Subgroups — C₃×#37682 #10656289

Order 768.

3174 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2671	C₂	1	4	yes	maximal, complemented
7	C₃×#2668	C₂	1	4	yes	maximal, complemented
8	C₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2443	C₂	1	4	yes	maximal, complemented
13	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2418	C₂	1	4	yes	maximal, complemented
18	C₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
20	#37682	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#41	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
25	C₃×#547	—	2	8	no	—
26	C₃×#546	—	2	8	no	—
27	C₃×#535	—	2	8	no	—
28	C₃×#532	—	2	8	no	—
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#127	C₂²	1	1	yes	characteristic
33	C₂×C₃×#127	C₂²	1	1	yes	characteristic
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#123	C₂²	1	2	yes	—
41	C₂×C₃×#123	C₂²	1	2	yes	—
42	C₂×C₃×#123	C₂²	1	2	yes	complemented
43	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#121	C₂²	1	4	yes	—
47	C₂×C₃×#121	C₂²	1	2	yes	—
48	C₂×C₃×#121	C₂²	1	1	yes	characteristic
49	C₂×C₃×#121	C₂²	1	2	yes	—
50	C₂×C₃×#121	C₂²	1	4	yes	complemented
51	C₂×C₃×#120	C₂²	1	4	yes	—
52	C₂×C₃×#120	C₂²	1	2	yes	—
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
56	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×#117	C₂²	1	1	yes	characteristic
58	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
61	C₃×#399	C₂²	1	4	yes	complemented
62	C₃×#399	C₂²	1	4	yes	complemented
63	C₃×#398	C₂²	1	4	yes	complemented
64	C₃×#397	C₂²	1	4	yes	—
65	C₃×#397	C₂²	1	4	yes	complemented
66	C₃×#394	C₂²	1	4	yes	—
67	C₃×#394	C₂²	1	4	yes	—
68	C₃×#394	C₂²	1	4	yes	complemented
69	C₃×#394	C₂²	1	4	yes	complemented
70	C₃×#392	C₂²	1	4	yes	complemented
71	C₃×#391	C₂²	1	1	yes	characteristic, complemented
72	C₃×#391	C₂²	1	1	yes	characteristic, complemented
73	C₃×#391	C₂²	1	1	yes	characteristic, complemented
74	C₃×#390	C₂²	1	1	yes	characteristic
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	1	yes	characteristic, complemented
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	4	yes	complemented
79	C₃×#387	C₂²	1	2	yes	complemented
80	C₃×#386	C₂²	1	2	yes	—
81	C₃×#386	C₂²	1	4	yes	complemented
82	C₃×#386	C₂²	1	4	yes	complemented
83	C₃×#386	C₂²	1	4	yes	complemented
84	C₃×#386	C₂²	1	4	yes	complemented
85	C₃×#386	C₂²	1	4	yes	complemented
86	C₃×#385	C₂²	1	2	yes	complemented
87	C₃×#385	C₂²	1	4	yes	complemented
88	C₃×#385	C₂²	1	4	yes	complemented
89	C₃×#382	C₂²	1	1	yes	characteristic, complemented
90	C₃×#380	C₂²	1	4	yes	complemented
91	C₃×#379	C₂²	1	4	yes	—
92	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
94	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₃×#376	C₂²	1	1	yes	characteristic, complemented
96	C₂×#547	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
98	C₂×#535	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂×#532	C₂×C₃	1	1	yes	characteristic, complemented
100	#2850	C₂×C₃	1	1	yes	characteristic, complemented
101	#2671	C₂×C₃	1	4	yes	complemented
102	#2668	C₂×C₃	1	4	yes	complemented
103	#2658	C₂×C₃	1	1	yes	characteristic, complemented
104	#2621	C₂×C₃	1	1	yes	characteristic, complemented
105	#2547	C₂×C₃	1	1	yes	characteristic, complemented
106	#2544	C₂×C₃	1	1	yes	characteristic, complemented
107	#2443	C₂×C₃	1	4	yes	complemented
108	#2435	C₂×C₃	1	1	yes	characteristic, complemented
109	#2432	C₂×C₃	1	1	yes	characteristic, complemented
110	#2432	C₂×C₃	1	1	yes	characteristic, complemented
111	#2431	C₂×C₃	1	1	yes	characteristic, complemented
112	#2418	C₂×C₃	1	4	yes	complemented
113	#2328	C₂×C₃	1	1	yes	characteristic, complemented
114	#2290	C₂×C₃	1	1	yes	characteristic, complemented
115	C₂⁵×C₃	C₂³	1	2	yes	—
116	C₂×C₃×#41	—	2	4	no	—
117	C₂×C₃×#41	—	2	4	no	—
118	C₂×C₃×#41	—	2	4	no	—
119	C₂×C₃×#41	—	2	4	no	—
120	C₂×C₃×#41	—	2	4	no	—
121	C₂×C₃×#41	—	2	4	no	—
122	C₂×C₃×#41	—	4	2	no	—
123	C₂×C₃×#41	—	4	2	no	—
124	C₂×C₃×#41	—	4	2	no	—
125	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×D₄	—	2	4	no	—
129	C₂²×C₃×D₄	—	2	4	no	—
130	C₂²×C₃×D₄	—	4	2	no	—
131	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₃×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
137	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂³	1	2	yes	—
139	C₂²×C₃×D₄	C₂³	1	4	yes	—
140	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
141	C₂²×C₃×D₄	C₂³	1	4	yes	—
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	2	yes	—
144	C₂³×C₃×C₄	C₂³	1	2	yes	—
145	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
147	C₂³×C₃×C₄	C₂³	1	2	yes	—
148	C₂³×C₃×C₄	C₂³	1	2	yes	—
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₃×C₄⋊Q₈	—	2	4	no	—
151	C₃×C₄⋊Q₈	—	2	4	no	—
152	C₃×C₄⋊Q₈	—	4	2	no	—
153	C₃×#127	—	2	4	no	—
154	C₃×#127	D₄	1	8	yes	complemented
155	C₃×#124	—	2	4	no	—
156	C₃×#124	—	2	4	no	—
157	C₃×#124	—	2	4	no	—
158	C₃×#124	—	2	4	no	—
159	C₃×#124	—	2	4	no	—
160	C₃×#124	—	4	2	no	—
161	C₃×#123	—	2	8	no	—
162	C₃×#123	—	2	8	no	—
163	C₃×#123	—	2	8	no	—
164	C₃×C₂²⋊Q₈	—	2	4	no	—
165	C₃×C₂²⋊Q₈	—	2	4	no	—
166	C₃×C₂²⋊Q₈	—	2	4	no	—
167	C₃×#121	—	2	16	no	—
168	C₃×#121	—	2	8	no	—
169	C₃×#121	—	2	16	no	—
170	C₃×#121	—	2	4	no	—
171	C₃×#121	—	2	8	no	—
172	C₃×#120	—	2	16	no	—
173	C₃×#120	—	2	8	no	—
174	C₃×C₄×D₄	—	2	16	no	—
175	C₃×C₄×D₄	—	2	4	no	—
176	C₃×C₄×D₄	—	2	4	no	—
177	C₃×C₄×D₄	D₄	1	8	yes	complemented
178	C₃×#117	—	2	4	no	—
179	C₂×C₃×C₄⋊C₄	—	2	8	no	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	4	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	4	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	4	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	—	2	4	no	—
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	2	yes	—
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	4	yes	—
227	C₃×#95	C₂³	1	4	yes	—
228	C₃×#95	C₂³	1	4	yes	—
229	C₃×#95	C₂³	1	4	yes	—
230	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
231	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
232	C₂²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
234	#547	—	2	8	no	—
235	#546	—	2	8	no	—
236	#535	—	2	8	no	—
237	#532	—	2	8	no	—
238	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
239	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
240	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₂×#127	C₂²×C₃	1	1	yes	characteristic
242	C₂×#127	C₂²×C₃	1	1	yes	characteristic
243	C₂×#124	C₂²×C₃	1	1	yes	characteristic
244	C₂×#124	C₂²×C₃	1	1	yes	characteristic
245	C₂×#124	C₂²×C₃	1	1	yes	characteristic
246	C₂×#124	C₂²×C₃	1	1	yes	characteristic
247	C₂×#124	C₂²×C₃	1	1	yes	characteristic
248	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
249	C₂×#123	C₂²×C₃	1	2	yes	—
250	C₂×#123	C₂²×C₃	1	2	yes	—
251	C₂×#123	C₂²×C₃	1	2	yes	complemented
252	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₂×#121	C₂²×C₃	1	1	yes	characteristic
256	C₂×#121	C₂²×C₃	1	2	yes	—
257	C₂×#121	C₂²×C₃	1	2	yes	—
258	C₂×#121	C₂²×C₃	1	4	yes	—
259	C₂×#121	C₂²×C₃	1	4	yes	complemented
260	C₂×#120	C₂²×C₃	1	2	yes	—
261	C₂×#120	C₂²×C₃	1	4	yes	—
262	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
265	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
266	C₂×#117	C₂²×C₃	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
268	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
269	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
270	#399	C₂²×C₃	1	4	yes	complemented
271	#399	C₂²×C₃	1	4	yes	complemented
272	#398	C₂²×C₃	1	4	yes	complemented
273	#397	C₂²×C₃	1	4	yes	—
274	#397	C₂²×C₃	1	4	yes	complemented
275	#394	C₂²×C₃	1	4	yes	—
276	#394	C₂²×C₃	1	4	yes	—
277	#394	C₂²×C₃	1	4	yes	complemented
278	#394	C₂²×C₃	1	4	yes	complemented
279	#392	C₂²×C₃	1	4	yes	complemented
280	#391	C₂²×C₃	1	1	yes	characteristic, complemented
281	#391	C₂²×C₃	1	1	yes	characteristic, complemented
282	#391	C₂²×C₃	1	1	yes	characteristic, complemented
283	#390	C₂²×C₃	1	1	yes	characteristic
284	#390	C₂²×C₃	1	1	yes	characteristic
285	#390	C₂²×C₃	1	1	yes	characteristic, complemented
286	#388	C₂²×C₃	1	2	yes	—
287	#388	C₂²×C₃	1	4	yes	complemented
288	#387	C₂²×C₃	1	2	yes	complemented
289	#386	C₂²×C₃	1	2	yes	—
290	#386	C₂²×C₃	1	4	yes	complemented
291	#386	C₂²×C₃	1	4	yes	complemented
292	#386	C₂²×C₃	1	4	yes	complemented
293	#386	C₂²×C₃	1	4	yes	complemented
294	#386	C₂²×C₃	1	4	yes	complemented
295	#385	C₂²×C₃	1	2	yes	complemented
296	#385	C₂²×C₃	1	4	yes	complemented
297	#385	C₂²×C₃	1	4	yes	complemented
298	#382	C₂²×C₃	1	1	yes	characteristic, complemented
299	#380	C₂²×C₃	1	4	yes	complemented
300	#379	C₂²×C₃	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
304	#376	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂⁴×C₃	—	2	4	no	—
306	C₂⁴×C₃	—	2	4	no	—
307	C₂⁴×C₃	—	4	4	no	—
308	C₂⁴×C₃	—	4	2	no	—
309	C₂⁴×C₃	—	4	4	no	—
310	C₂⁴×C₃	C₂⁴	1	2	yes	—
311	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
312	C₂⁴×C₃	C₂⁴	1	2	yes	—
313	C₂⁴×C₃	C₂⁴	1	2	yes	—
314	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
315	C₃×#41	—	4	16	no	—
316	C₃×#41	—	4	16	no	—
317	C₃×#41	—	4	16	no	—
318	C₂×C₃×Q₈	—	2	2	no	—
319	C₂×C₃×Q₈	—	2	2	no	—
320	C₂×C₃×Q₈	—	2	2	no	—
321	C₂×C₃×Q₈	—	2	2	no	—
322	C₂×C₃×Q₈	—	2	2	no	—
323	C₂×C₃×Q₈	—	2	2	no	—
324	C₂×C₃×Q₈	—	2	2	no	—
325	C₂×C₃×Q₈	—	2	2	no	—
326	C₂×C₃×Q₈	—	2	2	no	—
327	C₂×C₃×D₄	—	2	4	no	—
328	C₂×C₃×D₄	—	2	4	no	—
329	C₂×C₃×D₄	—	2	4	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	2	4	no	—
332	C₂×C₃×D₄	—	2	4	no	—
333	C₂×C₃×D₄	—	2	4	no	—
334	C₂×C₃×D₄	—	2	4	no	—
335	C₂×C₃×D₄	—	2	8	no	—
336	C₂×C₃×D₄	—	2	2	no	—
337	C₂×C₃×D₄	—	2	2	no	—
338	C₂×C₃×D₄	—	2	4	no	—
339	C₂×C₃×D₄	—	2	2	no	—
340	C₂×C₃×D₄	—	2	2	no	—
341	C₂×C₃×D₄	—	2	2	no	—
342	C₂×C₃×D₄	—	2	2	no	—
343	C₂×C₃×D₄	—	2	2	no	—
344	C₂×C₃×D₄	—	4	16	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂×C₃×D₄	—	4	2	no	—
347	C₂×C₃×D₄	—	4	4	no	—
348	C₂×C₃×D₄	—	4	4	no	—
349	C₂×C₃×D₄	—	4	2	no	—
350	C₂×C₃×D₄	—	4	2	no	—
351	C₂×C₃×D₄	—	4	2	no	—
352	C₂×C₃×D₄	—	4	4	no	—
353	C₂×C₃×D₄	—	4	4	no	—
354	C₂×C₃×D₄	—	4	4	no	—
355	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
356	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
357	C₂×C₃×D₄	C₂×D₄	1	16	yes	—
358	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
359	C₂²×C₃×C₄	—	2	2	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	2	no	—
363	C₂²×C₃×C₄	—	2	4	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	2	4	no	—
366	C₂²×C₃×C₄	—	2	4	no	—
367	C₂²×C₃×C₄	—	2	4	no	—
368	C₂²×C₃×C₄	—	2	4	no	—
369	C₂²×C₃×C₄	—	2	4	no	—
370	C₂²×C₃×C₄	—	2	4	no	—
371	C₂²×C₃×C₄	—	2	4	no	—
372	C₂²×C₃×C₄	—	4	4	no	—
373	C₂²×C₃×C₄	—	4	2	no	—
374	C₂²×C₃×C₄	—	4	2	no	—
375	C₂²×C₃×C₄	—	4	2	no	—
376	C₂²×C₃×C₄	—	4	2	no	—
377	C₂²×C₃×C₄	—	4	2	no	—
378	C₂²×C₃×C₄	—	4	4	no	—
379	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
380	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	2	4	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	8	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	4	no	—
403	C₃×C₄⋊C₄	—	2	4	no	—
404	C₃×C₄⋊C₄	—	4	2	no	—
405	C₃×C₄⋊C₄	—	4	4	no	—
406	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	8	no	—
409	C₃×C₂²⋊C₄	—	2	8	no	—
410	C₃×C₂²⋊C₄	—	2	8	no	—
411	C₃×C₂²⋊C₄	—	2	4	no	—
412	C₃×C₂²⋊C₄	—	2	4	no	—
413	C₃×C₂²⋊C₄	—	2	4	no	—
414	C₃×C₂²⋊C₄	—	2	4	no	—
415	C₃×C₂²⋊C₄	—	2	4	no	—
416	C₃×C₂²⋊C₄	—	2	4	no	—
417	C₃×C₂²⋊C₄	—	2	4	no	—
418	C₃×C₂²⋊C₄	—	2	8	no	—
419	C₃×C₂²⋊C₄	—	2	4	no	—
420	C₃×C₂²⋊C₄	—	4	4	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	4	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	4	no	—
425	C₃×C₂²⋊C₄	—	4	4	no	—
426	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
427	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	2	2	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	2	no	—
432	C₃×C₄²	C₂×D₄	1	4	yes	—
433	C₃×C₄²	C₂×D₄	1	4	yes	—
434	C₂⁵	C₂³×C₃	1	2	yes	—
435	C₂×#41	—	2	4	no	—
436	C₂×#41	—	2	4	no	—
437	C₂×#41	—	2	4	no	—
438	C₂×#41	—	2	4	no	—
439	C₂×#41	—	2	4	no	—
440	C₂×#41	—	2	4	no	—
441	C₂×#41	—	4	2	no	—
442	C₂×#41	—	4	2	no	—
443	C₂×#41	—	4	2	no	—
444	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
447	C₂²×D₄	—	2	4	no	—
448	C₂²×D₄	—	2	4	no	—
449	C₂²×D₄	—	4	2	no	—
450	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₃	1	2	yes	—
452	C₂²×D₄	C₂³×C₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₃	1	2	yes	—
454	C₂²×D₄	C₂³×C₃	1	2	yes	—
455	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₃	1	2	yes	—
458	C₂²×D₄	C₂³×C₃	1	4	yes	—
459	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₃	1	4	yes	—
461	C₂³×C₄	C₂³×C₃	1	2	yes	—
462	C₂³×C₄	C₂³×C₃	1	2	yes	—
463	C₂³×C₄	C₂³×C₃	1	2	yes	—
464	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₃	1	2	yes	—
467	C₂³×C₄	C₂³×C₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₃	1	2	yes	—
469	C₄⋊Q₈	—	2	4	no	—
470	C₄⋊Q₈	—	2	4	no	—
471	C₄⋊Q₈	—	4	2	no	—
472	#127	—	2	4	no	—
473	#127	C₃×D₄	1	8	yes	complemented
474	#124	—	2	4	no	—
475	#124	—	2	4	no	—
476	#124	—	2	4	no	—
477	#124	—	2	4	no	—
478	#124	—	2	4	no	—
479	#124	—	4	2	no	—
480	#123	—	2	8	no	—
481	#123	—	2	8	no	—
482	#123	—	2	8	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	#121	—	2	16	no	—
487	#121	—	2	8	no	—
488	#121	—	2	16	no	—
489	#121	—	2	4	no	—
490	#121	—	2	8	no	—
491	#120	—	2	16	no	—
492	#120	—	2	8	no	—
493	C₄×D₄	—	2	16	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	C₃×D₄	1	8	yes	complemented
497	#117	—	2	4	no	—
498	C₂×C₄⋊C₄	—	2	8	no	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	—	2	8	no	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	4	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	4	yes	—
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	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	—	2	4	no	—
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	4	yes	—
546	#95	C₂³×C₃	1	4	yes	—
547	#95	C₂³×C₃	1	4	yes	—
548	#95	C₂³×C₃	1	4	yes	—
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	1	no	—
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	2	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	2	no	—
558	C₂³×C₃	—	2	4	no	—
559	C₂³×C₃	—	2	4	no	—
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	4	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	4	no	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	2	no	—
567	C₂³×C₃	—	2	2	no	—
568	C₂³×C₃	—	2	4	no	—
569	C₂³×C₃	—	2	4	no	—
570	C₂³×C₃	—	4	8	no	—
571	C₂³×C₃	—	4	8	no	—
572	C₂³×C₃	—	8	8	no	—
573	C₂³×C₃	—	8	4	no	—
574	C₂³×C₃	—	8	8	no	—
575	C₂³×C₃	C₂²×D₄	1	2	yes	—
576	C₂³×C₃	C₂²×D₄	1	4	yes	—
577	C₂³×C₃	C₂²×D₄	1	2	yes	—
578	C₂³×C₃	C₂²×D₄	1	4	yes	—
579	C₂³×C₃	C₂⁵	1	1	yes	characteristic
580	C₃×Q₈	—	4	4	no	—
581	C₃×Q₈	—	4	4	no	—
582	C₃×Q₈	—	4	4	no	—
583	C₃×D₄	—	2	8	no	—
584	C₃×D₄	—	2	8	no	—
585	C₃×D₄	—	4	4	no	—
586	C₃×D₄	—	4	16	no	—
587	C₃×D₄	—	4	8	no	—
588	C₃×D₄	—	4	8	no	—
589	C₃×D₄	—	4	8	no	—
590	C₃×D₄	—	4	8	no	—
591	C₃×D₄	—	4	4	no	—
592	C₃×D₄	—	8	8	no	—
593	C₃×D₄	—	8	4	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	8	no	—
603	C₂×C₃×C₄	—	2	8	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	4	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	4	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	4	8	no	—
627	C₂×C₃×C₄	—	4	8	no	—
628	C₂×C₃×C₄	—	4	8	no	—
629	C₂×C₃×C₄	—	4	8	no	—
630	C₂×C₃×C₄	—	4	8	no	—
631	C₂×C₃×C₄	—	8	4	no	—
632	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
633	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
634	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
635	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
636	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
637	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
638	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
639	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
640	C₂⁴	—	2	4	no	—
641	C₂⁴	—	2	4	no	—
642	C₂⁴	—	4	2	no	—
643	C₂⁴	—	4	4	no	—
644	C₂⁴	—	4	4	no	—
645	C₂⁴	C₂⁴×C₃	1	2	yes	—
646	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₃	1	2	yes	—
648	C₂⁴	C₂⁴×C₃	1	2	yes	—
649	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
650	#41	—	4	16	no	—
651	#41	—	4	16	no	—
652	#41	—	4	16	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	16	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
691	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
692	C₂×D₄	C₂×C₃×D₄	1	16	yes	—
693	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	4	no	—
714	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
715	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	8	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	4	4	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	8	no	—
744	C₂²⋊C₄	—	2	8	no	—
745	C₂²⋊C₄	—	2	8	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	8	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	4	4	no	—
756	C₂²⋊C₄	—	4	4	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	4	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	4	no	—
761	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
762	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	C₂×C₃×D₄	1	4	yes	—
768	C₄²	C₂×C₃×D₄	1	4	yes	—
769	C₂²×C₃	—	2	2	no	—
770	C₂²×C₃	—	2	2	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	2	no	—
773	C₂²×C₃	—	2	4	no	—
774	C₂²×C₃	—	2	4	no	—
775	C₂²×C₃	—	2	8	no	—
776	C₂²×C₃	—	2	8	no	—
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	4	2	no	—
780	C₂²×C₃	—	4	2	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	2	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	2	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	4	no	—
787	C₂²×C₃	—	4	4	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	4	2	no	—
790	C₂²×C₃	—	4	2	no	—
791	C₂²×C₃	—	4	4	no	—
792	C₂²×C₃	—	4	2	no	—
793	C₂²×C₃	—	4	4	no	—
794	C₂²×C₃	—	8	16	no	—
795	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
796	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
797	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²×C₃	#585	1	2	yes	—
799	C₂²×C₃	#585	1	2	yes	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	2	4	no	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	4	2	no	—
806	C₃×C₄	—	4	2	no	—
807	C₃×C₄	—	4	2	no	—
808	C₃×C₄	—	4	2	no	—
809	C₃×C₄	—	4	2	no	—
810	C₃×C₄	—	4	2	no	—
811	C₃×C₄	—	4	2	no	—
812	C₃×C₄	—	4	2	no	—
813	C₃×C₄	D₄²	1	4	yes	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	4	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	4	no	—
834	C₂³	—	2	4	no	—
835	C₂³	—	4	8	no	—
836	C₂³	—	4	8	no	—
837	C₂³	—	8	8	no	—
838	C₂³	—	8	4	no	—
839	C₂³	—	8	8	no	—
840	C₂³	C₂²×C₃×D₄	1	2	yes	—
841	C₂³	C₂²×C₃×D₄	1	4	yes	—
842	C₂³	C₂²×C₃×D₄	1	2	yes	—
843	C₂³	C₂²×C₃×D₄	1	4	yes	—
844	C₂³	C₂⁵×C₃	1	1	yes	characteristic
845	Q₈	—	4	4	no	—
846	Q₈	—	4	4	no	—
847	Q₈	—	4	4	no	—
848	D₄	—	2	8	no	—
849	D₄	—	2	8	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	16	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	8	no	—
854	D₄	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	4	no	—
857	D₄	—	8	8	no	—
858	D₄	—	8	4	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	8	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	4	8	no	—
896	C₂×C₄	—	8	4	no	—
897	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
898	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
899	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
900	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
901	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
902	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
903	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
904	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
905	C₂×C₃	—	4	2	no	—
906	C₂×C₃	—	4	4	no	—
907	C₂×C₃	—	4	4	no	—
908	C₂×C₃	—	4	2	no	—
909	C₂×C₃	—	8	2	no	—
910	C₂×C₃	#3449	1	1	yes	characteristic
911	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
912	C₂×C₃	#3485	1	2	yes	—
913	C₂×C₃	#3500	1	1	yes	characteristic
914	C₂×C₃	#3562	1	2	yes	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	8	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	4	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	4	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	4	no	—
940	C₂²	—	8	16	no	—
941	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
942	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
943	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂²	C₃×#585	1	2	yes	—
945	C₂²	C₃×#585	1	2	yes	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	2	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	C₃×D₄²	1	4	yes	—
960	C₃	#37682	1	1	yes	characteristic, direct product factor, Sylow
961	C₂	—	4	2	no	—
962	C₂	—	4	4	no	—
963	C₂	—	4	2	no	—
964	C₂	—	4	4	no	—
965	C₂	—	8	2	no	—
966	C₂	C₃×#3449	1	1	yes	characteristic
967	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
968	C₂	C₃×#3485	1	2	yes	—
969	C₂	C₃×#3500	1	1	yes	characteristic
970	C₂	C₃×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#547	C₂	semidirect
2. C₂×C₃×#546	C₂	semidirect
3. C₂×C₃×#535	C₂	semidirect
4. C₂×C₃×#532	C₂	semidirect
5. C₃×#2850	C₂	semidirect
6. C₃×#2671	C₂	semidirect
7. C₃×#2668	C₂	semidirect
8. C₃×#2658	C₂	semidirect
9. C₃×#2621	C₂	semidirect
10. C₃×#2547	C₂	semidirect
11. C₃×#2544	C₂	semidirect
12. C₃×#2443	C₂	semidirect
13. C₃×#2435	C₂	semidirect
14. C₃×#2432	C₂	semidirect
15. C₃×#2432	C₂	semidirect
16. C₃×#2431	C₂	semidirect
17. C₃×#2418	C₂	semidirect
18. C₃×#2328	C₂	semidirect
19. C₃×#2290	C₂	semidirect
20. #37682	C₃	direct (N × H)
23. C₂²×C₃×#41	C₂²	semidirect
29. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₃×#124	C₂²	semidirect
42. C₂×C₃×#123	C₂²	semidirect
45. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₃×#121	C₂²	semidirect
55. C₂×C₃×C₄×D₄	C₂²	semidirect
56. C₂×C₃×C₄×D₄	C₂²	semidirect
58. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
60. C₂²×C₃×C₄²	C₂²	semidirect
61. C₃×#399	C₂²	semidirect
62. C₃×#399	C₂²	semidirect
63. C₃×#398	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#392	C₂²	semidirect
71. C₃×#391	C₂²	semidirect
72. C₃×#391	C₂²	semidirect
73. C₃×#391	C₂²	semidirect
76. C₃×#390	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
81. C₃×#386	C₂²	semidirect
82. C₃×#386	C₂²	semidirect
83. C₃×#386	C₂²	semidirect
84. C₃×#386	C₂²	semidirect
85. C₃×#386	C₂²	semidirect
86. C₃×#385	C₂²	semidirect
87. C₃×#385	C₂²	semidirect
88. C₃×#385	C₂²	semidirect
89. C₃×#382	C₂²	semidirect
90. C₃×#380	C₂²	semidirect
92. C₃×C₄×C₄⋊C₄	C₂²	semidirect
94. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
95. C₃×#376	C₂²	semidirect
96. C₂×#547	C₂×C₃	semidirect
97. C₂×#546	C₂×C₃	semidirect
98. C₂×#535	C₂×C₃	semidirect
99. C₂×#532	C₂×C₃	semidirect
100. #2850	C₂×C₃	semidirect
101. #2671	C₂×C₃	semidirect
102. #2668	C₂×C₃	semidirect
103. #2658	C₂×C₃	semidirect
104. #2621	C₂×C₃	semidirect
105. #2547	C₂×C₃	semidirect
106. #2544	C₂×C₃	semidirect
107. #2443	C₂×C₃	semidirect
108. #2435	C₂×C₃	semidirect
109. #2432	C₂×C₃	semidirect
110. #2432	C₂×C₃	semidirect
111. #2431	C₂×C₃	semidirect
112. #2418	C₂×C₃	semidirect
113. #2328	C₂×C₃	semidirect
114. #2290	C₂×C₃	semidirect
154. C₃×#127	D₄	semidirect
177. C₃×C₄×D₄	D₄	semidirect
232. C₂²×#41	C₂²×C₃	semidirect
238. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
240. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
248. C₂×#124	C₂²×C₃	semidirect
251. C₂×#123	C₂²×C₃	semidirect
254. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
259. C₂×#121	C₂²×C₃	semidirect
264. C₂×C₄×D₄	C₂²×C₃	semidirect
265. C₂×C₄×D₄	C₂²×C₃	semidirect
267. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
269. C₂²×C₄²	C₂²×C₃	semidirect
270. #399	C₂²×C₃	semidirect
271. #399	C₂²×C₃	semidirect
272. #398	C₂²×C₃	semidirect
274. #397	C₂²×C₃	semidirect
277. #394	C₂²×C₃	semidirect
278. #394	C₂²×C₃	semidirect
279. #392	C₂²×C₃	semidirect
280. #391	C₂²×C₃	semidirect
281. #391	C₂²×C₃	semidirect
282. #391	C₂²×C₃	semidirect
285. #390	C₂²×C₃	semidirect
287. #388	C₂²×C₃	semidirect
288. #387	C₂²×C₃	semidirect
290. #386	C₂²×C₃	semidirect
291. #386	C₂²×C₃	semidirect
292. #386	C₂²×C₃	semidirect
293. #386	C₂²×C₃	semidirect
294. #386	C₂²×C₃	semidirect
295. #385	C₂²×C₃	semidirect
296. #385	C₂²×C₃	semidirect
297. #385	C₂²×C₃	semidirect
298. #382	C₂²×C₃	semidirect
299. #380	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
303. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
304. #376	C₂²×C₃	semidirect
473. #127	C₃×D₄	semidirect
496. C₄×D₄	C₃×D₄	semidirect
960. C₃	#37682	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×#547	2
C₂×C₃×#546	2
C₂×C₃×#535	2
C₂×C₃×#532	2
C₃×#2850	2
C₃×#2671	2
C₃×#2668	2
C₃×#2658	2
C₃×#2621	2
C₃×#2547	2
C₃×#2544	2
C₃×#2443	2
C₃×#2435	2
C₃×#2432	2
C₃×#2431	2
C₃×#2418	2
C₃×#2328	2
C₃×#2290	2
#37682	3

Subgroups — C3×#37682 #10656289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37682 #10656289