Subgroups — C₃×#35732 #10654339

Order 768.

2642 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#551	C₂	1	2	yes	maximal, complemented
2	C₃×#2662	C₂	1	2	yes	maximal, complemented
3	C₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2601	C₂	1	2	yes	maximal, complemented
5	C₃×#2560	C₂	1	2	yes	maximal, complemented
6	C₃×#2554	C₂	1	2	yes	maximal, complemented
7	C₃×#2549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2544	C₂	1	2	yes	maximal, complemented
9	C₃×#2472	C₂	1	2	yes	maximal, complemented
10	C₃×#2461	C₂	1	2	yes	maximal, complemented
11	C₃×#2445	C₂	1	2	yes	maximal, complemented
12	C₃×#2433	C₂	1	1	yes	maximal, characteristic
13	C₃×#2411	C₂	1	2	yes	maximal, complemented
14	C₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2364	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2358	C₂	1	2	yes	maximal, complemented
18	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
20	#35732	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₃×#551	—	2	16	no	—
23	C₂×C₃×#127	C₂²	1	2	yes	—
24	C₂×C₃×#126	C₂²	1	2	yes	complemented
25	C₂×C₃×#126	C₂²	1	2	yes	complemented
26	C₂×C₃×#124	C₂²	1	2	yes	complemented
27	C₂×C₃×#124	C₂²	1	2	yes	complemented
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×#123	C₂²	1	2	yes	complemented
30	C₂×C₃×#123	C₂²	1	2	yes	complemented
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₃×#120	C₂²	1	2	yes	—
35	C₂×C₃×#120	C₂²	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
40	C₂×C₃×#117	C₂²	1	1	yes	characteristic
41	C₂×C₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	2	yes	complemented
43	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	1	yes	characteristic, complemented
48	C₃×#398	C₂²	1	1	yes	characteristic, complemented
49	C₃×#398	C₂²	1	2	yes	complemented
50	C₃×#397	C₂²	1	2	yes	complemented
51	C₃×#396	C₂²	1	2	yes	complemented
52	C₃×#396	C₂²	1	2	yes	complemented
53	C₃×#396	C₂²	1	2	yes	complemented
54	C₃×#396	C₂²	1	2	yes	complemented
55	C₃×#395	C₂²	1	2	yes	complemented
56	C₃×#394	C₂²	1	1	yes	characteristic
57	C₃×#394	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	1	yes	characteristic
60	C₃×#394	C₂²	1	2	yes	—
61	C₃×#394	C₂²	1	1	yes	characteristic
62	C₃×#394	C₂²	1	1	yes	characteristic, complemented
63	C₃×#394	C₂²	1	1	yes	characteristic, complemented
64	C₃×#394	C₂²	1	2	yes	complemented
65	C₃×#394	C₂²	1	2	yes	complemented
66	C₃×#394	C₂²	1	2	yes	complemented
67	C₃×#394	C₂²	1	2	yes	complemented
68	C₃×#393	C₂²	1	2	yes	complemented
69	C₃×#392	C₂²	1	2	yes	—
70	C₃×#392	C₂²	1	2	yes	—
71	C₃×#391	C₂²	1	2	yes	complemented
72	C₃×#390	C₂²	1	2	yes	—
73	C₃×#390	C₂²	1	2	yes	—
74	C₃×#390	C₂²	1	2	yes	complemented
75	C₃×#390	C₂²	1	2	yes	complemented
76	C₃×#390	C₂²	1	2	yes	complemented
77	C₃×#390	C₂²	1	2	yes	complemented
78	C₃×#389	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	2	yes	complemented
80	C₃×#388	C₂²	1	2	yes	complemented
81	C₃×#388	C₂²	1	2	yes	complemented
82	C₃×#388	C₂²	1	2	yes	complemented
83	C₃×#388	C₂²	1	2	yes	complemented
84	C₃×#388	C₂²	1	2	yes	complemented
85	C₃×#388	C₂²	1	2	yes	complemented
86	C₃×#387	C₂²	1	2	yes	complemented
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	complemented
92	C₃×#386	C₂²	1	2	yes	complemented
93	C₃×#386	C₂²	1	2	yes	complemented
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	complemented
96	C₃×#380	C₂²	1	1	yes	characteristic
97	C₃×#379	C₂²	1	2	yes	—
98	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
100	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
101	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	C₂×C₃×#95	C₂²	1	1	yes	characteristic
109	C₂×#551	C₂×C₃	1	2	yes	complemented
110	#2662	C₂×C₃	1	2	yes	complemented
111	#2618	C₂×C₃	1	1	yes	characteristic, complemented
112	#2601	C₂×C₃	1	2	yes	complemented
113	#2560	C₂×C₃	1	2	yes	complemented
114	#2554	C₂×C₃	1	2	yes	complemented
115	#2549	C₂×C₃	1	1	yes	characteristic, complemented
116	#2544	C₂×C₃	1	2	yes	complemented
117	#2472	C₂×C₃	1	2	yes	complemented
118	#2461	C₂×C₃	1	2	yes	complemented
119	#2445	C₂×C₃	1	2	yes	complemented
120	#2433	C₂×C₃	1	1	yes	characteristic
121	#2411	C₂×C₃	1	2	yes	complemented
122	#2392	C₂×C₃	1	2	yes	complemented
123	C₂×#394	C₂×C₃	1	1	yes	characteristic, complemented
124	#2364	C₂×C₃	1	1	yes	characteristic, complemented
125	#2358	C₂×C₃	1	2	yes	complemented
126	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
127	#2274	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁵×C₃	C₂³	1	2	yes	—
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×D₄	—	2	4	no	—
131	C₂²×C₃×D₄	—	4	4	no	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	2	yes	—
135	C₂²×C₃×D₄	C₂³	1	2	yes	—
136	C₂²×C₃×D₄	C₂³	1	2	yes	—
137	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
143	C₂³×C₃×C₄	C₂³	1	2	yes	—
144	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
145	C₂³×C₃×C₄	C₂³	1	2	yes	—
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
148	C₃×#127	—	4	4	no	—
149	C₃×#126	—	2	8	no	—
150	C₃×#126	—	2	8	no	—
151	C₃×#124	—	2	8	no	—
152	C₃×#124	—	4	4	no	—
153	C₃×#123	—	2	8	no	—
154	C₃×#123	—	2	8	no	—
155	C₃×#123	—	2	8	no	—
156	C₃×C₂²⋊Q₈	—	2	8	no	—
157	C₃×C₂²⋊Q₈	—	2	8	no	—
158	C₃×#121	—	2	4	no	—
159	C₃×#120	—	2	8	no	—
160	C₃×#120	—	2	8	no	—
161	C₃×C₄×D₄	—	2	8	no	—
162	C₃×C₄×D₄	—	2	8	no	—
163	C₃×C₄×D₄	—	4	4	no	—
164	C₃×C₄×D₄	—	4	4	no	—
165	C₃×#117	—	2	4	no	—
166	C₃×#117	—	2	8	no	—
167	C₃×#117	D₄	1	8	yes	complemented
168	C₂×C₃×C₄⋊C₄	—	2	4	no	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
186	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
187	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	2	yes	—
220	C₂×C₃×C₄²	C₂³	1	2	yes	—
221	C₂×C₃×C₄²	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	2	yes	—
223	C₂×C₃×C₄²	C₂³	1	2	yes	—
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	1	yes	characteristic
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
242	#551	—	2	16	no	—
243	C₂×#127	C₂²×C₃	1	2	yes	—
244	C₂×#126	C₂²×C₃	1	2	yes	complemented
245	C₂×#126	C₂²×C₃	1	2	yes	complemented
246	C₂×#124	C₂²×C₃	1	2	yes	complemented
247	C₂×#124	C₂²×C₃	1	2	yes	complemented
248	C₂×#123	C₂²×C₃	1	2	yes	—
249	C₂×#123	C₂²×C₃	1	2	yes	complemented
250	C₂×#123	C₂²×C₃	1	2	yes	complemented
251	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
253	C₂×#121	C₂²×C₃	1	1	yes	characteristic
254	C₂×#120	C₂²×C₃	1	2	yes	—
255	C₂×#120	C₂²×C₃	1	2	yes	—
256	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
257	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
259	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
260	C₂×#117	C₂²×C₃	1	1	yes	characteristic
261	C₂×#117	C₂²×C₃	1	1	yes	characteristic
262	C₂×#117	C₂²×C₃	1	2	yes	complemented
263	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
267	#398	C₂²×C₃	1	1	yes	characteristic, complemented
268	#398	C₂²×C₃	1	1	yes	characteristic, complemented
269	#398	C₂²×C₃	1	2	yes	complemented
270	#397	C₂²×C₃	1	2	yes	complemented
271	#396	C₂²×C₃	1	2	yes	complemented
272	#396	C₂²×C₃	1	2	yes	complemented
273	#396	C₂²×C₃	1	2	yes	complemented
274	#396	C₂²×C₃	1	2	yes	complemented
275	#395	C₂²×C₃	1	2	yes	complemented
276	#394	C₂²×C₃	1	2	yes	—
277	#394	C₂²×C₃	1	2	yes	—
278	#394	C₂²×C₃	1	1	yes	characteristic
279	#394	C₂²×C₃	1	1	yes	characteristic
280	#394	C₂²×C₃	1	1	yes	characteristic
281	#394	C₂²×C₃	1	1	yes	characteristic
282	#394	C₂²×C₃	1	1	yes	characteristic, complemented
283	#394	C₂²×C₃	1	1	yes	characteristic, complemented
284	#394	C₂²×C₃	1	2	yes	complemented
285	#394	C₂²×C₃	1	2	yes	complemented
286	#394	C₂²×C₃	1	2	yes	complemented
287	#394	C₂²×C₃	1	2	yes	complemented
288	#393	C₂²×C₃	1	2	yes	complemented
289	#392	C₂²×C₃	1	2	yes	—
290	#392	C₂²×C₃	1	2	yes	—
291	#391	C₂²×C₃	1	2	yes	complemented
292	#390	C₂²×C₃	1	2	yes	—
293	#390	C₂²×C₃	1	2	yes	—
294	#390	C₂²×C₃	1	2	yes	complemented
295	#390	C₂²×C₃	1	2	yes	complemented
296	#390	C₂²×C₃	1	2	yes	complemented
297	#390	C₂²×C₃	1	2	yes	complemented
298	#389	C₂²×C₃	1	2	yes	complemented
299	#388	C₂²×C₃	1	2	yes	complemented
300	#388	C₂²×C₃	1	2	yes	complemented
301	#388	C₂²×C₃	1	2	yes	complemented
302	#388	C₂²×C₃	1	2	yes	complemented
303	#388	C₂²×C₃	1	2	yes	complemented
304	#388	C₂²×C₃	1	2	yes	complemented
305	#388	C₂²×C₃	1	2	yes	complemented
306	#387	C₂²×C₃	1	2	yes	complemented
307	#386	C₂²×C₃	1	2	yes	—
308	#386	C₂²×C₃	1	2	yes	—
309	#386	C₂²×C₃	1	2	yes	—
310	#386	C₂²×C₃	1	2	yes	—
311	#386	C₂²×C₃	1	2	yes	complemented
312	#386	C₂²×C₃	1	2	yes	complemented
313	#386	C₂²×C₃	1	2	yes	complemented
314	#385	C₂²×C₃	1	2	yes	—
315	#385	C₂²×C₃	1	2	yes	complemented
316	#380	C₂²×C₃	1	1	yes	characteristic
317	#379	C₂²×C₃	1	2	yes	—
318	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
319	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
320	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
321	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
322	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
324	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
327	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
328	C₂×#95	C₂²×C₃	1	1	yes	characteristic
329	C₂⁴×C₃	—	2	4	no	—
330	C₂⁴×C₃	—	2	4	no	—
331	C₂⁴×C₃	—	2	4	no	—
332	C₂⁴×C₃	—	2	4	no	—
333	C₂⁴×C₃	—	4	2	no	—
334	C₂⁴×C₃	—	4	2	no	—
335	C₂⁴×C₃	—	4	2	no	—
336	C₂⁴×C₃	C₂⁴	1	2	yes	—
337	C₂⁴×C₃	C₂⁴	1	2	yes	—
338	C₂⁴×C₃	C₂⁴	1	2	yes	—
339	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₃×Q₈	—	2	4	no	—
341	C₂×C₃×Q₈	—	4	2	no	—
342	C₂×C₃×Q₈	—	4	2	no	—
343	C₂×C₃×D₄	—	2	4	no	—
344	C₂×C₃×D₄	—	2	4	no	—
345	C₂×C₃×D₄	—	2	4	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	4	no	—
348	C₂×C₃×D₄	—	2	4	no	—
349	C₂×C₃×D₄	—	2	4	no	—
350	C₂×C₃×D₄	—	2	4	no	—
351	C₂×C₃×D₄	—	2	4	no	—
352	C₂×C₃×D₄	—	2	2	no	—
353	C₂×C₃×D₄	—	2	4	no	—
354	C₂×C₃×D₄	—	2	2	no	—
355	C₂×C₃×D₄	—	2	4	no	—
356	C₂×C₃×D₄	—	2	4	no	—
357	C₂×C₃×D₄	—	2	2	no	—
358	C₂×C₃×D₄	—	4	2	no	—
359	C₂×C₃×D₄	—	4	2	no	—
360	C₂×C₃×D₄	—	4	2	no	—
361	C₂×C₃×D₄	—	4	2	no	—
362	C₂×C₃×D₄	—	4	2	no	—
363	C₂×C₃×D₄	—	4	2	no	—
364	C₂×C₃×D₄	—	4	2	no	—
365	C₂×C₃×D₄	—	4	2	no	—
366	C₂×C₃×D₄	—	4	2	no	—
367	C₂×C₃×D₄	—	4	16	no	—
368	C₂²×C₃×C₄	—	2	2	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	2	4	no	—
371	C₂²×C₃×C₄	—	2	4	no	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	4	no	—
375	C₂²×C₃×C₄	—	2	4	no	—
376	C₂²×C₃×C₄	—	4	2	no	—
377	C₂²×C₃×C₄	—	4	2	no	—
378	C₂²×C₃×C₄	—	4	2	no	—
379	C₂²×C₃×C₄	—	4	2	no	—
380	C₂²×C₃×C₄	—	4	2	no	—
381	C₂²×C₃×C₄	—	4	2	no	—
382	C₂²×C₃×C₄	—	4	2	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
386	C₂²×C₃×C₄	#41	1	4	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
394	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
395	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₃×C₄⋊C₄	—	2	4	no	—
403	C₃×C₄⋊C₄	—	2	4	no	—
404	C₃×C₄⋊C₄	—	2	4	no	—
405	C₃×C₄⋊C₄	—	2	4	no	—
406	C₃×C₄⋊C₄	—	2	4	no	—
407	C₃×C₄⋊C₄	—	2	4	no	—
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	2	2	no	—
410	C₃×C₄⋊C₄	—	2	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	4	no	—
413	C₃×C₄⋊C₄	—	2	2	no	—
414	C₃×C₄⋊C₄	—	4	2	no	—
415	C₃×C₄⋊C₄	—	4	2	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
418	C₃×C₂²⋊C₄	—	2	4	no	—
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₂²⋊C₄	—	2	4	no	—
421	C₃×C₂²⋊C₄	—	2	4	no	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	2	4	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	—	2	4	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
431	C₃×C₂²⋊C₄	—	2	4	no	—
432	C₃×C₂²⋊C₄	—	2	4	no	—
433	C₃×C₂²⋊C₄	—	2	4	no	—
434	C₃×C₂²⋊C₄	—	2	4	no	—
435	C₃×C₂²⋊C₄	—	2	4	no	—
436	C₃×C₂²⋊C₄	—	2	4	no	—
437	C₃×C₂²⋊C₄	—	4	2	no	—
438	C₃×C₂²⋊C₄	—	4	2	no	—
439	C₃×C₂²⋊C₄	—	4	2	no	—
440	C₃×C₂²⋊C₄	—	4	2	no	—
441	C₃×C₂²⋊C₄	—	4	2	no	—
442	C₃×C₂²⋊C₄	—	4	2	no	—
443	C₃×C₂²⋊C₄	—	4	2	no	—
444	C₃×C₂²⋊C₄	—	4	2	no	—
445	C₃×C₂²⋊C₄	—	4	2	no	—
446	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
447	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
448	C₃×C₂²⋊C₄	#41	1	4	yes	—
449	C₃×C₄²	—	2	4	no	—
450	C₃×C₄²	—	2	4	no	—
451	C₃×C₄²	—	4	2	no	—
452	C₃×C₄²	—	4	2	no	—
453	C₃×C₄²	—	4	2	no	—
454	C₃×C₄²	—	4	2	no	—
455	C₃×C₄²	C₂×D₄	1	8	yes	complemented
456	C₂⁵	C₂³×C₃	1	2	yes	—
457	C₂²×Q₈	C₂³×C₃	1	2	yes	—
458	C₂²×D₄	—	2	4	no	—
459	C₂²×D₄	—	4	4	no	—
460	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₃	1	2	yes	—
463	C₂²×D₄	C₂³×C₃	1	2	yes	—
464	C₂²×D₄	C₂³×C₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₃	1	2	yes	—
475	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
476	#127	—	4	4	no	—
477	#126	—	2	8	no	—
478	#126	—	2	8	no	—
479	#124	—	2	8	no	—
480	#124	—	4	4	no	—
481	#123	—	2	8	no	—
482	#123	—	2	8	no	—
483	#123	—	2	8	no	—
484	C₂²⋊Q₈	—	2	8	no	—
485	C₂²⋊Q₈	—	2	8	no	—
486	#121	—	2	4	no	—
487	#120	—	2	8	no	—
488	#120	—	2	8	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	4	4	no	—
492	C₄×D₄	—	4	4	no	—
493	#117	—	2	4	no	—
494	#117	—	2	8	no	—
495	#117	C₃×D₄	1	8	yes	complemented
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	—	2	8	no	—
514	C₂×C₂²⋊C₄	—	2	8	no	—
515	C₂×C₂²⋊C₄	—	4	4	no	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₃	1	2	yes	—
548	C₂×C₄²	C₂³×C₃	1	2	yes	—
549	C₂×C₄²	C₂³×C₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₃	1	2	yes	—
552	C₂×C₄²	C₂³×C₃	1	2	yes	—
553	C₂×C₄²	C₂³×C₃	1	2	yes	—
554	#95	C₂³×C₃	1	1	yes	characteristic
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	1	yes	characteristic
557	#95	C₂³×C₃	1	2	yes	—
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	2	yes	—
560	#95	C₂³×C₃	1	2	yes	—
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	C₂³×C₃	—	2	2	no	—
570	C₂³×C₃	—	2	2	no	—
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	2	2	no	—
575	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	2	2	no	—
578	C₂³×C₃	—	2	2	no	—
579	C₂³×C₃	—	2	2	no	—
580	C₂³×C₃	—	2	2	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	—	2	2	no	—
588	C₂³×C₃	—	2	2	no	—
589	C₂³×C₃	—	2	2	no	—
590	C₂³×C₃	—	2	2	no	—
591	C₂³×C₃	—	4	8	no	—
592	C₂³×C₃	—	4	8	no	—
593	C₂³×C₃	—	4	8	no	—
594	C₂³×C₃	—	4	8	no	—
595	C₂³×C₃	—	8	4	no	—
596	C₂³×C₃	—	8	4	no	—
597	C₂³×C₃	—	8	4	no	—
598	C₂³×C₃	C₂²×D₄	1	2	yes	—
599	C₂³×C₃	C₂×#41	1	2	yes	—
600	C₂³×C₃	C₂×#41	1	2	yes	—
601	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
602	C₂³×C₃	C₂⁵	1	1	yes	characteristic
603	C₃×Q₈	—	8	4	no	—
604	C₃×D₄	—	2	8	no	—
605	C₃×D₄	—	4	8	no	—
606	C₃×D₄	—	4	8	no	—
607	C₃×D₄	—	4	8	no	—
608	C₃×D₄	—	4	4	no	—
609	C₃×D₄	—	4	8	no	—
610	C₃×D₄	—	8	4	no	—
611	C₃×D₄	—	8	2	no	—
612	C₃×D₄	—	8	4	no	—
613	C₂×C₃×C₄	—	2	8	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	4	4	no	—
649	C₂×C₃×C₄	—	4	8	no	—
650	C₂×C₃×C₄	—	8	4	no	—
651	C₂×C₃×C₄	—	8	4	no	—
652	C₂×C₃×C₄	—	8	4	no	—
653	C₂×C₃×C₄	—	8	2	no	—
654	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
655	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
656	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
657	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
658	C₂×C₃×C₄	C₂×#41	1	4	yes	—
659	C₂×C₃×C₄	C₂×#41	1	2	yes	—
660	C₂×C₃×C₄	C₂×#41	1	2	yes	—
661	C₂⁴	—	2	4	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	2	4	no	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	4	2	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂⁴×C₃	1	2	yes	—
669	C₂⁴	C₂⁴×C₃	1	2	yes	—
670	C₂⁴	C₂⁴×C₃	1	2	yes	—
671	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	16	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
718	C₂²×C₄	C₃×#41	1	4	yes	—
719	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	complemented
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
779	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
780	C₂²⋊C₄	C₃×#41	1	4	yes	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	2	no	—
787	C₄²	C₂×C₃×D₄	1	8	yes	complemented
788	C₂²×C₃	—	2	4	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	2	2	no	—
791	C₂²×C₃	—	2	4	no	—
792	C₂²×C₃	—	2	4	no	—
793	C₂²×C₃	—	2	4	no	—
794	C₂²×C₃	—	2	4	no	—
795	C₂²×C₃	—	4	2	no	—
796	C₂²×C₃	—	4	2	no	—
797	C₂²×C₃	—	4	2	no	—
798	C₂²×C₃	—	4	2	no	—
799	C₂²×C₃	—	4	2	no	—
800	C₂²×C₃	—	4	2	no	—
801	C₂²×C₃	—	4	2	no	—
802	C₂²×C₃	—	4	2	no	—
803	C₂²×C₃	—	4	2	no	—
804	C₂²×C₃	—	4	2	no	—
805	C₂²×C₃	—	4	2	no	—
806	C₂²×C₃	—	4	2	no	—
807	C₂²×C₃	—	4	2	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	4	2	no	—
810	C₂²×C₃	—	4	2	no	—
811	C₂²×C₃	—	4	2	no	—
812	C₂²×C₃	—	4	2	no	—
813	C₂²×C₃	—	8	16	no	—
814	C₂²×C₃	#532	1	4	yes	—
815	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
816	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
817	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
818	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
819	C₂²×C₃	#585	1	2	yes	—
820	C₃×C₄	—	2	2	no	—
821	C₃×C₄	—	2	2	no	—
822	C₃×C₄	—	2	4	no	—
823	C₃×C₄	—	2	4	no	—
824	C₃×C₄	—	2	2	no	—
825	C₃×C₄	—	2	2	no	—
826	C₃×C₄	—	2	4	no	—
827	C₃×C₄	—	4	2	no	—
828	C₃×C₄	—	4	2	no	—
829	C₃×C₄	—	4	2	no	—
830	C₃×C₄	—	4	2	no	—
831	C₃×C₄	—	4	2	no	—
832	C₃×C₄	—	4	1	no	—
833	C₃×C₄	—	4	1	no	—
834	C₃×C₄	—	4	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	4	8	no	—
858	C₂³	—	4	8	no	—
859	C₂³	—	4	8	no	—
860	C₂³	—	4	8	no	—
861	C₂³	—	8	4	no	—
862	C₂³	—	8	4	no	—
863	C₂³	—	8	4	no	—
864	C₂³	C₂²×C₃×D₄	1	2	yes	—
865	C₂³	C₂×C₃×#41	1	2	yes	—
866	C₂³	C₂×C₃×#41	1	2	yes	—
867	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
868	C₂³	C₂⁵×C₃	1	1	yes	characteristic
869	Q₈	—	8	4	no	—
870	D₄	—	2	8	no	—
871	D₄	—	4	8	no	—
872	D₄	—	4	8	no	—
873	D₄	—	4	8	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	8	no	—
876	D₄	—	8	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	4	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	8	4	no	—
917	C₂×C₄	—	8	4	no	—
918	C₂×C₄	—	8	4	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
921	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
922	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
923	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
924	C₂×C₄	C₂×C₃×#41	1	4	yes	—
925	C₂×C₄	C₂×C₃×#41	1	2	yes	—
926	C₂×C₄	C₂×C₃×#41	1	2	yes	—
927	C₂×C₃	—	2	4	no	—
928	C₂×C₃	—	4	4	no	—
929	C₂×C₃	—	8	2	no	—
930	C₂×C₃	—	8	2	no	—
931	C₂×C₃	C₂×#532	1	1	yes	characteristic
932	C₂×C₃	#3488	1	2	yes	—
933	C₂×C₃	#3490	1	1	yes	characteristic
934	C₂×C₃	#3510	1	1	yes	characteristic
935	C₂×C₃	#3513	1	2	yes	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	4	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	8	16	no	—
962	C₂²	C₃×#532	1	4	yes	—
963	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
964	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
965	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
966	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
967	C₂²	C₃×#585	1	2	yes	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	2	no	—
983	C₃	#35732	1	1	yes	characteristic, direct product factor, Sylow
984	C₂	—	2	4	no	—
985	C₂	—	4	4	no	—
986	C₂	—	8	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×C₃×#532	1	1	yes	characteristic
989	C₂	C₃×#3488	1	2	yes	—
990	C₂	C₃×#3490	1	1	yes	characteristic
991	C₂	C₃×#3510	1	1	yes	characteristic
992	C₂	C₃×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2433	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#551	C₂	semidirect
2. C₃×#2662	C₂	semidirect
3. C₃×#2618	C₂	semidirect
4. C₃×#2601	C₂	semidirect
5. C₃×#2560	C₂	semidirect
6. C₃×#2554	C₂	semidirect
7. C₃×#2549	C₂	semidirect
8. C₃×#2544	C₂	semidirect
9. C₃×#2472	C₂	semidirect
10. C₃×#2461	C₂	semidirect
11. C₃×#2445	C₂	semidirect
13. C₃×#2411	C₂	semidirect
14. C₃×#2392	C₂	semidirect
15. C₂×C₃×#394	C₂	semidirect
16. C₃×#2364	C₂	semidirect
17. C₃×#2358	C₂	semidirect
18. C₃×D₄×C₂²⋊C₄	C₂	semidirect
19. C₃×#2274	C₂	semidirect
20. #35732	C₃	direct (N × H)
24. C₂×C₃×#126	C₂²	semidirect
25. C₂×C₃×#126	C₂²	semidirect
26. C₂×C₃×#124	C₂²	semidirect
27. C₂×C₃×#124	C₂²	semidirect
29. C₂×C₃×#123	C₂²	semidirect
30. C₂×C₃×#123	C₂²	semidirect
32. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×C₄×D₄	C₂²	semidirect
42. C₂×C₃×#117	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
49. C₃×#398	C₂²	semidirect
50. C₃×#397	C₂²	semidirect
51. C₃×#396	C₂²	semidirect
52. C₃×#396	C₂²	semidirect
53. C₃×#396	C₂²	semidirect
54. C₃×#396	C₂²	semidirect
55. C₃×#395	C₂²	semidirect
62. C₃×#394	C₂²	semidirect
63. C₃×#394	C₂²	semidirect
64. C₃×#394	C₂²	semidirect
65. C₃×#394	C₂²	semidirect
66. C₃×#394	C₂²	semidirect
67. C₃×#394	C₂²	semidirect
68. C₃×#393	C₂²	semidirect
71. C₃×#391	C₂²	semidirect
74. C₃×#390	C₂²	semidirect
75. C₃×#390	C₂²	semidirect
76. C₃×#390	C₂²	semidirect
77. C₃×#390	C₂²	semidirect
78. C₃×#389	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#388	C₂²	semidirect
82. C₃×#388	C₂²	semidirect
83. C₃×#388	C₂²	semidirect
84. C₃×#388	C₂²	semidirect
85. C₃×#388	C₂²	semidirect
86. C₃×#387	C₂²	semidirect
91. C₃×#386	C₂²	semidirect
92. C₃×#386	C₂²	semidirect
93. C₃×#386	C₂²	semidirect
95. C₃×#385	C₂²	semidirect
98. C₃×C₄×C₄⋊C₄	C₂²	semidirect
99. C₃×C₄×C₄⋊C₄	C₂²	semidirect
100. C₃×C₄×C₄⋊C₄	C₂²	semidirect
101. C₃×C₄×C₄⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
107. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
109. C₂×#551	C₂×C₃	semidirect
110. #2662	C₂×C₃	semidirect
111. #2618	C₂×C₃	semidirect
112. #2601	C₂×C₃	semidirect
113. #2560	C₂×C₃	semidirect
114. #2554	C₂×C₃	semidirect
115. #2549	C₂×C₃	semidirect
116. #2544	C₂×C₃	semidirect
117. #2472	C₂×C₃	semidirect
118. #2461	C₂×C₃	semidirect
119. #2445	C₂×C₃	semidirect
121. #2411	C₂×C₃	semidirect
122. #2392	C₂×C₃	semidirect
123. C₂×#394	C₂×C₃	semidirect
124. #2364	C₂×C₃	semidirect
125. #2358	C₂×C₃	semidirect
126. D₄×C₂²⋊C₄	C₂×C₃	semidirect
127. #2274	C₂×C₃	semidirect
167. C₃×#117	D₄	semidirect
244. C₂×#126	C₂²×C₃	semidirect
245. C₂×#126	C₂²×C₃	semidirect
246. C₂×#124	C₂²×C₃	semidirect
247. C₂×#124	C₂²×C₃	semidirect
249. C₂×#123	C₂²×C₃	semidirect
250. C₂×#123	C₂²×C₃	semidirect
252. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
258. C₂×C₄×D₄	C₂²×C₃	semidirect
259. C₂×C₄×D₄	C₂²×C₃	semidirect
262. C₂×#117	C₂²×C₃	semidirect
267. #398	C₂²×C₃	semidirect
268. #398	C₂²×C₃	semidirect
269. #398	C₂²×C₃	semidirect
270. #397	C₂²×C₃	semidirect
271. #396	C₂²×C₃	semidirect
272. #396	C₂²×C₃	semidirect
273. #396	C₂²×C₃	semidirect
274. #396	C₂²×C₃	semidirect
275. #395	C₂²×C₃	semidirect
282. #394	C₂²×C₃	semidirect
283. #394	C₂²×C₃	semidirect
284. #394	C₂²×C₃	semidirect
285. #394	C₂²×C₃	semidirect
286. #394	C₂²×C₃	semidirect
287. #394	C₂²×C₃	semidirect
288. #393	C₂²×C₃	semidirect
291. #391	C₂²×C₃	semidirect
294. #390	C₂²×C₃	semidirect
295. #390	C₂²×C₃	semidirect
296. #390	C₂²×C₃	semidirect
297. #390	C₂²×C₃	semidirect
298. #389	C₂²×C₃	semidirect
299. #388	C₂²×C₃	semidirect
300. #388	C₂²×C₃	semidirect
301. #388	C₂²×C₃	semidirect
302. #388	C₂²×C₃	semidirect
303. #388	C₂²×C₃	semidirect
304. #388	C₂²×C₃	semidirect
305. #388	C₂²×C₃	semidirect
306. #387	C₂²×C₃	semidirect
311. #386	C₂²×C₃	semidirect
312. #386	C₂²×C₃	semidirect
313. #386	C₂²×C₃	semidirect
315. #385	C₂²×C₃	semidirect
318. C₄×C₄⋊C₄	C₂²×C₃	semidirect
319. C₄×C₄⋊C₄	C₂²×C₃	semidirect
320. C₄×C₄⋊C₄	C₂²×C₃	semidirect
321. C₄×C₄⋊C₄	C₂²×C₃	semidirect
326. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
327. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
417. C₃×C₄⋊C₄	C₂×D₄	semidirect
455. C₃×C₄²	C₂×D₄	semidirect
495. #117	C₃×D₄	semidirect
749. C₄⋊C₄	C₂×C₃×D₄	semidirect
787. C₄²	C₂×C₃×D₄	semidirect
983. C₃	#35732	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#551	2
C₃×#2662	2
C₃×#2618	2
C₃×#2601	2
C₃×#2560	2
C₃×#2554	2
C₃×#2549	2
C₃×#2544	2
C₃×#2472	2
C₃×#2461	2
C₃×#2445	2
C₃×#2433	2
C₃×#2411	2
C₃×#2392	2
C₂×C₃×#394	2
C₃×#2364	2
C₃×#2358	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2274	2
#35732	3

Subgroups — C3×#35732 #10654339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35732 #10654339