Subgroups — C₃×#41437 #10660044

Order 768.

1578 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2837	C₂	1	2	yes	maximal, complemented
2	C₃×#2738	C₂	1	2	yes	maximal, complemented
3	C₃×#2735	C₂	1	2	yes	maximal, complemented
4	C₃×#2707	C₂	1	2	yes	maximal, complemented
5	C₃×#2685	C₂	1	2	yes	maximal
6	C₃×#2667	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2664	C₂	1	2	yes	maximal, complemented
8	C₃×#2651	C₂	1	2	yes	maximal, complemented
9	C₃×#2534	C₂	1	1	yes	maximal, characteristic
10	C₃×#2529	C₂	1	2	yes	maximal, complemented
11	C₃×#2526	C₂	1	2	yes	maximal, complemented
12	C₃×#2525	C₂	1	2	yes	maximal, complemented
13	C₃×#2519	C₂	1	2	yes	maximal, complemented
14	C₃×#2518	C₂	1	2	yes	maximal, complemented
15	C₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
20	#41437	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#126	C₂²	1	2	yes	—
22	C₂×C₃×#125	C₂²	1	2	yes	complemented
23	C₂×C₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₃×#120	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×#400	C₂²	1	1	yes	characteristic, complemented
29	C₃×#400	C₂²	1	2	yes	complemented
30	C₃×#400	C₂²	1	2	yes	complemented
31	C₃×#399	C₂²	1	2	yes	—
32	C₃×#399	C₂²	1	2	yes	—
33	C₃×#399	C₂²	1	2	yes	—
34	C₃×#399	C₂²	1	1	yes	characteristic, complemented
35	C₃×#398	C₂²	1	1	yes	characteristic, complemented
36	C₃×#398	C₂²	1	2	yes	complemented
37	C₃×#398	C₂²	1	2	yes	complemented
38	C₃×#398	C₂²	1	2	yes	complemented
39	C₃×#398	C₂²	1	2	yes	complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#397	C₂²	1	2	yes	—
43	C₃×#397	C₂²	1	2	yes	—
44	C₃×#397	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₃×#397	C₂²	1	2	yes	complemented
47	C₃×#396	C₂²	1	2	yes	—
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#396	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#396	C₂²	1	2	yes	complemented
52	C₃×#396	C₂²	1	2	yes	complemented
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	2	yes	—
58	C₃×#390	C₂²	1	2	yes	—
59	C₃×#390	C₂²	1	2	yes	—
60	C₃×#389	C₂²	1	2	yes	complemented
61	C₃×#389	C₂²	1	2	yes	complemented
62	C₃×#389	C₂²	1	2	yes	complemented
63	C₃×#389	C₂²	1	2	yes	complemented
64	C₃×#388	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	complemented
81	C₃×#388	C₂²	1	2	yes	complemented
82	C₃×#387	C₂²	1	2	yes	complemented
83	C₃×#387	C₂²	1	2	yes	complemented
84	C₃×#387	C₂²	1	2	yes	complemented
85	C₃×#387	C₂²	1	2	yes	complemented
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#383	C₂²	1	2	yes	complemented
89	C₃×#382	C₂²	1	2	yes	complemented
90	C₃×#382	C₂²	1	1	yes	characteristic, complemented
91	C₃×#381	C₂²	1	1	yes	characteristic
92	C₃×#381	C₂²	1	1	yes	characteristic
93	C₃×#381	C₂²	1	1	yes	characteristic, complemented
94	C₃×#380	C₂²	1	1	yes	characteristic
95	C₃×#380	C₂²	1	2	yes	—
96	C₃×#379	C₂²	1	2	yes	—
97	C₃×#379	C₂²	1	2	yes	—
98	C₃×#379	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
106	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₃×#376	C₂²	1	2	yes	complemented
108	#2837	C₂×C₃	1	2	yes	complemented
109	#2738	C₂×C₃	1	2	yes	complemented
110	#2735	C₂×C₃	1	2	yes	complemented
111	#2707	C₂×C₃	1	2	yes	complemented
112	#2685	C₂×C₃	1	2	yes	—
113	#2667	C₂×C₃	1	1	yes	characteristic, complemented
114	#2664	C₂×C₃	1	2	yes	complemented
115	#2651	C₂×C₃	1	2	yes	complemented
116	#2534	C₂×C₃	1	1	yes	characteristic
117	#2529	C₂×C₃	1	2	yes	complemented
118	#2526	C₂×C₃	1	2	yes	complemented
119	#2525	C₂×C₃	1	2	yes	complemented
120	#2519	C₂×C₃	1	2	yes	complemented
121	#2518	C₂×C₃	1	2	yes	complemented
122	#2482	C₂×C₃	1	1	yes	characteristic, complemented
123	#2395	C₂×C₃	1	1	yes	characteristic, complemented
124	#2357	C₂×C₃	1	1	yes	characteristic, complemented
125	#2346	C₂×C₃	1	1	yes	characteristic, complemented
126	#2312	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
133	C₃×#126	—	4	4	no	—
134	C₃×#125	—	4	4	no	—
135	C₃×#123	—	4	2	no	—
136	C₃×#120	—	4	2	no	—
137	C₃×C₄×D₄	—	2	4	no	—
138	C₃×#117	—	2	4	no	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	2	yes	—
191	C₂×C₃×C₄²	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	C₂³	1	2	yes	—
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₃×#95	C₂³	1	1	yes	characteristic
196	C₃×#95	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	1	yes	characteristic
200	C₃×#95	C₂³	1	1	yes	characteristic
201	C₃×#95	C₂³	1	1	yes	characteristic
202	C₃×#95	C₂³	1	1	yes	characteristic
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	1	yes	characteristic
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₂×#126	C₂²×C₃	1	2	yes	—
222	C₂×#125	C₂²×C₃	1	2	yes	complemented
223	C₂×#123	C₂²×C₃	1	1	yes	characteristic
224	C₂×#120	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
226	C₂×#117	C₂²×C₃	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	#400	C₂²×C₃	1	2	yes	complemented
229	#400	C₂²×C₃	1	1	yes	characteristic, complemented
230	#400	C₂²×C₃	1	2	yes	complemented
231	#399	C₂²×C₃	1	2	yes	—
232	#399	C₂²×C₃	1	2	yes	—
233	#399	C₂²×C₃	1	2	yes	—
234	#399	C₂²×C₃	1	1	yes	characteristic, complemented
235	#398	C₂²×C₃	1	2	yes	complemented
236	#398	C₂²×C₃	1	2	yes	complemented
237	#398	C₂²×C₃	1	1	yes	characteristic, complemented
238	#398	C₂²×C₃	1	2	yes	complemented
239	#398	C₂²×C₃	1	2	yes	complemented
240	#398	C₂²×C₃	1	2	yes	complemented
241	#397	C₂²×C₃	1	2	yes	—
242	#397	C₂²×C₃	1	2	yes	—
243	#397	C₂²×C₃	1	2	yes	—
244	#397	C₂²×C₃	1	2	yes	—
245	#397	C₂²×C₃	1	1	yes	characteristic, complemented
246	#397	C₂²×C₃	1	2	yes	complemented
247	#396	C₂²×C₃	1	2	yes	—
248	#396	C₂²×C₃	1	2	yes	—
249	#396	C₂²×C₃	1	2	yes	—
250	#396	C₂²×C₃	1	2	yes	—
251	#396	C₂²×C₃	1	2	yes	complemented
252	#396	C₂²×C₃	1	2	yes	complemented
253	#394	C₂²×C₃	1	2	yes	—
254	#394	C₂²×C₃	1	2	yes	—
255	#394	C₂²×C₃	1	2	yes	—
256	#394	C₂²×C₃	1	2	yes	—
257	#394	C₂²×C₃	1	2	yes	—
258	#390	C₂²×C₃	1	2	yes	—
259	#390	C₂²×C₃	1	2	yes	—
260	#389	C₂²×C₃	1	2	yes	complemented
261	#389	C₂²×C₃	1	2	yes	complemented
262	#389	C₂²×C₃	1	2	yes	complemented
263	#389	C₂²×C₃	1	2	yes	complemented
264	#388	C₂²×C₃	1	2	yes	—
265	#388	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	—
275	#388	C₂²×C₃	1	2	yes	—
276	#388	C₂²×C₃	1	2	yes	—
277	#388	C₂²×C₃	1	2	yes	—
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	complemented
281	#388	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#387	C₂²×C₃	1	2	yes	complemented
286	#386	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	2	yes	—
288	#383	C₂²×C₃	1	2	yes	complemented
289	#382	C₂²×C₃	1	2	yes	complemented
290	#382	C₂²×C₃	1	1	yes	characteristic, complemented
291	#381	C₂²×C₃	1	1	yes	characteristic
292	#381	C₂²×C₃	1	1	yes	characteristic
293	#381	C₂²×C₃	1	1	yes	characteristic, complemented
294	#380	C₂²×C₃	1	2	yes	—
295	#380	C₂²×C₃	1	1	yes	characteristic
296	#379	C₂²×C₃	1	2	yes	—
297	#379	C₂²×C₃	1	2	yes	—
298	#379	C₂²×C₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
301	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
303	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
307	#376	C₂²×C₃	1	2	yes	complemented
308	C₂⁴×C₃	—	2	2	no	—
309	C₂⁴×C₃	—	4	2	no	—
310	C₂⁴×C₃	—	4	2	no	—
311	C₂⁴×C₃	—	4	1	no	—
312	C₂⁴×C₃	—	4	1	no	—
313	C₂⁴×C₃	C₂⁴	1	2	yes	—
314	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₃×D₄	—	2	2	no	—
317	C₂×C₃×D₄	—	2	2	no	—
318	C₂×C₃×D₄	—	4	1	no	—
319	C₂×C₃×D₄	—	4	2	no	—
320	C₂×C₃×D₄	—	4	2	no	—
321	C₂×C₃×D₄	—	4	2	no	—
322	C₂²×C₃×C₄	—	2	2	no	—
323	C₂²×C₃×C₄	—	2	2	no	—
324	C₂²×C₃×C₄	—	4	2	no	—
325	C₂²×C₃×C₄	—	4	1	no	—
326	C₂²×C₃×C₄	—	4	2	no	—
327	C₂²×C₃×C₄	—	4	1	no	—
328	C₂²×C₃×C₄	#41	1	4	yes	—
329	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
332	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
334	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
338	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
339	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
345	C₃×C₄⋊C₄	—	2	2	no	—
346	C₃×C₄⋊C₄	—	2	2	no	—
347	C₃×C₄⋊C₄	—	2	2	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	4	2	no	—
351	C₃×C₄⋊C₄	—	4	2	no	—
352	C₃×C₄⋊C₄	—	4	2	no	—
353	C₃×C₄⋊C₄	—	4	2	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	2	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₂²⋊C₄	—	2	4	no	—
367	C₃×C₂²⋊C₄	—	2	2	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	4	no	—
370	C₃×C₂²⋊C₄	—	2	2	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	4	2	no	—
373	C₃×C₂²⋊C₄	—	4	2	no	—
374	C₃×C₂²⋊C₄	—	4	2	no	—
375	C₃×C₂²⋊C₄	—	4	2	no	—
376	C₃×C₂²⋊C₄	—	4	2	no	—
377	C₃×C₂²⋊C₄	—	4	2	no	—
378	C₃×C₂²⋊C₄	—	4	2	no	—
379	C₃×C₂²⋊C₄	—	4	2	no	—
380	C₃×C₂²⋊C₄	—	4	2	no	—
381	C₃×C₂²⋊C₄	—	4	2	no	—
382	C₃×C₂²⋊C₄	—	4	2	no	—
383	C₃×C₂²⋊C₄	—	4	2	no	—
384	C₃×C₂²⋊C₄	—	4	2	no	—
385	C₃×C₂²⋊C₄	—	4	2	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	—	4	1	no	—
388	C₃×C₂²⋊C₄	—	4	1	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₂²⋊C₄	—	4	2	no	—
391	C₃×C₂²⋊C₄	—	4	2	no	—
392	C₃×C₄²	—	2	4	no	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	4	no	—
395	C₃×C₄²	—	4	2	no	—
396	C₃×C₄²	—	4	2	no	—
397	C₃×C₄²	—	4	2	no	—
398	C₃×C₄²	—	4	2	no	—
399	C₃×C₄²	—	4	2	no	—
400	C₂⁵	C₂³×C₃	1	1	yes	characteristic
401	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
406	#126	—	4	4	no	—
407	#125	—	4	4	no	—
408	#123	—	4	2	no	—
409	#120	—	4	2	no	—
410	C₄×D₄	—	2	4	no	—
411	#117	—	2	4	no	—
412	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₂²⋊C₄	—	2	4	no	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₃	1	2	yes	—
464	C₂×C₄²	C₂³×C₃	1	2	yes	—
465	C₂×C₄²	C₂³×C₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₃	1	2	yes	—
468	#95	C₂³×C₃	1	1	yes	characteristic
469	#95	C₂³×C₃	1	2	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	C₂³×C₃	1	2	yes	—
472	#95	C₂³×C₃	1	1	yes	characteristic
473	#95	C₂³×C₃	1	1	yes	characteristic
474	#95	C₂³×C₃	1	1	yes	characteristic
475	#95	C₂³×C₃	1	1	yes	characteristic
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	1	yes	characteristic
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	2	yes	—
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	C₂³×C₃	—	2	1	no	—
495	C₂³×C₃	—	2	2	no	—
496	C₂³×C₃	—	2	2	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	2	1	no	—
500	C₂³×C₃	—	2	2	no	—
501	C₂³×C₃	—	2	1	no	—
502	C₂³×C₃	—	2	2	no	—
503	C₂³×C₃	—	2	1	no	—
504	C₂³×C₃	—	2	2	no	—
505	C₂³×C₃	—	2	2	no	—
506	C₂³×C₃	—	2	2	no	—
507	C₂³×C₃	—	2	2	no	—
508	C₂³×C₃	—	2	2	no	—
509	C₂³×C₃	—	2	2	no	—
510	C₂³×C₃	—	4	4	no	—
511	C₂³×C₃	—	8	2	no	—
512	C₂³×C₃	—	8	2	no	—
513	C₂³×C₃	—	8	4	no	—
514	C₂³×C₃	—	8	4	no	—
515	C₂³×C₃	C₂×#41	1	2	yes	—
516	C₂³×C₃	C₂⁵	1	1	yes	characteristic
517	C₃×D₄	—	4	4	no	—
518	C₃×D₄	—	8	4	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	4	4	no	—
561	C₂×C₃×C₄	—	8	2	no	—
562	C₂×C₃×C₄	—	8	2	no	—
563	C₂×C₃×C₄	C₂×#41	1	2	yes	—
564	C₂×C₃×C₄	C₂×#41	1	2	yes	—
565	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
566	C₂⁴	—	2	2	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	1	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	4	1	no	—
571	C₂⁴	C₂⁴×C₃	1	2	yes	—
572	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
573	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	1	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	C₃×#41	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	4	2	no	—
654	C₄²	—	4	2	no	—
655	C₄²	—	4	2	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₂²×C₃	—	2	2	no	—
659	C₂²×C₃	—	2	2	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	4	2	no	—
662	C₂²×C₃	—	4	2	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	—	4	2	no	—
665	C₂²×C₃	—	4	1	no	—
666	C₂²×C₃	—	4	2	no	—
667	C₂²×C₃	—	4	1	no	—
668	C₂²×C₃	—	4	2	no	—
669	C₂²×C₃	—	4	2	no	—
670	C₂²×C₃	—	4	2	no	—
671	C₂²×C₃	—	4	2	no	—
672	C₂²×C₃	—	4	2	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	—	4	2	no	—
675	C₂²×C₃	—	8	8	no	—
676	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
677	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²×C₃	#585	1	2	yes	—
679	C₂²×C₃	#585	1	2	yes	—
680	C₂²×C₃	#585	1	1	yes	characteristic
681	C₃×C₄	—	2	2	no	—
682	C₃×C₄	—	2	2	no	—
683	C₃×C₄	—	2	2	no	—
684	C₃×C₄	—	4	1	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	1	no	—
687	C₃×C₄	—	4	2	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	—	4	2	no	—
690	C₃×C₄	—	4	2	no	—
691	C₃×C₄	—	4	2	no	—
692	C₃×C₄	—	4	2	no	—
693	C₃×C₄	—	4	2	no	—
694	C₃×C₄	—	4	2	no	—
695	C₃×C₄	—	4	2	no	—
696	C₃×C₄	—	4	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	8	2	no	—
715	C₂³	—	8	2	no	—
716	C₂³	—	8	4	no	—
717	C₂³	—	8	4	no	—
718	C₂³	C₂×C₃×#41	1	2	yes	—
719	C₂³	C₂⁵×C₃	1	1	yes	characteristic
720	D₄	—	4	4	no	—
721	D₄	—	8	4	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	8	2	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	C₂×C₃×#41	1	2	yes	—
767	C₂×C₄	C₂×C₃×#41	1	2	yes	—
768	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
769	C₂×C₃	—	4	2	no	—
770	C₂×C₃	—	8	1	no	—
771	C₂×C₃	—	8	2	no	—
772	C₂×C₃	#3455	1	1	yes	characteristic
773	C₂×C₃	#3491	1	1	yes	characteristic
774	C₂×C₃	#3494	1	1	yes	characteristic
775	C₂×C₃	#3551	1	2	yes	—
776	C₂×C₃	#3566	1	2	yes	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	8	8	no	—
795	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
796	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂²	C₃×#585	1	2	yes	—
798	C₂²	C₃×#585	1	2	yes	—
799	C₂²	C₃×#585	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₃	#41437	1	1	yes	characteristic, direct product factor, Sylow
817	C₂	—	4	2	no	—
818	C₂	—	8	2	no	—
819	C₂	—	8	1	no	—
820	C₂	C₃×#3455	1	1	yes	characteristic
821	C₂	C₃×#3491	1	1	yes	characteristic
822	C₂	C₃×#3494	1	1	yes	characteristic
823	C₂	C₃×#3551	1	2	yes	—
824	C₂	C₃×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	C₂²
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×#2837	C₂	semidirect
2. C₃×#2738	C₂	semidirect
3. C₃×#2735	C₂	semidirect
4. C₃×#2707	C₂	semidirect
6. C₃×#2667	C₂	semidirect
7. C₃×#2664	C₂	semidirect
8. C₃×#2651	C₂	semidirect
10. C₃×#2529	C₂	semidirect
11. C₃×#2526	C₂	semidirect
12. C₃×#2525	C₂	semidirect
13. C₃×#2519	C₂	semidirect
14. C₃×#2518	C₂	semidirect
15. C₃×#2482	C₂	semidirect
16. C₃×#2395	C₂	semidirect
17. C₃×#2357	C₂	semidirect
18. C₃×#2346	C₂	semidirect
19. C₃×#2312	C₂	semidirect
20. #41437	C₃	direct (N × H)
22. C₂×C₃×#125	C₂²	semidirect
28. C₃×#400	C₂²	semidirect
29. C₃×#400	C₂²	semidirect
30. C₃×#400	C₂²	semidirect
34. C₃×#399	C₂²	semidirect
35. C₃×#398	C₂²	semidirect
36. C₃×#398	C₂²	semidirect
37. C₃×#398	C₂²	semidirect
38. C₃×#398	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
51. C₃×#396	C₂²	semidirect
52. C₃×#396	C₂²	semidirect
60. C₃×#389	C₂²	semidirect
61. C₃×#389	C₂²	semidirect
62. C₃×#389	C₂²	semidirect
63. C₃×#389	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#388	C₂²	semidirect
82. C₃×#387	C₂²	semidirect
83. C₃×#387	C₂²	semidirect
84. C₃×#387	C₂²	semidirect
85. C₃×#387	C₂²	semidirect
88. C₃×#383	C₂²	semidirect
89. C₃×#382	C₂²	semidirect
90. C₃×#382	C₂²	semidirect
93. C₃×#381	C₂²	semidirect
99. C₃×C₄×C₄⋊C₄	C₂²	semidirect
100. C₃×C₄×C₄⋊C₄	C₂²	semidirect
101. C₃×C₄×C₄⋊C₄	C₂²	semidirect
102. C₃×C₄×C₄⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
107. C₃×#376	C₂²	semidirect
108. #2837	C₂×C₃	semidirect
109. #2738	C₂×C₃	semidirect
110. #2735	C₂×C₃	semidirect
111. #2707	C₂×C₃	semidirect
113. #2667	C₂×C₃	semidirect
114. #2664	C₂×C₃	semidirect
115. #2651	C₂×C₃	semidirect
117. #2529	C₂×C₃	semidirect
118. #2526	C₂×C₃	semidirect
119. #2525	C₂×C₃	semidirect
120. #2519	C₂×C₃	semidirect
121. #2518	C₂×C₃	semidirect
122. #2482	C₂×C₃	semidirect
123. #2395	C₂×C₃	semidirect
124. #2357	C₂×C₃	semidirect
125. #2346	C₂×C₃	semidirect
126. #2312	C₂×C₃	semidirect
222. C₂×#125	C₂²×C₃	semidirect
228. #400	C₂²×C₃	semidirect
229. #400	C₂²×C₃	semidirect
230. #400	C₂²×C₃	semidirect
234. #399	C₂²×C₃	semidirect
235. #398	C₂²×C₃	semidirect
236. #398	C₂²×C₃	semidirect
237. #398	C₂²×C₃	semidirect
238. #398	C₂²×C₃	semidirect
239. #398	C₂²×C₃	semidirect
240. #398	C₂²×C₃	semidirect
245. #397	C₂²×C₃	semidirect
246. #397	C₂²×C₃	semidirect
251. #396	C₂²×C₃	semidirect
252. #396	C₂²×C₃	semidirect
260. #389	C₂²×C₃	semidirect
261. #389	C₂²×C₃	semidirect
262. #389	C₂²×C₃	semidirect
263. #389	C₂²×C₃	semidirect
280. #388	C₂²×C₃	semidirect
281. #388	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
285. #387	C₂²×C₃	semidirect
288. #383	C₂²×C₃	semidirect
289. #382	C₂²×C₃	semidirect
290. #382	C₂²×C₃	semidirect
293. #381	C₂²×C₃	semidirect
299. C₄×C₄⋊C₄	C₂²×C₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
302. C₄×C₄⋊C₄	C₂²×C₃	semidirect
305. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
306. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
307. #376	C₂²×C₃	semidirect
816. C₃	#41437	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×#2837	2
C₃×#2738	2
C₃×#2735	2
C₃×#2707	2
C₃×#2685	2
C₃×#2667	2
C₃×#2664	2
C₃×#2651	2
C₃×#2534	2
C₃×#2529	2
C₃×#2526	2
C₃×#2525	2
C₃×#2519	2
C₃×#2518	2
C₃×#2482	2
C₃×#2395	2
C₃×#2357	2
C₃×#2346	2
C₃×#2312	2
#41437	3

Subgroups — C3×#41437 #10660044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41437 #10660044