Subgroups — C₃×#10615519 #14415835

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65523	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65417	C₂	1	2	yes	maximal, complemented
6	C₃×#65416	C₂	1	2	yes	maximal, complemented
7	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65400	C₂	1	2	yes	maximal, complemented
9	C₃×#65399	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615519	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₃×C₅×#131	—	2	4	no	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
20	C₃×#4093	C₄	1	1	yes	characteristic
21	C₃×#4090	C₄	1	1	yes	characteristic
22	C₃×#4086	C₄	1	1	yes	characteristic
23	C₃×#4085	C₄	1	2	yes	—
24	C₃×#4085	C₄	1	2	yes	—
25	C₃×#4082	C₄	1	1	yes	characteristic
26	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
27	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×#681	C₂²	1	1	yes	characteristic
30	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
31	C₃×#4053	—	2	4	no	—
32	C₂×C₃×#676	C₂²	1	2	yes	—
33	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
34	C₃×C₂²⋊#168	C₂²	1	2	yes	—
35	C₃×C₂²⋊#168	C₂²	1	2	yes	—
36	C₃×#3952	C₂²	1	2	yes	—
37	C₃×#3952	C₂²	1	2	yes	—
38	C₃×#3947	C₂²	1	2	yes	—
39	C₃×#3946	C₂²	1	1	yes	characteristic
40	C₃×#3946	C₂²	1	1	yes	characteristic
41	C₃×#3946	C₂²	1	1	yes	characteristic
42	C₃×#3946	C₂²	1	1	yes	characteristic
43	C₃×C₈×Dic₅	C₂²	1	2	yes	—
44	C₃×#2935	—	5	1	no	maximal, Hall
45	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
46	#66166	C₂×C₃	1	1	yes	characteristic
47	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
48	#65523	C₂×C₃	1	1	yes	characteristic, complemented
49	#65417	C₂×C₃	1	2	yes	complemented
50	#65416	C₂×C₃	1	2	yes	complemented
51	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
52	#65400	C₂×C₃	1	2	yes	complemented
53	#65399	C₂×C₃	1	1	yes	characteristic, complemented
54	C₈×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
55	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
66	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₃×#709	—	2	2	no	—
69	C₃×#709	—	2	2	no	—
70	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
72	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
73	C₃×C₅×M₁₆	—	2	4	no	—
74	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
75	C₂×C₃×C₅×C₈	—	2	2	no	—
76	C₂×C₃×C₅×C₈	—	2	4	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
81	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
82	C₃×#685	C₂×C₄	1	2	yes	—
83	C₃×#685	C₂×C₄	1	2	yes	—
84	C₃×#683	C₂×C₄	1	2	yes	—
85	C₃×#683	C₂×C₄	1	2	yes	—
86	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
90	C₃×#681	—	2	2	no	—
91	C₂×C₃×#168	—	2	2	no	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×#168	C₂³	1	1	yes	characteristic
94	C₂×C₃×#168	C₂³	1	1	yes	characteristic
95	C₃×#676	—	2	4	no	—
96	C₃×C₈×D₅	—	2	4	no	—
97	C₂×C₃×#131	—	5	1	no	—
98	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
99	C₃×#532	—	5	1	no	—
100	C₃×#436	—	5	2	no	—
101	C₃×#435	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×C₈×D₄	—	5	2	no	—
104	C₂×C₃×C₄⋊C₈	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₃×#408	—	5	1	no	—
107	C₃×C₄×M₁₆	—	5	1	no	—
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂×#709	C₂²×C₃	1	1	yes	characteristic
110	C₅×#131	—	2	4	no	—
111	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
115	#4093	C₃×C₄	1	1	yes	characteristic
116	#4090	C₃×C₄	1	1	yes	characteristic
117	#4086	C₃×C₄	1	1	yes	characteristic
118	#4085	C₃×C₄	1	2	yes	—
119	#4085	C₃×C₄	1	2	yes	—
120	#4082	C₃×C₄	1	1	yes	characteristic
121	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
122	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
123	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
124	C₂×#681	C₂²×C₃	1	1	yes	characteristic
125	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
126	#4053	—	2	4	no	—
127	C₂×#676	C₂²×C₃	1	2	yes	—
128	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
129	C₂²⋊#168	C₂²×C₃	1	2	yes	—
130	C₂²⋊#168	C₂²×C₃	1	2	yes	—
131	#3952	C₂²×C₃	1	2	yes	—
132	#3952	C₂²×C₃	1	2	yes	—
133	#3947	C₂²×C₃	1	2	yes	—
134	#3946	C₂²×C₃	1	1	yes	characteristic
135	#3946	C₂²×C₃	1	1	yes	characteristic
136	#3946	C₂²×C₃	1	1	yes	characteristic
137	#3946	C₂²×C₃	1	1	yes	characteristic
138	C₈×Dic₅	C₂²×C₃	1	2	yes	—
139	#2935	—	5	1	no	Sylow
140	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
141	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×D₄	—	2	4	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₃×C₂²⋊D₅	—	2	4	no	—
154	C₃×C₂²⋊D₅	—	2	4	no	—
155	C₃×C₂²⋊D₅	—	4	2	no	—
156	C₂×C₃×Dic₅	—	2	2	no	—
157	C₂×C₃×Dic₅	—	4	1	no	—
158	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₃×D₂₀	—	2	2	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	2	no	—
166	C₃×Dic₁₀	—	2	2	no	—
167	C₃×C₅×C₈	—	2	1	no	—
168	C₃×C₅×C₈	—	2	1	no	—
169	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
170	C₃×#168	—	2	1	no	—
171	C₃×#168	—	2	1	no	—
172	C₃×#168	—	2	2	no	—
173	C₂×C₃×#41	—	5	1	no	—
174	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
175	C₃×#131	—	2	4	no	—
176	C₃×#131	—	10	4	no	—
177	C₂×C₃×M₁₆	—	5	1	no	—
178	C₂×C₃×M₁₆	—	5	2	no	—
179	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
180	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
181	C₂²×C₃×C₈	—	5	1	no	—
182	C₂²×C₃×C₈	—	5	2	no	—
183	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
184	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
185	C₃×C₄⋊Q₈	—	5	1	no	—
186	C₃×#127	—	5	1	no	—
187	C₃×#124	—	5	1	no	—
188	C₃×#124	—	5	1	no	—
189	C₃×#121	—	5	2	no	—
190	C₃×#121	—	5	2	no	—
191	C₃×C₄×D₄	—	5	2	no	—
192	C₃×C₄×D₄	—	5	2	no	—
193	C₂×C₃×C₄²	—	5	1	no	—
194	C₃×C₄⋊C₈	—	5	1	no	—
195	C₃×C₄⋊C₈	—	5	1	no	—
196	C₃×C₄⋊C₈	—	5	1	no	—
197	C₃×C₄⋊C₈	—	5	1	no	—
198	C₃×C₂²⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	2	no	—
200	C₃×C₂²⋊C₈	—	5	2	no	—
201	C₃×C₂²⋊C₈	—	5	2	no	—
202	C₃×#97	—	5	2	no	—
203	C₃×C₄×C₈	—	5	2	no	—
204	C₅×#41	—	2	2	no	—
205	C₅×#41	—	2	2	no	—
206	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
212	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
213	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
214	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
216	#709	—	2	2	no	—
217	#709	—	2	2	no	—
218	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
220	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
221	C₅×M₁₆	—	2	4	no	—
222	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
223	C₂×C₅×C₈	—	2	2	no	—
224	C₂×C₅×C₈	—	2	4	no	—
225	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
228	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
229	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
230	#685	C₂×C₃×C₄	1	2	yes	—
231	#685	C₂×C₃×C₄	1	2	yes	—
232	#683	C₂×C₃×C₄	1	2	yes	—
233	#683	C₂×C₃×C₄	1	2	yes	—
234	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
235	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
236	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
237	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
238	#681	—	2	2	no	—
239	C₂×#168	—	2	2	no	—
240	C₂×#168	C₂³×C₃	1	2	yes	—
241	C₂×#168	C₂³×C₃	1	1	yes	characteristic
242	C₂×#168	C₂³×C₃	1	1	yes	characteristic
243	#676	—	2	4	no	—
244	C₈×D₅	—	2	4	no	—
245	C₂×#131	—	5	1	no	—
246	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
247	#532	—	5	1	no	—
248	#436	—	5	2	no	—
249	#435	—	5	2	no	—
250	#435	—	5	2	no	—
251	C₈×D₄	—	5	2	no	—
252	C₂×C₄⋊C₈	—	5	1	no	—
253	#408	—	5	1	no	—
254	#408	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₂²×C₃×C₅	—	2	1	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	2	no	—
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₅	—	2	2	no	—
264	C₂×C₃×D₅	—	2	2	no	—
265	C₂×C₃×D₅	—	2	2	no	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
270	C₃×Dic₅	—	2	2	no	—
271	C₃×Dic₅	—	2	1	no	—
272	C₃×Dic₅	—	2	1	no	—
273	C₃×Dic₅	—	2	1	no	—
274	C₃×Dic₅	#131	1	2	yes	complemented
275	C₃×#41	—	2	2	no	—
276	C₃×#41	—	2	2	no	—
277	C₃×#41	—	10	2	no	—
278	C₃×#41	—	10	2	no	—
279	C₂×C₃×Q₈	—	5	1	no	—
280	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×D₄	—	5	2	no	—
282	C₂×C₃×D₄	—	5	2	no	—
283	C₂×C₃×D₄	—	5	2	no	—
284	C₂×C₃×D₄	—	5	1	no	—
285	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
286	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	—	5	1	no	—
288	C₂²×C₃×C₄	—	5	1	no	—
289	C₂²×C₃×C₄	—	5	2	no	—
290	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
291	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
292	C₃×M₁₆	—	2	4	no	—
293	C₃×M₁₆	—	10	2	no	—
294	C₃×M₁₆	—	10	4	no	—
295	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
296	C₂×C₃×C₈	—	2	2	no	—
297	C₂×C₃×C₈	—	2	4	no	—
298	C₂×C₃×C₈	—	5	2	no	—
299	C₂×C₃×C₈	—	5	1	no	—
300	C₂×C₃×C₈	—	5	1	no	—
301	C₂×C₃×C₈	—	10	2	no	—
302	C₂×C₃×C₈	—	10	4	no	—
303	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
304	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
305	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
306	C₃×C₄⋊C₄	—	5	2	no	—
307	C₃×C₄⋊C₄	—	5	2	no	—
308	C₃×C₂²⋊C₄	—	5	2	no	—
309	C₃×C₂²⋊C₄	—	5	2	no	—
310	C₃×C₂²⋊C₄	—	5	2	no	—
311	C₃×C₂²⋊C₄	—	5	2	no	—
312	C₃×C₄²	—	5	1	no	—
313	C₃×C₄²	—	5	1	no	—
314	C₃×C₄²	—	5	1	no	—
315	C₃×C₄²	—	5	1	no	—
316	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
317	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
319	C₅×Q₈	—	2	2	no	—
320	C₅×D₄	—	2	4	no	—
321	C₅×D₄	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
325	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
327	C₂×C₄×C₅	C₃×#41	1	2	yes	—
328	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
329	C₂²⋊D₅	—	2	4	no	—
330	C₂²⋊D₅	—	2	4	no	—
331	C₂²⋊D₅	—	4	2	no	—
332	C₂×Dic₅	—	2	2	no	—
333	C₂×Dic₅	—	4	1	no	—
334	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
336	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
338	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
339	D₂₀	—	2	2	no	—
340	C₄×D₅	—	2	2	no	—
341	C₄×D₅	—	2	2	no	—
342	Dic₁₀	—	2	2	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	2	1	no	—
345	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
346	#168	—	2	1	no	—
347	#168	—	2	1	no	—
348	#168	—	2	2	no	—
349	C₂×#41	—	5	1	no	—
350	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
351	#131	—	2	4	no	—
352	#131	—	10	4	no	—
353	C₂×M₁₆	—	5	1	no	—
354	C₂×M₁₆	—	5	2	no	—
355	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
356	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	5	2	no	—
359	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
360	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
361	C₄⋊Q₈	—	5	1	no	—
362	#127	—	5	1	no	—
363	#124	—	5	1	no	—
364	#124	—	5	1	no	—
365	#121	—	5	2	no	—
366	#121	—	5	2	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₂×C₄²	—	5	1	no	—
370	C₄⋊C₈	—	5	1	no	—
371	C₄⋊C₈	—	5	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₂²⋊C₈	—	5	2	no	—
375	C₂²⋊C₈	—	5	2	no	—
376	C₂²⋊C₈	—	5	2	no	—
377	C₂²⋊C₈	—	5	2	no	—
378	#97	—	5	2	no	—
379	C₄×C₈	—	5	2	no	—
380	C₂×C₃×C₅	—	2	2	no	—
381	C₂×C₃×C₅	—	4	2	no	—
382	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
383	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
384	C₂×C₃×C₅	#568	1	1	yes	characteristic
385	C₃×D₅	—	4	2	no	—
386	C₂³×C₃	—	5	2	no	—
387	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
388	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	10	2	no	—
391	C₃×D₄	—	2	4	no	—
392	C₃×D₄	—	2	2	no	—
393	C₃×D₄	—	10	4	no	—
394	C₃×D₄	—	10	4	no	—
395	C₃×D₄	—	10	2	no	—
396	C₃×D₄	—	20	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	5	1	no	—
400	C₂×C₃×C₄	—	5	1	no	—
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	1	no	—
403	C₂×C₃×C₄	—	5	2	no	—
404	C₂×C₃×C₄	—	10	2	no	—
405	C₂×C₃×C₄	—	10	2	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	20	1	no	—
408	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
409	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
410	C₂×C₃×C₄	#709	1	2	yes	—
411	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
412	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
413	C₃×C₈	—	2	1	no	—
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	—	10	2	no	—
416	C₃×C₈	—	10	1	no	—
417	C₃×C₈	—	10	1	no	—
418	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
425	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
426	C₂×D₅	—	2	2	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
431	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
432	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
433	Dic₅	—	2	1	no	—
434	Dic₅	—	2	1	no	—
435	Dic₅	—	2	1	no	—
436	Dic₅	—	2	2	no	—
437	Dic₅	C₃×#131	1	2	yes	complemented
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	10	2	no	—
441	#41	—	10	2	no	—
442	C₂×Q₈	—	5	1	no	—
443	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
444	C₂×D₄	—	5	2	no	—
445	C₂×D₄	—	5	2	no	—
446	C₂×D₄	—	5	2	no	—
447	C₂×D₄	—	5	1	no	—
448	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
449	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	1	no	—
452	C₂²×C₄	—	5	2	no	—
453	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
454	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
455	M₁₆	—	2	4	no	—
456	M₁₆	—	10	2	no	—
457	M₁₆	—	10	4	no	—
458	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	—	5	2	no	—
462	C₂×C₈	—	5	1	no	—
463	C₂×C₈	—	5	1	no	—
464	C₂×C₈	—	10	2	no	—
465	C₂×C₈	—	10	4	no	—
466	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
467	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₂²⋊C₄	—	5	2	no	—
472	C₂²⋊C₄	—	5	2	no	—
473	C₂²⋊C₄	—	5	2	no	—
474	C₂²⋊C₄	—	5	2	no	—
475	C₄²	—	5	1	no	—
476	C₄²	—	5	1	no	—
477	C₄²	—	5	1	no	—
478	C₄²	—	5	1	no	—
479	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	10	2	no	—
486	C₂²×C₃	—	10	2	no	—
487	C₂²×C₃	—	10	2	no	—
488	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
489	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	—	5	2	no	—
492	C₃×C₄	—	10	1	no	—
493	C₃×C₄	—	10	1	no	—
494	C₃×C₄	—	10	1	no	—
495	C₃×C₄	—	10	2	no	—
496	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
497	C₃×C₄	C₂×#709	1	1	yes	characteristic
498	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
499	C₂×C₅	—	2	2	no	—
500	C₂×C₅	—	4	2	no	—
501	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
502	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
503	C₂×C₅	C₃×#568	1	1	yes	characteristic
504	D₅	—	4	2	no	—
505	C₂³	—	5	2	no	—
506	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
507	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
508	Q₈	—	2	2	no	—
509	Q₈	—	10	2	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	2	no	—
512	D₄	—	10	4	no	—
513	D₄	—	10	4	no	—
514	D₄	—	10	2	no	—
515	D₄	—	20	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	5	1	no	—
519	C₂×C₄	—	5	1	no	—
520	C₂×C₄	—	5	1	no	—
521	C₂×C₄	—	5	1	no	—
522	C₂×C₄	—	5	2	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	2	no	—
525	C₂×C₄	—	10	2	no	—
526	C₂×C₄	—	20	1	no	—
527	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
528	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
529	C₂×C₄	C₃×#709	1	2	yes	—
530	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
531	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	10	2	no	—
535	C₈	—	10	1	no	—
536	C₈	—	10	1	no	—
537	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	—	4	2	no	—
540	C₂×C₃	—	20	2	no	—
541	C₂×C₃	D₅×#131	1	1	yes	characteristic
542	C₂×C₃	#66084	1	1	yes	characteristic
543	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
544	C₅	C₃×#2935	1	1	yes	characteristic, complemented, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	10	2	no	—
551	C₂²	—	10	2	no	—
552	C₂²	—	10	2	no	—
553	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
554	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	5	2	no	—
557	C₄	—	10	2	no	—
558	C₄	—	10	1	no	—
559	C₄	—	10	1	no	—
560	C₄	—	10	1	no	—
561	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
562	C₄	C₂×C₃×#709	1	1	yes	characteristic
563	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
564	C₃	#10615519	1	1	yes	characteristic, direct product factor, Sylow
565	C₂	—	2	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	20	2	no	—
568	C₂	C₃×D₅×#131	1	1	yes	characteristic
569	C₂	C₃×#66084	1	1	yes	characteristic
570	C₂	C₂×C₃×C₄×C₂²⋊D₅	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	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66166	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₃×#2935
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×C₃×#4053	C₂	semidirect
4. C₃×#65523	C₂	semidirect
5. C₃×#65417	C₂	semidirect
6. C₃×#65416	C₂	semidirect
7. C₃×M₁₆×Dic₅	C₂	semidirect
8. C₃×#65400	C₂	semidirect
9. C₃×#65399	C₂	semidirect
10. C₃×C₈×C₂²⋊D₅	C₂	semidirect
11. C₂×C₃×#3946	C₂	semidirect
12. #10615519	C₃	direct (N × H)
45. C₂×C₅×#131	C₂×C₃	semidirect
47. C₂×#4053	C₂×C₃	semidirect
48. #65523	C₂×C₃	semidirect
49. #65417	C₂×C₃	semidirect
50. #65416	C₂×C₃	semidirect
51. M₁₆×Dic₅	C₂×C₃	semidirect
52. #65400	C₂×C₃	semidirect
53. #65399	C₂×C₃	semidirect
54. C₈×C₂²⋊D₅	C₂×C₃	semidirect
55. C₂×#3946	C₂×C₃	semidirect
74. C₃×C₅×M₁₆	D₄	semidirect
98. C₂×C₃×#131	D₅	semidirect
222. C₅×M₁₆	C₃×D₄	semidirect
246. C₂×#131	C₃×D₅	semidirect
274. C₃×Dic₅	#131	semidirect
295. C₃×M₁₆	C₂²⋊D₅	semidirect
437. Dic₅	C₃×#131	semidirect
458. M₁₆	C₃×C₂²⋊D₅	semidirect
479. C₃×C₅	#2935	semidirect
544. C₅	C₃×#2935	semidirect
564. C₃	#10615519	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×C₅×#131	2
C₃×#66166	2
C₂×C₃×#4053	2
C₃×#65523	2
C₃×#65417	2
C₃×#65416	2
C₃×M₁₆×Dic₅	2
C₃×#65400	2
C₃×#65399	2
C₃×C₈×C₂²⋊D₅	2
C₂×C₃×#3946	2
#10615519	3
C₃×#2935	5

Subgroups — C3×#10615519 #14415835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615519 #14415835