Subgroups — C₃×#35890 #10654497

Order 768.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2648	C₂	1	2	yes	maximal, complemented
2	C₃×#2644	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2578	C₂	1	2	yes	maximal, complemented
4	C₃×#2558	C₂	1	2	yes	maximal, complemented
5	C₃×#2510	C₂	1	2	yes	maximal, complemented
6	C₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2490	C₂	1	2	yes	maximal, complemented
9	C₃×#2471	C₂	1	2	yes	maximal, complemented
10	C₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2428	C₂	1	1	yes	maximal, characteristic
13	C₃×#2425	C₂	1	2	yes	maximal, complemented
14	C₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2401	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2395	C₂	1	2	yes	maximal, complemented
17	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	#35890	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×#125	C₂²	1	2	yes	—
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×#117	C₂²	1	2	yes	—
40	C₃×#401	C₂²	1	1	yes	characteristic
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	1	yes	characteristic
43	C₃×#400	C₂²	1	1	yes	characteristic
44	C₃×#400	C₂²	1	1	yes	characteristic
45	C₃×#399	C₂²	1	2	yes	—
46	C₃×#398	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×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#397	C₂²	1	1	yes	characteristic
54	C₃×#397	C₂²	1	1	yes	characteristic
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#394	C₂²	1	2	yes	—
61	C₃×#394	C₂²	1	2	yes	—
62	C₃×#394	C₂²	1	2	yes	—
63	C₃×#392	C₂²	1	2	yes	—
64	C₃×#390	C₂²	1	1	yes	characteristic
65	C₃×#390	C₂²	1	2	yes	—
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#390	C₂²	1	2	yes	—
68	C₃×#390	C₂²	1	1	yes	characteristic
69	C₃×#390	C₂²	1	1	yes	characteristic
70	C₃×#390	C₂²	1	2	yes	—
71	C₃×#390	C₂²	1	1	yes	characteristic
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#390	C₂²	1	2	yes	—
74	C₃×#389	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	1	yes	characteristic
76	C₃×#389	C₂²	1	1	yes	characteristic
77	C₃×#389	C₂²	1	2	yes	—
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	1	yes	characteristic
80	C₃×#389	C₂²	1	1	yes	characteristic
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#388	C₂²	1	2	yes	—
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	2	yes	—
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#386	C₂²	1	2	yes	—
93	C₃×#386	C₂²	1	2	yes	—
94	C₃×#386	C₂²	1	2	yes	—
95	C₃×#386	C₂²	1	2	yes	—
96	C₃×#386	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	—
98	C₃×#385	C₂²	1	2	yes	—
99	C₃×#384	C₂²	1	1	yes	characteristic
100	C₃×#383	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	1	yes	characteristic
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	2	yes	—
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
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×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×#376	C₂²	1	1	yes	characteristic
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	#2648	C₂×C₃	1	2	yes	complemented
125	#2644	C₂×C₃	1	1	yes	characteristic, complemented
126	#2578	C₂×C₃	1	2	yes	complemented
127	#2558	C₂×C₃	1	2	yes	complemented
128	#2510	C₂×C₃	1	2	yes	complemented
129	#2506	C₂×C₃	1	1	yes	characteristic, complemented
130	#2490	C₂×C₃	1	1	yes	characteristic, complemented
131	#2490	C₂×C₃	1	2	yes	complemented
132	#2471	C₂×C₃	1	2	yes	complemented
133	#2454	C₂×C₃	1	1	yes	characteristic, complemented
134	#2445	C₂×C₃	1	1	yes	characteristic, complemented
135	#2428	C₂×C₃	1	1	yes	characteristic
136	#2425	C₂×C₃	1	2	yes	complemented
137	#2422	C₂×C₃	1	1	yes	characteristic, complemented
138	#2401	C₂×C₃	1	1	yes	characteristic, complemented
139	#2395	C₂×C₃	1	2	yes	complemented
140	#2370	C₂×C₃	1	1	yes	characteristic, complemented
141	#2366	C₂×C₃	1	1	yes	characteristic, complemented
142	#2363	C₂×C₃	1	1	yes	characteristic, complemented
143	#2363	C₂×C₃	1	1	yes	characteristic, complemented
144	#2354	C₂×C₃	1	1	yes	characteristic, complemented
145	#2347	C₂×C₃	1	1	yes	characteristic, complemented
146	#2275	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
148	C₂²×C₃×D₄	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	2	yes	—
152	C₂²×C₃×D₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
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	C₂³×C₃×C₄	C₂³	1	2	yes	—
158	C₃×#127	—	2	4	no	—
159	C₃×#125	—	2	4	no	—
160	C₃×#125	—	4	4	no	—
161	C₃×#123	—	4	4	no	—
162	C₃×#123	—	4	4	no	—
163	C₃×#121	—	2	4	no	—
164	C₃×#121	—	2	4	no	—
165	C₃×#121	—	4	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	4	no	—
168	C₃×C₄×D₄	—	2	4	no	—
169	C₃×C₄×D₄	—	2	4	no	—
170	C₃×C₄×D₄	—	4	4	no	—
171	C₃×#117	—	2	4	no	—
172	C₃×#117	—	4	4	no	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₂×C₃×C₄²	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₂×C₃×C₄²	C₂³	1	2	yes	—
232	C₂×C₃×C₄²	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₂×#127	C₂²×C₃	1	1	yes	characteristic
262	C₂×#125	C₂²×C₃	1	1	yes	characteristic
263	C₂×#125	C₂²×C₃	1	2	yes	—
264	C₂×#123	C₂²×C₃	1	2	yes	—
265	C₂×#123	C₂²×C₃	1	2	yes	—
266	C₂×#121	C₂²×C₃	1	1	yes	characteristic
267	C₂×#121	C₂²×C₃	1	1	yes	characteristic
268	C₂×#121	C₂²×C₃	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
274	C₂×#117	C₂²×C₃	1	1	yes	characteristic
275	C₂×#117	C₂²×C₃	1	2	yes	—
276	#401	C₂²×C₃	1	1	yes	characteristic
277	#400	C₂²×C₃	1	1	yes	characteristic
278	#400	C₂²×C₃	1	2	yes	—
279	#400	C₂²×C₃	1	1	yes	characteristic
280	#400	C₂²×C₃	1	1	yes	characteristic
281	#399	C₂²×C₃	1	2	yes	—
282	#398	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	#397	C₂²×C₃	1	2	yes	—
287	#397	C₂²×C₃	1	1	yes	characteristic
288	#397	C₂²×C₃	1	2	yes	—
289	#397	C₂²×C₃	1	1	yes	characteristic
290	#397	C₂²×C₃	1	1	yes	characteristic
291	#396	C₂²×C₃	1	2	yes	—
292	#396	C₂²×C₃	1	2	yes	—
293	#396	C₂²×C₃	1	1	yes	characteristic
294	#394	C₂²×C₃	1	2	yes	—
295	#394	C₂²×C₃	1	2	yes	—
296	#394	C₂²×C₃	1	2	yes	—
297	#394	C₂²×C₃	1	2	yes	—
298	#394	C₂²×C₃	1	2	yes	—
299	#392	C₂²×C₃	1	2	yes	—
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	2	yes	—
304	#390	C₂²×C₃	1	1	yes	characteristic
305	#390	C₂²×C₃	1	2	yes	—
306	#390	C₂²×C₃	1	1	yes	characteristic
307	#390	C₂²×C₃	1	1	yes	characteristic
308	#390	C₂²×C₃	1	2	yes	—
309	#390	C₂²×C₃	1	2	yes	—
310	#389	C₂²×C₃	1	1	yes	characteristic
311	#389	C₂²×C₃	1	1	yes	characteristic
312	#389	C₂²×C₃	1	1	yes	characteristic
313	#389	C₂²×C₃	1	1	yes	characteristic
314	#389	C₂²×C₃	1	1	yes	characteristic
315	#389	C₂²×C₃	1	2	yes	—
316	#389	C₂²×C₃	1	1	yes	characteristic
317	#388	C₂²×C₃	1	2	yes	—
318	#388	C₂²×C₃	1	2	yes	—
319	#388	C₂²×C₃	1	2	yes	—
320	#388	C₂²×C₃	1	2	yes	—
321	#388	C₂²×C₃	1	2	yes	—
322	#388	C₂²×C₃	1	2	yes	—
323	#388	C₂²×C₃	1	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#386	C₂²×C₃	1	2	yes	—
328	#386	C₂²×C₃	1	2	yes	—
329	#386	C₂²×C₃	1	2	yes	—
330	#386	C₂²×C₃	1	2	yes	—
331	#386	C₂²×C₃	1	2	yes	—
332	#386	C₂²×C₃	1	2	yes	—
333	#385	C₂²×C₃	1	2	yes	—
334	#385	C₂²×C₃	1	2	yes	—
335	#384	C₂²×C₃	1	1	yes	characteristic
336	#383	C₂²×C₃	1	2	yes	—
337	#380	C₂²×C₃	1	2	yes	—
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×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	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	#376	C₂²×C₃	1	1	yes	characteristic
359	C₂×#95	C₂²×C₃	1	2	yes	—
360	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
361	C₂⁴×C₃	C₂⁴	1	2	yes	—
362	C₂⁴×C₃	C₂⁴	1	2	yes	—
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	—	2	2	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	4	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	—	4	2	no	—
377	C₂×C₃×D₄	—	4	2	no	—
378	C₂×C₃×D₄	—	4	2	no	—
379	C₂×C₃×D₄	—	4	2	no	—
380	C₂×C₃×D₄	#41	1	4	yes	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	2	no	—
383	C₂²×C₃×C₄	—	2	4	no	—
384	C₂²×C₃×C₄	—	2	2	no	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	4	no	—
387	C₂²×C₃×C₄	—	2	4	no	—
388	C₂²×C₃×C₄	—	2	4	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	—	4	2	no	—
394	C₂²×C₃×C₄	—	4	2	no	—
395	C₂²×C₃×C₄	—	4	2	no	—
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	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	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	2	no	—
419	C₃×C₄⋊C₄	—	2	4	no	—
420	C₃×C₄⋊C₄	—	2	4	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	4	no	—
426	C₃×C₄⋊C₄	—	2	2	no	—
427	C₃×C₄⋊C₄	—	2	4	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	4	1	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	2	no	—
435	C₃×C₄⋊C₄	—	4	2	no	—
436	C₃×C₄⋊C₄	#41	1	4	yes	—
437	C₃×C₄⋊C₄	#41	1	4	yes	—
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	4	no	—
443	C₃×C₂²⋊C₄	—	2	4	no	—
444	C₃×C₂²⋊C₄	—	2	4	no	—
445	C₃×C₂²⋊C₄	—	2	4	no	—
446	C₃×C₂²⋊C₄	—	2	2	no	—
447	C₃×C₂²⋊C₄	—	2	2	no	—
448	C₃×C₂²⋊C₄	—	4	1	no	—
449	C₃×C₂²⋊C₄	—	4	1	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	—	4	2	no	—
452	C₃×C₂²⋊C₄	—	4	2	no	—
453	C₃×C₂²⋊C₄	—	4	2	no	—
454	C₃×C₂²⋊C₄	—	4	1	no	—
455	C₃×C₂²⋊C₄	—	4	1	no	—
456	C₃×C₂²⋊C₄	—	4	2	no	—
457	C₃×C₂²⋊C₄	—	4	2	no	—
458	C₃×C₂²⋊C₄	—	4	2	no	—
459	C₃×C₂²⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	4	2	no	—
461	C₃×C₂²⋊C₄	—	4	2	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	—	4	2	no	—
464	C₃×C₄²	—	2	4	no	—
465	C₃×C₄²	—	2	2	no	—
466	C₃×C₄²	—	2	2	no	—
467	C₃×C₄²	—	2	2	no	—
468	C₃×C₄²	—	2	2	no	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	4	2	no	—
472	C₃×C₄²	—	4	2	no	—
473	C₃×C₄²	—	4	2	no	—
474	C₃×C₄²	—	4	2	no	—
475	C₃×C₄²	—	4	2	no	—
476	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₃	1	2	yes	—
478	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₃	1	2	yes	—
480	C₂²×D₄	C₂³×C₃	1	2	yes	—
481	C₂²×D₄	C₂³×C₃	1	2	yes	—
482	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₃	1	2	yes	—
484	C₂³×C₄	C₂³×C₃	1	2	yes	—
485	C₂³×C₄	C₂³×C₃	1	2	yes	—
486	C₂³×C₄	C₂³×C₃	1	2	yes	—
487	#127	—	2	4	no	—
488	#125	—	2	4	no	—
489	#125	—	4	4	no	—
490	#123	—	4	4	no	—
491	#123	—	4	4	no	—
492	#121	—	2	4	no	—
493	#121	—	2	4	no	—
494	#121	—	4	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	—	4	4	no	—
500	#117	—	2	4	no	—
501	#117	—	4	4	no	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
567	#95	C₂³×C₃	1	1	yes	characteristic
568	#95	C₂³×C₃	1	1	yes	characteristic
569	#95	C₂³×C₃	1	1	yes	characteristic
570	#95	C₂³×C₃	1	1	yes	characteristic
571	#95	C₂³×C₃	1	1	yes	characteristic
572	#95	C₂³×C₃	1	1	yes	characteristic
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	1	yes	characteristic
577	#95	C₂³×C₃	1	1	yes	characteristic
578	#95	C₂³×C₃	1	1	yes	characteristic
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	1	yes	characteristic
584	#95	C₂³×C₃	1	1	yes	characteristic
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	1	yes	characteristic
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	C₂³×C₃	—	2	2	no	—
591	C₂³×C₃	—	2	2	no	—
592	C₂³×C₃	—	2	2	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	2	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	2	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	2	no	—
605	C₂³×C₃	—	2	2	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	2	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	2	no	—
610	C₂³×C₃	C₂×#41	1	4	yes	—
611	C₂³×C₃	C₂⁵	1	1	yes	characteristic
612	C₃×D₄	—	2	8	no	—
613	C₃×D₄	—	4	8	no	—
614	C₃×D₄	—	4	4	no	—
615	C₃×D₄	—	8	4	no	—
616	C₃×D₄	—	8	4	no	—
617	C₃×D₄	—	8	4	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	1	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	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	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	2	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	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	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	4	8	no	—
672	C₂×C₃×C₄	—	4	4	no	—
673	C₂×C₃×C₄	—	8	4	no	—
674	C₂×C₃×C₄	—	8	4	no	—
675	C₂×C₃×C₄	—	8	4	no	—
676	C₂×C₃×C₄	C₂×#41	1	4	yes	—
677	C₂×C₃×C₄	C₂×#41	1	4	yes	—
678	C₂×C₃×C₄	C₂×#41	1	2	yes	—
679	C₂×C₃×C₄	C₂×#41	1	2	yes	—
680	C₂×C₃×C₄	C₂×#41	1	2	yes	—
681	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
682	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
683	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
684	C₂⁴	C₂⁴×C₃	1	2	yes	—
685	C₂⁴	C₂⁴×C₃	1	2	yes	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	C₃×#41	1	4	yes	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
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	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₃×#41	1	4	yes	—
760	C₄⋊C₄	C₃×#41	1	4	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₂²⋊C₄	—	4	1	no	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₂²×C₃	—	2	4	no	—
800	C₂²×C₃	—	2	4	no	—
801	C₂²×C₃	—	2	4	no	—
802	C₂²×C₃	—	4	2	no	—
803	C₂²×C₃	—	4	2	no	—
804	C₂²×C₃	—	4	2	no	—
805	C₂²×C₃	—	4	2	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	2	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	4	1	no	—
810	C₂²×C₃	—	4	1	no	—
811	C₂²×C₃	—	4	2	no	—
812	C₂²×C₃	—	4	1	no	—
813	C₂²×C₃	—	4	2	no	—
814	C₂²×C₃	—	4	2	no	—
815	C₂²×C₃	—	4	1	no	—
816	C₂²×C₃	—	4	2	no	—
817	C₂²×C₃	—	4	1	no	—
818	C₂²×C₃	—	4	2	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
821	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
822	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
823	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
825	C₂²×C₃	#585	1	1	yes	characteristic
826	C₂²×C₃	#585	1	1	yes	characteristic
827	C₃×C₄	—	2	2	no	—
828	C₃×C₄	—	2	4	no	—
829	C₃×C₄	—	2	4	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	4	1	no	—
832	C₃×C₄	—	4	1	no	—
833	C₃×C₄	—	4	1	no	—
834	C₃×C₄	—	4	1	no	—
835	C₃×C₄	—	4	1	no	—
836	C₃×C₄	—	4	1	no	—
837	C₃×C₄	—	4	1	no	—
838	C₃×C₄	—	4	2	no	—
839	C₃×C₄	—	4	1	no	—
840	C₃×C₄	—	4	2	no	—
841	C₃×C₄	—	4	2	no	—
842	C₃×C₄	—	4	1	no	—
843	C₃×C₄	—	4	2	no	—
844	C₃×C₄	—	4	1	no	—
845	C₃×C₄	—	4	1	no	—
846	C₃×C₄	#529	1	4	yes	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	C₂×C₃×#41	1	4	yes	—
868	C₂³	C₂⁵×C₃	1	1	yes	characteristic
869	D₄	—	2	8	no	—
870	D₄	—	4	8	no	—
871	D₄	—	4	4	no	—
872	D₄	—	8	4	no	—
873	D₄	—	8	4	no	—
874	D₄	—	8	4	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	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	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	—	8	4	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	C₂×C₃×#41	1	4	yes	—
934	C₂×C₄	C₂×C₃×#41	1	4	yes	—
935	C₂×C₄	C₂×C₃×#41	1	2	yes	—
936	C₂×C₄	C₂×C₃×#41	1	2	yes	—
937	C₂×C₄	C₂×C₃×#41	1	2	yes	—
938	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
939	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
940	C₂×C₃	—	4	4	no	—
941	C₂×C₃	—	8	1	no	—
942	C₂×C₃	—	8	2	no	—
943	C₂×C₃	C₂×#529	1	1	yes	characteristic
944	C₂×C₃	#3513	1	1	yes	characteristic
945	C₂×C₃	#3514	1	1	yes	characteristic
946	C₂×C₃	#3517	1	1	yes	characteristic
947	C₂×C₃	#3517	1	1	yes	characteristic
948	C₂×C₃	#3519	1	1	yes	characteristic
949	C₂×C₃	#3521	1	1	yes	characteristic
950	C₂²	—	2	4	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	4	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
972	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
973	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
974	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
975	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂²	C₃×#585	1	1	yes	characteristic
977	C₂²	C₃×#585	1	1	yes	characteristic
978	C₄	—	2	2	no	—
979	C₄	—	2	4	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	C₃×#529	1	4	yes	—
998	C₃	#35890	1	1	yes	characteristic, direct product factor, Sylow
999	C₂	—	4	4	no	—
1000	C₂	—	8	1	no	—
1001	C₂	—	8	2	no	—
1002	C₂	C₂×C₃×#529	1	1	yes	characteristic
1003	C₂	C₃×#3513	1	1	yes	characteristic
1004	C₂	C₃×#3514	1	1	yes	characteristic
1005	C₂	C₃×#3517	1	1	yes	characteristic
1006	C₂	C₃×#3517	1	1	yes	characteristic
1007	C₂	C₃×#3519	1	1	yes	characteristic
1008	C₂	C₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2428	C₂
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×#2648	C₂	semidirect
2. C₃×#2644	C₂	semidirect
3. C₃×#2578	C₂	semidirect
4. C₃×#2558	C₂	semidirect
5. C₃×#2510	C₂	semidirect
6. C₃×#2506	C₂	semidirect
7. C₃×#2490	C₂	semidirect
8. C₃×#2490	C₂	semidirect
9. C₃×#2471	C₂	semidirect
10. C₃×#2454	C₂	semidirect
11. C₃×#2445	C₂	semidirect
13. C₃×#2425	C₂	semidirect
14. C₃×#2422	C₂	semidirect
15. C₃×#2401	C₂	semidirect
16. C₃×#2395	C₂	semidirect
17. C₃×#2370	C₂	semidirect
18. C₃×#2366	C₂	semidirect
19. C₃×#2363	C₂	semidirect
20. C₃×#2363	C₂	semidirect
21. C₃×#2354	C₂	semidirect
22. C₃×#2347	C₂	semidirect
23. C₃×#2275	C₂	semidirect
24. #35890	C₃	direct (N × H)
124. #2648	C₂×C₃	semidirect
125. #2644	C₂×C₃	semidirect
126. #2578	C₂×C₃	semidirect
127. #2558	C₂×C₃	semidirect
128. #2510	C₂×C₃	semidirect
129. #2506	C₂×C₃	semidirect
130. #2490	C₂×C₃	semidirect
131. #2490	C₂×C₃	semidirect
132. #2471	C₂×C₃	semidirect
133. #2454	C₂×C₃	semidirect
134. #2445	C₂×C₃	semidirect
136. #2425	C₂×C₃	semidirect
137. #2422	C₂×C₃	semidirect
138. #2401	C₂×C₃	semidirect
139. #2395	C₂×C₃	semidirect
140. #2370	C₂×C₃	semidirect
141. #2366	C₂×C₃	semidirect
142. #2363	C₂×C₃	semidirect
143. #2363	C₂×C₃	semidirect
144. #2354	C₂×C₃	semidirect
145. #2347	C₂×C₃	semidirect
146. #2275	C₂×C₃	semidirect
998. C₃	#35890	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×#2648	2
C₃×#2644	2
C₃×#2578	2
C₃×#2558	2
C₃×#2510	2
C₃×#2506	2
C₃×#2490	2
C₃×#2471	2
C₃×#2454	2
C₃×#2445	2
C₃×#2428	2
C₃×#2425	2
C₃×#2422	2
C₃×#2401	2
C₃×#2395	2
C₃×#2370	2
C₃×#2366	2
C₃×#2363	2
C₃×#2354	2
C₃×#2347	2
C₃×#2275	2
#35890	3

Subgroups — C3×#35890 #10654497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35890 #10654497