Subgroups — C₃×#10618776 #14484781

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66040	C₂	1	2	yes	maximal, complemented
3	C₃×#66036	C₂	1	2	yes	maximal, complemented
4	C₃×#66025	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66019	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65998	C₂	1	2	yes	maximal, complemented
7	C₃×#65983	C₂	1	2	yes	maximal, complemented
8	C₃×#65935	C₂	1	2	yes	maximal, complemented
9	C₃×#65934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65932	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65930	C₂	1	2	yes	maximal, complemented
14	C₃×#65893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65886	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65874	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×#711	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#65867	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#65856	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#65848	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
24	#10618776	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×#711	C₂²	1	2	yes	—
26	C₂×C₃×#711	C₂²	1	1	yes	characteristic
27	C₂×C₃×#711	C₂²	1	1	yes	characteristic
28	C₂×C₃×#709	C₂²	1	1	yes	characteristic
29	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	C₂²	1	2	yes	—
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic
32	C₃×C₅×#123	C₂²	1	2	yes	—
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic
34	C₃×C₅×#121	C₂²	1	2	yes	—
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×#4086	C₂²	1	1	yes	characteristic
42	C₃×#4086	C₂²	1	2	yes	—
43	C₃×#4085	C₂²	1	2	yes	—
44	C₃×#4085	C₂²	1	2	yes	—
45	C₃×#4085	C₂²	1	2	yes	—
46	C₃×#4085	C₂²	1	2	yes	—
47	C₃×#4082	C₂²	1	1	yes	characteristic
48	C₃×#4081	C₂²	1	2	yes	—
49	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
50	C₃×D₄×Dic₅	C₂²	1	2	yes	—
51	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
52	C₃×D₄×Dic₅	C₂²	1	2	yes	—
53	C₃×#4076	C₂²	1	2	yes	—
54	C₃×#4076	C₂²	1	1	yes	characteristic
55	C₃×#4075	C₂²	1	2	yes	—
56	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
57	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
58	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
60	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
61	C₃×#4070	C₂²	1	1	yes	characteristic
62	C₂×C₃×#683	C₂²	1	2	yes	—
63	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
64	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
65	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
66	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
67	C₃×#4044	C₂²	1	2	yes	—
68	C₃×#4044	C₂²	1	2	yes	—
69	C₃×#4043	C₂²	1	1	yes	characteristic
70	C₃×#4042	C₂²	1	2	yes	—
71	C₃×#4041	C₂²	1	1	yes	characteristic
72	C₃×#4040	C₂²	1	2	yes	—
73	C₃×#4040	C₂²	1	2	yes	—
74	C₃×#4039	C₂²	1	1	yes	characteristic
75	C₃×#4039	C₂²	1	1	yes	characteristic
76	C₃×#4039	C₂²	1	2	yes	—
77	C₃×#4038	C₂²	1	1	yes	characteristic
78	C₃×#4038	C₂²	1	2	yes	—
79	C₃×#4038	C₂²	1	1	yes	characteristic
80	C₃×#4036	C₂²	1	1	yes	characteristic
81	C₃×#4035	C₂²	1	2	yes	—
82	C₃×#4035	C₂²	1	2	yes	—
83	C₃×#4034	C₂²	1	1	yes	characteristic
84	C₃×#4034	C₂²	1	2	yes	—
85	C₃×#4033	C₂²	1	1	yes	characteristic
86	C₃×#4033	C₂²	1	1	yes	characteristic
87	C₃×#4033	C₂²	1	1	yes	characteristic
88	C₃×#4033	C₂²	1	2	yes	—
89	C₃×#4033	C₂²	1	1	yes	characteristic
90	C₃×#4033	C₂²	1	1	yes	characteristic
91	C₃×#4033	C₂²	1	1	yes	characteristic
92	C₃×#4033	C₂²	1	2	yes	—
93	C₃×#4033	C₂²	1	2	yes	—
94	C₃×#4031	C₂²	1	2	yes	—
95	C₃×#4031	C₂²	1	2	yes	—
96	C₃×#4031	C₂²	1	2	yes	—
97	C₃×#4031	C₂²	1	2	yes	—
98	C₃×#4031	C₂²	1	2	yes	—
99	C₃×#4030	C₂²	1	2	yes	—
100	C₃×#4029	C₂²	1	2	yes	—
101	C₃×#4027	C₂²	1	2	yes	—
102	C₃×#4027	C₂²	1	2	yes	—
103	C₃×#4027	C₂²	1	1	yes	characteristic
104	C₃×#4027	C₂²	1	2	yes	—
105	C₃×#4027	C₂²	1	2	yes	—
106	C₃×#4027	C₂²	1	2	yes	—
107	C₃×#4027	C₂²	1	1	yes	characteristic
108	C₃×#4027	C₂²	1	2	yes	—
109	C₃×#4025	C₂²	1	2	yes	—
110	C₃×#4025	C₂²	1	2	yes	—
111	C₃×#4024	C₂²	1	2	yes	—
112	C₃×#4023	C₂²	1	1	yes	characteristic
113	C₃×#4023	C₂²	1	2	yes	—
114	C₃×#4023	C₂²	1	2	yes	—
115	C₃×#4023	C₂²	1	1	yes	characteristic
116	C₃×#4022	C₂²	1	2	yes	—
117	C₃×#4021	C₂²	1	1	yes	characteristic
118	C₃×#4018	C₂²	1	2	yes	—
119	C₃×C₄²×D₅	C₂²	1	2	yes	—
120	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
121	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
122	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
124	C₃×#3480	—	5	1	no	maximal, Hall
125	C₅×#553	C₂×C₃	1	1	yes	characteristic, complemented
126	#66040	C₂×C₃	1	2	yes	complemented
127	#66036	C₂×C₃	1	2	yes	complemented
128	#66025	C₂×C₃	1	1	yes	characteristic, complemented
129	#66019	C₂×C₃	1	1	yes	characteristic, complemented
130	#65998	C₂×C₃	1	2	yes	complemented
131	#65983	C₂×C₃	1	2	yes	complemented
132	#65935	C₂×C₃	1	2	yes	complemented
133	#65934	C₂×C₃	1	1	yes	characteristic, complemented
134	#65933	C₂×C₃	1	1	yes	characteristic, complemented
135	#65932	C₂×C₃	1	1	yes	characteristic, complemented
136	#65930	C₂×C₃	1	1	yes	characteristic, complemented
137	#65930	C₂×C₃	1	2	yes	complemented
138	#65893	C₂×C₃	1	1	yes	characteristic, complemented
139	#65886	C₂×C₃	1	1	yes	characteristic, complemented
140	#65874	C₂×C₃	1	2	yes	complemented
141	C₄×#711	C₂×C₃	1	2	yes	complemented
142	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
143	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
144	#65867	C₂×C₃	1	1	yes	characteristic, complemented
145	#65856	C₂×C₃	1	1	yes	characteristic, complemented
146	#65848	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
150	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
155	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
163	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
164	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
165	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
166	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
167	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
168	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
169	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
170	C₃×#711	—	2	8	no	—
171	C₃×#711	—	2	4	no	—
172	C₃×#711	—	2	4	no	—
173	C₃×#709	—	2	4	no	—
174	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
175	C₂×C₃×D₂₀	C₂³	1	2	yes	—
176	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
177	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
178	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
182	C₂×C₃×Dic₁₀	—	2	4	no	—
183	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
184	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
185	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
186	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
187	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₃×C₄²×C₅	C₂³	1	2	yes	—
203	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
204	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
205	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
206	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
207	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
208	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
209	C₃×#685	C₂³	1	2	yes	—
210	C₃×#685	C₂³	1	2	yes	—
211	C₃×#685	C₂³	1	2	yes	—
212	C₃×#685	C₂³	1	2	yes	—
213	C₃×#685	C₂³	1	2	yes	—
214	C₃×#685	C₂³	1	2	yes	—
215	C₃×#685	C₂³	1	1	yes	characteristic
216	C₃×#685	C₂³	1	2	yes	—
217	C₃×#685	C₂³	1	1	yes	characteristic
218	C₃×#685	C₂³	1	2	yes	—
219	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
220	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
221	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
222	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
223	C₃×#683	C₂³	1	2	yes	—
224	C₃×#683	C₂³	1	2	yes	—
225	C₃×#683	C₂³	1	2	yes	—
226	C₃×#683	C₂³	1	2	yes	—
227	C₃×#683	C₂³	1	2	yes	—
228	C₃×#683	C₂³	1	2	yes	—
229	C₃×#683	C₂³	1	1	yes	characteristic
230	C₃×#683	C₂³	1	2	yes	—
231	C₃×#683	C₂³	1	1	yes	characteristic
232	C₃×#683	C₂³	1	1	yes	characteristic
233	C₃×#683	C₂³	1	2	yes	—
234	C₃×#683	C₂³	1	2	yes	—
235	C₃×#683	C₂³	1	1	yes	characteristic
236	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
237	C₃×C₄×Dic₅	C₂³	1	2	yes	—
238	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
239	C₃×C₄×Dic₅	C₂³	1	2	yes	—
240	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
241	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
242	C₃×C₄×Dic₅	C₂³	1	2	yes	—
243	C₃×C₄×Dic₅	C₂³	1	2	yes	—
244	C₃×C₄×Dic₅	C₂³	1	2	yes	—
245	C₃×C₄×Dic₅	C₂³	1	2	yes	—
246	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
247	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
248	C₃×C₄×Dic₅	C₂³	1	2	yes	—
249	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
250	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
251	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
252	C₃×#559	—	5	2	no	—
253	C₃×#559	—	5	1	no	—
254	C₃×#557	—	5	1	no	—
255	C₃×#556	—	5	2	no	—
256	C₃×#556	—	5	1	no	—
257	C₃×#553	—	5	2	no	—
258	C₃×#553	—	5	2	no	—
259	C₃×#553	—	5	1	no	—
260	C₃×#553	D₅	1	1	yes	characteristic, complemented
261	C₃×#550	—	5	1	no	—
262	C₃×#548	—	5	1	no	—
263	C₃×#548	—	5	1	no	—
264	C₃×#532	—	5	1	no	—
265	C₃×#532	—	5	2	no	—
266	C₃×#529	—	5	2	no	—
267	C₃×#529	—	5	1	no	—
268	C₃×#529	—	5	2	no	—
269	C₃×#529	—	5	1	no	—
270	C₃×C₄×#41	—	5	2	no	—
271	C₃×C₄×#41	—	5	1	no	—
272	C₃×C₄×#41	—	5	1	no	—
273	C₃×C₄×#41	—	5	1	no	—
274	C₂×C₃×C₄×Q₈	—	5	1	no	—
275	C₂×#711	C₂²×C₃	1	2	yes	—
276	C₂×#711	C₂²×C₃	1	1	yes	characteristic
277	C₂×#711	C₂²×C₃	1	1	yes	characteristic
278	C₂×#709	C₂²×C₃	1	1	yes	characteristic
279	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
280	C₅×#126	C₂²×C₃	1	2	yes	—
281	C₅×#125	C₂²×C₃	1	1	yes	characteristic
282	C₅×#123	C₂²×C₃	1	2	yes	—
283	C₅×#121	C₂²×C₃	1	1	yes	characteristic
284	C₅×#121	C₂²×C₃	1	2	yes	—
285	C₅×#121	C₂²×C₃	1	1	yes	characteristic
286	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
287	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
288	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
289	C₅×#117	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
291	#4086	C₂²×C₃	1	1	yes	characteristic
292	#4086	C₂²×C₃	1	2	yes	—
293	#4085	C₂²×C₃	1	2	yes	—
294	#4085	C₂²×C₃	1	2	yes	—
295	#4085	C₂²×C₃	1	2	yes	—
296	#4085	C₂²×C₃	1	2	yes	—
297	#4082	C₂²×C₃	1	1	yes	characteristic
298	#4081	C₂²×C₃	1	2	yes	—
299	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
300	D₄×Dic₅	C₂²×C₃	1	2	yes	—
301	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
302	D₄×Dic₅	C₂²×C₃	1	2	yes	—
303	#4076	C₂²×C₃	1	2	yes	—
304	#4076	C₂²×C₃	1	1	yes	characteristic
305	#4075	C₂²×C₃	1	2	yes	—
306	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
307	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
308	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
309	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
310	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
311	#4070	C₂²×C₃	1	1	yes	characteristic
312	C₂×#683	C₂²×C₃	1	2	yes	—
313	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
314	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
315	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
316	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
317	#4044	C₂²×C₃	1	2	yes	—
318	#4044	C₂²×C₃	1	2	yes	—
319	#4043	C₂²×C₃	1	1	yes	characteristic
320	#4042	C₂²×C₃	1	2	yes	—
321	#4041	C₂²×C₃	1	1	yes	characteristic
322	#4040	C₂²×C₃	1	2	yes	—
323	#4040	C₂²×C₃	1	2	yes	—
324	#4039	C₂²×C₃	1	1	yes	characteristic
325	#4039	C₂²×C₃	1	1	yes	characteristic
326	#4039	C₂²×C₃	1	2	yes	—
327	#4038	C₂²×C₃	1	1	yes	characteristic
328	#4038	C₂²×C₃	1	2	yes	—
329	#4038	C₂²×C₃	1	1	yes	characteristic
330	#4036	C₂²×C₃	1	1	yes	characteristic
331	#4035	C₂²×C₃	1	2	yes	—
332	#4035	C₂²×C₃	1	2	yes	—
333	#4034	C₂²×C₃	1	1	yes	characteristic
334	#4034	C₂²×C₃	1	2	yes	—
335	#4033	C₂²×C₃	1	1	yes	characteristic
336	#4033	C₂²×C₃	1	1	yes	characteristic
337	#4033	C₂²×C₃	1	1	yes	characteristic
338	#4033	C₂²×C₃	1	1	yes	characteristic
339	#4033	C₂²×C₃	1	2	yes	—
340	#4033	C₂²×C₃	1	2	yes	—
341	#4033	C₂²×C₃	1	1	yes	characteristic
342	#4033	C₂²×C₃	1	2	yes	—
343	#4033	C₂²×C₃	1	1	yes	characteristic
344	#4031	C₂²×C₃	1	2	yes	—
345	#4031	C₂²×C₃	1	2	yes	—
346	#4031	C₂²×C₃	1	2	yes	—
347	#4031	C₂²×C₃	1	2	yes	—
348	#4031	C₂²×C₃	1	2	yes	—
349	#4030	C₂²×C₃	1	2	yes	—
350	#4029	C₂²×C₃	1	2	yes	—
351	#4027	C₂²×C₃	1	2	yes	—
352	#4027	C₂²×C₃	1	2	yes	—
353	#4027	C₂²×C₃	1	1	yes	characteristic
354	#4027	C₂²×C₃	1	2	yes	—
355	#4027	C₂²×C₃	1	2	yes	—
356	#4027	C₂²×C₃	1	2	yes	—
357	#4027	C₂²×C₃	1	1	yes	characteristic
358	#4027	C₂²×C₃	1	2	yes	—
359	#4025	C₂²×C₃	1	2	yes	—
360	#4025	C₂²×C₃	1	2	yes	—
361	#4024	C₂²×C₃	1	2	yes	—
362	#4023	C₂²×C₃	1	1	yes	characteristic
363	#4023	C₂²×C₃	1	2	yes	—
364	#4023	C₂²×C₃	1	2	yes	—
365	#4023	C₂²×C₃	1	1	yes	characteristic
366	#4022	C₂²×C₃	1	2	yes	—
367	#4021	C₂²×C₃	1	1	yes	characteristic
368	#4018	C₂²×C₃	1	2	yes	—
369	C₄²×D₅	C₂²×C₃	1	2	yes	—
370	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
371	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
372	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
373	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
374	#3480	—	5	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
377	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
379	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
380	C₃×C₅×D₄	—	2	4	no	—
381	C₃×C₅×D₄	—	2	2	no	—
382	C₃×C₅×D₄	—	2	2	no	—
383	C₃×C₅×D₄	—	4	2	no	—
384	C₂×C₃×C₄×C₅	—	2	2	no	—
385	C₂×C₃×C₄×C₅	—	2	2	no	—
386	C₂×C₃×C₄×C₅	—	4	2	no	—
387	C₂×C₃×C₄×C₅	—	4	2	no	—
388	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
389	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
390	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
391	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
392	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
395	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₃×C₂²⋊D₅	—	2	2	no	—
397	C₃×C₂²⋊D₅	—	2	4	no	—
398	C₃×C₂²⋊D₅	—	2	4	no	—
399	C₃×C₂²⋊D₅	—	2	4	no	—
400	C₃×C₂²⋊D₅	—	2	2	no	—
401	C₃×C₂²⋊D₅	—	2	4	no	—
402	C₃×C₂²⋊D₅	—	4	2	no	—
403	C₂×C₃×Dic₅	—	2	4	no	—
404	C₂×C₃×Dic₅	—	2	4	no	—
405	C₂×C₃×Dic₅	—	2	2	no	—
406	C₂×C₃×Dic₅	—	2	4	no	—
407	C₂×C₃×Dic₅	—	4	1	no	—
408	C₂×C₃×Dic₅	—	4	1	no	—
409	C₂×C₃×Dic₅	#41	1	4	yes	complemented
410	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
413	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
414	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
415	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
416	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
417	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
418	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
419	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
420	C₃×D₂₀	—	2	2	no	—
421	C₃×D₂₀	—	4	2	no	—
422	C₃×C₄×D₅	—	2	2	no	—
423	C₃×C₄×D₅	—	2	4	no	—
424	C₃×C₄×D₅	—	2	4	no	—
425	C₃×C₄×D₅	—	2	2	no	—
426	C₃×C₄×D₅	—	4	2	no	—
427	C₃×C₄×D₅	—	4	1	no	—
428	C₃×Dic₁₀	—	2	2	no	—
429	C₃×Dic₁₀	—	2	4	no	—
430	C₃×Dic₁₀	—	2	4	no	—
431	C₃×Dic₁₀	—	2	2	no	—
432	C₃×Dic₁₀	#41	1	4	yes	complemented
433	C₂×C₃×#41	—	5	2	no	—
434	C₂×C₃×#41	—	5	1	no	—
435	C₂×C₃×#41	—	5	1	no	—
436	C₂×C₃×#41	—	5	1	no	—
437	C₂²×C₃×Q₈	—	5	1	no	—
438	C₃×C₄⋊Q₈	—	5	2	no	—
439	C₃×C₄⋊Q₈	—	5	1	no	—
440	C₃×#127	—	5	2	no	—
441	C₃×#127	—	5	1	no	—
442	C₃×#126	—	5	2	no	—
443	C₃×#126	—	5	2	no	—
444	C₃×#126	—	5	2	no	—
445	C₃×#126	—	5	2	no	—
446	C₃×#126	—	5	2	no	—
447	C₃×#126	C₂×D₅	1	2	yes	—
448	C₃×#125	—	5	2	no	—
449	C₃×#125	—	5	2	no	—
450	C₃×#125	—	5	1	no	—
451	C₃×#125	C₂×D₅	1	1	yes	characteristic
452	C₃×#124	—	5	1	no	—
453	C₃×#124	—	5	2	no	—
454	C₃×#124	—	5	2	no	—
455	C₃×#124	—	5	2	no	—
456	C₃×#124	—	5	2	no	—
457	C₃×#124	—	5	2	no	—
458	C₃×#124	—	5	1	no	—
459	C₃×#123	—	5	2	no	—
460	C₃×#123	—	5	2	no	—
461	C₃×#123	—	5	2	no	—
462	C₃×#123	—	5	2	no	—
463	C₃×#123	—	5	2	no	—
464	C₃×#123	C₂×D₅	1	2	yes	—
465	C₃×C₂²⋊Q₈	—	5	1	no	—
466	C₃×C₂²⋊Q₈	—	5	2	no	—
467	C₃×C₂²⋊Q₈	—	5	1	no	—
468	C₃×C₂²⋊Q₈	—	5	2	no	—
469	C₃×#121	—	5	2	no	—
470	C₃×#121	—	5	2	no	—
471	C₃×#121	—	5	2	no	—
472	C₃×#121	—	5	2	no	—
473	C₃×#121	—	5	1	no	—
474	C₃×#121	—	5	2	no	—
475	C₃×#121	—	5	1	no	—
476	C₃×#121	—	5	2	no	—
477	C₃×#121	C₂×D₅	1	1	yes	characteristic
478	C₃×#121	C₂×D₅	1	1	yes	characteristic
479	C₃×#121	C₂×D₅	1	2	yes	—
480	C₃×C₄×Q₈	—	5	2	no	—
481	C₃×C₄×Q₈	—	5	1	no	—
482	C₃×C₄×Q₈	—	5	2	no	—
483	C₃×C₄×Q₈	—	5	1	no	—
484	C₃×C₄×Q₈	—	5	2	no	—
485	C₃×C₄×Q₈	—	5	1	no	—
486	C₃×C₄×Q₈	—	5	1	no	—
487	C₃×C₄×Q₈	—	5	1	no	—
488	C₃×C₄×Q₈	—	5	1	no	—
489	C₃×C₄×Q₈	—	5	1	no	—
490	C₃×C₄×Q₈	—	5	1	no	—
491	C₃×C₄×Q₈	—	5	2	no	—
492	C₃×C₄×D₄	—	5	1	no	—
493	C₃×C₄×D₄	—	5	2	no	—
494	C₃×C₄×D₄	—	5	1	no	—
495	C₃×C₄×D₄	—	5	2	no	—
496	C₃×C₄×D₄	—	5	2	no	—
497	C₃×C₄×D₄	—	5	2	no	—
498	C₃×C₄×D₄	—	5	1	no	—
499	C₃×C₄×D₄	—	5	1	no	—
500	C₃×C₄×D₄	—	5	2	no	—
501	C₃×C₄×D₄	—	5	1	no	—
502	C₃×C₄×D₄	—	5	1	no	—
503	C₃×C₄×D₄	—	5	2	no	—
504	C₃×C₄×D₄	—	5	1	no	—
505	C₃×C₄×D₄	—	5	2	no	—
506	C₃×C₄×D₄	—	5	2	no	—
507	C₃×C₄×D₄	—	5	2	no	—
508	C₃×C₄×D₄	—	5	2	no	—
509	C₃×C₄×D₄	—	5	2	no	—
510	C₃×C₄×D₄	—	5	1	no	—
511	C₃×C₄×D₄	—	5	2	no	—
512	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
513	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
514	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
515	C₃×#117	—	5	2	no	—
516	C₃×#117	—	5	1	no	—
517	C₃×#117	—	5	1	no	—
518	C₃×#117	—	5	1	no	—
519	C₃×#117	—	5	1	no	—
520	C₃×#117	—	5	2	no	—
521	C₃×#117	—	5	2	no	—
522	C₃×#117	—	5	2	no	—
523	C₃×#117	C₂×D₅	1	1	yes	characteristic
524	C₂×C₃×C₄⋊C₄	—	5	2	no	—
525	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
526	C₂×C₃×C₄²	—	5	2	no	—
527	C₂×C₃×C₄²	—	5	1	no	—
528	C₂×C₃×C₄²	—	5	2	no	—
529	C₂×C₃×C₄²	—	5	1	no	—
530	C₂×C₃×C₄²	—	5	1	no	—
531	C₂×C₃×C₄²	—	5	2	no	—
532	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
534	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
536	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
537	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
538	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
539	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
547	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
548	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
549	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
550	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
551	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
552	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
553	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
554	#711	—	2	8	no	—
555	#711	—	2	4	no	—
556	#711	—	2	4	no	—
557	#709	—	2	4	no	—
558	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
559	C₂×D₂₀	C₂³×C₃	1	2	yes	—
560	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
561	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
562	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
566	C₂×Dic₁₀	—	2	4	no	—
567	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
568	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
569	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
570	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
571	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
572	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
573	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
575	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
577	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
579	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
582	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
584	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₄²×C₅	C₂³×C₃	1	2	yes	—
586	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
587	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
588	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
589	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
590	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
591	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
592	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
593	#685	C₂³×C₃	1	2	yes	—
594	#685	C₂³×C₃	1	2	yes	—
595	#685	C₂³×C₃	1	2	yes	—
596	#685	C₂³×C₃	1	2	yes	—
597	#685	C₂³×C₃	1	1	yes	characteristic
598	#685	C₂³×C₃	1	2	yes	—
599	#685	C₂³×C₃	1	2	yes	—
600	#685	C₂³×C₃	1	1	yes	characteristic
601	#685	C₂³×C₃	1	2	yes	—
602	#685	C₂³×C₃	1	2	yes	—
603	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
604	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
605	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
606	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
607	#683	C₂³×C₃	1	1	yes	characteristic
608	#683	C₂³×C₃	1	2	yes	—
609	#683	C₂³×C₃	1	1	yes	characteristic
610	#683	C₂³×C₃	1	2	yes	—
611	#683	C₂³×C₃	1	1	yes	characteristic
612	#683	C₂³×C₃	1	2	yes	—
613	#683	C₂³×C₃	1	2	yes	—
614	#683	C₂³×C₃	1	2	yes	—
615	#683	C₂³×C₃	1	2	yes	—
616	#683	C₂³×C₃	1	1	yes	characteristic
617	#683	C₂³×C₃	1	2	yes	—
618	#683	C₂³×C₃	1	2	yes	—
619	#683	C₂³×C₃	1	2	yes	—
620	C₄×Dic₅	C₂³×C₃	1	2	yes	—
621	C₄×Dic₅	C₂³×C₃	1	2	yes	—
622	C₄×Dic₅	C₂³×C₃	1	2	yes	—
623	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
624	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
625	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
626	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
627	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
628	C₄×Dic₅	C₂³×C₃	1	2	yes	—
629	C₄×Dic₅	C₂³×C₃	1	2	yes	—
630	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
631	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
632	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
633	C₄×Dic₅	C₂³×C₃	1	2	yes	—
634	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
635	C₄×Dic₅	C₂³×C₃	1	2	yes	—
636	#559	—	5	2	no	—
637	#559	—	5	1	no	—
638	#557	—	5	1	no	—
639	#556	—	5	2	no	—
640	#556	—	5	1	no	—
641	#553	—	5	2	no	—
642	#553	—	5	2	no	—
643	#553	—	5	1	no	—
644	#553	C₃×D₅	1	1	yes	characteristic, complemented
645	#550	—	5	1	no	—
646	#548	—	5	1	no	—
647	#548	—	5	1	no	—
648	#532	—	5	1	no	—
649	#532	—	5	2	no	—
650	#529	—	5	2	no	—
651	#529	—	5	1	no	—
652	#529	—	5	2	no	—
653	#529	—	5	1	no	—
654	C₄×#41	—	5	2	no	—
655	C₄×#41	—	5	1	no	—
656	C₄×#41	—	5	1	no	—
657	C₄×#41	—	5	1	no	—
658	C₂×C₄×Q₈	—	5	1	no	—
659	C₂²×C₃×C₅	—	2	1	no	—
660	C₂²×C₃×C₅	—	2	1	no	—
661	C₂²×C₃×C₅	—	2	2	no	—
662	C₂²×C₃×C₅	—	2	1	no	—
663	C₂²×C₃×C₅	—	2	2	no	—
664	C₂²×C₃×C₅	—	2	1	no	—
665	C₂²×C₃×C₅	—	2	1	no	—
666	C₂²×C₃×C₅	—	2	2	no	—
667	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
668	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
669	C₂×C₃×D₅	—	2	2	no	—
670	C₂×C₃×D₅	—	2	2	no	—
671	C₂×C₃×D₅	—	2	1	no	—
672	C₂×C₃×D₅	—	2	1	no	—
673	C₂×C₃×D₅	—	2	1	no	—
674	C₂×C₃×D₅	—	2	2	no	—
675	C₃×C₄×C₅	—	2	1	no	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	—	2	1	no	—
679	C₃×C₄×C₅	—	2	2	no	—
680	C₃×C₄×C₅	—	2	1	no	—
681	C₃×C₄×C₅	—	2	2	no	—
682	C₃×C₄×C₅	C₂×#41	1	2	yes	—
683	C₃×Dic₅	—	2	2	no	—
684	C₃×Dic₅	—	2	1	no	—
685	C₃×Dic₅	—	2	2	no	—
686	C₃×Dic₅	—	2	1	no	—
687	C₃×Dic₅	—	2	1	no	—
688	C₃×Dic₅	—	2	1	no	—
689	C₃×Dic₅	—	2	1	no	—
690	C₃×Dic₅	C₂×#41	1	2	yes	—
691	C₃×Dic₅	C₂×#41	1	4	yes	—
692	C₃×Dic₅	C₂×#41	1	2	yes	—
693	C₃×#41	—	10	4	no	—
694	C₃×#41	—	10	8	no	—
695	C₃×#41	—	10	4	no	—
696	C₃×#41	—	10	4	no	—
697	C₂×C₃×Q₈	—	5	1	no	—
698	C₂×C₃×Q₈	—	5	2	no	—
699	C₂×C₃×Q₈	—	5	1	no	—
700	C₂×C₃×Q₈	—	5	2	no	—
701	C₂×C₃×Q₈	—	5	1	no	—
702	C₂×C₃×Q₈	—	10	4	no	—
703	C₂×C₃×D₄	—	5	1	no	—
704	C₂×C₃×D₄	—	5	2	no	—
705	C₂×C₃×D₄	—	5	2	no	—
706	C₂×C₃×D₄	—	5	2	no	—
707	C₂×C₃×D₄	—	5	2	no	—
708	C₂×C₃×D₄	—	5	1	no	—
709	C₂×C₃×D₄	—	5	2	no	—
710	C₂×C₃×D₄	—	5	1	no	—
711	C₂×C₃×D₄	—	5	2	no	—
712	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
713	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
714	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
715	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
716	C₂²×C₃×C₄	—	5	1	no	—
717	C₂²×C₃×C₄	—	5	2	no	—
718	C₂²×C₃×C₄	—	5	2	no	—
719	C₂²×C₃×C₄	—	5	1	no	—
720	C₂²×C₃×C₄	—	5	2	no	—
721	C₂²×C₃×C₄	—	5	1	no	—
722	C₂²×C₃×C₄	—	5	1	no	—
723	C₂²×C₃×C₄	—	5	2	no	—
724	C₂²×C₃×C₄	—	5	1	no	—
725	C₂²×C₃×C₄	—	5	2	no	—
726	C₂²×C₃×C₄	—	5	1	no	—
727	C₂²×C₃×C₄	—	5	1	no	—
728	C₂²×C₃×C₄	—	5	2	no	—
729	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
730	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
731	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
732	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
733	C₃×C₄⋊C₄	—	5	2	no	—
734	C₃×C₄⋊C₄	—	5	2	no	—
735	C₃×C₄⋊C₄	—	5	2	no	—
736	C₃×C₄⋊C₄	—	5	2	no	—
737	C₃×C₄⋊C₄	—	5	1	no	—
738	C₃×C₄⋊C₄	—	5	1	no	—
739	C₃×C₄⋊C₄	—	5	2	no	—
740	C₃×C₄⋊C₄	—	5	2	no	—
741	C₃×C₄⋊C₄	—	5	1	no	—
742	C₃×C₄⋊C₄	—	5	2	no	—
743	C₃×C₄⋊C₄	—	5	2	no	—
744	C₃×C₄⋊C₄	—	5	1	no	—
745	C₃×C₄⋊C₄	—	5	2	no	—
746	C₃×C₄⋊C₄	—	5	1	no	—
747	C₃×C₄⋊C₄	—	5	2	no	—
748	C₃×C₄⋊C₄	—	5	1	no	—
749	C₃×C₄⋊C₄	—	5	2	no	—
750	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
751	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
752	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
753	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
754	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
755	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
756	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
757	C₃×C₂²⋊C₄	—	5	1	no	—
758	C₃×C₂²⋊C₄	—	5	1	no	—
759	C₃×C₂²⋊C₄	—	5	2	no	—
760	C₃×C₂²⋊C₄	—	5	2	no	—
761	C₃×C₂²⋊C₄	—	5	2	no	—
762	C₃×C₂²⋊C₄	—	5	2	no	—
763	C₃×C₂²⋊C₄	—	5	2	no	—
764	C₃×C₂²⋊C₄	—	5	1	no	—
765	C₃×C₂²⋊C₄	—	5	2	no	—
766	C₃×C₂²⋊C₄	—	5	2	no	—
767	C₃×C₂²⋊C₄	—	5	2	no	—
768	C₃×C₂²⋊C₄	—	5	1	no	—
769	C₃×C₂²⋊C₄	—	5	2	no	—
770	C₃×C₂²⋊C₄	—	5	2	no	—
771	C₃×C₂²⋊C₄	—	5	2	no	—
772	C₃×C₂²⋊C₄	—	5	2	no	—
773	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
774	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
775	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
776	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
777	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
778	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
779	C₃×C₄²	—	5	1	no	—
780	C₃×C₄²	—	5	1	no	—
781	C₃×C₄²	—	5	2	no	—
782	C₃×C₄²	—	5	1	no	—
783	C₃×C₄²	—	5	2	no	—
784	C₃×C₄²	—	5	1	no	—
785	C₃×C₄²	—	5	1	no	—
786	C₃×C₄²	—	5	2	no	—
787	C₃×C₄²	—	5	1	no	—
788	C₃×C₄²	—	5	2	no	—
789	C₃×C₄²	—	5	2	no	—
790	C₃×C₄²	—	5	1	no	—
791	C₃×C₄²	—	5	1	no	—
792	C₃×C₄²	—	5	2	no	—
793	C₃×C₄²	—	5	2	no	—
794	C₃×C₄²	—	5	1	no	—
795	C₃×C₄²	C₂²×D₅	1	2	yes	—
796	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
797	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
798	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
799	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
801	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
802	C₅×D₄	—	2	4	no	—
803	C₅×D₄	—	2	2	no	—
804	C₅×D₄	—	2	2	no	—
805	C₅×D₄	—	4	2	no	—
806	C₂×C₄×C₅	—	2	2	no	—
807	C₂×C₄×C₅	—	2	2	no	—
808	C₂×C₄×C₅	—	4	2	no	—
809	C₂×C₄×C₅	—	4	2	no	—
810	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
811	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
812	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
813	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
814	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
815	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
816	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
817	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
818	C₂²⋊D₅	—	2	2	no	—
819	C₂²⋊D₅	—	2	4	no	—
820	C₂²⋊D₅	—	2	4	no	—
821	C₂²⋊D₅	—	2	4	no	—
822	C₂²⋊D₅	—	2	2	no	—
823	C₂²⋊D₅	—	2	4	no	—
824	C₂²⋊D₅	—	4	2	no	—
825	C₂×Dic₅	—	2	4	no	—
826	C₂×Dic₅	—	2	4	no	—
827	C₂×Dic₅	—	2	2	no	—
828	C₂×Dic₅	—	2	4	no	—
829	C₂×Dic₅	—	4	1	no	—
830	C₂×Dic₅	—	4	1	no	—
831	C₂×Dic₅	C₃×#41	1	4	yes	complemented
832	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
833	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
834	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
835	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
836	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
837	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
838	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
839	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
840	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
841	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
842	D₂₀	—	2	2	no	—
843	D₂₀	—	4	2	no	—
844	C₄×D₅	—	2	2	no	—
845	C₄×D₅	—	2	4	no	—
846	C₄×D₅	—	2	4	no	—
847	C₄×D₅	—	2	2	no	—
848	C₄×D₅	—	4	2	no	—
849	C₄×D₅	—	4	1	no	—
850	Dic₁₀	—	2	2	no	—
851	Dic₁₀	—	2	4	no	—
852	Dic₁₀	—	2	4	no	—
853	Dic₁₀	—	2	2	no	—
854	Dic₁₀	C₃×#41	1	4	yes	complemented
855	C₂×#41	—	5	2	no	—
856	C₂×#41	—	5	1	no	—
857	C₂×#41	—	5	1	no	—
858	C₂×#41	—	5	1	no	—
859	C₂²×Q₈	—	5	1	no	—
860	C₄⋊Q₈	—	5	2	no	—
861	C₄⋊Q₈	—	5	1	no	—
862	#127	—	5	2	no	—
863	#127	—	5	1	no	—
864	#126	—	5	2	no	—
865	#126	—	5	2	no	—
866	#126	—	5	2	no	—
867	#126	—	5	2	no	—
868	#126	—	5	2	no	—
869	#126	C₂×C₃×D₅	1	2	yes	—
870	#125	—	5	2	no	—
871	#125	—	5	2	no	—
872	#125	—	5	1	no	—
873	#125	C₂×C₃×D₅	1	1	yes	characteristic
874	#124	—	5	1	no	—
875	#124	—	5	2	no	—
876	#124	—	5	2	no	—
877	#124	—	5	2	no	—
878	#124	—	5	2	no	—
879	#124	—	5	2	no	—
880	#124	—	5	1	no	—
881	#123	—	5	2	no	—
882	#123	—	5	2	no	—
883	#123	—	5	2	no	—
884	#123	—	5	2	no	—
885	#123	—	5	2	no	—
886	#123	C₂×C₃×D₅	1	2	yes	—
887	C₂²⋊Q₈	—	5	1	no	—
888	C₂²⋊Q₈	—	5	2	no	—
889	C₂²⋊Q₈	—	5	1	no	—
890	C₂²⋊Q₈	—	5	2	no	—
891	#121	—	5	2	no	—
892	#121	—	5	2	no	—
893	#121	—	5	2	no	—
894	#121	—	5	2	no	—
895	#121	—	5	1	no	—
896	#121	—	5	2	no	—
897	#121	—	5	1	no	—
898	#121	—	5	2	no	—
899	#121	C₂×C₃×D₅	1	1	yes	characteristic
900	#121	C₂×C₃×D₅	1	1	yes	characteristic
901	#121	C₂×C₃×D₅	1	2	yes	—
902	C₄×Q₈	—	5	1	no	—
903	C₄×Q₈	—	5	2	no	—
904	C₄×Q₈	—	5	1	no	—
905	C₄×Q₈	—	5	1	no	—
906	C₄×Q₈	—	5	2	no	—
907	C₄×Q₈	—	5	1	no	—
908	C₄×Q₈	—	5	1	no	—
909	C₄×Q₈	—	5	1	no	—
910	C₄×Q₈	—	5	2	no	—
911	C₄×Q₈	—	5	1	no	—
912	C₄×Q₈	—	5	2	no	—
913	C₄×Q₈	—	5	1	no	—
914	C₄×D₄	—	5	1	no	—
915	C₄×D₄	—	5	2	no	—
916	C₄×D₄	—	5	1	no	—
917	C₄×D₄	—	5	2	no	—
918	C₄×D₄	—	5	1	no	—
919	C₄×D₄	—	5	1	no	—
920	C₄×D₄	—	5	2	no	—
921	C₄×D₄	—	5	2	no	—
922	C₄×D₄	—	5	2	no	—
923	C₄×D₄	—	5	1	no	—
924	C₄×D₄	—	5	1	no	—
925	C₄×D₄	—	5	2	no	—
926	C₄×D₄	—	5	2	no	—
927	C₄×D₄	—	5	2	no	—
928	C₄×D₄	—	5	2	no	—
929	C₄×D₄	—	5	2	no	—
930	C₄×D₄	—	5	1	no	—
931	C₄×D₄	—	5	2	no	—
932	C₄×D₄	—	5	1	no	—
933	C₄×D₄	—	5	2	no	—
934	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
935	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
936	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
937	#117	—	5	2	no	—
938	#117	—	5	1	no	—
939	#117	—	5	1	no	—
940	#117	—	5	1	no	—
941	#117	—	5	1	no	—
942	#117	—	5	2	no	—
943	#117	—	5	2	no	—
944	#117	—	5	2	no	—
945	#117	C₂×C₃×D₅	1	1	yes	characteristic
946	C₂×C₄⋊C₄	—	5	2	no	—
947	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
948	C₂×C₄²	—	5	2	no	—
949	C₂×C₄²	—	5	1	no	—
950	C₂×C₄²	—	5	2	no	—
951	C₂×C₄²	—	5	1	no	—
952	C₂×C₄²	—	5	1	no	—
953	C₂×C₄²	—	5	2	no	—
954	C₂×C₃×C₅	—	2	2	no	—
955	C₂×C₃×C₅	—	4	2	no	—
956	C₂×C₃×C₅	—	4	1	no	—
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
959	C₂×C₃×C₅	#585	1	1	yes	characteristic
960	C₃×D₅	—	4	2	no	—
961	C₃×D₅	—	4	1	no	—
962	C₂³×C₃	—	5	1	no	—
963	C₂³×C₃	—	5	2	no	—
964	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
965	C₂³×C₃	C₂³×D₅	1	2	yes	—
966	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
967	C₃×Q₈	—	5	4	no	—
968	C₃×Q₈	—	10	4	no	—
969	C₃×Q₈	—	10	4	no	—
970	C₃×Q₈	—	10	2	no	—
971	C₃×Q₈	—	10	2	no	—
972	C₃×D₄	—	2	4	no	—
973	C₃×D₄	—	2	2	no	—
974	C₃×D₄	—	2	2	no	—
975	C₃×D₄	—	4	2	no	—
976	C₃×D₄	—	10	4	no	—
977	C₃×D₄	—	10	2	no	—
978	C₃×D₄	—	10	4	no	—
979	C₃×D₄	—	10	4	no	—
980	C₃×D₄	—	10	2	no	—
981	C₃×D₄	—	10	4	no	—
982	C₃×D₄	—	10	2	no	—
983	C₃×D₄	—	20	2	no	—
984	C₃×D₄	—	20	2	no	—
985	C₂×C₃×C₄	—	2	2	no	—
986	C₂×C₃×C₄	—	2	2	no	—
987	C₂×C₃×C₄	—	4	2	no	—
988	C₂×C₃×C₄	—	4	2	no	—
989	C₂×C₃×C₄	—	5	4	no	—
990	C₂×C₃×C₄	—	5	1	no	—
991	C₂×C₃×C₄	—	5	1	no	—
992	C₂×C₃×C₄	—	5	2	no	—
993	C₂×C₃×C₄	—	5	1	no	—
994	C₂×C₃×C₄	—	5	1	no	—
995	C₂×C₃×C₄	—	5	1	no	—
996	C₂×C₃×C₄	—	5	2	no	—
997	C₂×C₃×C₄	—	5	2	no	—
998	C₂×C₃×C₄	—	5	1	no	—
999	C₂×C₃×C₄	—	5	1	no	—
1000	C₂×C₃×C₄	—	10	4	no	—
1001	C₂×C₃×C₄	—	10	4	no	—
1002	C₂×C₃×C₄	—	10	2	no	—
1003	C₂×C₃×C₄	—	10	4	no	—
1004	C₂×C₃×C₄	—	10	4	no	—
1005	C₂×C₃×C₄	—	10	2	no	—
1006	C₂×C₃×C₄	—	10	4	no	—
1007	C₂×C₃×C₄	—	10	2	no	—
1008	C₂×C₃×C₄	—	20	2	no	—
1009	C₂×C₃×C₄	—	20	1	no	—
1010	C₂×C₃×C₄	—	20	1	no	—
1011	C₂×C₃×C₄	—	20	1	no	—
1012	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1013	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1014	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1017	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1019	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1020	C₂²×C₅	—	2	1	no	—
1021	C₂²×C₅	—	2	1	no	—
1022	C₂²×C₅	—	2	2	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	2	2	no	—
1025	C₂²×C₅	—	2	1	no	—
1026	C₂²×C₅	—	2	1	no	—
1027	C₂²×C₅	—	2	2	no	—
1028	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
1029	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1030	C₂×D₅	—	2	2	no	—
1031	C₂×D₅	—	2	2	no	—
1032	C₂×D₅	—	2	1	no	—
1033	C₂×D₅	—	2	1	no	—
1034	C₂×D₅	—	2	1	no	—
1035	C₂×D₅	—	2	2	no	—
1036	C₄×C₅	—	2	1	no	—
1037	C₄×C₅	—	2	1	no	—
1038	C₄×C₅	—	2	2	no	—
1039	C₄×C₅	—	2	1	no	—
1040	C₄×C₅	—	2	2	no	—
1041	C₄×C₅	—	2	1	no	—
1042	C₄×C₅	—	2	2	no	—
1043	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1044	Dic₅	—	2	2	no	—
1045	Dic₅	—	2	2	no	—
1046	Dic₅	—	2	1	no	—
1047	Dic₅	—	2	1	no	—
1048	Dic₅	—	2	1	no	—
1049	Dic₅	—	2	1	no	—
1050	Dic₅	—	2	1	no	—
1051	Dic₅	C₂×C₃×#41	1	2	yes	—
1052	Dic₅	C₂×C₃×#41	1	4	yes	—
1053	Dic₅	C₂×C₃×#41	1	2	yes	—
1054	#41	—	10	4	no	—
1055	#41	—	10	8	no	—
1056	#41	—	10	4	no	—
1057	#41	—	10	4	no	—
1058	C₂×Q₈	—	5	1	no	—
1059	C₂×Q₈	—	5	2	no	—
1060	C₂×Q₈	—	5	1	no	—
1061	C₂×Q₈	—	5	1	no	—
1062	C₂×Q₈	—	5	2	no	—
1063	C₂×Q₈	—	10	4	no	—
1064	C₂×D₄	—	5	1	no	—
1065	C₂×D₄	—	5	2	no	—
1066	C₂×D₄	—	5	2	no	—
1067	C₂×D₄	—	5	2	no	—
1068	C₂×D₄	—	5	1	no	—
1069	C₂×D₄	—	5	2	no	—
1070	C₂×D₄	—	5	2	no	—
1071	C₂×D₄	—	5	1	no	—
1072	C₂×D₄	—	5	2	no	—
1073	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
1074	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1075	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1076	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
1077	C₂²×C₄	—	5	1	no	—
1078	C₂²×C₄	—	5	2	no	—
1079	C₂²×C₄	—	5	2	no	—
1080	C₂²×C₄	—	5	1	no	—
1081	C₂²×C₄	—	5	2	no	—
1082	C₂²×C₄	—	5	1	no	—
1083	C₂²×C₄	—	5	1	no	—
1084	C₂²×C₄	—	5	2	no	—
1085	C₂²×C₄	—	5	1	no	—
1086	C₂²×C₄	—	5	2	no	—
1087	C₂²×C₄	—	5	1	no	—
1088	C₂²×C₄	—	5	2	no	—
1089	C₂²×C₄	—	5	1	no	—
1090	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1091	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1092	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1093	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1094	C₄⋊C₄	—	5	2	no	—
1095	C₄⋊C₄	—	5	2	no	—
1096	C₄⋊C₄	—	5	2	no	—
1097	C₄⋊C₄	—	5	2	no	—
1098	C₄⋊C₄	—	5	1	no	—
1099	C₄⋊C₄	—	5	1	no	—
1100	C₄⋊C₄	—	5	2	no	—
1101	C₄⋊C₄	—	5	2	no	—
1102	C₄⋊C₄	—	5	1	no	—
1103	C₄⋊C₄	—	5	1	no	—
1104	C₄⋊C₄	—	5	2	no	—
1105	C₄⋊C₄	—	5	2	no	—
1106	C₄⋊C₄	—	5	2	no	—
1107	C₄⋊C₄	—	5	1	no	—
1108	C₄⋊C₄	—	5	1	no	—
1109	C₄⋊C₄	—	5	2	no	—
1110	C₄⋊C₄	—	5	2	no	—
1111	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1112	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1113	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1114	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1116	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1118	C₂²⋊C₄	—	5	1	no	—
1119	C₂²⋊C₄	—	5	1	no	—
1120	C₂²⋊C₄	—	5	2	no	—
1121	C₂²⋊C₄	—	5	2	no	—
1122	C₂²⋊C₄	—	5	2	no	—
1123	C₂²⋊C₄	—	5	2	no	—
1124	C₂²⋊C₄	—	5	2	no	—
1125	C₂²⋊C₄	—	5	1	no	—
1126	C₂²⋊C₄	—	5	2	no	—
1127	C₂²⋊C₄	—	5	2	no	—
1128	C₂²⋊C₄	—	5	2	no	—
1129	C₂²⋊C₄	—	5	1	no	—
1130	C₂²⋊C₄	—	5	2	no	—
1131	C₂²⋊C₄	—	5	2	no	—
1132	C₂²⋊C₄	—	5	2	no	—
1133	C₂²⋊C₄	—	5	2	no	—
1134	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1135	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1136	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1137	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1138	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1139	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1140	C₄²	—	5	1	no	—
1141	C₄²	—	5	1	no	—
1142	C₄²	—	5	2	no	—
1143	C₄²	—	5	1	no	—
1144	C₄²	—	5	2	no	—
1145	C₄²	—	5	1	no	—
1146	C₄²	—	5	1	no	—
1147	C₄²	—	5	2	no	—
1148	C₄²	—	5	1	no	—
1149	C₄²	—	5	2	no	—
1150	C₄²	—	5	2	no	—
1151	C₄²	—	5	1	no	—
1152	C₄²	—	5	1	no	—
1153	C₄²	—	5	2	no	—
1154	C₄²	—	5	2	no	—
1155	C₄²	—	5	1	no	—
1156	C₄²	C₂²×C₃×D₅	1	2	yes	—
1157	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1158	C₃×C₅	#3480	1	1	yes	characteristic, complemented, Hall
1159	C₂²×C₃	—	2	1	no	—
1160	C₂²×C₃	—	2	1	no	—
1161	C₂²×C₃	—	2	1	no	—
1162	C₂²×C₃	—	2	1	no	—
1163	C₂²×C₃	—	2	2	no	—
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	2	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	—	10	1	no	—
1168	C₂²×C₃	—	10	2	no	—
1169	C₂²×C₃	—	10	2	no	—
1170	C₂²×C₃	—	10	1	no	—
1171	C₂²×C₃	—	10	1	no	—
1172	C₂²×C₃	—	10	2	no	—
1173	C₂²×C₃	D₅×#41	1	2	yes	—
1174	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1175	C₃×C₄	—	2	1	no	—
1176	C₃×C₄	—	2	1	no	—
1177	C₃×C₄	—	2	1	no	—
1178	C₃×C₄	—	2	2	no	—
1179	C₃×C₄	—	2	1	no	—
1180	C₃×C₄	—	2	2	no	—
1181	C₃×C₄	—	2	2	no	—
1182	C₃×C₄	—	5	2	no	—
1183	C₃×C₄	—	5	2	no	—
1184	C₃×C₄	—	5	4	no	—
1185	C₃×C₄	—	10	1	no	—
1186	C₃×C₄	—	10	2	no	—
1187	C₃×C₄	—	10	1	no	—
1188	C₃×C₄	—	10	2	no	—
1189	C₃×C₄	—	10	1	no	—
1190	C₃×C₄	—	10	1	no	—
1191	C₃×C₄	—	10	1	no	—
1192	C₃×C₄	D₅×#41	1	2	yes	—
1193	C₂×C₅	—	2	2	no	—
1194	C₂×C₅	—	4	2	no	—
1195	C₂×C₅	—	4	1	no	—
1196	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1197	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1198	C₂×C₅	C₃×#585	1	1	yes	characteristic
1199	D₅	—	4	2	no	—
1200	D₅	—	4	1	no	—
1201	C₂³	—	5	1	no	—
1202	C₂³	—	5	2	no	—
1203	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1204	C₂³	C₂³×C₃×D₅	1	2	yes	—
1205	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1206	Q₈	—	5	4	no	—
1207	Q₈	—	10	4	no	—
1208	Q₈	—	10	2	no	—
1209	Q₈	—	10	4	no	—
1210	Q₈	—	10	2	no	—
1211	D₄	—	2	4	no	—
1212	D₄	—	2	2	no	—
1213	D₄	—	2	2	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	10	2	no	—
1216	D₄	—	10	4	no	—
1217	D₄	—	10	4	no	—
1218	D₄	—	10	4	no	—
1219	D₄	—	10	2	no	—
1220	D₄	—	10	4	no	—
1221	D₄	—	10	2	no	—
1222	D₄	—	20	2	no	—
1223	D₄	—	20	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	4	2	no	—
1227	C₂×C₄	—	4	2	no	—
1228	C₂×C₄	—	5	4	no	—
1229	C₂×C₄	—	5	1	no	—
1230	C₂×C₄	—	5	1	no	—
1231	C₂×C₄	—	5	2	no	—
1232	C₂×C₄	—	5	1	no	—
1233	C₂×C₄	—	5	1	no	—
1234	C₂×C₄	—	5	1	no	—
1235	C₂×C₄	—	5	2	no	—
1236	C₂×C₄	—	5	2	no	—
1237	C₂×C₄	—	5	1	no	—
1238	C₂×C₄	—	5	1	no	—
1239	C₂×C₄	—	10	4	no	—
1240	C₂×C₄	—	10	4	no	—
1241	C₂×C₄	—	10	2	no	—
1242	C₂×C₄	—	10	4	no	—
1243	C₂×C₄	—	10	4	no	—
1244	C₂×C₄	—	10	2	no	—
1245	C₂×C₄	—	10	4	no	—
1246	C₂×C₄	—	10	2	no	—
1247	C₂×C₄	—	20	2	no	—
1248	C₂×C₄	—	20	1	no	—
1249	C₂×C₄	—	20	1	no	—
1250	C₂×C₄	—	20	1	no	—
1251	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1252	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1253	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1254	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1255	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1256	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1257	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1258	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1259	C₂×C₃	—	2	2	no	—
1260	C₂×C₃	—	4	1	no	—
1261	C₂×C₃	—	4	2	no	—
1262	C₂×C₃	—	20	2	no	—
1263	C₂×C₃	—	20	1	no	—
1264	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1265	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1266	C₂×C₃	#66285	1	1	yes	characteristic
1267	C₅	C₃×#3480	1	1	yes	characteristic, complemented, Sylow
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	2	no	—
1273	C₂²	—	2	2	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	10	1	no	—
1277	C₂²	—	10	2	no	—
1278	C₂²	—	10	2	no	—
1279	C₂²	—	10	1	no	—
1280	C₂²	—	10	1	no	—
1281	C₂²	—	10	2	no	—
1282	C₂²	C₃×D₅×#41	1	2	yes	—
1283	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	2	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	5	2	no	—
1292	C₄	—	5	2	no	—
1293	C₄	—	5	4	no	—
1294	C₄	—	10	1	no	—
1295	C₄	—	10	2	no	—
1296	C₄	—	10	1	no	—
1297	C₄	—	10	2	no	—
1298	C₄	—	10	1	no	—
1299	C₄	—	10	1	no	—
1300	C₄	—	10	1	no	—
1301	C₄	C₃×D₅×#41	1	2	yes	—
1302	C₃	#10618776	1	1	yes	characteristic, direct product factor, Sylow
1303	C₂	—	2	2	no	—
1304	C₂	—	4	1	no	—
1305	C₂	—	4	2	no	—
1306	C₂	—	20	2	no	—
1307	C₂	—	20	1	no	—
1308	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1309	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1310	C₂	C₃×#66285	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×#553	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#553	D₅
hypocenter	C₅	C₃×#3480
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#553

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#553	C₂	semidirect
2. C₃×#66040	C₂	semidirect
3. C₃×#66036	C₂	semidirect
4. C₃×#66025	C₂	semidirect
5. C₃×#66019	C₂	semidirect
6. C₃×#65998	C₂	semidirect
7. C₃×#65983	C₂	semidirect
8. C₃×#65935	C₂	semidirect
9. C₃×#65934	C₂	semidirect
10. C₃×#65933	C₂	semidirect
11. C₃×#65932	C₂	semidirect
12. C₃×#65930	C₂	semidirect
13. C₃×#65930	C₂	semidirect
14. C₃×#65893	C₂	semidirect
15. C₃×#65886	C₂	semidirect
16. C₃×#65874	C₂	semidirect
17. C₃×C₄×#711	C₂	semidirect
18. C₃×C₄×#711	C₂	semidirect
19. C₃×C₄×#711	C₂	semidirect
20. C₃×#65867	C₂	semidirect
21. C₃×#65856	C₂	semidirect
22. C₃×#65848	C₂	semidirect
23. C₂×C₃×#4033	C₂	semidirect
24. #10618776	C₃	direct (N × H)
125. C₅×#553	C₂×C₃	semidirect
126. #66040	C₂×C₃	semidirect
127. #66036	C₂×C₃	semidirect
128. #66025	C₂×C₃	semidirect
129. #66019	C₂×C₃	semidirect
130. #65998	C₂×C₃	semidirect
131. #65983	C₂×C₃	semidirect
132. #65935	C₂×C₃	semidirect
133. #65934	C₂×C₃	semidirect
134. #65933	C₂×C₃	semidirect
135. #65932	C₂×C₃	semidirect
136. #65930	C₂×C₃	semidirect
137. #65930	C₂×C₃	semidirect
138. #65893	C₂×C₃	semidirect
139. #65886	C₂×C₃	semidirect
140. #65874	C₂×C₃	semidirect
141. C₄×#711	C₂×C₃	semidirect
142. C₄×#711	C₂×C₃	semidirect
143. C₄×#711	C₂×C₃	semidirect
144. #65867	C₂×C₃	semidirect
145. #65856	C₂×C₃	semidirect
146. #65848	C₂×C₃	semidirect
147. C₂×#4033	C₂×C₃	semidirect
260. C₃×#553	D₅	semidirect
409. C₂×C₃×Dic₅	#41	semidirect
432. C₃×Dic₁₀	#41	semidirect
644. #553	C₃×D₅	semidirect
831. C₂×Dic₅	C₃×#41	semidirect
854. Dic₁₀	C₃×#41	semidirect
1158. C₃×C₅	#3480	semidirect
1267. C₅	C₃×#3480	semidirect
1302. C₃	#10618776	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×#553	2
C₃×#66040	2
C₃×#66036	2
C₃×#66025	2
C₃×#66019	2
C₃×#65998	2
C₃×#65983	2
C₃×#65935	2
C₃×#65934	2
C₃×#65933	2
C₃×#65932	2
C₃×#65930	2
C₃×#65893	2
C₃×#65886	2
C₃×#65874	2
C₃×C₄×#711	2
C₃×#65867	2
C₃×#65856	2
C₃×#65848	2
C₂×C₃×#4033	2
#10618776	3
C₃×#3480	5

Subgroups — C3×#10618776 #14484781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618776 #14484781