Subgroups — C₃×D₅×#508 #14478261

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	C₃×D₅×#135	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65483	C₂	1	2	yes	maximal, complemented
4	C₃×#65208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65205	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×SD₃₂	C₂	1	2	yes	maximal, complemented
8	C₃×#65201	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65193	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#508	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	—	2	2	no	—
14	C₃×C₅×#135	C₂²	1	2	yes	complemented
15	C₃×#4096	—	2	2	no	—
16	C₃×#4065	C₂²	1	2	yes	complemented
17	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
18	C₃×#4062	—	2	2	no	—
19	C₃×D₅×SD₁₆	—	2	2	no	—
20	C₃×#4058	C₂²	1	2	yes	complemented
21	C₃×D₅×D₈	C₂²	1	2	yes	—
22	C₃×#4050	C₂²	1	2	yes	complemented
23	C₂×C₃×C₈×D₅	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	C₃×#3961	C₂²	1	2	yes	complemented
29	C₃×#3960	C₂²	1	2	yes	complemented
30	C₃×#3959	C₂²	1	2	yes	complemented
31	C₃×#3958	C₂²	1	2	yes	complemented
32	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
33	C₃×Dic₄₀	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3932	C₂²	1	2	yes	complemented
35	C₃×D₈₀	C₂²	1	1	yes	characteristic, complemented
36	C₃×D₅×C₁₆	C₂²	1	1	yes	characteristic
37	C₃×D₅×C₁₆	C₂²	1	1	yes	characteristic
38	C₃×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#508	—	5	1	no	maximal, Hall
41	D₅×#135	C₂×C₃	1	2	yes	complemented
42	C₅×#508	C₂×C₃	1	1	yes	characteristic, complemented
43	#65483	C₂×C₃	1	2	yes	complemented
44	#65208	C₂×C₃	1	1	yes	characteristic, complemented
45	D₅×Q₃₂	C₂×C₃	1	1	yes	characteristic, complemented
46	#65205	C₂×C₃	1	2	yes	complemented
47	D₅×SD₃₂	C₂×C₃	1	2	yes	complemented
48	#65201	C₂×C₃	1	1	yes	characteristic, complemented
49	D₅×D₁₆	C₂×C₃	1	1	yes	characteristic, complemented
50	#65193	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×D₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×C₅×#41	—	2	2	no	—
53	C₃×#713	—	2	2	no	—
54	C₃×Q₈×D₅	—	2	2	no	—
55	C₃×#711	—	2	2	no	—
56	C₃×#711	—	4	2	no	—
57	C₃×D₄×D₅	—	2	2	no	—
58	C₃×D₄×D₅	—	4	2	no	—
59	C₃×#709	—	2	2	no	—
60	C₃×#709	—	4	2	no	—
61	C₂×C₃×C₄×D₅	—	4	2	no	—
62	C₂×C₃×C₄×D₅	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	C₃×#689	—	2	2	no	—
68	C₃×#688	—	2	2	no	—
69	C₃×#687	—	2	2	no	—
70	C₃×#686	—	2	2	no	—
71	C₂×C₃×#168	D₄	1	1	yes	characteristic
72	C₃×Dic₂₀	C₂³	1	2	yes	—
73	C₃×D₄₀	C₂³	1	2	yes	—
74	C₃×#677	—	2	2	no	—
75	C₃×C₈×D₅	D₄	1	1	yes	characteristic
76	C₃×C₈×D₅	D₄	1	1	yes	characteristic
77	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
78	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₁₆	C₂³	1	1	yes	characteristic
81	C₃×#672	C₂³	1	1	yes	characteristic
82	C₃×#672	C₂³	1	1	yes	characteristic
83	C₂×C₃×#135	—	5	2	no	—
84	C₃×#508	—	5	2	no	—
85	C₃×#508	—	5	1	no	—
86	C₃×#508	—	5	2	no	—
87	C₃×#508	—	5	1	no	—
88	C₃×#508	—	5	1	no	—
89	C₃×#508	D₅	1	1	yes	characteristic, direct product factor
90	C₂×C₃×Q₃₂	—	5	1	no	—
91	C₂×C₃×SD₃₂	—	5	2	no	—
92	C₂×C₃×D₁₆	—	5	1	no	—
93	C₂²×C₃×C₁₆	—	5	1	no	—
94	D₅×#41	—	2	2	no	—
95	C₅×#135	C₂²×C₃	1	2	yes	complemented
96	#4096	—	2	2	no	—
97	#4065	C₂²×C₃	1	2	yes	complemented
98	D₅×Q₁₆	C₂²×C₃	1	2	yes	—
99	#4062	—	2	2	no	—
100	D₅×SD₁₆	—	2	2	no	—
101	#4058	C₂²×C₃	1	2	yes	complemented
102	D₅×D₈	C₂²×C₃	1	2	yes	—
103	#4050	C₂²×C₃	1	2	yes	complemented
104	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
105	C₅×Q₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₅×SD₃₂	C₂²×C₃	1	2	yes	complemented
107	C₅×D₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
109	#3961	C₂²×C₃	1	2	yes	complemented
110	#3960	C₂²×C₃	1	2	yes	complemented
111	#3959	C₂²×C₃	1	2	yes	complemented
112	#3958	C₂²×C₃	1	2	yes	complemented
113	C₂×#672	C₂²×C₃	1	1	yes	characteristic, complemented
114	Dic₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
115	#3932	C₂²×C₃	1	2	yes	complemented
116	D₈₀	C₂²×C₃	1	1	yes	characteristic, complemented
117	D₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
118	D₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
119	D₅×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
120	D₅×C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₂×#508	—	5	1	no	Sylow
122	C₂²×C₃×D₅	—	4	2	no	—
123	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	4	2	no	—
130	C₃×C₂²⋊D₅	—	4	2	no	—
131	C₃×C₂²⋊D₅	—	4	2	no	—
132	C₂×C₃×Dic₅	—	4	2	no	—
133	C₂×C₃×Dic₅	D₈	1	1	yes	characteristic
134	C₃×D₂₀	—	2	2	no	—
135	C₃×D₂₀	—	4	2	no	—
136	C₃×C₄×D₅	—	4	2	no	—
137	C₃×C₄×D₅	—	4	2	no	—
138	C₃×C₄×D₅	—	4	2	no	—
139	C₃×C₄×D₅	D₈	1	1	yes	characteristic
140	C₃×C₄×D₅	D₈	1	1	yes	characteristic
141	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
142	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
143	C₃×Dic₁₀	—	2	2	no	—
144	C₃×Dic₁₀	—	4	2	no	—
145	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
147	C₃×#168	C₂×D₄	1	1	yes	characteristic
148	C₃×#168	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×#41	—	10	2	no	—
150	C₃×#135	—	5	2	no	—
151	C₃×#135	—	5	2	no	—
152	C₃×#135	—	5	2	no	—
153	C₃×#135	—	10	2	no	—
154	C₃×#135	—	10	2	no	—
155	C₃×#135	C₂×D₅	1	2	yes	complemented
156	C₂×C₃×Q₁₆	—	5	2	no	—
157	C₂×C₃×SD₁₆	—	10	2	no	—
158	C₂×C₃×D₈	—	5	2	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₃×Q₃₂	—	5	2	no	—
161	C₃×Q₃₂	—	5	1	no	—
162	C₃×Q₃₂	C₂×D₅	1	1	yes	characteristic, complemented
163	C₃×SD₃₂	—	5	2	no	—
164	C₃×SD₃₂	—	5	2	no	—
165	C₃×SD₃₂	—	5	2	no	—
166	C₃×SD₃₂	C₂×D₅	1	2	yes	complemented
167	C₃×D₁₆	—	5	2	no	—
168	C₃×D₁₆	—	5	1	no	—
169	C₃×D₁₆	C₂×D₅	1	1	yes	characteristic, complemented
170	C₂×C₃×C₁₆	—	5	1	no	—
171	C₂×C₃×C₁₆	—	5	1	no	—
172	C₂×C₃×C₁₆	—	5	1	no	—
173	C₂×C₃×C₁₆	—	5	1	no	—
174	C₂×C₃×C₁₆	—	5	1	no	—
175	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
176	C₅×#41	—	2	2	no	—
177	#713	—	2	2	no	—
178	Q₈×D₅	—	2	2	no	—
179	#711	—	2	2	no	—
180	#711	—	4	2	no	—
181	D₄×D₅	—	2	2	no	—
182	D₄×D₅	—	4	2	no	—
183	#709	—	2	2	no	—
184	#709	—	4	2	no	—
185	C₂×C₄×D₅	—	4	2	no	—
186	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
187	C₅×Q₁₆	C₂³×C₃	1	2	yes	—
188	C₅×SD₁₆	—	2	2	no	—
189	C₅×D₈	C₂³×C₃	1	2	yes	—
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	#689	—	2	2	no	—
192	#688	—	2	2	no	—
193	#687	—	2	2	no	—
194	#686	—	2	2	no	—
195	C₂×#168	C₃×D₄	1	1	yes	characteristic
196	Dic₂₀	C₂³×C₃	1	2	yes	—
197	D₄₀	C₂³×C₃	1	2	yes	—
198	#677	—	2	2	no	—
199	C₈×D₅	C₃×D₄	1	1	yes	characteristic
200	C₈×D₅	C₃×D₄	1	1	yes	characteristic
201	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
202	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₁₆	C₂³×C₃	1	1	yes	characteristic
204	C₅×C₁₆	C₂³×C₃	1	1	yes	characteristic
205	#672	C₂³×C₃	1	1	yes	characteristic
206	#672	C₂³×C₃	1	1	yes	characteristic
207	C₂×#135	—	5	2	no	—
208	#508	—	5	2	no	—
209	#508	—	5	1	no	—
210	#508	—	5	2	no	—
211	#508	—	5	1	no	—
212	#508	—	5	1	no	—
213	#508	C₃×D₅	1	1	yes	characteristic, direct product factor
214	C₂×Q₃₂	—	5	1	no	—
215	C₂×SD₃₂	—	5	2	no	—
216	C₂×D₁₆	—	5	1	no	—
217	C₂²×C₁₆	—	5	1	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×C₃×D₅	—	2	2	no	—
221	C₂×C₃×D₅	—	4	2	no	—
222	C₂×C₃×D₅	—	8	4	no	—
223	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
224	C₂×C₃×D₅	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	C₃×Dic₅	—	4	2	no	—
229	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
230	C₃×Dic₅	C₂×D₈	1	1	yes	characteristic
231	C₃×#41	—	2	2	no	—
232	C₃×#41	—	10	2	no	—
233	C₃×#41	—	10	2	no	—
234	C₃×#41	—	10	2	no	—
235	C₃×#41	—	20	2	no	—
236	C₃×#41	—	20	2	no	—
237	C₂×C₃×Q₈	—	10	2	no	—
238	C₂×C₃×D₄	—	10	2	no	—
239	C₂×C₃×D₄	—	20	2	no	—
240	C₂²×C₃×C₄	—	5	1	no	—
241	C₂²×C₃×C₄	—	20	2	no	—
242	C₃×Q₁₆	—	5	2	no	—
243	C₃×Q₁₆	—	10	2	no	—
244	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
245	C₃×SD₁₆	—	2	2	no	—
246	C₃×SD₁₆	—	10	2	no	—
247	C₃×SD₁₆	—	10	2	no	—
248	C₃×SD₁₆	—	10	2	no	—
249	C₃×D₈	—	5	2	no	—
250	C₃×D₈	—	10	2	no	—
251	C₃×D₈	C₂²×D₅	1	2	yes	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	1	no	—
257	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₁₆	—	5	1	no	—
259	C₃×C₁₆	—	5	1	no	—
260	C₃×C₁₆	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₁₆	C₂²×D₅	1	1	yes	characteristic
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
264	C₅×Q₈	—	2	2	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂²⋊D₅	—	4	2	no	—
270	C₂²⋊D₅	—	4	2	no	—
271	C₂²⋊D₅	—	4	2	no	—
272	C₂×Dic₅	—	4	2	no	—
273	C₂×Dic₅	C₃×D₈	1	1	yes	characteristic
274	D₂₀	—	2	2	no	—
275	D₂₀	—	4	2	no	—
276	C₄×D₅	—	4	2	no	—
277	C₄×D₅	—	4	2	no	—
278	C₄×D₅	—	4	2	no	—
279	C₄×D₅	C₃×D₈	1	1	yes	characteristic
280	C₄×D₅	C₃×D₈	1	1	yes	characteristic
281	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
283	Dic₁₀	—	2	2	no	—
284	Dic₁₀	—	4	2	no	—
285	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
286	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
287	#168	C₂×C₃×D₄	1	1	yes	characteristic
288	#168	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×#41	—	10	2	no	—
290	#135	—	5	2	no	—
291	#135	—	5	2	no	—
292	#135	—	5	2	no	—
293	#135	—	10	2	no	—
294	#135	—	10	2	no	—
295	#135	C₂×C₃×D₅	1	2	yes	complemented
296	C₂×Q₁₆	—	5	2	no	—
297	C₂×SD₁₆	—	10	2	no	—
298	C₂×D₈	—	5	2	no	—
299	C₂²×C₈	—	5	1	no	—
300	Q₃₂	—	5	2	no	—
301	Q₃₂	—	5	1	no	—
302	Q₃₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
303	SD₃₂	—	5	2	no	—
304	SD₃₂	—	5	2	no	—
305	SD₃₂	—	5	2	no	—
306	SD₃₂	C₂×C₃×D₅	1	2	yes	complemented
307	D₁₆	—	5	2	no	—
308	D₁₆	—	5	1	no	—
309	D₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
310	C₂×C₁₆	—	5	1	no	—
311	C₂×C₁₆	—	5	1	no	—
312	C₂×C₁₆	—	5	1	no	—
313	C₂×C₁₆	—	5	1	no	—
314	C₂×C₁₆	—	5	1	no	—
315	C₂×C₁₆	C₂×C₃×D₅	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	C₃×D₅	—	2	1	no	—
320	C₃×D₅	—	8	2	no	—
321	C₃×D₅	#508	1	2	yes	direct product factor
322	C₂³×C₃	—	5	1	no	—
323	C₂³×C₃	—	20	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	10	2	no	—
326	C₃×Q₈	—	20	2	no	—
327	C₃×D₄	—	2	2	no	—
328	C₃×D₄	—	4	2	no	—
329	C₃×D₄	—	10	2	no	—
330	C₃×D₄	—	20	2	no	—
331	C₃×D₄	—	20	2	no	—
332	C₃×D₄	—	20	2	no	—
333	C₃×D₄	—	20	2	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	5	1	no	—
336	C₂×C₃×C₄	—	5	1	no	—
337	C₂×C₃×C₄	—	5	1	no	—
338	C₂×C₃×C₄	—	5	1	no	—
339	C₂×C₃×C₄	—	5	1	no	—
340	C₂×C₃×C₄	—	20	2	no	—
341	C₂×C₃×C₄	—	20	2	no	—
342	C₂×C₃×C₄	—	20	2	no	—
343	C₂×C₃×C₄	—	20	2	no	—
344	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
345	C₃×C₈	—	5	1	no	—
346	C₃×C₈	—	5	1	no	—
347	C₃×C₈	D₄×D₅	1	1	yes	characteristic
348	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
351	C₂×D₅	—	2	2	no	—
352	C₂×D₅	—	4	2	no	—
353	C₂×D₅	—	8	4	no	—
354	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
355	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
358	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
359	Dic₅	—	4	2	no	—
360	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
361	Dic₅	C₂×C₃×D₈	1	1	yes	characteristic
362	#41	—	2	2	no	—
363	#41	—	10	2	no	—
364	#41	—	10	2	no	—
365	#41	—	10	2	no	—
366	#41	—	20	2	no	—
367	#41	—	20	2	no	—
368	C₂×Q₈	—	10	2	no	—
369	C₂×D₄	—	10	2	no	—
370	C₂×D₄	—	20	2	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	20	2	no	—
373	Q₁₆	—	5	2	no	—
374	Q₁₆	—	10	2	no	—
375	Q₁₆	C₂²×C₃×D₅	1	2	yes	—
376	SD₁₆	—	2	2	no	—
377	SD₁₆	—	10	2	no	—
378	SD₁₆	—	10	2	no	—
379	SD₁₆	—	10	2	no	—
380	D₈	—	5	2	no	—
381	D₈	—	10	2	no	—
382	D₈	C₂²×C₃×D₅	1	2	yes	—
383	C₂×C₈	—	5	1	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	—	5	1	no	—
387	C₂×C₈	—	5	1	no	—
388	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
389	C₁₆	—	5	1	no	—
390	C₁₆	—	5	1	no	—
391	C₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
393	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	5	1	no	—
396	C₂²×C₃	—	5	1	no	—
397	C₂²×C₃	—	10	2	no	—
398	C₂²×C₃	—	20	2	no	—
399	C₂²×C₃	—	40	4	no	—
400	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	5	1	no	—
403	C₃×C₄	—	5	1	no	—
404	C₃×C₄	—	20	2	no	—
405	C₃×C₄	D₅×D₈	1	1	yes	characteristic
406	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
407	C₂×C₅	—	2	1	no	—
408	C₂×C₅	—	8	2	no	—
409	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
410	D₅	—	2	1	no	—
411	D₅	—	8	2	no	—
412	D₅	C₃×#508	1	2	yes	direct product factor
413	C₂³	—	5	1	no	—
414	C₂³	—	20	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	10	2	no	—
417	Q₈	—	20	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	10	2	no	—
421	D₄	—	20	2	no	—
422	D₄	—	20	2	no	—
423	D₄	—	20	2	no	—
424	D₄	—	20	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	5	1	no	—
428	C₂×C₄	—	5	1	no	—
429	C₂×C₄	—	5	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	20	2	no	—
432	C₂×C₄	—	20	2	no	—
433	C₂×C₄	—	20	2	no	—
434	C₂×C₄	—	20	2	no	—
435	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
436	C₈	—	5	1	no	—
437	C₈	—	5	1	no	—
438	C₈	C₃×D₄×D₅	1	1	yes	characteristic
439	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	5	2	no	—
442	C₂×C₃	—	8	2	no	—
443	C₂×C₃	—	10	1	no	—
444	C₂×C₃	—	40	2	no	—
445	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
446	C₅	C₂×C₃×#508	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	4	2	no	—
448	C₂²	—	5	1	no	—
449	C₂²	—	5	1	no	—
450	C₂²	—	10	2	no	—
451	C₂²	—	20	2	no	—
452	C₂²	—	40	4	no	—
453	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
454	C₄	—	4	2	no	—
455	C₄	—	5	1	no	—
456	C₄	—	5	1	no	—
457	C₄	—	20	2	no	—
458	C₄	C₃×D₅×D₈	1	1	yes	characteristic
459	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
460	C₃	D₅×#508	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	5	2	no	—
463	C₂	—	8	2	no	—
464	C₂	—	10	1	no	—
465	C₂	—	40	2	no	—
466	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₃×C₅×#508	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₃×#508	D₅
hypocenter	C₅	C₂×C₃×#508
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#508

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×#135	C₂	semidirect
2. C₃×C₅×#508	C₂	semidirect
3. C₃×#65483	C₂	semidirect
4. C₃×#65208	C₂	semidirect
5. C₃×D₅×Q₃₂	C₂	semidirect
6. C₃×#65205	C₂	semidirect
7. C₃×D₅×SD₃₂	C₂	semidirect
8. C₃×#65201	C₂	semidirect
9. C₃×D₅×D₁₆	C₂	semidirect
10. C₃×#65193	C₂	semidirect
11. C₂×C₃×D₅×C₁₆	C₂	semidirect
12. D₅×#508	C₃	direct (N × H)
14. C₃×C₅×#135	C₂²	semidirect
16. C₃×#4065	C₂²	semidirect
20. C₃×#4058	C₂²	semidirect
22. C₃×#4050	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. C₃×#3961	C₂²	semidirect
29. C₃×#3960	C₂²	semidirect
30. C₃×#3959	C₂²	semidirect
31. C₃×#3958	C₂²	semidirect
32. C₂×C₃×#672	C₂²	semidirect
33. C₃×Dic₄₀	C₂²	semidirect
34. C₃×#3932	C₂²	semidirect
35. C₃×D₈₀	C₂²	semidirect
38. C₃×D₅×C₁₆	C₂²	semidirect
39. C₃×D₅×C₁₆	C₂²	semidirect
41. D₅×#135	C₂×C₃	semidirect
42. C₅×#508	C₂×C₃	semidirect
43. #65483	C₂×C₃	semidirect
44. #65208	C₂×C₃	semidirect
45. D₅×Q₃₂	C₂×C₃	semidirect
46. #65205	C₂×C₃	semidirect
47. D₅×SD₃₂	C₂×C₃	semidirect
48. #65201	C₂×C₃	semidirect
49. D₅×D₁₆	C₂×C₃	semidirect
50. #65193	C₂×C₃	semidirect
51. C₂×D₅×C₁₆	C₂×C₃	semidirect
89. C₃×#508	D₅	direct (N × H)
95. C₅×#135	C₂²×C₃	semidirect
97. #4065	C₂²×C₃	semidirect
101. #4058	C₂²×C₃	semidirect
103. #4050	C₂²×C₃	semidirect
105. C₅×Q₃₂	C₂²×C₃	semidirect
106. C₅×SD₃₂	C₂²×C₃	semidirect
107. C₅×D₁₆	C₂²×C₃	semidirect
108. C₂×C₅×C₁₆	C₂²×C₃	semidirect
109. #3961	C₂²×C₃	semidirect
110. #3960	C₂²×C₃	semidirect
111. #3959	C₂²×C₃	semidirect
112. #3958	C₂²×C₃	semidirect
113. C₂×#672	C₂²×C₃	semidirect
114. Dic₄₀	C₂²×C₃	semidirect
115. #3932	C₂²×C₃	semidirect
116. D₈₀	C₂²×C₃	semidirect
119. D₅×C₁₆	C₂²×C₃	semidirect
120. D₅×C₁₆	C₂²×C₃	semidirect
155. C₃×#135	C₂×D₅	semidirect
162. C₃×Q₃₂	C₂×D₅	semidirect
166. C₃×SD₃₂	C₂×D₅	semidirect
169. C₃×D₁₆	C₂×D₅	semidirect
175. C₂×C₃×C₁₆	C₂×D₅	semidirect
213. #508	C₃×D₅	direct (N × H)
295. #135	C₂×C₃×D₅	semidirect
302. Q₃₂	C₂×C₃×D₅	semidirect
306. SD₃₂	C₂×C₃×D₅	semidirect
309. D₁₆	C₂×C₃×D₅	semidirect
315. C₂×C₁₆	C₂×C₃×D₅	semidirect
321. C₃×D₅	#508	direct (N × H)
393. C₃×C₅	C₂×#508	semidirect
412. D₅	C₃×#508	direct (N × H)
446. C₅	C₂×C₃×#508	semidirect
460. C₃	D₅×#508	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×#135	2
C₃×C₅×#508	2
C₃×#65483	2
C₃×#65208	2
C₃×D₅×Q₃₂	2
C₃×#65205	2
C₃×D₅×SD₃₂	2
C₃×#65201	2
C₃×D₅×D₁₆	2
C₃×#65193	2
C₂×C₃×D₅×C₁₆	2
D₅×#508	3
C₂×C₃×#508	5

Subgroups — C3×D5×#508 #14478261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#508 #14478261