Subgroups — C₃×#10615493 #14411750

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65418	C₂	1	4	yes	maximal, complemented
5	C₃×#65415	C₂	1	4	yes	maximal, complemented
6	C₃×#65399	C₂	1	4	yes	maximal, complemented
7	#10615493	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₂²⋊D₅	C₄	1	2	yes	—
10	C₂×C₃×#709	—	2	4	no	—
11	C₂×C₃×#709	—	2	4	no	—
12	C₂×C₃×#709	C₄	1	2	yes	—
13	C₂×C₃×#709	C₄	1	2	yes	—
14	C₂×C₃×#709	C₂²	1	2	yes	—
15	C₂×C₃×#709	C₂²	1	2	yes	—
16	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×Dic₁₀	C₄	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	—	2	4	no	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
23	C₂×C₃×#681	—	2	4	no	—
24	C₂×C₃×#681	C₂²	1	2	yes	—
25	C₂×C₃×#681	C₂²	1	2	yes	complemented
26	C₂²×C₃×#168	C₂²	1	2	yes	complemented
27	C₃×#3952	C₂²	1	16	yes	complemented
28	C₃×#2879	—	5	1	no	maximal, Hall
29	C₂²×#709	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂²×#681	C₂×C₃	1	1	yes	characteristic, complemented
32	#65418	C₂×C₃	1	4	yes	complemented
33	#65415	C₂×C₃	1	4	yes	complemented
34	#65399	C₂×C₃	1	4	yes	complemented
35	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
46	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
48	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
49	C₃×#709	—	2	8	no	—
50	C₃×#709	—	2	8	no	—
51	C₃×#709	—	2	4	no	—
52	C₃×#709	—	2	4	no	—
53	C₃×#709	—	2	4	no	—
54	C₃×#709	—	2	4	no	—
55	C₂×C₃×D₂₀	—	2	4	no	—
56	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
57	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	4	no	—
59	C₂×C₃×C₄×D₅	—	2	4	no	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
61	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
62	C₂×C₃×Dic₁₀	—	2	4	no	—
63	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
64	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
65	C₃×C₅×M₁₆	—	2	4	no	—
66	C₃×C₅×M₁₆	—	2	4	no	—
67	C₂×C₃×C₅×C₈	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
69	C₃×#681	—	2	4	no	—
70	C₃×#681	—	2	4	no	—
71	C₂×C₃×#168	—	2	4	no	—
72	C₂×C₃×#168	C₂³	1	4	yes	—
73	C₂²×C₃×#41	—	5	1	no	—
74	C₂²×C₃×M₁₆	—	5	1	no	—
75	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
76	C₃×#408	—	5	4	no	—
77	C₃×#408	—	5	4	no	—
78	C₃×#407	—	5	4	no	—
79	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₂²⋊D₅	C₃×C₄	1	2	yes	—
81	C₂×#709	—	2	4	no	—
82	C₂×#709	—	2	4	no	—
83	C₂×#709	C₃×C₄	1	2	yes	—
84	C₂×#709	C₃×C₄	1	2	yes	—
85	C₂×#709	C₂²×C₃	1	2	yes	—
86	C₂×#709	C₂²×C₃	1	2	yes	—
87	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic
88	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
89	C₂²×Dic₁₀	C₃×C₄	1	1	yes	characteristic
90	C₂×C₅×M₁₆	—	2	4	no	—
91	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
92	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
93	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
94	C₂×#681	—	2	4	no	—
95	C₂×#681	C₂²×C₃	1	2	yes	—
96	C₂×#681	C₂²×C₃	1	2	yes	complemented
97	C₂²×#168	C₂²×C₃	1	2	yes	complemented
98	#3952	C₂²×C₃	1	16	yes	complemented
99	#2879	—	5	1	no	Sylow
100	C₂³×C₃×C₅	—	4	2	no	—
101	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	—	2	4	no	—
106	C₂²×C₃×D₅	—	4	4	no	—
107	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₃×C₂²⋊D₅	—	2	8	no	—
122	C₃×C₂²⋊D₅	—	2	8	no	—
123	C₂×C₃×Dic₅	—	2	4	no	—
124	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
125	C₃×D₂₀	—	2	4	no	—
126	C₃×D₂₀	—	2	4	no	—
127	C₃×C₄×D₅	—	2	8	no	—
128	C₃×C₄×D₅	—	2	4	no	—
129	C₃×C₄×D₅	—	2	4	no	—
130	C₃×Dic₁₀	—	2	4	no	—
131	C₃×Dic₁₀	—	2	4	no	—
132	C₃×C₅×C₈	—	2	4	no	—
133	C₃×#168	—	2	4	no	—
134	C₂×C₃×#41	—	5	2	no	—
135	C₂×C₃×#41	—	5	2	no	—
136	C₂×C₃×#41	—	5	2	no	—
137	C₂×C₃×#41	—	5	2	no	—
138	C₂×C₃×#41	—	10	4	no	—
139	C₂×C₃×#41	—	10	4	no	—
140	C₂²×C₃×Q₈	—	5	1	no	—
141	C₂²×C₃×D₄	—	5	2	no	—
142	C₂²×C₃×D₄	—	5	1	no	—
143	C₂³×C₃×C₄	—	5	2	no	—
144	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
145	C₂×C₃×M₁₆	—	2	4	no	—
146	C₂×C₃×M₁₆	—	5	2	no	—
147	C₂×C₃×M₁₆	—	5	2	no	—
148	C₂×C₃×M₁₆	—	10	4	no	—
149	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
150	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	complemented
151	C₂²×C₃×C₈	—	5	2	no	—
152	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
153	C₃×C₂²⋊C₈	—	5	16	no	—
154	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
156	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
160	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₂²⋊D₅	—	2	8	no	—
165	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
166	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
167	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
168	#709	—	2	8	no	—
169	#709	—	2	8	no	—
170	#709	—	2	4	no	—
171	#709	—	2	4	no	—
172	#709	—	2	4	no	—
173	#709	—	2	4	no	—
174	C₂×D₂₀	—	2	4	no	—
175	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
176	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
177	C₂×C₄×D₅	—	2	4	no	—
178	C₂×C₄×D₅	—	2	4	no	—
179	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
180	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
181	C₂×Dic₁₀	—	2	4	no	—
182	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
183	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
184	C₅×M₁₆	—	2	4	no	—
185	C₅×M₁₆	—	2	4	no	—
186	C₂×C₅×C₈	—	2	4	no	—
187	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
188	#681	—	2	4	no	—
189	#681	—	2	4	no	—
190	C₂×#168	—	2	4	no	—
191	C₂×#168	C₂³×C₃	1	4	yes	—
192	C₂²×#41	—	5	1	no	—
193	C₂²×M₁₆	—	5	1	no	—
194	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
195	#408	—	5	4	no	—
196	#408	—	5	4	no	—
197	#407	—	5	4	no	—
198	C₂²×C₃×C₅	—	2	2	no	—
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	2	2	no	—
201	C₂²×C₃×C₅	—	4	4	no	—
202	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₃×D₅	—	2	4	no	—
207	C₂×C₃×D₅	—	2	8	no	—
208	C₂×C₃×D₅	—	4	8	no	—
209	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
210	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
211	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
212	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×Dic₅	—	2	4	no	—
215	C₂⁴×C₃	—	5	2	no	—
216	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
217	C₃×#41	—	10	8	no	—
218	C₃×#41	—	10	8	no	—
219	C₃×#41	—	10	4	no	—
220	C₃×#41	—	10	4	no	—
221	C₃×#41	—	10	4	no	—
222	C₃×#41	—	10	4	no	—
223	C₂×C₃×Q₈	—	5	2	no	—
224	C₂×C₃×Q₈	—	5	2	no	—
225	C₂×C₃×Q₈	—	10	4	no	—
226	C₂×C₃×D₄	—	5	4	no	—
227	C₂×C₃×D₄	—	5	4	no	—
228	C₂×C₃×D₄	—	5	2	no	—
229	C₂×C₃×D₄	—	5	2	no	—
230	C₂×C₃×D₄	—	10	8	no	—
231	C₂×C₃×D₄	—	10	4	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	4	no	—
234	C₂²×C₃×C₄	—	5	4	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	—	10	4	no	—
237	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	D₂₀	1	4	yes	—
241	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
245	C₃×M₁₆	—	2	4	no	—
246	C₃×M₁₆	—	2	4	no	—
247	C₃×M₁₆	—	10	4	no	—
248	C₃×M₁₆	—	10	4	no	—
249	C₂×C₃×C₈	—	2	4	no	—
250	C₂×C₃×C₈	—	5	4	no	—
251	C₂×C₃×C₈	—	10	4	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
253	C₂³×C₅	—	4	2	no	—
254	C₂³×C₅	C₃×C₂²⋊C₄	1	4	yes	—
255	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂²×D₅	—	2	4	no	—
259	C₂²×D₅	—	4	4	no	—
260	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
261	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
262	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
263	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
264	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
274	C₂²⋊D₅	—	2	8	no	—
275	C₂²⋊D₅	—	2	8	no	—
276	C₂×Dic₅	—	2	4	no	—
277	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
278	D₂₀	—	2	4	no	—
279	D₂₀	—	2	4	no	—
280	C₄×D₅	—	2	8	no	—
281	C₄×D₅	—	2	4	no	—
282	C₄×D₅	—	2	4	no	—
283	Dic₁₀	—	2	4	no	—
284	Dic₁₀	—	2	4	no	—
285	C₅×C₈	—	2	4	no	—
286	#168	—	2	4	no	—
287	C₂×#41	—	5	2	no	—
288	C₂×#41	—	5	2	no	—
289	C₂×#41	—	5	2	no	—
290	C₂×#41	—	5	2	no	—
291	C₂×#41	—	10	4	no	—
292	C₂×#41	—	10	4	no	—
293	C₂²×Q₈	—	5	1	no	—
294	C₂²×D₄	—	5	2	no	—
295	C₂²×D₄	—	5	1	no	—
296	C₂³×C₄	—	5	2	no	—
297	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	5	2	no	—
300	C₂×M₁₆	—	5	2	no	—
301	C₂×M₁₆	—	10	4	no	—
302	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
303	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	complemented
304	C₂²×C₈	—	5	2	no	—
305	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
306	C₂²⋊C₈	—	5	16	no	—
307	C₂×C₃×C₅	—	2	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	—	2	2	no	—
310	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₃×C₅	#568	1	2	yes	—
312	C₃×D₅	—	4	4	no	—
313	C₂³×C₃	—	4	2	no	—
314	C₂³×C₃	—	5	4	no	—
315	C₂³×C₃	—	10	4	no	—
316	C₂³×C₃	—	20	4	no	—
317	C₂³×C₃	#685	1	4	yes	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
320	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
321	C₃×Q₈	—	10	4	no	—
322	C₃×Q₈	—	10	4	no	—
323	C₃×D₄	—	10	8	no	—
324	C₃×D₄	—	10	8	no	—
325	C₃×D₄	—	10	4	no	—
326	C₃×D₄	—	10	4	no	—
327	C₂×C₃×C₄	—	5	4	no	—
328	C₂×C₃×C₄	—	10	4	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	—	10	4	no	—
331	C₂×C₃×C₄	—	10	8	no	—
332	C₂×C₃×C₄	#685	1	4	yes	—
333	C₂×C₃×C₄	#685	1	4	yes	—
334	C₂×C₃×C₄	#685	1	4	yes	—
335	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
339	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
340	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₃×C₈	—	2	4	no	—
346	C₃×C₈	—	10	4	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	2	no	—
350	C₂²×C₅	—	4	4	no	—
351	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
352	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
353	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
354	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
355	C₂×D₅	—	2	8	no	—
356	C₂×D₅	—	2	4	no	—
357	C₂×D₅	—	4	8	no	—
358	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
359	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
360	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
361	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
362	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	Dic₅	—	2	4	no	—
364	C₂⁴	—	5	2	no	—
365	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
366	#41	—	10	8	no	—
367	#41	—	10	8	no	—
368	#41	—	10	4	no	—
369	#41	—	10	4	no	—
370	#41	—	10	4	no	—
371	#41	—	10	4	no	—
372	C₂×Q₈	—	5	2	no	—
373	C₂×Q₈	—	5	2	no	—
374	C₂×Q₈	—	10	4	no	—
375	C₂×D₄	—	5	4	no	—
376	C₂×D₄	—	5	4	no	—
377	C₂×D₄	—	5	2	no	—
378	C₂×D₄	—	5	2	no	—
379	C₂×D₄	—	10	8	no	—
380	C₂×D₄	—	10	4	no	—
381	C₂²×C₄	—	5	2	no	—
382	C₂²×C₄	—	5	4	no	—
383	C₂²×C₄	—	5	4	no	—
384	C₂²×C₄	—	10	4	no	—
385	C₂²×C₄	—	10	4	no	—
386	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
387	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
388	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
389	C₂²×C₄	C₃×D₂₀	1	4	yes	—
390	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
391	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
394	M₁₆	—	2	4	no	—
395	M₁₆	—	2	4	no	—
396	M₁₆	—	10	4	no	—
397	M₁₆	—	10	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	5	4	no	—
400	C₂×C₈	—	10	4	no	—
401	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
402	C₃×C₅	#2879	1	1	yes	characteristic, complemented, Hall
403	C₂²×C₃	—	2	2	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	4	4	no	—
407	C₂²×C₃	—	10	8	no	—
408	C₂²×C₃	—	10	4	no	—
409	C₂²×C₃	—	20	8	no	—
410	C₂²×C₃	C₂×#685	1	2	yes	—
411	C₂²×C₃	C₂×#685	1	2	yes	—
412	C₂²×C₃	C₂×#685	1	2	yes	—
413	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
414	C₃×C₄	—	10	4	no	—
415	C₃×C₄	C₂×#685	1	2	yes	—
416	C₃×C₄	C₂×#685	1	2	yes	—
417	C₃×C₄	C₂×#685	1	2	yes	—
418	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
419	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	2	2	no	—
422	C₂×C₅	—	2	2	no	—
423	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₅	C₃×#568	1	2	yes	—
425	D₅	—	4	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	5	4	no	—
428	C₂³	—	10	4	no	—
429	C₂³	—	20	4	no	—
430	C₂³	C₃×#685	1	4	yes	—
431	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
432	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
433	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
434	Q₈	—	10	4	no	—
435	Q₈	—	10	4	no	—
436	D₄	—	10	8	no	—
437	D₄	—	10	8	no	—
438	D₄	—	10	4	no	—
439	D₄	—	10	4	no	—
440	C₂×C₄	—	5	4	no	—
441	C₂×C₄	—	10	4	no	—
442	C₂×C₄	—	10	4	no	—
443	C₂×C₄	—	10	4	no	—
444	C₂×C₄	—	10	8	no	—
445	C₂×C₄	C₃×#685	1	4	yes	—
446	C₂×C₄	C₃×#685	1	4	yes	—
447	C₂×C₄	C₃×#685	1	4	yes	—
448	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
449	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
450	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
452	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
453	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
454	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
455	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
456	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
457	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	10	4	no	—
460	C₂×C₃	—	2	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	20	4	no	—
464	C₂×C₃	#66079	1	2	yes	—
465	C₂×C₃	C₂²×#685	1	1	yes	characteristic
466	C₅	C₃×#2879	1	1	yes	characteristic, complemented, Sylow
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	10	4	no	—
472	C₂²	—	10	8	no	—
473	C₂²	—	20	8	no	—
474	C₂²	C₂×C₃×#685	1	2	yes	—
475	C₂²	C₂×C₃×#685	1	2	yes	—
476	C₂²	C₂×C₃×#685	1	2	yes	—
477	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
478	C₄	—	10	4	no	—
479	C₄	C₂×C₃×#685	1	2	yes	—
480	C₄	C₂×C₃×#685	1	2	yes	—
481	C₄	C₂×C₃×#685	1	2	yes	—
482	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
483	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
484	C₃	#10615493	1	1	yes	characteristic, direct product factor, Sylow
485	C₂	—	2	2	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	20	4	no	—
489	C₂	C₃×#66079	1	2	yes	—
490	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₃×#2879
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₃×#681	C₂	semidirect
4. C₃×#65418	C₂	semidirect
5. C₃×#65415	C₂	semidirect
6. C₃×#65399	C₂	semidirect
7. #10615493	C₃	direct (N × H)
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₂×C₃×#681	C₂²	semidirect
26. C₂²×C₃×#168	C₂²	semidirect
27. C₃×#3952	C₂²	semidirect
30. C₂²×C₅×M₁₆	C₂×C₃	semidirect
31. C₂²×#681	C₂×C₃	semidirect
32. #65418	C₂×C₃	semidirect
33. #65415	C₂×C₃	semidirect
34. #65399	C₂×C₃	semidirect
75. C₂²×C₃×M₁₆	D₅	semidirect
92. C₂×C₅×M₁₆	C₂²×C₃	semidirect
93. C₂²×C₅×C₈	C₂²×C₃	semidirect
96. C₂×#681	C₂²×C₃	semidirect
97. C₂²×#168	C₂²×C₃	semidirect
98. #3952	C₂²×C₃	semidirect
150. C₂×C₃×M₁₆	C₂×D₅	semidirect
152. C₂²×C₃×C₈	C₂×D₅	semidirect
194. C₂²×M₁₆	C₃×D₅	semidirect
303. C₂×M₁₆	C₂×C₃×D₅	semidirect
305. C₂²×C₈	C₂×C₃×D₅	semidirect
402. C₃×C₅	#2879	semidirect
466. C₅	C₃×#2879	semidirect
484. C₃	#10615493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#709	2
C₂²×C₃×C₅×M₁₆	2
C₂²×C₃×#681	2
C₃×#65418	2
C₃×#65415	2
C₃×#65399	2
#10615493	3
C₃×#2879	5

Subgroups — C3×#10615493 #14411750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615493 #14411750