Finite Group Databasebeta

← C2×#11753258 #14482614

Subgroups — C2×#11753258 #14482614

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×#4031C211yesmaximal, characteristic, complemented
6C2×#91570C211yesmaximal, characteristic, complemented
7C2×#91562C211yesmaximal, characteristic, complemented
8C2×#91533C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91454C211yesmaximal, characteristic, complemented
12C2×#91452C211yesmaximal, characteristic, complemented
13C2×C4×#1203C211yesmaximal, characteristic, complemented
14C2×#91410C211yesmaximal, characteristic, complemented
15C2×#91405C211yesmaximal, characteristic, complemented
16#11753258C2116yesmaximal, direct product factor
17C2×#65824—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×Dic10C2211yescharacteristic, complemented
28C2×D3×C22⋊D5—28no—
29C2×D3×C22⋊D5C2218yescomplemented
30C22×#1203C2211yescharacteristic
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic, complemented
33C22×#1202C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C22×D3×Dic5C2211yescharacteristic
38C2×#6769—28no—
39C2×#6769C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43#91773C2218yescomplemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C5×D3×C22⋊C4C2218yescomplemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×C4×Dic5C2211yescharacteristic, complemented
52C3×#4031C2218yescomplemented
53#91570C2218yescomplemented
54#91562C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6668C2211yescharacteristic, complemented
57C2×#6668C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62#91533C2218yescomplemented
63#91476C2218yescomplemented
64#91473C2218yescomplemented
65#91454C2218yescomplemented
66#91452C2218yescomplemented
67C4×#1203C2218yescomplemented
68#91410C2218yescomplemented
69#91405C2218yescomplemented
70C2×#5676—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#709—31no—
73C22×C5×C22⋊C4—31no—
74C2×#4099—31no—
75C2×#4076—31no—
76C2×#4075—31no—
77C2×C4×C22⋊D5—31no—
78C2×#4031D311yescharacteristic, complemented
79#65824—316no—
80C2×#4030—31no—
81C2×#4030—31no—
82C2×#4029—31no—
83C2×#4028—31no—
84C2×#4027—31no—
85C2×D5×C22⋊C4—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—24no—
92C23×C5×D3—42no—
93C23×C5×D3C2314yes—
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220C2314yes—
106C2×#1220C2314yescomplemented
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×D60—24no—
110C2×D60C2314yescomplemented
111C2×C4×D15—42no—
112C2×C4×D15C2314yescomplemented
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C2×C4×C5×D3—24no—
116C2×C4×C5×D3—42no—
117C2×C4×C5×D3C2314yescomplemented
118C2×C4×C5×D3C2314yescomplemented
119C2×C3×C22⋊D5—24no—
120C2×C3×C22⋊D5C2314yes—
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2311yescharacteristic
124C2×C3×Dic10—24no—
125C2×C3×Dic10C2314yescomplemented
126D3×C22⋊D5—232no—
127C2×#1203—24no—
128C2×#1203—24no—
129C2×#1203D418yescomplemented
130C2×#1203C2314yes—
131C2×#1203C2314yes—
132C2×#1203C2314yescomplemented
133C2×#1202—42no—
134C2×#1202C2314yescomplemented
135C2×#1201—24no—
136C2×#1201C2314yes—
137C2×#1200—24no—
138C2×#1200—24no—
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141C2×D3×Dic5—24no—
142C2×D3×Dic5C2314yes—
143#6769—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yes—
149C5×(C2×D3)⋊C4C2314yes—
150C3×C22⋊Dic5C2314yescomplemented
151C3×#685C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×C4×Dic5C2314yescomplemented
154Dic3⋊Dic5C2314yescomplemented
155#6668C2314yescomplemented
156#6668C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yes—
159(C2×D3)⋊Dic5C2314yescomplemented
160#6665C2314yescomplemented
161C22×#239—51no—
162C22×D3×D4—51no—
163C2×C3×#124—51no—
164C2×#946—51no—
165C2×#938—51no—
166#5676—516no—
167C2×#884—51no—
168C2×#884—51no—
169C2×#883—51no—
170C2×#883—51no—
171C2×#882—51no—
172C2×#882—51no—
173C2×D3×C22⋊C4—51no—
174C2×D3×C22⋊C4D511yescharacteristic, complemented
175C2×C4×D12—51no—
176C2×C4×D12—51no—
177C25×C5—31no—
178C24×D5—31no—
179C23×C4×C5—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—38no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—68no—
189C22×C22⋊D5C2×D311yescharacteristic
190C23×Dic5—31no—
191C2×#709—38no—
192C2×#709—68no—
193C22×D20—31no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10C2×D311yescharacteristic, complemented
199C2×C5×C22⋊C4—31no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—38no—
203C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
204#4099—38no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5C2×D311yescharacteristic, complemented
208#4076—38no—
209#4075—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×#685C2×D311yescharacteristic, complemented
216C2×C4⋊Dic5—31no—
217C2×#683—31no—
218C2×#683—31no—
219C2×#683—31no—
220C2×C4×Dic5C2×D311yescharacteristic, complemented
221#4031C2×D318yescomplemented
222#4030—38no—
223#4030—38no—
224#4029—38no—
225#4028—38no—
226#4027—38no—
227D5×C22⋊C4—38no—
228#4024—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15C2×D414yes—
241C22×D15C2412yes—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—28no—
248C22×C5×D3—28no—
249C22×C5×D3—44no—
250C22×C5×D3—416no—
251C22×C5×D3C2×D414yes—
252C22×C5×D3#4114yescomplemented
253C22×C5×D3C2412yes—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268#1220—44no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—44no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C4×C5×D3—28no—
280C4×C5×D3—44no—
281C3×C22⋊D5—28no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2×D414yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C2×C3×Dic5C2412yes—
288C3×Dic10—28no—
289#1203—28no—
290#1203—28no—
291#1203C2×D4116yescomplemented
292#1202—44no—
293#1201—28no—
294#1200—28no—
295#1200—28no—
296D3×Dic5—28no—
297C24×D3—51no—
298C24×D3C2×D511yescharacteristic
299C22×C3×Q8—51no—
300C22×C3×D4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C2×#239—58no—
306C2×#239—108no—
307C2×D3×D4—58no—
308C2×D3×D4—108no—
309C22×D12—51no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×C4×D3—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×C4×D3C2×D511yescharacteristic, complemented
319C3×#124—58no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324C2×C3×C42—51no—
325C2×#217—51no—
326C2×#217C2×D511yescharacteristic, complemented
327#946—58no—
328#938—58no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4C2×D511yescharacteristic
334C2×(C2×D3)⋊C4C2×D511yescharacteristic
335C2×C4⋊Dic3—51no—
336C2×C4⋊Dic3—51no—
337C2×Dic3⋊C4—51no—
338C2×Dic3⋊C4—51no—
339#884—58no—
340#884—58no—
341#883—58no—
342#883—58no—
343#882—58no—
344#882—58no—
345D3×C22⋊C4—58no—
346D3×C22⋊C4C2×D518yescomplemented
347C4×D12—58no—
348C4×D12—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—34no—
352C24×C5—64no—
353C24×C5—64no—
354C24×C5—122no—
355C24×C5C22×D311yescharacteristic
356C23×D5—31no—
357C23×D5—31no—
358C23×D5—34no—
359C23×D5—64no—
360C23×D5—64no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C22×C4×C5—31no—
364C22×C4×C5—31no—
365C22×C4×C5—34no—
366C22×C4×C5—34no—
367C22×C4×C5—64no—
368C22×C4×C5—122no—
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C2×C22⋊D5—24no—
372C2×C22⋊D5—34no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—38no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—64no—
381C2×C22⋊D5—632no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C2×C22⋊D5C22×D314yes—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—64no—
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392C22×Dic5C22×D311yescharacteristic
393#709—632no—
394C2×D20—34no—
395C2×D20—34no—
396C2×D20—64no—
397C2×D20—122no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—24no—
405C2×Dic10C22×D314yescomplemented
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4C22×D314yescomplemented
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5C22×D314yescomplemented
413#685—34no—
414#685—34no—
415#685—34no—
416#685C22×D314yescomplemented
417#685C22×D314yescomplemented
418C4⋊Dic5—34no—
419#683—34no—
420#683—34no—
421#683—34no—
422C4×Dic5C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—51no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—31no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—28no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—44no—
454C2×D15C22×D414yes—
455C2×C5×D3—28no—
456C2×C5×D3—28no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—416no—
462C2×C5×D3C22×D414yes—
463C2×C5×D3C2×#4114yescomplemented
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—44no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5C22×D414yes—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C23×D3—24no—
481C23×D3—24no—
482C23×D3—42no—
483C23×D3—51no—
484C23×D3—51no—
485C23×D3—54no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×Q8—54no—
493C2×C3×Q8—104no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C22×C3×C4—51no—
497C22×C3×C4—51no—
498C22×C3×C4—51no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—54no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—104no—
506C2×#67—104no—
507C2×#67—202no—
508C2×#67—202no—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3C22×D511yescharacteristic
512C22×Dic3C22×D511yescharacteristic
513#239—1032no—
514D3×D4—1032no—
515C2×D12—58no—
516C2×D12—54no—
517C2×D12—54no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—104no—
521C2×D12—104no—
522C2×D12—104no—
523C2×C4×D3—24no—
524C2×C4×D3—42no—
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×C4×D3C22×D514yescomplemented
534C2×C4×D3C22×D514yescomplemented
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4C22×D514yescomplemented
539C3×C42—54no—
540#217—54no—
541#217C22×D514yescomplemented
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4C22×D514yes—
547(C2×D3)⋊C4C22×D514yes—
548C4⋊Dic3—54no—
549C4⋊Dic3—54no—
550Dic3⋊C4—54no—
551Dic3⋊C4—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—34no—
557C23×C5—32no—
558C23×C5—32no—
559C23×C5—68no—
560C23×C5—68no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5—62no—
564C23×C5—62no—
565C23×C5—124no—
566C23×C5—1216no—
567C23×C5C23×D312yes—
568C23×C5C23×D311yescharacteristic
569C22×D5—22no—
570C22×D5—22no—
571C22×D5—22no—
572C22×D5—34no—
573C22×D5—32no—
574C22×D5—32no—
575C22×D5—68no—
576C22×D5—68no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—62no—
581C22×D5—62no—
582C22×D5—124no—
583C22×D5—1216no—
584C22×D5C23×D312yes—
585C2×C4×C5—22no—
586C2×C4×C5—22no—
587C2×C4×C5—32no—
588C2×C4×C5—32no—
589C2×C4×C5—68no—
590C2×C4×C5—62no—
591C2×C4×C5—62no—
592C2×C4×C5—124no—
593C2×C4×C5C23×D312yes—
594C2×C4×C5C23×D312yes—
595C22⋊D5—28no—
596C22⋊D5—316no—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5—68no—
609C2×Dic5D3×D414yes—
610C2×Dic5C23×D312yes—
611C2×Dic5C23×D312yes—
612C2×Dic5C23×D312yes—
613D20—68no—
614D20—124no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—28no—
619C25—31no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—51no—
624C22×D4—51no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—31no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—58no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—151no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—38no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—51no—
662C2×C22⋊C4—51no—
663C2×C22⋊C4—158no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—51no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677D15—42no—
678C3×D5—42no—
679C5×D3—24no—
680C5×D3—24no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—52no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3C23×D512yes—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—28no—
695C22×D3—28no—
696C22×D3—44no—
697C22×D3—416no—
698C22×D3—54no—
699C22×D3—52no—
700C22×D3—52no—
701C22×D3—108no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—108no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3#70914yescomplemented
711C22×D3D4×D514yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×Q8—108no—
715C3×D4—108no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—108no—
727#67—108no—
728#67—204no—
729#67—204no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—102no—
735C2×Dic3—102no—
736C2×Dic3C23×D512yes—
737C2×Dic3C23×D512yes—
738D12—516no—
739D12—108no—
740D12—108no—
741D12—108no—
742C4×D3—28no—
743C4×D3—44no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—108no—
747C4×D3—204no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—34no—
753C22×C5—44no—
754C22×C5—68no—
755C22×C5—68no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—62no—
760C22×C5—1216no—
761C22×C5C2×D3×D412yes—
762C22×C5D3×#4112yes—
763C22×C5#100912yes—
764C22×C5C24×D311yescharacteristic
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—34no—
769C2×D5—44no—
770C2×D5—68no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—62no—
776C2×D5—1216no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—34no—
790C24—51no—
791C24—64no—
792C24—64no—
793C24—122no—
794C24—154no—
795C24—151no—
796C24—151no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—54no—
803C2×Q8—104no—
804C2×D4—54no—
805C2×D4—104no—
806C2×D4—154no—
807C2×D4—154no—
808C2×D4—158no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—304no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—3032no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—64no—
831C22×C4—122no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—154no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—54no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—54no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—204no—
870C22×C3C2×#70912yes—
871C22×C3C2×D4×D512yes—
872C22×C3#414412yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—28no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—416no—
881C2×D3—54no—
882C2×D3—108no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—204no—
890C2×D3C2×#70914yescomplemented
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—54no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—64no—
904C2×C5#567614yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—42no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—34no—
916C23—32no—
917C23—32no—
918C23—52no—
919C23—68no—
920C23—68no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—124no—
929C23—1216no—
930C23—154no—
931C23—152no—
932C23—152no—
933C23—308no—
934C23—308no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—108no—
945D4—108no—
946D4—1516no—
947D4—308no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—54no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—102no—
966C2×C4—102no—
967C2×C4—124no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—202no—
980C2×C3#6582414yescomplemented
981C2×C3C22×#70911yescharacteristic
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×#414411yescharacteristic
984D3—24no—
985D3—24no—
986D3—104no—
987D3—202no—
988C5C2×#567611yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—34no—
994C22—44no—
995C22—68no—
996C22—68no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—1216no—
1005C22—154no—
1006C22—204no—
1007C22—308no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22D3×#70912yes—
1016C22D3×D4×D512yes—
1017C22#9202712yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—54no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6582411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—64no—
1032C2—202no—
1033C2—304no—
1034C2—602no—
1035C2#1175325814yesdirect product factor
1036C2C2×D3×#70911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#546
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. C22×D3×C22⋊D5C2semidirect
2. C22×#6769C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×D3×C22⋊C4C2semidirect
5. C2×C3×#4031C2semidirect
6. C2×#91570C2semidirect
7. C2×#91562C2semidirect
8. C2×#91533C2semidirect
9. C2×#91476C2semidirect
10. C2×#91473C2semidirect
11. C2×#91454C2semidirect
12. C2×#91452C2semidirect
13. C2×C4×#1203C2semidirect
14. C2×#91410C2semidirect
15. C2×#91405C2semidirect
16. #11753258C2direct (N × H)
21. C22×#1220C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
24. C22×C4×C5×D3C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×Dic10C22semidirect
29. C2×D3×C22⋊D5C22semidirect
32. C22×#1203C22semidirect
33. C22×#1202C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
39. C2×#6769C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
43. #91773C22semidirect
44. C2×C5×#217C22semidirect
47. C5×D3×C22⋊C4C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×C4×Dic5C22semidirect
52. C3×#4031C22semidirect
53. #91570C22semidirect
54. #91562C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×#6668C22semidirect
57. C2×#6668C22semidirect
58. C2×#6667C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×#6665C22semidirect
62. #91533C22semidirect
63. #91476C22semidirect
64. #91473C22semidirect
65. #91454C22semidirect
66. #91452C22semidirect
67. C4×#1203C22semidirect
68. #91410C22semidirect
69. #91405C22semidirect
78. C2×#4031D3semidirect
106. C2×#1220C23semidirect
110. C2×D60C23semidirect
112. C2×C4×D15C23semidirect
117. C2×C4×C5×D3C23semidirect
118. C2×C4×C5×D3C23semidirect
125. C2×C3×Dic10C23semidirect
129. C2×#1203D4semidirect
132. C2×#1203C23semidirect
134. C2×#1202C23semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×#217C23semidirect
150. C3×C22⋊Dic5C23semidirect
151. C3×#685C23semidirect
152. C3×#685C23semidirect
153. C3×C4×Dic5C23semidirect
154. Dic3⋊Dic5C23semidirect
155. #6668C23semidirect
156. #6668C23semidirect
157. #6667C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
174. C2×D3×C22⋊C4D5semidirect
198. C22×Dic10C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
207. C2×C22⋊Dic5C2×D3semidirect
214. C2×#685C2×D3semidirect
215. C2×#685C2×D3semidirect
220. C2×C4×Dic5C2×D3semidirect
221. #4031C2×D3semidirect
252. C22×C5×D3#41semidirect
291. #1203C2×D4semidirect
317. C22×C4×D3C2×D5semidirect
318. C22×C4×D3C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
326. C2×#217C2×D5semidirect
346. D3×C22⋊C4C2×D5semidirect
405. C2×Dic10C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
412. C22⋊Dic5C22×D3semidirect
416. #685C22×D3semidirect
417. #685C22×D3semidirect
422. C4×Dic5C22×D3semidirect
463. C2×C5×D3C2×#41semidirect
533. C2×C4×D3C22×D5semidirect
534. C2×C4×D3C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
541. #217C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
710. C22×D3#709semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
890. C2×D3C2×#709semidirect
904. C2×C5#5676semidirect
980. C2×C3#65824semidirect
988. C5C2×#5676semidirect
1028. C3C2×#65824semidirect
1035. C2#11753258direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×#67692
C2×#917732
C2×C5×D3×C22⋊C42
C2×C3×#40312
C2×#915702
C2×#915622
C2×#915332
C2×#914762
C2×#914732
C2×#914542
C2×#914522
C2×C4×#12032
C2×#914102
C2×#914052
#117532582
C2×#658243
C2×#56765