Subgroups — C₃×D₅×#497 #14439013

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₅×SD₁₆	C₂	1	2	yes	maximal
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#124	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65479	C₂	1	2	yes	maximal, complemented
7	C₃×#65456	C₂	1	2	yes	maximal, complemented
8	C₃×#65375	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65349	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#497	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
15	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₃×#4093	C₂²	1	1	yes	characteristic
21	C₃×#4090	C₂²	1	2	yes	complemented
22	C₂×C₃×#689	C₂²	1	2	yes	complemented
23	C₂×C₃×#689	C₂²	1	2	yes	complemented
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₃×#4082	C₂²	1	1	yes	characteristic
26	C₂×C₃×#687	C₂²	1	2	yes	—
27	C₃×D₅×Q₁₆	—	2	8	no	—
28	C₃×D₅×SD₁₆	—	2	8	no	—
29	C₂×C₃×Dic₂₀	C₂²	1	2	yes	complemented
30	C₂×C₃×#677	C₂²	1	2	yes	—
31	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
32	C₃×D₅×C₄⋊C₄	—	2	2	no	—
33	C₃×#4034	—	2	2	no	—
34	C₃×#4031	—	2	2	no	—
35	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
36	C₃×#4021	C₂²	1	1	yes	characteristic
37	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
38	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3947	C₂²	1	2	yes	complemented
41	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×#497	—	5	1	no	maximal, Hall
43	C₂×D₅×Q₁₆	C₂×C₃	1	2	yes	complemented
44	C₂×D₅×SD₁₆	C₂×C₃	1	2	yes	—
45	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
46	D₅×#124	C₂×C₃	1	1	yes	characteristic
47	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
48	#65479	C₂×C₃	1	2	yes	complemented
49	#65456	C₂×C₃	1	2	yes	complemented
50	#65375	C₂×C₃	1	1	yes	characteristic, complemented
51	#65349	C₂×C₃	1	1	yes	characteristic, complemented
52	#65004	C₂×C₃	1	1	yes	characteristic, complemented
53	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×C₃×D₅	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
59	C₃×Q₈×D₅	—	2	4	no	—
60	C₃×Q₈×D₅	—	2	4	no	—
61	C₃×Q₈×D₅	—	2	4	no	—
62	C₃×D₄×D₅	—	2	4	no	—
63	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	—	2	1	no	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₁₀	—	2	1	no	—
69	C₂×C₃×Dic₁₀	—	2	2	no	—
70	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
71	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
72	C₃×C₅×Q₁₆	—	2	4	no	—
73	C₃×C₅×SD₁₆	—	2	4	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₂²⋊Dic₅	—	2	2	no	—
79	C₃×#689	—	2	4	no	—
80	C₃×#689	—	2	4	no	—
81	C₃×#688	—	2	4	no	—
82	C₃×#687	—	2	4	no	—
83	C₃×#685	—	2	2	no	—
84	C₃×#685	—	2	2	no	—
85	C₃×C₄⋊Dic₅	—	2	2	no	—
86	C₃×#683	—	2	4	no	—
87	C₃×C₄×Dic₅	D₄	1	2	yes	—
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	2	yes	—
90	C₃×Dic₂₀	—	2	4	no	—
91	C₃×#677	—	2	4	no	—
92	C₃×C₈×D₅	D₄	1	8	yes	—
93	C₂²×C₃×Q₁₆	—	5	2	no	—
94	C₂²×C₃×SD₁₆	—	5	2	no	—
95	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
96	C₂×C₃×#124	—	5	1	no	—
97	C₃×#497	—	5	2	no	—
98	C₃×#497	—	5	2	no	—
99	C₃×#497	—	5	1	no	—
100	C₃×#497	—	5	1	no	—
101	C₃×#497	—	5	1	no	—
102	C₃×#497	D₅	1	1	yes	characteristic, direct product factor
103	C₂×C₃×#97	—	5	1	no	—
104	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
105	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#124	C₂²×C₃	1	1	yes	characteristic
111	#4093	C₂²×C₃	1	1	yes	characteristic
112	#4090	C₂²×C₃	1	2	yes	complemented
113	C₂×#689	C₂²×C₃	1	2	yes	complemented
114	C₂×#689	C₂²×C₃	1	2	yes	complemented
115	C₂×#688	C₂²×C₃	1	2	yes	—
116	#4082	C₂²×C₃	1	1	yes	characteristic
117	C₂×#687	C₂²×C₃	1	2	yes	—
118	D₅×Q₁₆	—	2	8	no	—
119	D₅×SD₁₆	—	2	8	no	—
120	C₂×Dic₂₀	C₂²×C₃	1	2	yes	complemented
121	C₂×#677	C₂²×C₃	1	2	yes	—
122	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
123	D₅×C₄⋊C₄	—	2	2	no	—
124	#4034	—	2	2	no	—
125	#4031	—	2	2	no	—
126	D₅×C₂²⋊C₄	—	2	2	no	—
127	#4021	C₂²×C₃	1	1	yes	characteristic
128	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
129	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3947	C₂²×C₃	1	2	yes	complemented
132	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂×#497	—	5	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×D₅	—	2	1	no	—
136	C₂²×C₃×D₅	—	4	2	no	—
137	C₂²×C₃×D₅	—	4	4	no	—
138	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₃×C₂²⋊D₅	—	4	2	no	—
148	C₂×C₃×Dic₅	—	2	2	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
152	C₃×D₂₀	—	2	2	no	—
153	C₃×C₄×D₅	—	2	4	no	—
154	C₃×C₄×D₅	—	4	2	no	—
155	C₃×C₄×D₅	—	4	4	no	—
156	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
157	C₃×Dic₁₀	—	2	2	no	—
158	C₃×Dic₁₀	—	2	2	no	—
159	C₃×Dic₁₀	—	2	2	no	—
160	C₃×Dic₁₀	—	4	2	no	—
161	C₃×Dic₁₀	—	4	4	no	—
162	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
163	C₃×#168	C₂×D₄	1	4	yes	—
164	C₂²×C₃×Q₈	—	5	2	no	—
165	C₂²×C₃×Q₈	—	5	1	no	—
166	C₂²×C₃×D₄	—	5	1	no	—
167	C₂×C₃×Q₁₆	—	5	2	no	—
168	C₂×C₃×Q₁₆	—	5	2	no	—
169	C₂×C₃×Q₁₆	—	5	2	no	—
170	C₂×C₃×Q₁₆	—	10	8	no	—
171	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	complemented
172	C₂×C₃×SD₁₆	—	5	2	no	—
173	C₂×C₃×SD₁₆	—	5	2	no	—
174	C₂×C₃×SD₁₆	—	5	2	no	—
175	C₂×C₃×SD₁₆	—	10	8	no	—
176	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
177	C₂²×C₃×C₈	—	5	2	no	—
178	C₃×C₄⋊Q₈	—	5	2	no	—
179	C₃×C₄⋊Q₈	—	5	1	no	—
180	C₃×C₄⋊Q₈	—	10	2	no	—
181	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
182	C₃×#124	—	5	1	no	—
183	C₃×#124	—	5	1	no	—
184	C₃×#124	—	5	1	no	—
185	C₃×#124	—	10	2	no	—
186	C₃×#124	C₂×D₅	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	—	10	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
189	C₂×C₃×C₄²	—	5	1	no	—
190	C₃×#97	—	5	2	no	—
191	C₃×#97	—	5	1	no	—
192	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
193	C₂³×D₅	—	2	1	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
196	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₂²⋊D₅	—	2	1	no	—
198	Q₈×D₅	—	2	4	no	—
199	Q₈×D₅	—	2	4	no	—
200	Q₈×D₅	—	2	4	no	—
201	D₄×D₅	—	2	4	no	—
202	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₄×D₅	—	2	1	no	—
204	C₂×C₄×D₅	—	2	2	no	—
205	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
206	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×Dic₁₀	—	2	1	no	—
208	C₂×Dic₁₀	—	2	2	no	—
209	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
210	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
211	C₅×Q₁₆	—	2	4	no	—
212	C₅×SD₁₆	—	2	4	no	—
213	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₂²⋊Dic₅	—	2	2	no	—
218	#689	—	2	4	no	—
219	#689	—	2	4	no	—
220	#688	—	2	4	no	—
221	#687	—	2	4	no	—
222	#685	—	2	2	no	—
223	#685	—	2	2	no	—
224	C₄⋊Dic₅	—	2	2	no	—
225	#683	—	2	4	no	—
226	C₄×Dic₅	C₃×D₄	1	2	yes	—
227	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
228	C₂×#168	C₂³×C₃	1	2	yes	—
229	Dic₂₀	—	2	4	no	—
230	#677	—	2	4	no	—
231	C₈×D₅	C₃×D₄	1	8	yes	—
232	C₂²×Q₁₆	—	5	2	no	—
233	C₂²×SD₁₆	—	5	2	no	—
234	C₂×C₄⋊Q₈	—	5	1	no	—
235	C₂×#124	—	5	1	no	—
236	#497	—	5	2	no	—
237	#497	—	5	2	no	—
238	#497	—	5	1	no	—
239	#497	—	5	1	no	—
240	#497	—	5	1	no	—
241	#497	C₃×D₅	1	1	yes	characteristic, direct product factor
242	C₂×#97	—	5	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×D₅	—	4	1	no	—
247	C₂×C₃×D₅	—	4	2	no	—
248	C₂×C₃×D₅	—	8	4	no	—
249	C₂×C₃×D₅	#127	1	2	yes	—
250	C₂×C₃×D₅	#137	1	4	yes	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
255	C₃×Dic₅	—	2	2	no	—
256	C₃×Dic₅	—	4	2	no	—
257	C₃×Dic₅	—	4	1	no	—
258	C₃×Dic₅	#127	1	2	yes	—
259	C₂⁴×C₃	—	10	1	no	—
260	C₂×C₃×Q₈	—	5	1	no	—
261	C₂×C₃×Q₈	—	5	2	no	—
262	C₂×C₃×Q₈	—	10	1	no	—
263	C₂×C₃×Q₈	—	10	2	no	—
264	C₂×C₃×Q₈	—	10	4	no	—
265	C₂×C₃×Q₈	—	10	4	no	—
266	C₂×C₃×Q₈	—	10	4	no	—
267	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
269	C₂×C₃×D₄	—	5	1	no	—
270	C₂×C₃×D₄	—	10	4	no	—
271	C₂×C₃×D₄	—	10	1	no	—
272	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
273	C₂²×C₃×C₄	—	5	1	no	—
274	C₂²×C₃×C₄	—	5	2	no	—
275	C₂²×C₃×C₄	—	10	1	no	—
276	C₂²×C₃×C₄	—	10	2	no	—
277	C₃×Q₁₆	—	2	4	no	—
278	C₃×Q₁₆	—	10	4	no	—
279	C₃×Q₁₆	—	10	4	no	—
280	C₃×Q₁₆	—	10	4	no	—
281	C₃×SD₁₆	—	2	4	no	—
282	C₃×SD₁₆	—	10	4	no	—
283	C₃×SD₁₆	—	10	4	no	—
284	C₃×SD₁₆	—	10	4	no	—
285	C₂×C₃×C₈	—	5	2	no	—
286	C₂×C₃×C₈	—	5	8	no	—
287	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	10	4	no	—
290	C₃×C₄⋊C₄	—	10	2	no	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	10	2	no	—
293	C₃×C₂²⋊C₄	—	10	2	no	—
294	C₃×C₂²⋊C₄	—	10	2	no	—
295	C₃×C₄²	—	5	2	no	—
296	C₃×C₄²	—	5	1	no	—
297	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
298	C₂³×C₅	—	2	1	no	—
299	C₂²×D₅	—	2	1	no	—
300	C₂²×D₅	—	4	2	no	—
301	C₂²×D₅	—	4	4	no	—
302	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	2	2	no	—
306	C₅×D₄	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²⋊D₅	—	4	2	no	—
312	C₂×Dic₅	—	2	2	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
315	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
316	D₂₀	—	2	2	no	—
317	C₄×D₅	—	2	4	no	—
318	C₄×D₅	—	4	2	no	—
319	C₄×D₅	—	4	4	no	—
320	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
321	Dic₁₀	—	2	2	no	—
322	Dic₁₀	—	2	2	no	—
323	Dic₁₀	—	2	2	no	—
324	Dic₁₀	—	4	2	no	—
325	Dic₁₀	—	4	4	no	—
326	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
327	#168	C₂×C₃×D₄	1	4	yes	—
328	C₂²×Q₈	—	5	1	no	—
329	C₂²×Q₈	—	5	2	no	—
330	C₂²×D₄	—	5	1	no	—
331	C₂×Q₁₆	—	5	2	no	—
332	C₂×Q₁₆	—	5	2	no	—
333	C₂×Q₁₆	—	5	2	no	—
334	C₂×Q₁₆	—	10	8	no	—
335	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	complemented
336	C₂×SD₁₆	—	5	2	no	—
337	C₂×SD₁₆	—	5	2	no	—
338	C₂×SD₁₆	—	5	2	no	—
339	C₂×SD₁₆	—	10	8	no	—
340	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
341	C₂²×C₈	—	5	2	no	—
342	C₄⋊Q₈	—	5	2	no	—
343	C₄⋊Q₈	—	5	1	no	—
344	C₄⋊Q₈	—	10	2	no	—
345	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
346	#124	—	5	1	no	—
347	#124	—	5	1	no	—
348	#124	—	5	1	no	—
349	#124	—	10	2	no	—
350	#124	C₂×C₃×D₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	—	10	2	no	—
352	C₂×C₂²⋊C₄	—	10	2	no	—
353	C₂×C₄²	—	5	1	no	—
354	#97	—	5	2	no	—
355	#97	—	5	1	no	—
356	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
357	C₂×C₃×C₅	—	8	1	no	—
358	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
359	C₂×C₃×C₅	C₂×#137	1	2	yes	—
360	C₃×D₅	—	8	1	no	—
361	C₃×D₅	#497	1	4	yes	direct product factor
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	5	1	no	—
364	C₂³×C₃	—	10	1	no	—
365	C₂³×C₃	—	20	2	no	—
366	C₂³×C₃	—	20	4	no	—
367	C₃×Q₈	—	2	2	no	—
368	C₃×Q₈	—	2	2	no	—
369	C₃×Q₈	—	2	2	no	—
370	C₃×Q₈	—	10	2	no	—
371	C₃×Q₈	—	10	2	no	—
372	C₃×Q₈	—	10	2	no	—
373	C₃×Q₈	—	20	2	no	—
374	C₃×Q₈	—	20	4	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	10	2	no	—
377	C₃×D₄	—	20	2	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	5	1	no	—
381	C₂×C₃×C₄	—	5	4	no	—
382	C₂×C₃×C₄	—	5	2	no	—
383	C₂×C₃×C₄	—	10	4	no	—
384	C₂×C₃×C₄	—	10	1	no	—
385	C₂×C₃×C₄	—	10	2	no	—
386	C₂×C₃×C₄	—	20	2	no	—
387	C₂×C₃×C₄	—	20	4	no	—
388	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
389	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
390	C₃×C₈	—	5	4	no	—
391	C₃×C₈	D₄×D₅	1	4	yes	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
395	C₂×D₅	—	4	2	no	—
396	C₂×D₅	—	4	1	no	—
397	C₂×D₅	—	8	4	no	—
398	C₂×D₅	C₃×#127	1	2	yes	—
399	C₂×D₅	C₃×#137	1	4	yes	—
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
404	Dic₅	—	2	2	no	—
405	Dic₅	—	4	2	no	—
406	Dic₅	—	4	1	no	—
407	Dic₅	C₃×#127	1	2	yes	—
408	C₂⁴	—	10	1	no	—
409	C₂×Q₈	—	5	1	no	—
410	C₂×Q₈	—	5	2	no	—
411	C₂×Q₈	—	10	1	no	—
412	C₂×Q₈	—	10	2	no	—
413	C₂×Q₈	—	10	4	no	—
414	C₂×Q₈	—	10	4	no	—
415	C₂×Q₈	—	10	4	no	—
416	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
417	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
418	C₂×D₄	—	5	1	no	—
419	C₂×D₄	—	10	4	no	—
420	C₂×D₄	—	10	1	no	—
421	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂²×C₄	—	5	1	no	—
423	C₂²×C₄	—	5	2	no	—
424	C₂²×C₄	—	10	1	no	—
425	C₂²×C₄	—	10	2	no	—
426	Q₁₆	—	2	4	no	—
427	Q₁₆	—	10	4	no	—
428	Q₁₆	—	10	4	no	—
429	Q₁₆	—	10	4	no	—
430	SD₁₆	—	2	4	no	—
431	SD₁₆	—	10	4	no	—
432	SD₁₆	—	10	4	no	—
433	SD₁₆	—	10	4	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	5	8	no	—
436	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	10	4	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	10	2	no	—
442	C₂²⋊C₄	—	10	2	no	—
443	C₂²⋊C₄	—	10	2	no	—
444	C₄²	—	5	2	no	—
445	C₄²	—	5	1	no	—
446	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
447	C₃×C₅	C₂×#497	1	1	yes	characteristic, complemented, Hall
448	C₂²×C₃	—	4	1	no	—
449	C₂²×C₃	—	4	2	no	—
450	C₂²×C₃	—	5	2	no	—
451	C₂²×C₃	—	5	4	no	—
452	C₂²×C₃	—	20	1	no	—
453	C₂²×C₃	—	20	2	no	—
454	C₂²×C₃	—	40	4	no	—
455	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	4	1	no	—
458	C₃×C₄	—	4	2	no	—
459	C₃×C₄	—	5	2	no	—
460	C₃×C₄	—	10	2	no	—
461	C₃×C₄	—	20	1	no	—
462	C₃×C₄	—	20	2	no	—
463	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
464	C₂×C₅	—	8	1	no	—
465	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
466	C₂×C₅	C₂×C₃×#137	1	2	yes	—
467	D₅	—	8	1	no	—
468	D₅	C₃×#497	1	4	yes	direct product factor
469	C₂³	—	2	1	no	—
470	C₂³	—	5	1	no	—
471	C₂³	—	10	1	no	—
472	C₂³	—	20	2	no	—
473	C₂³	—	20	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	10	2	no	—
478	Q₈	—	10	2	no	—
479	Q₈	—	10	2	no	—
480	Q₈	—	20	2	no	—
481	Q₈	—	20	4	no	—
482	D₄	—	2	2	no	—
483	D₄	—	10	2	no	—
484	D₄	—	20	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	5	1	no	—
488	C₂×C₄	—	5	4	no	—
489	C₂×C₄	—	5	2	no	—
490	C₂×C₄	—	10	4	no	—
491	C₂×C₄	—	10	1	no	—
492	C₂×C₄	—	10	2	no	—
493	C₂×C₄	—	20	2	no	—
494	C₂×C₄	—	20	4	no	—
495	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
496	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
497	C₈	—	5	4	no	—
498	C₈	C₃×D₄×D₅	1	4	yes	—
499	C₂×C₃	—	5	4	no	—
500	C₂×C₃	—	8	1	no	—
501	C₂×C₃	—	40	1	no	—
502	C₂×C₃	D₅×#127	1	1	yes	characteristic
503	C₂×C₃	D₅×#137	1	2	yes	—
504	C₅	C₂×C₃×#497	1	1	yes	characteristic, complemented, Sylow
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	5	4	no	—
508	C₂²	—	5	2	no	—
509	C₂²	—	20	2	no	—
510	C₂²	—	20	1	no	—
511	C₂²	—	40	4	no	—
512	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	5	2	no	—
517	C₄	—	10	2	no	—
518	C₄	—	20	1	no	—
519	C₄	—	20	2	no	—
520	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
521	C₃	D₅×#497	1	1	yes	characteristic, direct product factor, Sylow
522	C₂	—	5	4	no	—
523	C₂	—	8	1	no	—
524	C₂	—	40	1	no	—
525	C₂	C₃×D₅×#127	1	1	yes	characteristic
526	C₂	C₃×D₅×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₄×D₅	C₂²
hypercenter	C₃×#497	D₅
hypocenter	C₅	C₂×C₃×#497
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×Q₁₆	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×#65479	C₂	semidirect
7. C₃×#65456	C₂	semidirect
8. C₃×#65375	C₂	semidirect
9. C₃×#65349	C₂	semidirect
10. C₃×#65004	C₂	semidirect
11. C₃×D₅×#97	C₂	semidirect
12. D₅×#497	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×#4090	C₂²	semidirect
22. C₂×C₃×#689	C₂²	semidirect
23. C₂×C₃×#689	C₂²	semidirect
29. C₂×C₃×Dic₂₀	C₂²	semidirect
38. C₃×#4015	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₃×#3947	C₂²	semidirect
41. C₃×#3935	C₂²	semidirect
43. C₂×D₅×Q₁₆	C₂×C₃	semidirect
45. D₅×C₄⋊Q₈	C₂×C₃	semidirect
47. C₅×#497	C₂×C₃	semidirect
48. #65479	C₂×C₃	semidirect
49. #65456	C₂×C₃	semidirect
50. #65375	C₂×C₃	semidirect
51. #65349	C₂×C₃	semidirect
52. #65004	C₂×C₃	semidirect
53. D₅×#97	C₂×C₃	semidirect
102. C₃×#497	D₅	direct (N × H)
107. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
109. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
112. #4090	C₂²×C₃	semidirect
113. C₂×#689	C₂²×C₃	semidirect
114. C₂×#689	C₂²×C₃	semidirect
120. C₂×Dic₂₀	C₂²×C₃	semidirect
129. #4015	C₂²×C₃	semidirect
130. C₅×#97	C₂²×C₃	semidirect
131. #3947	C₂²×C₃	semidirect
132. #3935	C₂²×C₃	semidirect
171. C₂×C₃×Q₁₆	C₂×D₅	semidirect
181. C₃×C₄⋊Q₈	C₂×D₅	semidirect
192. C₃×#97	C₂×D₅	semidirect
241. #497	C₃×D₅	direct (N × H)
335. C₂×Q₁₆	C₂×C₃×D₅	semidirect
345. C₄⋊Q₈	C₂×C₃×D₅	semidirect
356. #97	C₂×C₃×D₅	semidirect
361. C₃×D₅	#497	direct (N × H)
447. C₃×C₅	C₂×#497	semidirect
468. D₅	C₃×#497	direct (N × H)
504. C₅	C₂×C₃×#497	semidirect
521. C₃	D₅×#497	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×D₅×SD₁₆	2
C₃×D₅×C₄⋊Q₈	2
C₃×D₅×#124	2
C₃×C₅×#497	2
C₃×#65479	2
C₃×#65456	2
C₃×#65375	2
C₃×#65349	2
C₃×#65004	2
C₃×D₅×#97	2
D₅×#497	3
C₂×C₃×#497	5

Subgroups — C3×D5×#497 #14439013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#497 #14439013