Finite Group Databasebeta

← C2×#11754545 #14483007

Subgroups — C2×#11754545 #14483007

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#235C211yesmaximal, characteristic, complemented
2C22×#6773C211yesmaximal, characteristic, complemented
3C2×#91819C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×#91567C212yesmaximal, complemented
6C2×#91557C212yesmaximal, complemented
7#11754545C2116yesmaximal, direct product factor
8C2×#91454C212yesmaximal, complemented
9C2×#91451C211yesmaximal, characteristic, complemented
10C2×#91449C211yesmaximal, characteristic, complemented
11C2×#91446C212yesmaximal, complemented
12C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
13C2×#66168—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C22×C5×#67C2212yes—
18C2×C5×#235—28no—
19C2×C5×#235C2218yescomplemented
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2212yes—
22C22×C5×Dic6C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1203C2212yes—
26C22×#1203C2212yes—
27C22×#1202C2212yes—
28C22×#1201C2212yes—
29C22×#1200C2212yes—
30C2×#6773—28no—
31C2×#6773C2218yescomplemented
32#91819C2218yescomplemented
33C2×#6714C2212yes—
34C2×C4⋊Dic15C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C3×C4×C22⋊D5C2218yescomplemented
37C2×C3×#685C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40#91567C22116yescomplemented
41#91557C22116yescomplemented
42C2×Dic3⋊Dic5C2212yes—
43C2×(C2×D3)⋊Dic5C2212yes—
44C2×Dic3×Dic5C2212yes—
45#91454C22116yescomplemented
46#91451C2218yescomplemented
47#91449C2218yescomplemented
48#91446C22116yescomplemented
49Dic5×Dic6C2218yescomplemented
50C2×#5553—51nomaximal, Hall
51C22×C5×#41—31no—
52C22×#713—31no—
53#66168—316no—
54C2×Q8×Dic5—31no—
55C2×#4086—31no—
56C2×#4086—32no—
57C2×#4084—31no—
58C2×#4084—32no—
59C2×#4076—32no—
60C2×#4076—31no—
61C2×C4×C22⋊D5—32no—
62C2×C4×C22⋊D5D311yescharacteristic, complemented
63C24×C3×C5C2311yescharacteristic
64C23×D15C2312yes—
65C23×C5×D3C2312yes—
66C23×C3×D5C2311yescharacteristic
67C22×C3×C4×C5—24no—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2314yes—
70C22×C3×C4×C5C2311yescharacteristic
71C2×#1220—44no—
72C2×#1220C2318yes—
73C22×Dic15C2312yes—
74C2×D60—24no—
75C2×D60C2314yes—
76C2×C5×#67—28no—
77C2×C5×#67C2318yes—
78C22×C5×Dic3C2312yes—
79C5×#235—232no—
80C2×C5×D12—24no—
81C2×C5×D12C2314yes—
82C2×C4×C5×D3—28no—
83C2×C4×C5×D3C2318yes—
84C2×C5×Dic6D418yescomplemented
85C2×C5×Dic6C2314yes—
86C2×C3×C22⋊D5—24no—
87C2×C3×C22⋊D5C2314yes—
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×C3×C4×D5—24no—
92C2×C3×C4×D5C2314yes—
93C2×#1203—28no—
94C2×#1203—44no—
95C2×#1203C2318yes—
96C2×#1203C2318yes—
97C2×#1202—28no—
98C2×#1202C2318yes—
99C2×#1201—44no—
100C2×#1201C2318yes—
101C2×#1200—28no—
102C2×#1200C2318yes—
103#6773—232no—
104#6714C2318yes—
105C4⋊Dic15C2314yes—
106C3×C22⋊Dic5C2314yes—
107C3×#685C2314yes—
108C3×#683C2314yes—
109C3×C4×Dic5C2314yes—
110Dic3⋊Dic5C2318yes—
111(C2×D3)⋊Dic5C2318yes—
112Dic3×Dic5C2318yes—
113C22×#235—51no—
114C22×#235D511yescharacteristic, complemented
115C2×C3×C4×D4—51no—
116C2×#940—52no—
117C2×#930—51no—
118C2×#930—51no—
119#5553—516no—
120C2×#893—52no—
121C2×#884—52no—
122C2×#884—52no—
123C2×#874—51no—
124C2×C4×Dic6—51no—
125C2×C5×#41—38no—
126C2×C5×#41—68no—
127C22×C5×Q8—31no—
128C22×C5×D4—32no—
129C22×C5×D4—31no—
130C23×C4×C5—32no—
131C23×C4×C5C2×D311yescharacteristic
132C22×C22⋊D5—32no—
133C22×C22⋊D5—32no—
134C22×C22⋊D5—32no—
135C22×C22⋊D5—32no—
136C22×C22⋊D5C2×D311yescharacteristic
137C2×#713—38no—
138C2×#713—68no—
139C22×D20—32no—
140C22×D20—31no—
141C22×C4×D5—32no—
142C22×C4×D5C2×D311yescharacteristic
143C2×C22⋊Dic5—32no—
144C2×C22⋊Dic5C2×D311yescharacteristic
145Q8×Dic5—38no—
146#4086—316no—
147#4086—38no—
148#4084—38no—
149#4084—316no—
150#4076—38no—
151#4076—316no—
152C4×C22⋊D5—316no—
153C4×C22⋊D5C2×D318yescomplemented
154C2×#685—32no—
155C2×#685C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—32no—
158C2×#683C2×D311yescharacteristic
159C2×C4×Dic5—32no—
160C2×C4×Dic5C2×D311yescharacteristic
161C2×#550—151noSylow
162C23×C3×C5—22no—
163C23×C3×C5—22no—
164C23×C3×C5—22no—
165C23×C3×C5C2412yes—
166C23×C3×C5C2411yescharacteristic
167C22×D15—24no—
168C22×D15—24no—
169C22×D15—24no—
170C22×D15C2414yes—
171C22×C5×D3—24no—
172C22×C5×D3—24no—
173C22×C5×D3—24no—
174C22×C5×D3C2414yes—
175C22×C3×D5—22no—
176C22×C3×D5—22no—
177C22×C3×D5—22no—
178C22×C3×D5C2412yes—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—28no—
181C2×C3×C4×C5C2×D414yes—
182C2×C3×C4×C5C2412yes—
183C2×C3×C4×C5C2412yes—
184#1220—48no—
185C2×Dic15—24no—
186C2×Dic15C2414yes—
187D60—28no—
188C5×#67—216no—
189C2×C5×Dic3C2×D418yes—
190C2×C5×Dic3C2414yes—
191C5×D12—28no—
192C4×C5×D3—216no—
193C5×Dic6C2×D4116yescomplemented
194C3×C22⋊D5—28no—
195C2×C3×Dic5—22no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5#4114yescomplemented
198C2×C3×Dic5C2412yes—
199C2×C3×Dic5C2412yes—
200C2×C3×Dic5C2412yes—
201C3×C4×D5—28no—
202#1203—216no—
203#1203—48no—
204#1202—216no—
205#1201—48no—
206#1200—216no—
207C22×C3×D4—51no—
208C23×C3×C4—51no—
209C23×C3×C4C2×D511yescharacteristic
210C22×#67—52no—
211C22×#67—52no—
212C22×#67—52no—
213C22×#67C2×D512yes—
214C2×#235—28no—
215C2×#235—58no—
216C2×#235—108no—
217C2×#235C2×D518yescomplemented
218C22×D12—52no—
219C22×D12—51no—
220C22×D12—52no—
221C22×D12C2×D511yescharacteristic
222C22×C4×D3—52no—
223C22×C4×D3C2×D512yes—
224C22×Dic6C2×D511yescharacteristic
225C3×C4×D4—58no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4—51no—
229C2×C3×C42—51no—
230#940—516no—
231#930—58no—
232#930—58no—
233C2×(C2×D3)⋊C4—52no—
234C2×(C2×D3)⋊C4—52no—
235C2×C4⋊Dic3—51no—
236C2×Dic3⋊C4—52no—
237C2×C4×Dic3—52no—
238#893—516no—
239#884—516no—
240#884—516no—
241#874—58no—
242C4×Dic6—58no—
243C24×C5—32no—
244C24×C5C22×D311yescharacteristic
245C23×D5—32no—
246C23×D5C22×D311yescharacteristic
247C5×#41—632no—
248C2×C5×Q8—38no—
249C2×C5×Q8—34no—
250C2×C5×D4—38no—
251C2×C5×D4—34no—
252C2×C5×D4—68no—
253C2×C5×D4—64no—
254C22×C4×C5—24no—
255C22×C4×C5—32no—
256C22×C4×C5—38no—
257C22×C4×C5—68no—
258C22×C4×C5C22×D311yescharacteristic
259C22×C4×C5C22×D314yes—
260C22×C4×C5C22×D311yescharacteristic
261C2×C22⋊D5—24no—
262C2×C22⋊D5—38no—
263C2×C22⋊D5—38no—
264C2×C22⋊D5—38no—
265C2×C22⋊D5—38no—
266C2×C22⋊D5—68no—
267C2×C22⋊D5—124no—
268C2×C22⋊D5—124no—
269C2×C22⋊D5—124no—
270C2×C22⋊D5C22×D314yes—
271C22×Dic5—32no—
272C22×Dic5C22×D311yescharacteristic
273C22×Dic5C22×D311yescharacteristic
274C22×Dic5C22×D311yescharacteristic
275#713—632no—
276C2×D20—38no—
277C2×D20—34no—
278C2×D20—68no—
279C2×D20—64no—
280C2×C4×D5—24no—
281C2×C4×D5—38no—
282C2×C4×D5—68no—
283C2×C4×D5C22×D314yes—
284C22⋊Dic5—38no—
285C22⋊Dic5C22×D314yes—
286#685—38no—
287#685C22×D314yes—
288C4⋊Dic5—34no—
289C4⋊Dic5—38no—
290#683C22×D314yes—
291C4×Dic5—38no—
292C4×Dic5C22×D314yes—
293C22×#41—31no—
294C22×#41—151no—
295#550—1516no—
296C2×#127—151no—
297C2×#127—152no—
298C2×#121—152no—
299C2×#121—152no—
300C2×#121—151no—
301C2×#121—151no—
302C2×C4×Q8—151no—
303C2×C4×D4—51no—
304C2×C4×D4—152no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—22no—
308C22×C3×C5—44no—
309C22×C3×C5C22×D412yes—
310C22×C3×C5C2×#4112yes—
311C22×C3×C5H(5,𝔽2)12yes—
312C22×C3×C5C2511yescharacteristic
313C2×D15—24no—
314C2×D15—24no—
315C2×D15—24no—
316C2×D15—48no—
317C2×C5×D3—24no—
318C2×C5×D3—24no—
319C2×C5×D3—24no—
320C2×C5×D3—48no—
321C2×C3×D5—22no—
322C2×C3×D5—22no—
323C2×C3×D5—22no—
324C2×C3×D5—44no—
325C3×C4×C5—22no—
326C3×C4×C5C22×D414yes—
327Dic15—24no—
328C3×Dic5—22no—
329C3×Dic5—22no—
330C3×Dic5C2×#4114yescomplemented
331C5×Dic3C22×D418yes—
332C24×C3—51no—
333C24×C3C22×D511yescharacteristic
334C23×D3—52no—
335C23×D3C22×D512yes—
336C2×C3×D4—54no—
337C2×C3×D4—104no—
338C22×C3×C4—24no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—54no—
343C22×C3×C4—104no—
344C22×C3×C4C22×D511yescharacteristic
345C22×C3×C4C22×D514yes—
346C22×C3×C4C22×D511yescharacteristic
347C2×#67—28no—
348C2×#67—58no—
349C2×#67—58no—
350C2×#67—58no—
351C2×#67—108no—
352C2×#67—204no—
353C2×#67—204no—
354C2×#67C22×D518yes—
355C22×Dic3—52no—
356C22×Dic3C22×D512yes—
357#235—232no—
358#235—1032no—
359C2×D12—24no—
360C2×D12—58no—
361C2×D12—54no—
362C2×D12—58no—
363C2×D12—108no—
364C2×D12—104no—
365C2×D12—204no—
366C2×D12C22×D514yes—
367C2×C4×D3—28no—
368C2×C4×D3—58no—
369C2×C4×D3—108no—
370C2×C4×D3C22×D518yes—
371C2×Dic6C22⋊D518yescomplemented
372C2×Dic6C22×D514yes—
373C3×C4⋊C4—54no—
374C3×C22⋊C4—54no—
375C3×C22⋊C4—54no—
376C3×C42—54no—
377(C2×D3)⋊C4—58no—
378(C2×D3)⋊C4—58no—
379C4⋊Dic3—54no—
380Dic3⋊C4—58no—
381C4×Dic3—58no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—34no—
386C23×C5—64no—
387C23×C5—64no—
388C23×C5—64no—
389C23×C5C23×D312yes—
390C23×C5C23×D311yescharacteristic
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—34no—
395C22×D5—64no—
396C22×D5—64no—
397C22×D5—64no—
398C22×D5C23×D312yes—
399C5×Q8—316no—
400C5×D4—616no—
401C5×D4—68no—
402C2×C4×C5—22no—
403C2×C4×C5—28no—
404C2×C4×C5—38no—
405C2×C4×C5—34no—
406C2×C4×C5—616no—
407C2×C4×C5D3×D414yes—
408C2×C4×C5C23×D312yes—
409C2×C4×C5C23×D312yes—
410C22⋊D5—28no—
411C22⋊D5—616no—
412C22⋊D5—128no—
413C22⋊D5—128no—
414C22⋊D5—128no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—34no—
418C2×Dic5—64no—
419C2×Dic5#23514yescomplemented
420C2×Dic5C23×D312yes—
421C2×Dic5C23×D312yes—
422C2×Dic5C23×D312yes—
423D20—616no—
424D20—68no—
425C4×D5—28no—
426C4×D5—616no—
427C2×#41—38no—
428C2×#41—68no—
429C2×#41—158no—
430C2×#41—308no—
431C22×Q8—31no—
432C22×D4—32no—
433C22×D4—31no—
434C22×D4—51no—
435C22×D4—152no—
436C22×D4—152no—
437C22×D4—152no—
438C22×D4—152no—
439C22×D4—152no—
440C22×D4—151no—
441C23×C4—32no—
442C23×C4—51no—
443C23×C4—152no—
444C23×C4D3×D511yescharacteristic
445#127—158no—
446#127—1516no—
447#121—1516no—
448#121—1516no—
449#121—158no—
450#121—158no—
451C4×Q8—158no—
452C4×D4—58no—
453C4×D4—1516no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—152no—
456C2×C4⋊C4—151no—
457C2×C22⋊C4—51no—
458C2×C22⋊C4—51no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—152no—
461C2×C42—51no—
462C2×C42—152no—
463C2×C3×C5—42no—
464C2×C3×C5#55014yescomplemented
465C2×C3×C5C23×D411yescharacteristic
466C2×C3×C5C22×#4111yescharacteristic
467C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
468D15—44no—
469C3×D5—42no—
470C5×D3—44no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—52no—
475C23×C3—102no—
476C23×C3—102no—
477C23×C3—102no—
478C23×C3C23×D512yes—
479C23×C3C23×D511yescharacteristic
480C22×D3—24no—
481C22×D3—24no—
482C22×D3—24no—
483C22×D3—54no—
484C22×D3—104no—
485C22×D3—104no—
486C22×D3—104no—
487C22×D3C23×D514yes—
488C3×D4—108no—
489C2×C3×C4—22no—
490C2×C3×C4—28no—
491C2×C3×C4—54no—
492C2×C3×C4—52no—
493C2×C3×C4—52no—
494C2×C3×C4—52no—
495C2×C3×C4—102no—
496C2×C3×C4—102no—
497C2×C3×C4—108no—
498C2×C3×C4C2×C22⋊D514yes—
499C2×C3×C4C23×D512yes—
500C2×C3×C4C23×D512yes—
501#67—216no—
502#67—1016no—
503#67—208no—
504#67—208no—
505C2×Dic3—54no—
506C2×Dic3—104no—
507C2×Dic3C2×C22⋊D518yes—
508C2×Dic3C23×D514yes—
509D12—28no—
510D12—1016no—
511D12—108no—
512D12—208no—
513C4×D3—216no—
514C4×D3—1016no—
515Dic6C2×C22⋊D5116yescomplemented
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—44no—
520C22×C5—64no—
521C22×C5—64no—
522C22×C5—64no—
523C22×C5—128no—
524C22×C5C2×#23512yes—
525C22×C5C2×D3×D412yes—
526C22×C5#100912yes—
527C22×C5C24×D311yescharacteristic
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—44no—
532C2×D5—64no—
533C2×D5—64no—
534C2×D5—64no—
535C2×D5—128no—
536C4×C5—22no—
537C4×C5—38no—
538C4×C5C2×D3×D414yes—
539Dic5—22no—
540Dic5—22no—
541Dic5—64no—
542Dic5C2×#23514yescomplemented
543C24—32no—
544C24—51no—
545C24—152no—
546C24C2×D3×D511yescharacteristic
547#41—632no—
548#41—3032no—
549C2×Q8—38no—
550C2×Q8—34no—
551C2×D4—38no—
552C2×D4—34no—
553C2×D4—54no—
554C2×D4—68no—
555C2×D4—64no—
556C2×D4—104no—
557C2×D4—158no—
558C2×D4—158no—
559C2×D4—158no—
560C2×D4—158no—
561C2×D4—158no—
562C2×D4—154no—
563C2×D4—308no—
564C2×D4—308no—
565C2×D4—304no—
566C2×D4—604no—
567C2×D4—604no—
568C2×D4—604no—
569C22×C4—24no—
570C22×C4—32no—
571C22×C4—38no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—51no—
575C22×C4—54no—
576C22×C4—68no—
577C22×C4—104no—
578C22×C4—158no—
579C22×C4—152no—
580C22×C4—308no—
581C22×C4C2×D3×D514yes—
582C22×C4C2×D3×D511yescharacteristic
583C22×C4C2×D3×D511yescharacteristic
584C4⋊C4—54no—
585C4⋊C4—158no—
586C4⋊C4—154no—
587C22⋊C4—54no—
588C22⋊C4—54no—
589C22⋊C4—158no—
590C22⋊C4—158no—
591C42—54no—
592C42—158no—
593C3×C5C2×#55011yescharacteristic, complemented, Hall
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—44no—
598C22×C3—102no—
599C22×C3—102no—
600C22×C3—102no—
601C22×C3—204no—
602C22×C3D5×#4112yes—
603C22×C3#414912yes—
604C22×C3C22×C22⋊D512yes—
605C22×C3C24×D511yescharacteristic
606C2×D3—24no—
607C2×D3—24no—
608C2×D3—24no—
609C2×D3—48no—
610C2×D3—104no—
611C2×D3—104no—
612C2×D3—104no—
613C2×D3—208no—
614C3×C4—22no—
615C3×C4—54no—
616C3×C4—102no—
617C3×C4—102no—
618C3×C4C22×C22⋊D514yes—
619Dic3—104no—
620Dic3C22×C22⋊D518yes—
621C2×C5—42no—
622C2×C5—124no—
623C2×C5#555314yescomplemented
624C2×C5C22×#23511yescharacteristic
625C2×C5C22×D3×D411yescharacteristic
626C2×C5C2×#100911yescharacteristic
627D5—42no—
628D5—124no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—34no—
633C23—52no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—154no—
641C23—304no—
642C23—304no—
643C23—304no—
644C23C22×D3×D512yes—
645C23C22×D3×D511yescharacteristic
646Q8—316no—
647D4—616no—
648D4—68no—
649D4—108no—
650D4—3016no—
651D4—3016no—
652D4—308no—
653D4—608no—
654D4—608no—
655D4—608no—
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—38no—
659C2×C4—34no—
660C2×C4—54no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—52no—
664C2×C4—616no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—108no—
668C2×C4—154no—
669C2×C4—3016no—
670C2×C4—304no—
671C2×C4D3×C22⋊D514yes—
672C2×C4C22×D3×D512yes—
673C2×C4C22×D3×D512yes—
674C2×C3—42no—
675C2×C3—202no—
676C2×C3#6616814yescomplemented
677C2×C3C2×D5×#4111yescharacteristic
678C2×C3C2×#414911yescharacteristic
679C2×C3C23×C22⋊D511yescharacteristic
680D3—44no—
681D3—204no—
682C5C2×#555311yescharacteristic, complemented, Sylow
683C22—22no—
684C22—22no—
685C22—22no—
686C22—44no—
687C22—64no—
688C22—64no—
689C22—64no—
690C22—102no—
691C22—102no—
692C22—102no—
693C22—128no—
694C22—204no—
695C22—304no—
696C22—304no—
697C22—304no—
698C22—608no—
699C22D5×#23512yes—
700C22#9201912yes—
701C22C2×D3×C22⋊D512yes—
702C22C23×D3×D511yescharacteristic
703C4—22no—
704C4—38no—
705C4—54no—
706C4—102no—
707C4—102no—
708C4—304no—
709C4C2×D3×C22⋊D514yes—
710C3C2×#6616811yescharacteristic, complemented, Sylow
711C2—42no—
712C2—124no—
713C2—202no—
714C2—604no—
715C2#1175454514yesdirect product factor
716C2C2×D5×#23511yescharacteristic
717C2C2×#9201911yescharacteristic
718C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#550
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#235C2semidirect
2. C22×#6773C2semidirect
3. C2×#91819C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. C2×#91567C2semidirect
6. C2×#91557C2semidirect
7. #11754545C2direct (N × H)
8. C2×#91454C2semidirect
9. C2×#91451C2semidirect
10. C2×#91449C2semidirect
11. C2×#91446C2semidirect
12. C2×Dic5×Dic6C2semidirect
19. C2×C5×#235C22semidirect
31. C2×#6773C22semidirect
32. #91819C22semidirect
36. C3×C4×C22⋊D5C22semidirect
40. #91567C22semidirect
41. #91557C22semidirect
45. #91454C22semidirect
46. #91451C22semidirect
47. #91449C22semidirect
48. #91446C22semidirect
49. Dic5×Dic6C22semidirect
62. C2×C4×C22⋊D5D3semidirect
84. C2×C5×Dic6D4semidirect
114. C22×#235D5semidirect
153. C4×C22⋊D5C2×D3semidirect
193. C5×Dic6C2×D4semidirect
197. C2×C3×Dic5#41semidirect
217. C2×#235C2×D5semidirect
330. C3×Dic5C2×#41semidirect
371. C2×Dic6C22⋊D5semidirect
419. C2×Dic5#235semidirect
464. C2×C3×C5#550semidirect
515. Dic6C2×C22⋊D5semidirect
542. Dic5C2×#235semidirect
593. C3×C5C2×#550semidirect
623. C2×C5#5553semidirect
676. C2×C3#66168semidirect
682. C5C2×#5553semidirect
710. C3C2×#66168semidirect
715. C2#11754545direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C22×#67732
C2×#918192
C2×C3×C4×C22⋊D52
C2×#915672
C2×#915572
#117545452
C2×#914542
C2×#914512
C2×#914492
C2×#914462
C2×Dic5×Dic62
C2×#661683
C2×#55535