Subgroups — C₅×#86523 #14481508

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5707	C₂	1	2	yes	maximal, complemented
5	C₅×#5706	C₂	1	2	yes	maximal, complemented
6	C₅×#5682	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5680	C₂	1	2	yes	maximal, complemented
8	C₅×#5678	C₂	1	2	yes	maximal, complemented
9	C₅×#5668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5657	C₂	1	2	yes	maximal, complemented
11	C₅×#5649	C₂	1	2	yes	maximal, complemented
12	C₅×#5638	C₂	1	2	yes	maximal, complemented
13	C₅×#5627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5625	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5624	C₂	1	2	yes	maximal, complemented
16	C₅×#5619	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#5606	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#5583	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#5562	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3455	—	3	1	no	maximal, Hall
25	C₂×C₅×#239	C₂²	1	1	yes	characteristic
26	C₂×C₅×#237	C₂²	1	1	yes	characteristic
27	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#126	C₂²	1	2	yes	complemented
30	C₃×C₅×#124	C₂²	1	2	yes	—
31	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#123	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×#117	C₂²	1	1	yes	characteristic
39	C₅×#947	C₂²	1	2	yes	—
40	C₅×#946	C₂²	1	2	yes	—
41	C₅×#946	C₂²	1	1	yes	characteristic
42	C₅×#946	C₂²	1	2	yes	complemented
43	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
44	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₅×#944	C₂²	1	1	yes	characteristic, complemented
46	C₅×#940	C₂²	1	1	yes	characteristic, complemented
47	C₅×#939	C₂²	1	2	yes	—
48	C₅×#938	C₂²	1	2	yes	—
49	C₅×#938	C₂²	1	1	yes	characteristic
50	C₅×#937	C₂²	1	2	yes	—
51	C₅×D₄×Dic₃	C₂²	1	2	yes	—
52	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₅×#930	C₂²	1	2	yes	—
54	C₅×#930	C₂²	1	1	yes	characteristic
55	C₅×#929	C₂²	1	2	yes	complemented
56	C₄×C₅×#67	C₂²	1	2	yes	—
57	C₅×#926	C₂²	1	1	yes	characteristic
58	C₅×#924	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
60	C₅×#898	C₂²	1	2	yes	—
61	C₅×#898	C₂²	1	2	yes	complemented
62	C₅×#898	C₂²	1	2	yes	complemented
63	C₅×#897	C₂²	1	2	yes	—
64	C₅×#897	C₂²	1	1	yes	characteristic
65	C₅×#896	C₂²	1	2	yes	complemented
66	C₅×#895	C₂²	1	1	yes	characteristic
67	C₅×#894	C₂²	1	2	yes	—
68	C₅×#894	C₂²	1	2	yes	—
69	C₅×#893	C₂²	1	2	yes	—
70	C₅×#893	C₂²	1	2	yes	—
71	C₅×#893	C₂²	1	1	yes	characteristic, complemented
72	C₅×#892	C₂²	1	1	yes	characteristic
73	C₅×#892	C₂²	1	1	yes	characteristic
74	C₅×#892	C₂²	1	1	yes	characteristic
75	C₅×#892	C₂²	1	1	yes	characteristic
76	C₅×#892	C₂²	1	2	yes	complemented
77	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₅×#890	C₂²	1	2	yes	complemented
80	C₅×#890	C₂²	1	1	yes	characteristic, complemented
81	C₅×#890	C₂²	1	1	yes	characteristic, complemented
82	C₅×#889	C₂²	1	2	yes	complemented
83	C₅×#889	C₂²	1	2	yes	complemented
84	C₅×#887	C₂²	1	2	yes	complemented
85	C₅×#887	C₂²	1	1	yes	characteristic, complemented
86	C₅×#886	C₂²	1	2	yes	—
87	C₅×#886	C₂²	1	2	yes	complemented
88	C₅×#885	C₂²	1	2	yes	—
89	C₅×#885	C₂²	1	2	yes	—
90	C₅×#884	C₂²	1	2	yes	—
91	C₅×#884	C₂²	1	2	yes	—
92	C₅×#884	C₂²	1	2	yes	—
93	C₅×#883	C₂²	1	2	yes	—
94	C₅×#883	C₂²	1	2	yes	—
95	C₅×#883	C₂²	1	2	yes	complemented
96	C₅×#883	C₂²	1	2	yes	complemented
97	C₅×#882	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	complemented
102	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
103	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₅×#879	C₂²	1	2	yes	—
106	C₅×#879	C₂²	1	2	yes	—
107	C₅×#879	C₂²	1	2	yes	complemented
108	C₅×#878	C₂²	1	2	yes	complemented
109	C₅×#877	C₂²	1	1	yes	characteristic
110	C₅×#877	C₂²	1	1	yes	characteristic
111	C₅×#877	C₂²	1	2	yes	complemented
112	C₅×#876	C₂²	1	2	yes	—
113	C₅×#875	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₅×D₁₂	C₂²	1	2	yes	—
115	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
116	C₅×#872	C₂²	1	1	yes	characteristic
117	C₅×#872	C₂²	1	1	yes	characteristic
118	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
119	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
120	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
121	C₅×#870	C₂²	1	2	yes	complemented
122	C₅×#869	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#86523	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#542	—	3	1	no	—
126	C₅×#542	—	3	1	no	—
127	C₅×#542	—	3	1	no	—
128	C₅×#542	D₃	1	1	yes	characteristic, complemented
129	C₅×#541	—	3	1	no	—
130	C₅×#541	—	3	1	no	—
131	C₅×#540	—	3	1	no	—
132	C₅×#540	—	3	1	no	—
133	C₅×#539	—	3	2	no	—
134	C₅×#539	—	3	2	no	—
135	C₅×#538	—	3	2	no	—
136	C₅×#538	—	3	2	no	—
137	C₅×#533	—	3	1	no	—
138	C₅×#532	—	3	1	no	—
139	C₅×#529	—	3	2	no	—
140	C₅×#529	—	3	2	no	—
141	C₅×#529	—	3	2	no	—
142	C₅×#529	—	3	2	no	—
143	C₅×#525	—	3	1	no	—
144	C₅×#525	—	3	1	no	—
145	C₄×C₅×#41	—	3	1	no	—
146	C₄×C₅×#41	—	3	1	no	—
147	C₂×C₅×#117	—	3	1	no	—
148	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	2	yes	—
159	C₂×C₅×#67	C₂³	1	2	yes	—
160	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
161	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
162	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
163	C₅×#239	—	2	4	no	—
164	C₅×#237	—	2	4	no	—
165	C₂×C₅×D₁₂	C₂³	1	2	yes	—
166	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×C₅×D₁₂	C₂³	1	2	yes	—
168	C₂×C₄×C₅×D₃	—	2	4	no	—
169	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
170	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
171	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
178	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
179	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
181	C₂×C₅×Dic₆	C₂³	1	2	yes	—
182	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₃×C₄²×C₅	C₂³	1	2	yes	—
199	C₅×#217	C₂³	1	1	yes	characteristic
200	C₅×#217	C₂³	1	1	yes	characteristic
201	C₅×#217	C₂³	1	2	yes	—
202	C₅×#217	C₂³	1	2	yes	—
203	C₅×#217	C₂³	1	2	yes	—
204	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
205	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
206	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
207	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
208	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
219	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
221	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
229	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
230	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
232	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
233	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
251	#5733	C₂×C₅	1	1	yes	characteristic, complemented
252	#5728	C₂×C₅	1	1	yes	characteristic, complemented
253	#5707	C₂×C₅	1	2	yes	complemented
254	#5706	C₂×C₅	1	2	yes	complemented
255	#5682	C₂×C₅	1	1	yes	characteristic, complemented
256	#5680	C₂×C₅	1	2	yes	complemented
257	#5678	C₂×C₅	1	2	yes	complemented
258	#5668	C₂×C₅	1	1	yes	characteristic, complemented
259	#5657	C₂×C₅	1	2	yes	complemented
260	#5649	C₂×C₅	1	2	yes	complemented
261	#5638	C₂×C₅	1	2	yes	complemented
262	#5627	C₂×C₅	1	1	yes	characteristic, complemented
263	#5625	C₂×C₅	1	1	yes	characteristic, complemented
264	#5624	C₂×C₅	1	2	yes	complemented
265	#5619	C₂×C₅	1	1	yes	characteristic, complemented
266	#5606	C₂×C₅	1	1	yes	characteristic, complemented
267	#5583	C₂×C₅	1	1	yes	characteristic, complemented
268	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
269	#5562	C₂×C₅	1	1	yes	characteristic, complemented
270	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
271	#5534	C₂×C₅	1	1	yes	characteristic, complemented
272	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂×C₅×#41	—	3	1	no	—
274	C₂×C₅×#41	—	3	1	no	—
275	C₂³×C₄×C₅	—	3	1	no	—
276	C₅×C₄⋊Q₈	—	3	1	no	—
277	C₅×C₄⋊Q₈	—	3	1	no	—
278	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
279	C₅×#127	—	3	1	no	—
280	C₅×#126	—	3	2	no	—
281	C₅×#126	—	3	2	no	—
282	C₅×#126	—	3	2	no	—
283	C₅×#126	—	3	2	no	—
284	C₅×#126	—	3	2	no	—
285	C₅×#126	—	3	2	no	—
286	C₅×#126	—	3	2	no	—
287	C₅×#126	C₂×D₃	1	2	yes	complemented
288	C₅×#125	—	3	2	no	—
289	C₅×#125	—	3	2	no	—
290	C₅×#125	—	3	2	no	—
291	C₅×#125	—	3	1	no	—
292	C₅×#125	—	3	1	no	—
293	C₅×#125	—	3	2	no	—
294	C₅×#124	—	3	2	no	—
295	C₅×#124	—	3	2	no	—
296	C₅×#124	—	3	2	no	—
297	C₅×#124	—	3	1	no	—
298	C₅×#124	C₂×D₃	1	2	yes	—
299	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
300	C₅×#123	—	3	2	no	—
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	—	3	2	no	—
307	C₅×#123	—	3	2	no	—
308	C₅×#123	—	3	2	no	—
309	C₅×#123	C₂×D₃	1	2	yes	—
310	C₅×C₂²⋊Q₈	—	3	1	no	—
311	C₅×C₂²⋊Q₈	—	3	2	no	—
312	C₅×C₂²⋊Q₈	—	3	2	no	—
313	C₅×C₂²⋊Q₈	—	3	1	no	—
314	C₅×C₂²⋊Q₈	—	3	2	no	—
315	C₅×C₂²⋊Q₈	—	3	1	no	—
316	C₅×C₂²⋊Q₈	—	3	2	no	—
317	C₅×C₂²⋊Q₈	—	3	2	no	—
318	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
319	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
320	C₅×#121	—	3	1	no	—
321	C₅×#121	—	3	2	no	—
322	C₅×#121	—	3	2	no	—
323	C₅×#121	—	3	1	no	—
324	C₅×#121	—	3	2	no	—
325	C₅×#121	—	3	1	no	—
326	C₅×#121	—	3	2	no	—
327	C₅×#121	—	3	2	no	—
328	C₅×#121	—	3	2	no	—
329	C₅×#121	C₂×D₃	1	1	yes	characteristic
330	C₅×#120	—	3	2	no	—
331	C₅×#120	—	3	2	no	—
332	C₄×C₅×Q₈	—	3	1	no	—
333	C₄×C₅×Q₈	—	3	2	no	—
334	C₄×C₅×Q₈	—	3	1	no	—
335	C₄×C₅×Q₈	—	3	2	no	—
336	C₄×C₅×Q₈	—	3	1	no	—
337	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
338	C₄×C₅×D₄	—	3	2	no	—
339	C₄×C₅×D₄	—	3	1	no	—
340	C₄×C₅×D₄	—	3	2	no	—
341	C₄×C₅×D₄	—	3	2	no	—
342	C₄×C₅×D₄	—	3	2	no	—
343	C₄×C₅×D₄	—	3	1	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	C₂×D₃	1	1	yes	characteristic, complemented
352	C₅×#117	—	3	1	no	—
353	C₅×#117	—	3	1	no	—
354	C₅×#117	—	3	1	no	—
355	C₅×#117	—	3	1	no	—
356	C₅×#117	—	3	1	no	—
357	C₅×#117	—	3	2	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	1	no	—
363	C₅×#117	C₂×D₃	1	1	yes	characteristic
364	C₂×C₅×C₄⋊C₄	—	3	1	no	—
365	C₂×C₅×C₄⋊C₄	—	3	1	no	—
366	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
367	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
368	C₂×C₄²×C₅	—	3	2	no	—
369	C₂×C₄²×C₅	—	3	1	no	—
370	C₂×C₄²×C₅	—	3	1	no	—
371	C₂×C₄²×C₅	—	3	2	no	—
372	#3455	—	3	1	no	Sylow
373	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
374	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
375	C₂²×C₅×D₃	—	2	2	no	—
376	C₂²×C₅×D₃	—	4	1	no	—
377	C₂²×C₅×D₃	—	4	1	no	—
378	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
380	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
381	C₃×C₅×Q₈	—	2	2	no	—
382	C₃×C₅×Q₈	—	4	2	no	—
383	C₃×C₅×D₄	—	2	2	no	—
384	C₃×C₅×D₄	—	4	2	no	—
385	C₂×C₃×C₄×C₅	—	2	2	no	—
386	C₂×C₃×C₄×C₅	—	4	2	no	—
387	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
389	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
390	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
391	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
398	C₅×#67	—	4	2	no	—
399	C₅×#67	—	4	2	no	—
400	C₅×#67	—	4	2	no	—
401	C₂×C₅×Dic₃	—	2	2	no	—
402	C₂×C₅×Dic₃	—	2	4	no	—
403	C₂×C₅×Dic₃	—	4	2	no	—
404	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
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	C₅×D₁₂	—	2	4	no	—
414	C₅×D₁₂	—	2	2	no	—
415	C₅×D₁₂	—	4	2	no	—
416	C₄×C₅×D₃	—	2	2	no	—
417	C₄×C₅×D₃	—	2	2	no	—
418	C₄×C₅×D₃	—	2	2	no	—
419	C₄×C₅×D₃	—	2	4	no	—
420	C₄×C₅×D₃	—	4	2	no	—
421	C₄×C₅×D₃	—	4	1	no	—
422	C₄×C₅×D₃	—	4	2	no	—
423	C₄×C₅×D₃	—	4	1	no	—
424	C₄×C₅×D₃	—	4	1	no	—
425	C₄×C₅×D₃	—	4	1	no	—
426	C₄×C₅×D₃	#41	1	4	yes	—
427	C₅×Dic₆	—	2	2	no	—
428	C₅×Dic₆	—	4	2	no	—
429	C₂×#239	C₂²×C₅	1	1	yes	characteristic
430	C₂×#237	C₂²×C₅	1	1	yes	characteristic
431	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
432	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
433	C₃×#126	C₂²×C₅	1	2	yes	complemented
434	C₃×#124	C₂²×C₅	1	2	yes	—
435	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
436	C₃×#123	C₂²×C₅	1	2	yes	—
437	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
438	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
439	C₃×#121	C₂²×C₅	1	1	yes	characteristic
440	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
441	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₃×#117	C₂²×C₅	1	1	yes	characteristic
443	#947	C₂²×C₅	1	2	yes	—
444	#946	C₂²×C₅	1	2	yes	—
445	#946	C₂²×C₅	1	1	yes	characteristic
446	#946	C₂²×C₅	1	2	yes	complemented
447	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
448	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
449	#944	C₂²×C₅	1	1	yes	characteristic, complemented
450	#940	C₂²×C₅	1	1	yes	characteristic, complemented
451	#939	C₂²×C₅	1	2	yes	—
452	#938	C₂²×C₅	1	2	yes	—
453	#938	C₂²×C₅	1	1	yes	characteristic
454	#937	C₂²×C₅	1	2	yes	—
455	D₄×Dic₃	C₂²×C₅	1	2	yes	—
456	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
457	#930	C₂²×C₅	1	2	yes	—
458	#930	C₂²×C₅	1	1	yes	characteristic
459	#929	C₂²×C₅	1	2	yes	complemented
460	C₄×#67	C₂²×C₅	1	2	yes	—
461	#926	C₂²×C₅	1	1	yes	characteristic
462	#924	C₂²×C₅	1	1	yes	characteristic
463	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
464	#898	C₂²×C₅	1	2	yes	—
465	#898	C₂²×C₅	1	2	yes	complemented
466	#898	C₂²×C₅	1	2	yes	complemented
467	#897	C₂²×C₅	1	2	yes	—
468	#897	C₂²×C₅	1	1	yes	characteristic
469	#896	C₂²×C₅	1	2	yes	complemented
470	#895	C₂²×C₅	1	1	yes	characteristic
471	#894	C₂²×C₅	1	2	yes	—
472	#894	C₂²×C₅	1	2	yes	—
473	#893	C₂²×C₅	1	2	yes	—
474	#893	C₂²×C₅	1	2	yes	—
475	#893	C₂²×C₅	1	1	yes	characteristic, complemented
476	#892	C₂²×C₅	1	1	yes	characteristic
477	#892	C₂²×C₅	1	1	yes	characteristic
478	#892	C₂²×C₅	1	1	yes	characteristic
479	#892	C₂²×C₅	1	1	yes	characteristic
480	#892	C₂²×C₅	1	2	yes	complemented
481	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
482	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
483	#890	C₂²×C₅	1	2	yes	complemented
484	#890	C₂²×C₅	1	1	yes	characteristic, complemented
485	#890	C₂²×C₅	1	1	yes	characteristic, complemented
486	#889	C₂²×C₅	1	2	yes	complemented
487	#889	C₂²×C₅	1	2	yes	complemented
488	#887	C₂²×C₅	1	2	yes	complemented
489	#887	C₂²×C₅	1	1	yes	characteristic, complemented
490	#886	C₂²×C₅	1	2	yes	—
491	#886	C₂²×C₅	1	2	yes	complemented
492	#885	C₂²×C₅	1	2	yes	—
493	#885	C₂²×C₅	1	2	yes	—
494	#884	C₂²×C₅	1	2	yes	—
495	#884	C₂²×C₅	1	2	yes	—
496	#884	C₂²×C₅	1	2	yes	—
497	#883	C₂²×C₅	1	2	yes	—
498	#883	C₂²×C₅	1	2	yes	—
499	#883	C₂²×C₅	1	2	yes	complemented
500	#883	C₂²×C₅	1	2	yes	complemented
501	#882	C₂²×C₅	1	2	yes	—
502	#67⋊C₄	C₂²×C₅	1	2	yes	—
503	#67⋊C₄	C₂²×C₅	1	2	yes	—
504	#67⋊C₄	C₂²×C₅	1	2	yes	—
505	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
506	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
507	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
508	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
509	#879	C₂²×C₅	1	2	yes	—
510	#879	C₂²×C₅	1	2	yes	—
511	#879	C₂²×C₅	1	2	yes	complemented
512	#878	C₂²×C₅	1	2	yes	complemented
513	#877	C₂²×C₅	1	1	yes	characteristic
514	#877	C₂²×C₅	1	1	yes	characteristic
515	#877	C₂²×C₅	1	2	yes	complemented
516	#876	C₂²×C₅	1	2	yes	—
517	#875	C₂²×C₅	1	1	yes	characteristic, complemented
518	C₄×D₁₂	C₂²×C₅	1	2	yes	—
519	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
520	#872	C₂²×C₅	1	1	yes	characteristic
521	#872	C₂²×C₅	1	1	yes	characteristic
522	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
523	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
524	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
525	#870	C₂²×C₅	1	2	yes	complemented
526	#869	C₂²×C₅	1	1	yes	characteristic, complemented
527	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
528	C₂⁴×C₅	—	3	1	no	—
529	C₅×#41	—	6	4	no	—
530	C₅×#41	—	6	4	no	—
531	C₂×C₅×Q₈	—	3	1	no	—
532	C₂×C₅×Q₈	—	3	2	no	—
533	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
534	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
535	C₂×C₅×D₄	—	3	2	no	—
536	C₂×C₅×D₄	—	3	2	no	—
537	C₂×C₅×D₄	—	3	2	no	—
538	C₂×C₅×D₄	—	3	2	no	—
539	C₂×C₅×D₄	—	3	2	no	—
540	C₂×C₅×D₄	—	3	2	no	—
541	C₂×C₅×D₄	—	3	1	no	—
542	C₂×C₅×D₄	—	3	2	no	—
543	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
544	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
545	C₂²×C₄×C₅	—	3	1	no	—
546	C₂²×C₄×C₅	—	3	2	no	—
547	C₂²×C₄×C₅	—	3	1	no	—
548	C₂²×C₄×C₅	—	3	2	no	—
549	C₂²×C₄×C₅	—	3	2	no	—
550	C₂²×C₄×C₅	—	3	1	no	—
551	C₂²×C₄×C₅	—	3	1	no	—
552	C₂²×C₄×C₅	—	3	1	no	—
553	C₂²×C₄×C₅	—	3	1	no	—
554	C₂²×C₄×C₅	—	3	1	no	—
555	C₂²×C₄×C₅	—	3	1	no	—
556	C₂²×C₄×C₅	—	3	1	no	—
557	C₂²×C₄×C₅	—	3	2	no	—
558	C₂²×C₄×C₅	—	3	2	no	—
559	C₂²×C₄×C₅	—	6	4	no	—
560	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
561	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
562	C₅×C₄⋊C₄	—	3	1	no	—
563	C₅×C₄⋊C₄	—	3	1	no	—
564	C₅×C₄⋊C₄	—	3	1	no	—
565	C₅×C₄⋊C₄	—	3	1	no	—
566	C₅×C₄⋊C₄	—	3	1	no	—
567	C₅×C₄⋊C₄	—	3	1	no	—
568	C₅×C₄⋊C₄	—	3	1	no	—
569	C₅×C₄⋊C₄	—	3	1	no	—
570	C₅×C₄⋊C₄	—	3	2	no	—
571	C₅×C₄⋊C₄	—	3	2	no	—
572	C₅×C₄⋊C₄	—	3	2	no	—
573	C₅×C₄⋊C₄	—	3	2	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	2	no	—
578	C₅×C₄⋊C₄	—	3	2	no	—
579	C₅×C₄⋊C₄	—	3	2	no	—
580	C₅×C₄⋊C₄	—	3	2	no	—
581	C₅×C₄⋊C₄	—	3	2	no	—
582	C₅×C₄⋊C₄	—	3	2	no	—
583	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
584	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
585	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
586	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
587	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
588	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
589	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
590	C₅×C₂²⋊C₄	—	3	1	no	—
591	C₅×C₂²⋊C₄	—	3	1	no	—
592	C₅×C₂²⋊C₄	—	3	2	no	—
593	C₅×C₂²⋊C₄	—	3	2	no	—
594	C₅×C₂²⋊C₄	—	3	2	no	—
595	C₅×C₂²⋊C₄	—	3	1	no	—
596	C₅×C₂²⋊C₄	—	3	1	no	—
597	C₅×C₂²⋊C₄	—	3	1	no	—
598	C₅×C₂²⋊C₄	—	3	1	no	—
599	C₅×C₂²⋊C₄	—	3	2	no	—
600	C₅×C₂²⋊C₄	—	3	2	no	—
601	C₅×C₂²⋊C₄	—	3	2	no	—
602	C₅×C₂²⋊C₄	—	3	2	no	—
603	C₅×C₂²⋊C₄	—	3	2	no	—
604	C₅×C₂²⋊C₄	—	3	2	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	C₂²×D₃	1	1	yes	characteristic
610	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
611	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
612	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
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	C₄²×C₅	—	3	1	no	—
617	C₄²×C₅	—	3	1	no	—
618	C₄²×C₅	—	3	2	no	—
619	C₄²×C₅	—	3	2	no	—
620	C₄²×C₅	—	3	1	no	—
621	C₄²×C₅	—	3	1	no	—
622	C₄²×C₅	—	3	1	no	—
623	C₄²×C₅	—	3	1	no	—
624	C₄²×C₅	—	3	2	no	—
625	C₄²×C₅	—	3	2	no	—
626	C₄²×C₅	—	3	2	no	—
627	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
628	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
629	C₄²×C₅	C₂²×D₃	1	2	yes	—
630	#542	—	3	1	no	—
631	#542	—	3	1	no	—
632	#542	—	3	1	no	—
633	#542	C₅×D₃	1	1	yes	characteristic, complemented
634	#541	—	3	1	no	—
635	#541	—	3	1	no	—
636	#540	—	3	1	no	—
637	#540	—	3	1	no	—
638	#539	—	3	2	no	—
639	#539	—	3	2	no	—
640	#538	—	3	2	no	—
641	#538	—	3	2	no	—
642	#533	—	3	1	no	—
643	#532	—	3	1	no	—
644	#529	—	3	2	no	—
645	#529	—	3	2	no	—
646	#529	—	3	2	no	—
647	#529	—	3	2	no	—
648	#525	—	3	1	no	—
649	#525	—	3	1	no	—
650	C₄×#41	—	3	1	no	—
651	C₄×#41	—	3	1	no	—
652	C₂×#117	—	3	1	no	—
653	C₂²×C₃×C₅	—	2	2	no	—
654	C₂²×C₃×C₅	—	2	1	no	—
655	C₂²×C₃×C₅	—	2	2	no	—
656	C₂²×C₃×C₅	—	2	1	no	—
657	C₂²×C₃×C₅	—	2	2	no	—
658	C₂²×C₃×C₅	—	2	1	no	—
659	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
660	C₂×C₅×D₃	—	2	1	no	—
661	C₂×C₅×D₃	—	2	1	no	—
662	C₂×C₅×D₃	—	2	1	no	—
663	C₂×C₅×D₃	—	2	2	no	—
664	C₂×C₅×D₃	—	2	2	no	—
665	C₂×C₅×D₃	—	2	2	no	—
666	C₂×C₅×D₃	—	2	1	no	—
667	C₂×C₅×D₃	—	2	1	no	—
668	C₂×C₅×D₃	—	4	4	no	—
669	C₂×C₅×D₃	C₂×#41	1	2	yes	—
670	C₃×C₄×C₅	—	2	1	no	—
671	C₃×C₄×C₅	—	2	2	no	—
672	C₃×C₄×C₅	—	2	1	no	—
673	C₃×C₄×C₅	—	2	1	no	—
674	C₃×C₄×C₅	—	2	1	no	—
675	C₃×C₄×C₅	—	2	2	no	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	C₂×#41	1	2	yes	—
679	C₅×Dic₃	—	2	2	no	—
680	C₅×Dic₃	—	2	1	no	—
681	C₅×Dic₃	—	2	2	no	—
682	C₅×Dic₃	—	2	2	no	—
683	C₅×Dic₃	—	2	1	no	—
684	C₅×Dic₃	—	2	1	no	—
685	C₅×Dic₃	—	2	1	no	—
686	C₅×Dic₃	—	2	1	no	—
687	C₅×Dic₃	C₂×#41	1	2	yes	—
688	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
689	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
690	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
691	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
692	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
693	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
694	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
695	C₂×#67	C₂³×C₅	1	2	yes	—
696	C₂×#67	C₂³×C₅	1	2	yes	—
697	C₂×#67	C₂³×C₅	1	2	yes	—
698	C₂×#67	C₂³×C₅	1	2	yes	—
699	C₂×#67	C₂³×C₅	1	2	yes	—
700	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
701	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
702	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
703	#239	—	2	4	no	—
704	#237	—	2	4	no	—
705	C₂×D₁₂	C₂³×C₅	1	2	yes	—
706	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
707	C₂×D₁₂	C₂³×C₅	1	2	yes	—
708	C₂×C₄×D₃	—	2	4	no	—
709	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
710	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
711	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
713	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
714	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
715	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
716	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₄×D₃	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×Dic₆	C₂³×C₅	1	1	yes	characteristic
721	C₂×Dic₆	C₂³×C₅	1	2	yes	—
722	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
723	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
724	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
725	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
726	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
727	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
728	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
729	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
730	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
731	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
732	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
733	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
734	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
735	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
736	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
737	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
738	C₃×C₄²	C₂³×C₅	1	2	yes	—
739	#217	C₂³×C₅	1	1	yes	characteristic
740	#217	C₂³×C₅	1	1	yes	characteristic
741	#217	C₂³×C₅	1	2	yes	—
742	#217	C₂³×C₅	1	2	yes	—
743	#217	C₂³×C₅	1	2	yes	—
744	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
745	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
746	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
747	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
748	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
750	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
751	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
752	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
753	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
754	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
758	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
759	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
760	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
761	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
762	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
763	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
764	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
765	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
766	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
767	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
768	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
769	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
770	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
771	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
772	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
773	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
774	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
776	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
777	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
778	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
779	C₄×Dic₃	C₂³×C₅	1	2	yes	—
780	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
781	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
782	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
783	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
784	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
785	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₅	1	2	yes	—
787	C₄×Dic₃	C₂³×C₅	1	2	yes	—
788	C₄×Dic₃	C₂³×C₅	1	2	yes	—
789	C₄×Dic₃	C₂³×C₅	1	2	yes	—
790	C₂³×C₅	—	3	1	no	—
791	C₂³×C₅	—	3	1	no	—
792	C₂³×C₅	—	3	2	no	—
793	C₂³×C₅	—	6	2	no	—
794	C₂³×C₅	—	12	1	no	—
795	C₂³×C₅	—	12	1	no	—
796	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
797	C₂³×C₅	C₂³×D₃	1	2	yes	—
798	C₅×Q₈	—	2	2	no	—
799	C₅×Q₈	—	4	2	no	—
800	C₅×Q₈	—	6	2	no	—
801	C₅×Q₈	—	12	2	no	—
802	C₅×D₄	—	2	2	no	—
803	C₅×D₄	—	4	2	no	—
804	C₅×D₄	—	6	4	no	—
805	C₅×D₄	—	6	4	no	—
806	C₅×D₄	—	6	2	no	—
807	C₅×D₄	—	12	2	no	—
808	C₅×D₄	—	12	2	no	—
809	C₅×D₄	—	12	2	no	—
810	C₅×D₄	—	12	2	no	—
811	C₅×D₄	—	12	2	no	—
812	C₂×C₄×C₅	—	2	2	no	—
813	C₂×C₄×C₅	—	3	1	no	—
814	C₂×C₄×C₅	—	3	4	no	—
815	C₂×C₄×C₅	—	3	1	no	—
816	C₂×C₄×C₅	—	3	1	no	—
817	C₂×C₄×C₅	—	3	2	no	—
818	C₂×C₄×C₅	—	3	2	no	—
819	C₂×C₄×C₅	—	3	2	no	—
820	C₂×C₄×C₅	—	3	1	no	—
821	C₂×C₄×C₅	—	3	1	no	—
822	C₂×C₄×C₅	—	3	1	no	—
823	C₂×C₄×C₅	—	4	2	no	—
824	C₂×C₄×C₅	—	6	2	no	—
825	C₂×C₄×C₅	—	6	4	no	—
826	C₂×C₄×C₅	—	6	2	no	—
827	C₂×C₄×C₅	—	6	2	no	—
828	C₂×C₄×C₅	—	6	4	no	—
829	C₂×C₄×C₅	—	6	2	no	—
830	C₂×C₄×C₅	—	12	1	no	—
831	C₂×C₄×C₅	—	12	2	no	—
832	C₂×C₄×C₅	—	12	1	no	—
833	C₂×C₄×C₅	—	12	1	no	—
834	C₂×C₄×C₅	—	12	2	no	—
835	C₂×C₄×C₅	—	12	1	no	—
836	C₂×C₄×C₅	—	12	2	no	—
837	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
838	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
839	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
840	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
841	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
842	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
843	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
844	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
845	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
846	C₂×#41	—	3	1	no	—
847	C₂×#41	—	3	1	no	—
848	C₂³×C₄	—	3	1	no	—
849	C₄⋊Q₈	—	3	1	no	—
850	C₄⋊Q₈	—	3	1	no	—
851	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
852	#127	—	3	1	no	—
853	#126	—	3	2	no	—
854	#126	—	3	2	no	—
855	#126	—	3	2	no	—
856	#126	—	3	2	no	—
857	#126	—	3	2	no	—
858	#126	—	3	2	no	—
859	#126	—	3	2	no	—
860	#126	C₂×C₅×D₃	1	2	yes	complemented
861	#125	—	3	2	no	—
862	#125	—	3	2	no	—
863	#125	—	3	2	no	—
864	#125	—	3	1	no	—
865	#125	—	3	1	no	—
866	#125	—	3	2	no	—
867	#124	—	3	2	no	—
868	#124	—	3	2	no	—
869	#124	—	3	2	no	—
870	#124	—	3	1	no	—
871	#124	C₂×C₅×D₃	1	2	yes	—
872	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
873	#123	—	3	2	no	—
874	#123	—	3	2	no	—
875	#123	—	3	2	no	—
876	#123	—	3	2	no	—
877	#123	—	3	2	no	—
878	#123	—	3	2	no	—
879	#123	—	3	2	no	—
880	#123	—	3	2	no	—
881	#123	—	3	2	no	—
882	#123	C₂×C₅×D₃	1	2	yes	—
883	C₂²⋊Q₈	—	3	1	no	—
884	C₂²⋊Q₈	—	3	2	no	—
885	C₂²⋊Q₈	—	3	2	no	—
886	C₂²⋊Q₈	—	3	1	no	—
887	C₂²⋊Q₈	—	3	1	no	—
888	C₂²⋊Q₈	—	3	2	no	—
889	C₂²⋊Q₈	—	3	2	no	—
890	C₂²⋊Q₈	—	3	2	no	—
891	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
892	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
893	#121	—	3	1	no	—
894	#121	—	3	2	no	—
895	#121	—	3	2	no	—
896	#121	—	3	1	no	—
897	#121	—	3	2	no	—
898	#121	—	3	1	no	—
899	#121	—	3	2	no	—
900	#121	—	3	2	no	—
901	#121	—	3	2	no	—
902	#121	C₂×C₅×D₃	1	1	yes	characteristic
903	#120	—	3	2	no	—
904	#120	—	3	2	no	—
905	C₄×Q₈	—	3	1	no	—
906	C₄×Q₈	—	3	2	no	—
907	C₄×Q₈	—	3	1	no	—
908	C₄×Q₈	—	3	2	no	—
909	C₄×Q₈	—	3	1	no	—
910	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
911	C₄×D₄	—	3	1	no	—
912	C₄×D₄	—	3	2	no	—
913	C₄×D₄	—	3	2	no	—
914	C₄×D₄	—	3	2	no	—
915	C₄×D₄	—	3	1	no	—
916	C₄×D₄	—	3	2	no	—
917	C₄×D₄	—	3	2	no	—
918	C₄×D₄	—	3	2	no	—
919	C₄×D₄	—	3	2	no	—
920	C₄×D₄	—	3	2	no	—
921	C₄×D₄	—	3	2	no	—
922	C₄×D₄	—	3	2	no	—
923	C₄×D₄	—	3	1	no	—
924	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
925	#117	—	3	1	no	—
926	#117	—	3	1	no	—
927	#117	—	3	1	no	—
928	#117	—	3	1	no	—
929	#117	—	3	1	no	—
930	#117	—	3	2	no	—
931	#117	—	3	1	no	—
932	#117	—	3	1	no	—
933	#117	—	3	2	no	—
934	#117	—	3	1	no	—
935	#117	—	3	1	no	—
936	#117	C₂×C₅×D₃	1	1	yes	characteristic
937	C₂×C₄⋊C₄	—	3	1	no	—
938	C₂×C₄⋊C₄	—	3	1	no	—
939	C₂×C₂²⋊C₄	—	3	1	no	—
940	C₂×C₂²⋊C₄	—	3	1	no	—
941	C₂×C₄²	—	3	2	no	—
942	C₂×C₄²	—	3	1	no	—
943	C₂×C₄²	—	3	1	no	—
944	C₂×C₄²	—	3	2	no	—
945	C₂×C₃×C₅	—	4	1	no	—
946	C₂×C₃×C₅	—	4	2	no	—
947	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
948	C₂×C₃×C₅	#585	1	1	yes	characteristic
949	C₂×C₃×C₅	#585	1	1	yes	characteristic
950	C₅×D₃	—	2	2	no	—
951	C₅×D₃	—	4	2	no	—
952	C₅×D₃	—	4	1	no	—
953	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
954	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
955	C₂²×D₃	—	2	2	no	—
956	C₂²×D₃	—	4	1	no	—
957	C₂²×D₃	—	4	1	no	—
958	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
959	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
960	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
961	C₃×Q₈	—	2	2	no	—
962	C₃×Q₈	—	4	2	no	—
963	C₃×D₄	—	2	2	no	—
964	C₃×D₄	—	4	2	no	—
965	C₂×C₃×C₄	—	2	2	no	—
966	C₂×C₃×C₄	—	4	2	no	—
967	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
968	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
969	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
970	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
971	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
972	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
973	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
974	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
975	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
976	#67	—	2	4	no	—
977	#67	—	4	2	no	—
978	#67	—	4	2	no	—
979	#67	—	4	2	no	—
980	#67	—	4	2	no	—
981	C₂×Dic₃	—	2	2	no	—
982	C₂×Dic₃	—	2	4	no	—
983	C₂×Dic₃	—	4	2	no	—
984	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
985	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
986	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
987	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
988	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
989	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
990	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
991	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
992	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
993	D₁₂	—	2	4	no	—
994	D₁₂	—	2	2	no	—
995	D₁₂	—	4	2	no	—
996	C₄×D₃	—	2	2	no	—
997	C₄×D₃	—	2	2	no	—
998	C₄×D₃	—	2	2	no	—
999	C₄×D₃	—	2	4	no	—
1000	C₄×D₃	—	4	2	no	—
1001	C₄×D₃	—	4	1	no	—
1002	C₄×D₃	—	4	2	no	—
1003	C₄×D₃	—	4	1	no	—
1004	C₄×D₃	—	4	1	no	—
1005	C₄×D₃	—	4	1	no	—
1006	C₄×D₃	C₅×#41	1	4	yes	—
1007	Dic₆	—	2	2	no	—
1008	Dic₆	—	4	2	no	—
1009	C₂²×C₅	—	2	1	no	—
1010	C₂²×C₅	—	2	2	no	—
1011	C₂²×C₅	—	2	2	no	—
1012	C₂²×C₅	—	2	1	no	—
1013	C₂²×C₅	—	2	2	no	—
1014	C₂²×C₅	—	2	1	no	—
1015	C₂²×C₅	—	3	2	no	—
1016	C₂²×C₅	—	6	1	no	—
1017	C₂²×C₅	—	6	1	no	—
1018	C₂²×C₅	—	6	1	no	—
1019	C₂²×C₅	—	6	2	no	—
1020	C₂²×C₅	—	6	2	no	—
1021	C₂²×C₅	—	6	1	no	—
1022	C₂²×C₅	—	6	2	no	—
1023	C₂²×C₅	—	6	1	no	—
1024	C₂²×C₅	—	12	4	no	—
1025	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1026	C₄×C₅	—	2	1	no	—
1027	C₄×C₅	—	2	2	no	—
1028	C₄×C₅	—	2	1	no	—
1029	C₄×C₅	—	2	2	no	—
1030	C₄×C₅	—	2	2	no	—
1031	C₄×C₅	—	2	1	no	—
1032	C₄×C₅	—	2	1	no	—
1033	C₄×C₅	—	2	1	no	—
1034	C₄×C₅	—	3	2	no	—
1035	C₄×C₅	—	6	1	no	—
1036	C₄×C₅	—	6	2	no	—
1037	C₄×C₅	—	6	1	no	—
1038	C₄×C₅	—	6	1	no	—
1039	C₄×C₅	—	6	1	no	—
1040	C₄×C₅	—	6	1	no	—
1041	C₄×C₅	—	6	2	no	—
1042	C₄×C₅	—	6	2	no	—
1043	C₄×C₅	D₃×#41	1	2	yes	—
1044	C₂⁴	—	3	1	no	—
1045	#41	—	6	4	no	—
1046	#41	—	6	4	no	—
1047	C₂×Q₈	—	3	1	no	—
1048	C₂×Q₈	—	3	2	no	—
1049	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1050	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
1051	C₂×D₄	—	3	2	no	—
1052	C₂×D₄	—	3	2	no	—
1053	C₂×D₄	—	3	2	no	—
1054	C₂×D₄	—	3	2	no	—
1055	C₂×D₄	—	3	2	no	—
1056	C₂×D₄	—	3	2	no	—
1057	C₂×D₄	—	3	1	no	—
1058	C₂×D₄	—	3	2	no	—
1059	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1060	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1061	C₂²×C₄	—	3	1	no	—
1062	C₂²×C₄	—	3	2	no	—
1063	C₂²×C₄	—	3	1	no	—
1064	C₂²×C₄	—	3	2	no	—
1065	C₂²×C₄	—	3	2	no	—
1066	C₂²×C₄	—	3	1	no	—
1067	C₂²×C₄	—	3	1	no	—
1068	C₂²×C₄	—	3	1	no	—
1069	C₂²×C₄	—	3	1	no	—
1070	C₂²×C₄	—	3	1	no	—
1071	C₂²×C₄	—	3	1	no	—
1072	C₂²×C₄	—	3	1	no	—
1073	C₂²×C₄	—	3	2	no	—
1074	C₂²×C₄	—	3	2	no	—
1075	C₂²×C₄	—	6	4	no	—
1076	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1077	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1078	C₄⋊C₄	—	3	1	no	—
1079	C₄⋊C₄	—	3	1	no	—
1080	C₄⋊C₄	—	3	1	no	—
1081	C₄⋊C₄	—	3	1	no	—
1082	C₄⋊C₄	—	3	1	no	—
1083	C₄⋊C₄	—	3	1	no	—
1084	C₄⋊C₄	—	3	1	no	—
1085	C₄⋊C₄	—	3	1	no	—
1086	C₄⋊C₄	—	3	2	no	—
1087	C₄⋊C₄	—	3	2	no	—
1088	C₄⋊C₄	—	3	2	no	—
1089	C₄⋊C₄	—	3	2	no	—
1090	C₄⋊C₄	—	3	2	no	—
1091	C₄⋊C₄	—	3	2	no	—
1092	C₄⋊C₄	—	3	2	no	—
1093	C₄⋊C₄	—	3	2	no	—
1094	C₄⋊C₄	—	3	2	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	2	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1100	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1101	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1102	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1103	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1104	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1105	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1106	C₂²⋊C₄	—	3	1	no	—
1107	C₂²⋊C₄	—	3	1	no	—
1108	C₂²⋊C₄	—	3	2	no	—
1109	C₂²⋊C₄	—	3	2	no	—
1110	C₂²⋊C₄	—	3	2	no	—
1111	C₂²⋊C₄	—	3	1	no	—
1112	C₂²⋊C₄	—	3	1	no	—
1113	C₂²⋊C₄	—	3	1	no	—
1114	C₂²⋊C₄	—	3	1	no	—
1115	C₂²⋊C₄	—	3	2	no	—
1116	C₂²⋊C₄	—	3	2	no	—
1117	C₂²⋊C₄	—	3	2	no	—
1118	C₂²⋊C₄	—	3	2	no	—
1119	C₂²⋊C₄	—	3	2	no	—
1120	C₂²⋊C₄	—	3	2	no	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	2	no	—
1123	C₂²⋊C₄	—	3	2	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1127	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1128	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1129	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1130	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1131	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1132	C₄²	—	3	1	no	—
1133	C₄²	—	3	1	no	—
1134	C₄²	—	3	2	no	—
1135	C₄²	—	3	2	no	—
1136	C₄²	—	3	1	no	—
1137	C₄²	—	3	1	no	—
1138	C₄²	—	3	1	no	—
1139	C₄²	—	3	1	no	—
1140	C₄²	—	3	2	no	—
1141	C₄²	—	3	2	no	—
1142	C₄²	—	3	2	no	—
1143	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1144	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1145	C₄²	C₂²×C₅×D₃	1	2	yes	—
1146	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
1147	C₂²×C₃	—	2	2	no	—
1148	C₂²×C₃	—	2	1	no	—
1149	C₂²×C₃	—	2	2	no	—
1150	C₂²×C₃	—	2	1	no	—
1151	C₂²×C₃	—	2	2	no	—
1152	C₂²×C₃	—	2	1	no	—
1153	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1154	C₂×D₃	—	2	1	no	—
1155	C₂×D₃	—	2	1	no	—
1156	C₂×D₃	—	2	1	no	—
1157	C₂×D₃	—	2	2	no	—
1158	C₂×D₃	—	2	2	no	—
1159	C₂×D₃	—	2	2	no	—
1160	C₂×D₃	—	2	1	no	—
1161	C₂×D₃	—	2	1	no	—
1162	C₂×D₃	—	4	4	no	—
1163	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1164	C₃×C₄	—	2	1	no	—
1165	C₃×C₄	—	2	2	no	—
1166	C₃×C₄	—	2	1	no	—
1167	C₃×C₄	—	2	1	no	—
1168	C₃×C₄	—	2	1	no	—
1169	C₃×C₄	—	2	2	no	—
1170	C₃×C₄	—	2	1	no	—
1171	C₃×C₄	—	2	2	no	—
1172	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1173	Dic₃	—	2	2	no	—
1174	Dic₃	—	2	1	no	—
1175	Dic₃	—	2	2	no	—
1176	Dic₃	—	2	2	no	—
1177	Dic₃	—	2	1	no	—
1178	Dic₃	—	2	1	no	—
1179	Dic₃	—	2	1	no	—
1180	Dic₃	—	2	1	no	—
1181	Dic₃	C₂×C₅×#41	1	2	yes	—
1182	C₂×C₅	—	4	1	no	—
1183	C₂×C₅	—	4	2	no	—
1184	C₂×C₅	—	6	2	no	—
1185	C₂×C₅	—	12	1	no	—
1186	C₂×C₅	—	12	2	no	—
1187	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1188	C₂×C₅	#5966	1	1	yes	characteristic
1189	C₂×C₅	#5968	1	1	yes	characteristic
1190	C₂³	—	3	1	no	—
1191	C₂³	—	3	1	no	—
1192	C₂³	—	3	2	no	—
1193	C₂³	—	6	2	no	—
1194	C₂³	—	12	1	no	—
1195	C₂³	—	12	1	no	—
1196	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1197	C₂³	C₂³×C₅×D₃	1	2	yes	—
1198	Q₈	—	2	2	no	—
1199	Q₈	—	4	2	no	—
1200	Q₈	—	6	2	no	—
1201	Q₈	—	12	2	no	—
1202	D₄	—	2	2	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	6	4	no	—
1205	D₄	—	6	4	no	—
1206	D₄	—	6	2	no	—
1207	D₄	—	12	2	no	—
1208	D₄	—	12	2	no	—
1209	D₄	—	12	2	no	—
1210	D₄	—	12	2	no	—
1211	D₄	—	12	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	3	1	no	—
1214	C₂×C₄	—	3	4	no	—
1215	C₂×C₄	—	3	1	no	—
1216	C₂×C₄	—	3	1	no	—
1217	C₂×C₄	—	3	2	no	—
1218	C₂×C₄	—	3	2	no	—
1219	C₂×C₄	—	3	2	no	—
1220	C₂×C₄	—	3	1	no	—
1221	C₂×C₄	—	3	1	no	—
1222	C₂×C₄	—	3	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	6	2	no	—
1225	C₂×C₄	—	6	4	no	—
1226	C₂×C₄	—	6	2	no	—
1227	C₂×C₄	—	6	2	no	—
1228	C₂×C₄	—	6	4	no	—
1229	C₂×C₄	—	6	2	no	—
1230	C₂×C₄	—	12	1	no	—
1231	C₂×C₄	—	12	2	no	—
1232	C₂×C₄	—	12	1	no	—
1233	C₂×C₄	—	12	1	no	—
1234	C₂×C₄	—	12	2	no	—
1235	C₂×C₄	—	12	1	no	—
1236	C₂×C₄	—	12	2	no	—
1237	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1238	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1239	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1240	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1241	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1242	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1243	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1244	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1245	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1246	C₂×C₃	—	4	1	no	—
1247	C₂×C₃	—	4	2	no	—
1248	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1249	C₂×C₃	C₅×#585	1	1	yes	characteristic
1250	C₂×C₃	C₅×#585	1	1	yes	characteristic
1251	D₃	—	2	2	no	—
1252	D₃	—	4	1	no	—
1253	D₃	—	4	2	no	—
1254	C₅	#86523	1	1	yes	characteristic, direct product factor, Sylow
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	2	2	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	3	2	no	—
1262	C₂²	—	6	1	no	—
1263	C₂²	—	6	1	no	—
1264	C₂²	—	6	1	no	—
1265	C₂²	—	6	2	no	—
1266	C₂²	—	6	2	no	—
1267	C₂²	—	6	1	no	—
1268	C₂²	—	6	2	no	—
1269	C₂²	—	6	1	no	—
1270	C₂²	—	12	4	no	—
1271	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1272	C₄	—	2	1	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	2	2	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	2	1	no	—
1279	C₄	—	2	1	no	—
1280	C₄	—	3	2	no	—
1281	C₄	—	6	1	no	—
1282	C₄	—	6	2	no	—
1283	C₄	—	6	1	no	—
1284	C₄	—	6	1	no	—
1285	C₄	—	6	1	no	—
1286	C₄	—	6	1	no	—
1287	C₄	—	6	2	no	—
1288	C₄	—	6	2	no	—
1289	C₄	C₅×D₃×#41	1	2	yes	—
1290	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
1291	C₂	—	4	1	no	—
1292	C₂	—	4	2	no	—
1293	C₂	—	6	2	no	—
1294	C₂	—	12	1	no	—
1295	C₂	—	12	2	no	—
1296	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1297	C₂	C₅×#5966	1	1	yes	characteristic
1298	C₂	C₅×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#542	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#542	D₃
hypocenter	C₃	C₅×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#542

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₅×#5733	C₂	semidirect
3. C₅×#5728	C₂	semidirect
4. C₅×#5707	C₂	semidirect
5. C₅×#5706	C₂	semidirect
6. C₅×#5682	C₂	semidirect
7. C₅×#5680	C₂	semidirect
8. C₅×#5678	C₂	semidirect
9. C₅×#5668	C₂	semidirect
10. C₅×#5657	C₂	semidirect
11. C₅×#5649	C₂	semidirect
12. C₅×#5638	C₂	semidirect
13. C₅×#5627	C₂	semidirect
14. C₅×#5625	C₂	semidirect
15. C₅×#5624	C₂	semidirect
16. C₅×#5619	C₂	semidirect
17. C₅×#5606	C₂	semidirect
18. C₅×#5583	C₂	semidirect
19. C₄×C₅×#239	C₂	semidirect
20. C₅×#5562	C₂	semidirect
21. C₄×C₅×#237	C₂	semidirect
22. C₅×#5534	C₂	semidirect
23. C₅×D₃×#117	C₂	semidirect
28. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#124	C₂²	semidirect
34. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
37. C₃×C₄×C₅×D₄	C₂²	semidirect
42. C₅×#946	C₂²	semidirect
43. C₅×Q₈×Dic₃	C₂²	semidirect
44. C₅×Q₈×Dic₃	C₂²	semidirect
45. C₅×#944	C₂²	semidirect
46. C₅×#940	C₂²	semidirect
52. C₅×D₄×Dic₃	C₂²	semidirect
55. C₅×#929	C₂²	semidirect
59. C₂×C₄×C₅×Dic₃	C₂²	semidirect
61. C₅×#898	C₂²	semidirect
62. C₅×#898	C₂²	semidirect
65. C₅×#896	C₂²	semidirect
71. C₅×#893	C₂²	semidirect
76. C₅×#892	C₂²	semidirect
79. C₅×#890	C₂²	semidirect
80. C₅×#890	C₂²	semidirect
81. C₅×#890	C₂²	semidirect
82. C₅×#889	C₂²	semidirect
83. C₅×#889	C₂²	semidirect
84. C₅×#887	C₂²	semidirect
85. C₅×#887	C₂²	semidirect
87. C₅×#886	C₂²	semidirect
95. C₅×#883	C₂²	semidirect
96. C₅×#883	C₂²	semidirect
101. C₅×#67⋊C₄	C₂²	semidirect
102. C₅×#67⋊C₄	C₂²	semidirect
107. C₅×#879	C₂²	semidirect
108. C₅×#878	C₂²	semidirect
111. C₅×#877	C₂²	semidirect
113. C₅×#875	C₂²	semidirect
115. C₄×C₅×D₁₂	C₂²	semidirect
120. C₄²×C₅×D₃	C₂²	semidirect
121. C₅×#870	C₂²	semidirect
122. C₅×#869	C₂²	semidirect
123. C₄×C₅×Dic₆	C₂²	semidirect
124. #86523	C₅	direct (N × H)
128. C₅×#542	D₃	semidirect
250. C₃×#542	C₂×C₅	semidirect
251. #5733	C₂×C₅	semidirect
252. #5728	C₂×C₅	semidirect
253. #5707	C₂×C₅	semidirect
254. #5706	C₂×C₅	semidirect
255. #5682	C₂×C₅	semidirect
256. #5680	C₂×C₅	semidirect
257. #5678	C₂×C₅	semidirect
258. #5668	C₂×C₅	semidirect
259. #5657	C₂×C₅	semidirect
260. #5649	C₂×C₅	semidirect
261. #5638	C₂×C₅	semidirect
262. #5627	C₂×C₅	semidirect
263. #5625	C₂×C₅	semidirect
264. #5624	C₂×C₅	semidirect
265. #5619	C₂×C₅	semidirect
266. #5606	C₂×C₅	semidirect
267. #5583	C₂×C₅	semidirect
268. C₄×#239	C₂×C₅	semidirect
269. #5562	C₂×C₅	semidirect
270. C₄×#237	C₂×C₅	semidirect
271. #5534	C₂×C₅	semidirect
272. D₃×#117	C₂×C₅	semidirect
278. C₅×C₄⋊Q₈	C₂×D₃	semidirect
287. C₅×#126	C₂×D₃	semidirect
299. C₅×#124	C₂×D₃	semidirect
319. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
337. C₄×C₅×Q₈	C₂×D₃	semidirect
351. C₄×C₅×D₄	C₂×D₃	semidirect
432. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
433. C₃×#126	C₂²×C₅	semidirect
435. C₃×#124	C₂²×C₅	semidirect
438. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
440. C₃×C₄×Q₈	C₂²×C₅	semidirect
441. C₃×C₄×D₄	C₂²×C₅	semidirect
446. #946	C₂²×C₅	semidirect
447. Q₈×Dic₃	C₂²×C₅	semidirect
448. Q₈×Dic₃	C₂²×C₅	semidirect
449. #944	C₂²×C₅	semidirect
450. #940	C₂²×C₅	semidirect
456. D₄×Dic₃	C₂²×C₅	semidirect
459. #929	C₂²×C₅	semidirect
463. C₂×C₄×Dic₃	C₂²×C₅	semidirect
465. #898	C₂²×C₅	semidirect
466. #898	C₂²×C₅	semidirect
469. #896	C₂²×C₅	semidirect
475. #893	C₂²×C₅	semidirect
480. #892	C₂²×C₅	semidirect
483. #890	C₂²×C₅	semidirect
484. #890	C₂²×C₅	semidirect
485. #890	C₂²×C₅	semidirect
486. #889	C₂²×C₅	semidirect
487. #889	C₂²×C₅	semidirect
488. #887	C₂²×C₅	semidirect
489. #887	C₂²×C₅	semidirect
491. #886	C₂²×C₅	semidirect
499. #883	C₂²×C₅	semidirect
500. #883	C₂²×C₅	semidirect
505. #67⋊C₄	C₂²×C₅	semidirect
506. #67⋊C₄	C₂²×C₅	semidirect
511. #879	C₂²×C₅	semidirect
512. #878	C₂²×C₅	semidirect
515. #877	C₂²×C₅	semidirect
517. #875	C₂²×C₅	semidirect
519. C₄×D₁₂	C₂²×C₅	semidirect
524. C₄²×D₃	C₂²×C₅	semidirect
525. #870	C₂²×C₅	semidirect
526. #869	C₂²×C₅	semidirect
527. C₄×Dic₆	C₂²×C₅	semidirect
633. #542	C₅×D₃	semidirect
851. C₄⋊Q₈	C₂×C₅×D₃	semidirect
860. #126	C₂×C₅×D₃	semidirect
872. #124	C₂×C₅×D₃	semidirect
892. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
910. C₄×Q₈	C₂×C₅×D₃	semidirect
924. C₄×D₄	C₂×C₅×D₃	semidirect
1146. C₃×C₅	#3455	semidirect
1254. C₅	#86523	direct (N × H)
1290. C₃	C₅×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#542	2
C₅×#5733	2
C₅×#5728	2
C₅×#5707	2
C₅×#5706	2
C₅×#5682	2
C₅×#5680	2
C₅×#5678	2
C₅×#5668	2
C₅×#5657	2
C₅×#5649	2
C₅×#5638	2
C₅×#5627	2
C₅×#5625	2
C₅×#5624	2
C₅×#5619	2
C₅×#5606	2
C₅×#5583	2
C₄×C₅×#239	2
C₅×#5562	2
C₄×C₅×#237	2
C₅×#5534	2
C₅×D₃×#117	2
C₅×#3455	3
#86523	5

Subgroups — C5×#86523 #14481508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86523 #14481508