C4—54no—
814C2×C4⋊C4—58no—
815C2×C4⋊C4—54no—
816C2×C4⋊C4—54no—
817C2×C4⋊C4—54no—
818C2×C4⋊C4—58no—
819C2×C4⋊C4—516no—
820C2×C4⋊C4—516no—
821C2×C4⋊C4—516no—
822C2×C4⋊C4—58no—
823C2×C4⋊C4—58no—
824C2×C4⋊C4—54no—
825C2×C4⋊C4—54no—
826C2×C4⋊C4—58no—
827C2×C4⋊C4—54no—
828C2×C4⋊C4C22×D511yescharacteristic
829C2×C4⋊C4C22×D518yescomplemented
830C2×C4⋊C4C22×D514yescomplemented
831C2×C22⋊C4—52no—
832C2×C22⋊C4—58no—
833C2×C22⋊C4—52no—
834C2×C22⋊C4—52no—
835C2×C22⋊C4—58no—
836C2×C22⋊C4—58no—
837C2×C22⋊C4—58no—
838C2×C22⋊C4—58no—
839C2×C22⋊C4—516no—
840C2×C22⋊C4—58no—
841C2×C22⋊C4—516no—
842C2×C22⋊C4—516no—
843C2×C22⋊C4C22×D512yes—
844C2×C22⋊C4C22×D518yes—
845C2×C42—51no—
846C2×C42—51no—
847C2×C42—51no—
848C2×C42—58no—
849C2×C42—52no—
850C2×C42—52no—
851C2×C42—52no—
852C2×C42—52no—
853C2×C42C22×D511yescharacteristic
854C22×C5—24no—
855C22×C5—21no—
856C22×C5—24no—
857C22×C5—21no—
858C22×C5—48no—
859C22×C5C23×Q812yes—
860C22×C5C23×Q818yes—
861C22×C5C2611yescharacteristic
862C2×D5—24no—
863C2×D5—21no—
864C2×D5—24no—
865C2×D5—21no—
866C2×D5—28no—
867C2×D5—232no—
868C2×D5—416no—
869C2×D5—48no—
870C2×D5C23×Q812yes—
871C2×D5C23×Q818yes—
872C2×D5C23×Q812yes—
873C2×D5C2×H(5,𝔽2)12yes—
874C2×D5#58512yes—
875C4×C5—28no—
876C4×C5—24no—
877C4×C5—21no—
878C4×C5—22no—
879C4×C5—28no—
880C4×C5C23×Q814yes—
881C4×C5C2×H(5,𝔽2)12yes—
882Dic5—28no—
883Dic5—24no—
884Dic5—21no—
885Dic5—22no—
886Dic5—28no—
887Dic5C23×Q814yes—
888Dic5C2×H(5,𝔽2)12yes—
889C24—51no—
890C24—54no—
891C24—516no—
892C24—54no—
893C24—52no—
894C24—204no—
895C24—204no—
896C24C23×D512yes—
897C2×Q8—48no—
898C2×Q8—58no—
899C2×Q8—54no—
900C2×Q8—58no—
901C2×Q8—54no—
902C2×Q8—58no—
903C2×Q8—516no—
904C2×Q8—1016no—
905C2×Q8—208no—
906C2×Q8—2016no—
907C2×Q8—2016no—
908C2×Q8—208no—
909C2×Q8—2016no—
910C2×Q8—2016no—
911C2×Q8C23×D514yes—
912C2×Q8C23×D514yes—
913C2×Q8C23×D518yes—
914C2×D4—516no—
915C2×D4—58no—
916C2×D4—532no—
917C2×D4—532no—
918C2×D4—58no—
919C2×D4—54no—
920C2×D4Q8×D518yescomplemented
921C2×D4C23×D514yes—
922C22×C4—44no—
923C22×C4—51no—
924C22×C4—58no—
925C22×C4—52no—
926C22×C4—51no—
927C22×C4—52no—
928C22×C4—51no—
929C22×C4—54no—
930C22×C4—51no—
931C22×C4—58no—
932C22×C4—58no—
933C22×C4—52no—
934C22×C4—54no—
935C22×C4—52no—
936C22×C4—51no—
937C22×C4—51no—
938C22×C4—51no—
939C22×C4—58no—
940C22×C4—58no—
941C22×C4—54no—
942C22×C4—54no—
943C22×C4—54no—
944C22×C4—52no—
945C22×C4—516no—
946C22×C4—516no—
947C22×C4—54no—
948C22×C4—54no—
949C22×C4—54no—
950C22×C4—104no—
951C22×C4—1016no—
952C22×C4—204no—
953C22×C4—208no—
954C22×C4—208no—
955C22×C4—204no—
956C22×C4—208no—
957C22×C4—204no—
958C22×C4—2016no—
959C22×C4—2016no—
960C22×C4—202no—
961C22×C4—204no—
962C22×C4C23×D511yescharacteristic
963C22×C4C23×D514yes—
964C22×C4C23×D511yescharacteristic
965C22×C4C23×D518yes—
966C22×C4C23×D512yes—
967C22×C4C23×D518yes—
968C22×C4C23×D514yes—
969C22×C4C23×D511yescharacteristic
970C4⋊C4—58no—
971C4⋊C4—58no—
972C4⋊C4—58no—
973C4⋊C4—58no—
974C4⋊C4—54no—
975C4⋊C4—58no—
976C4⋊C4—54no—
977C4⋊C4—516no—
978C4⋊C4—58no—
979C4⋊C4—516no—
980C4⋊C4—516no—
981C4⋊C4—516no—
982C4⋊C4—58no—
983C4⋊C4—54no—
984C4⋊C4—58no—
985C4⋊C4—54no—
986C4⋊C4—58no—
987C4⋊C4—58no—
988C4⋊C4—58no—
989C4⋊C4—58no—
990C4⋊C4—54no—
991C4⋊C4C23×D518yes—
992C4⋊C4C23×D514yes—
993C4⋊C4C23×D514yes—
994C4⋊C4C23×D518yes—
995C4⋊C4C23×D5116yes—
996C4⋊C4C23×D514yes—
997C4⋊C4C23×D514yes—
998C4⋊C4C23×D518yes—
999C4⋊C4C23×D514yes—
1000C22⋊C4—58no—
1001C22⋊C4—58no—
1002C22⋊C4—516no—
1003C22⋊C4—58no—
1004C22⋊C4—58no—
1005C22⋊C4—58no—
1006C22⋊C4—516no—
1007C22⋊C4—516no—
1008C22⋊C4—58no—
1009C22⋊C4C23×D518yes—
1010C22⋊C4C23×D518yes—
1011C22⋊C4C23×D5116yes—
1012C42—52no—
1013C42—52no—
1014C42—52no—
1015C42—52no—
1016C42—52no—
1017C42—52no—
1018C42—58no—
1019C42—58no—
1020C42—58no—
1021C42C23×D512yes—
1022C42C23×D512yes—
1023C42C23×D518yes—
1024C2×C5—22no—
1025C2×C5—28no—
1026C2×C5C24×Q811yescharacteristic
1027C2×C5C22×H(5,𝔽2)11yescharacteristic
1028C2×C5C2×#58511yescharacteristic
1029D5—22no—
1030D5—28no—
1031D5#350114yesdirect product factor
1032C23—42no—
1033C23—42no—
1034C23—51no—
1035C23—54no—
1036C23—516no—
1037C23—51no—
1038C23—54no—
1039C23—516no—
1040C23—58no—
1041C23—108no—
1042C23—102no—
1043C23—108no—
1044C23—102no—
1045C23—204no—
1046C23—202no—
1047C23—204no—
1048C23—202no—
1049C23—2032no—
1050C23C2×Q8×D518yescomplemented
1051C23C24×D511yescharacteristic
1052C23C24×D514yes—
1053Q8—28no—
1054Q8—48no—
1055Q8—44no—
1056Q8—1016no—
1057Q8—108no—
1058Q8—208no—
1059Q8—2016no—
1060Q8—208no—
1061Q8—204no—
1062D4—532no—
1063D4—516no—
1064D4C2×Q8×D5116yescomplemented
1065C2×C4—22no—
1066C2×C4—28no—
1067C2×C4—44no—
1068C2×C4—42no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—41no—
1072C2×C4—54no—
1073C2×C4—52no—
1074C2×C4—51no—
1075C2×C4—58no—
1076C2×C4—58no—
1077C2×C4—54no—
1078C2×C4—52no—
1079C2×C4—51no—
1080C2×C4—58no—
1081C2×C4—58no—
1082C2×C4—54no—
1083C2×C4—102no—
1084C2×C4—108no—
1085C2×C4—102no—
1086C2×C4—108no—
1087C2×C4—1016no—
1088C2×C4—1016no—
1089C2×C4—104no—
1090C2×C4—102no—
1091C2×C4—108no—
1092C2×C4—102no—
1093C2×C4—108no—
1094C2×C4—204no—
1095C2×C4—204no—
1096C2×C4—204no—
1097C2×C4—2016no—
1098C2×C4—2016no—
1099C2×C4—202no—
1100C2×C4—204no—
1101C2×C4—202no—
1102C2×C4—208no—
1103C2×C4—208no—
1104C2×C4—201no—
1105C2×C4C2×Q8×D514yescomplemented
1106C2×C4C24×D512yes—
1107C2×C4C24×D511yescharacteristic
1108C2×C4C24×D518yes—
1109C2×C4C24×D518yes—
1110C2×C4C24×D514yes—
1111C2×C4C24×D512yes—
1112C2×C4C24×D511yescharacteristic
1113C5C2×#350111yescharacteristic, complemented, Sylow
1114C22—24no—
1115C22—21no—
1116C22—24no—
1117C22—21no—
1118C22—48no—
1119C22—52no—
1120C22—52no—
1121C22—52no—
1122C22—52no—
1123C22—58no—
1124C22—108no—
1125C22—1032no—
1126C22—104no—
1127C22—101no—
1128C22—104no—
1129C22—101no—
1130C22—208no—
1131C22—2016no—
1132C22C22×Q8×D512yes—
1133C22C22×Q8×D518yes—
1134C22C25×D511yescharacteristic
1135C4—21no—
1136C4—24no—
1137C4—28no—
1138C4—28no—
1139C4—22no—
1140C4—54no—
1141C4—52no—
1142C4—101no—
1143C4—104no—
1144C4—108no—
1145C4—108no—
1146C4—102no—
1147C4C22×Q8×D514yes—
1148C4D5×H(5,𝔽2)12yes—
1149C2—22no—
1150C2—28no—
1151C2—54no—
1152C2—102no—
1153C2—108no—
1154C2C23×Q8×D511yescharacteristic
1155C2C2×D5×H(5,𝔽2)11yescharacteristic
1156C2D5×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3501C2
prime radicalC22×D4×D5C22
hypercenter#3501D5
hypocenterC5C2×#3501
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C5×#3501C2semidirect
2. #10618850C2semidirect
3. #10618849C2semidirect
4. D5×#554C2semidirect
5. D5×#554C2semidirect
6. #10618662C2semidirect
7. D4×Q8×D5C2semidirect
8. #10618500C2semidirect
9. D5×#544C2semidirect
10. D5×#543C2semidirect
11. #10618475C2semidirect
12. #10618181C2semidirect
13. D5×#533C2semidirect
14. #10617887C2semidirect
15. C2×D5×C22⋊Q8C2semidirect
17. #10617761C2semidirect
19. #10617667C2semidirect
20. C22×Q8×D5C22semidirect
23. C5×#554C22semidirect
24. C5×#554C22semidirect
25. C5×D4×Q8C22semidirect
26. C5×#544C22semidirect
27. C5×#543C22semidirect
28. C5×#533C22semidirect
29. C2×C5×C22⋊Q8C22semidirect
32. Q8×C22⋊D5C22semidirect
33. C2×#4092C22semidirect
37. C2×#4070C22semidirect
38. #66064C22semidirect
39. #66064C22semidirect
40. #66063C22semidirect
41. #66062C22semidirect
42. #66062C22semidirect
43. #66061C22semidirect
44. #66061C22semidirect
45. D5×C4⋊Q8C22semidirect
46. D5×C4⋊Q8C22semidirect
47. D5×C4⋊Q8C22semidirect
48. #66024C22semidirect
49. #66024C22semidirect
50. #66024C22semidirect
51. #66023C22semidirect
52. #66022C22semidirect
53. D5×#125C22semidirect
54. D5×#125C22semidirect
55. #65970C22semidirect
56. #65970C22semidirect
57. #65970C22semidirect
58. #65969C22semidirect
59. #65969C22semidirect
60. #65968C22semidirect
61. #65968C22semidirect
62. #65968C22semidirect
63. #65968C22semidirect
64. #65966C22semidirect
65. #65966C22semidirect
69. D5×C22⋊Q8C22semidirect
70. D5×C22⋊Q8C22semidirect
71. D5×C22⋊Q8C22semidirect
72. D5×C22⋊Q8C22semidirect
73. D5×C22⋊Q8C22semidirect
74. D5×C22⋊Q8C22semidirect
75. D5×C22⋊Q8C22semidirect
76. D5×C22⋊Q8C22semidirect
77. #65957C22semidirect
78. #65956C22semidirect
79. #65956C22semidirect
80. #65913C22semidirect
81. #65913C22semidirect
82. #65912C22semidirect
83. #65912C22semidirect
84. Q8×D20C22semidirect
85. C4×Q8×D5C22semidirect
86. C4×Q8×D5C22semidirect
95. #65877C22semidirect
96. #65877C22semidirect
97. #65873C22semidirect
98. #65873C22semidirect
99. #65873C22semidirect
100. D4×Dic10C22semidirect
101. D4×Dic10C22semidirect
104. #65853C22semidirect
105. #65851C22semidirect
106. #65845C22semidirect
107. #65845C22semidirect
108. C2×#4043C22semidirect
109. C2×#4042C22semidirect
112. C2×D5×C4⋊C4C22semidirect
113. C2×D5×C4⋊C4C22semidirect
114. #65834C22semidirect
119. #65817C22semidirect
120. #65817C22semidirect
121. C2×#4024C22semidirect
124. #65804C22semidirect
127. C22×C5×Q8C23semidirect
136. C2×Q8×D5C23semidirect
137. C2×Q8×D5C23semidirect
138. C2×D4×D5Q8semidirect
155. C22×Dic10C23semidirect
156. C22×Dic10C23semidirect
157. C5×C4⋊Q8C23semidirect
158. C5×C4⋊Q8C23semidirect
159. C5×C4⋊Q8C23semidirect
160. C5×#125C23semidirect
161. C5×#125C23semidirect
165. C5×C22⋊Q8C23semidirect
166. C5×C22⋊Q8C23semidirect
167. C5×C22⋊Q8C23semidirect
168. C5×C22⋊Q8C23semidirect
169. C4×C5×Q8C23semidirect
170. C4×C5×Q8C23semidirect
177. C2×C5×C4⋊C4C23semidirect
178. C2×C5×C4⋊C4C23semidirect
187. #4092C23semidirect
188. #4092C23semidirect
189. #4092C23semidirect
190. #4092C23semidirect
191. Q8×Dic5C23semidirect
192. Q8×Dic5C23semidirect
193. #4090C23semidirect
194. #4090C23semidirect
195. #4090C23semidirect
210. C2×C4⋊Dic5C23semidirect
211. C2×C4⋊Dic5C23semidirect
215. #4070C23semidirect
216. #4070C23semidirect
217. #4070C23semidirect
218. #4070C23semidirect
220. C2×#683C23semidirect
221. C2×#683C23semidirect
222. C2×#683C23semidirect
229. #4043C23semidirect
230. #4043C23semidirect
231. #4043C23semidirect
232. #4043C23semidirect
236. #4042C23semidirect
237. #4042C23semidirect
238. #4042C23semidirect
239. #4042C23semidirect
240. #4042C23semidirect
241. #4042C23semidirect
258. D5×C4⋊C4C23semidirect
259. D5×C4⋊C4C23semidirect
260. D5×C4⋊C4C23semidirect
261. D5×C4⋊C4C23semidirect
262. #4036C23semidirect
263. #4036C23semidirect
264. #4036C23semidirect
265. #4036C23semidirect
266. #4035C23semidirect
267. #4035C23semidirect
268. #4035C23semidirect
269. #4035C23semidirect
270. #4034C23semidirect
271. #4034C23semidirect
272. #4034C23semidirect
273. #4034C23semidirect
274. #4034C23semidirect
275. #4034C23semidirect
276. #4034C23semidirect
277. #4033C23semidirect
278. #4033C23semidirect
279. #4033C23semidirect
280. #4033C23semidirect
294. #4024C23semidirect
295. #4024C23semidirect
296. #4024C23semidirect
297. #4024C23semidirect
298. #4024C23semidirect
299. #4024C23semidirect
311. #4016C23semidirect
312. #4016C23semidirect
313. #4015C23semidirect
314. #4015C23semidirect
315. #4015C23semidirect
316. C4×Dic10C23semidirect
317. C4×Dic10C23semidirect
318. C4×Dic10C23semidirect
319. C4×Dic10C23semidirect
329. #3501D5direct (N × H)
342. C23×D5C2×Q8semidirect
351. C2×C5×D4C2×Q8semidirect
362. C2×C22⋊D5C2×Q8semidirect
378. D4×D5C2×Q8semidirect
379. D4×D5C2×Q8semidirect
380. C2×D20C2×Q8semidirect
393. C2×C4×D5C2×Q8semidirect
496. #554C2×D5semidirect
497. #554C2×D5semidirect
506. D4×Q8C2×D5semidirect
512. #544C2×D5semidirect
519. #543C2×D5semidirect
529. #533C2×D5semidirect
551. C2×C22⋊Q8C2×D5semidirect
581. C23×C5C22×Q8semidirect
595. C22×D5C22×Q8semidirect
596. C22×D5C22×Q8semidirect
603. C5×D4C22×Q8semidirect
611. C2×C4×C5C22×Q8semidirect
619. C22⋊D5C22×Q8semidirect
627. C2×Dic5C22×Q8semidirect
635. D20C22×Q8semidirect
652. C4×D5C22×Q8semidirect
669. C22×Q8C22×D5semidirect
704. C4⋊Q8C22×D5semidirect
705. C4⋊Q8C22×D5semidirect
706. C4⋊Q8C22×D5semidirect
717. #125C22×D5semidirect
718. #125C22×D5semidirect
761. C22⋊Q8C22×D5semidirect
762. C22⋊Q8C22×D5semidirect
763. C22⋊Q8C22×D5semidirect
764. C22⋊Q8C22×D5semidirect
775. C4×Q8C22×D5semidirect
776. C4×Q8C22×D5semidirect
829. C2×C4⋊C4C22×D5semidirect
830. C2×C4⋊C4C22×D5semidirect
920. C2×D4Q8×D5semidirect
1031. D5#3501direct (N × H)
1050. C23C2×Q8×D5semidirect
1064. D4C2×Q8×D5semidirect
1105. C2×C4C2×Q8×D5semidirect
1113. C5C2×#3501semidirect

Maximal subgroups

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

subgroupindex
C5×#35012
#106188502
#106188492
D5×#5542
#106186622
D4×Q8×D52
#106185002
D5×#5442
D5×#5432
#106184752
#106181812
D5×#5332
#106178872
C2×D5×C22⋊Q82
D5×#5182
#106177612
C2×C4×D4×D52
#106176672
C2×#35015