Subgroups — C₃×#10610565 #14424217

Order 1920.

1568 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	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65290	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65100	C₂	1	4	yes	maximal, complemented
9	C₃×#65062	C₂	1	4	yes	maximal, complemented
10	#10610565	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₃×#4149	—	2	4	no	—
13	C₃×#4149	—	2	4	no	—
14	C₂×C₃×#713	C₂²	1	2	yes	complemented
15	C₂×C₃×D₄×D₅	—	2	2	no	—
16	C₂×C₃×D₄×D₅	C₂²	1	2	yes	complemented
17	C₂×C₃×#709	—	2	1	no	—
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂²×C₃×D₂₀	—	2	1	no	—
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
24	C₃×#4095	—	2	4	no	—
25	C₂×C₃×#688	C₂²	1	2	yes	complemented
26	C₂×C₃×#686	C₂²	1	2	yes	complemented
27	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×D₄₀	—	2	4	no	—
29	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
30	C₃×#4041	C₂²	1	4	yes	complemented
31	C₃×#4028	—	2	2	no	—
32	C₃×#4021	—	2	1	no	—
33	C₃×#4020	—	2	1	no	—
34	C₃×C₅×#103	C₂²	1	2	yes	complemented
35	C₃×C₅×#102	C₂²	1	2	yes	complemented
36	C₃×#3952	C₂²	1	4	yes	complemented
37	C₃×#3941	C₂²	1	4	yes	complemented
38	C₃×#3008	—	5	1	no	maximal, Hall
39	C₂×#4149	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#4095	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
42	#65859	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
44	#65399	C₂×C₃	1	1	yes	characteristic, complemented
45	#65290	C₂×C₃	1	1	yes	characteristic, complemented
46	#65100	C₂×C₃	1	4	yes	complemented
47	#65062	C₂×C₃	1	4	yes	complemented
48	C₂³×C₃×D₅	—	2	1	no	—
49	C₂³×C₃×D₅	—	2	2	no	—
50	C₂³×C₃×D₅	—	2	1	no	—
51	C₃×C₅×#41	—	2	2	no	—
52	C₃×C₅×#41	D₄	1	4	yes	complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×D₄	—	2	1	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
60	C₃×#713	—	2	4	no	—
61	C₃×#713	—	2	4	no	—
62	C₃×D₄×D₅	—	2	16	no	—
63	C₃×D₄×D₅	—	2	4	no	—
64	C₃×D₄×D₅	—	2	4	no	—
65	C₃×#709	—	2	8	no	—
66	C₃×#709	—	2	2	no	—
67	C₃×#709	—	2	2	no	—
68	C₂×C₃×D₂₀	—	2	8	no	—
69	C₂×C₃×D₂₀	—	2	2	no	—
70	C₂×C₃×D₂₀	—	2	1	no	—
71	C₂×C₃×D₂₀	—	2	2	no	—
72	C₂×C₃×D₂₀	—	2	2	no	—
73	C₂×C₃×D₂₀	—	2	2	no	—
74	C₂×C₃×D₂₀	—	2	1	no	—
75	C₂×C₃×D₂₀	—	2	4	no	—
76	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
77	C₂×C₃×D₂₀	D₄	1	4	yes	complemented
78	C₂×C₃×D₂₀	C₂³	1	2	yes	—
79	C₂×C₃×D₂₀	C₂³	1	2	yes	—
80	C₂×C₃×C₄×D₅	—	2	2	no	—
81	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
82	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	—	2	2	no	—
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
86	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×#688	—	2	4	no	—
89	C₃×#686	—	2	4	no	—
90	C₃×#685	—	2	4	no	—
91	C₃×#681	—	2	2	no	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₃×D₄₀	—	2	8	no	—
94	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
95	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
96	C₂²×C₃×D₈	—	5	1	no	—
97	C₃×#535	—	5	1	no	—
98	C₃×#449	—	5	4	no	—
99	C₃×#447	—	5	4	no	—
100	C₃×#418	—	5	1	no	—
101	C₃×#416	D₅	1	1	yes	characteristic, complemented
102	C₃×#408	—	5	1	no	—
103	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
104	#4149	—	2	4	no	—
105	#4149	—	2	4	no	—
106	C₂×#713	C₂²×C₃	1	2	yes	complemented
107	C₂×D₄×D₅	—	2	2	no	—
108	C₂×D₄×D₅	C₂²×C₃	1	2	yes	complemented
109	C₂×#709	—	2	1	no	—
110	C₂×#709	C₂²×C₃	1	1	yes	characteristic
111	C₂²×D₂₀	—	2	1	no	—
112	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
113	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
116	#4095	—	2	4	no	—
117	C₂×#688	C₂²×C₃	1	2	yes	complemented
118	C₂×#686	C₂²×C₃	1	2	yes	complemented
119	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₂×D₄₀	—	2	4	no	—
121	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
122	#4041	C₂²×C₃	1	4	yes	complemented
123	#4028	—	2	2	no	—
124	#4021	—	2	1	no	—
125	#4020	—	2	1	no	—
126	C₅×#103	C₂²×C₃	1	2	yes	complemented
127	C₅×#102	C₂²×C₃	1	2	yes	complemented
128	#3952	C₂²×C₃	1	4	yes	complemented
129	#3941	C₂²×C₃	1	4	yes	complemented
130	#3008	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₃×D₅	—	2	2	no	—
134	C₂²×C₃×D₅	—	2	8	no	—
135	C₂²×C₃×D₅	—	2	4	no	—
136	C₂²×C₃×D₅	—	2	2	no	—
137	C₂²×C₃×D₅	—	4	2	no	—
138	C₂²×C₃×D₅	—	8	4	no	—
139	C₂²×C₃×D₅	—	8	2	no	—
140	C₂²×C₃×D₅	—	8	2	no	—
141	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
142	C₃×C₅×Q₈	—	2	1	no	—
143	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
144	C₃×C₅×D₄	—	2	4	no	—
145	C₃×C₅×D₄	—	2	1	no	—
146	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	4	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₂²⋊D₅	—	2	8	no	—
155	C₃×C₂²⋊D₅	—	2	4	no	—
156	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
157	C₃×D₂₀	—	2	8	no	—
158	C₃×D₂₀	—	2	2	no	—
159	C₃×D₂₀	—	2	4	no	—
160	C₃×D₂₀	—	2	2	no	—
161	C₃×D₂₀	—	2	2	no	—
162	C₃×D₂₀	—	2	2	no	—
163	C₃×D₂₀	—	4	2	no	—
164	C₃×D₂₀	—	8	4	no	—
165	C₃×D₂₀	C₂×D₄	1	4	yes	—
166	C₃×C₄×D₅	—	2	8	no	—
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×Dic₁₀	—	2	2	no	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₃×#168	—	2	2	no	—
172	C₃×H(5,𝔽₂)	—	10	4	no	—
173	C₃×H(5,𝔽₂)	—	10	4	no	—
174	C₂×C₃×#41	—	5	1	no	—
175	C₂×C₃×#41	—	5	2	no	—
176	C₂×C₃×#41	—	10	1	no	—
177	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
178	C₂²×C₃×D₄	—	5	2	no	—
179	C₂²×C₃×D₄	—	5	1	no	—
180	C₂²×C₃×D₄	—	5	1	no	—
181	C₂²×C₃×D₄	—	10	1	no	—
182	C₂²×C₃×D₄	—	10	2	no	—
183	C₃×AGL(1,ℤ/8)	—	10	4	no	—
184	C₂×C₃×SD₁₆	—	5	2	no	—
185	C₂×C₃×D₈	—	5	2	no	—
186	C₂×C₃×D₈	—	5	4	no	—
187	C₂×C₃×D₈	—	10	4	no	—
188	C₂×C₃×M₁₆	—	5	1	no	—
189	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×#127	—	10	1	no	—
191	C₃×#124	—	10	1	no	—
192	C₃×#121	—	5	4	no	—
193	C₃×#120	—	10	2	no	—
194	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
195	C₃×#103	C₂×D₅	1	2	yes	complemented
196	C₃×#102	—	5	4	no	—
197	C₃×#102	C₂×D₅	1	2	yes	complemented
198	C₃×C₂²⋊C₈	—	5	4	no	—
199	C₂³×D₅	—	2	1	no	—
200	C₂³×D₅	—	2	2	no	—
201	C₂³×D₅	—	2	1	no	—
202	C₅×#41	—	2	2	no	—
203	C₅×#41	C₃×D₄	1	4	yes	complemented
204	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	2	no	—
210	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
211	#713	—	2	4	no	—
212	#713	—	2	4	no	—
213	D₄×D₅	—	2	16	no	—
214	D₄×D₅	—	2	4	no	—
215	D₄×D₅	—	2	4	no	—
216	#709	—	2	8	no	—
217	#709	—	2	2	no	—
218	#709	—	2	2	no	—
219	C₂×D₂₀	—	2	8	no	—
220	C₂×D₂₀	—	2	2	no	—
221	C₂×D₂₀	—	2	1	no	—
222	C₂×D₂₀	—	2	2	no	—
223	C₂×D₂₀	—	2	2	no	—
224	C₂×D₂₀	—	2	2	no	—
225	C₂×D₂₀	—	2	1	no	—
226	C₂×D₂₀	—	2	4	no	—
227	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
228	C₂×D₂₀	C₃×D₄	1	4	yes	complemented
229	C₂×D₂₀	C₂³×C₃	1	2	yes	—
230	C₂×D₂₀	C₂³×C₃	1	2	yes	—
231	C₂×C₄×D₅	—	2	2	no	—
232	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
233	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
234	C₂×C₅×C₈	—	2	2	no	—
235	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
236	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
237	C₅×C₂²⋊C₄	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	#688	—	2	4	no	—
240	#686	—	2	4	no	—
241	#685	—	2	4	no	—
242	#681	—	2	2	no	—
243	C₂×#168	C₂³×C₃	1	2	yes	—
244	D₄₀	—	2	8	no	—
245	C₂×H(5,𝔽₂)	—	5	1	no	—
246	C₂×AGL(1,ℤ/8)	—	5	1	no	—
247	C₂²×D₈	—	5	1	no	—
248	#535	—	5	1	no	—
249	#449	—	5	4	no	—
250	#447	—	5	4	no	—
251	#418	—	5	1	no	—
252	#416	C₃×D₅	1	1	yes	characteristic, complemented
253	#408	—	5	1	no	—
254	C₂²×C₃×C₅	—	2	2	no	—
255	C₂²×C₃×C₅	—	2	2	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	#120	1	2	yes	—
258	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₃×D₅	—	2	2	no	—
260	C₂×C₃×D₅	—	2	4	no	—
261	C₂×C₃×D₅	—	2	4	no	—
262	C₂×C₃×D₅	—	4	4	no	—
263	C₂×C₃×D₅	—	4	2	no	—
264	C₂×C₃×D₅	—	4	4	no	—
265	C₂×C₃×D₅	—	8	4	no	—
266	C₂×C₃×D₅	—	8	8	no	—
267	C₂×C₃×D₅	—	8	4	no	—
268	C₃×C₄×C₅	—	2	2	no	—
269	C₃×C₄×C₅	—	4	2	no	—
270	C₃×C₄×C₅	#120	1	2	yes	—
271	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₃×Dic₅	—	2	2	no	—
274	C₂⁴×C₃	—	10	2	no	—
275	C₂⁴×C₃	—	10	1	no	—
276	C₂⁴×C₃	—	10	1	no	—
277	C₃×#41	—	2	2	no	—
278	C₃×#41	—	10	8	no	—
279	C₃×#41	—	10	4	no	—
280	C₃×#41	—	10	4	no	—
281	C₃×#41	—	10	2	no	—
282	C₃×#41	—	10	2	no	—
283	C₃×#41	D₂₀	1	4	yes	complemented
284	C₂×C₃×Q₈	—	5	1	no	—
285	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
286	C₂×C₃×D₄	—	2	1	no	—
287	C₂×C₃×D₄	—	5	2	no	—
288	C₂×C₃×D₄	—	5	4	no	—
289	C₂×C₃×D₄	—	5	1	no	—
290	C₂×C₃×D₄	—	5	2	no	—
291	C₂×C₃×D₄	—	5	2	no	—
292	C₂×C₃×D₄	—	10	2	no	—
293	C₂×C₃×D₄	—	10	8	no	—
294	C₂×C₃×D₄	—	10	4	no	—
295	C₂×C₃×D₄	—	10	2	no	—
296	C₂×C₃×D₄	—	10	4	no	—
297	C₂×C₃×D₄	—	10	16	no	—
298	C₂×C₃×D₄	—	10	4	no	—
299	C₂×C₃×D₄	—	10	2	no	—
300	C₂×C₃×D₄	—	10	2	no	—
301	C₂×C₃×D₄	—	10	1	no	—
302	C₂×C₃×D₄	—	10	2	no	—
303	C₂×C₃×D₄	—	10	1	no	—
304	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	—	5	2	no	—
307	C₂²×C₃×C₄	—	10	2	no	—
308	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
309	C₃×SD₁₆	—	10	4	no	—
310	C₃×D₈	—	10	8	no	—
311	C₃×D₈	—	10	4	no	—
312	C₃×M₁₆	—	10	2	no	—
313	C₂×C₃×C₈	—	2	2	no	—
314	C₂×C₃×C₈	—	5	2	no	—
315	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
316	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
317	C₃×C₂²⋊C₄	—	2	1	no	—
318	C₃×C₂²⋊C₄	—	10	4	no	—
319	C₃×C₄²	—	2	1	no	—
320	C₂³×C₅	—	2	1	no	—
321	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂²×D₅	—	2	2	no	—
323	C₂²×D₅	—	2	8	no	—
324	C₂²×D₅	—	2	4	no	—
325	C₂²×D₅	—	2	2	no	—
326	C₂²×D₅	—	4	2	no	—
327	C₂²×D₅	—	8	4	no	—
328	C₂²×D₅	—	8	2	no	—
329	C₂²×D₅	—	8	2	no	—
330	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
331	C₅×Q₈	—	2	1	no	—
332	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
333	C₅×D₄	—	2	4	no	—
334	C₅×D₄	—	2	1	no	—
335	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	4	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
342	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
343	C₂²⋊D₅	—	2	8	no	—
344	C₂²⋊D₅	—	2	4	no	—
345	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
346	D₂₀	—	2	8	no	—
347	D₂₀	—	2	2	no	—
348	D₂₀	—	2	4	no	—
349	D₂₀	—	2	2	no	—
350	D₂₀	—	2	2	no	—
351	D₂₀	—	2	2	no	—
352	D₂₀	—	4	2	no	—
353	D₂₀	—	8	4	no	—
354	D₂₀	C₂×C₃×D₄	1	4	yes	—
355	C₄×D₅	—	2	8	no	—
356	C₄×D₅	—	2	2	no	—
357	C₄×D₅	—	2	2	no	—
358	Dic₁₀	—	2	2	no	—
359	C₅×C₈	—	2	2	no	—
360	#168	—	2	2	no	—
361	H(5,𝔽₂)	—	10	4	no	—
362	H(5,𝔽₂)	—	10	4	no	—
363	C₂×#41	—	5	1	no	—
364	C₂×#41	—	5	2	no	—
365	C₂×#41	—	10	1	no	—
366	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
367	C₂²×D₄	—	5	2	no	—
368	C₂²×D₄	—	5	1	no	—
369	C₂²×D₄	—	5	1	no	—
370	C₂²×D₄	—	10	1	no	—
371	C₂²×D₄	—	10	2	no	—
372	AGL(1,ℤ/8)	—	10	4	no	—
373	C₂×SD₁₆	—	5	2	no	—
374	C₂×D₈	—	5	2	no	—
375	C₂×D₈	—	5	4	no	—
376	C₂×D₈	—	10	4	no	—
377	C₂×M₁₆	—	5	1	no	—
378	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
379	#127	—	10	1	no	—
380	#124	—	10	1	no	—
381	#121	—	5	4	no	—
382	#120	—	10	2	no	—
383	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
384	#103	C₂×C₃×D₅	1	2	yes	complemented
385	#102	—	5	4	no	—
386	#102	C₂×C₃×D₅	1	2	yes	complemented
387	C₂²⋊C₈	—	5	4	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	—	4	2	no	—
390	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
391	C₂×C₃×C₅	#576	1	2	yes	—
392	C₃×D₅	—	4	2	no	—
393	C₃×D₅	—	4	4	no	—
394	C₃×D₅	—	8	2	no	—
395	C₂³×C₃	—	2	1	no	—
396	C₂³×C₃	—	5	2	no	—
397	C₂³×C₃	—	10	8	no	—
398	C₂³×C₃	—	10	2	no	—
399	C₂³×C₃	—	10	4	no	—
400	C₂³×C₃	—	10	2	no	—
401	C₂³×C₃	—	20	2	no	—
402	C₂³×C₃	—	40	2	no	—
403	C₂³×C₃	—	40	2	no	—
404	C₂³×C₃	—	40	4	no	—
405	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
406	C₃×Q₈	—	2	1	no	—
407	C₃×Q₈	—	10	2	no	—
408	C₃×Q₈	C₂×D₂₀	1	2	yes	—
409	C₃×D₄	—	2	4	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	5	4	no	—
412	C₃×D₄	—	10	8	no	—
413	C₃×D₄	—	10	8	no	—
414	C₃×D₄	—	10	4	no	—
415	C₃×D₄	—	10	2	no	—
416	C₃×D₄	—	10	2	no	—
417	C₃×D₄	—	10	2	no	—
418	C₃×D₄	—	10	4	no	—
419	C₃×D₄	—	10	2	no	—
420	C₃×D₄	—	20	2	no	—
421	C₃×D₄	—	40	4	no	—
422	C₃×D₄	C₂×D₂₀	1	2	yes	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	2	no	—
426	C₂×C₃×C₄	—	5	2	no	—
427	C₂×C₃×C₄	—	10	8	no	—
428	C₂×C₃×C₄	—	10	2	no	—
429	C₂×C₃×C₄	—	10	2	no	—
430	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
431	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
432	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
434	C₃×C₈	—	2	2	no	—
435	C₃×C₈	—	10	2	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	4	2	no	—
439	C₂²×C₅	C₃×#120	1	2	yes	—
440	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
441	C₂×D₅	—	2	4	no	—
442	C₂×D₅	—	2	2	no	—
443	C₂×D₅	—	2	4	no	—
444	C₂×D₅	—	4	4	no	—
445	C₂×D₅	—	4	4	no	—
446	C₂×D₅	—	4	2	no	—
447	C₂×D₅	—	8	4	no	—
448	C₂×D₅	—	8	8	no	—
449	C₂×D₅	—	8	4	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	4	2	no	—
452	C₄×C₅	C₃×#120	1	2	yes	—
453	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
454	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
455	Dic₅	—	2	2	no	—
456	C₂⁴	—	10	2	no	—
457	C₂⁴	—	10	1	no	—
458	C₂⁴	—	10	1	no	—
459	#41	—	2	2	no	—
460	#41	—	10	8	no	—
461	#41	—	10	4	no	—
462	#41	—	10	4	no	—
463	#41	—	10	2	no	—
464	#41	—	10	2	no	—
465	#41	C₃×D₂₀	1	4	yes	complemented
466	C₂×Q₈	—	5	1	no	—
467	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	5	2	no	—
470	C₂×D₄	—	5	4	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	10	2	no	—
475	C₂×D₄	—	10	8	no	—
476	C₂×D₄	—	10	4	no	—
477	C₂×D₄	—	10	2	no	—
478	C₂×D₄	—	10	4	no	—
479	C₂×D₄	—	10	16	no	—
480	C₂×D₄	—	10	4	no	—
481	C₂×D₄	—	10	2	no	—
482	C₂×D₄	—	10	2	no	—
483	C₂×D₄	—	10	1	no	—
484	C₂×D₄	—	10	2	no	—
485	C₂×D₄	—	10	1	no	—
486	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	10	2	no	—
490	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
491	SD₁₆	—	10	4	no	—
492	D₈	—	10	8	no	—
493	D₈	—	10	4	no	—
494	M₁₆	—	10	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	5	2	no	—
497	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
498	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	10	4	no	—
501	C₄²	—	2	1	no	—
502	C₃×C₅	#3008	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	4	2	no	—
506	C₂²×C₃	—	10	4	no	—
507	C₂²×C₃	—	10	2	no	—
508	C₂²×C₃	—	10	4	no	—
509	C₂²×C₃	—	20	4	no	—
510	C₂²×C₃	—	20	2	no	—
511	C₂²×C₃	—	20	4	no	—
512	C₂²×C₃	—	40	4	no	—
513	C₂²×C₃	—	40	4	no	—
514	C₂²×C₃	—	40	8	no	—
515	C₂²×C₃	#4028	1	2	yes	—
516	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	4	2	no	—
519	C₃×C₄	—	10	2	no	—
520	C₃×C₄	#4028	1	2	yes	—
521	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
522	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
523	C₂×C₅	—	2	2	no	—
524	C₂×C₅	—	4	2	no	—
525	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
526	C₂×C₅	C₃×#576	1	2	yes	—
527	D₅	—	4	2	no	—
528	D₅	—	4	4	no	—
529	D₅	—	8	2	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	5	2	no	—
532	C₂³	—	10	8	no	—
533	C₂³	—	10	2	no	—
534	C₂³	—	10	4	no	—
535	C₂³	—	10	2	no	—
536	C₂³	—	20	2	no	—
537	C₂³	—	40	2	no	—
538	C₂³	—	40	2	no	—
539	C₂³	—	40	4	no	—
540	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
541	Q₈	—	2	1	no	—
542	Q₈	—	10	2	no	—
543	Q₈	C₂×C₃×D₂₀	1	2	yes	—
544	D₄	—	2	4	no	—
545	D₄	—	2	1	no	—
546	D₄	—	5	4	no	—
547	D₄	—	10	8	no	—
548	D₄	—	10	8	no	—
549	D₄	—	10	4	no	—
550	D₄	—	10	2	no	—
551	D₄	—	10	2	no	—
552	D₄	—	10	2	no	—
553	D₄	—	10	4	no	—
554	D₄	—	10	2	no	—
555	D₄	—	20	2	no	—
556	D₄	—	40	4	no	—
557	D₄	C₂×C₃×D₂₀	1	2	yes	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	5	2	no	—
562	C₂×C₄	—	10	8	no	—
563	C₂×C₄	—	10	2	no	—
564	C₂×C₄	—	10	2	no	—
565	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
566	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
567	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
568	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	10	2	no	—
571	C₂×C₃	—	2	2	no	—
572	C₂×C₃	—	4	2	no	—
573	C₂×C₃	—	20	2	no	—
574	C₂×C₃	—	20	4	no	—
575	C₂×C₃	—	40	2	no	—
576	C₂×C₃	C₂×#4028	1	1	yes	characteristic
577	C₂×C₃	#66103	1	2	yes	—
578	C₅	C₃×#3008	1	1	yes	characteristic, complemented, Sylow
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	10	4	no	—
583	C₂²	—	10	4	no	—
584	C₂²	—	10	2	no	—
585	C₂²	—	20	4	no	—
586	C₂²	—	20	4	no	—
587	C₂²	—	20	2	no	—
588	C₂²	—	40	4	no	—
589	C₂²	—	40	4	no	—
590	C₂²	—	40	8	no	—
591	C₂²	C₃×#4028	1	2	yes	—
592	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	10	2	no	—
596	C₄	C₃×#4028	1	2	yes	—
597	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
598	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
599	C₃	#10610565	1	1	yes	characteristic, direct product factor, Sylow
600	C₂	—	2	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	20	2	no	—
603	C₂	—	20	4	no	—
604	C₂	—	40	2	no	—
605	C₂	C₂×C₃×#4028	1	1	yes	characteristic
606	C₂	C₃×#66103	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#416	D₅
hypocenter	C₅	C₃×#3008
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#416

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4149	C₂	semidirect
2. C₂×C₃×#4095	C₂	semidirect
3. C₂²×C₃×D₄₀	C₂	semidirect
4. C₃×#65859	C₂	semidirect
5. C₃×C₅×#416	C₂	semidirect
6. C₃×#65399	C₂	semidirect
7. C₃×#65290	C₂	semidirect
8. C₃×#65100	C₂	semidirect
9. C₃×#65062	C₂	semidirect
10. #10610565	C₃	direct (N × H)
14. C₂×C₃×#713	C₂²	semidirect
16. C₂×C₃×D₄×D₅	C₂²	semidirect
21. C₂²×C₃×D₂₀	C₂²	semidirect
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
23. C₃×C₅×#117	C₂²	semidirect
25. C₂×C₃×#688	C₂²	semidirect
26. C₂×C₃×#686	C₂²	semidirect
27. C₂×C₃×#681	C₂²	semidirect
29. C₂×C₃×D₄₀	C₂²	semidirect
30. C₃×#4041	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
35. C₃×C₅×#102	C₂²	semidirect
36. C₃×#3952	C₂²	semidirect
37. C₃×#3941	C₂²	semidirect
39. C₂×#4149	C₂×C₃	semidirect
40. C₂×#4095	C₂×C₃	semidirect
41. C₂²×D₄₀	C₂×C₃	semidirect
42. #65859	C₂×C₃	semidirect
43. C₅×#416	C₂×C₃	semidirect
44. #65399	C₂×C₃	semidirect
45. #65290	C₂×C₃	semidirect
46. #65100	C₂×C₃	semidirect
47. #65062	C₂×C₃	semidirect
52. C₃×C₅×#41	D₄	semidirect
77. C₂×C₃×D₂₀	D₄	semidirect
101. C₃×#416	D₅	semidirect
106. C₂×#713	C₂²×C₃	semidirect
108. C₂×D₄×D₅	C₂²×C₃	semidirect
113. C₂²×D₂₀	C₂²×C₃	semidirect
114. C₂²×C₅×C₈	C₂²×C₃	semidirect
115. C₅×#117	C₂²×C₃	semidirect
117. C₂×#688	C₂²×C₃	semidirect
118. C₂×#686	C₂²×C₃	semidirect
119. C₂×#681	C₂²×C₃	semidirect
121. C₂×D₄₀	C₂²×C₃	semidirect
122. #4041	C₂²×C₃	semidirect
126. C₅×#103	C₂²×C₃	semidirect
127. C₅×#102	C₂²×C₃	semidirect
128. #3952	C₂²×C₃	semidirect
129. #3941	C₂²×C₃	semidirect
189. C₂²×C₃×C₈	C₂×D₅	semidirect
194. C₃×#117	C₂×D₅	semidirect
195. C₃×#103	C₂×D₅	semidirect
197. C₃×#102	C₂×D₅	semidirect
203. C₅×#41	C₃×D₄	semidirect
228. C₂×D₂₀	C₃×D₄	semidirect
252. #416	C₃×D₅	semidirect
283. C₃×#41	D₂₀	semidirect
378. C₂²×C₈	C₂×C₃×D₅	semidirect
383. #117	C₂×C₃×D₅	semidirect
384. #103	C₂×C₃×D₅	semidirect
386. #102	C₂×C₃×D₅	semidirect
465. #41	C₃×D₂₀	semidirect
502. C₃×C₅	#3008	semidirect
578. C₅	C₃×#3008	semidirect
599. C₃	#10610565	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4149	2
C₂×C₃×#4095	2
C₂²×C₃×D₄₀	2
C₃×#65859	2
C₃×C₅×#416	2
C₃×#65399	2
C₃×#65290	2
C₃×#65100	2
C₃×#65062	2
#10610565	3
C₃×#3008	5

Subgroups — C3×#10610565 #14424217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610565 #14424217