Subgroups — C₃×#61872 #10680479

Order 768.

1722 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₃×#3384	C₂	1	2	yes	maximal, complemented
6	C₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₃×#3370	C₂	1	2	yes	maximal, complemented
9	C₃×#3370	C₂	1	2	yes	maximal, complemented
10	C₃×#3366	C₂	1	2	yes	maximal, complemented
11	C₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3122	C₂	1	2	yes	maximal, complemented
16	C₃×#3118	C₂	1	2	yes	maximal, complemented
17	C₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	#61872	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#562	—	2	2	no	—
22	C₃×#559	C₂²	1	1	yes	characteristic, complemented
23	C₃×#559	C₂²	1	2	yes	complemented
24	C₃×#557	C₂²	1	1	yes	characteristic, complemented
25	C₃×#554	—	2	1	no	—
26	C₃×#554	—	2	2	no	—
27	C₃×#554	C₂²	1	2	yes	—
28	C₃×#554	C₂²	1	2	yes	—
29	C₃×#554	C₂²	1	2	yes	—
30	C₃×#554	C₂²	1	2	yes	complemented
31	C₃×#550	C₂²	1	1	yes	characteristic, complemented
32	C₃×D₄×Q₈	—	2	1	no	—
33	C₃×D₄×Q₈	C₂²	1	2	yes	—
34	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×#548	—	2	1	no	—
36	C₃×#547	—	2	1	no	—
37	C₃×#544	C₂²	1	2	yes	—
38	C₃×#543	—	2	1	no	—
39	C₃×#543	—	2	1	no	—
40	C₃×#542	—	2	1	no	—
41	C₃×#542	C₂²	1	2	yes	—
42	C₃×#540	C₂²	1	2	yes	—
43	C₃×#539	—	2	2	no	—
44	C₃×#536	—	2	1	no	—
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	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
50	C₃×#518	C₂²	1	2	yes	—
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₃×#501	C₂²	1	1	yes	characteristic, complemented
53	C₃×#501	C₂²	1	2	yes	complemented
54	C₃×#501	C₂²	1	2	yes	complemented
55	C₃×#501	C₂²	1	2	yes	complemented
56	C₃×#501	C₂²	1	1	yes	characteristic, complemented
57	C₃×#499	C₂²	1	2	yes	complemented
58	C₃×#498	C₂²	1	2	yes	complemented
59	C₃×#490	C₂²	1	2	yes	complemented
60	C₃×#490	C₂²	1	2	yes	complemented
61	C₃×#489	C₂²	1	1	yes	characteristic, complemented
62	C₃×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃×#489	C₂²	1	2	yes	complemented
64	C₃×#488	C₂²	1	2	yes	complemented
65	C₃×#486	C₂²	1	2	yes	complemented
66	C₃×#485	C₂²	1	2	yes	—
67	C₃×#483	C₂²	1	1	yes	characteristic
68	C₃×#482	C₂²	1	2	yes	—
69	C₃×#482	C₂²	1	2	yes	—
70	C₃×#482	C₂²	1	2	yes	—
71	C₃×#481	C₂²	1	2	yes	—
72	C₃×#480	C₂²	1	1	yes	characteristic
73	C₃×#479	C₂²	1	2	yes	complemented
74	C₃×#479	C₂²	1	2	yes	complemented
75	C₃×#478	C₂²	1	2	yes	—
76	C₃×#478	C₂²	1	2	yes	—
77	C₃×#478	C₂²	1	2	yes	—
78	C₃×#478	C₂²	1	2	yes	complemented
79	C₃×#478	C₂²	1	2	yes	complemented
80	C₃×#478	C₂²	1	2	yes	complemented
81	C₃×#478	C₂²	1	2	yes	complemented
82	C₃×#476	C₂²	1	2	yes	—
83	C₃×#476	C₂²	1	2	yes	—
84	C₃×#476	C₂²	1	2	yes	complemented
85	C₃×#476	C₂²	1	2	yes	complemented
86	C₃×#476	C₂²	1	2	yes	complemented
87	C₃×#475	C₂²	1	2	yes	complemented
88	C₃×#474	C₂²	1	2	yes	—
89	C₃×#474	C₂²	1	2	yes	complemented
90	C₃×#474	C₂²	1	2	yes	complemented
91	C₃×#463	C₂²	1	2	yes	—
92	C₃×#463	C₂²	1	2	yes	—
93	C₃×#463	C₂²	1	2	yes	—
94	C₃×#459	C₂²	1	2	yes	—
95	C₃×#459	C₂²	1	2	yes	—
96	C₃×#459	C₂²	1	2	yes	—
97	C₃×#450	C₂²	1	1	yes	characteristic
98	C₃×#447	C₂²	1	2	yes	—
99	C₃×#447	C₂²	1	1	yes	characteristic
100	C₃×#446	C₂²	1	2	yes	complemented
101	C₃×#446	C₂²	1	2	yes	complemented
102	C₃×#446	C₂²	1	2	yes	complemented
103	C₃×#446	C₂²	1	2	yes	complemented
104	C₃×#442	C₂²	1	2	yes	—
105	C₃×#442	C₂²	1	2	yes	—
106	C₃×#442	C₂²	1	2	yes	—
107	C₃×#442	C₂²	1	2	yes	—
108	C₃×#442	C₂²	1	2	yes	—
109	C₃×#442	C₂²	1	2	yes	—
110	C₃×#440	C₂²	1	2	yes	—
111	C₃×#440	C₂²	1	2	yes	—
112	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
113	C₃×C₄×D₈	C₂²	1	2	yes	—
114	C₃×C₄×D₈	C₂²	1	2	yes	—
115	C₃×C₄×D₈	C₂²	1	2	yes	—
116	C₃×#433	C₂²	1	2	yes	—
117	C₃×#433	C₂²	1	2	yes	—
118	C₃×#432	C₂²	1	1	yes	characteristic
119	C₃×#432	C₂²	1	1	yes	characteristic
120	#3554	C₂×C₃	1	1	yes	characteristic, complemented
121	#3501	C₂×C₃	1	1	yes	characteristic, complemented
122	#3389	C₂×C₃	1	2	yes	complemented
123	#3388	C₂×C₃	1	2	yes	complemented
124	#3384	C₂×C₃	1	2	yes	complemented
125	#3384	C₂×C₃	1	2	yes	complemented
126	#3373	C₂×C₃	1	2	yes	complemented
127	#3370	C₂×C₃	1	2	yes	complemented
128	#3370	C₂×C₃	1	2	yes	complemented
129	#3366	C₂×C₃	1	2	yes	complemented
130	#3244	C₂×C₃	1	2	yes	complemented
131	#3241	C₂×C₃	1	2	yes	complemented
132	#3240	C₂×C₃	1	1	yes	characteristic, complemented
133	#3235	C₂×C₃	1	1	yes	characteristic, complemented
134	#3122	C₂×C₃	1	2	yes	complemented
135	#3118	C₂×C₃	1	2	yes	complemented
136	#3114	C₂×C₃	1	1	yes	characteristic, complemented
137	#3109	C₂×C₃	1	1	yes	characteristic, complemented
138	#2987	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×C₃×#41	—	2	1	no	—
140	C₂×C₃×#41	—	2	1	no	—
141	C₂²×C₃×Q₈	—	2	2	no	—
142	C₂²×C₃×Q₈	—	2	1	no	—
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×D₈	C₂³	1	2	yes	—
147	C₂×C₃×D₈	C₂³	1	2	yes	—
148	C₂×C₃×D₈	C₂³	1	2	yes	—
149	C₃×C₄⋊Q₈	—	2	1	no	—
150	C₃×C₄⋊Q₈	—	2	2	no	—
151	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
152	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
153	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃×#127	C₂³	1	1	yes	characteristic
160	C₃×#127	C₂³	1	2	yes	—
161	C₃×#126	—	2	2	no	—
162	C₃×#126	—	2	1	no	—
163	C₃×#125	—	2	2	no	—
164	C₃×#125	—	2	2	no	—
165	C₃×#125	D₄	1	2	yes	—
166	C₃×#125	C₂³	1	1	yes	characteristic
167	C₃×#125	C₂³	1	2	yes	—
168	C₃×#125	C₂³	1	2	yes	—
169	C₃×#125	C₂³	1	2	yes	—
170	C₃×#125	C₂³	1	2	yes	—
171	C₃×#124	—	2	2	no	—
172	C₃×#124	—	2	1	no	—
173	C₃×#124	—	2	2	no	—
174	C₃×#124	—	2	1	no	—
175	C₃×#124	C₂³	1	1	yes	characteristic
176	C₃×#124	C₂³	1	2	yes	—
177	C₃×#123	—	2	1	no	—
178	C₃×#123	—	2	2	no	—
179	C₃×#123	—	2	2	no	—
180	C₃×#123	—	2	2	no	—
181	C₃×#123	—	2	2	no	—
182	C₃×#123	—	2	2	no	—
183	C₃×#123	—	2	2	no	—
184	C₃×C₂²⋊Q₈	—	2	2	no	—
185	C₃×C₂²⋊Q₈	—	2	2	no	—
186	C₃×C₂²⋊Q₈	—	2	2	no	—
187	C₃×C₂²⋊Q₈	—	2	2	no	—
188	C₃×C₂²⋊Q₈	—	2	1	no	—
189	C₃×C₂²⋊Q₈	—	2	1	no	—
190	C₃×C₂²⋊Q₈	—	2	2	no	—
191	C₃×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
197	C₃×C₂²⋊Q₈	—	2	1	no	—
198	C₃×C₂²⋊Q₈	—	2	2	no	—
199	C₃×C₂²⋊Q₈	—	2	2	no	—
200	C₃×C₂²⋊Q₈	—	2	2	no	—
201	C₃×C₂²⋊Q₈	—	2	2	no	—
202	C₃×C₂²⋊Q₈	—	2	2	no	—
203	C₃×C₂²⋊Q₈	—	2	2	no	—
204	C₃×C₂²⋊Q₈	—	2	2	no	—
205	C₃×C₂²⋊Q₈	—	2	2	no	—
206	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
207	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃×#121	—	2	1	no	—
211	C₃×#121	—	2	2	no	—
212	C₃×#121	—	2	1	no	—
213	C₃×#121	—	2	2	no	—
214	C₃×#121	—	2	2	no	—
215	C₃×#121	C₂³	1	1	yes	characteristic
216	C₃×#121	C₂³	1	2	yes	—
217	C₃×C₄×Q₈	—	2	1	no	—
218	C₃×C₄×Q₈	—	2	1	no	—
219	C₃×C₄×Q₈	—	2	1	no	—
220	C₃×C₄×Q₈	C₂³	1	2	yes	—
221	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₃×C₄×Q₈	C₂³	1	2	yes	—
223	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₃×C₄×D₄	—	2	1	no	—
226	C₃×C₄×D₄	—	2	2	no	—
227	C₃×C₄×D₄	—	2	1	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	C₂³	1	2	yes	—
234	C₃×C₄×D₄	C₂³	1	2	yes	—
235	C₃×C₄×D₄	C₂³	1	2	yes	—
236	C₃×C₄×D₄	C₂³	1	2	yes	—
237	C₃×C₄×D₄	C₂³	1	2	yes	—
238	C₃×C₄×D₄	C₂³	1	2	yes	—
239	C₃×C₄×D₄	C₂³	1	2	yes	—
240	C₃×C₄×D₄	C₂³	1	2	yes	—
241	C₃×C₄×D₄	C₂³	1	2	yes	—
242	C₃×C₄×D₄	C₂³	1	2	yes	—
243	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
244	C₃×#117	—	2	1	no	—
245	C₃×#117	C₂³	1	2	yes	—
246	C₃×#117	C₂³	1	2	yes	—
247	C₂×C₃×C₄⋊C₄	—	2	2	no	—
248	C₂×C₃×C₄⋊C₄	—	2	2	no	—
249	C₂×C₃×C₄⋊C₄	—	2	2	no	—
250	C₂×C₃×C₄⋊C₄	—	2	2	no	—
251	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₃×#107	C₂³	1	2	yes	—
257	C₃×#107	C₂³	1	2	yes	—
258	C₃×#107	C₂³	1	2	yes	—
259	C₃×#107	C₂³	1	2	yes	—
260	C₃×#107	C₂³	1	2	yes	—
261	C₃×#106	C₂³	1	2	yes	—
262	C₃×#106	C₂³	1	2	yes	—
263	C₃×#106	C₂³	1	2	yes	—
264	C₃×#106	C₂³	1	2	yes	—
265	C₃×#106	C₂³	1	2	yes	—
266	C₃×#106	C₂³	1	2	yes	—
267	C₃×#106	C₂³	1	2	yes	—
268	C₃×C₄⋊C₈	C₂³	1	2	yes	—
269	C₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₃×C₄⋊C₈	C₂³	1	2	yes	—
271	C₃×C₄⋊C₈	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×#102	C₂³	1	2	yes	—
278	C₃×#102	C₂³	1	2	yes	—
279	C₃×#102	C₂³	1	2	yes	—
280	C₃×#102	C₂³	1	2	yes	—
281	C₃×#102	C₂³	1	2	yes	—
282	C₃×#102	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	2	yes	—
291	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₃×#97	C₂³	1	2	yes	—
294	C₃×#97	C₂³	1	1	yes	characteristic
295	C₃×#97	C₂³	1	1	yes	characteristic
296	C₃×#97	C₂³	1	2	yes	—
297	C₃×#97	C₂³	1	2	yes	—
298	C₃×C₄×C₈	C₂³	1	2	yes	—
299	C₃×C₄×C₈	C₂³	1	2	yes	—
300	#562	—	2	2	no	—
301	#559	C₂²×C₃	1	1	yes	characteristic, complemented
302	#559	C₂²×C₃	1	2	yes	complemented
303	#557	C₂²×C₃	1	1	yes	characteristic, complemented
304	#554	—	2	1	no	—
305	#554	—	2	2	no	—
306	#554	C₂²×C₃	1	2	yes	—
307	#554	C₂²×C₃	1	2	yes	—
308	#554	C₂²×C₃	1	2	yes	—
309	#554	C₂²×C₃	1	2	yes	complemented
310	#550	C₂²×C₃	1	1	yes	characteristic, complemented
311	D₄×Q₈	—	2	1	no	—
312	D₄×Q₈	C₂²×C₃	1	2	yes	—
313	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
314	#548	—	2	1	no	—
315	#547	—	2	1	no	—
316	#544	C₂²×C₃	1	2	yes	—
317	#543	—	2	1	no	—
318	#543	—	2	1	no	—
319	#542	—	2	1	no	—
320	#542	C₂²×C₃	1	2	yes	—
321	#540	C₂²×C₃	1	2	yes	—
322	#539	—	2	2	no	—
323	#536	—	2	1	no	—
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	C₂×C₂²⋊Q₈	—	2	2	no	—
329	#518	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	2	yes	complemented
334	#501	C₂²×C₃	1	2	yes	complemented
335	#501	C₂²×C₃	1	1	yes	characteristic, complemented
336	#499	C₂²×C₃	1	2	yes	complemented
337	#498	C₂²×C₃	1	2	yes	complemented
338	#490	C₂²×C₃	1	2	yes	complemented
339	#490	C₂²×C₃	1	2	yes	complemented
340	#489	C₂²×C₃	1	1	yes	characteristic, complemented
341	#489	C₂²×C₃	1	2	yes	complemented
342	#489	C₂²×C₃	1	1	yes	characteristic, complemented
343	#488	C₂²×C₃	1	2	yes	complemented
344	#486	C₂²×C₃	1	2	yes	complemented
345	#485	C₂²×C₃	1	2	yes	—
346	#483	C₂²×C₃	1	1	yes	characteristic
347	#482	C₂²×C₃	1	2	yes	—
348	#482	C₂²×C₃	1	2	yes	—
349	#482	C₂²×C₃	1	2	yes	—
350	#481	C₂²×C₃	1	2	yes	—
351	#480	C₂²×C₃	1	1	yes	characteristic
352	#479	C₂²×C₃	1	2	yes	complemented
353	#479	C₂²×C₃	1	2	yes	complemented
354	#478	C₂²×C₃	1	2	yes	—
355	#478	C₂²×C₃	1	2	yes	—
356	#478	C₂²×C₃	1	2	yes	—
357	#478	C₂²×C₃	1	2	yes	complemented
358	#478	C₂²×C₃	1	2	yes	complemented
359	#478	C₂²×C₃	1	2	yes	complemented
360	#478	C₂²×C₃	1	2	yes	complemented
361	#476	C₂²×C₃	1	2	yes	—
362	#476	C₂²×C₃	1	2	yes	—
363	#476	C₂²×C₃	1	2	yes	complemented
364	#476	C₂²×C₃	1	2	yes	complemented
365	#476	C₂²×C₃	1	2	yes	complemented
366	#475	C₂²×C₃	1	2	yes	complemented
367	#474	C₂²×C₃	1	2	yes	—
368	#474	C₂²×C₃	1	2	yes	complemented
369	#474	C₂²×C₃	1	2	yes	complemented
370	#463	C₂²×C₃	1	2	yes	—
371	#463	C₂²×C₃	1	2	yes	—
372	#463	C₂²×C₃	1	2	yes	—
373	#459	C₂²×C₃	1	2	yes	—
374	#459	C₂²×C₃	1	2	yes	—
375	#459	C₂²×C₃	1	2	yes	—
376	#450	C₂²×C₃	1	1	yes	characteristic
377	#447	C₂²×C₃	1	2	yes	—
378	#447	C₂²×C₃	1	1	yes	characteristic
379	#446	C₂²×C₃	1	2	yes	complemented
380	#446	C₂²×C₃	1	2	yes	complemented
381	#446	C₂²×C₃	1	2	yes	complemented
382	#446	C₂²×C₃	1	2	yes	complemented
383	#442	C₂²×C₃	1	2	yes	—
384	#442	C₂²×C₃	1	2	yes	—
385	#442	C₂²×C₃	1	2	yes	—
386	#442	C₂²×C₃	1	2	yes	—
387	#442	C₂²×C₃	1	2	yes	—
388	#442	C₂²×C₃	1	2	yes	—
389	#440	C₂²×C₃	1	2	yes	—
390	#440	C₂²×C₃	1	2	yes	—
391	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
392	C₄×D₈	C₂²×C₃	1	2	yes	—
393	C₄×D₈	C₂²×C₃	1	2	yes	—
394	C₄×D₈	C₂²×C₃	1	2	yes	—
395	#433	C₂²×C₃	1	2	yes	—
396	#433	C₂²×C₃	1	2	yes	—
397	#432	C₂²×C₃	1	1	yes	characteristic
398	#432	C₂²×C₃	1	1	yes	characteristic
399	C₂⁴×C₃	—	2	1	no	—
400	C₃×#41	—	8	2	no	—
401	C₃×#41	—	8	2	no	—
402	C₂×C₃×Q₈	—	2	1	no	—
403	C₂×C₃×Q₈	—	2	1	no	—
404	C₂×C₃×Q₈	—	2	1	no	—
405	C₂×C₃×Q₈	—	2	2	no	—
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	—	2	2	no	—
408	C₂×C₃×Q₈	—	8	4	no	—
409	C₂×C₃×Q₈	—	8	2	no	—
410	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
411	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
412	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
413	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₃×D₄	—	2	4	no	—
415	C₂×C₃×D₄	—	2	1	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	1	no	—
418	C₂×C₃×D₄	—	2	1	no	—
419	C₂×C₃×D₄	—	2	1	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	2	2	no	—
422	C₂×C₃×D₄	C₂⁴	1	2	yes	—
423	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
424	C₂×C₃×D₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	—	2	1	no	—
426	C₂²×C₃×C₄	—	2	2	no	—
427	C₂²×C₃×C₄	—	2	1	no	—
428	C₂²×C₃×C₄	—	2	2	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	—	2	2	no	—
431	C₂²×C₃×C₄	—	2	2	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	2	no	—
437	C₂²×C₃×C₄	—	8	2	no	—
438	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
441	C₃×SD₁₆	—	2	4	no	—
442	C₃×D₈	—	2	4	no	—
443	C₃×D₈	—	2	4	no	—
444	C₃×D₈	—	2	4	no	—
445	C₂×C₃×C₈	C₂⁴	1	2	yes	—
446	C₂×C₃×C₈	C₂⁴	1	2	yes	—
447	C₂×C₃×C₈	C₂⁴	1	2	yes	—
448	C₂×C₃×C₈	C₂⁴	1	2	yes	—
449	C₃×C₄⋊C₄	—	2	1	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	1	no	—
452	C₃×C₄⋊C₄	—	2	2	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	2	no	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₄⋊C₄	—	2	2	no	—
458	C₃×C₄⋊C₄	—	2	2	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	1	no	—
461	C₃×C₄⋊C₄	—	2	1	no	—
462	C₃×C₄⋊C₄	—	2	1	no	—
463	C₃×C₄⋊C₄	—	2	1	no	—
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
470	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
471	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
472	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
473	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
474	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
475	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
476	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
478	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
479	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
480	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
481	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
482	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
483	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	2	1	no	—
486	C₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
493	C₃×C₂²⋊C₄	—	2	1	no	—
494	C₃×C₂²⋊C₄	—	2	1	no	—
495	C₃×C₂²⋊C₄	—	2	2	no	—
496	C₃×C₂²⋊C₄	—	2	2	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	2	1	no	—
499	C₃×C₂²⋊C₄	—	2	2	no	—
500	C₃×C₂²⋊C₄	—	2	2	no	—
501	C₃×C₂²⋊C₄	—	2	2	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
504	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
505	C₃×C₄²	—	2	1	no	—
506	C₃×C₄²	—	2	2	no	—
507	C₃×C₄²	—	2	2	no	—
508	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
509	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
510	C₃×C₄²	C₂⁴	1	2	yes	—
511	C₃×C₄²	C₂⁴	1	2	yes	—
512	C₃×C₄²	C₂⁴	1	1	yes	characteristic
513	C₃×C₄²	C₂⁴	1	1	yes	characteristic
514	C₂×#41	—	2	1	no	—
515	C₂×#41	—	2	1	no	—
516	C₂²×Q₈	—	2	2	no	—
517	C₂²×Q₈	—	2	1	no	—
518	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
521	C₂×D₈	C₂³×C₃	1	2	yes	—
522	C₂×D₈	C₂³×C₃	1	2	yes	—
523	C₂×D₈	C₂³×C₃	1	2	yes	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
527	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
534	#127	C₂³×C₃	1	1	yes	characteristic
535	#127	C₂³×C₃	1	2	yes	—
536	#126	—	2	2	no	—
537	#126	—	2	1	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	C₃×D₄	1	2	yes	—
541	#125	C₂³×C₃	1	1	yes	characteristic
542	#125	C₂³×C₃	1	2	yes	—
543	#125	C₂³×C₃	1	2	yes	—
544	#125	C₂³×C₃	1	2	yes	—
545	#125	C₂³×C₃	1	2	yes	—
546	#124	—	2	1	no	—
547	#124	—	2	2	no	—
548	#124	—	2	2	no	—
549	#124	—	2	1	no	—
550	#124	C₂³×C₃	1	1	yes	characteristic
551	#124	C₂³×C₃	1	2	yes	—
552	#123	—	2	1	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
582	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
583	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	C₂³×C₃	1	1	yes	characteristic
591	#121	C₂³×C₃	1	2	yes	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	C₂³×C₃	1	2	yes	—
609	C₄×D₄	C₂³×C₃	1	2	yes	—
610	C₄×D₄	C₂³×C₃	1	2	yes	—
611	C₄×D₄	C₂³×C₃	1	2	yes	—
612	C₄×D₄	C₂³×C₃	1	2	yes	—
613	C₄×D₄	C₂³×C₃	1	2	yes	—
614	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₃	1	2	yes	—
616	C₄×D₄	C₂³×C₃	1	2	yes	—
617	C₄×D₄	C₂³×C₃	1	2	yes	—
618	C₄×D₄	C₂³×C₃	1	2	yes	—
619	#117	—	2	1	no	—
620	#117	C₂³×C₃	1	2	yes	—
621	#117	C₂³×C₃	1	2	yes	—
622	C₂×C₄⋊C₄	—	2	2	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
631	#107	C₂³×C₃	1	2	yes	—
632	#107	C₂³×C₃	1	2	yes	—
633	#107	C₂³×C₃	1	2	yes	—
634	#107	C₂³×C₃	1	2	yes	—
635	#107	C₂³×C₃	1	2	yes	—
636	#106	C₂³×C₃	1	2	yes	—
637	#106	C₂³×C₃	1	2	yes	—
638	#106	C₂³×C₃	1	2	yes	—
639	#106	C₂³×C₃	1	2	yes	—
640	#106	C₂³×C₃	1	2	yes	—
641	#106	C₂³×C₃	1	2	yes	—
642	#106	C₂³×C₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₃	1	2	yes	—
644	C₄⋊C₈	C₂³×C₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₃	1	2	yes	—
649	#103	C₂³×C₃	1	2	yes	—
650	#103	C₂³×C₃	1	2	yes	—
651	#103	C₂³×C₃	1	2	yes	—
652	#102	C₂³×C₃	1	2	yes	—
653	#102	C₂³×C₃	1	2	yes	—
654	#102	C₂³×C₃	1	2	yes	—
655	#102	C₂³×C₃	1	2	yes	—
656	#102	C₂³×C₃	1	2	yes	—
657	#102	C₂³×C₃	1	2	yes	—
658	#102	C₂³×C₃	1	2	yes	—
659	#102	C₂³×C₃	1	2	yes	—
660	#102	C₂³×C₃	1	2	yes	—
661	#102	C₂³×C₃	1	2	yes	—
662	#102	C₂³×C₃	1	2	yes	—
663	#102	C₂³×C₃	1	2	yes	—
664	#102	C₂³×C₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
667	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
668	#97	C₂³×C₃	1	2	yes	—
669	#97	C₂³×C₃	1	1	yes	characteristic
670	#97	C₂³×C₃	1	1	yes	characteristic
671	#97	C₂³×C₃	1	2	yes	—
672	#97	C₂³×C₃	1	2	yes	—
673	C₄×C₈	C₂³×C₃	1	2	yes	—
674	C₄×C₈	C₂³×C₃	1	2	yes	—
675	C₂³×C₃	—	2	4	no	—
676	C₂³×C₃	—	2	2	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	8	1	no	—
680	C₂³×C₃	—	8	1	no	—
681	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
682	C₃×Q₈	—	2	2	no	—
683	C₃×Q₈	—	4	2	no	—
684	C₃×Q₈	—	4	1	no	—
685	C₃×Q₈	—	4	1	no	—
686	C₃×Q₈	—	4	2	no	—
687	C₃×Q₈	—	4	2	no	—
688	C₃×Q₈	—	8	1	no	—
689	C₃×Q₈	—	8	2	no	—
690	C₃×Q₈	—	8	2	no	—
691	C₃×Q₈	—	8	2	no	—
692	C₃×D₄	—	2	4	no	—
693	C₃×D₄	—	2	2	no	—
694	C₃×D₄	—	2	2	no	—
695	C₃×D₄	—	2	2	no	—
696	C₃×D₄	—	2	2	no	—
697	C₃×D₄	—	4	2	no	—
698	C₃×D₄	—	8	1	no	—
699	C₃×D₄	—	8	2	no	—
700	C₃×D₄	—	8	2	no	—
701	C₃×D₄	—	8	1	no	—
702	C₃×D₄	—	8	2	no	—
703	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
704	C₂×C₃×C₄	—	2	2	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	2	no	—
712	C₂×C₃×C₄	—	4	1	no	—
713	C₂×C₃×C₄	—	4	1	no	—
714	C₂×C₃×C₄	—	4	4	no	—
715	C₂×C₃×C₄	—	4	2	no	—
716	C₂×C₃×C₄	—	8	2	no	—
717	C₂×C₃×C₄	—	8	2	no	—
718	C₂×C₃×C₄	—	8	2	no	—
719	C₂×C₃×C₄	—	8	2	no	—
720	C₂×C₃×C₄	—	8	2	no	—
721	C₂×C₃×C₄	—	8	2	no	—
722	C₂×C₃×C₄	—	8	2	no	—
723	C₂×C₃×C₄	—	8	2	no	—
724	C₂×C₃×C₄	—	8	2	no	—
725	C₂×C₃×C₄	—	8	1	no	—
726	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
727	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
728	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
729	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
730	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
731	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
732	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
733	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
734	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
735	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
736	C₃×C₈	—	2	2	no	—
737	C₃×C₈	—	2	2	no	—
738	C₃×C₈	—	2	2	no	—
739	C₃×C₈	—	2	2	no	—
740	C₂⁴	—	2	1	no	—
741	#41	—	8	2	no	—
742	#41	—	8	2	no	—
743	C₂×Q₈	—	2	1	no	—
744	C₂×Q₈	—	2	1	no	—
745	C₂×Q₈	—	2	1	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	8	4	no	—
750	C₂×Q₈	—	8	2	no	—
751	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
752	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
753	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
754	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	1	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	C₂⁴×C₃	1	2	yes	—
764	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂×D₄	C₂⁴×C₃	1	2	yes	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	8	2	no	—
779	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
780	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
782	SD₁₆	—	2	4	no	—
783	D₈	—	2	4	no	—
784	D₈	—	2	4	no	—
785	D₈	—	2	4	no	—
786	C₂×C₈	C₂⁴×C₃	1	2	yes	—
787	C₂×C₈	C₂⁴×C₃	1	2	yes	—
788	C₂×C₈	C₂⁴×C₃	1	2	yes	—
789	C₂×C₈	C₂⁴×C₃	1	2	yes	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
811	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
812	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
813	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
814	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
815	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
816	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
817	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
818	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	1	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	1	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	C₂×C₃×D₄	1	2	yes	—
845	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
846	C₄²	—	2	1	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
850	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
851	C₄²	C₂⁴×C₃	1	2	yes	—
852	C₄²	C₂⁴×C₃	1	2	yes	—
853	C₄²	C₂⁴×C₃	1	1	yes	characteristic
854	C₄²	C₂⁴×C₃	1	1	yes	characteristic
855	C₂²×C₃	—	2	1	no	—
856	C₂²×C₃	—	2	1	no	—
857	C₂²×C₃	—	2	1	no	—
858	C₂²×C₃	—	2	4	no	—
859	C₂²×C₃	—	4	2	no	—
860	C₂²×C₃	—	4	2	no	—
861	C₂²×C₃	—	4	1	no	—
862	C₂²×C₃	—	4	2	no	—
863	C₂²×C₃	—	4	2	no	—
864	C₂²×C₃	—	4	1	no	—
865	C₂²×C₃	—	4	1	no	—
866	C₂²×C₃	—	4	2	no	—
867	C₂²×C₃	—	8	4	no	—
868	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
869	C₃×C₄	—	2	1	no	—
870	C₃×C₄	—	2	1	no	—
871	C₃×C₄	—	2	1	no	—
872	C₃×C₄	—	2	1	no	—
873	C₃×C₄	—	2	2	no	—
874	C₃×C₄	—	2	2	no	—
875	C₃×C₄	—	2	2	no	—
876	C₃×C₄	—	2	2	no	—
877	C₃×C₄	—	2	1	no	—
878	C₃×C₄	—	4	1	no	—
879	C₃×C₄	—	4	2	no	—
880	C₃×C₄	—	4	1	no	—
881	C₃×C₄	—	4	2	no	—
882	C₃×C₄	—	4	2	no	—
883	C₃×C₄	—	4	2	no	—
884	C₃×C₄	—	4	1	no	—
885	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
886	C₂³	—	2	4	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	8	1	no	—
891	C₂³	—	8	1	no	—
892	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
893	Q₈	—	2	2	no	—
894	Q₈	—	4	2	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	4	1	no	—
897	Q₈	—	4	2	no	—
898	Q₈	—	4	2	no	—
899	Q₈	—	8	2	no	—
900	Q₈	—	8	2	no	—
901	Q₈	—	8	2	no	—
902	Q₈	—	8	1	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	2	no	—
909	D₄	—	8	2	no	—
910	D₄	—	8	1	no	—
911	D₄	—	8	2	no	—
912	D₄	—	8	2	no	—
913	D₄	—	8	1	no	—
914	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	1	no	—
937	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
938	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
939	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
940	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
941	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
942	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
943	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
944	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
945	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
946	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
947	C₈	—	2	2	no	—
948	C₈	—	2	2	no	—
949	C₈	—	2	2	no	—
950	C₈	—	2	2	no	—
951	C₂×C₃	—	4	1	no	—
952	C₂×C₃	—	4	4	no	—
953	C₂×C₃	—	8	1	no	—
954	C₂×C₃	—	8	2	no	—
955	C₂×C₃	#3486	1	1	yes	characteristic
956	C₂×C₃	#3585	1	1	yes	characteristic
957	C₂×C₃	#3585	1	1	yes	characteristic
958	C₂²	—	2	1	no	—
959	C₂²	—	2	4	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	8	4	no	—
971	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
972	C₄	—	2	1	no	—
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
989	C₃	#61872	1	1	yes	characteristic, direct product factor, Sylow
990	C₂	—	4	1	no	—
991	C₂	—	4	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₃×#3486	1	1	yes	characteristic
995	C₂	C₃×#3585	1	1	yes	characteristic
996	C₂	C₃×#3585	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3554	C₂	semidirect
2. C₃×#3501	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. C₃×#3388	C₂	semidirect
5. C₃×#3384	C₂	semidirect
6. C₃×#3384	C₂	semidirect
7. C₃×#3373	C₂	semidirect
8. C₃×#3370	C₂	semidirect
9. C₃×#3370	C₂	semidirect
10. C₃×#3366	C₂	semidirect
11. C₃×#3244	C₂	semidirect
12. C₃×#3241	C₂	semidirect
13. C₃×#3240	C₂	semidirect
14. C₃×#3235	C₂	semidirect
15. C₃×#3122	C₂	semidirect
16. C₃×#3118	C₂	semidirect
17. C₃×#3114	C₂	semidirect
18. C₃×#3109	C₂	semidirect
19. C₃×#2987	C₂	semidirect
20. #61872	C₃	direct (N × H)
22. C₃×#559	C₂²	semidirect
23. C₃×#559	C₂²	semidirect
24. C₃×#557	C₂²	semidirect
30. C₃×#554	C₂²	semidirect
31. C₃×#550	C₂²	semidirect
34. C₃×D₄×Q₈	C₂²	semidirect
52. C₃×#501	C₂²	semidirect
53. C₃×#501	C₂²	semidirect
54. C₃×#501	C₂²	semidirect
55. C₃×#501	C₂²	semidirect
56. C₃×#501	C₂²	semidirect
57. C₃×#499	C₂²	semidirect
58. C₃×#498	C₂²	semidirect
59. C₃×#490	C₂²	semidirect
60. C₃×#490	C₂²	semidirect
61. C₃×#489	C₂²	semidirect
62. C₃×#489	C₂²	semidirect
63. C₃×#489	C₂²	semidirect
64. C₃×#488	C₂²	semidirect
65. C₃×#486	C₂²	semidirect
73. C₃×#479	C₂²	semidirect
74. C₃×#479	C₂²	semidirect
78. C₃×#478	C₂²	semidirect
79. C₃×#478	C₂²	semidirect
80. C₃×#478	C₂²	semidirect
81. C₃×#478	C₂²	semidirect
84. C₃×#476	C₂²	semidirect
85. C₃×#476	C₂²	semidirect
86. C₃×#476	C₂²	semidirect
87. C₃×#475	C₂²	semidirect
89. C₃×#474	C₂²	semidirect
90. C₃×#474	C₂²	semidirect
100. C₃×#446	C₂²	semidirect
101. C₃×#446	C₂²	semidirect
102. C₃×#446	C₂²	semidirect
103. C₃×#446	C₂²	semidirect
120. #3554	C₂×C₃	semidirect
121. #3501	C₂×C₃	semidirect
122. #3389	C₂×C₃	semidirect
123. #3388	C₂×C₃	semidirect
124. #3384	C₂×C₃	semidirect
125. #3384	C₂×C₃	semidirect
126. #3373	C₂×C₃	semidirect
127. #3370	C₂×C₃	semidirect
128. #3370	C₂×C₃	semidirect
129. #3366	C₂×C₃	semidirect
130. #3244	C₂×C₃	semidirect
131. #3241	C₂×C₃	semidirect
132. #3240	C₂×C₃	semidirect
133. #3235	C₂×C₃	semidirect
134. #3122	C₂×C₃	semidirect
135. #3118	C₂×C₃	semidirect
136. #3114	C₂×C₃	semidirect
137. #3109	C₂×C₃	semidirect
138. #2987	C₂×C₃	semidirect
301. #559	C₂²×C₃	semidirect
302. #559	C₂²×C₃	semidirect
303. #557	C₂²×C₃	semidirect
309. #554	C₂²×C₃	semidirect
310. #550	C₂²×C₃	semidirect
313. D₄×Q₈	C₂²×C₃	semidirect
331. #501	C₂²×C₃	semidirect
332. #501	C₂²×C₃	semidirect
333. #501	C₂²×C₃	semidirect
334. #501	C₂²×C₃	semidirect
335. #501	C₂²×C₃	semidirect
336. #499	C₂²×C₃	semidirect
337. #498	C₂²×C₃	semidirect
338. #490	C₂²×C₃	semidirect
339. #490	C₂²×C₃	semidirect
340. #489	C₂²×C₃	semidirect
341. #489	C₂²×C₃	semidirect
342. #489	C₂²×C₃	semidirect
343. #488	C₂²×C₃	semidirect
344. #486	C₂²×C₃	semidirect
352. #479	C₂²×C₃	semidirect
353. #479	C₂²×C₃	semidirect
357. #478	C₂²×C₃	semidirect
358. #478	C₂²×C₃	semidirect
359. #478	C₂²×C₃	semidirect
360. #478	C₂²×C₃	semidirect
363. #476	C₂²×C₃	semidirect
364. #476	C₂²×C₃	semidirect
365. #476	C₂²×C₃	semidirect
366. #475	C₂²×C₃	semidirect
368. #474	C₂²×C₃	semidirect
369. #474	C₂²×C₃	semidirect
379. #446	C₂²×C₃	semidirect
380. #446	C₂²×C₃	semidirect
381. #446	C₂²×C₃	semidirect
382. #446	C₂²×C₃	semidirect
989. C₃	#61872	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×#3554	2
C₃×#3501	2
C₃×#3389	2
C₃×#3388	2
C₃×#3384	2
C₃×#3373	2
C₃×#3370	2
C₃×#3366	2
C₃×#3244	2
C₃×#3241	2
C₃×#3240	2
C₃×#3235	2
C₃×#3122	2
C₃×#3118	2
C₃×#3114	2
C₃×#3109	2
C₃×#2987	2
#61872	3

Subgroups — C3×#61872 #10680479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61872 #10680479