Subgroups — C₅×D₃×#510 #14478374

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5195	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5179	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4918	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×Q₃₂	C₂	1	2	yes	maximal, complemented
8	C₅×#4915	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₅×#4909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#510	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	—	2	1	no	—
14	C₂×C₅×D₃×Q₈	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₅×#950	—	2	1	no	—
18	C₂×C₅×#216	—	2	1	no	—
19	C₅×#919	C₂²	1	1	yes	characteristic
20	C₅×D₃×Q₁₆	—	2	1	no	—
21	C₅×D₃×Q₁₆	—	2	1	no	—
22	C₅×D₃×Q₁₆	C₂²	1	2	yes	—
23	C₅×D₃×Q₁₆	C₂²	1	1	yes	characteristic
24	C₅×D₃×Q₁₆	C₂²	1	2	yes	complemented
25	C₅×#916	—	2	1	no	—
26	C₅×D₃×SD₁₆	—	2	1	no	—
27	C₅×#912	C₂²	1	1	yes	characteristic
28	C₅×D₃×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₅×#904	C₂²	1	1	yes	characteristic
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×Q₃₂	C₂²	1	2	yes	complemented
33	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
34	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₅×#829	C₂²	1	2	yes	complemented
36	C₅×#829	C₂²	1	2	yes	complemented
37	C₅×#828	C₂²	1	2	yes	complemented
38	C₅×#827	C₂²	1	2	yes	complemented
39	C₅×#812	C₂²	1	1	yes	characteristic, complemented
40	C₅×Dic₂₄	C₂²	1	2	yes	complemented
41	C₅×#800	C₂²	1	2	yes	complemented
42	C₅×#798	C₂²	1	2	yes	complemented
43	C₅×D₃×C₁₆	C₂²	1	2	yes	—
44	D₃×#510	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#135	—	3	1	no	—
46	C₂²×C₅×Q₁₆	—	3	1	no	—
47	C₅×#510	—	3	2	no	—
48	C₅×#510	—	3	2	no	—
49	C₅×#510	—	3	1	no	—
50	C₅×#510	—	3	1	no	—
51	C₅×#510	—	3	1	no	—
52	C₅×#510	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×Q₃₂	—	3	2	no	—
54	C₂×C₅×SD₃₂	—	3	2	no	—
55	C₂×C₅×M₃₂	—	3	1	no	—
56	C₃×C₅×#41	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₅×#239	—	2	1	no	—
59	C₅×D₃×Q₈	—	2	1	no	—
60	C₅×D₃×Q₈	—	2	2	no	—
61	C₅×D₃×Q₈	—	2	2	no	—
62	C₅×D₃×Q₈	—	4	1	no	—
63	C₅×D₃×Q₈	—	4	1	no	—
64	C₅×#237	—	2	1	no	—
65	C₅×#237	—	4	1	no	—
66	C₅×D₃×D₄	—	2	1	no	—
67	C₅×D₃×D₄	—	4	1	no	—
68	C₅×#235	—	2	1	no	—
69	C₅×#235	—	4	1	no	—
70	C₂×C₄×C₅×D₃	—	4	1	no	—
71	C₂×C₄×C₅×D₃	—	4	1	no	—
72	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
73	C₂×C₅×Dic₆	—	2	1	no	—
74	C₂×C₅×Dic₆	—	4	1	no	—
75	C₃×C₅×Q₁₆	—	2	1	no	—
76	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
77	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
78	C₃×C₅×SD₁₆	—	2	1	no	—
79	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₅×#216	—	2	1	no	—
82	C₅×#216	—	2	2	no	—
83	C₅×#216	—	2	2	no	—
84	C₅×#215	—	2	1	no	—
85	C₅×#214	—	2	1	no	—
86	C₅×#213	—	2	1	no	—
87	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
88	C₅×Dic₁₂	—	2	1	no	—
89	C₅×Dic₁₂	C₂³	1	1	yes	characteristic
90	C₅×Dic₁₂	C₂³	1	2	yes	—
91	C₅×D₂₄	C₂³	1	1	yes	characteristic
92	C₅×#204	—	2	1	no	—
93	C₅×D₃×C₈	D₄	1	1	yes	characteristic
94	C₅×D₃×C₈	D₄	1	1	yes	characteristic
95	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
96	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₁₆	C₂³	1	2	yes	—
98	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
99	D₃×#135	C₂×C₅	1	1	yes	characteristic
100	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#510	C₂×C₅	1	1	yes	characteristic, complemented
102	#5195	C₂×C₅	1	1	yes	characteristic, complemented
103	#5179	C₂×C₅	1	1	yes	characteristic, complemented
104	#4918	C₂×C₅	1	2	yes	complemented
105	D₃×Q₃₂	C₂×C₅	1	2	yes	complemented
106	#4915	C₂×C₅	1	2	yes	complemented
107	D₃×SD₃₂	C₂×C₅	1	2	yes	complemented
108	#4909	C₂×C₅	1	1	yes	characteristic, complemented
109	D₃×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₅×#41	—	6	1	no	—
111	C₂²×C₅×Q₈	—	6	1	no	—
112	C₅×#135	—	3	1	no	—
113	C₅×#135	—	3	1	no	—
114	C₅×#135	—	3	1	no	—
115	C₅×#135	—	6	1	no	—
116	C₅×#135	—	6	1	no	—
117	C₅×#135	C₂×D₃	1	1	yes	characteristic
118	C₂×C₅×Q₁₆	—	3	2	no	—
119	C₂×C₅×Q₁₆	—	3	1	no	—
120	C₂×C₅×Q₁₆	—	3	2	no	—
121	C₂×C₅×Q₁₆	—	3	1	no	—
122	C₂×C₅×Q₁₆	—	6	1	no	—
123	C₂×C₅×Q₁₆	—	6	1	no	—
124	C₂×C₅×Q₁₆	—	6	1	no	—
125	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
126	C₂×C₅×SD₁₆	—	6	1	no	—
127	C₂×C₅×D₈	—	3	1	no	—
128	C₂²×C₅×C₈	—	3	1	no	—
129	C₅×Q₃₂	—	3	2	no	—
130	C₅×Q₃₂	—	3	2	no	—
131	C₅×Q₃₂	—	3	2	no	—
132	C₅×Q₃₂	C₂×D₃	1	2	yes	complemented
133	C₅×SD₃₂	—	3	2	no	—
134	C₅×SD₃₂	—	3	2	no	—
135	C₅×SD₃₂	—	3	2	no	—
136	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
137	C₅×M₃₂	—	3	1	no	—
138	C₅×M₃₂	—	3	2	no	—
139	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
140	C₂×C₅×C₁₆	—	3	2	no	—
141	C₂×#510	—	3	1	no	Sylow
142	C₂²×C₅×D₃	—	4	1	no	—
143	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
144	C₃×C₅×Q₈	—	2	1	no	—
145	C₃×C₅×Q₈	—	2	2	no	—
146	C₃×C₅×Q₈	—	4	1	no	—
147	C₃×C₅×D₄	—	2	1	no	—
148	C₃×C₅×D₄	—	4	1	no	—
149	C₂×C₃×C₄×C₅	—	4	1	no	—
150	C₂×C₃×C₄×C₅	—	4	1	no	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₅×#67	—	4	1	no	—
153	C₅×#67	—	4	1	no	—
154	C₅×#67	—	4	1	no	—
155	C₂×C₅×Dic₃	—	4	1	no	—
156	C₂×C₅×Dic₃	—	4	1	no	—
157	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
158	C₅×D₁₂	—	2	1	no	—
159	C₅×D₁₂	—	4	1	no	—
160	C₄×C₅×D₃	—	4	1	no	—
161	C₄×C₅×D₃	—	4	2	no	—
162	C₄×C₅×D₃	—	4	2	no	—
163	C₄×C₅×D₃	—	4	1	no	—
164	C₄×C₅×D₃	—	4	1	no	—
165	C₄×C₅×D₃	D₈	1	1	yes	characteristic
166	C₄×C₅×D₃	D₈	1	1	yes	characteristic
167	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
168	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
169	C₅×Dic₆	—	2	1	no	—
170	C₅×Dic₆	—	2	2	no	—
171	C₅×Dic₆	—	4	1	no	—
172	C₅×Dic₆	—	4	2	no	—
173	C₅×Dic₆	—	4	2	no	—
174	C₅×Dic₆	—	4	1	no	—
175	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
176	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
177	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
178	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
179	D₃×#41	—	2	1	no	—
180	C₂×D₃×Q₈	—	2	1	no	—
181	C₃×#135	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
183	#950	—	2	1	no	—
184	C₂×#216	—	2	1	no	—
185	#919	C₂²×C₅	1	1	yes	characteristic
186	D₃×Q₁₆	—	2	1	no	—
187	D₃×Q₁₆	—	2	1	no	—
188	D₃×Q₁₆	C₂²×C₅	1	2	yes	—
189	D₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
190	D₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
191	#916	—	2	1	no	—
192	D₃×SD₁₆	—	2	1	no	—
193	#912	C₂²×C₅	1	1	yes	characteristic
194	D₃×D₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
196	#904	C₂²×C₅	1	1	yes	characteristic
197	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
198	C₃×Q₃₂	C₂²×C₅	1	2	yes	complemented
199	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
200	C₃×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
201	#829	C₂²×C₅	1	2	yes	complemented
202	#829	C₂²×C₅	1	2	yes	complemented
203	#828	C₂²×C₅	1	2	yes	complemented
204	#827	C₂²×C₅	1	2	yes	complemented
205	#812	C₂²×C₅	1	1	yes	characteristic, complemented
206	Dic₂₄	C₂²×C₅	1	2	yes	complemented
207	#800	C₂²×C₅	1	2	yes	complemented
208	#798	C₂²×C₅	1	2	yes	complemented
209	D₃×C₁₆	C₂²×C₅	1	2	yes	—
210	C₅×#41	—	2	1	no	—
211	C₅×#41	—	6	1	no	—
212	C₅×#41	—	6	1	no	—
213	C₅×#41	—	6	1	no	—
214	C₅×#41	—	12	1	no	—
215	C₅×#41	—	12	1	no	—
216	C₂×C₅×Q₈	—	2	1	no	—
217	C₂×C₅×Q₈	—	6	1	no	—
218	C₂×C₅×Q₈	—	6	2	no	—
219	C₂×C₅×Q₈	—	6	2	no	—
220	C₂×C₅×Q₈	—	6	1	no	—
221	C₂×C₅×Q₈	—	12	1	no	—
222	C₂×C₅×Q₈	—	12	1	no	—
223	C₂×C₅×Q₈	—	12	1	no	—
224	C₂×C₅×D₄	—	6	1	no	—
225	C₂×C₅×D₄	—	12	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	12	1	no	—
228	C₂²×C₄×C₅	—	12	1	no	—
229	C₅×Q₁₆	—	2	1	no	—
230	C₅×Q₁₆	—	3	2	no	—
231	C₅×Q₁₆	—	3	1	no	—
232	C₅×Q₁₆	—	6	2	no	—
233	C₅×Q₁₆	—	6	2	no	—
234	C₅×Q₁₆	—	6	1	no	—
235	C₅×Q₁₆	—	6	1	no	—
236	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
237	C₅×Q₁₆	C₂²×D₃	1	1	yes	characteristic
238	C₅×SD₁₆	—	2	1	no	—
239	C₅×SD₁₆	—	6	1	no	—
240	C₅×SD₁₆	—	6	1	no	—
241	C₅×SD₁₆	—	6	1	no	—
242	C₅×D₈	—	3	1	no	—
243	C₅×D₈	—	6	1	no	—
244	C₅×D₈	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₅×C₈	—	3	1	no	—
246	C₂×C₅×C₈	—	3	1	no	—
247	C₂×C₅×C₈	—	3	1	no	—
248	C₂×C₅×C₈	—	3	1	no	—
249	C₂×C₅×C₈	—	3	1	no	—
250	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
251	C₅×C₁₆	—	3	2	no	—
252	C₅×C₁₆	C₂²×D₃	1	2	yes	—
253	C₂×#135	—	3	1	no	—
254	C₂²×Q₁₆	—	3	1	no	—
255	#510	—	3	1	no	—
256	#510	—	3	1	no	—
257	#510	—	3	2	no	—
258	#510	—	3	2	no	—
259	#510	—	3	1	no	—
260	#510	C₅×D₃	1	1	yes	characteristic, direct product factor
261	C₂×Q₃₂	—	3	2	no	—
262	C₂×SD₃₂	—	3	2	no	—
263	C₂×M₃₂	—	3	1	no	—
264	C₂²×C₃×C₅	—	4	1	no	—
265	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
266	C₂×C₅×D₃	—	2	2	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₂×C₅×D₃	—	8	2	no	—
269	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
270	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
271	C₃×C₄×C₅	—	4	2	no	—
272	C₃×C₄×C₅	—	4	1	no	—
273	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₅×Dic₃	—	4	2	no	—
276	C₅×Dic₃	—	4	1	no	—
277	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
278	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
279	C₃×#41	—	2	1	no	—
280	C₂×C₃×Q₈	—	2	1	no	—
281	#239	—	2	1	no	—
282	D₃×Q₈	—	2	1	no	—
283	D₃×Q₈	—	2	2	no	—
284	D₃×Q₈	—	2	2	no	—
285	D₃×Q₈	—	4	1	no	—
286	D₃×Q₈	—	4	1	no	—
287	#237	—	2	1	no	—
288	#237	—	4	1	no	—
289	D₃×D₄	—	2	1	no	—
290	D₃×D₄	—	4	1	no	—
291	#235	—	2	1	no	—
292	#235	—	4	1	no	—
293	C₂×C₄×D₃	—	4	1	no	—
294	C₂×C₄×D₃	—	4	1	no	—
295	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
296	C₂×Dic₆	—	2	1	no	—
297	C₂×Dic₆	—	4	1	no	—
298	C₃×Q₁₆	—	2	1	no	—
299	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
300	C₃×Q₁₆	C₂³×C₅	1	1	yes	characteristic
301	C₃×SD₁₆	—	2	1	no	—
302	C₃×D₈	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
304	#216	—	2	1	no	—
305	#216	—	2	2	no	—
306	#216	—	2	2	no	—
307	#215	—	2	1	no	—
308	#214	—	2	1	no	—
309	#213	—	2	1	no	—
310	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
311	Dic₁₂	—	2	1	no	—
312	Dic₁₂	C₂³×C₅	1	2	yes	—
313	Dic₁₂	C₂³×C₅	1	1	yes	characteristic
314	D₂₄	C₂³×C₅	1	1	yes	characteristic
315	#204	—	2	1	no	—
316	D₃×C₈	C₅×D₄	1	1	yes	characteristic
317	D₃×C₈	C₅×D₄	1	1	yes	characteristic
318	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
319	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₃×C₁₆	C₂³×C₅	1	2	yes	—
321	C₃⋊C₁₆	C₂³×C₅	1	2	yes	—
322	C₂³×C₅	—	3	1	no	—
323	C₂³×C₅	—	12	1	no	—
324	C₅×Q₈	—	2	1	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	4	1	no	—
327	C₅×Q₈	—	6	1	no	—
328	C₅×Q₈	—	6	2	no	—
329	C₅×Q₈	—	12	2	no	—
330	C₅×Q₈	—	12	2	no	—
331	C₅×Q₈	—	12	1	no	—
332	C₅×Q₈	—	12	1	no	—
333	C₅×D₄	—	2	1	no	—
334	C₅×D₄	—	4	1	no	—
335	C₅×D₄	—	6	1	no	—
336	C₅×D₄	—	12	1	no	—
337	C₅×D₄	—	12	1	no	—
338	C₅×D₄	—	12	1	no	—
339	C₅×D₄	—	12	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	3	1	no	—
342	C₂×C₄×C₅	—	3	1	no	—
343	C₂×C₄×C₅	—	3	1	no	—
344	C₂×C₄×C₅	—	3	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	12	1	no	—
348	C₂×C₄×C₅	—	12	1	no	—
349	C₂×C₄×C₅	—	12	1	no	—
350	C₂×C₄×C₅	—	12	2	no	—
351	C₂×C₄×C₅	—	12	2	no	—
352	C₂×C₄×C₅	—	12	1	no	—
353	C₂×C₄×C₅	—	12	1	no	—
354	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
355	C₅×C₈	—	3	1	no	—
356	C₅×C₈	—	3	1	no	—
357	C₅×C₈	D₃×D₄	1	1	yes	characteristic
358	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
359	C₂×#41	—	6	1	no	—
360	C₂²×Q₈	—	6	1	no	—
361	#135	—	3	1	no	—
362	#135	—	3	1	no	—
363	#135	—	3	1	no	—
364	#135	—	6	1	no	—
365	#135	—	6	1	no	—
366	#135	C₂×C₅×D₃	1	1	yes	characteristic
367	C₂×Q₁₆	—	3	2	no	—
368	C₂×Q₁₆	—	3	2	no	—
369	C₂×Q₁₆	—	3	1	no	—
370	C₂×Q₁₆	—	3	1	no	—
371	C₂×Q₁₆	—	6	1	no	—
372	C₂×Q₁₆	—	6	1	no	—
373	C₂×Q₁₆	—	6	1	no	—
374	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
375	C₂×SD₁₆	—	6	1	no	—
376	C₂×D₈	—	3	1	no	—
377	C₂²×C₈	—	3	1	no	—
378	Q₃₂	—	3	2	no	—
379	Q₃₂	—	3	2	no	—
380	Q₃₂	—	3	2	no	—
381	Q₃₂	C₂×C₅×D₃	1	2	yes	complemented
382	SD₃₂	—	3	2	no	—
383	SD₃₂	—	3	2	no	—
384	SD₃₂	—	3	2	no	—
385	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
386	M₃₂	—	3	1	no	—
387	M₃₂	—	3	2	no	—
388	M₃₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
389	C₂×C₁₆	—	3	2	no	—
390	C₂×C₃×C₅	—	2	1	no	—
391	C₂×C₃×C₅	—	8	1	no	—
392	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
393	C₅×D₃	—	2	1	no	—
394	C₅×D₃	—	8	1	no	—
395	C₅×D₃	#510	1	2	yes	direct product factor
396	C₂²×D₃	—	4	1	no	—
397	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
398	C₃×Q₈	—	2	1	no	—
399	C₃×Q₈	—	2	2	no	—
400	C₃×Q₈	—	4	1	no	—
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	—	4	1	no	—
403	C₂×C₃×C₄	—	4	1	no	—
404	C₂×C₃×C₄	—	4	1	no	—
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	#67	—	4	1	no	—
407	#67	—	4	1	no	—
408	#67	—	4	1	no	—
409	C₂×Dic₃	—	4	1	no	—
410	C₂×Dic₃	—	4	1	no	—
411	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
412	D₁₂	—	2	1	no	—
413	D₁₂	—	4	1	no	—
414	C₄×D₃	—	4	1	no	—
415	C₄×D₃	—	4	2	no	—
416	C₄×D₃	—	4	2	no	—
417	C₄×D₃	—	4	1	no	—
418	C₄×D₃	—	4	1	no	—
419	C₄×D₃	C₅×D₈	1	1	yes	characteristic
420	C₄×D₃	C₅×D₈	1	1	yes	characteristic
421	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
422	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
423	Dic₆	—	2	1	no	—
424	Dic₆	—	2	2	no	—
425	Dic₆	—	4	1	no	—
426	Dic₆	—	4	2	no	—
427	Dic₆	—	4	2	no	—
428	Dic₆	—	4	1	no	—
429	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
430	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
431	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
432	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₅	—	3	1	no	—
434	C₂²×C₅	—	3	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	6	2	no	—
437	C₂²×C₅	—	12	1	no	—
438	C₂²×C₅	—	24	2	no	—
439	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
440	C₄×C₅	—	3	1	no	—
441	C₄×C₅	—	3	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	2	no	—
444	C₄×C₅	—	12	1	no	—
445	C₄×C₅	—	12	2	no	—
446	C₄×C₅	D₃×D₈	1	1	yes	characteristic
447	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
448	#41	—	2	1	no	—
449	#41	—	6	1	no	—
450	#41	—	6	1	no	—
451	#41	—	6	1	no	—
452	#41	—	12	1	no	—
453	#41	—	12	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	6	1	no	—
456	C₂×Q₈	—	6	2	no	—
457	C₂×Q₈	—	6	2	no	—
458	C₂×Q₈	—	6	1	no	—
459	C₂×Q₈	—	12	1	no	—
460	C₂×Q₈	—	12	1	no	—
461	C₂×Q₈	—	12	1	no	—
462	C₂×D₄	—	6	1	no	—
463	C₂×D₄	—	12	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	12	1	no	—
466	C₂²×C₄	—	12	1	no	—
467	Q₁₆	—	2	1	no	—
468	Q₁₆	—	3	2	no	—
469	Q₁₆	—	3	1	no	—
470	Q₁₆	—	6	2	no	—
471	Q₁₆	—	6	2	no	—
472	Q₁₆	—	6	1	no	—
473	Q₁₆	—	6	1	no	—
474	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
475	Q₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
476	SD₁₆	—	2	1	no	—
477	SD₁₆	—	6	1	no	—
478	SD₁₆	—	6	1	no	—
479	SD₁₆	—	6	1	no	—
480	D₈	—	3	1	no	—
481	D₈	—	6	1	no	—
482	D₈	C₂²×C₅×D₃	1	1	yes	characteristic
483	C₂×C₈	—	3	1	no	—
484	C₂×C₈	—	3	1	no	—
485	C₂×C₈	—	3	1	no	—
486	C₂×C₈	—	3	1	no	—
487	C₂×C₈	—	3	1	no	—
488	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
489	C₁₆	—	3	2	no	—
490	C₁₆	C₂²×C₅×D₃	1	2	yes	—
491	C₃×C₅	C₂×#510	1	1	yes	characteristic, complemented, Hall
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	4	1	no	—
496	C₂×D₃	—	8	2	no	—
497	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
498	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
499	C₃×C₄	—	4	2	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
502	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
503	Dic₃	—	4	2	no	—
504	Dic₃	—	4	1	no	—
505	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
506	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
507	C₂×C₅	—	2	1	no	—
508	C₂×C₅	—	3	2	no	—
509	C₂×C₅	—	6	1	no	—
510	C₂×C₅	—	8	1	no	—
511	C₂×C₅	—	24	1	no	—
512	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
513	C₂³	—	3	1	no	—
514	C₂³	—	12	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	6	1	no	—
519	Q₈	—	6	2	no	—
520	Q₈	—	12	2	no	—
521	Q₈	—	12	2	no	—
522	Q₈	—	12	1	no	—
523	Q₈	—	12	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	6	1	no	—
527	D₄	—	12	1	no	—
528	D₄	—	12	1	no	—
529	D₄	—	12	1	no	—
530	D₄	—	12	1	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	3	1	no	—
534	C₂×C₄	—	3	1	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	12	1	no	—
539	C₂×C₄	—	12	1	no	—
540	C₂×C₄	—	12	1	no	—
541	C₂×C₄	—	12	2	no	—
542	C₂×C₄	—	12	2	no	—
543	C₂×C₄	—	12	1	no	—
544	C₂×C₄	—	12	1	no	—
545	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
546	C₈	—	3	1	no	—
547	C₈	—	3	1	no	—
548	C₈	C₅×D₃×D₄	1	1	yes	characteristic
549	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	8	1	no	—
552	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
553	D₃	—	2	1	no	—
554	D₃	—	8	1	no	—
555	D₃	C₅×#510	1	2	yes	direct product factor
556	C₅	D₃×#510	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	3	1	no	—
558	C₂²	—	3	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	12	1	no	—
562	C₂²	—	24	2	no	—
563	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
564	C₄	—	3	1	no	—
565	C₄	—	3	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	12	1	no	—
569	C₄	—	12	2	no	—
570	C₄	C₅×D₃×D₈	1	1	yes	characteristic
571	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
572	C₃	C₂×C₅×#510	1	1	yes	characteristic, complemented, Sylow
573	C₂	—	2	1	no	—
574	C₂	—	3	2	no	—
575	C₂	—	6	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	24	1	no	—
578	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#510	C₂
socle	C₂×C₃×C₅	C₂²×D₈
prime radical	C₅×D₃×#135	C₂
hypercenter	C₅×#510	D₃
hypocenter	C₃	C₂×C₅×#510
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#510

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×Q₁₆	C₂	semidirect
3. C₃×C₅×#510	C₂	semidirect
4. C₅×#5195	C₂	semidirect
5. C₅×#5179	C₂	semidirect
6. C₅×#4918	C₂	semidirect
7. C₅×D₃×Q₃₂	C₂	semidirect
8. C₅×#4915	C₂	semidirect
9. C₅×D₃×SD₃₂	C₂	semidirect
10. C₅×#4909	C₂	semidirect
11. C₅×D₃×M₃₂	C₂	semidirect
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
24. C₅×D₃×Q₁₆	C₂²	semidirect
29. C₂×C₅×Dic₁₂	C₂²	semidirect
32. C₃×C₅×Q₃₂	C₂²	semidirect
33. C₃×C₅×SD₃₂	C₂²	semidirect
34. C₃×C₅×M₃₂	C₂²	semidirect
35. C₅×#829	C₂²	semidirect
36. C₅×#829	C₂²	semidirect
37. C₅×#828	C₂²	semidirect
38. C₅×#827	C₂²	semidirect
39. C₅×#812	C₂²	semidirect
40. C₅×Dic₂₄	C₂²	semidirect
41. C₅×#800	C₂²	semidirect
42. C₅×#798	C₂²	semidirect
44. D₃×#510	C₅	direct (N × H)
52. C₅×#510	D₃	direct (N × H)
100. C₂×D₃×Q₁₆	C₂×C₅	semidirect
101. C₃×#510	C₂×C₅	semidirect
102. #5195	C₂×C₅	semidirect
103. #5179	C₂×C₅	semidirect
104. #4918	C₂×C₅	semidirect
105. D₃×Q₃₂	C₂×C₅	semidirect
106. #4915	C₂×C₅	semidirect
107. D₃×SD₃₂	C₂×C₅	semidirect
108. #4909	C₂×C₅	semidirect
109. D₃×M₃₂	C₂×C₅	semidirect
125. C₂×C₅×Q₁₆	C₂×D₃	semidirect
132. C₅×Q₃₂	C₂×D₃	semidirect
136. C₅×SD₃₂	C₂×D₃	semidirect
139. C₅×M₃₂	C₂×D₃	semidirect
182. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
190. D₃×Q₁₆	C₂²×C₅	semidirect
195. C₂×Dic₁₂	C₂²×C₅	semidirect
198. C₃×Q₃₂	C₂²×C₅	semidirect
199. C₃×SD₃₂	C₂²×C₅	semidirect
200. C₃×M₃₂	C₂²×C₅	semidirect
201. #829	C₂²×C₅	semidirect
202. #829	C₂²×C₅	semidirect
203. #828	C₂²×C₅	semidirect
204. #827	C₂²×C₅	semidirect
205. #812	C₂²×C₅	semidirect
206. Dic₂₄	C₂²×C₅	semidirect
207. #800	C₂²×C₅	semidirect
208. #798	C₂²×C₅	semidirect
260. #510	C₅×D₃	direct (N × H)
374. C₂×Q₁₆	C₂×C₅×D₃	semidirect
381. Q₃₂	C₂×C₅×D₃	semidirect
385. SD₃₂	C₂×C₅×D₃	semidirect
388. M₃₂	C₂×C₅×D₃	semidirect
395. C₅×D₃	#510	direct (N × H)
491. C₃×C₅	C₂×#510	semidirect
555. D₃	C₅×#510	direct (N × H)
556. C₅	D₃×#510	direct (N × H)
572. C₃	C₂×C₅×#510	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#135	2
C₂×C₅×D₃×Q₁₆	2
C₃×C₅×#510	2
C₅×#5195	2
C₅×#5179	2
C₅×#4918	2
C₅×D₃×Q₃₂	2
C₅×#4915	2
C₅×D₃×SD₃₂	2
C₅×#4909	2
C₅×D₃×M₃₂	2
C₂×C₅×#510	3
D₃×#510	5

Subgroups — C5×D3×#510 #14478374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#510 #14478374