Finite Group Databasebeta

← #14289606

Subgroups — #14289606

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5563C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3#11747103C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602721—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#938—21no—
11C5×#930—21no—
12C5×#926—21no—
13C5×#892—21no—
14C5×#885—22no—
15C4×C5×D12C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3964—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90986—21no—
25#90966—21no—
26#71145—51nomaximal, Hall
27C5×#555—31no—
28#65381—31no—
29#65297—31no—
30#65297D311yescharacteristic, complemented
31#64766—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6D412yes—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×#217—22no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C4×C5×Dic3—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6661—44no—
57#5563D511yescharacteristic
58C3×#476—51no—
59#5092—51no—
60#5084—51no—
61D4⋊(C3⋊C8)—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8—31no—
65C5×#124—62no—
66C5×#121—61no—
67C5×#121—61no—
68C4×C5×D4—31no—
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—61no—
71C5×#117—61no—
72C2×#689—62no—
73#4015C2×D311yescharacteristic
74#3964—21no—
75#3964—61no—
76#3940—21no—
77#3940—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1634—151noSylow
82C23×C3×C5—21no—
83C22×C5×D3—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C5×#67—82no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—22no—
95C5×D12—21no—
96C5×D12—21no—
97C4×C5×D3—41no—
98C4×C5×D3—41no—
99C5×Dic6—42no—
100C2×C3×Dic5—41no—
101C3×Dic10—42no—
102C3⋊#168—22no—
103C3⋊#168—41no—
104C3×#168—41no—
105C3×C4⋊Q8—51no—
106C3×C4×D4C2×D511yescharacteristic
107C2×#216—102no—
108#938—21no—
109#930—21no—
110#926—21no—
111#892—21no—
112#885—22no—
113C4×D12C2×D511yescharacteristic
114#869C2×D511yescharacteristic
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×#102—101no—
118#809—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C4×C3⋊C8—51no—
122C2×C5×Q8—32no—
123C2×C5×D4—31no—
124C2×C5×D4—62no—
125C2×C5×D4#6711yescharacteristic
126C22×C4×C5—21no—
127C22×C4×C5—61no—
128C2×Dic10—21no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—61no—
137C42×C5—62no—
138C42×C5C22×D311yescharacteristic
139#689—124no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C2×#168—21no—
143C2×#168—61no—
144C2×#168—61no—
145#555—31no—
146#494—151no—
147#476—51no—
148#476—151no—
149#333—151no—
150D4⋊C8—151no—
151D4⋊C8—151no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—81no—
166C5×Dic3—41no—
167C5×Dic3—42no—
168C2×C3×Q8—101no—
169C2×C3×D4C22⋊D511yescharacteristic
170C22×C3×C4—21no—
171C2×#67—22no—
172C2×D12C22⋊D511yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C22⋊D512yes—
175C2×C3×C8—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4C22⋊D511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C42C22×D511yescharacteristic
181#217—22no—
182#216—204no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3C22⋊D511yescharacteristic
188C4×Dic3—22no—
189C2×C3⋊C8—101no—
190C2×C3⋊C8—101no—
191C23×C5—21no—
192C23×C5—61no—
193C5×Q8—122no—
194C5×D4—21no—
195C5×D4—21no—
196C5×D4—61no—
197C5×D4—61no—
198C5×D4—242no—
199C2×C4×C5—21no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—61no—
203C2×C4×C5—62no—
204C2×C4×C5—121no—
205C2×C4×C5—121no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—41no—
210Dic10—42no—
211#168—41no—
212#168—62no—
213#168—121no—
214C2×Q16—302no—
215C4⋊Q8—31no—
216C4⋊Q8—51no—
217#124—62no—
218#121—61no—
219#121—61no—
220C4×D4—31no—
221C4×D4D3×D511yescharacteristic
222#117—61no—
223#117—61no—
224#106—101no—
225#106—301no—
226C4⋊C8—51no—
227C4⋊C8—151no—
228#102—101no—
229#102—301no—
230C4×C8—151no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C5×D3—81no—
236C23×C3—21no—
237C22×D3—21no—
238C3×Q8—202no—
239C3×D4—21no—
240C3×D4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—201no—
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—82no—
249C2×Dic3—21no—
250C2×Dic3—22no—
251D12—21no—
252D12—21no—
253C4×D3—41no—
254C4×D3—41no—
255Dic6—42no—
256C3×C8—201no—
257C3⋊C8—102no—
258C3⋊C8—201no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#93711yescharacteristic
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—122no—
269C4×C5—121no—
270C4×C5#91511yescharacteristic
271C4×C5#91611yescharacteristic
272C4×C5#94211yescharacteristic
273C4×C5#95011yescharacteristic
274Dic5—81no—
275C2×Q8—32no—
276C2×Q8—101no—
277C2×D4—31no—
278C2×D4—62no—
279C2×D4#120111yescharacteristic
280C22×C4—21no—
281C22×C4—61no—
282Q16—604no—
283C2×C8—101no—
284C2×C8—301no—
285C2×C8—301no—
286C4⋊C4—31no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4#120111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—62no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3#409911yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—401no—
309C3×C4#409611yescharacteristic
310C3×C4#409611yescharacteristic
311C3×C4#409711yescharacteristic
312C3×C4#409711yescharacteristic
313Dic3—41no—
314Dic3—42no—
315C2×C5—81no—
316C2×C5—241no—
317C2×C5#504711yescharacteristic
318C2×C5#517311yescharacteristic
319C2×C5#519811yescharacteristic
320C23—21no—
321C23—61no—
322Q8—122no—
323Q8—202no—
324D4—21no—
325D4—21no—
326D4—61no—
327D4—61no—
328D4—242no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—61no—
333C2×C4—62no—
334C2×C4—121no—
335C2×C4—121no—
336C2×C4—201no—
337C2×C4C2×#120111yescharacteristic
338C2×C4D3×C22⋊D511yescharacteristic
339C2×C4D3×C22⋊D511yescharacteristic
340C8—201no—
341C8—302no—
342C8—601no—
343C2×C3—81no—
344C2×C3#6552811yescharacteristic
345C2×C3#6552811yescharacteristic
346C2×C3#6553011yescharacteristic
347D3—81no—
348C5#7114511yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22#9156811yescharacteristic
356C4—21no—
357C4—41no—
358C4—122no—
359C4—121no—
360C4—401no—
361C4#9129711yescharacteristic
362C4#9130911yescharacteristic
363C4#9148611yescharacteristic
364C4#9149511yescharacteristic
365C3#1060272111yescharacteristic, complemented, Sylow
366C2—81no—
367C2—241no—
368C2#1174853811yescharacteristic
369C2#1174905911yescharacteristic
370C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65297C2semidirect
3. #11747103C2semidirect
4. #11746882C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745862C2semidirect
7. #11745836C2semidirect
30. #65297D3semidirect
298. C3×C5#1634semidirect
348. C5#71145semidirect
365. C3#10602721semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C3×#652972
#117471032
#117468822
D4⋊(C3⋊#168)2
#117458622
#117458362
#106027213
#711455