Subgroups — C₃×#86558 #11909737

Order 1152.

2316 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5726	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5710	C₂	1	2	yes	maximal, complemented
5	C₃×#5706	C₂	1	2	yes	maximal, complemented
6	C₃×#5681	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5669	C₂	1	2	yes	maximal, complemented
9	C₃×#5668	C₂	1	2	yes	maximal, complemented
10	C₃×#5664	C₂	1	2	yes	maximal, complemented
11	C₃×#5655	C₂	1	2	yes	maximal, complemented
12	C₃×#5636	C₂	1	2	yes	maximal, complemented
13	C₃×#5635	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5633	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5631	C₂	1	2	yes	maximal, complemented
16	C₃×#5611	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5599	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5582	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5548	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#5546	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5528	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#5523	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3522	—	3	1	no	maximal
25	#86558	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×#239	C₂²	1	2	yes	—
27	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#237	C₂²	1	1	yes	characteristic
29	C₂×C₃×#237	C₂²	1	2	yes	—
30	C₂×C₃×#235	C₂²	1	1	yes	characteristic
31	C₂×C₃×#235	C₂²	1	2	yes	—
32	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃²×#126	C₂²	1	2	yes	—
34	C₃²×#124	C₂²	1	2	yes	—
35	C₃²×#124	C₂²	1	1	yes	characteristic
36	C₃²×#123	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃²×#121	C₂²	1	1	yes	characteristic
40	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
41	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₃²×#117	C₂²	1	1	yes	characteristic
43	C₃×#947	C₂²	1	1	yes	characteristic
44	C₃×#946	C₂²	1	1	yes	characteristic
45	C₃×#946	C₂²	1	2	yes	—
46	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
47	C₃×#944	C₂²	1	2	yes	—
48	C₃×#944	C₂²	1	2	yes	—
49	C₃×#940	C₂²	1	1	yes	characteristic
50	C₃×#940	C₂²	1	2	yes	—
51	C₃×#939	C₂²	1	2	yes	—
52	C₃×#938	C₂²	1	1	yes	characteristic
53	C₃×#935	C₂²	1	2	yes	—
54	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
55	C₃×C₄×#67	C₂²	1	1	yes	characteristic
56	C₃×C₄×#67	C₂²	1	1	yes	characteristic
57	C₃×C₄×#67	C₂²	1	2	yes	—
58	C₃×C₄×#67	C₂²	1	2	yes	—
59	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
60	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
61	C₃×#898	C₂²	1	1	yes	characteristic
62	C₃×#897	C₂²	1	2	yes	—
63	C₃×#896	C₂²	1	1	yes	characteristic
64	C₃×#896	C₂²	1	2	yes	—
65	C₃×#896	C₂²	1	2	yes	—
66	C₃×#895	C₂²	1	1	yes	characteristic
67	C₃×#895	C₂²	1	1	yes	characteristic
68	C₃×#894	C₂²	1	1	yes	characteristic
69	C₃×#894	C₂²	1	2	yes	—
70	C₃×#894	C₂²	1	2	yes	—
71	C₃×#894	C₂²	1	2	yes	—
72	C₃×#893	C₂²	1	2	yes	—
73	C₃×#892	C₂²	1	2	yes	—
74	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₃×#889	C₂²	1	1	yes	characteristic
79	C₃×#889	C₂²	1	2	yes	—
80	C₃×#888	C₂²	1	1	yes	characteristic
81	C₃×#888	C₂²	1	1	yes	characteristic
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	2	yes	—
86	C₃×#887	C₂²	1	2	yes	—
87	C₃×#886	C₂²	1	2	yes	—
88	C₃×#885	C₂²	1	1	yes	characteristic
89	C₃×#885	C₂²	1	2	yes	—
90	C₃×#885	C₂²	1	2	yes	—
91	C₃×#885	C₂²	1	2	yes	—
92	C₃×#885	C₂²	1	2	yes	—
93	C₃×#884	C₂²	1	1	yes	characteristic
94	C₃×#884	C₂²	1	2	yes	—
95	C₃×#884	C₂²	1	2	yes	—
96	C₃×#884	C₂²	1	2	yes	—
97	C₃×#884	C₂²	1	2	yes	—
98	C₃×#883	C₂²	1	1	yes	characteristic
99	C₃×#883	C₂²	1	2	yes	—
100	C₃×#883	C₂²	1	2	yes	—
101	C₃×#67⋊C₄	C₂²	1	2	yes	—
102	C₃×#67⋊C₄	C₂²	1	2	yes	—
103	C₃×#67⋊C₄	C₂²	1	2	yes	—
104	C₃×#67⋊C₄	C₂²	1	2	yes	—
105	C₃×#67⋊C₄	C₂²	1	2	yes	—
106	C₃×#67⋊C₄	C₂²	1	2	yes	—
107	C₃×#67⋊C₄	C₂²	1	2	yes	—
108	C₃×#879	C₂²	1	1	yes	characteristic
109	C₃×#878	C₂²	1	2	yes	—
110	C₃×#878	C₂²	1	2	yes	—
111	C₃×#878	C₂²	1	2	yes	—
112	C₃×#877	C₂²	1	2	yes	—
113	C₃×#876	C₂²	1	2	yes	—
114	C₃×#875	C₂²	1	2	yes	—
115	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
116	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
117	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
118	C₃×#872	C₂²	1	1	yes	characteristic
119	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₃×C₄²×D₃	C₂²	1	2	yes	—
121	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
122	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
123	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
124	C₃×C₄×Dic₆	C₂²	1	2	yes	—
125	C₃×#559	—	3	1	no	—
126	C₃×#559	—	3	2	no	—
127	C₃×Q₈²	—	3	1	no	—
128	C₃×#554	—	3	1	no	—
129	C₃×#554	—	3	2	no	—
130	C₃×#550	—	3	1	no	—
131	C₃×#548	—	3	1	no	—
132	C₃×#548	—	3	1	no	—
133	C₃×#547	—	3	1	no	—
134	C₃×#547	—	3	2	no	—
135	C₃×#547	—	3	2	no	—
136	C₃×#547	—	3	1	no	—
137	C₃×#542	—	2	1	no	—
138	C₃×#542	—	3	2	no	—
139	C₃×#542	—	3	2	no	—
140	C₃×#542	—	3	1	no	—
141	C₃×#542	D₃	1	1	yes	characteristic, complemented
142	C₃×#542	C₂×C₃	1	1	yes	characteristic, complemented
143	C₃×#532	—	3	2	no	—
144	C₃×#532	—	3	1	no	—
145	C₃×#529	—	3	2	no	—
146	C₃×#529	—	3	1	no	—
147	C₃×#520	—	3	1	no	—
148	C₃×#520	—	3	1	no	—
149	C₂×C₃×C₄×Q₈	—	3	1	no	—
150	#5726	C₂×C₃	1	1	yes	characteristic, complemented
151	#5722	C₂×C₃	1	1	yes	characteristic, complemented
152	#5710	C₂×C₃	1	2	yes	complemented
153	#5706	C₂×C₃	1	2	yes	complemented
154	#5681	C₂×C₃	1	1	yes	characteristic, complemented
155	#5677	C₂×C₃	1	1	yes	characteristic, complemented
156	#5669	C₂×C₃	1	2	yes	complemented
157	#5668	C₂×C₃	1	2	yes	complemented
158	#5664	C₂×C₃	1	2	yes	complemented
159	#5655	C₂×C₃	1	2	yes	complemented
160	#5636	C₂×C₃	1	2	yes	complemented
161	#5635	C₂×C₃	1	1	yes	characteristic, complemented
162	#5633	C₂×C₃	1	1	yes	characteristic, complemented
163	#5631	C₂×C₃	1	2	yes	complemented
164	#5611	C₂×C₃	1	1	yes	characteristic, complemented
165	#5599	C₂×C₃	1	1	yes	characteristic, complemented
166	#5582	C₂×C₃	1	1	yes	characteristic, complemented
167	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
168	#5548	C₂×C₃	1	1	yes	characteristic, complemented
169	#5546	C₂×C₃	1	1	yes	characteristic, complemented
170	#5528	C₂×C₃	1	1	yes	characteristic, complemented
171	#5523	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
173	C₂×C₃²×Q₈	C₂³	1	2	yes	—
174	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
175	C₂×C₃²×D₄	C₂³	1	2	yes	—
176	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	2	yes	—
178	C₂×C₃×#67	C₂³	1	2	yes	—
179	C₂×C₃×#67	C₂³	1	1	yes	characteristic
180	C₂×C₃×#67	C₂³	1	2	yes	—
181	C₂×C₃×#67	C₂³	1	2	yes	—
182	C₂×C₃×#67	C₂³	1	2	yes	—
183	C₂×C₃×#67	C₂³	1	1	yes	characteristic
184	C₂×C₃×#67	C₂³	1	2	yes	—
185	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
186	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
187	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
188	C₃×#239	—	4	4	no	—
189	C₃×D₃×Q₈	—	2	4	no	—
190	C₃×#237	—	2	4	no	—
191	C₃×#237	—	4	4	no	—
192	C₃×#235	—	2	4	no	—
193	C₃×#235	—	4	4	no	—
194	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
195	C₂×C₃×D₁₂	C₂³	1	2	yes	—
196	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
197	C₂×C₃×D₁₂	C₂³	1	2	yes	—
198	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
202	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
206	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
207	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
208	C₂×C₃×Dic₆	C₂³	1	2	yes	—
209	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
210	C₂×C₃×Dic₆	C₂³	1	2	yes	—
211	C₂×C₃×Dic₆	C₂³	1	2	yes	—
212	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
213	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
216	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
219	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃²×C₄²	C₂³	1	1	yes	characteristic
228	C₃²×C₄²	C₂³	1	1	yes	characteristic
229	C₃²×C₄²	C₂³	1	2	yes	—
230	C₃×#217	C₂³	1	2	yes	—
231	C₃×#217	C₂³	1	1	yes	characteristic
232	C₃×#217	C₂³	1	2	yes	—
233	C₃×#217	C₂³	1	1	yes	characteristic
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
236	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
243	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
244	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
245	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
246	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
247	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
248	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
249	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
250	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
251	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
252	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
253	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
256	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
263	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
264	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
265	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
266	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	2	yes	—
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	2	yes	—
273	C₃×C₄×Dic₃	C₂³	1	2	yes	—
274	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
275	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
276	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
277	#3522	—	3	1	no	Sylow
278	C₂×C₃×#41	—	3	2	no	—
279	C₂×C₃×#41	—	3	1	no	—
280	C₂×C₃×#41	—	3	2	no	—
281	C₂×C₃×#41	—	3	1	no	—
282	C₂×C₃×#41	—	3	2	no	—
283	C₂²×C₃×Q₈	—	3	1	no	—
284	C₂×#239	C₂²×C₃	1	2	yes	—
285	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
286	C₂×#237	C₂²×C₃	1	1	yes	characteristic
287	C₂×#237	C₂²×C₃	1	2	yes	—
288	C₂×#235	C₂²×C₃	1	1	yes	characteristic
289	C₂×#235	C₂²×C₃	1	2	yes	—
290	C₃×C₄⋊Q₈	—	2	1	no	—
291	C₃×C₄⋊Q₈	—	3	2	no	—
292	C₃×C₄⋊Q₈	—	3	2	no	—
293	C₃×C₄⋊Q₈	—	3	1	no	—
294	C₃×C₄⋊Q₈	—	3	2	no	—
295	C₃×C₄⋊Q₈	—	3	1	no	—
296	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
297	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₃×#127	—	3	2	no	—
299	C₃×#127	—	3	1	no	—
300	C₃×#126	—	2	2	no	—
301	C₃×#126	—	3	1	no	—
302	C₃×#126	—	3	1	no	—
303	C₃×#126	—	3	2	no	—
304	C₃×#126	C₂×D₃	1	2	yes	—
305	C₃×#126	C₂²×C₃	1	2	yes	—
306	C₃×#125	—	3	2	no	—
307	C₃×#125	—	3	1	no	—
308	C₃×#124	—	2	2	no	—
309	C₃×#124	—	2	1	no	—
310	C₃×#124	—	3	1	no	—
311	C₃×#124	—	3	2	no	—
312	C₃×#124	—	3	1	no	—
313	C₃×#124	—	3	2	no	—
314	C₃×#124	—	3	2	no	—
315	C₃×#124	—	3	2	no	—
316	C₃×#124	—	3	2	no	—
317	C₃×#124	C₂×D₃	1	1	yes	characteristic
318	C₃×#124	C₂×D₃	1	2	yes	—
319	C₃×#124	C₂²×C₃	1	2	yes	—
320	C₃×#124	C₂²×C₃	1	1	yes	characteristic
321	C₃×#123	—	2	2	no	—
322	C₃×#123	—	3	2	no	—
323	C₃×#123	—	3	2	no	—
324	C₃×#123	—	3	2	no	—
325	C₃×#123	—	3	2	no	—
326	C₃×#123	—	3	1	no	—
327	C₃×#123	—	3	2	no	—
328	C₃×#123	—	3	2	no	—
329	C₃×#123	—	3	2	no	—
330	C₃×#123	—	3	1	no	—
331	C₃×#123	C₂×D₃	1	2	yes	—
332	C₃×#123	C₂²×C₃	1	2	yes	—
333	C₃×C₂²⋊Q₈	—	2	2	no	—
334	C₃×C₂²⋊Q₈	—	2	1	no	—
335	C₃×C₂²⋊Q₈	—	3	2	no	—
336	C₃×C₂²⋊Q₈	—	3	1	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	—	3	2	no	—
343	C₃×C₂²⋊Q₈	—	3	2	no	—
344	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
345	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
346	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
347	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
348	C₃×#121	—	2	1	no	—
349	C₃×#121	—	3	1	no	—
350	C₃×#121	—	3	2	no	—
351	C₃×#121	—	3	1	no	—
352	C₃×#121	—	3	1	no	—
353	C₃×#121	—	3	2	no	—
354	C₃×#121	—	3	1	no	—
355	C₃×#121	—	3	2	no	—
356	C₃×#121	—	3	2	no	—
357	C₃×#121	—	3	2	no	—
358	C₃×#121	C₂×D₃	1	1	yes	characteristic
359	C₃×#121	C₂²×C₃	1	1	yes	characteristic
360	C₃×C₄×Q₈	—	2	1	no	—
361	C₃×C₄×Q₈	—	3	1	no	—
362	C₃×C₄×Q₈	—	3	2	no	—
363	C₃×C₄×Q₈	—	3	1	no	—
364	C₃×C₄×Q₈	—	3	1	no	—
365	C₃×C₄×Q₈	—	3	2	no	—
366	C₃×C₄×Q₈	—	3	1	no	—
367	C₃×C₄×Q₈	—	3	1	no	—
368	C₃×C₄×Q₈	—	3	1	no	—
369	C₃×C₄×Q₈	—	3	2	no	—
370	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
371	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
372	C₃×C₄×D₄	—	2	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	—	3	1	no	—
377	C₃×C₄×D₄	—	3	1	no	—
378	C₃×C₄×D₄	—	3	2	no	—
379	C₃×C₄×D₄	—	3	2	no	—
380	C₃×C₄×D₄	—	3	2	no	—
381	C₃×C₄×D₄	—	3	2	no	—
382	C₃×C₄×D₄	—	3	2	no	—
383	C₃×C₄×D₄	—	3	2	no	—
384	C₃×C₄×D₄	—	3	2	no	—
385	C₃×C₄×D₄	—	3	2	no	—
386	C₃×C₄×D₄	—	3	1	no	—
387	C₃×C₄×D₄	—	3	1	no	—
388	C₃×C₄×D₄	—	3	1	no	—
389	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
390	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
391	C₃×#117	—	2	1	no	—
392	C₃×#117	—	3	2	no	—
393	C₃×#117	—	3	2	no	—
394	C₃×#117	—	3	1	no	—
395	C₃×#117	C₂×D₃	1	1	yes	characteristic
396	C₃×#117	C₂²×C₃	1	1	yes	characteristic
397	C₂×C₃×C₄⋊C₄	—	3	2	no	—
398	C₂×C₃×C₄⋊C₄	—	3	1	no	—
399	C₂×C₃×C₄⋊C₄	—	3	2	no	—
400	C₂×C₃×C₄⋊C₄	—	3	1	no	—
401	C₂×C₃×C₄⋊C₄	—	3	2	no	—
402	C₂×C₃×C₄⋊C₄	—	3	1	no	—
403	C₂×C₃×C₄²	—	3	2	no	—
404	C₂×C₃×C₄²	—	3	1	no	—
405	#947	C₂²×C₃	1	1	yes	characteristic
406	#946	C₂²×C₃	1	1	yes	characteristic
407	#946	C₂²×C₃	1	2	yes	—
408	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
409	#944	C₂²×C₃	1	2	yes	—
410	#944	C₂²×C₃	1	2	yes	—
411	#940	C₂²×C₃	1	2	yes	—
412	#940	C₂²×C₃	1	1	yes	characteristic
413	#939	C₂²×C₃	1	2	yes	—
414	#938	C₂²×C₃	1	1	yes	characteristic
415	#935	C₂²×C₃	1	2	yes	—
416	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
417	C₄×#67	C₂²×C₃	1	1	yes	characteristic
418	C₄×#67	C₂²×C₃	1	1	yes	characteristic
419	C₄×#67	C₂²×C₃	1	2	yes	—
420	C₄×#67	C₂²×C₃	1	2	yes	—
421	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
422	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
423	#898	C₂²×C₃	1	1	yes	characteristic
424	#897	C₂²×C₃	1	2	yes	—
425	#896	C₂²×C₃	1	2	yes	—
426	#896	C₂²×C₃	1	2	yes	—
427	#896	C₂²×C₃	1	1	yes	characteristic
428	#895	C₂²×C₃	1	1	yes	characteristic
429	#895	C₂²×C₃	1	1	yes	characteristic
430	#894	C₂²×C₃	1	2	yes	—
431	#894	C₂²×C₃	1	2	yes	—
432	#894	C₂²×C₃	1	2	yes	—
433	#894	C₂²×C₃	1	1	yes	characteristic
434	#893	C₂²×C₃	1	2	yes	—
435	#892	C₂²×C₃	1	2	yes	—
436	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
437	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
438	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
439	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
440	#889	C₂²×C₃	1	2	yes	—
441	#889	C₂²×C₃	1	1	yes	characteristic
442	#888	C₂²×C₃	1	1	yes	characteristic
443	#888	C₂²×C₃	1	2	yes	—
444	#888	C₂²×C₃	1	1	yes	characteristic
445	#887	C₂²×C₃	1	1	yes	characteristic
446	#887	C₂²×C₃	1	2	yes	—
447	#887	C₂²×C₃	1	2	yes	—
448	#887	C₂²×C₃	1	1	yes	characteristic
449	#886	C₂²×C₃	1	2	yes	—
450	#885	C₂²×C₃	1	2	yes	—
451	#885	C₂²×C₃	1	1	yes	characteristic
452	#885	C₂²×C₃	1	2	yes	—
453	#885	C₂²×C₃	1	2	yes	—
454	#885	C₂²×C₃	1	2	yes	—
455	#884	C₂²×C₃	1	2	yes	—
456	#884	C₂²×C₃	1	1	yes	characteristic
457	#884	C₂²×C₃	1	2	yes	—
458	#884	C₂²×C₃	1	2	yes	—
459	#884	C₂²×C₃	1	2	yes	—
460	#883	C₂²×C₃	1	1	yes	characteristic
461	#883	C₂²×C₃	1	2	yes	—
462	#883	C₂²×C₃	1	2	yes	—
463	#67⋊C₄	C₂²×C₃	1	2	yes	—
464	#67⋊C₄	C₂²×C₃	1	2	yes	—
465	#67⋊C₄	C₂²×C₃	1	2	yes	—
466	#67⋊C₄	C₂²×C₃	1	2	yes	—
467	#67⋊C₄	C₂²×C₃	1	2	yes	—
468	#67⋊C₄	C₂²×C₃	1	2	yes	—
469	#67⋊C₄	C₂²×C₃	1	2	yes	—
470	#879	C₂²×C₃	1	1	yes	characteristic
471	#878	C₂²×C₃	1	2	yes	—
472	#878	C₂²×C₃	1	2	yes	—
473	#878	C₂²×C₃	1	2	yes	—
474	#877	C₂²×C₃	1	2	yes	—
475	#876	C₂²×C₃	1	2	yes	—
476	#875	C₂²×C₃	1	2	yes	—
477	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
478	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
479	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
480	#872	C₂²×C₃	1	1	yes	characteristic
481	C₄²×D₃	C₂²×C₃	1	2	yes	—
482	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
483	C₄×Dic₆	C₂²×C₃	1	2	yes	—
484	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
485	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
486	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
487	C₂³×C₃²	C₂⁴	1	2	yes	—
488	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
489	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
490	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
492	C₃²×Q₈	—	2	2	no	—
493	C₃²×Q₈	—	4	2	no	—
494	C₃²×D₄	—	2	2	no	—
495	C₃²×D₄	—	4	2	no	—
496	C₂×C₃²×C₄	—	2	2	no	—
497	C₂×C₃²×C₄	—	4	2	no	—
498	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
499	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
500	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
501	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
503	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₃×#67	—	2	4	no	—
508	C₃×#67	—	2	2	no	—
509	C₃×#67	—	2	4	no	—
510	C₃×#67	—	2	4	no	—
511	C₃×#67	—	2	4	no	—
512	C₃×#67	—	2	2	no	—
513	C₃×#67	—	4	2	no	—
514	C₂×C₃×Dic₃	—	2	4	no	—
515	C₂×C₃×Dic₃	—	4	2	no	—
516	C₂×C₃×Dic₃	—	4	2	no	—
517	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
518	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
519	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
520	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
521	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
522	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
525	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
526	C₃×D₁₂	—	2	4	no	—
527	C₃×D₁₂	—	2	2	no	—
528	C₃×D₁₂	—	2	2	no	—
529	C₃×D₁₂	—	4	2	no	—
530	C₃×C₄×D₃	—	2	2	no	—
531	C₃×C₄×D₃	—	2	4	no	—
532	C₃×C₄×D₃	—	2	2	no	—
533	C₃×C₄×D₃	—	2	2	no	—
534	C₃×C₄×D₃	—	2	4	no	—
535	C₃×C₄×D₃	—	2	4	no	—
536	C₃×C₄×D₃	—	2	2	no	—
537	C₃×C₄×D₃	—	4	2	no	—
538	C₃×C₄×D₃	—	4	2	no	—
539	C₃×C₄×D₃	—	4	2	no	—
540	C₃×Dic₆	—	2	4	no	—
541	C₃×Dic₆	—	2	2	no	—
542	C₃×Dic₆	—	4	2	no	—
543	C₃×Dic₆	—	4	2	no	—
544	C₃×Dic₆	#41	1	4	yes	complemented
545	#559	—	3	1	no	—
546	#559	—	3	2	no	—
547	Q₈²	—	3	1	no	—
548	#554	—	3	1	no	—
549	#554	—	3	2	no	—
550	#550	—	3	1	no	—
551	#548	—	3	1	no	—
552	#548	—	3	1	no	—
553	#547	—	3	1	no	—
554	#547	—	3	2	no	—
555	#547	—	3	2	no	—
556	#547	—	3	1	no	—
557	#542	—	3	2	no	—
558	#542	—	3	2	no	—
559	#542	—	3	1	no	—
560	#542	C₃×D₃	1	1	yes	characteristic, complemented
561	#532	—	3	2	no	—
562	#532	—	3	1	no	—
563	#529	—	3	2	no	—
564	#529	—	3	1	no	—
565	#520	—	3	1	no	—
566	#520	—	3	1	no	—
567	C₂×C₄×Q₈	—	3	1	no	—
568	C₃×#41	—	6	4	no	—
569	C₃×#41	—	6	4	no	—
570	C₃×#41	—	12	4	no	—
571	C₃×#41	—	12	4	no	—
572	C₃×#41	—	12	4	no	—
573	C₂×C₃×Q₈	—	2	1	no	—
574	C₂×C₃×Q₈	—	2	2	no	—
575	C₂×C₃×Q₈	—	3	1	no	—
576	C₂×C₃×Q₈	—	3	1	no	—
577	C₂×C₃×Q₈	—	3	2	no	—
578	C₂×C₃×Q₈	—	3	2	no	—
579	C₂×C₃×Q₈	—	3	2	no	—
580	C₂×C₃×Q₈	—	6	4	no	—
581	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
582	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
583	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
585	C₂×C₃×D₄	—	2	1	no	—
586	C₂×C₃×D₄	—	2	2	no	—
587	C₂×C₃×D₄	—	3	2	no	—
588	C₂×C₃×D₄	—	3	1	no	—
589	C₂×C₃×D₄	—	3	2	no	—
590	C₂×C₃×D₄	—	3	2	no	—
591	C₂×C₃×D₄	—	3	1	no	—
592	C₂×C₃×D₄	—	3	2	no	—
593	C₂×C₃×D₄	—	3	2	no	—
594	C₂×C₃×D₄	—	3	1	no	—
595	C₂×C₃×D₄	—	3	2	no	—
596	C₂×C₃×D₄	—	3	1	no	—
597	C₂×C₃×D₄	—	3	2	no	—
598	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
599	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
600	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
602	C₂²×C₃×C₄	—	2	1	no	—
603	C₂²×C₃×C₄	—	2	2	no	—
604	C₂²×C₃×C₄	—	3	2	no	—
605	C₂²×C₃×C₄	—	3	2	no	—
606	C₂²×C₃×C₄	—	3	2	no	—
607	C₂²×C₃×C₄	—	3	1	no	—
608	C₂²×C₃×C₄	—	3	2	no	—
609	C₂²×C₃×C₄	—	3	1	no	—
610	C₂²×C₃×C₄	—	3	2	no	—
611	C₂²×C₃×C₄	—	3	1	no	—
612	C₂²×C₃×C₄	—	3	2	no	—
613	C₂²×C₃×C₄	—	3	1	no	—
614	C₂²×C₃×C₄	—	3	2	no	—
615	C₂²×C₃×C₄	—	3	2	no	—
616	C₂²×C₃×C₄	—	3	2	no	—
617	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
618	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
619	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
621	C₂×#67	C₂³×C₃	1	1	yes	characteristic
622	C₂×#67	C₂³×C₃	1	2	yes	—
623	C₂×#67	C₂³×C₃	1	2	yes	—
624	C₂×#67	C₂³×C₃	1	2	yes	—
625	C₂×#67	C₂³×C₃	1	2	yes	—
626	C₂×#67	C₂³×C₃	1	1	yes	characteristic
627	C₂×#67	C₂³×C₃	1	2	yes	—
628	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
629	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
630	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
631	#239	—	4	4	no	—
632	D₃×Q₈	—	2	4	no	—
633	#237	—	2	4	no	—
634	#237	—	4	4	no	—
635	#235	—	2	4	no	—
636	#235	—	4	4	no	—
637	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
638	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
639	C₂×D₁₂	C₂³×C₃	1	2	yes	—
640	C₂×D₁₂	C₂³×C₃	1	2	yes	—
641	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
642	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
643	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
644	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
645	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
646	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
648	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
649	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
650	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
651	C₂×Dic₆	C₂³×C₃	1	2	yes	—
652	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
653	C₂×Dic₆	C₂³×C₃	1	2	yes	—
654	C₂×Dic₆	C₂³×C₃	1	2	yes	—
655	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
656	C₃×C₄⋊C₄	—	2	1	no	—
657	C₃×C₄⋊C₄	—	2	1	no	—
658	C₃×C₄⋊C₄	—	2	1	no	—
659	C₃×C₄⋊C₄	—	2	1	no	—
660	C₃×C₄⋊C₄	—	2	2	no	—
661	C₃×C₄⋊C₄	—	2	2	no	—
662	C₃×C₄⋊C₄	—	2	2	no	—
663	C₃×C₄⋊C₄	—	3	2	no	—
664	C₃×C₄⋊C₄	—	3	2	no	—
665	C₃×C₄⋊C₄	—	3	1	no	—
666	C₃×C₄⋊C₄	—	3	2	no	—
667	C₃×C₄⋊C₄	—	3	2	no	—
668	C₃×C₄⋊C₄	—	3	2	no	—
669	C₃×C₄⋊C₄	—	3	2	no	—
670	C₃×C₄⋊C₄	—	3	1	no	—
671	C₃×C₄⋊C₄	—	3	1	no	—
672	C₃×C₄⋊C₄	—	3	2	no	—
673	C₃×C₄⋊C₄	—	3	1	no	—
674	C₃×C₄⋊C₄	—	3	1	no	—
675	C₃×C₄⋊C₄	—	3	2	no	—
676	C₃×C₄⋊C₄	—	3	1	no	—
677	C₃×C₄⋊C₄	—	3	2	no	—
678	C₃×C₄⋊C₄	—	3	1	no	—
679	C₃×C₄⋊C₄	—	3	2	no	—
680	C₃×C₄⋊C₄	—	3	1	no	—
681	C₃×C₄⋊C₄	—	3	2	no	—
682	C₃×C₄⋊C₄	—	3	1	no	—
683	C₃×C₄⋊C₄	—	3	1	no	—
684	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
685	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
686	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
687	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
688	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
689	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
690	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
691	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
692	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
693	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
694	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
695	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
696	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
697	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
698	C₃×C₂²⋊C₄	—	2	1	no	—
699	C₃×C₂²⋊C₄	—	2	1	no	—
700	C₃×C₂²⋊C₄	—	2	2	no	—
701	C₃×C₂²⋊C₄	—	2	2	no	—
702	C₃×C₂²⋊C₄	—	2	2	no	—
703	C₃×C₂²⋊C₄	—	2	2	no	—
704	C₃×C₂²⋊C₄	—	2	2	no	—
705	C₃×C₂²⋊C₄	—	3	2	no	—
706	C₃×C₂²⋊C₄	—	3	1	no	—
707	C₃×C₂²⋊C₄	—	3	2	no	—
708	C₃×C₂²⋊C₄	—	3	1	no	—
709	C₃×C₂²⋊C₄	—	3	1	no	—
710	C₃×C₂²⋊C₄	—	3	2	no	—
711	C₃×C₂²⋊C₄	—	3	1	no	—
712	C₃×C₂²⋊C₄	—	3	2	no	—
713	C₃×C₂²⋊C₄	—	3	1	no	—
714	C₃×C₂²⋊C₄	—	3	1	no	—
715	C₃×C₂²⋊C₄	—	3	1	no	—
716	C₃×C₂²⋊C₄	—	3	2	no	—
717	C₃×C₂²⋊C₄	—	3	2	no	—
718	C₃×C₂²⋊C₄	—	3	2	no	—
719	C₃×C₂²⋊C₄	—	3	2	no	—
720	C₃×C₂²⋊C₄	—	3	2	no	—
721	C₃×C₂²⋊C₄	—	3	1	no	—
722	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
723	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
724	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
725	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
726	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
727	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
728	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
729	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
730	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
731	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
732	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
733	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
734	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
735	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
736	C₃×C₄²	—	2	1	no	—
737	C₃×C₄²	—	2	1	no	—
738	C₃×C₄²	—	2	2	no	—
739	C₃×C₄²	—	3	2	no	—
740	C₃×C₄²	—	3	1	no	—
741	C₃×C₄²	—	3	2	no	—
742	C₃×C₄²	—	3	2	no	—
743	C₃×C₄²	—	3	1	no	—
744	C₃×C₄²	—	3	1	no	—
745	C₃×C₄²	—	3	2	no	—
746	C₃×C₄²	—	3	2	no	—
747	C₃×C₄²	—	3	1	no	—
748	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
749	C₃×C₄²	C₂²×D₃	1	2	yes	—
750	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
751	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
752	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
753	C₃×C₄²	C₂³×C₃	1	2	yes	—
754	#217	C₂³×C₃	1	2	yes	—
755	#217	C₂³×C₃	1	1	yes	characteristic
756	#217	C₂³×C₃	1	2	yes	—
757	#217	C₂³×C₃	1	1	yes	characteristic
758	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
759	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
760	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
761	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
762	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
763	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
764	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
766	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
767	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
768	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
769	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
770	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
771	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
772	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
773	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
774	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
775	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
776	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
777	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
778	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
780	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
781	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
784	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
785	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
788	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
789	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
790	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
791	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
792	C₄×Dic₃	C₂³×C₃	1	2	yes	—
793	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
795	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₃	1	2	yes	—
797	C₄×Dic₃	C₂³×C₃	1	2	yes	—
798	C₄×Dic₃	C₂³×C₃	1	2	yes	—
799	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
800	C₄×Dic₃	C₂³×C₃	1	2	yes	—
801	C₂²×C₃²	—	2	2	no	—
802	C₂²×C₃²	—	2	1	no	—
803	C₂²×C₃²	—	2	1	no	—
804	C₂²×C₃²	—	2	2	no	—
805	C₂²×C₃²	—	2	2	no	—
806	C₂²×C₃²	—	2	1	no	—
807	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
808	C₂×C₃×D₃	—	2	1	no	—
809	C₂×C₃×D₃	—	2	1	no	—
810	C₂×C₃×D₃	—	2	2	no	—
811	C₂×C₃×D₃	—	2	1	no	—
812	C₂×C₃×D₃	—	2	1	no	—
813	C₂×C₃×D₃	—	2	2	no	—
814	C₂×C₃×D₃	—	2	2	no	—
815	C₂×C₃×D₃	—	2	1	no	—
816	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
817	C₃²×C₄	—	2	2	no	—
818	C₃²×C₄	—	2	1	no	—
819	C₃²×C₄	—	2	2	no	—
820	C₃²×C₄	—	2	2	no	—
821	C₃²×C₄	—	2	1	no	—
822	C₃²×C₄	—	2	1	no	—
823	C₃²×C₄	—	2	1	no	—
824	C₃²×C₄	—	2	1	no	—
825	C₃²×C₄	C₂×#41	1	2	yes	—
826	C₃×Dic₃	—	2	1	no	—
827	C₃×Dic₃	—	2	1	no	—
828	C₃×Dic₃	—	2	1	no	—
829	C₃×Dic₃	—	2	2	no	—
830	C₃×Dic₃	—	2	1	no	—
831	C₃×Dic₃	—	2	2	no	—
832	C₃×Dic₃	—	2	1	no	—
833	C₃×Dic₃	C₂×#41	1	4	yes	—
834	C₃×Dic₃	2₋¹⁺⁴	1	2	yes	—
835	C₂×#41	—	3	2	no	—
836	C₂×#41	—	3	1	no	—
837	C₂×#41	—	3	2	no	—
838	C₂×#41	—	3	1	no	—
839	C₂×#41	—	3	2	no	—
840	C₂²×Q₈	—	3	1	no	—
841	C₄⋊Q₈	—	3	2	no	—
842	C₄⋊Q₈	—	3	2	no	—
843	C₄⋊Q₈	—	3	1	no	—
844	C₄⋊Q₈	—	3	2	no	—
845	C₄⋊Q₈	—	3	1	no	—
846	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
847	#127	—	3	2	no	—
848	#127	—	3	1	no	—
849	#126	—	3	1	no	—
850	#126	—	3	1	no	—
851	#126	—	3	2	no	—
852	#126	C₂×C₃×D₃	1	2	yes	—
853	#125	—	3	2	no	—
854	#125	—	3	1	no	—
855	#124	—	3	1	no	—
856	#124	—	3	2	no	—
857	#124	—	3	1	no	—
858	#124	—	3	2	no	—
859	#124	—	3	2	no	—
860	#124	—	3	2	no	—
861	#124	—	3	2	no	—
862	#124	C₂×C₃×D₃	1	2	yes	—
863	#124	C₂×C₃×D₃	1	1	yes	characteristic
864	#123	—	3	2	no	—
865	#123	—	3	2	no	—
866	#123	—	3	1	no	—
867	#123	—	3	2	no	—
868	#123	—	3	2	no	—
869	#123	—	3	2	no	—
870	#123	—	3	1	no	—
871	#123	—	3	2	no	—
872	#123	—	3	2	no	—
873	#123	C₂×C₃×D₃	1	2	yes	—
874	C₂²⋊Q₈	—	3	2	no	—
875	C₂²⋊Q₈	—	3	1	no	—
876	C₂²⋊Q₈	—	3	1	no	—
877	C₂²⋊Q₈	—	3	2	no	—
878	C₂²⋊Q₈	—	3	2	no	—
879	C₂²⋊Q₈	—	3	2	no	—
880	C₂²⋊Q₈	—	3	2	no	—
881	C₂²⋊Q₈	—	3	2	no	—
882	C₂²⋊Q₈	—	3	2	no	—
883	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
884	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
885	#121	—	3	1	no	—
886	#121	—	3	2	no	—
887	#121	—	3	1	no	—
888	#121	—	3	1	no	—
889	#121	—	3	2	no	—
890	#121	—	3	1	no	—
891	#121	—	3	2	no	—
892	#121	—	3	2	no	—
893	#121	—	3	2	no	—
894	#121	C₂×C₃×D₃	1	1	yes	characteristic
895	C₄×Q₈	—	3	1	no	—
896	C₄×Q₈	—	3	1	no	—
897	C₄×Q₈	—	3	2	no	—
898	C₄×Q₈	—	3	1	no	—
899	C₄×Q₈	—	3	2	no	—
900	C₄×Q₈	—	3	1	no	—
901	C₄×Q₈	—	3	2	no	—
902	C₄×Q₈	—	3	1	no	—
903	C₄×Q₈	—	3	1	no	—
904	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
905	C₄×D₄	—	3	1	no	—
906	C₄×D₄	—	3	2	no	—
907	C₄×D₄	—	3	1	no	—
908	C₄×D₄	—	3	1	no	—
909	C₄×D₄	—	3	2	no	—
910	C₄×D₄	—	3	2	no	—
911	C₄×D₄	—	3	2	no	—
912	C₄×D₄	—	3	2	no	—
913	C₄×D₄	—	3	2	no	—
914	C₄×D₄	—	3	2	no	—
915	C₄×D₄	—	3	2	no	—
916	C₄×D₄	—	3	2	no	—
917	C₄×D₄	—	3	2	no	—
918	C₄×D₄	—	3	1	no	—
919	C₄×D₄	—	3	1	no	—
920	C₄×D₄	—	3	1	no	—
921	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
922	#117	—	3	2	no	—
923	#117	—	3	2	no	—
924	#117	—	3	1	no	—
925	#117	C₂×C₃×D₃	1	1	yes	characteristic
926	C₂×C₄⋊C₄	—	3	2	no	—
927	C₂×C₄⋊C₄	—	3	1	no	—
928	C₂×C₄⋊C₄	—	3	2	no	—
929	C₂×C₄⋊C₄	—	3	1	no	—
930	C₂×C₄⋊C₄	—	3	2	no	—
931	C₂×C₄⋊C₄	—	3	1	no	—
932	C₂×C₄²	—	3	2	no	—
933	C₂×C₄²	—	3	1	no	—
934	C₂³×C₃	—	2	1	no	—
935	C₂³×C₃	—	2	2	no	—
936	C₂³×C₃	—	3	1	no	—
937	C₂³×C₃	—	3	1	no	—
938	C₂³×C₃	—	3	2	no	—
939	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
940	C₂³×C₃	C₂³×D₃	1	2	yes	—
941	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
942	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
943	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
944	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
945	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
946	C₃×Q₈	—	2	2	no	—
947	C₃×Q₈	—	2	2	no	—
948	C₃×Q₈	—	3	4	no	—
949	C₃×Q₈	—	4	2	no	—
950	C₃×Q₈	—	4	2	no	—
951	C₃×Q₈	—	4	2	no	—
952	C₃×Q₈	—	6	2	no	—
953	C₃×Q₈	—	6	4	no	—
954	C₃×Q₈	—	8	2	no	—
955	C₃×Q₈	—	12	2	no	—
956	C₃×Q₈	—	12	2	no	—
957	C₃×D₄	—	2	2	no	—
958	C₃×D₄	—	2	2	no	—
959	C₃×D₄	—	4	2	no	—
960	C₃×D₄	—	4	2	no	—
961	C₃×D₄	—	4	2	no	—
962	C₃×D₄	—	6	4	no	—
963	C₃×D₄	—	6	2	no	—
964	C₃×D₄	—	6	4	no	—
965	C₃×D₄	—	6	2	no	—
966	C₃×D₄	—	6	4	no	—
967	C₃×D₄	—	6	4	no	—
968	C₃×D₄	—	6	4	no	—
969	C₃×D₄	—	6	2	no	—
970	C₃×D₄	—	6	2	no	—
971	C₃×D₄	—	8	2	no	—
972	C₃×D₄	—	12	2	no	—
973	C₃×D₄	—	12	2	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	2	1	no	—
977	C₂×C₃×C₄	—	2	1	no	—
978	C₂×C₃×C₄	—	2	1	no	—
979	C₂×C₃×C₄	—	2	2	no	—
980	C₂×C₃×C₄	—	2	1	no	—
981	C₂×C₃×C₄	—	2	1	no	—
982	C₂×C₃×C₄	—	2	2	no	—
983	C₂×C₃×C₄	—	2	1	no	—
984	C₂×C₃×C₄	—	2	2	no	—
985	C₂×C₃×C₄	—	3	1	no	—
986	C₂×C₃×C₄	—	3	2	no	—
987	C₂×C₃×C₄	—	3	1	no	—
988	C₂×C₃×C₄	—	3	1	no	—
989	C₂×C₃×C₄	—	3	2	no	—
990	C₂×C₃×C₄	—	3	1	no	—
991	C₂×C₃×C₄	—	3	1	no	—
992	C₂×C₃×C₄	—	3	2	no	—
993	C₂×C₃×C₄	—	3	1	no	—
994	C₂×C₃×C₄	—	4	2	no	—
995	C₂×C₃×C₄	—	4	2	no	—
996	C₂×C₃×C₄	—	4	2	no	—
997	C₂×C₃×C₄	—	6	2	no	—
998	C₂×C₃×C₄	—	6	4	no	—
999	C₂×C₃×C₄	—	6	4	no	—
1000	C₂×C₃×C₄	—	6	2	no	—
1001	C₂×C₃×C₄	—	6	4	no	—
1002	C₂×C₃×C₄	—	6	4	no	—
1003	C₂×C₃×C₄	—	6	2	no	—
1004	C₂×C₃×C₄	—	6	2	no	—
1005	C₂×C₃×C₄	—	8	2	no	—
1006	C₂×C₃×C₄	—	12	2	no	—
1007	C₂×C₃×C₄	—	12	2	no	—
1008	C₂×C₃×C₄	—	12	2	no	—
1009	C₂×C₃×C₄	—	12	2	no	—
1010	C₂×C₃×C₄	—	12	2	no	—
1011	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1012	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1013	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1014	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1016	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1017	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1019	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1020	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1021	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1022	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1023	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1024	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1025	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1026	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1027	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1028	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1029	#67	—	2	4	no	—
1030	#67	—	2	2	no	—
1031	#67	—	2	4	no	—
1032	#67	—	2	4	no	—
1033	#67	—	2	2	no	—
1034	#67	—	2	4	no	—
1035	#67	—	4	2	no	—
1036	C₂×Dic₃	—	2	4	no	—
1037	C₂×Dic₃	—	4	2	no	—
1038	C₂×Dic₃	—	4	2	no	—
1039	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1040	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1041	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1042	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1043	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1044	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1045	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1046	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1047	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1048	D₁₂	—	2	4	no	—
1049	D₁₂	—	2	2	no	—
1050	D₁₂	—	2	2	no	—
1051	D₁₂	—	4	2	no	—
1052	C₄×D₃	—	2	2	no	—
1053	C₄×D₃	—	2	4	no	—
1054	C₄×D₃	—	2	2	no	—
1055	C₄×D₃	—	2	2	no	—
1056	C₄×D₃	—	2	4	no	—
1057	C₄×D₃	—	2	4	no	—
1058	C₄×D₃	—	2	2	no	—
1059	C₄×D₃	—	4	2	no	—
1060	C₄×D₃	—	4	2	no	—
1061	C₄×D₃	—	4	2	no	—
1062	Dic₆	—	2	4	no	—
1063	Dic₆	—	2	2	no	—
1064	Dic₆	—	4	2	no	—
1065	Dic₆	—	4	2	no	—
1066	Dic₆	C₃×#41	1	4	yes	complemented
1067	C₂×C₃²	—	4	2	no	—
1068	C₂×C₃²	—	4	1	no	—
1069	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1070	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1071	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1072	C₃×D₃	—	2	2	no	—
1073	C₃×D₃	—	4	2	no	—
1074	C₃×D₃	—	4	1	no	—
1075	#41	—	6	4	no	—
1076	#41	—	6	4	no	—
1077	#41	—	12	4	no	—
1078	#41	—	12	4	no	—
1079	#41	—	12	4	no	—
1080	C₂×Q₈	—	3	1	no	—
1081	C₂×Q₈	—	3	1	no	—
1082	C₂×Q₈	—	3	2	no	—
1083	C₂×Q₈	—	3	2	no	—
1084	C₂×Q₈	—	3	2	no	—
1085	C₂×Q₈	—	6	4	no	—
1086	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1087	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
1088	C₂×D₄	—	3	1	no	—
1089	C₂×D₄	—	3	2	no	—
1090	C₂×D₄	—	3	2	no	—
1091	C₂×D₄	—	3	2	no	—
1092	C₂×D₄	—	3	1	no	—
1093	C₂×D₄	—	3	2	no	—
1094	C₂×D₄	—	3	2	no	—
1095	C₂×D₄	—	3	1	no	—
1096	C₂×D₄	—	3	2	no	—
1097	C₂×D₄	—	3	1	no	—
1098	C₂×D₄	—	3	2	no	—
1099	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1100	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1101	C₂²×C₄	—	3	2	no	—
1102	C₂²×C₄	—	3	2	no	—
1103	C₂²×C₄	—	3	2	no	—
1104	C₂²×C₄	—	3	1	no	—
1105	C₂²×C₄	—	3	2	no	—
1106	C₂²×C₄	—	3	1	no	—
1107	C₂²×C₄	—	3	2	no	—
1108	C₂²×C₄	—	3	1	no	—
1109	C₂²×C₄	—	3	2	no	—
1110	C₂²×C₄	—	3	1	no	—
1111	C₂²×C₄	—	3	2	no	—
1112	C₂²×C₄	—	3	2	no	—
1113	C₂²×C₄	—	3	2	no	—
1114	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1115	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1116	C₄⋊C₄	—	3	2	no	—
1117	C₄⋊C₄	—	3	1	no	—
1118	C₄⋊C₄	—	3	2	no	—
1119	C₄⋊C₄	—	3	1	no	—
1120	C₄⋊C₄	—	3	2	no	—
1121	C₄⋊C₄	—	3	2	no	—
1122	C₄⋊C₄	—	3	2	no	—
1123	C₄⋊C₄	—	3	1	no	—
1124	C₄⋊C₄	—	3	2	no	—
1125	C₄⋊C₄	—	3	2	no	—
1126	C₄⋊C₄	—	3	2	no	—
1127	C₄⋊C₄	—	3	1	no	—
1128	C₄⋊C₄	—	3	1	no	—
1129	C₄⋊C₄	—	3	2	no	—
1130	C₄⋊C₄	—	3	1	no	—
1131	C₄⋊C₄	—	3	1	no	—
1132	C₄⋊C₄	—	3	2	no	—
1133	C₄⋊C₄	—	3	1	no	—
1134	C₄⋊C₄	—	3	1	no	—
1135	C₄⋊C₄	—	3	2	no	—
1136	C₄⋊C₄	—	3	1	no	—
1137	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1138	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1139	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1140	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1141	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1142	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1143	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1144	C₂²⋊C₄	—	3	2	no	—
1145	C₂²⋊C₄	—	3	1	no	—
1146	C₂²⋊C₄	—	3	2	no	—
1147	C₂²⋊C₄	—	3	1	no	—
1148	C₂²⋊C₄	—	3	2	no	—
1149	C₂²⋊C₄	—	3	1	no	—
1150	C₂²⋊C₄	—	3	1	no	—
1151	C₂²⋊C₄	—	3	2	no	—
1152	C₂²⋊C₄	—	3	1	no	—
1153	C₂²⋊C₄	—	3	1	no	—
1154	C₂²⋊C₄	—	3	1	no	—
1155	C₂²⋊C₄	—	3	2	no	—
1156	C₂²⋊C₄	—	3	2	no	—
1157	C₂²⋊C₄	—	3	2	no	—
1158	C₂²⋊C₄	—	3	2	no	—
1159	C₂²⋊C₄	—	3	2	no	—
1160	C₂²⋊C₄	—	3	1	no	—
1161	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1162	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1163	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1164	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1165	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1166	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1167	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1168	C₄²	—	3	2	no	—
1169	C₄²	—	3	1	no	—
1170	C₄²	—	3	2	no	—
1171	C₄²	—	3	2	no	—
1172	C₄²	—	3	1	no	—
1173	C₄²	—	3	1	no	—
1174	C₄²	—	3	2	no	—
1175	C₄²	—	3	2	no	—
1176	C₄²	—	3	1	no	—
1177	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1178	C₄²	C₂²×C₃×D₃	1	2	yes	—
1179	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1180	C₂²×C₃	—	2	1	no	—
1181	C₂²×C₃	—	2	2	no	—
1182	C₂²×C₃	—	2	2	no	—
1183	C₂²×C₃	—	2	1	no	—
1184	C₂²×C₃	—	2	1	no	—
1185	C₂²×C₃	—	2	2	no	—
1186	C₂²×C₃	—	2	2	no	—
1187	C₂²×C₃	—	2	1	no	—
1188	C₂²×C₃	—	2	1	no	—
1189	C₂²×C₃	—	2	2	no	—
1190	C₂²×C₃	—	2	2	no	—
1191	C₂²×C₃	—	2	1	no	—
1192	C₂²×C₃	—	2	1	no	—
1193	C₂²×C₃	—	3	2	no	—
1194	C₂²×C₃	—	4	1	no	—
1195	C₂²×C₃	—	4	2	no	—
1196	C₂²×C₃	—	4	2	no	—
1197	C₂²×C₃	—	4	1	no	—
1198	C₂²×C₃	—	4	1	no	—
1199	C₂²×C₃	—	4	2	no	—
1200	C₂²×C₃	—	6	1	no	—
1201	C₂²×C₃	—	6	1	no	—
1202	C₂²×C₃	—	6	2	no	—
1203	C₂²×C₃	—	6	1	no	—
1204	C₂²×C₃	—	6	1	no	—
1205	C₂²×C₃	—	6	2	no	—
1206	C₂²×C₃	—	6	1	no	—
1207	C₂²×C₃	—	6	2	no	—
1208	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1209	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1210	C₂×D₃	—	2	1	no	—
1211	C₂×D₃	—	2	1	no	—
1212	C₂×D₃	—	2	2	no	—
1213	C₂×D₃	—	2	1	no	—
1214	C₂×D₃	—	2	1	no	—
1215	C₂×D₃	—	2	2	no	—
1216	C₂×D₃	—	2	2	no	—
1217	C₂×D₃	—	2	1	no	—
1218	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
1219	C₃×C₄	—	2	1	no	—
1220	C₃×C₄	—	2	2	no	—
1221	C₃×C₄	—	2	1	no	—
1222	C₃×C₄	—	2	2	no	—
1223	C₃×C₄	—	2	2	no	—
1224	C₃×C₄	—	2	1	no	—
1225	C₃×C₄	—	2	1	no	—
1226	C₃×C₄	—	2	1	no	—
1227	C₃×C₄	—	2	2	no	—
1228	C₃×C₄	—	2	1	no	—
1229	C₃×C₄	—	2	2	no	—
1230	C₃×C₄	—	2	2	no	—
1231	C₃×C₄	—	2	1	no	—
1232	C₃×C₄	—	2	1	no	—
1233	C₃×C₄	—	2	1	no	—
1234	C₃×C₄	—	2	1	no	—
1235	C₃×C₄	—	2	2	no	—
1236	C₃×C₄	—	3	4	no	—
1237	C₃×C₄	—	3	2	no	—
1238	C₃×C₄	—	4	1	no	—
1239	C₃×C₄	—	4	1	no	—
1240	C₃×C₄	—	4	2	no	—
1241	C₃×C₄	—	4	2	no	—
1242	C₃×C₄	—	4	2	no	—
1243	C₃×C₄	—	4	1	no	—
1244	C₃×C₄	—	4	1	no	—
1245	C₃×C₄	—	4	1	no	—
1246	C₃×C₄	—	6	1	no	—
1247	C₃×C₄	—	6	1	no	—
1248	C₃×C₄	—	6	2	no	—
1249	C₃×C₄	—	6	1	no	—
1250	C₃×C₄	—	6	2	no	—
1251	C₃×C₄	—	6	1	no	—
1252	C₃×C₄	—	6	1	no	—
1253	C₃×C₄	D₃×#41	1	2	yes	—
1254	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1255	Dic₃	—	2	1	no	—
1256	Dic₃	—	2	1	no	—
1257	Dic₃	—	2	1	no	—
1258	Dic₃	—	2	2	no	—
1259	Dic₃	—	2	1	no	—
1260	Dic₃	—	2	2	no	—
1261	Dic₃	—	2	1	no	—
1262	Dic₃	C₂×C₃×#41	1	4	yes	—
1263	Dic₃	C₃×2₋¹⁺⁴	1	2	yes	—
1264	C₃²	#3522	1	1	yes	characteristic, complemented, Sylow
1265	C₂³	—	3	1	no	—
1266	C₂³	—	3	1	no	—
1267	C₂³	—	3	2	no	—
1268	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1269	C₂³	C₂³×C₃×D₃	1	2	yes	—
1270	Q₈	—	2	2	no	—
1271	Q₈	—	3	4	no	—
1272	Q₈	—	4	2	no	—
1273	Q₈	—	6	4	no	—
1274	Q₈	—	6	2	no	—
1275	Q₈	—	12	2	no	—
1276	Q₈	—	12	2	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	4	2	no	—
1279	D₄	—	6	4	no	—
1280	D₄	—	6	2	no	—
1281	D₄	—	6	4	no	—
1282	D₄	—	6	4	no	—
1283	D₄	—	6	2	no	—
1284	D₄	—	6	4	no	—
1285	D₄	—	6	4	no	—
1286	D₄	—	6	2	no	—
1287	D₄	—	6	2	no	—
1288	D₄	—	12	2	no	—
1289	D₄	—	12	2	no	—
1290	C₂×C₄	—	2	2	no	—
1291	C₂×C₄	—	3	1	no	—
1292	C₂×C₄	—	3	2	no	—
1293	C₂×C₄	—	3	1	no	—
1294	C₂×C₄	—	3	1	no	—
1295	C₂×C₄	—	3	2	no	—
1296	C₂×C₄	—	3	1	no	—
1297	C₂×C₄	—	3	2	no	—
1298	C₂×C₄	—	3	1	no	—
1299	C₂×C₄	—	3	1	no	—
1300	C₂×C₄	—	4	2	no	—
1301	C₂×C₄	—	6	4	no	—
1302	C₂×C₄	—	6	4	no	—
1303	C₂×C₄	—	6	2	no	—
1304	C₂×C₄	—	6	2	no	—
1305	C₂×C₄	—	6	4	no	—
1306	C₂×C₄	—	6	4	no	—
1307	C₂×C₄	—	6	2	no	—
1308	C₂×C₄	—	6	2	no	—
1309	C₂×C₄	—	12	2	no	—
1310	C₂×C₄	—	12	2	no	—
1311	C₂×C₄	—	12	2	no	—
1312	C₂×C₄	—	12	2	no	—
1313	C₂×C₄	—	12	2	no	—
1314	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1315	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1316	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1317	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1318	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1319	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1320	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1321	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1322	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1323	C₂×C₃	—	2	1	no	—
1324	C₂×C₃	—	2	1	no	—
1325	C₂×C₃	—	2	1	no	—
1326	C₂×C₃	—	4	1	no	—
1327	C₂×C₃	—	4	2	no	—
1328	C₂×C₃	—	4	2	no	—
1329	C₂×C₃	—	4	1	no	—
1330	C₂×C₃	—	6	2	no	—
1331	C₂×C₃	—	8	1	no	—
1332	C₂×C₃	—	8	2	no	—
1333	C₂×C₃	—	12	2	no	—
1334	C₂×C₃	—	12	1	no	—
1335	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1336	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1337	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1338	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1339	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1340	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1341	D₃	—	2	2	no	—
1342	D₃	—	4	2	no	—
1343	D₃	—	4	1	no	—
1344	C₂²	—	2	1	no	—
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	2	1	no	—
1348	C₂²	—	2	1	no	—
1349	C₂²	—	2	2	no	—
1350	C₂²	—	3	2	no	—
1351	C₂²	—	6	1	no	—
1352	C₂²	—	6	1	no	—
1353	C₂²	—	6	2	no	—
1354	C₂²	—	6	1	no	—
1355	C₂²	—	6	1	no	—
1356	C₂²	—	6	2	no	—
1357	C₂²	—	6	1	no	—
1358	C₂²	—	6	2	no	—
1359	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1360	C₄	—	2	1	no	—
1361	C₄	—	2	2	no	—
1362	C₄	—	2	1	no	—
1363	C₄	—	2	2	no	—
1364	C₄	—	2	2	no	—
1365	C₄	—	2	1	no	—
1366	C₄	—	2	1	no	—
1367	C₄	—	2	1	no	—
1368	C₄	—	3	4	no	—
1369	C₄	—	3	2	no	—
1370	C₄	—	6	1	no	—
1371	C₄	—	6	1	no	—
1372	C₄	—	6	2	no	—
1373	C₄	—	6	1	no	—
1374	C₄	—	6	2	no	—
1375	C₄	—	6	1	no	—
1376	C₄	—	6	1	no	—
1377	C₄	C₃×D₃×#41	1	2	yes	—
1378	C₃	—	2	1	no	—
1379	C₃	#86558	1	1	yes	characteristic, direct product factor
1380	C₃	C₃×#3522	1	1	yes	characteristic, complemented
1381	C₂	—	4	1	no	—
1382	C₂	—	4	2	no	—
1383	C₂	—	6	2	no	—
1384	C₂	—	12	2	no	—
1385	C₂	—	12	1	no	—
1386	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1387	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1388	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×#542	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#542	D₃
hypocenter	C₃	C₃×#3522
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#542

Complements

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

N	H ≅ G/N	type
1. C₃²×#542	C₂	semidirect
2. C₃×#5726	C₂	semidirect
3. C₃×#5722	C₂	semidirect
4. C₃×#5710	C₂	semidirect
5. C₃×#5706	C₂	semidirect
6. C₃×#5681	C₂	semidirect
7. C₃×#5677	C₂	semidirect
8. C₃×#5669	C₂	semidirect
9. C₃×#5668	C₂	semidirect
10. C₃×#5664	C₂	semidirect
11. C₃×#5655	C₂	semidirect
12. C₃×#5636	C₂	semidirect
13. C₃×#5635	C₂	semidirect
14. C₃×#5633	C₂	semidirect
15. C₃×#5631	C₂	semidirect
16. C₃×#5611	C₂	semidirect
17. C₃×#5599	C₂	semidirect
18. C₃×#5582	C₂	semidirect
19. C₃×C₄×D₃×Q₈	C₂	semidirect
20. C₃×#5548	C₂	semidirect
21. C₃×#5546	C₂	semidirect
22. C₃×#5528	C₂	semidirect
23. C₃×#5523	C₂	semidirect
25. #86558	C₃	direct (N × H)
141. C₃×#542	D₃	semidirect
142. C₃×#542	C₂×C₃	semidirect
150. #5726	C₂×C₃	semidirect
151. #5722	C₂×C₃	semidirect
152. #5710	C₂×C₃	semidirect
153. #5706	C₂×C₃	semidirect
154. #5681	C₂×C₃	semidirect
155. #5677	C₂×C₃	semidirect
156. #5669	C₂×C₃	semidirect
157. #5668	C₂×C₃	semidirect
158. #5664	C₂×C₃	semidirect
159. #5655	C₂×C₃	semidirect
160. #5636	C₂×C₃	semidirect
161. #5635	C₂×C₃	semidirect
162. #5633	C₂×C₃	semidirect
163. #5631	C₂×C₃	semidirect
164. #5611	C₂×C₃	semidirect
165. #5599	C₂×C₃	semidirect
166. #5582	C₂×C₃	semidirect
167. C₄×D₃×Q₈	C₂×C₃	semidirect
168. #5548	C₂×C₃	semidirect
169. #5546	C₂×C₃	semidirect
170. #5528	C₂×C₃	semidirect
171. #5523	C₂×C₃	semidirect
544. C₃×Dic₆	#41	semidirect
560. #542	C₃×D₃	semidirect
1066. Dic₆	C₃×#41	semidirect
1264. C₃²	#3522	semidirect
1379. C₃	#86558	direct (N × H)
1380. C₃	C₃×#3522	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#542	2
C₃×#5726	2
C₃×#5722	2
C₃×#5710	2
C₃×#5706	2
C₃×#5681	2
C₃×#5677	2
C₃×#5669	2
C₃×#5668	2
C₃×#5664	2
C₃×#5655	2
C₃×#5636	2
C₃×#5635	2
C₃×#5633	2
C₃×#5631	2
C₃×#5611	2
C₃×#5599	2
C₃×#5582	2
C₃×C₄×D₃×Q₈	2
C₃×#5548	2
C₃×#5546	2
C₃×#5528	2
C₃×#5523	2
C₃×#3522	3
#86558	3

Subgroups — C3×#86558 #11909737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86558 #11909737