Finite Group Databasebeta

← #13007852

Subgroups — #13007852

Order 1280.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3501C211yesmaximal, characteristic, complemented
2#10618828C218yesmaximal, complemented
3#10618827C214yesmaximal, complemented
4#10618824C218yesmaximal, complemented
5#10618824C214yesmaximal, complemented
6#10618648C214yesmaximal, complemented
7Q8×#711C214yesmaximal, complemented
8#10618486C212yesmaximal, complemented
9#10618482C212yesmaximal, complemented
10#10618475C214yesmaximal, complemented
11#10618472C214yesmaximal, complemented
12D5×#533C212yesmaximal, complemented
13#10618159C212yesmaximal, complemented
14#10617887C214yesmaximal, complemented
15C2×#65956C214yesmaximal, complemented
16#10617761C212yesmaximal, complemented
17#10617757C212yesmaximal
18#10617667C211yesmaximal, characteristic, complemented
19C2×C4×#711C211yesmaximal, characteristic
20C22×#711C2211yescharacteristic
21C5×#554C2214yescomplemented
22C5×#554C2218yescomplemented
23C5×D4×Q8C2214yescomplemented
24C5×#544C2212yes—
25C5×#543C2214yes—
26C5×#533C2212yes—
27C2×C5×C22⋊Q8C2214yes—
28C5×#518C2212yes—
29C2×C4×C5×D4C2211yescharacteristic
30Q8×C22⋊D5C2218yescomplemented
31C2×Q8×Dic5C2214yescomplemented
32C2×#4090C2214yescomplemented
33#66132C2212yes—
34C2×D4×Dic5C2211yescharacteristic
35C2×C4×C22⋊D5C2212yes—
36C2×#4070C2214yes—
37C22×C4×Dic5C2212yes—
38#66063C2218yescomplemented
39#66062C2212yescomplemented
40#66062C2218yescomplemented
41#66062C2212yescomplemented
42D5×C4⋊Q8C2212yescomplemented
43D5×C4⋊Q8C2212yescomplemented
44#66056C2218yescomplemented
45#66056C2214yescomplemented
46#66055C2214yescomplemented
47#66055C2218yescomplemented
48#66023C2218yescomplemented
49#66022C2214yescomplemented
50#66022C2218yescomplemented
51D5×#125C2214yescomplemented
52#66019C2218yescomplemented
53#66019C2218yescomplemented
54#66019C2218yescomplemented
55#65970C22116yescomplemented
56#65970C22116yescomplemented
57#65970C22116yescomplemented
58#65969C2218yescomplemented
59#65969C22116yescomplemented
60#65968C2218yes—
61#65966C2218yescomplemented
62#65966C22116yescomplemented
63D5×C22⋊Q8C2214yes—
64D5×C22⋊Q8C2214yes—
65#65957C2218yes—
66#65957C2218yes—
67#65957C22116yescomplemented
68#65957C22116yescomplemented
69#65956C2214yes—
70#65956C2218yes—
71#65956C2218yes—
72#65956C2218yes—
73#65956C2214yes—
74#65956C2218yescomplemented
75#65956C2218yescomplemented
76#65956C2218yescomplemented
77#65956C2218yescomplemented
78#65956C22116yescomplemented
79#65956C22116yescomplemented
80#65912C2214yescomplemented
81#65912C2214yescomplemented
82C4×Q8×D5C2214yescomplemented
83C4×Q8×D5C2214yescomplemented
84#65901C2214yescomplemented
85#65901C2218yescomplemented
86Q8×Dic10C2214yescomplemented
87#65880C2218yes—
88#65880C2218yes—
89#65877C2214yescomplemented
90#65877C2218yescomplemented
91#65873C2218yescomplemented
92#65873C2218yescomplemented
93#65873C2218yescomplemented
94D4×Dic10C2214yescomplemented
95D4×Dic10C2218yescomplemented
96C4×#711C2214yes—
97C4×#711C2218yes—
98C4×#711C2214yes—
99C4×#711C2214yes—
100C4×#711C2214yes—
101C4×#711C2218yes—
102D5×#117C2214yes—
103#65853C2214yes—
104#65851C2214yes—
105#65850C2214yes—
106#65845C2218yescomplemented
107#65845C22116yescomplemented
108C2×#4038C2211yescharacteristic
109#65834C2212yes—
110C2×#4035C2218yescomplemented
111C2×#4034C2214yescomplemented
112C2×#4033C2211yescharacteristic
113C2×#4033C2214yescomplemented
114C2×#4033C2218yescomplemented
115#65820C2218yes—
116C2×#4027C2212yes—
117#65817C2218yes—
118#65817C2214yes—
119C2×#4024C2218yes—
120C2×#4023C2218yes—
121C2×#4023C2212yes—
122C2×C42×D5C2211yescharacteristic
123#65804C2212yes—
124C2×C4×Dic10C2211yescharacteristic
125#62813—51nomaximal, Sylow
126C22×C5×Q8C2314yes—
127C22×C5×D4C2311yescharacteristic
128C23×C4×C5C2312yes—
129C22×C22⋊D5C2312yes—
130C23×Dic5C2312yes—
131C23×Dic5C2312yes—
132C2×Q8×D5C2314yes—
133C2×Q8×D5C2314yes—
134C2×#711Q8116yescomplemented
135C2×#711C2314yes—
136C2×#711C2314yes—
137C22×C4×D5C2311yescharacteristic
138C22×C4×D5C2311yescharacteristic
139C22×C4×D5C2311yescharacteristic
140C22×Dic10C2318yes—
141C22×Dic10C2314yes—
142C22×Dic10C2311yescharacteristic
143C5×C4⋊Q8C2312yes—
144C5×C4⋊Q8C2318yes—
145C5×C4⋊Q8C2312yes—
146C5×#125C2314yes—
147C5×#125C2318yes—
148C5×C22⋊Q8C2314yes—
149C5×C22⋊Q8C2318yes—
150C5×C22⋊Q8C2318yes—
151C5×C22⋊Q8C2318yes—
152C5×C22⋊Q8C2314yes—
153C5×C22⋊Q8C23116yes—
154C5×C22⋊Q8C23116yes—
155C4×C5×Q8C2314yes—
156C4×C5×Q8C2314yes—
157C4×C5×D4C2314yes—
158C4×C5×D4C2314yes—
159C4×C5×D4C2318yes—
160C4×C5×D4C2318yes—
161C5×#117C2314yes—
162C2×C5×C4⋊C4C2311yescharacteristic
163C2×C5×C4⋊C4C2314yes—
164C2×C5×C4⋊C4C2318yes—
165C2×C5×C22⋊C4C2318yes—
166C2×C5×C22⋊C4C2312yes—
167C2×C42×C5C2311yescharacteristic
168C2×C22⋊Dic5C2318yes—
169C2×C22⋊Dic5C2312yes—
170#4092C23116yes—
171#4092C2314yes—
172#4092C2314yes—
173Q8×Dic5C2318yes—
174Q8×Dic5C2318yes—
175Q8×Dic5C2318yes—
176Q8×Dic5C2314yes—
177Q8×Dic5C2314yes—
178#4090C23116yes—
179#4090C2318yes—
180#4090C2318yes—
181#4090C23116yes—
182#4090C2314yes—
183#4090C2314yes—
184#4090C2318yes—
185D4×Dic5C2314yes—
186D4×Dic5C2314yes—
187D4×Dic5C2318yes—
188D4×Dic5C2318yes—
189C4×C22⋊D5C23116yes—
190C4×C22⋊D5C23116yes—
191C4×C22⋊D5C2318yes—
192C4×C22⋊D5C2318yes—
193C2×#685C2312yes—
194#4072C2314yes—
195C2×C4⋊Dic5C2311yescharacteristic
196C2×C4⋊Dic5C2318yes—
197C2×C4⋊Dic5C2314yes—
198#4070C2314yes—
199#4070C2314yes—
200#4070C2318yes—
201#4070C23116yes—
202#4070C23116yes—
203#4070C2318yes—
204#4070C2318yes—
205C2×#683C2312yes—
206C2×#683C2312yes—
207C2×#683C2318yes—
208C2×#683C2318yes—
209C2×#683C2318yes—
210C2×#683C2318yes—
211C2×#683C2318yes—
212C2×C4×Dic5C2312yes—
213C2×C4×Dic5C2311yescharacteristic
214C2×C4×Dic5C2311yescharacteristic
215C2×C4×Dic5C2311yescharacteristic
216C2×C4×Dic5C2318yes—
217C2×C4×Dic5C2318yes—
218C2×C4×Dic5C2312yes—
219C2×C4×Dic5C2312yes—
220C2×C4×Dic5C2314yes—
221C2×C4×Dic5C2314yes—
222C2×C4×Dic5C2314yes—
223C2×C4×Dic5C2314yes—
224#4043C2314yes—
225#4043C23116yes—
226#4043C2314yes—
227#4042C23116yes—
228#4042C2318yes—
229#4042C23116yes—
230#4042C2318yes—
231#4038C2314yes—
232#4038C2314yes—
233#4038C2314yes—
234#4038C2314yes—
235D5×C4⋊C4C2314yes—
236D5×C4⋊C4C2314yes—
237D5×C4⋊C4C2314yes—
238D5×C4⋊C4C2314yes—
239D5×C4⋊C4C2318yes—
240D5×C4⋊C4C2318yes—
241#4036C2314yes—
242#4036C2318yes—
243#4036C2318yes—
244#4036C2314yes—
245#4035C23116yes—
246#4035C23116yes—
247#4035C23116yes—
248#4035C23116yes—
249#4035C2318yes—
250#4035C23116yes—
251#4035C23116yes—
252#4035C23116yes—
253#4035C2318yes—
254#4034C2314yes—
255#4034C2318yes—
256#4034C2318yes—
257#4034C23116yes—
258#4034C2318yes—
259#4034C2314yes—
260#4034C2314yes—
261#4034C2314yes—
262#4034C2318yes—
263#4034C2318yes—
264#4034C23116yes—
265#4033C2318yes—
266#4033C2314yes—
267#4033C2314yes—
268#4033C2318yes—
269#4033C23116yes—
270#4033C2318yes—
271#4033C2314yes—
272#4033C23116yes—
273#4033C2314yes—
274#4033C2318yes—
275#4033C23116yes—
276#4033C2318yes—
277#4033C2318yes—
278#4033C2318yes—
279#4027C2318yes—
280#4027C2318yes—
281#4027C23116yes—
282#4027C23116yes—
283D5×C22⋊C4C2318yes—
284#4024C2318yes—
285#4024C23116yes—
286#4024C23116yes—
287#4024C23116yes—
288#4024C2318yes—
289#4024C23116yes—
290#4024C23116yes—
291#4024C23116yes—
292#4024C23116yes—
293#4023C2318yes—
294#4023C23116yes—
295#4023C2318yes—
296#4023C23116yes—
297#4023C2318yes—
298#4023C23116yes—
299#4018C2318yes—
300C42×D5C2312yes—
301C42×D5C2312yes—
302C42×D5C2312yes—
303C42×D5C2312yes—
304C42×D5C2318yes—
305#4016C2314yes—
306#4016C2318yes—
307#4015C2312yes—
308#4015C2312yes—
309#4015C2318yes—
310C4×Dic10C2314yes—
311C4×Dic10C2314yes—
312C4×Dic10C2318yes—
313C4×Dic10C2318yes—
314C4×Dic10C2318yes—
315C4×Dic10C2318yes—
316C4×Dic10C2314yes—
317C4×Dic10C2314yes—
318#3504—58no—
319#3503—54no—
320#3503—54no—
321#3502—52no—
322#3502—52no—
323#3501—54no—
324#3501—54no—
325#3501—52no—
326#3501—51no—
327#3501D511yescharacteristic, complemented
328Q8×#41—54no—
329Q8×#41—58no—
330Q8×#41—54no—
331#3458—52no—
332#3458—54no—
333C2×#533—52no—
334C2×#533—54no—
335#3428—52no—
336C2×C4×#41—51no—
337C24×C5C2412yes—
338C23×D5C2411yescharacteristic
339C2×C5×Q8—48no—
340C2×C5×Q8C2414yes—
341C2×C5×Q8C2414yes—
342C2×C5×Q8C2418yes—
343C2×C5×D4C2×Q818yescomplemented
344C2×C5×D4C2414yes—
345C22×C4×C5—44no—
346C22×C4×C5C2411yescharacteristic
347C22×C4×C5C2414yes—
348C22×C4×C5C2411yescharacteristic
349C22×C4×C5C2418yes—
350C22×C4×C5C2418yes—
351C22×C4×C5C2412yes—
352C22×C4×C5C2414yes—
353C22×C4×C5C2411yescharacteristic
354C2×C22⋊D5C2×Q8116yescomplemented
355C2×C22⋊D5C2418yes—
356C22×Dic5—44no—
357C22×Dic5C2×Q8116yescomplemented
358C22×Dic5C2414yes—
359C22×Dic5C2411yescharacteristic
360C22×Dic5C2411yescharacteristic
361C22×Dic5C2418yes—
362C22×Dic5C2418yes—
363C22×Dic5C2412yes—
364C22×Dic5C2414yes—
365C22×Dic5C2412yes—
366C22×Dic5C2411yescharacteristic
367C22×Dic5C2414yes—
368C22×Dic5C2414yes—
369Q8×D5—48no—
370Q8×D5—48no—
371#711C2×Q8132yescomplemented
372#711C2×Q8132yescomplemented
373C2×C4×D5—42no—
374C2×C4×D5—42no—
375C2×C4×D5C2×Q818yescomplemented
376C2×C4×D5C2412yes—
377C2×C4×D5C2412yes—
378C2×C4×D5C2412yes—
379C2×C4×D5C2412yes—
380C2×C4×D5C2418yes—
381C2×C4×D5C2418yes—
382C2×C4×D5C2412yes—
383C2×C4×D5C2412yes—
384C2×Dic10—416no—
385C2×Dic10—48no—
386C2×Dic10C2×Q818yescomplemented
387C2×Dic10C2414yes—
388C2×Dic10C2418yes—
389C2×Dic10C24116yes—
390C2×Dic10C2418yes—
391C2×Dic10C2414yes—
392C2×Dic10C2418yes—
393C2×Dic10C2414yes—
394C5×C4⋊C4C2418yes—
395C5×C4⋊C4C2414yes—
396C5×C4⋊C4C2414yes—
397C5×C4⋊C4C2418yes—
398C5×C4⋊C4C24116yes—
399C5×C4⋊C4C2414yes—
400C5×C4⋊C4C2414yes—
401C5×C4⋊C4C2418yes—
402C5×C4⋊C4C2414yes—
403C5×C22⋊C4C2418yes—
404C5×C22⋊C4C2418yes—
405C5×C22⋊C4C24116yes—
406C42×C5C2412yes—
407C42×C5C2412yes—
408C42×C5C2418yes—
409C22⋊Dic5C2418yes—
410C22⋊Dic5C24116yes—
411C22⋊Dic5C2418yes—
412#685C2418yes—
413#685C2418yes—
414#685C2418yes—
415C4⋊Dic5C2414yes—
416C4⋊Dic5C2414yes—
417C4⋊Dic5C2414yes—
418C4⋊Dic5C2414yes—
419C4⋊Dic5C2414yes—
420C4⋊Dic5C2418yes—
421C4⋊Dic5C2418yes—
422C4⋊Dic5C24116yes—
423C4⋊Dic5C2418yes—
424#683C2418yes—
425#683C2418yes—
426#683C2418yes—
427#683C24116yes—
428#683C24116yes—
429#683C2418yes—
430#683C2418yes—
431#683C2418yes—
432#683C2418yes—
433#683C24116yes—
434#683C24116yes—
435#683C2418yes—
436#683C2418yes—
437#683C2418yes—
438#683C24116yes—
439C4×Dic5C2412yes—
440C4×Dic5C2412yes—
441C4×Dic5C2418yes—
442C4×Dic5C2414yes—
443C4×Dic5C2414yes—
444C4×Dic5C24116yes—
445C4×Dic5C24116yes—
446C4×Dic5C2412yes—
447C4×Dic5C2412yes—
448C4×Dic5C2411yescharacteristic
449C4×Dic5C2411yescharacteristic
450C4×Dic5C2411yescharacteristic
451C4×Dic5C2411yescharacteristic
452C4×Dic5C2418yes—
453C4×Dic5C2418yes—
454C4×Dic5C2414yes—
455C4×Dic5C2414yes—
456C4×Dic5C2414yes—
457C4×Dic5C2414yes—
458C22×#41—51no—
459Q82—58no—
460Q82—54no—
461Q82—54no—
462#557—54no—
463#557—58no—
464#557—58no—
465#557—58no—
466#557—58no—
467#557—54no—
468#557—58no—
469#554—58no—
470#554—516no—
471#554—516no—
472#554—516no—
473#554—516no—
474#554—58no—
475#554—58no—
476#554—58no—
477#554—54no—
478#554—58no—
479#554—58no—
480#554—516no—
481#554C2×D514yescomplemented
482#554C2×D518yescomplemented
483D4×Q8—58no—
484D4×Q8—58no—
485D4×Q8—516no—
486D4×Q8—58no—
487D4×Q8—54no—
488D4×Q8C2×D514yescomplemented
489#544—58no—
490#544—58no—
491#544—58no—
492#544—58no—
493#544—516no—
494#544—516no—
495#544—54no—
496#544—52no—
497#544C2×D512yes—
498#543—58no—
499#543—58no—
500#543—54no—
501#543C2×D514yes—
502#533—52no—
503#533—52no—
504#533—58no—
505#533—54no—
506#533—58no—
507#533—54no—
508#533—54no—
509#533—58no—
510#533—58no—
511#533—58no—
512#533—58no—
513#533—58no—
514#533—58no—
515#533—58no—
516#533—516no—
517#533—516no—
518#533—54no—
519#533—54no—
520#533—54no—
521#533—52no—
522#533C2×D512yes—
523C2×C4⋊Q8—54no—
524C2×C4⋊Q8—52no—
525C2×C4⋊Q8—52no—
526C2×C4⋊Q8—54no—
527C2×#125—54no—
528C2×#125—58no—
529C2×C22⋊Q8—54no—
530C2×C22⋊Q8—54no—
531C2×C22⋊Q8—54no—
532C2×C22⋊Q8—58no—
533C2×C22⋊Q8C2×D514yes—
534#520—58no—
535#520—58no—
536#519—54no—
537#518—52no—
538#518—58no—
539#518C2×D512yes—
540C4×#41—54no—
541C4×#41—54no—
542C4×#41—54no—
543C4×#41—54no—
544C4×#41—58no—
545C4×#41—58no—
546C2×C4×Q8—54no—
547C2×C4×Q8—54no—
548C2×C4×Q8—54no—
549C2×C4×Q8—51no—
550C2×C4×Q8—54no—
551C2×C4×Q8—58no—
552C2×C4×Q8—51no—
553C2×C4×D4—51no—
554C2×C4×D4—52no—
555C2×C4×D4—52no—
556C2×C4×D4C2×D511yescharacteristic
557C2×#117—54no—
558C2×#117—51no—
559C2×#117—52no—
560C2×#117—58no—
561C22×C42—52no—
562C22×C42—51no—
563C23×C5—42no—
564C23×C5—42no—
565C23×C5C22×Q818yes—
566C23×C5C2511yescharacteristic
567C23×C5C2514yes—
568C22×D5—41no—
569C22×D5—41no—
570C22×D5C22×Q814yes—
571C22×D5C2512yes—
572C5×Q8—28no—
573C5×Q8—44no—
574C5×Q8—48no—
575C5×D4C22×Q8116yes—
576C2×C4×C5—28no—
577C2×C4×C5—22no—
578C2×C4×C5—48no—
579C2×C4×C5—41no—
580C2×C4×C5—42no—
581C2×C4×C5—44no—
582C2×C4×C5—48no—
583C2×C4×C5C22×Q814yes—
584C2×C4×C5C2511yescharacteristic
585C2×C4×C5C2514yes—
586C2×C4×C5C2518yes—
587C2×C4×C5C2518yes—
588C2×C4×C5C2512yes—
589C2×C4×C5C2512yes—
590C2×C4×C5C2511yescharacteristic
591C22⋊D5C22×Q8132yes—
592C2×Dic5—28no—
593C2×Dic5—22no—
594C2×Dic5—48no—
595C2×Dic5—48no—
596C2×Dic5—41no—
597C2×Dic5—42no—
598C2×Dic5—44no—
599C2×Dic5C22×Q818yes—
600C2×Dic5C22×Q814yes—
601C2×Dic5C22×Q8116yes—
602C2×Dic5C22×Q8116yes—
603C2×Dic5C2511yescharacteristic
604C2×Dic5C2518yes—
605C2×Dic5C2512yes—
606C2×Dic5C2514yes—
607C2×Dic5C2518yes—
608C2×Dic5C2511yescharacteristic
609C2×Dic5C2514yes—
610C2×Dic5C2511yescharacteristic
611C2×Dic5C2511yescharacteristic
612C4×D5—24no—
613C4×D5—24no—
614C4×D5—42no—
615C4×D5—42no—
616C4×D5—48no—
617C4×D5—48no—
618C4×D5C22×Q818yes—
619C4×D5C22×Q818yes—
620Dic10—28no—
621Dic10—216no—
622Dic10—48no—
623Dic10—416no—
624Dic10—44no—
625Dic10—48no—
626Dic10C22×Q8116yes—
627C2×#41—516no—
628C2×#41—54no—
629C2×#41—54no—
630C22×Q8—54no—
631C22×Q8—54no—
632C22×Q8—51no—
633C22×Q8—58no—
634C22×Q8—54no—
635C22×Q8C22×D514yes—
636C22×D4—52no—
637C22×D4C22×D511yescharacteristic
638C23×C4—52no—
639C23×C4—51no—
640C23×C4—52no—
641C23×C4—51no—
642C23×C4—51no—
643C23×C4C22×D512yes—
644C4⋊Q8—54no—
645C4⋊Q8—58no—
646C4⋊Q8—54no—
647C4⋊Q8—58no—
648C4⋊Q8—58no—
649C4⋊Q8—516no—
650C4⋊Q8—516no—
651C4⋊Q8—54no—
652C4⋊Q8—54no—
653C4⋊Q8—58no—
654C4⋊Q8—58no—
655C4⋊Q8—54no—
656C4⋊Q8—54no—
657C4⋊Q8—58no—
658C4⋊Q8—516no—
659C4⋊Q8—516no—
660C4⋊Q8—58no—
661C4⋊Q8—58no—
662C4⋊Q8—52no—
663C4⋊Q8—52no—
664C4⋊Q8—58no—
665C4⋊Q8C22×D512yes—
666C4⋊Q8C22×D512yes—
667C4⋊Q8C22×D518yes—
668#125—58no—
669#125—58no—
670#125—516no—
671#125—516no—
672#125—516no—
673#125—54no—
674#125—54no—
675#125—516no—
676#125—516no—
677#125—516no—
678#125—516no—
679#125—58no—
680#125—58no—
681#125—54no—
682#125—58no—
683#125C22×D514yes—
684#125C22×D518yes—
685C22⋊Q8—54no—
686C22⋊Q8—54no—
687C22⋊Q8—516no—
688C22⋊Q8—54no—
689C22⋊Q8—58no—
690C22⋊Q8—54no—
691C22⋊Q8—58no—
692C22⋊Q8—58no—
693C22⋊Q8—516no—
694C22⋊Q8—516no—
695C22⋊Q8—58no—
696C22⋊Q8—54no—
697C22⋊Q8—58no—
698C22⋊Q8—54no—
699C22⋊Q8—516no—
700C22⋊Q8—516no—
701C22⋊Q8—516no—
702C22⋊Q8—58no—
703C22⋊Q8—58no—
704C22⋊Q8—516no—
705C22⋊Q8—516no—
706C22⋊Q8—516no—
707C22⋊Q8—516no—
708C22⋊Q8—516no—
709C22⋊Q8—516no—
710C22⋊Q8—516no—
711C22⋊Q8C22×D514yes—
712C22⋊Q8C22×D514yes—
713C22⋊Q8C22×D518yes—
714C22⋊Q8C22×D518yes—
715C22⋊Q8C22×D518yes—
716C22⋊Q8C22×D5116yes—
717C22⋊Q8C22×D5116yes—
718C4×Q8—54no—
719C4×Q8—58no—
720C4×Q8—54no—
721C4×Q8—58no—
722C4×Q8—58no—
723C4×Q8—54no—
724C4×Q8—58no—
725C4×Q8—54no—
726C4×Q8—54no—
727C4×Q8—54no—
728C4×Q8—58no—
729C4×Q8—516no—
730C4×Q8—58no—
731C4×Q8—516no—
732C4×Q8—58no—
733C4×Q8—58no—
734C4×Q8—516no—
735C4×Q8—58no—
736C4×Q8—58no—
737C4×Q8—54no—
738C4×Q8—54no—
739C4×Q8—58no—
740C4×Q8—54no—
741C4×Q8—58no—
742C4×Q8—54no—
743C4×Q8—58no—
744C4×Q8—58no—
745C4×Q8C22×D514yes—
746C4×Q8C22×D514yes—
747C4×D4—54no—
748C4×D4—54no—
749C4×D4—58no—
750C4×D4—58no—
751C4×D4—58no—
752C4×D4—58no—
753C4×D4—516no—
754C4×D4—516no—
755C4×D4—58no—
756C4×D4—58no—
757C4×D4—516no—
758C4×D4—516no—
759C4×D4C22×D514yes—
760C4×D4C22×D514yes—
761C4×D4C22×D518yes—
762C4×D4C22×D518yes—
763#117—54no—
764#117—54no—
765#117—54no—
766#117—54no—
767#117—54no—
768#117—58no—
769#117—58no—
770#117—516no—
771#117—58no—
772#117—516no—
773#117—516no—
774#117—58no—
775#117C22×D514yes—
776C2×C4⋊C4—52no—
777C2×C4⋊C4—52no—
778C2×C4⋊C4—51no—
779C2×C4⋊C4—58no—
780C2×C4⋊C4—58no—
781C2×C4⋊C4—58no—
782C2×C4⋊C4—58no—
783C2×C4⋊C4—58no—
784C2×C4⋊C4—58no—
785C2×C4⋊C4—54no—
786C2×C4⋊C4—54no—
787C2×C4⋊C4—54no—
788C2×C4⋊C4—58no—
789C2×C4⋊C4—58no—
790C2×C4⋊C4—54no—
791C2×C4⋊C4—54no—
792C2×C4⋊C4C22×D511yescharacteristic
793C2×C4⋊C4C22×D518yes—
794C2×C4⋊C4C22×D514yes—
795C2×C22⋊C4—52no—
796C2×C22⋊C4—58no—
797C2×C22⋊C4—52no—
798C2×C22⋊C4—58no—
799C2×C22⋊C4C22×D512yes—
800C2×C22⋊C4C22×D518yes—
801C2×C42—52no—
802C2×C42—51no—
803C2×C42—58no—
804C2×C42—58no—
805C2×C42—52no—
806C2×C42—52no—
807C2×C42—51no—
808C2×C42—54no—
809C2×C42—54no—
810C2×C42—54no—
811C2×C42—54no—
812C2×C42—51no—
813C2×C42—58no—
814C2×C42—52no—
815C2×C42—52no—
816C2×C42—52no—
817C2×C42—52no—
818C2×C42C22×D511yescharacteristic
819C22×C5—24no—
820C22×C5—21no—
821C22×C5—24no—
822C22×C5—21no—
823C22×C5—48no—
824C22×C5C23×Q812yes—
825C22×C5C23×Q818yes—
826C22×C5C2611yescharacteristic
827C2×D5—22no—
828C2×D5—22no—
829C2×D5—44no—
830C2×D5C23×Q814yes—
831C4×C5—28no—
832C4×C5—22no—
833C4×C5—24no—
834C4×C5—28no—
835C4×C5—21no—
836C4×C5C23×Q814yes—
837C4×C5#58512yes—
838Dic5—28no—
839Dic5—28no—
840Dic5—22no—
841Dic5—24no—
842Dic5—21no—
843Dic5C23×Q818yes—
844Dic5C23×Q812yes—
845Dic5C23×Q812yes—
846Dic5#58512yes—
847C24—51no—
848C24C23×D512yes—
849#41—532no—
850#41—532no—
851C2×Q8—48no—
852C2×Q8—58no—
853C2×Q8—54no—
854C2×Q8—58no—
855C2×Q8—54no—
856C2×Q8—58no—
857C2×Q8—58no—
858C2×Q8—516no—
859C2×Q8—54no—
860C2×Q8—208no—
861C2×Q8—2016no—
862C2×Q8—208no—
863C2×Q8—208no—
864C2×Q8C23×D514yes—
865C2×Q8C23×D518yes—
866C2×Q8C23×D514yes—
867C2×D4—516no—
868C2×D4—58no—
869C2×D4Q8×D518yescomplemented
870C2×D4C23×D514yes—
871C22×C4—44no—
872C22×C4—516no—
873C22×C4—54no—
874C22×C4—51no—
875C22×C4—54no—
876C22×C4—52no—
877C22×C4—58no—
878C22×C4—52no—
879C22×C4—52no—
880C22×C4—51no—
881C22×C4—54no—
882C22×C4—51no—
883C22×C4—52no—
884C22×C4—54no—
885C22×C4—58no—
886C22×C4—58no—
887C22×C4—52no—
888C22×C4—52no—
889C22×C4—52no—
890C22×C4—52no—
891C22×C4—58no—
892C22×C4—58no—
893C22×C4—202no—
894C22×C4—202no—
895C22×C4—204no—
896C22×C4C23×D511yescharacteristic
897C22×C4C23×D514yes—
898C22×C4C23×D512yes—
899C22×C4C23×D514yes—
900C22×C4C23×D511yescharacteristic
901C22×C4C23×D518yes—
902C22×C4C23×D518yes—
903C22×C4C23×D511yescharacteristic
904C4⋊C4—58no—
905C4⋊C4—58no—
906C4⋊C4—58no—
907C4⋊C4—58no—
908C4⋊C4—58no—
909C4⋊C4—58no—
910C4⋊C4—54no—
911C4⋊C4—58no—
912C4⋊C4—516no—
913C4⋊C4—516no—
914C4⋊C4—58no—
915C4⋊C4—54no—
916C4⋊C4—54no—
917C4⋊C4—54no—
918C4⋊C4—516no—
919C4⋊C4—516no—
920C4⋊C4—58no—
921C4⋊C4—516no—
922C4⋊C4—58no—
923C4⋊C4—58no—
924C4⋊C4—58no—
925C4⋊C4—516no—
926C4⋊C4—58no—
927C4⋊C4—54no—
928C4⋊C4C23×D518yes—
929C4⋊C4C23×D514yes—
930C4⋊C4C23×D514yes—
931C4⋊C4C23×D514yes—
932C4⋊C4C23×D514yes—
933C4⋊C4C23×D518yes—
934C4⋊C4C23×D514yes—
935C4⋊C4C23×D5116yes—
936C4⋊C4C23×D518yes—
937C22⋊C4—58no—
938C22⋊C4—58no—
939C22⋊C4—516no—
940C22⋊C4—58no—
941C22⋊C4—58no—
942C22⋊C4—58no—
943C22⋊C4C23×D518yes—
944C22⋊C4C23×D518yes—
945C22⋊C4C23×D5116yes—
946C42—51no—
947C42—51no—
948C42—51no—
949C42—51no—
950C42—54no—
951C42—58no—
952C42—58no—
953C42—52no—
954C42—54no—
955C42—52no—
956C42—54no—
957C42—54no—
958C42—52no—
959C42—54no—
960C42—54no—
961C42—52no—
962C42—516no—
963C42—516no—
964C42—58no—
965C42C23×D512yes—
966C42C23×D512yes—
967C42C23×D518yes—
968C2×C5—22no—
969C2×C5—28no—
970C2×C5C24×Q811yescharacteristic
971C2×C5C2×#58511yescharacteristic
972C2×C5C2×#58511yescharacteristic
973D5—24no—
974C23—42no—
975C23—42no—
976C23—52no—
977C23—54no—
978C23—201no—
979C23—201no—
980C23C2×Q8×D518yes—
981C23C24×D511yescharacteristic
982C23C24×D514yes—
983Q8—28no—
984Q8—48no—
985Q8—44no—
986Q8—516no—
987Q8—1016no—
988Q8—108no—
989Q8—208no—
990Q8—208no—
991Q8—2016no—
992Q8—204no—
993D4—532no—
994D4C2×Q8×D5116yes—
995C2×C4—22no—
996C2×C4—28no—
997C2×C4—44no—
998C2×C4—42no—
999C2×C4—41no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—54no—
1003C2×C4—58no—
1004C2×C4—516no—
1005C2×C4—516no—
1006C2×C4—51no—
1007C2×C4—54no—
1008C2×C4—51no—
1009C2×C4—51no—
1010C2×C4—58no—
1011C2×C4—58no—
1012C2×C4—51no—
1013C2×C4—52no—
1014C2×C4—58no—
1015C2×C4—54no—
1016C2×C4—58no—
1017C2×C4—104no—
1018C2×C4—102no—
1019C2×C4—108no—
1020C2×C4—104no—
1021C2×C4—202no—
1022C2×C4—202no—
1023C2×C4—208no—
1024C2×C4—208no—
1025C2×C4—201no—
1026C2×C4—204no—
1027C2×C4—202no—
1028C2×C4—208no—
1029C2×C4—208no—
1030C2×C4C2×Q8×D514yes—
1031C2×C4C24×D511yescharacteristic
1032C2×C4C24×D514yes—
1033C2×C4C24×D518yes—
1034C2×C4C24×D518yes—
1035C2×C4C24×D512yes—
1036C2×C4C24×D512yes—
1037C2×C4C24×D511yescharacteristic
1038C5#6281311yescharacteristic, complemented, Sylow
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—54no—
1045C22—102no—
1046C22—102no—
1047C22—204no—
1048C22C22×Q8×D512yes—
1049C22C22×Q8×D518yes—
1050C22C25×D511yescharacteristic
1051C4—21no—
1052C4—24no—
1053C4—28no—
1054C4—28no—
1055C4—22no—
1056C4—52no—
1057C4—52no—
1058C4—58no—
1059C4—52no—
1060C4—102no—
1061C4—108no—
1062C4—101no—
1063C4—104no—
1064C4—108no—
1065C4C22×Q8×D514yes—
1066C4#6628512yes—
1067C2—22no—
1068C2—28no—
1069C2—104no—
1070C2C23×Q8×D511yescharacteristic
1071C2C2×#6628511yescharacteristic
1072C2D5×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3501C2
prime radicalC22×#711C22
hypercenter#3501D5
hypocenterC5#62813
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. #10618828C2semidirect
3. #10618827C2semidirect
4. #10618824C2semidirect
5. #10618824C2semidirect
6. #10618648C2semidirect
7. Q8×#711C2semidirect
8. #10618486C2semidirect
9. #10618482C2semidirect
10. #10618475C2semidirect
11. #10618472C2semidirect
12. D5×#533C2semidirect
13. #10618159C2semidirect
14. #10617887C2semidirect
15. C2×#65956C2semidirect
16. #10617761C2semidirect
18. #10617667C2semidirect
21. C5×#554C22semidirect
22. C5×#554C22semidirect
23. C5×D4×Q8C22semidirect
30. Q8×C22⋊D5C22semidirect
31. C2×Q8×Dic5C22semidirect
32. C2×#4090C22semidirect
38. #66063C22semidirect
39. #66062C22semidirect
40. #66062C22semidirect
41. #66062C22semidirect
42. D5×C4⋊Q8C22semidirect
43. D5×C4⋊Q8C22semidirect
44. #66056C22semidirect
45. #66056C22semidirect
46. #66055C22semidirect
47. #66055C22semidirect
48. #66023C22semidirect
49. #66022C22semidirect
50. #66022C22semidirect
51. D5×#125C22semidirect
52. #66019C22semidirect
53. #66019C22semidirect
54. #66019C22semidirect
55. #65970C22semidirect
56. #65970C22semidirect
57. #65970C22semidirect
58. #65969C22semidirect
59. #65969C22semidirect
61. #65966C22semidirect
62. #65966C22semidirect
67. #65957C22semidirect
68. #65957C22semidirect
74. #65956C22semidirect
75. #65956C22semidirect
76. #65956C22semidirect
77. #65956C22semidirect
78. #65956C22semidirect
79. #65956C22semidirect
80. #65912C22semidirect
81. #65912C22semidirect
82. C4×Q8×D5C22semidirect
83. C4×Q8×D5C22semidirect
84. #65901C22semidirect
85. #65901C22semidirect
86. Q8×Dic10C22semidirect
89. #65877C22semidirect
90. #65877C22semidirect
91. #65873C22semidirect
92. #65873C22semidirect
93. #65873C22semidirect
94. D4×Dic10C22semidirect
95. D4×Dic10C22semidirect
106. #65845C22semidirect
107. #65845C22semidirect
110. C2×#4035C22semidirect
111. C2×#4034C22semidirect
113. C2×#4033C22semidirect
114. C2×#4033C22semidirect
134. C2×#711Q8semidirect
327. #3501D5semidirect
343. C2×C5×D4C2×Q8semidirect
354. C2×C22⋊D5C2×Q8semidirect
357. C22×Dic5C2×Q8semidirect
371. #711C2×Q8semidirect
372. #711C2×Q8semidirect
375. C2×C4×D5C2×Q8semidirect
386. C2×Dic10C2×Q8semidirect
481. #554C2×D5semidirect
482. #554C2×D5semidirect
488. D4×Q8C2×D5semidirect
869. C2×D4Q8×D5semidirect
1038. C5#62813semidirect

Maximal subgroups

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

subgroupindex
C5×#35012
#106188282
#106188272
#106188242
#106186482
Q8×#7112
#106184862
#106184822
#106184752
#106184722
D5×#5332
#106181592
#106178872
C2×#659562
#106177612
#106177572
#106176672
C2×C4×#7112
#628135