Subgroups — C₃×#10613767 #14478495

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66103	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66091	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3958	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65205	C₂	1	2	yes	maximal, complemented
7	C₃×#65203	C₂	1	2	yes	maximal, complemented
8	C₃×#65200	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×D₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×#65197	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65196	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613767	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×#4149	—	2	1	no	—
14	C₃×#4144	—	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	C₃×#4095	—	2	1	no	—
18	C₃×#4078	—	2	1	no	—
19	C₃×#4065	C₂²	1	2	yes	complemented
20	C₃×#4060	—	2	2	no	—
21	C₃×#4058	C₂²	1	2	yes	complemented
22	C₃×#4057	—	2	2	no	—
23	C₃×D₅×D₈	C₂²	1	2	yes	complemented
24	C₃×D₅×D₈	C₂²	1	2	yes	complemented
25	C₃×#4050	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
27	C₃×#4047	C₂²	1	1	yes	characteristic
28	C₃×C₅×SD₃₂	C₂²	1	2	yes	complemented
29	C₃×C₅×D₁₆	C₂²	1	2	yes	complemented
30	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3961	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3960	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3959	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3958	C₂²	1	2	yes	complemented
35	C₃×#3958	C₂²	1	2	yes	complemented
36	C₃×#3958	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3932	C₂²	1	2	yes	complemented
39	C₃×D₈₀	C₂²	1	2	yes	complemented
40	C₃×#3930	C₂²	1	2	yes	complemented
41	C₃×D₅×C₁₆	C₂²	1	2	yes	complemented
42	C₃×#3415	—	5	1	no	maximal, Hall
43	#66103	C₂×C₃	1	1	yes	characteristic, complemented
44	#66091	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#509	C₂×C₃	1	1	yes	characteristic, complemented
46	#65483	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3958	C₂×C₃	1	1	yes	characteristic, complemented
48	#65205	C₂×C₃	1	2	yes	complemented
49	#65203	C₂×C₃	1	2	yes	complemented
50	#65200	C₂×C₃	1	2	yes	complemented
51	D₅×D₁₆	C₂×C₃	1	2	yes	complemented
52	#65197	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×D₄	—	2	1	no	—
56	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
57	C₃×#713	—	2	2	no	—
58	C₃×#711	—	2	2	no	—
59	C₃×#711	—	4	1	no	—
60	C₃×D₄×D₅	—	2	2	no	—
61	C₃×D₄×D₅	—	2	2	no	—
62	C₃×D₄×D₅	—	4	2	no	—
63	C₃×D₄×D₅	—	4	1	no	—
64	C₃×#709	—	2	1	no	—
65	C₃×#709	—	4	1	no	—
66	C₃×#709	D₄	1	1	yes	characteristic
67	C₂×C₃×D₂₀	—	2	1	no	—
68	C₂×C₃×D₂₀	—	4	1	no	—
69	C₃×C₅×Q₁₆	C₂³	1	1	yes	characteristic
70	C₃×C₅×SD₁₆	—	2	1	no	—
71	C₃×C₅×D₈	—	2	1	no	—
72	C₃×C₅×D₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×D₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×#688	—	2	2	no	—
76	C₃×#687	—	2	2	no	—
77	C₃×#686	—	2	2	no	—
78	C₃×#686	—	2	2	no	—
79	C₃×#681	D₄	1	1	yes	characteristic
80	C₃×Dic₂₀	C₂³	1	1	yes	characteristic
81	C₃×D₄₀	—	2	1	no	—
82	C₃×D₄₀	C₂³	1	1	yes	characteristic
83	C₃×D₄₀	C₂³	1	2	yes	—
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×#576	—	5	1	no	—
91	C₃×#576	—	5	1	no	—
92	C₃×#509	—	5	2	no	—
93	C₃×#509	—	5	2	no	—
94	C₃×#509	—	5	1	no	—
95	C₃×#509	D₅	1	1	yes	characteristic, complemented
96	C₃×#508	—	5	1	no	—
97	C₃×#508	—	5	2	no	—
98	C₂×C₃×D₁₆	—	5	1	no	—
99	C₂×C₃×D₁₆	—	5	2	no	—
100	C₃×#504	—	5	1	no	—
101	#4149	—	2	1	no	—
102	#4144	—	2	1	no	—
103	C₅×#135	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
105	#4095	—	2	1	no	—
106	#4078	—	2	1	no	—
107	#4065	C₂²×C₃	1	2	yes	complemented
108	#4060	—	2	2	no	—
109	#4058	C₂²×C₃	1	2	yes	complemented
110	#4057	—	2	2	no	—
111	D₅×D₈	C₂²×C₃	1	2	yes	complemented
112	D₅×D₈	C₂²×C₃	1	2	yes	complemented
113	#4050	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
115	#4047	C₂²×C₃	1	1	yes	characteristic
116	C₅×SD₃₂	C₂²×C₃	1	2	yes	complemented
117	C₅×D₁₆	C₂²×C₃	1	2	yes	complemented
118	C₅×M₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
119	#3961	C₂²×C₃	1	1	yes	characteristic, complemented
120	#3960	C₂²×C₃	1	1	yes	characteristic, complemented
121	#3959	C₂²×C₃	1	1	yes	characteristic, complemented
122	#3958	C₂²×C₃	1	2	yes	complemented
123	#3958	C₂²×C₃	1	2	yes	complemented
124	#3958	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×#672	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3932	C₂²×C₃	1	2	yes	complemented
127	D₈₀	C₂²×C₃	1	2	yes	complemented
128	#3930	C₂²×C₃	1	2	yes	complemented
129	D₅×C₁₆	C₂²×C₃	1	2	yes	complemented
130	#3415	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	4	1	no	—
132	C₂²×C₃×D₅	—	4	1	no	—
133	C₂²×C₃×D₅	—	4	2	no	—
134	C₂²×C₃×D₅	—	4	2	no	—
135	C₃×C₅×Q₈	—	2	1	no	—
136	C₃×C₅×D₄	—	2	1	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	4	1	no	—
139	C₃×C₅×D₄	—	4	1	no	—
140	C₂×C₃×C₄×C₅	—	4	1	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₃×C₂²⋊D₅	—	4	1	no	—
143	C₃×C₂²⋊D₅	—	4	2	no	—
144	C₃×C₂²⋊D₅	—	4	2	no	—
145	C₃×C₂²⋊D₅	—	4	2	no	—
146	C₃×C₂²⋊D₅	D₈	1	2	yes	—
147	C₂×C₃×Dic₅	—	4	2	no	—
148	C₃×D₂₀	—	2	1	no	—
149	C₃×D₂₀	—	2	2	no	—
150	C₃×D₂₀	—	4	2	no	—
151	C₃×D₂₀	—	4	1	no	—
152	C₃×D₂₀	D₈	1	1	yes	characteristic
153	C₃×C₄×D₅	—	4	1	no	—
154	C₃×C₄×D₅	—	4	2	no	—
155	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
156	C₃×Dic₁₀	—	2	1	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×H(5,𝔽₂)	—	10	1	no	—
162	C₃×H(5,𝔽₂)	—	10	1	no	—
163	C₃×AGL(1,ℤ/8)	—	10	2	no	—
164	C₃×AGL(1,ℤ/8)	—	10	2	no	—
165	C₃×AGL(1,ℤ/8)	—	10	1	no	—
166	C₃×AGL(1,ℤ/8)	—	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, complemented
171	C₂×C₃×D₈	—	5	2	no	—
172	C₂×C₃×D₈	—	5	2	no	—
173	C₂×C₃×D₈	—	5	1	no	—
174	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
175	C₃×#131	—	5	1	no	—
176	C₃×Q₃₂	—	5	1	no	—
177	C₃×SD₃₂	—	5	1	no	—
178	C₃×SD₃₂	—	5	1	no	—
179	C₃×SD₃₂	—	5	2	no	—
180	C₃×SD₃₂	C₂×D₅	1	2	yes	complemented
181	C₃×D₁₆	—	5	2	no	—
182	C₃×D₁₆	—	5	1	no	—
183	C₃×D₁₆	—	5	2	no	—
184	C₃×D₁₆	—	5	2	no	—
185	C₃×D₁₆	C₂×D₅	1	2	yes	complemented
186	C₃×M₃₂	—	5	2	no	—
187	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
188	C₂×C₃×C₁₆	—	5	1	no	—
189	C₂×C₃×C₁₆	—	5	2	no	—
190	C₅×#41	—	2	1	no	—
191	C₂×C₅×D₄	—	2	1	no	—
192	C₂×C₂²⋊D₅	—	4	2	no	—
193	#713	—	2	2	no	—
194	#711	—	2	2	no	—
195	#711	—	4	1	no	—
196	D₄×D₅	—	2	2	no	—
197	D₄×D₅	—	2	2	no	—
198	D₄×D₅	—	4	2	no	—
199	D₄×D₅	—	4	1	no	—
200	#709	—	2	1	no	—
201	#709	—	4	1	no	—
202	#709	C₃×D₄	1	1	yes	characteristic
203	C₂×D₂₀	—	2	1	no	—
204	C₂×D₂₀	—	4	1	no	—
205	C₅×Q₁₆	C₂³×C₃	1	1	yes	characteristic
206	C₅×SD₁₆	—	2	1	no	—
207	C₅×D₈	—	2	1	no	—
208	C₅×D₈	C₂³×C₃	1	2	yes	—
209	C₅×D₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	#688	—	2	2	no	—
212	#687	—	2	2	no	—
213	#686	—	2	2	no	—
214	#686	—	2	2	no	—
215	#681	C₃×D₄	1	1	yes	characteristic
216	Dic₂₀	C₂³×C₃	1	1	yes	characteristic
217	D₄₀	—	2	1	no	—
218	D₄₀	C₂³×C₃	1	1	yes	characteristic
219	D₄₀	C₂³×C₃	1	2	yes	—
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	#576	—	5	1	no	—
227	#576	—	5	1	no	—
228	#509	—	5	2	no	—
229	#509	—	5	2	no	—
230	#509	—	5	1	no	—
231	#509	C₃×D₅	1	1	yes	characteristic, complemented
232	#508	—	5	1	no	—
233	#508	—	5	2	no	—
234	C₂×D₁₆	—	5	1	no	—
235	C₂×D₁₆	—	5	2	no	—
236	#504	—	5	1	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	—	16	1	no	—
240	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
241	C₂×C₃×D₅	—	4	2	no	—
242	C₂×C₃×D₅	—	4	1	no	—
243	C₂×C₃×D₅	—	16	2	no	—
244	C₂×C₃×D₅	—	16	2	no	—
245	C₂×C₃×D₅	—	16	1	no	—
246	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
249	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₃×Dic₅	—	4	1	no	—
251	C₃×Dic₅	C₂×D₈	1	2	yes	—
252	C₃×#41	—	2	1	no	—
253	C₃×#41	—	5	1	no	—
254	C₃×#41	—	10	2	no	—
255	C₃×#41	—	10	2	no	—
256	C₃×#41	—	10	1	no	—
257	C₃×#41	—	20	1	no	—
258	C₃×#41	—	20	1	no	—
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	10	2	no	—
261	C₂×C₃×D₄	—	10	2	no	—
262	C₂×C₃×D₄	—	10	1	no	—
263	C₂×C₃×D₄	—	20	1	no	—
264	C₂×C₃×D₄	—	20	2	no	—
265	C₂×C₃×D₄	—	20	1	no	—
266	C₂×C₃×D₄	—	20	2	no	—
267	C₃×Q₁₆	—	5	1	no	—
268	C₃×Q₁₆	C₂²×D₅	1	1	yes	characteristic
269	C₃×SD₁₆	—	2	1	no	—
270	C₃×SD₁₆	—	10	2	no	—
271	C₃×SD₁₆	—	10	2	no	—
272	C₃×SD₁₆	—	10	1	no	—
273	C₃×D₈	—	2	1	no	—
274	C₃×D₈	—	5	1	no	—
275	C₃×D₈	—	5	2	no	—
276	C₃×D₈	—	10	2	no	—
277	C₃×D₈	—	10	2	no	—
278	C₃×D₈	—	10	1	no	—
279	C₃×D₈	C₂²×D₅	1	2	yes	—
280	C₃×D₈	C₂²×D₅	1	1	yes	characteristic
281	C₃×M₁₆	—	5	1	no	—
282	C₃×M₁₆	—	5	2	no	—
283	C₂×C₃×C₈	—	5	2	no	—
284	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
285	C₃×C₁₆	—	5	1	no	—
286	C₃×C₁₆	—	5	1	no	—
287	C₃×C₁₆	C₂²×D₅	1	2	yes	—
288	C₂³×C₅	—	4	1	no	—
289	C₂²×D₅	—	4	1	no	—
290	C₂²×D₅	—	4	2	no	—
291	C₂²×D₅	—	4	2	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	4	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂²⋊D₅	—	4	1	no	—
300	C₂²⋊D₅	—	4	2	no	—
301	C₂²⋊D₅	—	4	2	no	—
302	C₂²⋊D₅	—	4	2	no	—
303	C₂²⋊D₅	C₃×D₈	1	2	yes	—
304	C₂×Dic₅	—	4	2	no	—
305	D₂₀	—	2	1	no	—
306	D₂₀	—	2	2	no	—
307	D₂₀	—	4	2	no	—
308	D₂₀	—	4	1	no	—
309	D₂₀	C₃×D₈	1	1	yes	characteristic
310	C₄×D₅	—	4	1	no	—
311	C₄×D₅	—	4	2	no	—
312	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
313	Dic₁₀	—	2	1	no	—
314	Dic₁₀	C₃×D₈	1	1	yes	characteristic
315	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
316	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
317	#168	C₂×C₃×D₄	1	2	yes	—
318	H(5,𝔽₂)	—	10	1	no	—
319	H(5,𝔽₂)	—	10	1	no	—
320	AGL(1,ℤ/8)	—	10	2	no	—
321	AGL(1,ℤ/8)	—	10	2	no	—
322	AGL(1,ℤ/8)	—	10	1	no	—
323	AGL(1,ℤ/8)	—	10	1	no	—
324	#135	—	5	2	no	—
325	#135	—	5	2	no	—
326	#135	—	5	1	no	—
327	#135	C₂×C₃×D₅	1	1	yes	characteristic, complemented
328	C₂×D₈	—	5	2	no	—
329	C₂×D₈	—	5	2	no	—
330	C₂×D₈	—	5	1	no	—
331	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
332	#131	—	5	1	no	—
333	Q₃₂	—	5	1	no	—
334	SD₃₂	—	5	1	no	—
335	SD₃₂	—	5	1	no	—
336	SD₃₂	—	5	2	no	—
337	SD₃₂	C₂×C₃×D₅	1	2	yes	complemented
338	D₁₆	—	5	2	no	—
339	D₁₆	—	5	1	no	—
340	D₁₆	—	5	2	no	—
341	D₁₆	—	5	2	no	—
342	D₁₆	C₂×C₃×D₅	1	2	yes	complemented
343	M₃₂	—	5	2	no	—
344	M₃₂	C₂×C₃×D₅	1	1	yes	characteristic, complemented
345	C₂×C₁₆	—	5	1	no	—
346	C₂×C₁₆	—	5	2	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	8	1	no	—
349	C₂×C₃×C₅	—	8	2	no	—
350	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
351	C₃×D₅	—	2	2	no	—
352	C₃×D₅	—	8	2	no	—
353	C₃×D₅	—	8	1	no	—
354	C₂³×C₃	—	4	1	no	—
355	C₂³×C₃	—	20	2	no	—
356	C₂³×C₃	—	20	2	no	—
357	C₂³×C₃	—	20	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	5	1	no	—
360	C₃×Q₈	—	10	1	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	4	1	no	—
364	C₃×D₄	—	4	1	no	—
365	C₃×D₄	—	5	2	no	—
366	C₃×D₄	—	5	1	no	—
367	C₃×D₄	—	10	1	no	—
368	C₃×D₄	—	10	2	no	—
369	C₃×D₄	—	20	2	no	—
370	C₃×D₄	—	20	2	no	—
371	C₃×D₄	—	20	2	no	—
372	C₃×D₄	—	20	2	no	—
373	C₃×D₄	—	20	1	no	—
374	C₃×D₄	—	20	1	no	—
375	C₂×C₃×C₄	—	4	1	no	—
376	C₂×C₃×C₄	—	5	2	no	—
377	C₂×C₃×C₄	—	20	2	no	—
378	C₂×C₃×C₄	—	20	2	no	—
379	C₂×C₃×C₄	—	20	1	no	—
380	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
381	C₃×C₈	—	5	2	no	—
382	C₃×C₈	D₄×D₅	1	1	yes	characteristic
383	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
384	C₂²×C₅	—	4	2	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	16	1	no	—
387	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
388	C₂×D₅	—	4	2	no	—
389	C₂×D₅	—	4	1	no	—
390	C₂×D₅	—	16	2	no	—
391	C₂×D₅	—	16	2	no	—
392	C₂×D₅	—	16	1	no	—
393	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
396	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
397	Dic₅	—	4	1	no	—
398	Dic₅	C₂×C₃×D₈	1	2	yes	—
399	#41	—	2	1	no	—
400	#41	—	5	1	no	—
401	#41	—	10	2	no	—
402	#41	—	10	2	no	—
403	#41	—	10	1	no	—
404	#41	—	20	1	no	—
405	#41	—	20	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	10	2	no	—
408	C₂×D₄	—	10	2	no	—
409	C₂×D₄	—	10	1	no	—
410	C₂×D₄	—	20	1	no	—
411	C₂×D₄	—	20	2	no	—
412	C₂×D₄	—	20	1	no	—
413	C₂×D₄	—	20	2	no	—
414	Q₁₆	—	5	1	no	—
415	Q₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
416	SD₁₆	—	2	1	no	—
417	SD₁₆	—	10	2	no	—
418	SD₁₆	—	10	2	no	—
419	SD₁₆	—	10	1	no	—
420	D₈	—	2	1	no	—
421	D₈	—	5	2	no	—
422	D₈	—	5	1	no	—
423	D₈	—	10	2	no	—
424	D₈	—	10	2	no	—
425	D₈	—	10	1	no	—
426	D₈	C₂²×C₃×D₅	1	2	yes	—
427	D₈	C₂²×C₃×D₅	1	1	yes	characteristic
428	M₁₆	—	5	1	no	—
429	M₁₆	—	5	2	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
432	C₁₆	—	5	1	no	—
433	C₁₆	—	5	1	no	—
434	C₁₆	C₂²×C₃×D₅	1	2	yes	—
435	C₃×C₅	#3415	1	1	yes	characteristic, complemented, Hall
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	5	2	no	—
439	C₂²×C₃	—	16	1	no	—
440	C₂²×C₃	—	20	2	no	—
441	C₂²×C₃	—	20	1	no	—
442	C₂²×C₃	—	80	1	no	—
443	C₂²×C₃	—	80	2	no	—
444	C₂²×C₃	—	80	2	no	—
445	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	—	5	2	no	—
448	C₃×C₄	—	20	1	no	—
449	C₃×C₄	D₅×D₈	1	1	yes	characteristic
450	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	8	1	no	—
453	C₂×C₅	—	8	2	no	—
454	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
455	D₅	—	2	2	no	—
456	D₅	—	8	2	no	—
457	D₅	—	8	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	20	2	no	—
460	C₂³	—	20	2	no	—
461	C₂³	—	20	1	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	5	1	no	—
464	Q₈	—	10	1	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	4	1	no	—
468	D₄	—	4	1	no	—
469	D₄	—	5	2	no	—
470	D₄	—	5	1	no	—
471	D₄	—	10	1	no	—
472	D₄	—	10	2	no	—
473	D₄	—	20	2	no	—
474	D₄	—	20	2	no	—
475	D₄	—	20	2	no	—
476	D₄	—	20	2	no	—
477	D₄	—	20	1	no	—
478	D₄	—	20	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	5	2	no	—
481	C₂×C₄	—	20	2	no	—
482	C₂×C₄	—	20	2	no	—
483	C₂×C₄	—	20	1	no	—
484	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
485	C₈	—	5	2	no	—
486	C₈	C₃×D₄×D₅	1	1	yes	characteristic
487	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	8	2	no	—
490	C₂×C₃	—	8	1	no	—
491	C₂×C₃	—	10	2	no	—
492	C₂×C₃	—	40	2	no	—
493	C₂×C₃	—	40	1	no	—
494	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
495	C₅	C₃×#3415	1	1	yes	characteristic, complemented, Sylow
496	C₂²	—	4	1	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	5	2	no	—
499	C₂²	—	16	1	no	—
500	C₂²	—	20	2	no	—
501	C₂²	—	20	1	no	—
502	C₂²	—	80	1	no	—
503	C₂²	—	80	2	no	—
504	C₂²	—	80	2	no	—
505	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
506	C₄	—	4	1	no	—
507	C₄	—	5	2	no	—
508	C₄	—	20	1	no	—
509	C₄	C₃×D₅×D₈	1	1	yes	characteristic
510	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
511	C₃	#10613767	1	1	yes	characteristic, direct product factor, Sylow
512	C₂	—	2	1	no	—
513	C₂	—	8	2	no	—
514	C₂	—	8	1	no	—
515	C₂	—	10	2	no	—
516	C₂	—	40	2	no	—
517	C₂	—	40	1	no	—
518	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×#509	C₂
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₃×#509	D₅
hypocenter	C₅	C₃×#3415
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#509

Complements

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

N	H ≅ G/N	type
1. C₃×#66103	C₂	semidirect
2. C₃×#66091	C₂	semidirect
3. C₃×C₅×#509	C₂	semidirect
4. C₃×#65483	C₂	semidirect
5. C₂×C₃×#3958	C₂	semidirect
6. C₃×#65205	C₂	semidirect
7. C₃×#65203	C₂	semidirect
8. C₃×#65200	C₂	semidirect
9. C₃×D₅×D₁₆	C₂	semidirect
10. C₃×#65197	C₂	semidirect
11. C₃×#65196	C₂	semidirect
12. #10613767	C₃	direct (N × H)
15. C₃×C₅×#135	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₃×#4065	C₂²	semidirect
21. C₃×#4058	C₂²	semidirect
23. C₃×D₅×D₈	C₂²	semidirect
24. C₃×D₅×D₈	C₂²	semidirect
25. C₃×#4050	C₂²	semidirect
26. C₂×C₃×D₄₀	C₂²	semidirect
28. C₃×C₅×SD₃₂	C₂²	semidirect
29. C₃×C₅×D₁₆	C₂²	semidirect
30. C₃×C₅×M₃₂	C₂²	semidirect
31. C₃×#3961	C₂²	semidirect
32. C₃×#3960	C₂²	semidirect
33. C₃×#3959	C₂²	semidirect
34. C₃×#3958	C₂²	semidirect
35. C₃×#3958	C₂²	semidirect
36. C₃×#3958	C₂²	semidirect
37. C₂×C₃×#672	C₂²	semidirect
38. C₃×#3932	C₂²	semidirect
39. C₃×D₈₀	C₂²	semidirect
40. C₃×#3930	C₂²	semidirect
41. C₃×D₅×C₁₆	C₂²	semidirect
43. #66103	C₂×C₃	semidirect
44. #66091	C₂×C₃	semidirect
45. C₅×#509	C₂×C₃	semidirect
46. #65483	C₂×C₃	semidirect
47. C₂×#3958	C₂×C₃	semidirect
48. #65205	C₂×C₃	semidirect
49. #65203	C₂×C₃	semidirect
50. #65200	C₂×C₃	semidirect
51. D₅×D₁₆	C₂×C₃	semidirect
52. #65197	C₂×C₃	semidirect
53. #65196	C₂×C₃	semidirect
95. C₃×#509	D₅	semidirect
103. C₅×#135	C₂²×C₃	semidirect
104. C₂×C₅×D₈	C₂²×C₃	semidirect
107. #4065	C₂²×C₃	semidirect
109. #4058	C₂²×C₃	semidirect
111. D₅×D₈	C₂²×C₃	semidirect
112. D₅×D₈	C₂²×C₃	semidirect
113. #4050	C₂²×C₃	semidirect
114. C₂×D₄₀	C₂²×C₃	semidirect
116. C₅×SD₃₂	C₂²×C₃	semidirect
117. C₅×D₁₆	C₂²×C₃	semidirect
118. C₅×M₃₂	C₂²×C₃	semidirect
119. #3961	C₂²×C₃	semidirect
120. #3960	C₂²×C₃	semidirect
121. #3959	C₂²×C₃	semidirect
122. #3958	C₂²×C₃	semidirect
123. #3958	C₂²×C₃	semidirect
124. #3958	C₂²×C₃	semidirect
125. C₂×#672	C₂²×C₃	semidirect
126. #3932	C₂²×C₃	semidirect
127. D₈₀	C₂²×C₃	semidirect
128. #3930	C₂²×C₃	semidirect
129. D₅×C₁₆	C₂²×C₃	semidirect
170. C₃×#135	C₂×D₅	semidirect
174. C₂×C₃×D₈	C₂×D₅	semidirect
180. C₃×SD₃₂	C₂×D₅	semidirect
185. C₃×D₁₆	C₂×D₅	semidirect
187. C₃×M₃₂	C₂×D₅	semidirect
231. #509	C₃×D₅	semidirect
327. #135	C₂×C₃×D₅	semidirect
331. C₂×D₈	C₂×C₃×D₅	semidirect
337. SD₃₂	C₂×C₃×D₅	semidirect
342. D₁₆	C₂×C₃×D₅	semidirect
344. M₃₂	C₂×C₃×D₅	semidirect
435. C₃×C₅	#3415	semidirect
495. C₅	C₃×#3415	semidirect
511. C₃	#10613767	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×#66103	2
C₃×#66091	2
C₃×C₅×#509	2
C₃×#65483	2
C₂×C₃×#3958	2
C₃×#65205	2
C₃×#65203	2
C₃×#65200	2
C₃×D₅×D₁₆	2
C₃×#65197	2
C₃×#65196	2
#10613767	3
C₃×#3415	5

Subgroups — C3×#10613767 #14478495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613767 #14478495