Subgroups — C₅×#86152 #14484771

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×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5709	C₂	1	2	yes	maximal, complemented
3	C₅×#5702	C₂	1	2	yes	maximal, complemented
4	C₅×#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5685	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5681	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5664	C₂	1	2	yes	maximal, complemented
9	C₅×#5661	C₂	1	2	yes	maximal, complemented
10	C₅×#5641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5614	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5599	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5580	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5548	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#5548	C₂	1	2	yes	maximal, complemented
18	C₅×#5538	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#5528	C₂	1	2	yes	maximal, complemented
21	C₅×#5522	C₂	1	2	yes	maximal, complemented
22	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3480	—	3	1	no	maximal, Hall
25	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#237	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	C₂²	1	1	yes	characteristic
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂×C₅×#235	C₂²	1	2	yes	—
30	C₃×C₅×#126	C₂²	1	2	yes	—
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#123	C₂²	1	2	yes	—
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
39	C₃×C₅×#117	C₂²	1	2	yes	—
40	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
41	C₅×#947	C₂²	1	1	yes	characteristic
42	C₅×#946	C₂²	1	1	yes	characteristic
43	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
44	C₅×#940	C₂²	1	2	yes	—
45	C₅×#940	C₂²	1	1	yes	characteristic
46	C₅×#939	C₂²	1	2	yes	—
47	C₅×#938	C₂²	1	2	yes	—
48	C₅×#938	C₂²	1	1	yes	characteristic
49	C₅×#935	C₂²	1	2	yes	—
50	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₅×#67	C₂²	1	1	yes	characteristic
52	C₄×C₅×#67	C₂²	1	2	yes	—
53	C₄×C₅×#67	C₂²	1	1	yes	characteristic
54	C₄×C₅×#67	C₂²	1	2	yes	—
55	C₄×C₅×#67	C₂²	1	1	yes	characteristic
56	C₄×C₅×#67	C₂²	1	1	yes	characteristic
57	C₄×C₅×#67	C₂²	1	2	yes	—
58	C₄×C₅×#67	C₂²	1	2	yes	—
59	C₅×#926	C₂²	1	1	yes	characteristic
60	C₅×#926	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
62	C₅×#898	C₂²	1	2	yes	—
63	C₅×#898	C₂²	1	2	yes	—
64	C₅×#898	C₂²	1	2	yes	—
65	C₅×#896	C₂²	1	2	yes	—
66	C₅×#895	C₂²	1	2	yes	—
67	C₅×#895	C₂²	1	1	yes	characteristic
68	C₅×#895	C₂²	1	1	yes	characteristic
69	C₅×#894	C₂²	1	2	yes	—
70	C₅×#894	C₂²	1	2	yes	—
71	C₅×#893	C₂²	1	2	yes	—
72	C₅×#893	C₂²	1	2	yes	—
73	C₅×#892	C₂²	1	1	yes	characteristic
74	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₅×#890	C₂²	1	1	yes	characteristic
77	C₅×#889	C₂²	1	2	yes	—
78	C₅×#889	C₂²	1	2	yes	—
79	C₅×#888	C₂²	1	2	yes	—
80	C₅×#888	C₂²	1	1	yes	characteristic
81	C₅×#887	C₂²	1	2	yes	—
82	C₅×#887	C₂²	1	2	yes	—
83	C₅×#887	C₂²	1	1	yes	characteristic
84	C₅×#887	C₂²	1	1	yes	characteristic
85	C₅×#887	C₂²	1	2	yes	—
86	C₅×#886	C₂²	1	2	yes	—
87	C₅×#885	C₂²	1	2	yes	—
88	C₅×#885	C₂²	1	2	yes	—
89	C₅×#885	C₂²	1	2	yes	—
90	C₅×#885	C₂²	1	2	yes	—
91	C₅×#885	C₂²	1	2	yes	—
92	C₅×#884	C₂²	1	2	yes	—
93	C₅×#884	C₂²	1	2	yes	—
94	C₅×#884	C₂²	1	2	yes	—
95	C₅×#884	C₂²	1	2	yes	—
96	C₅×#883	C₂²	1	2	yes	—
97	C₅×#67⋊C₄	C₂²	1	2	yes	—
98	C₅×#67⋊C₄	C₂²	1	2	yes	—
99	C₅×#67⋊C₄	C₂²	1	2	yes	—
100	C₅×#67⋊C₄	C₂²	1	2	yes	—
101	C₅×#67⋊C₄	C₂²	1	2	yes	—
102	C₅×#879	C₂²	1	2	yes	—
103	C₅×#879	C₂²	1	2	yes	—
104	C₅×#878	C₂²	1	2	yes	—
105	C₅×#877	C₂²	1	2	yes	—
106	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
107	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
108	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
109	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
110	C₄×C₅×D₁₂	C₂²	1	2	yes	—
111	C₅×#872	C₂²	1	2	yes	—
112	C₅×#872	C₂²	1	1	yes	characteristic
113	C₅×#872	C₂²	1	1	yes	characteristic
114	C₅×#872	C₂²	1	2	yes	—
115	C₄²×C₅×D₃	C₂²	1	2	yes	—
116	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
117	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
118	C₄²×C₅×D₃	C₂²	1	2	yes	—
119	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
120	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
121	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
122	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
123	C₄×C₅×Dic₆	C₂²	1	2	yes	—
124	#86152	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#559	—	3	1	no	—
126	C₅×#559	—	3	2	no	—
127	C₅×#557	—	3	1	no	—
128	C₅×#556	—	3	2	no	—
129	C₅×#556	—	3	1	no	—
130	C₅×#553	—	3	2	no	—
131	C₅×#553	—	3	1	no	—
132	C₅×#553	—	3	2	no	—
133	C₅×#553	—	3	1	no	—
134	C₅×#550	—	3	1	no	—
135	C₅×#548	—	3	1	no	—
136	C₅×#548	—	3	1	no	—
137	C₅×#532	—	3	2	no	—
138	C₅×#532	—	3	1	no	—
139	C₅×#529	—	3	1	no	—
140	C₅×#529	—	3	2	no	—
141	C₅×#529	—	3	2	no	—
142	C₅×#529	D₃	1	1	yes	characteristic, complemented
143	C₄×C₅×#41	—	3	1	no	—
144	C₄×C₅×#41	—	3	2	no	—
145	C₄×C₅×#41	—	3	1	no	—
146	C₄×C₅×#41	—	3	1	no	—
147	C₂×C₄×C₅×Q₈	—	3	1	no	—
148	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
151	C₂²×C₃×C₄×C₅	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	1	yes	characteristic
155	C₂×C₅×#67	C₂³	1	2	yes	—
156	C₂×C₅×#67	C₂³	1	2	yes	—
157	C₂×C₅×#67	C₂³	1	2	yes	—
158	C₂×C₅×#67	C₂³	1	1	yes	characteristic
159	C₂×C₅×#67	C₂³	1	2	yes	—
160	C₂×C₅×#67	C₂³	1	1	yes	characteristic
161	C₂×C₅×#67	C₂³	1	2	yes	—
162	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
163	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
164	C₅×D₃×Q₈	—	2	4	no	—
165	C₅×#237	—	2	4	no	—
166	C₅×#235	—	2	4	no	—
167	C₅×#235	—	2	8	no	—
168	C₅×#235	—	2	4	no	—
169	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
170	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×C₅×D₁₂	C₂³	1	2	yes	—
172	C₂×C₅×D₁₂	C₂³	1	2	yes	—
173	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
174	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
176	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
179	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
181	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
183	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
185	C₂×C₅×Dic₆	C₂³	1	2	yes	—
186	C₂×C₅×Dic₆	C₂³	1	2	yes	—
187	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₃×C₄²×C₅	C₂³	1	2	yes	—
202	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
203	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₅×#217	C₂³	1	2	yes	—
205	C₅×#217	C₂³	1	2	yes	—
206	C₅×#217	C₂³	1	1	yes	characteristic
207	C₅×#217	C₂³	1	2	yes	—
208	C₅×#217	C₂³	1	1	yes	characteristic
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
210	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
211	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
212	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
233	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₄×C₅×Dic₃	C₂³	1	2	yes	—
240	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×C₅×Dic₃	C₂³	1	2	yes	—
243	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×C₅×Dic₃	C₂³	1	2	yes	—
248	C₄×C₅×Dic₃	C₂³	1	2	yes	—
249	C₄×C₅×Dic₃	C₂³	1	2	yes	—
250	C₄×C₅×Dic₃	C₂³	1	2	yes	—
251	C₄×C₅×Dic₃	C₂³	1	2	yes	—
252	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
253	#5709	C₂×C₅	1	2	yes	complemented
254	#5702	C₂×C₅	1	2	yes	complemented
255	#5695	C₂×C₅	1	1	yes	characteristic, complemented
256	#5685	C₂×C₅	1	1	yes	characteristic, complemented
257	#5681	C₂×C₅	1	1	yes	characteristic, complemented
258	#5677	C₂×C₅	1	1	yes	characteristic, complemented
259	#5664	C₂×C₅	1	2	yes	complemented
260	#5661	C₂×C₅	1	2	yes	complemented
261	#5641	C₂×C₅	1	1	yes	characteristic, complemented
262	#5633	C₂×C₅	1	1	yes	characteristic, complemented
263	#5614	C₂×C₅	1	1	yes	characteristic, complemented
264	#5599	C₂×C₅	1	1	yes	characteristic, complemented
265	#5580	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
267	#5548	C₂×C₅	1	1	yes	characteristic, complemented
268	#5548	C₂×C₅	1	2	yes	complemented
269	#5538	C₂×C₅	1	2	yes	complemented
270	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
271	#5528	C₂×C₅	1	2	yes	complemented
272	#5522	C₂×C₅	1	2	yes	complemented
273	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
274	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
275	C₂×C₅×#41	—	3	1	no	—
276	C₂×C₅×#41	—	3	2	no	—
277	C₂×C₅×#41	—	3	1	no	—
278	C₂×C₅×#41	—	3	1	no	—
279	C₂²×C₅×Q₈	—	3	1	no	—
280	C₅×C₄⋊Q₈	—	3	2	no	—
281	C₅×C₄⋊Q₈	—	3	1	no	—
282	C₅×#127	—	3	2	no	—
283	C₅×#127	—	3	1	no	—
284	C₅×#126	—	3	2	no	—
285	C₅×#126	—	3	2	no	—
286	C₅×#126	—	3	2	no	—
287	C₅×#126	—	3	2	no	—
288	C₅×#126	—	3	2	no	—
289	C₅×#126	C₂×D₃	1	2	yes	—
290	C₅×#125	—	3	2	no	—
291	C₅×#125	—	3	2	no	—
292	C₅×#125	—	3	1	no	—
293	C₅×#125	C₂×D₃	1	1	yes	characteristic
294	C₅×#124	—	3	1	no	—
295	C₅×#124	—	3	2	no	—
296	C₅×#124	—	3	2	no	—
297	C₅×#124	—	3	2	no	—
298	C₅×#124	—	3	2	no	—
299	C₅×#124	—	3	2	no	—
300	C₅×#124	C₂×D₃	1	1	yes	characteristic
301	C₅×#123	—	3	2	no	—
302	C₅×#123	—	3	2	no	—
303	C₅×#123	—	3	2	no	—
304	C₅×#123	—	3	2	no	—
305	C₅×#123	—	3	2	no	—
306	C₅×#123	C₂×D₃	1	2	yes	—
307	C₅×C₂²⋊Q₈	—	3	1	no	—
308	C₅×C₂²⋊Q₈	—	3	2	no	—
309	C₅×C₂²⋊Q₈	—	3	2	no	—
310	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
311	C₅×#121	—	3	1	no	—
312	C₅×#121	—	3	2	no	—
313	C₅×#121	—	3	2	no	—
314	C₅×#121	—	3	1	no	—
315	C₅×#121	—	3	1	no	—
316	C₅×#121	—	3	2	no	—
317	C₅×#121	—	3	2	no	—
318	C₅×#121	—	3	2	no	—
319	C₅×#121	—	3	2	no	—
320	C₅×#121	—	3	2	no	—
321	C₅×#121	C₂×D₃	1	1	yes	characteristic
322	C₄×C₅×Q₈	—	3	1	no	—
323	C₄×C₅×Q₈	—	3	1	no	—
324	C₄×C₅×Q₈	—	3	2	no	—
325	C₄×C₅×Q₈	—	3	1	no	—
326	C₄×C₅×Q₈	—	3	2	no	—
327	C₄×C₅×Q₈	—	3	2	no	—
328	C₄×C₅×Q₈	—	3	1	no	—
329	C₄×C₅×Q₈	—	3	2	no	—
330	C₄×C₅×Q₈	—	3	1	no	—
331	C₄×C₅×Q₈	—	3	1	no	—
332	C₄×C₅×Q₈	—	3	1	no	—
333	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
334	C₄×C₅×D₄	—	3	1	no	—
335	C₄×C₅×D₄	—	3	2	no	—
336	C₄×C₅×D₄	—	3	2	no	—
337	C₄×C₅×D₄	—	3	1	no	—
338	C₄×C₅×D₄	—	3	1	no	—
339	C₄×C₅×D₄	—	3	1	no	—
340	C₄×C₅×D₄	—	3	2	no	—
341	C₄×C₅×D₄	—	3	1	no	—
342	C₄×C₅×D₄	—	3	2	no	—
343	C₄×C₅×D₄	—	3	2	no	—
344	C₄×C₅×D₄	—	3	2	no	—
345	C₄×C₅×D₄	—	3	2	no	—
346	C₄×C₅×D₄	—	3	2	no	—
347	C₄×C₅×D₄	—	3	2	no	—
348	C₄×C₅×D₄	—	3	2	no	—
349	C₄×C₅×D₄	—	3	2	no	—
350	C₄×C₅×D₄	—	3	1	no	—
351	C₄×C₅×D₄	—	3	1	no	—
352	C₄×C₅×D₄	—	3	1	no	—
353	C₄×C₅×D₄	—	3	1	no	—
354	C₄×C₅×D₄	—	3	2	no	—
355	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
356	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
357	C₅×#117	—	3	1	no	—
358	C₅×#117	—	3	1	no	—
359	C₅×#117	—	3	1	no	—
360	C₅×#117	—	3	2	no	—
361	C₅×#117	—	3	1	no	—
362	C₅×#117	—	3	2	no	—
363	C₅×#117	—	3	1	no	—
364	C₅×#117	—	3	2	no	—
365	C₅×#117	C₂×D₃	1	2	yes	—
366	C₂×C₅×C₄⋊C₄	—	3	2	no	—
367	C₂×C₅×C₄⋊C₄	—	3	1	no	—
368	C₂×C₄²×C₅	—	3	2	no	—
369	C₂×C₄²×C₅	—	3	2	no	—
370	C₂×C₄²×C₅	—	3	1	no	—
371	C₂×C₄²×C₅	—	3	1	no	—
372	C₂×C₄²×C₅	—	3	2	no	—
373	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
374	#3480	—	3	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
376	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
377	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
378	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
380	C₃×C₅×Q₈	—	2	2	no	—
381	C₃×C₅×D₄	—	2	2	no	—
382	C₃×C₅×D₄	—	4	2	no	—
383	C₂×C₃×C₄×C₅	—	2	4	no	—
384	C₂×C₃×C₄×C₅	—	2	2	no	—
385	C₂×C₃×C₄×C₅	—	2	2	no	—
386	C₂×C₃×C₄×C₅	—	4	1	no	—
387	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
392	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
393	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
395	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₅×#67	—	2	4	no	—
397	C₅×#67	—	2	2	no	—
398	C₅×#67	—	2	4	no	—
399	C₅×#67	—	2	2	no	—
400	C₅×#67	—	2	4	no	—
401	C₅×#67	—	2	4	no	—
402	C₅×#67	—	4	2	no	—
403	C₂×C₅×Dic₃	—	2	4	no	—
404	C₂×C₅×Dic₃	—	4	2	no	—
405	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
408	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
411	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
414	C₅×D₁₂	—	2	2	no	—
415	C₅×D₁₂	—	2	4	no	—
416	C₅×D₁₂	—	2	2	no	—
417	C₅×D₁₂	—	4	2	no	—
418	C₄×C₅×D₃	—	2	4	no	—
419	C₄×C₅×D₃	—	2	2	no	—
420	C₄×C₅×D₃	—	2	2	no	—
421	C₄×C₅×D₃	—	2	2	no	—
422	C₄×C₅×D₃	—	2	4	no	—
423	C₄×C₅×D₃	—	2	4	no	—
424	C₄×C₅×D₃	—	4	2	no	—
425	C₄×C₅×D₃	—	4	2	no	—
426	C₄×C₅×D₃	—	4	1	no	—
427	C₄×C₅×D₃	—	4	1	no	—
428	C₄×C₅×D₃	#41	1	4	yes	complemented
429	C₅×Dic₆	—	2	2	no	—
430	C₅×Dic₆	—	2	4	no	—
431	C₅×Dic₆	—	2	4	no	—
432	C₅×Dic₆	#41	1	4	yes	complemented
433	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
434	C₂×#237	C₂²×C₅	1	1	yes	characteristic
435	C₂×#235	C₂²×C₅	1	1	yes	characteristic
436	C₂×#235	C₂²×C₅	1	1	yes	characteristic
437	C₂×#235	C₂²×C₅	1	2	yes	—
438	C₃×#126	C₂²×C₅	1	2	yes	—
439	C₃×#125	C₂²×C₅	1	1	yes	characteristic
440	C₃×#124	C₂²×C₅	1	1	yes	characteristic
441	C₃×#123	C₂²×C₅	1	2	yes	—
442	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
443	C₃×#121	C₂²×C₅	1	1	yes	characteristic
444	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
445	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
446	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
447	C₃×#117	C₂²×C₅	1	2	yes	—
448	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
449	#947	C₂²×C₅	1	1	yes	characteristic
450	#946	C₂²×C₅	1	1	yes	characteristic
451	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
452	#940	C₂²×C₅	1	2	yes	—
453	#940	C₂²×C₅	1	1	yes	characteristic
454	#939	C₂²×C₅	1	2	yes	—
455	#938	C₂²×C₅	1	2	yes	—
456	#938	C₂²×C₅	1	1	yes	characteristic
457	#935	C₂²×C₅	1	2	yes	—
458	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
459	C₄×#67	C₂²×C₅	1	1	yes	characteristic
460	C₄×#67	C₂²×C₅	1	1	yes	characteristic
461	C₄×#67	C₂²×C₅	1	1	yes	characteristic
462	C₄×#67	C₂²×C₅	1	2	yes	—
463	C₄×#67	C₂²×C₅	1	1	yes	characteristic
464	C₄×#67	C₂²×C₅	1	2	yes	—
465	C₄×#67	C₂²×C₅	1	2	yes	—
466	C₄×#67	C₂²×C₅	1	2	yes	—
467	#926	C₂²×C₅	1	1	yes	characteristic
468	#926	C₂²×C₅	1	1	yes	characteristic
469	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
470	#898	C₂²×C₅	1	2	yes	—
471	#898	C₂²×C₅	1	2	yes	—
472	#898	C₂²×C₅	1	2	yes	—
473	#896	C₂²×C₅	1	2	yes	—
474	#895	C₂²×C₅	1	1	yes	characteristic
475	#895	C₂²×C₅	1	2	yes	—
476	#895	C₂²×C₅	1	1	yes	characteristic
477	#894	C₂²×C₅	1	2	yes	—
478	#894	C₂²×C₅	1	2	yes	—
479	#893	C₂²×C₅	1	2	yes	—
480	#893	C₂²×C₅	1	2	yes	—
481	#892	C₂²×C₅	1	1	yes	characteristic
482	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
483	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
484	#890	C₂²×C₅	1	1	yes	characteristic
485	#889	C₂²×C₅	1	2	yes	—
486	#889	C₂²×C₅	1	2	yes	—
487	#888	C₂²×C₅	1	1	yes	characteristic
488	#888	C₂²×C₅	1	2	yes	—
489	#887	C₂²×C₅	1	1	yes	characteristic
490	#887	C₂²×C₅	1	2	yes	—
491	#887	C₂²×C₅	1	2	yes	—
492	#887	C₂²×C₅	1	2	yes	—
493	#887	C₂²×C₅	1	1	yes	characteristic
494	#886	C₂²×C₅	1	2	yes	—
495	#885	C₂²×C₅	1	2	yes	—
496	#885	C₂²×C₅	1	2	yes	—
497	#885	C₂²×C₅	1	2	yes	—
498	#885	C₂²×C₅	1	2	yes	—
499	#885	C₂²×C₅	1	2	yes	—
500	#884	C₂²×C₅	1	2	yes	—
501	#884	C₂²×C₅	1	2	yes	—
502	#884	C₂²×C₅	1	2	yes	—
503	#884	C₂²×C₅	1	2	yes	—
504	#883	C₂²×C₅	1	2	yes	—
505	#67⋊C₄	C₂²×C₅	1	2	yes	—
506	#67⋊C₄	C₂²×C₅	1	2	yes	—
507	#67⋊C₄	C₂²×C₅	1	2	yes	—
508	#67⋊C₄	C₂²×C₅	1	2	yes	—
509	#67⋊C₄	C₂²×C₅	1	2	yes	—
510	#879	C₂²×C₅	1	2	yes	—
511	#879	C₂²×C₅	1	2	yes	—
512	#878	C₂²×C₅	1	2	yes	—
513	#877	C₂²×C₅	1	2	yes	—
514	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
515	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
516	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
517	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
518	C₄×D₁₂	C₂²×C₅	1	2	yes	—
519	#872	C₂²×C₅	1	2	yes	—
520	#872	C₂²×C₅	1	1	yes	characteristic
521	#872	C₂²×C₅	1	1	yes	characteristic
522	#872	C₂²×C₅	1	2	yes	—
523	C₄²×D₃	C₂²×C₅	1	2	yes	—
524	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
525	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
526	C₄²×D₃	C₂²×C₅	1	2	yes	—
527	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
528	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
529	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
530	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
531	C₄×Dic₆	C₂²×C₅	1	2	yes	—
532	C₅×#41	—	6	8	no	—
533	C₅×#41	—	6	4	no	—
534	C₅×#41	—	6	4	no	—
535	C₅×#41	—	6	4	no	—
536	C₂×C₅×Q₈	—	3	1	no	—
537	C₂×C₅×Q₈	—	3	2	no	—
538	C₂×C₅×Q₈	—	3	2	no	—
539	C₂×C₅×Q₈	—	3	1	no	—
540	C₂×C₅×Q₈	—	6	4	no	—
541	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
542	C₂×C₅×D₄	—	3	1	no	—
543	C₂×C₅×D₄	—	3	2	no	—
544	C₂×C₅×D₄	—	3	2	no	—
545	C₂×C₅×D₄	—	3	2	no	—
546	C₂×C₅×D₄	—	3	1	no	—
547	C₂×C₅×D₄	—	3	2	no	—
548	C₂×C₅×D₄	—	3	2	no	—
549	C₂×C₅×D₄	—	3	2	no	—
550	C₂×C₅×D₄	—	3	1	no	—
551	C₂×C₅×D₄	—	3	1	no	—
552	C₂×C₅×D₄	—	3	2	no	—
553	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
554	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
555	C₂²×C₄×C₅	—	3	1	no	—
556	C₂²×C₄×C₅	—	3	2	no	—
557	C₂²×C₄×C₅	—	3	2	no	—
558	C₂²×C₄×C₅	—	3	2	no	—
559	C₂²×C₄×C₅	—	3	1	no	—
560	C₂²×C₄×C₅	—	3	2	no	—
561	C₂²×C₄×C₅	—	3	1	no	—
562	C₂²×C₄×C₅	—	3	1	no	—
563	C₂²×C₄×C₅	—	3	2	no	—
564	C₂²×C₄×C₅	—	3	2	no	—
565	C₂²×C₄×C₅	—	3	1	no	—
566	C₂²×C₄×C₅	—	3	2	no	—
567	C₂²×C₄×C₅	—	3	1	no	—
568	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
569	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
570	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
571	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
572	C₅×C₄⋊C₄	—	3	2	no	—
573	C₅×C₄⋊C₄	—	3	1	no	—
574	C₅×C₄⋊C₄	—	3	2	no	—
575	C₅×C₄⋊C₄	—	3	2	no	—
576	C₅×C₄⋊C₄	—	3	2	no	—
577	C₅×C₄⋊C₄	—	3	1	no	—
578	C₅×C₄⋊C₄	—	3	1	no	—
579	C₅×C₄⋊C₄	—	3	2	no	—
580	C₅×C₄⋊C₄	—	3	2	no	—
581	C₅×C₄⋊C₄	—	3	1	no	—
582	C₅×C₄⋊C₄	—	3	2	no	—
583	C₅×C₄⋊C₄	—	3	1	no	—
584	C₅×C₄⋊C₄	—	3	1	no	—
585	C₅×C₄⋊C₄	—	3	2	no	—
586	C₅×C₄⋊C₄	—	3	1	no	—
587	C₅×C₄⋊C₄	—	3	1	no	—
588	C₅×C₄⋊C₄	—	3	2	no	—
589	C₅×C₄⋊C₄	—	3	2	no	—
590	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
591	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
592	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
593	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
594	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
595	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
596	C₅×C₂²⋊C₄	—	3	1	no	—
597	C₅×C₂²⋊C₄	—	3	2	no	—
598	C₅×C₂²⋊C₄	—	3	2	no	—
599	C₅×C₂²⋊C₄	—	3	1	no	—
600	C₅×C₂²⋊C₄	—	3	2	no	—
601	C₅×C₂²⋊C₄	—	3	1	no	—
602	C₅×C₂²⋊C₄	—	3	1	no	—
603	C₅×C₂²⋊C₄	—	3	2	no	—
604	C₅×C₂²⋊C₄	—	3	1	no	—
605	C₅×C₂²⋊C₄	—	3	2	no	—
606	C₅×C₂²⋊C₄	—	3	2	no	—
607	C₅×C₂²⋊C₄	—	3	2	no	—
608	C₅×C₂²⋊C₄	—	3	2	no	—
609	C₅×C₂²⋊C₄	—	3	1	no	—
610	C₅×C₂²⋊C₄	—	3	2	no	—
611	C₅×C₂²⋊C₄	—	3	2	no	—
612	C₅×C₂²⋊C₄	—	3	2	no	—
613	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
614	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
615	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
616	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
617	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
618	C₄²×C₅	—	3	2	no	—
619	C₄²×C₅	—	3	2	no	—
620	C₄²×C₅	—	3	1	no	—
621	C₄²×C₅	—	3	2	no	—
622	C₄²×C₅	—	3	2	no	—
623	C₄²×C₅	—	3	1	no	—
624	C₄²×C₅	—	3	2	no	—
625	C₄²×C₅	—	3	1	no	—
626	C₄²×C₅	—	3	2	no	—
627	C₄²×C₅	—	3	1	no	—
628	C₄²×C₅	—	3	1	no	—
629	C₄²×C₅	—	3	2	no	—
630	C₄²×C₅	—	3	1	no	—
631	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
632	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
633	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
634	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
635	C₄²×C₅	C₂²×D₃	1	2	yes	—
636	#559	—	3	1	no	—
637	#559	—	3	2	no	—
638	#557	—	3	1	no	—
639	#556	—	3	2	no	—
640	#556	—	3	1	no	—
641	#553	—	3	2	no	—
642	#553	—	3	1	no	—
643	#553	—	3	2	no	—
644	#553	—	3	1	no	—
645	#550	—	3	1	no	—
646	#548	—	3	1	no	—
647	#548	—	3	1	no	—
648	#532	—	3	2	no	—
649	#532	—	3	1	no	—
650	#529	—	3	1	no	—
651	#529	—	3	2	no	—
652	#529	—	3	2	no	—
653	#529	C₅×D₃	1	1	yes	characteristic, complemented
654	C₄×#41	—	3	1	no	—
655	C₄×#41	—	3	2	no	—
656	C₄×#41	—	3	1	no	—
657	C₄×#41	—	3	1	no	—
658	C₂×C₄×Q₈	—	3	1	no	—
659	C₂²×C₃×C₅	—	2	2	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	C₂⁵	1	1	yes	characteristic
666	C₂×C₅×D₃	—	2	1	no	—
667	C₂×C₅×D₃	—	2	1	no	—
668	C₂×C₅×D₃	—	2	2	no	—
669	C₂×C₅×D₃	—	2	1	no	—
670	C₂×C₅×D₃	—	2	2	no	—
671	C₂×C₅×D₃	—	2	1	no	—
672	C₂×C₅×D₃	—	2	1	no	—
673	C₂×C₅×D₃	—	2	2	no	—
674	C₂×C₅×D₃	C₂×#41	1	2	yes	—
675	C₃×C₄×C₅	—	2	2	no	—
676	C₃×C₄×C₅	—	2	2	no	—
677	C₃×C₄×C₅	—	2	1	no	—
678	C₃×C₄×C₅	—	2	1	no	—
679	C₃×C₄×C₅	—	2	1	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×C₄×C₅	C₂×#41	1	2	yes	—
684	C₅×Dic₃	—	2	1	no	—
685	C₅×Dic₃	—	2	1	no	—
686	C₅×Dic₃	—	2	2	no	—
687	C₅×Dic₃	—	2	1	no	—
688	C₅×Dic₃	—	2	2	no	—
689	C₅×Dic₃	—	2	1	no	—
690	C₅×Dic₃	—	2	1	no	—
691	C₅×Dic₃	C₂×#41	1	2	yes	—
692	C₅×Dic₃	C₂×#41	1	4	yes	—
693	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
694	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
695	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
696	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
697	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
698	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
699	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
700	C₂×#67	C₂³×C₅	1	2	yes	—
701	C₂×#67	C₂³×C₅	1	2	yes	—
702	C₂×#67	C₂³×C₅	1	2	yes	—
703	C₂×#67	C₂³×C₅	1	1	yes	characteristic
704	C₂×#67	C₂³×C₅	1	2	yes	—
705	C₂×#67	C₂³×C₅	1	1	yes	characteristic
706	C₂×#67	C₂³×C₅	1	2	yes	—
707	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
708	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
709	D₃×Q₈	—	2	4	no	—
710	#237	—	2	4	no	—
711	#235	—	2	4	no	—
712	#235	—	2	8	no	—
713	#235	—	2	4	no	—
714	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
715	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
716	C₂×D₁₂	C₂³×C₅	1	2	yes	—
717	C₂×D₁₂	C₂³×C₅	1	2	yes	—
718	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
719	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
720	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
721	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
724	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
725	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
726	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
727	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
728	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
729	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
730	C₂×Dic₆	C₂³×C₅	1	2	yes	—
731	C₂×Dic₆	C₂³×C₅	1	2	yes	—
732	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
733	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
734	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
735	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
736	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
737	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
738	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
740	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
741	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
742	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
743	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
744	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
746	C₃×C₄²	C₂³×C₅	1	2	yes	—
747	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
748	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
749	#217	C₂³×C₅	1	2	yes	—
750	#217	C₂³×C₅	1	2	yes	—
751	#217	C₂³×C₅	1	1	yes	characteristic
752	#217	C₂³×C₅	1	2	yes	—
753	#217	C₂³×C₅	1	1	yes	characteristic
754	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
755	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
756	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
757	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
758	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
759	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
761	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
762	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
763	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
764	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
766	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
767	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
768	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
769	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
770	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
771	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
772	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
773	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
775	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
778	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
781	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
784	C₄×Dic₃	C₂³×C₅	1	2	yes	—
785	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
787	C₄×Dic₃	C₂³×C₅	1	2	yes	—
788	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
789	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
790	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
791	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
792	C₄×Dic₃	C₂³×C₅	1	2	yes	—
793	C₄×Dic₃	C₂³×C₅	1	2	yes	—
794	C₄×Dic₃	C₂³×C₅	1	2	yes	—
795	C₄×Dic₃	C₂³×C₅	1	2	yes	—
796	C₄×Dic₃	C₂³×C₅	1	2	yes	—
797	C₂³×C₅	—	3	1	no	—
798	C₂³×C₅	—	3	1	no	—
799	C₂³×C₅	—	3	2	no	—
800	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
801	C₂³×C₅	C₂³×D₃	1	2	yes	—
802	C₅×Q₈	—	2	2	no	—
803	C₅×Q₈	—	3	4	no	—
804	C₅×Q₈	—	6	4	no	—
805	C₅×Q₈	—	6	4	no	—
806	C₅×Q₈	—	6	2	no	—
807	C₅×D₄	—	2	2	no	—
808	C₅×D₄	—	4	2	no	—
809	C₅×D₄	—	6	4	no	—
810	C₅×D₄	—	6	2	no	—
811	C₅×D₄	—	6	2	no	—
812	C₅×D₄	—	6	4	no	—
813	C₅×D₄	—	6	4	no	—
814	C₅×D₄	—	6	4	no	—
815	C₅×D₄	—	6	2	no	—
816	C₅×D₄	—	6	4	no	—
817	C₅×D₄	—	6	2	no	—
818	C₅×D₄	—	12	2	no	—
819	C₅×D₄	—	12	2	no	—
820	C₂×C₄×C₅	—	2	2	no	—
821	C₂×C₄×C₅	—	2	4	no	—
822	C₂×C₄×C₅	—	2	2	no	—
823	C₂×C₄×C₅	—	3	1	no	—
824	C₂×C₄×C₅	—	3	2	no	—
825	C₂×C₄×C₅	—	3	4	no	—
826	C₂×C₄×C₅	—	3	1	no	—
827	C₂×C₄×C₅	—	3	2	no	—
828	C₂×C₄×C₅	—	3	1	no	—
829	C₂×C₄×C₅	—	3	1	no	—
830	C₂×C₄×C₅	—	3	1	no	—
831	C₂×C₄×C₅	—	3	2	no	—
832	C₂×C₄×C₅	—	3	1	no	—
833	C₂×C₄×C₅	—	4	1	no	—
834	C₂×C₄×C₅	—	6	4	no	—
835	C₂×C₄×C₅	—	6	4	no	—
836	C₂×C₄×C₅	—	6	4	no	—
837	C₂×C₄×C₅	—	6	2	no	—
838	C₂×C₄×C₅	—	6	2	no	—
839	C₂×C₄×C₅	—	6	2	no	—
840	C₂×C₄×C₅	—	6	4	no	—
841	C₂×C₄×C₅	—	12	2	no	—
842	C₂×C₄×C₅	—	12	1	no	—
843	C₂×C₄×C₅	—	12	1	no	—
844	C₂×C₄×C₅	—	12	2	no	—
845	C₂×C₄×C₅	—	12	2	no	—
846	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
847	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
848	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
849	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
850	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
851	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
852	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
853	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
854	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
855	C₂×#41	—	3	1	no	—
856	C₂×#41	—	3	2	no	—
857	C₂×#41	—	3	1	no	—
858	C₂×#41	—	3	1	no	—
859	C₂²×Q₈	—	3	1	no	—
860	C₄⋊Q₈	—	3	2	no	—
861	C₄⋊Q₈	—	3	1	no	—
862	#127	—	3	2	no	—
863	#127	—	3	1	no	—
864	#126	—	3	2	no	—
865	#126	—	3	2	no	—
866	#126	—	3	2	no	—
867	#126	—	3	2	no	—
868	#126	—	3	2	no	—
869	#126	C₂×C₅×D₃	1	2	yes	—
870	#125	—	3	2	no	—
871	#125	—	3	2	no	—
872	#125	—	3	1	no	—
873	#125	C₂×C₅×D₃	1	1	yes	characteristic
874	#124	—	3	1	no	—
875	#124	—	3	2	no	—
876	#124	—	3	2	no	—
877	#124	—	3	2	no	—
878	#124	—	3	2	no	—
879	#124	—	3	2	no	—
880	#124	C₂×C₅×D₃	1	1	yes	characteristic
881	#123	—	3	2	no	—
882	#123	—	3	2	no	—
883	#123	—	3	2	no	—
884	#123	—	3	2	no	—
885	#123	—	3	2	no	—
886	#123	C₂×C₅×D₃	1	2	yes	—
887	C₂²⋊Q₈	—	3	1	no	—
888	C₂²⋊Q₈	—	3	2	no	—
889	C₂²⋊Q₈	—	3	2	no	—
890	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
891	#121	—	3	2	no	—
892	#121	—	3	1	no	—
893	#121	—	3	2	no	—
894	#121	—	3	1	no	—
895	#121	—	3	1	no	—
896	#121	—	3	2	no	—
897	#121	—	3	2	no	—
898	#121	—	3	2	no	—
899	#121	—	3	2	no	—
900	#121	—	3	2	no	—
901	#121	C₂×C₅×D₃	1	1	yes	characteristic
902	C₄×Q₈	—	3	1	no	—
903	C₄×Q₈	—	3	1	no	—
904	C₄×Q₈	—	3	2	no	—
905	C₄×Q₈	—	3	1	no	—
906	C₄×Q₈	—	3	2	no	—
907	C₄×Q₈	—	3	2	no	—
908	C₄×Q₈	—	3	1	no	—
909	C₄×Q₈	—	3	2	no	—
910	C₄×Q₈	—	3	1	no	—
911	C₄×Q₈	—	3	1	no	—
912	C₄×Q₈	—	3	1	no	—
913	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
914	C₄×D₄	—	3	1	no	—
915	C₄×D₄	—	3	2	no	—
916	C₄×D₄	—	3	2	no	—
917	C₄×D₄	—	3	1	no	—
918	C₄×D₄	—	3	1	no	—
919	C₄×D₄	—	3	1	no	—
920	C₄×D₄	—	3	2	no	—
921	C₄×D₄	—	3	1	no	—
922	C₄×D₄	—	3	2	no	—
923	C₄×D₄	—	3	2	no	—
924	C₄×D₄	—	3	2	no	—
925	C₄×D₄	—	3	2	no	—
926	C₄×D₄	—	3	2	no	—
927	C₄×D₄	—	3	2	no	—
928	C₄×D₄	—	3	2	no	—
929	C₄×D₄	—	3	2	no	—
930	C₄×D₄	—	3	1	no	—
931	C₄×D₄	—	3	1	no	—
932	C₄×D₄	—	3	1	no	—
933	C₄×D₄	—	3	1	no	—
934	C₄×D₄	—	3	2	no	—
935	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
936	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
937	#117	—	3	1	no	—
938	#117	—	3	1	no	—
939	#117	—	3	1	no	—
940	#117	—	3	2	no	—
941	#117	—	3	1	no	—
942	#117	—	3	2	no	—
943	#117	—	3	1	no	—
944	#117	—	3	2	no	—
945	#117	C₂×C₅×D₃	1	2	yes	—
946	C₂×C₄⋊C₄	—	3	2	no	—
947	C₂×C₄⋊C₄	—	3	1	no	—
948	C₂×C₄²	—	3	2	no	—
949	C₂×C₄²	—	3	2	no	—
950	C₂×C₄²	—	3	1	no	—
951	C₂×C₄²	—	3	1	no	—
952	C₂×C₄²	—	3	2	no	—
953	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
954	C₂×C₃×C₅	—	4	2	no	—
955	C₂×C₃×C₅	—	4	1	no	—
956	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	#585	1	1	yes	characteristic
959	C₅×D₃	—	2	2	no	—
960	C₅×D₃	—	4	2	no	—
961	C₅×D₃	—	4	1	no	—
962	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
963	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
964	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
965	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
966	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
967	C₃×Q₈	—	2	2	no	—
968	C₃×D₄	—	2	2	no	—
969	C₃×D₄	—	4	2	no	—
970	C₂×C₃×C₄	—	2	4	no	—
971	C₂×C₃×C₄	—	2	2	no	—
972	C₂×C₃×C₄	—	2	2	no	—
973	C₂×C₃×C₄	—	4	1	no	—
974	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
975	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
976	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
977	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
978	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
979	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
980	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
981	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
982	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
983	#67	—	2	4	no	—
984	#67	—	2	2	no	—
985	#67	—	2	4	no	—
986	#67	—	2	2	no	—
987	#67	—	2	4	no	—
988	#67	—	2	4	no	—
989	#67	—	4	2	no	—
990	C₂×Dic₃	—	2	4	no	—
991	C₂×Dic₃	—	4	2	no	—
992	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
993	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
994	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
995	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
996	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
997	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
998	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1000	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1001	D₁₂	—	2	2	no	—
1002	D₁₂	—	2	4	no	—
1003	D₁₂	—	2	2	no	—
1004	D₁₂	—	4	2	no	—
1005	C₄×D₃	—	2	4	no	—
1006	C₄×D₃	—	2	2	no	—
1007	C₄×D₃	—	2	2	no	—
1008	C₄×D₃	—	2	2	no	—
1009	C₄×D₃	—	2	4	no	—
1010	C₄×D₃	—	2	4	no	—
1011	C₄×D₃	—	4	2	no	—
1012	C₄×D₃	—	4	2	no	—
1013	C₄×D₃	—	4	1	no	—
1014	C₄×D₃	—	4	1	no	—
1015	C₄×D₃	C₅×#41	1	4	yes	complemented
1016	Dic₆	—	2	2	no	—
1017	Dic₆	—	2	4	no	—
1018	Dic₆	—	2	4	no	—
1019	Dic₆	C₅×#41	1	4	yes	complemented
1020	C₂²×C₅	—	2	1	no	—
1021	C₂²×C₅	—	2	1	no	—
1022	C₂²×C₅	—	2	2	no	—
1023	C₂²×C₅	—	2	2	no	—
1024	C₂²×C₅	—	2	1	no	—
1025	C₂²×C₅	—	2	2	no	—
1026	C₂²×C₅	—	3	2	no	—
1027	C₂²×C₅	—	6	1	no	—
1028	C₂²×C₅	—	6	1	no	—
1029	C₂²×C₅	—	6	2	no	—
1030	C₂²×C₅	—	6	1	no	—
1031	C₂²×C₅	—	6	1	no	—
1032	C₂²×C₅	—	6	2	no	—
1033	C₂²×C₅	—	6	1	no	—
1034	C₂²×C₅	—	6	2	no	—
1035	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1036	C₄×C₅	—	2	1	no	—
1037	C₄×C₅	—	2	2	no	—
1038	C₄×C₅	—	2	1	no	—
1039	C₄×C₅	—	2	2	no	—
1040	C₄×C₅	—	2	1	no	—
1041	C₄×C₅	—	2	1	no	—
1042	C₄×C₅	—	2	2	no	—
1043	C₄×C₅	—	3	2	no	—
1044	C₄×C₅	—	3	4	no	—
1045	C₄×C₅	—	6	1	no	—
1046	C₄×C₅	—	6	1	no	—
1047	C₄×C₅	—	6	2	no	—
1048	C₄×C₅	—	6	1	no	—
1049	C₄×C₅	—	6	2	no	—
1050	C₄×C₅	—	6	1	no	—
1051	C₄×C₅	—	6	1	no	—
1052	C₄×C₅	D₃×#41	1	2	yes	—
1053	C₄×C₅	D₃×#41	1	2	yes	—
1054	#41	—	6	8	no	—
1055	#41	—	6	4	no	—
1056	#41	—	6	4	no	—
1057	#41	—	6	4	no	—
1058	C₂×Q₈	—	3	1	no	—
1059	C₂×Q₈	—	3	2	no	—
1060	C₂×Q₈	—	3	2	no	—
1061	C₂×Q₈	—	3	1	no	—
1062	C₂×Q₈	—	6	4	no	—
1063	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1064	C₂×D₄	—	3	1	no	—
1065	C₂×D₄	—	3	2	no	—
1066	C₂×D₄	—	3	2	no	—
1067	C₂×D₄	—	3	2	no	—
1068	C₂×D₄	—	3	1	no	—
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	3	2	no	—
1071	C₂×D₄	—	3	2	no	—
1072	C₂×D₄	—	3	1	no	—
1073	C₂×D₄	—	3	1	no	—
1074	C₂×D₄	—	3	2	no	—
1075	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1076	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1077	C₂²×C₄	—	3	1	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	2	no	—
1081	C₂²×C₄	—	3	1	no	—
1082	C₂²×C₄	—	3	1	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	—	3	1	no	—
1086	C₂²×C₄	—	3	2	no	—
1087	C₂²×C₄	—	3	1	no	—
1088	C₂²×C₄	—	3	2	no	—
1089	C₂²×C₄	—	3	1	no	—
1090	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1091	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1092	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1094	C₄⋊C₄	—	3	2	no	—
1095	C₄⋊C₄	—	3	1	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	2	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	—	3	1	no	—
1100	C₄⋊C₄	—	3	1	no	—
1101	C₄⋊C₄	—	3	2	no	—
1102	C₄⋊C₄	—	3	2	no	—
1103	C₄⋊C₄	—	3	1	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	1	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	1	no	—
1109	C₄⋊C₄	—	3	1	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1114	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1116	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1117	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1118	C₂²⋊C₄	—	3	1	no	—
1119	C₂²⋊C₄	—	3	2	no	—
1120	C₂²⋊C₄	—	3	2	no	—
1121	C₂²⋊C₄	—	3	1	no	—
1122	C₂²⋊C₄	—	3	2	no	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	1	no	—
1125	C₂²⋊C₄	—	3	2	no	—
1126	C₂²⋊C₄	—	3	1	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	2	no	—
1130	C₂²⋊C₄	—	3	2	no	—
1131	C₂²⋊C₄	—	3	1	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	2	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1136	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1137	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1138	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1139	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1140	C₄²	—	3	1	no	—
1141	C₄²	—	3	2	no	—
1142	C₄²	—	3	1	no	—
1143	C₄²	—	3	2	no	—
1144	C₄²	—	3	2	no	—
1145	C₄²	—	3	1	no	—
1146	C₄²	—	3	2	no	—
1147	C₄²	—	3	2	no	—
1148	C₄²	—	3	1	no	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	1	no	—
1151	C₄²	—	3	2	no	—
1152	C₄²	—	3	1	no	—
1153	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1154	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1155	C₄²	C₂²×C₅×D₃	1	2	yes	—
1156	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1157	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1158	C₃×C₅	#3480	1	1	yes	characteristic, complemented, Hall
1159	C₂²×C₃	—	2	2	no	—
1160	C₂²×C₃	—	2	1	no	—
1161	C₂²×C₃	—	2	2	no	—
1162	C₂²×C₃	—	2	1	no	—
1163	C₂²×C₃	—	2	2	no	—
1164	C₂²×C₃	—	2	1	no	—
1165	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1166	C₂×D₃	—	2	1	no	—
1167	C₂×D₃	—	2	1	no	—
1168	C₂×D₃	—	2	2	no	—
1169	C₂×D₃	—	2	1	no	—
1170	C₂×D₃	—	2	2	no	—
1171	C₂×D₃	—	2	1	no	—
1172	C₂×D₃	—	2	1	no	—
1173	C₂×D₃	—	2	2	no	—
1174	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1175	C₃×C₄	—	2	2	no	—
1176	C₃×C₄	—	2	2	no	—
1177	C₃×C₄	—	2	1	no	—
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	1	no	—
1180	C₃×C₄	—	2	1	no	—
1181	C₃×C₄	—	2	2	no	—
1182	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1183	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1184	Dic₃	—	2	1	no	—
1185	Dic₃	—	2	1	no	—
1186	Dic₃	—	2	2	no	—
1187	Dic₃	—	2	1	no	—
1188	Dic₃	—	2	2	no	—
1189	Dic₃	—	2	1	no	—
1190	Dic₃	—	2	1	no	—
1191	Dic₃	C₂×C₅×#41	1	2	yes	—
1192	Dic₃	C₂×C₅×#41	1	4	yes	—
1193	C₂×C₅	—	4	1	no	—
1194	C₂×C₅	—	4	2	no	—
1195	C₂×C₅	—	6	2	no	—
1196	C₂×C₅	—	12	2	no	—
1197	C₂×C₅	—	12	1	no	—
1198	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1199	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1200	C₂×C₅	#5964	1	1	yes	characteristic
1201	C₂³	—	3	1	no	—
1202	C₂³	—	3	1	no	—
1203	C₂³	—	3	2	no	—
1204	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1205	C₂³	C₂³×C₅×D₃	1	2	yes	—
1206	Q₈	—	2	2	no	—
1207	Q₈	—	3	4	no	—
1208	Q₈	—	6	4	no	—
1209	Q₈	—	6	4	no	—
1210	Q₈	—	6	2	no	—
1211	D₄	—	2	2	no	—
1212	D₄	—	4	2	no	—
1213	D₄	—	6	4	no	—
1214	D₄	—	6	2	no	—
1215	D₄	—	6	2	no	—
1216	D₄	—	6	4	no	—
1217	D₄	—	6	4	no	—
1218	D₄	—	6	4	no	—
1219	D₄	—	6	2	no	—
1220	D₄	—	6	4	no	—
1221	D₄	—	6	2	no	—
1222	D₄	—	12	2	no	—
1223	D₄	—	12	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	4	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	3	1	no	—
1228	C₂×C₄	—	3	2	no	—
1229	C₂×C₄	—	3	4	no	—
1230	C₂×C₄	—	3	1	no	—
1231	C₂×C₄	—	3	1	no	—
1232	C₂×C₄	—	3	2	no	—
1233	C₂×C₄	—	3	1	no	—
1234	C₂×C₄	—	3	1	no	—
1235	C₂×C₄	—	3	2	no	—
1236	C₂×C₄	—	3	1	no	—
1237	C₂×C₄	—	4	1	no	—
1238	C₂×C₄	—	6	4	no	—
1239	C₂×C₄	—	6	4	no	—
1240	C₂×C₄	—	6	4	no	—
1241	C₂×C₄	—	6	2	no	—
1242	C₂×C₄	—	6	2	no	—
1243	C₂×C₄	—	6	2	no	—
1244	C₂×C₄	—	6	4	no	—
1245	C₂×C₄	—	12	2	no	—
1246	C₂×C₄	—	12	1	no	—
1247	C₂×C₄	—	12	1	no	—
1248	C₂×C₄	—	12	2	no	—
1249	C₂×C₄	—	12	2	no	—
1250	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1251	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1252	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1253	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1254	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1255	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1256	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1257	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1258	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1259	C₂×C₃	—	4	2	no	—
1260	C₂×C₃	—	4	1	no	—
1261	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1262	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1263	C₂×C₃	C₅×#585	1	1	yes	characteristic
1264	D₃	—	2	2	no	—
1265	D₃	—	4	2	no	—
1266	D₃	—	4	1	no	—
1267	C₅	#86152	1	1	yes	characteristic, direct product factor, Sylow
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	2	no	—
1274	C₂²	—	3	2	no	—
1275	C₂²	—	6	1	no	—
1276	C₂²	—	6	1	no	—
1277	C₂²	—	6	2	no	—
1278	C₂²	—	6	1	no	—
1279	C₂²	—	6	1	no	—
1280	C₂²	—	6	2	no	—
1281	C₂²	—	6	1	no	—
1282	C₂²	—	6	2	no	—
1283	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	2	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	2	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	3	2	no	—
1292	C₄	—	3	4	no	—
1293	C₄	—	6	1	no	—
1294	C₄	—	6	1	no	—
1295	C₄	—	6	2	no	—
1296	C₄	—	6	1	no	—
1297	C₄	—	6	2	no	—
1298	C₄	—	6	1	no	—
1299	C₄	—	6	1	no	—
1300	C₄	C₅×D₃×#41	1	2	yes	—
1301	C₄	C₅×D₃×#41	1	2	yes	—
1302	C₃	C₅×#3480	1	1	yes	characteristic, complemented, Sylow
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	6	2	no	—
1306	C₂	—	12	2	no	—
1307	C₂	—	12	1	no	—
1308	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1309	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1310	C₂	C₅×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#3480
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#529	C₂	semidirect
2. C₅×#5709	C₂	semidirect
3. C₅×#5702	C₂	semidirect
4. C₅×#5695	C₂	semidirect
5. C₅×#5685	C₂	semidirect
6. C₅×#5681	C₂	semidirect
7. C₅×#5677	C₂	semidirect
8. C₅×#5664	C₂	semidirect
9. C₅×#5661	C₂	semidirect
10. C₅×#5641	C₂	semidirect
11. C₅×#5633	C₂	semidirect
12. C₅×#5614	C₂	semidirect
13. C₅×#5599	C₂	semidirect
14. C₅×#5580	C₂	semidirect
15. C₄×C₅×D₃×Q₈	C₂	semidirect
16. C₅×#5548	C₂	semidirect
17. C₅×#5548	C₂	semidirect
18. C₅×#5538	C₂	semidirect
19. C₄×C₅×#237	C₂	semidirect
20. C₅×#5528	C₂	semidirect
21. C₅×#5522	C₂	semidirect
22. C₄×C₅×#235	C₂	semidirect
23. C₄×C₅×#235	C₂	semidirect
124. #86152	C₅	direct (N × H)
142. C₅×#529	D₃	semidirect
252. C₃×#529	C₂×C₅	semidirect
253. #5709	C₂×C₅	semidirect
254. #5702	C₂×C₅	semidirect
255. #5695	C₂×C₅	semidirect
256. #5685	C₂×C₅	semidirect
257. #5681	C₂×C₅	semidirect
258. #5677	C₂×C₅	semidirect
259. #5664	C₂×C₅	semidirect
260. #5661	C₂×C₅	semidirect
261. #5641	C₂×C₅	semidirect
262. #5633	C₂×C₅	semidirect
263. #5614	C₂×C₅	semidirect
264. #5599	C₂×C₅	semidirect
265. #5580	C₂×C₅	semidirect
266. C₄×D₃×Q₈	C₂×C₅	semidirect
267. #5548	C₂×C₅	semidirect
268. #5548	C₂×C₅	semidirect
269. #5538	C₂×C₅	semidirect
270. C₄×#237	C₂×C₅	semidirect
271. #5528	C₂×C₅	semidirect
272. #5522	C₂×C₅	semidirect
273. C₄×#235	C₂×C₅	semidirect
274. C₄×#235	C₂×C₅	semidirect
428. C₄×C₅×D₃	#41	semidirect
432. C₅×Dic₆	#41	semidirect
653. #529	C₅×D₃	semidirect
1015. C₄×D₃	C₅×#41	semidirect
1019. Dic₆	C₅×#41	semidirect
1158. C₃×C₅	#3480	semidirect
1267. C₅	#86152	direct (N × H)
1302. C₃	C₅×#3480	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₅×#5709	2
C₅×#5702	2
C₅×#5695	2
C₅×#5685	2
C₅×#5681	2
C₅×#5677	2
C₅×#5664	2
C₅×#5661	2
C₅×#5641	2
C₅×#5633	2
C₅×#5614	2
C₅×#5599	2
C₅×#5580	2
C₄×C₅×D₃×Q₈	2
C₅×#5548	2
C₅×#5538	2
C₄×C₅×#237	2
C₅×#5528	2
C₅×#5522	2
C₄×C₅×#235	2
C₅×#3480	3
#86152	5

Subgroups — C5×#86152 #14484771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86152 #14484771