Subgroups — C₃×#86842 #11909850

Order 1152.

2091 conjugacy classes of subgroups.

The subgroup lattice has 1297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5702	C₂	1	2	yes	maximal, complemented
3	C₃×#5701	C₂	1	2	yes	maximal, complemented
4	C₃×#5698	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5696	C₂	1	2	yes	maximal, complemented
6	C₃×#5685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5685	C₂	1	2	yes	maximal, complemented
8	C₃×#5650	C₂	1	2	yes	maximal, complemented
9	C₃×#5649	C₂	1	2	yes	maximal
10	C₃×#5632	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5632	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5572	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5567	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5538	C₂	1	1	yes	maximal, characteristic
17	C₃×D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5531	C₂	1	2	yes	maximal, complemented
20	C₃×#5517	C₂	1	2	yes	maximal, complemented
21	C₃×#5516	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5513	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#887	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3523	—	3	1	no	maximal
25	#86842	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
27	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
28	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
29	C₃²×#126	C₂²	1	2	yes	—
30	C₃²×#125	C₂²	1	2	yes	—
31	C₃²×#125	C₂²	1	1	yes	characteristic
32	C₃²×#123	C₂²	1	2	yes	—
33	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃²×#117	C₂²	1	1	yes	characteristic
38	C₃²×#117	C₂²	1	2	yes	—
39	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
41	C₃×#944	C₂²	1	1	yes	characteristic
42	C₃×#944	C₂²	1	1	yes	characteristic
43	C₃×#939	C₂²	1	1	yes	characteristic
44	C₃×#935	C₂²	1	1	yes	characteristic
45	C₃×D₄×Dic₃	C₂²	1	2	yes	—
46	C₃×#929	C₂²	1	2	yes	—
47	C₃×C₄×#67	C₂²	1	1	yes	characteristic
48	C₃×C₄×#67	C₂²	1	1	yes	characteristic
49	C₃×#926	C₂²	1	2	yes	—
50	C₃×#926	C₂²	1	1	yes	characteristic
51	C₃×#924	C₂²	1	1	yes	characteristic
52	C₃×#924	C₂²	1	1	yes	characteristic
53	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
54	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
55	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
56	C₃×#898	C₂²	1	2	yes	—
57	C₃×#898	C₂²	1	2	yes	—
58	C₃×#898	C₂²	1	1	yes	characteristic
59	C₃×#898	C₂²	1	2	yes	—
60	C₃×#897	C₂²	1	1	yes	characteristic
61	C₃×#897	C₂²	1	1	yes	characteristic
62	C₃×#896	C₂²	1	2	yes	—
63	C₃×#896	C₂²	1	2	yes	—
64	C₃×#892	C₂²	1	1	yes	characteristic
65	C₃×#892	C₂²	1	2	yes	—
66	C₃×#890	C₂²	1	1	yes	characteristic
67	C₃×#890	C₂²	1	2	yes	—
68	C₃×#890	C₂²	1	2	yes	—
69	C₃×#890	C₂²	1	2	yes	—
70	C₃×#889	C₂²	1	2	yes	—
71	C₃×#889	C₂²	1	2	yes	—
72	C₃×#889	C₂²	1	2	yes	—
73	C₃×#889	C₂²	1	1	yes	characteristic
74	C₃×#889	C₂²	1	2	yes	—
75	C₃×#889	C₂²	1	2	yes	—
76	C₃×#889	C₂²	1	2	yes	—
77	C₃×#889	C₂²	1	2	yes	—
78	C₃×#888	C₂²	1	2	yes	—
79	C₃×#888	C₂²	1	2	yes	—
80	C₃×#888	C₂²	1	1	yes	characteristic
81	C₃×#888	C₂²	1	2	yes	—
82	C₃×#888	C₂²	1	2	yes	—
83	C₃×#887	C₂²	1	1	yes	characteristic
84	C₃×#887	C₂²	1	1	yes	characteristic
85	C₃×#887	C₂²	1	1	yes	characteristic
86	C₃×#887	C₂²	1	1	yes	characteristic
87	C₃×#887	C₂²	1	2	yes	—
88	C₃×#887	C₂²	1	2	yes	—
89	C₃×#887	C₂²	1	1	yes	characteristic
90	C₃×#887	C₂²	1	1	yes	characteristic
91	C₃×#887	C₂²	1	1	yes	characteristic
92	C₃×#887	C₂²	1	2	yes	—
93	C₃×#887	C₂²	1	2	yes	—
94	C₃×#887	C₂²	1	2	yes	—
95	C₃×#886	C₂²	1	1	yes	characteristic
96	C₃×#885	C₂²	1	2	yes	—
97	C₃×#885	C₂²	1	1	yes	characteristic
98	C₃×#67⋊C₄	C₂²	1	2	yes	—
99	C₃×#67⋊C₄	C₂²	1	2	yes	—
100	C₃×#879	C₂²	1	2	yes	—
101	C₃×#879	C₂²	1	1	yes	characteristic
102	C₃×#879	C₂²	1	2	yes	—
103	C₃×#879	C₂²	1	2	yes	—
104	C₃×#878	C₂²	1	1	yes	characteristic
105	C₃×#878	C₂²	1	2	yes	—
106	C₃×#878	C₂²	1	2	yes	—
107	C₃×#878	C₂²	1	2	yes	—
108	C₃×#878	C₂²	1	2	yes	—
109	C₃×#878	C₂²	1	2	yes	—
110	C₃×#877	C₂²	1	2	yes	—
111	C₃×#877	C₂²	1	2	yes	—
112	C₃×#877	C₂²	1	2	yes	—
113	C₃×#876	C₂²	1	2	yes	—
114	C₃×#872	C₂²	1	2	yes	—
115	C₃×#872	C₂²	1	1	yes	characteristic
116	C₃×#870	C₂²	1	2	yes	—
117	C₃×#869	C₂²	1	1	yes	characteristic
118	C₃×C₄×Dic₆	C₂²	1	2	yes	—
119	C₃×C₄×Dic₆	C₂²	1	2	yes	—
120	C₃×C₄×Dic₆	C₂²	1	2	yes	—
121	C₃×C₄×Dic₆	C₂²	1	2	yes	—
122	C₃×C₄×Dic₆	C₂²	1	2	yes	—
123	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
125	C₃×#557	—	3	1	no	—
126	C₃×#557	—	3	2	no	—
127	C₃×#557	—	3	1	no	—
128	C₃×#556	—	3	2	no	—
129	C₃×#556	—	3	1	no	—
130	C₃×#552	—	2	1	no	—
131	C₃×#552	—	3	2	no	—
132	C₃×#552	—	3	2	no	—
133	C₃×#552	—	3	1	no	—
134	C₃×#552	D₃	1	1	yes	characteristic, complemented
135	C₃×#552	C₂×C₃	1	1	yes	characteristic, complemented
136	C₃×D₄×Q₈	—	3	1	no	—
137	C₃×D₄×Q₈	—	3	1	no	—
138	C₃×D₄×Q₈	—	3	1	no	—
139	C₃×#541	—	3	2	no	—
140	C₃×#541	—	3	2	no	—
141	C₃×#541	—	3	1	no	—
142	C₃×#541	—	3	1	no	—
143	C₃×#533	—	3	1	no	—
144	C₃×#533	—	3	2	no	—
145	C₃×#529	—	3	2	no	—
146	C₃×#529	—	3	1	no	—
147	C₃×#519	—	3	1	no	—
148	C₃×#519	—	3	1	no	—
149	C₂×C₃×C₄×Q₈	—	3	1	no	—
150	#5702	C₂×C₃	1	2	yes	complemented
151	#5701	C₂×C₃	1	2	yes	complemented
152	#5698	C₂×C₃	1	1	yes	characteristic, complemented
153	#5696	C₂×C₃	1	2	yes	complemented
154	#5685	C₂×C₃	1	2	yes	complemented
155	#5685	C₂×C₃	1	1	yes	characteristic, complemented
156	#5650	C₂×C₃	1	2	yes	complemented
157	#5649	C₂×C₃	1	2	yes	—
158	#5632	C₂×C₃	1	1	yes	characteristic, complemented
159	#5632	C₂×C₃	1	1	yes	characteristic, complemented
160	#5625	C₂×C₃	1	1	yes	characteristic, complemented
161	#5622	C₂×C₃	1	1	yes	characteristic, complemented
162	#5572	C₂×C₃	1	1	yes	characteristic, complemented
163	#5567	C₂×C₃	1	1	yes	characteristic, complemented
164	#5538	C₂×C₃	1	1	yes	characteristic
165	D₄×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
166	#5533	C₂×C₃	1	1	yes	characteristic, complemented
167	#5531	C₂×C₃	1	2	yes	complemented
168	#5517	C₂×C₃	1	2	yes	complemented
169	#5516	C₂×C₃	1	1	yes	characteristic, complemented
170	#5513	C₂×C₃	1	1	yes	characteristic, complemented
171	C₂×#887	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
173	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃²×C₄	C₂³	1	2	yes	—
175	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×#67	C₂³	1	1	yes	characteristic
178	C₂×C₃×#67	C₂³	1	1	yes	characteristic
179	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
180	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
181	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
182	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
183	C₃×D₃×Q₈	—	2	4	no	—
184	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
186	C₂×C₃×Dic₆	—	2	4	no	—
187	C₂×C₃×Dic₆	—	2	4	no	—
188	C₂×C₃×Dic₆	C₂³	1	2	yes	—
189	C₂×C₃×Dic₆	C₂³	1	2	yes	—
190	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
191	C₂×C₃×Dic₆	C₂³	1	2	yes	—
192	C₂×C₃×Dic₆	C₂³	1	2	yes	—
193	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
194	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
195	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
196	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
203	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
205	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
206	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₄²	C₂³	1	2	yes	—
212	C₃²×C₄²	C₂³	1	2	yes	—
213	C₃²×C₄²	C₂³	1	1	yes	characteristic
214	C₃×#217	C₂³	1	1	yes	characteristic
215	C₃×#217	C₂³	1	1	yes	characteristic
216	C₃×#217	C₂³	1	2	yes	—
217	C₃×#217	C₂³	1	1	yes	characteristic
218	C₃×#217	C₂³	1	1	yes	characteristic
219	C₃×#217	C₂³	1	2	yes	—
220	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
235	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
236	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
237	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
241	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
242	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
244	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
245	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
246	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
247	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
248	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
249	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
250	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
251	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
252	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
253	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
258	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
259	C₃×C₄×Dic₃	C₂³	1	2	yes	—
260	C₃×C₄×Dic₃	C₂³	1	2	yes	—
261	C₃×C₄×Dic₃	C₂³	1	2	yes	—
262	C₃×C₄×Dic₃	C₂³	1	2	yes	—
263	C₃×C₄×Dic₃	C₂³	1	2	yes	—
264	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
265	C₃×C₄×Dic₃	C₂³	1	2	yes	—
266	C₃×C₄×Dic₃	C₂³	1	2	yes	—
267	C₃×C₄×Dic₃	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
269	C₃×C₄×Dic₃	C₂³	1	2	yes	—
270	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
271	C₃×C₄×Dic₃	C₂³	1	2	yes	—
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	#3523	—	3	1	no	Sylow
275	C₂²×C₃×Q₈	—	3	1	no	—
276	C₂²×C₃×Q₈	—	3	1	no	—
277	C₂²×C₃×Q₈	—	3	1	no	—
278	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
279	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
280	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
281	C₃×C₄⋊Q₈	—	3	1	no	—
282	C₃×C₄⋊Q₈	—	3	1	no	—
283	C₃×C₄⋊Q₈	—	3	2	no	—
284	C₃×C₄⋊Q₈	—	3	2	no	—
285	C₃×C₄⋊Q₈	—	3	1	no	—
286	C₃×C₄⋊Q₈	—	3	2	no	—
287	C₃×C₄⋊Q₈	—	3	2	no	—
288	C₃×C₄⋊Q₈	—	3	1	no	—
289	C₃×#126	—	2	2	no	—
290	C₃×#126	—	3	2	no	—
291	C₃×#126	—	3	1	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	1	no	—
295	C₃×#126	—	3	2	no	—
296	C₃×#126	—	3	2	no	—
297	C₃×#126	—	3	2	no	—
298	C₃×#126	—	3	2	no	—
299	C₃×#126	C₂×D₃	1	2	yes	—
300	C₃×#126	C₂²×C₃	1	2	yes	—
301	C₃×#125	—	2	2	no	—
302	C₃×#125	—	2	1	no	—
303	C₃×#125	—	3	1	no	—
304	C₃×#125	—	3	2	no	—
305	C₃×#125	—	3	2	no	—
306	C₃×#125	—	3	2	no	—
307	C₃×#125	—	3	2	no	—
308	C₃×#125	—	3	2	no	—
309	C₃×#125	—	3	2	no	—
310	C₃×#125	—	3	2	no	—
311	C₃×#125	—	3	2	no	—
312	C₃×#125	—	3	2	no	—
313	C₃×#125	—	3	2	no	—
314	C₃×#125	—	3	1	no	—
315	C₃×#125	—	3	2	no	—
316	C₃×#125	C₂×D₃	1	1	yes	characteristic
317	C₃×#125	C₂×D₃	1	2	yes	—
318	C₃×#125	C₂²×C₃	1	2	yes	—
319	C₃×#125	C₂²×C₃	1	1	yes	characteristic
320	C₃×#124	—	3	1	no	—
321	C₃×#124	—	3	2	no	—
322	C₃×#123	—	2	2	no	—
323	C₃×#123	—	3	1	no	—
324	C₃×#123	—	3	2	no	—
325	C₃×#123	—	3	1	no	—
326	C₃×#123	C₂×D₃	1	2	yes	—
327	C₃×#123	C₂²×C₃	1	2	yes	—
328	C₃×C₂²⋊Q₈	—	2	1	no	—
329	C₃×C₂²⋊Q₈	—	2	1	no	—
330	C₃×C₂²⋊Q₈	—	3	1	no	—
331	C₃×C₂²⋊Q₈	—	3	1	no	—
332	C₃×C₂²⋊Q₈	—	3	2	no	—
333	C₃×C₂²⋊Q₈	—	3	2	no	—
334	C₃×C₂²⋊Q₈	—	3	1	no	—
335	C₃×C₂²⋊Q₈	—	3	1	no	—
336	C₃×C₂²⋊Q₈	—	3	2	no	—
337	C₃×C₂²⋊Q₈	—	3	1	no	—
338	C₃×C₂²⋊Q₈	—	3	2	no	—
339	C₃×C₂²⋊Q₈	—	3	2	no	—
340	C₃×C₂²⋊Q₈	—	3	2	no	—
341	C₃×C₂²⋊Q₈	—	3	2	no	—
342	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
343	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
344	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
345	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
346	C₃×#121	—	3	1	no	—
347	C₃×C₄×Q₈	—	2	1	no	—
348	C₃×C₄×Q₈	—	3	1	no	—
349	C₃×C₄×Q₈	—	3	1	no	—
350	C₃×C₄×Q₈	—	3	2	no	—
351	C₃×C₄×Q₈	—	3	1	no	—
352	C₃×C₄×Q₈	—	3	1	no	—
353	C₃×C₄×Q₈	—	3	2	no	—
354	C₃×C₄×Q₈	—	3	1	no	—
355	C₃×C₄×Q₈	—	3	1	no	—
356	C₃×C₄×Q₈	—	3	1	no	—
357	C₃×C₄×Q₈	—	3	2	no	—
358	C₃×C₄×Q₈	—	3	1	no	—
359	C₃×C₄×Q₈	—	3	2	no	—
360	C₃×C₄×Q₈	—	3	2	no	—
361	C₃×C₄×Q₈	—	3	2	no	—
362	C₃×C₄×Q₈	—	3	2	no	—
363	C₃×C₄×Q₈	—	3	1	no	—
364	C₃×C₄×Q₈	—	3	2	no	—
365	C₃×C₄×Q₈	—	3	1	no	—
366	C₃×C₄×Q₈	—	3	2	no	—
367	C₃×C₄×Q₈	—	3	2	no	—
368	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
369	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
370	C₃×C₄×D₄	—	2	1	no	—
371	C₃×C₄×D₄	—	3	2	no	—
372	C₃×C₄×D₄	—	3	1	no	—
373	C₃×C₄×D₄	—	3	1	no	—
374	C₃×C₄×D₄	—	3	2	no	—
375	C₃×C₄×D₄	—	3	2	no	—
376	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
377	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
378	C₃×#117	—	2	1	no	—
379	C₃×#117	—	2	2	no	—
380	C₃×#117	—	3	1	no	—
381	C₃×#117	—	3	2	no	—
382	C₃×#117	—	3	2	no	—
383	C₃×#117	—	3	1	no	—
384	C₃×#117	—	3	2	no	—
385	C₃×#117	—	3	2	no	—
386	C₃×#117	—	3	2	no	—
387	C₃×#117	—	3	1	no	—
388	C₃×#117	—	3	2	no	—
389	C₃×#117	C₂×D₃	1	1	yes	characteristic
390	C₃×#117	C₂×D₃	1	2	yes	—
391	C₃×#117	C₂²×C₃	1	1	yes	characteristic
392	C₃×#117	C₂²×C₃	1	2	yes	—
393	C₂×C₃×C₄⋊C₄	—	2	1	no	—
394	C₂×C₃×C₄⋊C₄	—	3	2	no	—
395	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
396	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	—	3	2	no	—
399	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
400	#944	C₂²×C₃	1	1	yes	characteristic
401	#944	C₂²×C₃	1	1	yes	characteristic
402	#939	C₂²×C₃	1	1	yes	characteristic
403	#935	C₂²×C₃	1	1	yes	characteristic
404	D₄×Dic₃	C₂²×C₃	1	2	yes	—
405	#929	C₂²×C₃	1	2	yes	—
406	C₄×#67	C₂²×C₃	1	1	yes	characteristic
407	C₄×#67	C₂²×C₃	1	1	yes	characteristic
408	#926	C₂²×C₃	1	2	yes	—
409	#926	C₂²×C₃	1	1	yes	characteristic
410	#924	C₂²×C₃	1	1	yes	characteristic
411	#924	C₂²×C₃	1	1	yes	characteristic
412	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
413	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
414	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
415	#898	C₂²×C₃	1	2	yes	—
416	#898	C₂²×C₃	1	1	yes	characteristic
417	#898	C₂²×C₃	1	2	yes	—
418	#898	C₂²×C₃	1	2	yes	—
419	#897	C₂²×C₃	1	1	yes	characteristic
420	#897	C₂²×C₃	1	1	yes	characteristic
421	#896	C₂²×C₃	1	2	yes	—
422	#896	C₂²×C₃	1	2	yes	—
423	#892	C₂²×C₃	1	2	yes	—
424	#892	C₂²×C₃	1	1	yes	characteristic
425	#890	C₂²×C₃	1	2	yes	—
426	#890	C₂²×C₃	1	1	yes	characteristic
427	#890	C₂²×C₃	1	2	yes	—
428	#890	C₂²×C₃	1	2	yes	—
429	#889	C₂²×C₃	1	2	yes	—
430	#889	C₂²×C₃	1	2	yes	—
431	#889	C₂²×C₃	1	2	yes	—
432	#889	C₂²×C₃	1	1	yes	characteristic
433	#889	C₂²×C₃	1	2	yes	—
434	#889	C₂²×C₃	1	2	yes	—
435	#889	C₂²×C₃	1	2	yes	—
436	#889	C₂²×C₃	1	2	yes	—
437	#888	C₂²×C₃	1	2	yes	—
438	#888	C₂²×C₃	1	2	yes	—
439	#888	C₂²×C₃	1	2	yes	—
440	#888	C₂²×C₃	1	2	yes	—
441	#888	C₂²×C₃	1	1	yes	characteristic
442	#887	C₂²×C₃	1	1	yes	characteristic
443	#887	C₂²×C₃	1	1	yes	characteristic
444	#887	C₂²×C₃	1	2	yes	—
445	#887	C₂²×C₃	1	2	yes	—
446	#887	C₂²×C₃	1	2	yes	—
447	#887	C₂²×C₃	1	2	yes	—
448	#887	C₂²×C₃	1	2	yes	—
449	#887	C₂²×C₃	1	1	yes	characteristic
450	#887	C₂²×C₃	1	1	yes	characteristic
451	#887	C₂²×C₃	1	1	yes	characteristic
452	#887	C₂²×C₃	1	1	yes	characteristic
453	#887	C₂²×C₃	1	1	yes	characteristic
454	#886	C₂²×C₃	1	1	yes	characteristic
455	#885	C₂²×C₃	1	2	yes	—
456	#885	C₂²×C₃	1	1	yes	characteristic
457	#67⋊C₄	C₂²×C₃	1	2	yes	—
458	#67⋊C₄	C₂²×C₃	1	2	yes	—
459	#879	C₂²×C₃	1	2	yes	—
460	#879	C₂²×C₃	1	2	yes	—
461	#879	C₂²×C₃	1	2	yes	—
462	#879	C₂²×C₃	1	1	yes	characteristic
463	#878	C₂²×C₃	1	2	yes	—
464	#878	C₂²×C₃	1	2	yes	—
465	#878	C₂²×C₃	1	2	yes	—
466	#878	C₂²×C₃	1	2	yes	—
467	#878	C₂²×C₃	1	1	yes	characteristic
468	#878	C₂²×C₃	1	2	yes	—
469	#877	C₂²×C₃	1	2	yes	—
470	#877	C₂²×C₃	1	2	yes	—
471	#877	C₂²×C₃	1	2	yes	—
472	#876	C₂²×C₃	1	2	yes	—
473	#872	C₂²×C₃	1	1	yes	characteristic
474	#872	C₂²×C₃	1	2	yes	—
475	#870	C₂²×C₃	1	2	yes	—
476	#869	C₂²×C₃	1	1	yes	characteristic
477	C₄×Dic₆	C₂²×C₃	1	2	yes	—
478	C₄×Dic₆	C₂²×C₃	1	2	yes	—
479	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
480	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
481	C₄×Dic₆	C₂²×C₃	1	2	yes	—
482	C₄×Dic₆	C₂²×C₃	1	2	yes	—
483	C₄×Dic₆	C₂²×C₃	1	2	yes	—
484	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
485	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
486	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
487	C₃²×Q₈	—	2	2	no	—
488	C₃²×D₄	—	2	2	no	—
489	C₂×C₃²×C₄	—	2	4	no	—
490	C₂×C₃²×C₄	—	2	2	no	—
491	C₂×C₃²×C₄	—	2	2	no	—
492	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
493	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
494	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
495	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
496	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
497	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
498	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
499	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
500	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
501	C₃×#67	—	2	2	no	—
502	C₃×#67	—	2	2	no	—
503	C₂×C₃×Dic₃	—	2	2	no	—
504	C₂×C₃×Dic₃	—	2	4	no	—
505	C₂×C₃×Dic₃	—	2	4	no	—
506	C₂×C₃×Dic₃	—	2	2	no	—
507	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
508	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
509	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
510	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
511	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
512	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
513	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
514	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
515	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
516	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
517	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
518	C₃×C₄×D₃	—	2	2	no	—
519	C₃×C₄×D₃	—	2	4	no	—
520	C₃×Dic₆	—	2	2	no	—
521	C₃×Dic₆	—	2	2	no	—
522	C₃×Dic₆	—	2	4	no	—
523	C₃×Dic₆	—	2	4	no	—
524	C₃×Dic₆	—	2	4	no	—
525	C₃×Dic₆	—	2	4	no	—
526	C₃×Dic₆	—	2	2	no	—
527	C₃×Dic₆	#41	1	4	yes	—
528	#557	—	3	1	no	—
529	#557	—	3	2	no	—
530	#557	—	3	1	no	—
531	#556	—	3	2	no	—
532	#556	—	3	1	no	—
533	#552	—	3	2	no	—
534	#552	—	3	2	no	—
535	#552	—	3	1	no	—
536	#552	C₃×D₃	1	1	yes	characteristic, complemented
537	D₄×Q₈	—	3	1	no	—
538	D₄×Q₈	—	3	1	no	—
539	D₄×Q₈	—	3	1	no	—
540	#541	—	3	2	no	—
541	#541	—	3	2	no	—
542	#541	—	3	1	no	—
543	#541	—	3	1	no	—
544	#533	—	3	1	no	—
545	#533	—	3	2	no	—
546	#529	—	3	2	no	—
547	#529	—	3	1	no	—
548	#519	—	3	1	no	—
549	#519	—	3	1	no	—
550	C₂×C₄×Q₈	—	3	1	no	—
551	C₂×C₃×Q₈	—	2	1	no	—
552	C₂×C₃×Q₈	—	3	1	no	—
553	C₂×C₃×Q₈	—	3	2	no	—
554	C₂×C₃×Q₈	—	3	1	no	—
555	C₂×C₃×Q₈	—	3	2	no	—
556	C₂×C₃×Q₈	—	3	2	no	—
557	C₂×C₃×Q₈	—	3	2	no	—
558	C₂×C₃×Q₈	—	3	1	no	—
559	C₂×C₃×Q₈	—	3	1	no	—
560	C₂×C₃×Q₈	—	6	4	no	—
561	C₂×C₃×Q₈	—	6	4	no	—
562	C₂×C₃×Q₈	—	6	4	no	—
563	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
564	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₃×D₄	—	2	1	no	—
566	C₂×C₃×D₄	—	3	1	no	—
567	C₂×C₃×D₄	—	3	1	no	—
568	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
569	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
570	C₂²×C₃×C₄	—	2	2	no	—
571	C₂²×C₃×C₄	—	2	1	no	—
572	C₂²×C₃×C₄	—	2	1	no	—
573	C₂²×C₃×C₄	—	3	1	no	—
574	C₂²×C₃×C₄	—	3	1	no	—
575	C₂²×C₃×C₄	—	3	2	no	—
576	C₂²×C₃×C₄	—	3	2	no	—
577	C₂²×C₃×C₄	—	3	2	no	—
578	C₂²×C₃×C₄	—	3	1	no	—
579	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
580	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
581	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
582	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
583	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
584	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
585	C₂×#67	C₂³×C₃	1	1	yes	characteristic
586	C₂×#67	C₂³×C₃	1	1	yes	characteristic
587	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
588	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
589	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
590	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
591	D₃×Q₈	—	2	4	no	—
592	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
593	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
594	C₂×Dic₆	—	2	4	no	—
595	C₂×Dic₆	—	2	4	no	—
596	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
597	C₂×Dic₆	C₂³×C₃	1	2	yes	—
598	C₂×Dic₆	C₂³×C₃	1	2	yes	—
599	C₂×Dic₆	C₂³×C₃	1	2	yes	—
600	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
601	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
602	C₂×Dic₆	C₂³×C₃	1	2	yes	—
603	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
604	C₃×C₄⋊C₄	—	2	1	no	—
605	C₃×C₄⋊C₄	—	2	1	no	—
606	C₃×C₄⋊C₄	—	2	2	no	—
607	C₃×C₄⋊C₄	—	2	1	no	—
608	C₃×C₄⋊C₄	—	2	2	no	—
609	C₃×C₄⋊C₄	—	2	2	no	—
610	C₃×C₄⋊C₄	—	2	1	no	—
611	C₃×C₄⋊C₄	—	2	2	no	—
612	C₃×C₄⋊C₄	—	2	2	no	—
613	C₃×C₄⋊C₄	—	2	2	no	—
614	C₃×C₄⋊C₄	—	3	2	no	—
615	C₃×C₄⋊C₄	—	3	2	no	—
616	C₃×C₄⋊C₄	—	3	2	no	—
617	C₃×C₄⋊C₄	—	3	2	no	—
618	C₃×C₄⋊C₄	—	3	2	no	—
619	C₃×C₄⋊C₄	—	3	2	no	—
620	C₃×C₄⋊C₄	—	3	2	no	—
621	C₃×C₄⋊C₄	—	3	1	no	—
622	C₃×C₄⋊C₄	—	3	1	no	—
623	C₃×C₄⋊C₄	—	3	2	no	—
624	C₃×C₄⋊C₄	—	3	2	no	—
625	C₃×C₄⋊C₄	—	3	2	no	—
626	C₃×C₄⋊C₄	—	3	2	no	—
627	C₃×C₄⋊C₄	—	3	1	no	—
628	C₃×C₄⋊C₄	—	3	1	no	—
629	C₃×C₄⋊C₄	—	3	2	no	—
630	C₃×C₄⋊C₄	—	3	1	no	—
631	C₃×C₄⋊C₄	—	3	2	no	—
632	C₃×C₄⋊C₄	—	3	2	no	—
633	C₃×C₄⋊C₄	—	3	2	no	—
634	C₃×C₄⋊C₄	—	3	2	no	—
635	C₃×C₄⋊C₄	—	3	1	no	—
636	C₃×C₄⋊C₄	—	3	1	no	—
637	C₃×C₄⋊C₄	—	3	2	no	—
638	C₃×C₄⋊C₄	—	3	1	no	—
639	C₃×C₄⋊C₄	—	3	1	no	—
640	C₃×C₄⋊C₄	—	3	2	no	—
641	C₃×C₄⋊C₄	—	3	2	no	—
642	C₃×C₄⋊C₄	—	3	2	no	—
643	C₃×C₄⋊C₄	—	3	2	no	—
644	C₃×C₄⋊C₄	—	3	2	no	—
645	C₃×C₄⋊C₄	—	3	1	no	—
646	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
647	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
648	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
649	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
650	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
651	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
652	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
653	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
654	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
655	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
656	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
657	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
658	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
659	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
660	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
661	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
662	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
663	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
664	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
665	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
666	C₃×C₂²⋊C₄	—	2	1	no	—
667	C₃×C₂²⋊C₄	—	2	2	no	—
668	C₃×C₂²⋊C₄	—	2	2	no	—
669	C₃×C₂²⋊C₄	—	2	1	no	—
670	C₃×C₂²⋊C₄	—	2	2	no	—
671	C₃×C₂²⋊C₄	—	3	1	no	—
672	C₃×C₂²⋊C₄	—	3	1	no	—
673	C₃×C₂²⋊C₄	—	3	2	no	—
674	C₃×C₂²⋊C₄	—	3	1	no	—
675	C₃×C₂²⋊C₄	—	3	1	no	—
676	C₃×C₂²⋊C₄	—	3	2	no	—
677	C₃×C₂²⋊C₄	—	3	1	no	—
678	C₃×C₂²⋊C₄	—	3	1	no	—
679	C₃×C₂²⋊C₄	—	3	2	no	—
680	C₃×C₂²⋊C₄	—	3	1	no	—
681	C₃×C₂²⋊C₄	—	3	2	no	—
682	C₃×C₂²⋊C₄	—	3	1	no	—
683	C₃×C₂²⋊C₄	—	3	2	no	—
684	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
686	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
687	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
688	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
689	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
690	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
691	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
692	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
693	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
694	C₃×C₄²	—	2	2	no	—
695	C₃×C₄²	—	2	2	no	—
696	C₃×C₄²	—	2	1	no	—
697	C₃×C₄²	—	3	2	no	—
698	C₃×C₄²	—	3	1	no	—
699	C₃×C₄²	—	3	2	no	—
700	C₃×C₄²	—	3	1	no	—
701	C₃×C₄²	—	3	1	no	—
702	C₃×C₄²	—	3	2	no	—
703	C₃×C₄²	—	3	1	no	—
704	C₃×C₄²	—	3	2	no	—
705	C₃×C₄²	—	3	2	no	—
706	C₃×C₄²	—	3	2	no	—
707	C₃×C₄²	—	3	2	no	—
708	C₃×C₄²	—	3	2	no	—
709	C₃×C₄²	—	3	2	no	—
710	C₃×C₄²	—	3	2	no	—
711	C₃×C₄²	—	3	1	no	—
712	C₃×C₄²	C₂²×D₃	1	2	yes	—
713	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
714	C₃×C₄²	C₂²×D₃	1	2	yes	—
715	C₃×C₄²	C₂³×C₃	1	2	yes	—
716	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
717	C₃×C₄²	C₂³×C₃	1	2	yes	—
718	#217	C₂³×C₃	1	1	yes	characteristic
719	#217	C₂³×C₃	1	1	yes	characteristic
720	#217	C₂³×C₃	1	2	yes	—
721	#217	C₂³×C₃	1	1	yes	characteristic
722	#217	C₂³×C₃	1	1	yes	characteristic
723	#217	C₂³×C₃	1	2	yes	—
724	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
725	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
726	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
727	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
728	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
729	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
730	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
731	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
732	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
733	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
734	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
735	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
736	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
737	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
738	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
739	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
740	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
741	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
742	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
743	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
744	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
745	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
746	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
747	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
748	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
749	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
750	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
751	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
752	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
753	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
754	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
755	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
756	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
757	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
758	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
759	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
760	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
761	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
762	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
763	C₄×Dic₃	C₂³×C₃	1	2	yes	—
764	C₄×Dic₃	C₂³×C₃	1	2	yes	—
765	C₄×Dic₃	C₂³×C₃	1	2	yes	—
766	C₄×Dic₃	C₂³×C₃	1	2	yes	—
767	C₄×Dic₃	C₂³×C₃	1	2	yes	—
768	C₄×Dic₃	C₂³×C₃	1	2	yes	—
769	C₄×Dic₃	C₂³×C₃	1	2	yes	—
770	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
771	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
772	C₄×Dic₃	C₂³×C₃	1	2	yes	—
773	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
774	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
775	C₄×Dic₃	C₂³×C₃	1	2	yes	—
776	C₄×Dic₃	C₂³×C₃	1	2	yes	—
777	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
778	C₂²×C₃²	—	2	1	no	—
779	C₂²×C₃²	—	2	1	no	—
780	C₂²×C₃²	—	2	1	no	—
781	C₂²×C₃²	—	2	1	no	—
782	C₂²×C₃²	—	2	1	no	—
783	C₂²×C₃²	2₋¹⁺⁴	1	2	yes	—
784	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
785	C₂×C₃×D₃	—	2	1	no	—
786	C₂×C₃×D₃	—	2	1	no	—
787	C₂×C₃×D₃	—	2	1	no	—
788	C₃²×C₄	—	2	1	no	—
789	C₃²×C₄	—	2	1	no	—
790	C₃²×C₄	—	2	2	no	—
791	C₃²×C₄	—	2	2	no	—
792	C₃²×C₄	—	2	1	no	—
793	C₃²×C₄	—	2	2	no	—
794	C₃²×C₄	—	2	2	no	—
795	C₃²×C₄	—	2	1	no	—
796	C₃²×C₄	C₂×#41	1	2	yes	—
797	C₃×Dic₃	—	2	1	no	—
798	C₃×Dic₃	—	2	2	no	—
799	C₃×Dic₃	—	2	2	no	—
800	C₃×Dic₃	—	2	2	no	—
801	C₃×Dic₃	—	2	1	no	—
802	C₃×Dic₃	—	2	1	no	—
803	C₃×Dic₃	—	2	1	no	—
804	C₃×Dic₃	—	2	1	no	—
805	C₃×Dic₃	—	2	1	no	—
806	C₃×Dic₃	C₂×#41	1	4	yes	—
807	C₃×Dic₃	2₋¹⁺⁴	1	2	yes	—
808	C₂²×Q₈	—	3	1	no	—
809	C₂²×Q₈	—	3	1	no	—
810	C₂²×Q₈	—	3	1	no	—
811	C₄⋊Q₈	—	3	1	no	—
812	C₄⋊Q₈	—	3	1	no	—
813	C₄⋊Q₈	—	3	2	no	—
814	C₄⋊Q₈	—	3	2	no	—
815	C₄⋊Q₈	—	3	1	no	—
816	C₄⋊Q₈	—	3	2	no	—
817	C₄⋊Q₈	—	3	2	no	—
818	C₄⋊Q₈	—	3	1	no	—
819	#126	—	3	2	no	—
820	#126	—	3	1	no	—
821	#126	—	3	2	no	—
822	#126	—	3	2	no	—
823	#126	—	3	1	no	—
824	#126	—	3	2	no	—
825	#126	—	3	2	no	—
826	#126	—	3	2	no	—
827	#126	—	3	2	no	—
828	#126	C₂×C₃×D₃	1	2	yes	—
829	#125	—	3	1	no	—
830	#125	—	3	2	no	—
831	#125	—	3	2	no	—
832	#125	—	3	2	no	—
833	#125	—	3	2	no	—
834	#125	—	3	2	no	—
835	#125	—	3	2	no	—
836	#125	—	3	2	no	—
837	#125	—	3	2	no	—
838	#125	—	3	2	no	—
839	#125	—	3	2	no	—
840	#125	—	3	1	no	—
841	#125	—	3	2	no	—
842	#125	C₂×C₃×D₃	1	1	yes	characteristic
843	#125	C₂×C₃×D₃	1	2	yes	—
844	#124	—	3	1	no	—
845	#124	—	3	2	no	—
846	#123	—	3	1	no	—
847	#123	—	3	2	no	—
848	#123	—	3	1	no	—
849	#123	C₂×C₃×D₃	1	2	yes	—
850	C₂²⋊Q₈	—	3	1	no	—
851	C₂²⋊Q₈	—	3	1	no	—
852	C₂²⋊Q₈	—	3	2	no	—
853	C₂²⋊Q₈	—	3	1	no	—
854	C₂²⋊Q₈	—	3	2	no	—
855	C₂²⋊Q₈	—	3	1	no	—
856	C₂²⋊Q₈	—	3	2	no	—
857	C₂²⋊Q₈	—	3	1	no	—
858	C₂²⋊Q₈	—	3	2	no	—
859	C₂²⋊Q₈	—	3	2	no	—
860	C₂²⋊Q₈	—	3	2	no	—
861	C₂²⋊Q₈	—	3	2	no	—
862	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
864	#121	—	3	1	no	—
865	C₄×Q₈	—	3	1	no	—
866	C₄×Q₈	—	3	1	no	—
867	C₄×Q₈	—	3	2	no	—
868	C₄×Q₈	—	3	1	no	—
869	C₄×Q₈	—	3	1	no	—
870	C₄×Q₈	—	3	2	no	—
871	C₄×Q₈	—	3	1	no	—
872	C₄×Q₈	—	3	1	no	—
873	C₄×Q₈	—	3	1	no	—
874	C₄×Q₈	—	3	2	no	—
875	C₄×Q₈	—	3	1	no	—
876	C₄×Q₈	—	3	2	no	—
877	C₄×Q₈	—	3	2	no	—
878	C₄×Q₈	—	3	2	no	—
879	C₄×Q₈	—	3	2	no	—
880	C₄×Q₈	—	3	1	no	—
881	C₄×Q₈	—	3	2	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	2	no	—
884	C₄×Q₈	—	3	2	no	—
885	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
886	C₄×D₄	—	3	2	no	—
887	C₄×D₄	—	3	1	no	—
888	C₄×D₄	—	3	1	no	—
889	C₄×D₄	—	3	2	no	—
890	C₄×D₄	—	3	2	no	—
891	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
892	#117	—	3	1	no	—
893	#117	—	3	2	no	—
894	#117	—	3	2	no	—
895	#117	—	3	1	no	—
896	#117	—	3	2	no	—
897	#117	—	3	2	no	—
898	#117	—	3	2	no	—
899	#117	—	3	1	no	—
900	#117	—	3	2	no	—
901	#117	C₂×C₃×D₃	1	1	yes	characteristic
902	#117	C₂×C₃×D₃	1	2	yes	—
903	C₂×C₄⋊C₄	—	3	2	no	—
904	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
905	C₂×C₄²	—	3	1	no	—
906	C₂×C₄²	—	3	2	no	—
907	C₂³×C₃	—	2	1	no	—
908	C₂³×C₃	—	2	1	no	—
909	C₂³×C₃	—	3	1	no	—
910	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
911	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
912	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
913	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
914	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
915	C₃×Q₈	—	2	2	no	—
916	C₃×Q₈	—	2	2	no	—
917	C₃×Q₈	—	3	4	no	—
918	C₃×Q₈	—	4	2	no	—
919	C₃×Q₈	—	6	4	no	—
920	C₃×Q₈	—	6	2	no	—
921	C₃×Q₈	—	6	4	no	—
922	C₃×Q₈	—	6	4	no	—
923	C₃×Q₈	—	6	4	no	—
924	C₃×Q₈	—	6	2	no	—
925	C₃×Q₈	—	6	2	no	—
926	C₃×D₄	—	2	2	no	—
927	C₃×D₄	—	2	2	no	—
928	C₃×D₄	—	4	2	no	—
929	C₃×D₄	—	6	2	no	—
930	C₃×D₄	—	6	2	no	—
931	C₂×C₃×C₄	—	2	4	no	—
932	C₂×C₃×C₄	—	2	4	no	—
933	C₂×C₃×C₄	—	2	2	no	—
934	C₂×C₃×C₄	—	2	2	no	—
935	C₂×C₃×C₄	—	2	2	no	—
936	C₂×C₃×C₄	—	2	2	no	—
937	C₂×C₃×C₄	—	2	1	no	—
938	C₂×C₃×C₄	—	2	1	no	—
939	C₂×C₃×C₄	—	2	2	no	—
940	C₂×C₃×C₄	—	2	1	no	—
941	C₂×C₃×C₄	—	2	2	no	—
942	C₂×C₃×C₄	—	2	2	no	—
943	C₂×C₃×C₄	—	2	1	no	—
944	C₂×C₃×C₄	—	2	2	no	—
945	C₂×C₃×C₄	—	2	1	no	—
946	C₂×C₃×C₄	—	3	1	no	—
947	C₂×C₃×C₄	—	3	2	no	—
948	C₂×C₃×C₄	—	3	1	no	—
949	C₂×C₃×C₄	—	3	1	no	—
950	C₂×C₃×C₄	—	3	1	no	—
951	C₂×C₃×C₄	—	3	2	no	—
952	C₂×C₃×C₄	—	3	1	no	—
953	C₂×C₃×C₄	—	3	1	no	—
954	C₂×C₃×C₄	—	3	2	no	—
955	C₂×C₃×C₄	—	3	2	no	—
956	C₂×C₃×C₄	—	3	1	no	—
957	C₂×C₃×C₄	—	4	2	no	—
958	C₂×C₃×C₄	—	4	2	no	—
959	C₂×C₃×C₄	—	4	4	no	—
960	C₂×C₃×C₄	—	6	4	no	—
961	C₂×C₃×C₄	—	6	2	no	—
962	C₂×C₃×C₄	—	6	4	no	—
963	C₂×C₃×C₄	—	6	4	no	—
964	C₂×C₃×C₄	—	6	2	no	—
965	C₂×C₃×C₄	—	6	2	no	—
966	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
967	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
968	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
969	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
970	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
971	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
972	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
973	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
974	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
975	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
976	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
977	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
978	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
979	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
980	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
981	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
982	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
983	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
984	#67	—	2	2	no	—
985	#67	—	2	2	no	—
986	C₂×Dic₃	—	2	2	no	—
987	C₂×Dic₃	—	2	4	no	—
988	C₂×Dic₃	—	2	4	no	—
989	C₂×Dic₃	—	2	2	no	—
990	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
991	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
992	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
993	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
994	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
995	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
996	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
997	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
998	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
999	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1000	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1001	C₄×D₃	—	2	2	no	—
1002	C₄×D₃	—	2	4	no	—
1003	Dic₆	—	2	2	no	—
1004	Dic₆	—	2	2	no	—
1005	Dic₆	—	2	4	no	—
1006	Dic₆	—	2	4	no	—
1007	Dic₆	—	2	4	no	—
1008	Dic₆	—	2	2	no	—
1009	Dic₆	—	2	4	no	—
1010	Dic₆	C₃×#41	1	4	yes	—
1011	C₂×C₃²	—	2	2	no	—
1012	C₂×C₃²	—	4	1	no	—
1013	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1014	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1015	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1016	C₃×D₃	—	4	1	no	—
1017	C₂×Q₈	—	3	1	no	—
1018	C₂×Q₈	—	3	2	no	—
1019	C₂×Q₈	—	3	1	no	—
1020	C₂×Q₈	—	3	2	no	—
1021	C₂×Q₈	—	3	2	no	—
1022	C₂×Q₈	—	3	2	no	—
1023	C₂×Q₈	—	3	1	no	—
1024	C₂×Q₈	—	3	1	no	—
1025	C₂×Q₈	—	6	4	no	—
1026	C₂×Q₈	—	6	4	no	—
1027	C₂×Q₈	—	6	4	no	—
1028	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1029	C₂×D₄	—	3	1	no	—
1030	C₂×D₄	—	3	1	no	—
1031	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1032	C₂²×C₄	—	3	1	no	—
1033	C₂²×C₄	—	3	1	no	—
1034	C₂²×C₄	—	3	2	no	—
1035	C₂²×C₄	—	3	2	no	—
1036	C₂²×C₄	—	3	2	no	—
1037	C₂²×C₄	—	3	1	no	—
1038	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1039	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1040	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1041	C₄⋊C₄	—	3	2	no	—
1042	C₄⋊C₄	—	3	2	no	—
1043	C₄⋊C₄	—	3	2	no	—
1044	C₄⋊C₄	—	3	2	no	—
1045	C₄⋊C₄	—	3	2	no	—
1046	C₄⋊C₄	—	3	2	no	—
1047	C₄⋊C₄	—	3	1	no	—
1048	C₄⋊C₄	—	3	2	no	—
1049	C₄⋊C₄	—	3	1	no	—
1050	C₄⋊C₄	—	3	2	no	—
1051	C₄⋊C₄	—	3	1	no	—
1052	C₄⋊C₄	—	3	1	no	—
1053	C₄⋊C₄	—	3	2	no	—
1054	C₄⋊C₄	—	3	1	no	—
1055	C₄⋊C₄	—	3	2	no	—
1056	C₄⋊C₄	—	3	2	no	—
1057	C₄⋊C₄	—	3	2	no	—
1058	C₄⋊C₄	—	3	2	no	—
1059	C₄⋊C₄	—	3	2	no	—
1060	C₄⋊C₄	—	3	1	no	—
1061	C₄⋊C₄	—	3	1	no	—
1062	C₄⋊C₄	—	3	2	no	—
1063	C₄⋊C₄	—	3	2	no	—
1064	C₄⋊C₄	—	3	1	no	—
1065	C₄⋊C₄	—	3	2	no	—
1066	C₄⋊C₄	—	3	2	no	—
1067	C₄⋊C₄	—	3	2	no	—
1068	C₄⋊C₄	—	3	2	no	—
1069	C₄⋊C₄	—	3	2	no	—
1070	C₄⋊C₄	—	3	2	no	—
1071	C₄⋊C₄	—	3	1	no	—
1072	C₄⋊C₄	—	3	1	no	—
1073	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1075	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1076	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1077	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1079	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1080	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1082	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1083	C₂²⋊C₄	—	3	1	no	—
1084	C₂²⋊C₄	—	3	1	no	—
1085	C₂²⋊C₄	—	3	1	no	—
1086	C₂²⋊C₄	—	3	2	no	—
1087	C₂²⋊C₄	—	3	1	no	—
1088	C₂²⋊C₄	—	3	2	no	—
1089	C₂²⋊C₄	—	3	1	no	—
1090	C₂²⋊C₄	—	3	1	no	—
1091	C₂²⋊C₄	—	3	2	no	—
1092	C₂²⋊C₄	—	3	1	no	—
1093	C₂²⋊C₄	—	3	2	no	—
1094	C₂²⋊C₄	—	3	1	no	—
1095	C₂²⋊C₄	—	3	2	no	—
1096	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1097	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1098	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1099	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1100	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1101	C₄²	—	3	2	no	—
1102	C₄²	—	3	1	no	—
1103	C₄²	—	3	2	no	—
1104	C₄²	—	3	1	no	—
1105	C₄²	—	3	1	no	—
1106	C₄²	—	3	2	no	—
1107	C₄²	—	3	1	no	—
1108	C₄²	—	3	2	no	—
1109	C₄²	—	3	2	no	—
1110	C₄²	—	3	2	no	—
1111	C₄²	—	3	2	no	—
1112	C₄²	—	3	2	no	—
1113	C₄²	—	3	2	no	—
1114	C₄²	—	3	2	no	—
1115	C₄²	—	3	1	no	—
1116	C₄²	C₂²×C₃×D₃	1	2	yes	—
1117	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1118	C₄²	C₂²×C₃×D₃	1	2	yes	—
1119	C₂²×C₃	—	2	1	no	—
1120	C₂²×C₃	—	2	1	no	—
1121	C₂²×C₃	—	2	1	no	—
1122	C₂²×C₃	—	2	1	no	—
1123	C₂²×C₃	—	2	1	no	—
1124	C₂²×C₃	—	2	1	no	—
1125	C₂²×C₃	—	2	1	no	—
1126	C₂²×C₃	—	2	1	no	—
1127	C₂²×C₃	—	2	1	no	—
1128	C₂²×C₃	—	2	1	no	—
1129	C₂²×C₃	—	2	2	no	—
1130	C₂²×C₃	—	2	1	no	—
1131	C₂²×C₃	—	4	1	no	—
1132	C₂²×C₃	—	4	1	no	—
1133	C₂²×C₃	—	4	1	no	—
1134	C₂²×C₃	—	4	1	no	—
1135	C₂²×C₃	—	4	1	no	—
1136	C₂²×C₃	—	6	1	no	—
1137	C₂²×C₃	—	6	1	no	—
1138	C₂²×C₃	—	6	1	no	—
1139	C₂²×C₃	#1010	1	2	yes	—
1140	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
1141	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1142	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1143	C₂×D₃	—	2	1	no	—
1144	C₂×D₃	—	2	1	no	—
1145	C₂×D₃	—	2	1	no	—
1146	C₃×C₄	—	2	1	no	—
1147	C₃×C₄	—	2	1	no	—
1148	C₃×C₄	—	2	2	no	—
1149	C₃×C₄	—	2	2	no	—
1150	C₃×C₄	—	2	2	no	—
1151	C₃×C₄	—	2	1	no	—
1152	C₃×C₄	—	2	2	no	—
1153	C₃×C₄	—	2	1	no	—
1154	C₃×C₄	—	2	1	no	—
1155	C₃×C₄	—	2	1	no	—
1156	C₃×C₄	—	2	2	no	—
1157	C₃×C₄	—	2	2	no	—
1158	C₃×C₄	—	2	1	no	—
1159	C₃×C₄	—	2	2	no	—
1160	C₃×C₄	—	2	2	no	—
1161	C₃×C₄	—	2	1	no	—
1162	C₃×C₄	—	2	2	no	—
1163	C₃×C₄	—	3	4	no	—
1164	C₃×C₄	—	3	2	no	—
1165	C₃×C₄	—	4	1	no	—
1166	C₃×C₄	—	4	1	no	—
1167	C₃×C₄	—	4	2	no	—
1168	C₃×C₄	—	4	2	no	—
1169	C₃×C₄	—	4	1	no	—
1170	C₃×C₄	—	4	2	no	—
1171	C₃×C₄	—	4	1	no	—
1172	C₃×C₄	—	4	2	no	—
1173	C₃×C₄	—	6	2	no	—
1174	C₃×C₄	—	6	2	no	—
1175	C₃×C₄	—	6	1	no	—
1176	C₃×C₄	—	6	1	no	—
1177	C₃×C₄	—	6	1	no	—
1178	C₃×C₄	—	6	1	no	—
1179	C₃×C₄	—	6	1	no	—
1180	C₃×C₄	—	6	1	no	—
1181	C₃×C₄	—	6	2	no	—
1182	C₃×C₄	D₃×#41	1	2	yes	—
1183	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1184	Dic₃	—	2	1	no	—
1185	Dic₃	—	2	2	no	—
1186	Dic₃	—	2	2	no	—
1187	Dic₃	—	2	1	no	—
1188	Dic₃	—	2	2	no	—
1189	Dic₃	—	2	1	no	—
1190	Dic₃	—	2	1	no	—
1191	Dic₃	—	2	1	no	—
1192	Dic₃	—	2	1	no	—
1193	Dic₃	C₂×C₃×#41	1	4	yes	—
1194	Dic₃	C₃×2₋¹⁺⁴	1	2	yes	—
1195	C₃²	#3523	1	1	yes	characteristic, complemented, Sylow
1196	C₂³	—	3	1	no	—
1197	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1198	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1199	Q₈	—	2	2	no	—
1200	Q₈	—	3	4	no	—
1201	Q₈	—	6	4	no	—
1202	Q₈	—	6	4	no	—
1203	Q₈	—	6	4	no	—
1204	Q₈	—	6	4	no	—
1205	Q₈	—	6	2	no	—
1206	Q₈	—	6	2	no	—
1207	Q₈	—	6	2	no	—
1208	D₄	—	2	2	no	—
1209	D₄	—	6	2	no	—
1210	D₄	—	6	2	no	—
1211	C₂×C₄	—	2	4	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	3	1	no	—
1215	C₂×C₄	—	3	2	no	—
1216	C₂×C₄	—	3	1	no	—
1217	C₂×C₄	—	3	1	no	—
1218	C₂×C₄	—	3	1	no	—
1219	C₂×C₄	—	3	2	no	—
1220	C₂×C₄	—	3	1	no	—
1221	C₂×C₄	—	3	1	no	—
1222	C₂×C₄	—	3	2	no	—
1223	C₂×C₄	—	3	1	no	—
1224	C₂×C₄	—	3	2	no	—
1225	C₂×C₄	—	6	4	no	—
1226	C₂×C₄	—	6	4	no	—
1227	C₂×C₄	—	6	4	no	—
1228	C₂×C₄	—	6	2	no	—
1229	C₂×C₄	—	6	2	no	—
1230	C₂×C₄	—	6	2	no	—
1231	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1232	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1233	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1234	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1235	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1236	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1237	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1238	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1239	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1240	C₂×C₃	—	2	2	no	—
1241	C₂×C₃	—	2	2	no	—
1242	C₂×C₃	—	2	1	no	—
1243	C₂×C₃	—	2	1	no	—
1244	C₂×C₃	—	2	1	no	—
1245	C₂×C₃	—	4	2	no	—
1246	C₂×C₃	—	4	1	no	—
1247	C₂×C₃	—	4	1	no	—
1248	C₂×C₃	—	8	1	no	—
1249	C₂×C₃	—	12	1	no	—
1250	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1251	C₂×C₃	C₂×#1010	1	1	yes	characteristic
1252	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1253	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1254	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1255	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1256	D₃	—	4	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	6	1	no	—
1263	C₂²	—	6	1	no	—
1264	C₂²	—	6	1	no	—
1265	C₂²	C₃×#1010	1	2	yes	—
1266	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	3	4	no	—
1276	C₄	—	3	2	no	—
1277	C₄	—	6	2	no	—
1278	C₄	—	6	2	no	—
1279	C₄	—	6	1	no	—
1280	C₄	—	6	1	no	—
1281	C₄	—	6	1	no	—
1282	C₄	—	6	1	no	—
1283	C₄	—	6	1	no	—
1284	C₄	—	6	1	no	—
1285	C₄	—	6	2	no	—
1286	C₄	C₃×D₃×#41	1	2	yes	—
1287	C₃	—	2	1	no	—
1288	C₃	#86842	1	1	yes	characteristic, direct product factor
1289	C₃	C₃×#3523	1	1	yes	characteristic, complemented
1290	C₂	—	2	2	no	—
1291	C₂	—	4	1	no	—
1292	C₂	—	12	1	no	—
1293	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1294	C₂	C₂×C₃×#1010	1	1	yes	characteristic
1295	C₂	C₃×D₃×2₋¹⁺⁴	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×#552	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₃×#939	C₂²
hypercenter	C₃×#552	D₃
hypocenter	C₃	C₃×#3523
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#552

Complements

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

N	H ≅ G/N	type
1. C₃²×#552	C₂	semidirect
2. C₃×#5702	C₂	semidirect
3. C₃×#5701	C₂	semidirect
4. C₃×#5698	C₂	semidirect
5. C₃×#5696	C₂	semidirect
6. C₃×#5685	C₂	semidirect
7. C₃×#5685	C₂	semidirect
8. C₃×#5650	C₂	semidirect
10. C₃×#5632	C₂	semidirect
11. C₃×#5632	C₂	semidirect
12. C₃×#5625	C₂	semidirect
13. C₃×#5622	C₂	semidirect
14. C₃×#5572	C₂	semidirect
15. C₃×#5567	C₂	semidirect
17. C₃×D₄×Dic₆	C₂	semidirect
18. C₃×#5533	C₂	semidirect
19. C₃×#5531	C₂	semidirect
20. C₃×#5517	C₂	semidirect
21. C₃×#5516	C₂	semidirect
22. C₃×#5513	C₂	semidirect
23. C₂×C₃×#887	C₂	semidirect
25. #86842	C₃	direct (N × H)
134. C₃×#552	D₃	semidirect
135. C₃×#552	C₂×C₃	semidirect
150. #5702	C₂×C₃	semidirect
151. #5701	C₂×C₃	semidirect
152. #5698	C₂×C₃	semidirect
153. #5696	C₂×C₃	semidirect
154. #5685	C₂×C₃	semidirect
155. #5685	C₂×C₃	semidirect
156. #5650	C₂×C₃	semidirect
158. #5632	C₂×C₃	semidirect
159. #5632	C₂×C₃	semidirect
160. #5625	C₂×C₃	semidirect
161. #5622	C₂×C₃	semidirect
162. #5572	C₂×C₃	semidirect
163. #5567	C₂×C₃	semidirect
165. D₄×Dic₆	C₂×C₃	semidirect
166. #5533	C₂×C₃	semidirect
167. #5531	C₂×C₃	semidirect
168. #5517	C₂×C₃	semidirect
169. #5516	C₂×C₃	semidirect
170. #5513	C₂×C₃	semidirect
171. C₂×#887	C₂×C₃	semidirect
536. #552	C₃×D₃	semidirect
1195. C₃²	#3523	semidirect
1288. C₃	#86842	direct (N × H)
1289. C₃	C₃×#3523	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#552	2
C₃×#5702	2
C₃×#5701	2
C₃×#5698	2
C₃×#5696	2
C₃×#5685	2
C₃×#5650	2
C₃×#5649	2
C₃×#5632	2
C₃×#5625	2
C₃×#5622	2
C₃×#5572	2
C₃×#5567	2
C₃×#5538	2
C₃×D₄×Dic₆	2
C₃×#5533	2
C₃×#5531	2
C₃×#5517	2
C₃×#5516	2
C₃×#5513	2
C₂×C₃×#887	2
C₃×#3523	3
#86842	3

Subgroups — C3×#86842 #11909850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86842 #11909850