Subgroups — C₃×#37664 #10656271

Order 768.

2868 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2701	C₂	1	2	yes	maximal, complemented
5	C₃×#2691	C₂	1	2	yes	maximal, complemented
6	C₃×#2686	C₂	1	2	yes	maximal, complemented
7	C₃×#2672	C₂	1	2	yes	maximal, complemented
8	C₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2437	C₂	1	2	yes	maximal, complemented
14	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2435	C₂	1	2	yes	maximal, complemented
16	C₃×#2427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2405	C₂	1	2	yes	maximal, complemented
20	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
24	#37664	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	2	yes	—
27	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
28	C₃×#542	—	2	8	no	—
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#126	C₂²	1	2	yes	complemented
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#124	C₂²	1	2	yes	complemented
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#124	C₂²	1	2	yes	complemented
35	C₂×C₃×#123	C₂²	1	2	yes	complemented
36	C₂×C₃×#123	C₂²	1	2	yes	complemented
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×#121	—	2	8	no	—
43	C₂×C₃×#121	C₂²	1	1	yes	characteristic
44	C₂×C₃×#121	C₂²	1	2	yes	—
45	C₂×C₃×#121	C₂²	1	1	yes	characteristic
46	C₂×C₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃×#121	C₂²	1	2	yes	—
48	C₂×C₃×#121	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₃×#399	C₂²	1	2	yes	complemented
58	C₃×#398	C₂²	1	2	yes	complemented
59	C₃×#397	C₂²	1	2	yes	complemented
60	C₃×#397	C₂²	1	2	yes	complemented
61	C₃×#397	C₂²	1	2	yes	complemented
62	C₃×#396	C₂²	1	2	yes	complemented
63	C₃×#396	C₂²	1	2	yes	complemented
64	C₃×#396	C₂²	1	2	yes	complemented
65	C₃×#395	C₂²	1	2	yes	complemented
66	C₃×#394	C₂²	1	2	yes	complemented
67	C₃×#394	C₂²	1	2	yes	complemented
68	C₃×#394	C₂²	1	2	yes	complemented
69	C₃×#394	C₂²	1	2	yes	complemented
70	C₃×#394	C₂²	1	2	yes	complemented
71	C₃×#394	C₂²	1	2	yes	complemented
72	C₃×#394	C₂²	1	2	yes	complemented
73	C₃×#394	C₂²	1	2	yes	complemented
74	C₃×#394	C₂²	1	2	yes	complemented
75	C₃×#394	C₂²	1	2	yes	complemented
76	C₃×#393	C₂²	1	2	yes	complemented
77	C₃×#391	C₂²	1	1	yes	characteristic, complemented
78	C₃×#390	C₂²	1	1	yes	characteristic, complemented
79	C₃×#390	C₂²	1	1	yes	characteristic, complemented
80	C₃×#390	C₂²	1	1	yes	characteristic, complemented
81	C₃×#390	C₂²	1	1	yes	characteristic, complemented
82	C₃×#390	C₂²	1	2	yes	complemented
83	C₃×#390	C₂²	1	2	yes	complemented
84	C₃×#389	C₂²	1	1	yes	characteristic, complemented
85	C₃×#389	C₂²	1	2	yes	complemented
86	C₃×#389	C₂²	1	1	yes	characteristic, complemented
87	C₃×#389	C₂²	1	1	yes	characteristic, complemented
88	C₃×#388	C₂²	1	2	yes	complemented
89	C₃×#388	C₂²	1	2	yes	complemented
90	C₃×#388	C₂²	1	2	yes	complemented
91	C₃×#387	C₂²	1	2	yes	complemented
92	C₃×#386	C₂²	1	2	yes	complemented
93	C₃×#386	C₂²	1	2	yes	complemented
94	C₃×#386	C₂²	1	2	yes	complemented
95	C₃×#386	C₂²	1	2	yes	complemented
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#385	C₂²	1	2	yes	—
99	C₃×#385	C₂²	1	2	yes	complemented
100	C₃×#385	C₂²	1	2	yes	complemented
101	C₃×#385	C₂²	1	2	yes	complemented
102	C₃×#385	C₂²	1	2	yes	complemented
103	C₃×#384	C₂²	1	1	yes	characteristic, complemented
104	C₃×#381	C₂²	1	1	yes	characteristic, complemented
105	C₃×#381	C₂²	1	1	yes	characteristic, complemented
106	C₃×#380	C₂²	1	1	yes	characteristic
107	C₃×#380	C₂²	1	1	yes	characteristic
108	C₃×#380	C₂²	1	1	yes	characteristic
109	C₃×#380	C₂²	1	1	yes	characteristic, complemented
110	C₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₃×#380	C₂²	1	1	yes	characteristic, complemented
112	C₃×#380	C₂²	1	2	yes	complemented
113	C₃×#380	C₂²	1	1	yes	characteristic, complemented
114	C₃×#379	C₂²	1	1	yes	characteristic
115	C₃×#379	C₂²	1	2	yes	—
116	C₃×#379	C₂²	1	2	yes	—
117	C₃×#379	C₂²	1	2	yes	—
118	C₃×#379	C₂²	1	1	yes	characteristic
119	C₃×#379	C₂²	1	2	yes	—
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
126	C₂×#542	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×#121	C₂×C₃	1	1	yes	characteristic
128	#2848	C₂×C₃	1	1	yes	characteristic, complemented
129	#2701	C₂×C₃	1	2	yes	complemented
130	#2691	C₂×C₃	1	2	yes	complemented
131	#2686	C₂×C₃	1	2	yes	complemented
132	#2672	C₂×C₃	1	2	yes	complemented
133	#2624	C₂×C₃	1	1	yes	characteristic, complemented
134	#2620	C₂×C₃	1	1	yes	characteristic, complemented
135	#2491	C₂×C₃	1	1	yes	characteristic, complemented
136	#2480	C₂×C₃	1	2	yes	complemented
137	#2440	C₂×C₃	1	1	yes	characteristic, complemented
138	#2437	C₂×C₃	1	2	yes	complemented
139	#2435	C₂×C₃	1	1	yes	characteristic, complemented
140	#2435	C₂×C₃	1	2	yes	complemented
141	#2427	C₂×C₃	1	1	yes	characteristic, complemented
142	#2426	C₂×C₃	1	1	yes	characteristic, complemented
143	#2422	C₂×C₃	1	1	yes	characteristic, complemented
144	#2405	C₂×C₃	1	2	yes	complemented
145	#2360	C₂×C₃	1	1	yes	characteristic, complemented
146	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
147	#2324	C₂×C₃	1	1	yes	characteristic, complemented
148	#2280	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	1	yes	characteristic
150	C₂⁵×C₃	C₂³	1	2	yes	—
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₃×Q₈	C₂³	1	2	yes	—
153	C₂²×C₃×D₄	—	2	4	no	—
154	C₂²×C₃×D₄	—	2	8	no	—
155	C₂²×C₃×D₄	—	2	4	no	—
156	C₂²×C₃×D₄	—	4	2	no	—
157	C₂²×C₃×D₄	—	4	4	no	—
158	C₂²×C₃×D₄	—	4	4	no	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	2	yes	—
163	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂³	1	2	yes	—
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	—	2	4	no	—
167	C₂³×C₃×C₄	—	2	4	no	—
168	C₂³×C₃×C₄	—	4	2	no	—
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₂³×C₃×C₄	C₂³	1	2	yes	—
177	C₂³×C₃×C₄	C₂³	1	2	yes	—
178	C₃×C₄⋊Q₈	—	2	4	no	—
179	C₃×#126	—	2	8	no	—
180	C₃×#124	—	2	4	no	—
181	C₃×#124	—	2	8	no	—
182	C₃×#124	—	4	2	no	—
183	C₃×#124	—	4	4	no	—
184	C₃×#123	—	2	8	no	—
185	C₃×#123	—	4	4	no	—
186	C₃×C₂²⋊Q₈	—	2	4	no	—
187	C₃×C₂²⋊Q₈	—	2	4	no	—
188	C₃×C₂²⋊Q₈	—	2	8	no	—
189	C₃×C₂²⋊Q₈	—	4	4	no	—
190	C₃×C₂²⋊Q₈	—	4	2	no	—
191	C₃×#121	—	2	4	no	—
192	C₃×#121	—	2	8	no	—
193	C₃×#121	—	2	4	no	—
194	C₃×#121	—	2	4	no	—
195	C₃×#121	—	2	8	no	—
196	C₃×#121	D₄	1	8	yes	—
197	C₃×C₄×Q₈	—	2	4	no	—
198	C₃×C₄×D₄	—	2	4	no	—
199	C₃×C₄×D₄	—	4	2	no	—
200	C₃×#117	—	2	4	no	—
201	C₃×#117	—	4	2	no	—
202	C₂×C₃×C₄⋊C₄	—	2	4	no	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
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	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
256	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
257	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
259	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
260	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
261	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
263	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
264	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
265	C₂×C₃×C₄²	C₂³	1	2	yes	—
266	C₂×C₃×C₄²	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	1	yes	characteristic
268	C₃×#95	C₂³	1	1	yes	characteristic
269	C₃×#95	C₂³	1	1	yes	characteristic
270	C₃×#95	C₂³	1	1	yes	characteristic
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	1	yes	characteristic
274	C₃×#95	C₂³	1	1	yes	characteristic
275	C₃×#95	C₂³	1	1	yes	characteristic
276	C₃×#95	C₂³	1	1	yes	characteristic
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₃×#95	C₂³	1	2	yes	—
283	C₃×#95	C₂³	1	2	yes	—
284	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
285	C₂³×D₄	C₂²×C₃	1	2	yes	—
286	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
287	#542	—	2	8	no	—
288	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₂×#126	C₂²×C₃	1	2	yes	complemented
290	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂×#124	C₂²×C₃	1	2	yes	complemented
292	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₂×#124	C₂²×C₃	1	2	yes	complemented
294	C₂×#123	C₂²×C₃	1	2	yes	complemented
295	C₂×#123	C₂²×C₃	1	2	yes	complemented
296	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
300	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂×#121	—	2	8	no	—
302	C₂×#121	C₂²×C₃	1	1	yes	characteristic
303	C₂×#121	C₂²×C₃	1	2	yes	—
304	C₂×#121	C₂²×C₃	1	1	yes	characteristic
305	C₂×#121	C₂²×C₃	1	1	yes	characteristic
306	C₂×#121	C₂²×C₃	1	2	yes	—
307	C₂×#121	C₂²×C₃	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
311	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	#399	C₂²×C₃	1	2	yes	complemented
317	#398	C₂²×C₃	1	2	yes	complemented
318	#397	C₂²×C₃	1	2	yes	complemented
319	#397	C₂²×C₃	1	2	yes	complemented
320	#397	C₂²×C₃	1	2	yes	complemented
321	#396	C₂²×C₃	1	2	yes	complemented
322	#396	C₂²×C₃	1	2	yes	complemented
323	#396	C₂²×C₃	1	2	yes	complemented
324	#395	C₂²×C₃	1	2	yes	complemented
325	#394	C₂²×C₃	1	2	yes	complemented
326	#394	C₂²×C₃	1	2	yes	complemented
327	#394	C₂²×C₃	1	2	yes	complemented
328	#394	C₂²×C₃	1	2	yes	complemented
329	#394	C₂²×C₃	1	2	yes	complemented
330	#394	C₂²×C₃	1	2	yes	complemented
331	#394	C₂²×C₃	1	2	yes	complemented
332	#394	C₂²×C₃	1	2	yes	complemented
333	#394	C₂²×C₃	1	2	yes	complemented
334	#394	C₂²×C₃	1	2	yes	complemented
335	#393	C₂²×C₃	1	2	yes	complemented
336	#391	C₂²×C₃	1	1	yes	characteristic, complemented
337	#390	C₂²×C₃	1	1	yes	characteristic, complemented
338	#390	C₂²×C₃	1	2	yes	complemented
339	#390	C₂²×C₃	1	1	yes	characteristic, complemented
340	#390	C₂²×C₃	1	1	yes	characteristic, complemented
341	#390	C₂²×C₃	1	1	yes	characteristic, complemented
342	#390	C₂²×C₃	1	2	yes	complemented
343	#389	C₂²×C₃	1	1	yes	characteristic, complemented
344	#389	C₂²×C₃	1	1	yes	characteristic, complemented
345	#389	C₂²×C₃	1	2	yes	complemented
346	#389	C₂²×C₃	1	1	yes	characteristic, complemented
347	#388	C₂²×C₃	1	2	yes	complemented
348	#388	C₂²×C₃	1	2	yes	complemented
349	#388	C₂²×C₃	1	2	yes	complemented
350	#387	C₂²×C₃	1	2	yes	complemented
351	#386	C₂²×C₃	1	2	yes	complemented
352	#386	C₂²×C₃	1	2	yes	complemented
353	#386	C₂²×C₃	1	2	yes	complemented
354	#386	C₂²×C₃	1	2	yes	complemented
355	#385	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	complemented
359	#385	C₂²×C₃	1	2	yes	complemented
360	#385	C₂²×C₃	1	2	yes	complemented
361	#385	C₂²×C₃	1	2	yes	complemented
362	#384	C₂²×C₃	1	1	yes	characteristic, complemented
363	#381	C₂²×C₃	1	1	yes	characteristic, complemented
364	#381	C₂²×C₃	1	1	yes	characteristic, complemented
365	#380	C₂²×C₃	1	1	yes	characteristic
366	#380	C₂²×C₃	1	1	yes	characteristic
367	#380	C₂²×C₃	1	1	yes	characteristic
368	#380	C₂²×C₃	1	1	yes	characteristic, complemented
369	#380	C₂²×C₃	1	1	yes	characteristic, complemented
370	#380	C₂²×C₃	1	1	yes	characteristic, complemented
371	#380	C₂²×C₃	1	2	yes	complemented
372	#380	C₂²×C₃	1	1	yes	characteristic, complemented
373	#379	C₂²×C₃	1	2	yes	—
374	#379	C₂²×C₃	1	2	yes	—
375	#379	C₂²×C₃	1	1	yes	characteristic
376	#379	C₂²×C₃	1	2	yes	—
377	#379	C₂²×C₃	1	2	yes	—
378	#379	C₂²×C₃	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
380	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
383	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
384	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
385	C₂⁴×C₃	—	2	2	no	—
386	C₂⁴×C₃	—	2	2	no	—
387	C₂⁴×C₃	—	2	2	no	—
388	C₂⁴×C₃	—	2	4	no	—
389	C₂⁴×C₃	—	2	2	no	—
390	C₂⁴×C₃	—	2	2	no	—
391	C₂⁴×C₃	—	2	4	no	—
392	C₂⁴×C₃	—	2	4	no	—
393	C₂⁴×C₃	—	2	4	no	—
394	C₂⁴×C₃	—	4	1	no	—
395	C₂⁴×C₃	—	4	1	no	—
396	C₂⁴×C₃	—	4	2	no	—
397	C₂⁴×C₃	—	4	2	no	—
398	C₂⁴×C₃	—	4	2	no	—
399	C₂⁴×C₃	C₂⁴	1	2	yes	—
400	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
401	C₂⁴×C₃	C₂⁴	1	2	yes	—
402	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
403	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₃×Q₈	—	2	2	no	—
405	C₂×C₃×Q₈	—	2	4	no	—
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	—	2	2	no	—
408	C₂×C₃×Q₈	—	4	2	no	—
409	C₂×C₃×Q₈	—	4	2	no	—
410	C₂×C₃×D₄	—	2	4	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	4	no	—
414	C₂×C₃×D₄	—	2	4	no	—
415	C₂×C₃×D₄	—	2	4	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	4	no	—
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	2	2	no	—
422	C₂×C₃×D₄	—	4	16	no	—
423	C₂×C₃×D₄	—	4	2	no	—
424	C₂×C₃×D₄	—	4	2	no	—
425	C₂×C₃×D₄	—	4	2	no	—
426	C₂×C₃×D₄	—	4	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	2	no	—
430	C₂×C₃×D₄	—	4	32	no	—
431	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
432	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	2	no	—
435	C₂²×C₃×C₄	—	2	2	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	4	no	—
440	C₂²×C₃×C₄	—	2	4	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	4	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	2	2	no	—
449	C₂²×C₃×C₄	—	4	1	no	—
450	C₂²×C₃×C₄	—	4	1	no	—
451	C₂²×C₃×C₄	—	4	1	no	—
452	C₂²×C₃×C₄	—	4	2	no	—
453	C₂²×C₃×C₄	—	4	16	no	—
454	C₂²×C₃×C₄	—	4	2	no	—
455	C₂²×C₃×C₄	—	4	2	no	—
456	C₂²×C₃×C₄	—	4	2	no	—
457	C₂²×C₃×C₄	—	4	2	no	—
458	C₂²×C₃×C₄	—	4	2	no	—
459	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
460	C₂²×C₃×C₄	#41	1	4	yes	—
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
465	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
466	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
467	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
468	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
475	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
476	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₃×C₄⋊C₄	—	2	4	no	—
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	2	2	no	—
483	C₃×C₄⋊C₄	—	2	2	no	—
484	C₃×C₄⋊C₄	—	2	4	no	—
485	C₃×C₄⋊C₄	—	2	4	no	—
486	C₃×C₄⋊C₄	—	2	4	no	—
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	—	2	4	no	—
489	C₃×C₄⋊C₄	—	2	2	no	—
490	C₃×C₄⋊C₄	—	4	1	no	—
491	C₃×C₄⋊C₄	—	4	1	no	—
492	C₃×C₄⋊C₄	—	4	2	no	—
493	C₃×C₄⋊C₄	—	4	2	no	—
494	C₃×C₄⋊C₄	—	4	2	no	—
495	C₃×C₄⋊C₄	—	4	2	no	—
496	C₃×C₄⋊C₄	—	4	2	no	—
497	C₃×C₄⋊C₄	—	4	2	no	—
498	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
499	C₃×C₂²⋊C₄	—	2	4	no	—
500	C₃×C₂²⋊C₄	—	2	2	no	—
501	C₃×C₂²⋊C₄	—	2	2	no	—
502	C₃×C₂²⋊C₄	—	2	4	no	—
503	C₃×C₂²⋊C₄	—	2	4	no	—
504	C₃×C₂²⋊C₄	—	2	4	no	—
505	C₃×C₂²⋊C₄	—	2	4	no	—
506	C₃×C₂²⋊C₄	—	2	4	no	—
507	C₃×C₂²⋊C₄	—	2	2	no	—
508	C₃×C₂²⋊C₄	—	2	4	no	—
509	C₃×C₂²⋊C₄	—	2	2	no	—
510	C₃×C₂²⋊C₄	—	2	2	no	—
511	C₃×C₂²⋊C₄	—	2	4	no	—
512	C₃×C₂²⋊C₄	—	2	2	no	—
513	C₃×C₂²⋊C₄	—	2	2	no	—
514	C₃×C₂²⋊C₄	—	2	2	no	—
515	C₃×C₂²⋊C₄	—	2	4	no	—
516	C₃×C₂²⋊C₄	—	2	4	no	—
517	C₃×C₂²⋊C₄	—	4	2	no	—
518	C₃×C₂²⋊C₄	—	4	2	no	—
519	C₃×C₂²⋊C₄	—	4	1	no	—
520	C₃×C₂²⋊C₄	—	4	2	no	—
521	C₃×C₂²⋊C₄	—	4	2	no	—
522	C₃×C₂²⋊C₄	—	4	2	no	—
523	C₃×C₂²⋊C₄	—	4	2	no	—
524	C₃×C₂²⋊C₄	—	4	1	no	—
525	C₃×C₂²⋊C₄	—	4	1	no	—
526	C₃×C₂²⋊C₄	—	4	1	no	—
527	C₃×C₂²⋊C₄	—	4	2	no	—
528	C₃×C₂²⋊C₄	—	4	2	no	—
529	C₃×C₂²⋊C₄	—	4	2	no	—
530	C₃×C₂²⋊C₄	—	4	2	no	—
531	C₃×C₂²⋊C₄	—	4	2	no	—
532	C₃×C₂²⋊C₄	—	4	2	no	—
533	C₃×C₂²⋊C₄	—	4	2	no	—
534	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
535	C₃×C₄²	—	2	2	no	—
536	C₃×C₄²	—	2	2	no	—
537	C₃×C₄²	—	2	4	no	—
538	C₃×C₄²	—	2	2	no	—
539	C₃×C₄²	—	2	2	no	—
540	C₃×C₄²	—	4	2	no	—
541	C₂⁵	C₂³×C₃	1	1	yes	characteristic
542	C₂⁵	C₂³×C₃	1	2	yes	—
543	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₃	1	2	yes	—
545	C₂²×D₄	—	2	4	no	—
546	C₂²×D₄	—	2	8	no	—
547	C₂²×D₄	—	2	4	no	—
548	C₂²×D₄	—	4	2	no	—
549	C₂²×D₄	—	4	4	no	—
550	C₂²×D₄	—	4	4	no	—
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	2	yes	—
553	C₂²×D₄	C₂³×C₃	1	2	yes	—
554	C₂²×D₄	C₂³×C₃	1	2	yes	—
555	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₃	1	2	yes	—
557	C₂²×D₄	C₂³×C₃	1	2	yes	—
558	C₂³×C₄	—	2	4	no	—
559	C₂³×C₄	—	2	4	no	—
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	2	yes	—
564	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₃	1	2	yes	—
569	C₂³×C₄	C₂³×C₃	1	2	yes	—
570	C₄⋊Q₈	—	2	4	no	—
571	#126	—	2	8	no	—
572	#124	—	2	4	no	—
573	#124	—	2	8	no	—
574	#124	—	4	2	no	—
575	#124	—	4	4	no	—
576	#123	—	2	8	no	—
577	#123	—	4	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	C₂²⋊Q₈	—	4	4	no	—
582	C₂²⋊Q₈	—	4	2	no	—
583	#121	—	2	4	no	—
584	#121	—	2	8	no	—
585	#121	—	2	4	no	—
586	#121	—	2	4	no	—
587	#121	—	2	8	no	—
588	#121	C₃×D₄	1	8	yes	—
589	C₄×Q₈	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	4	2	no	—
592	#117	—	2	4	no	—
593	#117	—	4	2	no	—
594	C₂×C₄⋊C₄	—	2	4	no	—
595	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	—	2	8	no	—
616	C₂×C₂²⋊C₄	—	4	4	no	—
617	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₃	1	2	yes	—
658	C₂×C₄²	C₂³×C₃	1	2	yes	—
659	#95	C₂³×C₃	1	1	yes	characteristic
660	#95	C₂³×C₃	1	1	yes	characteristic
661	#95	C₂³×C₃	1	1	yes	characteristic
662	#95	C₂³×C₃	1	1	yes	characteristic
663	#95	C₂³×C₃	1	2	yes	—
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	1	yes	characteristic
666	#95	C₂³×C₃	1	1	yes	characteristic
667	#95	C₂³×C₃	1	1	yes	characteristic
668	#95	C₂³×C₃	1	1	yes	characteristic
669	#95	C₂³×C₃	1	2	yes	—
670	#95	C₂³×C₃	1	2	yes	—
671	#95	C₂³×C₃	1	2	yes	—
672	#95	C₂³×C₃	1	2	yes	—
673	#95	C₂³×C₃	1	2	yes	—
674	#95	C₂³×C₃	1	2	yes	—
675	#95	C₂³×C₃	1	2	yes	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	1	no	—
679	C₂³×C₃	—	2	1	no	—
680	C₂³×C₃	—	2	8	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	—	2	1	no	—
683	C₂³×C₃	—	2	1	no	—
684	C₂³×C₃	—	2	2	no	—
685	C₂³×C₃	—	2	1	no	—
686	C₂³×C₃	—	2	1	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	2	no	—
690	C₂³×C₃	—	2	1	no	—
691	C₂³×C₃	—	2	1	no	—
692	C₂³×C₃	—	2	1	no	—
693	C₂³×C₃	—	2	1	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	1	no	—
696	C₂³×C₃	—	2	1	no	—
697	C₂³×C₃	—	2	1	no	—
698	C₂³×C₃	—	2	2	no	—
699	C₂³×C₃	—	2	2	no	—
700	C₂³×C₃	—	2	2	no	—
701	C₂³×C₃	—	2	2	no	—
702	C₂³×C₃	—	2	2	no	—
703	C₂³×C₃	—	2	2	no	—
704	C₂³×C₃	—	2	2	no	—
705	C₂³×C₃	—	2	2	no	—
706	C₂³×C₃	—	4	4	no	—
707	C₂³×C₃	—	4	4	no	—
708	C₂³×C₃	—	4	4	no	—
709	C₂³×C₃	—	4	4	no	—
710	C₂³×C₃	—	4	8	no	—
711	C₂³×C₃	—	4	8	no	—
712	C₂³×C₃	—	4	8	no	—
713	C₂³×C₃	—	4	4	no	—
714	C₂³×C₃	—	4	4	no	—
715	C₂³×C₃	—	4	8	no	—
716	C₂³×C₃	—	8	4	no	—
717	C₂³×C₃	—	8	4	no	—
718	C₂³×C₃	—	8	4	no	—
719	C₂³×C₃	C₂²×D₄	1	4	yes	—
720	C₂³×C₃	C₂²×D₄	1	2	yes	—
721	C₂³×C₃	C₂×#41	1	2	yes	—
722	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
723	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
724	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
725	C₂³×C₃	C₂⁵	1	1	yes	characteristic
726	C₃×Q₈	—	4	4	no	—
727	C₃×Q₈	—	8	4	no	—
728	C₃×D₄	—	2	8	no	—
729	C₃×D₄	—	4	8	no	—
730	C₃×D₄	—	4	8	no	—
731	C₃×D₄	—	4	8	no	—
732	C₃×D₄	—	4	8	no	—
733	C₃×D₄	—	4	8	no	—
734	C₃×D₄	—	4	4	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	2	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	2	no	—
740	C₂×C₃×C₄	—	2	1	no	—
741	C₂×C₃×C₄	—	2	8	no	—
742	C₂×C₃×C₄	—	2	8	no	—
743	C₂×C₃×C₄	—	2	1	no	—
744	C₂×C₃×C₄	—	2	1	no	—
745	C₂×C₃×C₄	—	2	2	no	—
746	C₂×C₃×C₄	—	2	1	no	—
747	C₂×C₃×C₄	—	2	1	no	—
748	C₂×C₃×C₄	—	2	1	no	—
749	C₂×C₃×C₄	—	2	2	no	—
750	C₂×C₃×C₄	—	2	2	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	2	no	—
753	C₂×C₃×C₄	—	2	1	no	—
754	C₂×C₃×C₄	—	2	1	no	—
755	C₂×C₃×C₄	—	2	1	no	—
756	C₂×C₃×C₄	—	2	1	no	—
757	C₂×C₃×C₄	—	2	1	no	—
758	C₂×C₃×C₄	—	2	1	no	—
759	C₂×C₃×C₄	—	2	2	no	—
760	C₂×C₃×C₄	—	2	1	no	—
761	C₂×C₃×C₄	—	2	1	no	—
762	C₂×C₃×C₄	—	2	1	no	—
763	C₂×C₃×C₄	—	2	1	no	—
764	C₂×C₃×C₄	—	2	2	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	1	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	1	no	—
770	C₂×C₃×C₄	—	2	2	no	—
771	C₂×C₃×C₄	—	2	2	no	—
772	C₂×C₃×C₄	—	2	1	no	—
773	C₂×C₃×C₄	—	2	2	no	—
774	C₂×C₃×C₄	—	2	2	no	—
775	C₂×C₃×C₄	—	2	1	no	—
776	C₂×C₃×C₄	—	2	1	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	1	no	—
779	C₂×C₃×C₄	—	2	1	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	2	no	—
782	C₂×C₃×C₄	—	2	1	no	—
783	C₂×C₃×C₄	—	2	2	no	—
784	C₂×C₃×C₄	—	2	1	no	—
785	C₂×C₃×C₄	—	4	4	no	—
786	C₂×C₃×C₄	—	4	4	no	—
787	C₂×C₃×C₄	—	4	4	no	—
788	C₂×C₃×C₄	—	4	8	no	—
789	C₂×C₃×C₄	—	4	4	no	—
790	C₂×C₃×C₄	—	8	4	no	—
791	C₂×C₃×C₄	—	8	4	no	—
792	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
793	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
794	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
795	C₂×C₃×C₄	C₂×#41	1	2	yes	—
796	C₂×C₃×C₄	C₂×#41	1	2	yes	—
797	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
798	C₂⁴	—	2	2	no	—
799	C₂⁴	—	2	2	no	—
800	C₂⁴	—	2	2	no	—
801	C₂⁴	—	2	4	no	—
802	C₂⁴	—	2	2	no	—
803	C₂⁴	—	2	2	no	—
804	C₂⁴	—	2	4	no	—
805	C₂⁴	—	2	4	no	—
806	C₂⁴	—	2	4	no	—
807	C₂⁴	—	4	1	no	—
808	C₂⁴	—	4	1	no	—
809	C₂⁴	—	4	2	no	—
810	C₂⁴	—	4	2	no	—
811	C₂⁴	—	4	2	no	—
812	C₂⁴	C₂⁴×C₃	1	2	yes	—
813	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
814	C₂⁴	C₂⁴×C₃	1	2	yes	—
815	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
816	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	4	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	4	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	4	16	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	32	no	—
844	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
845	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	1	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	16	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
873	C₂²×C₄	C₃×#41	1	4	yes	—
874	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	4	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	4	1	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	1	no	—
933	C₂²⋊C₄	—	4	1	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	1	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	1	no	—
947	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	4	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	4	2	no	—
954	C₂²×C₃	—	2	2	no	—
955	C₂²×C₃	—	2	2	no	—
956	C₂²×C₃	—	2	2	no	—
957	C₂²×C₃	—	2	2	no	—
958	C₂²×C₃	—	2	2	no	—
959	C₂²×C₃	—	2	2	no	—
960	C₂²×C₃	—	2	2	no	—
961	C₂²×C₃	—	2	4	no	—
962	C₂²×C₃	—	2	4	no	—
963	C₂²×C₃	—	2	2	no	—
964	C₂²×C₃	—	2	2	no	—
965	C₂²×C₃	—	2	2	no	—
966	C₂²×C₃	—	2	4	no	—
967	C₂²×C₃	—	2	2	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	4	16	no	—
970	C₂²×C₃	—	4	1	no	—
971	C₂²×C₃	—	4	1	no	—
972	C₂²×C₃	—	4	2	no	—
973	C₂²×C₃	—	4	1	no	—
974	C₂²×C₃	—	4	1	no	—
975	C₂²×C₃	—	4	1	no	—
976	C₂²×C₃	—	4	2	no	—
977	C₂²×C₃	—	4	1	no	—
978	C₂²×C₃	—	4	2	no	—
979	C₂²×C₃	—	4	2	no	—
980	C₂²×C₃	—	4	1	no	—
981	C₂²×C₃	—	4	1	no	—
982	C₂²×C₃	—	4	2	no	—
983	C₂²×C₃	—	4	2	no	—
984	C₂²×C₃	—	4	2	no	—
985	C₂²×C₃	—	4	2	no	—
986	C₂²×C₃	—	4	2	no	—
987	C₂²×C₃	—	4	2	no	—
988	C₂²×C₃	—	4	2	no	—
989	C₂²×C₃	—	8	16	no	—
990	C₂²×C₃	#542	1	4	yes	complemented
991	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
992	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
993	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
994	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
995	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
996	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
997	C₂²×C₃	#585	1	1	yes	characteristic
998	C₃×C₄	—	2	2	no	—
999	C₃×C₄	—	2	2	no	—
1000	C₃×C₄	—	2	4	no	—
1001	C₃×C₄	—	4	1	no	—
1002	C₃×C₄	—	4	2	no	—
1003	C₃×C₄	—	4	2	no	—
1004	C₃×C₄	—	4	1	no	—
1005	C₃×C₄	—	4	2	no	—
1006	C₃×C₄	—	4	1	no	—
1007	C₃×C₄	—	4	1	no	—
1008	C₃×C₄	—	4	1	no	—
1009	C₃×C₄	—	4	2	no	—
1010	C₃×C₄	—	4	1	no	—
1011	C₃×C₄	—	4	1	no	—
1012	C₃×C₄	—	4	1	no	—
1013	C₃×C₄	—	4	2	no	—
1014	C₃×C₄	—	4	1	no	—
1015	C₃×C₄	#546	1	4	yes	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	8	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	4	no	—
1047	C₂³	—	4	4	no	—
1048	C₂³	—	4	4	no	—
1049	C₂³	—	4	4	no	—
1050	C₂³	—	4	8	no	—
1051	C₂³	—	4	8	no	—
1052	C₂³	—	4	8	no	—
1053	C₂³	—	4	4	no	—
1054	C₂³	—	4	4	no	—
1055	C₂³	—	4	8	no	—
1056	C₂³	—	8	4	no	—
1057	C₂³	—	8	4	no	—
1058	C₂³	—	8	4	no	—
1059	C₂³	C₂²×C₃×D₄	1	4	yes	—
1060	C₂³	C₂²×C₃×D₄	1	2	yes	—
1061	C₂³	C₂×C₃×#41	1	2	yes	—
1062	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1063	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1064	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
1065	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1066	Q₈	—	4	4	no	—
1067	Q₈	—	8	4	no	—
1068	D₄	—	2	8	no	—
1069	D₄	—	4	8	no	—
1070	D₄	—	4	8	no	—
1071	D₄	—	4	8	no	—
1072	D₄	—	4	8	no	—
1073	D₄	—	4	8	no	—
1074	D₄	—	4	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	8	no	—
1082	C₂×C₄	—	2	8	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	4	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	8	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	8	4	no	—
1131	C₂×C₄	—	8	4	no	—
1132	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1133	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1134	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1135	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1136	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1137	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1138	C₂×C₃	—	2	4	no	—
1139	C₂×C₃	—	4	2	no	—
1140	C₂×C₃	—	4	2	no	—
1141	C₂×C₃	—	4	4	no	—
1142	C₂×C₃	—	8	2	no	—
1143	C₂×C₃	C₂×#542	1	1	yes	characteristic
1144	C₂×C₃	C₂×#546	1	1	yes	characteristic
1145	C₂×C₃	#3484	1	1	yes	characteristic
1146	C₂×C₃	#3489	1	1	yes	characteristic
1147	C₂×C₃	#3494	1	1	yes	characteristic
1148	C₂×C₃	#3536	1	1	yes	characteristic
1149	C₂×C₃	#3542	1	1	yes	characteristic
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	4	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	4	16	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	8	16	no	—
1186	C₂²	C₃×#542	1	4	yes	complemented
1187	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1188	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1189	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1193	C₂²	C₃×#585	1	1	yes	characteristic
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	4	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	2	no	—
1199	C₄	—	4	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	C₃×#546	1	4	yes	—
1212	C₃	#37664	1	1	yes	characteristic, direct product factor, Sylow
1213	C₂	—	2	4	no	—
1214	C₂	—	4	2	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	4	4	no	—
1217	C₂	—	8	2	no	—
1218	C₂	C₂×C₃×#542	1	1	yes	characteristic
1219	C₂	C₂×C₃×#546	1	1	yes	characteristic
1220	C₂	C₃×#3484	1	1	yes	characteristic
1221	C₂	C₃×#3489	1	1	yes	characteristic
1222	C₂	C₃×#3494	1	1	yes	characteristic
1223	C₂	C₃×#3536	1	1	yes	characteristic
1224	C₂	C₃×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×#121	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. C₂×C₃×#542	C₂	semidirect
3. C₃×#2848	C₂	semidirect
4. C₃×#2701	C₂	semidirect
5. C₃×#2691	C₂	semidirect
6. C₃×#2686	C₂	semidirect
7. C₃×#2672	C₂	semidirect
8. C₃×#2624	C₂	semidirect
9. C₃×#2620	C₂	semidirect
10. C₃×#2491	C₂	semidirect
11. C₃×#2480	C₂	semidirect
12. C₃×#2440	C₂	semidirect
13. C₃×#2437	C₂	semidirect
14. C₃×#2435	C₂	semidirect
15. C₃×#2435	C₂	semidirect
16. C₃×#2427	C₂	semidirect
17. C₃×#2426	C₂	semidirect
18. C₃×#2422	C₂	semidirect
19. C₃×#2405	C₂	semidirect
20. C₃×#2360	C₂	semidirect
21. C₃×D₄×C₂²⋊C₄	C₂	semidirect
22. C₃×#2324	C₂	semidirect
23. C₃×#2280	C₂	semidirect
24. #37664	C₃	direct (N × H)
29. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×#126	C₂²	semidirect
31. C₂×C₃×#124	C₂²	semidirect
32. C₂×C₃×#124	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
34. C₂×C₃×#124	C₂²	semidirect
35. C₂×C₃×#123	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
39. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₃×C₄×Q₈	C₂²	semidirect
50. C₂×C₃×C₄×D₄	C₂²	semidirect
51. C₂×C₃×C₄×D₄	C₂²	semidirect
52. C₂×C₃×#117	C₂²	semidirect
53. C₂×C₃×#117	C₂²	semidirect
57. C₃×#399	C₂²	semidirect
58. C₃×#398	C₂²	semidirect
59. C₃×#397	C₂²	semidirect
60. C₃×#397	C₂²	semidirect
61. C₃×#397	C₂²	semidirect
62. C₃×#396	C₂²	semidirect
63. C₃×#396	C₂²	semidirect
64. C₃×#396	C₂²	semidirect
65. C₃×#395	C₂²	semidirect
66. C₃×#394	C₂²	semidirect
67. C₃×#394	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#394	C₂²	semidirect
71. C₃×#394	C₂²	semidirect
72. C₃×#394	C₂²	semidirect
73. C₃×#394	C₂²	semidirect
74. C₃×#394	C₂²	semidirect
75. C₃×#394	C₂²	semidirect
76. C₃×#393	C₂²	semidirect
77. C₃×#391	C₂²	semidirect
78. C₃×#390	C₂²	semidirect
79. C₃×#390	C₂²	semidirect
80. C₃×#390	C₂²	semidirect
81. C₃×#390	C₂²	semidirect
82. C₃×#390	C₂²	semidirect
83. C₃×#390	C₂²	semidirect
84. C₃×#389	C₂²	semidirect
85. C₃×#389	C₂²	semidirect
86. C₃×#389	C₂²	semidirect
87. C₃×#389	C₂²	semidirect
88. C₃×#388	C₂²	semidirect
89. C₃×#388	C₂²	semidirect
90. C₃×#388	C₂²	semidirect
91. C₃×#387	C₂²	semidirect
92. C₃×#386	C₂²	semidirect
93. C₃×#386	C₂²	semidirect
94. C₃×#386	C₂²	semidirect
95. C₃×#386	C₂²	semidirect
99. C₃×#385	C₂²	semidirect
100. C₃×#385	C₂²	semidirect
101. C₃×#385	C₂²	semidirect
102. C₃×#385	C₂²	semidirect
103. C₃×#384	C₂²	semidirect
104. C₃×#381	C₂²	semidirect
105. C₃×#381	C₂²	semidirect
109. C₃×#380	C₂²	semidirect
110. C₃×#380	C₂²	semidirect
111. C₃×#380	C₂²	semidirect
112. C₃×#380	C₂²	semidirect
113. C₃×#380	C₂²	semidirect
120. C₃×C₄×C₄⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
126. C₂×#542	C₂×C₃	semidirect
128. #2848	C₂×C₃	semidirect
129. #2701	C₂×C₃	semidirect
130. #2691	C₂×C₃	semidirect
131. #2686	C₂×C₃	semidirect
132. #2672	C₂×C₃	semidirect
133. #2624	C₂×C₃	semidirect
134. #2620	C₂×C₃	semidirect
135. #2491	C₂×C₃	semidirect
136. #2480	C₂×C₃	semidirect
137. #2440	C₂×C₃	semidirect
138. #2437	C₂×C₃	semidirect
139. #2435	C₂×C₃	semidirect
140. #2435	C₂×C₃	semidirect
141. #2427	C₂×C₃	semidirect
142. #2426	C₂×C₃	semidirect
143. #2422	C₂×C₃	semidirect
144. #2405	C₂×C₃	semidirect
145. #2360	C₂×C₃	semidirect
146. D₄×C₂²⋊C₄	C₂×C₃	semidirect
147. #2324	C₂×C₃	semidirect
148. #2280	C₂×C₃	semidirect
288. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
289. C₂×#126	C₂²×C₃	semidirect
290. C₂×#124	C₂²×C₃	semidirect
291. C₂×#124	C₂²×C₃	semidirect
292. C₂×#124	C₂²×C₃	semidirect
293. C₂×#124	C₂²×C₃	semidirect
294. C₂×#123	C₂²×C₃	semidirect
295. C₂×#123	C₂²×C₃	semidirect
298. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
299. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
308. C₂×C₄×Q₈	C₂²×C₃	semidirect
309. C₂×C₄×D₄	C₂²×C₃	semidirect
310. C₂×C₄×D₄	C₂²×C₃	semidirect
311. C₂×#117	C₂²×C₃	semidirect
312. C₂×#117	C₂²×C₃	semidirect
316. #399	C₂²×C₃	semidirect
317. #398	C₂²×C₃	semidirect
318. #397	C₂²×C₃	semidirect
319. #397	C₂²×C₃	semidirect
320. #397	C₂²×C₃	semidirect
321. #396	C₂²×C₃	semidirect
322. #396	C₂²×C₃	semidirect
323. #396	C₂²×C₃	semidirect
324. #395	C₂²×C₃	semidirect
325. #394	C₂²×C₃	semidirect
326. #394	C₂²×C₃	semidirect
327. #394	C₂²×C₃	semidirect
328. #394	C₂²×C₃	semidirect
329. #394	C₂²×C₃	semidirect
330. #394	C₂²×C₃	semidirect
331. #394	C₂²×C₃	semidirect
332. #394	C₂²×C₃	semidirect
333. #394	C₂²×C₃	semidirect
334. #394	C₂²×C₃	semidirect
335. #393	C₂²×C₃	semidirect
336. #391	C₂²×C₃	semidirect
337. #390	C₂²×C₃	semidirect
338. #390	C₂²×C₃	semidirect
339. #390	C₂²×C₃	semidirect
340. #390	C₂²×C₃	semidirect
341. #390	C₂²×C₃	semidirect
342. #390	C₂²×C₃	semidirect
343. #389	C₂²×C₃	semidirect
344. #389	C₂²×C₃	semidirect
345. #389	C₂²×C₃	semidirect
346. #389	C₂²×C₃	semidirect
347. #388	C₂²×C₃	semidirect
348. #388	C₂²×C₃	semidirect
349. #388	C₂²×C₃	semidirect
350. #387	C₂²×C₃	semidirect
351. #386	C₂²×C₃	semidirect
352. #386	C₂²×C₃	semidirect
353. #386	C₂²×C₃	semidirect
354. #386	C₂²×C₃	semidirect
358. #385	C₂²×C₃	semidirect
359. #385	C₂²×C₃	semidirect
360. #385	C₂²×C₃	semidirect
361. #385	C₂²×C₃	semidirect
362. #384	C₂²×C₃	semidirect
363. #381	C₂²×C₃	semidirect
364. #381	C₂²×C₃	semidirect
368. #380	C₂²×C₃	semidirect
369. #380	C₂²×C₃	semidirect
370. #380	C₂²×C₃	semidirect
371. #380	C₂²×C₃	semidirect
372. #380	C₂²×C₃	semidirect
379. C₄×C₄⋊C₄	C₂²×C₃	semidirect
383. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
384. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
990. C₂²×C₃	#542	semidirect
1186. C₂²	C₃×#542	semidirect
1212. C₃	#37664	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×#542	2
C₂²×C₃×#121	2
C₃×#2848	2
C₃×#2701	2
C₃×#2691	2
C₃×#2686	2
C₃×#2672	2
C₃×#2624	2
C₃×#2620	2
C₃×#2491	2
C₃×#2480	2
C₃×#2440	2
C₃×#2437	2
C₃×#2435	2
C₃×#2427	2
C₃×#2426	2
C₃×#2422	2
C₃×#2405	2
C₃×#2360	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2324	2
C₃×#2280	2
#37664	3

Subgroups — C3×#37664 #10656271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37664 #10656271