Subgroups — C₃×#61795 #10680402

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3350	C₂	1	2	yes	maximal, complemented
4	C₃×#3347	C₂	1	2	yes	maximal, complemented
5	C₃×#3345	C₂	1	2	yes	maximal, complemented
6	C₃×#3345	C₂	1	2	yes	maximal, complemented
7	C₃×#3319	C₂	1	2	yes	maximal, complemented
8	C₃×#3318	C₂	1	2	yes	maximal, complemented
9	C₃×#3309	C₂	1	2	yes	maximal, complemented
10	C₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3199	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×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3099	C₂	1	2	yes	maximal, complemented
18	C₃×#3096	C₂	1	2	yes	maximal, complemented
19	C₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	#61795	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#560	—	2	2	no	—
22	C₃×#559	—	2	2	no	—
23	C₃×#556	—	2	1	no	—
24	C₃×#556	C₂²	1	1	yes	characteristic, complemented
25	C₃×#555	C₂²	1	2	yes	complemented
26	C₃×#553	C₂²	1	2	yes	—
27	C₃×#553	C₂²	1	2	yes	complemented
28	C₃×#553	C₂²	1	2	yes	complemented
29	C₃×#550	—	2	1	no	—
30	C₃×#550	—	2	1	no	—
31	C₃×#550	C₂²	1	1	yes	characteristic, complemented
32	C₃×#547	C₂²	1	2	yes	complemented
33	C₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₃×#546	—	2	1	no	—
35	C₃×#546	C₂²	1	2	yes	complemented
36	C₃×D₄²	C₂²	1	1	yes	characteristic, complemented
37	C₃×#542	—	2	1	no	—
38	C₃×#538	—	2	2	no	—
39	C₃×#538	—	2	1	no	—
40	C₃×#538	—	2	1	no	—
41	C₃×#537	C₂²	1	2	yes	—
42	C₃×#535	—	2	1	no	—
43	C₃×#535	C₂²	1	2	yes	—
44	C₃×#535	C₂²	1	2	yes	complemented
45	C₃×#533	C₂²	1	1	yes	characteristic, complemented
46	C₃×#532	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	complemented
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
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×#490	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	complemented
59	C₃×#485	C₂²	1	2	yes	complemented
60	C₃×#483	C₂²	1	2	yes	complemented
61	C₃×#483	C₂²	1	1	yes	characteristic, complemented
62	C₃×#482	C₂²	1	2	yes	—
63	C₃×#482	C₂²	1	2	yes	complemented
64	C₃×#482	C₂²	1	2	yes	complemented
65	C₃×#482	C₂²	1	2	yes	complemented
66	C₃×#482	C₂²	1	2	yes	complemented
67	C₃×#482	C₂²	1	2	yes	complemented
68	C₃×#482	C₂²	1	2	yes	complemented
69	C₃×#482	C₂²	1	2	yes	complemented
70	C₃×#481	C₂²	1	2	yes	complemented
71	C₃×#481	C₂²	1	2	yes	complemented
72	C₃×#481	C₂²	1	2	yes	complemented
73	C₃×#481	C₂²	1	2	yes	complemented
74	C₃×#480	C₂²	1	1	yes	characteristic
75	C₃×#480	C₂²	1	2	yes	complemented
76	C₃×#480	C₂²	1	2	yes	complemented
77	C₃×#479	C₂²	1	2	yes	complemented
78	C₃×#478	C₂²	1	2	yes	complemented
79	C₃×#478	C₂²	1	2	yes	complemented
80	C₃×#476	C₂²	1	2	yes	complemented
81	C₃×#476	C₂²	1	2	yes	complemented
82	C₃×#474	C₂²	1	2	yes	complemented
83	C₃×#469	C₂²	1	2	yes	—
84	C₃×#469	C₂²	1	2	yes	—
85	C₃×#469	C₂²	1	2	yes	complemented
86	C₃×#468	C₂²	1	2	yes	complemented
87	C₃×#466	C₂²	1	2	yes	—
88	C₃×#466	C₂²	1	2	yes	—
89	C₃×#466	C₂²	1	2	yes	complemented
90	C₃×#465	C₂²	1	2	yes	complemented
91	C₃×#463	C₂²	1	2	yes	—
92	C₃×#459	C₂²	1	2	yes	—
93	C₃×#450	C₂²	1	1	yes	characteristic, complemented
94	C₃×#449	C₂²	1	2	yes	complemented
95	C₃×#449	C₂²	1	2	yes	complemented
96	C₃×#447	C₂²	1	1	yes	characteristic
97	C₃×#447	C₂²	1	2	yes	—
98	C₃×#447	C₂²	1	2	yes	—
99	C₃×#447	C₂²	1	2	yes	complemented
100	C₃×#442	C₂²	1	2	yes	—
101	C₃×#442	C₂²	1	2	yes	complemented
102	C₃×#442	C₂²	1	2	yes	complemented
103	C₃×#440	C₂²	1	2	yes	complemented
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, complemented
109	C₃×#432	C₂²	1	1	yes	characteristic, complemented
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×#106	C₂²	1	2	yes	complemented
114	C₃×#418	C₂²	1	2	yes	complemented
115	C₃×#417	C₂²	1	2	yes	complemented
116	C₃×#416	C₂²	1	2	yes	complemented
117	C₂×C₃×#102	C₂²	1	2	yes	complemented
118	C₃×#408	C₂²	1	2	yes	complemented
119	C₃×#408	C₂²	1	2	yes	complemented
120	#3546	C₂×C₃	1	1	yes	characteristic, complemented
121	#3506	C₂×C₃	1	1	yes	characteristic, complemented
122	#3350	C₂×C₃	1	2	yes	complemented
123	#3347	C₂×C₃	1	2	yes	complemented
124	#3345	C₂×C₃	1	2	yes	complemented
125	#3345	C₂×C₃	1	2	yes	complemented
126	#3319	C₂×C₃	1	2	yes	complemented
127	#3318	C₂×C₃	1	2	yes	complemented
128	#3309	C₂×C₃	1	2	yes	complemented
129	#3306	C₂×C₃	1	2	yes	complemented
130	#3240	C₂×C₃	1	1	yes	characteristic, complemented
131	#3235	C₂×C₃	1	1	yes	characteristic, complemented
132	#3199	C₂×C₃	1	2	yes	complemented
133	#3198	C₂×C₃	1	2	yes	complemented
134	#3114	C₂×C₃	1	1	yes	characteristic, complemented
135	#3109	C₂×C₃	1	1	yes	characteristic, complemented
136	#3099	C₂×C₃	1	2	yes	complemented
137	#3096	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	—	2	1	no	—
141	C₂×C₃×#41	—	2	1	no	—
142	C₂×C₃×#41	C₂³	1	2	yes	—
143	C₂×C₃×#41	C₂³	1	2	yes	—
144	C₂²×C₃×D₄	—	2	1	no	—
145	C₂²×C₃×D₄	C₂³	1	2	yes	—
146	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
147	C₂³×C₃×C₄	—	2	1	no	—
148	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₃×D₈	C₂³	1	2	yes	—
150	C₂×C₃×D₈	C₂³	1	2	yes	—
151	C₂×C₃×D₈	C₂³	1	2	yes	—
152	C₂×C₃×M₁₆	C₂³	1	2	yes	—
153	C₂×C₃×M₁₆	C₂³	1	2	yes	—
154	C₂²×C₃×C₈	C₂³	1	2	yes	—
155	C₂²×C₃×C₈	C₂³	1	2	yes	—
156	C₃×C₄⋊Q₈	D₄	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	—	2	2	no	—
162	C₃×#127	—	2	1	no	—
163	C₃×#127	D₄	1	1	yes	characteristic
164	C₃×#127	C₂³	1	1	yes	characteristic
165	C₃×#126	—	2	2	no	—
166	C₃×#126	—	2	2	no	—
167	C₃×#126	—	2	2	no	—
168	C₃×#126	—	2	2	no	—
169	C₃×#126	—	2	1	no	—
170	C₃×#125	C₂³	1	1	yes	characteristic
171	C₃×#125	C₂³	1	2	yes	—
172	C₃×#124	—	2	2	no	—
173	C₃×#124	—	2	2	no	—
174	C₃×#124	—	2	1	no	—
175	C₃×#124	—	2	2	no	—
176	C₃×#124	—	2	2	no	—
177	C₃×#124	—	2	1	no	—
178	C₃×#124	D₄	1	2	yes	—
179	C₃×#124	C₂³	1	1	yes	characteristic
180	C₃×#123	—	2	1	no	—
181	C₃×#123	—	2	2	no	—
182	C₃×#123	—	2	2	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	2	no	—
192	C₃×C₂²⋊Q₈	—	2	1	no	—
193	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃×#121	—	2	2	no	—
196	C₃×#121	—	2	2	no	—
197	C₃×#121	—	2	2	no	—
198	C₃×#121	—	2	2	no	—
199	C₃×#121	—	2	2	no	—
200	C₃×#121	—	2	2	no	—
201	C₃×#121	—	2	2	no	—
202	C₃×#121	—	2	1	no	—
203	C₃×#121	—	2	1	no	—
204	C₃×#121	—	2	2	no	—
205	C₃×#121	—	2	2	no	—
206	C₃×#121	D₄	1	2	yes	—
207	C₃×#121	D₄	1	1	yes	characteristic
208	C₃×#121	D₄	1	1	yes	characteristic
209	C₃×#121	C₂³	1	2	yes	—
210	C₃×#121	C₂³	1	2	yes	—
211	C₃×#121	C₂³	1	1	yes	characteristic
212	C₃×#121	C₂³	1	2	yes	—
213	C₃×#121	C₂³	1	2	yes	—
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×#120	—	2	2	no	—
219	C₃×#120	—	2	2	no	—
220	C₃×#120	—	2	2	no	—
221	C₃×#120	—	2	2	no	—
222	C₃×#120	—	2	2	no	—
223	C₃×#120	—	2	2	no	—
224	C₃×C₄×Q₈	—	2	2	no	—
225	C₃×C₄×Q₈	—	2	1	no	—
226	C₃×C₄×Q₈	—	2	1	no	—
227	C₃×C₄×Q₈	—	2	1	no	—
228	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₃×C₄×D₄	—	2	2	no	—
230	C₃×C₄×D₄	—	2	2	no	—
231	C₃×C₄×D₄	—	2	2	no	—
232	C₃×C₄×D₄	—	2	1	no	—
233	C₃×C₄×D₄	—	2	1	no	—
234	C₃×C₄×D₄	—	2	2	no	—
235	C₃×C₄×D₄	—	2	2	no	—
236	C₃×C₄×D₄	—	2	2	no	—
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	—	2	1	no	—
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	C₂³	1	2	yes	—
241	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
242	C₃×C₄×D₄	C₂³	1	2	yes	—
243	C₃×C₄×D₄	C₂³	1	2	yes	—
244	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
245	C₃×C₄×D₄	C₂³	1	2	yes	—
246	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
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	1	yes	characteristic
257	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₃×C₂²⋊C₄	—	2	2	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×#106	C₂³	1	2	yes	—
266	C₃×#106	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×#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	1	yes	characteristic
291	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
292	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
298	C₃×#97	C₂³	1	1	yes	characteristic
299	C₃×#97	C₂³	1	1	yes	characteristic
300	#560	—	2	2	no	—
301	#559	—	2	2	no	—
302	#556	—	2	1	no	—
303	#556	C₂²×C₃	1	1	yes	characteristic, complemented
304	#555	C₂²×C₃	1	2	yes	complemented
305	#553	C₂²×C₃	1	2	yes	—
306	#553	C₂²×C₃	1	2	yes	complemented
307	#553	C₂²×C₃	1	2	yes	complemented
308	#550	—	2	1	no	—
309	#550	—	2	1	no	—
310	#550	C₂²×C₃	1	1	yes	characteristic, complemented
311	#547	C₂²×C₃	1	1	yes	characteristic, complemented
312	#547	C₂²×C₃	1	2	yes	complemented
313	#546	—	2	1	no	—
314	#546	C₂²×C₃	1	2	yes	complemented
315	D₄²	C₂²×C₃	1	1	yes	characteristic, complemented
316	#542	—	2	1	no	—
317	#538	—	2	2	no	—
318	#538	—	2	1	no	—
319	#538	—	2	1	no	—
320	#537	C₂²×C₃	1	2	yes	—
321	#535	—	2	1	no	—
322	#535	C₂²×C₃	1	2	yes	—
323	#535	C₂²×C₃	1	2	yes	complemented
324	#533	C₂²×C₃	1	1	yes	characteristic, complemented
325	#532	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	complemented
330	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
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	#490	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	complemented
338	#485	C₂²×C₃	1	2	yes	complemented
339	#483	C₂²×C₃	1	2	yes	complemented
340	#483	C₂²×C₃	1	1	yes	characteristic, complemented
341	#482	C₂²×C₃	1	2	yes	—
342	#482	C₂²×C₃	1	2	yes	complemented
343	#482	C₂²×C₃	1	2	yes	complemented
344	#482	C₂²×C₃	1	2	yes	complemented
345	#482	C₂²×C₃	1	2	yes	complemented
346	#482	C₂²×C₃	1	2	yes	complemented
347	#482	C₂²×C₃	1	2	yes	complemented
348	#482	C₂²×C₃	1	2	yes	complemented
349	#481	C₂²×C₃	1	2	yes	complemented
350	#481	C₂²×C₃	1	2	yes	complemented
351	#481	C₂²×C₃	1	2	yes	complemented
352	#481	C₂²×C₃	1	2	yes	complemented
353	#480	C₂²×C₃	1	1	yes	characteristic
354	#480	C₂²×C₃	1	2	yes	complemented
355	#480	C₂²×C₃	1	2	yes	complemented
356	#479	C₂²×C₃	1	2	yes	complemented
357	#478	C₂²×C₃	1	2	yes	complemented
358	#478	C₂²×C₃	1	2	yes	complemented
359	#476	C₂²×C₃	1	2	yes	complemented
360	#476	C₂²×C₃	1	2	yes	complemented
361	#474	C₂²×C₃	1	2	yes	complemented
362	#469	C₂²×C₃	1	2	yes	—
363	#469	C₂²×C₃	1	2	yes	—
364	#469	C₂²×C₃	1	2	yes	complemented
365	#468	C₂²×C₃	1	2	yes	complemented
366	#466	C₂²×C₃	1	2	yes	—
367	#466	C₂²×C₃	1	2	yes	—
368	#466	C₂²×C₃	1	2	yes	complemented
369	#465	C₂²×C₃	1	2	yes	complemented
370	#463	C₂²×C₃	1	2	yes	—
371	#459	C₂²×C₃	1	2	yes	—
372	#450	C₂²×C₃	1	1	yes	characteristic, complemented
373	#449	C₂²×C₃	1	2	yes	complemented
374	#449	C₂²×C₃	1	2	yes	complemented
375	#447	C₂²×C₃	1	1	yes	characteristic
376	#447	C₂²×C₃	1	2	yes	—
377	#447	C₂²×C₃	1	2	yes	—
378	#447	C₂²×C₃	1	2	yes	complemented
379	#442	C₂²×C₃	1	2	yes	—
380	#442	C₂²×C₃	1	2	yes	complemented
381	#442	C₂²×C₃	1	2	yes	complemented
382	#440	C₂²×C₃	1	2	yes	complemented
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, complemented
388	#432	C₂²×C₃	1	1	yes	characteristic, complemented
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×#106	C₂²×C₃	1	2	yes	complemented
393	#418	C₂²×C₃	1	2	yes	complemented
394	#417	C₂²×C₃	1	2	yes	complemented
395	#416	C₂²×C₃	1	2	yes	complemented
396	C₂×#102	C₂²×C₃	1	2	yes	complemented
397	#408	C₂²×C₃	1	2	yes	complemented
398	#408	C₂²×C₃	1	2	yes	complemented
399	C₂⁴×C₃	—	2	1	no	—
400	C₂⁴×C₃	—	2	2	no	—
401	C₃×#41	—	4	2	no	—
402	C₃×#41	—	4	2	no	—
403	C₃×#41	—	4	2	no	—
404	C₃×#41	—	4	2	no	—
405	C₃×#41	—	8	2	no	—
406	C₃×#41	—	8	4	no	—
407	C₃×#41	—	8	2	no	—
408	C₂×C₃×Q₈	—	2	1	no	—
409	C₂×C₃×Q₈	—	2	1	no	—
410	C₂×C₃×Q₈	—	2	1	no	—
411	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
412	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	2	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	2	no	—
422	C₂×C₃×D₄	—	2	2	no	—
423	C₂×C₃×D₄	—	2	1	no	—
424	C₂×C₃×D₄	—	2	1	no	—
425	C₂×C₃×D₄	—	2	1	no	—
426	C₂×C₃×D₄	—	2	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	2	no	—
430	C₂×C₃×D₄	—	8	2	no	—
431	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
432	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
433	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
434	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
435	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
436	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
437	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
438	C₂×C₃×D₄	C₂⁴	1	2	yes	—
439	C₂×C₃×D₄	C₂⁴	1	2	yes	—
440	C₂²×C₃×C₄	—	2	1	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	2	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	1	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	2	2	no	—
449	C₂²×C₃×C₄	—	8	2	no	—
450	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
454	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
455	C₃×SD₁₆	—	4	2	no	—
456	C₃×D₈	—	4	2	no	—
457	C₃×D₈	—	4	2	no	—
458	C₃×D₈	—	4	2	no	—
459	C₃×M₁₆	—	4	2	no	—
460	C₃×M₁₆	—	4	2	no	—
461	C₂×C₃×C₈	—	4	2	no	—
462	C₂×C₃×C₈	—	4	2	no	—
463	C₂×C₃×C₈	C₂⁴	1	2	yes	—
464	C₂×C₃×C₈	C₂⁴	1	2	yes	—
465	C₂×C₃×C₈	C₂⁴	1	2	yes	—
466	C₂×C₃×C₈	C₂⁴	1	2	yes	—
467	C₃×C₄⋊C₄	—	2	1	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	2	2	no	—
470	C₃×C₄⋊C₄	—	2	2	no	—
471	C₃×C₄⋊C₄	—	2	1	no	—
472	C₃×C₄⋊C₄	—	2	1	no	—
473	C₃×C₄⋊C₄	—	2	1	no	—
474	C₃×C₄⋊C₄	—	2	1	no	—
475	C₃×C₄⋊C₄	—	2	2	no	—
476	C₃×C₄⋊C₄	—	2	1	no	—
477	C₃×C₄⋊C₄	—	2	2	no	—
478	C₃×C₄⋊C₄	—	2	2	no	—
479	C₃×C₄⋊C₄	—	2	1	no	—
480	C₃×C₄⋊C₄	—	2	1	no	—
481	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
482	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
488	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
489	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	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	2	no	—
504	C₃×C₂²⋊C₄	—	2	2	no	—
505	C₃×C₂²⋊C₄	—	2	2	no	—
506	C₃×C₂²⋊C₄	—	2	2	no	—
507	C₃×C₂²⋊C₄	—	2	2	no	—
508	C₃×C₂²⋊C₄	—	2	2	no	—
509	C₃×C₂²⋊C₄	—	2	1	no	—
510	C₃×C₂²⋊C₄	—	2	2	no	—
511	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
512	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
513	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
514	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
515	C₃×C₄²	—	2	2	no	—
516	C₃×C₄²	—	2	2	no	—
517	C₃×C₄²	—	2	1	no	—
518	C₃×C₄²	—	2	2	no	—
519	C₃×C₄²	—	2	2	no	—
520	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
521	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
522	C₃×C₄²	C₂⁴	1	1	yes	characteristic
523	C₃×C₄²	C₂⁴	1	1	yes	characteristic
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	C₂³×C₃	1	2	yes	—
528	C₂×#41	C₂³×C₃	1	2	yes	—
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₃	1	2	yes	—
532	C₂³×C₄	—	2	1	no	—
533	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
534	C₂×D₈	C₂³×C₃	1	2	yes	—
535	C₂×D₈	C₂³×C₃	1	2	yes	—
536	C₂×D₈	C₂³×C₃	1	2	yes	—
537	C₂×M₁₆	C₂³×C₃	1	2	yes	—
538	C₂×M₁₆	C₂³×C₃	1	2	yes	—
539	C₂²×C₈	C₂³×C₃	1	2	yes	—
540	C₂²×C₈	C₂³×C₃	1	2	yes	—
541	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
545	#127	—	2	1	no	—
546	#127	—	2	2	no	—
547	#127	—	2	2	no	—
548	#127	C₃×D₄	1	1	yes	characteristic
549	#127	C₂³×C₃	1	1	yes	characteristic
550	#126	—	2	2	no	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	1	no	—
555	#125	C₂³×C₃	1	1	yes	characteristic
556	#125	C₂³×C₃	1	2	yes	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	1	no	—
563	#124	C₃×D₄	1	2	yes	—
564	#124	C₂³×C₃	1	1	yes	characteristic
565	#123	—	2	1	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
579	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	C₃×D₄	1	2	yes	—
592	#121	C₃×D₄	1	1	yes	characteristic
593	#121	C₃×D₄	1	1	yes	characteristic
594	#121	C₂³×C₃	1	1	yes	characteristic
595	#121	C₂³×C₃	1	2	yes	—
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	#121	C₂³×C₃	1	2	yes	—
602	#121	C₂³×C₃	1	2	yes	—
603	#120	—	2	2	no	—
604	#120	—	2	2	no	—
605	#120	—	2	2	no	—
606	#120	—	2	2	no	—
607	#120	—	2	2	no	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	C₂³×C₃	1	2	yes	—
626	C₄×D₄	C₂³×C₃	1	2	yes	—
627	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₃	1	2	yes	—
629	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₃	1	2	yes	—
631	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
632	#117	—	2	2	no	—
633	#117	—	2	1	no	—
634	#117	C₂³×C₃	1	2	yes	—
635	#117	C₂³×C₃	1	2	yes	—
636	#117	C₂³×C₃	1	2	yes	—
637	#117	C₂³×C₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	2	no	—
644	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	#107	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	#106	C₂³×C₃	1	2	yes	—
655	#106	C₂³×C₃	1	2	yes	—
656	#106	C₂³×C₃	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃	1	2	yes	—
658	C₄⋊C₈	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	#102	C₂³×C₃	1	2	yes	—
663	#102	C₂³×C₃	1	2	yes	—
664	#102	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	#102	C₂³×C₃	1	2	yes	—
673	#102	C₂³×C₃	1	2	yes	—
674	#102	C₂³×C₃	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
676	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
678	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
682	#97	C₂³×C₃	1	2	yes	—
683	#97	C₂³×C₃	1	1	yes	characteristic
684	#97	C₂³×C₃	1	1	yes	characteristic
685	C₂³×C₃	—	2	2	no	—
686	C₂³×C₃	—	2	1	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	4	2	no	—
689	C₂³×C₃	—	8	1	no	—
690	C₂³×C₃	—	8	1	no	—
691	C₂³×C₃	—	8	2	no	—
692	C₂³×C₃	—	8	2	no	—
693	C₂³×C₃	—	8	2	no	—
694	C₂³×C₃	C₂²×D₄	1	2	yes	—
695	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
696	C₂³×C₃	C₂²×D₄	1	2	yes	—
697	C₃×Q₈	—	2	2	no	—
698	C₃×Q₈	—	4	2	no	—
699	C₃×Q₈	—	4	2	no	—
700	C₃×Q₈	—	4	2	no	—
701	C₃×Q₈	—	8	1	no	—
702	C₃×D₄	—	2	2	no	—
703	C₃×D₄	—	2	2	no	—
704	C₃×D₄	—	2	2	no	—
705	C₃×D₄	—	2	2	no	—
706	C₃×D₄	—	2	2	no	—
707	C₃×D₄	—	4	1	no	—
708	C₃×D₄	—	4	2	no	—
709	C₃×D₄	—	4	2	no	—
710	C₃×D₄	—	4	2	no	—
711	C₃×D₄	—	4	2	no	—
712	C₃×D₄	—	4	1	no	—
713	C₃×D₄	—	4	2	no	—
714	C₃×D₄	—	4	2	no	—
715	C₃×D₄	—	8	1	no	—
716	C₃×D₄	—	8	2	no	—
717	C₃×D₄	—	8	1	no	—
718	C₃×D₄	—	8	2	no	—
719	C₃×D₄	—	8	2	no	—
720	C₃×D₄	—	8	2	no	—
721	C₃×D₄	—	8	2	no	—
722	C₃×D₄	—	8	2	no	—
723	C₃×D₄	—	8	2	no	—
724	C₃×D₄	—	8	2	no	—
725	C₃×D₄	—	8	2	no	—
726	C₃×D₄	—	8	2	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	2	no	—
729	C₂×C₃×C₄	—	2	2	no	—
730	C₂×C₃×C₄	—	2	2	no	—
731	C₂×C₃×C₄	—	2	2	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	2	no	—
734	C₂×C₃×C₄	—	2	2	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	2	no	—
737	C₂×C₃×C₄	—	2	2	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	4	1	no	—
740	C₂×C₃×C₄	—	4	1	no	—
741	C₂×C₃×C₄	—	4	4	no	—
742	C₂×C₃×C₄	—	4	2	no	—
743	C₂×C₃×C₄	—	8	2	no	—
744	C₂×C₃×C₄	—	8	2	no	—
745	C₂×C₃×C₄	—	8	2	no	—
746	C₂×C₃×C₄	—	8	1	no	—
747	C₂×C₃×C₄	—	8	2	no	—
748	C₂×C₃×C₄	—	8	2	no	—
749	C₂×C₃×C₄	—	8	2	no	—
750	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
752	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
754	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
758	C₃×C₈	—	2	2	no	—
759	C₃×C₈	—	2	2	no	—
760	C₃×C₈	—	2	2	no	—
761	C₃×C₈	—	2	2	no	—
762	C₂⁴	—	2	1	no	—
763	C₂⁴	—	2	2	no	—
764	#41	—	4	2	no	—
765	#41	—	4	2	no	—
766	#41	—	4	2	no	—
767	#41	—	4	2	no	—
768	#41	—	8	2	no	—
769	#41	—	8	4	no	—
770	#41	—	8	2	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
775	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	8	2	no	—
794	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
795	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
796	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
797	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
798	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
799	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
800	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
801	C₂×D₄	C₂⁴×C₃	1	2	yes	—
802	C₂×D₄	C₂⁴×C₃	1	2	yes	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	8	2	no	—
813	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
814	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
818	SD₁₆	—	4	2	no	—
819	D₈	—	4	2	no	—
820	D₈	—	4	2	no	—
821	D₈	—	4	2	no	—
822	M₁₆	—	4	2	no	—
823	M₁₆	—	4	2	no	—
824	C₂×C₈	—	4	2	no	—
825	C₂×C₈	—	4	2	no	—
826	C₂×C₈	C₂⁴×C₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₃	1	2	yes	—
829	C₂×C₈	C₂⁴×C₃	1	2	yes	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
845	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
846	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
851	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	2	1	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	1	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
875	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
876	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
877	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	1	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
884	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
885	C₄²	C₂⁴×C₃	1	1	yes	characteristic
886	C₄²	C₂⁴×C₃	1	1	yes	characteristic
887	C₂²×C₃	—	2	1	no	—
888	C₂²×C₃	—	2	1	no	—
889	C₂²×C₃	—	2	2	no	—
890	C₂²×C₃	—	2	2	no	—
891	C₂²×C₃	—	2	2	no	—
892	C₂²×C₃	—	2	2	no	—
893	C₂²×C₃	—	2	1	no	—
894	C₂²×C₃	—	2	2	no	—
895	C₂²×C₃	—	2	2	no	—
896	C₂²×C₃	—	4	2	no	—
897	C₂²×C₃	—	4	1	no	—
898	C₂²×C₃	—	4	2	no	—
899	C₂²×C₃	—	4	2	no	—
900	C₂²×C₃	—	4	2	no	—
901	C₂²×C₃	—	4	1	no	—
902	C₂²×C₃	—	4	2	no	—
903	C₂²×C₃	—	4	2	no	—
904	C₂²×C₃	—	4	1	no	—
905	C₂²×C₃	—	8	4	no	—
906	C₂²×C₃	—	16	4	no	—
907	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
908	C₃×C₄	—	2	1	no	—
909	C₃×C₄	—	2	1	no	—
910	C₃×C₄	—	2	1	no	—
911	C₃×C₄	—	2	1	no	—
912	C₃×C₄	—	2	2	no	—
913	C₃×C₄	—	2	1	no	—
914	C₃×C₄	—	2	2	no	—
915	C₃×C₄	—	4	2	no	—
916	C₃×C₄	—	4	1	no	—
917	C₃×C₄	—	4	2	no	—
918	C₃×C₄	—	4	2	no	—
919	C₃×C₄	—	4	1	no	—
920	C₃×C₄	—	4	2	no	—
921	C₃×C₄	—	4	1	no	—
922	C₃×C₄	#585	1	2	yes	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	4	2	no	—
927	C₂³	—	8	1	no	—
928	C₂³	—	8	1	no	—
929	C₂³	—	8	2	no	—
930	C₂³	—	8	2	no	—
931	C₂³	—	8	2	no	—
932	C₂³	C₂²×C₃×D₄	1	2	yes	—
933	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
934	C₂³	C₂²×C₃×D₄	1	2	yes	—
935	Q₈	—	2	2	no	—
936	Q₈	—	4	2	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	4	2	no	—
939	Q₈	—	8	1	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	4	1	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	1	no	—
951	D₄	—	4	2	no	—
952	D₄	—	4	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	D₄	—	8	2	no	—
959	D₄	—	8	2	no	—
960	D₄	—	8	2	no	—
961	D₄	—	8	1	no	—
962	D₄	—	8	2	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	4	1	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	—	8	2	no	—
984	C₂×C₄	—	8	1	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
989	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
990	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
991	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
992	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
993	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
994	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₈	—	2	2	no	—
999	C₈	—	2	2	no	—
1000	C₂×C₃	—	4	2	no	—
1001	C₂×C₃	—	4	1	no	—
1002	C₂×C₃	—	4	2	no	—
1003	C₂×C₃	—	8	2	no	—
1004	C₂×C₃	—	8	2	no	—
1005	C₂×C₃	—	8	1	no	—
1006	C₂×C₃	#3485	1	1	yes	characteristic
1007	C₂×C₃	#3585	1	1	yes	characteristic
1008	C₂×C₃	#3585	1	1	yes	characteristic
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	8	4	no	—
1028	C₂²	—	16	4	no	—
1029	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1030	C₄	—	2	2	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	2	no	—
1044	C₄	C₃×#585	1	2	yes	—
1045	C₃	#61795	1	1	yes	characteristic, direct product factor, Sylow
1046	C₂	—	4	1	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	4	2	no	—
1049	C₂	—	8	2	no	—
1050	C₂	—	8	1	no	—
1051	C₂	—	8	2	no	—
1052	C₂	C₃×#3485	1	1	yes	characteristic
1053	C₂	C₃×#3585	1	1	yes	characteristic
1054	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3546	C₂	semidirect
2. C₃×#3506	C₂	semidirect
3. C₃×#3350	C₂	semidirect
4. C₃×#3347	C₂	semidirect
5. C₃×#3345	C₂	semidirect
6. C₃×#3345	C₂	semidirect
7. C₃×#3319	C₂	semidirect
8. C₃×#3318	C₂	semidirect
9. C₃×#3309	C₂	semidirect
10. C₃×#3306	C₂	semidirect
11. C₃×#3240	C₂	semidirect
12. C₃×#3235	C₂	semidirect
13. C₃×#3199	C₂	semidirect
14. C₃×#3198	C₂	semidirect
15. C₃×#3114	C₂	semidirect
16. C₃×#3109	C₂	semidirect
17. C₃×#3099	C₂	semidirect
18. C₃×#3096	C₂	semidirect
19. C₃×#2980	C₂	semidirect
20. #61795	C₃	direct (N × H)
24. C₃×#556	C₂²	semidirect
25. C₃×#555	C₂²	semidirect
27. C₃×#553	C₂²	semidirect
28. C₃×#553	C₂²	semidirect
31. C₃×#550	C₂²	semidirect
32. C₃×#547	C₂²	semidirect
33. C₃×#547	C₂²	semidirect
35. C₃×#546	C₂²	semidirect
36. C₃×D₄²	C₂²	semidirect
44. C₃×#535	C₂²	semidirect
45. C₃×#533	C₂²	semidirect
50. C₃×#520	C₂²	semidirect
51. C₂×C₃×C₄×D₄	C₂²	semidirect
52. C₃×#501	C₂²	semidirect
53. C₃×#501	C₂²	semidirect
54. C₃×#501	C₂²	semidirect
55. C₃×#490	C₂²	semidirect
56. C₃×#489	C₂²	semidirect
57. C₃×#489	C₂²	semidirect
58. C₃×#485	C₂²	semidirect
59. C₃×#485	C₂²	semidirect
60. C₃×#483	C₂²	semidirect
61. C₃×#483	C₂²	semidirect
63. C₃×#482	C₂²	semidirect
64. C₃×#482	C₂²	semidirect
65. C₃×#482	C₂²	semidirect
66. C₃×#482	C₂²	semidirect
67. C₃×#482	C₂²	semidirect
68. C₃×#482	C₂²	semidirect
69. C₃×#482	C₂²	semidirect
70. C₃×#481	C₂²	semidirect
71. C₃×#481	C₂²	semidirect
72. C₃×#481	C₂²	semidirect
73. C₃×#481	C₂²	semidirect
75. C₃×#480	C₂²	semidirect
76. C₃×#480	C₂²	semidirect
77. C₃×#479	C₂²	semidirect
78. C₃×#478	C₂²	semidirect
79. C₃×#478	C₂²	semidirect
80. C₃×#476	C₂²	semidirect
81. C₃×#476	C₂²	semidirect
82. C₃×#474	C₂²	semidirect
85. C₃×#469	C₂²	semidirect
86. C₃×#468	C₂²	semidirect
89. C₃×#466	C₂²	semidirect
90. C₃×#465	C₂²	semidirect
93. C₃×#450	C₂²	semidirect
94. C₃×#449	C₂²	semidirect
95. C₃×#449	C₂²	semidirect
99. C₃×#447	C₂²	semidirect
101. C₃×#442	C₂²	semidirect
102. C₃×#442	C₂²	semidirect
103. C₃×#440	C₂²	semidirect
104. C₃×#435	C₂²	semidirect
105. C₃×#435	C₂²	semidirect
106. C₃×#435	C₂²	semidirect
107. C₃×#435	C₂²	semidirect
108. C₃×#432	C₂²	semidirect
109. C₃×#432	C₂²	semidirect
110. C₃×#428	C₂²	semidirect
111. C₃×#428	C₂²	semidirect
112. C₃×#427	C₂²	semidirect
113. C₂×C₃×#106	C₂²	semidirect
114. C₃×#418	C₂²	semidirect
115. C₃×#417	C₂²	semidirect
116. C₃×#416	C₂²	semidirect
117. C₂×C₃×#102	C₂²	semidirect
118. C₃×#408	C₂²	semidirect
119. C₃×#408	C₂²	semidirect
120. #3546	C₂×C₃	semidirect
121. #3506	C₂×C₃	semidirect
122. #3350	C₂×C₃	semidirect
123. #3347	C₂×C₃	semidirect
124. #3345	C₂×C₃	semidirect
125. #3345	C₂×C₃	semidirect
126. #3319	C₂×C₃	semidirect
127. #3318	C₂×C₃	semidirect
128. #3309	C₂×C₃	semidirect
129. #3306	C₂×C₃	semidirect
130. #3240	C₂×C₃	semidirect
131. #3235	C₂×C₃	semidirect
132. #3199	C₂×C₃	semidirect
133. #3198	C₂×C₃	semidirect
134. #3114	C₂×C₃	semidirect
135. #3109	C₂×C₃	semidirect
136. #3099	C₂×C₃	semidirect
137. #3096	C₂×C₃	semidirect
138. #2980	C₂×C₃	semidirect
303. #556	C₂²×C₃	semidirect
304. #555	C₂²×C₃	semidirect
306. #553	C₂²×C₃	semidirect
307. #553	C₂²×C₃	semidirect
310. #550	C₂²×C₃	semidirect
311. #547	C₂²×C₃	semidirect
312. #547	C₂²×C₃	semidirect
314. #546	C₂²×C₃	semidirect
315. D₄²	C₂²×C₃	semidirect
323. #535	C₂²×C₃	semidirect
324. #533	C₂²×C₃	semidirect
329. #520	C₂²×C₃	semidirect
330. C₂×C₄×D₄	C₂²×C₃	semidirect
331. #501	C₂²×C₃	semidirect
332. #501	C₂²×C₃	semidirect
333. #501	C₂²×C₃	semidirect
334. #490	C₂²×C₃	semidirect
335. #489	C₂²×C₃	semidirect
336. #489	C₂²×C₃	semidirect
337. #485	C₂²×C₃	semidirect
338. #485	C₂²×C₃	semidirect
339. #483	C₂²×C₃	semidirect
340. #483	C₂²×C₃	semidirect
342. #482	C₂²×C₃	semidirect
343. #482	C₂²×C₃	semidirect
344. #482	C₂²×C₃	semidirect
345. #482	C₂²×C₃	semidirect
346. #482	C₂²×C₃	semidirect
347. #482	C₂²×C₃	semidirect
348. #482	C₂²×C₃	semidirect
349. #481	C₂²×C₃	semidirect
350. #481	C₂²×C₃	semidirect
351. #481	C₂²×C₃	semidirect
352. #481	C₂²×C₃	semidirect
354. #480	C₂²×C₃	semidirect
355. #480	C₂²×C₃	semidirect
356. #479	C₂²×C₃	semidirect
357. #478	C₂²×C₃	semidirect
358. #478	C₂²×C₃	semidirect
359. #476	C₂²×C₃	semidirect
360. #476	C₂²×C₃	semidirect
361. #474	C₂²×C₃	semidirect
364. #469	C₂²×C₃	semidirect
365. #468	C₂²×C₃	semidirect
368. #466	C₂²×C₃	semidirect
369. #465	C₂²×C₃	semidirect
372. #450	C₂²×C₃	semidirect
373. #449	C₂²×C₃	semidirect
374. #449	C₂²×C₃	semidirect
378. #447	C₂²×C₃	semidirect
380. #442	C₂²×C₃	semidirect
381. #442	C₂²×C₃	semidirect
382. #440	C₂²×C₃	semidirect
383. #435	C₂²×C₃	semidirect
384. #435	C₂²×C₃	semidirect
385. #435	C₂²×C₃	semidirect
386. #435	C₂²×C₃	semidirect
387. #432	C₂²×C₃	semidirect
388. #432	C₂²×C₃	semidirect
389. #428	C₂²×C₃	semidirect
390. #428	C₂²×C₃	semidirect
391. #427	C₂²×C₃	semidirect
392. C₂×#106	C₂²×C₃	semidirect
393. #418	C₂²×C₃	semidirect
394. #417	C₂²×C₃	semidirect
395. #416	C₂²×C₃	semidirect
396. C₂×#102	C₂²×C₃	semidirect
397. #408	C₂²×C₃	semidirect
398. #408	C₂²×C₃	semidirect
1045. C₃	#61795	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3546	2
C₃×#3506	2
C₃×#3350	2
C₃×#3347	2
C₃×#3345	2
C₃×#3319	2
C₃×#3318	2
C₃×#3309	2
C₃×#3306	2
C₃×#3240	2
C₃×#3235	2
C₃×#3199	2
C₃×#3198	2
C₃×#3114	2
C₃×#3109	2
C₃×#3099	2
C₃×#3096	2
C₃×#2980	2
#61795	3

Subgroups — C3×#61795 #10680402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61795 #10680402