Subgroups — C₃×#41427 #10660034

Order 768.

1858 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2827	C₂	1	2	yes	maximal, complemented
2	C₃×#2771	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2765	C₂	1	2	yes	maximal, complemented
4	C₃×#2764	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2736	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2735	C₂	1	2	yes	maximal, complemented
7	C₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2653	C₂	1	2	yes	maximal, complemented
9	C₃×#2649	C₂	1	2	yes	maximal, complemented
10	C₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2518	C₂	1	2	yes	maximal, complemented
12	C₃×#2510	C₂	1	2	yes	maximal, complemented
13	C₃×#2498	C₂	1	2	yes	maximal, complemented
14	C₃×#2488	C₂	1	2	yes	maximal, complemented
15	C₃×#2413	C₂	1	2	yes	maximal, complemented
16	C₃×#2405	C₂	1	2	yes	maximal
17	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2342	C₂	1	2	yes	maximal, complemented
19	C₃×#2308	C₂	1	1	yes	maximal, characteristic
20	#41427	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#123	C₂²	1	2	yes	—
23	C₂×C₃×#123	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#117	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×#401	C₂²	1	2	yes	complemented
31	C₃×#400	C₂²	1	2	yes	complemented
32	C₃×#400	C₂²	1	2	yes	complemented
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
35	C₃×#399	C₂²	1	1	yes	characteristic
36	C₃×#399	C₂²	1	1	yes	characteristic, complemented
37	C₃×#399	C₂²	1	2	yes	complemented
38	C₃×#398	C₂²	1	2	yes	complemented
39	C₃×#398	C₂²	1	2	yes	complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#397	C₂²	1	1	yes	characteristic
42	C₃×#397	C₂²	1	2	yes	—
43	C₃×#397	C₂²	1	1	yes	characteristic
44	C₃×#397	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₃×#397	C₂²	1	1	yes	characteristic, complemented
47	C₃×#397	C₂²	1	2	yes	complemented
48	C₃×#397	C₂²	1	2	yes	complemented
49	C₃×#397	C₂²	1	2	yes	complemented
50	C₃×#397	C₂²	1	2	yes	complemented
51	C₃×#396	C₂²	1	2	yes	—
52	C₃×#396	C₂²	1	2	yes	complemented
53	C₃×#396	C₂²	1	2	yes	complemented
54	C₃×#396	C₂²	1	2	yes	complemented
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	2	yes	—
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#393	C₂²	1	1	yes	characteristic
60	C₃×#393	C₂²	1	1	yes	characteristic, complemented
61	C₃×#393	C₂²	1	2	yes	complemented
62	C₃×#391	C₂²	1	2	yes	complemented
63	C₃×#389	C₂²	1	2	yes	complemented
64	C₃×#389	C₂²	1	2	yes	complemented
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	complemented
70	C₃×#388	C₂²	1	2	yes	complemented
71	C₃×#388	C₂²	1	2	yes	complemented
72	C₃×#388	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	2	yes	complemented
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	2	yes	complemented
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#387	C₂²	1	2	yes	complemented
79	C₃×#387	C₂²	1	2	yes	complemented
80	C₃×#386	C₂²	1	2	yes	—
81	C₃×#386	C₂²	1	2	yes	—
82	C₃×#386	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#386	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	complemented
89	C₃×#385	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	2	yes	complemented
91	C₃×#383	C₂²	1	2	yes	complemented
92	C₃×#382	C₂²	1	2	yes	complemented
93	C₃×#381	C₂²	1	1	yes	characteristic
94	C₃×#381	C₂²	1	1	yes	characteristic
95	C₃×#381	C₂²	1	2	yes	complemented
96	C₃×#380	C₂²	1	1	yes	characteristic, complemented
97	C₃×#380	C₂²	1	2	yes	complemented
98	C₃×#379	C₂²	1	2	yes	—
99	C₃×#379	C₂²	1	2	yes	—
100	C₃×#379	C₂²	1	2	yes	—
101	C₃×#379	C₂²	1	1	yes	characteristic
102	C₃×#379	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₂×C₃×#95	C₂²	1	2	yes	complemented
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
108	#2827	C₂×C₃	1	2	yes	complemented
109	#2771	C₂×C₃	1	1	yes	characteristic, complemented
110	#2765	C₂×C₃	1	2	yes	complemented
111	#2764	C₂×C₃	1	1	yes	characteristic, complemented
112	#2736	C₂×C₃	1	1	yes	characteristic, complemented
113	#2735	C₂×C₃	1	2	yes	complemented
114	#2735	C₂×C₃	1	1	yes	characteristic, complemented
115	#2653	C₂×C₃	1	2	yes	complemented
116	#2649	C₂×C₃	1	2	yes	complemented
117	#2626	C₂×C₃	1	1	yes	characteristic, complemented
118	#2518	C₂×C₃	1	2	yes	complemented
119	#2510	C₂×C₃	1	2	yes	complemented
120	#2498	C₂×C₃	1	2	yes	complemented
121	#2488	C₂×C₃	1	2	yes	complemented
122	#2413	C₂×C₃	1	2	yes	complemented
123	#2405	C₂×C₃	1	2	yes	—
124	C₂×#397	C₂×C₃	1	1	yes	characteristic, complemented
125	#2342	C₂×C₃	1	2	yes	complemented
126	#2308	C₂×C₃	1	1	yes	characteristic
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×D₄	—	2	4	no	—
131	C₂²×C₃×D₄	—	4	2	no	—
132	C₂²×C₃×D₄	—	4	2	no	—
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	2	yes	—
135	C₂³×C₃×C₄	C₂³	1	2	yes	—
136	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂³	1	2	yes	—
138	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₃×#123	—	4	4	no	—
142	C₃×#123	—	4	4	no	—
143	C₃×C₂²⋊Q₈	—	4	2	no	—
144	C₃×#117	—	4	4	no	—
145	C₂×C₃×C₄⋊C₄	—	4	2	no	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
163	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
164	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	1	yes	characteristic
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	1	yes	characteristic
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	1	yes	characteristic
212	C₃×#95	C₂³	1	1	yes	characteristic
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
226	C₂×#123	C₂²×C₃	1	2	yes	—
227	C₂×#123	C₂²×C₃	1	2	yes	—
228	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
229	C₂×#117	C₂²×C₃	1	2	yes	complemented
230	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
231	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
234	#401	C₂²×C₃	1	2	yes	complemented
235	#400	C₂²×C₃	1	2	yes	complemented
236	#400	C₂²×C₃	1	2	yes	complemented
237	#400	C₂²×C₃	1	2	yes	complemented
238	#400	C₂²×C₃	1	2	yes	complemented
239	#399	C₂²×C₃	1	1	yes	characteristic
240	#399	C₂²×C₃	1	2	yes	complemented
241	#399	C₂²×C₃	1	1	yes	characteristic, complemented
242	#398	C₂²×C₃	1	2	yes	complemented
243	#398	C₂²×C₃	1	2	yes	complemented
244	#398	C₂²×C₃	1	2	yes	complemented
245	#397	C₂²×C₃	1	1	yes	characteristic
246	#397	C₂²×C₃	1	2	yes	—
247	#397	C₂²×C₃	1	1	yes	characteristic
248	#397	C₂²×C₃	1	1	yes	characteristic, complemented
249	#397	C₂²×C₃	1	2	yes	complemented
250	#397	C₂²×C₃	1	2	yes	complemented
251	#397	C₂²×C₃	1	2	yes	complemented
252	#397	C₂²×C₃	1	1	yes	characteristic, complemented
253	#397	C₂²×C₃	1	2	yes	complemented
254	#397	C₂²×C₃	1	2	yes	complemented
255	#396	C₂²×C₃	1	2	yes	—
256	#396	C₂²×C₃	1	2	yes	complemented
257	#396	C₂²×C₃	1	2	yes	complemented
258	#396	C₂²×C₃	1	2	yes	complemented
259	#394	C₂²×C₃	1	2	yes	—
260	#394	C₂²×C₃	1	2	yes	—
261	#394	C₂²×C₃	1	2	yes	—
262	#394	C₂²×C₃	1	2	yes	—
263	#393	C₂²×C₃	1	1	yes	characteristic
264	#393	C₂²×C₃	1	1	yes	characteristic, complemented
265	#393	C₂²×C₃	1	2	yes	complemented
266	#391	C₂²×C₃	1	2	yes	complemented
267	#389	C₂²×C₃	1	2	yes	complemented
268	#389	C₂²×C₃	1	2	yes	complemented
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	complemented
274	#388	C₂²×C₃	1	2	yes	complemented
275	#388	C₂²×C₃	1	2	yes	complemented
276	#388	C₂²×C₃	1	2	yes	complemented
277	#388	C₂²×C₃	1	2	yes	complemented
278	#388	C₂²×C₃	1	2	yes	complemented
279	#388	C₂²×C₃	1	2	yes	complemented
280	#388	C₂²×C₃	1	2	yes	complemented
281	#387	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#386	C₂²×C₃	1	2	yes	—
285	#386	C₂²×C₃	1	2	yes	—
286	#386	C₂²×C₃	1	2	yes	—
287	#386	C₂²×C₃	1	2	yes	—
288	#386	C₂²×C₃	1	2	yes	—
289	#386	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	complemented
293	#385	C₂²×C₃	1	2	yes	complemented
294	#385	C₂²×C₃	1	2	yes	complemented
295	#383	C₂²×C₃	1	2	yes	complemented
296	#382	C₂²×C₃	1	2	yes	complemented
297	#381	C₂²×C₃	1	1	yes	characteristic
298	#381	C₂²×C₃	1	1	yes	characteristic
299	#381	C₂²×C₃	1	2	yes	complemented
300	#380	C₂²×C₃	1	2	yes	complemented
301	#380	C₂²×C₃	1	1	yes	characteristic, complemented
302	#379	C₂²×C₃	1	1	yes	characteristic
303	#379	C₂²×C₃	1	1	yes	characteristic
304	#379	C₂²×C₃	1	2	yes	—
305	#379	C₂²×C₃	1	2	yes	—
306	#379	C₂²×C₃	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
308	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
310	C₂×#95	C₂²×C₃	1	2	yes	complemented
311	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂⁴×C₃	—	2	2	no	—
313	C₂⁴×C₃	—	2	2	no	—
314	C₂⁴×C₃	—	2	2	no	—
315	C₂⁴×C₃	—	4	2	no	—
316	C₂⁴×C₃	—	4	2	no	—
317	C₂⁴×C₃	—	4	1	no	—
318	C₂⁴×C₃	—	4	1	no	—
319	C₂⁴×C₃	—	4	2	no	—
320	C₂⁴×C₃	—	4	2	no	—
321	C₂⁴×C₃	#41	1	4	yes	—
322	C₂⁴×C₃	C₂⁴	1	2	yes	—
323	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
325	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₃×Q₈	—	4	1	no	—
327	C₂×C₃×Q₈	—	4	2	no	—
328	C₂×C₃×D₄	—	2	4	no	—
329	C₂×C₃×D₄	—	2	4	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	2	4	no	—
332	C₂×C₃×D₄	—	4	2	no	—
333	C₂×C₃×D₄	—	4	2	no	—
334	C₂×C₃×D₄	—	4	16	no	—
335	C₂²×C₃×C₄	—	2	4	no	—
336	C₂²×C₃×C₄	—	2	2	no	—
337	C₂²×C₃×C₄	—	2	2	no	—
338	C₂²×C₃×C₄	—	2	4	no	—
339	C₂²×C₃×C₄	—	2	4	no	—
340	C₂²×C₃×C₄	—	2	4	no	—
341	C₂²×C₃×C₄	—	2	2	no	—
342	C₂²×C₃×C₄	—	4	2	no	—
343	C₂²×C₃×C₄	—	4	1	no	—
344	C₂²×C₃×C₄	—	4	1	no	—
345	C₂²×C₃×C₄	—	4	2	no	—
346	C₂²×C₃×C₄	—	4	2	no	—
347	C₂²×C₃×C₄	—	4	2	no	—
348	C₂²×C₃×C₄	—	4	2	no	—
349	C₂²×C₃×C₄	—	4	2	no	—
350	C₂²×C₃×C₄	—	4	2	no	—
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
362	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
364	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
366	C₃×C₄⋊C₄	—	4	1	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	1	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₄⋊C₄	—	4	1	no	—
377	C₃×C₄⋊C₄	—	4	2	no	—
378	C₃×C₄⋊C₄	—	4	2	no	—
379	C₃×C₄⋊C₄	—	4	2	no	—
380	C₃×C₄⋊C₄	—	4	2	no	—
381	C₃×C₄⋊C₄	—	4	2	no	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	4	no	—
385	C₃×C₂²⋊C₄	—	2	4	no	—
386	C₃×C₂²⋊C₄	—	2	4	no	—
387	C₃×C₂²⋊C₄	—	2	4	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	4	1	no	—
390	C₃×C₂²⋊C₄	—	4	1	no	—
391	C₃×C₂²⋊C₄	—	4	1	no	—
392	C₃×C₂²⋊C₄	—	4	1	no	—
393	C₃×C₂²⋊C₄	—	4	1	no	—
394	C₃×C₂²⋊C₄	—	4	1	no	—
395	C₃×C₂²⋊C₄	—	4	2	no	—
396	C₃×C₂²⋊C₄	—	4	2	no	—
397	C₃×C₂²⋊C₄	—	4	2	no	—
398	C₃×C₂²⋊C₄	—	4	2	no	—
399	C₃×C₂²⋊C₄	—	4	2	no	—
400	C₃×C₂²⋊C₄	—	4	2	no	—
401	C₃×C₂²⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	4	2	no	—
403	C₃×C₂²⋊C₄	—	4	2	no	—
404	C₃×C₂²⋊C₄	—	4	2	no	—
405	C₃×C₂²⋊C₄	—	4	2	no	—
406	C₃×C₂²⋊C₄	—	4	2	no	—
407	C₃×C₂²⋊C₄	—	4	2	no	—
408	C₃×C₂²⋊C₄	—	4	2	no	—
409	C₃×C₂²⋊C₄	—	4	2	no	—
410	C₃×C₂²⋊C₄	—	4	2	no	—
411	C₃×C₄²	—	4	2	no	—
412	C₃×C₄²	—	4	2	no	—
413	C₃×C₄²	—	4	2	no	—
414	C₃×C₄²	—	4	2	no	—
415	C₂⁵	C₂³×C₃	1	1	yes	characteristic
416	C₂⁵	C₂³×C₃	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
418	C₂²×D₄	—	2	4	no	—
419	C₂²×D₄	—	4	2	no	—
420	C₂²×D₄	—	4	2	no	—
421	C₂²×D₄	C₂³×C₃	1	2	yes	—
422	C₂²×D₄	C₂³×C₃	1	2	yes	—
423	C₂³×C₄	C₂³×C₃	1	2	yes	—
424	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₃	1	2	yes	—
427	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₃	1	2	yes	—
429	#123	—	4	4	no	—
430	#123	—	4	4	no	—
431	C₂²⋊Q₈	—	4	2	no	—
432	#117	—	4	4	no	—
433	C₂×C₄⋊C₄	—	4	2	no	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	—	2	8	no	—
451	C₂×C₂²⋊C₄	—	4	2	no	—
452	C₂×C₂²⋊C₄	—	4	2	no	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₃	1	2	yes	—
483	C₂×C₄²	C₂³×C₃	1	2	yes	—
484	C₂×C₄²	C₂³×C₃	1	2	yes	—
485	C₂×C₄²	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	1	yes	characteristic
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	1	yes	characteristic
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	2	yes	—
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	1	yes	characteristic
500	#95	C₂³×C₃	1	1	yes	characteristic
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	2	yes	—
504	#95	C₂³×C₃	1	2	yes	—
505	#95	C₂³×C₃	1	2	yes	—
506	#95	C₂³×C₃	1	2	yes	—
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	2	yes	—
510	#95	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	2	yes	—
512	#95	C₂³×C₃	1	2	yes	—
513	C₂³×C₃	—	2	2	no	—
514	C₂³×C₃	—	2	2	no	—
515	C₂³×C₃	—	2	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	2	2	no	—
520	C₂³×C₃	—	2	2	no	—
521	C₂³×C₃	—	2	2	no	—
522	C₂³×C₃	—	2	2	no	—
523	C₂³×C₃	—	2	8	no	—
524	C₂³×C₃	—	2	2	no	—
525	C₂³×C₃	—	2	2	no	—
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	—	2	2	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	4	8	no	—
532	C₂³×C₃	—	4	4	no	—
533	C₂³×C₃	—	8	2	no	—
534	C₂³×C₃	—	8	2	no	—
535	C₂³×C₃	—	8	4	no	—
536	C₂³×C₃	—	8	4	no	—
537	C₂³×C₃	—	8	2	no	—
538	C₂³×C₃	—	8	2	no	—
539	C₂³×C₃	—	8	4	no	—
540	C₂³×C₃	C₂×#41	1	2	yes	—
541	C₂³×C₃	C₂×#41	1	2	yes	—
542	C₂³×C₃	C₂×#41	1	2	yes	—
543	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
544	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
545	C₂³×C₃	C₂⁵	1	1	yes	characteristic
546	C₃×Q₈	—	8	2	no	—
547	C₃×D₄	—	4	8	no	—
548	C₃×D₄	—	4	8	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	4	4	no	—
591	C₂×C₃×C₄	—	4	4	no	—
592	C₂×C₃×C₄	—	4	8	no	—
593	C₂×C₃×C₄	—	8	4	no	—
594	C₂×C₃×C₄	—	8	2	no	—
595	C₂×C₃×C₄	—	8	4	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	4	1	no	—
600	C₂⁴	—	4	1	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	4	2	no	—
604	C₂⁴	—	4	2	no	—
605	C₂⁴	C₃×#41	1	4	yes	—
606	C₂⁴	C₂⁴×C₃	1	2	yes	—
607	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
608	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
609	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
610	C₂×Q₈	—	4	1	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	16	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	1	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	4	1	no	—
674	C₂²⋊C₄	—	4	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₂²⋊C₄	—	4	2	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₂²×C₃	—	2	4	no	—
700	C₂²×C₃	—	2	2	no	—
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	2	4	no	—
703	C₂²×C₃	—	2	2	no	—
704	C₂²×C₃	—	2	2	no	—
705	C₂²×C₃	—	2	4	no	—
706	C₂²×C₃	—	2	4	no	—
707	C₂²×C₃	—	4	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	2	no	—
712	C₂²×C₃	—	4	2	no	—
713	C₂²×C₃	—	4	2	no	—
714	C₂²×C₃	—	4	2	no	—
715	C₂²×C₃	—	4	2	no	—
716	C₂²×C₃	—	4	2	no	—
717	C₂²×C₃	—	4	2	no	—
718	C₂²×C₃	—	4	2	no	—
719	C₂²×C₃	—	4	2	no	—
720	C₂²×C₃	—	8	8	no	—
721	C₂²×C₃	—	8	8	no	—
722	C₂²×C₃	#538	1	4	yes	—
723	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
724	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
725	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂²×C₃	#585	1	2	yes	—
727	C₂²×C₃	#585	1	2	yes	—
728	C₃×C₄	—	4	2	no	—
729	C₃×C₄	—	4	2	no	—
730	C₃×C₄	—	4	2	no	—
731	C₃×C₄	—	4	2	no	—
732	C₃×C₄	—	4	2	no	—
733	C₃×C₄	—	4	2	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	1	no	—
738	C₃×C₄	—	4	2	no	—
739	C₃×C₄	—	4	2	no	—
740	C₃×C₄	—	4	2	no	—
741	C₃×C₄	—	4	2	no	—
742	C₃×C₄	—	4	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	2	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	—	8	4	no	—
770	C₂³	C₂×C₃×#41	1	2	yes	—
771	C₂³	C₂×C₃×#41	1	2	yes	—
772	C₂³	C₂×C₃×#41	1	2	yes	—
773	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
774	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
775	C₂³	C₂⁵×C₃	1	1	yes	characteristic
776	Q₈	—	8	2	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	8	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₃	—	2	4	no	—
827	C₂×C₃	—	4	2	no	—
828	C₂×C₃	—	4	2	no	—
829	C₂×C₃	—	8	2	no	—
830	C₂×C₃	C₂×#538	1	1	yes	characteristic
831	C₂×C₃	#3491	1	2	yes	—
832	C₂×C₃	#3533	1	1	yes	characteristic
833	C₂×C₃	#3545	1	1	yes	characteristic
834	C₂×C₃	#3560	1	2	yes	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	8	8	no	—
857	C₂²	—	8	8	no	—
858	C₂²	C₃×#538	1	4	yes	—
859	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
860	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²	C₃×#585	1	2	yes	—
863	C₂²	C₃×#585	1	2	yes	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₃	#41427	1	1	yes	characteristic, direct product factor, Sylow
880	C₂	—	2	4	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	8	2	no	—
884	C₂	C₂×C₃×#538	1	1	yes	characteristic
885	C₂	C₃×#3491	1	2	yes	—
886	C₂	C₃×#3533	1	1	yes	characteristic
887	C₂	C₃×#3545	1	1	yes	characteristic
888	C₂	C₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2827	C₂	semidirect
2. C₃×#2771	C₂	semidirect
3. C₃×#2765	C₂	semidirect
4. C₃×#2764	C₂	semidirect
5. C₃×#2736	C₂	semidirect
6. C₃×#2735	C₂	semidirect
7. C₃×#2735	C₂	semidirect
8. C₃×#2653	C₂	semidirect
9. C₃×#2649	C₂	semidirect
10. C₃×#2626	C₂	semidirect
11. C₃×#2518	C₂	semidirect
12. C₃×#2510	C₂	semidirect
13. C₃×#2498	C₂	semidirect
14. C₃×#2488	C₂	semidirect
15. C₃×#2413	C₂	semidirect
17. C₂×C₃×#397	C₂	semidirect
18. C₃×#2342	C₂	semidirect
20. #41427	C₃	direct (N × H)
24. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₃×#117	C₂²	semidirect
26. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
30. C₃×#401	C₂²	semidirect
31. C₃×#400	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
36. C₃×#399	C₂²	semidirect
37. C₃×#399	C₂²	semidirect
38. C₃×#398	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#397	C₂²	semidirect
48. C₃×#397	C₂²	semidirect
49. C₃×#397	C₂²	semidirect
50. C₃×#397	C₂²	semidirect
52. C₃×#396	C₂²	semidirect
53. C₃×#396	C₂²	semidirect
54. C₃×#396	C₂²	semidirect
60. C₃×#393	C₂²	semidirect
61. C₃×#393	C₂²	semidirect
62. C₃×#391	C₂²	semidirect
63. C₃×#389	C₂²	semidirect
64. C₃×#389	C₂²	semidirect
69. C₃×#388	C₂²	semidirect
70. C₃×#388	C₂²	semidirect
71. C₃×#388	C₂²	semidirect
72. C₃×#388	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
88. C₃×#385	C₂²	semidirect
89. C₃×#385	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#383	C₂²	semidirect
92. C₃×#382	C₂²	semidirect
95. C₃×#381	C₂²	semidirect
96. C₃×#380	C₂²	semidirect
97. C₃×#380	C₂²	semidirect
103. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₂×C₃×#95	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2827	C₂×C₃	semidirect
109. #2771	C₂×C₃	semidirect
110. #2765	C₂×C₃	semidirect
111. #2764	C₂×C₃	semidirect
112. #2736	C₂×C₃	semidirect
113. #2735	C₂×C₃	semidirect
114. #2735	C₂×C₃	semidirect
115. #2653	C₂×C₃	semidirect
116. #2649	C₂×C₃	semidirect
117. #2626	C₂×C₃	semidirect
118. #2518	C₂×C₃	semidirect
119. #2510	C₂×C₃	semidirect
120. #2498	C₂×C₃	semidirect
121. #2488	C₂×C₃	semidirect
122. #2413	C₂×C₃	semidirect
124. C₂×#397	C₂×C₃	semidirect
125. #2342	C₂×C₃	semidirect
228. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
229. C₂×#117	C₂²×C₃	semidirect
230. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
234. #401	C₂²×C₃	semidirect
235. #400	C₂²×C₃	semidirect
236. #400	C₂²×C₃	semidirect
237. #400	C₂²×C₃	semidirect
238. #400	C₂²×C₃	semidirect
240. #399	C₂²×C₃	semidirect
241. #399	C₂²×C₃	semidirect
242. #398	C₂²×C₃	semidirect
243. #398	C₂²×C₃	semidirect
244. #398	C₂²×C₃	semidirect
248. #397	C₂²×C₃	semidirect
249. #397	C₂²×C₃	semidirect
250. #397	C₂²×C₃	semidirect
251. #397	C₂²×C₃	semidirect
252. #397	C₂²×C₃	semidirect
253. #397	C₂²×C₃	semidirect
254. #397	C₂²×C₃	semidirect
256. #396	C₂²×C₃	semidirect
257. #396	C₂²×C₃	semidirect
258. #396	C₂²×C₃	semidirect
264. #393	C₂²×C₃	semidirect
265. #393	C₂²×C₃	semidirect
266. #391	C₂²×C₃	semidirect
267. #389	C₂²×C₃	semidirect
268. #389	C₂²×C₃	semidirect
273. #388	C₂²×C₃	semidirect
274. #388	C₂²×C₃	semidirect
275. #388	C₂²×C₃	semidirect
276. #388	C₂²×C₃	semidirect
277. #388	C₂²×C₃	semidirect
278. #388	C₂²×C₃	semidirect
279. #388	C₂²×C₃	semidirect
280. #388	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
292. #385	C₂²×C₃	semidirect
293. #385	C₂²×C₃	semidirect
294. #385	C₂²×C₃	semidirect
295. #383	C₂²×C₃	semidirect
296. #382	C₂²×C₃	semidirect
299. #381	C₂²×C₃	semidirect
300. #380	C₂²×C₃	semidirect
301. #380	C₂²×C₃	semidirect
307. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
308. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
309. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
310. C₂×#95	C₂²×C₃	semidirect
311. C₂×#95	C₂²×C₃	semidirect
879. C₃	#41427	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×#2827	2
C₃×#2771	2
C₃×#2765	2
C₃×#2764	2
C₃×#2736	2
C₃×#2735	2
C₃×#2653	2
C₃×#2649	2
C₃×#2626	2
C₃×#2518	2
C₃×#2510	2
C₃×#2498	2
C₃×#2488	2
C₃×#2413	2
C₃×#2405	2
C₂×C₃×#397	2
C₃×#2342	2
C₃×#2308	2
#41427	3

Subgroups — C3×#41427 #10660034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41427 #10660034