Subgroups — C₃×#35270 #10653877

Order 768.

1766 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2854	C₂	1	1	yes	maximal, characteristic
4	C₃×#2850	C₂	1	1	yes	maximal, characteristic
5	C₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2645	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2532	C₂	1	2	yes	maximal, complemented
10	C₃×#2530	C₂	1	2	yes	maximal, complemented
11	C₃×#2529	C₂	1	2	yes	maximal, complemented
12	C₃×#2527	C₂	1	2	yes	maximal, complemented
13	C₃×#2510	C₂	1	2	yes	maximal, complemented
14	C₃×#2488	C₂	1	2	yes	maximal, complemented
15	C₃×#2450	C₂	1	2	yes	maximal, complemented
16	C₃×#2419	C₂	1	2	yes	maximal, complemented
17	C₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic
23	C₂×C₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
24	#35270	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃×#123	C₂²	1	2	yes	—
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
35	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₃×#401	C₂²	1	2	yes	—
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×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#393	C₂²	1	2	yes	—
52	C₃×#393	C₂²	1	2	yes	—
53	C₃×#391	C₂²	1	1	yes	characteristic
54	C₃×#391	C₂²	1	1	yes	characteristic
55	C₃×#391	C₂²	1	1	yes	characteristic
56	C₃×#391	C₂²	1	1	yes	characteristic
57	C₃×#391	C₂²	1	2	yes	—
58	C₃×#391	C₂²	1	2	yes	—
59	C₃×#391	C₂²	1	2	yes	—
60	C₃×#390	C₂²	1	1	yes	characteristic
61	C₃×#390	C₂²	1	1	yes	characteristic
62	C₃×#390	C₂²	1	1	yes	characteristic
63	C₃×#390	C₂²	1	1	yes	characteristic
64	C₃×#389	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×#389	C₂²	1	1	yes	characteristic
72	C₃×#389	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#386	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#384	C₂²	1	1	yes	characteristic
98	C₃×#383	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	1	yes	characteristic
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×#381	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	2	yes	—
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₃×#376	C₂²	1	1	yes	characteristic
113	C₃×#376	C₂²	1	1	yes	characteristic
114	C₃×#376	C₂²	1	1	yes	characteristic
115	C₃×#376	C₂²	1	1	yes	characteristic
116	C₃×#376	C₂²	1	1	yes	characteristic
117	C₃×#376	C₂²	1	1	yes	characteristic
118	C₃×#376	C₂²	1	1	yes	characteristic
119	C₃×#376	C₂²	1	1	yes	characteristic
120	C₂×C₃×#95	C₂²	1	1	yes	characteristic
121	C₂×C₃×#95	C₂²	1	1	yes	characteristic
122	C₂×C₃×#95	C₂²	1	1	yes	characteristic
123	C₂×C₃×#95	C₂²	1	1	yes	characteristic
124	#2857	C₂×C₃	1	1	yes	characteristic, complemented
125	#2855	C₂×C₃	1	1	yes	characteristic, complemented
126	#2854	C₂×C₃	1	1	yes	characteristic
127	#2850	C₂×C₃	1	1	yes	characteristic
128	#2647	C₂×C₃	1	1	yes	characteristic, complemented
129	#2645	C₂×C₃	1	1	yes	characteristic, complemented
130	#2644	C₂×C₃	1	1	yes	characteristic, complemented
131	#2640	C₂×C₃	1	1	yes	characteristic, complemented
132	#2532	C₂×C₃	1	2	yes	complemented
133	#2530	C₂×C₃	1	2	yes	complemented
134	#2529	C₂×C₃	1	2	yes	complemented
135	#2527	C₂×C₃	1	2	yes	complemented
136	#2510	C₂×C₃	1	2	yes	complemented
137	#2488	C₂×C₃	1	2	yes	complemented
138	#2450	C₂×C₃	1	2	yes	complemented
139	#2419	C₂×C₃	1	2	yes	complemented
140	#2331	C₂×C₃	1	1	yes	characteristic, complemented
141	#2326	C₂×C₃	1	1	yes	characteristic, complemented
142	#2320	C₂×C₃	1	1	yes	characteristic, complemented
143	#2319	C₂×C₃	1	1	yes	characteristic, complemented
144	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×#121	C₂×C₃	1	1	yes	characteristic
146	C₂×#376	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	2	yes	—
149	C₂²×C₃×D₄	C₂³	1	2	yes	—
150	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₃×C₄⋊Q₈	—	2	4	no	—
160	C₃×#124	—	2	4	no	—
161	C₃×#123	—	4	4	no	—
162	C₃×C₂²⋊Q₈	—	2	4	no	—
163	C₃×C₂²⋊Q₈	—	4	4	no	—
164	C₃×#121	—	2	4	no	—
165	C₃×C₄×Q₈	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	4	4	no	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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×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	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	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄²	—	2	4	no	—
203	C₂×C₃×C₄²	—	2	4	no	—
204	C₂×C₃×C₄²	—	2	4	no	—
205	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	2	yes	—
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₃×#95	C₂³	1	1	yes	characteristic
221	C₃×#95	C₂³	1	1	yes	characteristic
222	C₃×#95	C₂³	1	1	yes	characteristic
223	C₃×#95	C₂³	1	1	yes	characteristic
224	C₃×#95	C₂³	1	1	yes	characteristic
225	C₃×#95	C₂³	1	1	yes	characteristic
226	C₃×#95	C₂³	1	1	yes	characteristic
227	C₃×#95	C₂³	1	1	yes	characteristic
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
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	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
259	C₂×#124	C₂²×C₃	1	1	yes	characteristic
260	C₂×#123	C₂²×C₃	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
263	C₂×#121	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
267	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
268	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
269	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
270	#401	C₂²×C₃	1	2	yes	—
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	#398	C₂²×C₃	1	2	yes	—
277	#398	C₂²×C₃	1	2	yes	—
278	#397	C₂²×C₃	1	2	yes	—
279	#397	C₂²×C₃	1	2	yes	—
280	#397	C₂²×C₃	1	2	yes	—
281	#397	C₂²×C₃	1	2	yes	—
282	#397	C₂²×C₃	1	2	yes	—
283	#396	C₂²×C₃	1	2	yes	—
284	#393	C₂²×C₃	1	2	yes	—
285	#393	C₂²×C₃	1	2	yes	—
286	#391	C₂²×C₃	1	1	yes	characteristic
287	#391	C₂²×C₃	1	1	yes	characteristic
288	#391	C₂²×C₃	1	1	yes	characteristic
289	#391	C₂²×C₃	1	2	yes	—
290	#391	C₂²×C₃	1	2	yes	—
291	#391	C₂²×C₃	1	2	yes	—
292	#391	C₂²×C₃	1	1	yes	characteristic
293	#390	C₂²×C₃	1	1	yes	characteristic
294	#390	C₂²×C₃	1	1	yes	characteristic
295	#390	C₂²×C₃	1	1	yes	characteristic
296	#390	C₂²×C₃	1	1	yes	characteristic
297	#389	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	2	yes	—
304	#389	C₂²×C₃	1	1	yes	characteristic
305	#389	C₂²×C₃	1	1	yes	characteristic
306	#388	C₂²×C₃	1	2	yes	—
307	#388	C₂²×C₃	1	2	yes	—
308	#388	C₂²×C₃	1	2	yes	—
309	#388	C₂²×C₃	1	2	yes	—
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#386	C₂²×C₃	1	2	yes	—
323	#386	C₂²×C₃	1	2	yes	—
324	#386	C₂²×C₃	1	2	yes	—
325	#386	C₂²×C₃	1	2	yes	—
326	#385	C₂²×C₃	1	2	yes	—
327	#385	C₂²×C₃	1	2	yes	—
328	#385	C₂²×C₃	1	2	yes	—
329	#385	C₂²×C₃	1	2	yes	—
330	#384	C₂²×C₃	1	1	yes	characteristic
331	#383	C₂²×C₃	1	2	yes	—
332	#382	C₂²×C₃	1	2	yes	—
333	#382	C₂²×C₃	1	1	yes	characteristic
334	#381	C₂²×C₃	1	2	yes	—
335	#381	C₂²×C₃	1	2	yes	—
336	#380	C₂²×C₃	1	2	yes	—
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	C₂²×C₃	1	1	yes	characteristic
339	#380	C₂²×C₃	1	2	yes	—
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	2	yes	—
343	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
344	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
345	#376	C₂²×C₃	1	1	yes	characteristic
346	#376	C₂²×C₃	1	1	yes	characteristic
347	#376	C₂²×C₃	1	1	yes	characteristic
348	#376	C₂²×C₃	1	1	yes	characteristic
349	#376	C₂²×C₃	1	1	yes	characteristic
350	#376	C₂²×C₃	1	1	yes	characteristic
351	#376	C₂²×C₃	1	1	yes	characteristic
352	#376	C₂²×C₃	1	1	yes	characteristic
353	C₂×#95	C₂²×C₃	1	1	yes	characteristic
354	C₂×#95	C₂²×C₃	1	1	yes	characteristic
355	C₂×#95	C₂²×C₃	1	1	yes	characteristic
356	C₂×#95	C₂²×C₃	1	1	yes	characteristic
357	C₂⁴×C₃	C₂⁴	1	2	yes	—
358	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₃×Q₈	—	2	2	no	—
360	C₂×C₃×Q₈	—	2	2	no	—
361	C₂×C₃×Q₈	—	2	2	no	—
362	C₂×C₃×Q₈	—	2	4	no	—
363	C₂×C₃×Q₈	—	4	2	no	—
364	C₂×C₃×Q₈	—	4	2	no	—
365	C₂×C₃×D₄	—	2	4	no	—
366	C₂×C₃×D₄	—	2	4	no	—
367	C₂×C₃×D₄	—	2	4	no	—
368	C₂×C₃×D₄	—	2	2	no	—
369	C₂×C₃×D₄	—	2	2	no	—
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	2	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	2	no	—
382	C₂²×C₃×C₄	—	2	2	no	—
383	C₂²×C₃×C₄	—	2	2	no	—
384	C₂²×C₃×C₄	—	2	2	no	—
385	C₂²×C₃×C₄	—	2	4	no	—
386	C₂²×C₃×C₄	—	4	1	no	—
387	C₂²×C₃×C₄	—	4	1	no	—
388	C₂²×C₃×C₄	—	4	1	no	—
389	C₂²×C₃×C₄	—	4	1	no	—
390	C₂²×C₃×C₄	—	4	1	no	—
391	C₂²×C₃×C₄	—	4	1	no	—
392	C₂²×C₃×C₄	—	4	2	no	—
393	C₂²×C₃×C₄	—	4	2	no	—
394	C₂²×C₃×C₄	#41	1	4	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	1	yes	characteristic
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
409	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
410	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	2	4	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	4	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	4	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	2	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	2	no	—
435	C₃×C₂²⋊C₄	—	2	4	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	—	4	2	no	—
443	C₃×C₂²⋊C₄	—	4	2	no	—
444	C₃×C₂²⋊C₄	—	4	2	no	—
445	C₃×C₂²⋊C₄	—	4	2	no	—
446	C₃×C₂²⋊C₄	—	4	2	no	—
447	C₃×C₂²⋊C₄	—	4	2	no	—
448	C₃×C₂²⋊C₄	—	4	2	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₄²	—	2	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	—	2	2	no	—
458	C₃×C₄²	—	2	2	no	—
459	C₃×C₄²	—	2	2	no	—
460	C₃×C₄²	—	2	4	no	—
461	C₃×C₄²	—	4	2	no	—
462	C₃×C₄²	—	4	2	no	—
463	C₃×C₄²	#41	1	4	yes	—
464	C₃×C₄²	#41	1	4	yes	—
465	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₃	1	2	yes	—
476	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
477	C₄⋊Q₈	—	2	4	no	—
478	#124	—	2	4	no	—
479	#123	—	4	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	4	4	no	—
482	#121	—	2	4	no	—
483	C₄×Q₈	—	2	4	no	—
484	C₄×D₄	—	2	4	no	—
485	C₄×D₄	—	4	4	no	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
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	2	yes	—
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	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₄²	—	2	4	no	—
521	C₂×C₄²	—	2	4	no	—
522	C₂×C₄²	—	2	4	no	—
523	C₂×C₄²	C₂³×C₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
538	#95	C₂³×C₃	1	1	yes	characteristic
539	#95	C₂³×C₃	1	1	yes	characteristic
540	#95	C₂³×C₃	1	1	yes	characteristic
541	#95	C₂³×C₃	1	1	yes	characteristic
542	#95	C₂³×C₃	1	1	yes	characteristic
543	#95	C₂³×C₃	1	1	yes	characteristic
544	#95	C₂³×C₃	1	1	yes	characteristic
545	#95	C₂³×C₃	1	1	yes	characteristic
546	#95	C₂³×C₃	1	1	yes	characteristic
547	#95	C₂³×C₃	1	1	yes	characteristic
548	#95	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	2	yes	—
557	#95	C₂³×C₃	1	2	yes	—
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	2	yes	—
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	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	2	yes	—
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
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	2	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	C₂×#41	1	2	yes	—
588	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
589	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
590	C₂³×C₃	C₂⁵	1	1	yes	characteristic
591	C₃×Q₈	—	4	4	no	—
592	C₃×Q₈	—	8	4	no	—
593	C₃×D₄	—	4	8	no	—
594	C₃×D₄	—	4	4	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	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	8	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	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	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	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	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	1	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	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	4	4	no	—
652	C₂×C₃×C₄	—	4	4	no	—
653	C₂×C₃×C₄	—	4	4	no	—
654	C₂×C₃×C₄	—	4	4	no	—
655	C₂×C₃×C₄	—	4	4	no	—
656	C₂×C₃×C₄	—	4	4	no	—
657	C₂×C₃×C₄	—	8	4	no	—
658	C₂×C₃×C₄	C₂×#41	1	2	yes	—
659	C₂×C₃×C₄	C₂×#41	1	2	yes	—
660	C₂×C₃×C₄	C₂×#41	1	2	yes	—
661	C₂×C₃×C₄	C₂×#41	1	2	yes	—
662	C₂×C₃×C₄	C₂×#41	1	2	yes	—
663	C₂×C₃×C₄	C₂×#41	1	2	yes	—
664	C₂×C₃×C₄	C₂×#41	1	2	yes	—
665	C₂×C₃×C₄	C₂×#41	1	2	yes	—
666	C₂⁴	C₂⁴×C₃	1	2	yes	—
667	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	C₃×#41	1	4	yes	—
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	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	4	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	C₃×#41	1	4	yes	—
773	C₄²	C₃×#41	1	4	yes	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	2	no	—
776	C₂²×C₃	—	2	2	no	—
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	4	2	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	2	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	2	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	2	no	—
787	C₂²×C₃	#542	1	4	yes	—
788	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
789	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
790	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
791	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂²×C₃	#585	1	1	yes	characteristic
794	C₂²×C₃	#585	1	1	yes	characteristic
795	C₃×C₄	—	2	2	no	—
796	C₃×C₄	—	2	2	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	4	2	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	1	no	—
803	C₃×C₄	—	4	2	no	—
804	C₃×C₄	—	4	2	no	—
805	C₃×C₄	—	4	1	no	—
806	C₃×C₄	—	4	1	no	—
807	C₃×C₄	—	4	2	no	—
808	C₃×C₄	—	4	1	no	—
809	C₃×C₄	—	4	1	no	—
810	C₃×C₄	—	4	2	no	—
811	C₃×C₄	—	4	2	no	—
812	C₃×C₄	—	4	2	no	—
813	C₃×C₄	—	4	1	no	—
814	C₃×C₄	—	4	1	no	—
815	C₃×C₄	#529	1	4	yes	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	C₂×C₃×#41	1	2	yes	—
828	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
829	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
830	C₂³	C₂⁵×C₃	1	1	yes	characteristic
831	Q₈	—	4	4	no	—
832	Q₈	—	8	4	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	4	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	C₂×C₃×#41	1	2	yes	—
899	C₂×C₄	C₂×C₃×#41	1	2	yes	—
900	C₂×C₄	C₂×C₃×#41	1	2	yes	—
901	C₂×C₄	C₂×C₃×#41	1	2	yes	—
902	C₂×C₄	C₂×C₃×#41	1	2	yes	—
903	C₂×C₄	C₂×C₃×#41	1	2	yes	—
904	C₂×C₄	C₂×C₃×#41	1	2	yes	—
905	C₂×C₄	C₂×C₃×#41	1	2	yes	—
906	C₂×C₃	—	2	4	no	—
907	C₂×C₃	—	8	2	no	—
908	C₂×C₃	C₂×#529	1	1	yes	characteristic
909	C₂×C₃	C₂×#542	1	1	yes	characteristic
910	C₂×C₃	#3455	1	1	yes	characteristic
911	C₂×C₃	#3494	1	1	yes	characteristic
912	C₂×C₃	#3494	1	1	yes	characteristic
913	C₂×C₃	#3495	1	1	yes	characteristic
914	C₂×C₃	#3495	1	1	yes	characteristic
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	C₃×#542	1	4	yes	—
929	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
930	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
931	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
932	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
934	C₂²	C₃×#585	1	1	yes	characteristic
935	C₂²	C₃×#585	1	1	yes	characteristic
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	C₃×#529	1	4	yes	—
957	C₃	#35270	1	1	yes	characteristic, direct product factor, Sylow
958	C₂	—	2	4	no	—
959	C₂	—	8	2	no	—
960	C₂	C₂×C₃×#529	1	1	yes	characteristic
961	C₂	C₂×C₃×#542	1	1	yes	characteristic
962	C₂	C₃×#3455	1	1	yes	characteristic
963	C₂	C₃×#3494	1	1	yes	characteristic
964	C₂	C₃×#3494	1	1	yes	characteristic
965	C₂	C₃×#3495	1	1	yes	characteristic
966	C₂	C₃×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#121	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×#2857	C₂	semidirect
2. C₃×#2855	C₂	semidirect
5. C₃×#2647	C₂	semidirect
6. C₃×#2645	C₂	semidirect
7. C₃×#2644	C₂	semidirect
8. C₃×#2640	C₂	semidirect
9. C₃×#2532	C₂	semidirect
10. C₃×#2530	C₂	semidirect
11. C₃×#2529	C₂	semidirect
12. C₃×#2527	C₂	semidirect
13. C₃×#2510	C₂	semidirect
14. C₃×#2488	C₂	semidirect
15. C₃×#2450	C₂	semidirect
16. C₃×#2419	C₂	semidirect
17. C₃×#2331	C₂	semidirect
18. C₃×#2326	C₂	semidirect
19. C₃×#2320	C₂	semidirect
20. C₃×#2319	C₂	semidirect
21. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
23. C₂×C₃×#376	C₂	semidirect
24. #35270	C₃	direct (N × H)
124. #2857	C₂×C₃	semidirect
125. #2855	C₂×C₃	semidirect
128. #2647	C₂×C₃	semidirect
129. #2645	C₂×C₃	semidirect
130. #2644	C₂×C₃	semidirect
131. #2640	C₂×C₃	semidirect
132. #2532	C₂×C₃	semidirect
133. #2530	C₂×C₃	semidirect
134. #2529	C₂×C₃	semidirect
135. #2527	C₂×C₃	semidirect
136. #2510	C₂×C₃	semidirect
137. #2488	C₂×C₃	semidirect
138. #2450	C₂×C₃	semidirect
139. #2419	C₂×C₃	semidirect
140. #2331	C₂×C₃	semidirect
141. #2326	C₂×C₃	semidirect
142. #2320	C₂×C₃	semidirect
143. #2319	C₂×C₃	semidirect
144. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
146. C₂×#376	C₂×C₃	semidirect
957. C₃	#35270	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×#2857	2
C₃×#2855	2
C₃×#2854	2
C₃×#2850	2
C₃×#2647	2
C₃×#2645	2
C₃×#2644	2
C₃×#2640	2
C₃×#2532	2
C₃×#2530	2
C₃×#2529	2
C₃×#2527	2
C₃×#2510	2
C₃×#2488	2
C₃×#2450	2
C₃×#2419	2
C₃×#2331	2
C₃×#2326	2
C₃×#2320	2
C₃×#2319	2
C₃×C₄×C₂²⋊Q₈	2
C₃×C₄×#121	2
C₂×C₃×#376	2
#35270	3

Subgroups — C3×#35270 #10653877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35270 #10653877