Subgroups — C₃×#10618033 #14495595

Order 1920.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1068 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	C₃×#66046	C₂	1	2	yes	maximal, complemented
3	C₃×#66046	C₂	1	2	yes	maximal, complemented
4	C₃×#66033	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66018	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#66006	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#66001	C₂	1	2	yes	maximal, complemented
9	C₃×#65985	C₂	1	2	yes	maximal, complemented
10	C₃×#65980	C₂	1	2	yes	maximal, complemented
11	C₃×#65955	C₂	1	2	yes	maximal, complemented
12	C₃×#65912	C₂	1	2	yes	maximal, complemented
13	C₃×#65891	C₂	1	2	yes	maximal, complemented
14	C₃×#65872	C₂	1	2	yes	maximal, complemented
15	C₃×#65872	C₂	1	2	yes	maximal, complemented
16	C₃×#65862	C₂	1	2	yes	maximal, complemented
17	C₃×#65851	C₂	1	2	yes	maximal, complemented
18	C₃×#65813	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
20	#10618033	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃×C₅×#126	C₂²	1	2	yes	—
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₂²	1	1	yes	characteristic
24	C₃×C₅×#123	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×#4092	C₂²	1	2	yes	—
33	C₃×#4090	C₂²	1	2	yes	—
34	C₃×#4085	C₂²	1	2	yes	—
35	C₃×#4085	C₂²	1	2	yes	—
36	C₃×#4084	C₂²	1	2	yes	—
37	C₃×#4082	C₂²	1	2	yes	—
38	C₃×#4081	C₂²	1	2	yes	—
39	C₃×#4081	C₂²	1	2	yes	—
40	C₃×#4076	C₂²	1	1	yes	characteristic
41	C₃×#4075	C₂²	1	2	yes	—
42	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
43	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
44	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
45	C₃×#4072	C₂²	1	2	yes	—
46	C₃×#4072	C₂²	1	1	yes	characteristic
47	C₃×#4072	C₂²	1	1	yes	characteristic
48	C₃×#4070	C₂²	1	2	yes	—
49	C₃×#4070	C₂²	1	1	yes	characteristic
50	C₃×#4070	C₂²	1	2	yes	—
51	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
52	C₃×#4044	C₂²	1	2	yes	—
53	C₃×#4044	C₂²	1	2	yes	—
54	C₃×#4044	C₂²	1	2	yes	—
55	C₃×#4043	C₂²	1	2	yes	—
56	C₃×#4043	C₂²	1	2	yes	—
57	C₃×#4042	C₂²	1	2	yes	—
58	C₃×#4042	C₂²	1	2	yes	—
59	C₃×#4042	C₂²	1	2	yes	—
60	C₃×#4040	C₂²	1	2	yes	—
61	C₃×#4036	C₂²	1	2	yes	—
62	C₃×#4036	C₂²	1	2	yes	—
63	C₃×#4036	C₂²	1	2	yes	—
64	C₃×#4035	C₂²	1	2	yes	—
65	C₃×#4035	C₂²	1	2	yes	—
66	C₃×#4035	C₂²	1	2	yes	—
67	C₃×#4035	C₂²	1	2	yes	—
68	C₃×#4035	C₂²	1	2	yes	—
69	C₃×#4034	C₂²	1	2	yes	—
70	C₃×#4034	C₂²	1	2	yes	—
71	C₃×#4034	C₂²	1	2	yes	—
72	C₃×#4032	C₂²	1	2	yes	—
73	C₃×#4032	C₂²	1	2	yes	—
74	C₃×#4031	C₂²	1	2	yes	—
75	C₃×#4031	C₂²	1	2	yes	—
76	C₃×#4031	C₂²	1	2	yes	—
77	C₃×#4030	C₂²	1	2	yes	—
78	C₃×#4029	C₂²	1	2	yes	—
79	C₃×#4029	C₂²	1	2	yes	—
80	C₃×#4029	C₂²	1	2	yes	—
81	C₃×#4025	C₂²	1	2	yes	—
82	C₃×#4025	C₂²	1	2	yes	—
83	C₃×#4025	C₂²	1	2	yes	—
84	C₃×#4025	C₂²	1	2	yes	—
85	C₃×#4025	C₂²	1	2	yes	—
86	C₃×#4024	C₂²	1	2	yes	—
87	C₃×#4024	C₂²	1	2	yes	—
88	C₃×#4024	C₂²	1	2	yes	—
89	C₃×#4024	C₂²	1	2	yes	—
90	C₃×#4024	C₂²	1	2	yes	—
91	C₃×#4024	C₂²	1	2	yes	—
92	C₃×#4022	C₂²	1	2	yes	—
93	C₃×#4021	C₂²	1	1	yes	characteristic
94	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
95	C₃×#4018	C₂²	1	2	yes	—
96	C₃×#4018	C₂²	1	2	yes	—
97	C₃×C₄²×D₅	C₂²	1	2	yes	—
98	C₃×#4016	C₂²	1	1	yes	characteristic
99	C₃×#4016	C₂²	1	1	yes	characteristic
100	C₃×#4016	C₂²	1	1	yes	characteristic
101	C₃×#4015	C₂²	1	1	yes	characteristic
102	C₃×#4015	C₂²	1	1	yes	characteristic
103	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
104	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
105	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
106	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
107	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
108	C₃×#3531	—	5	1	no	maximal, Hall
109	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
110	#66046	C₂×C₃	1	2	yes	complemented
111	#66046	C₂×C₃	1	2	yes	complemented
112	#66033	C₂×C₃	1	1	yes	characteristic, complemented
113	C₅⋊#564	C₂×C₃	1	1	yes	characteristic, complemented
114	#66018	C₂×C₃	1	1	yes	characteristic, complemented
115	#66006	C₂×C₃	1	1	yes	characteristic, complemented
116	#66001	C₂×C₃	1	2	yes	complemented
117	#65985	C₂×C₃	1	2	yes	complemented
118	#65980	C₂×C₃	1	2	yes	complemented
119	#65955	C₂×C₃	1	2	yes	complemented
120	#65912	C₂×C₃	1	2	yes	complemented
121	#65891	C₂×C₃	1	2	yes	complemented
122	#65872	C₂×C₃	1	2	yes	complemented
123	#65872	C₂×C₃	1	2	yes	complemented
124	#65862	C₂×C₃	1	2	yes	complemented
125	#65851	C₂×C₃	1	2	yes	complemented
126	#65813	C₂×C₃	1	1	yes	characteristic, complemented
127	#65804	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
133	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
136	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
139	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
140	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
144	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
145	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
146	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
147	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
148	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
149	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₃×C₄²×C₅	C₂³	1	2	yes	—
163	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
166	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
167	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
168	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
169	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
170	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
171	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
172	C₃×#685	C₂³	1	2	yes	—
173	C₃×#685	C₂³	1	2	yes	—
174	C₃×#685	C₂³	1	2	yes	—
175	C₃×#685	C₂³	1	2	yes	—
176	C₃×#685	C₂³	1	2	yes	—
177	C₃×#685	C₂³	1	2	yes	—
178	C₃×#685	C₂³	1	2	yes	—
179	C₃×#685	C₂³	1	2	yes	—
180	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
181	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
182	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
184	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
189	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
191	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₃×#683	C₂³	1	2	yes	—
193	C₃×#683	C₂³	1	2	yes	—
194	C₃×#683	C₂³	1	2	yes	—
195	C₃×#683	C₂³	1	2	yes	—
196	C₃×#683	C₂³	1	2	yes	—
197	C₃×#683	C₂³	1	2	yes	—
198	C₃×#683	C₂³	1	2	yes	—
199	C₃×#683	C₂³	1	2	yes	—
200	C₃×#683	C₂³	1	2	yes	—
201	C₃×#683	C₂³	1	2	yes	—
202	C₃×#683	C₂³	1	2	yes	—
203	C₃×#683	C₂³	1	2	yes	—
204	C₃×#683	C₂³	1	2	yes	—
205	C₃×#683	C₂³	1	2	yes	—
206	C₃×#683	C₂³	1	2	yes	—
207	C₃×#683	C₂³	1	2	yes	—
208	C₃×C₄×Dic₅	C₂³	1	2	yes	—
209	C₃×C₄×Dic₅	C₂³	1	2	yes	—
210	C₃×C₄×Dic₅	C₂³	1	2	yes	—
211	C₃×C₄×Dic₅	C₂³	1	2	yes	—
212	C₃×C₄×Dic₅	C₂³	1	2	yes	—
213	C₃×C₄×Dic₅	C₂³	1	2	yes	—
214	C₃×C₄×Dic₅	C₂³	1	2	yes	—
215	C₃×#564	—	5	1	no	—
216	C₃×#563	—	5	2	no	—
217	C₃×#563	—	5	2	no	—
218	C₃×#563	—	5	1	no	—
219	C₃×#563	—	5	1	no	—
220	C₃×#563	—	5	2	no	—
221	C₃×#563	—	5	2	no	—
222	C₃×#562	—	5	1	no	—
223	C₃×#562	—	5	2	no	—
224	C₃×#562	—	5	2	no	—
225	C₃×#533	—	5	2	no	—
226	C₃×#533	—	5	2	no	—
227	C₃×#533	—	5	1	no	—
228	C₃×#529	—	5	2	no	—
229	C₃×#529	—	5	2	no	—
230	C₃×#529	—	5	2	no	—
231	C₃×#529	—	5	2	no	—
232	C₃×#529	—	5	1	no	—
233	C₃×#529	D₅	1	1	yes	characteristic, complemented
234	C₅×#126	C₂²×C₃	1	2	yes	—
235	C₅×#125	C₂²×C₃	1	1	yes	characteristic
236	C₅×#124	C₂²×C₃	1	1	yes	characteristic
237	C₅×#123	C₂²×C₃	1	2	yes	—
238	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
239	C₅×#121	C₂²×C₃	1	1	yes	characteristic
240	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
241	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
242	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
243	C₅×#117	C₂²×C₃	1	2	yes	—
244	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
245	#4092	C₂²×C₃	1	2	yes	—
246	#4090	C₂²×C₃	1	2	yes	—
247	#4085	C₂²×C₃	1	2	yes	—
248	#4085	C₂²×C₃	1	2	yes	—
249	#4084	C₂²×C₃	1	2	yes	—
250	#4082	C₂²×C₃	1	2	yes	—
251	#4081	C₂²×C₃	1	2	yes	—
252	#4081	C₂²×C₃	1	2	yes	—
253	#4076	C₂²×C₃	1	1	yes	characteristic
254	#4075	C₂²×C₃	1	2	yes	—
255	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
256	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
257	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
258	#4072	C₂²×C₃	1	1	yes	characteristic
259	#4072	C₂²×C₃	1	1	yes	characteristic
260	#4072	C₂²×C₃	1	2	yes	—
261	#4070	C₂²×C₃	1	2	yes	—
262	#4070	C₂²×C₃	1	2	yes	—
263	#4070	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
265	#4044	C₂²×C₃	1	2	yes	—
266	#4044	C₂²×C₃	1	2	yes	—
267	#4044	C₂²×C₃	1	2	yes	—
268	#4043	C₂²×C₃	1	2	yes	—
269	#4043	C₂²×C₃	1	2	yes	—
270	#4042	C₂²×C₃	1	2	yes	—
271	#4042	C₂²×C₃	1	2	yes	—
272	#4042	C₂²×C₃	1	2	yes	—
273	#4040	C₂²×C₃	1	2	yes	—
274	#4036	C₂²×C₃	1	2	yes	—
275	#4036	C₂²×C₃	1	2	yes	—
276	#4036	C₂²×C₃	1	2	yes	—
277	#4035	C₂²×C₃	1	2	yes	—
278	#4035	C₂²×C₃	1	2	yes	—
279	#4035	C₂²×C₃	1	2	yes	—
280	#4035	C₂²×C₃	1	2	yes	—
281	#4035	C₂²×C₃	1	2	yes	—
282	#4034	C₂²×C₃	1	2	yes	—
283	#4034	C₂²×C₃	1	2	yes	—
284	#4034	C₂²×C₃	1	2	yes	—
285	#4032	C₂²×C₃	1	2	yes	—
286	#4032	C₂²×C₃	1	2	yes	—
287	#4031	C₂²×C₃	1	2	yes	—
288	#4031	C₂²×C₃	1	2	yes	—
289	#4031	C₂²×C₃	1	2	yes	—
290	#4030	C₂²×C₃	1	2	yes	—
291	#4029	C₂²×C₃	1	2	yes	—
292	#4029	C₂²×C₃	1	2	yes	—
293	#4029	C₂²×C₃	1	2	yes	—
294	#4025	C₂²×C₃	1	2	yes	—
295	#4025	C₂²×C₃	1	2	yes	—
296	#4025	C₂²×C₃	1	2	yes	—
297	#4025	C₂²×C₃	1	2	yes	—
298	#4025	C₂²×C₃	1	2	yes	—
299	#4024	C₂²×C₃	1	2	yes	—
300	#4024	C₂²×C₃	1	2	yes	—
301	#4024	C₂²×C₃	1	2	yes	—
302	#4024	C₂²×C₃	1	2	yes	—
303	#4024	C₂²×C₃	1	2	yes	—
304	#4024	C₂²×C₃	1	2	yes	—
305	#4022	C₂²×C₃	1	2	yes	—
306	#4021	C₂²×C₃	1	1	yes	characteristic
307	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
308	#4018	C₂²×C₃	1	2	yes	—
309	#4018	C₂²×C₃	1	2	yes	—
310	C₄²×D₅	C₂²×C₃	1	2	yes	—
311	#4016	C₂²×C₃	1	1	yes	characteristic
312	#4016	C₂²×C₃	1	1	yes	characteristic
313	#4016	C₂²×C₃	1	1	yes	characteristic
314	#4015	C₂²×C₃	1	1	yes	characteristic
315	#4015	C₂²×C₃	1	1	yes	characteristic
316	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
317	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
318	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
319	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
320	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
321	#3531	—	5	1	no	Sylow
322	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
323	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
324	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
325	C₃×C₅×Q₈	—	4	1	no	—
326	C₃×C₅×D₄	—	4	2	no	—
327	C₃×C₅×D₄	—	4	1	no	—
328	C₂×C₃×C₄×C₅	—	2	2	no	—
329	C₂×C₃×C₄×C₅	—	2	4	no	—
330	C₂×C₃×C₄×C₅	—	4	1	no	—
331	C₂×C₃×C₄×C₅	—	4	1	no	—
332	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
333	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
334	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
335	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
336	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
339	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
340	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₃×C₂²⋊D₅	—	4	2	no	—
342	C₃×C₂²⋊D₅	—	4	2	no	—
343	C₃×C₂²⋊D₅	—	4	2	no	—
344	C₂×C₃×Dic₅	—	4	2	no	—
345	C₂×C₃×Dic₅	—	4	2	no	—
346	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
347	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
348	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
349	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
350	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
351	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
353	C₃×D₂₀	—	4	1	no	—
354	C₃×C₄×D₅	—	2	4	no	—
355	C₃×C₄×D₅	—	4	2	no	—
356	C₃×C₄×D₅	—	4	2	no	—
357	C₃×Dic₁₀	—	4	2	no	—
358	C₃×Dic₁₀	—	4	2	no	—
359	C₃×Dic₁₀	—	4	1	no	—
360	C₃×Dic₁₀	—	4	2	no	—
361	C₃×Dic₁₀	—	4	2	no	—
362	C₃×C₄⋊Q₈	—	5	2	no	—
363	C₃×C₄⋊Q₈	—	5	2	no	—
364	C₃×C₄⋊Q₈	—	5	2	no	—
365	C₃×C₄⋊Q₈	—	5	2	no	—
366	C₃×C₄⋊Q₈	—	5	1	no	—
367	C₃×C₄⋊Q₈	—	5	1	no	—
368	C₃×#126	—	5	2	no	—
369	C₃×#126	—	5	2	no	—
370	C₃×#126	—	5	2	no	—
371	C₃×#126	—	5	2	no	—
372	C₃×#126	—	5	2	no	—
373	C₃×#126	—	5	2	no	—
374	C₃×#126	—	5	2	no	—
375	C₃×#126	—	5	2	no	—
376	C₃×#126	—	5	2	no	—
377	C₃×#126	C₂×D₅	1	2	yes	—
378	C₃×#125	—	5	2	no	—
379	C₃×#125	—	5	2	no	—
380	C₃×#125	—	5	2	no	—
381	C₃×#125	—	5	2	no	—
382	C₃×#125	—	5	2	no	—
383	C₃×#125	—	5	2	no	—
384	C₃×#125	—	5	2	no	—
385	C₃×#125	—	5	2	no	—
386	C₃×#125	—	5	1	no	—
387	C₃×#125	—	5	1	no	—
388	C₃×#125	—	5	1	no	—
389	C₃×#125	C₂×D₅	1	1	yes	characteristic
390	C₃×#124	—	5	2	no	—
391	C₃×#124	—	5	2	no	—
392	C₃×#124	—	5	2	no	—
393	C₃×#124	—	5	2	no	—
394	C₃×#124	—	5	1	no	—
395	C₃×#124	C₂×D₅	1	1	yes	characteristic
396	C₃×#123	—	5	2	no	—
397	C₃×#123	—	5	2	no	—
398	C₃×#123	—	5	2	no	—
399	C₃×#123	—	5	2	no	—
400	C₃×#123	—	5	2	no	—
401	C₃×#123	—	5	2	no	—
402	C₃×#123	—	5	2	no	—
403	C₃×#123	—	5	2	no	—
404	C₃×#123	—	5	2	no	—
405	C₃×#123	C₂×D₅	1	2	yes	—
406	C₃×C₂²⋊Q₈	—	5	2	no	—
407	C₃×C₂²⋊Q₈	—	5	2	no	—
408	C₃×C₂²⋊Q₈	—	5	2	no	—
409	C₃×C₂²⋊Q₈	—	5	1	no	—
410	C₃×C₂²⋊Q₈	—	5	2	no	—
411	C₃×C₂²⋊Q₈	—	5	2	no	—
412	C₃×C₂²⋊Q₈	—	5	2	no	—
413	C₃×C₂²⋊Q₈	—	5	2	no	—
414	C₃×C₂²⋊Q₈	—	5	2	no	—
415	C₃×C₂²⋊Q₈	—	5	2	no	—
416	C₃×C₂²⋊Q₈	—	5	2	no	—
417	C₃×C₂²⋊Q₈	—	5	2	no	—
418	C₃×C₂²⋊Q₈	—	5	2	no	—
419	C₃×C₂²⋊Q₈	—	5	2	no	—
420	C₃×C₂²⋊Q₈	—	5	2	no	—
421	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
422	C₃×#121	—	5	2	no	—
423	C₃×#121	—	5	2	no	—
424	C₃×#121	—	5	2	no	—
425	C₃×#121	—	5	1	no	—
426	C₃×#121	—	5	2	no	—
427	C₃×#121	C₂×D₅	1	1	yes	characteristic
428	C₃×C₄×Q₈	—	5	2	no	—
429	C₃×C₄×Q₈	—	5	2	no	—
430	C₃×C₄×Q₈	—	5	2	no	—
431	C₃×C₄×Q₈	—	5	2	no	—
432	C₃×C₄×Q₈	—	5	1	no	—
433	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
434	C₃×C₄×D₄	—	5	2	no	—
435	C₃×C₄×D₄	—	5	2	no	—
436	C₃×C₄×D₄	—	5	2	no	—
437	C₃×C₄×D₄	—	5	1	no	—
438	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
439	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
440	C₃×#117	—	5	2	no	—
441	C₃×#117	—	5	1	no	—
442	C₃×#117	—	5	1	no	—
443	C₃×#117	—	5	2	no	—
444	C₃×#117	—	5	2	no	—
445	C₃×#117	C₂×D₅	1	2	yes	—
446	C₂×C₃×C₄²	—	5	2	no	—
447	C₂×C₃×C₄²	—	5	2	no	—
448	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
449	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
451	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
452	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
453	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
454	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
455	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
459	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
460	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
461	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
463	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
464	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
465	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
466	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
467	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
468	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
469	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
470	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
472	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
474	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
478	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
480	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
482	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
483	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
484	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
485	C₄²×C₅	C₂³×C₃	1	2	yes	—
486	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
487	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
488	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
489	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
490	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
491	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
492	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
493	#685	C₂³×C₃	1	2	yes	—
494	#685	C₂³×C₃	1	2	yes	—
495	#685	C₂³×C₃	1	2	yes	—
496	#685	C₂³×C₃	1	2	yes	—
497	#685	C₂³×C₃	1	2	yes	—
498	#685	C₂³×C₃	1	2	yes	—
499	#685	C₂³×C₃	1	2	yes	—
500	#685	C₂³×C₃	1	2	yes	—
501	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
502	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
503	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
504	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
505	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
506	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
507	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
508	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
509	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
510	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
511	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
512	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
513	#683	C₂³×C₃	1	2	yes	—
514	#683	C₂³×C₃	1	2	yes	—
515	#683	C₂³×C₃	1	2	yes	—
516	#683	C₂³×C₃	1	2	yes	—
517	#683	C₂³×C₃	1	2	yes	—
518	#683	C₂³×C₃	1	2	yes	—
519	#683	C₂³×C₃	1	2	yes	—
520	#683	C₂³×C₃	1	2	yes	—
521	#683	C₂³×C₃	1	2	yes	—
522	#683	C₂³×C₃	1	2	yes	—
523	#683	C₂³×C₃	1	2	yes	—
524	#683	C₂³×C₃	1	2	yes	—
525	#683	C₂³×C₃	1	2	yes	—
526	#683	C₂³×C₃	1	2	yes	—
527	#683	C₂³×C₃	1	2	yes	—
528	#683	C₂³×C₃	1	2	yes	—
529	C₄×Dic₅	C₂³×C₃	1	2	yes	—
530	C₄×Dic₅	C₂³×C₃	1	2	yes	—
531	C₄×Dic₅	C₂³×C₃	1	2	yes	—
532	C₄×Dic₅	C₂³×C₃	1	2	yes	—
533	C₄×Dic₅	C₂³×C₃	1	2	yes	—
534	C₄×Dic₅	C₂³×C₃	1	2	yes	—
535	C₄×Dic₅	C₂³×C₃	1	2	yes	—
536	#564	—	5	1	no	—
537	#563	—	5	2	no	—
538	#563	—	5	2	no	—
539	#563	—	5	1	no	—
540	#563	—	5	1	no	—
541	#563	—	5	2	no	—
542	#563	—	5	2	no	—
543	#562	—	5	1	no	—
544	#562	—	5	2	no	—
545	#562	—	5	2	no	—
546	#533	—	5	2	no	—
547	#533	—	5	2	no	—
548	#533	—	5	1	no	—
549	#529	—	5	2	no	—
550	#529	—	5	2	no	—
551	#529	—	5	2	no	—
552	#529	—	5	2	no	—
553	#529	—	5	1	no	—
554	#529	C₃×D₅	1	1	yes	characteristic, complemented
555	C₂²×C₃×C₅	—	2	1	no	—
556	C₂²×C₃×C₅	—	2	2	no	—
557	C₂²×C₃×C₅	—	2	2	no	—
558	C₂²×C₃×C₅	—	2	2	no	—
559	C₂²×C₃×C₅	—	2	1	no	—
560	C₂²×C₃×C₅	—	2	1	no	—
561	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
562	C₂×C₃×D₅	—	2	2	no	—
563	C₂×C₃×D₅	—	2	2	no	—
564	C₂×C₃×D₅	—	2	2	no	—
565	C₃×C₄×C₅	—	2	2	no	—
566	C₃×C₄×C₅	—	2	1	no	—
567	C₃×C₄×C₅	—	2	1	no	—
568	C₃×C₄×C₅	—	2	1	no	—
569	C₃×C₄×C₅	—	2	2	no	—
570	C₃×C₄×C₅	—	2	2	no	—
571	C₃×C₄×C₅	—	2	1	no	—
572	C₃×C₄×C₅	—	2	1	no	—
573	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
574	C₃×Dic₅	—	2	2	no	—
575	C₃×Dic₅	—	2	2	no	—
576	C₃×Dic₅	—	2	2	no	—
577	C₃×Dic₅	—	2	2	no	—
578	C₃×Dic₅	—	2	2	no	—
579	C₃×Dic₅	—	2	2	no	—
580	C₃×Dic₅	—	2	2	no	—
581	C₂×C₃×Q₈	—	5	2	no	—
582	C₂×C₃×Q₈	—	5	1	no	—
583	C₂×C₃×Q₈	—	5	2	no	—
584	C₂×C₃×Q₈	—	5	2	no	—
585	C₂×C₃×Q₈	—	5	2	no	—
586	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
587	C₂×C₃×D₄	—	5	2	no	—
588	C₂×C₃×D₄	—	5	2	no	—
589	C₂×C₃×D₄	—	5	2	no	—
590	C₂×C₃×D₄	—	5	1	no	—
591	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
592	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
593	C₂²×C₃×C₄	—	5	2	no	—
594	C₂²×C₃×C₄	—	5	2	no	—
595	C₂²×C₃×C₄	—	5	2	no	—
596	C₂²×C₃×C₄	—	5	2	no	—
597	C₂²×C₃×C₄	—	5	2	no	—
598	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
599	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
600	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
601	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
602	C₃×C₄⋊C₄	—	5	2	no	—
603	C₃×C₄⋊C₄	—	5	2	no	—
604	C₃×C₄⋊C₄	—	5	2	no	—
605	C₃×C₄⋊C₄	—	5	2	no	—
606	C₃×C₄⋊C₄	—	5	2	no	—
607	C₃×C₄⋊C₄	—	5	2	no	—
608	C₃×C₄⋊C₄	—	5	2	no	—
609	C₃×C₄⋊C₄	—	5	2	no	—
610	C₃×C₄⋊C₄	—	5	2	no	—
611	C₃×C₄⋊C₄	—	5	2	no	—
612	C₃×C₄⋊C₄	—	5	2	no	—
613	C₃×C₄⋊C₄	—	5	2	no	—
614	C₃×C₄⋊C₄	—	5	2	no	—
615	C₃×C₄⋊C₄	—	5	2	no	—
616	C₃×C₄⋊C₄	—	5	2	no	—
617	C₃×C₄⋊C₄	—	5	2	no	—
618	C₃×C₄⋊C₄	—	5	2	no	—
619	C₃×C₄⋊C₄	—	5	1	no	—
620	C₃×C₄⋊C₄	—	5	1	no	—
621	C₃×C₄⋊C₄	—	5	2	no	—
622	C₃×C₄⋊C₄	—	5	1	no	—
623	C₃×C₄⋊C₄	—	5	1	no	—
624	C₃×C₄⋊C₄	—	5	1	no	—
625	C₃×C₄⋊C₄	—	5	2	no	—
626	C₃×C₄⋊C₄	—	5	1	no	—
627	C₃×C₄⋊C₄	—	5	2	no	—
628	C₃×C₄⋊C₄	—	5	2	no	—
629	C₃×C₄⋊C₄	—	5	2	no	—
630	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
631	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
632	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
633	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
634	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
635	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
636	C₃×C₂²⋊C₄	—	5	2	no	—
637	C₃×C₂²⋊C₄	—	5	2	no	—
638	C₃×C₂²⋊C₄	—	5	2	no	—
639	C₃×C₂²⋊C₄	—	5	2	no	—
640	C₃×C₂²⋊C₄	—	5	2	no	—
641	C₃×C₂²⋊C₄	—	5	2	no	—
642	C₃×C₂²⋊C₄	—	5	2	no	—
643	C₃×C₂²⋊C₄	—	5	2	no	—
644	C₃×C₂²⋊C₄	—	5	2	no	—
645	C₃×C₂²⋊C₄	—	5	2	no	—
646	C₃×C₂²⋊C₄	—	5	2	no	—
647	C₃×C₂²⋊C₄	—	5	2	no	—
648	C₃×C₂²⋊C₄	—	5	2	no	—
649	C₃×C₂²⋊C₄	—	5	2	no	—
650	C₃×C₂²⋊C₄	—	5	2	no	—
651	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
652	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
653	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
654	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
655	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
656	C₃×C₄²	—	5	2	no	—
657	C₃×C₄²	—	5	2	no	—
658	C₃×C₄²	—	5	2	no	—
659	C₃×C₄²	—	5	2	no	—
660	C₃×C₄²	—	5	2	no	—
661	C₃×C₄²	—	5	2	no	—
662	C₃×C₄²	—	5	2	no	—
663	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
664	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
665	C₃×C₄²	C₂²×D₅	1	2	yes	—
666	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
667	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
668	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
669	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
670	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
671	C₅×Q₈	—	4	1	no	—
672	C₅×D₄	—	4	2	no	—
673	C₅×D₄	—	4	1	no	—
674	C₂×C₄×C₅	—	2	2	no	—
675	C₂×C₄×C₅	—	2	4	no	—
676	C₂×C₄×C₅	—	4	1	no	—
677	C₂×C₄×C₅	—	4	1	no	—
678	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
679	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
680	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
681	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
682	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
683	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
684	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
685	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
686	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
687	C₂²⋊D₅	—	4	2	no	—
688	C₂²⋊D₅	—	4	2	no	—
689	C₂²⋊D₅	—	4	2	no	—
690	C₂×Dic₅	—	4	2	no	—
691	C₂×Dic₅	—	4	2	no	—
692	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
693	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
694	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
695	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
696	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
697	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
698	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
699	D₂₀	—	4	1	no	—
700	C₄×D₅	—	2	4	no	—
701	C₄×D₅	—	4	2	no	—
702	C₄×D₅	—	4	2	no	—
703	Dic₁₀	—	4	2	no	—
704	Dic₁₀	—	4	2	no	—
705	Dic₁₀	—	4	1	no	—
706	Dic₁₀	—	4	2	no	—
707	Dic₁₀	—	4	2	no	—
708	C₄⋊Q₈	—	5	2	no	—
709	C₄⋊Q₈	—	5	2	no	—
710	C₄⋊Q₈	—	5	2	no	—
711	C₄⋊Q₈	—	5	2	no	—
712	C₄⋊Q₈	—	5	1	no	—
713	C₄⋊Q₈	—	5	1	no	—
714	#126	—	5	2	no	—
715	#126	—	5	2	no	—
716	#126	—	5	2	no	—
717	#126	—	5	2	no	—
718	#126	—	5	2	no	—
719	#126	—	5	2	no	—
720	#126	—	5	2	no	—
721	#126	—	5	2	no	—
722	#126	—	5	2	no	—
723	#126	C₂×C₃×D₅	1	2	yes	—
724	#125	—	5	2	no	—
725	#125	—	5	2	no	—
726	#125	—	5	2	no	—
727	#125	—	5	2	no	—
728	#125	—	5	2	no	—
729	#125	—	5	2	no	—
730	#125	—	5	2	no	—
731	#125	—	5	2	no	—
732	#125	—	5	1	no	—
733	#125	—	5	1	no	—
734	#125	—	5	1	no	—
735	#125	C₂×C₃×D₅	1	1	yes	characteristic
736	#124	—	5	2	no	—
737	#124	—	5	2	no	—
738	#124	—	5	2	no	—
739	#124	—	5	2	no	—
740	#124	—	5	1	no	—
741	#124	C₂×C₃×D₅	1	1	yes	characteristic
742	#123	—	5	2	no	—
743	#123	—	5	2	no	—
744	#123	—	5	2	no	—
745	#123	—	5	2	no	—
746	#123	—	5	2	no	—
747	#123	—	5	2	no	—
748	#123	—	5	2	no	—
749	#123	—	5	2	no	—
750	#123	—	5	2	no	—
751	#123	C₂×C₃×D₅	1	2	yes	—
752	C₂²⋊Q₈	—	5	2	no	—
753	C₂²⋊Q₈	—	5	1	no	—
754	C₂²⋊Q₈	—	5	2	no	—
755	C₂²⋊Q₈	—	5	2	no	—
756	C₂²⋊Q₈	—	5	2	no	—
757	C₂²⋊Q₈	—	5	2	no	—
758	C₂²⋊Q₈	—	5	2	no	—
759	C₂²⋊Q₈	—	5	2	no	—
760	C₂²⋊Q₈	—	5	2	no	—
761	C₂²⋊Q₈	—	5	2	no	—
762	C₂²⋊Q₈	—	5	2	no	—
763	C₂²⋊Q₈	—	5	2	no	—
764	C₂²⋊Q₈	—	5	2	no	—
765	C₂²⋊Q₈	—	5	2	no	—
766	C₂²⋊Q₈	—	5	2	no	—
767	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
768	#121	—	5	2	no	—
769	#121	—	5	2	no	—
770	#121	—	5	2	no	—
771	#121	—	5	1	no	—
772	#121	—	5	2	no	—
773	#121	C₂×C₃×D₅	1	1	yes	characteristic
774	C₄×Q₈	—	5	2	no	—
775	C₄×Q₈	—	5	2	no	—
776	C₄×Q₈	—	5	2	no	—
777	C₄×Q₈	—	5	2	no	—
778	C₄×Q₈	—	5	1	no	—
779	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
780	C₄×D₄	—	5	2	no	—
781	C₄×D₄	—	5	2	no	—
782	C₄×D₄	—	5	2	no	—
783	C₄×D₄	—	5	1	no	—
784	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
785	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
786	#117	—	5	2	no	—
787	#117	—	5	1	no	—
788	#117	—	5	1	no	—
789	#117	—	5	2	no	—
790	#117	—	5	2	no	—
791	#117	C₂×C₃×D₅	1	2	yes	—
792	C₂×C₄²	—	5	2	no	—
793	C₂×C₄²	—	5	2	no	—
794	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
795	C₂×C₃×C₅	—	4	2	no	—
796	C₂×C₃×C₅	—	4	1	no	—
797	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
798	C₂×C₃×C₅	#585	1	1	yes	characteristic
799	C₂×C₃×C₅	#585	1	1	yes	characteristic
800	C₃×D₅	—	4	2	no	—
801	C₂³×C₃	—	5	2	no	—
802	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
803	C₂³×C₃	C₂³×D₅	1	2	yes	—
804	C₃×Q₈	—	4	1	no	—
805	C₃×Q₈	—	20	1	no	—
806	C₃×Q₈	—	20	2	no	—
807	C₃×Q₈	—	20	2	no	—
808	C₃×Q₈	—	20	2	no	—
809	C₃×Q₈	—	20	2	no	—
810	C₃×D₄	—	4	1	no	—
811	C₃×D₄	—	4	2	no	—
812	C₃×D₄	—	20	1	no	—
813	C₃×D₄	—	20	2	no	—
814	C₃×D₄	—	20	2	no	—
815	C₃×D₄	—	20	2	no	—
816	C₂×C₃×C₄	—	2	4	no	—
817	C₂×C₃×C₄	—	2	2	no	—
818	C₂×C₃×C₄	—	4	1	no	—
819	C₂×C₃×C₄	—	4	1	no	—
820	C₂×C₃×C₄	—	5	2	no	—
821	C₂×C₃×C₄	—	5	2	no	—
822	C₂×C₃×C₄	—	5	2	no	—
823	C₂×C₃×C₄	—	5	2	no	—
824	C₂×C₃×C₄	—	5	2	no	—
825	C₂×C₃×C₄	—	5	2	no	—
826	C₂×C₃×C₄	—	5	2	no	—
827	C₂×C₃×C₄	—	10	4	no	—
828	C₂×C₃×C₄	—	20	2	no	—
829	C₂×C₃×C₄	—	20	2	no	—
830	C₂×C₃×C₄	—	20	2	no	—
831	C₂×C₃×C₄	—	20	2	no	—
832	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
833	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
834	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
835	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
836	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
837	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
838	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
839	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
840	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
841	C₂²×C₅	—	2	1	no	—
842	C₂²×C₅	—	2	2	no	—
843	C₂²×C₅	—	2	2	no	—
844	C₂²×C₅	—	2	2	no	—
845	C₂²×C₅	—	2	1	no	—
846	C₂²×C₅	—	2	1	no	—
847	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
848	C₂×D₅	—	2	2	no	—
849	C₂×D₅	—	2	2	no	—
850	C₂×D₅	—	2	2	no	—
851	C₄×C₅	—	2	2	no	—
852	C₄×C₅	—	2	1	no	—
853	C₄×C₅	—	2	1	no	—
854	C₄×C₅	—	2	1	no	—
855	C₄×C₅	—	2	2	no	—
856	C₄×C₅	—	2	2	no	—
857	C₄×C₅	—	2	1	no	—
858	C₄×C₅	—	2	1	no	—
859	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
860	Dic₅	—	2	2	no	—
861	Dic₅	—	2	2	no	—
862	Dic₅	—	2	2	no	—
863	Dic₅	—	2	2	no	—
864	Dic₅	—	2	2	no	—
865	Dic₅	—	2	2	no	—
866	Dic₅	—	2	2	no	—
867	C₂×Q₈	—	5	2	no	—
868	C₂×Q₈	—	5	1	no	—
869	C₂×Q₈	—	5	2	no	—
870	C₂×Q₈	—	5	2	no	—
871	C₂×Q₈	—	5	2	no	—
872	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
873	C₂×D₄	—	5	2	no	—
874	C₂×D₄	—	5	2	no	—
875	C₂×D₄	—	5	2	no	—
876	C₂×D₄	—	5	1	no	—
877	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
878	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
879	C₂²×C₄	—	5	2	no	—
880	C₂²×C₄	—	5	2	no	—
881	C₂²×C₄	—	5	2	no	—
882	C₂²×C₄	—	5	2	no	—
883	C₂²×C₄	—	5	2	no	—
884	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
885	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
886	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
887	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
888	C₄⋊C₄	—	5	2	no	—
889	C₄⋊C₄	—	5	2	no	—
890	C₄⋊C₄	—	5	2	no	—
891	C₄⋊C₄	—	5	1	no	—
892	C₄⋊C₄	—	5	1	no	—
893	C₄⋊C₄	—	5	2	no	—
894	C₄⋊C₄	—	5	2	no	—
895	C₄⋊C₄	—	5	2	no	—
896	C₄⋊C₄	—	5	1	no	—
897	C₄⋊C₄	—	5	1	no	—
898	C₄⋊C₄	—	5	2	no	—
899	C₄⋊C₄	—	5	2	no	—
900	C₄⋊C₄	—	5	2	no	—
901	C₄⋊C₄	—	5	1	no	—
902	C₄⋊C₄	—	5	2	no	—
903	C₄⋊C₄	—	5	2	no	—
904	C₄⋊C₄	—	5	2	no	—
905	C₄⋊C₄	—	5	2	no	—
906	C₄⋊C₄	—	5	1	no	—
907	C₄⋊C₄	—	5	2	no	—
908	C₄⋊C₄	—	5	2	no	—
909	C₄⋊C₄	—	5	2	no	—
910	C₄⋊C₄	—	5	2	no	—
911	C₄⋊C₄	—	5	2	no	—
912	C₄⋊C₄	—	5	2	no	—
913	C₄⋊C₄	—	5	2	no	—
914	C₄⋊C₄	—	5	2	no	—
915	C₄⋊C₄	—	5	2	no	—
916	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
917	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
918	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
919	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
922	C₂²⋊C₄	—	5	2	no	—
923	C₂²⋊C₄	—	5	2	no	—
924	C₂²⋊C₄	—	5	2	no	—
925	C₂²⋊C₄	—	5	2	no	—
926	C₂²⋊C₄	—	5	2	no	—
927	C₂²⋊C₄	—	5	2	no	—
928	C₂²⋊C₄	—	5	2	no	—
929	C₂²⋊C₄	—	5	2	no	—
930	C₂²⋊C₄	—	5	2	no	—
931	C₂²⋊C₄	—	5	2	no	—
932	C₂²⋊C₄	—	5	2	no	—
933	C₂²⋊C₄	—	5	2	no	—
934	C₂²⋊C₄	—	5	2	no	—
935	C₂²⋊C₄	—	5	2	no	—
936	C₂²⋊C₄	—	5	2	no	—
937	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
938	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
939	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
940	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
941	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
942	C₄²	—	5	2	no	—
943	C₄²	—	5	2	no	—
944	C₄²	—	5	2	no	—
945	C₄²	—	5	2	no	—
946	C₄²	—	5	2	no	—
947	C₄²	—	5	2	no	—
948	C₄²	—	5	2	no	—
949	C₄²	C₂²×C₃×D₅	1	2	yes	—
950	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
951	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
952	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
953	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
954	C₃×C₅	#3531	1	1	yes	characteristic, complemented, Hall
955	C₂²×C₃	—	2	1	no	—
956	C₂²×C₃	—	2	2	no	—
957	C₂²×C₃	—	2	1	no	—
958	C₂²×C₃	—	2	1	no	—
959	C₂²×C₃	—	2	2	no	—
960	C₂²×C₃	—	2	2	no	—
961	C₂²×C₃	—	10	2	no	—
962	C₂²×C₃	—	10	2	no	—
963	C₂²×C₃	—	10	2	no	—
964	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
965	C₃×C₄	—	2	2	no	—
966	C₃×C₄	—	2	1	no	—
967	C₃×C₄	—	2	1	no	—
968	C₃×C₄	—	2	1	no	—
969	C₃×C₄	—	2	1	no	—
970	C₃×C₄	—	2	1	no	—
971	C₃×C₄	—	2	2	no	—
972	C₃×C₄	—	2	2	no	—
973	C₃×C₄	—	10	2	no	—
974	C₃×C₄	—	10	2	no	—
975	C₃×C₄	—	10	2	no	—
976	C₃×C₄	—	10	2	no	—
977	C₃×C₄	—	10	2	no	—
978	C₃×C₄	—	10	2	no	—
979	C₃×C₄	—	10	2	no	—
980	C₃×C₄	#4150	1	2	yes	—
981	C₂×C₅	—	4	2	no	—
982	C₂×C₅	—	4	1	no	—
983	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
984	C₂×C₅	C₃×#585	1	1	yes	characteristic
985	C₂×C₅	C₃×#585	1	1	yes	characteristic
986	D₅	—	4	2	no	—
987	C₂³	—	5	2	no	—
988	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
989	C₂³	C₂³×C₃×D₅	1	2	yes	—
990	Q₈	—	4	1	no	—
991	Q₈	—	20	1	no	—
992	Q₈	—	20	2	no	—
993	Q₈	—	20	2	no	—
994	Q₈	—	20	2	no	—
995	Q₈	—	20	2	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	20	1	no	—
999	D₄	—	20	2	no	—
1000	D₄	—	20	2	no	—
1001	D₄	—	20	2	no	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	5	2	no	—
1007	C₂×C₄	—	5	2	no	—
1008	C₂×C₄	—	5	2	no	—
1009	C₂×C₄	—	5	2	no	—
1010	C₂×C₄	—	5	2	no	—
1011	C₂×C₄	—	5	2	no	—
1012	C₂×C₄	—	5	2	no	—
1013	C₂×C₄	—	10	4	no	—
1014	C₂×C₄	—	20	2	no	—
1015	C₂×C₄	—	20	2	no	—
1016	C₂×C₄	—	20	2	no	—
1017	C₂×C₄	—	20	2	no	—
1018	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1019	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1020	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1021	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1022	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1023	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1024	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1025	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1026	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1027	C₂×C₃	—	4	1	no	—
1028	C₂×C₃	—	4	2	no	—
1029	C₂×C₃	—	20	2	no	—
1030	C₂×C₃	C₂×#4150	1	1	yes	characteristic
1031	C₂×C₃	#66283	1	1	yes	characteristic
1032	C₂×C₃	#66283	1	1	yes	characteristic
1033	C₅	C₃×#3531	1	1	yes	characteristic, complemented, Sylow
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	10	2	no	—
1041	C₂²	—	10	2	no	—
1042	C₂²	—	10	2	no	—
1043	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	10	2	no	—
1053	C₄	—	10	2	no	—
1054	C₄	—	10	2	no	—
1055	C₄	—	10	2	no	—
1056	C₄	—	10	2	no	—
1057	C₄	—	10	2	no	—
1058	C₄	—	10	2	no	—
1059	C₄	C₃×#4150	1	2	yes	—
1060	C₃	#10618033	1	1	yes	characteristic, direct product factor, Sylow
1061	C₂	—	4	1	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	20	2	no	—
1064	C₂	C₂×C₃×#4150	1	1	yes	characteristic
1065	C₂	C₃×#66283	1	1	yes	characteristic
1066	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#3531
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#529	C₂	semidirect
2. C₃×#66046	C₂	semidirect
3. C₃×#66046	C₂	semidirect
4. C₃×#66033	C₂	semidirect
5. C₃×C₅⋊#564	C₂	semidirect
6. C₃×#66018	C₂	semidirect
7. C₃×#66006	C₂	semidirect
8. C₃×#66001	C₂	semidirect
9. C₃×#65985	C₂	semidirect
10. C₃×#65980	C₂	semidirect
11. C₃×#65955	C₂	semidirect
12. C₃×#65912	C₂	semidirect
13. C₃×#65891	C₂	semidirect
14. C₃×#65872	C₂	semidirect
15. C₃×#65872	C₂	semidirect
16. C₃×#65862	C₂	semidirect
17. C₃×#65851	C₂	semidirect
18. C₃×#65813	C₂	semidirect
19. C₃×#65804	C₂	semidirect
20. #10618033	C₃	direct (N × H)
109. C₅×#529	C₂×C₃	semidirect
110. #66046	C₂×C₃	semidirect
111. #66046	C₂×C₃	semidirect
112. #66033	C₂×C₃	semidirect
113. C₅⋊#564	C₂×C₃	semidirect
114. #66018	C₂×C₃	semidirect
115. #66006	C₂×C₃	semidirect
116. #66001	C₂×C₃	semidirect
117. #65985	C₂×C₃	semidirect
118. #65980	C₂×C₃	semidirect
119. #65955	C₂×C₃	semidirect
120. #65912	C₂×C₃	semidirect
121. #65891	C₂×C₃	semidirect
122. #65872	C₂×C₃	semidirect
123. #65872	C₂×C₃	semidirect
124. #65862	C₂×C₃	semidirect
125. #65851	C₂×C₃	semidirect
126. #65813	C₂×C₃	semidirect
127. #65804	C₂×C₃	semidirect
233. C₃×#529	D₅	semidirect
554. #529	C₃×D₅	semidirect
954. C₃×C₅	#3531	semidirect
1033. C₅	C₃×#3531	semidirect
1060. C₃	#10618033	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×#529	2
C₃×#66046	2
C₃×#66033	2
C₃×C₅⋊#564	2
C₃×#66018	2
C₃×#66006	2
C₃×#66001	2
C₃×#65985	2
C₃×#65980	2
C₃×#65955	2
C₃×#65912	2
C₃×#65891	2
C₃×#65872	2
C₃×#65862	2
C₃×#65851	2
C₃×#65813	2
C₃×#65804	2
#10618033	3
C₃×#3531	5

Subgroups — C3×#10618033 #14495595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618033 #14495595