Subgroups — C₃×#10615488 #14415443

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66125	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65417	C₂	1	2	yes	maximal, complemented
7	C₃×#65416	C₂	1	2	yes	maximal, complemented
8	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65400	C₂	1	2	yes	maximal, complemented
11	C₃×C₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
12	#10615488	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	—	2	4	no	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
20	C₃×#4099	C₄	1	2	yes	—
21	C₃×#4076	C₄	1	1	yes	characteristic
22	C₃×#4076	C₄	1	1	yes	characteristic
23	C₃×#4075	C₄	1	2	yes	—
24	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
25	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
26	C₃×#4072	C₂²	1	1	yes	characteristic
27	C₃×#4070	C₄	1	1	yes	characteristic
28	C₃×#4070	C₄	1	1	yes	characteristic
29	C₂²×C₃×#168	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	complemented
33	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
37	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
38	C₃×#3952	C₂²	1	2	yes	complemented
39	C₃×#3952	C₂²	1	2	yes	complemented
40	C₃×#3947	C₂²	1	2	yes	complemented
41	C₃×#3946	C₂²	1	2	yes	complemented
42	C₃×#3946	C₂²	1	2	yes	complemented
43	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
44	C₃×#2933	—	5	1	no	maximal, Hall
45	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
46	#66125	C₂×C₃	1	1	yes	characteristic
47	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
49	#65418	C₂×C₃	1	1	yes	characteristic, complemented
50	#65417	C₂×C₃	1	2	yes	complemented
51	#65416	C₂×C₃	1	2	yes	complemented
52	#65411	C₂×C₃	1	1	yes	characteristic, complemented
53	#65408	C₂×C₃	1	1	yes	characteristic, complemented
54	#65400	C₂×C₃	1	2	yes	complemented
55	C₈×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
56	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	2	no	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
66	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
67	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
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	2	no	—
74	C₃×C₅×M₁₆	—	2	4	no	—
75	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
76	C₂×C₃×C₅×C₈	—	2	4	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
79	C₃×C₂²⋊Dic₅	C₂×C₄	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×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₃×#683	C₂×C₄	1	2	yes	—
87	C₃×#683	C₂×C₄	1	2	yes	—
88	C₃×C₄×Dic₅	C₂³	1	2	yes	—
89	C₂×C₃×#168	—	2	2	no	—
90	C₂×C₃×#168	—	2	2	no	—
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	1	yes	characteristic
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	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
99	C₃×#525	—	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	C₃×#424	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
107	C₃×#405	—	5	1	no	—
108	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×#709	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×M₁₆	—	2	4	no	—
111	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
113	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
115	#4099	C₃×C₄	1	2	yes	—
116	#4076	C₃×C₄	1	1	yes	characteristic
117	#4076	C₃×C₄	1	1	yes	characteristic
118	#4075	C₃×C₄	1	2	yes	—
119	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
120	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
121	#4072	C₂²×C₃	1	1	yes	characteristic
122	#4070	C₃×C₄	1	1	yes	characteristic
123	#4070	C₃×C₄	1	1	yes	characteristic
124	C₂²×#168	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	complemented
128	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
129	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
130	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
131	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
132	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
133	#3952	C₂²×C₃	1	2	yes	complemented
134	#3952	C₂²×C₃	1	2	yes	complemented
135	#3947	C₂²×C₃	1	2	yes	complemented
136	#3946	C₂²×C₃	1	2	yes	complemented
137	#3946	C₂²×C₃	1	2	yes	complemented
138	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
139	#2933	—	5	1	no	Sylow
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	4	1	no	—
143	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	#41	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₃×C₂²⋊D₅	—	2	4	no	—
161	C₃×C₂²⋊D₅	—	2	4	no	—
162	C₃×C₂²⋊D₅	—	4	2	no	—
163	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
164	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
165	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
166	C₃×D₂₀	—	2	2	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×C₅×C₈	C₂×D₄	1	4	yes	—
172	C₃×#168	—	2	1	no	—
173	C₃×#168	—	2	1	no	—
174	C₃×#168	—	2	1	no	—
175	C₃×#168	—	2	1	no	—
176	C₂×C₃×#41	—	5	1	no	—
177	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
178	C₃×#131	—	10	4	no	—
179	C₂×C₃×M₁₆	—	2	4	no	—
180	C₂×C₃×M₁₆	—	5	2	no	—
181	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
182	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
183	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
184	C₂²×C₃×C₈	—	5	1	no	—
185	C₂²×C₃×C₈	—	5	1	no	—
186	C₂²×C₃×C₈	—	5	2	no	—
187	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
188	C₃×#123	—	5	2	no	—
189	C₃×C₂²⋊Q₈	—	5	1	no	—
190	C₃×C₂²⋊Q₈	—	5	1	no	—
191	C₃×#121	—	5	1	no	—
192	C₃×#121	—	5	1	no	—
193	C₃×#120	—	5	2	no	—
194	C₃×C₄×D₄	—	5	2	no	—
195	C₃×C₄×D₄	—	5	2	no	—
196	C₃×#117	—	5	1	no	—
197	C₃×C₄⋊C₈	—	5	2	no	—
198	C₃×C₄⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	1	no	—
200	C₃×C₂²⋊C₈	—	5	1	no	—
201	C₃×C₂²⋊C₈	—	5	1	no	—
202	C₃×C₂²⋊C₈	—	5	1	no	—
203	C₃×C₂²⋊C₈	—	5	2	no	—
204	C₃×C₂²⋊C₈	—	5	2	no	—
205	C₃×#97	—	5	2	no	—
206	C₃×C₄×C₈	—	5	2	no	—
207	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	—	2	2	no	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
217	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
218	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
219	#709	—	2	2	no	—
220	#709	—	2	2	no	—
221	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
223	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
224	C₅×M₁₆	—	2	2	no	—
225	C₅×M₁₆	—	2	4	no	—
226	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
227	C₂×C₅×C₈	—	2	4	no	—
228	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
229	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
230	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
231	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
232	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
233	#685	C₂×C₃×C₄	1	2	yes	—
234	#685	C₂×C₃×C₄	1	2	yes	—
235	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
236	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
237	#683	C₂×C₃×C₄	1	2	yes	—
238	#683	C₂×C₃×C₄	1	2	yes	—
239	C₄×Dic₅	C₂³×C₃	1	2	yes	—
240	C₂×#168	—	2	2	no	—
241	C₂×#168	—	2	2	no	—
242	C₂×#168	C₂³×C₃	1	1	yes	characteristic
243	C₂×#168	C₂³×C₃	1	1	yes	characteristic
244	C₂×#168	C₂³×C₃	1	1	yes	characteristic
245	C₂×#168	C₂³×C₃	1	1	yes	characteristic
246	#676	—	2	4	no	—
247	C₈×D₅	—	2	4	no	—
248	C₂×#131	—	5	1	no	—
249	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
250	#525	—	5	1	no	—
251	#436	—	5	2	no	—
252	#435	—	5	2	no	—
253	#435	—	5	2	no	—
254	C₈×D₄	—	5	2	no	—
255	#424	—	5	1	no	—
256	#408	—	5	1	no	—
257	C₂×C₂²⋊C₈	—	5	1	no	—
258	#405	—	5	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	1	no	—
265	C₂²×C₃×C₅	—	2	1	no	—
266	C₂²×C₃×C₅	—	4	4	no	—
267	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
268	C₂²×C₃×C₅	#131	1	2	yes	complemented
269	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₃×D₅	—	2	2	no	—
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	—	2	2	no	—
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	1	no	—
275	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
276	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
278	C₃×Dic₅	—	2	2	no	—
279	C₃×Dic₅	—	2	2	no	—
280	C₃×Dic₅	—	2	2	no	—
281	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
282	C₃×#41	—	10	2	no	—
283	C₃×#41	—	10	2	no	—
284	C₂×C₃×Q₈	—	5	1	no	—
285	C₂×C₃×D₄	—	5	2	no	—
286	C₂×C₃×D₄	—	5	2	no	—
287	C₂×C₃×D₄	—	5	2	no	—
288	C₂×C₃×D₄	—	5	1	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	—	5	2	no	—
292	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×M₁₆	—	2	2	no	—
299	C₃×M₁₆	—	2	4	no	—
300	C₃×M₁₆	—	10	4	no	—
301	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
302	C₂×C₃×C₈	—	2	4	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	1	no	—
305	C₂×C₃×C₈	—	5	1	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	10	2	no	—
308	C₂×C₃×C₈	—	10	2	no	—
309	C₂×C₃×C₈	—	10	4	no	—
310	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
311	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
312	C₃×C₄⋊C₄	—	5	2	no	—
313	C₃×C₄⋊C₄	—	5	2	no	—
314	C₃×C₄⋊C₄	—	5	1	no	—
315	C₃×C₄⋊C₄	—	5	1	no	—
316	C₃×C₂²⋊C₄	—	5	2	no	—
317	C₃×C₂²⋊C₄	—	5	2	no	—
318	C₃×C₂²⋊C₄	—	5	2	no	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	—	5	2	no	—
321	C₃×C₄²	—	5	2	no	—
322	C₂³×C₅	—	2	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	4	1	no	—
325	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₃×#41	1	2	yes	—
341	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
342	C₂²⋊D₅	—	2	4	no	—
343	C₂²⋊D₅	—	2	4	no	—
344	C₂²⋊D₅	—	4	2	no	—
345	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
346	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
347	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
348	D₂₀	—	2	2	no	—
349	C₄×D₅	—	2	2	no	—
350	C₄×D₅	—	2	2	no	—
351	Dic₁₀	—	2	2	no	—
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
354	#168	—	2	1	no	—
355	#168	—	2	1	no	—
356	#168	—	2	1	no	—
357	#168	—	2	1	no	—
358	C₂×#41	—	5	1	no	—
359	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
360	#131	—	10	4	no	—
361	C₂×M₁₆	—	2	4	no	—
362	C₂×M₁₆	—	5	2	no	—
363	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
364	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
365	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	5	2	no	—
369	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
370	#123	—	5	2	no	—
371	C₂²⋊Q₈	—	5	1	no	—
372	C₂²⋊Q₈	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	—	5	1	no	—
375	#120	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	2	no	—
378	#117	—	5	1	no	—
379	C₄⋊C₈	—	5	2	no	—
380	C₄⋊C₈	—	5	2	no	—
381	C₂²⋊C₈	—	5	1	no	—
382	C₂²⋊C₈	—	5	1	no	—
383	C₂²⋊C₈	—	5	1	no	—
384	C₂²⋊C₈	—	5	1	no	—
385	C₂²⋊C₈	—	5	2	no	—
386	C₂²⋊C₈	—	5	2	no	—
387	#97	—	5	2	no	—
388	C₄×C₈	—	5	2	no	—
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	—	2	2	no	—
391	C₂×C₃×C₅	—	4	1	no	—
392	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
393	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
394	C₂×C₃×C₅	#568	1	1	yes	characteristic
395	C₃×D₅	—	4	2	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	—	4	1	no	—
399	C₂³×C₃	—	5	2	no	—
400	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
402	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
403	C₃×Q₈	—	10	2	no	—
404	C₃×D₄	—	10	4	no	—
405	C₃×D₄	—	10	4	no	—
406	C₃×D₄	—	10	2	no	—
407	C₃×D₄	—	20	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	5	2	no	—
416	C₂×C₃×C₄	—	5	2	no	—
417	C₂×C₃×C₄	—	5	2	no	—
418	C₂×C₃×C₄	—	10	2	no	—
419	C₂×C₃×C₄	—	10	2	no	—
420	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
423	C₂×C₃×C₄	#709	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
425	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
426	C₃×C₈	—	2	2	no	—
427	C₃×C₈	—	10	1	no	—
428	C₃×C₈	—	10	1	no	—
429	C₃×C₈	—	10	1	no	—
430	C₃×C₈	—	10	1	no	—
431	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	1	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	2	1	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	4	4	no	—
440	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
441	C₂²×C₅	C₃×#131	1	2	yes	complemented
442	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
443	C₂×D₅	—	2	2	no	—
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	2	2	no	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
449	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
451	Dic₅	—	2	2	no	—
452	Dic₅	—	2	2	no	—
453	Dic₅	—	2	2	no	—
454	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
455	#41	—	10	2	no	—
456	#41	—	10	2	no	—
457	C₂×Q₈	—	5	1	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
466	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
467	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	4	no	—
473	M₁₆	—	10	4	no	—
474	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	10	2	no	—
481	C₂×C₈	—	10	2	no	—
482	C₂×C₈	—	10	4	no	—
483	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
484	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₂²⋊C₄	—	5	2	no	—
490	C₂²⋊C₄	—	5	2	no	—
491	C₂²⋊C₄	—	5	2	no	—
492	C₂²⋊C₄	—	5	2	no	—
493	C₂²⋊C₄	—	5	2	no	—
494	C₄²	—	5	2	no	—
495	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	—	2	1	no	—
503	C₂²×C₃	—	4	4	no	—
504	C₂²×C₃	—	10	2	no	—
505	C₂²×C₃	—	10	2	no	—
506	C₂²×C₃	—	10	2	no	—
507	C₂²×C₃	#4053	1	2	yes	complemented
508	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
509	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	10	2	no	—
513	C₃×C₄	—	10	2	no	—
514	C₃×C₄	—	10	2	no	—
515	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
516	C₃×C₄	C₂×#709	1	1	yes	characteristic
517	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	2	2	no	—
520	C₂×C₅	—	4	1	no	—
521	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
522	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
523	C₂×C₅	C₃×#568	1	1	yes	characteristic
524	D₅	—	4	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	5	2	no	—
529	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
530	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
531	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
532	Q₈	—	10	2	no	—
533	D₄	—	10	4	no	—
534	D₄	—	10	4	no	—
535	D₄	—	10	2	no	—
536	D₄	—	20	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	5	2	no	—
545	C₂×C₄	—	5	2	no	—
546	C₂×C₄	—	5	2	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
550	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
551	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
552	C₂×C₄	C₃×#709	1	2	yes	—
553	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
554	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	10	1	no	—
557	C₈	—	10	1	no	—
558	C₈	—	10	1	no	—
559	C₈	—	10	1	no	—
560	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	20	2	no	—
565	C₂×C₃	C₂×#4053	1	1	yes	characteristic
566	C₂×C₃	#66079	1	1	yes	characteristic
567	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
568	C₅	C₃×#2933	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	10	2	no	—
578	C₂²	—	10	2	no	—
579	C₂²	—	10	2	no	—
580	C₂²	C₃×#4053	1	2	yes	complemented
581	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
582	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	10	2	no	—
586	C₄	—	10	2	no	—
587	C₄	—	10	2	no	—
588	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
589	C₄	C₂×C₃×#709	1	1	yes	characteristic
590	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
591	C₃	#10615488	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	20	2	no	—
596	C₂	C₂×C₃×#4053	1	1	yes	characteristic
597	C₂	C₃×#66079	1	1	yes	characteristic
598	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	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66125	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₃×#2933
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
1. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂×C₃×#4053	C₂	semidirect
4. C₂×C₃×C₂²⋊#168	C₂	semidirect
5. C₃×#65418	C₂	semidirect
6. C₃×#65417	C₂	semidirect
7. C₃×#65416	C₂	semidirect
8. C₃×#65411	C₂	semidirect
9. C₃×#65408	C₂	semidirect
10. C₃×#65400	C₂	semidirect
11. C₃×C₈×C₂²⋊D₅	C₂	semidirect
12. #10615488	C₃	direct (N × H)
32. C₂×C₃×#676	C₂²	semidirect
33. C₂×C₃×C₈×D₅	C₂²	semidirect
38. C₃×#3952	C₂²	semidirect
39. C₃×#3952	C₂²	semidirect
40. C₃×#3947	C₂²	semidirect
41. C₃×#3946	C₂²	semidirect
42. C₃×#3946	C₂²	semidirect
43. C₃×C₈×Dic₅	C₂²	semidirect
45. C₂²×C₅×M₁₆	C₂×C₃	semidirect
47. C₂×#4053	C₂×C₃	semidirect
48. C₂×C₂²⋊#168	C₂×C₃	semidirect
49. #65418	C₂×C₃	semidirect
50. #65417	C₂×C₃	semidirect
51. #65416	C₂×C₃	semidirect
52. #65411	C₂×C₃	semidirect
53. #65408	C₂×C₃	semidirect
54. #65400	C₂×C₃	semidirect
55. C₈×C₂²⋊D₅	C₂×C₃	semidirect
75. C₃×C₅×M₁₆	D₄	semidirect
98. C₂²×C₃×M₁₆	D₅	semidirect
127. C₂×#676	C₂²×C₃	semidirect
128. C₂×C₈×D₅	C₂²×C₃	semidirect
133. #3952	C₂²×C₃	semidirect
134. #3952	C₂²×C₃	semidirect
135. #3947	C₂²×C₃	semidirect
136. #3946	C₂²×C₃	semidirect
137. #3946	C₂²×C₃	semidirect
138. C₈×Dic₅	C₂²×C₃	semidirect
226. C₅×M₁₆	C₃×D₄	semidirect
249. C₂²×M₁₆	C₃×D₅	semidirect
268. C₂²×C₃×C₅	#131	semidirect
301. C₃×M₁₆	C₂²⋊D₅	semidirect
441. C₂²×C₅	C₃×#131	semidirect
474. M₁₆	C₃×C₂²⋊D₅	semidirect
495. C₃×C₅	#2933	semidirect
507. C₂²×C₃	#4053	semidirect
568. C₅	C₃×#2933	semidirect
580. C₂²	C₃×#4053	semidirect
591. C₃	#10615488	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×C₅×M₁₆	2
C₃×#66125	2
C₂×C₃×#4053	2
C₂×C₃×C₂²⋊#168	2
C₃×#65418	2
C₃×#65417	2
C₃×#65416	2
C₃×#65411	2
C₃×#65408	2
C₃×#65400	2
C₃×C₈×C₂²⋊D₅	2
#10615488	3
C₃×#2933	5

Subgroups — C3×#10615488 #14415443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615488 #14415443