Finite Group Databasebeta

← C2×#11752904 #14479897

Subgroups — C2×#11752904 #14479897

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×#91773C211yesmaximal, characteristic
2C2×C5×#879C211yesmaximal, characteristic, complemented
3C2×C3×#4023C211yesmaximal, characteristic, complemented
4C2×#91562C211yesmaximal, characteristic, complemented
5C2×#91552C211yesmaximal, characteristic, complemented
6C2×#91552C211yesmaximal, characteristic, complemented
7C2×#91526C211yesmaximal, characteristic, complemented
8C2×#91433C211yesmaximal, characteristic, complemented
9C2×#91418C211yesmaximal, characteristic, complemented
10C2×#91402C211yesmaximal, characteristic, complemented
11C2×C4×#1200C211yesmaximal, characteristic, complemented
12C2×#91380C211yesmaximal, characteristic, complemented
13C2×#91377C211yesmaximal, characteristic, complemented
14C2×#91336C211yesmaximal, characteristic, complemented
15C2×#91323C211yesmaximal, characteristic, complemented
16#11752904C2116yesmaximal, direct product factor
17C2×#66040—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30#91773C2218yes—
31C2×C5×#217C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic
33C2×C5×C4⋊Dic3C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C5×#879C2218yescomplemented
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4023C2218yescomplemented
44#91562C2218yescomplemented
45#91552C2218yescomplemented
46#91552C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6667C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59#91526C2218yescomplemented
60#91433C2218yescomplemented
61#91418C2218yescomplemented
62#91402C2218yescomplemented
63C4×#1200C2218yescomplemented
64#91380C2218yescomplemented
65#91377C2218yescomplemented
66#91336C2218yescomplemented
67#91323C2218yescomplemented
68C2×#5528—51nomaximal, Hall
69C2×C5×#126—31no—
70#66040—316no—
71C2×#4042—31no—
72C2×#4040—31no—
73C2×#4039—31no—
74C2×#4038—31no—
75C2×#4035—31no—
76C2×#4033—31no—
77C2×#4031—31no—
78C2×#4030—31no—
79C2×#4029—31no—
80C2×#4027—31no—
81C2×#4027—31no—
82C2×#4023D311yescharacteristic, complemented
83C2×#4022—31no—
84C2×C42×D5—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—24no—
91C2×#1220—24no—
92C2×#1220C2314yes—
93C2×#1220C2314yes—
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C2×D60—24no—
97C2×D60C2314yes—
98C2×C4×D15—24no—
99C2×C4×D15C2314yes—
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C3×Dic5—24no—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C2×#1204—24no—
111C2×#1204C2314yes—
112C2×#1200—24no—
113C2×#1200—24no—
114C2×#1200—24no—
115C2×#1200C2314yes—
116C2×#1200C2314yes—
117C2×#1200C2314yes—
118C3×C5×C22⋊C4C2314yes—
119#6714C2314yes—
120#6712C2314yes—
121C5×#217C2314yes—
122C5×#217C2314yes—
123C5×C4⋊Dic3C2314yes—
124C5×Dic3⋊C4C2314yes—
125C5×Dic3⋊C4C2314yes—
126C4×C5×Dic3C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×#683C2314yes—
129C3×#683C2314yes—
130C3×C4×Dic5C2314yes—
131C3×C4×Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133#6669C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6667C2314yes—
137#6667C2314yes—
138#6667C2314yes—
139#6667C2314yes—
140#6667C2314yes—
141Dic3×Dic5C2314yes—
142Dic3×Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#117—51no—
145C2×C4×#67—51no—
146C2×C4×#67—51no—
147#5528—516no—
148C2×#898—51no—
149C2×#896—51no—
150C2×#894—51no—
151C2×#889—51no—
152C2×#885—51no—
153C2×#884—51no—
154C2×#883—51no—
155C2×#879D511yescharacteristic, complemented
156C2×C4×D12—51no—
157C2×#872—51no—
158C2×C42×D3—51no—
159C2×C4×Dic6—51no—
160C22×C22⋊D5—31no—
161C22×C22⋊D5—31no—
162C23×Dic5C2×D311yescharacteristic
163C22×D20—31no—
164C22×C4×D5—31no—
165C22×C4×D5—31no—
166C22×C4×D5—31no—
167C22×C4×D5—31no—
168C22×Dic10—31no—
169C5×#126—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C4⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4—31no—
175C2×C5×C22⋊C4C2×D311yescharacteristic
176C2×C42×C5—31no—
177C2×C22⋊Dic5C2×D311yescharacteristic
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×C4⋊Dic5—31no—
185C2×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683C2×D311yescharacteristic
190C2×#683C2×D311yescharacteristic
191C2×C4×Dic5—31no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5C2×D311yescharacteristic
195C2×C4×Dic5C2×D311yescharacteristic
196#4042—38no—
197#4040—38no—
198#4039—38no—
199#4038—38no—
200#4035—38no—
201#4033—38no—
202#4031—38no—
203#4030—38no—
204#4029—38no—
205#4027—38no—
206#4027—38no—
207#4023C2×D318yescomplemented
208#4022—38no—
209C42×D5—38no—
210C2×#529—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2412yes—
215C23×C3×C5C2411yescharacteristic
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15#4114yes—
222C22×D15C2412yes—
223C22×D15C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228#1220—28no—
229#1220—28no—
230C2×Dic15—22no—
231C2×Dic15#4114yes—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234D60—28no—
235C4×D15—28no—
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—28no—
248C2×C3×Dic5#4114yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253#1204—28no—
254#1200—28no—
255#1200—28no—
256#1200—28no—
257C23×C3×C4—51no—
258C22×#67—51no—
259C22×#67—51no—
260C22×D12—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×C4×D3—51no—
265C22×Dic6—51no—
266C3×#117—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C42—51no—
272C2×C3×C42—51no—
273C2×#217C2×D511yescharacteristic
274C2×#217C2×D511yescharacteristic
275C4×#67—58no—
276C4×#67—58no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3C2×D511yescharacteristic
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4C2×D511yescharacteristic
290C2×Dic3⋊C4C2×D511yescharacteristic
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293C2×C4×Dic3—51no—
294C2×C4×Dic3C2×D511yescharacteristic
295#898—58no—
296#896—58no—
297#894—58no—
298#889—58no—
299#885—58no—
300#884—58no—
301#883—58no—
302#879C2×D518yescomplemented
303C4×D12—58no—
304#872—58no—
305C42×D3—58no—
306C4×Dic6—58no—
307C24×C5C22×D311yescharacteristic
308C23×D5—31no—
309C23×D5—31no—
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C2×C22⋊D5—34no—
317C2×C22⋊D5—34no—
318C2×C22⋊D5—64no—
319C2×C22⋊D5—64no—
320C22×Dic5—24no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5C22×D311yescharacteristic
324C22×Dic5C22×D311yescharacteristic
325C22×Dic5C22×D314yes—
326C22×Dic5C22×D311yescharacteristic
327C22×Dic5C22×D311yescharacteristic
328C2×D20—34no—
329C2×D20—64no—
330C2×C4×D5—34no—
331C2×C4×D5—34no—
332C2×C4×D5—34no—
333C2×C4×D5—34no—
334C2×C4×D5—64no—
335C2×C4×D5—64no—
336C2×C4×D5—64no—
337C2×C4×D5—64no—
338C2×Dic10—34no—
339C2×Dic10—64no—
340C5×C4⋊C4—34no—
341C5×C4⋊C4—34no—
342C5×C4⋊C4—34no—
343C5×C22⋊C4—34no—
344C5×C22⋊C4—34no—
345C5×C22⋊C4C22×D314yes—
346C42×C5—34no—
347C22⋊Dic5C22×D314yes—
348#685—34no—
349#685—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354C4⋊Dic5—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683C22×D314yes—
360#683C22×D314yes—
361C4×Dic5—34no—
362C4×Dic5—34no—
363C4×Dic5—34no—
364C4×Dic5C22×D314yes—
365C4×Dic5C22×D314yes—
366#529—1516no—
367C2×#126—31no—
368C2×#126—151no—
369C2×#125—151no—
370C2×#124—151no—
371C2×#123—151no—
372C2×#123—151no—
373C2×C22⋊Q8—151no—
374C2×#121—151no—
375C2×C4×Q8—151no—
376C2×C4×D4—151no—
377C2×C4×D4—151no—
378C2×C4×D4—151no—
379C2×#117—51no—
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×D15—28no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—22no—
394C2×D15—22no—
395C2×D15—22no—
396C2×D15—44no—
397C2×D15C2×#4114yes—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400Dic15—22no—
401Dic15C2×#4114yes—
402C3×Dic5—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5C2×#4114yes—
406C5×Dic3—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3—51no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—54no—
418C22×C3×C4—104no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C2×#67—54no—
422C2×#67—54no—
423C2×#67—104no—
424C2×#67—104no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3C22×D511yescharacteristic
428C22×Dic3C22×D511yescharacteristic
429C22×Dic3C22×D511yescharacteristic
430C22×Dic3C22×D511yescharacteristic
431C2×D12—54no—
432C2×D12—104no—
433C2×C4×D3—54no—
434C2×C4×D3—54no—
435C2×C4×D3—54no—
436C2×C4×D3—54no—
437C2×C4×D3—104no—
438C2×C4×D3—104no—
439C2×C4×D3—104no—
440C2×C4×D3—104no—
441C2×Dic6—54no—
442C2×Dic6—104no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4C22×D514yes—
447C3×C42—54no—
448C3×C42—54no—
449#217C22×D514yes—
450#217C22×D514yes—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457C4⋊Dic3—54no—
458C4⋊Dic3C22×D514yes—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4C22×D514yes—
464Dic3⋊C4C22×D514yes—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3C22×D514yes—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5C23×D312yes—
473C23×C5C23×D311yescharacteristic
474C22×D5—34no—
475C22×D5—32no—
476C22×D5—32no—
477C22×D5—62no—
478C22×D5—62no—
479C22×D5—62no—
480C22×D5—62no—
481C22×D5—62no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—32no—
485C2×C4×C5—32no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—62no—
489C2×C4×C5—62no—
490C2×C4×C5—62no—
491C2×C4×C5—62no—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C22⋊D5—68no—
495C22⋊D5—68no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—28no—
500C2×Dic5—34no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—62no—
504C2×Dic5#23514yes—
505C2×Dic5C23×D312yes—
506C2×Dic5C23×D312yes—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D312yes—
509D20—68no—
510C4×D5—68no—
511C4×D5—68no—
512C4×D5—68no—
513C4×D5—68no—
514Dic10—68no—
515C22×Q8—151no—
516C22×D4—151no—
517C22×D4—151no—
518C22×D4—151no—
519C23×C4—51no—
520C23×C4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524#126—38no—
525#126—158no—
526#125—158no—
527#124—158no—
528#123—158no—
529#123—158no—
530C22⋊Q8—158no—
531#121—158no—
532C4×Q8—158no—
533C4×D4—158no—
534C4×D4—158no—
535C4×D4—158no—
536#117—58no—
537#117—158no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—51no—
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—31no—
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—51no—
560C2×C42—51no—
561C2×C42—158no—
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
570D15—24no—
571D15—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3C23×D512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—54no—
578C22×D3—52no—
579C22×D3—52no—
580C22×D3—102no—
581C22×D3—102no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3—102no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—54no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—108no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4—102no—
596C2×C3×C4C23×D512yes—
597C2×C3×C4C23×D512yes—
598#67—108no—
599#67—108no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—54no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—102no—
608C2×Dic3C23×D512yes—
609C2×Dic3C23×D512yes—
610C2×Dic3C23×D512yes—
611C2×Dic3C23×D512yes—
612D12—108no—
613C4×D3—108no—
614C4×D3—108no—
615C4×D3—108no—
616C4×D3—108no—
617Dic6—108no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—44no—
622C22×C5C2×#23512yes—
623C22×C5D3×#4112yes—
624C22×C5D3×#4112yes—
625C22×C5C24×D311yescharacteristic
626C2×D5—34no—
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—68no—
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—62no—
637C4×C5—62no—
638C4×C5—62no—
639C4×C5—62no—
640Dic5—22no—
641Dic5—22no—
642Dic5—22no—
643Dic5—34no—
644Dic5—62no—
645Dic5C2×#23514yes—
646C24—151no—
647C24—151no—
648C24C2×D3×D511yescharacteristic
649C2×Q8—154no—
650C2×Q8—304no—
651C2×D4—154no—
652C2×D4—154no—
653C2×D4—154no—
654C2×D4—304no—
655C2×D4—304no—
656C2×D4—304no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—51no—
662C22×C4—54no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—104no—
667C22×C4—154no—
668C22×C4—154no—
669C22×C4—154no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—154no—
673C22×C4—304no—
674C22×C4—304no—
675C22×C4—304no—
676C22×C4—304no—
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—34no—
681C4⋊C4—34no—
682C4⋊C4—54no—
683C4⋊C4—54no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—34no—
690C22⋊C4—34no—
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—54no—
701C42—54no—
702C42—154no—
703C42—154no—
704C42—154no—
705C3×C5C2×#52911yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—44no—
710C22×C3D5×#4112yes—
711C22×C3D5×#4112yes—
712C22×C3D5×#4112yes—
713C22×C3C24×D511yescharacteristic
714C2×D3—54no—
715C2×D3—102no—
716C2×D3—102no—
717C2×D3—108no—
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—102no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—54no—
725C3×C4—102no—
726C3×C4—102no—
727C3×C4—102no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—22no—
732Dic3—54no—
733Dic3—102no—
734C2×C5—42no—
735C2×C5#552814yescomplemented
736C2×C5C22×#23511yescharacteristic
737C2×C5C2×D3×#4111yescharacteristic
738C2×C5C2×D3×#4111yescharacteristic
739D5—64no—
740D5—122no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—154no—
745C23—152no—
746C23—152no—
747C23—302no—
748C23—302no—
749C23—302no—
750C23—302no—
751C23—302no—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—308no—
755D4—308no—
756D4—308no—
757D4—308no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—54no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—108no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—154no—
778C2×C4—152no—
779C2×C4—152no—
780C2×C4—308no—
781C2×C4—308no—
782C2×C4—308no—
783C2×C4—308no—
784C2×C4—302no—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3#6604014yescomplemented
789C2×C3C2×D5×#4111yescharacteristic
790C2×C3C2×D5×#4111yescharacteristic
791C2×C3C2×D5×#4111yescharacteristic
792D3—104no—
793D3—202no—
794C5C2×#552811yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—154no—
800C22—308no—
801C22—302no—
802C22—302no—
803C22—302no—
804C22—302no—
805C22—302no—
806C22—604no—
807C22D5×#23512yes—
808C22#9202412yes—
809C22#9202412yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—54no—
814C4—62no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—102no—
819C4—102no—
820C4—102no—
821C4—154no—
822C4—302no—
823C3C2×#6604011yescharacteristic, complemented, Sylow
824C2—42no—
825C2—304no—
826C2—602no—
827C2#1175290414yesdirect product factor
828C2C2×D5×#23511yescharacteristic
829C2C2×#9202411yescharacteristic
830C2C2×#9202411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91773C2
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
2. C2×C5×#879C2semidirect
3. C2×C3×#4023C2semidirect
4. C2×#91562C2semidirect
5. C2×#91552C2semidirect
6. C2×#91552C2semidirect
7. C2×#91526C2semidirect
8. C2×#91433C2semidirect
9. C2×#91418C2semidirect
10. C2×#91402C2semidirect
11. C2×C4×#1200C2semidirect
12. C2×#91380C2semidirect
13. C2×#91377C2semidirect
14. C2×#91336C2semidirect
15. C2×#91323C2semidirect
16. #11752904C2direct (N × H)
37. C5×#879C22semidirect
43. C3×#4023C22semidirect
44. #91562C22semidirect
45. #91552C22semidirect
46. #91552C22semidirect
59. #91526C22semidirect
60. #91433C22semidirect
61. #91418C22semidirect
62. #91402C22semidirect
63. C4×#1200C22semidirect
64. #91380C22semidirect
65. #91377C22semidirect
66. #91336C22semidirect
67. #91323C22semidirect
82. C2×#4023D3semidirect
155. C2×#879D5semidirect
207. #4023C2×D3semidirect
302. #879C2×D5semidirect
566. C2×C3×C5#529semidirect
705. C3×C5C2×#529semidirect
735. C2×C5#5528semidirect
788. C2×C3#66040semidirect
794. C5C2×#5528semidirect
823. C3C2×#66040semidirect
827. C2#11752904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917732
C2×C5×#8792
C2×C3×#40232
C2×#915622
C2×#915522
C2×#915262
C2×#914332
C2×#914182
C2×#914022
C2×C4×#12002
C2×#913802
C2×#913772
C2×#913362
C2×#913232
#117529042
C2×#660403
C2×#55285