Subgroups — C₃×#61657 #10680264

Order 768.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3322	C₂	1	2	yes	maximal, complemented
6	C₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3297	C₂	1	2	yes	maximal, complemented
8	C₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3280	C₂	1	2	yes	maximal, complemented
11	C₃×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3203	C₂	1	2	yes	maximal, complemented
18	C₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₃×#3008	C₂	1	2	yes	maximal, complemented
23	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#61657	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
26	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂×C₃×#135	C₂²	1	2	yes	complemented
29	C₂²×C₃×D₈	C₂²	1	2	yes	complemented
30	C₃×#560	—	2	2	no	—
31	C₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃×#553	C₂²	1	2	yes	complemented
33	C₃×#550	—	2	1	no	—
34	C₃×#550	C₂²	1	1	yes	characteristic, complemented
35	C₃×#547	—	2	1	no	—
36	C₃×#547	C₂²	1	1	yes	characteristic
37	C₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃×#546	—	2	2	no	—
40	C₃×#546	—	2	1	no	—
41	C₃×#546	C₂²	1	2	yes	complemented
42	C₃×#546	C₂²	1	2	yes	complemented
43	C₃×#546	C₂²	1	2	yes	complemented
44	C₃×D₄²	—	2	1	no	—
45	C₃×D₄²	C₂²	1	1	yes	characteristic
46	C₃×D₄²	C₂²	1	1	yes	characteristic, complemented
47	C₃×D₄²	C₂²	1	1	yes	characteristic, complemented
48	C₃×#542	—	2	1	no	—
49	C₃×#538	—	2	2	no	—
50	C₃×#537	C₂²	1	2	yes	complemented
51	C₃×#537	C₂²	1	2	yes	complemented
52	C₃×#535	—	2	1	no	—
53	C₃×#535	C₂²	1	2	yes	complemented
54	C₃×#534	—	2	2	no	—
55	C₃×#532	C₂²	1	1	yes	characteristic
56	C₃×#532	C₂²	1	1	yes	characteristic, complemented
57	C₃×#532	C₂²	1	1	yes	characteristic, complemented
58	C₃×#529	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×#121	—	2	1	no	—
60	C₂×C₃×#121	—	2	1	no	—
61	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
62	C₃×#495	C₂²	1	2	yes	complemented
63	C₃×#493	C₂²	1	1	yes	characteristic, complemented
64	C₃×#492	C₂²	1	1	yes	characteristic, complemented
65	C₃×#488	C₂²	1	2	yes	complemented
66	C₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃×#485	C₂²	1	2	yes	complemented
69	C₃×#484	C₂²	1	1	yes	characteristic, complemented
70	C₃×#484	C₂²	1	2	yes	complemented
71	C₃×#482	C₂²	1	2	yes	complemented
72	C₃×#481	C₂²	1	1	yes	characteristic, complemented
73	C₃×#480	C₂²	1	2	yes	complemented
74	C₃×#480	C₂²	1	2	yes	complemented
75	C₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₃×#478	C₂²	1	1	yes	characteristic, complemented
77	C₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₃×#469	C₂²	1	2	yes	complemented
80	C₃×#468	C₂²	1	2	yes	complemented
81	C₃×#468	C₂²	1	2	yes	complemented
82	C₃×#468	C₂²	1	2	yes	complemented
83	C₃×#467	C₂²	1	2	yes	complemented
84	C₃×#466	C₂²	1	2	yes	complemented
85	C₃×#466	C₂²	1	2	yes	complemented
86	C₃×#465	C₂²	1	2	yes	complemented
87	C₃×#463	C₂²	1	2	yes	complemented
88	C₃×#463	C₂²	1	2	yes	complemented
89	C₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₃×#463	C₂²	1	1	yes	characteristic, complemented
91	C₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₃×#459	C₂²	1	1	yes	characteristic, complemented
97	C₃×#452	C₂²	1	2	yes	complemented
98	C₃×#452	C₂²	1	2	yes	complemented
99	C₃×#452	C₂²	1	2	yes	complemented
100	C₃×#450	C₂²	1	2	yes	complemented
101	C₃×#450	C₂²	1	1	yes	characteristic, complemented
102	C₃×#450	C₂²	1	2	yes	complemented
103	C₃×#449	C₂²	1	2	yes	complemented
104	C₃×#449	C₂²	1	2	yes	complemented
105	C₃×#449	C₂²	1	2	yes	complemented
106	C₃×#449	C₂²	1	2	yes	complemented
107	C₃×#449	C₂²	1	2	yes	complemented
108	C₃×#449	C₂²	1	2	yes	complemented
109	C₃×#449	C₂²	1	2	yes	complemented
110	C₃×#447	C₂²	1	1	yes	characteristic
111	C₃×#447	C₂²	1	2	yes	complemented
112	C₃×#447	C₂²	1	2	yes	complemented
113	C₃×#447	C₂²	1	2	yes	complemented
114	C₃×#447	C₂²	1	2	yes	complemented
115	C₃×#447	C₂²	1	2	yes	complemented
116	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
119	C₃×C₄×D₈	C₂²	1	2	yes	complemented
120	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×D₈	C₂²	1	2	yes	complemented
122	C₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₃×#436	C₂²	1	2	yes	complemented
124	C₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₃×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
126	C₃×C₈×D₄	C₂²	1	2	yes	complemented
127	C₃×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₃×#418	C₂²	1	2	yes	complemented
131	C₃×#417	C₂²	1	2	yes	complemented
132	C₃×#416	C₂²	1	2	yes	complemented
133	C₂×C₃×#102	C₂²	1	2	yes	complemented
134	C₃×#408	C₂²	1	2	yes	complemented
135	C₃×#408	C₂²	1	2	yes	complemented
136	#3546	C₂×C₃	1	1	yes	characteristic, complemented
137	#3496	C₂×C₃	1	1	yes	characteristic, complemented
138	#3330	C₂×C₃	1	1	yes	characteristic, complemented
139	#3324	C₂×C₃	1	1	yes	characteristic, complemented
140	#3322	C₂×C₃	1	2	yes	complemented
141	#3302	C₂×C₃	1	1	yes	characteristic, complemented
142	#3297	C₂×C₃	1	2	yes	complemented
143	#3294	C₂×C₃	1	1	yes	characteristic, complemented
144	#3284	C₂×C₃	1	1	yes	characteristic, complemented
145	#3280	C₂×C₃	1	2	yes	complemented
146	D₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
147	#3274	C₂×C₃	1	1	yes	characteristic, complemented
148	#3273	C₂×C₃	1	2	yes	complemented
149	#3272	C₂×C₃	1	1	yes	characteristic, complemented
150	#3212	C₂×C₃	1	1	yes	characteristic, complemented
151	#3207	C₂×C₃	1	1	yes	characteristic, complemented
152	#3203	C₂×C₃	1	2	yes	complemented
153	#3198	C₂×C₃	1	2	yes	complemented
154	#3105	C₂×C₃	1	1	yes	characteristic, complemented
155	#3100	C₂×C₃	1	1	yes	characteristic, complemented
156	#3012	C₂×C₃	1	2	yes	complemented
157	#3008	C₂×C₃	1	2	yes	complemented
158	#2979	C₂×C₃	1	1	yes	characteristic, complemented
159	C₃×H(5,𝔽₂)	—	4	4	no	—
160	C₃×H(5,𝔽₂)	—	4	4	no	—
161	C₂×C₃×#41	—	2	2	no	—
162	C₂×C₃×#41	—	2	1	no	—
163	C₂×C₃×#41	—	2	1	no	—
164	C₂×C₃×#41	C₂³	1	2	yes	—
165	C₂×C₃×#41	C₂³	1	2	yes	—
166	C₂×C₃×#41	C₂³	1	2	yes	—
167	C₂×C₃×#41	C₂³	1	2	yes	—
168	C₂×C₃×#41	C₂³	1	2	yes	—
169	C₂²×C₃×D₄	—	2	2	no	—
170	C₂²×C₃×D₄	—	2	2	no	—
171	C₂²×C₃×D₄	—	2	2	no	—
172	C₂²×C₃×D₄	—	2	1	no	—
173	C₂²×C₃×D₄	—	2	1	no	—
174	C₂²×C₃×D₄	—	2	1	no	—
175	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃×D₄	C₂³	1	2	yes	—
177	C₂²×C₃×D₄	C₂³	1	2	yes	—
178	C₂²×C₃×D₄	C₂³	1	2	yes	—
179	C₂³×C₃×C₄	—	2	1	no	—
180	C₃×AGL(1,ℤ/8)	—	4	4	no	—
181	C₃×AGL(1,ℤ/8)	—	4	4	no	—
182	C₃×#135	—	4	4	no	—
183	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
184	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
185	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
187	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
188	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
189	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
190	C₂×C₃×D₈	—	4	4	no	—
191	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
192	C₂×C₃×D₈	C₂³	1	2	yes	—
193	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
194	C₂×C₃×D₈	C₂³	1	2	yes	—
195	C₂×C₃×D₈	C₂³	1	2	yes	—
196	C₂×C₃×D₈	C₂³	1	2	yes	—
197	C₂×C₃×D₈	C₂³	1	2	yes	—
198	C₂×C₃×M₁₆	C₂³	1	2	yes	—
199	C₂×C₃×M₁₆	C₂³	1	2	yes	—
200	C₂²×C₃×C₈	C₂³	1	2	yes	—
201	C₂²×C₃×C₈	C₂³	1	2	yes	—
202	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
203	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
204	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
205	C₃×#127	—	2	2	no	—
206	C₃×#127	—	2	1	no	—
207	C₃×#127	D₄	1	1	yes	characteristic
208	C₃×#127	C₂³	1	1	yes	characteristic
209	C₃×#127	C₂³	1	1	yes	characteristic
210	C₃×#126	—	2	2	no	—
211	C₃×#126	—	2	2	no	—
212	C₃×#126	—	2	1	no	—
213	C₃×#125	C₂³	1	1	yes	characteristic
214	C₃×#124	—	2	2	no	—
215	C₃×#124	—	2	1	no	—
216	C₃×#124	—	2	1	no	—
217	C₃×#124	D₄	1	2	yes	—
218	C₃×#124	C₂³	1	1	yes	characteristic
219	C₃×#124	C₂³	1	2	yes	—
220	C₃×#123	—	2	1	no	—
221	C₃×#123	—	2	2	no	—
222	C₃×#123	—	2	2	no	—
223	C₃×#123	—	2	2	no	—
224	C₃×#123	—	2	2	no	—
225	C₃×#123	—	2	2	no	—
226	C₃×#123	—	2	2	no	—
227	C₃×#123	—	2	2	no	—
228	C₃×C₂²⋊Q₈	—	2	2	no	—
229	C₃×C₂²⋊Q₈	—	2	2	no	—
230	C₃×C₂²⋊Q₈	—	2	1	no	—
231	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
233	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
234	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
235	C₃×#121	—	2	2	no	—
236	C₃×#121	—	2	2	no	—
237	C₃×#121	—	2	2	no	—
238	C₃×#121	—	2	2	no	—
239	C₃×#121	—	2	2	no	—
240	C₃×#121	—	2	1	no	—
241	C₃×#121	—	2	1	no	—
242	C₃×#121	—	2	2	no	—
243	C₃×#121	—	2	2	no	—
244	C₃×#121	—	2	1	no	—
245	C₃×#121	—	2	1	no	—
246	C₃×#121	—	2	1	no	—
247	C₃×#121	—	2	1	no	—
248	C₃×#121	—	2	1	no	—
249	C₃×#121	—	2	1	no	—
250	C₃×#121	—	2	2	no	—
251	C₃×#121	—	2	2	no	—
252	C₃×#121	—	2	2	no	—
253	C₃×#121	—	2	2	no	—
254	C₃×#121	D₄	1	2	yes	—
255	C₃×#121	D₄	1	1	yes	characteristic
256	C₃×#121	D₄	1	1	yes	characteristic
257	C₃×#121	C₂³	1	1	yes	characteristic
258	C₃×#121	C₂³	1	2	yes	—
259	C₃×#121	C₂³	1	2	yes	—
260	C₃×#121	C₂³	1	2	yes	—
261	C₃×#121	C₂³	1	2	yes	—
262	C₃×#121	C₂³	1	2	yes	—
263	C₃×#121	C₂³	1	2	yes	—
264	C₃×#120	—	2	2	no	—
265	C₃×#120	—	2	2	no	—
266	C₃×#120	—	2	2	no	—
267	C₃×#120	—	2	2	no	—
268	C₃×#120	—	2	2	no	—
269	C₃×#120	—	2	2	no	—
270	C₃×#120	—	2	2	no	—
271	C₃×#120	—	2	2	no	—
272	C₃×C₄×Q₈	—	2	1	no	—
273	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
274	C₃×C₄×D₄	—	2	1	no	—
275	C₃×C₄×D₄	—	2	1	no	—
276	C₃×C₄×D₄	—	2	2	no	—
277	C₃×C₄×D₄	—	2	1	no	—
278	C₃×C₄×D₄	—	2	1	no	—
279	C₃×C₄×D₄	—	2	1	no	—
280	C₃×C₄×D₄	—	2	1	no	—
281	C₃×C₄×D₄	—	2	1	no	—
282	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
283	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
284	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
285	C₃×C₄×D₄	C₂³	1	2	yes	—
286	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
287	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
288	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
289	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
290	C₃×C₄×D₄	C₂³	1	2	yes	—
291	C₃×#117	—	2	1	no	—
292	C₃×#117	C₂³	1	2	yes	—
293	C₂×C₃×C₄⋊C₄	—	2	1	no	—
294	C₂×C₃×C₄⋊C₄	—	2	1	no	—
295	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
296	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
302	C₃×#107	C₂³	1	1	yes	characteristic
303	C₃×#107	C₂³	1	2	yes	—
304	C₃×#107	C₂³	1	2	yes	—
305	C₃×#107	C₂³	1	1	yes	characteristic
306	C₃×#106	C₂³	1	1	yes	characteristic
307	C₃×#106	C₂³	1	1	yes	characteristic
308	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
309	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
310	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
311	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
312	C₃×#103	C₂³	1	2	yes	—
313	C₃×#103	C₂³	1	2	yes	—
314	C₃×#103	C₂³	1	2	yes	—
315	C₃×#103	C₂³	1	2	yes	—
316	C₃×#103	C₂³	1	1	yes	characteristic
317	C₃×#103	C₂³	1	1	yes	characteristic
318	C₃×#102	C₂³	1	1	yes	characteristic
319	C₃×#102	C₂³	1	2	yes	—
320	C₃×#102	C₂³	1	2	yes	—
321	C₃×#102	C₂³	1	2	yes	—
322	C₃×#102	C₂³	1	1	yes	characteristic
323	C₃×#102	C₂³	1	1	yes	characteristic
324	C₃×#102	C₂³	1	2	yes	—
325	C₃×#102	C₂³	1	1	yes	characteristic
326	C₃×#102	C₂³	1	2	yes	—
327	C₃×#102	C₂³	1	2	yes	—
328	C₃×#102	C₂³	1	1	yes	characteristic
329	C₃×#102	C₂³	1	2	yes	—
330	C₃×#102	C₂³	1	2	yes	—
331	C₃×#102	C₂³	1	1	yes	characteristic
332	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃×C₄×C₈	C₂³	1	2	yes	—
340	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
342	C₂×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
343	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
344	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
345	C₂×#135	C₂²×C₃	1	2	yes	complemented
346	C₂²×D₈	C₂²×C₃	1	2	yes	complemented
347	#560	—	2	2	no	—
348	#556	C₂²×C₃	1	1	yes	characteristic, complemented
349	#553	C₂²×C₃	1	2	yes	complemented
350	#550	—	2	1	no	—
351	#550	C₂²×C₃	1	1	yes	characteristic, complemented
352	#547	—	2	1	no	—
353	#547	C₂²×C₃	1	1	yes	characteristic
354	#547	C₂²×C₃	1	1	yes	characteristic, complemented
355	#547	C₂²×C₃	1	1	yes	characteristic, complemented
356	#546	—	2	2	no	—
357	#546	—	2	1	no	—
358	#546	C₂²×C₃	1	2	yes	complemented
359	#546	C₂²×C₃	1	2	yes	complemented
360	#546	C₂²×C₃	1	2	yes	complemented
361	D₄²	—	2	1	no	—
362	D₄²	C₂²×C₃	1	1	yes	characteristic
363	D₄²	C₂²×C₃	1	1	yes	characteristic, complemented
364	D₄²	C₂²×C₃	1	1	yes	characteristic, complemented
365	#542	—	2	1	no	—
366	#538	—	2	2	no	—
367	#537	C₂²×C₃	1	2	yes	complemented
368	#537	C₂²×C₃	1	2	yes	complemented
369	#535	—	2	1	no	—
370	#535	C₂²×C₃	1	2	yes	complemented
371	#534	—	2	2	no	—
372	#532	C₂²×C₃	1	1	yes	characteristic
373	#532	C₂²×C₃	1	1	yes	characteristic, complemented
374	#532	C₂²×C₃	1	1	yes	characteristic, complemented
375	#529	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₂×#121	—	2	1	no	—
377	C₂×#121	—	2	1	no	—
378	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
379	#495	C₂²×C₃	1	2	yes	complemented
380	#493	C₂²×C₃	1	1	yes	characteristic, complemented
381	#492	C₂²×C₃	1	1	yes	characteristic, complemented
382	#488	C₂²×C₃	1	2	yes	complemented
383	#487	C₂²×C₃	1	1	yes	characteristic, complemented
384	#486	C₂²×C₃	1	1	yes	characteristic, complemented
385	#485	C₂²×C₃	1	2	yes	complemented
386	#484	C₂²×C₃	1	2	yes	complemented
387	#484	C₂²×C₃	1	1	yes	characteristic, complemented
388	#482	C₂²×C₃	1	2	yes	complemented
389	#481	C₂²×C₃	1	1	yes	characteristic, complemented
390	#480	C₂²×C₃	1	2	yes	complemented
391	#480	C₂²×C₃	1	2	yes	complemented
392	#478	C₂²×C₃	1	1	yes	characteristic, complemented
393	#478	C₂²×C₃	1	1	yes	characteristic, complemented
394	#474	C₂²×C₃	1	1	yes	characteristic, complemented
395	#474	C₂²×C₃	1	1	yes	characteristic, complemented
396	#469	C₂²×C₃	1	2	yes	complemented
397	#468	C₂²×C₃	1	2	yes	complemented
398	#468	C₂²×C₃	1	2	yes	complemented
399	#468	C₂²×C₃	1	2	yes	complemented
400	#467	C₂²×C₃	1	2	yes	complemented
401	#466	C₂²×C₃	1	2	yes	complemented
402	#466	C₂²×C₃	1	2	yes	complemented
403	#465	C₂²×C₃	1	2	yes	complemented
404	#463	C₂²×C₃	1	1	yes	characteristic, complemented
405	#463	C₂²×C₃	1	1	yes	characteristic, complemented
406	#463	C₂²×C₃	1	2	yes	complemented
407	#463	C₂²×C₃	1	2	yes	complemented
408	#462	C₂²×C₃	1	1	yes	characteristic, complemented
409	#461	C₂²×C₃	1	1	yes	characteristic, complemented
410	#460	C₂²×C₃	1	1	yes	characteristic, complemented
411	#459	C₂²×C₃	1	1	yes	characteristic, complemented
412	#459	C₂²×C₃	1	1	yes	characteristic, complemented
413	#459	C₂²×C₃	1	1	yes	characteristic, complemented
414	#452	C₂²×C₃	1	2	yes	complemented
415	#452	C₂²×C₃	1	2	yes	complemented
416	#452	C₂²×C₃	1	2	yes	complemented
417	#450	C₂²×C₃	1	1	yes	characteristic, complemented
418	#450	C₂²×C₃	1	2	yes	complemented
419	#450	C₂²×C₃	1	2	yes	complemented
420	#449	C₂²×C₃	1	2	yes	complemented
421	#449	C₂²×C₃	1	2	yes	complemented
422	#449	C₂²×C₃	1	2	yes	complemented
423	#449	C₂²×C₃	1	2	yes	complemented
424	#449	C₂²×C₃	1	2	yes	complemented
425	#449	C₂²×C₃	1	2	yes	complemented
426	#449	C₂²×C₃	1	2	yes	complemented
427	#447	C₂²×C₃	1	1	yes	characteristic
428	#447	C₂²×C₃	1	2	yes	complemented
429	#447	C₂²×C₃	1	2	yes	complemented
430	#447	C₂²×C₃	1	2	yes	complemented
431	#447	C₂²×C₃	1	2	yes	complemented
432	#447	C₂²×C₃	1	2	yes	complemented
433	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
434	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
435	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
436	C₄×D₈	C₂²×C₃	1	2	yes	complemented
437	C₄×D₈	C₂²×C₃	1	2	yes	complemented
438	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
439	#436	C₂²×C₃	1	1	yes	characteristic, complemented
440	#436	C₂²×C₃	1	1	yes	characteristic, complemented
441	#436	C₂²×C₃	1	2	yes	complemented
442	C₈×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
443	C₈×D₄	C₂²×C₃	1	2	yes	complemented
444	C₈×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
445	#431	C₂²×C₃	1	1	yes	characteristic, complemented
446	#431	C₂²×C₃	1	1	yes	characteristic, complemented
447	#418	C₂²×C₃	1	2	yes	complemented
448	#417	C₂²×C₃	1	2	yes	complemented
449	#416	C₂²×C₃	1	2	yes	complemented
450	C₂×#102	C₂²×C₃	1	2	yes	complemented
451	#408	C₂²×C₃	1	2	yes	complemented
452	#408	C₂²×C₃	1	2	yes	complemented
453	C₂⁴×C₃	—	2	1	no	—
454	C₂⁴×C₃	—	2	2	no	—
455	C₂⁴×C₃	—	2	2	no	—
456	C₂⁴×C₃	—	2	2	no	—
457	C₃×#41	—	2	4	no	—
458	C₃×#41	—	2	4	no	—
459	C₃×#41	—	4	2	no	—
460	C₃×#41	—	4	2	no	—
461	C₃×#41	—	4	2	no	—
462	C₃×#41	—	4	2	no	—
463	C₃×#41	—	4	2	no	—
464	C₃×#41	—	4	2	no	—
465	C₃×#41	—	4	2	no	—
466	C₃×#41	—	4	2	no	—
467	C₃×#41	—	4	8	no	—
468	C₃×#41	—	8	2	no	—
469	C₃×#41	—	8	2	no	—
470	C₂×C₃×Q₈	—	2	1	no	—
471	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
472	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
473	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
474	C₂×C₃×D₄	—	2	2	no	—
475	C₂×C₃×D₄	—	2	2	no	—
476	C₂×C₃×D₄	—	2	4	no	—
477	C₂×C₃×D₄	—	2	4	no	—
478	C₂×C₃×D₄	—	2	2	no	—
479	C₂×C₃×D₄	—	2	2	no	—
480	C₂×C₃×D₄	—	2	2	no	—
481	C₂×C₃×D₄	—	2	1	no	—
482	C₂×C₃×D₄	—	2	2	no	—
483	C₂×C₃×D₄	—	2	2	no	—
484	C₂×C₃×D₄	—	2	2	no	—
485	C₂×C₃×D₄	—	2	2	no	—
486	C₂×C₃×D₄	—	2	2	no	—
487	C₂×C₃×D₄	—	2	2	no	—
488	C₂×C₃×D₄	—	2	2	no	—
489	C₂×C₃×D₄	—	2	1	no	—
490	C₂×C₃×D₄	—	2	1	no	—
491	C₂×C₃×D₄	—	2	1	no	—
492	C₂×C₃×D₄	—	2	2	no	—
493	C₂×C₃×D₄	—	2	2	no	—
494	C₂×C₃×D₄	—	2	1	no	—
495	C₂×C₃×D₄	—	2	1	no	—
496	C₂×C₃×D₄	—	2	2	no	—
497	C₂×C₃×D₄	—	4	2	no	—
498	C₂×C₃×D₄	—	4	2	no	—
499	C₂×C₃×D₄	—	4	2	no	—
500	C₂×C₃×D₄	—	4	2	no	—
501	C₂×C₃×D₄	—	4	8	no	—
502	C₂×C₃×D₄	—	4	8	no	—
503	C₂×C₃×D₄	—	4	8	no	—
504	C₂×C₃×D₄	—	8	2	no	—
505	C₂×C₃×D₄	—	8	2	no	—
506	C₂×C₃×D₄	—	8	2	no	—
507	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
508	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
509	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
510	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
511	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
512	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
513	C₂×C₃×D₄	C₂⁴	1	2	yes	—
514	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
515	C₂×C₃×D₄	C₂⁴	1	2	yes	—
516	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
517	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
518	C₂²×C₃×C₄	—	2	1	no	—
519	C₂²×C₃×C₄	—	2	2	no	—
520	C₂²×C₃×C₄	—	2	2	no	—
521	C₂²×C₃×C₄	—	2	2	no	—
522	C₂²×C₃×C₄	—	2	1	no	—
523	C₂²×C₃×C₄	—	2	1	no	—
524	C₂²×C₃×C₄	—	2	1	no	—
525	C₂²×C₃×C₄	—	2	2	no	—
526	C₂²×C₃×C₄	—	2	1	no	—
527	C₂²×C₃×C₄	—	2	1	no	—
528	C₂²×C₃×C₄	—	2	2	no	—
529	C₂²×C₃×C₄	—	2	2	no	—
530	C₂²×C₃×C₄	—	8	2	no	—
531	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
532	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
534	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
535	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
536	C₃×Q₁₆	—	4	2	no	—
537	C₃×SD₁₆	—	2	2	no	—
538	C₃×SD₁₆	—	2	2	no	—
539	C₃×SD₁₆	—	4	2	no	—
540	C₃×SD₁₆	—	4	2	no	—
541	C₃×SD₁₆	—	4	2	no	—
542	C₃×SD₁₆	—	4	2	no	—
543	C₃×D₈	—	2	2	no	—
544	C₃×D₈	—	2	4	no	—
545	C₃×D₈	—	2	4	no	—
546	C₃×D₈	—	2	2	no	—
547	C₃×D₈	—	4	2	no	—
548	C₃×D₈	—	4	2	no	—
549	C₃×D₈	—	4	2	no	—
550	C₃×M₁₆	—	4	2	no	—
551	C₃×M₁₆	—	4	2	no	—
552	C₂×C₃×C₈	—	4	2	no	—
553	C₂×C₃×C₈	—	4	2	no	—
554	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
555	C₂×C₃×C₈	C₂⁴	1	2	yes	—
556	C₂×C₃×C₈	C₂⁴	1	2	yes	—
557	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
558	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
559	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
560	C₃×C₄⋊C₄	—	2	1	no	—
561	C₃×C₄⋊C₄	—	2	2	no	—
562	C₃×C₄⋊C₄	—	2	2	no	—
563	C₃×C₄⋊C₄	—	2	1	no	—
564	C₃×C₄⋊C₄	—	2	2	no	—
565	C₃×C₄⋊C₄	—	2	1	no	—
566	C₃×C₄⋊C₄	—	2	1	no	—
567	C₃×C₄⋊C₄	—	2	1	no	—
568	C₃×C₄⋊C₄	—	2	1	no	—
569	C₃×C₄⋊C₄	—	2	1	no	—
570	C₃×C₄⋊C₄	—	2	2	no	—
571	C₃×C₄⋊C₄	—	2	1	no	—
572	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
573	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
574	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
575	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
576	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
577	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
578	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
579	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
580	C₃×C₂²⋊C₄	—	2	2	no	—
581	C₃×C₂²⋊C₄	—	2	2	no	—
582	C₃×C₂²⋊C₄	—	2	2	no	—
583	C₃×C₂²⋊C₄	—	2	2	no	—
584	C₃×C₂²⋊C₄	—	2	1	no	—
585	C₃×C₂²⋊C₄	—	2	2	no	—
586	C₃×C₂²⋊C₄	—	2	1	no	—
587	C₃×C₂²⋊C₄	—	2	1	no	—
588	C₃×C₂²⋊C₄	—	2	1	no	—
589	C₃×C₂²⋊C₄	—	2	1	no	—
590	C₃×C₂²⋊C₄	—	2	1	no	—
591	C₃×C₂²⋊C₄	—	2	2	no	—
592	C₃×C₂²⋊C₄	—	2	2	no	—
593	C₃×C₂²⋊C₄	—	2	2	no	—
594	C₃×C₂²⋊C₄	—	2	1	no	—
595	C₃×C₂²⋊C₄	—	2	1	no	—
596	C₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
601	C₃×C₂²⋊C₄	—	2	2	no	—
602	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
603	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
604	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
605	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
606	C₃×C₄²	—	2	1	no	—
607	C₃×C₄²	—	2	2	no	—
608	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
609	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
610	C₃×C₄²	C₂⁴	1	1	yes	characteristic
611	C₃×C₄²	C₂⁴	1	1	yes	characteristic
612	H(5,𝔽₂)	—	4	4	no	—
613	H(5,𝔽₂)	—	4	4	no	—
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	1	no	—
616	C₂×#41	—	2	1	no	—
617	C₂×#41	C₂³×C₃	1	2	yes	—
618	C₂×#41	C₂³×C₃	1	2	yes	—
619	C₂×#41	C₂³×C₃	1	2	yes	—
620	C₂×#41	C₂³×C₃	1	2	yes	—
621	C₂×#41	C₂³×C₃	1	2	yes	—
622	C₂²×D₄	—	2	2	no	—
623	C₂²×D₄	—	2	2	no	—
624	C₂²×D₄	—	2	2	no	—
625	C₂²×D₄	—	2	1	no	—
626	C₂²×D₄	—	2	1	no	—
627	C₂²×D₄	—	2	1	no	—
628	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
629	C₂²×D₄	C₂³×C₃	1	2	yes	—
630	C₂²×D₄	C₂³×C₃	1	2	yes	—
631	C₂²×D₄	C₂³×C₃	1	2	yes	—
632	C₂³×C₄	—	2	1	no	—
633	AGL(1,ℤ/8)	—	4	4	no	—
634	AGL(1,ℤ/8)	—	4	4	no	—
635	#135	—	4	4	no	—
636	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
637	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
638	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
639	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
643	C₂×D₈	—	4	4	no	—
644	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
645	C₂×D₈	C₂³×C₃	1	2	yes	—
646	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
647	C₂×D₈	C₂³×C₃	1	2	yes	—
648	C₂×D₈	C₂³×C₃	1	2	yes	—
649	C₂×D₈	C₂³×C₃	1	2	yes	—
650	C₂×D₈	C₂³×C₃	1	2	yes	—
651	C₂×M₁₆	C₂³×C₃	1	2	yes	—
652	C₂×M₁₆	C₂³×C₃	1	2	yes	—
653	C₂²×C₈	C₂³×C₃	1	2	yes	—
654	C₂²×C₈	C₂³×C₃	1	2	yes	—
655	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
656	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
657	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
658	#127	—	2	1	no	—
659	#127	—	2	2	no	—
660	#127	C₃×D₄	1	1	yes	characteristic
661	#127	C₂³×C₃	1	1	yes	characteristic
662	#127	C₂³×C₃	1	1	yes	characteristic
663	#126	—	2	2	no	—
664	#126	—	2	2	no	—
665	#126	—	2	1	no	—
666	#125	C₂³×C₃	1	1	yes	characteristic
667	#124	—	2	2	no	—
668	#124	—	2	1	no	—
669	#124	—	2	1	no	—
670	#124	C₃×D₄	1	2	yes	—
671	#124	C₂³×C₃	1	1	yes	characteristic
672	#124	C₂³×C₃	1	2	yes	—
673	#123	—	2	1	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	1	no	—
691	#121	—	2	1	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	1	no	—
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	C₃×D₄	1	1	yes	characteristic
708	#121	C₃×D₄	1	1	yes	characteristic
709	#121	C₃×D₄	1	2	yes	—
710	#121	C₂³×C₃	1	1	yes	characteristic
711	#121	C₂³×C₃	1	2	yes	—
712	#121	C₂³×C₃	1	2	yes	—
713	#121	C₂³×C₃	1	2	yes	—
714	#121	C₂³×C₃	1	2	yes	—
715	#121	C₂³×C₃	1	2	yes	—
716	#121	C₂³×C₃	1	2	yes	—
717	#120	—	2	2	no	—
718	#120	—	2	2	no	—
719	#120	—	2	2	no	—
720	#120	—	2	2	no	—
721	#120	—	2	2	no	—
722	#120	—	2	2	no	—
723	#120	—	2	2	no	—
724	#120	—	2	2	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
738	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
739	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
740	C₄×D₄	C₂³×C₃	1	2	yes	—
741	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
742	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₃	1	2	yes	—
744	#117	—	2	1	no	—
745	#117	C₂³×C₃	1	2	yes	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
755	#107	C₂³×C₃	1	1	yes	characteristic
756	#107	C₂³×C₃	1	2	yes	—
757	#107	C₂³×C₃	1	2	yes	—
758	#107	C₂³×C₃	1	1	yes	characteristic
759	#106	C₂³×C₃	1	1	yes	characteristic
760	#106	C₂³×C₃	1	1	yes	characteristic
761	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
762	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
763	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
764	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
765	#103	C₂³×C₃	1	2	yes	—
766	#103	C₂³×C₃	1	2	yes	—
767	#103	C₂³×C₃	1	2	yes	—
768	#103	C₂³×C₃	1	2	yes	—
769	#103	C₂³×C₃	1	1	yes	characteristic
770	#103	C₂³×C₃	1	1	yes	characteristic
771	#102	C₂³×C₃	1	1	yes	characteristic
772	#102	C₂³×C₃	1	2	yes	—
773	#102	C₂³×C₃	1	2	yes	—
774	#102	C₂³×C₃	1	2	yes	—
775	#102	C₂³×C₃	1	1	yes	characteristic
776	#102	C₂³×C₃	1	1	yes	characteristic
777	#102	C₂³×C₃	1	2	yes	—
778	#102	C₂³×C₃	1	1	yes	characteristic
779	#102	C₂³×C₃	1	2	yes	—
780	#102	C₂³×C₃	1	2	yes	—
781	#102	C₂³×C₃	1	1	yes	characteristic
782	#102	C₂³×C₃	1	2	yes	—
783	#102	C₂³×C₃	1	2	yes	—
784	#102	C₂³×C₃	1	1	yes	characteristic
785	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
786	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
788	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
792	C₄×C₈	C₂³×C₃	1	2	yes	—
793	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
794	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
795	C₂³×C₃	—	2	4	no	—
796	C₂³×C₃	—	2	1	no	—
797	C₂³×C₃	—	2	1	no	—
798	C₂³×C₃	—	2	1	no	—
799	C₂³×C₃	—	2	2	no	—
800	C₂³×C₃	—	2	2	no	—
801	C₂³×C₃	—	4	4	no	—
802	C₂³×C₃	—	4	4	no	—
803	C₂³×C₃	—	8	1	no	—
804	C₂³×C₃	—	8	1	no	—
805	C₂³×C₃	—	8	2	no	—
806	C₂³×C₃	—	8	2	no	—
807	C₂³×C₃	—	8	2	no	—
808	C₂³×C₃	—	8	2	no	—
809	C₂³×C₃	—	8	2	no	—
810	C₂³×C₃	—	8	2	no	—
811	C₂³×C₃	—	8	2	no	—
812	C₂³×C₃	C₂²×D₄	1	2	yes	—
813	C₂³×C₃	C₂²×D₄	1	2	yes	—
814	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
815	C₃×Q₈	—	2	1	no	—
816	C₃×Q₈	—	2	1	no	—
817	C₃×Q₈	—	2	2	no	—
818	C₃×Q₈	—	2	2	no	—
819	C₃×Q₈	—	4	2	no	—
820	C₃×Q₈	—	4	2	no	—
821	C₃×D₄	—	2	4	no	—
822	C₃×D₄	—	2	2	no	—
823	C₃×D₄	—	2	2	no	—
824	C₃×D₄	—	2	1	no	—
825	C₃×D₄	—	2	1	no	—
826	C₃×D₄	—	2	1	no	—
827	C₃×D₄	—	2	2	no	—
828	C₃×D₄	—	2	2	no	—
829	C₃×D₄	—	2	1	no	—
830	C₃×D₄	—	2	2	no	—
831	C₃×D₄	—	2	2	no	—
832	C₃×D₄	—	4	2	no	—
833	C₃×D₄	—	4	2	no	—
834	C₃×D₄	—	4	2	no	—
835	C₃×D₄	—	4	2	no	—
836	C₃×D₄	—	4	4	no	—
837	C₃×D₄	—	4	4	no	—
838	C₃×D₄	—	4	4	no	—
839	C₃×D₄	—	4	4	no	—
840	C₃×D₄	—	4	4	no	—
841	C₃×D₄	—	4	2	no	—
842	C₃×D₄	—	4	2	no	—
843	C₃×D₄	—	8	1	no	—
844	C₃×D₄	—	8	1	no	—
845	C₃×D₄	—	8	2	no	—
846	C₃×D₄	—	8	1	no	—
847	C₃×D₄	—	8	2	no	—
848	C₃×D₄	—	8	2	no	—
849	C₃×D₄	—	8	2	no	—
850	C₃×D₄	—	8	2	no	—
851	C₃×D₄	—	8	2	no	—
852	C₃×D₄	—	8	2	no	—
853	C₃×D₄	—	8	2	no	—
854	C₃×D₄	H(5,𝔽₂)	1	2	yes	—
855	C₃×D₄	H(5,𝔽₂)	1	2	yes	—
856	C₂×C₃×C₄	—	2	2	no	—
857	C₂×C₃×C₄	—	2	2	no	—
858	C₂×C₃×C₄	—	2	2	no	—
859	C₂×C₃×C₄	—	2	2	no	—
860	C₂×C₃×C₄	—	2	2	no	—
861	C₂×C₃×C₄	—	2	1	no	—
862	C₂×C₃×C₄	—	2	1	no	—
863	C₂×C₃×C₄	—	2	1	no	—
864	C₂×C₃×C₄	—	2	1	no	—
865	C₂×C₃×C₄	—	2	2	no	—
866	C₂×C₃×C₄	—	2	1	no	—
867	C₂×C₃×C₄	—	2	1	no	—
868	C₂×C₃×C₄	—	2	1	no	—
869	C₂×C₃×C₄	—	2	2	no	—
870	C₂×C₃×C₄	—	4	1	no	—
871	C₂×C₃×C₄	—	4	4	no	—
872	C₂×C₃×C₄	—	4	4	no	—
873	C₂×C₃×C₄	—	4	4	no	—
874	C₂×C₃×C₄	—	4	2	no	—
875	C₂×C₃×C₄	—	4	2	no	—
876	C₂×C₃×C₄	—	4	2	no	—
877	C₂×C₃×C₄	—	8	1	no	—
878	C₂×C₃×C₄	—	8	1	no	—
879	C₂×C₃×C₄	—	8	2	no	—
880	C₂×C₃×C₄	—	8	2	no	—
881	C₂×C₃×C₄	—	8	1	no	—
882	C₂×C₃×C₄	—	8	2	no	—
883	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
884	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
889	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
891	C₃×C₈	—	2	1	no	—
892	C₃×C₈	—	2	2	no	—
893	C₃×C₈	—	2	1	no	—
894	C₃×C₈	—	2	2	no	—
895	C₃×C₈	—	2	1	no	—
896	C₃×C₈	—	2	1	no	—
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	2	2	no	—
899	C₂⁴	—	2	2	no	—
900	C₂⁴	—	2	2	no	—
901	#41	—	2	4	no	—
902	#41	—	2	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	8	no	—
912	#41	—	8	2	no	—
913	#41	—	8	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
916	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	4	no	—
921	C₂×D₄	—	2	4	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	4	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	4	8	no	—
946	C₂×D₄	—	4	8	no	—
947	C₂×D₄	—	4	8	no	—
948	C₂×D₄	—	8	2	no	—
949	C₂×D₄	—	8	2	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
952	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
953	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
954	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
955	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
956	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
957	C₂×D₄	C₂⁴×C₃	1	2	yes	—
958	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₃	1	2	yes	—
960	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
961	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	8	2	no	—
975	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
976	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
980	Q₁₆	—	4	2	no	—
981	SD₁₆	—	2	2	no	—
982	SD₁₆	—	2	2	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	D₈	—	2	2	no	—
988	D₈	—	2	4	no	—
989	D₈	—	2	4	no	—
990	D₈	—	2	2	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	2	no	—
993	D₈	—	4	2	no	—
994	M₁₆	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₃	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1047	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1048	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1049	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1053	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1056	C₂²×C₃	—	2	1	no	—
1057	C₂²×C₃	—	2	2	no	—
1058	C₂²×C₃	—	2	2	no	—
1059	C₂²×C₃	—	2	1	no	—
1060	C₂²×C₃	—	2	2	no	—
1061	C₂²×C₃	—	2	2	no	—
1062	C₂²×C₃	—	2	2	no	—
1063	C₂²×C₃	—	2	2	no	—
1064	C₂²×C₃	—	2	1	no	—
1065	C₂²×C₃	—	2	2	no	—
1066	C₂²×C₃	—	2	2	no	—
1067	C₂²×C₃	—	4	1	no	—
1068	C₂²×C₃	—	4	1	no	—
1069	C₂²×C₃	—	4	1	no	—
1070	C₂²×C₃	—	4	1	no	—
1071	C₂²×C₃	—	4	2	no	—
1072	C₂²×C₃	—	4	2	no	—
1073	C₂²×C₃	—	4	1	no	—
1074	C₂²×C₃	—	4	2	no	—
1075	C₂²×C₃	—	4	2	no	—
1076	C₂²×C₃	—	4	1	no	—
1077	C₂²×C₃	—	4	1	no	—
1078	C₂²×C₃	—	4	2	no	—
1079	C₂²×C₃	—	4	2	no	—
1080	C₂²×C₃	—	8	4	no	—
1081	C₂²×C₃	—	16	4	no	—
1082	C₂²×C₃	—	16	4	no	—
1083	C₂²×C₃	—	16	4	no	—
1084	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1085	C₃×C₄	—	2	1	no	—
1086	C₃×C₄	—	2	1	no	—
1087	C₃×C₄	—	2	1	no	—
1088	C₃×C₄	—	2	2	no	—
1089	C₃×C₄	—	2	2	no	—
1090	C₃×C₄	—	2	1	no	—
1091	C₃×C₄	—	4	1	no	—
1092	C₃×C₄	—	4	2	no	—
1093	C₃×C₄	—	4	1	no	—
1094	C₃×C₄	—	4	1	no	—
1095	C₃×C₄	—	4	1	no	—
1096	C₃×C₄	—	4	1	no	—
1097	C₃×C₄	—	4	2	no	—
1098	C₃×C₄	#576	1	2	yes	—
1099	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1100	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1101	C₂³	—	2	4	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	4	4	no	—
1108	C₂³	—	4	4	no	—
1109	C₂³	—	8	1	no	—
1110	C₂³	—	8	1	no	—
1111	C₂³	—	8	2	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	—	8	2	no	—
1116	C₂³	—	8	2	no	—
1117	C₂³	—	8	2	no	—
1118	C₂³	C₂²×C₃×D₄	1	2	yes	—
1119	C₂³	C₂²×C₃×D₄	1	2	yes	—
1120	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	2	2	no	—
1124	Q₈	—	2	2	no	—
1125	Q₈	—	4	2	no	—
1126	Q₈	—	4	2	no	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	2	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	2	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	4	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	1	no	—
1151	D₄	—	8	1	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	2	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	1	no	—
1159	D₄	—	8	2	no	—
1160	D₄	C₃×H(5,𝔽₂)	1	2	yes	—
1161	D₄	C₃×H(5,𝔽₂)	1	2	yes	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	4	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	4	2	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	8	2	no	—
1186	C₂×C₄	—	8	2	no	—
1187	C₂×C₄	—	8	1	no	—
1188	C₂×C₄	—	8	2	no	—
1189	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1190	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1191	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1192	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1193	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1195	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1196	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1197	C₈	—	2	1	no	—
1198	C₈	—	2	2	no	—
1199	C₈	—	2	1	no	—
1200	C₈	—	2	2	no	—
1201	C₈	—	2	1	no	—
1202	C₈	—	2	1	no	—
1203	C₂×C₃	—	4	1	no	—
1204	C₂×C₃	—	4	2	no	—
1205	C₂×C₃	—	4	2	no	—
1206	C₂×C₃	—	4	2	no	—
1207	C₂×C₃	—	4	2	no	—
1208	C₂×C₃	—	8	2	no	—
1209	C₂×C₃	—	8	2	no	—
1210	C₂×C₃	—	8	1	no	—
1211	C₂×C₃	#3484	1	1	yes	characteristic
1212	C₂×C₃	C₂×#576	1	1	yes	characteristic
1213	C₂×C₃	#3584	1	1	yes	characteristic
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	2	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	8	4	no	—
1239	C₂²	—	16	4	no	—
1240	C₂²	—	16	4	no	—
1241	C₂²	—	16	4	no	—
1242	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	2	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	2	no	—
1255	C₄	—	4	1	no	—
1256	C₄	C₃×#576	1	2	yes	—
1257	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1258	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1259	C₃	#61657	1	1	yes	characteristic, direct product factor, Sylow
1260	C₂	—	4	1	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	4	2	no	—
1265	C₂	—	8	2	no	—
1266	C₂	—	8	1	no	—
1267	C₂	—	8	2	no	—
1268	C₂	C₃×#3484	1	1	yes	characteristic
1269	C₂	C₂×C₃×#576	1	1	yes	characteristic
1270	C₂	C₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3546	C₂	semidirect
2. C₃×#3496	C₂	semidirect
3. C₃×#3330	C₂	semidirect
4. C₃×#3324	C₂	semidirect
5. C₃×#3322	C₂	semidirect
6. C₃×#3302	C₂	semidirect
7. C₃×#3297	C₂	semidirect
8. C₃×#3294	C₂	semidirect
9. C₃×#3284	C₂	semidirect
10. C₃×#3280	C₂	semidirect
11. C₃×D₄×D₈	C₂	semidirect
12. C₃×#3274	C₂	semidirect
13. C₃×#3273	C₂	semidirect
14. C₃×#3272	C₂	semidirect
15. C₃×#3212	C₂	semidirect
16. C₃×#3207	C₂	semidirect
17. C₃×#3203	C₂	semidirect
18. C₃×#3198	C₂	semidirect
19. C₃×#3105	C₂	semidirect
20. C₃×#3100	C₂	semidirect
21. C₃×#3012	C₂	semidirect
22. C₃×#3008	C₂	semidirect
23. C₃×#2979	C₂	semidirect
24. #61657	C₃	direct (N × H)
25. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
26. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₃×#135	C₂²	semidirect
29. C₂²×C₃×D₈	C₂²	semidirect
31. C₃×#556	C₂²	semidirect
32. C₃×#553	C₂²	semidirect
34. C₃×#550	C₂²	semidirect
37. C₃×#547	C₂²	semidirect
38. C₃×#547	C₂²	semidirect
41. C₃×#546	C₂²	semidirect
42. C₃×#546	C₂²	semidirect
43. C₃×#546	C₂²	semidirect
46. C₃×D₄²	C₂²	semidirect
47. C₃×D₄²	C₂²	semidirect
50. C₃×#537	C₂²	semidirect
51. C₃×#537	C₂²	semidirect
53. C₃×#535	C₂²	semidirect
56. C₃×#532	C₂²	semidirect
57. C₃×#532	C₂²	semidirect
58. C₃×#529	C₂²	semidirect
61. C₂×C₃×C₄×D₄	C₂²	semidirect
62. C₃×#495	C₂²	semidirect
63. C₃×#493	C₂²	semidirect
64. C₃×#492	C₂²	semidirect
65. C₃×#488	C₂²	semidirect
66. C₃×#487	C₂²	semidirect
67. C₃×#486	C₂²	semidirect
68. C₃×#485	C₂²	semidirect
69. C₃×#484	C₂²	semidirect
70. C₃×#484	C₂²	semidirect
71. C₃×#482	C₂²	semidirect
72. C₃×#481	C₂²	semidirect
73. C₃×#480	C₂²	semidirect
74. C₃×#480	C₂²	semidirect
75. C₃×#478	C₂²	semidirect
76. C₃×#478	C₂²	semidirect
77. C₃×#474	C₂²	semidirect
78. C₃×#474	C₂²	semidirect
79. C₃×#469	C₂²	semidirect
80. C₃×#468	C₂²	semidirect
81. C₃×#468	C₂²	semidirect
82. C₃×#468	C₂²	semidirect
83. C₃×#467	C₂²	semidirect
84. C₃×#466	C₂²	semidirect
85. C₃×#466	C₂²	semidirect
86. C₃×#465	C₂²	semidirect
87. C₃×#463	C₂²	semidirect
88. C₃×#463	C₂²	semidirect
89. C₃×#463	C₂²	semidirect
90. C₃×#463	C₂²	semidirect
91. C₃×#462	C₂²	semidirect
92. C₃×#461	C₂²	semidirect
93. C₃×#460	C₂²	semidirect
94. C₃×#459	C₂²	semidirect
95. C₃×#459	C₂²	semidirect
96. C₃×#459	C₂²	semidirect
97. C₃×#452	C₂²	semidirect
98. C₃×#452	C₂²	semidirect
99. C₃×#452	C₂²	semidirect
100. C₃×#450	C₂²	semidirect
101. C₃×#450	C₂²	semidirect
102. C₃×#450	C₂²	semidirect
103. C₃×#449	C₂²	semidirect
104. C₃×#449	C₂²	semidirect
105. C₃×#449	C₂²	semidirect
106. C₃×#449	C₂²	semidirect
107. C₃×#449	C₂²	semidirect
108. C₃×#449	C₂²	semidirect
109. C₃×#449	C₂²	semidirect
111. C₃×#447	C₂²	semidirect
112. C₃×#447	C₂²	semidirect
113. C₃×#447	C₂²	semidirect
114. C₃×#447	C₂²	semidirect
115. C₃×#447	C₂²	semidirect
116. C₃×C₄×SD₁₆	C₂²	semidirect
117. C₃×C₄×SD₁₆	C₂²	semidirect
118. C₃×C₄×D₈	C₂²	semidirect
119. C₃×C₄×D₈	C₂²	semidirect
120. C₃×C₄×D₈	C₂²	semidirect
121. C₃×C₄×D₈	C₂²	semidirect
122. C₃×#436	C₂²	semidirect
123. C₃×#436	C₂²	semidirect
124. C₃×#436	C₂²	semidirect
125. C₃×C₈×D₄	C₂²	semidirect
126. C₃×C₈×D₄	C₂²	semidirect
127. C₃×C₈×D₄	C₂²	semidirect
128. C₃×#431	C₂²	semidirect
129. C₃×#431	C₂²	semidirect
130. C₃×#418	C₂²	semidirect
131. C₃×#417	C₂²	semidirect
132. C₃×#416	C₂²	semidirect
133. C₂×C₃×#102	C₂²	semidirect
134. C₃×#408	C₂²	semidirect
135. C₃×#408	C₂²	semidirect
136. #3546	C₂×C₃	semidirect
137. #3496	C₂×C₃	semidirect
138. #3330	C₂×C₃	semidirect
139. #3324	C₂×C₃	semidirect
140. #3322	C₂×C₃	semidirect
141. #3302	C₂×C₃	semidirect
142. #3297	C₂×C₃	semidirect
143. #3294	C₂×C₃	semidirect
144. #3284	C₂×C₃	semidirect
145. #3280	C₂×C₃	semidirect
146. D₄×D₈	C₂×C₃	semidirect
147. #3274	C₂×C₃	semidirect
148. #3273	C₂×C₃	semidirect
149. #3272	C₂×C₃	semidirect
150. #3212	C₂×C₃	semidirect
151. #3207	C₂×C₃	semidirect
152. #3203	C₂×C₃	semidirect
153. #3198	C₂×C₃	semidirect
154. #3105	C₂×C₃	semidirect
155. #3100	C₂×C₃	semidirect
156. #3012	C₂×C₃	semidirect
157. #3008	C₂×C₃	semidirect
158. #2979	C₂×C₃	semidirect
342. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
343. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
344. C₂×AGL(1,ℤ/8)	C₂²×C₃	semidirect
345. C₂×#135	C₂²×C₃	semidirect
346. C₂²×D₈	C₂²×C₃	semidirect
348. #556	C₂²×C₃	semidirect
349. #553	C₂²×C₃	semidirect
351. #550	C₂²×C₃	semidirect
354. #547	C₂²×C₃	semidirect
355. #547	C₂²×C₃	semidirect
358. #546	C₂²×C₃	semidirect
359. #546	C₂²×C₃	semidirect
360. #546	C₂²×C₃	semidirect
363. D₄²	C₂²×C₃	semidirect
364. D₄²	C₂²×C₃	semidirect
367. #537	C₂²×C₃	semidirect
368. #537	C₂²×C₃	semidirect
370. #535	C₂²×C₃	semidirect
373. #532	C₂²×C₃	semidirect
374. #532	C₂²×C₃	semidirect
375. #529	C₂²×C₃	semidirect
378. C₂×C₄×D₄	C₂²×C₃	semidirect
379. #495	C₂²×C₃	semidirect
380. #493	C₂²×C₃	semidirect
381. #492	C₂²×C₃	semidirect
382. #488	C₂²×C₃	semidirect
383. #487	C₂²×C₃	semidirect
384. #486	C₂²×C₃	semidirect
385. #485	C₂²×C₃	semidirect
386. #484	C₂²×C₃	semidirect
387. #484	C₂²×C₃	semidirect
388. #482	C₂²×C₃	semidirect
389. #481	C₂²×C₃	semidirect
390. #480	C₂²×C₃	semidirect
391. #480	C₂²×C₃	semidirect
392. #478	C₂²×C₃	semidirect
393. #478	C₂²×C₃	semidirect
394. #474	C₂²×C₃	semidirect
395. #474	C₂²×C₃	semidirect
396. #469	C₂²×C₃	semidirect
397. #468	C₂²×C₃	semidirect
398. #468	C₂²×C₃	semidirect
399. #468	C₂²×C₃	semidirect
400. #467	C₂²×C₃	semidirect
401. #466	C₂²×C₃	semidirect
402. #466	C₂²×C₃	semidirect
403. #465	C₂²×C₃	semidirect
404. #463	C₂²×C₃	semidirect
405. #463	C₂²×C₃	semidirect
406. #463	C₂²×C₃	semidirect
407. #463	C₂²×C₃	semidirect
408. #462	C₂²×C₃	semidirect
409. #461	C₂²×C₃	semidirect
410. #460	C₂²×C₃	semidirect
411. #459	C₂²×C₃	semidirect
412. #459	C₂²×C₃	semidirect
413. #459	C₂²×C₃	semidirect
414. #452	C₂²×C₃	semidirect
415. #452	C₂²×C₃	semidirect
416. #452	C₂²×C₃	semidirect
417. #450	C₂²×C₃	semidirect
418. #450	C₂²×C₃	semidirect
419. #450	C₂²×C₃	semidirect
420. #449	C₂²×C₃	semidirect
421. #449	C₂²×C₃	semidirect
422. #449	C₂²×C₃	semidirect
423. #449	C₂²×C₃	semidirect
424. #449	C₂²×C₃	semidirect
425. #449	C₂²×C₃	semidirect
426. #449	C₂²×C₃	semidirect
428. #447	C₂²×C₃	semidirect
429. #447	C₂²×C₃	semidirect
430. #447	C₂²×C₃	semidirect
431. #447	C₂²×C₃	semidirect
432. #447	C₂²×C₃	semidirect
433. C₄×SD₁₆	C₂²×C₃	semidirect
434. C₄×SD₁₆	C₂²×C₃	semidirect
435. C₄×D₈	C₂²×C₃	semidirect
436. C₄×D₈	C₂²×C₃	semidirect
437. C₄×D₈	C₂²×C₃	semidirect
438. C₄×D₈	C₂²×C₃	semidirect
439. #436	C₂²×C₃	semidirect
440. #436	C₂²×C₃	semidirect
441. #436	C₂²×C₃	semidirect
442. C₈×D₄	C₂²×C₃	semidirect
443. C₈×D₄	C₂²×C₃	semidirect
444. C₈×D₄	C₂²×C₃	semidirect
445. #431	C₂²×C₃	semidirect
446. #431	C₂²×C₃	semidirect
447. #418	C₂²×C₃	semidirect
448. #417	C₂²×C₃	semidirect
449. #416	C₂²×C₃	semidirect
450. C₂×#102	C₂²×C₃	semidirect
451. #408	C₂²×C₃	semidirect
452. #408	C₂²×C₃	semidirect
1259. C₃	#61657	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3546	2
C₃×#3496	2
C₃×#3330	2
C₃×#3324	2
C₃×#3322	2
C₃×#3302	2
C₃×#3297	2
C₃×#3294	2
C₃×#3284	2
C₃×#3280	2
C₃×D₄×D₈	2
C₃×#3274	2
C₃×#3273	2
C₃×#3272	2
C₃×#3212	2
C₃×#3207	2
C₃×#3203	2
C₃×#3198	2
C₃×#3105	2
C₃×#3100	2
C₃×#3012	2
C₃×#3008	2
C₃×#2979	2
#61657	3

Subgroups — C3×#61657 #10680264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61657 #10680264