Subgroups — C₃×#61796 #10680403

Order 768.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1026 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, complemented
2	C₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3348	C₂	1	2	yes	maximal, complemented
4	C₃×#3347	C₂	1	2	yes	maximal, complemented
5	C₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₃×#3321	C₂	1	2	yes	maximal, complemented
8	C₃×#3320	C₂	1	2	yes	maximal, complemented
9	C₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₃×#3307	C₂	1	2	yes	maximal, complemented
11	C₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3200	C₂	1	2	yes	maximal, complemented
14	C₃×#3198	C₂	1	2	yes	maximal, complemented
15	C₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3098	C₂	1	2	yes	maximal, complemented
18	C₃×#3097	C₂	1	2	yes	maximal, complemented
19	C₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	#61796	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#562	—	2	2	no	—
22	C₃×#559	—	2	2	no	—
23	C₃×#556	—	2	1	no	—
24	C₃×#555	—	2	1	no	—
25	C₃×#555	C₂²	1	2	yes	—
26	C₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₃×#553	—	2	1	no	—
29	C₃×#553	C₂²	1	2	yes	—
30	C₃×#553	C₂²	1	2	yes	—
31	C₃×#552	C₂²	1	2	yes	complemented
32	C₃×#550	—	2	1	no	—
33	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#548	C₂²	1	2	yes	complemented
35	C₃×#547	C₂²	1	2	yes	—
36	C₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₃×#544	—	2	1	no	—
38	C₃×#542	—	2	2	no	—
39	C₃×#540	—	2	1	no	—
40	C₃×#538	—	2	1	no	—
41	C₃×#538	—	2	1	no	—
42	C₃×#537	C₂²	1	2	yes	—
43	C₃×#536	C₂²	1	2	yes	—
44	C₃×#535	C₂²	1	2	yes	—
45	C₃×#533	C₂²	1	1	yes	characteristic
46	C₃×#533	C₂²	1	1	yes	characteristic
47	C₃×#532	C₂²	1	1	yes	characteristic
48	C₃×#529	C₂²	1	1	yes	characteristic
49	C₃×#525	—	2	2	no	—
50	C₃×#520	C₂²	1	2	yes	—
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₃×#501	C₂²	1	2	yes	complemented
53	C₃×#501	C₂²	1	1	yes	characteristic, complemented
54	C₃×#501	C₂²	1	1	yes	characteristic, complemented
55	C₃×#491	C₂²	1	2	yes	complemented
56	C₃×#489	C₂²	1	1	yes	characteristic, complemented
57	C₃×#489	C₂²	1	1	yes	characteristic, complemented
58	C₃×#485	C₂²	1	2	yes	—
59	C₃×#485	C₂²	1	2	yes	—
60	C₃×#485	C₂²	1	2	yes	—
61	C₃×#485	C₂²	1	2	yes	complemented
62	C₃×#485	C₂²	1	2	yes	complemented
63	C₃×#485	C₂²	1	2	yes	complemented
64	C₃×#484	C₂²	1	2	yes	—
65	C₃×#484	C₂²	1	2	yes	complemented
66	C₃×#484	C₂²	1	2	yes	complemented
67	C₃×#483	C₂²	1	1	yes	characteristic
68	C₃×#483	C₂²	1	2	yes	complemented
69	C₃×#482	C₂²	1	2	yes	—
70	C₃×#482	C₂²	1	2	yes	—
71	C₃×#482	C₂²	1	2	yes	—
72	C₃×#482	C₂²	1	2	yes	complemented
73	C₃×#481	C₂²	1	2	yes	—
74	C₃×#480	C₂²	1	2	yes	—
75	C₃×#480	C₂²	1	1	yes	characteristic
76	C₃×#480	C₂²	1	2	yes	complemented
77	C₃×#479	C₂²	1	2	yes	complemented
78	C₃×#478	C₂²	1	2	yes	—
79	C₃×#478	C₂²	1	2	yes	complemented
80	C₃×#477	C₂²	1	2	yes	complemented
81	C₃×#475	C₂²	1	2	yes	complemented
82	C₃×#474	C₂²	1	2	yes	—
83	C₃×#469	C₂²	1	2	yes	—
84	C₃×#468	C₂²	1	2	yes	—
85	C₃×#468	C₂²	1	2	yes	—
86	C₃×#468	C₂²	1	2	yes	—
87	C₃×#466	C₂²	1	2	yes	—
88	C₃×#465	C₂²	1	2	yes	—
89	C₃×#465	C₂²	1	2	yes	—
90	C₃×#465	C₂²	1	2	yes	—
91	C₃×#463	C₂²	1	2	yes	—
92	C₃×#461	C₂²	1	2	yes	—
93	C₃×#450	C₂²	1	2	yes	—
94	C₃×#450	C₂²	1	1	yes	characteristic
95	C₃×#449	C₂²	1	2	yes	—
96	C₃×#449	C₂²	1	2	yes	—
97	C₃×#448	C₂²	1	2	yes	—
98	C₃×#448	C₂²	1	2	yes	—
99	C₃×#447	C₂²	1	1	yes	characteristic
100	C₃×#442	C₂²	1	2	yes	—
101	C₃×#440	C₂²	1	2	yes	—
102	C₃×#440	C₂²	1	2	yes	—
103	C₃×#440	C₂²	1	2	yes	—
104	C₃×#435	C₂²	1	2	yes	complemented
105	C₃×#435	C₂²	1	2	yes	complemented
106	C₃×#435	C₂²	1	2	yes	complemented
107	C₃×#435	C₂²	1	2	yes	complemented
108	C₃×#432	C₂²	1	1	yes	characteristic
109	C₃×#432	C₂²	1	1	yes	characteristic
110	C₃×#428	C₂²	1	2	yes	complemented
111	C₃×#428	C₂²	1	2	yes	complemented
112	C₃×#427	C₂²	1	2	yes	complemented
113	C₂×C₃×#107	C₂²	1	2	yes	complemented
114	C₃×#419	C₂²	1	2	yes	complemented
115	C₃×#417	C₂²	1	2	yes	complemented
116	C₃×#416	C₂²	1	2	yes	complemented
117	C₂×C₃×#103	C₂²	1	2	yes	complemented
118	C₃×#408	C₂²	1	2	yes	—
119	C₃×#408	C₂²	1	2	yes	—
120	#3547	C₂×C₃	1	1	yes	characteristic, complemented
121	#3506	C₂×C₃	1	1	yes	characteristic, complemented
122	#3348	C₂×C₃	1	2	yes	complemented
123	#3347	C₂×C₃	1	2	yes	complemented
124	#3346	C₂×C₃	1	2	yes	complemented
125	#3343	C₂×C₃	1	2	yes	complemented
126	#3321	C₂×C₃	1	2	yes	complemented
127	#3320	C₂×C₃	1	2	yes	complemented
128	#3308	C₂×C₃	1	2	yes	complemented
129	#3307	C₂×C₃	1	2	yes	complemented
130	#3240	C₂×C₃	1	1	yes	characteristic, complemented
131	#3237	C₂×C₃	1	1	yes	characteristic, complemented
132	#3200	C₂×C₃	1	2	yes	complemented
133	#3198	C₂×C₃	1	2	yes	complemented
134	#3114	C₂×C₃	1	1	yes	characteristic, complemented
135	#3110	C₂×C₃	1	1	yes	characteristic, complemented
136	#3098	C₂×C₃	1	2	yes	complemented
137	#3097	C₂×C₃	1	2	yes	complemented
138	#2980	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×C₃×#41	—	2	2	no	—
140	C₂×C₃×#41	C₂³	1	2	yes	—
141	C₂×C₃×#41	C₂³	1	2	yes	—
142	C₂²×C₃×Q₈	C₂³	1	2	yes	—
143	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
144	C₂³×C₃×C₄	—	2	1	no	—
145	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₃×D₈	C₂³	1	2	yes	—
149	C₂×C₃×M₁₆	C₂³	1	2	yes	—
150	C₂×C₃×M₁₆	C₂³	1	2	yes	—
151	C₂²×C₃×C₈	C₂³	1	2	yes	—
152	C₂²×C₃×C₈	C₂³	1	2	yes	—
153	C₃×C₄⋊Q₈	—	2	2	no	—
154	C₃×C₄⋊Q₈	—	2	1	no	—
155	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃×#127	—	2	2	no	—
161	C₃×#127	D₄	1	1	yes	characteristic
162	C₃×#126	—	2	2	no	—
163	C₃×#126	—	2	2	no	—
164	C₃×#126	—	2	2	no	—
165	C₃×#126	—	2	1	no	—
166	C₃×#125	—	2	2	no	—
167	C₃×#125	—	2	1	no	—
168	C₃×#125	—	2	1	no	—
169	C₃×#125	C₂³	1	1	yes	characteristic
170	C₃×#125	C₂³	1	2	yes	—
171	C₃×#124	—	2	2	no	—
172	C₃×#124	—	2	2	no	—
173	C₃×#124	—	2	2	no	—
174	C₃×#124	—	2	2	no	—
175	C₃×#124	—	2	2	no	—
176	C₃×#124	—	2	2	no	—
177	C₃×#124	D₄	1	2	yes	—
178	C₃×#124	C₂³	1	1	yes	characteristic
179	C₃×#123	—	2	2	no	—
180	C₃×#123	—	2	2	no	—
181	C₃×#123	—	2	2	no	—
182	C₃×#123	—	2	1	no	—
183	C₃×#123	—	2	2	no	—
184	C₃×#123	—	2	2	no	—
185	C₃×#123	—	2	2	no	—
186	C₃×#123	—	2	2	no	—
187	C₃×#123	—	2	2	no	—
188	C₃×C₂²⋊Q₈	—	2	2	no	—
189	C₃×C₂²⋊Q₈	—	2	1	no	—
190	C₃×C₂²⋊Q₈	—	2	1	no	—
191	C₃×C₂²⋊Q₈	—	2	1	no	—
192	C₃×C₂²⋊Q₈	—	2	2	no	—
193	C₃×C₂²⋊Q₈	—	2	2	no	—
194	C₃×C₂²⋊Q₈	—	2	2	no	—
195	C₃×C₂²⋊Q₈	—	2	2	no	—
196	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃×#121	—	2	2	no	—
202	C₃×#121	—	2	2	no	—
203	C₃×#121	—	2	2	no	—
204	C₃×#121	—	2	2	no	—
205	C₃×#121	—	2	2	no	—
206	C₃×#121	—	2	2	no	—
207	C₃×#121	—	2	2	no	—
208	C₃×#121	—	2	1	no	—
209	C₃×#121	—	2	1	no	—
210	C₃×#121	D₄	1	2	yes	—
211	C₃×#121	D₄	1	1	yes	characteristic
212	C₃×#121	D₄	1	1	yes	characteristic
213	C₃×#121	C₂³	1	1	yes	characteristic
214	C₃×#121	C₂³	1	2	yes	—
215	C₃×#121	C₂³	1	2	yes	—
216	C₃×#121	C₂³	1	2	yes	—
217	C₃×#121	C₂³	1	2	yes	—
218	C₃×#121	C₂³	1	2	yes	—
219	C₃×#120	—	2	2	no	—
220	C₃×#120	—	2	2	no	—
221	C₃×C₄×Q₈	—	2	2	no	—
222	C₃×C₄×Q₈	—	2	1	no	—
223	C₃×C₄×Q₈	—	2	1	no	—
224	C₃×C₄×Q₈	—	2	1	no	—
225	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₃×C₄×Q₈	C₂³	1	2	yes	—
227	C₃×C₄×D₄	—	2	2	no	—
228	C₃×C₄×D₄	—	2	2	no	—
229	C₃×C₄×D₄	—	2	2	no	—
230	C₃×C₄×D₄	—	2	1	no	—
231	C₃×C₄×D₄	—	2	1	no	—
232	C₃×C₄×D₄	—	2	1	no	—
233	C₃×C₄×D₄	—	2	2	no	—
234	C₃×C₄×D₄	—	2	2	no	—
235	C₃×C₄×D₄	—	2	2	no	—
236	C₃×C₄×D₄	—	2	1	no	—
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	C₂³	1	2	yes	—
239	C₃×C₄×D₄	C₂³	1	2	yes	—
240	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₃×C₄×D₄	C₂³	1	2	yes	—
242	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
243	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
244	C₃×#117	—	2	1	no	—
245	C₃×#117	—	2	2	no	—
246	C₃×#117	—	2	1	no	—
247	C₃×#117	—	2	2	no	—
248	C₃×#117	—	2	1	no	—
249	C₃×#117	C₂³	1	2	yes	—
250	C₃×#117	C₂³	1	2	yes	—
251	C₃×#117	C₂³	1	2	yes	—
252	C₃×#117	C₂³	1	2	yes	—
253	C₂×C₃×C₄⋊C₄	—	2	1	no	—
254	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
260	C₃×#107	C₂³	1	2	yes	—
261	C₃×#107	C₂³	1	2	yes	—
262	C₃×#107	C₂³	1	2	yes	—
263	C₃×#107	C₂³	1	2	yes	—
264	C₃×#107	C₂³	1	2	yes	—
265	C₃×#107	C₂³	1	2	yes	—
266	C₃×#107	C₂³	1	2	yes	—
267	C₃×#106	C₂³	1	2	yes	—
268	C₃×#106	C₂³	1	2	yes	—
269	C₃×#106	C₂³	1	2	yes	—
270	C₃×#106	C₂³	1	2	yes	—
271	C₃×#106	C₂³	1	2	yes	—
272	C₃×C₄⋊C₈	C₂³	1	2	yes	—
273	C₃×C₄⋊C₈	C₂³	1	2	yes	—
274	C₃×#103	C₂³	1	2	yes	—
275	C₃×#103	C₂³	1	2	yes	—
276	C₃×#103	C₂³	1	2	yes	—
277	C₃×#103	C₂³	1	2	yes	—
278	C₃×#103	C₂³	1	2	yes	—
279	C₃×#103	C₂³	1	2	yes	—
280	C₃×#103	C₂³	1	2	yes	—
281	C₃×#103	C₂³	1	2	yes	—
282	C₃×#103	C₂³	1	2	yes	—
283	C₃×#102	C₂³	1	2	yes	—
284	C₃×#102	C₂³	1	2	yes	—
285	C₃×#102	C₂³	1	2	yes	—
286	C₃×#102	C₂³	1	2	yes	—
287	C₃×#102	C₂³	1	2	yes	—
288	C₃×#102	C₂³	1	2	yes	—
289	C₃×#102	C₂³	1	2	yes	—
290	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
293	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
294	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
295	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
297	C₃×#97	C₂³	1	1	yes	characteristic
298	C₃×#97	C₂³	1	1	yes	characteristic
299	C₃×#97	C₂³	1	2	yes	—
300	#562	—	2	2	no	—
301	#559	—	2	2	no	—
302	#556	—	2	1	no	—
303	#555	—	2	1	no	—
304	#555	C₂²×C₃	1	2	yes	—
305	#555	C₂²×C₃	1	1	yes	characteristic, complemented
306	#554	C₂²×C₃	1	1	yes	characteristic, complemented
307	#553	—	2	1	no	—
308	#553	C₂²×C₃	1	2	yes	—
309	#553	C₂²×C₃	1	2	yes	—
310	#552	C₂²×C₃	1	2	yes	complemented
311	#550	—	2	1	no	—
312	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
313	#548	C₂²×C₃	1	2	yes	complemented
314	#547	C₂²×C₃	1	2	yes	—
315	#547	C₂²×C₃	1	1	yes	characteristic, complemented
316	#544	—	2	1	no	—
317	#542	—	2	2	no	—
318	#540	—	2	1	no	—
319	#538	—	2	1	no	—
320	#538	—	2	1	no	—
321	#537	C₂²×C₃	1	2	yes	—
322	#536	C₂²×C₃	1	2	yes	—
323	#535	C₂²×C₃	1	2	yes	—
324	#533	C₂²×C₃	1	1	yes	characteristic
325	#533	C₂²×C₃	1	1	yes	characteristic
326	#532	C₂²×C₃	1	1	yes	characteristic
327	#529	C₂²×C₃	1	1	yes	characteristic
328	#525	—	2	2	no	—
329	#520	C₂²×C₃	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
331	#501	C₂²×C₃	1	1	yes	characteristic, complemented
332	#501	C₂²×C₃	1	2	yes	complemented
333	#501	C₂²×C₃	1	1	yes	characteristic, complemented
334	#491	C₂²×C₃	1	2	yes	complemented
335	#489	C₂²×C₃	1	1	yes	characteristic, complemented
336	#489	C₂²×C₃	1	1	yes	characteristic, complemented
337	#485	C₂²×C₃	1	2	yes	—
338	#485	C₂²×C₃	1	2	yes	—
339	#485	C₂²×C₃	1	2	yes	—
340	#485	C₂²×C₃	1	2	yes	complemented
341	#485	C₂²×C₃	1	2	yes	complemented
342	#485	C₂²×C₃	1	2	yes	complemented
343	#484	C₂²×C₃	1	2	yes	—
344	#484	C₂²×C₃	1	2	yes	complemented
345	#484	C₂²×C₃	1	2	yes	complemented
346	#483	C₂²×C₃	1	1	yes	characteristic
347	#483	C₂²×C₃	1	2	yes	complemented
348	#482	C₂²×C₃	1	2	yes	—
349	#482	C₂²×C₃	1	2	yes	—
350	#482	C₂²×C₃	1	2	yes	—
351	#482	C₂²×C₃	1	2	yes	complemented
352	#481	C₂²×C₃	1	2	yes	—
353	#480	C₂²×C₃	1	2	yes	—
354	#480	C₂²×C₃	1	1	yes	characteristic
355	#480	C₂²×C₃	1	2	yes	complemented
356	#479	C₂²×C₃	1	2	yes	complemented
357	#478	C₂²×C₃	1	2	yes	—
358	#478	C₂²×C₃	1	2	yes	complemented
359	#477	C₂²×C₃	1	2	yes	complemented
360	#475	C₂²×C₃	1	2	yes	complemented
361	#474	C₂²×C₃	1	2	yes	—
362	#469	C₂²×C₃	1	2	yes	—
363	#468	C₂²×C₃	1	2	yes	—
364	#468	C₂²×C₃	1	2	yes	—
365	#468	C₂²×C₃	1	2	yes	—
366	#466	C₂²×C₃	1	2	yes	—
367	#465	C₂²×C₃	1	2	yes	—
368	#465	C₂²×C₃	1	2	yes	—
369	#465	C₂²×C₃	1	2	yes	—
370	#463	C₂²×C₃	1	2	yes	—
371	#461	C₂²×C₃	1	2	yes	—
372	#450	C₂²×C₃	1	2	yes	—
373	#450	C₂²×C₃	1	1	yes	characteristic
374	#449	C₂²×C₃	1	2	yes	—
375	#449	C₂²×C₃	1	2	yes	—
376	#448	C₂²×C₃	1	2	yes	—
377	#448	C₂²×C₃	1	2	yes	—
378	#447	C₂²×C₃	1	1	yes	characteristic
379	#442	C₂²×C₃	1	2	yes	—
380	#440	C₂²×C₃	1	2	yes	—
381	#440	C₂²×C₃	1	2	yes	—
382	#440	C₂²×C₃	1	2	yes	—
383	#435	C₂²×C₃	1	2	yes	complemented
384	#435	C₂²×C₃	1	2	yes	complemented
385	#435	C₂²×C₃	1	2	yes	complemented
386	#435	C₂²×C₃	1	2	yes	complemented
387	#432	C₂²×C₃	1	1	yes	characteristic
388	#432	C₂²×C₃	1	1	yes	characteristic
389	#428	C₂²×C₃	1	2	yes	complemented
390	#428	C₂²×C₃	1	2	yes	complemented
391	#427	C₂²×C₃	1	2	yes	complemented
392	C₂×#107	C₂²×C₃	1	2	yes	complemented
393	#419	C₂²×C₃	1	2	yes	complemented
394	#417	C₂²×C₃	1	2	yes	complemented
395	#416	C₂²×C₃	1	2	yes	complemented
396	C₂×#103	C₂²×C₃	1	2	yes	complemented
397	#408	C₂²×C₃	1	2	yes	—
398	#408	C₂²×C₃	1	2	yes	—
399	C₂⁴×C₃	—	2	1	no	—
400	C₃×#41	—	4	2	no	—
401	C₃×#41	—	4	2	no	—
402	C₃×#41	—	4	2	no	—
403	C₃×#41	—	4	2	no	—
404	C₃×#41	—	8	4	no	—
405	C₂×C₃×Q₈	—	2	1	no	—
406	C₂×C₃×Q₈	—	2	1	no	—
407	C₂×C₃×Q₈	—	2	1	no	—
408	C₂×C₃×Q₈	—	2	2	no	—
409	C₂×C₃×Q₈	—	4	2	no	—
410	C₂×C₃×Q₈	—	4	2	no	—
411	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
412	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	1	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	2	1	no	—
422	C₂×C₃×D₄	—	4	2	no	—
423	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
424	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
425	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
426	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
427	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
428	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
429	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
430	C₂×C₃×D₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	—	2	1	no	—
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	2	no	—
435	C₂²×C₃×C₄	—	2	2	no	—
436	C₂²×C₃×C₄	—	2	1	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	2	no	—
440	C₂²×C₃×C₄	—	8	2	no	—
441	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₃×SD₁₆	—	4	2	no	—
447	C₃×SD₁₆	—	4	2	no	—
448	C₃×SD₁₆	—	4	2	no	—
449	C₃×D₈	—	4	2	no	—
450	C₃×M₁₆	—	4	2	no	—
451	C₃×M₁₆	—	4	2	no	—
452	C₂×C₃×C₈	—	4	2	no	—
453	C₂×C₃×C₈	—	4	2	no	—
454	C₂×C₃×C₈	C₂⁴	1	2	yes	—
455	C₂×C₃×C₈	C₂⁴	1	2	yes	—
456	C₂×C₃×C₈	C₂⁴	1	2	yes	—
457	C₂×C₃×C₈	C₂⁴	1	2	yes	—
458	C₃×C₄⋊C₄	—	2	1	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	1	no	—
461	C₃×C₄⋊C₄	—	2	2	no	—
462	C₃×C₄⋊C₄	—	2	2	no	—
463	C₃×C₄⋊C₄	—	2	2	no	—
464	C₃×C₄⋊C₄	—	2	1	no	—
465	C₃×C₄⋊C₄	—	2	1	no	—
466	C₃×C₄⋊C₄	—	2	1	no	—
467	C₃×C₄⋊C₄	—	2	2	no	—
468	C₃×C₄⋊C₄	—	2	1	no	—
469	C₃×C₄⋊C₄	—	2	1	no	—
470	C₃×C₄⋊C₄	—	2	2	no	—
471	C₃×C₄⋊C₄	—	2	2	no	—
472	C₃×C₄⋊C₄	—	2	2	no	—
473	C₃×C₄⋊C₄	—	2	2	no	—
474	C₃×C₄⋊C₄	—	2	1	no	—
475	C₃×C₄⋊C₄	—	2	1	no	—
476	C₃×C₄⋊C₄	—	2	2	no	—
477	C₃×C₄⋊C₄	—	2	1	no	—
478	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
479	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
480	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
482	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
483	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
484	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
485	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
486	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
487	C₃×C₂²⋊C₄	—	2	2	no	—
488	C₃×C₂²⋊C₄	—	2	2	no	—
489	C₃×C₂²⋊C₄	—	2	2	no	—
490	C₃×C₂²⋊C₄	—	2	2	no	—
491	C₃×C₂²⋊C₄	—	2	2	no	—
492	C₃×C₂²⋊C₄	—	2	2	no	—
493	C₃×C₂²⋊C₄	—	2	2	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	1	no	—
496	C₃×C₂²⋊C₄	—	2	2	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	2	2	no	—
499	C₃×C₂²⋊C₄	—	2	2	no	—
500	C₃×C₂²⋊C₄	—	2	1	no	—
501	C₃×C₂²⋊C₄	—	2	1	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	—	2	1	no	—
504	C₃×C₂²⋊C₄	—	2	2	no	—
505	C₃×C₂²⋊C₄	—	2	2	no	—
506	C₃×C₂²⋊C₄	—	2	1	no	—
507	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
508	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
509	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
510	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
511	C₃×C₄²	—	2	2	no	—
512	C₃×C₄²	—	2	2	no	—
513	C₃×C₄²	—	2	2	no	—
514	C₃×C₄²	—	2	2	no	—
515	C₃×C₄²	—	2	1	no	—
516	C₃×C₄²	—	2	2	no	—
517	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
518	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
519	C₃×C₄²	C₂⁴	1	1	yes	characteristic
520	C₃×C₄²	C₂⁴	1	1	yes	characteristic
521	C₂×#41	—	2	2	no	—
522	C₂×#41	C₂³×C₃	1	2	yes	—
523	C₂×#41	C₂³×C₃	1	2	yes	—
524	C₂²×Q₈	C₂³×C₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
529	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
530	C₂×D₈	C₂³×C₃	1	2	yes	—
531	C₂×M₁₆	C₂³×C₃	1	2	yes	—
532	C₂×M₁₆	C₂³×C₃	1	2	yes	—
533	C₂²×C₈	C₂³×C₃	1	2	yes	—
534	C₂²×C₈	C₂³×C₃	1	2	yes	—
535	C₄⋊Q₈	—	2	2	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
542	#127	—	2	2	no	—
543	#127	C₃×D₄	1	1	yes	characteristic
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	—	2	1	no	—
551	#125	C₂³×C₃	1	1	yes	characteristic
552	#125	C₂³×C₃	1	2	yes	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	C₃×D₄	1	2	yes	—
560	#124	C₂³×C₃	1	1	yes	characteristic
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	1	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
579	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	C₃×D₄	1	2	yes	—
593	#121	C₃×D₄	1	1	yes	characteristic
594	#121	C₃×D₄	1	1	yes	characteristic
595	#121	C₂³×C₃	1	1	yes	characteristic
596	#121	C₂³×C₃	1	2	yes	—
597	#121	C₂³×C₃	1	2	yes	—
598	#121	C₂³×C₃	1	2	yes	—
599	#121	C₂³×C₃	1	2	yes	—
600	#121	C₂³×C₃	1	2	yes	—
601	#120	—	2	2	no	—
602	#120	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃	1	2	yes	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	C₂³×C₃	1	2	yes	—
621	C₄×D₄	C₂³×C₃	1	2	yes	—
622	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₃	1	2	yes	—
624	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	—	2	1	no	—
631	#117	C₂³×C₃	1	2	yes	—
632	#117	C₂³×C₃	1	2	yes	—
633	#117	C₂³×C₃	1	2	yes	—
634	#117	C₂³×C₃	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
642	#107	C₂³×C₃	1	2	yes	—
643	#107	C₂³×C₃	1	2	yes	—
644	#107	C₂³×C₃	1	2	yes	—
645	#107	C₂³×C₃	1	2	yes	—
646	#107	C₂³×C₃	1	2	yes	—
647	#107	C₂³×C₃	1	2	yes	—
648	#107	C₂³×C₃	1	2	yes	—
649	#106	C₂³×C₃	1	2	yes	—
650	#106	C₂³×C₃	1	2	yes	—
651	#106	C₂³×C₃	1	2	yes	—
652	#106	C₂³×C₃	1	2	yes	—
653	#106	C₂³×C₃	1	2	yes	—
654	C₄⋊C₈	C₂³×C₃	1	2	yes	—
655	C₄⋊C₈	C₂³×C₃	1	2	yes	—
656	#103	C₂³×C₃	1	2	yes	—
657	#103	C₂³×C₃	1	2	yes	—
658	#103	C₂³×C₃	1	2	yes	—
659	#103	C₂³×C₃	1	2	yes	—
660	#103	C₂³×C₃	1	2	yes	—
661	#103	C₂³×C₃	1	2	yes	—
662	#103	C₂³×C₃	1	2	yes	—
663	#103	C₂³×C₃	1	2	yes	—
664	#103	C₂³×C₃	1	2	yes	—
665	#102	C₂³×C₃	1	2	yes	—
666	#102	C₂³×C₃	1	2	yes	—
667	#102	C₂³×C₃	1	2	yes	—
668	#102	C₂³×C₃	1	2	yes	—
669	#102	C₂³×C₃	1	2	yes	—
670	#102	C₂³×C₃	1	2	yes	—
671	#102	C₂³×C₃	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
674	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
679	#97	C₂³×C₃	1	1	yes	characteristic
680	#97	C₂³×C₃	1	1	yes	characteristic
681	#97	C₂³×C₃	1	2	yes	—
682	C₂³×C₃	—	2	1	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	4	2	no	—
685	C₂³×C₃	—	8	1	no	—
686	C₂³×C₃	—	8	1	no	—
687	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
688	C₂³×C₃	C₂²×D₄	1	2	yes	—
689	C₂³×C₃	C₂²×D₄	1	2	yes	—
690	C₃×Q₈	—	2	2	no	—
691	C₃×Q₈	—	2	2	no	—
692	C₃×Q₈	—	2	2	no	—
693	C₃×Q₈	—	4	2	no	—
694	C₃×Q₈	—	4	2	no	—
695	C₃×Q₈	—	8	1	no	—
696	C₃×Q₈	—	8	1	no	—
697	C₃×Q₈	—	8	2	no	—
698	C₃×D₄	—	2	2	no	—
699	C₃×D₄	—	2	2	no	—
700	C₃×D₄	—	2	2	no	—
701	C₃×D₄	—	4	1	no	—
702	C₃×D₄	—	4	1	no	—
703	C₃×D₄	—	4	2	no	—
704	C₃×D₄	—	4	2	no	—
705	C₃×D₄	—	4	2	no	—
706	C₃×D₄	—	4	2	no	—
707	C₃×D₄	—	4	2	no	—
708	C₃×D₄	—	8	1	no	—
709	C₃×D₄	—	8	2	no	—
710	C₃×D₄	—	8	2	no	—
711	C₃×D₄	—	8	2	no	—
712	C₃×D₄	—	8	2	no	—
713	C₃×D₄	—	8	2	no	—
714	C₃×D₄	—	8	2	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	2	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	2	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	2	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	4	1	no	—
729	C₂×C₃×C₄	—	4	1	no	—
730	C₂×C₃×C₄	—	4	2	no	—
731	C₂×C₃×C₄	—	4	4	no	—
732	C₂×C₃×C₄	—	8	2	no	—
733	C₂×C₃×C₄	—	8	2	no	—
734	C₂×C₃×C₄	—	8	2	no	—
735	C₂×C₃×C₄	—	8	1	no	—
736	C₂×C₃×C₄	—	8	2	no	—
737	C₂×C₃×C₄	—	8	2	no	—
738	C₂×C₃×C₄	—	8	2	no	—
739	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
740	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
742	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
744	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
747	C₃×C₈	—	2	2	no	—
748	C₃×C₈	—	2	2	no	—
749	C₃×C₈	—	2	2	no	—
750	C₃×C₈	—	2	2	no	—
751	C₂⁴	—	2	1	no	—
752	#41	—	4	2	no	—
753	#41	—	4	2	no	—
754	#41	—	4	2	no	—
755	#41	—	4	2	no	—
756	#41	—	8	4	no	—
757	C₂×Q₈	—	2	1	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	4	2	no	—
762	C₂×Q₈	—	4	2	no	—
763	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
764	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
765	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
776	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
777	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
778	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
779	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
780	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
781	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
782	C₂×D₄	C₂⁴×C₃	1	2	yes	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	8	2	no	—
793	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
794	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
798	SD₁₆	—	4	2	no	—
799	SD₁₆	—	4	2	no	—
800	SD₁₆	—	4	2	no	—
801	D₈	—	4	2	no	—
802	M₁₆	—	4	2	no	—
803	M₁₆	—	4	2	no	—
804	C₂×C₈	—	4	2	no	—
805	C₂×C₈	—	4	2	no	—
806	C₂×C₈	C₂⁴×C₃	1	2	yes	—
807	C₂×C₈	C₂⁴×C₃	1	2	yes	—
808	C₂×C₈	C₂⁴×C₃	1	2	yes	—
809	C₂×C₈	C₂⁴×C₃	1	2	yes	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
831	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
832	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
833	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
834	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	1	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
860	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
861	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
862	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	1	no	—
868	C₄²	—	2	2	no	—
869	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
870	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
871	C₄²	C₂⁴×C₃	1	1	yes	characteristic
872	C₄²	C₂⁴×C₃	1	1	yes	characteristic
873	C₂²×C₃	—	2	1	no	—
874	C₂²×C₃	—	2	2	no	—
875	C₂²×C₃	—	2	2	no	—
876	C₂²×C₃	—	2	1	no	—
877	C₂²×C₃	—	2	2	no	—
878	C₂²×C₃	—	2	2	no	—
879	C₂²×C₃	—	2	2	no	—
880	C₂²×C₃	—	2	1	no	—
881	C₂²×C₃	—	2	2	no	—
882	C₂²×C₃	—	4	2	no	—
883	C₂²×C₃	—	4	1	no	—
884	C₂²×C₃	—	4	1	no	—
885	C₂²×C₃	—	4	2	no	—
886	C₂²×C₃	—	4	1	no	—
887	C₂²×C₃	—	4	2	no	—
888	C₂²×C₃	—	8	4	no	—
889	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
890	C₃×C₄	—	2	1	no	—
891	C₃×C₄	—	2	1	no	—
892	C₃×C₄	—	2	1	no	—
893	C₃×C₄	—	2	1	no	—
894	C₃×C₄	—	2	2	no	—
895	C₃×C₄	—	2	1	no	—
896	C₃×C₄	—	2	2	no	—
897	C₃×C₄	—	4	2	no	—
898	C₃×C₄	—	4	1	no	—
899	C₃×C₄	—	4	2	no	—
900	C₃×C₄	—	4	2	no	—
901	C₃×C₄	—	4	1	no	—
902	C₃×C₄	—	4	2	no	—
903	C₃×C₄	—	4	2	no	—
904	C₃×C₄	—	4	1	no	—
905	C₃×C₄	#585	1	2	yes	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	4	2	no	—
909	C₂³	—	8	1	no	—
910	C₂³	—	8	1	no	—
911	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
912	C₂³	C₂²×C₃×D₄	1	2	yes	—
913	C₂³	C₂²×C₃×D₄	1	2	yes	—
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	4	2	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	8	2	no	—
920	Q₈	—	8	1	no	—
921	Q₈	—	8	1	no	—
922	D₄	—	2	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	2	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	2	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	2	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	4	1	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	8	2	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	1	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
964	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
965	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
966	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
967	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
968	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
969	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
970	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
971	C₈	—	2	2	no	—
972	C₈	—	2	2	no	—
973	C₈	—	2	2	no	—
974	C₈	—	2	2	no	—
975	C₂×C₃	—	4	2	no	—
976	C₂×C₃	—	4	2	no	—
977	C₂×C₃	—	4	1	no	—
978	C₂×C₃	—	8	1	no	—
979	C₂×C₃	—	8	2	no	—
980	C₂×C₃	#3485	1	1	yes	characteristic
981	C₂×C₃	#3585	1	1	yes	characteristic
982	C₂×C₃	#3586	1	1	yes	characteristic
983	C₂²	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	8	4	no	—
999	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1000	C₄	—	2	2	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	2	no	—
1015	C₄	C₃×#585	1	2	yes	—
1016	C₃	#61796	1	1	yes	characteristic, direct product factor, Sylow
1017	C₂	—	4	1	no	—
1018	C₂	—	4	2	no	—
1019	C₂	—	4	2	no	—
1020	C₂	—	8	2	no	—
1021	C₂	—	8	1	no	—
1022	C₂	C₃×#3485	1	1	yes	characteristic
1023	C₂	C₃×#3585	1	1	yes	characteristic
1024	C₂	C₃×#3586	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×#3547	C₂	semidirect
2. C₃×#3506	C₂	semidirect
3. C₃×#3348	C₂	semidirect
4. C₃×#3347	C₂	semidirect
5. C₃×#3346	C₂	semidirect
6. C₃×#3343	C₂	semidirect
7. C₃×#3321	C₂	semidirect
8. C₃×#3320	C₂	semidirect
9. C₃×#3308	C₂	semidirect
10. C₃×#3307	C₂	semidirect
11. C₃×#3240	C₂	semidirect
12. C₃×#3237	C₂	semidirect
13. C₃×#3200	C₂	semidirect
14. C₃×#3198	C₂	semidirect
15. C₃×#3114	C₂	semidirect
16. C₃×#3110	C₂	semidirect
17. C₃×#3098	C₂	semidirect
18. C₃×#3097	C₂	semidirect
19. C₃×#2980	C₂	semidirect
20. #61796	C₃	direct (N × H)
26. C₃×#555	C₂²	semidirect
27. C₃×#554	C₂²	semidirect
31. C₃×#552	C₂²	semidirect
33. C₃×D₄×Q₈	C₂²	semidirect
34. C₃×#548	C₂²	semidirect
36. C₃×#547	C₂²	semidirect
52. C₃×#501	C₂²	semidirect
53. C₃×#501	C₂²	semidirect
54. C₃×#501	C₂²	semidirect
55. C₃×#491	C₂²	semidirect
56. C₃×#489	C₂²	semidirect
57. C₃×#489	C₂²	semidirect
61. C₃×#485	C₂²	semidirect
62. C₃×#485	C₂²	semidirect
63. C₃×#485	C₂²	semidirect
65. C₃×#484	C₂²	semidirect
66. C₃×#484	C₂²	semidirect
68. C₃×#483	C₂²	semidirect
72. C₃×#482	C₂²	semidirect
76. C₃×#480	C₂²	semidirect
77. C₃×#479	C₂²	semidirect
79. C₃×#478	C₂²	semidirect
80. C₃×#477	C₂²	semidirect
81. C₃×#475	C₂²	semidirect
104. C₃×#435	C₂²	semidirect
105. C₃×#435	C₂²	semidirect
106. C₃×#435	C₂²	semidirect
107. C₃×#435	C₂²	semidirect
110. C₃×#428	C₂²	semidirect
111. C₃×#428	C₂²	semidirect
112. C₃×#427	C₂²	semidirect
113. C₂×C₃×#107	C₂²	semidirect
114. C₃×#419	C₂²	semidirect
115. C₃×#417	C₂²	semidirect
116. C₃×#416	C₂²	semidirect
117. C₂×C₃×#103	C₂²	semidirect
120. #3547	C₂×C₃	semidirect
121. #3506	C₂×C₃	semidirect
122. #3348	C₂×C₃	semidirect
123. #3347	C₂×C₃	semidirect
124. #3346	C₂×C₃	semidirect
125. #3343	C₂×C₃	semidirect
126. #3321	C₂×C₃	semidirect
127. #3320	C₂×C₃	semidirect
128. #3308	C₂×C₃	semidirect
129. #3307	C₂×C₃	semidirect
130. #3240	C₂×C₃	semidirect
131. #3237	C₂×C₃	semidirect
132. #3200	C₂×C₃	semidirect
133. #3198	C₂×C₃	semidirect
134. #3114	C₂×C₃	semidirect
135. #3110	C₂×C₃	semidirect
136. #3098	C₂×C₃	semidirect
137. #3097	C₂×C₃	semidirect
138. #2980	C₂×C₃	semidirect
305. #555	C₂²×C₃	semidirect
306. #554	C₂²×C₃	semidirect
310. #552	C₂²×C₃	semidirect
312. D₄×Q₈	C₂²×C₃	semidirect
313. #548	C₂²×C₃	semidirect
315. #547	C₂²×C₃	semidirect
331. #501	C₂²×C₃	semidirect
332. #501	C₂²×C₃	semidirect
333. #501	C₂²×C₃	semidirect
334. #491	C₂²×C₃	semidirect
335. #489	C₂²×C₃	semidirect
336. #489	C₂²×C₃	semidirect
340. #485	C₂²×C₃	semidirect
341. #485	C₂²×C₃	semidirect
342. #485	C₂²×C₃	semidirect
344. #484	C₂²×C₃	semidirect
345. #484	C₂²×C₃	semidirect
347. #483	C₂²×C₃	semidirect
351. #482	C₂²×C₃	semidirect
355. #480	C₂²×C₃	semidirect
356. #479	C₂²×C₃	semidirect
358. #478	C₂²×C₃	semidirect
359. #477	C₂²×C₃	semidirect
360. #475	C₂²×C₃	semidirect
383. #435	C₂²×C₃	semidirect
384. #435	C₂²×C₃	semidirect
385. #435	C₂²×C₃	semidirect
386. #435	C₂²×C₃	semidirect
389. #428	C₂²×C₃	semidirect
390. #428	C₂²×C₃	semidirect
391. #427	C₂²×C₃	semidirect
392. C₂×#107	C₂²×C₃	semidirect
393. #419	C₂²×C₃	semidirect
394. #417	C₂²×C₃	semidirect
395. #416	C₂²×C₃	semidirect
396. C₂×#103	C₂²×C₃	semidirect
1016. C₃	#61796	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×#3506	2
C₃×#3348	2
C₃×#3347	2
C₃×#3346	2
C₃×#3343	2
C₃×#3321	2
C₃×#3320	2
C₃×#3308	2
C₃×#3307	2
C₃×#3240	2
C₃×#3237	2
C₃×#3200	2
C₃×#3198	2
C₃×#3114	2
C₃×#3110	2
C₃×#3098	2
C₃×#3097	2
C₃×#2980	2
#61796	3

Subgroups — C3×#61796 #10680403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61796 #10680403