Subgroups — C₃×#10618881 #14484775

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66043	C₂	1	4	yes	maximal, complemented
5	C₃×#66040	C₂	1	4	yes	maximal, complemented
6	C₃×#66015	C₂	1	2	yes	maximal, complemented
7	C₃×#66002	C₂	1	2	yes	maximal, complemented
8	C₃×#65967	C₂	1	2	yes	maximal, complemented
9	C₃×#65958	C₂	1	2	yes	maximal, complemented
10	C₃×#65919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#713	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65902	C₂	1	2	yes	maximal, complemented
14	C₃×#65887	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65864	C₂	1	2	yes	maximal, complemented
17	C₃×#65856	C₂	1	2	yes	maximal, complemented
18	#10618881	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×#713	C₂²	1	2	yes	—
20	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#711	C₂²	1	1	yes	characteristic
22	C₂×C₃×#709	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#126	C₂²	1	4	yes	—
25	C₃×C₅×#124	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
28	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₃×#4093	C₂²	1	2	yes	—
32	C₃×#4093	C₂²	1	2	yes	—
33	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
34	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
35	C₃×#4090	C₂²	1	2	yes	—
36	C₃×#4086	C₂²	1	2	yes	—
37	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#4076	C₂²	1	2	yes	—
39	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
40	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
41	C₃×#4044	C₂²	1	4	yes	—
42	C₃×#4042	C₂²	1	4	yes	—
43	C₃×#4041	C₂²	1	2	yes	—
44	C₃×#4041	C₂²	1	2	yes	—
45	C₃×#4040	C₂²	1	4	yes	—
46	C₃×#4039	C₂²	1	2	yes	—
47	C₃×#4039	C₂²	1	2	yes	—
48	C₃×#4039	C₂²	1	2	yes	—
49	C₃×#4039	C₂²	1	4	yes	—
50	C₃×#4039	C₂²	1	2	yes	—
51	C₃×#4038	C₂²	1	1	yes	characteristic
52	C₃×#4038	C₂²	1	4	yes	—
53	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
55	C₃×#4036	C₂²	1	2	yes	—
56	C₃×#4035	C₂²	1	4	yes	—
57	C₃×#4033	C₂²	1	1	yes	characteristic
58	C₃×#4033	C₂²	1	2	yes	—
59	C₃×#4033	C₂²	1	1	yes	characteristic
60	C₃×#4033	C₂²	1	2	yes	—
61	C₃×#4032	C₂²	1	4	yes	—
62	C₃×#4031	C₂²	1	4	yes	—
63	C₃×#4030	C₂²	1	4	yes	—
64	C₃×#4030	C₂²	1	4	yes	—
65	C₃×#4030	C₂²	1	4	yes	—
66	C₃×#4029	C₂²	1	4	yes	—
67	C₃×#4027	C₂²	1	4	yes	—
68	C₃×#4027	C₂²	1	4	yes	—
69	C₃×#4027	C₂²	1	2	yes	—
70	C₃×#4027	C₂²	1	4	yes	—
71	C₃×#4023	C₂²	1	2	yes	—
72	C₃×#4022	C₂²	1	4	yes	—
73	C₃×#4021	C₂²	1	2	yes	—
74	C₃×#4020	C₂²	1	1	yes	characteristic
75	C₃×C₄×D₂₀	C₂²	1	4	yes	—
76	C₃×C₄×D₂₀	C₂²	1	2	yes	—
77	C₃×#4018	C₂²	1	4	yes	—
78	C₃×C₄²×D₅	C₂²	1	4	yes	—
79	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
80	C₃×C₄²×D₅	C₂²	1	2	yes	—
81	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
82	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
83	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
84	C₃×#3480	—	5	1	no	maximal, Hall
85	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
86	#66059	C₂×C₃	1	1	yes	characteristic, complemented
87	#66055	C₂×C₃	1	1	yes	characteristic, complemented
88	#66043	C₂×C₃	1	4	yes	complemented
89	#66040	C₂×C₃	1	4	yes	complemented
90	#66015	C₂×C₃	1	2	yes	complemented
91	#66002	C₂×C₃	1	2	yes	complemented
92	#65967	C₂×C₃	1	2	yes	complemented
93	#65958	C₂×C₃	1	2	yes	complemented
94	#65919	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×#713	C₂×C₃	1	2	yes	complemented
96	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
97	#65902	C₂×C₃	1	2	yes	complemented
98	#65887	C₂×C₃	1	1	yes	characteristic, complemented
99	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
100	#65864	C₂×C₃	1	2	yes	complemented
101	#65856	C₂×C₃	1	2	yes	complemented
102	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
106	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
107	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
108	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
109	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
110	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
111	C₃×#713	—	2	8	no	—
112	C₃×Q₈×D₅	—	2	4	no	—
113	C₃×#711	—	2	4	no	—
114	C₃×#709	—	2	8	no	—
115	C₂×C₃×D₂₀	C₂³	1	2	yes	—
116	C₂×C₃×D₂₀	C₂³	1	2	yes	—
117	C₂×C₃×D₂₀	C₂³	1	4	yes	—
118	C₂×C₃×D₂₀	C₂³	1	2	yes	—
119	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
120	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
121	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
123	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
124	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
125	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
127	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
128	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
129	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
130	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₃×C₄²×C₅	C₂³	1	2	yes	—
141	C₃×C₄²×C₅	C₂³	1	4	yes	—
142	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
143	C₃×#685	C₂³	1	4	yes	—
144	C₃×#685	C₂³	1	4	yes	—
145	C₃×#685	C₂³	1	4	yes	—
146	C₃×#685	C₂³	1	4	yes	—
147	C₃×#685	C₂³	1	4	yes	—
148	C₃×#685	C₂³	1	2	yes	—
149	C₃×#685	C₂³	1	4	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
151	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
152	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
153	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
154	C₃×#683	C₂³	1	4	yes	—
155	C₃×#683	C₂³	1	4	yes	—
156	C₃×#683	C₂³	1	2	yes	—
157	C₃×#683	C₂³	1	2	yes	—
158	C₃×#683	C₂³	1	2	yes	—
159	C₃×#683	C₂³	1	2	yes	—
160	C₃×#683	C₂³	1	2	yes	—
161	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
162	C₃×C₄×Dic₅	C₂³	1	2	yes	—
163	C₃×C₄×Dic₅	C₂³	1	2	yes	—
164	C₃×C₄×Dic₅	C₂³	1	4	yes	—
165	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
166	C₃×C₄×Dic₅	C₂³	1	2	yes	—
167	C₃×C₄×Dic₅	C₂³	1	2	yes	—
168	C₃×C₄×Dic₅	C₂³	1	2	yes	—
169	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
170	C₃×C₄×Dic₅	C₂³	1	2	yes	—
171	C₃×#559	—	5	2	no	—
172	C₃×#559	—	5	1	no	—
173	C₃×#557	—	5	1	no	—
174	C₃×#556	—	5	2	no	—
175	C₃×#556	D₅	1	1	yes	characteristic, complemented
176	C₃×#553	—	5	4	no	—
177	C₃×#553	—	5	2	no	—
178	C₃×#550	—	5	1	no	—
179	C₃×#548	—	5	2	no	—
180	C₃×#532	—	5	1	no	—
181	C₃×#532	—	5	2	no	—
182	C₃×#529	—	5	4	no	—
183	C₃×#529	—	5	2	no	—
184	C₃×C₄×#41	—	5	2	no	—
185	C₃×C₄×#41	—	5	1	no	—
186	C₃×C₄×#41	—	5	2	no	—
187	C₂×C₃×C₄×Q₈	—	5	1	no	—
188	C₂×#713	C₂²×C₃	1	2	yes	—
189	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×#711	C₂²×C₃	1	1	yes	characteristic
191	C₂×#709	C₂²×C₃	1	2	yes	—
192	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₅×#126	C₂²×C₃	1	4	yes	—
194	C₅×#124	C₂²×C₃	1	2	yes	—
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
196	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
197	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
198	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₅×#117	C₂²×C₃	1	2	yes	—
200	#4093	C₂²×C₃	1	2	yes	—
201	#4093	C₂²×C₃	1	2	yes	—
202	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
203	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
204	#4090	C₂²×C₃	1	2	yes	—
205	#4086	C₂²×C₃	1	2	yes	—
206	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
207	#4076	C₂²×C₃	1	2	yes	—
208	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
209	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
210	#4044	C₂²×C₃	1	4	yes	—
211	#4042	C₂²×C₃	1	4	yes	—
212	#4041	C₂²×C₃	1	2	yes	—
213	#4041	C₂²×C₃	1	2	yes	—
214	#4040	C₂²×C₃	1	4	yes	—
215	#4039	C₂²×C₃	1	2	yes	—
216	#4039	C₂²×C₃	1	2	yes	—
217	#4039	C₂²×C₃	1	2	yes	—
218	#4039	C₂²×C₃	1	2	yes	—
219	#4039	C₂²×C₃	1	4	yes	—
220	#4038	C₂²×C₃	1	1	yes	characteristic
221	#4038	C₂²×C₃	1	4	yes	—
222	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
223	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
224	#4036	C₂²×C₃	1	2	yes	—
225	#4035	C₂²×C₃	1	4	yes	—
226	#4033	C₂²×C₃	1	2	yes	—
227	#4033	C₂²×C₃	1	1	yes	characteristic
228	#4033	C₂²×C₃	1	1	yes	characteristic
229	#4033	C₂²×C₃	1	2	yes	—
230	#4032	C₂²×C₃	1	4	yes	—
231	#4031	C₂²×C₃	1	4	yes	—
232	#4030	C₂²×C₃	1	4	yes	—
233	#4030	C₂²×C₃	1	4	yes	—
234	#4030	C₂²×C₃	1	4	yes	—
235	#4029	C₂²×C₃	1	4	yes	—
236	#4027	C₂²×C₃	1	4	yes	—
237	#4027	C₂²×C₃	1	4	yes	—
238	#4027	C₂²×C₃	1	2	yes	—
239	#4027	C₂²×C₃	1	4	yes	—
240	#4023	C₂²×C₃	1	2	yes	—
241	#4022	C₂²×C₃	1	4	yes	—
242	#4021	C₂²×C₃	1	2	yes	—
243	#4020	C₂²×C₃	1	1	yes	characteristic
244	C₄×D₂₀	C₂²×C₃	1	4	yes	—
245	C₄×D₂₀	C₂²×C₃	1	2	yes	—
246	#4018	C₂²×C₃	1	4	yes	—
247	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
248	C₄²×D₅	C₂²×C₃	1	4	yes	—
249	C₄²×D₅	C₂²×C₃	1	2	yes	—
250	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
251	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
252	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
253	#3480	—	5	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
256	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
257	C₃×C₅×Q₈	—	2	2	no	—
258	C₃×C₅×Q₈	—	2	4	no	—
259	C₃×C₅×D₄	—	2	2	no	—
260	C₂×C₃×C₄×C₅	—	2	4	no	—
261	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
262	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
264	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₃×C₂²⋊D₅	—	2	4	no	—
269	C₃×C₂²⋊D₅	—	2	8	no	—
270	C₃×C₂²⋊D₅	—	4	4	no	—
271	C₂×C₃×Dic₅	—	2	4	no	—
272	C₂×C₃×Dic₅	—	4	2	no	—
273	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
275	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
276	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
277	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
280	C₃×D₂₀	—	2	8	no	—
281	C₃×D₂₀	—	2	4	no	—
282	C₃×D₂₀	—	2	4	no	—
283	C₃×D₂₀	—	4	2	no	—
284	C₃×C₄×D₅	—	2	2	no	—
285	C₃×C₄×D₅	—	2	8	no	—
286	C₃×C₄×D₅	—	2	4	no	—
287	C₃×C₄×D₅	—	2	8	no	—
288	C₃×C₄×D₅	—	4	4	no	—
289	C₃×C₄×D₅	—	4	1	no	—
290	C₃×C₄×D₅	—	4	2	no	—
291	C₃×C₄×D₅	#41	1	4	yes	complemented
292	C₃×Dic₁₀	—	2	2	no	—
293	C₃×Dic₁₀	—	2	4	no	—
294	C₃×Dic₁₀	#41	1	4	yes	complemented
295	C₂×C₃×#41	—	5	2	no	—
296	C₂×C₃×#41	—	5	1	no	—
297	C₂×C₃×#41	—	5	2	no	—
298	C₂²×C₃×Q₈	—	5	1	no	—
299	C₃×C₄⋊Q₈	—	5	2	no	—
300	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
301	C₃×#127	—	5	2	no	—
302	C₃×#127	—	5	1	no	—
303	C₃×#126	—	5	4	no	—
304	C₃×#126	—	5	4	no	—
305	C₃×#126	C₂×D₅	1	4	yes	—
306	C₃×#125	—	5	4	no	—
307	C₃×#125	—	5	2	no	—
308	C₃×#124	—	5	2	no	—
309	C₃×#124	—	5	2	no	—
310	C₃×#124	—	5	4	no	—
311	C₃×#124	—	5	2	no	—
312	C₃×#124	C₂×D₅	1	2	yes	—
313	C₃×#123	—	5	4	no	—
314	C₃×#123	—	5	4	no	—
315	C₃×#123	—	5	4	no	—
316	C₃×C₂²⋊Q₈	—	5	4	no	—
317	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
318	C₃×#121	—	5	2	no	—
319	C₃×#121	—	5	2	no	—
320	C₃×#121	—	5	2	no	—
321	C₃×#121	—	5	4	no	—
322	C₃×#121	—	5	4	no	—
323	C₃×#121	—	5	4	no	—
324	C₃×C₄×Q₈	—	5	2	no	—
325	C₃×C₄×Q₈	—	5	1	no	—
326	C₃×C₄×Q₈	—	5	1	no	—
327	C₃×C₄×Q₈	—	5	2	no	—
328	C₃×C₄×Q₈	—	5	2	no	—
329	C₃×C₄×Q₈	—	5	1	no	—
330	C₃×C₄×Q₈	—	5	2	no	—
331	C₃×C₄×Q₈	—	5	1	no	—
332	C₃×C₄×Q₈	—	5	1	no	—
333	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
334	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
335	C₃×C₄×D₄	—	5	1	no	—
336	C₃×C₄×D₄	—	5	2	no	—
337	C₃×C₄×D₄	—	5	2	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	4	no	—
340	C₃×C₄×D₄	—	5	2	no	—
341	C₃×C₄×D₄	—	5	2	no	—
342	C₃×C₄×D₄	—	5	4	no	—
343	C₃×C₄×D₄	—	5	4	no	—
344	C₃×C₄×D₄	—	5	2	no	—
345	C₃×C₄×D₄	—	5	4	no	—
346	C₃×C₄×D₄	—	5	2	no	—
347	C₃×C₄×D₄	—	5	4	no	—
348	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
349	C₃×#117	—	5	1	no	—
350	C₃×#117	—	5	4	no	—
351	C₃×#117	—	5	2	no	—
352	C₃×#117	—	5	4	no	—
353	C₃×#117	C₂×D₅	1	2	yes	—
354	C₂×C₃×C₄⋊C₄	—	5	2	no	—
355	C₂×C₃×C₄⋊C₄	—	5	1	no	—
356	C₂×C₃×C₄²	—	5	2	no	—
357	C₂×C₃×C₄²	—	5	1	no	—
358	C₂×C₃×C₄²	—	5	2	no	—
359	C₂×C₃×C₄²	—	5	4	no	—
360	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
361	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
362	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
364	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
365	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
366	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
367	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
368	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
369	#713	—	2	8	no	—
370	Q₈×D₅	—	2	4	no	—
371	#711	—	2	4	no	—
372	#709	—	2	8	no	—
373	C₂×D₂₀	C₂³×C₃	1	2	yes	—
374	C₂×D₂₀	C₂³×C₃	1	2	yes	—
375	C₂×D₂₀	C₂³×C₃	1	4	yes	—
376	C₂×D₂₀	C₂³×C₃	1	2	yes	—
377	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
378	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
379	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
381	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
382	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
383	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
384	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
385	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
386	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
387	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
388	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
389	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
390	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
391	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
392	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
395	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
396	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
397	C₄²×C₅	C₂³×C₃	1	4	yes	—
398	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
399	C₄²×C₅	C₂³×C₃	1	2	yes	—
400	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
401	#685	C₂³×C₃	1	4	yes	—
402	#685	C₂³×C₃	1	4	yes	—
403	#685	C₂³×C₃	1	2	yes	—
404	#685	C₂³×C₃	1	4	yes	—
405	#685	C₂³×C₃	1	4	yes	—
406	#685	C₂³×C₃	1	4	yes	—
407	#685	C₂³×C₃	1	4	yes	—
408	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
409	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
410	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
411	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
412	#683	C₂³×C₃	1	2	yes	—
413	#683	C₂³×C₃	1	2	yes	—
414	#683	C₂³×C₃	1	2	yes	—
415	#683	C₂³×C₃	1	2	yes	—
416	#683	C₂³×C₃	1	4	yes	—
417	#683	C₂³×C₃	1	2	yes	—
418	#683	C₂³×C₃	1	4	yes	—
419	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
420	C₄×Dic₅	C₂³×C₃	1	2	yes	—
421	C₄×Dic₅	C₂³×C₃	1	2	yes	—
422	C₄×Dic₅	C₂³×C₃	1	2	yes	—
423	C₄×Dic₅	C₂³×C₃	1	2	yes	—
424	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
425	C₄×Dic₅	C₂³×C₃	1	2	yes	—
426	C₄×Dic₅	C₂³×C₃	1	4	yes	—
427	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
428	C₄×Dic₅	C₂³×C₃	1	2	yes	—
429	#559	—	5	2	no	—
430	#559	—	5	1	no	—
431	#557	—	5	1	no	—
432	#556	—	5	2	no	—
433	#556	C₃×D₅	1	1	yes	characteristic, complemented
434	#553	—	5	4	no	—
435	#553	—	5	2	no	—
436	#550	—	5	1	no	—
437	#548	—	5	2	no	—
438	#532	—	5	1	no	—
439	#532	—	5	2	no	—
440	#529	—	5	4	no	—
441	#529	—	5	2	no	—
442	C₄×#41	—	5	2	no	—
443	C₄×#41	—	5	1	no	—
444	C₄×#41	—	5	2	no	—
445	C₂×C₄×Q₈	—	5	1	no	—
446	C₂²×C₃×C₅	—	2	2	no	—
447	C₂²×C₃×C₅	—	2	2	no	—
448	C₂²×C₃×C₅	—	2	2	no	—
449	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
450	C₂×C₃×D₅	—	2	1	no	—
451	C₂×C₃×D₅	—	2	1	no	—
452	C₂×C₃×D₅	—	2	4	no	—
453	C₂×C₃×D₅	—	2	4	no	—
454	C₂×C₃×D₅	—	2	4	no	—
455	C₂×C₃×D₅	C₂×#41	1	2	yes	—
456	C₃×C₄×C₅	—	2	2	no	—
457	C₃×C₄×C₅	—	2	2	no	—
458	C₃×C₄×C₅	—	2	4	no	—
459	C₃×C₄×C₅	—	2	2	no	—
460	C₃×C₄×C₅	—	2	1	no	—
461	C₃×C₄×C₅	C₂×#41	1	2	yes	—
462	C₃×C₄×C₅	C₂×#41	1	2	yes	—
463	C₃×Dic₅	—	2	1	no	—
464	C₃×Dic₅	—	2	2	no	—
465	C₃×Dic₅	—	2	2	no	—
466	C₃×Dic₅	—	2	1	no	—
467	C₃×Dic₅	—	2	2	no	—
468	C₃×Dic₅	C₂×#41	1	4	yes	—
469	C₃×Dic₅	C₂×#41	1	2	yes	—
470	C₃×#41	—	10	8	no	—
471	C₃×#41	—	10	4	no	—
472	C₃×#41	—	10	8	no	—
473	C₂×C₃×Q₈	—	5	1	no	—
474	C₂×C₃×Q₈	—	5	2	no	—
475	C₂×C₃×Q₈	—	5	1	no	—
476	C₂×C₃×Q₈	—	10	4	no	—
477	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
478	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
479	C₂×C₃×D₄	—	5	2	no	—
480	C₂×C₃×D₄	—	5	4	no	—
481	C₂×C₃×D₄	—	5	4	no	—
482	C₂×C₃×D₄	—	5	4	no	—
483	C₂×C₃×D₄	—	5	2	no	—
484	C₂×C₃×D₄	—	5	2	no	—
485	C₂×C₃×D₄	—	5	2	no	—
486	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
487	C₂²×C₃×C₄	—	5	1	no	—
488	C₂²×C₃×C₄	—	5	2	no	—
489	C₂²×C₃×C₄	—	5	2	no	—
490	C₂²×C₃×C₄	—	5	2	no	—
491	C₂²×C₃×C₄	—	5	1	no	—
492	C₂²×C₃×C₄	—	5	4	no	—
493	C₂²×C₃×C₄	—	5	4	no	—
494	C₂²×C₃×C₄	—	5	1	no	—
495	C₂²×C₃×C₄	—	5	2	no	—
496	C₂²×C₃×C₄	—	5	4	no	—
497	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
498	C₃×C₄⋊C₄	—	5	2	no	—
499	C₃×C₄⋊C₄	—	5	2	no	—
500	C₃×C₄⋊C₄	—	5	2	no	—
501	C₃×C₄⋊C₄	—	5	4	no	—
502	C₃×C₄⋊C₄	—	5	2	no	—
503	C₃×C₄⋊C₄	—	5	2	no	—
504	C₃×C₄⋊C₄	—	5	4	no	—
505	C₃×C₄⋊C₄	—	5	1	no	—
506	C₃×C₄⋊C₄	—	5	2	no	—
507	C₃×C₄⋊C₄	—	5	1	no	—
508	C₃×C₄⋊C₄	—	5	4	no	—
509	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
511	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
512	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
513	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
514	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
515	C₃×C₂²⋊C₄	—	5	2	no	—
516	C₃×C₂²⋊C₄	—	5	2	no	—
517	C₃×C₂²⋊C₄	—	5	4	no	—
518	C₃×C₂²⋊C₄	—	5	4	no	—
519	C₃×C₂²⋊C₄	—	5	4	no	—
520	C₃×C₂²⋊C₄	—	5	4	no	—
521	C₃×C₂²⋊C₄	—	5	4	no	—
522	C₃×C₂²⋊C₄	—	5	4	no	—
523	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
524	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
525	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
526	C₃×C₄²	—	5	2	no	—
527	C₃×C₄²	—	5	2	no	—
528	C₃×C₄²	—	5	1	no	—
529	C₃×C₄²	—	5	1	no	—
530	C₃×C₄²	—	5	2	no	—
531	C₃×C₄²	—	5	2	no	—
532	C₃×C₄²	—	5	4	no	—
533	C₃×C₄²	—	5	2	no	—
534	C₃×C₄²	—	5	1	no	—
535	C₃×C₄²	—	5	2	no	—
536	C₃×C₄²	C₂²×D₅	1	4	yes	—
537	C₃×C₄²	C₂²×D₅	1	2	yes	—
538	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
539	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
540	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
541	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
542	C₅×Q₈	—	2	2	no	—
543	C₅×Q₈	—	2	4	no	—
544	C₅×D₄	—	2	2	no	—
545	C₂×C₄×C₅	—	2	4	no	—
546	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
547	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
548	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
549	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
550	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
551	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
552	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
553	C₂²⋊D₅	—	2	4	no	—
554	C₂²⋊D₅	—	2	8	no	—
555	C₂²⋊D₅	—	4	4	no	—
556	C₂×Dic₅	—	2	4	no	—
557	C₂×Dic₅	—	4	2	no	—
558	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
559	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
560	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
561	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
562	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
563	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
564	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
565	D₂₀	—	2	8	no	—
566	D₂₀	—	2	4	no	—
567	D₂₀	—	2	4	no	—
568	D₂₀	—	4	2	no	—
569	C₄×D₅	—	2	2	no	—
570	C₄×D₅	—	2	8	no	—
571	C₄×D₅	—	2	4	no	—
572	C₄×D₅	—	2	8	no	—
573	C₄×D₅	—	4	4	no	—
574	C₄×D₅	—	4	1	no	—
575	C₄×D₅	—	4	2	no	—
576	C₄×D₅	C₃×#41	1	4	yes	complemented
577	Dic₁₀	—	2	2	no	—
578	Dic₁₀	—	2	4	no	—
579	Dic₁₀	C₃×#41	1	4	yes	complemented
580	C₂×#41	—	5	2	no	—
581	C₂×#41	—	5	1	no	—
582	C₂×#41	—	5	2	no	—
583	C₂²×Q₈	—	5	1	no	—
584	C₄⋊Q₈	—	5	2	no	—
585	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
586	#127	—	5	2	no	—
587	#127	—	5	1	no	—
588	#126	—	5	4	no	—
589	#126	—	5	4	no	—
590	#126	C₂×C₃×D₅	1	4	yes	—
591	#125	—	5	4	no	—
592	#125	—	5	2	no	—
593	#124	—	5	2	no	—
594	#124	—	5	2	no	—
595	#124	—	5	4	no	—
596	#124	—	5	2	no	—
597	#124	C₂×C₃×D₅	1	2	yes	—
598	#123	—	5	4	no	—
599	#123	—	5	4	no	—
600	#123	—	5	4	no	—
601	C₂²⋊Q₈	—	5	4	no	—
602	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
603	#121	—	5	2	no	—
604	#121	—	5	2	no	—
605	#121	—	5	2	no	—
606	#121	—	5	4	no	—
607	#121	—	5	4	no	—
608	#121	—	5	4	no	—
609	C₄×Q₈	—	5	1	no	—
610	C₄×Q₈	—	5	2	no	—
611	C₄×Q₈	—	5	1	no	—
612	C₄×Q₈	—	5	2	no	—
613	C₄×Q₈	—	5	2	no	—
614	C₄×Q₈	—	5	1	no	—
615	C₄×Q₈	—	5	1	no	—
616	C₄×Q₈	—	5	2	no	—
617	C₄×Q₈	—	5	1	no	—
618	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
619	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
620	C₄×D₄	—	5	1	no	—
621	C₄×D₄	—	5	2	no	—
622	C₄×D₄	—	5	2	no	—
623	C₄×D₄	—	5	4	no	—
624	C₄×D₄	—	5	2	no	—
625	C₄×D₄	—	5	2	no	—
626	C₄×D₄	—	5	2	no	—
627	C₄×D₄	—	5	4	no	—
628	C₄×D₄	—	5	2	no	—
629	C₄×D₄	—	5	4	no	—
630	C₄×D₄	—	5	4	no	—
631	C₄×D₄	—	5	4	no	—
632	C₄×D₄	—	5	2	no	—
633	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
634	#117	—	5	1	no	—
635	#117	—	5	4	no	—
636	#117	—	5	2	no	—
637	#117	—	5	4	no	—
638	#117	C₂×C₃×D₅	1	2	yes	—
639	C₂×C₄⋊C₄	—	5	2	no	—
640	C₂×C₄⋊C₄	—	5	1	no	—
641	C₂×C₄²	—	5	2	no	—
642	C₂×C₄²	—	5	1	no	—
643	C₂×C₄²	—	5	2	no	—
644	C₂×C₄²	—	5	4	no	—
645	C₂×C₃×C₅	—	4	2	no	—
646	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
647	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
648	C₂×C₃×C₅	#585	1	1	yes	characteristic
649	C₃×D₅	—	2	2	no	—
650	C₃×D₅	—	4	4	no	—
651	C₂³×C₃	—	5	1	no	—
652	C₂³×C₃	—	5	4	no	—
653	C₂³×C₃	C₂³×D₅	1	2	yes	—
654	C₃×Q₈	—	2	2	no	—
655	C₃×Q₈	—	2	4	no	—
656	C₃×Q₈	—	5	4	no	—
657	C₃×Q₈	—	10	4	no	—
658	C₃×Q₈	—	10	2	no	—
659	C₃×D₄	—	2	2	no	—
660	C₃×D₄	—	10	8	no	—
661	C₃×D₄	—	10	8	no	—
662	C₃×D₄	—	10	4	no	—
663	C₃×D₄	—	10	4	no	—
664	C₃×D₄	—	10	4	no	—
665	C₃×D₄	—	20	2	no	—
666	C₃×D₄	—	20	4	no	—
667	C₂×C₃×C₄	—	2	4	no	—
668	C₂×C₃×C₄	—	5	1	no	—
669	C₂×C₃×C₄	—	5	2	no	—
670	C₂×C₃×C₄	—	5	4	no	—
671	C₂×C₃×C₄	—	5	1	no	—
672	C₂×C₃×C₄	—	5	2	no	—
673	C₂×C₃×C₄	—	5	1	no	—
674	C₂×C₃×C₄	—	5	2	no	—
675	C₂×C₃×C₄	—	5	2	no	—
676	C₂×C₃×C₄	—	10	4	no	—
677	C₂×C₃×C₄	—	10	8	no	—
678	C₂×C₃×C₄	—	10	8	no	—
679	C₂×C₃×C₄	—	10	4	no	—
680	C₂×C₃×C₄	—	10	2	no	—
681	C₂×C₃×C₄	—	20	4	no	—
682	C₂×C₃×C₄	—	20	2	no	—
683	C₂×C₃×C₄	—	20	1	no	—
684	C₂×C₃×C₄	—	20	2	no	—
685	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
686	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
687	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
688	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
689	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
691	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
692	C₂²×C₅	—	2	2	no	—
693	C₂²×C₅	—	2	2	no	—
694	C₂²×C₅	—	2	2	no	—
695	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
696	C₂×D₅	—	2	1	no	—
697	C₂×D₅	—	2	1	no	—
698	C₂×D₅	—	2	4	no	—
699	C₂×D₅	—	2	4	no	—
700	C₂×D₅	—	2	4	no	—
701	C₂×D₅	C₂×C₃×#41	1	2	yes	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	2	4	no	—
705	C₄×C₅	—	2	2	no	—
706	C₄×C₅	—	2	1	no	—
707	C₄×C₅	C₂×C₃×#41	1	2	yes	—
708	C₄×C₅	C₂×C₃×#41	1	2	yes	—
709	Dic₅	—	2	1	no	—
710	Dic₅	—	2	2	no	—
711	Dic₅	—	2	2	no	—
712	Dic₅	—	2	1	no	—
713	Dic₅	—	2	2	no	—
714	Dic₅	C₂×C₃×#41	1	4	yes	—
715	Dic₅	C₂×C₃×#41	1	2	yes	—
716	#41	—	10	8	no	—
717	#41	—	10	4	no	—
718	#41	—	10	8	no	—
719	C₂×Q₈	—	5	1	no	—
720	C₂×Q₈	—	5	2	no	—
721	C₂×Q₈	—	5	1	no	—
722	C₂×Q₈	—	10	4	no	—
723	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
724	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
725	C₂×D₄	—	5	2	no	—
726	C₂×D₄	—	5	4	no	—
727	C₂×D₄	—	5	4	no	—
728	C₂×D₄	—	5	4	no	—
729	C₂×D₄	—	5	2	no	—
730	C₂×D₄	—	5	2	no	—
731	C₂×D₄	—	5	2	no	—
732	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
733	C₂²×C₄	—	5	1	no	—
734	C₂²×C₄	—	5	2	no	—
735	C₂²×C₄	—	5	2	no	—
736	C₂²×C₄	—	5	2	no	—
737	C₂²×C₄	—	5	1	no	—
738	C₂²×C₄	—	5	4	no	—
739	C₂²×C₄	—	5	4	no	—
740	C₂²×C₄	—	5	1	no	—
741	C₂²×C₄	—	5	2	no	—
742	C₂²×C₄	—	5	4	no	—
743	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
744	C₄⋊C₄	—	5	2	no	—
745	C₄⋊C₄	—	5	2	no	—
746	C₄⋊C₄	—	5	1	no	—
747	C₄⋊C₄	—	5	2	no	—
748	C₄⋊C₄	—	5	2	no	—
749	C₄⋊C₄	—	5	1	no	—
750	C₄⋊C₄	—	5	4	no	—
751	C₄⋊C₄	—	5	2	no	—
752	C₄⋊C₄	—	5	2	no	—
753	C₄⋊C₄	—	5	4	no	—
754	C₄⋊C₄	—	5	4	no	—
755	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
757	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
759	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
760	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
761	C₂²⋊C₄	—	5	2	no	—
762	C₂²⋊C₄	—	5	2	no	—
763	C₂²⋊C₄	—	5	4	no	—
764	C₂²⋊C₄	—	5	4	no	—
765	C₂²⋊C₄	—	5	4	no	—
766	C₂²⋊C₄	—	5	4	no	—
767	C₂²⋊C₄	—	5	4	no	—
768	C₂²⋊C₄	—	5	4	no	—
769	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
770	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
771	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
772	C₄²	—	5	2	no	—
773	C₄²	—	5	2	no	—
774	C₄²	—	5	1	no	—
775	C₄²	—	5	1	no	—
776	C₄²	—	5	2	no	—
777	C₄²	—	5	2	no	—
778	C₄²	—	5	4	no	—
779	C₄²	—	5	2	no	—
780	C₄²	—	5	1	no	—
781	C₄²	—	5	2	no	—
782	C₄²	C₂²×C₃×D₅	1	4	yes	—
783	C₄²	C₂²×C₃×D₅	1	2	yes	—
784	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
785	C₃×C₅	#3480	1	1	yes	characteristic, complemented, Hall
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	5	2	no	—
790	C₂²×C₃	—	10	1	no	—
791	C₂²×C₃	—	10	1	no	—
792	C₂²×C₃	—	10	4	no	—
793	C₂²×C₃	—	10	4	no	—
794	C₂²×C₃	—	10	4	no	—
795	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
796	C₃×C₄	—	2	2	no	—
797	C₃×C₄	—	2	4	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	—	5	2	no	—
802	C₃×C₄	—	5	4	no	—
803	C₃×C₄	—	10	2	no	—
804	C₃×C₄	—	10	1	no	—
805	C₃×C₄	—	10	2	no	—
806	C₃×C₄	—	10	1	no	—
807	C₃×C₄	—	10	2	no	—
808	C₃×C₄	D₅×#41	1	2	yes	—
809	C₃×C₄	D₅×#41	1	2	yes	—
810	C₂×C₅	—	4	2	no	—
811	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
812	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
813	C₂×C₅	C₃×#585	1	1	yes	characteristic
814	D₅	—	2	2	no	—
815	D₅	—	4	4	no	—
816	C₂³	—	5	1	no	—
817	C₂³	—	5	4	no	—
818	C₂³	C₂³×C₃×D₅	1	2	yes	—
819	Q₈	—	2	2	no	—
820	Q₈	—	2	4	no	—
821	Q₈	—	5	4	no	—
822	Q₈	—	10	4	no	—
823	Q₈	—	10	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	10	8	no	—
826	D₄	—	10	8	no	—
827	D₄	—	10	4	no	—
828	D₄	—	10	4	no	—
829	D₄	—	10	4	no	—
830	D₄	—	20	2	no	—
831	D₄	—	20	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	5	1	no	—
834	C₂×C₄	—	5	2	no	—
835	C₂×C₄	—	5	4	no	—
836	C₂×C₄	—	5	2	no	—
837	C₂×C₄	—	5	1	no	—
838	C₂×C₄	—	5	1	no	—
839	C₂×C₄	—	5	2	no	—
840	C₂×C₄	—	5	2	no	—
841	C₂×C₄	—	10	4	no	—
842	C₂×C₄	—	10	8	no	—
843	C₂×C₄	—	10	8	no	—
844	C₂×C₄	—	10	4	no	—
845	C₂×C₄	—	10	2	no	—
846	C₂×C₄	—	20	4	no	—
847	C₂×C₄	—	20	2	no	—
848	C₂×C₄	—	20	1	no	—
849	C₂×C₄	—	20	2	no	—
850	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
851	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
852	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
853	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
854	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
855	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
856	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
857	C₂×C₃	—	4	2	no	—
858	C₂×C₃	—	10	2	no	—
859	C₂×C₃	—	20	4	no	—
860	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
861	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
862	C₂×C₃	#66287	1	1	yes	characteristic
863	C₅	C₃×#3480	1	1	yes	characteristic, complemented, Sylow
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	5	2	no	—
868	C₂²	—	10	1	no	—
869	C₂²	—	10	1	no	—
870	C₂²	—	10	4	no	—
871	C₂²	—	10	4	no	—
872	C₂²	—	10	4	no	—
873	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
874	C₄	—	2	2	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	1	no	—
879	C₄	—	5	2	no	—
880	C₄	—	5	4	no	—
881	C₄	—	10	2	no	—
882	C₄	—	10	1	no	—
883	C₄	—	10	2	no	—
884	C₄	—	10	1	no	—
885	C₄	—	10	2	no	—
886	C₄	C₃×D₅×#41	1	2	yes	—
887	C₄	C₃×D₅×#41	1	2	yes	—
888	C₃	#10618881	1	1	yes	characteristic, direct product factor, Sylow
889	C₂	—	4	2	no	—
890	C₂	—	10	2	no	—
891	C₂	—	20	4	no	—
892	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
893	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
894	C₂	C₃×#66287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#556	D₅
hypocenter	C₅	C₃×#3480
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
2. C₃×#66059	C₂	semidirect
3. C₃×#66055	C₂	semidirect
4. C₃×#66043	C₂	semidirect
5. C₃×#66040	C₂	semidirect
6. C₃×#66015	C₂	semidirect
7. C₃×#66002	C₂	semidirect
8. C₃×#65967	C₂	semidirect
9. C₃×#65958	C₂	semidirect
10. C₃×#65919	C₂	semidirect
11. C₃×C₄×#713	C₂	semidirect
12. C₃×C₄×Q₈×D₅	C₂	semidirect
13. C₃×#65902	C₂	semidirect
14. C₃×#65887	C₂	semidirect
15. C₃×C₄×#711	C₂	semidirect
16. C₃×#65864	C₂	semidirect
17. C₃×#65856	C₂	semidirect
18. #10618881	C₃	direct (N × H)
85. C₅×#556	C₂×C₃	semidirect
86. #66059	C₂×C₃	semidirect
87. #66055	C₂×C₃	semidirect
88. #66043	C₂×C₃	semidirect
89. #66040	C₂×C₃	semidirect
90. #66015	C₂×C₃	semidirect
91. #66002	C₂×C₃	semidirect
92. #65967	C₂×C₃	semidirect
93. #65958	C₂×C₃	semidirect
94. #65919	C₂×C₃	semidirect
95. C₄×#713	C₂×C₃	semidirect
96. C₄×Q₈×D₅	C₂×C₃	semidirect
97. #65902	C₂×C₃	semidirect
98. #65887	C₂×C₃	semidirect
99. C₄×#711	C₂×C₃	semidirect
100. #65864	C₂×C₃	semidirect
101. #65856	C₂×C₃	semidirect
175. C₃×#556	D₅	semidirect
291. C₃×C₄×D₅	#41	semidirect
294. C₃×Dic₁₀	#41	semidirect
433. #556	C₃×D₅	semidirect
576. C₄×D₅	C₃×#41	semidirect
579. Dic₁₀	C₃×#41	semidirect
785. C₃×C₅	#3480	semidirect
863. C₅	C₃×#3480	semidirect
888. C₃	#10618881	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×C₅×#556	2
C₃×#66059	2
C₃×#66055	2
C₃×#66043	2
C₃×#66040	2
C₃×#66015	2
C₃×#66002	2
C₃×#65967	2
C₃×#65958	2
C₃×#65919	2
C₃×C₄×#713	2
C₃×C₄×Q₈×D₅	2
C₃×#65902	2
C₃×#65887	2
C₃×C₄×#711	2
C₃×#65864	2
C₃×#65856	2
#10618881	3
C₃×#3480	5

Subgroups — C3×#10618881 #14484775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618881 #14484775