Subgroups — C₃×#61787 #10680394

Order 768.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3547	C₂	1	1	yes	maximal, characteristic
2	C₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#3352	C₂	1	2	yes	maximal, complemented
6	C₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3336	C₂	1	2	yes	maximal, complemented
9	C₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3327	C₂	1	2	yes	maximal, complemented
12	C₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3300	C₂	1	2	yes	maximal, complemented
14	C₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3202	C₂	1	2	yes	maximal, complemented
18	C₃×#3201	C₂	1	2	yes	maximal, complemented
19	C₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#3098	C₂	1	2	yes	maximal, complemented
22	C₃×#3097	C₂	1	2	yes	maximal, complemented
23	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	#61787	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#562	—	2	2	no	—
26	C₃×#559	—	2	1	no	—
27	C₃×#557	—	2	1	no	—
28	C₃×#556	—	2	2	no	—
29	C₃×#556	C₂²	1	1	yes	characteristic
30	C₃×#556	C₂²	1	1	yes	characteristic
31	C₃×#555	—	2	1	no	—
32	C₃×#555	C₂²	1	1	yes	characteristic
33	C₃×#554	C₂²	1	1	yes	characteristic
34	C₃×#554	C₂²	1	1	yes	characteristic
35	C₃×#554	C₂²	1	1	yes	characteristic
36	C₃×#553	—	2	1	no	—
37	C₃×#552	C₂²	1	2	yes	—
38	C₃×#552	C₂²	1	2	yes	—
39	C₃×#552	C₂²	1	2	yes	—
40	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
41	C₃×#548	C₂²	1	2	yes	—
42	C₃×#547	C₂²	1	1	yes	characteristic
43	C₃×#544	—	2	1	no	—
44	C₃×#542	—	2	2	no	—
45	C₃×#540	—	2	1	no	—
46	C₃×#539	—	2	2	no	—
47	C₃×#537	C₂²	1	2	yes	—
48	C₃×#536	C₂²	1	2	yes	—
49	C₃×#536	C₂²	1	2	yes	—
50	C₃×#533	C₂²	1	1	yes	characteristic
51	C₃×#533	C₂²	1	1	yes	characteristic
52	C₃×#532	C₂²	1	1	yes	characteristic
53	C₃×#529	—	2	1	no	—
54	C₃×#529	—	2	1	no	—
55	C₃×#529	C₂²	1	1	yes	characteristic
56	C₃×#520	C₂²	1	2	yes	—
57	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
58	C₃×#500	C₂²	1	1	yes	characteristic
59	C₃×#499	C₂²	1	2	yes	—
60	C₃×#498	C₂²	1	1	yes	characteristic
61	C₃×#488	C₂²	1	2	yes	—
62	C₃×#487	C₂²	1	1	yes	characteristic
63	C₃×#487	C₂²	1	1	yes	characteristic
64	C₃×#485	C₂²	1	2	yes	—
65	C₃×#485	C₂²	1	2	yes	—
66	C₃×#485	C₂²	1	2	yes	—
67	C₃×#485	C₂²	1	2	yes	—
68	C₃×#485	C₂²	1	2	yes	—
69	C₃×#485	C₂²	1	2	yes	—
70	C₃×#485	C₂²	1	2	yes	—
71	C₃×#485	C₂²	1	2	yes	—
72	C₃×#484	C₂²	1	2	yes	—
73	C₃×#484	C₂²	1	2	yes	—
74	C₃×#484	C₂²	1	2	yes	—
75	C₃×#484	C₂²	1	2	yes	—
76	C₃×#483	C₂²	1	2	yes	—
77	C₃×#483	C₂²	1	2	yes	—
78	C₃×#483	C₂²	1	1	yes	characteristic
79	C₃×#482	C₂²	1	2	yes	—
80	C₃×#482	C₂²	1	2	yes	—
81	C₃×#480	C₂²	1	2	yes	—
82	C₃×#480	C₂²	1	1	yes	characteristic
83	C₃×#479	C₂²	1	2	yes	—
84	C₃×#479	C₂²	1	2	yes	—
85	C₃×#479	C₂²	1	1	yes	characteristic
86	C₃×#479	C₂²	1	1	yes	characteristic
87	C₃×#477	C₂²	1	1	yes	characteristic
88	C₃×#477	C₂²	1	1	yes	characteristic
89	C₃×#477	C₂²	1	1	yes	characteristic
90	C₃×#476	C₂²	1	1	yes	characteristic
91	C₃×#475	C₂²	1	1	yes	characteristic
92	C₃×#474	C₂²	1	1	yes	characteristic
93	C₃×#470	C₂²	1	2	yes	—
94	C₃×#470	C₂²	1	2	yes	—
95	C₃×#470	C₂²	1	2	yes	—
96	C₃×#468	C₂²	1	2	yes	—
97	C₃×#467	C₂²	1	2	yes	—
98	C₃×#467	C₂²	1	2	yes	—
99	C₃×#467	C₂²	1	2	yes	—
100	C₃×#465	C₂²	1	2	yes	—
101	C₃×#464	C₂²	1	1	yes	characteristic
102	C₃×#464	C₂²	1	1	yes	characteristic
103	C₃×#462	C₂²	1	1	yes	characteristic
104	C₃×#462	C₂²	1	1	yes	characteristic
105	C₃×#452	C₂²	1	2	yes	—
106	C₃×#452	C₂²	1	2	yes	—
107	C₃×#451	C₂²	1	2	yes	—
108	C₃×#451	C₂²	1	1	yes	characteristic
109	C₃×#451	C₂²	1	2	yes	—
110	C₃×#451	C₂²	1	2	yes	—
111	C₃×#448	C₂²	1	1	yes	characteristic
112	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
113	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
114	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
115	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
116	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₃×#436	C₂²	1	2	yes	—
119	C₃×#436	C₂²	1	1	yes	characteristic
120	C₃×#436	C₂²	1	1	yes	characteristic
121	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
122	C₃×C₈×D₄	C₂²	1	2	yes	—
123	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
124	C₃×#431	C₂²	1	1	yes	characteristic
125	C₃×#431	C₂²	1	1	yes	characteristic
126	C₃×#428	C₂²	1	2	yes	—
127	C₃×#428	C₂²	1	2	yes	—
128	C₃×#427	C₂²	1	2	yes	—
129	C₂×C₃×#107	C₂²	1	2	yes	—
130	C₃×#419	C₂²	1	2	yes	—
131	C₃×#417	C₂²	1	2	yes	—
132	C₃×#416	C₂²	1	2	yes	—
133	C₂×C₃×#103	C₂²	1	2	yes	—
134	C₃×#408	C₂²	1	2	yes	—
135	C₃×#408	C₂²	1	2	yes	—
136	#3547	C₂×C₃	1	1	yes	characteristic
137	#3507	C₂×C₃	1	1	yes	characteristic, complemented
138	#3357	C₂×C₃	1	1	yes	characteristic, complemented
139	#3356	C₂×C₃	1	1	yes	characteristic, complemented
140	#3352	C₂×C₃	1	2	yes	complemented
141	#3340	C₂×C₃	1	1	yes	characteristic, complemented
142	#3338	C₂×C₃	1	1	yes	characteristic, complemented
143	#3336	C₂×C₃	1	2	yes	complemented
144	#3331	C₂×C₃	1	1	yes	characteristic, complemented
145	#3328	C₂×C₃	1	1	yes	characteristic, complemented
146	#3327	C₂×C₃	1	2	yes	complemented
147	#3302	C₂×C₃	1	1	yes	characteristic, complemented
148	#3300	C₂×C₃	1	2	yes	complemented
149	#3299	C₂×C₃	1	1	yes	characteristic, complemented
150	#3233	C₂×C₃	1	1	yes	characteristic, complemented
151	#3231	C₂×C₃	1	1	yes	characteristic, complemented
152	#3202	C₂×C₃	1	2	yes	complemented
153	#3201	C₂×C₃	1	2	yes	complemented
154	#3108	C₂×C₃	1	1	yes	characteristic, complemented
155	#3104	C₂×C₃	1	1	yes	characteristic, complemented
156	#3098	C₂×C₃	1	2	yes	complemented
157	#3097	C₂×C₃	1	2	yes	complemented
158	#2979	C₂×C₃	1	1	yes	characteristic, complemented
159	C₂×C₃×#41	C₂³	1	2	yes	—
160	C₂×C₃×#41	C₂³	1	2	yes	—
161	C₂²×C₃×Q₈	C₂³	1	2	yes	—
162	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
163	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
167	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₃×M₁₆	C₂³	1	2	yes	—
170	C₂×C₃×M₁₆	C₂³	1	2	yes	—
171	C₂²×C₃×C₈	C₂³	1	2	yes	—
172	C₂²×C₃×C₈	C₂³	1	2	yes	—
173	C₃×C₄⋊Q₈	—	2	2	no	—
174	C₃×C₄⋊Q₈	—	2	2	no	—
175	C₃×C₄⋊Q₈	—	2	1	no	—
176	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
177	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₃×#127	D₄	1	1	yes	characteristic
182	C₃×#126	—	2	2	no	—
183	C₃×#126	—	2	2	no	—
184	C₃×#126	—	2	2	no	—
185	C₃×#126	—	2	2	no	—
186	C₃×#126	—	2	2	no	—
187	C₃×#126	—	2	1	no	—
188	C₃×#125	—	2	2	no	—
189	C₃×#125	—	2	1	no	—
190	C₃×#125	—	2	1	no	—
191	C₃×#125	—	2	2	no	—
192	C₃×#125	—	2	2	no	—
193	C₃×#125	—	2	1	no	—
194	C₃×#125	—	2	1	no	—
195	C₃×#125	C₂³	1	1	yes	characteristic
196	C₃×#125	C₂³	1	2	yes	—
197	C₃×#124	—	2	1	no	—
198	C₃×#124	—	2	1	no	—
199	C₃×#124	—	2	2	no	—
200	C₃×#124	—	2	2	no	—
201	C₃×#124	—	2	2	no	—
202	C₃×#124	—	2	2	no	—
203	C₃×#124	D₄	1	2	yes	—
204	C₃×#124	C₂³	1	1	yes	characteristic
205	C₃×#123	—	2	2	no	—
206	C₃×#123	—	2	2	no	—
207	C₃×#123	—	2	2	no	—
208	C₃×#123	—	2	2	no	—
209	C₃×#123	—	2	2	no	—
210	C₃×#123	—	2	2	no	—
211	C₃×#123	—	2	2	no	—
212	C₃×#123	—	2	1	no	—
213	C₃×#123	—	2	2	no	—
214	C₃×C₂²⋊Q₈	—	2	2	no	—
215	C₃×C₂²⋊Q₈	—	2	1	no	—
216	C₃×C₂²⋊Q₈	—	2	1	no	—
217	C₃×C₂²⋊Q₈	—	2	1	no	—
218	C₃×C₂²⋊Q₈	—	2	2	no	—
219	C₃×C₂²⋊Q₈	—	2	2	no	—
220	C₃×C₂²⋊Q₈	—	2	2	no	—
221	C₃×C₂²⋊Q₈	—	2	2	no	—
222	C₃×C₂²⋊Q₈	—	2	2	no	—
223	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₃×#121	—	2	2	no	—
233	C₃×#121	—	2	2	no	—
234	C₃×#121	—	2	2	no	—
235	C₃×#121	—	2	2	no	—
236	C₃×#121	—	2	1	no	—
237	C₃×#121	—	2	1	no	—
238	C₃×#121	D₄	1	2	yes	—
239	C₃×#121	D₄	1	1	yes	characteristic
240	C₃×#121	D₄	1	1	yes	characteristic
241	C₃×#121	C₂³	1	1	yes	characteristic
242	C₃×#121	C₂³	1	2	yes	—
243	C₃×C₄×Q₈	—	2	2	no	—
244	C₃×C₄×Q₈	—	2	1	no	—
245	C₃×C₄×Q₈	—	2	1	no	—
246	C₃×C₄×Q₈	—	2	1	no	—
247	C₃×C₄×Q₈	—	2	1	no	—
248	C₃×C₄×Q₈	—	2	1	no	—
249	C₃×C₄×Q₈	—	2	1	no	—
250	C₃×C₄×Q₈	—	2	1	no	—
251	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
255	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
256	C₃×C₄×Q₈	C₂³	1	2	yes	—
257	C₃×C₄×D₄	—	2	2	no	—
258	C₃×C₄×D₄	—	2	1	no	—
259	C₃×C₄×D₄	—	2	1	no	—
260	C₃×C₄×D₄	—	2	2	no	—
261	C₃×C₄×D₄	—	2	2	no	—
262	C₃×C₄×D₄	—	2	1	no	—
263	C₃×C₄×D₄	—	2	1	no	—
264	C₃×C₄×D₄	—	2	1	no	—
265	C₃×C₄×D₄	—	2	2	no	—
266	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
267	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
268	C₃×C₄×D₄	C₂³	1	2	yes	—
269	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
270	C₃×#117	—	2	1	no	—
271	C₃×#117	—	2	1	no	—
272	C₃×#117	—	2	2	no	—
273	C₃×#117	—	2	2	no	—
274	C₃×#117	—	2	2	no	—
275	C₃×#117	—	2	1	no	—
276	C₃×#117	C₂³	1	2	yes	—
277	C₃×#117	C₂³	1	2	yes	—
278	C₃×#117	C₂³	1	2	yes	—
279	C₃×#117	C₂³	1	2	yes	—
280	C₂×C₃×C₄⋊C₄	—	2	1	no	—
281	C₂×C₃×C₄⋊C₄	—	2	1	no	—
282	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
284	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₃×C₄²	—	2	1	no	—
287	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
288	C₃×#107	C₂³	1	1	yes	characteristic
289	C₃×#107	C₂³	1	2	yes	—
290	C₃×#107	C₂³	1	2	yes	—
291	C₃×#107	C₂³	1	2	yes	—
292	C₃×#107	C₂³	1	2	yes	—
293	C₃×#107	C₂³	1	2	yes	—
294	C₃×#107	C₂³	1	1	yes	characteristic
295	C₃×#107	C₂³	1	2	yes	—
296	C₃×#106	C₂³	1	1	yes	characteristic
297	C₃×#106	C₂³	1	2	yes	—
298	C₃×#106	C₂³	1	1	yes	characteristic
299	C₃×#106	C₂³	1	2	yes	—
300	C₃×#106	C₂³	1	2	yes	—
301	C₃×#106	C₂³	1	2	yes	—
302	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
303	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
304	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
305	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
306	C₃×#103	C₂³	1	1	yes	characteristic
307	C₃×#103	C₂³	1	2	yes	—
308	C₃×#103	C₂³	1	2	yes	—
309	C₃×#103	C₂³	1	2	yes	—
310	C₃×#103	C₂³	1	2	yes	—
311	C₃×#103	C₂³	1	2	yes	—
312	C₃×#103	C₂³	1	2	yes	—
313	C₃×#103	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
319	C₃×#103	C₂³	1	1	yes	characteristic
320	C₃×#103	C₂³	1	2	yes	—
321	C₃×#103	C₂³	1	2	yes	—
322	C₃×#102	C₂³	1	1	yes	characteristic
323	C₃×#102	C₂³	1	2	yes	—
324	C₃×#102	C₂³	1	1	yes	characteristic
325	C₃×#102	C₂³	1	2	yes	—
326	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
327	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
328	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
329	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
330	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
331	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
332	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
334	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
335	C₃×C₄×C₈	C₂³	1	2	yes	—
336	#562	—	2	2	no	—
337	#559	—	2	1	no	—
338	#557	—	2	1	no	—
339	#556	—	2	2	no	—
340	#556	C₂²×C₃	1	1	yes	characteristic
341	#556	C₂²×C₃	1	1	yes	characteristic
342	#555	—	2	1	no	—
343	#555	C₂²×C₃	1	1	yes	characteristic
344	#554	C₂²×C₃	1	1	yes	characteristic
345	#554	C₂²×C₃	1	1	yes	characteristic
346	#554	C₂²×C₃	1	1	yes	characteristic
347	#553	—	2	1	no	—
348	#552	C₂²×C₃	1	2	yes	—
349	#552	C₂²×C₃	1	2	yes	—
350	#552	C₂²×C₃	1	2	yes	—
351	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
352	#548	C₂²×C₃	1	2	yes	—
353	#547	C₂²×C₃	1	1	yes	characteristic
354	#544	—	2	1	no	—
355	#542	—	2	2	no	—
356	#540	—	2	1	no	—
357	#539	—	2	2	no	—
358	#537	C₂²×C₃	1	2	yes	—
359	#536	C₂²×C₃	1	2	yes	—
360	#536	C₂²×C₃	1	2	yes	—
361	#533	C₂²×C₃	1	1	yes	characteristic
362	#533	C₂²×C₃	1	1	yes	characteristic
363	#532	C₂²×C₃	1	1	yes	characteristic
364	#529	—	2	1	no	—
365	#529	—	2	1	no	—
366	#529	C₂²×C₃	1	1	yes	characteristic
367	#520	C₂²×C₃	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
369	#500	C₂²×C₃	1	1	yes	characteristic
370	#499	C₂²×C₃	1	2	yes	—
371	#498	C₂²×C₃	1	1	yes	characteristic
372	#488	C₂²×C₃	1	2	yes	—
373	#487	C₂²×C₃	1	1	yes	characteristic
374	#487	C₂²×C₃	1	1	yes	characteristic
375	#485	C₂²×C₃	1	2	yes	—
376	#485	C₂²×C₃	1	2	yes	—
377	#485	C₂²×C₃	1	2	yes	—
378	#485	C₂²×C₃	1	2	yes	—
379	#485	C₂²×C₃	1	2	yes	—
380	#485	C₂²×C₃	1	2	yes	—
381	#485	C₂²×C₃	1	2	yes	—
382	#485	C₂²×C₃	1	2	yes	—
383	#484	C₂²×C₃	1	2	yes	—
384	#484	C₂²×C₃	1	2	yes	—
385	#484	C₂²×C₃	1	2	yes	—
386	#484	C₂²×C₃	1	2	yes	—
387	#483	C₂²×C₃	1	2	yes	—
388	#483	C₂²×C₃	1	2	yes	—
389	#483	C₂²×C₃	1	1	yes	characteristic
390	#482	C₂²×C₃	1	2	yes	—
391	#482	C₂²×C₃	1	2	yes	—
392	#480	C₂²×C₃	1	1	yes	characteristic
393	#480	C₂²×C₃	1	2	yes	—
394	#479	C₂²×C₃	1	1	yes	characteristic
395	#479	C₂²×C₃	1	2	yes	—
396	#479	C₂²×C₃	1	1	yes	characteristic
397	#479	C₂²×C₃	1	2	yes	—
398	#477	C₂²×C₃	1	1	yes	characteristic
399	#477	C₂²×C₃	1	1	yes	characteristic
400	#477	C₂²×C₃	1	1	yes	characteristic
401	#476	C₂²×C₃	1	1	yes	characteristic
402	#475	C₂²×C₃	1	1	yes	characteristic
403	#474	C₂²×C₃	1	1	yes	characteristic
404	#470	C₂²×C₃	1	2	yes	—
405	#470	C₂²×C₃	1	2	yes	—
406	#470	C₂²×C₃	1	2	yes	—
407	#468	C₂²×C₃	1	2	yes	—
408	#467	C₂²×C₃	1	2	yes	—
409	#467	C₂²×C₃	1	2	yes	—
410	#467	C₂²×C₃	1	2	yes	—
411	#465	C₂²×C₃	1	2	yes	—
412	#464	C₂²×C₃	1	1	yes	characteristic
413	#464	C₂²×C₃	1	1	yes	characteristic
414	#462	C₂²×C₃	1	1	yes	characteristic
415	#462	C₂²×C₃	1	1	yes	characteristic
416	#452	C₂²×C₃	1	2	yes	—
417	#452	C₂²×C₃	1	2	yes	—
418	#451	C₂²×C₃	1	2	yes	—
419	#451	C₂²×C₃	1	2	yes	—
420	#451	C₂²×C₃	1	1	yes	characteristic
421	#451	C₂²×C₃	1	2	yes	—
422	#448	C₂²×C₃	1	1	yes	characteristic
423	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
424	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
426	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
427	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
428	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
429	#436	C₂²×C₃	1	1	yes	characteristic
430	#436	C₂²×C₃	1	1	yes	characteristic
431	#436	C₂²×C₃	1	2	yes	—
432	C₈×D₄	C₂²×C₃	1	2	yes	—
433	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
434	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
435	#431	C₂²×C₃	1	1	yes	characteristic
436	#431	C₂²×C₃	1	1	yes	characteristic
437	#428	C₂²×C₃	1	2	yes	—
438	#428	C₂²×C₃	1	2	yes	—
439	#427	C₂²×C₃	1	2	yes	—
440	C₂×#107	C₂²×C₃	1	2	yes	—
441	#419	C₂²×C₃	1	2	yes	—
442	#417	C₂²×C₃	1	2	yes	—
443	#416	C₂²×C₃	1	2	yes	—
444	C₂×#103	C₂²×C₃	1	2	yes	—
445	#408	C₂²×C₃	1	2	yes	—
446	#408	C₂²×C₃	1	2	yes	—
447	C₃×#41	—	4	2	no	—
448	C₃×#41	—	4	2	no	—
449	C₃×#41	—	4	2	no	—
450	C₃×#41	—	4	2	no	—
451	C₂×C₃×Q₈	—	2	1	no	—
452	C₂×C₃×Q₈	—	2	1	no	—
453	C₂×C₃×Q₈	—	2	1	no	—
454	C₂×C₃×Q₈	—	2	1	no	—
455	C₂×C₃×Q₈	—	2	2	no	—
456	C₂×C₃×Q₈	—	4	1	no	—
457	C₂×C₃×Q₈	—	4	1	no	—
458	C₂×C₃×Q₈	—	4	2	no	—
459	C₂×C₃×Q₈	—	4	2	no	—
460	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
461	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
462	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
463	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
464	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
465	C₂×C₃×D₄	—	2	1	no	—
466	C₂×C₃×D₄	—	2	2	no	—
467	C₂×C₃×D₄	—	2	2	no	—
468	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
469	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
470	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
471	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
472	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
473	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
474	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₃×C₄	—	2	1	no	—
476	C₂²×C₃×C₄	—	2	1	no	—
477	C₂²×C₃×C₄	—	2	2	no	—
478	C₂²×C₃×C₄	—	2	2	no	—
479	C₂²×C₃×C₄	—	2	2	no	—
480	C₂²×C₃×C₄	—	2	2	no	—
481	C₂²×C₃×C₄	—	2	1	no	—
482	C₂²×C₃×C₄	—	2	2	no	—
483	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
486	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
487	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
488	C₃×Q₁₆	—	4	1	no	—
489	C₃×Q₁₆	—	4	2	no	—
490	C₃×Q₁₆	—	4	1	no	—
491	C₃×Q₁₆	—	4	2	no	—
492	C₃×SD₁₆	—	4	1	no	—
493	C₃×SD₁₆	—	4	1	no	—
494	C₃×M₁₆	—	4	2	no	—
495	C₃×M₁₆	—	4	2	no	—
496	C₂×C₃×C₈	—	4	2	no	—
497	C₂×C₃×C₈	—	4	2	no	—
498	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
499	C₂×C₃×C₈	C₂⁴	1	2	yes	—
500	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
501	C₂×C₃×C₈	C₂⁴	1	2	yes	—
502	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
503	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
504	C₃×C₄⋊C₄	—	2	1	no	—
505	C₃×C₄⋊C₄	—	2	1	no	—
506	C₃×C₄⋊C₄	—	2	1	no	—
507	C₃×C₄⋊C₄	—	2	1	no	—
508	C₃×C₄⋊C₄	—	2	1	no	—
509	C₃×C₄⋊C₄	—	2	2	no	—
510	C₃×C₄⋊C₄	—	2	1	no	—
511	C₃×C₄⋊C₄	—	2	2	no	—
512	C₃×C₄⋊C₄	—	2	2	no	—
513	C₃×C₄⋊C₄	—	2	2	no	—
514	C₃×C₄⋊C₄	—	2	1	no	—
515	C₃×C₄⋊C₄	—	2	1	no	—
516	C₃×C₄⋊C₄	—	2	2	no	—
517	C₃×C₄⋊C₄	—	2	2	no	—
518	C₃×C₄⋊C₄	—	2	2	no	—
519	C₃×C₄⋊C₄	—	2	2	no	—
520	C₃×C₄⋊C₄	—	2	1	no	—
521	C₃×C₄⋊C₄	—	2	1	no	—
522	C₃×C₄⋊C₄	—	2	1	no	—
523	C₃×C₄⋊C₄	—	2	2	no	—
524	C₃×C₄⋊C₄	—	2	2	no	—
525	C₃×C₄⋊C₄	—	2	1	no	—
526	C₃×C₄⋊C₄	—	2	2	no	—
527	C₃×C₄⋊C₄	—	2	1	no	—
528	C₃×C₄⋊C₄	—	2	2	no	—
529	C₃×C₄⋊C₄	—	2	2	no	—
530	C₃×C₄⋊C₄	—	2	2	no	—
531	C₃×C₄⋊C₄	—	2	1	no	—
532	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
533	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
534	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
535	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
536	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
537	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
538	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
539	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
540	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
541	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
542	C₃×C₂²⋊C₄	—	2	2	no	—
543	C₃×C₂²⋊C₄	—	2	2	no	—
544	C₃×C₂²⋊C₄	—	2	2	no	—
545	C₃×C₂²⋊C₄	—	2	2	no	—
546	C₃×C₂²⋊C₄	—	2	2	no	—
547	C₃×C₂²⋊C₄	—	2	2	no	—
548	C₃×C₂²⋊C₄	—	2	2	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	2	no	—
551	C₃×C₂²⋊C₄	—	2	2	no	—
552	C₃×C₂²⋊C₄	—	2	2	no	—
553	C₃×C₂²⋊C₄	—	2	2	no	—
554	C₃×C₂²⋊C₄	—	2	1	no	—
555	C₃×C₂²⋊C₄	—	2	1	no	—
556	C₃×C₂²⋊C₄	—	2	1	no	—
557	C₃×C₂²⋊C₄	—	2	2	no	—
558	C₃×C₂²⋊C₄	—	2	1	no	—
559	C₃×C₂²⋊C₄	—	2	1	no	—
560	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
561	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
562	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
563	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
564	C₃×C₄²	—	2	1	no	—
565	C₃×C₄²	—	2	1	no	—
566	C₃×C₄²	—	2	1	no	—
567	C₃×C₄²	—	2	1	no	—
568	C₃×C₄²	—	2	2	no	—
569	C₃×C₄²	—	2	2	no	—
570	C₃×C₄²	—	2	2	no	—
571	C₃×C₄²	—	2	2	no	—
572	C₃×C₄²	—	2	1	no	—
573	C₃×C₄²	—	2	2	no	—
574	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
575	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
576	C₃×C₄²	C₂⁴	1	1	yes	characteristic
577	C₃×C₄²	C₂⁴	1	1	yes	characteristic
578	C₂×#41	C₂³×C₃	1	2	yes	—
579	C₂×#41	C₂³×C₃	1	2	yes	—
580	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
581	C₂²×Q₈	C₂³×C₃	1	2	yes	—
582	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
583	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
584	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
585	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
587	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₃	1	2	yes	—
589	C₂×M₁₆	C₂³×C₃	1	2	yes	—
590	C₂²×C₈	C₂³×C₃	1	2	yes	—
591	C₂²×C₈	C₂³×C₃	1	2	yes	—
592	C₄⋊Q₈	—	2	2	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	—	2	1	no	—
595	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
596	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
597	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
598	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
600	#127	C₃×D₄	1	1	yes	characteristic
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	1	no	—
607	#125	—	2	1	no	—
608	#125	—	2	1	no	—
609	#125	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	1	no	—
613	#125	—	2	1	no	—
614	#125	C₂³×C₃	1	1	yes	characteristic
615	#125	C₂³×C₃	1	2	yes	—
616	#124	—	2	1	no	—
617	#124	—	2	1	no	—
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	C₃×D₄	1	2	yes	—
623	#124	C₂³×C₃	1	1	yes	characteristic
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	1	no	—
632	#123	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	—	2	1	no	—
636	C₂²⋊Q₈	—	2	1	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
643	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	1	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	C₃×D₄	1	1	yes	characteristic
658	#121	C₃×D₄	1	1	yes	characteristic
659	#121	C₃×D₄	1	2	yes	—
660	#121	C₂³×C₃	1	1	yes	characteristic
661	#121	C₂³×C₃	1	2	yes	—
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	—	2	1	no	—
669	C₄×Q₈	—	2	1	no	—
670	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
671	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
672	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
673	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
674	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
675	C₄×Q₈	C₂³×C₃	1	2	yes	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
687	C₄×D₄	C₂³×C₃	1	2	yes	—
688	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
689	#117	—	2	1	no	—
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	1	no	—
695	#117	C₂³×C₃	1	2	yes	—
696	#117	C₂³×C₃	1	2	yes	—
697	#117	C₂³×C₃	1	2	yes	—
698	#117	C₂³×C₃	1	2	yes	—
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
707	#107	C₂³×C₃	1	1	yes	characteristic
708	#107	C₂³×C₃	1	2	yes	—
709	#107	C₂³×C₃	1	2	yes	—
710	#107	C₂³×C₃	1	2	yes	—
711	#107	C₂³×C₃	1	2	yes	—
712	#107	C₂³×C₃	1	2	yes	—
713	#107	C₂³×C₃	1	1	yes	characteristic
714	#107	C₂³×C₃	1	2	yes	—
715	#106	C₂³×C₃	1	1	yes	characteristic
716	#106	C₂³×C₃	1	2	yes	—
717	#106	C₂³×C₃	1	1	yes	characteristic
718	#106	C₂³×C₃	1	2	yes	—
719	#106	C₂³×C₃	1	2	yes	—
720	#106	C₂³×C₃	1	2	yes	—
721	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
722	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
723	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
724	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
725	#103	C₂³×C₃	1	1	yes	characteristic
726	#103	C₂³×C₃	1	2	yes	—
727	#103	C₂³×C₃	1	2	yes	—
728	#103	C₂³×C₃	1	2	yes	—
729	#103	C₂³×C₃	1	2	yes	—
730	#103	C₂³×C₃	1	2	yes	—
731	#103	C₂³×C₃	1	2	yes	—
732	#103	C₂³×C₃	1	1	yes	characteristic
733	#103	C₂³×C₃	1	2	yes	—
734	#103	C₂³×C₃	1	2	yes	—
735	#103	C₂³×C₃	1	1	yes	characteristic
736	#103	C₂³×C₃	1	1	yes	characteristic
737	#103	C₂³×C₃	1	1	yes	characteristic
738	#103	C₂³×C₃	1	1	yes	characteristic
739	#103	C₂³×C₃	1	2	yes	—
740	#103	C₂³×C₃	1	2	yes	—
741	#102	C₂³×C₃	1	1	yes	characteristic
742	#102	C₂³×C₃	1	2	yes	—
743	#102	C₂³×C₃	1	1	yes	characteristic
744	#102	C₂³×C₃	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
746	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
747	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
752	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
753	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
754	C₄×C₈	C₂³×C₃	1	2	yes	—
755	C₂³×C₃	—	2	1	no	—
756	C₂³×C₃	C₂²×D₄	1	2	yes	—
757	C₂³×C₃	C₂²×D₄	1	2	yes	—
758	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
759	C₃×Q₈	—	2	1	no	—
760	C₃×Q₈	—	2	1	no	—
761	C₃×Q₈	—	2	1	no	—
762	C₃×Q₈	—	2	1	no	—
763	C₃×Q₈	—	2	1	no	—
764	C₃×Q₈	—	2	1	no	—
765	C₃×Q₈	—	2	2	no	—
766	C₃×Q₈	—	2	2	no	—
767	C₃×Q₈	—	4	2	no	—
768	C₃×Q₈	—	4	2	no	—
769	C₃×Q₈	—	4	2	no	—
770	C₃×Q₈	—	8	1	no	—
771	C₃×Q₈	—	8	1	no	—
772	C₃×Q₈	—	8	2	no	—
773	C₃×D₄	—	2	2	no	—
774	C₃×D₄	—	2	2	no	—
775	C₃×D₄	—	2	1	no	—
776	C₃×D₄	—	2	1	no	—
777	C₃×D₄	—	4	2	no	—
778	C₃×D₄	—	4	2	no	—
779	C₃×D₄	—	4	2	no	—
780	C₃×D₄	—	4	2	no	—
781	C₃×D₄	—	8	1	no	—
782	C₃×D₄	—	8	2	no	—
783	C₃×D₄	—	8	2	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	2	no	—
786	C₂×C₃×C₄	—	2	2	no	—
787	C₂×C₃×C₄	—	2	2	no	—
788	C₂×C₃×C₄	—	2	2	no	—
789	C₂×C₃×C₄	—	2	1	no	—
790	C₂×C₃×C₄	—	2	1	no	—
791	C₂×C₃×C₄	—	2	1	no	—
792	C₂×C₃×C₄	—	2	1	no	—
793	C₂×C₃×C₄	—	2	2	no	—
794	C₂×C₃×C₄	—	2	1	no	—
795	C₂×C₃×C₄	—	2	1	no	—
796	C₂×C₃×C₄	—	2	1	no	—
797	C₂×C₃×C₄	—	2	2	no	—
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	2	no	—
802	C₂×C₃×C₄	—	4	1	no	—
803	C₂×C₃×C₄	—	4	2	no	—
804	C₂×C₃×C₄	—	4	2	no	—
805	C₂×C₃×C₄	—	8	2	no	—
806	C₂×C₃×C₄	—	8	1	no	—
807	C₂×C₃×C₄	—	8	2	no	—
808	C₂×C₃×C₄	—	8	2	no	—
809	C₂×C₃×C₄	—	8	2	no	—
810	C₂×C₃×C₄	—	8	2	no	—
811	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
814	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
815	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
816	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
817	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
818	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
819	C₃×C₈	—	2	1	no	—
820	C₃×C₈	—	2	2	no	—
821	C₃×C₈	—	2	1	no	—
822	C₃×C₈	—	2	1	no	—
823	C₃×C₈	—	2	1	no	—
824	C₃×C₈	—	2	2	no	—
825	#41	—	4	2	no	—
826	#41	—	4	2	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	4	1	no	—
835	C₂×Q₈	—	4	1	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
839	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
840	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
841	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
842	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
847	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
848	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
849	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
850	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
851	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
852	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
866	Q₁₆	—	4	1	no	—
867	Q₁₆	—	4	2	no	—
868	Q₁₆	—	4	1	no	—
869	Q₁₆	—	4	2	no	—
870	SD₁₆	—	4	1	no	—
871	SD₁₆	—	4	1	no	—
872	M₁₆	—	4	2	no	—
873	M₁₆	—	4	2	no	—
874	C₂×C₈	—	4	2	no	—
875	C₂×C₈	—	4	2	no	—
876	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
877	C₂×C₈	C₂⁴×C₃	1	2	yes	—
878	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₃	1	2	yes	—
880	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
911	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
912	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
913	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
914	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
915	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
917	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
919	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	1	no	—
934	C₂²⋊C₄	—	2	1	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
939	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
940	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
941	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	1	no	—
945	C₄²	—	2	1	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	2	no	—
952	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
953	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
954	C₄²	C₂⁴×C₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₃	1	1	yes	characteristic
956	C₂²×C₃	—	2	1	no	—
957	C₂²×C₃	—	2	2	no	—
958	C₂²×C₃	—	2	2	no	—
959	C₂²×C₃	—	2	1	no	—
960	C₂²×C₃	—	2	2	no	—
961	C₂²×C₃	—	2	2	no	—
962	C₂²×C₃	—	2	1	no	—
963	C₂²×C₃	—	2	2	no	—
964	C₂²×C₃	—	2	2	no	—
965	C₂²×C₃	—	4	1	no	—
966	C₂²×C₃	—	4	1	no	—
967	C₂²×C₃	—	4	1	no	—
968	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
969	C₃×C₄	—	2	1	no	—
970	C₃×C₄	—	2	1	no	—
971	C₃×C₄	—	2	2	no	—
972	C₃×C₄	—	2	1	no	—
973	C₃×C₄	—	2	2	no	—
974	C₃×C₄	—	2	1	no	—
975	C₃×C₄	—	4	1	no	—
976	C₃×C₄	—	4	1	no	—
977	C₃×C₄	—	4	1	no	—
978	C₃×C₄	—	4	2	no	—
979	C₃×C₄	—	4	2	no	—
980	C₃×C₄	—	4	1	no	—
981	C₃×C₄	—	4	1	no	—
982	C₃×C₄	—	4	2	no	—
983	C₃×C₄	—	4	1	no	—
984	C₃×C₄	—	4	1	no	—
985	C₃×C₄	—	4	2	no	—
986	C₃×C₄	#578	1	2	yes	—
987	C₃×C₄	#585	1	1	yes	characteristic
988	C₃×C₄	#585	1	1	yes	characteristic
989	C₂³	—	2	1	no	—
990	C₂³	C₂²×C₃×D₄	1	2	yes	—
991	C₂³	C₂²×C₃×D₄	1	2	yes	—
992	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	1	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	8	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	4	1	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1046	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1047	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1048	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1049	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1050	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1051	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1053	C₈	—	2	1	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	2	no	—
1059	C₂×C₃	—	4	1	no	—
1060	C₂×C₃	—	4	2	no	—
1061	C₂×C₃	—	4	2	no	—
1062	C₂×C₃	—	8	1	no	—
1063	C₂×C₃	#3485	1	1	yes	characteristic
1064	C₂×C₃	C₂×#578	1	1	yes	characteristic
1065	C₂×C₃	#3584	1	1	yes	characteristic
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	C₃×#578	1	2	yes	—
1097	C₄	C₃×#585	1	1	yes	characteristic
1098	C₄	C₃×#585	1	1	yes	characteristic
1099	C₃	#61787	1	1	yes	characteristic, direct product factor, Sylow
1100	C₂	—	4	1	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	1	no	—
1104	C₂	C₃×#3485	1	1	yes	characteristic
1105	C₂	C₂×C₃×#578	1	1	yes	characteristic
1106	C₂	C₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3547	C₂
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
2. C₃×#3507	C₂	semidirect
3. C₃×#3357	C₂	semidirect
4. C₃×#3356	C₂	semidirect
5. C₃×#3352	C₂	semidirect
6. C₃×#3340	C₂	semidirect
7. C₃×#3338	C₂	semidirect
8. C₃×#3336	C₂	semidirect
9. C₃×#3331	C₂	semidirect
10. C₃×#3328	C₂	semidirect
11. C₃×#3327	C₂	semidirect
12. C₃×#3302	C₂	semidirect
13. C₃×#3300	C₂	semidirect
14. C₃×#3299	C₂	semidirect
15. C₃×#3233	C₂	semidirect
16. C₃×#3231	C₂	semidirect
17. C₃×#3202	C₂	semidirect
18. C₃×#3201	C₂	semidirect
19. C₃×#3108	C₂	semidirect
20. C₃×#3104	C₂	semidirect
21. C₃×#3098	C₂	semidirect
22. C₃×#3097	C₂	semidirect
23. C₃×#2979	C₂	semidirect
24. #61787	C₃	direct (N × H)
137. #3507	C₂×C₃	semidirect
138. #3357	C₂×C₃	semidirect
139. #3356	C₂×C₃	semidirect
140. #3352	C₂×C₃	semidirect
141. #3340	C₂×C₃	semidirect
142. #3338	C₂×C₃	semidirect
143. #3336	C₂×C₃	semidirect
144. #3331	C₂×C₃	semidirect
145. #3328	C₂×C₃	semidirect
146. #3327	C₂×C₃	semidirect
147. #3302	C₂×C₃	semidirect
148. #3300	C₂×C₃	semidirect
149. #3299	C₂×C₃	semidirect
150. #3233	C₂×C₃	semidirect
151. #3231	C₂×C₃	semidirect
152. #3202	C₂×C₃	semidirect
153. #3201	C₂×C₃	semidirect
154. #3108	C₂×C₃	semidirect
155. #3104	C₂×C₃	semidirect
156. #3098	C₂×C₃	semidirect
157. #3097	C₂×C₃	semidirect
158. #2979	C₂×C₃	semidirect
1099. C₃	#61787	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×#3547	2
C₃×#3507	2
C₃×#3357	2
C₃×#3356	2
C₃×#3352	2
C₃×#3340	2
C₃×#3338	2
C₃×#3336	2
C₃×#3331	2
C₃×#3328	2
C₃×#3327	2
C₃×#3302	2
C₃×#3300	2
C₃×#3299	2
C₃×#3233	2
C₃×#3231	2
C₃×#3202	2
C₃×#3201	2
C₃×#3108	2
C₃×#3104	2
C₃×#3098	2
C₃×#3097	2
C₃×#2979	2
#61787	3

Subgroups — C3×#61787 #10680394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61787 #10680394