Subgroups — C₃×#35970 #10654577

Order 768.

1780 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2653	C₂	1	2	yes	maximal, complemented
2	C₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2578	C₂	1	2	yes	maximal, complemented
4	C₃×#2572	C₂	1	2	yes	maximal, complemented
5	C₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2544	C₂	1	1	yes	maximal, characteristic
7	C₃×#2531	C₂	1	2	yes	maximal, complemented
8	C₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2510	C₂	1	2	yes	maximal, complemented
11	C₃×#2458	C₂	1	2	yes	maximal, complemented
12	C₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2445	C₂	1	1	yes	maximal, characteristic
14	C₃×#2419	C₂	1	2	yes	maximal, complemented
15	C₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2398	C₂	1	2	yes	maximal, complemented
17	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2366	C₂	1	1	yes	maximal, characteristic
20	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	#35970	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#127	C₂²	1	1	yes	characteristic
27	C₂×C₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₃×#401	C₂²	1	2	yes	—
38	C₃×#400	C₂²	1	1	yes	characteristic
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	1	yes	characteristic
41	C₃×#400	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	1	yes	characteristic
43	C₃×#398	C₂²	1	1	yes	characteristic
44	C₃×#398	C₂²	1	1	yes	characteristic
45	C₃×#398	C₂²	1	1	yes	characteristic
46	C₃×#398	C₂²	1	1	yes	characteristic
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#393	C₂²	1	2	yes	—
58	C₃×#393	C₂²	1	2	yes	—
59	C₃×#393	C₂²	1	2	yes	—
60	C₃×#393	C₂²	1	2	yes	—
61	C₃×#391	C₂²	1	2	yes	—
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×#391	C₂²	1	1	yes	characteristic
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#390	C₂²	1	1	yes	characteristic
68	C₃×#390	C₂²	1	2	yes	—
69	C₃×#390	C₂²	1	1	yes	characteristic
70	C₃×#390	C₂²	1	1	yes	characteristic
71	C₃×#390	C₂²	1	1	yes	characteristic
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	C₂²	1	1	yes	characteristic
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×#388	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×#386	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×#383	C₂²	1	2	yes	—
97	C₃×#383	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	1	yes	characteristic
100	C₃×#381	C₂²	1	2	yes	—
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊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×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	#2653	C₂×C₃	1	2	yes	complemented
125	#2640	C₂×C₃	1	1	yes	characteristic, complemented
126	#2578	C₂×C₃	1	2	yes	complemented
127	#2572	C₂×C₃	1	2	yes	complemented
128	#2563	C₂×C₃	1	1	yes	characteristic, complemented
129	#2544	C₂×C₃	1	1	yes	characteristic
130	#2531	C₂×C₃	1	2	yes	complemented
131	#2514	C₂×C₃	1	1	yes	characteristic, complemented
132	#2513	C₂×C₃	1	1	yes	characteristic, complemented
133	#2510	C₂×C₃	1	2	yes	complemented
134	#2458	C₂×C₃	1	2	yes	complemented
135	#2447	C₂×C₃	1	1	yes	characteristic, complemented
136	#2445	C₂×C₃	1	1	yes	characteristic
137	#2419	C₂×C₃	1	2	yes	complemented
138	#2402	C₂×C₃	1	1	yes	characteristic, complemented
139	#2398	C₂×C₃	1	2	yes	complemented
140	#2367	C₂×C₃	1	1	yes	characteristic, complemented
141	#2367	C₂×C₃	1	1	yes	characteristic, complemented
142	#2366	C₂×C₃	1	1	yes	characteristic
143	#2365	C₂×C₃	1	1	yes	characteristic, complemented
144	#2357	C₂×C₃	1	1	yes	characteristic, complemented
145	#2356	C₂×C₃	1	1	yes	characteristic, complemented
146	#2275	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	1	yes	characteristic
150	C₂²×C₃×D₄	C₂³	1	2	yes	—
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	2	yes	—
157	C₃×C₄⋊Q₈	—	2	4	no	—
158	C₃×#127	—	2	4	no	—
159	C₃×#124	—	2	4	no	—
160	C₃×#124	—	2	4	no	—
161	C₃×#123	—	4	4	no	—
162	C₃×C₄×Q₈	—	2	4	no	—
163	C₃×C₄×Q₈	—	4	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	C₃×C₄×D₄	—	4	4	no	—
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	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	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	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	2	yes	—
219	C₂×C₃×C₄²	C₂³	1	2	yes	—
220	C₂×C₃×C₄²	C₂³	1	2	yes	—
221	C₂×C₃×C₄²	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₃×#95	C₂³	1	1	yes	characteristic
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	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	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
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×#127	C₂²×C₃	1	1	yes	characteristic
260	C₂×#124	C₂²×C₃	1	1	yes	characteristic
261	C₂×#124	C₂²×C₃	1	1	yes	characteristic
262	C₂×#123	C₂²×C₃	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
270	#401	C₂²×C₃	1	2	yes	—
271	#400	C₂²×C₃	1	1	yes	characteristic
272	#400	C₂²×C₃	1	1	yes	characteristic
273	#400	C₂²×C₃	1	1	yes	characteristic
274	#400	C₂²×C₃	1	2	yes	—
275	#400	C₂²×C₃	1	1	yes	characteristic
276	#398	C₂²×C₃	1	1	yes	characteristic
277	#398	C₂²×C₃	1	1	yes	characteristic
278	#398	C₂²×C₃	1	1	yes	characteristic
279	#398	C₂²×C₃	1	1	yes	characteristic
280	#397	C₂²×C₃	1	2	yes	—
281	#397	C₂²×C₃	1	2	yes	—
282	#397	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	2	yes	—
284	#397	C₂²×C₃	1	2	yes	—
285	#397	C₂²×C₃	1	2	yes	—
286	#394	C₂²×C₃	1	2	yes	—
287	#394	C₂²×C₃	1	2	yes	—
288	#394	C₂²×C₃	1	2	yes	—
289	#394	C₂²×C₃	1	2	yes	—
290	#393	C₂²×C₃	1	2	yes	—
291	#393	C₂²×C₃	1	2	yes	—
292	#393	C₂²×C₃	1	2	yes	—
293	#393	C₂²×C₃	1	2	yes	—
294	#391	C₂²×C₃	1	2	yes	—
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	#391	C₂²×C₃	1	1	yes	characteristic
299	#390	C₂²×C₃	1	1	yes	characteristic
300	#390	C₂²×C₃	1	1	yes	characteristic
301	#390	C₂²×C₃	1	1	yes	characteristic
302	#390	C₂²×C₃	1	1	yes	characteristic
303	#390	C₂²×C₃	1	1	yes	characteristic
304	#390	C₂²×C₃	1	2	yes	—
305	#390	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
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	#388	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	#386	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	#383	C₂²×C₃	1	2	yes	—
330	#383	C₂²×C₃	1	2	yes	—
331	#382	C₂²×C₃	1	1	yes	characteristic
332	#382	C₂²×C₃	1	1	yes	characteristic
333	#381	C₂²×C₃	1	2	yes	—
334	#381	C₂²×C₃	1	2	yes	—
335	#380	C₂²×C₃	1	2	yes	—
336	#380	C₂²×C₃	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₄⋊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	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	#376	C₂²×C₃	1	2	yes	—
355	#376	C₂²×C₃	1	1	yes	characteristic
356	C₂×#95	C₂²×C₃	1	2	yes	—
357	C₂⁴×C₃	C₂⁴	1	2	yes	—
358	C₂⁴×C₃	C₂⁴	1	2	yes	—
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	2	no	—
368	C₂×C₃×D₄	—	2	2	no	—
369	C₂×C₃×D₄	—	2	2	no	—
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	4	no	—
373	C₂×C₃×D₄	—	4	2	no	—
374	C₂×C₃×D₄	—	4	2	no	—
375	C₂×C₃×D₄	—	4	2	no	—
376	C₂×C₃×D₄	#41	1	4	yes	—
377	C₂²×C₃×C₄	—	2	4	no	—
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	—	2	4	no	—
380	C₂²×C₃×C₄	—	2	4	no	—
381	C₂²×C₃×C₄	—	4	2	no	—
382	C₂²×C₃×C₄	—	4	2	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	C₂⁴	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	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	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₃×C₄⋊C₄	—	2	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	4	no	—
413	C₃×C₄⋊C₄	—	2	4	no	—
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	4	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	4	1	no	—
421	C₃×C₄⋊C₄	—	4	1	no	—
422	C₃×C₄⋊C₄	—	4	1	no	—
423	C₃×C₄⋊C₄	—	4	1	no	—
424	C₃×C₄⋊C₄	—	4	1	no	—
425	C₃×C₄⋊C₄	—	4	1	no	—
426	C₃×C₄⋊C₄	—	4	1	no	—
427	C₃×C₄⋊C₄	—	4	1	no	—
428	C₃×C₄⋊C₄	—	4	1	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	#41	1	4	yes	—
431	C₃×C₂²⋊C₄	—	2	4	no	—
432	C₃×C₂²⋊C₄	—	2	4	no	—
433	C₃×C₂²⋊C₄	—	2	4	no	—
434	C₃×C₂²⋊C₄	—	2	4	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	—	4	2	no	—
440	C₃×C₂²⋊C₄	—	4	2	no	—
441	C₃×C₂²⋊C₄	—	4	2	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×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	4	no	—
456	C₃×C₄²	—	2	2	no	—
457	C₃×C₄²	—	2	2	no	—
458	C₃×C₄²	—	2	4	no	—
459	C₃×C₄²	—	4	2	no	—
460	C₃×C₄²	—	4	2	no	—
461	C₃×C₄²	—	4	2	no	—
462	C₃×C₄²	—	4	2	no	—
463	C₃×C₄²	#41	1	4	yes	—
464	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₂²×D₄	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	C₄⋊Q₈	—	2	4	no	—
475	#127	—	2	4	no	—
476	#124	—	2	4	no	—
477	#124	—	2	4	no	—
478	#123	—	4	4	no	—
479	C₄×Q₈	—	2	4	no	—
480	C₄×Q₈	—	4	4	no	—
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	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	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	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	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	2	yes	—
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
540	#95	C₂³×C₃	1	1	yes	characteristic
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	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	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	1	yes	characteristic
564	#95	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	1	yes	characteristic
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	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	2	2	no	—
578	C₂³×C₃	—	2	2	no	—
579	C₂³×C₃	—	2	2	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	—	2	2	no	—
588	C₂³×C₃	C₂×#41	1	4	yes	—
589	C₂³×C₃	C₂⁵	1	1	yes	characteristic
590	C₃×Q₈	—	4	8	no	—
591	C₃×Q₈	—	4	4	no	—
592	C₃×D₄	—	2	8	no	—
593	C₃×D₄	—	4	8	no	—
594	C₃×D₄	—	4	4	no	—
595	C₃×D₄	—	8	4	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	2	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	1	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	2	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	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	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	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	1	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	1	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	1	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	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	1	no	—
651	C₂×C₃×C₄	—	2	1	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	—	8	4	no	—
656	C₂×C₃×C₄	C₂×#41	1	4	yes	—
657	C₂×C₃×C₄	C₂×#41	1	2	yes	—
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	H(5,𝔽₂)	1	2	yes	—
663	C₂⁴	C₂⁴×C₃	1	2	yes	—
664	C₂⁴	C₂⁴×C₃	1	2	yes	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	4	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	C₃×#41	1	4	yes	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	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	C₂⁴×C₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	2	yes	—
709	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	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	4	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	C₃×#41	1	4	yes	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	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	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	C₃×#41	1	4	yes	—
770	C₂²×C₃	—	2	4	no	—
771	C₂²×C₃	—	2	4	no	—
772	C₂²×C₃	—	2	4	no	—
773	C₂²×C₃	—	4	2	no	—
774	C₂²×C₃	—	4	2	no	—
775	C₂²×C₃	—	4	2	no	—
776	C₂²×C₃	—	4	2	no	—
777	C₂²×C₃	—	4	2	no	—
778	C₂²×C₃	—	4	2	no	—
779	C₂²×C₃	—	4	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	C₂²×#41	1	1	yes	characteristic
785	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
786	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
787	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
788	C₂²×C₃	#585	1	1	yes	characteristic
789	C₂²×C₃	#585	1	1	yes	characteristic
790	C₂²×C₃	#585	1	1	yes	characteristic
791	C₃×C₄	—	2	2	no	—
792	C₃×C₄	—	2	2	no	—
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	4	no	—
795	C₃×C₄	—	4	2	no	—
796	C₃×C₄	—	4	2	no	—
797	C₃×C₄	—	4	2	no	—
798	C₃×C₄	—	4	2	no	—
799	C₃×C₄	—	4	1	no	—
800	C₃×C₄	—	4	2	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	1	no	—
803	C₃×C₄	—	4	1	no	—
804	C₃×C₄	—	4	1	no	—
805	C₃×C₄	—	4	1	no	—
806	C₃×C₄	—	4	1	no	—
807	C₃×C₄	—	4	1	no	—
808	C₃×C₄	—	4	1	no	—
809	C₃×C₄	—	4	1	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	#529	1	4	yes	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	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	C₂×C₃×#41	1	4	yes	—
826	C₂³	C₂⁵×C₃	1	1	yes	characteristic
827	Q₈	—	4	8	no	—
828	Q₈	—	4	4	no	—
829	D₄	—	2	8	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	4	no	—
832	D₄	—	8	4	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	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	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	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	2	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	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	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	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	—	8	4	no	—
891	C₂×C₄	—	8	4	no	—
892	C₂×C₄	—	8	4	no	—
893	C₂×C₄	C₂×C₃×#41	1	4	yes	—
894	C₂×C₄	C₂×C₃×#41	1	2	yes	—
895	C₂×C₄	C₂×C₃×#41	1	2	yes	—
896	C₂×C₄	C₂×C₃×#41	1	2	yes	—
897	C₂×C₄	C₂×C₃×#41	1	2	yes	—
898	C₂×C₄	C₂×C₃×#41	1	2	yes	—
899	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
900	C₂×C₃	—	4	4	no	—
901	C₂×C₃	—	8	2	no	—
902	C₂×C₃	C₂×#529	1	1	yes	characteristic
903	C₂×C₃	#3506	1	1	yes	characteristic
904	C₂×C₃	#3510	1	1	yes	characteristic
905	C₂×C₃	#3513	1	1	yes	characteristic
906	C₂×C₃	#3514	1	1	yes	characteristic
907	C₂×C₃	#3521	1	1	yes	characteristic
908	C₂×C₃	#3524	1	1	yes	characteristic
909	C₂²	—	2	4	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
924	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
925	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
926	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
927	C₂²	C₃×#585	1	1	yes	characteristic
928	C₂²	C₃×#585	1	1	yes	characteristic
929	C₂²	C₃×#585	1	1	yes	characteristic
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	4	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	C₃×#529	1	4	yes	—
951	C₃	#35970	1	1	yes	characteristic, direct product factor, Sylow
952	C₂	—	4	4	no	—
953	C₂	—	8	2	no	—
954	C₂	C₂×C₃×#529	1	1	yes	characteristic
955	C₂	C₃×#3506	1	1	yes	characteristic
956	C₂	C₃×#3510	1	1	yes	characteristic
957	C₂	C₃×#3513	1	1	yes	characteristic
958	C₂	C₃×#3514	1	1	yes	characteristic
959	C₂	C₃×#3521	1	1	yes	characteristic
960	C₂	C₃×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#127	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×#2653	C₂	semidirect
2. C₃×#2640	C₂	semidirect
3. C₃×#2578	C₂	semidirect
4. C₃×#2572	C₂	semidirect
5. C₃×#2563	C₂	semidirect
7. C₃×#2531	C₂	semidirect
8. C₃×#2514	C₂	semidirect
9. C₃×#2513	C₂	semidirect
10. C₃×#2510	C₂	semidirect
11. C₃×#2458	C₂	semidirect
12. C₃×#2447	C₂	semidirect
14. C₃×#2419	C₂	semidirect
15. C₃×#2402	C₂	semidirect
16. C₃×#2398	C₂	semidirect
17. C₃×#2367	C₂	semidirect
18. C₃×#2367	C₂	semidirect
20. C₃×#2365	C₂	semidirect
21. C₃×#2357	C₂	semidirect
22. C₃×#2356	C₂	semidirect
23. C₃×#2275	C₂	semidirect
24. #35970	C₃	direct (N × H)
124. #2653	C₂×C₃	semidirect
125. #2640	C₂×C₃	semidirect
126. #2578	C₂×C₃	semidirect
127. #2572	C₂×C₃	semidirect
128. #2563	C₂×C₃	semidirect
130. #2531	C₂×C₃	semidirect
131. #2514	C₂×C₃	semidirect
132. #2513	C₂×C₃	semidirect
133. #2510	C₂×C₃	semidirect
134. #2458	C₂×C₃	semidirect
135. #2447	C₂×C₃	semidirect
137. #2419	C₂×C₃	semidirect
138. #2402	C₂×C₃	semidirect
139. #2398	C₂×C₃	semidirect
140. #2367	C₂×C₃	semidirect
141. #2367	C₂×C₃	semidirect
143. #2365	C₂×C₃	semidirect
144. #2357	C₂×C₃	semidirect
145. #2356	C₂×C₃	semidirect
146. #2275	C₂×C₃	semidirect
951. C₃	#35970	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×#2653	2
C₃×#2640	2
C₃×#2578	2
C₃×#2572	2
C₃×#2563	2
C₃×#2544	2
C₃×#2531	2
C₃×#2514	2
C₃×#2513	2
C₃×#2510	2
C₃×#2458	2
C₃×#2447	2
C₃×#2445	2
C₃×#2419	2
C₃×#2402	2
C₃×#2398	2
C₃×#2367	2
C₃×#2366	2
C₃×#2365	2
C₃×#2357	2
C₃×#2356	2
C₃×#2275	2
#35970	3

Subgroups — C3×#35970 #10654577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35970 #10654577