Finite Group Databasebeta

← C2×#11752924 #14479882

Subgroups — C2×#11752924 #14479882

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91768C211yesmaximal, characteristic, complemented
2C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4029C211yesmaximal, characteristic, complemented
4C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×#91549C211yesmaximal, characteristic
6C2×#91529C211yesmaximal, characteristic, complemented
7C2×#91525C211yesmaximal, characteristic, complemented
8C2×#91447C211yesmaximal, characteristic, complemented
9C2×#91441C211yesmaximal, characteristic, complemented
10C2×#91422C211yesmaximal, characteristic, complemented
11C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
12C2×#91367C211yesmaximal, characteristic, complemented
13C2×#91346C211yesmaximal, characteristic, complemented
14C2×#91338C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11752924C2116yesmaximal, direct product factor
17C2×#65891—31nomaximal, Hall
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34#91768C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C5×#67⋊C4C2218yescomplemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×C4⋊Dic5C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C3×#4029C2218yescomplemented
44Dic3×C22⋊D5C2218yescomplemented
45#91549C2218yes—
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54#91529C2218yescomplemented
55C2×Dic3×Dic5C2211yescharacteristic
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59#91525C2218yescomplemented
60#91447C2218yescomplemented
61#91441C2218yescomplemented
62#91422C2218yescomplemented
63C4×D5×Dic3C2218yescomplemented
64#91367C2218yescomplemented
65#91346C2218yescomplemented
66#91338C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5649—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4084—31no—
71C2×#4082—31no—
72C2×C4×C22⋊D5—31no—
73C2×C4×C22⋊D5—31no—
74C2×#4072—31no—
75C2×#4072—31no—
76#65891—316no—
77C2×#4043—31no—
78C2×#4036—31no—
79C2×#4029—31no—
80C2×#4029D311yescharacteristic, complemented
81C2×#4025—31no—
82C2×#4025—31no—
83C2×C42×D5—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×C5×#67—24no—
95C2×C5×#67C2314yes—
96C22×C5×Dic3—24no—
97C22×C5×Dic3C2314yes—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C4×C5×D3—24no—
102C2×C4×C5×D3C2314yes—
103C2×C3×C22⋊D5—24no—
104C2×C3×C22⋊D5C2314yes—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×C4×D5—24no—
109C2×C3×C4×D5C2314yes—
110C2×#1204—24no—
111C2×#1204C2314yes—
112C2×#1201—24no—
113C2×#1201C2314yes—
114C2×D5×Dic3—24no—
115C2×D5×Dic3—24no—
116C2×D5×Dic3C2314yes—
117C2×D5×Dic3C2314yes—
118C3×C5×C22⋊C4C2314yes—
119#6719C2314yes—
120#6719C2314yes—
121C4⋊Dic15C2314yes—
122#6712C2314yes—
123#6712C2314yes—
124C4×Dic15C2314yes—
125C5×(C2×D3)⋊C4C2314yes—
126C5×Dic3⋊C4C2314yes—
127C4×C5×Dic3C2314yes—
128C3×C22⋊Dic5C2314yes—
129C3×#685C2314yes—
130C3×C4⋊Dic5C2314yes—
131C3×#683C2314yes—
132Dic3⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134Dic3⋊Dic5C2314yes—
135#6668C2314yes—
136(C2×D3)⋊Dic5C2314yes—
137(C2×D3)⋊Dic5C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139#6665C2314yes—
140Dic3×Dic5C2314yes—
141Dic3×Dic5C2314yes—
142Dic3×Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#123—51no—
145C2×#939—51no—
146C2×D4×Dic3—51no—
147C2×#929—51no—
148C22×C4×Dic3—51no—
149#5649—516no—
150C2×#898—51no—
151C2×#892—51no—
152C2×#889—51no—
153C2×#887—51no—
154C2×#885—51no—
155C2×#67⋊C4—51no—
156C2×#67⋊C4D511yescharacteristic, complemented
157C2×#879—51no—
158C2×#878—51no—
159C2×#877—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5C2×D311yescharacteristic
165C22×C4×D5—31no—
166C22×C4×D5—31no—
167C22×C4×D5C2×D311yescharacteristic
168C22×Dic10—31no—
169C4×C5×D4—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4C2×D311yescharacteristic
173C2×C42×C5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5C2×D311yescharacteristic
180#4084—38no—
181#4082—38no—
182C4×C22⋊D5—38no—
183C4×C22⋊D5—38no—
184C2×#685—31no—
185C2×#685C2×D311yescharacteristic
186#4072—38no—
187#4072—38no—
188C2×C4⋊Dic5—31no—
189C2×C4⋊Dic5—31no—
190C2×C4⋊Dic5—31no—
191C2×C4⋊Dic5—31no—
192C2×C4⋊Dic5C2×D311yescharacteristic
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683C2×D311yescharacteristic
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202#4043—38no—
203#4036—38no—
204#4029—38no—
205#4029C2×D318yescomplemented
206#4025—38no—
207#4025—38no—
208C42×D5—38no—
209C4×Dic10—38no—
210C2×#529—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2412yes—
215C23×C3×C5C2411yescharacteristic
216C22×C5×D3—22no—
217C22×C5×D3—22no—
218C22×C5×D3—22no—
219C22×C5×D3C2412yes—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5#4114yes—
223C22×C3×D5C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228C2×Dic15—22no—
229C2×Dic15—22no—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C5×#67—28no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—28no—
239C2×C5×Dic3#4114yes—
240C2×C5×Dic3#4114yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C4×C5×D3—28no—
245C3×C22⋊D5—28no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C3×C4×D5—28no—
253#1204—28no—
254#1201—28no—
255D5×Dic3—28no—
256D5×Dic3—28no—
257C22×C3×D4—51no—
258C23×C3×C4—51no—
259C22×#67—51no—
260C22×#67C2×D511yescharacteristic
261C23×Dic3—51no—
262C23×Dic3—51no—
263C23×Dic3C2×D511yescharacteristic
264C22×C4×D3C2×D511yescharacteristic
265C22×Dic6—51no—
266C3×#123—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275#939—58no—
276D4×Dic3—58no—
277#929—58no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4C2×D511yescharacteristic
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293C2×C4×Dic3—51no—
294C2×C4×Dic3—51no—
295C2×C4×Dic3—58no—
296C2×C4×Dic3C2×D511yescharacteristic
297#898—58no—
298#892—58no—
299#889—58no—
300#887—58no—
301#885—58no—
302#67⋊C4—58no—
303#67⋊C4C2×D518yescomplemented
304#879—58no—
305#878—58no—
306#877—58no—
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C23×D5C22×D311yescharacteristic
310C2×C5×D4—34no—
311C2×C5×D4—64no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—31no—
315C22×C4×C5—34no—
316C22×C4×C5—34no—
317C22×C4×C5—64no—
318C22×C4×C5—64no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—24no—
322C2×C22⋊D5—34no—
323C2×C22⋊D5—64no—
324C2×C22⋊D5C22×D314yes—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C2×C4×D5—24no—
333C2×C4×D5—34no—
334C2×C4×D5—34no—
335C2×C4×D5—64no—
336C2×C4×D5—64no—
337C2×C4×D5C22×D314yes—
338C2×Dic10—34no—
339C2×Dic10—64no—
340C5×C4⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4C22×D314yes—
343C42×C5—34no—
344C22⋊Dic5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5C22×D314yes—
350#685—34no—
351#685C22×D314yes—
352C4⋊Dic5—34no—
353C4⋊Dic5—34no—
354C4⋊Dic5—34no—
355C4⋊Dic5—34no—
356C4⋊Dic5C22×D314yes—
357#683—34no—
358#683—34no—
359#683—34no—
360#683C22×D314yes—
361C4×Dic5—34no—
362C4×Dic5—34no—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5—34no—
366#529—1516no—
367C2×#126—151no—
368C2×#126—151no—
369C2×#125—151no—
370C2×#124—151no—
371C2×#123—51no—
372C2×#123—151no—
373C2×C22⋊Q8—151no—
374C2×#121—151no—
375C2×C4×Q8—151no—
376C2×C4×D4—31no—
377C2×C4×D4—151no—
378C2×C4×D4—151no—
379C2×#117—151no—
380C2×#117—151no—
381C22×C42—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—44no—
386C22×C3×C5C2×#4112yes—
387C22×C3×C5C2×#4112yes—
388C22×C3×C5C2×#4112yes—
389C22×C3×C5C2511yescharacteristic
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—44no—
394C2×C3×D5—28no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5C2×#4114yes—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400Dic15—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C5×Dic3—22no—
408C5×Dic3C2×#4114yes—
409C5×Dic3C2×#4114yes—
410C24×C3—51no—
411C24×C3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C2×C3×D4—54no—
414C2×C3×D4—104no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—54no—
419C22×C3×C4—104no—
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C2×#67—24no—
423C2×#67—54no—
424C2×#67—104no—
425C2×#67C22×D514yes—
426C22×Dic3—24no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—54no—
432C22×Dic3—54no—
433C22×Dic3—104no—
434C22×Dic3—104no—
435C22×Dic3C22×D514yes—
436C22×Dic3C22×D511yescharacteristic
437C22×Dic3C22×D511yescharacteristic
438C22×Dic3C22×D511yescharacteristic
439C2×C4×D3—24no—
440C2×C4×D3C22×D514yes—
441C2×Dic6—54no—
442C2×Dic6—104no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4—54no—
447C3×C22⋊C4C22×D514yes—
448#217—54no—
449#217—54no—
450#217—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4C22×D514yes—
455C4⋊Dic3—54no—
456C4⋊Dic3—54no—
457Dic3⋊C4—54no—
458Dic3⋊C4—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4C22×D514yes—
463C4×Dic3—54no—
464C4×Dic3—54no—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3C22×D514yes—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5—32no—
473C23×C5—62no—
474C23×C5—62no—
475C23×C5—62no—
476C23×C5C23×D312yes—
477C23×C5C23×D311yescharacteristic
478C22×D5—22no—
479C22×D5—22no—
480C22×D5#23714yes—
481C22×D5C23×D312yes—
482C5×D4—68no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—34no—
486C2×C4×C5—34no—
487C2×C4×C5—32no—
488C2×C4×C5—32no—
489C2×C4×C5—32no—
490C2×C4×C5—68no—
491C2×C4×C5—68no—
492C2×C4×C5—62no—
493C2×C4×C5C23×D312yes—
494C2×C4×C5C23×D312yes—
495C22⋊D5—28no—
496C22⋊D5—68no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—22no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—62no—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D312yes—
510C2×Dic5C23×D312yes—
511C4×D5—28no—
512C4×D5—68no—
513C4×D5—68no—
514Dic10—68no—
515C22×Q8—151no—
516C22×D4—31no—
517C22×D4—51no—
518C22×D4—151no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—51no—
522C23×C4—151no—
523C23×C4—151no—
524#126—158no—
525#126—158no—
526#125—158no—
527#124—158no—
528#123—58no—
529#123—158no—
530C22⋊Q8—158no—
531#121—158no—
532C4×Q8—158no—
533C4×D4—38no—
534C4×D4—158no—
535C4×D4—158no—
536#117—158no—
537#117—158no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—151no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—51no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—151no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4D3×D511yescharacteristic
558C2×C42—31no—
559C2×C42—158no—
560C2×C42—151no—
561C2×C42—151no—
562C2×C42—151no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C3×C5—42no—
566C2×C3×C5#52914yescomplemented
567C2×C3×C5C22×#4111yescharacteristic
568C2×C3×C5C22×#4111yescharacteristic
569C2×C3×C5C22×#4111yescharacteristic
570C3×D5—24no—
571C5×D3—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—54no—
576C23×C3—52no—
577C23×C3—102no—
578C23×C3—102no—
579C23×C3C23×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3C23×D512yes—
585C3×D4—108no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—108no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597#67—28no—
598#67—108no—
599C2×Dic3—22no—
600C2×Dic3—28no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—108no—
610C2×Dic3—108no—
611C2×Dic3#70914yes—
612C2×Dic3#71114yes—
613C2×Dic3C23×D512yes—
614C2×Dic3C23×D512yes—
615C2×Dic3C23×D512yes—
616C4×D3—28no—
617Dic6—108no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—44no—
622C22×C5—62no—
623C22×C5—62no—
624C22×C5—62no—
625C22×C5—124no—
626C22×C5C2×#23712yes—
627C22×C5D3×#4112yes—
628C22×C5D3×#4112yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—28no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5C2×#23714yes—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—34no—
637C4×C5—34no—
638C4×C5—62no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—31no—
647C24—51no—
648C24C2×D3×D511yescharacteristic
649C2×Q8—154no—
650C2×Q8—304no—
651C2×D4—34no—
652C2×D4—54no—
653C2×D4—64no—
654C2×D4—104no—
655C2×D4—154no—
656C2×D4—304no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—34no—
660C22×C4—31no—
661C22×C4—34no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—54no—
666C22×C4—64no—
667C22×C4—64no—
668C22×C4—104no—
669C22×C4—154no—
670C22×C4—154no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—151no—
674C22×C4—151no—
675C22×C4—304no—
676C22×C4—304no—
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—54no—
681C4⋊C4—54no—
682C4⋊C4—154no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—34no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4C2×D3×D514yes—
699C42—34no—
700C42—154no—
701C42—154no—
702C42—154no—
703C42—154no—
704C42—154no—
705C3×C5C2×#52911yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—44no—
710C22×C3—54no—
711C22×C3—108no—
712C22×C3—102no—
713C22×C3—102no—
714C22×C3C2×#70912yes—
715C22×C3C2×#71112yes—
716C22×C3D5×#4112yes—
717C22×C3C24×D511yescharacteristic
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—44no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—102no—
725C3×C4—102no—
726C3×C4—102no—
727Dic3—22no—
728Dic3—102no—
729Dic3—102no—
730Dic3—102no—
731Dic3—102no—
732Dic3C2×#70914yes—
733Dic3C2×#71114yes—
734C2×C5—42no—
735C2×C5—122no—
736C2×C5#564914yescomplemented
737C2×C5C22×#23711yescharacteristic
738C2×C5C2×D3×#4111yescharacteristic
739C2×C5C2×D3×#4111yescharacteristic
740D5—24no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—32no—
745C23—54no—
746C23—52no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—102no—
751C23—102no—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—308no—
755D4—68no—
756D4—108no—
757D4—308no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—34no—
761C2×C4—34no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—68no—
769C2×C4—68no—
770C2×C4—62no—
771C2×C4—108no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—152no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—308no—
780C2×C4—308no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—302no—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3—104no—
789C2×C3#6589114yescomplemented
790C2×C3C22×#70911yescharacteristic
791C2×C3C22×#71111yescharacteristic
792C2×C3C2×D5×#4111yescharacteristic
793D3—42no—
794C5C2×#564911yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—54no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—102no—
804C22—108no—
805C22—102no—
806C22—124no—
807C22D3×#70912yes—
808C22D5×#23712yes—
809C22D3×#71112yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—34no—
814C4—34no—
815C4—62no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6589111yescharacteristic, complemented, Sylow
824C2—42no—
825C2—104no—
826C2—122no—
827C2#1175292414yesdirect product factor
828C2C2×D3×#70911yescharacteristic
829C2C2×D5×#23711yescharacteristic
830C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91549C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#529
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
1. C2×#91768C2semidirect
2. C2×C5×#67⋊C4C2semidirect
3. C2×C3×#4029C2semidirect
4. C2×Dic3×C22⋊D5C2semidirect
6. C2×#91529C2semidirect
7. C2×#91525C2semidirect
8. C2×#91447C2semidirect
9. C2×#91441C2semidirect
10. C2×#91422C2semidirect
11. C2×C4×D5×Dic3C2semidirect
12. C2×#91367C2semidirect
13. C2×#91346C2semidirect
14. C2×#91338C2semidirect
15. C2×#91324C2semidirect
16. #11752924C2direct (N × H)
34. #91768C22semidirect
38. C5×#67⋊C4C22semidirect
43. C3×#4029C22semidirect
44. Dic3×C22⋊D5C22semidirect
54. #91529C22semidirect
59. #91525C22semidirect
60. #91447C22semidirect
61. #91441C22semidirect
62. #91422C22semidirect
63. C4×D5×Dic3C22semidirect
64. #91367C22semidirect
65. #91346C22semidirect
66. #91338C22semidirect
67. #91324C22semidirect
80. C2×#4029D3semidirect
156. C2×#67⋊C4D5semidirect
205. #4029C2×D3semidirect
303. #67⋊C4C2×D5semidirect
566. C2×C3×C5#529semidirect
705. C3×C5C2×#529semidirect
736. C2×C5#5649semidirect
789. C2×C3#65891semidirect
794. C5C2×#5649semidirect
823. C3C2×#65891semidirect
827. C2#11752924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917682
C2×C5×#67⋊C42
C2×C3×#40292
C2×Dic3×C22⋊D52
C2×#915492
C2×#915292
C2×#915252
C2×#914472
C2×#914412
C2×#914222
C2×C4×D5×Dic32
C2×#913672
C2×#913462
C2×#913382
C2×#913242
#117529242
C2×#658913
C2×#56495