Finite Group Databasebeta

← #14289585

Subgroups — #14289585

Order 1920.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756322C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3#11751193C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746302C211yesmaximal, characteristic, complemented
8#10601938—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×#6718—22no—
12#91827—21no—
13#91819—21no—
14#91815—21no—
15#91781—21no—
16#91774—22no—
17C4×D60C2211yescharacteristic
18#91758C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22#91093—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71145—51nomaximal, Hall
27#65897—31no—
28C5×#476D311yescharacteristic, complemented
29#65381—31no—
30#65373—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×#1220—22no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×Dic30D412yes—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6719—22no—
48#6718—44no—
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15D411yescharacteristic
54C4×Dic15—22no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5563—51no—
58C3×#476D511yescharacteristic, complemented
59#5092—51no—
60#5084—51no—
61D4⋊(C3⋊C8)—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×D4C2×D311yescharacteristic
66C2×#689—62no—
67#4084—61no—
68#4076—61no—
69#4072—61no—
70#4038—61no—
71#4031—62no—
72C4×D20—31no—
73#4015—31no—
74C5×#106—21no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#102—21no—
77#3941—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1634—151noSylow
82C23×C3×C5—21no—
83C22×D15—21no—
84C3×C5×Q8—42no—
85C3×C5×D4—21no—
86C3×C5×D4—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—82no—
95C2×Dic15—21no—
96C2×Dic15—22no—
97D60—21no—
98D60—21no—
99C4×D15—41no—
100C4×D15—41no—
101Dic30—42no—
102C3×C5×C8—41no—
103C3⋊#168—22no—
104C3⋊#168—41no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×D4C2×D511yescharacteristic
107C2×#216—102no—
108#938—101no—
109#930—101no—
110#926—101no—
111#892—101no—
112#885—102no—
113C4×D12—51no—
114#869—51no—
115C3×#106—21no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#102—21no—
118#809—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C4×C3⋊C8—51no—
122C2×C5×Q8—21no—
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C2×C22⋊D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×Dic10—32no—
129C2×C5×C8—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—62no—
136#689—124no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4×Dic5—62no—
143C2×#168—61no—
144C2×#168—61no—
145#555—151no—
146#494—151no—
147#476—151no—
148#476D1511yescharacteristic, complemented
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×D15—41no—
157C2×D15—41no—
158C2×D15—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—81no—
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×C4×C5#13711yescharacteristic
166Dic15—41no—
167Dic15—42no—
168C2×C3×Q8—21no—
169C2×C3×D4C22⋊D511yescharacteristic
170C22×C3×C4—21no—
171C2×#67—102no—
172C2×D12—51no—
173C2×C4×D3—101no—
174C2×Dic6—52no—
175C2×C3×C8—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4C22⋊D511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C42C22×D511yescharacteristic
181#217—102no—
182#216—204no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—51no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4×Dic3—102no—
189C2×C3⋊C8—101no—
190C2×C3⋊C8—101no—
191C23×C5—21no—
192C22×D5—61no—
193C5×Q8—42no—
194C5×D4—21no—
195C5×D4—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—242no—
204C2×Dic5—61no—
205C2×Dic5—62no—
206D20—61no—
207D20—61no—
208C4×D5—121no—
209C4×D5—121no—
210Dic10—122no—
211C5×C8—41no—
212#168—62no—
213#168—121no—
214C2×Q16—302no—
215C4⋊Q8—151no—
216C4⋊Q8C2×D1511yescharacteristic
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—151no—
221C4×D4C2×D1511yescharacteristic
222#117—301no—
223#117—301no—
224#106—21no—
225#106—301no—
226C4⋊C8—151no—
227C4⋊C8C2×D1511yescharacteristic
228#102—21no—
229#102—301no—
230C4×C8—151no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235D15—81no—
236C23×C3—21no—
237C22×D3—101no—
238C3×Q8—42no—
239C3×D4—21no—
240C3×D4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—402no—
249C2×Dic3—101no—
250C2×Dic3—102no—
251D12—101no—
252D12—101no—
253C4×D3—201no—
254C4×D3—201no—
255Dic6—202no—
256C3×C8—41no—
257C3⋊C8—102no—
258C3⋊C8—201no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#93711yescharacteristic
263C2×D5—121no—
264C2×D5—121no—
265C2×D5—121no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—81no—
269C4×C5#91511yescharacteristic
270C4×C5#91611yescharacteristic
271C4×C5#94211yescharacteristic
272C4×C5#95011yescharacteristic
273Dic5—122no—
274Dic5—121no—
275C2×Q8—21no—
276C2×Q8—152no—
277C2×D4—151no—
278C2×D4—302no—
279C2×D4#122011yescharacteristic
280C22×C4—21no—
281C22×C4—301no—
282Q16—604no—
283C2×C8—21no—
284C2×C8—301no—
285C2×C8—301no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—151no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#122011yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—301no—
296C42—302no—
297C42C22×D1511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3#408311yescharacteristic
303C2×D3—201no—
304C2×D3—201no—
305C2×D3—201no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—81no—
309C3×C4#406111yescharacteristic
310C3×C4#406211yescharacteristic
311C3×C4#408811yescharacteristic
312C3×C4#409611yescharacteristic
313Dic3—201no—
314Dic3—202no—
315C2×C5—81no—
316C2×C5#504711yescharacteristic
317C2×C5#517311yescharacteristic
318C2×C5#519811yescharacteristic
319D5—241no—
320C23—21no—
321C23—301no—
322Q8—42no—
323Q8—602no—
324D4—21no—
325D4—21no—
326D4—301no—
327D4—301no—
328D4—1202no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—301no—
334C2×C4—302no—
335C2×C4—601no—
336C2×C4—601no—
337C2×C4D4×D1511yescharacteristic
338C2×C4D4×D1511yescharacteristic
339C2×C4C2×#122011yescharacteristic
340C8—41no—
341C8—302no—
342C8—601no—
343C2×C3—81no—
344C2×C3#6533611yescharacteristic
345C2×C3#6546211yescharacteristic
346C2×C3#6548711yescharacteristic
347D3—401no—
348C5#7114511yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—601no—
353C22—601no—
354C22—601no—
355C22#9182611yescharacteristic
356C4—21no—
357C4—41no—
358C4—81no—
359C4—602no—
360C4—601no—
361C4#9180411yescharacteristic
362C4#9180511yescharacteristic
363C4#9183111yescharacteristic
364C4#9183911yescharacteristic
365C3#1060193811yescharacteristic, complemented, Sylow
366C2—81no—
367C2—1201no—
368C2#1175114811yescharacteristic
369C2#1175127411yescharacteristic
370C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radical#11756322C2
hypercenter#476D15
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. #11751193C2semidirect
4. #11751185C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746304C2semidirect
7. #11746302C2semidirect
28. C5×#476D3semidirect
58. C3×#476D5semidirect
148. #476D15semidirect
298. C3×C5#1634semidirect
348. C5#71145semidirect
365. C3#10601938semidirect

Maximal subgroups

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

subgroupindex
#117563222
C3×C5×#4762
#117511932
#117511852
D4⋊(C3⋊#168)2
#117463042
#117463022
#106019383
#711455