Subgroups — C₃×#10613772 #14478623

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66105	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3961	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65207	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×Q₃₂	C₂	1	2	yes	maximal, complemented
8	C₃×#65205	C₂	1	2	yes	maximal, complemented
9	C₃×#65204	C₂	1	2	yes	maximal, complemented
10	C₃×#65198	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65196	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613772	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×#4150	—	2	1	no	—
14	C₃×#4147	—	2	1	no	—
15	C₃×C₅×#135	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₃×#4097	—	2	1	no	—
18	C₃×#4088	—	2	1	no	—
19	C₃×#4065	C₂²	1	2	yes	—
20	C₃×#4064	—	2	2	no	—
21	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
22	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
23	C₃×#4061	—	2	2	no	—
24	C₃×#4058	C₂²	1	2	yes	—
25	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
26	C₃×#4050	C₂²	1	1	yes	characteristic
27	C₃×#4047	C₂²	1	1	yes	characteristic
28	C₃×C₅×Q₃₂	C₂²	1	2	yes	—
29	C₃×C₅×SD₃₂	C₂²	1	2	yes	—
30	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic
31	C₃×#3961	C₂²	1	2	yes	—
32	C₃×#3961	C₂²	1	2	yes	—
33	C₃×#3961	C₂²	1	1	yes	characteristic
34	C₃×#3960	C₂²	1	1	yes	characteristic
35	C₃×#3959	C₂²	1	1	yes	characteristic
36	C₃×#3958	C₂²	1	1	yes	characteristic
37	C₂×C₃×#672	C₂²	1	1	yes	characteristic
38	C₃×Dic₄₀	C₂²	1	2	yes	—
39	C₃×#3932	C₂²	1	2	yes	—
40	C₃×#3930	C₂²	1	2	yes	—
41	C₃×D₅×C₁₆	C₂²	1	2	yes	—
42	C₃×#3417	—	5	1	no	maximal, Hall
43	#66105	C₂×C₃	1	1	yes	characteristic, complemented
44	#66100	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#510	C₂×C₃	1	1	yes	characteristic, complemented
46	#65483	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3961	C₂×C₃	1	1	yes	characteristic, complemented
48	#65207	C₂×C₃	1	2	yes	complemented
49	D₅×Q₃₂	C₂×C₃	1	2	yes	complemented
50	#65205	C₂×C₃	1	2	yes	complemented
51	#65204	C₂×C₃	1	2	yes	complemented
52	#65198	C₂×C₃	1	1	yes	characteristic, complemented
53	#65196	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₅×#41	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₃×#713	—	2	2	no	—
57	C₃×#713	—	4	1	no	—
58	C₃×Q₈×D₅	—	2	2	no	—
59	C₃×Q₈×D₅	—	2	2	no	—
60	C₃×Q₈×D₅	—	4	1	no	—
61	C₃×#711	—	2	2	no	—
62	C₃×#711	—	4	2	no	—
63	C₃×#709	—	2	1	no	—
64	C₃×#709	—	4	2	no	—
65	C₃×#709	—	4	1	no	—
66	C₃×#709	D₄	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₂×C₃×Dic₁₀	—	4	1	no	—
69	C₃×C₅×Q₁₆	—	2	1	no	—
70	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
71	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
72	C₃×C₅×SD₁₆	—	2	1	no	—
73	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×#689	—	2	2	no	—
76	C₃×#689	—	2	2	no	—
77	C₃×#688	—	2	2	no	—
78	C₃×#687	—	2	2	no	—
79	C₃×#681	D₄	1	1	yes	characteristic
80	C₃×Dic₂₀	—	2	1	no	—
81	C₃×Dic₂₀	C₂³	1	2	yes	—
82	C₃×Dic₂₀	C₂³	1	1	yes	characteristic
83	C₃×D₄₀	C₂³	1	1	yes	characteristic
84	C₃×#677	—	2	1	no	—
85	C₃×#676	D₄	1	2	yes	—
86	C₃×C₈×D₅	C₂³	1	2	yes	—
87	C₃×C₅×C₁₆	C₂³	1	2	yes	—
88	C₃×#672	C₂³	1	1	yes	characteristic
89	C₃×#672	C₂³	1	1	yes	characteristic
90	C₃×#578	—	5	1	no	—
91	C₃×#578	—	5	1	no	—
92	C₃×#510	—	5	2	no	—
93	C₃×#510	—	5	2	no	—
94	C₃×#510	—	5	1	no	—
95	C₃×#510	D₅	1	1	yes	characteristic, complemented
96	C₃×#508	—	5	1	no	—
97	C₃×#508	—	5	2	no	—
98	C₂×C₃×Q₃₂	—	5	1	no	—
99	C₂×C₃×Q₃₂	—	5	2	no	—
100	C₃×#504	—	5	1	no	—
101	#4150	—	2	1	no	—
102	#4147	—	2	1	no	—
103	C₅×#135	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
105	#4097	—	2	1	no	—
106	#4088	—	2	1	no	—
107	#4065	C₂²×C₃	1	2	yes	—
108	#4064	—	2	2	no	—
109	D₅×Q₁₆	C₂²×C₃	1	2	yes	—
110	D₅×Q₁₆	C₂²×C₃	1	2	yes	—
111	#4061	—	2	2	no	—
112	#4058	C₂²×C₃	1	2	yes	—
113	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
114	#4050	C₂²×C₃	1	1	yes	characteristic
115	#4047	C₂²×C₃	1	1	yes	characteristic
116	C₅×Q₃₂	C₂²×C₃	1	2	yes	—
117	C₅×SD₃₂	C₂²×C₃	1	2	yes	—
118	C₅×M₃₂	C₂²×C₃	1	1	yes	characteristic
119	#3961	C₂²×C₃	1	2	yes	—
120	#3961	C₂²×C₃	1	2	yes	—
121	#3961	C₂²×C₃	1	1	yes	characteristic
122	#3960	C₂²×C₃	1	1	yes	characteristic
123	#3959	C₂²×C₃	1	1	yes	characteristic
124	#3958	C₂²×C₃	1	1	yes	characteristic
125	C₂×#672	C₂²×C₃	1	1	yes	characteristic
126	Dic₄₀	C₂²×C₃	1	2	yes	—
127	#3932	C₂²×C₃	1	2	yes	—
128	#3930	C₂²×C₃	1	2	yes	—
129	D₅×C₁₆	C₂²×C₃	1	2	yes	—
130	#3417	—	5	1	no	Sylow
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	4	1	no	—
134	C₃×C₅×D₄	—	2	1	no	—
135	C₃×C₅×D₄	—	4	1	no	—
136	C₂×C₃×C₄×C₅	—	4	1	no	—
137	C₂×C₃×C₄×C₅	—	4	1	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₂²⋊D₅	—	4	1	no	—
140	C₃×C₂²⋊D₅	—	4	2	no	—
141	C₃×C₂²⋊D₅	D₈	1	2	yes	—
142	C₂×C₃×Dic₅	—	4	1	no	—
143	C₂×C₃×Dic₅	—	4	2	no	—
144	C₃×D₂₀	—	2	1	no	—
145	C₃×D₂₀	—	4	2	no	—
146	C₃×D₂₀	D₈	1	1	yes	characteristic
147	C₃×C₄×D₅	—	4	2	no	—
148	C₃×C₄×D₅	—	4	2	no	—
149	C₃×C₄×D₅	—	4	1	no	—
150	C₃×C₄×D₅	—	4	2	no	—
151	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
152	C₃×Dic₁₀	—	2	1	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×Dic₁₀	—	4	1	no	—
155	C₃×Dic₁₀	—	4	2	no	—
156	C₃×Dic₁₀	—	4	2	no	—
157	C₃×Dic₁₀	D₈	1	1	yes	characteristic
158	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
160	C₃×#168	C₂×D₄	1	2	yes	—
161	C₃×2₋¹⁺⁴	—	10	1	no	—
162	C₃×2₋¹⁺⁴	—	10	1	no	—
163	C₃×#137	—	10	2	no	—
164	C₃×#137	—	10	2	no	—
165	C₃×#137	—	10	1	no	—
166	C₃×#137	—	10	1	no	—
167	C₃×#135	—	5	2	no	—
168	C₃×#135	—	5	2	no	—
169	C₃×#135	—	5	1	no	—
170	C₃×#135	C₂×D₅	1	1	yes	characteristic
171	C₂×C₃×Q₁₆	—	5	2	no	—
172	C₂×C₃×Q₁₆	—	5	2	no	—
173	C₂×C₃×Q₁₆	—	5	1	no	—
174	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
175	C₃×#131	—	5	1	no	—
176	C₃×Q₃₂	—	5	1	no	—
177	C₃×Q₃₂	—	5	2	no	—
178	C₃×Q₃₂	—	5	2	no	—
179	C₃×Q₃₂	—	5	2	no	—
180	C₃×Q₃₂	C₂×D₅	1	2	yes	—
181	C₃×SD₃₂	—	5	1	no	—
182	C₃×SD₃₂	—	5	1	no	—
183	C₃×SD₃₂	—	5	2	no	—
184	C₃×SD₃₂	C₂×D₅	1	2	yes	—
185	C₃×D₁₆	—	5	1	no	—
186	C₃×M₃₂	—	5	2	no	—
187	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic
188	C₂×C₃×C₁₆	—	5	1	no	—
189	C₂×C₃×C₁₆	—	5	2	no	—
190	C₅×#41	—	2	1	no	—
191	C₂×C₅×Q₈	—	2	1	no	—
192	#713	—	2	2	no	—
193	#713	—	4	1	no	—
194	Q₈×D₅	—	2	2	no	—
195	Q₈×D₅	—	2	2	no	—
196	Q₈×D₅	—	4	1	no	—
197	#711	—	2	2	no	—
198	#711	—	4	2	no	—
199	#709	—	2	1	no	—
200	#709	—	4	2	no	—
201	#709	—	4	1	no	—
202	#709	C₃×D₄	1	1	yes	characteristic
203	C₂×Dic₁₀	—	2	1	no	—
204	C₂×Dic₁₀	—	4	1	no	—
205	C₅×Q₁₆	—	2	1	no	—
206	C₅×Q₁₆	C₂³×C₃	1	2	yes	—
207	C₅×Q₁₆	C₂³×C₃	1	1	yes	characteristic
208	C₅×SD₁₆	—	2	1	no	—
209	C₅×D₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	#689	—	2	2	no	—
212	#689	—	2	2	no	—
213	#688	—	2	2	no	—
214	#687	—	2	2	no	—
215	#681	C₃×D₄	1	1	yes	characteristic
216	Dic₂₀	—	2	1	no	—
217	Dic₂₀	C₂³×C₃	1	2	yes	—
218	Dic₂₀	C₂³×C₃	1	1	yes	characteristic
219	D₄₀	C₂³×C₃	1	1	yes	characteristic
220	#677	—	2	1	no	—
221	#676	C₃×D₄	1	2	yes	—
222	C₈×D₅	C₂³×C₃	1	2	yes	—
223	C₅×C₁₆	C₂³×C₃	1	2	yes	—
224	#672	C₂³×C₃	1	1	yes	characteristic
225	#672	C₂³×C₃	1	1	yes	characteristic
226	#578	—	5	1	no	—
227	#578	—	5	1	no	—
228	#510	—	5	2	no	—
229	#510	—	5	2	no	—
230	#510	—	5	1	no	—
231	#510	C₃×D₅	1	1	yes	characteristic, complemented
232	#508	—	5	1	no	—
233	#508	—	5	2	no	—
234	C₂×Q₃₂	—	5	1	no	—
235	C₂×Q₃₂	—	5	2	no	—
236	#504	—	5	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
239	C₂×C₃×D₅	—	4	1	no	—
240	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₃×Dic₅	—	4	1	no	—
246	C₃×Dic₅	—	4	2	no	—
247	C₃×Dic₅	C₂×D₈	1	2	yes	—
248	C₃×#41	—	2	1	no	—
249	C₃×#41	—	5	1	no	—
250	C₃×#41	—	10	2	no	—
251	C₃×#41	—	10	2	no	—
252	C₃×#41	—	10	1	no	—
253	C₃×#41	—	20	2	no	—
254	C₃×#41	—	20	1	no	—
255	C₃×#41	—	20	2	no	—
256	C₃×#41	—	20	1	no	—
257	C₂×C₃×Q₈	—	2	1	no	—
258	C₂×C₃×Q₈	—	10	2	no	—
259	C₂×C₃×Q₈	—	10	2	no	—
260	C₂×C₃×Q₈	—	10	1	no	—
261	C₂×C₃×Q₈	—	20	1	no	—
262	C₂×C₃×Q₈	—	20	1	no	—
263	C₃×Q₁₆	—	2	1	no	—
264	C₃×Q₁₆	—	5	2	no	—
265	C₃×Q₁₆	—	5	1	no	—
266	C₃×Q₁₆	—	10	2	no	—
267	C₃×Q₁₆	—	10	2	no	—
268	C₃×Q₁₆	—	10	1	no	—
269	C₃×Q₁₆	C₂²×D₅	1	1	yes	characteristic
270	C₃×Q₁₆	C₂²×D₅	1	2	yes	—
271	C₃×SD₁₆	—	2	1	no	—
272	C₃×SD₁₆	—	10	2	no	—
273	C₃×SD₁₆	—	10	2	no	—
274	C₃×SD₁₆	—	10	1	no	—
275	C₃×D₈	—	5	1	no	—
276	C₃×D₈	C₂²×D₅	1	1	yes	characteristic
277	C₃×M₁₆	—	5	1	no	—
278	C₃×M₁₆	—	5	2	no	—
279	C₂×C₃×C₈	—	5	2	no	—
280	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
281	C₃×C₁₆	—	5	1	no	—
282	C₃×C₁₆	—	5	1	no	—
283	C₃×C₁₆	C₂²×D₅	1	2	yes	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	1	no	—
286	C₅×Q₈	—	4	1	no	—
287	C₅×D₄	—	2	1	no	—
288	C₅×D₄	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂²⋊D₅	—	4	1	no	—
293	C₂²⋊D₅	—	4	2	no	—
294	C₂²⋊D₅	C₃×D₈	1	2	yes	—
295	C₂×Dic₅	—	4	1	no	—
296	C₂×Dic₅	—	4	2	no	—
297	D₂₀	—	2	1	no	—
298	D₂₀	—	4	2	no	—
299	D₂₀	C₃×D₈	1	1	yes	characteristic
300	C₄×D₅	—	4	2	no	—
301	C₄×D₅	—	4	2	no	—
302	C₄×D₅	—	4	1	no	—
303	C₄×D₅	—	4	2	no	—
304	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
305	Dic₁₀	—	2	1	no	—
306	Dic₁₀	—	2	2	no	—
307	Dic₁₀	—	4	1	no	—
308	Dic₁₀	—	4	2	no	—
309	Dic₁₀	—	4	2	no	—
310	Dic₁₀	C₃×D₈	1	1	yes	characteristic
311	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
312	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
313	#168	C₂×C₃×D₄	1	2	yes	—
314	2₋¹⁺⁴	—	10	1	no	—
315	2₋¹⁺⁴	—	10	1	no	—
316	#137	—	10	2	no	—
317	#137	—	10	2	no	—
318	#137	—	10	1	no	—
319	#137	—	10	1	no	—
320	#135	—	5	2	no	—
321	#135	—	5	2	no	—
322	#135	—	5	1	no	—
323	#135	C₂×C₃×D₅	1	1	yes	characteristic
324	C₂×Q₁₆	—	5	2	no	—
325	C₂×Q₁₆	—	5	2	no	—
326	C₂×Q₁₆	—	5	1	no	—
327	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
328	#131	—	5	1	no	—
329	Q₃₂	—	5	1	no	—
330	Q₃₂	—	5	2	no	—
331	Q₃₂	—	5	2	no	—
332	Q₃₂	—	5	2	no	—
333	Q₃₂	C₂×C₃×D₅	1	2	yes	—
334	SD₃₂	—	5	1	no	—
335	SD₃₂	—	5	1	no	—
336	SD₃₂	—	5	2	no	—
337	SD₃₂	C₂×C₃×D₅	1	2	yes	—
338	D₁₆	—	5	1	no	—
339	M₃₂	—	5	2	no	—
340	M₃₂	C₂×C₃×D₅	1	1	yes	characteristic
341	C₂×C₁₆	—	5	1	no	—
342	C₂×C₁₆	—	5	2	no	—
343	C₂×C₃×C₅	—	2	1	no	—
344	C₂×C₃×C₅	—	8	1	no	—
345	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
346	C₃×D₅	—	2	2	no	—
347	C₃×D₅	—	8	1	no	—
348	C₃×Q₈	—	2	1	no	—
349	C₃×Q₈	—	2	2	no	—
350	C₃×Q₈	—	4	1	no	—
351	C₃×Q₈	—	5	1	no	—
352	C₃×Q₈	—	10	1	no	—
353	C₃×Q₈	—	10	2	no	—
354	C₃×Q₈	—	20	2	no	—
355	C₃×Q₈	—	20	2	no	—
356	C₃×Q₈	—	20	1	no	—
357	C₃×D₄	—	2	1	no	—
358	C₃×D₄	—	4	1	no	—
359	C₃×D₄	—	5	2	no	—
360	C₃×D₄	—	5	1	no	—
361	C₃×D₄	—	10	1	no	—
362	C₃×D₄	—	20	2	no	—
363	C₃×D₄	—	20	2	no	—
364	C₃×D₄	—	20	1	no	—
365	C₂×C₃×C₄	—	4	1	no	—
366	C₂×C₃×C₄	—	4	1	no	—
367	C₂×C₃×C₄	—	5	2	no	—
368	C₂×C₃×C₄	—	20	2	no	—
369	C₂×C₃×C₄	—	20	2	no	—
370	C₂×C₃×C₄	—	20	2	no	—
371	C₂×C₃×C₄	—	20	2	no	—
372	C₂×C₃×C₄	—	20	1	no	—
373	C₂×C₃×C₄	—	20	1	no	—
374	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
375	C₃×C₈	—	5	2	no	—
376	C₃×C₈	D₄×D₅	1	1	yes	characteristic
377	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
380	C₂×D₅	—	4	1	no	—
381	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
382	C₄×C₅	—	4	1	no	—
383	C₄×C₅	—	4	2	no	—
384	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
385	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
386	Dic₅	—	4	1	no	—
387	Dic₅	—	4	2	no	—
388	Dic₅	C₂×C₃×D₈	1	2	yes	—
389	#41	—	2	1	no	—
390	#41	—	5	1	no	—
391	#41	—	10	2	no	—
392	#41	—	10	2	no	—
393	#41	—	10	1	no	—
394	#41	—	20	2	no	—
395	#41	—	20	1	no	—
396	#41	—	20	2	no	—
397	#41	—	20	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	10	2	no	—
400	C₂×Q₈	—	10	2	no	—
401	C₂×Q₈	—	10	1	no	—
402	C₂×Q₈	—	20	1	no	—
403	C₂×Q₈	—	20	1	no	—
404	Q₁₆	—	2	1	no	—
405	Q₁₆	—	5	1	no	—
406	Q₁₆	—	5	2	no	—
407	Q₁₆	—	10	2	no	—
408	Q₁₆	—	10	2	no	—
409	Q₁₆	—	10	1	no	—
410	Q₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
411	Q₁₆	C₂²×C₃×D₅	1	2	yes	—
412	SD₁₆	—	2	1	no	—
413	SD₁₆	—	10	2	no	—
414	SD₁₆	—	10	2	no	—
415	SD₁₆	—	10	1	no	—
416	D₈	—	5	1	no	—
417	D₈	C₂²×C₃×D₅	1	1	yes	characteristic
418	M₁₆	—	5	1	no	—
419	M₁₆	—	5	2	no	—
420	C₂×C₈	—	5	2	no	—
421	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₁₆	—	5	1	no	—
423	C₁₆	—	5	1	no	—
424	C₁₆	C₂²×C₃×D₅	1	2	yes	—
425	C₃×C₅	#3417	1	1	yes	characteristic, complemented, Hall
426	C₂²×C₃	—	4	1	no	—
427	C₂²×C₃	—	5	2	no	—
428	C₂²×C₃	—	20	1	no	—
429	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	5	2	no	—
433	C₃×C₄	—	20	1	no	—
434	C₃×C₄	—	20	2	no	—
435	C₃×C₄	D₅×D₈	1	1	yes	characteristic
436	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
437	C₂×C₅	—	2	1	no	—
438	C₂×C₅	—	8	1	no	—
439	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
440	D₅	—	2	2	no	—
441	D₅	—	8	1	no	—
442	Q₈	—	2	1	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	5	1	no	—
446	Q₈	—	10	2	no	—
447	Q₈	—	10	1	no	—
448	Q₈	—	20	2	no	—
449	Q₈	—	20	2	no	—
450	Q₈	—	20	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	4	1	no	—
453	D₄	—	5	2	no	—
454	D₄	—	5	1	no	—
455	D₄	—	10	1	no	—
456	D₄	—	20	2	no	—
457	D₄	—	20	2	no	—
458	D₄	—	20	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	5	2	no	—
462	C₂×C₄	—	20	2	no	—
463	C₂×C₄	—	20	2	no	—
464	C₂×C₄	—	20	2	no	—
465	C₂×C₄	—	20	2	no	—
466	C₂×C₄	—	20	1	no	—
467	C₂×C₄	—	20	1	no	—
468	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
469	C₈	—	5	2	no	—
470	C₈	C₃×D₄×D₅	1	1	yes	characteristic
471	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	8	1	no	—
474	C₂×C₃	—	10	2	no	—
475	C₂×C₃	—	40	1	no	—
476	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
477	C₅	C₃×#3417	1	1	yes	characteristic, complemented, Sylow
478	C₂²	—	4	1	no	—
479	C₂²	—	5	2	no	—
480	C₂²	—	20	1	no	—
481	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
482	C₄	—	4	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	5	2	no	—
485	C₄	—	20	1	no	—
486	C₄	—	20	2	no	—
487	C₄	C₃×D₅×D₈	1	1	yes	characteristic
488	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
489	C₃	#10613772	1	1	yes	characteristic, direct product factor, Sylow
490	C₂	—	2	1	no	—
491	C₂	—	8	1	no	—
492	C₂	—	10	2	no	—
493	C₂	—	40	1	no	—
494	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₅×D₈
commutator, cosocle	C₅×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₃×C₅×#510	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₃×#510	D₅
hypocenter	C₅	C₃×#3417
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#510

Complements

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

N	H ≅ G/N	type
1. C₃×#66105	C₂	semidirect
2. C₃×#66100	C₂	semidirect
3. C₃×C₅×#510	C₂	semidirect
4. C₃×#65483	C₂	semidirect
5. C₂×C₃×#3961	C₂	semidirect
6. C₃×#65207	C₂	semidirect
7. C₃×D₅×Q₃₂	C₂	semidirect
8. C₃×#65205	C₂	semidirect
9. C₃×#65204	C₂	semidirect
10. C₃×#65198	C₂	semidirect
11. C₃×#65196	C₂	semidirect
12. #10613772	C₃	direct (N × H)
43. #66105	C₂×C₃	semidirect
44. #66100	C₂×C₃	semidirect
45. C₅×#510	C₂×C₃	semidirect
46. #65483	C₂×C₃	semidirect
47. C₂×#3961	C₂×C₃	semidirect
48. #65207	C₂×C₃	semidirect
49. D₅×Q₃₂	C₂×C₃	semidirect
50. #65205	C₂×C₃	semidirect
51. #65204	C₂×C₃	semidirect
52. #65198	C₂×C₃	semidirect
53. #65196	C₂×C₃	semidirect
95. C₃×#510	D₅	semidirect
231. #510	C₃×D₅	semidirect
425. C₃×C₅	#3417	semidirect
477. C₅	C₃×#3417	semidirect
489. C₃	#10613772	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×#66105	2
C₃×#66100	2
C₃×C₅×#510	2
C₃×#65483	2
C₂×C₃×#3961	2
C₃×#65207	2
C₃×D₅×Q₃₂	2
C₃×#65205	2
C₃×#65204	2
C₃×#65198	2
C₃×#65196	2
#10613772	3
C₃×#3417	5

Subgroups — C3×#10613772 #14478623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613772 #14478623