Subgroups — C₅×D₃×#509 #14478317

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 608 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, complemented
2	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5193	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4914	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×SD₃₂	C₂	1	2	yes	maximal, complemented
8	C₅×#4911	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×D₁₆	C₂	1	2	yes	maximal, complemented
10	C₅×#4908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#509	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	—	2	1	no	—
14	C₂×C₅×D₃×D₄	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₅×#950	—	2	1	no	—
18	C₂×C₅×#213	—	2	1	no	—
19	C₅×#919	C₂²	1	1	yes	characteristic, complemented
20	C₅×D₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₅×#916	—	2	1	no	—
22	C₅×D₃×SD₁₆	—	2	1	no	—
23	C₅×#912	C₂²	1	1	yes	characteristic, complemented
24	C₅×D₃×D₈	—	2	1	no	—
25	C₅×D₃×D₈	—	2	1	no	—
26	C₅×D₃×D₈	C₂²	1	2	yes	—
27	C₅×D₃×D₈	C₂²	1	2	yes	complemented
28	C₅×D₃×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#904	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
33	C₃×C₅×D₁₆	C₂²	1	2	yes	complemented
34	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
35	C₅×#828	C₂²	1	2	yes	complemented
36	C₅×#827	C₂²	1	2	yes	complemented
37	C₅×#826	C₂²	1	2	yes	complemented
38	C₅×#826	C₂²	1	2	yes	complemented
39	C₅×#812	C₂²	1	1	yes	characteristic, complemented
40	C₅×#800	C₂²	1	2	yes	complemented
41	C₅×D₄₈	C₂²	1	2	yes	complemented
42	C₅×#798	C₂²	1	2	yes	complemented
43	C₅×D₃×C₁₆	C₂²	1	2	yes	complemented
44	D₃×#509	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#135	—	3	1	no	—
46	C₂²×C₅×D₈	—	3	1	no	—
47	C₅×#509	—	3	2	no	—
48	C₅×#509	—	3	2	no	—
49	C₅×#509	—	3	1	no	—
50	C₅×#509	—	3	1	no	—
51	C₅×#509	—	3	1	no	—
52	C₅×#509	D₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×SD₃₂	—	3	2	no	—
54	C₂×C₅×D₁₆	—	3	2	no	—
55	C₂×C₅×M₃₂	—	3	1	no	—
56	C₂³×C₅×D₃	—	4	1	no	—
57	C₃×C₅×#41	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₅×#67	—	4	1	no	—
60	C₅×#239	—	2	1	no	—
61	C₅×D₃×Q₈	—	2	1	no	—
62	C₅×#237	—	2	1	no	—
63	C₅×#237	—	4	1	no	—
64	C₅×D₃×D₄	—	2	2	no	—
65	C₅×D₃×D₄	—	2	2	no	—
66	C₅×D₃×D₄	—	2	1	no	—
67	C₅×D₃×D₄	—	4	1	no	—
68	C₅×D₃×D₄	—	4	1	no	—
69	C₅×D₃×D₄	—	4	1	no	—
70	C₅×#235	—	2	1	no	—
71	C₅×#235	—	4	1	no	—
72	C₂×C₅×D₁₂	—	2	1	no	—
73	C₂×C₄×C₅×D₃	—	4	1	no	—
74	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
75	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic, complemented
76	C₃×C₅×SD₁₆	—	2	1	no	—
77	C₃×C₅×D₈	—	2	1	no	—
78	C₃×C₅×D₈	C₂³	1	2	yes	—
79	C₃×C₅×D₈	C₂³	1	1	yes	characteristic, complemented
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₅×#216	—	2	1	no	—
82	C₅×#215	—	2	1	no	—
83	C₅×#214	—	2	1	no	—
84	C₅×#213	—	2	2	no	—
85	C₅×#213	—	2	2	no	—
86	C₅×#213	—	2	1	no	—
87	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
88	C₅×Dic₁₂	C₂³	1	1	yes	characteristic, complemented
89	C₅×D₂₄	—	2	1	no	—
90	C₅×D₂₄	C₂³	1	2	yes	—
91	C₅×D₂₄	C₂³	1	1	yes	characteristic, complemented
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	complemented
98	C₅×C₃⋊C₁₆	C₂³	1	2	yes	complemented
99	D₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#509	C₂×C₅	1	1	yes	characteristic, complemented
102	#5193	C₂×C₅	1	1	yes	characteristic, complemented
103	#5147	C₂×C₅	1	1	yes	characteristic, complemented
104	#4914	C₂×C₅	1	2	yes	complemented
105	D₃×SD₃₂	C₂×C₅	1	2	yes	complemented
106	#4911	C₂×C₅	1	2	yes	complemented
107	D₃×D₁₆	C₂×C₅	1	2	yes	complemented
108	#4908	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×D₄	—	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, complemented
118	C₂×C₅×Q₁₆	—	3	1	no	—
119	C₂×C₅×SD₁₆	—	6	1	no	—
120	C₂×C₅×D₈	—	3	2	no	—
121	C₂×C₅×D₈	—	3	2	no	—
122	C₂×C₅×D₈	—	3	1	no	—
123	C₂×C₅×D₈	—	3	1	no	—
124	C₂×C₅×D₈	—	6	1	no	—
125	C₂×C₅×D₈	—	6	1	no	—
126	C₂×C₅×D₈	—	6	1	no	—
127	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂²×C₅×C₈	—	3	1	no	—
129	C₅×SD₃₂	—	3	2	no	—
130	C₅×SD₃₂	—	3	2	no	—
131	C₅×SD₃₂	—	3	2	no	—
132	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
133	C₅×D₁₆	—	3	2	no	—
134	C₅×D₁₆	—	3	2	no	—
135	C₅×D₁₆	—	3	2	no	—
136	C₅×D₁₆	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×#509	—	3	1	no	Sylow
142	C₂³×C₃×C₅	—	4	1	no	—
143	C₂²×C₅×D₃	—	4	1	no	—
144	C₂²×C₅×D₃	—	4	1	no	—
145	C₂²×C₅×D₃	—	4	2	no	—
146	C₂²×C₅×D₃	—	4	2	no	—
147	C₂²×C₅×D₃	—	8	4	no	—
148	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
149	C₃×C₅×Q₈	—	2	1	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	2	1	no	—
152	C₃×C₅×D₄	—	4	1	no	—
153	C₃×C₅×D₄	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	1	no	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₅×#67	—	4	1	no	—
157	C₅×#67	—	4	1	no	—
158	C₅×#67	—	4	1	no	—
159	C₅×#67	—	4	2	no	—
160	C₅×#67	—	4	2	no	—
161	C₂×C₅×Dic₃	—	4	1	no	—
162	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
163	C₅×D₁₂	—	2	1	no	—
164	C₅×D₁₂	—	2	2	no	—
165	C₅×D₁₂	—	4	1	no	—
166	C₅×D₁₂	—	4	1	no	—
167	C₄×C₅×D₃	—	4	1	no	—
168	C₄×C₅×D₃	—	4	1	no	—
169	C₄×C₅×D₃	—	4	1	no	—
170	C₄×C₅×D₃	D₈	1	1	yes	characteristic
171	C₄×C₅×D₃	D₈	1	1	yes	characteristic
172	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
173	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
174	C₅×Dic₆	—	2	1	no	—
175	C₅×Dic₆	—	4	1	no	—
176	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
177	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
178	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
179	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
180	D₃×#41	—	2	1	no	—
181	C₂×D₃×D₄	—	2	1	no	—
182	C₃×#135	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
184	#950	—	2	1	no	—
185	C₂×#213	—	2	1	no	—
186	#919	C₂²×C₅	1	1	yes	characteristic, complemented
187	D₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
188	#916	—	2	1	no	—
189	D₃×SD₁₆	—	2	1	no	—
190	#912	C₂²×C₅	1	1	yes	characteristic, complemented
191	D₃×D₈	—	2	1	no	—
192	D₃×D₈	—	2	1	no	—
193	D₃×D₈	C₂²×C₅	1	2	yes	—
194	D₃×D₈	C₂²×C₅	1	2	yes	complemented
195	D₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
196	#904	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
198	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
199	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
200	C₃×D₁₆	C₂²×C₅	1	2	yes	complemented
201	C₃×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
202	#828	C₂²×C₅	1	2	yes	complemented
203	#827	C₂²×C₅	1	2	yes	complemented
204	#826	C₂²×C₅	1	2	yes	complemented
205	#826	C₂²×C₅	1	2	yes	complemented
206	#812	C₂²×C₅	1	1	yes	characteristic, complemented
207	#800	C₂²×C₅	1	2	yes	complemented
208	D₄₈	C₂²×C₅	1	2	yes	complemented
209	#798	C₂²×C₅	1	2	yes	complemented
210	D₃×C₁₆	C₂²×C₅	1	2	yes	complemented
211	C₂⁴×C₅	—	12	1	no	—
212	C₅×#41	—	2	1	no	—
213	C₅×#41	—	6	1	no	—
214	C₅×#41	—	6	1	no	—
215	C₅×#41	—	6	1	no	—
216	C₅×#41	—	12	1	no	—
217	C₅×#41	—	12	1	no	—
218	C₂×C₅×Q₈	—	6	1	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	—	6	2	no	—
221	C₂×C₅×D₄	—	6	2	no	—
222	C₂×C₅×D₄	—	6	1	no	—
223	C₂×C₅×D₄	—	6	1	no	—
224	C₂×C₅×D₄	—	12	1	no	—
225	C₂×C₅×D₄	—	12	1	no	—
226	C₂×C₅×D₄	—	12	1	no	—
227	C₂×C₅×D₄	—	12	1	no	—
228	C₂²×C₄×C₅	—	3	1	no	—
229	C₂²×C₄×C₅	—	12	1	no	—
230	C₅×Q₁₆	—	3	1	no	—
231	C₅×Q₁₆	—	6	1	no	—
232	C₅×Q₁₆	C₂²×D₃	1	1	yes	characteristic, complemented
233	C₅×SD₁₆	—	2	1	no	—
234	C₅×SD₁₆	—	6	1	no	—
235	C₅×SD₁₆	—	6	1	no	—
236	C₅×SD₁₆	—	6	1	no	—
237	C₅×D₈	—	2	1	no	—
238	C₅×D₈	—	3	2	no	—
239	C₅×D₈	—	3	1	no	—
240	C₅×D₈	—	6	2	no	—
241	C₅×D₈	—	6	2	no	—
242	C₅×D₈	—	6	1	no	—
243	C₅×D₈	—	6	1	no	—
244	C₅×D₈	C₂²×D₃	1	2	yes	—
245	C₅×D₈	C₂²×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
251	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
252	C₅×C₁₆	—	3	2	no	—
253	C₅×C₁₆	C₂²×D₃	1	2	yes	complemented
254	C₂×#135	—	3	1	no	—
255	C₂²×D₈	—	3	1	no	—
256	#509	—	3	1	no	—
257	#509	—	3	1	no	—
258	#509	—	3	2	no	—
259	#509	—	3	2	no	—
260	#509	—	3	1	no	—
261	#509	C₅×D₃	1	1	yes	characteristic, direct product factor
262	C₂×SD₃₂	—	3	2	no	—
263	C₂×D₁₆	—	3	2	no	—
264	C₂×M₃₂	—	3	1	no	—
265	C₂²×C₃×C₅	—	4	1	no	—
266	C₂²×C₃×C₅	—	4	2	no	—
267	C₂²×C₃×C₅	—	8	2	no	—
268	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
269	C₂×C₅×D₃	—	2	2	no	—
270	C₂×C₅×D₃	—	4	1	no	—
271	C₂×C₅×D₃	—	4	2	no	—
272	C₂×C₅×D₃	—	8	4	no	—
273	C₂×C₅×D₃	—	8	2	no	—
274	C₂×C₅×D₃	—	8	2	no	—
275	C₂×C₅×D₃	—	8	4	no	—
276	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
277	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
278	C₃×C₄×C₅	—	4	1	no	—
279	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₅×Dic₃	—	4	1	no	—
282	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
283	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
284	C₂³×D₃	—	4	1	no	—
285	C₃×#41	—	2	1	no	—
286	C₂×C₃×D₄	—	2	1	no	—
287	C₂×#67	—	4	1	no	—
288	#239	—	2	1	no	—
289	D₃×Q₈	—	2	1	no	—
290	#237	—	2	1	no	—
291	#237	—	4	1	no	—
292	D₃×D₄	—	2	2	no	—
293	D₃×D₄	—	2	2	no	—
294	D₃×D₄	—	2	1	no	—
295	D₃×D₄	—	4	1	no	—
296	D₃×D₄	—	4	1	no	—
297	D₃×D₄	—	4	1	no	—
298	#235	—	2	1	no	—
299	#235	—	4	1	no	—
300	C₂×D₁₂	—	2	1	no	—
301	C₂×C₄×D₃	—	4	1	no	—
302	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
303	C₃×Q₁₆	C₂³×C₅	1	1	yes	characteristic, complemented
304	C₃×SD₁₆	—	2	1	no	—
305	C₃×D₈	—	2	1	no	—
306	C₃×D₈	C₂³×C₅	1	2	yes	—
307	C₃×D₈	C₂³×C₅	1	1	yes	characteristic, complemented
308	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
309	#216	—	2	1	no	—
310	#215	—	2	1	no	—
311	#214	—	2	1	no	—
312	#213	—	2	2	no	—
313	#213	—	2	2	no	—
314	#213	—	2	1	no	—
315	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
316	Dic₁₂	C₂³×C₅	1	1	yes	characteristic, complemented
317	D₂₄	—	2	1	no	—
318	D₂₄	C₂³×C₅	1	2	yes	—
319	D₂₄	C₂³×C₅	1	1	yes	characteristic, complemented
320	#204	—	2	1	no	—
321	D₃×C₈	C₅×D₄	1	1	yes	characteristic
322	D₃×C₈	C₅×D₄	1	1	yes	characteristic
323	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
324	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
325	C₃×C₁₆	C₂³×C₅	1	2	yes	complemented
326	C₃⋊C₁₆	C₂³×C₅	1	2	yes	complemented
327	C₂³×C₅	—	3	1	no	—
328	C₂³×C₅	—	4	1	no	—
329	C₂³×C₅	—	12	1	no	—
330	C₂³×C₅	—	12	2	no	—
331	C₂³×C₅	—	12	2	no	—
332	C₂³×C₅	—	12	1	no	—
333	C₂³×C₅	—	24	4	no	—
334	C₅×Q₈	—	2	1	no	—
335	C₅×Q₈	—	6	1	no	—
336	C₅×Q₈	—	12	1	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	4	1	no	—
340	C₅×D₄	—	4	1	no	—
341	C₅×D₄	—	6	2	no	—
342	C₅×D₄	—	6	1	no	—
343	C₅×D₄	—	12	2	no	—
344	C₅×D₄	—	12	2	no	—
345	C₅×D₄	—	12	1	no	—
346	C₅×D₄	—	12	1	no	—
347	C₅×D₄	—	12	1	no	—
348	C₅×D₄	—	12	1	no	—
349	C₅×D₄	—	12	1	no	—
350	C₂×C₄×C₅	—	3	1	no	—
351	C₂×C₄×C₅	—	3	1	no	—
352	C₂×C₄×C₅	—	3	1	no	—
353	C₂×C₄×C₅	—	3	1	no	—
354	C₂×C₄×C₅	—	3	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	12	1	no	—
357	C₂×C₄×C₅	—	12	1	no	—
358	C₂×C₄×C₅	—	12	1	no	—
359	C₂×C₄×C₅	—	12	1	no	—
360	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
361	C₅×C₈	—	3	1	no	—
362	C₅×C₈	—	3	1	no	—
363	C₅×C₈	D₃×D₄	1	1	yes	characteristic
364	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
365	C₂×#41	—	6	1	no	—
366	C₂²×D₄	—	6	1	no	—
367	#135	—	3	1	no	—
368	#135	—	3	1	no	—
369	#135	—	3	1	no	—
370	#135	—	6	1	no	—
371	#135	—	6	1	no	—
372	#135	C₂×C₅×D₃	1	1	yes	characteristic, complemented
373	C₂×Q₁₆	—	3	1	no	—
374	C₂×SD₁₆	—	6	1	no	—
375	C₂×D₈	—	3	2	no	—
376	C₂×D₈	—	3	2	no	—
377	C₂×D₈	—	3	1	no	—
378	C₂×D₈	—	3	1	no	—
379	C₂×D₈	—	6	1	no	—
380	C₂×D₈	—	6	1	no	—
381	C₂×D₈	—	6	1	no	—
382	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
383	C₂²×C₈	—	3	1	no	—
384	SD₃₂	—	3	2	no	—
385	SD₃₂	—	3	2	no	—
386	SD₃₂	—	3	2	no	—
387	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
388	D₁₆	—	3	2	no	—
389	D₁₆	—	3	2	no	—
390	D₁₆	—	3	2	no	—
391	D₁₆	C₂×C₅×D₃	1	2	yes	complemented
392	M₃₂	—	3	1	no	—
393	M₃₂	—	3	2	no	—
394	M₃₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
395	C₂×C₁₆	—	3	2	no	—
396	C₂×C₃×C₅	—	2	1	no	—
397	C₂×C₃×C₅	—	8	2	no	—
398	C₂×C₃×C₅	—	8	1	no	—
399	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
400	C₅×D₃	—	2	1	no	—
401	C₅×D₃	—	8	1	no	—
402	C₅×D₃	—	8	2	no	—
403	C₅×D₃	#509	1	2	yes	direct product factor
404	C₂³×C₃	—	4	1	no	—
405	C₂²×D₃	—	4	1	no	—
406	C₂²×D₃	—	4	1	no	—
407	C₂²×D₃	—	4	2	no	—
408	C₂²×D₃	—	4	2	no	—
409	C₂²×D₃	—	8	4	no	—
410	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
411	C₃×Q₈	—	2	1	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	2	1	no	—
414	C₃×D₄	—	4	1	no	—
415	C₃×D₄	—	4	1	no	—
416	C₂×C₃×C₄	—	4	1	no	—
417	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	#67	—	4	1	no	—
419	#67	—	4	1	no	—
420	#67	—	4	1	no	—
421	#67	—	4	2	no	—
422	#67	—	4	2	no	—
423	C₂×Dic₃	—	4	1	no	—
424	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
425	D₁₂	—	2	1	no	—
426	D₁₂	—	2	2	no	—
427	D₁₂	—	4	1	no	—
428	D₁₂	—	4	1	no	—
429	C₄×D₃	—	4	1	no	—
430	C₄×D₃	—	4	1	no	—
431	C₄×D₃	—	4	1	no	—
432	C₄×D₃	C₅×D₈	1	1	yes	characteristic
433	C₄×D₃	C₅×D₈	1	1	yes	characteristic
434	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
435	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
436	Dic₆	—	2	1	no	—
437	Dic₆	—	4	1	no	—
438	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
439	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
440	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
441	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂²×C₅	—	3	1	no	—
443	C₂²×C₅	—	3	1	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	6	2	no	—
447	C₂²×C₅	—	8	2	no	—
448	C₂²×C₅	—	12	1	no	—
449	C₂²×C₅	—	12	2	no	—
450	C₂²×C₅	—	24	2	no	—
451	C₂²×C₅	—	24	2	no	—
452	C₂²×C₅	—	24	4	no	—
453	C₂²×C₅	—	24	4	no	—
454	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
455	C₄×C₅	—	3	1	no	—
456	C₄×C₅	—	3	1	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	12	1	no	—
459	C₄×C₅	D₃×D₈	1	1	yes	characteristic
460	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
461	C₂⁴	—	12	1	no	—
462	#41	—	2	1	no	—
463	#41	—	6	1	no	—
464	#41	—	6	1	no	—
465	#41	—	6	1	no	—
466	#41	—	12	1	no	—
467	#41	—	12	1	no	—
468	C₂×Q₈	—	6	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	6	2	no	—
471	C₂×D₄	—	6	2	no	—
472	C₂×D₄	—	6	1	no	—
473	C₂×D₄	—	6	1	no	—
474	C₂×D₄	—	12	1	no	—
475	C₂×D₄	—	12	1	no	—
476	C₂×D₄	—	12	1	no	—
477	C₂×D₄	—	12	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	12	1	no	—
480	Q₁₆	—	3	1	no	—
481	Q₁₆	—	6	1	no	—
482	Q₁₆	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
483	SD₁₆	—	2	1	no	—
484	SD₁₆	—	6	1	no	—
485	SD₁₆	—	6	1	no	—
486	SD₁₆	—	6	1	no	—
487	D₈	—	2	1	no	—
488	D₈	—	3	1	no	—
489	D₈	—	3	2	no	—
490	D₈	—	6	2	no	—
491	D₈	—	6	2	no	—
492	D₈	—	6	1	no	—
493	D₈	—	6	1	no	—
494	D₈	C₂²×C₅×D₃	1	2	yes	—
495	D₈	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
496	C₂×C₈	—	3	1	no	—
497	C₂×C₈	—	3	1	no	—
498	C₂×C₈	—	3	1	no	—
499	C₂×C₈	—	3	1	no	—
500	C₂×C₈	—	3	1	no	—
501	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
502	C₁₆	—	3	2	no	—
503	C₁₆	C₂²×C₅×D₃	1	2	yes	complemented
504	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	8	2	no	—
508	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	4	1	no	—
511	C₂×D₃	—	4	2	no	—
512	C₂×D₃	—	8	4	no	—
513	C₂×D₃	—	8	2	no	—
514	C₂×D₃	—	8	2	no	—
515	C₂×D₃	—	8	4	no	—
516	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
517	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
520	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
521	Dic₃	—	4	1	no	—
522	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
523	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
524	C₂×C₅	—	2	1	no	—
525	C₂×C₅	—	3	2	no	—
526	C₂×C₅	—	6	1	no	—
527	C₂×C₅	—	8	2	no	—
528	C₂×C₅	—	8	1	no	—
529	C₂×C₅	—	24	2	no	—
530	C₂×C₅	—	24	1	no	—
531	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
532	C₂³	—	3	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	12	1	no	—
535	C₂³	—	12	2	no	—
536	C₂³	—	12	2	no	—
537	C₂³	—	12	1	no	—
538	C₂³	—	24	4	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	6	1	no	—
541	Q₈	—	12	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	6	2	no	—
547	D₄	—	6	1	no	—
548	D₄	—	12	2	no	—
549	D₄	—	12	2	no	—
550	D₄	—	12	1	no	—
551	D₄	—	12	1	no	—
552	D₄	—	12	1	no	—
553	D₄	—	12	1	no	—
554	D₄	—	12	1	no	—
555	C₂×C₄	—	3	1	no	—
556	C₂×C₄	—	3	1	no	—
557	C₂×C₄	—	3	1	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	12	1	no	—
562	C₂×C₄	—	12	1	no	—
563	C₂×C₄	—	12	1	no	—
564	C₂×C₄	—	12	1	no	—
565	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
566	C₈	—	3	1	no	—
567	C₈	—	3	1	no	—
568	C₈	C₅×D₃×D₄	1	1	yes	characteristic
569	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	8	2	no	—
572	C₂×C₃	—	8	1	no	—
573	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
574	D₃	—	2	1	no	—
575	D₃	—	8	2	no	—
576	D₃	—	8	1	no	—
577	D₃	C₅×#509	1	2	yes	direct product factor
578	C₅	D₃×#509	1	1	yes	characteristic, direct product factor, Sylow
579	C₂²	—	3	1	no	—
580	C₂²	—	3	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	6	2	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	12	1	no	—
586	C₂²	—	12	2	no	—
587	C₂²	—	24	2	no	—
588	C₂²	—	24	4	no	—
589	C₂²	—	24	2	no	—
590	C₂²	—	24	4	no	—
591	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
592	C₄	—	3	1	no	—
593	C₄	—	3	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	12	1	no	—
596	C₄	C₅×D₃×D₈	1	1	yes	characteristic
597	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
598	C₃	C₂×C₅×#509	1	1	yes	characteristic, complemented, Sylow
599	C₂	—	2	1	no	—
600	C₂	—	3	2	no	—
601	C₂	—	6	1	no	—
602	C₂	—	8	2	no	—
603	C₂	—	8	1	no	—
604	C₂	—	24	2	no	—
605	C₂	—	24	1	no	—
606	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×#509	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#509	D₃
hypocenter	C₃	C₂×C₅×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#509

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×#135	C₂	semidirect
2. C₂×C₅×D₃×D₈	C₂	semidirect
3. C₃×C₅×#509	C₂	semidirect
4. C₅×#5193	C₂	semidirect
5. C₅×#5147	C₂	semidirect
6. C₅×#4914	C₂	semidirect
7. C₅×D₃×SD₃₂	C₂	semidirect
8. C₅×#4911	C₂	semidirect
9. C₅×D₃×D₁₆	C₂	semidirect
10. C₅×#4908	C₂	semidirect
11. C₅×D₃×M₃₂	C₂	semidirect
15. C₃×C₅×#135	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₅×#919	C₂²	semidirect
20. C₅×D₃×Q₁₆	C₂²	semidirect
23. C₅×#912	C₂²	semidirect
27. C₅×D₃×D₈	C₂²	semidirect
28. C₅×D₃×D₈	C₂²	semidirect
29. C₅×#904	C₂²	semidirect
30. C₂×C₅×D₂₄	C₂²	semidirect
32. C₃×C₅×SD₃₂	C₂²	semidirect
33. C₃×C₅×D₁₆	C₂²	semidirect
34. C₃×C₅×M₃₂	C₂²	semidirect
35. C₅×#828	C₂²	semidirect
36. C₅×#827	C₂²	semidirect
37. C₅×#826	C₂²	semidirect
38. C₅×#826	C₂²	semidirect
39. C₅×#812	C₂²	semidirect
40. C₅×#800	C₂²	semidirect
41. C₅×D₄₈	C₂²	semidirect
42. C₅×#798	C₂²	semidirect
43. C₅×D₃×C₁₆	C₂²	semidirect
44. D₃×#509	C₅	direct (N × H)
52. C₅×#509	D₃	direct (N × H)
75. C₃×C₅×Q₁₆	C₂³	semidirect
79. C₃×C₅×D₈	C₂³	semidirect
88. C₅×Dic₁₂	C₂³	semidirect
91. C₅×D₂₄	C₂³	semidirect
97. C₃×C₅×C₁₆	C₂³	semidirect
98. C₅×C₃⋊C₁₆	C₂³	semidirect
99. D₃×#135	C₂×C₅	semidirect
100. C₂×D₃×D₈	C₂×C₅	semidirect
101. C₃×#509	C₂×C₅	semidirect
102. #5193	C₂×C₅	semidirect
103. #5147	C₂×C₅	semidirect
104. #4914	C₂×C₅	semidirect
105. D₃×SD₃₂	C₂×C₅	semidirect
106. #4911	C₂×C₅	semidirect
107. D₃×D₁₆	C₂×C₅	semidirect
108. #4908	C₂×C₅	semidirect
109. D₃×M₃₂	C₂×C₅	semidirect
117. C₅×#135	C₂×D₃	semidirect
127. C₂×C₅×D₈	C₂×D₃	semidirect
132. C₅×SD₃₂	C₂×D₃	semidirect
136. C₅×D₁₆	C₂×D₃	semidirect
139. C₅×M₃₂	C₂×D₃	semidirect
182. C₃×#135	C₂²×C₅	semidirect
183. C₂×C₃×D₈	C₂²×C₅	semidirect
186. #919	C₂²×C₅	semidirect
187. D₃×Q₁₆	C₂²×C₅	semidirect
190. #912	C₂²×C₅	semidirect
194. D₃×D₈	C₂²×C₅	semidirect
195. D₃×D₈	C₂²×C₅	semidirect
196. #904	C₂²×C₅	semidirect
197. C₂×D₂₄	C₂²×C₅	semidirect
199. C₃×SD₃₂	C₂²×C₅	semidirect
200. C₃×D₁₆	C₂²×C₅	semidirect
201. C₃×M₃₂	C₂²×C₅	semidirect
202. #828	C₂²×C₅	semidirect
203. #827	C₂²×C₅	semidirect
204. #826	C₂²×C₅	semidirect
205. #826	C₂²×C₅	semidirect
206. #812	C₂²×C₅	semidirect
207. #800	C₂²×C₅	semidirect
208. D₄₈	C₂²×C₅	semidirect
209. #798	C₂²×C₅	semidirect
210. D₃×C₁₆	C₂²×C₅	semidirect
232. C₅×Q₁₆	C₂²×D₃	semidirect
245. C₅×D₈	C₂²×D₃	semidirect
253. C₅×C₁₆	C₂²×D₃	semidirect
261. #509	C₅×D₃	direct (N × H)
303. C₃×Q₁₆	C₂³×C₅	semidirect
307. C₃×D₈	C₂³×C₅	semidirect
316. Dic₁₂	C₂³×C₅	semidirect
319. D₂₄	C₂³×C₅	semidirect
325. C₃×C₁₆	C₂³×C₅	semidirect
326. C₃⋊C₁₆	C₂³×C₅	semidirect
372. #135	C₂×C₅×D₃	semidirect
382. C₂×D₈	C₂×C₅×D₃	semidirect
387. SD₃₂	C₂×C₅×D₃	semidirect
391. D₁₆	C₂×C₅×D₃	semidirect
394. M₃₂	C₂×C₅×D₃	semidirect
403. C₅×D₃	#509	direct (N × H)
482. Q₁₆	C₂²×C₅×D₃	semidirect
495. D₈	C₂²×C₅×D₃	semidirect
503. C₁₆	C₂²×C₅×D₃	semidirect
504. C₃×C₅	C₂×#509	semidirect
577. D₃	C₅×#509	direct (N × H)
578. C₅	D₃×#509	direct (N × H)
598. C₃	C₂×C₅×#509	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×D₈	2
C₃×C₅×#509	2
C₅×#5193	2
C₅×#5147	2
C₅×#4914	2
C₅×D₃×SD₃₂	2
C₅×#4911	2
C₅×D₃×D₁₆	2
C₅×#4908	2
C₅×D₃×M₃₂	2
C₂×C₅×#509	3
D₃×#509	5

Subgroups — C5×D3×#509 #14478317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#509 #14478317