Finite Group Databasebeta

← #14291108

Subgroups — #14291108

Order 1920.

416 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×#5700C211yesmaximal, characteristic
2C3×#65354C211yesmaximal, characteristic, complemented
3#11747082C211yesmaximal, characteristic, complemented
4#11746904C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602746—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#896—21no—
11C5×#896—21no—
12C5×#895—21no—
13C5×#895—21no—
14C5×#894—21no—
15C5×#894—21no—
16C5×#875C2211yescharacteristic
17C5×#875C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C2×#6661—21no—
20C2×#6656—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C3×#3940—21no—
24C3×#3939—21no—
25C3×#3935C2211yescharacteristic
26#90972—21no—
27#90966—21no—
28#71392—51nomaximal, Hall
29C5×#562—31no—
30#65354D311yescharacteristic, complemented
31#65349—31no—
32#65344—31no—
33#64763—31no—
34#64760—31no—
35#64760—31no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12D411yescharacteristic
39C2×C5×D12D411yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C4×C5×D3—21no—
42C2×C5×Dic6D411yescharacteristic
43C2×C5×Dic6D411yescharacteristic
44C2×C3×Dic10—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C42×C5C2311yescharacteristic
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C5×Dic3⋊C4—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63#6661—42no—
64#6656—42no—
65#5700D511yescharacteristic
66C3×#501—51no—
67#5089—51no—
68#5086—51no—
69#4543—51no—
70#4464—51no—
71#4464—51no—
72C5×#125C2×D311yescharacteristic
73C5×#124—31no—
74C5×#124—31no—
75C5×#123—61no—
76C5×#123—61no—
77C5×C22⋊Q8—61no—
78C5×C22⋊Q8—61no—
79C5×#121—61no—
80C5×#121—61no—
81C2×#689—61no—
82C2×#687—61no—
83#4015C2×D311yescharacteristic
84#3967—61no—
85#3964—61no—
86#3940—21no—
87#3939—21no—
88#3935—31no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1661—151noSylow
92C22×C5×D3—21no—
93C22×C5×D3—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C5×D12—41no—
102C5×D12—41no—
103C5×D12—81no—
104C5×D12—81no—
105C4×C5×D3—81no—
106C4×C5×D3—81no—
107C5×Dic6—41no—
108C5×Dic6—41no—
109C2×C3×Dic5—41no—
110C3×Dic10—41no—
111C3×Dic10—41no—
112C3⋊#168—22no—
113C3⋊#168—41no—
114C3×#168—22no—
115C3×C4⋊Q8—51no—
116C3×#125C2×D511yescharacteristic
117C2×#216—101no—
118C2×#215—101no—
119#896—21no—
120#896—21no—
121#895—21no—
122#895—21no—
123#894—21no—
124#894—21no—
125#875C2×D511yescharacteristic
126#875C2×D511yescharacteristic
127C3×#107—101no—
128C3×#106—101no—
129C3×#97—51no—
130#810—101no—
131#809—101no—
132#803—51no—
133#803—51no—
134C2×C5×Q8—31no—
135C2×C5×Q8—31no—
136C2×C5×D4—31no—
137C2×C5×D4—31no—
138C2×C5×D4—61no—
139C2×C5×D4—61no—
140C22×C4×C5—61no—
141C22×C4×C5—61no—
142C2×Dic10—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4#6711yescharacteristic
148C5×C4⋊C4#6711yescharacteristic
149C5×C22⋊C4—61no—
150C5×C22⋊C4—61no—
151C5×C22⋊C4—61no—
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C42×C5C22×D311yescharacteristic
156#689—122no—
157#687—122no—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C2×#168—21no—
161C2×#168—61no—
162C2×#168—61no—
163#562—31no—
164#501—51no—
165#497—151no—
166#489—151no—
167#330—151no—
168#329—151no—
169#329—151no—
170C22×C3×C5#12011yescharacteristic
171C2×C5×D3—41no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3—41no—
176C2×C5×D3—41no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×Dic5—81no—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C2×C3×Q8—101no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12C22⋊D511yescharacteristic
189C2×D12C22⋊D511yescharacteristic
190C2×C4×D3—21no—
191C2×C4×D3—21no—
192C2×Dic6C22⋊D511yescharacteristic
193C2×Dic6C22⋊D511yescharacteristic
194C2×C3×C8—101no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4C22⋊D511yescharacteristic
200C3×C4⋊C4C22⋊D511yescharacteristic
201C3×C42C22×D511yescharacteristic
202#216—202no—
203#215—202no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—61no—
215C23×C5—61no—
216C5×Q8—121no—
217C5×Q8—121no—
218C5×D4—121no—
219C5×D4—121no—
220C5×D4—241no—
221C5×D4—241no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—241no—
227C2×C4×C5—241no—
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×C4×C5C2×#6711yescharacteristic
231C2×Dic5—41no—
232Dic10—41no—
233Dic10—41no—
234#168—22no—
235#168—62no—
236#168—121no—
237C2×Q16—301no—
238C2×SD16—301no—
239C4⋊Q8—51no—
240#125D3×D511yescharacteristic
241#124—31no—
242#124—31no—
243#123—61no—
244#123—61no—
245C22⋊Q8—61no—
246C22⋊Q8—61no—
247#121—61no—
248#121—61no—
249#107—101no—
250#106—101no—
251#103—301no—
252#102—301no—
253#97—51no—
254#97—151no—
255#97—151no—
256C2×C3×C5#45311yescharacteristic
257C2×C3×C5#45511yescharacteristic
258C2×C3×C5#45611yescharacteristic
259C5×D3—81no—
260C5×D3—81no—
261C22×D3—21no—
262C22×D3—21no—
263C3×Q8—201no—
264C3×Q8—201no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—201no—
268C2×C3×C4C2×C22⋊D511yescharacteristic
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273D12—41no—
274D12—41no—
275D12—81no—
276D12—81no—
277C4×D3—81no—
278C4×D3—81no—
279Dic6—41no—
280Dic6—41no—
281C3×C8—102no—
282C3⋊C8—102no—
283C3⋊C8—201no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5—121no—
287C22×C5—121no—
288C22×C5—121no—
289C22×C5—121no—
290C22×C5#93711yescharacteristic
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—41no—
295C4×C5—41no—
296C4×C5—121no—
297C4×C5—121no—
298Dic5—81no—
299C2×Q8—31no—
300C2×Q8—31no—
301C2×Q8—101no—
302C2×D4—31no—
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—61no—
306C22×C4—61no—
307C22×C4—61no—
308Q16—602no—
309SD16—602no—
310C2×C8—101no—
311C2×C8—301no—
312C2×C8—301no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C4⋊C4#120111yescharacteristic
320C4⋊C4#120111yescharacteristic
321C22⋊C4—61no—
322C22⋊C4—61no—
323C22⋊C4—61no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—61no—
327C42C2×D3×D511yescharacteristic
328C3×C5#166111yescharacteristic, complemented, Hall
329C22×C3#409911yescharacteristic
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—401no—
342Dic3—41no—
343Dic3—41no—
344C2×C5—241no—
345C2×C5—241no—
346C2×C5#509511yescharacteristic
347C2×C5#519811yescharacteristic
348C2×C5#520211yescharacteristic
349C23—61no—
350C23—61no—
351Q8—121no—
352Q8—121no—
353Q8—201no—
354Q8—201no—
355D4—121no—
356D4—121no—
357D4—241no—
358D4—241no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—201no—
364C2×C4—241no—
365C2×C4—241no—
366C2×C4C2×#120111yescharacteristic
367C2×C4D3×C22⋊D511yescharacteristic
368C2×C4D3×C22⋊D511yescharacteristic
369C8—102no—
370C8—302no—
371C8—601no—
372C2×C3#6553011yescharacteristic
373C2×C3#6553111yescharacteristic
374C2×C3#6553511yescharacteristic
375D3—81no—
376D3—81no—
377C5#7139211yescharacteristic, complemented, Sylow
378C22—121no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22#9156811yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—121no—
391C4—121no—
392C4—401no—
393C3#1060274611yescharacteristic, complemented, Sylow
394C2—241no—
395C2—241no—
396C2#1174939311yescharacteristic
397C2#1174941611yescharacteristic
398C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC5×#5700C2
hypercenter#125D3×D5
hypocenterC3×C5#1661
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C3×#65354C2semidirect
3. #11747082C2semidirect
4. #11746904C2semidirect
5. #11746364C2semidirect
6. #11745847C2semidirect
7. #11745847C2semidirect
30. #65354D3semidirect
328. C3×C5#1661semidirect
377. C5#71392semidirect
393. C3#10602746semidirect

Maximal subgroups

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

subgroupindex
C5×#57002
C3×#653542
#117470822
#117469042
#117463642
#117458472
#106027463
#713925