Finite Group Databasebeta

← #14289444

Subgroups — #14289444

Order 1920.

512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5718C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic, complemented
3#11746959C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10602712—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C5×#127C2211yescharacteristic
11C5×#940—21no—
12C5×#939—22no—
13C5×#938—21no—
14C5×D4×Dic3—21no—
15C4×C5×D12C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#687—22no—
18C3×#4015C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C3×C4×#168C2211yescharacteristic
22#90989—21no—
23#90986—21no—
24#90972—21no—
25#90966—21no—
26#71271—51nomaximal, Hall
27C5×#550—31no—
28#65365D311yescharacteristic, complemented
29#65310—31no—
30#65297—31no—
31#64764—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×C5×#67—22no—
38C2×C5×#67—22no—
39C22×C5×Dic3—22no—
40C5×#237—42no—
41C5×#237—42no—
42C2×C5×D12D411yescharacteristic
43C2×C4×C5×D3—21no—
44C2×C5×Dic6D411yescharacteristic
45C2×C3×Dic10—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C5×#217—22no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C3×#687—44no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C2×C3×#168—21no—
59#5718D511yescharacteristic
60C3×#492—51no—
61#5091—51no—
62#5084—51no—
63#4544—51no—
64#4459—51no—
65#4456—51no—
66C2×C5×#41—61no—
67C5×#127—61no—
68C5×#127C2×D311yescharacteristic
69C5×#121—61no—
70C5×#121—62no—
71C4×C5×Q8—31no—
72C4×C5×D4—31no—
73C4×C5×D4—61no—
74C2×#687—22no—
75#4015C2×D311yescharacteristic
76#3967—61no—
77#3964—61no—
78#3940—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1631—151noSylow
84C23×C3×C5—22no—
85C22×C5×D3—21no—
86C3×C5×D4—42no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C5×#67—44no—
95C5×#67—82no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—44no—
100C5×D12—21no—
101C5×D12—21no—
102C4×C5×D3—41no—
103C4×C5×D3—41no—
104C5×Dic6—21no—
105C5×Dic6SD1612yescomplemented
106C2×C3×Dic5—41no—
107C3×Dic10—42no—
108C3⋊#168—41no—
109C3⋊#168—41no—
110C3×#168—22no—
111C2×#237—21no—
112C2×C3×SD16—102no—
113C3×C4⋊Q8—51no—
114C3×#127C2×D511yescharacteristic
115#940—21no—
116#939—22no—
117#938—21no—
118D4×Dic3—21no—
119C4×D12C2×D511yescharacteristic
120C4×Dic6C2×D511yescharacteristic
121C3×C4×C8—51no—
122#810—101no—
123#809—101no—
124#808—101no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)—51no—
128C5×#41—122no—
129C5×#41—122no—
130C2×C5×Q8—31no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—31no—
134C2×C5×D4—62no—
135C2×C5×D4—62no—
136C2×C5×D4#6712yes—
137C22×C4×C5—62no—
138C22×C4×C5—61no—
139C2×Dic10—21no—
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4—61no—
143C5×C22⋊C4—62no—
144C5×C22⋊C4—61no—
145C42×C5—61no—
146C42×C5C22×D311yescharacteristic
147#687—44no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150C2×#168—21no—
151C2×#168—61no—
152C2×#168—61no—
153#550—31no—
154#492—51no—
155#477—151no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5#12011yescharacteristic
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172C3×Dic5—81no—
173C5×Dic3—22no—
174C5×Dic3—41no—
175C5×Dic3—41no—
176C2×C3×Q8—101no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4C22⋊D512yes—
180C2×#67—22no—
181C2×#67—22no—
182C22×Dic3—22no—
183#237—42no—
184#237—42no—
185C2×D12C22⋊D511yescharacteristic
186C2×C4×D3—21no—
187C2×Dic6C22⋊D511yescharacteristic
188C3×SD16—204no—
189C2×C3×C8—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193#217—22no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3C22⋊D511yescharacteristic
196C4⋊Dic3C22⋊D511yescharacteristic
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—22no—
202C23×C5—61no—
203C5×Q8—32no—
204C5×Q8—61no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—61no—
211C5×D4—61no—
212C5×D4—124no—
213C5×D4—242no—
214C2×C4×C5—61no—
215C2×C4×C5—61no—
216C2×C4×C5—61no—
217C2×C4×C5—124no—
218C2×C4×C5—121no—
219C2×C4×C5—121no—
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×Dic5—41no—
224Dic10—42no—
225#168—22no—
226#168—121no—
227#168—121no—
228C2×#41—61no—
229C2×SD16—102no—
230C4⋊Q8—51no—
231#127—61no—
232#127D3×D511yescharacteristic
233#121—61no—
234#121—62no—
235C4×Q8—31no—
236C4×D4—31no—
237C4×D4—61no—
238#107—301no—
239#106—301no—
240C4⋊C8—151no—
241C4⋊C8—151no—
242#103—301no—
243#102—301no—
244C4×C8—51no—
245C2×C3×C5—82no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249C5×D3—81no—
250C23×C3—22no—
251C22×D3—21no—
252C3×Q8—202no—
253C3×D4—42no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C2×C3×C4—201no—
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—44no—
263#67—82no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—44no—
268D12—21no—
269D12—21no—
270C4×D3—41no—
271C4×D3—41no—
272Dic6—21no—
273Dic6#68712yescomplemented
274C3×C8—102no—
275C3⋊C8—201no—
276C3⋊C8—201no—
277C22×C5—42no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#93711yescharacteristic
284C4×C5—21no—
285C4×C5—62no—
286C4×C5—121no—
287C4×C5—121no—
288C4×C5D3×SD1611yescharacteristic
289C4×C5#91411yescharacteristic
290C4×C5#91511yescharacteristic
291C4×C5#91611yescharacteristic
292Dic5—81no—
293#41—122no—
294#41—122no—
295C2×Q8—31no—
296C2×Q8—101no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—31no—
300C2×D4—62no—
301C2×D4—62no—
302C2×D4#120112yes—
303C22×C4—62no—
304C22×C4—61no—
305SD16—204no—
306C2×C8—101no—
307C2×C8—301no—
308C2×C8—301no—
309C4⋊C4—31no—
310C4⋊C4—31no—
311C4⋊C4—61no—
312C4⋊C4—101no—
313C4⋊C4—101no—
314C22⋊C4—62no—
315C22⋊C4—61no—
316C42—61no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3#409911yescharacteristic
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—21no—
327C3×C4—401no—
328C3×C4#407811yescharacteristic
329C3×C4C2×#68711yescharacteristic
330C3×C4#409611yescharacteristic
331C3×C4#409711yescharacteristic
332Dic3—22no—
333Dic3—41no—
334Dic3—41no—
335C2×C5—82no—
336C2×C5—241no—
337C2×C5#507711yescharacteristic
338C2×C5#516911yescharacteristic
339C2×C5#517311yescharacteristic
340C23—22no—
341C23—61no—
342Q8—32no—
343Q8—61no—
344Q8—202no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—61no—
351D4—61no—
352D4—124no—
353D4—242no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—124no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—201no—
361C2×C4C2×#120111yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—102no—
365C8—601no—
366C8—601no—
367C2×C3—82no—
368C2×C3#6550711yescharacteristic
369C2×C3#6552811yescharacteristic
370C2×C3#6553011yescharacteristic
371D3—81no—
372C5#7127111yescharacteristic, complemented, Sylow
373C22—42no—
374C22—42no—
375C22—42no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22#9156811yescharacteristic
380C4—21no—
381C4—62no—
382C4—121no—
383C4—121no—
384C4—401no—
385C4D3×#68711yescharacteristic
386C4#9148611yescharacteristic
387C4#9149511yescharacteristic
388C4#9149611yescharacteristic
389C3#1060271211yescharacteristic, complemented, Sylow
390C2—82no—
391C2—241no—
392C2#1174905811yescharacteristic
393C2#1174905911yescharacteristic
394C2#1174914011yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC5×#5718C2
hypercenter#127D3×D5
hypocenterC3×C5#1631
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
2. C3×#65365C2semidirect
3. #11746959C2semidirect
4. #11746882C2semidirect
5. #11746365C2semidirect
6. #11745843C2semidirect
7. #11745837C2semidirect
28. #65365D3semidirect
105. C5×Dic6SD16semidirect
273. Dic6#687semidirect
318. C3×C5#1631semidirect
372. C5#71271semidirect
389. C3#10602712semidirect

Maximal subgroups

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

subgroupindex
C5×#57182
C3×#653652
#117469592
#117468822
#117463652
#117458432
#117458372
#106027123
#712715