Finite Group Databasebeta

← #14288906

Subgroups — #14288906

Order 1920.

556 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752554C211yesmaximal, characteristic, complemented
2#11751176C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic, complemented
4C3×#65362C211yesmaximal, characteristic, complemented
5#11745852C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601806—31nomaximal, Hall
9C2×#6765—21no—
10C3×C5×#127C2211yescharacteristic
11C2×#6716—21no—
12C4×Dic30C2211yescharacteristic
13C2×C5×#213—21no—
14C4×C5×D12C2211yescharacteristic
15C2×C3×#686—22no—
16C3×#4020C2211yescharacteristic
17#91463—21no—
18#91456—21no—
19#91434—21no—
20#91408—22no—
21#91116—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#71285—51nomaximal, Hall
27#65887—31no—
28C5×#459—31no—
29#65364—31no—
30#65362D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20D412yes—
43C2×#1201—22no—
44C2×#1201—22no—
45C2×D5×Dic3—22no—
46#6765—42no—
47#6765—42no—
48C3×C42×C5C2311yescharacteristic
49#6716—42no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53C2×C3⋊#168—21no—
54C5×#213—42no—
55C5×(C2×D3)⋊C4—21no—
56C5×C4⋊Dic3D411yescharacteristic
57C2×C5×C3⋊C8—21no—
58C3×#686—44no—
59C2×C3×#168—21no—
60#6665—22no—
61#5718—51no—
62C3×#493—51no—
63#5075—51no—
64#5072D511yescharacteristic, complemented
65#4544—51no—
66#4459—51no—
67#4456—51no—
68C2×#709—61no—
69C2×C5×D8—61no—
70C5×#127C2×D311yescharacteristic
71C4×C5×D4—31no—
72#4086—61no—
73C2×#687—61no—
74C2×#686—22no—
75#4076—61no—
76#4039—61no—
77#4030—62no—
78#4020C2×D311yescharacteristic
79C4×Dic10—31no—
80C5×C4⋊C8—31no—
81C5×#102—61no—
82#3964—61no—
83C4⋊#168—31no—
84C4×#168C2×D311yescharacteristic
85#1621—151noSylow
86C23×C3×C5—41no—
87C22×C5×D3—21no—
88C22×C3×D5—22no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99Dic30—21no—
100Dic30D812yescomplemented
101C2×C5×Dic3—21no—
102C5×D12—21no—
103C5×D12—21no—
104C4×C5×D3—41no—
105C4×C5×D3—41no—
106C3×D20—42no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—41no—
111#1201—44no—
112#1201—82no—
113D5×Dic3—44no—
114C3⋊#168—41no—
115C3×#168—22no—
116C5×C3⋊C8—41no—
117C2×#237—101no—
118C2×C3×D8—102no—
119C3×#127—51no—
120C3×#127C2×D511yescharacteristic
121#940—101no—
122#939—102no—
123#938—101no—
124D4×Dic3—101no—
125C2×#214—101no—
126C2×#213—21no—
127C4×D12C2×D511yescharacteristic
128C4×Dic6—51no—
129C3×C4×C8—51no—
130#832—21no—
131#832—101no—
132C4⋊(C3⋊C8)—51no—
133C4⋊(C3⋊C8)C2×D511yescharacteristic
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—31no—
138C22×C4×C5—61no—
139C2×C22⋊D5—62no—
140C2×C22⋊D5—62no—
141#709—122no—
142#709—122no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20#6712yes—
146C2×C4×D5—62no—
147C2×Dic10—31no—
148C5×D8—122no—
149C2×C5×C8—61no—
150C5×C4⋊C4—31no—
151C5×C22⋊C4—61no—
152C42×C5C22×D311yescharacteristic
153#687—122no—
154#686—44no—
155#685—62no—
156C4⋊Dic5—31no—
157#683—61no—
158C4×Dic5—61no—
159C2×#168—21no—
160C2×#168—61no—
161#550—151no—
162#493—51no—
163#460—151no—
164#459—31no—
165#331—151no—
166Q8⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—81no—
169C22×C3×C5—81no—
170C22×C3×C5—81no—
171C22×C3×C5#12011yescharacteristic
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C3×D5—42no—
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C3×C4×C5—21no—
179C3×C4×C5C2×D811yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183Dic15—22no—
184Dic15—41no—
185C5×Dic3—41no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—52no—
190C2×C3×D4—101no—
191C2×C3×D4—101no—
192C2×#67—102no—
193C2×#67—102no—
194C22×Dic3—102no—
195#237—202no—
196#237—202no—
197C2×D12C22⋊D511yescharacteristic
198C2×C4×D3—21no—
199C2×Dic6—51no—
200C3×D8—204no—
201C2×C3×C8—101no—
202C3×C42C22×D511yescharacteristic
203#217—102no—
204#214—202no—
205#213—42no—
206(C2×D3)⋊C4—21no—
207C4⋊Dic3—51no—
208C4⋊Dic3C22⋊D511yescharacteristic
209Dic3⋊C4—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C23×C5—41no—
214C23×C5—61no—
215C22×D5—22no—
216C5×D4—42no—
217C5×D4—41no—
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C5×D4—61no—
222C5×D4—61no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5—121no—
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C22⋊D5—124no—
230C22⋊D5—242no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233D20—42no—
234D20—41no—
235D20—41no—
236D20—41no—
237D20—41no—
238C4×D5—124no—
239Dic10—32no—
240Dic10—61no—
241C5×C8—121no—
242#168—22no—
243#168—121no—
244C2×#41—301no—
245C2×SD16—301no—
246C2×D8—61no—
247C2×D8—102no—
248#127—51no—
249#127—301no—
250#127D3×D511yescharacteristic
251#121—302no—
252#121—301no—
253C4×Q8—151no—
254C4×D4—31no—
255C4×D4—301no—
256C4⋊C8—31no—
257C4⋊C8—151no—
258#102—61no—
259#102—301no—
260C4×C8—51no—
261C2×C3×C5—161no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265C3×D5—82no—
266C5×D3—81no—
267C23×C3—41no—
268C23×C3—102no—
269C22×D3—21no—
270C3×D4—42no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—202no—
276C3×D4—201no—
277C3×D4—201no—
278C3×D4—201no—
279C3×D4—201no—
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4C2×C22⋊D511yescharacteristic
283#67—204no—
284#67—402no—
285C2×Dic3—21no—
286C2×Dic3—101no—
287C2×Dic3—101no—
288C2×Dic3—204no—
289D12—21no—
290D12—21no—
291C4×D3—41no—
292C4×D3—41no—
293Dic6—52no—
294Dic6—101no—
295C3×C8—102no—
296C3⋊C8—41no—
297C3⋊C8—201no—
298C22×C5—81no—
299C22×C5—81no—
300C22×C5—81no—
301C22×C5—121no—
302C22×C5—121no—
303C22×C5—121no—
304C22×C5#93711yescharacteristic
305C2×D5—42no—
306C2×D5—42no—
307C2×D5—42no—
308C4×C5—21no—
309C4×C5—121no—
310C4×C5D3×D811yescharacteristic
311C4×C5#91111yescharacteristic
312C4×C5#91111yescharacteristic
313C4×C5#91211yescharacteristic
314Dic5—62no—
315Dic5—121no—
316#41—602no—
317#41—602no—
318C2×Q8—151no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—31no—
323C2×D4—52no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—302no—
327C2×D4—302no—
328C22×C4—61no—
329C22×C4—302no—
330SD16—602no—
331D8—122no—
332D8—204no—
333C2×C8—61no—
334C2×C8—101no—
335C2×C8—301no—
336C4⋊C4—31no—
337C4⋊C4—151no—
338C4⋊C4—301no—
339C22⋊C4—61no—
340C22⋊C4—302no—
341C42—301no—
342C42C2×D3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—81no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—202no—
348C22×C3—202no—
349C22×C3—202no—
350C22×C3#408311yescharacteristic
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—41no—
354C3×C4—21no—
355C3×C4D5×D811yescharacteristic
356C3×C4#405711yescharacteristic
357C3×C4#407811yescharacteristic
358C3×C4#409611yescharacteristic
359Dic3—41no—
360Dic3—102no—
361Dic3—201no—
362C2×C5—161no—
363C2×C5—241no—
364C2×C5#507711yescharacteristic
365C2×C5#515611yescharacteristic
366C2×C5#515811yescharacteristic
367D5—82no—
368C23—41no—
369C23—61no—
370C23—102no—
371Q8—152no—
372Q8—301no—
373D4—42no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—61no—
379D4—61no—
380D4—202no—
381D4—201no—
382D4—201no—
383D4—201no—
384D4—201no—
385D4—604no—
386D4—1202no—
387C2×C4—61no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—301no—
391C2×C4—301no—
392C2×C4—604no—
393C2×C4D5×#6711yescharacteristic
394C2×C4D3×C22⋊D511yescharacteristic
395C2×C4#679011yescharacteristic
396C8—102no—
397C8—121no—
398C8—601no—
399C2×C3—161no—
400C2×C3—402no—
401C2×C3#6532611yescharacteristic
402C2×C3#6544511yescharacteristic
403C2×C3#6548711yescharacteristic
404D3—81no—
405C5#7128511yescharacteristic, complemented, Sylow
406C22—81no—
407C22—81no—
408C22—81no—
409C22—121no—
410C22—121no—
411C22—121no—
412C22—202no—
413C22—202no—
414C22—202no—
415C22#9157711yescharacteristic
416C4—21no—
417C4—121no—
418C4—302no—
419C4—601no—
420C4#9148111yescharacteristic
421C4#9148211yescharacteristic
422C4#9149311yescharacteristic
423C4#9149411yescharacteristic
424C3#1060180611yescharacteristic, complemented, Sylow
425C2—161no—
426C2—241no—
427C2—402no—
428C2#1174915311yescharacteristic
429C2#1174915711yescharacteristic
430C2#1174916311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752554C2semidirect
2. #11751176C2semidirect
3. C5×#5072C2semidirect
4. C3×#65362C2semidirect
5. #11745852C2semidirect
6. #11745845C2semidirect
7. #11745837C2semidirect
30. #65362D3semidirect
64. #5072D5semidirect
100. Dic30D8semidirect
343. C3×C5#1621semidirect
405. C5#71285semidirect
424. C3#10601806semidirect

Maximal subgroups

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

subgroupindex
#117525542
#117511762
C5×#50722
C3×#653622
#117458522
#117458452
#117458372
#106018063
#712855