Subgroups — C₃×#41418 #10660025

Order 768.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#551	C₂	1	1	yes	maximal, characteristic
3	C₃×#2821	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2717	C₂	1	2	yes	maximal, complemented
6	C₃×#2715	C₂	1	2	yes	maximal, complemented
7	C₃×#2695	C₂	1	2	yes	maximal, complemented
8	C₃×#2684	C₂	1	2	yes	maximal
9	C₃×#2663	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2599	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2564	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2498	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2480	C₂	1	2	yes	maximal, complemented
19	C₃×#2478	C₂	1	2	yes	maximal, complemented
20	C₃×#2469	C₂	1	2	yes	maximal, complemented
21	C₃×#2465	C₂	1	2	yes	maximal, complemented
22	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
24	#41418	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#556	—	2	8	no	—
26	C₃×#551	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#126	C₂²	1	1	yes	characteristic
29	C₂×C₃×#126	C₂²	1	1	yes	characteristic
30	C₂×C₃×#126	C₂²	1	2	yes	—
31	C₂×C₃×#126	C₂²	1	2	yes	complemented
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₃×#124	C₂²	1	2	yes	—
34	C₂×C₃×#123	C₂²	1	1	yes	characteristic
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#120	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×#117	C₂²	1	1	yes	characteristic
47	C₂×C₃×#117	C₂²	1	1	yes	characteristic
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×#400	C₂²	1	1	yes	characteristic, complemented
53	C₃×#400	C₂²	1	1	yes	characteristic, complemented
54	C₃×#400	C₂²	1	1	yes	characteristic, complemented
55	C₃×#400	C₂²	1	1	yes	characteristic, complemented
56	C₃×#400	C₂²	1	2	yes	complemented
57	C₃×#399	C₂²	1	1	yes	characteristic
58	C₃×#399	C₂²	1	1	yes	characteristic
59	C₃×#399	C₂²	1	1	yes	characteristic
60	C₃×#399	C₂²	1	1	yes	characteristic
61	C₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₃×#398	C₂²	1	1	yes	characteristic, complemented
63	C₃×#398	C₂²	1	2	yes	complemented
64	C₃×#398	C₂²	1	2	yes	complemented
65	C₃×#397	C₂²	1	2	yes	—
66	C₃×#397	C₂²	1	2	yes	—
67	C₃×#397	C₂²	1	1	yes	characteristic
68	C₃×#397	C₂²	1	1	yes	characteristic
69	C₃×#397	C₂²	1	2	yes	—
70	C₃×#397	C₂²	1	2	yes	—
71	C₃×#397	C₂²	1	2	yes	—
72	C₃×#397	C₂²	1	2	yes	complemented
73	C₃×#397	C₂²	1	2	yes	complemented
74	C₃×#396	C₂²	1	2	yes	—
75	C₃×#396	C₂²	1	2	yes	—
76	C₃×#396	C₂²	1	2	yes	—
77	C₃×#395	C₂²	1	2	yes	complemented
78	C₃×#395	C₂²	1	1	yes	characteristic, complemented
79	C₃×#395	C₂²	1	1	yes	characteristic, complemented
80	C₃×#395	C₂²	1	2	yes	complemented
81	C₃×#395	C₂²	1	2	yes	complemented
82	C₃×#394	C₂²	1	2	yes	—
83	C₃×#394	C₂²	1	2	yes	—
84	C₃×#393	C₂²	1	1	yes	characteristic
85	C₃×#393	C₂²	1	1	yes	characteristic
86	C₃×#393	C₂²	1	2	yes	—
87	C₃×#393	C₂²	1	2	yes	—
88	C₃×#391	C₂²	1	2	yes	complemented
89	C₃×#389	C₂²	1	2	yes	complemented
90	C₃×#389	C₂²	1	2	yes	complemented
91	C₃×#389	C₂²	1	2	yes	complemented
92	C₃×#388	C₂²	1	2	yes	—
93	C₃×#388	C₂²	1	2	yes	—
94	C₃×#388	C₂²	1	2	yes	—
95	C₃×#388	C₂²	1	2	yes	—
96	C₃×#388	C₂²	1	2	yes	—
97	C₃×#388	C₂²	1	2	yes	—
98	C₃×#388	C₂²	1	2	yes	—
99	C₃×#387	C₂²	1	2	yes	complemented
100	C₃×#387	C₂²	1	2	yes	complemented
101	C₃×#387	C₂²	1	2	yes	complemented
102	C₃×#387	C₂²	1	2	yes	complemented
103	C₃×#387	C₂²	1	2	yes	complemented
104	C₃×#387	C₂²	1	2	yes	complemented
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#386	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	2	yes	—
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#385	C₂²	1	2	yes	—
110	C₃×#385	C₂²	1	2	yes	—
111	C₃×#385	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	complemented
113	C₃×#383	C₂²	1	1	yes	characteristic, complemented
114	C₃×#382	C₂²	1	1	yes	characteristic, complemented
115	C₃×#381	C₂²	1	1	yes	characteristic
116	C₃×#380	C₂²	1	1	yes	characteristic
117	C₃×#380	C₂²	1	2	yes	—
118	C₃×#380	C₂²	1	2	yes	complemented
119	C₃×#380	C₂²	1	2	yes	complemented
120	C₃×#379	C₂²	1	2	yes	—
121	C₃×#379	C₂²	1	2	yes	—
122	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
126	C₂×#556	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#551	C₂×C₃	1	1	yes	characteristic
128	#2821	C₂×C₃	1	1	yes	characteristic, complemented
129	#2817	C₂×C₃	1	1	yes	characteristic, complemented
130	#2717	C₂×C₃	1	2	yes	complemented
131	#2715	C₂×C₃	1	2	yes	complemented
132	#2695	C₂×C₃	1	2	yes	complemented
133	#2684	C₂×C₃	1	2	yes	—
134	#2663	C₂×C₃	1	1	yes	characteristic, complemented
135	#2637	C₂×C₃	1	1	yes	characteristic, complemented
136	#2628	C₂×C₃	1	1	yes	characteristic, complemented
137	#2626	C₂×C₃	1	1	yes	characteristic, complemented
138	#2625	C₂×C₃	1	1	yes	characteristic, complemented
139	#2599	C₂×C₃	1	1	yes	characteristic, complemented
140	#2564	C₂×C₃	1	1	yes	characteristic, complemented
141	#2498	C₂×C₃	1	1	yes	characteristic, complemented
142	#2482	C₂×C₃	1	1	yes	characteristic, complemented
143	#2480	C₂×C₃	1	2	yes	complemented
144	#2478	C₂×C₃	1	2	yes	complemented
145	#2469	C₂×C₃	1	2	yes	complemented
146	#2465	C₂×C₃	1	2	yes	complemented
147	#2395	C₂×C₃	1	1	yes	characteristic, complemented
148	#2318	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₃×Q₈	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	—	2	4	no	—
163	C₃×#126	—	2	4	no	—
164	C₃×#126	—	2	8	no	—
165	C₃×#126	—	2	8	no	—
166	C₃×#126	—	2	4	no	—
167	C₃×#124	—	2	8	no	—
168	C₃×#124	—	2	4	no	—
169	C₃×#123	—	2	4	no	—
170	C₃×#123	—	2	4	no	—
171	C₃×#123	—	2	4	no	—
172	C₃×C₂²⋊Q₈	—	2	4	no	—
173	C₃×C₂²⋊Q₈	—	2	4	no	—
174	C₃×C₂²⋊Q₈	—	2	4	no	—
175	C₃×C₂²⋊Q₈	—	2	4	no	—
176	C₃×#120	—	2	4	no	—
177	C₃×C₄×Q₈	—	2	8	no	—
178	C₃×C₄×Q₈	—	2	4	no	—
179	C₃×C₄×D₄	—	2	4	no	—
180	C₃×C₄×D₄	D₄	1	8	yes	—
181	C₃×#117	—	2	4	no	—
182	C₃×#117	—	2	4	no	—
183	C₃×#117	—	2	4	no	—
184	C₃×#117	—	2	4	no	—
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	2	yes	—
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	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
211	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	C₂³	1	2	yes	—
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	2	yes	—
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	2	yes	—
246	C₂×C₃×C₄²	C₂³	1	2	yes	—
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	#556	—	2	8	no	—
274	#551	—	2	8	no	—
275	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
276	C₂×#126	C₂²×C₃	1	1	yes	characteristic
277	C₂×#126	C₂²×C₃	1	1	yes	characteristic
278	C₂×#126	C₂²×C₃	1	2	yes	—
279	C₂×#126	C₂²×C₃	1	2	yes	complemented
280	C₂×#124	C₂²×C₃	1	2	yes	—
281	C₂×#124	C₂²×C₃	1	1	yes	characteristic
282	C₂×#123	C₂²×C₃	1	1	yes	characteristic
283	C₂×#123	C₂²×C₃	1	1	yes	characteristic
284	C₂×#123	C₂²×C₃	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
287	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₂×#120	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
292	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
294	C₂×#117	C₂²×C₃	1	1	yes	characteristic
295	C₂×#117	C₂²×C₃	1	1	yes	characteristic
296	C₂×#117	C₂²×C₃	1	1	yes	characteristic
297	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
300	#400	C₂²×C₃	1	1	yes	characteristic, complemented
301	#400	C₂²×C₃	1	1	yes	characteristic, complemented
302	#400	C₂²×C₃	1	2	yes	complemented
303	#400	C₂²×C₃	1	1	yes	characteristic, complemented
304	#400	C₂²×C₃	1	1	yes	characteristic, complemented
305	#399	C₂²×C₃	1	1	yes	characteristic
306	#399	C₂²×C₃	1	1	yes	characteristic
307	#399	C₂²×C₃	1	1	yes	characteristic
308	#399	C₂²×C₃	1	1	yes	characteristic
309	#398	C₂²×C₃	1	2	yes	complemented
310	#398	C₂²×C₃	1	1	yes	characteristic, complemented
311	#398	C₂²×C₃	1	1	yes	characteristic, complemented
312	#398	C₂²×C₃	1	2	yes	complemented
313	#397	C₂²×C₃	1	2	yes	—
314	#397	C₂²×C₃	1	2	yes	—
315	#397	C₂²×C₃	1	2	yes	—
316	#397	C₂²×C₃	1	1	yes	characteristic
317	#397	C₂²×C₃	1	2	yes	—
318	#397	C₂²×C₃	1	2	yes	—
319	#397	C₂²×C₃	1	1	yes	characteristic
320	#397	C₂²×C₃	1	2	yes	complemented
321	#397	C₂²×C₃	1	2	yes	complemented
322	#396	C₂²×C₃	1	2	yes	—
323	#396	C₂²×C₃	1	2	yes	—
324	#396	C₂²×C₃	1	2	yes	—
325	#395	C₂²×C₃	1	1	yes	characteristic, complemented
326	#395	C₂²×C₃	1	1	yes	characteristic, complemented
327	#395	C₂²×C₃	1	2	yes	complemented
328	#395	C₂²×C₃	1	2	yes	complemented
329	#395	C₂²×C₃	1	2	yes	complemented
330	#394	C₂²×C₃	1	2	yes	—
331	#394	C₂²×C₃	1	2	yes	—
332	#393	C₂²×C₃	1	1	yes	characteristic
333	#393	C₂²×C₃	1	2	yes	—
334	#393	C₂²×C₃	1	1	yes	characteristic
335	#393	C₂²×C₃	1	2	yes	—
336	#391	C₂²×C₃	1	2	yes	complemented
337	#389	C₂²×C₃	1	2	yes	complemented
338	#389	C₂²×C₃	1	2	yes	complemented
339	#389	C₂²×C₃	1	2	yes	complemented
340	#388	C₂²×C₃	1	2	yes	—
341	#388	C₂²×C₃	1	2	yes	—
342	#388	C₂²×C₃	1	2	yes	—
343	#388	C₂²×C₃	1	2	yes	—
344	#388	C₂²×C₃	1	2	yes	—
345	#388	C₂²×C₃	1	2	yes	—
346	#388	C₂²×C₃	1	2	yes	—
347	#387	C₂²×C₃	1	2	yes	complemented
348	#387	C₂²×C₃	1	2	yes	complemented
349	#387	C₂²×C₃	1	2	yes	complemented
350	#387	C₂²×C₃	1	2	yes	complemented
351	#387	C₂²×C₃	1	2	yes	complemented
352	#387	C₂²×C₃	1	2	yes	complemented
353	#386	C₂²×C₃	1	2	yes	—
354	#386	C₂²×C₃	1	2	yes	—
355	#386	C₂²×C₃	1	2	yes	—
356	#385	C₂²×C₃	1	2	yes	—
357	#385	C₂²×C₃	1	2	yes	—
358	#385	C₂²×C₃	1	2	yes	—
359	#385	C₂²×C₃	1	2	yes	—
360	#385	C₂²×C₃	1	2	yes	complemented
361	#383	C₂²×C₃	1	1	yes	characteristic, complemented
362	#382	C₂²×C₃	1	1	yes	characteristic, complemented
363	#381	C₂²×C₃	1	1	yes	characteristic
364	#380	C₂²×C₃	1	1	yes	characteristic
365	#380	C₂²×C₃	1	2	yes	—
366	#380	C₂²×C₃	1	2	yes	complemented
367	#380	C₂²×C₃	1	2	yes	complemented
368	#379	C₂²×C₃	1	2	yes	—
369	#379	C₂²×C₃	1	2	yes	—
370	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₂⁴×C₃	—	2	2	no	—
375	C₂⁴×C₃	—	2	2	no	—
376	C₂⁴×C₃	—	4	1	no	—
377	C₂⁴×C₃	—	4	2	no	—
378	C₂⁴×C₃	—	4	2	no	—
379	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
382	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₃×Q₈	—	2	2	no	—
384	C₂×C₃×Q₈	—	2	4	no	—
385	C₂×C₃×Q₈	—	2	2	no	—
386	C₂×C₃×Q₈	—	4	2	no	—
387	C₂×C₃×Q₈	—	4	2	no	—
388	C₂×C₃×Q₈	—	4	2	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	4	2	no	—
394	C₂×C₃×D₄	—	4	1	no	—
395	C₂×C₃×D₄	—	4	2	no	—
396	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
399	C₂²×C₃×C₄	—	2	2	no	—
400	C₂²×C₃×C₄	—	2	2	no	—
401	C₂²×C₃×C₄	—	4	2	no	—
402	C₂²×C₃×C₄	—	4	1	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	—	4	2	no	—
405	C₂²×C₃×C₄	—	4	2	no	—
406	C₂²×C₃×C₄	—	4	2	no	—
407	C₂²×C₃×C₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
410	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
422	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₃×C₄⋊C₄	—	2	2	no	—
431	C₃×C₄⋊C₄	—	2	2	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	2	4	no	—
440	C₃×C₄⋊C₄	—	2	4	no	—
441	C₃×C₄⋊C₄	—	2	2	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	4	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	2	no	—
447	C₃×C₄⋊C₄	—	4	2	no	—
448	C₃×C₄⋊C₄	—	4	2	no	—
449	C₃×C₄⋊C₄	—	4	2	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₄⋊C₄	—	4	2	no	—
452	C₃×C₄⋊C₄	—	4	2	no	—
453	C₃×C₄⋊C₄	—	4	2	no	—
454	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
455	C₃×C₂²⋊C₄	—	2	2	no	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	4	no	—
458	C₃×C₂²⋊C₄	—	2	4	no	—
459	C₃×C₂²⋊C₄	—	2	2	no	—
460	C₃×C₂²⋊C₄	—	2	4	no	—
461	C₃×C₂²⋊C₄	—	2	4	no	—
462	C₃×C₂²⋊C₄	—	2	2	no	—
463	C₃×C₂²⋊C₄	—	2	4	no	—
464	C₃×C₂²⋊C₄	—	2	2	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	2	2	no	—
467	C₃×C₂²⋊C₄	—	2	2	no	—
468	C₃×C₂²⋊C₄	—	2	2	no	—
469	C₃×C₂²⋊C₄	—	2	2	no	—
470	C₃×C₂²⋊C₄	—	2	2	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	2	no	—
475	C₃×C₂²⋊C₄	—	4	2	no	—
476	C₃×C₂²⋊C₄	—	4	2	no	—
477	C₃×C₂²⋊C₄	—	4	2	no	—
478	C₃×C₂²⋊C₄	—	4	2	no	—
479	C₃×C₂²⋊C₄	—	4	2	no	—
480	C₃×C₂²⋊C₄	—	4	2	no	—
481	C₃×C₂²⋊C₄	—	4	2	no	—
482	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
483	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
484	C₃×C₄²	—	2	2	no	—
485	C₃×C₄²	—	2	2	no	—
486	C₃×C₄²	—	2	4	no	—
487	C₃×C₄²	—	2	4	no	—
488	C₃×C₄²	—	2	4	no	—
489	C₃×C₄²	—	4	2	no	—
490	C₃×C₄²	C₂×D₄	1	4	yes	—
491	C₂⁵	C₂³×C₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₃	1	2	yes	—
494	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₃	1	2	yes	—
502	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
504	C₄⋊Q₈	—	2	4	no	—
505	#126	—	2	4	no	—
506	#126	—	2	8	no	—
507	#126	—	2	8	no	—
508	#126	—	2	4	no	—
509	#124	—	2	8	no	—
510	#124	—	2	4	no	—
511	#123	—	2	4	no	—
512	#123	—	2	4	no	—
513	#123	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	#120	—	2	4	no	—
519	C₄×Q₈	—	2	8	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	C₃×D₄	1	8	yes	—
523	#117	—	2	4	no	—
524	#117	—	2	4	no	—
525	#117	—	2	4	no	—
526	#117	—	2	4	no	—
527	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₃	1	2	yes	—
587	C₂×C₄²	C₂³×C₃	1	2	yes	—
588	C₂×C₄²	C₂³×C₃	1	2	yes	—
589	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
590	#95	C₂³×C₃	1	1	yes	characteristic
591	#95	C₂³×C₃	1	1	yes	characteristic
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	2	yes	—
595	#95	C₂³×C₃	1	1	yes	characteristic
596	#95	C₂³×C₃	1	1	yes	characteristic
597	#95	C₂³×C₃	1	2	yes	—
598	#95	C₂³×C₃	1	2	yes	—
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	2	yes	—
602	#95	C₂³×C₃	1	2	yes	—
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	2	yes	—
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	2	yes	—
608	#95	C₂³×C₃	1	2	yes	—
609	#95	C₂³×C₃	1	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	2	yes	—
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	2	no	—
620	C₂³×C₃	—	2	2	no	—
621	C₂³×C₃	—	2	2	no	—
622	C₂³×C₃	—	2	2	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	2	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	2	no	—
630	C₂³×C₃	—	2	1	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	4	4	no	—
633	C₂³×C₃	—	4	4	no	—
634	C₂³×C₃	—	8	2	no	—
635	C₂³×C₃	—	8	4	no	—
636	C₂³×C₃	—	8	4	no	—
637	C₂³×C₃	C₂²×D₄	1	2	yes	—
638	C₂³×C₃	C₂²×D₄	1	2	yes	—
639	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
640	C₂³×C₃	C₂⁵	1	1	yes	characteristic
641	C₃×Q₈	—	4	8	no	—
642	C₃×Q₈	—	4	4	no	—
643	C₃×Q₈	—	8	2	no	—
644	C₃×D₄	—	4	4	no	—
645	C₃×D₄	—	4	4	no	—
646	C₃×D₄	—	8	2	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	2	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	2	2	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	2	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	1	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	4	4	no	—
692	C₂×C₃×C₄	—	4	4	no	—
693	C₂×C₃×C₄	—	4	4	no	—
694	C₂×C₃×C₄	—	4	4	no	—
695	C₂×C₃×C₄	—	8	2	no	—
696	C₂×C₃×C₄	—	8	4	no	—
697	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
698	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
699	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
700	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
701	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
702	C₂⁴	—	2	2	no	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	—	4	1	no	—
705	C₂⁴	—	4	2	no	—
706	C₂⁴	—	4	2	no	—
707	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
708	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
709	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
710	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	4	2	no	—
715	C₂×Q₈	—	4	2	no	—
716	C₂×Q₈	—	4	2	no	—
717	C₂×Q₈	—	4	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	1	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
738	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
811	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	4	no	—
815	C₄²	—	2	4	no	—
816	C₄²	—	2	4	no	—
817	C₄²	—	4	2	no	—
818	C₄²	C₂×C₃×D₄	1	4	yes	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	2	2	no	—
823	C₂²×C₃	—	2	2	no	—
824	C₂²×C₃	—	2	2	no	—
825	C₂²×C₃	—	2	2	no	—
826	C₂²×C₃	—	2	4	no	—
827	C₂²×C₃	—	4	1	no	—
828	C₂²×C₃	—	4	1	no	—
829	C₂²×C₃	—	4	2	no	—
830	C₂²×C₃	—	4	2	no	—
831	C₂²×C₃	—	4	2	no	—
832	C₂²×C₃	—	4	2	no	—
833	C₂²×C₃	—	4	2	no	—
834	C₂²×C₃	—	4	1	no	—
835	C₂²×C₃	—	4	1	no	—
836	C₂²×C₃	—	4	1	no	—
837	C₂²×C₃	—	4	2	no	—
838	C₂²×C₃	—	4	2	no	—
839	C₂²×C₃	—	8	8	no	—
840	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
841	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
842	C₂²×C₃	#585	1	2	yes	—
843	C₂²×C₃	#585	1	2	yes	—
844	C₂²×C₃	#585	1	1	yes	characteristic
845	C₃×C₄	—	2	2	no	—
846	C₃×C₄	—	2	2	no	—
847	C₃×C₄	—	2	2	no	—
848	C₃×C₄	—	2	2	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	4	1	no	—
851	C₃×C₄	—	4	1	no	—
852	C₃×C₄	—	4	2	no	—
853	C₃×C₄	—	4	2	no	—
854	C₃×C₄	—	4	1	no	—
855	C₃×C₄	—	4	1	no	—
856	C₃×C₄	—	4	2	no	—
857	C₃×C₄	—	4	2	no	—
858	C₃×C₄	—	4	1	no	—
859	C₃×C₄	—	4	1	no	—
860	C₃×C₄	—	4	2	no	—
861	C₃×C₄	—	4	2	no	—
862	C₃×C₄	—	4	2	no	—
863	C₃×C₄	—	4	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	4	4	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	8	2	no	—
884	C₂³	—	8	4	no	—
885	C₂³	—	8	4	no	—
886	C₂³	C₂²×C₃×D₄	1	2	yes	—
887	C₂³	C₂²×C₃×D₄	1	2	yes	—
888	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
889	C₂³	C₂⁵×C₃	1	1	yes	characteristic
890	Q₈	—	4	8	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	8	2	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	D₄	—	8	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	4	no	—
946	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
947	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
948	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
949	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
950	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
951	C₂×C₃	—	4	2	no	—
952	C₂×C₃	—	4	2	no	—
953	C₂×C₃	—	4	2	no	—
954	C₂×C₃	—	8	1	no	—
955	C₂×C₃	#3449	1	1	yes	characteristic
956	C₂×C₃	#3485	1	1	yes	characteristic
957	C₂×C₃	#3489	1	1	yes	characteristic
958	C₂×C₃	#3564	1	2	yes	—
959	C₂×C₃	#3568	1	2	yes	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	4	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	8	8	no	—
981	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
982	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
983	C₂²	C₃×#585	1	2	yes	—
984	C₂²	C₃×#585	1	2	yes	—
985	C₂²	C₃×#585	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₃	#41418	1	1	yes	characteristic, direct product factor, Sylow
1006	C₂	—	4	2	no	—
1007	C₂	—	4	2	no	—
1008	C₂	—	4	2	no	—
1009	C₂	—	8	1	no	—
1010	C₂	C₃×#3449	1	1	yes	characteristic
1011	C₂	C₃×#3485	1	1	yes	characteristic
1012	C₂	C₃×#3489	1	1	yes	characteristic
1013	C₂	C₃×#3564	1	2	yes	—
1014	C₂	C₃×#3568	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. C₂×C₃×#556	C₂	semidirect
3. C₃×#2821	C₂	semidirect
4. C₃×#2817	C₂	semidirect
5. C₃×#2717	C₂	semidirect
6. C₃×#2715	C₂	semidirect
7. C₃×#2695	C₂	semidirect
9. C₃×#2663	C₂	semidirect
10. C₃×#2637	C₂	semidirect
11. C₃×#2628	C₂	semidirect
12. C₃×#2626	C₂	semidirect
13. C₃×#2625	C₂	semidirect
14. C₃×#2599	C₂	semidirect
15. C₃×#2564	C₂	semidirect
16. C₃×#2498	C₂	semidirect
17. C₃×#2482	C₂	semidirect
18. C₃×#2480	C₂	semidirect
19. C₃×#2478	C₂	semidirect
20. C₃×#2469	C₂	semidirect
21. C₃×#2465	C₂	semidirect
22. C₃×#2395	C₂	semidirect
23. C₃×#2318	C₂	semidirect
24. #41418	C₃	direct (N × H)
27. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₃×#126	C₂²	semidirect
40. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₃×C₄×Q₈	C₂²	semidirect
43. C₂×C₃×C₄×Q₈	C₂²	semidirect
49. C₂×C₃×#117	C₂²	semidirect
52. C₃×#400	C₂²	semidirect
53. C₃×#400	C₂²	semidirect
54. C₃×#400	C₂²	semidirect
55. C₃×#400	C₂²	semidirect
56. C₃×#400	C₂²	semidirect
61. C₃×#398	C₂²	semidirect
62. C₃×#398	C₂²	semidirect
63. C₃×#398	C₂²	semidirect
64. C₃×#398	C₂²	semidirect
72. C₃×#397	C₂²	semidirect
73. C₃×#397	C₂²	semidirect
77. C₃×#395	C₂²	semidirect
78. C₃×#395	C₂²	semidirect
79. C₃×#395	C₂²	semidirect
80. C₃×#395	C₂²	semidirect
81. C₃×#395	C₂²	semidirect
88. C₃×#391	C₂²	semidirect
89. C₃×#389	C₂²	semidirect
90. C₃×#389	C₂²	semidirect
91. C₃×#389	C₂²	semidirect
99. C₃×#387	C₂²	semidirect
100. C₃×#387	C₂²	semidirect
101. C₃×#387	C₂²	semidirect
102. C₃×#387	C₂²	semidirect
103. C₃×#387	C₂²	semidirect
104. C₃×#387	C₂²	semidirect
112. C₃×#385	C₂²	semidirect
113. C₃×#383	C₂²	semidirect
114. C₃×#382	C₂²	semidirect
118. C₃×#380	C₂²	semidirect
119. C₃×#380	C₂²	semidirect
122. C₃×C₄×C₄⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₂×C₃×#95	C₂²	semidirect
126. C₂×#556	C₂×C₃	semidirect
128. #2821	C₂×C₃	semidirect
129. #2817	C₂×C₃	semidirect
130. #2717	C₂×C₃	semidirect
131. #2715	C₂×C₃	semidirect
132. #2695	C₂×C₃	semidirect
134. #2663	C₂×C₃	semidirect
135. #2637	C₂×C₃	semidirect
136. #2628	C₂×C₃	semidirect
137. #2626	C₂×C₃	semidirect
138. #2625	C₂×C₃	semidirect
139. #2599	C₂×C₃	semidirect
140. #2564	C₂×C₃	semidirect
141. #2498	C₂×C₃	semidirect
142. #2482	C₂×C₃	semidirect
143. #2480	C₂×C₃	semidirect
144. #2478	C₂×C₃	semidirect
145. #2469	C₂×C₃	semidirect
146. #2465	C₂×C₃	semidirect
147. #2395	C₂×C₃	semidirect
148. #2318	C₂×C₃	semidirect
275. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
279. C₂×#126	C₂²×C₃	semidirect
288. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
290. C₂×C₄×Q₈	C₂²×C₃	semidirect
291. C₂×C₄×Q₈	C₂²×C₃	semidirect
297. C₂×#117	C₂²×C₃	semidirect
300. #400	C₂²×C₃	semidirect
301. #400	C₂²×C₃	semidirect
302. #400	C₂²×C₃	semidirect
303. #400	C₂²×C₃	semidirect
304. #400	C₂²×C₃	semidirect
309. #398	C₂²×C₃	semidirect
310. #398	C₂²×C₃	semidirect
311. #398	C₂²×C₃	semidirect
312. #398	C₂²×C₃	semidirect
320. #397	C₂²×C₃	semidirect
321. #397	C₂²×C₃	semidirect
325. #395	C₂²×C₃	semidirect
326. #395	C₂²×C₃	semidirect
327. #395	C₂²×C₃	semidirect
328. #395	C₂²×C₃	semidirect
329. #395	C₂²×C₃	semidirect
336. #391	C₂²×C₃	semidirect
337. #389	C₂²×C₃	semidirect
338. #389	C₂²×C₃	semidirect
339. #389	C₂²×C₃	semidirect
347. #387	C₂²×C₃	semidirect
348. #387	C₂²×C₃	semidirect
349. #387	C₂²×C₃	semidirect
350. #387	C₂²×C₃	semidirect
351. #387	C₂²×C₃	semidirect
352. #387	C₂²×C₃	semidirect
360. #385	C₂²×C₃	semidirect
361. #383	C₂²×C₃	semidirect
362. #382	C₂²×C₃	semidirect
366. #380	C₂²×C₃	semidirect
367. #380	C₂²×C₃	semidirect
370. C₄×C₄⋊C₄	C₂²×C₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
373. C₂×#95	C₂²×C₃	semidirect
1005. C₃	#41418	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×#556	2
C₂×C₃×#551	2
C₃×#2821	2
C₃×#2817	2
C₃×#2717	2
C₃×#2715	2
C₃×#2695	2
C₃×#2684	2
C₃×#2663	2
C₃×#2637	2
C₃×#2628	2
C₃×#2626	2
C₃×#2625	2
C₃×#2599	2
C₃×#2564	2
C₃×#2498	2
C₃×#2482	2
C₃×#2480	2
C₃×#2478	2
C₃×#2469	2
C₃×#2465	2
C₃×#2395	2
C₃×#2318	2
#41418	3

Subgroups — C3×#41418 #10660025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41418 #10660025