Subgroups — C₅×D₃×#508 #14478260

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 468 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	2	yes	maximal, complemented
2	C₃×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5194	C₂	1	2	yes	maximal, complemented
4	C₅×#4919	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4916	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×SD₃₂	C₂	1	2	yes	maximal, complemented
8	C₅×#4912	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4904	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#508	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	—	2	2	no	—
14	C₃×C₅×#135	C₂²	1	2	yes	complemented
15	C₅×#950	—	2	2	no	—
16	C₅×#919	C₂²	1	2	yes	complemented
17	C₅×D₃×Q₁₆	C₂²	1	2	yes	—
18	C₅×#916	—	2	2	no	—
19	C₅×D₃×SD₁₆	—	2	2	no	—
20	C₅×#912	C₂²	1	2	yes	complemented
21	C₅×D₃×D₈	C₂²	1	2	yes	—
22	C₅×#904	C₂²	1	2	yes	complemented
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
26	C₃×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₅×#829	C₂²	1	2	yes	complemented
29	C₅×#828	C₂²	1	2	yes	complemented
30	C₅×#827	C₂²	1	2	yes	complemented
31	C₅×#826	C₂²	1	2	yes	complemented
32	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₅×Dic₂₄	C₂²	1	1	yes	characteristic, complemented
34	C₅×#800	C₂²	1	2	yes	complemented
35	C₅×D₄₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×D₃×C₁₆	C₂²	1	1	yes	characteristic
37	C₅×D₃×C₁₆	C₂²	1	1	yes	characteristic
38	C₅×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₅×D₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
40	D₃×#508	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#135	—	3	2	no	—
42	C₅×#508	—	3	1	no	—
43	C₅×#508	—	3	2	no	—
44	C₅×#508	—	3	1	no	—
45	C₅×#508	—	3	1	no	—
46	C₅×#508	—	3	2	no	—
47	C₅×#508	D₃	1	1	yes	characteristic, direct product factor
48	C₂×C₅×Q₃₂	—	3	1	no	—
49	C₂×C₅×SD₃₂	—	3	2	no	—
50	C₂×C₅×D₁₆	—	3	1	no	—
51	C₂²×C₅×C₁₆	—	3	1	no	—
52	C₃×C₅×#41	—	2	2	no	—
53	C₅×#239	—	2	2	no	—
54	C₅×D₃×Q₈	—	2	2	no	—
55	C₅×#237	—	2	2	no	—
56	C₅×#237	—	4	2	no	—
57	C₅×D₃×D₄	—	2	2	no	—
58	C₅×D₃×D₄	—	4	2	no	—
59	C₅×#235	—	2	2	no	—
60	C₅×#235	—	4	2	no	—
61	C₂×C₄×C₅×D₃	—	4	2	no	—
62	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
64	C₃×C₅×SD₁₆	—	2	2	no	—
65	C₃×C₅×D₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₅×#216	—	2	2	no	—
68	C₅×#215	—	2	2	no	—
69	C₅×#214	—	2	2	no	—
70	C₅×#213	—	2	2	no	—
71	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
72	C₅×Dic₁₂	C₂³	1	2	yes	—
73	C₅×D₂₄	C₂³	1	2	yes	—
74	C₅×#204	—	2	2	no	—
75	C₅×D₃×C₈	D₄	1	1	yes	characteristic
76	C₅×D₃×C₈	D₄	1	1	yes	characteristic
77	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
78	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
81	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
82	C₅×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
83	D₃×#135	C₂×C₅	1	2	yes	complemented
84	C₃×#508	C₂×C₅	1	1	yes	characteristic, complemented
85	#5194	C₂×C₅	1	2	yes	complemented
86	#4919	C₂×C₅	1	1	yes	characteristic, complemented
87	D₃×Q₃₂	C₂×C₅	1	1	yes	characteristic, complemented
88	#4916	C₂×C₅	1	2	yes	complemented
89	D₃×SD₃₂	C₂×C₅	1	2	yes	complemented
90	#4912	C₂×C₅	1	1	yes	characteristic, complemented
91	D₃×D₁₆	C₂×C₅	1	1	yes	characteristic, complemented
92	#4904	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×D₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×C₅×#41	—	6	2	no	—
95	C₅×#135	—	3	2	no	—
96	C₅×#135	—	3	2	no	—
97	C₅×#135	—	3	2	no	—
98	C₅×#135	—	6	2	no	—
99	C₅×#135	—	6	2	no	—
100	C₅×#135	C₂×D₃	1	2	yes	complemented
101	C₂×C₅×Q₁₆	—	3	2	no	—
102	C₂×C₅×SD₁₆	—	6	2	no	—
103	C₂×C₅×D₈	—	3	2	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₅×Q₃₂	—	3	2	no	—
106	C₅×Q₃₂	—	3	1	no	—
107	C₅×Q₃₂	C₂×D₃	1	1	yes	characteristic, complemented
108	C₅×SD₃₂	—	3	2	no	—
109	C₅×SD₃₂	—	3	2	no	—
110	C₅×SD₃₂	—	3	2	no	—
111	C₅×SD₃₂	C₂×D₃	1	2	yes	complemented
112	C₅×D₁₆	—	3	2	no	—
113	C₅×D₁₆	—	3	1	no	—
114	C₅×D₁₆	C₂×D₃	1	1	yes	characteristic, complemented
115	C₂×C₅×C₁₆	—	3	1	no	—
116	C₂×C₅×C₁₆	—	3	1	no	—
117	C₂×C₅×C₁₆	—	3	1	no	—
118	C₂×C₅×C₁₆	—	3	1	no	—
119	C₂×C₅×C₁₆	—	3	1	no	—
120	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×#508	—	3	1	no	Sylow
122	C₂²×C₅×D₃	—	4	2	no	—
123	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	4	2	no	—
127	C₂×C₃×C₄×C₅	—	4	2	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₅×#67	—	4	2	no	—
130	C₅×#67	—	4	2	no	—
131	C₅×#67	—	4	2	no	—
132	C₂×C₅×Dic₃	—	4	2	no	—
133	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
134	C₅×D₁₂	—	2	2	no	—
135	C₅×D₁₂	—	4	2	no	—
136	C₄×C₅×D₃	—	4	2	no	—
137	C₄×C₅×D₃	—	4	2	no	—
138	C₄×C₅×D₃	—	4	2	no	—
139	C₄×C₅×D₃	D₈	1	1	yes	characteristic
140	C₄×C₅×D₃	D₈	1	1	yes	characteristic
141	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
142	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
143	C₅×Dic₆	—	2	2	no	—
144	C₅×Dic₆	—	4	2	no	—
145	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
147	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
149	D₃×#41	—	2	2	no	—
150	C₃×#135	C₂²×C₅	1	2	yes	complemented
151	#950	—	2	2	no	—
152	#919	C₂²×C₅	1	2	yes	complemented
153	D₃×Q₁₆	C₂²×C₅	1	2	yes	—
154	#916	—	2	2	no	—
155	D₃×SD₁₆	—	2	2	no	—
156	#912	C₂²×C₅	1	2	yes	complemented
157	D₃×D₈	C₂²×C₅	1	2	yes	—
158	#904	C₂²×C₅	1	2	yes	complemented
159	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
160	C₃×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₃×SD₃₂	C₂²×C₅	1	2	yes	complemented
162	C₃×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
164	#829	C₂²×C₅	1	2	yes	complemented
165	#828	C₂²×C₅	1	2	yes	complemented
166	#827	C₂²×C₅	1	2	yes	complemented
167	#826	C₂²×C₅	1	2	yes	complemented
168	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
169	Dic₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
170	#800	C₂²×C₅	1	2	yes	complemented
171	D₄₈	C₂²×C₅	1	1	yes	characteristic, complemented
172	D₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
173	D₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
174	D₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
175	D₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₅×#41	—	2	2	no	—
177	C₅×#41	—	6	2	no	—
178	C₅×#41	—	6	2	no	—
179	C₅×#41	—	6	2	no	—
180	C₅×#41	—	12	2	no	—
181	C₅×#41	—	12	2	no	—
182	C₂×C₅×Q₈	—	6	2	no	—
183	C₂×C₅×D₄	—	6	2	no	—
184	C₂×C₅×D₄	—	12	2	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂²×C₄×C₅	—	12	2	no	—
187	C₅×Q₁₆	—	3	2	no	—
188	C₅×Q₁₆	—	6	2	no	—
189	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
190	C₅×SD₁₆	—	2	2	no	—
191	C₅×SD₁₆	—	6	2	no	—
192	C₅×SD₁₆	—	6	2	no	—
193	C₅×SD₁₆	—	6	2	no	—
194	C₅×D₈	—	3	2	no	—
195	C₅×D₈	—	6	2	no	—
196	C₅×D₈	C₂²×D₃	1	2	yes	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	3	1	no	—
201	C₂×C₅×C₈	—	3	1	no	—
202	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
203	C₅×C₁₆	—	3	1	no	—
204	C₅×C₁₆	—	3	1	no	—
205	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
206	C₅×C₁₆	C₂²×D₃	1	1	yes	characteristic
207	C₂×#135	—	3	2	no	—
208	#508	—	3	2	no	—
209	#508	—	3	1	no	—
210	#508	—	3	2	no	—
211	#508	—	3	1	no	—
212	#508	—	3	1	no	—
213	#508	C₅×D₃	1	1	yes	characteristic, direct product factor
214	C₂×Q₃₂	—	3	1	no	—
215	C₂×SD₃₂	—	3	2	no	—
216	C₂×D₁₆	—	3	1	no	—
217	C₂²×C₁₆	—	3	1	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×C₅×D₃	—	2	2	no	—
221	C₂×C₅×D₃	—	4	2	no	—
222	C₂×C₅×D₃	—	8	4	no	—
223	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
224	C₂×C₅×D₃	C₂×D₈	1	1	yes	characteristic
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₅×Dic₃	—	4	2	no	—
229	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
230	C₅×Dic₃	C₂×D₈	1	1	yes	characteristic
231	C₃×#41	—	2	2	no	—
232	#239	—	2	2	no	—
233	D₃×Q₈	—	2	2	no	—
234	#237	—	2	2	no	—
235	#237	—	4	2	no	—
236	D₃×D₄	—	2	2	no	—
237	D₃×D₄	—	4	2	no	—
238	#235	—	2	2	no	—
239	#235	—	4	2	no	—
240	C₂×C₄×D₃	—	4	2	no	—
241	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
242	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
243	C₃×SD₁₆	—	2	2	no	—
244	C₃×D₈	C₂³×C₅	1	2	yes	—
245	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
246	#216	—	2	2	no	—
247	#215	—	2	2	no	—
248	#214	—	2	2	no	—
249	#213	—	2	2	no	—
250	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
251	Dic₁₂	C₂³×C₅	1	2	yes	—
252	D₂₄	C₂³×C₅	1	2	yes	—
253	#204	—	2	2	no	—
254	D₃×C₈	C₅×D₄	1	1	yes	characteristic
255	D₃×C₈	C₅×D₄	1	1	yes	characteristic
256	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
257	D₃×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₃×C₁₆	C₂³×C₅	1	1	yes	characteristic
259	C₃×C₁₆	C₂³×C₅	1	1	yes	characteristic
260	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
261	C₃⋊C₁₆	C₂³×C₅	1	1	yes	characteristic
262	C₂³×C₅	—	3	1	no	—
263	C₂³×C₅	—	12	2	no	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	6	2	no	—
266	C₅×Q₈	—	12	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	4	2	no	—
269	C₅×D₄	—	6	2	no	—
270	C₅×D₄	—	12	2	no	—
271	C₅×D₄	—	12	2	no	—
272	C₅×D₄	—	12	2	no	—
273	C₅×D₄	—	12	2	no	—
274	C₂×C₄×C₅	—	3	1	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	1	no	—
277	C₂×C₄×C₅	—	3	1	no	—
278	C₂×C₄×C₅	—	3	1	no	—
279	C₂×C₄×C₅	—	4	2	no	—
280	C₂×C₄×C₅	—	12	2	no	—
281	C₂×C₄×C₅	—	12	2	no	—
282	C₂×C₄×C₅	—	12	2	no	—
283	C₂×C₄×C₅	—	12	2	no	—
284	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
285	C₅×C₈	—	3	1	no	—
286	C₅×C₈	—	3	1	no	—
287	C₅×C₈	D₃×D₄	1	1	yes	characteristic
288	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
289	C₂×#41	—	6	2	no	—
290	#135	—	3	2	no	—
291	#135	—	3	2	no	—
292	#135	—	3	2	no	—
293	#135	—	6	2	no	—
294	#135	—	6	2	no	—
295	#135	C₂×C₅×D₃	1	2	yes	complemented
296	C₂×Q₁₆	—	3	2	no	—
297	C₂×SD₁₆	—	6	2	no	—
298	C₂×D₈	—	3	2	no	—
299	C₂²×C₈	—	3	1	no	—
300	Q₃₂	—	3	2	no	—
301	Q₃₂	—	3	1	no	—
302	Q₃₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
303	SD₃₂	—	3	2	no	—
304	SD₃₂	—	3	2	no	—
305	SD₃₂	—	3	2	no	—
306	SD₃₂	C₂×C₅×D₃	1	2	yes	complemented
307	D₁₆	—	3	2	no	—
308	D₁₆	—	3	1	no	—
309	D₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
310	C₂×C₁₆	—	3	1	no	—
311	C₂×C₁₆	—	3	1	no	—
312	C₂×C₁₆	—	3	1	no	—
313	C₂×C₁₆	—	3	1	no	—
314	C₂×C₁₆	—	3	1	no	—
315	C₂×C₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
316	C₂×C₃×C₅	—	2	1	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
319	C₅×D₃	—	2	1	no	—
320	C₅×D₃	—	8	2	no	—
321	C₅×D₃	#508	1	2	yes	direct product factor
322	C₂²×D₃	—	4	2	no	—
323	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
324	C₃×Q₈	—	2	2	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	—	4	2	no	—
327	C₂×C₃×C₄	—	4	2	no	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	#67	—	4	2	no	—
330	#67	—	4	2	no	—
331	#67	—	4	2	no	—
332	C₂×Dic₃	—	4	2	no	—
333	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
334	D₁₂	—	2	2	no	—
335	D₁₂	—	4	2	no	—
336	C₄×D₃	—	4	2	no	—
337	C₄×D₃	—	4	2	no	—
338	C₄×D₃	—	4	2	no	—
339	C₄×D₃	C₅×D₈	1	1	yes	characteristic
340	C₄×D₃	C₅×D₈	1	1	yes	characteristic
341	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
343	Dic₆	—	2	2	no	—
344	Dic₆	—	4	2	no	—
345	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
346	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
347	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
348	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂²×C₅	—	3	1	no	—
350	C₂²×C₅	—	3	1	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	6	2	no	—
353	C₂²×C₅	—	12	2	no	—
354	C₂²×C₅	—	24	4	no	—
355	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
356	C₄×C₅	—	3	1	no	—
357	C₄×C₅	—	3	1	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	12	2	no	—
360	C₄×C₅	D₃×D₈	1	1	yes	characteristic
361	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
362	#41	—	2	2	no	—
363	#41	—	6	2	no	—
364	#41	—	6	2	no	—
365	#41	—	6	2	no	—
366	#41	—	12	2	no	—
367	#41	—	12	2	no	—
368	C₂×Q₈	—	6	2	no	—
369	C₂×D₄	—	6	2	no	—
370	C₂×D₄	—	12	2	no	—
371	C₂²×C₄	—	3	1	no	—
372	C₂²×C₄	—	12	2	no	—
373	Q₁₆	—	3	2	no	—
374	Q₁₆	—	6	2	no	—
375	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
376	SD₁₆	—	2	2	no	—
377	SD₁₆	—	6	2	no	—
378	SD₁₆	—	6	2	no	—
379	SD₁₆	—	6	2	no	—
380	D₈	—	3	2	no	—
381	D₈	—	6	2	no	—
382	D₈	C₂²×C₅×D₃	1	2	yes	—
383	C₂×C₈	—	3	1	no	—
384	C₂×C₈	—	3	1	no	—
385	C₂×C₈	—	3	1	no	—
386	C₂×C₈	—	3	1	no	—
387	C₂×C₈	—	3	1	no	—
388	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
389	C₁₆	—	3	1	no	—
390	C₁₆	—	3	1	no	—
391	C₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
392	C₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
393	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
396	C₂×D₃	—	2	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₂×D₃	—	8	4	no	—
399	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
400	C₂×D₃	C₂×C₅×D₈	1	1	yes	characteristic
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
403	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
404	Dic₃	—	4	2	no	—
405	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
406	Dic₃	C₂×C₅×D₈	1	1	yes	characteristic
407	C₂×C₅	—	2	1	no	—
408	C₂×C₅	—	3	2	no	—
409	C₂×C₅	—	6	1	no	—
410	C₂×C₅	—	8	2	no	—
411	C₂×C₅	—	24	2	no	—
412	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
413	C₂³	—	3	1	no	—
414	C₂³	—	12	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	6	2	no	—
417	Q₈	—	12	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	6	2	no	—
421	D₄	—	12	2	no	—
422	D₄	—	12	2	no	—
423	D₄	—	12	2	no	—
424	D₄	—	12	2	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	12	2	no	—
432	C₂×C₄	—	12	2	no	—
433	C₂×C₄	—	12	2	no	—
434	C₂×C₄	—	12	2	no	—
435	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
436	C₈	—	3	1	no	—
437	C₈	—	3	1	no	—
438	C₈	C₅×D₃×D₄	1	1	yes	characteristic
439	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	8	2	no	—
442	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
443	D₃	—	2	1	no	—
444	D₃	—	8	2	no	—
445	D₃	C₅×#508	1	2	yes	direct product factor
446	C₅	D₃×#508	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	3	1	no	—
448	C₂²	—	3	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	6	2	no	—
451	C₂²	—	12	2	no	—
452	C₂²	—	24	4	no	—
453	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
454	C₄	—	3	1	no	—
455	C₄	—	3	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	12	2	no	—
458	C₄	C₅×D₃×D₈	1	1	yes	characteristic
459	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
460	C₃	C₂×C₅×#508	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	3	2	no	—
463	C₂	—	6	1	no	—
464	C₂	—	8	2	no	—
465	C₂	—	24	2	no	—
466	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₃×C₅×#508	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₅×#508	D₃
hypocenter	C₃	C₂×C₅×#508
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#508

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×#135	C₂	semidirect
2. C₃×C₅×#508	C₂	semidirect
3. C₅×#5194	C₂	semidirect
4. C₅×#4919	C₂	semidirect
5. C₅×D₃×Q₃₂	C₂	semidirect
6. C₅×#4916	C₂	semidirect
7. C₅×D₃×SD₃₂	C₂	semidirect
8. C₅×#4912	C₂	semidirect
9. C₅×D₃×D₁₆	C₂	semidirect
10. C₅×#4904	C₂	semidirect
11. C₂×C₅×D₃×C₁₆	C₂	semidirect
14. C₃×C₅×#135	C₂²	semidirect
16. C₅×#919	C₂²	semidirect
20. C₅×#912	C₂²	semidirect
22. C₅×#904	C₂²	semidirect
24. C₃×C₅×Q₃₂	C₂²	semidirect
25. C₃×C₅×SD₃₂	C₂²	semidirect
26. C₃×C₅×D₁₆	C₂²	semidirect
27. C₂×C₃×C₅×C₁₆	C₂²	semidirect
28. C₅×#829	C₂²	semidirect
29. C₅×#828	C₂²	semidirect
30. C₅×#827	C₂²	semidirect
31. C₅×#826	C₂²	semidirect
32. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
33. C₅×Dic₂₄	C₂²	semidirect
34. C₅×#800	C₂²	semidirect
35. C₅×D₄₈	C₂²	semidirect
38. C₅×D₃×C₁₆	C₂²	semidirect
39. C₅×D₃×C₁₆	C₂²	semidirect
40. D₃×#508	C₅	direct (N × H)
47. C₅×#508	D₃	direct (N × H)
83. D₃×#135	C₂×C₅	semidirect
84. C₃×#508	C₂×C₅	semidirect
85. #5194	C₂×C₅	semidirect
86. #4919	C₂×C₅	semidirect
87. D₃×Q₃₂	C₂×C₅	semidirect
88. #4916	C₂×C₅	semidirect
89. D₃×SD₃₂	C₂×C₅	semidirect
90. #4912	C₂×C₅	semidirect
91. D₃×D₁₆	C₂×C₅	semidirect
92. #4904	C₂×C₅	semidirect
93. C₂×D₃×C₁₆	C₂×C₅	semidirect
100. C₅×#135	C₂×D₃	semidirect
107. C₅×Q₃₂	C₂×D₃	semidirect
111. C₅×SD₃₂	C₂×D₃	semidirect
114. C₅×D₁₆	C₂×D₃	semidirect
120. C₂×C₅×C₁₆	C₂×D₃	semidirect
150. C₃×#135	C₂²×C₅	semidirect
152. #919	C₂²×C₅	semidirect
156. #912	C₂²×C₅	semidirect
158. #904	C₂²×C₅	semidirect
160. C₃×Q₃₂	C₂²×C₅	semidirect
161. C₃×SD₃₂	C₂²×C₅	semidirect
162. C₃×D₁₆	C₂²×C₅	semidirect
163. C₂×C₃×C₁₆	C₂²×C₅	semidirect
164. #829	C₂²×C₅	semidirect
165. #828	C₂²×C₅	semidirect
166. #827	C₂²×C₅	semidirect
167. #826	C₂²×C₅	semidirect
168. C₂×C₃⋊C₁₆	C₂²×C₅	semidirect
169. Dic₂₄	C₂²×C₅	semidirect
170. #800	C₂²×C₅	semidirect
171. D₄₈	C₂²×C₅	semidirect
174. D₃×C₁₆	C₂²×C₅	semidirect
175. D₃×C₁₆	C₂²×C₅	semidirect
213. #508	C₅×D₃	direct (N × H)
295. #135	C₂×C₅×D₃	semidirect
302. Q₃₂	C₂×C₅×D₃	semidirect
306. SD₃₂	C₂×C₅×D₃	semidirect
309. D₁₆	C₂×C₅×D₃	semidirect
315. C₂×C₁₆	C₂×C₅×D₃	semidirect
321. C₅×D₃	#508	direct (N × H)
393. C₃×C₅	C₂×#508	semidirect
445. D₃	C₅×#508	direct (N × H)
446. C₅	D₃×#508	direct (N × H)
460. C₃	C₂×C₅×#508	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
C₃×C₅×#508	2
C₅×#5194	2
C₅×#4919	2
C₅×D₃×Q₃₂	2
C₅×#4916	2
C₅×D₃×SD₃₂	2
C₅×#4912	2
C₅×D₃×D₁₆	2
C₅×#4904	2
C₂×C₅×D₃×C₁₆	2
C₂×C₅×#508	3
D₃×#508	5

Subgroups — C5×D3×#508 #14478260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#508 #14478260