Subgroups — C₃×#35888 #10654495

Order 768.

1848 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2645	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2643	C₂	1	2	yes	maximal, complemented
3	C₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2510	C₂	1	2	yes	maximal, complemented
7	C₃×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2493	C₂	1	2	yes	maximal, complemented
11	C₃×#2493	C₂	1	2	yes	maximal, complemented
12	C₃×#2493	C₂	1	2	yes	maximal, complemented
13	C₃×#2481	C₂	1	2	yes	maximal, complemented
14	C₃×#2481	C₂	1	2	yes	maximal, complemented
15	C₃×#2401	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#400	C₂	1	2	yes	maximal, complemented
17	C₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2339	C₂	1	1	yes	maximal, characteristic
21	C₃×#2339	C₂	1	1	yes	maximal, characteristic
22	C₃×#2339	C₂	1	1	yes	maximal, characteristic
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	#35888	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#126	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₃×#401	C₂²	1	2	yes	—
36	C₃×#401	C₂²	1	2	yes	—
37	C₃×#401	C₂²	1	1	yes	characteristic
38	C₃×#400	C₂²	1	2	yes	—
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	2	yes	—
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	1	yes	characteristic
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#400	C₂²	1	2	yes	—
46	C₃×#400	C₂²	1	2	yes	—
47	C₃×#400	C₂²	1	2	yes	—
48	C₃×#400	C₂²	1	2	yes	—
49	C₃×#400	C₂²	1	2	yes	—
50	C₃×#400	C₂²	1	1	yes	characteristic
51	C₃×#400	C₂²	1	1	yes	characteristic
52	C₃×#397	C₂²	1	1	yes	characteristic
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#397	C₂²	1	1	yes	characteristic
56	C₃×#397	C₂²	1	1	yes	characteristic
57	C₃×#396	C₂²	1	2	yes	—
58	C₃×#396	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#391	C₂²	1	1	yes	characteristic
62	C₃×#391	C₂²	1	1	yes	characteristic
63	C₃×#391	C₂²	1	1	yes	characteristic
64	C₃×#391	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
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	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#384	C₂²	1	1	yes	characteristic
93	C₃×#384	C₂²	1	1	yes	characteristic
94	C₃×#383	C₂²	1	2	yes	—
95	C₃×#383	C₂²	1	2	yes	—
96	C₃×#382	C₂²	1	1	yes	characteristic
97	C₃×#381	C₂²	1	2	yes	—
98	C₃×#381	C₂²	1	2	yes	—
99	C₃×#381	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×#376	C₂²	1	1	yes	characteristic
119	C₂×C₃×#95	C₂²	1	2	yes	—
120	C₂×C₃×#95	C₂²	1	2	yes	—
121	C₂×C₃×#95	C₂²	1	2	yes	—
122	C₂×C₃×#95	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	#2645	C₂×C₃	1	1	yes	characteristic, complemented
125	#2643	C₂×C₃	1	2	yes	complemented
126	#2514	C₂×C₃	1	1	yes	characteristic, complemented
127	#2511	C₂×C₃	1	1	yes	characteristic, complemented
128	#2511	C₂×C₃	1	1	yes	characteristic, complemented
129	#2510	C₂×C₃	1	2	yes	complemented
130	#2497	C₂×C₃	1	1	yes	characteristic, complemented
131	#2496	C₂×C₃	1	1	yes	characteristic, complemented
132	#2495	C₂×C₃	1	1	yes	characteristic, complemented
133	#2493	C₂×C₃	1	2	yes	complemented
134	#2493	C₂×C₃	1	2	yes	complemented
135	#2493	C₂×C₃	1	2	yes	complemented
136	#2481	C₂×C₃	1	2	yes	complemented
137	#2481	C₂×C₃	1	2	yes	complemented
138	#2401	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×#400	C₂×C₃	1	2	yes	complemented
140	#2349	C₂×C₃	1	1	yes	characteristic, complemented
141	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
142	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
143	#2339	C₂×C₃	1	1	yes	characteristic
144	#2339	C₂×C₃	1	1	yes	characteristic
145	#2339	C₂×C₃	1	1	yes	characteristic
146	#2275	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×C₃×#41	—	2	4	no	—
148	C₂×C₃×#41	—	2	4	no	—
149	C₂×C₃×#41	—	2	4	no	—
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	2	yes	—
157	C₂³×C₃×C₄	C₂³	1	2	yes	—
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₃×#126	—	4	4	no	—
162	C₃×C₄×D₄	—	2	4	no	—
163	C₃×C₄×D₄	—	2	4	no	—
164	C₃×C₄×D₄	—	2	4	no	—
165	C₃×C₄×D₄	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	4	no	—
168	C₂×C₃×C₄⋊C₄	—	4	4	no	—
169	C₂×C₃×C₄⋊C₄	—	4	4	no	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	C₂³	1	2	yes	—
214	C₂×C₃×C₄²	C₂³	1	2	yes	—
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	1	yes	characteristic
217	C₃×#95	C₂³	1	1	yes	characteristic
218	C₃×#95	C₂³	1	1	yes	characteristic
219	C₃×#95	C₂³	1	1	yes	characteristic
220	C₃×#95	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
259	C₂×#126	C₂²×C₃	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
268	#401	C₂²×C₃	1	2	yes	—
269	#401	C₂²×C₃	1	2	yes	—
270	#401	C₂²×C₃	1	1	yes	characteristic
271	#400	C₂²×C₃	1	2	yes	—
272	#400	C₂²×C₃	1	2	yes	—
273	#400	C₂²×C₃	1	2	yes	—
274	#400	C₂²×C₃	1	2	yes	—
275	#400	C₂²×C₃	1	2	yes	—
276	#400	C₂²×C₃	1	1	yes	characteristic
277	#400	C₂²×C₃	1	2	yes	—
278	#400	C₂²×C₃	1	2	yes	—
279	#400	C₂²×C₃	1	2	yes	—
280	#400	C₂²×C₃	1	2	yes	—
281	#400	C₂²×C₃	1	2	yes	—
282	#400	C₂²×C₃	1	2	yes	—
283	#400	C₂²×C₃	1	1	yes	characteristic
284	#400	C₂²×C₃	1	1	yes	characteristic
285	#397	C₂²×C₃	1	1	yes	characteristic
286	#397	C₂²×C₃	1	2	yes	—
287	#397	C₂²×C₃	1	2	yes	—
288	#397	C₂²×C₃	1	1	yes	characteristic
289	#397	C₂²×C₃	1	1	yes	characteristic
290	#396	C₂²×C₃	1	2	yes	—
291	#396	C₂²×C₃	1	1	yes	characteristic
292	#391	C₂²×C₃	1	1	yes	characteristic
293	#391	C₂²×C₃	1	1	yes	characteristic
294	#391	C₂²×C₃	1	1	yes	characteristic
295	#391	C₂²×C₃	1	1	yes	characteristic
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#389	C₂²×C₃	1	1	yes	characteristic
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	1	yes	characteristic
301	#389	C₂²×C₃	1	1	yes	characteristic
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#388	C₂²×C₃	1	2	yes	—
305	#388	C₂²×C₃	1	2	yes	—
306	#387	C₂²×C₃	1	2	yes	—
307	#387	C₂²×C₃	1	2	yes	—
308	#387	C₂²×C₃	1	2	yes	—
309	#387	C₂²×C₃	1	2	yes	—
310	#387	C₂²×C₃	1	2	yes	—
311	#387	C₂²×C₃	1	2	yes	—
312	#387	C₂²×C₃	1	2	yes	—
313	#386	C₂²×C₃	1	2	yes	—
314	#386	C₂²×C₃	1	2	yes	—
315	#386	C₂²×C₃	1	2	yes	—
316	#386	C₂²×C₃	1	2	yes	—
317	#386	C₂²×C₃	1	2	yes	—
318	#386	C₂²×C₃	1	2	yes	—
319	#385	C₂²×C₃	1	2	yes	—
320	#385	C₂²×C₃	1	2	yes	—
321	#385	C₂²×C₃	1	2	yes	—
322	#385	C₂²×C₃	1	2	yes	—
323	#385	C₂²×C₃	1	2	yes	—
324	#385	C₂²×C₃	1	2	yes	—
325	#384	C₂²×C₃	1	1	yes	characteristic
326	#384	C₂²×C₃	1	1	yes	characteristic
327	#383	C₂²×C₃	1	2	yes	—
328	#383	C₂²×C₃	1	2	yes	—
329	#382	C₂²×C₃	1	1	yes	characteristic
330	#381	C₂²×C₃	1	2	yes	—
331	#381	C₂²×C₃	1	2	yes	—
332	#381	C₂²×C₃	1	2	yes	—
333	#380	C₂²×C₃	1	1	yes	characteristic
334	#380	C₂²×C₃	1	1	yes	characteristic
335	#380	C₂²×C₃	1	1	yes	characteristic
336	#380	C₂²×C₃	1	2	yes	—
337	#380	C₂²×C₃	1	2	yes	—
338	#380	C₂²×C₃	1	2	yes	—
339	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	#376	C₂²×C₃	1	1	yes	characteristic
352	C₂×#95	C₂²×C₃	1	2	yes	—
353	C₂×#95	C₂²×C₃	1	2	yes	—
354	C₂×#95	C₂²×C₃	1	2	yes	—
355	C₂×#95	C₂²×C₃	1	2	yes	—
356	C₂×#95	C₂²×C₃	1	2	yes	—
357	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₃	C₂⁴	1	2	yes	—
359	C₃×#41	—	4	16	no	—
360	C₂×C₃×Q₈	—	2	2	no	—
361	C₂×C₃×Q₈	—	2	2	no	—
362	C₂×C₃×Q₈	—	2	2	no	—
363	C₂×C₃×D₄	—	2	4	no	—
364	C₂×C₃×D₄	—	2	4	no	—
365	C₂×C₃×D₄	—	2	4	no	—
366	C₂×C₃×D₄	#41	1	4	yes	—
367	C₂×C₃×D₄	#41	1	4	yes	—
368	C₂×C₃×D₄	#41	1	4	yes	—
369	C₂²×C₃×C₄	—	2	4	no	—
370	C₂²×C₃×C₄	—	2	4	no	—
371	C₂²×C₃×C₄	—	2	4	no	—
372	C₂²×C₃×C₄	—	2	4	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	4	no	—
375	C₂²×C₃×C₄	—	2	4	no	—
376	C₂²×C₃×C₄	—	2	4	no	—
377	C₂²×C₃×C₄	—	2	4	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	4	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	—	4	2	no	—
386	C₂²×C₃×C₄	—	4	2	no	—
387	C₂²×C₃×C₄	—	4	2	no	—
388	C₂²×C₃×C₄	—	4	2	no	—
389	C₂²×C₃×C₄	—	4	2	no	—
390	C₂²×C₃×C₄	—	4	2	no	—
391	C₂²×C₃×C₄	—	4	2	no	—
392	C₂²×C₃×C₄	—	4	2	no	—
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
410	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	2	2	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	4	2	no	—
427	C₃×C₄⋊C₄	—	4	2	no	—
428	C₃×C₄⋊C₄	—	4	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	1	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	—	4	2	no	—
434	C₃×C₄⋊C₄	—	4	1	no	—
435	C₃×C₄⋊C₄	—	4	2	no	—
436	C₃×C₂²⋊C₄	—	2	4	no	—
437	C₃×C₂²⋊C₄	—	2	4	no	—
438	C₃×C₂²⋊C₄	—	2	4	no	—
439	C₃×C₂²⋊C₄	—	2	4	no	—
440	C₃×C₂²⋊C₄	—	2	4	no	—
441	C₃×C₂²⋊C₄	—	2	4	no	—
442	C₃×C₂²⋊C₄	—	2	2	no	—
443	C₃×C₂²⋊C₄	—	2	2	no	—
444	C₃×C₂²⋊C₄	—	4	1	no	—
445	C₃×C₂²⋊C₄	—	4	2	no	—
446	C₃×C₂²⋊C₄	—	4	1	no	—
447	C₃×C₂²⋊C₄	—	4	1	no	—
448	C₃×C₂²⋊C₄	—	4	1	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₄²	—	2	2	no	—
452	C₃×C₄²	—	2	2	no	—
453	C₃×C₄²	—	2	2	no	—
454	C₃×C₄²	—	2	2	no	—
455	C₃×C₄²	—	2	2	no	—
456	C₃×C₄²	—	2	2	no	—
457	C₃×C₄²	—	4	2	no	—
458	C₃×C₄²	—	4	2	no	—
459	C₃×C₄²	—	4	2	no	—
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	4	no	—
463	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₃	1	2	yes	—
467	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₃	1	2	yes	—
469	C₂³×C₄	C₂³×C₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₃	1	2	yes	—
474	#126	—	4	4	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	4	4	no	—
482	C₂×C₄⋊C₄	—	4	4	no	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	#95	C₂³×C₃	1	1	yes	characteristic
530	#95	C₂³×C₃	1	1	yes	characteristic
531	#95	C₂³×C₃	1	1	yes	characteristic
532	#95	C₂³×C₃	1	1	yes	characteristic
533	#95	C₂³×C₃	1	1	yes	characteristic
534	#95	C₂³×C₃	1	2	yes	—
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	1	yes	characteristic
550	#95	C₂³×C₃	1	1	yes	characteristic
551	#95	C₂³×C₃	1	1	yes	characteristic
552	#95	C₂³×C₃	1	1	yes	characteristic
553	#95	C₂³×C₃	1	1	yes	characteristic
554	#95	C₂³×C₃	1	1	yes	characteristic
555	#95	C₂³×C₃	1	1	yes	characteristic
556	#95	C₂³×C₃	1	1	yes	characteristic
557	#95	C₂³×C₃	1	1	yes	characteristic
558	#95	C₂³×C₃	1	1	yes	characteristic
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	2	yes	—
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	2	2	no	—
575	C₂³×C₃	—	2	1	no	—
576	C₂³×C₃	—	2	1	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	2	1	no	—
579	C₂³×C₃	—	2	1	no	—
580	C₂³×C₃	—	2	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	C₂×#41	1	4	yes	—
583	C₂³×C₃	C₂×#41	1	4	yes	—
584	C₂³×C₃	C₂×#41	1	4	yes	—
585	C₂³×C₃	C₂⁵	1	1	yes	characteristic
586	C₃×Q₈	—	4	4	no	—
587	C₃×D₄	—	4	8	no	—
588	C₃×D₄	#126	1	16	yes	complemented
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	4	8	no	—
648	C₂×C₃×C₄	—	4	8	no	—
649	C₂×C₃×C₄	—	4	8	no	—
650	C₂×C₃×C₄	—	4	4	no	—
651	C₂×C₃×C₄	—	8	4	no	—
652	C₂×C₃×C₄	—	8	4	no	—
653	C₂×C₃×C₄	—	8	4	no	—
654	C₂×C₃×C₄	—	8	4	no	—
655	C₂×C₃×C₄	C₂×#41	1	2	yes	—
656	C₂×C₃×C₄	C₂×#41	1	2	yes	—
657	C₂×C₃×C₄	C₂×#41	1	2	yes	—
658	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
659	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
660	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
661	C₂⁴	C₂⁴×C₃	1	2	yes	—
662	#41	—	4	16	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	C₃×#41	1	4	yes	—
670	C₂×D₄	C₃×#41	1	4	yes	—
671	C₂×D₄	C₃×#41	1	4	yes	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	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	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	1	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₂²×C₃	—	2	4	no	—
764	C₂²×C₃	—	2	4	no	—
765	C₂²×C₃	—	2	4	no	—
766	C₂²×C₃	—	2	4	no	—
767	C₂²×C₃	—	2	4	no	—
768	C₂²×C₃	—	2	4	no	—
769	C₂²×C₃	—	4	1	no	—
770	C₂²×C₃	—	4	1	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	—	4	1	no	—
773	C₂²×C₃	—	4	1	no	—
774	C₂²×C₃	—	4	1	no	—
775	C₂²×C₃	—	4	1	no	—
776	C₂²×C₃	C₂×#126	1	8	yes	—
777	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
778	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
779	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
780	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
781	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
782	C₂²×C₃	#585	1	1	yes	characteristic
783	C₂²×C₃	#585	1	1	yes	characteristic
784	C₃×C₄	—	2	2	no	—
785	C₃×C₄	—	2	2	no	—
786	C₃×C₄	—	4	1	no	—
787	C₃×C₄	—	4	2	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	2	no	—
790	C₃×C₄	—	4	1	no	—
791	C₃×C₄	—	4	2	no	—
792	C₃×C₄	—	4	2	no	—
793	C₃×C₄	—	4	1	no	—
794	C₃×C₄	—	4	1	no	—
795	C₃×C₄	—	4	1	no	—
796	C₃×C₄	—	4	1	no	—
797	C₃×C₄	—	4	1	no	—
798	C₃×C₄	—	4	1	no	—
799	C₃×C₄	—	4	1	no	—
800	C₃×C₄	—	4	2	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	2	no	—
803	C₃×C₄	—	4	1	no	—
804	C₃×C₄	C₂×#126	1	4	yes	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	C₂×C₃×#41	1	4	yes	—
817	C₂³	C₂×C₃×#41	1	4	yes	—
818	C₂³	C₂×C₃×#41	1	4	yes	—
819	C₂³	C₂⁵×C₃	1	1	yes	characteristic
820	Q₈	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	C₃×#126	1	16	yes	complemented
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	8	4	no	—
886	C₂×C₄	—	8	4	no	—
887	C₂×C₄	—	8	4	no	—
888	C₂×C₄	—	8	4	no	—
889	C₂×C₄	C₂×C₃×#41	1	2	yes	—
890	C₂×C₄	C₂×C₃×#41	1	2	yes	—
891	C₂×C₄	C₂×C₃×#41	1	2	yes	—
892	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
893	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
894	C₂×C₃	—	2	8	no	—
895	C₂×C₃	—	8	1	no	—
896	C₂×C₃	C₂²×#126	1	1	yes	characteristic
897	C₂×C₃	#3513	1	1	yes	characteristic
898	C₂×C₃	#3514	1	1	yes	characteristic
899	C₂×C₃	#3515	1	1	yes	characteristic
900	C₂×C₃	#3515	1	1	yes	characteristic
901	C₂×C₃	#3520	1	1	yes	characteristic
902	C₂×C₃	#3521	1	1	yes	characteristic
903	C₂²	—	2	4	no	—
904	C₂²	—	2	4	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂×C₃×#126	1	8	yes	—
917	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
918	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
919	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
920	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
921	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
922	C₂²	C₃×#585	1	1	yes	characteristic
923	C₂²	C₃×#585	1	1	yes	characteristic
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	C₂×C₃×#126	1	4	yes	—
945	C₃	#35888	1	1	yes	characteristic, direct product factor, Sylow
946	C₂	—	2	8	no	—
947	C₂	—	8	1	no	—
948	C₂	C₂²×C₃×#126	1	1	yes	characteristic
949	C₂	C₃×#3513	1	1	yes	characteristic
950	C₂	C₃×#3514	1	1	yes	characteristic
951	C₂	C₃×#3515	1	1	yes	characteristic
952	C₂	C₃×#3515	1	1	yes	characteristic
953	C₂	C₃×#3520	1	1	yes	characteristic
954	C₂	C₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×#41	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×#2645	C₂	semidirect
2. C₃×#2643	C₂	semidirect
3. C₃×#2514	C₂	semidirect
4. C₃×#2511	C₂	semidirect
5. C₃×#2511	C₂	semidirect
6. C₃×#2510	C₂	semidirect
7. C₃×#2497	C₂	semidirect
8. C₃×#2496	C₂	semidirect
9. C₃×#2495	C₂	semidirect
10. C₃×#2493	C₂	semidirect
11. C₃×#2493	C₂	semidirect
12. C₃×#2493	C₂	semidirect
13. C₃×#2481	C₂	semidirect
14. C₃×#2481	C₂	semidirect
15. C₃×#2401	C₂	semidirect
16. C₂×C₃×#400	C₂	semidirect
17. C₃×#2349	C₂	semidirect
18. C₃×D₄×C₄⋊C₄	C₂	semidirect
19. C₃×D₄×C₄⋊C₄	C₂	semidirect
23. C₃×#2275	C₂	semidirect
24. #35888	C₃	direct (N × H)
124. #2645	C₂×C₃	semidirect
125. #2643	C₂×C₃	semidirect
126. #2514	C₂×C₃	semidirect
127. #2511	C₂×C₃	semidirect
128. #2511	C₂×C₃	semidirect
129. #2510	C₂×C₃	semidirect
130. #2497	C₂×C₃	semidirect
131. #2496	C₂×C₃	semidirect
132. #2495	C₂×C₃	semidirect
133. #2493	C₂×C₃	semidirect
134. #2493	C₂×C₃	semidirect
135. #2493	C₂×C₃	semidirect
136. #2481	C₂×C₃	semidirect
137. #2481	C₂×C₃	semidirect
138. #2401	C₂×C₃	semidirect
139. C₂×#400	C₂×C₃	semidirect
140. #2349	C₂×C₃	semidirect
141. D₄×C₄⋊C₄	C₂×C₃	semidirect
142. D₄×C₄⋊C₄	C₂×C₃	semidirect
146. #2275	C₂×C₃	semidirect
588. C₃×D₄	#126	semidirect
822. D₄	C₃×#126	semidirect
945. C₃	#35888	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×#2645	2
C₃×#2643	2
C₃×#2514	2
C₃×#2511	2
C₃×#2510	2
C₃×#2497	2
C₃×#2496	2
C₃×#2495	2
C₃×#2493	2
C₃×#2481	2
C₃×#2401	2
C₂×C₃×#400	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×#2339	2
C₃×#2275	2
#35888	3

Subgroups — C3×#35888 #10654495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35888 #10654495