Finite Group Databasebeta

← #14327167

Subgroups — #14327167

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#67⋊C4C211yesmaximal, characteristic
2C2×#67⋊Dic5C211yesmaximal, characteristic
3C2×Dic5×#67C211yesmaximal, characteristic
4#11751051C211yesmaximal, characteristic, complemented
5C3×#65239C211yesmaximal, characteristic, complemented
6#11749513C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748903C211yesmaximal, characteristic, complemented
9#11748897C211yesmaximal, characteristic, complemented
10D3×#3963C211yesmaximal, characteristic, complemented
11#11748786C211yesmaximal, characteristic, complemented
12Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
13#11748693C211yesmaximal, characteristic, complemented
14#11748677C211yesmaximal, characteristic, complemented
15#11748600C211yesmaximal, characteristic, complemented
16#10614064—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C5×#67⋊C4C418yescomplemented
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35#67⋊Dic5—24no—
36Dic5×#67—24no—
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74394—51nomaximal, Hall
56C2×C4×C5×D4—31no—
57C2×D4×Dic5—31no—
58C2×D4×Dic5—31no—
59#65501—31no—
60#65501—31no—
61C2×#3963—31no—
62C2×#3963—31no—
63#65274—31no—
64#65274—31no—
65#65239—31no—
66#65239—31no—
67#65239—31no—
68#65239D311yescharacteristic, complemented
69#65225—31no—
70C4×C4⋊Dic5—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15—22no—
76C22×Dic15—22no—
77C22×Dic15—41no—
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C2×C5×#67C2×C414yes—
83C2×C5×#67D414yes—
84C2×C5×#67Q814yes—
85C22×C5×Dic3—41no—
86C22×C5×Dic3—41no—
87C22×C5×Dic3C2×C414yescomplemented
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C2×C4×C5×D3—41no—
92C2×C4×C5×D3—41no—
93C2×C4×C5×D3C2×C414yescomplemented
94C22×C3×Dic5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5—41no—
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5—22no—
104C2×D3×Dic5—22no—
105C2×D3×Dic5—41no—
106C2×D3×Dic5—41no—
107C3×C5×C22⋊C4C2×C414yescomplemented
108#6719—22no—
109C4⋊Dic15—22no—
110C4⋊Dic15—41no—
111C5×(C2×D3)⋊C4C2×C414yescomplemented
112C5×Dic3⋊C4C2×C414yescomplemented
113C4×C5×Dic3C2×C414yescomplemented
114C3×C22⋊Dic5—22no—
115C3×C4⋊Dic5—22no—
116C3×C4⋊Dic5—41no—
117Dic3⋊Dic5—22no—
118Dic3⋊Dic5—22no—
119Dic3⋊Dic5—41no—
120Dic3⋊Dic5—41no—
121(C2×D3)⋊Dic5—22no—
122(C2×D3)⋊Dic5—22no—
123Dic3×Dic5—22no—
124Dic3×Dic5—22no—
125C2×C4×#67—51no—
126C2×#67⋊C4—51no—
127C2×#67⋊C4D511yescharacteristic
128C3×#385—51no—
129C2×C3⋊#95—51no—
130#4989—51no—
131#4987—51no—
132#4976—51no—
133Dic3×C4⋊C4—51no—
134#4950—51no—
135#4942—51no—
136#4668—51no—
137D3×#95—51no—
138#4650—51no—
139#4647—51no—
140C22×C5×D4—31no—
141C23×C4×C5—31no—
142C23×C4×C5—31no—
143C23×Dic5—31no—
144C23×Dic5—31no—
145C23×Dic5—31no—
146C23×Dic5C2×D311yescharacteristic
147C4×C5×D4—38no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4C2×D311yescharacteristic
151C2×C42×C5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5C2×D311yescharacteristic
156D4×Dic5—64no—
157D4×Dic5—64no—
158C2×C4⋊Dic5—31no—
159C2×C4⋊Dic5—31no—
160C2×C4⋊Dic5—31no—
161C2×C4⋊Dic5—31no—
162C2×C4⋊Dic5—31no—
163C2×C4⋊Dic5—31no—
164C2×C4⋊Dic5C2×D311yescharacteristic
165C2×C4⋊Dic5C2×D311yescharacteristic
166C2×C4×Dic5—31no—
167C2×C4×Dic5—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963C2×D311yescharacteristic
177#3963C2×D311yescharacteristic
178#2349—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5C22×C412yes—
184C23×C3×C5C2×D412yes—
185C23×C3×C5C2×Q812yes—
186C23×C3×C5C2411yescharacteristic
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3C22×C412yes—
192C22×C5×D3C2×D412yes—
193C22×C5×D3C2×Q812yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C22×C412yes—
199C2×C3×C4×C5C22×C412yes—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—44no—
212C2×Dic15#4112yes—
213C5×#67C4⋊C4116yescomplemented
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—44no—
219C2×C5×Dic3C22×C412yes—
220C2×C5×Dic3C22×C412yes—
221C2×C5×Dic3C22×C412yes—
222C2×C5×Dic3C2×D412yes—
223C2×C5×Dic3C2×Q812yes—
224C4×C5×D3—44no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—44no—
237C2×C3×Dic5#4112yes—
238D3×Dic5—44no—
239D3×Dic5—44no—
240C23×C3×C4—51no—
241C22×#67C2×D511yescharacteristic
242C23×Dic3—51no—
243C23×Dic3C2×D511yescharacteristic
244C22×C4×D3—51no—
245C22×C4×D3—51no—
246C22×C4×D3C2×D511yescharacteristic
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4C2×D511yescharacteristic
251C2×#217—51no—
252C4×#67—104no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4C2×D511yescharacteristic
256C2×C4⋊Dic3—51no—
257C2×C4⋊Dic3—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×Dic3⋊C4C2×D511yescharacteristic
263C2×C4×Dic3—51no—
264C2×C4×Dic3—51no—
265C2×C4×Dic3C2×D511yescharacteristic
266#67⋊C4—104no—
267#67⋊C4Dic518yescomplemented
268C3×#95—51no—
269C3×#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95—51no—
275C3⋊#95—51no—
276C3⋊#95—51no—
277C3⋊#95—51no—
278C24×C5—31no—
279C24×C5C22×D311yescharacteristic
280C2×C5×D4—34no—
281C2×C5×D4—34no—
282C2×C5×D4—34no—
283C22×C4×C5—31no—
284C22×C4×C5—31no—
285C22×C4×C5—31no—
286C22×C4×C5—34no—
287C22×C4×C5—34no—
288C22×C4×C5—121no—
289C22×C4×C5—121no—
290C22×C4×C5—121no—
291C22×C4×C5—121no—
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C22×Dic5—22no—
295C22×Dic5—22no—
296C22×Dic5—31no—
297C22×Dic5—31no—
298C22×Dic5—31no—
299C22×Dic5—31no—
300C22×Dic5—41no—
301C22×Dic5—62no—
302C22×Dic5—62no—
303C22×Dic5—62no—
304C22×Dic5—62no—
305C22×Dic5—62no—
306C22×Dic5—62no—
307C22×Dic5—121no—
308C22×Dic5—121no—
309C22×Dic5—121no—
310C22×Dic5C22×D311yescharacteristic
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C5×C4⋊C4—34no—
315C5×C22⋊C4—34no—
316C5×C22⋊C4C4×D314yescomplemented
317C42×C5—34no—
318C22⋊Dic5—22no—
319C22⋊Dic5—62no—
320C22⋊Dic5—62no—
321C22⋊Dic5—62no—
322C4⋊Dic5—22no—
323C4⋊Dic5—41no—
324C4⋊Dic5—62no—
325C4⋊Dic5—62no—
326C4⋊Dic5—62no—
327C4⋊Dic5—121no—
328C4⋊Dic5—121no—
329C4⋊Dic5—121no—
330C4×Dic5—62no—
331C4×Dic5—62no—
332C2×C4×D4—31no—
333C2×C4×D4—151no—
334C2×C4×D4—151no—
335#389—151no—
336#389—151no—
337#385—51no—
338#385—151no—
339#385—151no—
340#385—151no—
341#382—151no—
342#380—151no—
343#380—151no—
344C4×C4⋊C4—151no—
345C2×#95—151no—
346C2×#95—151no—
347C22×C3×C5—22no—
348C22×C3×C5—22no—
349C22×C3×C5—22no—
350C22×C3×C5—22no—
351C22×C3×C5—22no—
352C22×C3×C5—22no—
353C22×C3×C5C2×C4⋊C414yes—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C22×Q811yescharacteristic
357C22×C3×C5C2×#4111yescharacteristic
358C22×C3×C5C2×#4111yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C5H(5,𝔽2)11yescharacteristic
361C2×C5×D3—22no—
362C2×C5×D3—22no—
363C2×C5×D3—22no—
364C2×C5×D3—22no—
365C2×C5×D3—22no—
366C2×C5×D3—22no—
367C2×C5×D3C2×C4⋊C414yes—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370Dic15—22no—
371Dic15—41no—
372Dic15—41no—
373Dic15—41no—
374C3×Dic5—22no—
375C3×Dic5—41no—
376C3×Dic5—41no—
377C3×Dic5—41no—
378C5×Dic3—22no—
379C5×Dic3—22no—
380C5×Dic3C2×C4⋊C414yes—
381C24×C3C22×D511yescharacteristic
382C23×D3C22×D511yescharacteristic
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—102no—
388C22×C3×C4—102no—
389C22×C3×C4—201no—
390C22×C3×C4C22×D511yescharacteristic
391C22×C3×C4C22×D511yescharacteristic
392C2×#67Dic1014yes—
393C2×#67D2014yes—
394C2×#67C2×Dic514yes—
395C22×Dic3—41no—
396C22×Dic3—41no—
397C22×Dic3—51no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—102no—
402C22×Dic3—102no—
403C22×Dic3—201no—
404C22×Dic3C2×Dic514yescomplemented
405C22×Dic3C22×D511yescharacteristic
406C22×Dic3C22×D511yescharacteristic
407C22×Dic3C22×D511yescharacteristic
408C2×C4×D3—41no—
409C2×C4×D3—41no—
410C2×C4×D3—102no—
411C2×C4×D3—102no—
412C2×C4×D3—102no—
413C2×C4×D3—102no—
414C2×C4×D3—201no—
415C2×C4×D3—201no—
416C2×C4×D3C2×Dic514yescomplemented
417C3×C4⋊C4—102no—
418C3×C4⋊C4—201no—
419C3×C22⋊C4—102no—
420C3×C22⋊C4C2×Dic514yescomplemented
421#217—102no—
422(C2×D3)⋊C4—102no—
423(C2×D3)⋊C4—102no—
424(C2×D3)⋊C4C2×Dic514yescomplemented
425C4⋊Dic3—102no—
426C4⋊Dic3—201no—
427Dic3⋊C4—102no—
428Dic3⋊C4—102no—
429Dic3⋊C4—201no—
430Dic3⋊C4—201no—
431Dic3⋊C4C2×Dic514yescomplemented
432C4×Dic3—102no—
433C4×Dic3—102no—
434C4×Dic3C2×Dic514yescomplemented
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—32no—
440C23×C5—32no—
441C23×C5—32no—
442C23×C5—61no—
443C23×C5—61no—
444C23×C5—61no—
445C23×C5—61no—
446C23×C5C2×C4×D312yes—
447C23×C5D3×D412yes—
448C23×C5D3×Q812yes—
449C23×C5C23×D311yescharacteristic
450C5×D4—316no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—32no—
456C2×C4×C5—32no—
457C2×C4×C5—32no—
458C2×C4×C5—32no—
459C2×C4×C5—32no—
460C2×C4×C5—61no—
461C2×C4×C5—61no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—124no—
465C2×C4×C5—124no—
466C2×C4×C5C2×C4×D312yes—
467C2×C4×C5C2×C4×D312yes—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—32no—
480C2×Dic5—44no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—124no—
493C2×Dic5—124no—
494C2×Dic5—124no—
495C2×Dic5#23712yes—
496C22×D4—31no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—51no—
500C23×C4—151no—
501C23×C4—151no—
502C23×C4—151no—
503C4×D4—38no—
504C4×D4—304no—
505C4×D4—304no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—151no—
510C2×C4⋊C4—151no—
511C2×C4⋊C4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4—151no—
514C2×C4⋊C4—151no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4D3×D511yescharacteristic
521C2×C42—31no—
522C2×C42—151no—
523C2×C42—151no—
524#95—51no—
525#95—51no—
526#95—151no—
527#95—151no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532#95—151no—
533#95—151no—
534C2×C3×C5—24no—
535C2×C3×C5C22×C4⋊C411yescharacteristic
536C2×C3×C5C4×#4111yescharacteristic
537C2×C3×C5#51811yescharacteristic
538C2×C3×C5#54611yescharacteristic
539C2×C3×C5#54611yescharacteristic
540C2×C3×C5#55411yescharacteristic
541C2×C3×C5#55411yescharacteristic
542C5×D3—24no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3C2×Dic1012yes—
548C23×C3C2×D2012yes—
549C23×C3C22×Dic512yes—
550C23×C3C23×D511yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3C2×Dic1012yes—
556C22×D3C2×D2012yes—
557C22×D3C22×Dic512yes—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—52no—
563C2×C3×C4—101no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—204no—
575C2×C3×C4C22×Dic512yes—
576C2×C3×C4C22×Dic512yes—
577#67C4⋊Dic5116yescomplemented
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—44no—
583C2×Dic3—52no—
584C2×Dic3—101no—
585C2×Dic3—101no—
586C2×Dic3—101no—
587C2×Dic3—101no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—204no—
596C2×Dic3C2×Dic1012yes—
597C2×Dic3C2×D2012yes—
598C2×Dic3C22×Dic512yes—
599C2×Dic3C22×Dic512yes—
600C2×Dic3C22×Dic512yes—
601C4×D3—44no—
602C4×D3—204no—
603C4×D3—204no—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5—34no—
611C22×C5—62no—
612C22×C5—62no—
613C22×C5—62no—
614C22×C5—62no—
615C22×C5—62no—
616C22×C5—62no—
617C22×C5D3×C4⋊C414yes—
618C22×C5C22×C4×D311yescharacteristic
619C22×C5C2×D3×D411yescharacteristic
620C22×C5C2×#23711yescharacteristic
621C22×C5#100411yescharacteristic
622C22×C5C2×D3×Q811yescharacteristic
623C22×C5D3×#4111yescharacteristic
624C22×C5#100911yescharacteristic
625C4×C5—22no—
626C4×C5—22no—
627C4×C5—34no—
628C4×C5—62no—
629C4×C5—62no—
630Dic5—22no—
631Dic5—41no—
632Dic5—41no—
633Dic5—41no—
634Dic5—62no—
635Dic5—121no—
636Dic5—121no—
637Dic5—121no—
638C24—31no—
639C24C2×D3×D511yescharacteristic
640C2×D4—34no—
641C2×D4—34no—
642C2×D4—34no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—34no—
647C22×C4—34no—
648C22×C4—51no—
649C22×C4—51no—
650C22×C4—51no—
651C22×C4—51no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—121no—
655C22×C4—121no—
656C22×C4—121no—
657C22×C4—121no—
658C22×C4—151no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—151no—
662C22×C4—201no—
663C22×C4—302no—
664C22×C4—302no—
665C22×C4—302no—
666C22×C4—302no—
667C22×C4—302no—
668C22×C4—302no—
669C22×C4—601no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D511yescharacteristic
674C4⋊C4—34no—
675C4⋊C4—102no—
676C4⋊C4—201no—
677C4⋊C4—302no—
678C4⋊C4—302no—
679C4⋊C4—302no—
680C4⋊C4—601no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C22⋊C4—34no—
684C22⋊C4—102no—
685C22⋊C4—302no—
686C22⋊C4—302no—
687C22⋊C4—302no—
688C22⋊C4D3×Dic514yescomplemented
689C42—34no—
690C42—302no—
691C42—302no—
692C3×C5#234911yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3C2×C4⋊Dic514yes—
700C22×C3C22×Dic1011yescharacteristic
701C22×C3C22×D2011yescharacteristic
702C22×C3#414411yescharacteristic
703C22×C3#414411yescharacteristic
704C22×C3D5×#4111yescharacteristic
705C22×C3D5×#4111yescharacteristic
706C22×C3C23×Dic511yescharacteristic
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3C2×C4⋊Dic514yes—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—102no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720Dic3—22no—
721Dic3—22no—
722Dic3—102no—
723Dic3—201no—
724Dic3—201no—
725Dic3—201no—
726Dic3C2×C4⋊Dic514yes—
727C2×C5—24no—
728C2×C5—64no—
729C2×C5C2×D3×C4⋊C411yescharacteristic
730C2×C5C4×#23711yescharacteristic
731C2×C5#554511yescharacteristic
732C2×C5#559111yescharacteristic
733C2×C5#563511yescharacteristic
734C2×C5#563611yescharacteristic
735C2×C5#565411yescharacteristic
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—32no—
741C23—32no—
742C23—32no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23D3×Dic1012yes—
748C23D3×D2012yes—
749C23C2×D3×Dic512yes—
750C23C22×D3×D511yescharacteristic
751D4—316no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—52no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—101no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—124no—
778C2×C4—124no—
779C2×C4—152no—
780C2×C4—204no—
781C2×C4—301no—
782C2×C4—301no—
783C2×C4—301no—
784C2×C4—301no—
785C2×C4—301no—
786C2×C4—301no—
787C2×C4—301no—
788C2×C4—301no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—301no—
792C2×C4—604no—
793C2×C4—604no—
794C2×C4—604no—
795C2×C4C2×D3×Dic512yes—
796C2×C4C2×D3×Dic512yes—
797C2×C3—24no—
798C2×C3#6587311yescharacteristic
799C2×C3#6587311yescharacteristic
800C2×C3#6588811yescharacteristic
801C2×C3#6588811yescharacteristic
802C2×C3C22×C4⋊Dic511yescharacteristic
803C2×C3#6613211yescharacteristic
804C2×C3#41×Dic511yescharacteristic
805D3—24no—
806C5#7439411yescharacteristic, complemented, Sylow
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—34no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—62no—
819C22—62no—
820C22D3×C4⋊Dic514yes—
821C22C2×D3×Dic1011yescharacteristic
822C22C2×D3×D2011yescharacteristic
823C22D5×#23711yescharacteristic
824C22#9202411yescharacteristic
825C22#9202511yescharacteristic
826C22#9202711yescharacteristic
827C22C22×D3×Dic511yescharacteristic
828C4—22no—
829C4—22no—
830C4—34no—
831C4—62no—
832C4—62no—
833C4—102no—
834C4—201no—
835C4—201no—
836C4—201no—
837C4—302no—
838C4—601no—
839C4—601no—
840C4—601no—
841C3#1061406411yescharacteristic, complemented, Sylow
842C2—24no—
843C2—64no—
844C2#1175294211yescharacteristic
845C2#1175303111yescharacteristic
846C2#1175326711yescharacteristic
847C2#1175327111yescharacteristic
848C2C2×D3×C4⋊Dic511yescharacteristic
849C2Dic5×#23711yescharacteristic
850C2#1175491411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751051C2semidirect
5. C3×#65239C2semidirect
6. #11749513C2semidirect
7. C2×#90994C2semidirect
8. #11748903C2semidirect
9. #11748897C2semidirect
10. D3×#3963C2semidirect
11. #11748786C2semidirect
12. Dic3×C4⋊Dic5C2semidirect
13. #11748693C2semidirect
14. #11748677C2semidirect
15. #11748600C2semidirect
31. C5×#67⋊C4C4semidirect
68. #65239D3semidirect
87. C22×C5×Dic3C2×C4semidirect
93. C2×C4×C5×D3C2×C4semidirect
107. C3×C5×C22⋊C4C2×C4semidirect
111. C5×(C2×D3)⋊C4C2×C4semidirect
112. C5×Dic3⋊C4C2×C4semidirect
113. C4×C5×Dic3C2×C4semidirect
213. C5×#67C4⋊C4semidirect
267. #67⋊C4Dic5semidirect
316. C5×C22⋊C4C4×D3semidirect
404. C22×Dic3C2×Dic5semidirect
416. C2×C4×D3C2×Dic5semidirect
420. C3×C22⋊C4C2×Dic5semidirect
424. (C2×D3)⋊C4C2×Dic5semidirect
431. Dic3⋊C4C2×Dic5semidirect
434. C4×Dic3C2×Dic5semidirect
577. #67C4⋊Dic5semidirect
688. C22⋊C4D3×Dic5semidirect
692. C3×C5#2349semidirect
806. C5#74394semidirect
841. C3#10614064semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#67⋊C42
C2×#67⋊Dic52
C2×Dic5×#672
#117510512
C3×#652392
#117495132
C2×#909942
#117489032
#117488972
D3×#39632
#117487862
Dic3×C4⋊Dic52
#117486932
#117486772
#117486002
#106140643
#743945