Subgroups — C₃×#35858 #10654465

Order 768.

1836 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2646	C₂	1	2	yes	maximal, complemented
3	C₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2569	C₂	1	2	yes	maximal, complemented
5	C₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2505	C₂	1	2	yes	maximal, complemented
11	C₃×#2473	C₂	1	2	yes	maximal, complemented
12	C₃×#2473	C₂	1	2	yes	maximal, complemented
13	C₃×#2473	C₂	1	2	yes	maximal, complemented
14	C₃×#2442	C₂	1	2	yes	maximal, complemented
15	C₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#398	C₂	1	2	yes	maximal, complemented
17	C₃×#2349	C₂	1	1	yes	maximal, characteristic
18	C₃×#2349	C₂	1	1	yes	maximal, characteristic
19	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
20	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
21	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
22	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic
24	#35858	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#125	C₂²	1	2	yes	—
26	C₂×C₃×#125	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₃×#400	C₂²	1	1	yes	characteristic
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	2	yes	—
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	1	yes	characteristic
45	C₃×#400	C₂²	1	1	yes	characteristic
46	C₃×#400	C₂²	1	1	yes	characteristic
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#398	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	2	yes	—
51	C₃×#398	C₂²	1	1	yes	characteristic
52	C₃×#398	C₂²	1	2	yes	—
53	C₃×#398	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	2	yes	—
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#398	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#398	C₂²	1	1	yes	characteristic
60	C₃×#398	C₂²	1	1	yes	characteristic
61	C₃×#398	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#389	C₂²	1	1	yes	characteristic
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	1	yes	characteristic
76	C₃×#389	C₂²	1	1	yes	characteristic
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#384	C₂²	1	1	yes	characteristic
96	C₃×#384	C₂²	1	1	yes	characteristic
97	C₃×#384	C₂²	1	1	yes	characteristic
98	C₃×#384	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	1	yes	characteristic
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#382	C₂²	1	1	yes	characteristic
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	2	yes	—
105	C₃×#380	C₂²	1	2	yes	—
106	C₃×#380	C₂²	1	2	yes	—
107	C₃×#380	C₂²	1	2	yes	—
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×#376	C₂²	1	1	yes	characteristic
121	C₂×C₃×#95	C₂²	1	2	yes	—
122	C₂×C₃×#95	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	#2647	C₂×C₃	1	1	yes	characteristic, complemented
125	#2646	C₂×C₃	1	2	yes	complemented
126	#2570	C₂×C₃	1	1	yes	characteristic, complemented
127	#2569	C₂×C₃	1	2	yes	complemented
128	#2552	C₂×C₃	1	1	yes	characteristic, complemented
129	#2508	C₂×C₃	1	1	yes	characteristic, complemented
130	#2507	C₂×C₃	1	1	yes	characteristic, complemented
131	#2507	C₂×C₃	1	1	yes	characteristic, complemented
132	#2506	C₂×C₃	1	1	yes	characteristic, complemented
133	#2505	C₂×C₃	1	2	yes	complemented
134	#2473	C₂×C₃	1	2	yes	complemented
135	#2473	C₂×C₃	1	2	yes	complemented
136	#2473	C₂×C₃	1	2	yes	complemented
137	#2442	C₂×C₃	1	2	yes	complemented
138	#2402	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×#398	C₂×C₃	1	2	yes	complemented
140	#2349	C₂×C₃	1	1	yes	characteristic
141	#2349	C₂×C₃	1	1	yes	characteristic
142	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
143	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
144	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
145	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
146	#2275	C₂×C₃	1	1	yes	characteristic
147	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
148	C₂³×C₃×C₄	C₂³	1	2	yes	—
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₂³×C₃×C₄	C₂³	1	2	yes	—
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₃×#125	—	4	4	no	—
156	C₃×#125	—	4	4	no	—
157	C₃×C₄×D₄	—	2	4	no	—
158	C₃×C₄×D₄	—	2	4	no	—
159	C₃×C₄×D₄	—	2	4	no	—
160	C₃×C₄×D₄	—	2	4	no	—
161	C₃×C₄×D₄	—	2	4	no	—
162	C₃×C₄×D₄	—	2	4	no	—
163	C₃×C₄×D₄	Q₈	1	8	yes	—
164	C₂×C₃×C₄⋊C₄	—	4	4	no	—
165	C₂×C₃×C₄⋊C₄	—	4	4	no	—
166	C₂×C₃×C₄⋊C₄	—	4	4	no	—
167	C₂×C₃×C₄⋊C₄	—	4	4	no	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
224	C₃×#95	C₂³	1	1	yes	characteristic
225	C₃×#95	C₂³	1	1	yes	characteristic
226	C₃×#95	C₂³	1	1	yes	characteristic
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₂×#125	C₂²×C₃	1	2	yes	—
260	C₂×#125	C₂²×C₃	1	2	yes	—
261	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
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
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
270	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
272	#400	C₂²×C₃	1	2	yes	—
273	#400	C₂²×C₃	1	2	yes	—
274	#400	C₂²×C₃	1	1	yes	characteristic
275	#400	C₂²×C₃	1	2	yes	—
276	#400	C₂²×C₃	1	2	yes	—
277	#400	C₂²×C₃	1	2	yes	—
278	#400	C₂²×C₃	1	1	yes	characteristic
279	#400	C₂²×C₃	1	1	yes	characteristic
280	#400	C₂²×C₃	1	1	yes	characteristic
281	#398	C₂²×C₃	1	1	yes	characteristic
282	#398	C₂²×C₃	1	2	yes	—
283	#398	C₂²×C₃	1	2	yes	—
284	#398	C₂²×C₃	1	2	yes	—
285	#398	C₂²×C₃	1	2	yes	—
286	#398	C₂²×C₃	1	2	yes	—
287	#398	C₂²×C₃	1	2	yes	—
288	#398	C₂²×C₃	1	1	yes	characteristic
289	#398	C₂²×C₃	1	2	yes	—
290	#398	C₂²×C₃	1	2	yes	—
291	#398	C₂²×C₃	1	2	yes	—
292	#398	C₂²×C₃	1	2	yes	—
293	#398	C₂²×C₃	1	2	yes	—
294	#398	C₂²×C₃	1	1	yes	characteristic
295	#398	C₂²×C₃	1	1	yes	characteristic
296	#389	C₂²×C₃	1	1	yes	characteristic
297	#389	C₂²×C₃	1	1	yes	characteristic
298	#389	C₂²×C₃	1	1	yes	characteristic
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	1	yes	characteristic
301	#389	C₂²×C₃	1	1	yes	characteristic
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	1	yes	characteristic
305	#389	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	2	yes	—
309	#389	C₂²×C₃	1	2	yes	—
310	#389	C₂²×C₃	1	2	yes	—
311	#387	C₂²×C₃	1	2	yes	—
312	#387	C₂²×C₃	1	2	yes	—
313	#387	C₂²×C₃	1	2	yes	—
314	#387	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#385	C₂²×C₃	1	2	yes	—
318	#385	C₂²×C₃	1	2	yes	—
319	#385	C₂²×C₃	1	2	yes	—
320	#385	C₂²×C₃	1	2	yes	—
321	#385	C₂²×C₃	1	2	yes	—
322	#385	C₂²×C₃	1	2	yes	—
323	#385	C₂²×C₃	1	2	yes	—
324	#385	C₂²×C₃	1	2	yes	—
325	#385	C₂²×C₃	1	2	yes	—
326	#385	C₂²×C₃	1	2	yes	—
327	#385	C₂²×C₃	1	2	yes	—
328	#385	C₂²×C₃	1	2	yes	—
329	#384	C₂²×C₃	1	1	yes	characteristic
330	#384	C₂²×C₃	1	1	yes	characteristic
331	#384	C₂²×C₃	1	1	yes	characteristic
332	#384	C₂²×C₃	1	1	yes	characteristic
333	#382	C₂²×C₃	1	1	yes	characteristic
334	#382	C₂²×C₃	1	1	yes	characteristic
335	#382	C₂²×C₃	1	2	yes	—
336	#380	C₂²×C₃	1	2	yes	—
337	#380	C₂²×C₃	1	2	yes	—
338	#380	C₂²×C₃	1	2	yes	—
339	#380	C₂²×C₃	1	2	yes	—
340	#380	C₂²×C₃	1	2	yes	—
341	#380	C₂²×C₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	#376	C₂²×C₃	1	1	yes	characteristic
355	C₂×#95	C₂²×C₃	1	2	yes	—
356	C₂×#95	C₂²×C₃	1	2	yes	—
357	C₂×#95	C₂²×C₃	1	2	yes	—
358	C₂⁴×C₃	C₂⁴	1	2	yes	—
359	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
360	C₂×C₃×D₄	#41	1	4	yes	—
361	C₂×C₃×D₄	#41	1	4	yes	—
362	C₂²×C₃×C₄	—	2	4	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	—	4	2	no	—
372	C₂²×C₃×C₄	—	4	2	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	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	C₂×Q₈	1	8	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
394	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	2	2	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	2	no	—
413	C₃×C₄⋊C₄	—	2	2	no	—
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	4	no	—
416	C₃×C₄⋊C₄	—	2	4	no	—
417	C₃×C₄⋊C₄	—	2	4	no	—
418	C₃×C₄⋊C₄	—	2	4	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	4	2	no	—
425	C₃×C₄⋊C₄	—	4	2	no	—
426	C₃×C₄⋊C₄	—	4	2	no	—
427	C₃×C₄⋊C₄	—	4	2	no	—
428	C₃×C₄⋊C₄	—	4	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	2	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	—	4	1	no	—
434	C₃×C₄⋊C₄	—	4	1	no	—
435	C₃×C₄⋊C₄	—	4	2	no	—
436	C₃×C₄⋊C₄	—	4	1	no	—
437	C₃×C₄⋊C₄	—	4	2	no	—
438	C₃×C₄⋊C₄	—	4	2	no	—
439	C₃×C₄⋊C₄	—	4	2	no	—
440	C₃×C₄⋊C₄	—	4	2	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	2	no	—
443	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
444	C₃×C₂²⋊C₄	—	2	4	no	—
445	C₃×C₂²⋊C₄	—	2	4	no	—
446	C₃×C₂²⋊C₄	—	2	4	no	—
447	C₃×C₂²⋊C₄	—	2	4	no	—
448	C₃×C₂²⋊C₄	—	2	4	no	—
449	C₃×C₂²⋊C₄	—	2	4	no	—
450	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
451	C₃×C₄²	—	2	2	no	—
452	C₃×C₄²	—	2	2	no	—
453	C₃×C₄²	—	2	2	no	—
454	C₃×C₄²	—	2	2	no	—
455	C₃×C₄²	—	2	2	no	—
456	C₃×C₄²	—	2	2	no	—
457	C₃×C₄²	—	4	2	no	—
458	C₃×C₄²	—	4	2	no	—
459	C₃×C₄²	—	4	2	no	—
460	C₃×C₄²	C₂×Q₈	1	4	yes	—
461	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₃	1	2	yes	—
463	C₂³×C₄	C₂³×C₃	1	2	yes	—
464	C₂³×C₄	C₂³×C₃	1	2	yes	—
465	C₂³×C₄	C₂³×C₃	1	2	yes	—
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	#125	—	4	4	no	—
470	#125	—	4	4	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	C₃×Q₈	1	8	yes	—
478	C₂×C₄⋊C₄	—	4	4	no	—
479	C₂×C₄⋊C₄	—	4	4	no	—
480	C₂×C₄⋊C₄	—	4	4	no	—
481	C₂×C₄⋊C₄	—	4	4	no	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
538	#95	C₂³×C₃	1	1	yes	characteristic
539	#95	C₂³×C₃	1	1	yes	characteristic
540	#95	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	1	yes	characteristic
551	#95	C₂³×C₃	1	1	yes	characteristic
552	#95	C₂³×C₃	1	1	yes	characteristic
553	#95	C₂³×C₃	1	1	yes	characteristic
554	#95	C₂³×C₃	1	1	yes	characteristic
555	#95	C₂³×C₃	1	1	yes	characteristic
556	#95	C₂³×C₃	1	1	yes	characteristic
557	#95	C₂³×C₃	1	1	yes	characteristic
558	#95	C₂³×C₃	1	1	yes	characteristic
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	1	yes	characteristic
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
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	C₂²×Q₈	1	4	yes	—
578	C₂³×C₃	C₂×#41	1	4	yes	—
579	C₂³×C₃	C₂×#41	1	4	yes	—
580	C₂³×C₃	C₂⁵	1	1	yes	characteristic
581	C₃×D₄	#125	1	16	yes	complemented
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	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	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	2	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	1	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	1	no	—
614	C₂×C₃×C₄	—	2	1	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	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	1	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	1	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	4	8	no	—
640	C₂×C₃×C₄	—	4	8	no	—
641	C₂×C₃×C₄	—	4	8	no	—
642	C₂×C₃×C₄	—	4	8	no	—
643	C₂×C₃×C₄	—	8	4	no	—
644	C₂×C₃×C₄	—	8	4	no	—
645	C₂×C₃×C₄	—	8	4	no	—
646	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
647	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
648	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
649	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
650	C₂×C₃×C₄	C₂×#41	1	2	yes	—
651	C₂×C₃×C₄	C₂×#41	1	2	yes	—
652	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
653	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
654	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
655	C₂⁴	C₂⁴×C₃	1	2	yes	—
656	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
657	C₂×D₄	C₃×#41	1	4	yes	—
658	C₂×D₄	C₃×#41	1	4	yes	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
680	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	4	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	C₂×C₃×Q₈	1	4	yes	—
758	C₂²×C₃	—	2	4	no	—
759	C₂²×C₃	—	2	4	no	—
760	C₂²×C₃	—	2	4	no	—
761	C₂²×C₃	—	2	4	no	—
762	C₂²×C₃	—	2	4	no	—
763	C₂²×C₃	—	2	4	no	—
764	C₂²×C₃	C₂×#125	1	8	yes	—
765	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
766	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
767	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
768	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
769	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
770	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
771	C₂²×C₃	#585	1	1	yes	characteristic
772	C₃×C₄	—	2	2	no	—
773	C₃×C₄	—	2	4	no	—
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	2	2	no	—
776	C₃×C₄	—	2	2	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	4	1	no	—
779	C₃×C₄	—	4	2	no	—
780	C₃×C₄	—	4	2	no	—
781	C₃×C₄	—	4	1	no	—
782	C₃×C₄	—	4	1	no	—
783	C₃×C₄	—	4	1	no	—
784	C₃×C₄	—	4	1	no	—
785	C₃×C₄	—	4	2	no	—
786	C₃×C₄	—	4	2	no	—
787	C₃×C₄	—	4	2	no	—
788	C₃×C₄	—	4	1	no	—
789	C₃×C₄	—	4	1	no	—
790	C₃×C₄	—	4	1	no	—
791	C₃×C₄	—	4	1	no	—
792	C₃×C₄	—	4	2	no	—
793	C₃×C₄	C₂×#125	1	4	yes	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	C₂²×C₃×Q₈	1	4	yes	—
799	C₂³	C₂×C₃×#41	1	4	yes	—
800	C₂³	C₂×C₃×#41	1	4	yes	—
801	C₂³	C₂⁵×C₃	1	1	yes	characteristic
802	D₄	C₃×#125	1	16	yes	complemented
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	—	8	4	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
868	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
869	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
870	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
871	C₂×C₄	C₂×C₃×#41	1	2	yes	—
872	C₂×C₄	C₂×C₃×#41	1	2	yes	—
873	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
874	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
875	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
876	C₂×C₃	—	2	8	no	—
877	C₂×C₃	C₂²×#125	1	1	yes	characteristic
878	C₂×C₃	#3501	1	1	yes	characteristic
879	C₂×C₃	#3503	1	1	yes	characteristic
880	C₂×C₃	#3513	1	1	yes	characteristic
881	C₂×C₃	#3515	1	1	yes	characteristic
882	C₂×C₃	#3519	1	1	yes	characteristic
883	C₂×C₃	#3520	1	1	yes	characteristic
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	C₂×C₃×#125	1	8	yes	—
891	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
892	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
893	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
894	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
895	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
897	C₂²	C₃×#585	1	1	yes	characteristic
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	C₂×C₃×#125	1	4	yes	—
920	C₃	#35858	1	1	yes	characteristic, direct product factor, Sylow
921	C₂	—	2	8	no	—
922	C₂	C₂²×C₃×#125	1	1	yes	characteristic
923	C₂	C₃×#3501	1	1	yes	characteristic
924	C₂	C₃×#3503	1	1	yes	characteristic
925	C₂	C₃×#3513	1	1	yes	characteristic
926	C₂	C₃×#3515	1	1	yes	characteristic
927	C₂	C₃×#3519	1	1	yes	characteristic
928	C₂	C₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
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. C₃×#2647	C₂	semidirect
2. C₃×#2646	C₂	semidirect
3. C₃×#2570	C₂	semidirect
4. C₃×#2569	C₂	semidirect
5. C₃×#2552	C₂	semidirect
6. C₃×#2508	C₂	semidirect
7. C₃×#2507	C₂	semidirect
8. C₃×#2507	C₂	semidirect
9. C₃×#2506	C₂	semidirect
10. C₃×#2505	C₂	semidirect
11. C₃×#2473	C₂	semidirect
12. C₃×#2473	C₂	semidirect
13. C₃×#2473	C₂	semidirect
14. C₃×#2442	C₂	semidirect
15. C₃×#2402	C₂	semidirect
16. C₂×C₃×#398	C₂	semidirect
24. #35858	C₃	direct (N × H)
124. #2647	C₂×C₃	semidirect
125. #2646	C₂×C₃	semidirect
126. #2570	C₂×C₃	semidirect
127. #2569	C₂×C₃	semidirect
128. #2552	C₂×C₃	semidirect
129. #2508	C₂×C₃	semidirect
130. #2507	C₂×C₃	semidirect
131. #2507	C₂×C₃	semidirect
132. #2506	C₂×C₃	semidirect
133. #2505	C₂×C₃	semidirect
134. #2473	C₂×C₃	semidirect
135. #2473	C₂×C₃	semidirect
136. #2473	C₂×C₃	semidirect
137. #2442	C₂×C₃	semidirect
138. #2402	C₂×C₃	semidirect
139. C₂×#398	C₂×C₃	semidirect
581. C₃×D₄	#125	semidirect
802. D₄	C₃×#125	semidirect
920. C₃	#35858	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×#2647	2
C₃×#2646	2
C₃×#2570	2
C₃×#2569	2
C₃×#2552	2
C₃×#2508	2
C₃×#2507	2
C₃×#2506	2
C₃×#2505	2
C₃×#2473	2
C₃×#2442	2
C₃×#2402	2
C₂×C₃×#398	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×#2275	2
#35858	3

Subgroups — C3×#35858 #10654465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35858 #10654465