Subgroups — C₃×#40638 #10659245

Order 768.

2378 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2826	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2824	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2706	C₂	1	2	yes	maximal, complemented
4	C₃×#2705	C₂	1	2	yes	maximal, complemented
5	C₃×#2696	C₂	1	2	yes	maximal, complemented
6	C₃×#2693	C₂	1	2	yes	maximal, complemented
7	C₃×#2636	C₂	1	2	yes	maximal, complemented
8	C₃×#2630	C₂	1	2	yes	maximal, complemented
9	C₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2505	C₂	1	2	yes	maximal, complemented
11	C₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₃×#2463	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2437	C₂	1	2	yes	maximal, complemented
15	C₃×#2405	C₂	1	2	yes	maximal, complemented
16	C₃×#2405	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#392	C₂	1	1	yes	maximal, characteristic
18	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
19	C₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
20	#40638	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×D₄	C₂²	1	2	yes	—
22	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×#126	C₂²	1	2	yes	complemented
24	C₂×C₃×#123	C₂²	1	2	yes	complemented
25	C₂×C₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₃×#123	C₂²	1	2	yes	complemented
27	C₂×C₃×#123	C₂²	1	2	yes	complemented
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×#400	C₂²	1	2	yes	complemented
38	C₃×#400	C₂²	1	2	yes	complemented
39	C₃×#400	C₂²	1	2	yes	complemented
40	C₃×#399	C₂²	1	1	yes	characteristic, complemented
41	C₃×#399	C₂²	1	1	yes	characteristic, complemented
42	C₃×#399	C₂²	1	2	yes	complemented
43	C₃×#398	C₂²	1	2	yes	complemented
44	C₃×#397	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	2	yes	complemented
46	C₃×#397	C₂²	1	2	yes	complemented
47	C₃×#396	C₂²	1	2	yes	complemented
48	C₃×#396	C₂²	1	2	yes	complemented
49	C₃×#396	C₂²	1	2	yes	complemented
50	C₃×#396	C₂²	1	2	yes	complemented
51	C₃×#396	C₂²	1	2	yes	complemented
52	C₃×#394	C₂²	1	2	yes	complemented
53	C₃×#394	C₂²	1	2	yes	complemented
54	C₃×#394	C₂²	1	2	yes	complemented
55	C₃×#394	C₂²	1	2	yes	complemented
56	C₃×#394	C₂²	1	2	yes	complemented
57	C₃×#394	C₂²	1	2	yes	complemented
58	C₃×#394	C₂²	1	2	yes	complemented
59	C₃×#394	C₂²	1	2	yes	complemented
60	C₃×#393	C₂²	1	1	yes	characteristic, complemented
61	C₃×#393	C₂²	1	1	yes	characteristic, complemented
62	C₃×#393	C₂²	1	2	yes	complemented
63	C₃×#392	C₂²	1	2	yes	—
64	C₃×#392	C₂²	1	1	yes	characteristic
65	C₃×#392	C₂²	1	2	yes	—
66	C₃×#392	C₂²	1	1	yes	characteristic
67	C₃×#392	C₂²	1	1	yes	characteristic
68	C₃×#392	C₂²	1	1	yes	characteristic
69	C₃×#390	C₂²	1	2	yes	complemented
70	C₃×#390	C₂²	1	2	yes	complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#388	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	2	yes	complemented
75	C₃×#387	C₂²	1	2	yes	complemented
76	C₃×#387	C₂²	1	2	yes	complemented
77	C₃×#386	C₂²	1	2	yes	complemented
78	C₃×#386	C₂²	1	2	yes	complemented
79	C₃×#386	C₂²	1	2	yes	complemented
80	C₃×#386	C₂²	1	2	yes	complemented
81	C₃×#386	C₂²	1	2	yes	complemented
82	C₃×#386	C₂²	1	2	yes	complemented
83	C₃×#386	C₂²	1	2	yes	complemented
84	C₃×#386	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
91	C₃×#385	C₂²	1	1	yes	characteristic, complemented
92	C₃×#385	C₂²	1	2	yes	complemented
93	C₃×#385	C₂²	1	2	yes	complemented
94	C₃×#385	C₂²	1	1	yes	characteristic, complemented
95	C₃×#385	C₂²	1	1	yes	characteristic, complemented
96	C₃×#382	C₂²	1	2	yes	complemented
97	C₃×#380	C₂²	1	1	yes	characteristic
98	C₃×#380	C₂²	1	2	yes	—
99	C₃×#380	C₂²	1	2	yes	complemented
100	C₃×#380	C₂²	1	2	yes	complemented
101	C₃×#380	C₂²	1	2	yes	complemented
102	C₃×#379	C₂²	1	2	yes	—
103	C₃×#379	C₂²	1	2	yes	—
104	C₃×#379	C₂²	1	2	yes	—
105	C₃×#379	C₂²	1	2	yes	—
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic
108	#2826	C₂×C₃	1	1	yes	characteristic, complemented
109	#2824	C₂×C₃	1	1	yes	characteristic, complemented
110	#2706	C₂×C₃	1	2	yes	complemented
111	#2705	C₂×C₃	1	2	yes	complemented
112	#2696	C₂×C₃	1	2	yes	complemented
113	#2693	C₂×C₃	1	2	yes	complemented
114	#2636	C₂×C₃	1	2	yes	complemented
115	#2630	C₂×C₃	1	2	yes	complemented
116	#2626	C₂×C₃	1	1	yes	characteristic, complemented
117	#2505	C₂×C₃	1	2	yes	complemented
118	#2480	C₂×C₃	1	2	yes	complemented
119	#2463	C₂×C₃	1	1	yes	characteristic, complemented
120	#2455	C₂×C₃	1	1	yes	characteristic, complemented
121	#2437	C₂×C₃	1	2	yes	complemented
122	#2405	C₂×C₃	1	2	yes	complemented
123	#2405	C₂×C₃	1	2	yes	complemented
124	C₂×#392	C₂×C₃	1	1	yes	characteristic
125	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
126	#2315	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	2	yes	—
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×D₄	—	2	8	no	—
131	C₂²×C₃×D₄	—	4	4	no	—
132	C₂²×C₃×D₄	—	4	2	no	—
133	C₂²×C₃×D₄	—	4	4	no	—
134	C₂²×C₃×D₄	—	4	4	no	—
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	2	yes	—
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	2	yes	—
141	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
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	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₃×#126	—	4	4	no	—
151	C₃×#123	—	4	4	no	—
152	C₃×#123	—	4	4	no	—
153	C₃×#123	—	4	4	no	—
154	C₃×#123	—	4	4	no	—
155	C₃×C₂²⋊Q₈	—	4	2	no	—
156	C₃×C₂²⋊Q₈	—	4	4	no	—
157	C₃×C₄×D₄	—	4	4	no	—
158	C₃×C₄×D₄	—	4	4	no	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
175	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
176	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
177	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
178	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
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	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	1	yes	characteristic
216	C₃×#95	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	1	yes	characteristic
222	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	C₂³×D₄	C₂²×C₃	1	2	yes	—
234	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
235	C₂×#126	C₂²×C₃	1	2	yes	complemented
236	C₂×#123	C₂²×C₃	1	2	yes	complemented
237	C₂×#123	C₂²×C₃	1	2	yes	complemented
238	C₂×#123	C₂²×C₃	1	2	yes	complemented
239	C₂×#123	C₂²×C₃	1	2	yes	complemented
240	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
242	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
243	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
244	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
249	#400	C₂²×C₃	1	2	yes	complemented
250	#400	C₂²×C₃	1	2	yes	complemented
251	#400	C₂²×C₃	1	2	yes	complemented
252	#399	C₂²×C₃	1	1	yes	characteristic, complemented
253	#399	C₂²×C₃	1	1	yes	characteristic, complemented
254	#399	C₂²×C₃	1	2	yes	complemented
255	#398	C₂²×C₃	1	2	yes	complemented
256	#397	C₂²×C₃	1	2	yes	complemented
257	#397	C₂²×C₃	1	2	yes	complemented
258	#397	C₂²×C₃	1	2	yes	complemented
259	#396	C₂²×C₃	1	2	yes	complemented
260	#396	C₂²×C₃	1	2	yes	complemented
261	#396	C₂²×C₃	1	2	yes	complemented
262	#396	C₂²×C₃	1	2	yes	complemented
263	#396	C₂²×C₃	1	2	yes	complemented
264	#394	C₂²×C₃	1	2	yes	complemented
265	#394	C₂²×C₃	1	2	yes	complemented
266	#394	C₂²×C₃	1	2	yes	complemented
267	#394	C₂²×C₃	1	2	yes	complemented
268	#394	C₂²×C₃	1	2	yes	complemented
269	#394	C₂²×C₃	1	2	yes	complemented
270	#394	C₂²×C₃	1	2	yes	complemented
271	#394	C₂²×C₃	1	2	yes	complemented
272	#393	C₂²×C₃	1	1	yes	characteristic, complemented
273	#393	C₂²×C₃	1	2	yes	complemented
274	#393	C₂²×C₃	1	1	yes	characteristic, complemented
275	#392	C₂²×C₃	1	1	yes	characteristic
276	#392	C₂²×C₃	1	2	yes	—
277	#392	C₂²×C₃	1	1	yes	characteristic
278	#392	C₂²×C₃	1	2	yes	—
279	#392	C₂²×C₃	1	1	yes	characteristic
280	#392	C₂²×C₃	1	1	yes	characteristic
281	#390	C₂²×C₃	1	2	yes	complemented
282	#390	C₂²×C₃	1	2	yes	complemented
283	#389	C₂²×C₃	1	2	yes	complemented
284	#388	C₂²×C₃	1	2	yes	complemented
285	#388	C₂²×C₃	1	2	yes	complemented
286	#388	C₂²×C₃	1	2	yes	complemented
287	#387	C₂²×C₃	1	2	yes	complemented
288	#387	C₂²×C₃	1	2	yes	complemented
289	#386	C₂²×C₃	1	2	yes	complemented
290	#386	C₂²×C₃	1	2	yes	complemented
291	#386	C₂²×C₃	1	2	yes	complemented
292	#386	C₂²×C₃	1	2	yes	complemented
293	#386	C₂²×C₃	1	2	yes	complemented
294	#386	C₂²×C₃	1	2	yes	complemented
295	#386	C₂²×C₃	1	2	yes	complemented
296	#386	C₂²×C₃	1	2	yes	complemented
297	#385	C₂²×C₃	1	2	yes	—
298	#385	C₂²×C₃	1	2	yes	—
299	#385	C₂²×C₃	1	2	yes	—
300	#385	C₂²×C₃	1	2	yes	—
301	#385	C₂²×C₃	1	2	yes	—
302	#385	C₂²×C₃	1	1	yes	characteristic, complemented
303	#385	C₂²×C₃	1	1	yes	characteristic, complemented
304	#385	C₂²×C₃	1	1	yes	characteristic, complemented
305	#385	C₂²×C₃	1	1	yes	characteristic, complemented
306	#385	C₂²×C₃	1	2	yes	complemented
307	#385	C₂²×C₃	1	2	yes	complemented
308	#382	C₂²×C₃	1	2	yes	complemented
309	#380	C₂²×C₃	1	2	yes	—
310	#380	C₂²×C₃	1	1	yes	characteristic
311	#380	C₂²×C₃	1	2	yes	complemented
312	#380	C₂²×C₃	1	2	yes	complemented
313	#380	C₂²×C₃	1	2	yes	complemented
314	#379	C₂²×C₃	1	2	yes	—
315	#379	C₂²×C₃	1	2	yes	—
316	#379	C₂²×C₃	1	2	yes	—
317	#379	C₂²×C₃	1	2	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
319	C₂×#95	C₂²×C₃	1	1	yes	characteristic
320	C₂⁴×C₃	—	2	2	no	—
321	C₂⁴×C₃	—	2	2	no	—
322	C₂⁴×C₃	—	2	4	no	—
323	C₂⁴×C₃	—	2	4	no	—
324	C₂⁴×C₃	—	2	4	no	—
325	C₂⁴×C₃	—	2	4	no	—
326	C₂⁴×C₃	—	4	2	no	—
327	C₂⁴×C₃	—	4	2	no	—
328	C₂⁴×C₃	—	4	2	no	—
329	C₂⁴×C₃	—	4	2	no	—
330	C₂⁴×C₃	—	4	2	no	—
331	C₂⁴×C₃	#41	1	4	yes	—
332	C₂⁴×C₃	C₂⁴	1	2	yes	—
333	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
334	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
335	C₂⁴×C₃	C₂⁴	1	2	yes	—
336	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
337	C₂×C₃×Q₈	—	4	1	no	—
338	C₂×C₃×Q₈	—	4	2	no	—
339	C₂×C₃×D₄	—	2	4	no	—
340	C₂×C₃×D₄	—	2	4	no	—
341	C₂×C₃×D₄	—	2	4	no	—
342	C₂×C₃×D₄	—	2	4	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	—	4	2	no	—
350	C₂×C₃×D₄	—	4	2	no	—
351	C₂×C₃×D₄	—	4	1	no	—
352	C₂×C₃×D₄	—	4	2	no	—
353	C₂×C₃×D₄	—	4	2	no	—
354	C₂×C₃×D₄	—	4	1	no	—
355	C₂×C₃×D₄	—	4	2	no	—
356	C₂×C₃×D₄	—	4	2	no	—
357	C₂×C₃×D₄	—	4	2	no	—
358	C₂×C₃×D₄	—	4	32	no	—
359	C₂×C₃×D₄	—	4	16	no	—
360	C₂²×C₃×C₄	—	2	4	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	4	no	—
363	C₂²×C₃×C₄	—	2	2	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	2	4	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	1	no	—
369	C₂²×C₃×C₄	—	4	1	no	—
370	C₂²×C₃×C₄	—	4	2	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	C₂⁴	1	2	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	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	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
394	C₃×C₄⋊C₄	—	2	4	no	—
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	4	2	no	—
398	C₃×C₄⋊C₄	—	4	1	no	—
399	C₃×C₄⋊C₄	—	4	2	no	—
400	C₃×C₄⋊C₄	—	4	2	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	2	no	—
404	C₃×C₄⋊C₄	—	4	2	no	—
405	C₃×C₄⋊C₄	—	4	2	no	—
406	C₃×C₄⋊C₄	—	4	2	no	—
407	C₃×C₄⋊C₄	—	4	2	no	—
408	C₃×C₄⋊C₄	—	4	2	no	—
409	C₃×C₂²⋊C₄	—	2	2	no	—
410	C₃×C₂²⋊C₄	—	2	2	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	4	no	—
419	C₃×C₂²⋊C₄	—	2	4	no	—
420	C₃×C₂²⋊C₄	—	4	2	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	2	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₂²⋊C₄	—	4	1	no	—
426	C₃×C₂²⋊C₄	—	4	1	no	—
427	C₃×C₂²⋊C₄	—	4	1	no	—
428	C₃×C₂²⋊C₄	—	4	1	no	—
429	C₃×C₂²⋊C₄	—	4	2	no	—
430	C₃×C₂²⋊C₄	—	4	2	no	—
431	C₃×C₂²⋊C₄	—	4	2	no	—
432	C₃×C₂²⋊C₄	—	4	2	no	—
433	C₃×C₂²⋊C₄	—	4	2	no	—
434	C₃×C₂²⋊C₄	—	4	2	no	—
435	C₃×C₂²⋊C₄	—	4	2	no	—
436	C₃×C₂²⋊C₄	—	4	2	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×C₄²	—	2	4	no	—
443	C₃×C₄²	—	4	2	no	—
444	C₂⁵	C₂³×C₃	1	2	yes	—
445	C₂⁵	C₂³×C₃	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
447	C₂²×D₄	—	2	8	no	—
448	C₂²×D₄	—	4	4	no	—
449	C₂²×D₄	—	4	2	no	—
450	C₂²×D₄	—	4	4	no	—
451	C₂²×D₄	—	4	4	no	—
452	C₂²×D₄	C₂³×C₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₃	1	2	yes	—
455	C₂²×D₄	C₂³×C₃	1	2	yes	—
456	C₂²×D₄	C₂³×C₃	1	2	yes	—
457	C₂²×D₄	C₂³×C₃	1	2	yes	—
458	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃	1	2	yes	—
460	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₃	1	2	yes	—
462	C₂³×C₄	C₂³×C₃	1	2	yes	—
463	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
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	#126	—	4	4	no	—
468	#123	—	4	4	no	—
469	#123	—	4	4	no	—
470	#123	—	4	4	no	—
471	#123	—	4	4	no	—
472	C₂²⋊Q₈	—	4	2	no	—
473	C₂²⋊Q₈	—	4	4	no	—
474	C₄×D₄	—	4	4	no	—
475	C₄×D₄	—	4	4	no	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	4	4	no	—
493	C₂×C₂²⋊C₄	—	4	2	no	—
494	C₂×C₂²⋊C₄	—	4	4	no	—
495	C₂×C₂²⋊C₄	—	4	2	no	—
496	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	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	2	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	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	2	yes	—
531	#95	C₂³×C₃	1	2	yes	—
532	#95	C₂³×C₃	1	1	yes	characteristic
533	#95	C₂³×C₃	1	1	yes	characteristic
534	#95	C₂³×C₃	1	2	yes	—
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	1	yes	characteristic
539	#95	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	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	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	2	no	—
553	C₂³×C₃	—	2	2	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	2	no	—
558	C₂³×C₃	—	2	2	no	—
559	C₂³×C₃	—	2	2	no	—
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	2	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	8	no	—
567	C₂³×C₃	—	2	2	no	—
568	C₂³×C₃	—	2	2	no	—
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	—	4	8	no	—
575	C₂³×C₃	—	4	8	no	—
576	C₂³×C₃	—	4	8	no	—
577	C₂³×C₃	—	4	8	no	—
578	C₂³×C₃	—	4	8	no	—
579	C₂³×C₃	—	8	4	no	—
580	C₂³×C₃	—	8	2	no	—
581	C₂³×C₃	—	8	4	no	—
582	C₂³×C₃	—	8	4	no	—
583	C₂³×C₃	—	8	2	no	—
584	C₂³×C₃	—	8	4	no	—
585	C₂³×C₃	C₂×#41	1	2	yes	—
586	C₂³×C₃	C₂×#41	1	2	yes	—
587	C₂³×C₃	C₂×#41	1	2	yes	—
588	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
589	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
590	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
591	C₂³×C₃	C₂⁵	1	1	yes	characteristic
592	C₃×Q₈	—	8	2	no	—
593	C₃×D₄	—	2	16	no	—
594	C₃×D₄	—	4	8	no	—
595	C₃×D₄	—	4	8	no	—
596	C₃×D₄	—	4	4	no	—
597	C₃×D₄	—	4	8	no	—
598	C₃×D₄	—	4	8	no	—
599	C₃×D₄	—	4	4	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	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	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	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	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	2	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	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	4	8	no	—
638	C₂×C₃×C₄	—	4	4	no	—
639	C₂×C₃×C₄	—	8	4	no	—
640	C₂×C₃×C₄	—	8	4	no	—
641	C₂×C₃×C₄	—	8	2	no	—
642	C₂×C₃×C₄	—	8	2	no	—
643	C₂×C₃×C₄	—	8	2	no	—
644	C₂×C₃×C₄	—	8	4	no	—
645	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
646	C₂⁴	—	2	2	no	—
647	C₂⁴	—	2	2	no	—
648	C₂⁴	—	2	4	no	—
649	C₂⁴	—	2	4	no	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	4	2	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	4	2	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	2	no	—
657	C₂⁴	C₃×#41	1	4	yes	—
658	C₂⁴	C₂⁴×C₃	1	2	yes	—
659	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
661	C₂⁴	C₂⁴×C₃	1	2	yes	—
662	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	—	4	2	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	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	1	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	1	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	32	no	—
685	C₂×D₄	—	4	16	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	1	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	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
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	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	4	2	no	—
770	C₂²×C₃	—	2	4	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	4	no	—
773	C₂²×C₃	—	2	2	no	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	2	no	—
776	C₂²×C₃	—	2	4	no	—
777	C₂²×C₃	—	2	4	no	—
778	C₂²×C₃	—	2	4	no	—
779	C₂²×C₃	—	2	4	no	—
780	C₂²×C₃	—	2	4	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	2	no	—
783	C₂²×C₃	—	4	1	no	—
784	C₂²×C₃	—	4	1	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	2	no	—
787	C₂²×C₃	—	4	2	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	2	no	—
792	C₂²×C₃	—	4	2	no	—
793	C₂²×C₃	—	4	2	no	—
794	C₂²×C₃	—	4	2	no	—
795	C₂²×C₃	—	4	2	no	—
796	C₂²×C₃	—	4	2	no	—
797	C₂²×C₃	—	4	2	no	—
798	C₂²×C₃	—	8	8	no	—
799	C₂²×C₃	—	8	16	no	—
800	C₂²×C₃	#539	1	4	yes	—
801	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
802	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
804	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
805	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
806	C₃×C₄	—	2	4	no	—
807	C₃×C₄	—	4	2	no	—
808	C₃×C₄	—	4	2	no	—
809	C₃×C₄	—	4	2	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	—	4	1	no	—
812	C₃×C₄	—	4	2	no	—
813	C₃×C₄	—	4	2	no	—
814	C₃×C₄	—	4	2	no	—
815	C₃×C₄	—	4	2	no	—
816	C₃×C₄	—	4	1	no	—
817	C₃×C₄	—	4	2	no	—
818	C₃×C₄	—	4	1	no	—
819	C₃×C₄	—	4	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	8	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	—	4	8	no	—
845	C₂³	—	4	8	no	—
846	C₂³	—	4	8	no	—
847	C₂³	—	4	8	no	—
848	C₂³	—	4	8	no	—
849	C₂³	—	8	4	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	4	no	—
852	C₂³	—	8	4	no	—
853	C₂³	—	8	2	no	—
854	C₂³	—	8	4	no	—
855	C₂³	C₂×C₃×#41	1	2	yes	—
856	C₂³	C₂×C₃×#41	1	2	yes	—
857	C₂³	C₂×C₃×#41	1	2	yes	—
858	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
859	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
860	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
861	C₂³	C₂⁵×C₃	1	1	yes	characteristic
862	Q₈	—	8	2	no	—
863	D₄	—	2	16	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	8	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	4	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	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	2	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	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	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	—	4	8	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	8	4	no	—
910	C₂×C₄	—	8	4	no	—
911	C₂×C₄	—	8	2	no	—
912	C₂×C₄	—	8	2	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	—	8	4	no	—
915	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
916	C₂×C₃	—	2	4	no	—
917	C₂×C₃	—	4	2	no	—
918	C₂×C₃	—	4	2	no	—
919	C₂×C₃	—	4	4	no	—
920	C₂×C₃	—	8	2	no	—
921	C₂×C₃	C₂×#539	1	1	yes	characteristic
922	C₂×C₃	#3490	1	2	yes	—
923	C₂×C₃	#3532	1	1	yes	characteristic
924	C₂×C₃	#3536	1	2	yes	—
925	C₂×C₃	#3543	1	1	yes	characteristic
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	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	—	8	8	no	—
955	C₂²	—	8	16	no	—
956	C₂²	C₃×#539	1	4	yes	—
957	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
958	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
960	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
961	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
962	C₄	—	2	4	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₃	#40638	1	1	yes	characteristic, direct product factor, Sylow
977	C₂	—	2	4	no	—
978	C₂	—	4	2	no	—
979	C₂	—	4	2	no	—
980	C₂	—	4	4	no	—
981	C₂	—	8	2	no	—
982	C₂	C₂×C₃×#539	1	1	yes	characteristic
983	C₂	C₃×#3490	1	2	yes	—
984	C₂	C₃×#3532	1	1	yes	characteristic
985	C₂	C₃×#3536	1	2	yes	—
986	C₂	C₃×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#392	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. C₃×#2826	C₂	semidirect
2. C₃×#2824	C₂	semidirect
3. C₃×#2706	C₂	semidirect
4. C₃×#2705	C₂	semidirect
5. C₃×#2696	C₂	semidirect
6. C₃×#2693	C₂	semidirect
7. C₃×#2636	C₂	semidirect
8. C₃×#2630	C₂	semidirect
9. C₃×#2626	C₂	semidirect
10. C₃×#2505	C₂	semidirect
11. C₃×#2480	C₂	semidirect
12. C₃×#2463	C₂	semidirect
13. C₃×#2455	C₂	semidirect
14. C₃×#2437	C₂	semidirect
15. C₃×#2405	C₂	semidirect
16. C₃×#2405	C₂	semidirect
18. C₃×D₄×C₂²⋊C₄	C₂	semidirect
19. C₃×#2315	C₂	semidirect
20. #40638	C₃	direct (N × H)
23. C₂×C₃×#126	C₂²	semidirect
24. C₂×C₃×#123	C₂²	semidirect
25. C₂×C₃×#123	C₂²	semidirect
26. C₂×C₃×#123	C₂²	semidirect
27. C₂×C₃×#123	C₂²	semidirect
29. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃×C₄×D₄	C₂²	semidirect
31. C₂×C₃×C₄×D₄	C₂²	semidirect
37. C₃×#400	C₂²	semidirect
38. C₃×#400	C₂²	semidirect
39. C₃×#400	C₂²	semidirect
40. C₃×#399	C₂²	semidirect
41. C₃×#399	C₂²	semidirect
42. C₃×#399	C₂²	semidirect
43. C₃×#398	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#396	C₂²	semidirect
48. C₃×#396	C₂²	semidirect
49. C₃×#396	C₂²	semidirect
50. C₃×#396	C₂²	semidirect
51. C₃×#396	C₂²	semidirect
52. C₃×#394	C₂²	semidirect
53. C₃×#394	C₂²	semidirect
54. C₃×#394	C₂²	semidirect
55. C₃×#394	C₂²	semidirect
56. C₃×#394	C₂²	semidirect
57. C₃×#394	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
59. C₃×#394	C₂²	semidirect
60. C₃×#393	C₂²	semidirect
61. C₃×#393	C₂²	semidirect
62. C₃×#393	C₂²	semidirect
69. C₃×#390	C₂²	semidirect
70. C₃×#390	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#388	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
77. C₃×#386	C₂²	semidirect
78. C₃×#386	C₂²	semidirect
79. C₃×#386	C₂²	semidirect
80. C₃×#386	C₂²	semidirect
81. C₃×#386	C₂²	semidirect
82. C₃×#386	C₂²	semidirect
83. C₃×#386	C₂²	semidirect
84. C₃×#386	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#385	C₂²	semidirect
92. C₃×#385	C₂²	semidirect
93. C₃×#385	C₂²	semidirect
94. C₃×#385	C₂²	semidirect
95. C₃×#385	C₂²	semidirect
96. C₃×#382	C₂²	semidirect
99. C₃×#380	C₂²	semidirect
100. C₃×#380	C₂²	semidirect
101. C₃×#380	C₂²	semidirect
108. #2826	C₂×C₃	semidirect
109. #2824	C₂×C₃	semidirect
110. #2706	C₂×C₃	semidirect
111. #2705	C₂×C₃	semidirect
112. #2696	C₂×C₃	semidirect
113. #2693	C₂×C₃	semidirect
114. #2636	C₂×C₃	semidirect
115. #2630	C₂×C₃	semidirect
116. #2626	C₂×C₃	semidirect
117. #2505	C₂×C₃	semidirect
118. #2480	C₂×C₃	semidirect
119. #2463	C₂×C₃	semidirect
120. #2455	C₂×C₃	semidirect
121. #2437	C₂×C₃	semidirect
122. #2405	C₂×C₃	semidirect
123. #2405	C₂×C₃	semidirect
125. D₄×C₂²⋊C₄	C₂×C₃	semidirect
126. #2315	C₂×C₃	semidirect
235. C₂×#126	C₂²×C₃	semidirect
236. C₂×#123	C₂²×C₃	semidirect
237. C₂×#123	C₂²×C₃	semidirect
238. C₂×#123	C₂²×C₃	semidirect
239. C₂×#123	C₂²×C₃	semidirect
241. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
242. C₂×C₄×D₄	C₂²×C₃	semidirect
243. C₂×C₄×D₄	C₂²×C₃	semidirect
249. #400	C₂²×C₃	semidirect
250. #400	C₂²×C₃	semidirect
251. #400	C₂²×C₃	semidirect
252. #399	C₂²×C₃	semidirect
253. #399	C₂²×C₃	semidirect
254. #399	C₂²×C₃	semidirect
255. #398	C₂²×C₃	semidirect
256. #397	C₂²×C₃	semidirect
257. #397	C₂²×C₃	semidirect
258. #397	C₂²×C₃	semidirect
259. #396	C₂²×C₃	semidirect
260. #396	C₂²×C₃	semidirect
261. #396	C₂²×C₃	semidirect
262. #396	C₂²×C₃	semidirect
263. #396	C₂²×C₃	semidirect
264. #394	C₂²×C₃	semidirect
265. #394	C₂²×C₃	semidirect
266. #394	C₂²×C₃	semidirect
267. #394	C₂²×C₃	semidirect
268. #394	C₂²×C₃	semidirect
269. #394	C₂²×C₃	semidirect
270. #394	C₂²×C₃	semidirect
271. #394	C₂²×C₃	semidirect
272. #393	C₂²×C₃	semidirect
273. #393	C₂²×C₃	semidirect
274. #393	C₂²×C₃	semidirect
281. #390	C₂²×C₃	semidirect
282. #390	C₂²×C₃	semidirect
283. #389	C₂²×C₃	semidirect
284. #388	C₂²×C₃	semidirect
285. #388	C₂²×C₃	semidirect
286. #388	C₂²×C₃	semidirect
287. #387	C₂²×C₃	semidirect
288. #387	C₂²×C₃	semidirect
289. #386	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. #386	C₂²×C₃	semidirect
296. #386	C₂²×C₃	semidirect
302. #385	C₂²×C₃	semidirect
303. #385	C₂²×C₃	semidirect
304. #385	C₂²×C₃	semidirect
305. #385	C₂²×C₃	semidirect
306. #385	C₂²×C₃	semidirect
307. #385	C₂²×C₃	semidirect
308. #382	C₂²×C₃	semidirect
311. #380	C₂²×C₃	semidirect
312. #380	C₂²×C₃	semidirect
313. #380	C₂²×C₃	semidirect
976. C₃	#40638	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×#2826	2
C₃×#2824	2
C₃×#2706	2
C₃×#2705	2
C₃×#2696	2
C₃×#2693	2
C₃×#2636	2
C₃×#2630	2
C₃×#2626	2
C₃×#2505	2
C₃×#2480	2
C₃×#2463	2
C₃×#2455	2
C₃×#2437	2
C₃×#2405	2
C₂×C₃×#392	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2315	2
#40638	3

Subgroups — C3×#40638 #10659245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40638 #10659245