Subgroups — C₃×#86453 #11904947

Order 1152.

2213 conjugacy classes of subgroups.

The subgroup lattice has 1203 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5708	C₂	1	2	yes	maximal, complemented
3	C₃×#5705	C₂	1	2	yes	maximal, complemented
4	C₃×#5694	C₂	1	2	yes	maximal, complemented
5	C₃×#5693	C₂	1	2	yes	maximal, complemented
6	C₃×#5665	C₂	1	2	yes	maximal, complemented
7	C₃×#5659	C₂	1	2	yes	maximal, complemented
8	C₃×#5658	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×#123	C₂	1	2	yes	maximal, complemented
10	C₃×#5639	C₂	1	2	yes	maximal, complemented
11	C₃×#5637	C₂	1	2	yes	maximal, complemented
12	C₃×#5634	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5605	C₂	1	1	yes	maximal, characteristic
15	C₃×#5600	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5545	C₂	1	2	yes	maximal, complemented
17	C₃×#5538	C₂	1	2	yes	maximal, complemented
18	C₃×#5515	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#892	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3491	—	3	1	no	maximal
21	#86453	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
23	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
24	C₃²×#126	C₂²	1	2	yes	complemented
25	C₃²×#125	C₂²	1	2	yes	complemented
26	C₃²×#123	C₂²	1	2	yes	complemented
27	C₃²×#123	C₂²	1	2	yes	complemented
28	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₃²×#121	C₂²	1	1	yes	characteristic
31	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
32	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃×#947	C₂²	1	1	yes	characteristic, complemented
34	C₃×#946	C₂²	1	2	yes	complemented
35	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₃×#939	C₂²	1	2	yes	—
37	C₃×#937	C₂²	1	2	yes	—
38	C₃×#936	C₂²	1	1	yes	characteristic, complemented
39	C₃×#935	C₂²	1	2	yes	complemented
40	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
41	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
42	C₃×#930	C₂²	1	1	yes	characteristic
43	C₃×#929	C₂²	1	2	yes	complemented
44	C₃×C₄×#67	C₂²	1	2	yes	—
45	C₃×C₄×#67	C₂²	1	2	yes	complemented
46	C₃×C₄×#67	C₂²	1	2	yes	complemented
47	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
50	C₃×#926	C₂²	1	2	yes	complemented
51	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₃×#924	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
55	C₃×#898	C₂²	1	2	yes	complemented
56	C₃×#898	C₂²	1	2	yes	complemented
57	C₃×#898	C₂²	1	2	yes	complemented
58	C₃×#898	C₂²	1	2	yes	complemented
59	C₃×#897	C₂²	1	2	yes	complemented
60	C₃×#897	C₂²	1	2	yes	complemented
61	C₃×#896	C₂²	1	2	yes	complemented
62	C₃×#896	C₂²	1	2	yes	complemented
63	C₃×#896	C₂²	1	2	yes	complemented
64	C₃×#894	C₂²	1	2	yes	—
65	C₃×#894	C₂²	1	2	yes	—
66	C₃×#894	C₂²	1	2	yes	—
67	C₃×#894	C₂²	1	2	yes	complemented
68	C₃×#893	C₂²	1	2	yes	—
69	C₃×#893	C₂²	1	1	yes	characteristic, complemented
70	C₃×#892	C₂²	1	2	yes	complemented
71	C₃×#892	C₂²	1	2	yes	complemented
72	C₃×#892	C₂²	1	2	yes	complemented
73	C₃×#892	C₂²	1	2	yes	complemented
74	C₃×#892	C₂²	1	2	yes	complemented
75	C₃×#892	C₂²	1	2	yes	complemented
76	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
77	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₃×#890	C₂²	1	1	yes	characteristic, complemented
79	C₃×#890	C₂²	1	1	yes	characteristic, complemented
80	C₃×#890	C₂²	1	2	yes	complemented
81	C₃×#889	C₂²	1	2	yes	complemented
82	C₃×#889	C₂²	1	2	yes	complemented
83	C₃×#889	C₂²	1	2	yes	complemented
84	C₃×#887	C₂²	1	1	yes	characteristic, complemented
85	C₃×#886	C₂²	1	2	yes	complemented
86	C₃×#886	C₂²	1	2	yes	complemented
87	C₃×#885	C₂²	1	2	yes	complemented
88	C₃×#883	C₂²	1	2	yes	—
89	C₃×#883	C₂²	1	2	yes	—
90	C₃×#883	C₂²	1	2	yes	—
91	C₃×#883	C₂²	1	2	yes	complemented
92	C₃×#882	C₂²	1	2	yes	—
93	C₃×#67⋊C₄	C₂²	1	2	yes	—
94	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
95	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
97	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	C₃×#879	C₂²	1	2	yes	complemented
100	C₃×#879	C₂²	1	2	yes	complemented
101	C₃×#879	C₂²	1	2	yes	complemented
102	C₃×#878	C₂²	1	2	yes	complemented
103	C₃×#878	C₂²	1	2	yes	complemented
104	C₃×#877	C₂²	1	2	yes	complemented
105	C₃×C₄×D₁₂	C₂²	1	2	yes	—
106	C₃×#872	C₂²	1	2	yes	complemented
107	C₃×#872	C₂²	1	2	yes	complemented
108	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
109	C₃×#552	—	3	2	no	—
110	C₃×#552	—	3	2	no	—
111	C₃×#552	—	3	2	no	—
112	C₃×#552	—	3	2	no	—
113	C₃×#551	—	3	2	no	—
114	C₃×#551	—	3	2	no	—
115	C₃×#551	—	3	2	no	—
116	C₃×#551	—	3	2	no	—
117	C₃×#543	—	3	1	no	—
118	C₃×#539	—	2	1	no	—
119	C₃×#539	—	3	2	no	—
120	C₃×#539	—	3	1	no	—
121	C₃×#539	D₃	1	1	yes	characteristic, complemented
122	C₃×#539	C₂×C₃	1	1	yes	characteristic, complemented
123	C₃×#534	—	3	1	no	—
124	C₃×#529	—	3	1	no	—
125	C₃×#529	—	3	1	no	—
126	C₃×#529	—	3	2	no	—
127	C₂×C₃×#123	—	3	2	no	—
128	C₃×#518	—	3	2	no	—
129	C₂×C₃×#117	—	3	1	no	—
130	#5708	C₂×C₃	1	2	yes	complemented
131	#5705	C₂×C₃	1	2	yes	complemented
132	#5694	C₂×C₃	1	2	yes	complemented
133	#5693	C₂×C₃	1	2	yes	complemented
134	#5665	C₂×C₃	1	2	yes	complemented
135	#5659	C₂×C₃	1	2	yes	complemented
136	#5658	C₂×C₃	1	2	yes	complemented
137	D₃×#123	C₂×C₃	1	2	yes	complemented
138	#5639	C₂×C₃	1	2	yes	complemented
139	#5637	C₂×C₃	1	2	yes	complemented
140	#5634	C₂×C₃	1	1	yes	characteristic, complemented
141	#5624	C₂×C₃	1	1	yes	characteristic, complemented
142	#5605	C₂×C₃	1	1	yes	characteristic
143	#5600	C₂×C₃	1	1	yes	characteristic, complemented
144	#5545	C₂×C₃	1	2	yes	complemented
145	#5538	C₂×C₃	1	2	yes	complemented
146	#5515	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#892	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃×D₃	C₂³	1	2	yes	—
149	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
150	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃²×D₄	C₂³	1	2	yes	—
152	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃²×C₄	C₂³	1	2	yes	—
157	C₂×C₃×#67	C₂³	1	2	yes	—
158	C₂×C₃×#67	C₂³	1	2	yes	—
159	C₂×C₃×#67	C₂³	1	2	yes	—
160	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
161	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
162	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
163	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
164	C₃×D₃×D₄	—	2	8	no	—
165	C₂×C₃×D₁₂	C₂³	1	2	yes	—
166	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄×D₃	—	2	4	no	—
168	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
169	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
170	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
171	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
172	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
173	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
174	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
175	C₂×C₃×Dic₆	C₂³	1	2	yes	—
176	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
177	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
180	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₄²	C₂³	1	2	yes	—
191	C₃×#217	C₂³	1	2	yes	—
192	C₃×#217	C₂³	1	2	yes	—
193	C₃×#217	C₂³	1	2	yes	—
194	C₃×#217	C₂³	1	2	yes	—
195	C₃×#217	C₂³	1	2	yes	—
196	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
197	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
198	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
199	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
200	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
201	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
202	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
203	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
204	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
205	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
206	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
211	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
212	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
213	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
214	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
215	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
216	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
217	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
219	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
220	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
221	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
222	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
223	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
224	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
225	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
226	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
227	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
229	C₃×C₄×Dic₃	C₂³	1	2	yes	—
230	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
231	C₃×C₄×Dic₃	C₂³	1	2	yes	—
232	C₃×C₄×Dic₃	C₂³	1	2	yes	—
233	C₃×C₄×Dic₃	C₂³	1	2	yes	—
234	C₃×C₄×Dic₃	C₂³	1	2	yes	—
235	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
236	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
237	#3491	—	3	1	no	Sylow
238	C₂²×C₃×D₄	—	3	2	no	—
239	C₂³×C₃×C₄	—	3	1	no	—
240	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
241	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
242	C₃×#126	—	2	2	no	—
243	C₃×#126	—	3	2	no	—
244	C₃×#126	—	3	2	no	—
245	C₃×#126	—	3	2	no	—
246	C₃×#126	—	3	2	no	—
247	C₃×#126	—	3	2	no	—
248	C₃×#126	—	3	2	no	—
249	C₃×#126	—	3	2	no	—
250	C₃×#126	C₂×D₃	1	2	yes	complemented
251	C₃×#126	C₂²×C₃	1	2	yes	complemented
252	C₃×#125	—	2	2	no	—
253	C₃×#125	—	3	2	no	—
254	C₃×#125	—	3	2	no	—
255	C₃×#125	—	3	2	no	—
256	C₃×#125	—	3	1	no	—
257	C₃×#125	—	3	1	no	—
258	C₃×#125	—	3	2	no	—
259	C₃×#125	C₂×D₃	1	2	yes	complemented
260	C₃×#125	C₂²×C₃	1	2	yes	complemented
261	C₃×#124	—	3	1	no	—
262	C₃×#124	—	3	1	no	—
263	C₃×#124	—	3	2	no	—
264	C₃×#123	—	2	2	no	—
265	C₃×#123	—	2	2	no	—
266	C₃×#123	—	3	2	no	—
267	C₃×#123	—	3	2	no	—
268	C₃×#123	—	3	2	no	—
269	C₃×#123	—	3	2	no	—
270	C₃×#123	—	3	2	no	—
271	C₃×#123	—	3	2	no	—
272	C₃×#123	—	3	2	no	—
273	C₃×#123	—	3	2	no	—
274	C₃×#123	—	3	2	no	—
275	C₃×#123	—	3	2	no	—
276	C₃×#123	—	3	2	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	C₂×D₃	1	2	yes	complemented
279	C₃×#123	C₂×D₃	1	2	yes	complemented
280	C₃×#123	C₂²×C₃	1	2	yes	complemented
281	C₃×#123	C₂²×C₃	1	2	yes	complemented
282	C₃×C₂²⋊Q₈	—	2	1	no	—
283	C₃×C₂²⋊Q₈	—	2	2	no	—
284	C₃×C₂²⋊Q₈	—	3	2	no	—
285	C₃×C₂²⋊Q₈	—	3	1	no	—
286	C₃×C₂²⋊Q₈	—	3	2	no	—
287	C₃×C₂²⋊Q₈	—	3	2	no	—
288	C₃×C₂²⋊Q₈	—	3	2	no	—
289	C₃×C₂²⋊Q₈	—	3	2	no	—
290	C₃×C₂²⋊Q₈	—	3	2	no	—
291	C₃×C₂²⋊Q₈	—	3	2	no	—
292	C₃×C₂²⋊Q₈	—	3	2	no	—
293	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
294	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
295	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
297	C₃×#121	—	2	1	no	—
298	C₃×#121	—	3	2	no	—
299	C₃×#121	—	3	1	no	—
300	C₃×#121	C₂×D₃	1	1	yes	characteristic
301	C₃×#121	C₂²×C₃	1	1	yes	characteristic
302	C₃×#120	—	3	2	no	—
303	C₃×#120	—	3	2	no	—
304	C₃×C₄×Q₈	—	3	1	no	—
305	C₃×C₄×Q₈	—	3	1	no	—
306	C₃×C₄×Q₈	—	3	2	no	—
307	C₃×C₄×D₄	—	2	2	no	—
308	C₃×C₄×D₄	—	3	2	no	—
309	C₃×C₄×D₄	—	3	1	no	—
310	C₃×C₄×D₄	—	3	2	no	—
311	C₃×C₄×D₄	—	3	2	no	—
312	C₃×C₄×D₄	—	3	2	no	—
313	C₃×C₄×D₄	—	3	2	no	—
314	C₃×C₄×D₄	—	3	1	no	—
315	C₃×C₄×D₄	—	3	2	no	—
316	C₃×C₄×D₄	—	3	2	no	—
317	C₃×C₄×D₄	—	3	2	no	—
318	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
319	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
320	C₃×#117	—	3	2	no	—
321	C₃×#117	—	3	2	no	—
322	C₃×#117	—	3	2	no	—
323	C₃×#117	—	3	2	no	—
324	C₃×#117	—	3	2	no	—
325	C₃×#117	—	3	2	no	—
326	C₃×#117	—	3	2	no	—
327	C₃×#117	—	3	2	no	—
328	C₃×#117	—	3	2	no	—
329	C₃×#117	—	3	2	no	—
330	C₂×C₃×C₄⋊C₄	—	2	1	no	—
331	C₂×C₃×C₄⋊C₄	—	3	1	no	—
332	C₂×C₃×C₄⋊C₄	—	3	2	no	—
333	C₂×C₃×C₄⋊C₄	—	3	2	no	—
334	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
335	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
336	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
337	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
338	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
339	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
340	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
341	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
342	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₃×C₄²	—	3	1	no	—
344	C₂×C₃×C₄²	—	3	1	no	—
345	#947	C₂²×C₃	1	1	yes	characteristic, complemented
346	#946	C₂²×C₃	1	2	yes	complemented
347	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
348	#939	C₂²×C₃	1	2	yes	—
349	#937	C₂²×C₃	1	2	yes	—
350	#936	C₂²×C₃	1	1	yes	characteristic, complemented
351	#935	C₂²×C₃	1	2	yes	complemented
352	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
353	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
354	#930	C₂²×C₃	1	1	yes	characteristic
355	#929	C₂²×C₃	1	2	yes	complemented
356	C₄×#67	C₂²×C₃	1	2	yes	—
357	C₄×#67	C₂²×C₃	1	2	yes	complemented
358	C₄×#67	C₂²×C₃	1	2	yes	complemented
359	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
360	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
361	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
362	#926	C₂²×C₃	1	2	yes	complemented
363	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
364	#924	C₂²×C₃	1	1	yes	characteristic, complemented
365	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
367	#898	C₂²×C₃	1	2	yes	complemented
368	#898	C₂²×C₃	1	2	yes	complemented
369	#898	C₂²×C₃	1	2	yes	complemented
370	#898	C₂²×C₃	1	2	yes	complemented
371	#897	C₂²×C₃	1	2	yes	complemented
372	#897	C₂²×C₃	1	2	yes	complemented
373	#896	C₂²×C₃	1	2	yes	complemented
374	#896	C₂²×C₃	1	2	yes	complemented
375	#896	C₂²×C₃	1	2	yes	complemented
376	#894	C₂²×C₃	1	2	yes	—
377	#894	C₂²×C₃	1	2	yes	—
378	#894	C₂²×C₃	1	2	yes	—
379	#894	C₂²×C₃	1	2	yes	complemented
380	#893	C₂²×C₃	1	2	yes	—
381	#893	C₂²×C₃	1	1	yes	characteristic, complemented
382	#892	C₂²×C₃	1	2	yes	complemented
383	#892	C₂²×C₃	1	2	yes	complemented
384	#892	C₂²×C₃	1	2	yes	complemented
385	#892	C₂²×C₃	1	2	yes	complemented
386	#892	C₂²×C₃	1	2	yes	complemented
387	#892	C₂²×C₃	1	2	yes	complemented
388	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
389	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
390	#890	C₂²×C₃	1	2	yes	complemented
391	#890	C₂²×C₃	1	1	yes	characteristic, complemented
392	#890	C₂²×C₃	1	1	yes	characteristic, complemented
393	#889	C₂²×C₃	1	2	yes	complemented
394	#889	C₂²×C₃	1	2	yes	complemented
395	#889	C₂²×C₃	1	2	yes	complemented
396	#887	C₂²×C₃	1	1	yes	characteristic, complemented
397	#886	C₂²×C₃	1	2	yes	complemented
398	#886	C₂²×C₃	1	2	yes	complemented
399	#885	C₂²×C₃	1	2	yes	complemented
400	#883	C₂²×C₃	1	2	yes	—
401	#883	C₂²×C₃	1	2	yes	—
402	#883	C₂²×C₃	1	2	yes	—
403	#883	C₂²×C₃	1	2	yes	complemented
404	#882	C₂²×C₃	1	2	yes	—
405	#67⋊C₄	C₂²×C₃	1	2	yes	—
406	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
407	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
408	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
409	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
410	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
411	#879	C₂²×C₃	1	2	yes	complemented
412	#879	C₂²×C₃	1	2	yes	complemented
413	#879	C₂²×C₃	1	2	yes	complemented
414	#878	C₂²×C₃	1	2	yes	complemented
415	#878	C₂²×C₃	1	2	yes	complemented
416	#877	C₂²×C₃	1	2	yes	complemented
417	C₄×D₁₂	C₂²×C₃	1	2	yes	—
418	#872	C₂²×C₃	1	2	yes	complemented
419	#872	C₂²×C₃	1	2	yes	complemented
420	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
421	C₂³×C₃²	C₂⁴	1	2	yes	—
422	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
423	C₂²×C₃×D₃	—	2	4	no	—
424	C₂²×C₃×D₃	—	4	1	no	—
425	C₂²×C₃×D₃	—	4	1	no	—
426	C₂²×C₃×D₃	—	4	2	no	—
427	C₂²×C₃×D₃	—	4	2	no	—
428	C₂²×C₃×D₃	#41	1	4	yes	—
429	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
430	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
431	C₃²×Q₈	—	4	1	no	—
432	C₃²×D₄	—	2	4	no	—
433	C₃²×D₄	—	4	1	no	—
434	C₂×C₃²×C₄	—	2	2	no	—
435	C₂×C₃²×C₄	—	4	1	no	—
436	C₂×C₃²×C₄	—	4	1	no	—
437	C₂×C₃²×C₄	—	4	2	no	—
438	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
439	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
440	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
441	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
442	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
443	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
444	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
445	C₃×#67	—	2	4	no	—
446	C₃×#67	—	2	4	no	—
447	C₃×#67	—	4	2	no	—
448	C₂×C₃×Dic₃	—	2	2	no	—
449	C₂×C₃×Dic₃	—	4	2	no	—
450	C₂×C₃×Dic₃	—	4	1	no	—
451	C₂×C₃×Dic₃	—	4	1	no	—
452	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
453	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
454	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
455	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
456	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
457	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
458	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
459	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
460	C₃×D₁₂	—	2	4	no	—
461	C₃×D₁₂	—	4	1	no	—
462	C₃×C₄×D₃	—	2	4	no	—
463	C₃×C₄×D₃	—	2	4	no	—
464	C₃×C₄×D₃	—	2	4	no	—
465	C₃×C₄×D₃	—	4	2	no	—
466	C₃×C₄×D₃	—	4	2	no	—
467	C₃×C₄×D₃	—	4	2	no	—
468	C₃×C₄×D₃	—	4	2	no	—
469	C₃×Dic₆	—	4	1	no	—
470	C₃×Dic₆	—	4	2	no	—
471	#552	—	3	2	no	—
472	#552	—	3	2	no	—
473	#552	—	3	2	no	—
474	#552	—	3	2	no	—
475	#551	—	3	2	no	—
476	#551	—	3	2	no	—
477	#551	—	3	2	no	—
478	#551	—	3	2	no	—
479	#543	—	3	1	no	—
480	#539	—	3	2	no	—
481	#539	—	3	1	no	—
482	#539	C₃×D₃	1	1	yes	characteristic, complemented
483	#534	—	3	1	no	—
484	#529	—	3	1	no	—
485	#529	—	3	1	no	—
486	#529	—	3	2	no	—
487	C₂×#123	—	3	2	no	—
488	#518	—	3	2	no	—
489	C₂×#117	—	3	1	no	—
490	C₂⁴×C₃	—	3	1	no	—
491	C₂⁴×C₃	—	3	2	no	—
492	C₂³×D₃	C₂³×C₃	1	2	yes	—
493	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₃×Q₈	—	2	1	no	—
495	C₂×C₃×Q₈	—	3	2	no	—
496	C₂×C₃×Q₈	—	3	1	no	—
497	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
498	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₃×D₄	—	2	2	no	—
500	C₂×C₃×D₄	—	2	1	no	—
501	C₂×C₃×D₄	—	3	2	no	—
502	C₂×C₃×D₄	—	3	2	no	—
503	C₂×C₃×D₄	—	3	2	no	—
504	C₂×C₃×D₄	—	3	2	no	—
505	C₂×C₃×D₄	—	3	1	no	—
506	C₂×C₃×D₄	—	6	8	no	—
507	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
508	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
509	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
510	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
511	C₂²×C₃×C₄	—	2	1	no	—
512	C₂²×C₃×C₄	—	2	1	no	—
513	C₂²×C₃×C₄	—	2	1	no	—
514	C₂²×C₃×C₄	—	2	2	no	—
515	C₂²×C₃×C₄	—	3	1	no	—
516	C₂²×C₃×C₄	—	3	1	no	—
517	C₂²×C₃×C₄	—	3	1	no	—
518	C₂²×C₃×C₄	—	3	2	no	—
519	C₂²×C₃×C₄	—	3	2	no	—
520	C₂²×C₃×C₄	—	3	2	no	—
521	C₂²×C₃×C₄	—	3	2	no	—
522	C₂²×C₃×C₄	—	3	2	no	—
523	C₂²×C₃×C₄	—	3	2	no	—
524	C₂²×C₃×C₄	—	3	2	no	—
525	C₂²×C₃×C₄	—	3	2	no	—
526	C₂²×C₃×C₄	—	6	4	no	—
527	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
528	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
529	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
530	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
531	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
535	C₂×#67	C₂³×C₃	1	2	yes	—
536	C₂×#67	C₂³×C₃	1	2	yes	—
537	C₂×#67	C₂³×C₃	1	2	yes	—
538	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
539	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
540	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
541	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
542	D₃×D₄	—	2	8	no	—
543	C₂×D₁₂	C₂³×C₃	1	2	yes	—
544	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄×D₃	—	2	4	no	—
546	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
547	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
548	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
549	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
550	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
551	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
552	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
553	C₂×Dic₆	C₂³×C₃	1	2	yes	—
554	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
555	C₃×C₄⋊C₄	—	2	2	no	—
556	C₃×C₄⋊C₄	—	2	2	no	—
557	C₃×C₄⋊C₄	—	2	2	no	—
558	C₃×C₄⋊C₄	—	2	1	no	—
559	C₃×C₄⋊C₄	—	2	2	no	—
560	C₃×C₄⋊C₄	—	2	2	no	—
561	C₃×C₄⋊C₄	—	2	1	no	—
562	C₃×C₄⋊C₄	—	2	2	no	—
563	C₃×C₄⋊C₄	—	3	2	no	—
564	C₃×C₄⋊C₄	—	3	2	no	—
565	C₃×C₄⋊C₄	—	3	2	no	—
566	C₃×C₄⋊C₄	—	3	2	no	—
567	C₃×C₄⋊C₄	—	3	2	no	—
568	C₃×C₄⋊C₄	—	3	2	no	—
569	C₃×C₄⋊C₄	—	3	2	no	—
570	C₃×C₄⋊C₄	—	3	2	no	—
571	C₃×C₄⋊C₄	—	3	2	no	—
572	C₃×C₄⋊C₄	—	3	2	no	—
573	C₃×C₄⋊C₄	—	3	2	no	—
574	C₃×C₄⋊C₄	—	3	2	no	—
575	C₃×C₄⋊C₄	—	3	2	no	—
576	C₃×C₄⋊C₄	—	3	2	no	—
577	C₃×C₄⋊C₄	—	3	2	no	—
578	C₃×C₄⋊C₄	—	3	2	no	—
579	C₃×C₄⋊C₄	—	3	1	no	—
580	C₃×C₄⋊C₄	—	3	1	no	—
581	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
582	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
583	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
584	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
585	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
586	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
587	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
588	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
589	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
591	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
592	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
593	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
594	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
596	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
597	C₃×C₂²⋊C₄	—	2	2	no	—
598	C₃×C₂²⋊C₄	—	2	2	no	—
599	C₃×C₂²⋊C₄	—	2	2	no	—
600	C₃×C₂²⋊C₄	—	2	2	no	—
601	C₃×C₂²⋊C₄	—	2	2	no	—
602	C₃×C₂²⋊C₄	—	3	2	no	—
603	C₃×C₂²⋊C₄	—	3	2	no	—
604	C₃×C₂²⋊C₄	—	3	2	no	—
605	C₃×C₂²⋊C₄	—	3	2	no	—
606	C₃×C₂²⋊C₄	—	3	2	no	—
607	C₃×C₂²⋊C₄	—	3	2	no	—
608	C₃×C₂²⋊C₄	—	3	2	no	—
609	C₃×C₂²⋊C₄	—	3	2	no	—
610	C₃×C₂²⋊C₄	—	3	2	no	—
611	C₃×C₂²⋊C₄	—	3	2	no	—
612	C₃×C₂²⋊C₄	—	3	2	no	—
613	C₃×C₂²⋊C₄	—	3	2	no	—
614	C₃×C₂²⋊C₄	—	3	2	no	—
615	C₃×C₂²⋊C₄	—	3	2	no	—
616	C₃×C₂²⋊C₄	—	3	2	no	—
617	C₃×C₂²⋊C₄	—	3	2	no	—
618	C₃×C₂²⋊C₄	—	3	2	no	—
619	C₃×C₂²⋊C₄	—	3	2	no	—
620	C₃×C₂²⋊C₄	—	3	2	no	—
621	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
622	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
623	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
624	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
625	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
626	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
630	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₃×C₄²	—	2	2	no	—
632	C₃×C₄²	—	3	1	no	—
633	C₃×C₄²	—	3	1	no	—
634	C₃×C₄²	—	3	2	no	—
635	C₃×C₄²	—	3	1	no	—
636	C₃×C₄²	—	3	1	no	—
637	C₃×C₄²	—	3	2	no	—
638	C₃×C₄²	—	3	2	no	—
639	C₃×C₄²	—	3	2	no	—
640	C₃×C₄²	—	3	2	no	—
641	C₃×C₄²	C₂²×D₃	1	2	yes	—
642	C₃×C₄²	C₂³×C₃	1	2	yes	—
643	#217	C₂³×C₃	1	2	yes	—
644	#217	C₂³×C₃	1	2	yes	—
645	#217	C₂³×C₃	1	2	yes	—
646	#217	C₂³×C₃	1	2	yes	—
647	#217	C₂³×C₃	1	2	yes	—
648	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
649	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
650	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
651	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
652	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
653	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
654	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
655	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
656	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
657	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
658	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
659	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
660	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
661	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
662	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
663	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
664	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
665	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
666	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
667	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
668	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
669	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
670	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
671	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
672	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
673	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
674	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
675	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
676	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
677	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
678	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
679	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
680	C₄×Dic₃	C₂³×C₃	1	2	yes	—
681	C₄×Dic₃	C₂³×C₃	1	2	yes	—
682	C₄×Dic₃	C₂³×C₃	1	2	yes	—
683	C₄×Dic₃	C₂³×C₃	1	2	yes	—
684	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
685	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
686	C₄×Dic₃	C₂³×C₃	1	2	yes	—
687	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
688	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
689	C₂²×C₃²	—	2	1	no	—
690	C₂²×C₃²	—	2	1	no	—
691	C₂²×C₃²	—	2	2	no	—
692	C₂²×C₃²	—	2	2	no	—
693	C₂²×C₃²	—	2	2	no	—
694	C₂²×C₃²	C₂×#41	1	2	yes	—
695	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
696	C₂×C₃×D₃	—	2	2	no	—
697	C₂×C₃×D₃	—	2	2	no	—
698	C₂×C₃×D₃	—	2	2	no	—
699	C₂×C₃×D₃	—	2	2	no	—
700	C₂×C₃×D₃	—	2	2	no	—
701	C₂×C₃×D₃	—	4	4	no	—
702	C₂×C₃×D₃	—	8	4	no	—
703	C₂×C₃×D₃	C₂×#41	1	4	yes	—
704	C₃²×C₄	—	2	2	no	—
705	C₃²×C₄	—	2	2	no	—
706	C₃²×C₄	—	2	2	no	—
707	C₃²×C₄	—	2	1	no	—
708	C₃²×C₄	—	2	2	no	—
709	C₃²×C₄	—	2	2	no	—
710	C₃²×C₄	—	2	1	no	—
711	C₃×Dic₃	—	2	1	no	—
712	C₃×Dic₃	—	2	1	no	—
713	C₃×Dic₃	—	2	2	no	—
714	C₃×Dic₃	—	2	2	no	—
715	C₃×Dic₃	—	2	2	no	—
716	C₃×Dic₃	—	2	2	no	—
717	C₃×Dic₃	—	2	1	no	—
718	C₃×Dic₃	—	2	1	no	—
719	C₂²×D₄	—	3	2	no	—
720	C₂³×C₄	—	3	1	no	—
721	#126	—	3	2	no	—
722	#126	—	3	2	no	—
723	#126	—	3	2	no	—
724	#126	—	3	2	no	—
725	#126	—	3	2	no	—
726	#126	—	3	2	no	—
727	#126	—	3	2	no	—
728	#126	C₂×C₃×D₃	1	2	yes	complemented
729	#125	—	3	2	no	—
730	#125	—	3	1	no	—
731	#125	—	3	1	no	—
732	#125	—	3	2	no	—
733	#125	—	3	2	no	—
734	#125	—	3	2	no	—
735	#125	C₂×C₃×D₃	1	2	yes	complemented
736	#124	—	3	1	no	—
737	#124	—	3	1	no	—
738	#124	—	3	2	no	—
739	#123	—	3	2	no	—
740	#123	—	3	2	no	—
741	#123	—	3	2	no	—
742	#123	—	3	2	no	—
743	#123	—	3	2	no	—
744	#123	—	3	2	no	—
745	#123	—	3	2	no	—
746	#123	—	3	2	no	—
747	#123	—	3	2	no	—
748	#123	—	3	2	no	—
749	#123	—	3	2	no	—
750	#123	—	3	2	no	—
751	#123	C₂×C₃×D₃	1	2	yes	complemented
752	#123	C₂×C₃×D₃	1	2	yes	complemented
753	C₂²⋊Q₈	—	3	2	no	—
754	C₂²⋊Q₈	—	3	1	no	—
755	C₂²⋊Q₈	—	3	2	no	—
756	C₂²⋊Q₈	—	3	2	no	—
757	C₂²⋊Q₈	—	3	2	no	—
758	C₂²⋊Q₈	—	3	2	no	—
759	C₂²⋊Q₈	—	3	2	no	—
760	C₂²⋊Q₈	—	3	2	no	—
761	C₂²⋊Q₈	—	3	2	no	—
762	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
763	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
764	#121	—	3	2	no	—
765	#121	—	3	1	no	—
766	#121	C₂×C₃×D₃	1	1	yes	characteristic
767	#120	—	3	2	no	—
768	#120	—	3	2	no	—
769	C₄×Q₈	—	3	1	no	—
770	C₄×Q₈	—	3	1	no	—
771	C₄×Q₈	—	3	2	no	—
772	C₄×D₄	—	3	2	no	—
773	C₄×D₄	—	3	1	no	—
774	C₄×D₄	—	3	2	no	—
775	C₄×D₄	—	3	2	no	—
776	C₄×D₄	—	3	2	no	—
777	C₄×D₄	—	3	2	no	—
778	C₄×D₄	—	3	1	no	—
779	C₄×D₄	—	3	2	no	—
780	C₄×D₄	—	3	2	no	—
781	C₄×D₄	—	3	2	no	—
782	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
783	#117	—	3	2	no	—
784	#117	—	3	2	no	—
785	#117	—	3	2	no	—
786	#117	—	3	2	no	—
787	#117	—	3	2	no	—
788	#117	—	3	2	no	—
789	#117	—	3	2	no	—
790	#117	—	3	2	no	—
791	#117	—	3	2	no	—
792	#117	—	3	2	no	—
793	C₂×C₄⋊C₄	—	3	1	no	—
794	C₂×C₄⋊C₄	—	3	2	no	—
795	C₂×C₄⋊C₄	—	3	2	no	—
796	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
797	C₂×C₂²⋊C₄	—	3	1	no	—
798	C₂×C₂²⋊C₄	—	3	1	no	—
799	C₂×C₂²⋊C₄	—	3	2	no	—
800	C₂×C₂²⋊C₄	—	3	2	no	—
801	C₂×C₂²⋊C₄	—	3	2	no	—
802	C₂×C₂²⋊C₄	—	3	2	no	—
803	C₂×C₂²⋊C₄	—	3	2	no	—
804	C₂×C₄²	—	3	1	no	—
805	C₂×C₄²	—	3	1	no	—
806	C₂³×C₃	—	2	1	no	—
807	C₂³×C₃	—	2	2	no	—
808	C₂³×C₃	—	3	2	no	—
809	C₂³×C₃	—	3	4	no	—
810	C₂³×C₃	—	3	2	no	—
811	C₂³×C₃	—	6	4	no	—
812	C₂³×C₃	—	12	1	no	—
813	C₂³×C₃	—	12	1	no	—
814	C₂³×C₃	—	12	2	no	—
815	C₂³×C₃	—	12	2	no	—
816	C₂³×C₃	C₂³×D₃	1	2	yes	—
817	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
818	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
819	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
820	C₂²×D₃	—	2	4	no	—
821	C₂²×D₃	—	4	1	no	—
822	C₂²×D₃	—	4	1	no	—
823	C₂²×D₃	—	4	2	no	—
824	C₂²×D₃	—	4	2	no	—
825	C₂²×D₃	C₃×#41	1	4	yes	—
826	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
827	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
828	C₃×Q₈	—	4	1	no	—
829	C₃×Q₈	—	4	1	no	—
830	C₃×Q₈	—	8	1	no	—
831	C₃×Q₈	—	12	1	no	—
832	C₃×Q₈	—	12	2	no	—
833	C₃×D₄	—	2	4	no	—
834	C₃×D₄	—	2	4	no	—
835	C₃×D₄	—	4	4	no	—
836	C₃×D₄	—	4	1	no	—
837	C₃×D₄	—	4	1	no	—
838	C₃×D₄	—	6	4	no	—
839	C₃×D₄	—	6	4	no	—
840	C₃×D₄	—	6	4	no	—
841	C₃×D₄	—	8	1	no	—
842	C₃×D₄	—	12	1	no	—
843	C₃×D₄	—	12	2	no	—
844	C₂×C₃×C₄	—	2	2	no	—
845	C₂×C₃×C₄	—	2	2	no	—
846	C₂×C₃×C₄	—	2	2	no	—
847	C₂×C₃×C₄	—	2	2	no	—
848	C₂×C₃×C₄	—	2	2	no	—
849	C₂×C₃×C₄	—	2	2	no	—
850	C₂×C₃×C₄	—	2	1	no	—
851	C₂×C₃×C₄	—	2	2	no	—
852	C₂×C₃×C₄	—	2	1	no	—
853	C₂×C₃×C₄	—	3	1	no	—
854	C₂×C₃×C₄	—	3	1	no	—
855	C₂×C₃×C₄	—	3	1	no	—
856	C₂×C₃×C₄	—	3	1	no	—
857	C₂×C₃×C₄	—	3	2	no	—
858	C₂×C₃×C₄	—	3	2	no	—
859	C₂×C₃×C₄	—	3	2	no	—
860	C₂×C₃×C₄	—	3	2	no	—
861	C₂×C₃×C₄	—	4	2	no	—
862	C₂×C₃×C₄	—	4	1	no	—
863	C₂×C₃×C₄	—	4	2	no	—
864	C₂×C₃×C₄	—	4	1	no	—
865	C₂×C₃×C₄	—	4	1	no	—
866	C₂×C₃×C₄	—	4	1	no	—
867	C₂×C₃×C₄	—	4	2	no	—
868	C₂×C₃×C₄	—	6	4	no	—
869	C₂×C₃×C₄	—	6	4	no	—
870	C₂×C₃×C₄	—	6	4	no	—
871	C₂×C₃×C₄	—	6	2	no	—
872	C₂×C₃×C₄	—	8	1	no	—
873	C₂×C₃×C₄	—	8	2	no	—
874	C₂×C₃×C₄	—	8	1	no	—
875	C₂×C₃×C₄	—	12	2	no	—
876	C₂×C₃×C₄	—	12	2	no	—
877	C₂×C₃×C₄	—	12	2	no	—
878	C₂×C₃×C₄	—	12	2	no	—
879	C₂×C₃×C₄	—	12	1	no	—
880	C₂×C₃×C₄	—	12	2	no	—
881	C₂×C₃×C₄	—	12	1	no	—
882	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
883	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
884	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
885	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
886	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
887	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
888	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
889	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
890	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
891	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
892	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
893	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
894	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
895	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
896	#67	—	2	4	no	—
897	#67	—	2	4	no	—
898	#67	—	4	2	no	—
899	C₂×Dic₃	—	2	2	no	—
900	C₂×Dic₃	—	4	2	no	—
901	C₂×Dic₃	—	4	1	no	—
902	C₂×Dic₃	—	4	1	no	—
903	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
904	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
905	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
906	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
907	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
908	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
909	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
910	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
911	D₁₂	—	2	4	no	—
912	D₁₂	—	4	1	no	—
913	C₄×D₃	—	2	4	no	—
914	C₄×D₃	—	2	4	no	—
915	C₄×D₃	—	2	4	no	—
916	C₄×D₃	—	4	2	no	—
917	C₄×D₃	—	4	2	no	—
918	C₄×D₃	—	4	2	no	—
919	C₄×D₃	—	4	2	no	—
920	Dic₆	—	4	1	no	—
921	Dic₆	—	4	2	no	—
922	C₂×C₃²	—	2	2	no	—
923	C₂×C₃²	—	4	2	no	—
924	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
925	C₂×C₃²	#585	1	1	yes	characteristic
926	C₂×C₃²	#585	1	1	yes	characteristic
927	C₃×D₃	—	2	4	no	—
928	C₃×D₃	—	4	2	no	—
929	C₂⁴	—	3	1	no	—
930	C₂⁴	—	3	2	no	—
931	C₂×Q₈	—	3	2	no	—
932	C₂×Q₈	—	3	1	no	—
933	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
934	C₂×D₄	—	3	2	no	—
935	C₂×D₄	—	3	2	no	—
936	C₂×D₄	—	3	2	no	—
937	C₂×D₄	—	3	2	no	—
938	C₂×D₄	—	3	1	no	—
939	C₂×D₄	—	6	8	no	—
940	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
941	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
942	C₂²×C₄	—	3	1	no	—
943	C₂²×C₄	—	3	1	no	—
944	C₂²×C₄	—	3	1	no	—
945	C₂²×C₄	—	3	2	no	—
946	C₂²×C₄	—	3	2	no	—
947	C₂²×C₄	—	3	2	no	—
948	C₂²×C₄	—	3	2	no	—
949	C₂²×C₄	—	3	2	no	—
950	C₂²×C₄	—	3	2	no	—
951	C₂²×C₄	—	3	2	no	—
952	C₂²×C₄	—	3	2	no	—
953	C₂²×C₄	—	6	4	no	—
954	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
955	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
956	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
957	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
958	C₄⋊C₄	—	3	2	no	—
959	C₄⋊C₄	—	3	2	no	—
960	C₄⋊C₄	—	3	2	no	—
961	C₄⋊C₄	—	3	2	no	—
962	C₄⋊C₄	—	3	2	no	—
963	C₄⋊C₄	—	3	2	no	—
964	C₄⋊C₄	—	3	2	no	—
965	C₄⋊C₄	—	3	2	no	—
966	C₄⋊C₄	—	3	2	no	—
967	C₄⋊C₄	—	3	2	no	—
968	C₄⋊C₄	—	3	2	no	—
969	C₄⋊C₄	—	3	2	no	—
970	C₄⋊C₄	—	3	2	no	—
971	C₄⋊C₄	—	3	2	no	—
972	C₄⋊C₄	—	3	2	no	—
973	C₄⋊C₄	—	3	1	no	—
974	C₄⋊C₄	—	3	2	no	—
975	C₄⋊C₄	—	3	1	no	—
976	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
977	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
978	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
979	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
980	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
981	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
982	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
984	C₂²⋊C₄	—	3	2	no	—
985	C₂²⋊C₄	—	3	2	no	—
986	C₂²⋊C₄	—	3	2	no	—
987	C₂²⋊C₄	—	3	2	no	—
988	C₂²⋊C₄	—	3	2	no	—
989	C₂²⋊C₄	—	3	2	no	—
990	C₂²⋊C₄	—	3	2	no	—
991	C₂²⋊C₄	—	3	2	no	—
992	C₂²⋊C₄	—	3	2	no	—
993	C₂²⋊C₄	—	3	2	no	—
994	C₂²⋊C₄	—	3	2	no	—
995	C₂²⋊C₄	—	3	2	no	—
996	C₂²⋊C₄	—	3	2	no	—
997	C₂²⋊C₄	—	3	2	no	—
998	C₂²⋊C₄	—	3	2	no	—
999	C₂²⋊C₄	—	3	2	no	—
1000	C₂²⋊C₄	—	3	2	no	—
1001	C₂²⋊C₄	—	3	2	no	—
1002	C₂²⋊C₄	—	3	2	no	—
1003	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1004	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1005	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1006	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1007	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1008	C₄²	—	3	1	no	—
1009	C₄²	—	3	1	no	—
1010	C₄²	—	3	2	no	—
1011	C₄²	—	3	1	no	—
1012	C₄²	—	3	1	no	—
1013	C₄²	—	3	2	no	—
1014	C₄²	—	3	2	no	—
1015	C₄²	—	3	2	no	—
1016	C₄²	—	3	2	no	—
1017	C₄²	C₂²×C₃×D₃	1	2	yes	—
1018	C₂²×C₃	—	2	1	no	—
1019	C₂²×C₃	—	2	1	no	—
1020	C₂²×C₃	—	2	1	no	—
1021	C₂²×C₃	—	2	1	no	—
1022	C₂²×C₃	—	2	2	no	—
1023	C₂²×C₃	—	2	2	no	—
1024	C₂²×C₃	—	2	2	no	—
1025	C₂²×C₃	—	2	2	no	—
1026	C₂²×C₃	—	2	2	no	—
1027	C₂²×C₃	—	2	2	no	—
1028	C₂²×C₃	—	2	2	no	—
1029	C₂²×C₃	—	2	1	no	—
1030	C₂²×C₃	—	3	4	no	—
1031	C₂²×C₃	—	4	1	no	—
1032	C₂²×C₃	—	4	1	no	—
1033	C₂²×C₃	—	4	2	no	—
1034	C₂²×C₃	—	4	2	no	—
1035	C₂²×C₃	—	4	2	no	—
1036	C₂²×C₃	—	6	2	no	—
1037	C₂²×C₃	—	6	2	no	—
1038	C₂²×C₃	—	6	2	no	—
1039	C₂²×C₃	—	6	2	no	—
1040	C₂²×C₃	—	6	2	no	—
1041	C₂²×C₃	—	12	4	no	—
1042	C₂²×C₃	—	24	4	no	—
1043	C₂²×C₃	D₃×#41	1	2	yes	—
1044	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
1045	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1046	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1047	C₂×D₃	—	2	2	no	—
1048	C₂×D₃	—	2	2	no	—
1049	C₂×D₃	—	2	2	no	—
1050	C₂×D₃	—	2	2	no	—
1051	C₂×D₃	—	2	2	no	—
1052	C₂×D₃	—	4	4	no	—
1053	C₂×D₃	—	8	4	no	—
1054	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1055	C₃×C₄	—	2	2	no	—
1056	C₃×C₄	—	2	2	no	—
1057	C₃×C₄	—	2	2	no	—
1058	C₃×C₄	—	2	2	no	—
1059	C₃×C₄	—	2	1	no	—
1060	C₃×C₄	—	2	1	no	—
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	2	no	—
1065	C₃×C₄	—	2	1	no	—
1066	C₃×C₄	—	2	2	no	—
1067	C₃×C₄	—	2	2	no	—
1068	C₃×C₄	—	2	1	no	—
1069	C₃×C₄	—	4	2	no	—
1070	C₃×C₄	—	4	2	no	—
1071	C₃×C₄	—	4	1	no	—
1072	C₃×C₄	—	4	2	no	—
1073	C₃×C₄	—	4	1	no	—
1074	C₃×C₄	—	4	2	no	—
1075	C₃×C₄	—	4	2	no	—
1076	C₃×C₄	—	6	1	no	—
1077	C₃×C₄	—	6	1	no	—
1078	C₃×C₄	—	6	2	no	—
1079	C₃×C₄	—	6	2	no	—
1080	C₃×C₄	—	6	1	no	—
1081	C₃×C₄	—	6	1	no	—
1082	C₃×C₄	—	6	2	no	—
1083	C₃×C₄	—	6	2	no	—
1084	Dic₃	—	2	1	no	—
1085	Dic₃	—	2	1	no	—
1086	Dic₃	—	2	2	no	—
1087	Dic₃	—	2	2	no	—
1088	Dic₃	—	2	2	no	—
1089	Dic₃	—	2	2	no	—
1090	Dic₃	—	2	1	no	—
1091	Dic₃	—	2	1	no	—
1092	C₃²	#3491	1	1	yes	characteristic, complemented, Sylow
1093	C₂³	—	3	2	no	—
1094	C₂³	—	3	4	no	—
1095	C₂³	—	3	2	no	—
1096	C₂³	—	6	4	no	—
1097	C₂³	—	12	1	no	—
1098	C₂³	—	12	1	no	—
1099	C₂³	—	12	2	no	—
1100	C₂³	—	12	2	no	—
1101	C₂³	C₂³×C₃×D₃	1	2	yes	—
1102	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1103	Q₈	—	4	1	no	—
1104	Q₈	—	12	1	no	—
1105	Q₈	—	12	2	no	—
1106	D₄	—	2	4	no	—
1107	D₄	—	4	1	no	—
1108	D₄	—	6	4	no	—
1109	D₄	—	6	4	no	—
1110	D₄	—	6	4	no	—
1111	D₄	—	12	1	no	—
1112	D₄	—	12	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	3	1	no	—
1115	C₂×C₄	—	3	1	no	—
1116	C₂×C₄	—	3	1	no	—
1117	C₂×C₄	—	3	1	no	—
1118	C₂×C₄	—	3	2	no	—
1119	C₂×C₄	—	3	2	no	—
1120	C₂×C₄	—	3	2	no	—
1121	C₂×C₄	—	3	2	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	6	4	no	—
1126	C₂×C₄	—	6	4	no	—
1127	C₂×C₄	—	6	4	no	—
1128	C₂×C₄	—	6	2	no	—
1129	C₂×C₄	—	12	2	no	—
1130	C₂×C₄	—	12	2	no	—
1131	C₂×C₄	—	12	2	no	—
1132	C₂×C₄	—	12	2	no	—
1133	C₂×C₄	—	12	1	no	—
1134	C₂×C₄	—	12	2	no	—
1135	C₂×C₄	—	12	1	no	—
1136	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1137	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1138	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1139	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1140	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1141	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1142	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1143	C₂×C₃	—	2	2	no	—
1144	C₂×C₃	—	2	2	no	—
1145	C₂×C₃	—	2	1	no	—
1146	C₂×C₃	—	2	1	no	—
1147	C₂×C₃	—	2	1	no	—
1148	C₂×C₃	—	4	2	no	—
1149	C₂×C₃	—	4	2	no	—
1150	C₂×C₃	—	4	2	no	—
1151	C₂×C₃	—	6	4	no	—
1152	C₂×C₃	—	8	2	no	—
1153	C₂×C₃	—	12	2	no	—
1154	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1155	C₂×C₃	#5966	1	1	yes	characteristic
1156	C₂×C₃	#5968	1	1	yes	characteristic
1157	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1158	C₂×C₃	C₃×#585	1	1	yes	characteristic
1159	C₂×C₃	C₃×#585	1	1	yes	characteristic
1160	D₃	—	2	4	no	—
1161	D₃	—	4	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	3	4	no	—
1168	C₂²	—	6	2	no	—
1169	C₂²	—	6	2	no	—
1170	C₂²	—	6	2	no	—
1171	C₂²	—	6	2	no	—
1172	C₂²	—	6	2	no	—
1173	C₂²	—	12	4	no	—
1174	C₂²	—	24	4	no	—
1175	C₂²	C₃×D₃×#41	1	2	yes	—
1176	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	6	1	no	—
1185	C₄	—	6	1	no	—
1186	C₄	—	6	2	no	—
1187	C₄	—	6	2	no	—
1188	C₄	—	6	1	no	—
1189	C₄	—	6	1	no	—
1190	C₄	—	6	2	no	—
1191	C₄	—	6	2	no	—
1192	C₃	—	2	1	no	—
1193	C₃	#86453	1	1	yes	characteristic, direct product factor
1194	C₃	C₃×#3491	1	1	yes	characteristic, complemented
1195	C₂	—	2	2	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	6	4	no	—
1198	C₂	—	12	2	no	—
1199	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1200	C₂	C₃×#5966	1	1	yes	characteristic
1201	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#539	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₃×#5605	C₂
hypercenter	C₃×#539	D₃
hypocenter	C₃	C₃×#3491
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#539

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×#539	C₂	semidirect
2. C₃×#5708	C₂	semidirect
3. C₃×#5705	C₂	semidirect
4. C₃×#5694	C₂	semidirect
5. C₃×#5693	C₂	semidirect
6. C₃×#5665	C₂	semidirect
7. C₃×#5659	C₂	semidirect
8. C₃×#5658	C₂	semidirect
9. C₃×D₃×#123	C₂	semidirect
10. C₃×#5639	C₂	semidirect
11. C₃×#5637	C₂	semidirect
12. C₃×#5634	C₂	semidirect
13. C₃×#5624	C₂	semidirect
15. C₃×#5600	C₂	semidirect
16. C₃×#5545	C₂	semidirect
17. C₃×#5538	C₂	semidirect
18. C₃×#5515	C₂	semidirect
19. C₂×C₃×#892	C₂	semidirect
21. #86453	C₃	direct (N × H)
24. C₃²×#126	C₂²	semidirect
25. C₃²×#125	C₂²	semidirect
26. C₃²×#123	C₂²	semidirect
27. C₃²×#123	C₂²	semidirect
28. C₃²×C₂²⋊Q₈	C₂²	semidirect
29. C₃²×C₂²⋊Q₈	C₂²	semidirect
31. C₃²×C₄×D₄	C₂²	semidirect
32. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
33. C₃×#947	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×Q₈×Dic₃	C₂²	semidirect
38. C₃×#936	C₂²	semidirect
39. C₃×#935	C₂²	semidirect
40. C₃×D₄×Dic₃	C₂²	semidirect
41. C₃×D₄×Dic₃	C₂²	semidirect
43. C₃×#929	C₂²	semidirect
45. C₃×C₄×#67	C₂²	semidirect
46. C₃×C₄×#67	C₂²	semidirect
49. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
50. C₃×#926	C₂²	semidirect
51. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
52. C₃×#924	C₂²	semidirect
53. C₂×C₃×C₄×Dic₃	C₂²	semidirect
54. C₂×C₃×C₄×Dic₃	C₂²	semidirect
55. C₃×#898	C₂²	semidirect
56. C₃×#898	C₂²	semidirect
57. C₃×#898	C₂²	semidirect
58. C₃×#898	C₂²	semidirect
59. C₃×#897	C₂²	semidirect
60. C₃×#897	C₂²	semidirect
61. C₃×#896	C₂²	semidirect
62. C₃×#896	C₂²	semidirect
63. C₃×#896	C₂²	semidirect
67. C₃×#894	C₂²	semidirect
69. C₃×#893	C₂²	semidirect
70. C₃×#892	C₂²	semidirect
71. C₃×#892	C₂²	semidirect
72. C₃×#892	C₂²	semidirect
73. C₃×#892	C₂²	semidirect
74. C₃×#892	C₂²	semidirect
75. C₃×#892	C₂²	semidirect
76. C₃×D₃×C₄⋊C₄	C₂²	semidirect
77. C₃×D₃×C₄⋊C₄	C₂²	semidirect
78. C₃×#890	C₂²	semidirect
79. C₃×#890	C₂²	semidirect
80. C₃×#890	C₂²	semidirect
81. C₃×#889	C₂²	semidirect
82. C₃×#889	C₂²	semidirect
83. C₃×#889	C₂²	semidirect
84. C₃×#887	C₂²	semidirect
85. C₃×#886	C₂²	semidirect
86. C₃×#886	C₂²	semidirect
87. C₃×#885	C₂²	semidirect
91. C₃×#883	C₂²	semidirect
94. C₃×#67⋊C₄	C₂²	semidirect
96. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
97. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
98. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
99. C₃×#879	C₂²	semidirect
100. C₃×#879	C₂²	semidirect
101. C₃×#879	C₂²	semidirect
102. C₃×#878	C₂²	semidirect
103. C₃×#878	C₂²	semidirect
104. C₃×#877	C₂²	semidirect
106. C₃×#872	C₂²	semidirect
107. C₃×#872	C₂²	semidirect
108. C₃×C₄×Dic₆	C₂²	semidirect
121. C₃×#539	D₃	semidirect
122. C₃×#539	C₂×C₃	semidirect
130. #5708	C₂×C₃	semidirect
131. #5705	C₂×C₃	semidirect
132. #5694	C₂×C₃	semidirect
133. #5693	C₂×C₃	semidirect
134. #5665	C₂×C₃	semidirect
135. #5659	C₂×C₃	semidirect
136. #5658	C₂×C₃	semidirect
137. D₃×#123	C₂×C₃	semidirect
138. #5639	C₂×C₃	semidirect
139. #5637	C₂×C₃	semidirect
140. #5634	C₂×C₃	semidirect
141. #5624	C₂×C₃	semidirect
143. #5600	C₂×C₃	semidirect
144. #5545	C₂×C₃	semidirect
145. #5538	C₂×C₃	semidirect
146. #5515	C₂×C₃	semidirect
147. C₂×#892	C₂×C₃	semidirect
250. C₃×#126	C₂×D₃	semidirect
251. C₃×#126	C₂²×C₃	semidirect
259. C₃×#125	C₂×D₃	semidirect
260. C₃×#125	C₂²×C₃	semidirect
278. C₃×#123	C₂×D₃	semidirect
279. C₃×#123	C₂×D₃	semidirect
280. C₃×#123	C₂²×C₃	semidirect
281. C₃×#123	C₂²×C₃	semidirect
293. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
294. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
295. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
296. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
318. C₃×C₄×D₄	C₂×D₃	semidirect
319. C₃×C₄×D₄	C₂²×C₃	semidirect
334. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
335. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
345. #947	C₂²×C₃	semidirect
346. #946	C₂²×C₃	semidirect
347. Q₈×Dic₃	C₂²×C₃	semidirect
350. #936	C₂²×C₃	semidirect
351. #935	C₂²×C₃	semidirect
352. D₄×Dic₃	C₂²×C₃	semidirect
353. D₄×Dic₃	C₂²×C₃	semidirect
355. #929	C₂²×C₃	semidirect
357. C₄×#67	C₂²×C₃	semidirect
358. C₄×#67	C₂²×C₃	semidirect
361. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
362. #926	C₂²×C₃	semidirect
363. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
364. #924	C₂²×C₃	semidirect
365. C₂×C₄×Dic₃	C₂²×C₃	semidirect
366. C₂×C₄×Dic₃	C₂²×C₃	semidirect
367. #898	C₂²×C₃	semidirect
368. #898	C₂²×C₃	semidirect
369. #898	C₂²×C₃	semidirect
370. #898	C₂²×C₃	semidirect
371. #897	C₂²×C₃	semidirect
372. #897	C₂²×C₃	semidirect
373. #896	C₂²×C₃	semidirect
374. #896	C₂²×C₃	semidirect
375. #896	C₂²×C₃	semidirect
379. #894	C₂²×C₃	semidirect
381. #893	C₂²×C₃	semidirect
382. #892	C₂²×C₃	semidirect
383. #892	C₂²×C₃	semidirect
384. #892	C₂²×C₃	semidirect
385. #892	C₂²×C₃	semidirect
386. #892	C₂²×C₃	semidirect
387. #892	C₂²×C₃	semidirect
388. D₃×C₄⋊C₄	C₂²×C₃	semidirect
389. D₃×C₄⋊C₄	C₂²×C₃	semidirect
390. #890	C₂²×C₃	semidirect
391. #890	C₂²×C₃	semidirect
392. #890	C₂²×C₃	semidirect
393. #889	C₂²×C₃	semidirect
394. #889	C₂²×C₃	semidirect
395. #889	C₂²×C₃	semidirect
396. #887	C₂²×C₃	semidirect
397. #886	C₂²×C₃	semidirect
398. #886	C₂²×C₃	semidirect
399. #885	C₂²×C₃	semidirect
403. #883	C₂²×C₃	semidirect
406. #67⋊C₄	C₂²×C₃	semidirect
408. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
409. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
410. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
411. #879	C₂²×C₃	semidirect
412. #879	C₂²×C₃	semidirect
413. #879	C₂²×C₃	semidirect
414. #878	C₂²×C₃	semidirect
415. #878	C₂²×C₃	semidirect
416. #877	C₂²×C₃	semidirect
418. #872	C₂²×C₃	semidirect
419. #872	C₂²×C₃	semidirect
420. C₄×Dic₆	C₂²×C₃	semidirect
482. #539	C₃×D₃	semidirect
728. #126	C₂×C₃×D₃	semidirect
735. #125	C₂×C₃×D₃	semidirect
751. #123	C₂×C₃×D₃	semidirect
752. #123	C₂×C₃×D₃	semidirect
762. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
763. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
782. C₄×D₄	C₂×C₃×D₃	semidirect
796. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
1092. C₃²	#3491	semidirect
1193. C₃	#86453	direct (N × H)
1194. C₃	C₃×#3491	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#539	2
C₃×#5708	2
C₃×#5705	2
C₃×#5694	2
C₃×#5693	2
C₃×#5665	2
C₃×#5659	2
C₃×#5658	2
C₃×D₃×#123	2
C₃×#5639	2
C₃×#5637	2
C₃×#5634	2
C₃×#5624	2
C₃×#5605	2
C₃×#5600	2
C₃×#5545	2
C₃×#5538	2
C₃×#5515	2
C₂×C₃×#892	2
C₃×#3491	3
#86453	3

Subgroups — C3×#86453 #11904947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86453 #11904947