Subgroups — C₃×#37132 #10655739

Order 768.

2456 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#538	C₂	1	2	yes	maximal, complemented
2	C₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2727	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2705	C₂	1	2	yes	maximal, complemented
6	C₃×#2682	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2678	C₂	1	2	yes	maximal, complemented
10	C₃×#2674	C₂	1	2	yes	maximal, complemented
11	C₃×#2672	C₂	1	2	yes	maximal, complemented
12	C₃×#2670	C₂	1	2	yes	maximal, complemented
13	C₃×#2669	C₂	1	2	yes	maximal, complemented
14	C₃×#2662	C₂	1	2	yes	maximal, complemented
15	C₃×#2602	C₂	1	2	yes	maximal, complemented
16	C₃×#2539	C₂	1	2	yes	maximal, complemented
17	C₃×#2414	C₂	1	2	yes	maximal, complemented
18	C₃×#2411	C₂	1	2	yes	maximal, complemented
19	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	#37132	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#538	—	2	16	no	—
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₃×#126	C₂²	1	2	yes	complemented
25	C₂×C₃×#126	C₂²	1	2	yes	complemented
26	C₂×C₃×#124	C₂²	1	2	yes	—
27	C₂×C₃×#124	C₂²	1	2	yes	complemented
28	C₂×C₃×#124	C₂²	1	2	yes	complemented
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×#123	C₂²	1	2	yes	—
31	C₂×C₃×#123	C₂²	1	2	yes	complemented
32	C₂×C₃×#123	C₂²	1	2	yes	complemented
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₃×#121	C₂²	1	2	yes	—
35	C₂×C₃×#121	C₂²	1	2	yes	—
36	C₂×C₃×#121	C₂²	1	2	yes	—
37	C₂×C₃×#121	C₂²	1	2	yes	complemented
38	C₂×C₃×#120	C₂²	1	2	yes	—
39	C₂×C₃×#120	C₂²	1	2	yes	—
40	C₂×C₃×#120	C₂²	1	2	yes	—
41	C₂×C₃×#120	C₂²	1	2	yes	complemented
42	C₂×C₃×#120	C₂²	1	2	yes	complemented
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
45	C₂×C₃×#117	C₂²	1	2	yes	complemented
46	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₃×#399	C₂²	1	2	yes	complemented
48	C₃×#399	C₂²	1	2	yes	complemented
49	C₃×#397	C₂²	1	2	yes	complemented
50	C₃×#396	C₂²	1	2	yes	complemented
51	C₃×#396	C₂²	1	2	yes	complemented
52	C₃×#396	C₂²	1	2	yes	complemented
53	C₃×#396	C₂²	1	2	yes	complemented
54	C₃×#395	C₂²	1	2	yes	complemented
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#394	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	2	yes	—
58	C₃×#394	C₂²	1	2	yes	—
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#394	C₂²	1	2	yes	complemented
61	C₃×#394	C₂²	1	2	yes	complemented
62	C₃×#394	C₂²	1	2	yes	complemented
63	C₃×#394	C₂²	1	2	yes	complemented
64	C₃×#393	C₂²	1	2	yes	complemented
65	C₃×#392	C₂²	1	2	yes	—
66	C₃×#392	C₂²	1	2	yes	—
67	C₃×#392	C₂²	1	2	yes	—
68	C₃×#392	C₂²	1	2	yes	—
69	C₃×#392	C₂²	1	2	yes	—
70	C₃×#392	C₂²	1	2	yes	complemented
71	C₃×#390	C₂²	1	2	yes	—
72	C₃×#390	C₂²	1	1	yes	characteristic
73	C₃×#390	C₂²	1	1	yes	characteristic
74	C₃×#390	C₂²	1	1	yes	characteristic
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	1	yes	characteristic
78	C₃×#390	C₂²	1	1	yes	characteristic
79	C₃×#390	C₂²	1	2	yes	complemented
80	C₃×#390	C₂²	1	1	yes	characteristic, complemented
81	C₃×#390	C₂²	1	2	yes	complemented
82	C₃×#390	C₂²	1	2	yes	complemented
83	C₃×#390	C₂²	1	1	yes	characteristic, complemented
84	C₃×#390	C₂²	1	2	yes	complemented
85	C₃×#389	C₂²	1	2	yes	complemented
86	C₃×#389	C₂²	1	1	yes	characteristic, complemented
87	C₃×#389	C₂²	1	1	yes	characteristic, complemented
88	C₃×#389	C₂²	1	1	yes	characteristic, complemented
89	C₃×#389	C₂²	1	1	yes	characteristic, complemented
90	C₃×#389	C₂²	1	1	yes	characteristic, complemented
91	C₃×#388	C₂²	1	2	yes	complemented
92	C₃×#388	C₂²	1	2	yes	complemented
93	C₃×#388	C₂²	1	2	yes	complemented
94	C₃×#388	C₂²	1	2	yes	complemented
95	C₃×#388	C₂²	1	2	yes	complemented
96	C₃×#388	C₂²	1	2	yes	complemented
97	C₃×#388	C₂²	1	2	yes	complemented
98	C₃×#388	C₂²	1	2	yes	complemented
99	C₃×#387	C₂²	1	2	yes	complemented
100	C₃×#386	C₂²	1	2	yes	—
101	C₃×#386	C₂²	1	2	yes	complemented
102	C₃×#385	C₂²	1	2	yes	complemented
103	C₃×#385	C₂²	1	2	yes	complemented
104	C₃×#380	C₂²	1	2	yes	complemented
105	C₃×#379	C₂²	1	2	yes	complemented
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
109	C₂×#538	C₂×C₃	1	2	yes	complemented
110	#2860	C₂×C₃	1	1	yes	characteristic, complemented
111	#2858	C₂×C₃	1	1	yes	characteristic, complemented
112	#2727	C₂×C₃	1	1	yes	characteristic, complemented
113	#2705	C₂×C₃	1	2	yes	complemented
114	#2682	C₂×C₃	1	1	yes	characteristic, complemented
115	#2682	C₂×C₃	1	1	yes	characteristic, complemented
116	#2679	C₂×C₃	1	1	yes	characteristic, complemented
117	#2678	C₂×C₃	1	2	yes	complemented
118	#2674	C₂×C₃	1	2	yes	complemented
119	#2672	C₂×C₃	1	2	yes	complemented
120	#2670	C₂×C₃	1	2	yes	complemented
121	#2669	C₂×C₃	1	2	yes	complemented
122	#2662	C₂×C₃	1	2	yes	complemented
123	#2602	C₂×C₃	1	2	yes	complemented
124	#2539	C₂×C₃	1	2	yes	complemented
125	#2414	C₂×C₃	1	2	yes	complemented
126	#2411	C₂×C₃	1	2	yes	complemented
127	#2293	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁵×C₃	C₂³	1	2	yes	—
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×D₄	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₃×D₄	C₂³	1	2	yes	—
136	C₂²×C₃×D₄	C₂³	1	2	yes	—
137	C₂²×C₃×D₄	C₂³	1	2	yes	—
138	C₂²×C₃×D₄	C₂³	1	2	yes	—
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	2	yes	—
141	C₂²×C₃×D₄	C₂³	1	2	yes	—
142	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
143	C₂³×C₃×C₄	C₂³	1	2	yes	—
144	C₂³×C₃×C₄	C₂³	1	2	yes	—
145	C₂³×C₃×C₄	C₂³	1	2	yes	—
146	C₃×C₄⋊Q₈	—	4	2	no	—
147	C₃×#127	—	4	2	no	—
148	C₃×#126	—	2	8	no	—
149	C₃×#126	—	2	8	no	—
150	C₃×#124	—	2	8	no	—
151	C₃×#124	—	2	8	no	—
152	C₃×#124	—	4	4	no	—
153	C₃×#123	—	2	8	no	—
154	C₃×#123	—	2	8	no	—
155	C₃×#123	—	4	4	no	—
156	C₃×#123	—	4	4	no	—
157	C₃×C₂²⋊Q₈	—	2	8	no	—
158	C₃×#121	—	2	8	no	—
159	C₃×#121	—	2	8	no	—
160	C₃×#121	—	2	8	no	—
161	C₃×#121	—	4	4	no	—
162	C₃×#120	—	2	8	no	—
163	C₃×#120	—	2	8	no	—
164	C₃×#120	—	4	4	no	—
165	C₃×#120	—	4	4	no	—
166	C₃×#120	—	4	4	no	—
167	C₃×C₄×D₄	—	2	8	no	—
168	C₃×C₄×D₄	D₄	1	8	yes	complemented
169	C₃×#117	—	4	4	no	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
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×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×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	#538	—	2	16	no	—
241	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₂×#127	C₂²×C₃	1	1	yes	characteristic
243	C₂×#126	C₂²×C₃	1	2	yes	complemented
244	C₂×#126	C₂²×C₃	1	2	yes	complemented
245	C₂×#124	C₂²×C₃	1	2	yes	—
246	C₂×#124	C₂²×C₃	1	2	yes	complemented
247	C₂×#124	C₂²×C₃	1	2	yes	complemented
248	C₂×#123	C₂²×C₃	1	2	yes	—
249	C₂×#123	C₂²×C₃	1	2	yes	—
250	C₂×#123	C₂²×C₃	1	2	yes	complemented
251	C₂×#123	C₂²×C₃	1	2	yes	complemented
252	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
253	C₂×#121	C₂²×C₃	1	2	yes	—
254	C₂×#121	C₂²×C₃	1	2	yes	—
255	C₂×#121	C₂²×C₃	1	2	yes	—
256	C₂×#121	C₂²×C₃	1	2	yes	complemented
257	C₂×#120	C₂²×C₃	1	2	yes	—
258	C₂×#120	C₂²×C₃	1	2	yes	—
259	C₂×#120	C₂²×C₃	1	2	yes	—
260	C₂×#120	C₂²×C₃	1	2	yes	complemented
261	C₂×#120	C₂²×C₃	1	2	yes	complemented
262	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
264	C₂×#117	C₂²×C₃	1	2	yes	complemented
265	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
266	#399	C₂²×C₃	1	2	yes	complemented
267	#399	C₂²×C₃	1	2	yes	complemented
268	#397	C₂²×C₃	1	2	yes	complemented
269	#396	C₂²×C₃	1	2	yes	complemented
270	#396	C₂²×C₃	1	2	yes	complemented
271	#396	C₂²×C₃	1	2	yes	complemented
272	#396	C₂²×C₃	1	2	yes	complemented
273	#395	C₂²×C₃	1	2	yes	complemented
274	#394	C₂²×C₃	1	2	yes	—
275	#394	C₂²×C₃	1	2	yes	—
276	#394	C₂²×C₃	1	2	yes	—
277	#394	C₂²×C₃	1	2	yes	—
278	#394	C₂²×C₃	1	2	yes	—
279	#394	C₂²×C₃	1	2	yes	complemented
280	#394	C₂²×C₃	1	2	yes	complemented
281	#394	C₂²×C₃	1	2	yes	complemented
282	#394	C₂²×C₃	1	2	yes	complemented
283	#393	C₂²×C₃	1	2	yes	complemented
284	#392	C₂²×C₃	1	2	yes	—
285	#392	C₂²×C₃	1	2	yes	—
286	#392	C₂²×C₃	1	2	yes	—
287	#392	C₂²×C₃	1	2	yes	—
288	#392	C₂²×C₃	1	2	yes	—
289	#392	C₂²×C₃	1	2	yes	complemented
290	#390	C₂²×C₃	1	1	yes	characteristic
291	#390	C₂²×C₃	1	1	yes	characteristic
292	#390	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	2	yes	—
296	#390	C₂²×C₃	1	1	yes	characteristic
297	#390	C₂²×C₃	1	1	yes	characteristic
298	#390	C₂²×C₃	1	2	yes	complemented
299	#390	C₂²×C₃	1	1	yes	characteristic, complemented
300	#390	C₂²×C₃	1	2	yes	complemented
301	#390	C₂²×C₃	1	1	yes	characteristic, complemented
302	#390	C₂²×C₃	1	2	yes	complemented
303	#390	C₂²×C₃	1	2	yes	complemented
304	#389	C₂²×C₃	1	1	yes	characteristic, complemented
305	#389	C₂²×C₃	1	1	yes	characteristic, complemented
306	#389	C₂²×C₃	1	1	yes	characteristic, complemented
307	#389	C₂²×C₃	1	2	yes	complemented
308	#389	C₂²×C₃	1	1	yes	characteristic, complemented
309	#389	C₂²×C₃	1	1	yes	characteristic, complemented
310	#388	C₂²×C₃	1	2	yes	complemented
311	#388	C₂²×C₃	1	2	yes	complemented
312	#388	C₂²×C₃	1	2	yes	complemented
313	#388	C₂²×C₃	1	2	yes	complemented
314	#388	C₂²×C₃	1	2	yes	complemented
315	#388	C₂²×C₃	1	2	yes	complemented
316	#388	C₂²×C₃	1	2	yes	complemented
317	#388	C₂²×C₃	1	2	yes	complemented
318	#387	C₂²×C₃	1	2	yes	complemented
319	#386	C₂²×C₃	1	2	yes	—
320	#386	C₂²×C₃	1	2	yes	complemented
321	#385	C₂²×C₃	1	2	yes	complemented
322	#385	C₂²×C₃	1	2	yes	complemented
323	#380	C₂²×C₃	1	2	yes	complemented
324	#379	C₂²×C₃	1	2	yes	complemented
325	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
327	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₂⁴×C₃	—	2	4	no	—
329	C₂⁴×C₃	—	4	2	no	—
330	C₂⁴×C₃	—	4	2	no	—
331	C₂⁴×C₃	—	4	2	no	—
332	C₂⁴×C₃	—	4	2	no	—
333	C₂⁴×C₃	—	4	2	no	—
334	C₂⁴×C₃	—	4	2	no	—
335	C₂⁴×C₃	C₂⁴	1	2	yes	—
336	C₂⁴×C₃	C₂⁴	1	2	yes	—
337	C₂⁴×C₃	C₂⁴	1	2	yes	—
338	C₂⁴×C₃	C₂⁴	1	2	yes	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	—	4	2	no	—
341	C₂×C₃×Q₈	—	4	2	no	—
342	C₂×C₃×D₄	—	2	4	no	—
343	C₂×C₃×D₄	—	2	4	no	—
344	C₂×C₃×D₄	—	2	4	no	—
345	C₂×C₃×D₄	—	2	4	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	4	no	—
348	C₂×C₃×D₄	—	2	2	no	—
349	C₂×C₃×D₄	—	2	2	no	—
350	C₂×C₃×D₄	—	2	4	no	—
351	C₂×C₃×D₄	—	2	2	no	—
352	C₂×C₃×D₄	—	4	1	no	—
353	C₂×C₃×D₄	—	4	1	no	—
354	C₂×C₃×D₄	—	4	2	no	—
355	C₂×C₃×D₄	—	4	2	no	—
356	C₂×C₃×D₄	—	4	2	no	—
357	C₂×C₃×D₄	—	4	2	no	—
358	C₂×C₃×D₄	—	4	2	no	—
359	C₂×C₃×D₄	—	4	2	no	—
360	C₂×C₃×D₄	—	4	2	no	—
361	C₂×C₃×D₄	—	4	2	no	—
362	C₂×C₃×D₄	—	4	2	no	—
363	C₂×C₃×D₄	—	4	2	no	—
364	C₂×C₃×D₄	—	4	2	no	—
365	C₂×C₃×D₄	—	4	2	no	—
366	C₂×C₃×D₄	—	4	2	no	—
367	C₂×C₃×D₄	—	4	1	no	—
368	C₂×C₃×D₄	—	4	1	no	—
369	C₂×C₃×D₄	—	4	2	no	—
370	C₂×C₃×D₄	—	4	1	no	—
371	C₂×C₃×D₄	—	4	1	no	—
372	C₂×C₃×D₄	—	4	2	no	—
373	C₂×C₃×D₄	—	4	1	no	—
374	C₂×C₃×D₄	—	4	2	no	—
375	C₂×C₃×D₄	—	4	1	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	C₂×D₄	1	4	yes	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	4	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	—	4	2	no	—
386	C₂²×C₃×C₄	—	4	2	no	—
387	C₂²×C₃×C₄	—	4	2	no	—
388	C₂²×C₃×C₄	—	4	2	no	—
389	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
392	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	C₃×C₄⋊C₄	—	2	4	no	—
406	C₃×C₄⋊C₄	—	2	4	no	—
407	C₃×C₄⋊C₄	—	2	4	no	—
408	C₃×C₄⋊C₄	—	2	4	no	—
409	C₃×C₄⋊C₄	—	2	4	no	—
410	C₃×C₄⋊C₄	—	2	4	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	4	no	—
413	C₃×C₄⋊C₄	—	4	1	no	—
414	C₃×C₄⋊C₄	—	4	1	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	1	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₄⋊C₄	—	4	2	no	—
420	C₃×C₄⋊C₄	—	4	1	no	—
421	C₃×C₄⋊C₄	—	4	1	no	—
422	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
423	C₃×C₂²⋊C₄	—	2	4	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	—	2	4	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
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	—	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×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	C₂×D₄	1	8	yes	—
455	C₃×C₄²	—	2	4	no	—
456	C₃×C₄²	—	2	2	no	—
457	C₃×C₄²	—	2	2	no	—
458	C₃×C₄²	—	2	2	no	—
459	C₃×C₄²	—	4	1	no	—
460	C₃×C₄²	—	4	1	no	—
461	C₃×C₄²	—	4	1	no	—
462	C₃×C₄²	—	4	2	no	—
463	C₃×C₄²	C₂×D₄	1	4	yes	—
464	C₂⁵	C₂³×C₃	1	2	yes	—
465	C₂²×Q₈	C₂³×C₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₃	1	2	yes	—
469	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₃	1	2	yes	—
472	C₂²×D₄	C₂³×C₃	1	2	yes	—
473	C₂²×D₄	C₂³×C₃	1	2	yes	—
474	C₂²×D₄	C₂³×C₃	1	2	yes	—
475	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₃	1	2	yes	—
477	C₂²×D₄	C₂³×C₃	1	2	yes	—
478	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₃	1	2	yes	—
481	C₂³×C₄	C₂³×C₃	1	2	yes	—
482	C₄⋊Q₈	—	4	2	no	—
483	#127	—	4	2	no	—
484	#126	—	2	8	no	—
485	#126	—	2	8	no	—
486	#124	—	2	8	no	—
487	#124	—	2	8	no	—
488	#124	—	4	4	no	—
489	#123	—	2	8	no	—
490	#123	—	2	8	no	—
491	#123	—	4	4	no	—
492	#123	—	4	4	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	#121	—	2	8	no	—
495	#121	—	2	8	no	—
496	#121	—	2	8	no	—
497	#121	—	4	4	no	—
498	#120	—	2	8	no	—
499	#120	—	2	8	no	—
500	#120	—	4	4	no	—
501	#120	—	4	4	no	—
502	#120	—	4	4	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	C₃×D₄	1	8	yes	complemented
505	#117	—	4	4	no	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	—	2	8	no	—
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	2	yes	—
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	2	yes	—
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	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	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	—	2	2	no	—
589	C₂³×C₃	—	2	2	no	—
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	2	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	—	2	2	no	—
601	C₂³×C₃	—	2	2	no	—
602	C₂³×C₃	—	2	2	no	—
603	C₂³×C₃	—	4	8	no	—
604	C₂³×C₃	—	8	4	no	—
605	C₂³×C₃	—	8	4	no	—
606	C₂³×C₃	—	8	4	no	—
607	C₂³×C₃	—	8	4	no	—
608	C₂³×C₃	—	8	4	no	—
609	C₂³×C₃	—	8	4	no	—
610	C₂³×C₃	C₂²×D₄	1	4	yes	—
611	C₂³×C₃	C₂⁵	1	1	yes	characteristic
612	C₃×Q₈	—	8	4	no	—
613	C₃×D₄	—	4	4	no	—
614	C₃×D₄	—	4	8	no	—
615	C₃×D₄	—	8	4	no	—
616	C₃×D₄	—	8	4	no	—
617	C₃×D₄	—	8	4	no	—
618	C₃×D₄	—	8	2	no	—
619	C₃×D₄	—	8	2	no	—
620	C₃×D₄	—	8	2	no	—
621	C₃×D₄	—	8	4	no	—
622	C₃×D₄	—	8	4	no	—
623	C₃×D₄	—	8	4	no	—
624	C₃×D₄	—	8	4	no	—
625	C₃×D₄	—	8	4	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	2	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	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	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	2	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	2	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	2	no	—
664	C₂×C₃×C₄	—	4	8	no	—
665	C₂×C₃×C₄	—	8	4	no	—
666	C₂×C₃×C₄	—	8	4	no	—
667	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
668	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
669	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
670	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
671	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
672	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
673	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
674	C₂⁴	—	2	4	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	—	4	2	no	—
677	C₂⁴	—	4	2	no	—
678	C₂⁴	—	4	2	no	—
679	C₂⁴	—	4	2	no	—
680	C₂⁴	—	4	2	no	—
681	C₂⁴	C₂⁴×C₃	1	2	yes	—
682	C₂⁴	C₂⁴×C₃	1	2	yes	—
683	C₂⁴	C₂⁴×C₃	1	2	yes	—
684	C₂⁴	C₂⁴×C₃	1	2	yes	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	4	1	no	—
699	C₂×D₄	—	4	1	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	2	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
801	C₄²	—	2	4	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	1	no	—
807	C₄²	—	4	1	no	—
808	C₄²	—	4	1	no	—
809	C₄²	C₂×C₃×D₄	1	4	yes	—
810	C₂²×C₃	—	2	4	no	—
811	C₂²×C₃	—	2	4	no	—
812	C₂²×C₃	—	2	4	no	—
813	C₂²×C₃	—	4	2	no	—
814	C₂²×C₃	—	4	2	no	—
815	C₂²×C₃	—	4	2	no	—
816	C₂²×C₃	—	4	2	no	—
817	C₂²×C₃	—	4	2	no	—
818	C₂²×C₃	—	4	2	no	—
819	C₂²×C₃	—	4	2	no	—
820	C₂²×C₃	—	4	2	no	—
821	C₂²×C₃	—	4	2	no	—
822	C₂²×C₃	—	4	2	no	—
823	C₂²×C₃	—	4	2	no	—
824	C₂²×C₃	—	4	2	no	—
825	C₂²×C₃	—	4	2	no	—
826	C₂²×C₃	—	4	2	no	—
827	C₂²×C₃	—	4	2	no	—
828	C₂²×C₃	—	4	2	no	—
829	C₂²×C₃	—	4	2	no	—
830	C₂²×C₃	—	4	2	no	—
831	C₂²×C₃	—	4	2	no	—
832	C₂²×C₃	—	4	2	no	—
833	C₂²×C₃	—	4	2	no	—
834	C₂²×C₃	—	4	2	no	—
835	C₂²×C₃	—	4	2	no	—
836	C₂²×C₃	—	4	2	no	—
837	C₂²×C₃	—	4	2	no	—
838	C₂²×C₃	—	8	16	no	—
839	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
840	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
841	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
843	C₂²×C₃	#585	1	1	yes	characteristic
844	C₂²×C₃	#585	1	1	yes	characteristic
845	C₂²×C₃	#585	1	1	yes	characteristic
846	C₃×C₄	—	2	2	no	—
847	C₃×C₄	—	2	2	no	—
848	C₃×C₄	—	2	4	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	2	2	no	—
852	C₃×C₄	—	2	2	no	—
853	C₃×C₄	—	4	2	no	—
854	C₃×C₄	—	4	2	no	—
855	C₃×C₄	—	4	2	no	—
856	C₃×C₄	—	4	2	no	—
857	C₃×C₄	—	4	2	no	—
858	C₃×C₄	—	4	1	no	—
859	C₃×C₄	—	4	2	no	—
860	C₃×C₄	—	4	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	2	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	4	8	no	—
889	C₂³	—	8	4	no	—
890	C₂³	—	8	4	no	—
891	C₂³	—	8	4	no	—
892	C₂³	—	8	4	no	—
893	C₂³	—	8	4	no	—
894	C₂³	—	8	4	no	—
895	C₂³	C₂²×C₃×D₄	1	4	yes	—
896	C₂³	C₂⁵×C₃	1	1	yes	characteristic
897	Q₈	—	8	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	8	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	4	no	—
902	D₄	—	8	4	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	D₄	—	8	4	no	—
907	D₄	—	8	4	no	—
908	D₄	—	8	4	no	—
909	D₄	—	8	4	no	—
910	D₄	—	8	4	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	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	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	4	8	no	—
950	C₂×C₄	—	8	4	no	—
951	C₂×C₄	—	8	4	no	—
952	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
953	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
954	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
955	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
956	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
957	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
958	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
959	C₂×C₃	—	4	4	no	—
960	C₂×C₃	—	8	2	no	—
961	C₂×C₃	—	8	2	no	—
962	C₂×C₃	—	8	2	no	—
963	C₂×C₃	#3449	1	1	yes	characteristic
964	C₂×C₃	#3496	1	1	yes	characteristic
965	C₂×C₃	#3498	1	1	yes	characteristic
966	C₂×C₃	#3545	1	1	yes	characteristic
967	C₂×C₃	#3546	1	1	yes	characteristic
968	C₂×C₃	#3558	1	1	yes	characteristic
969	C₂×C₃	#3560	1	1	yes	characteristic
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	4	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	8	16	no	—
999	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1000	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1001	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1002	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1003	C₂²	C₃×#585	1	1	yes	characteristic
1004	C₂²	C₃×#585	1	1	yes	characteristic
1005	C₂²	C₃×#585	1	1	yes	characteristic
1006	C₄	—	2	2	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₃	#37132	1	1	yes	characteristic, direct product factor, Sylow
1022	C₂	—	4	4	no	—
1023	C₂	—	8	2	no	—
1024	C₂	—	8	2	no	—
1025	C₂	—	8	2	no	—
1026	C₂	C₃×#3449	1	1	yes	characteristic
1027	C₂	C₃×#3496	1	1	yes	characteristic
1028	C₂	C₃×#3498	1	1	yes	characteristic
1029	C₂	C₃×#3545	1	1	yes	characteristic
1030	C₂	C₃×#3546	1	1	yes	characteristic
1031	C₂	C₃×#3558	1	1	yes	characteristic
1032	C₂	C₃×#3560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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. C₂×C₃×#538	C₂	semidirect
2. C₃×#2860	C₂	semidirect
3. C₃×#2858	C₂	semidirect
4. C₃×#2727	C₂	semidirect
5. C₃×#2705	C₂	semidirect
6. C₃×#2682	C₂	semidirect
7. C₃×#2682	C₂	semidirect
8. C₃×#2679	C₂	semidirect
9. C₃×#2678	C₂	semidirect
10. C₃×#2674	C₂	semidirect
11. C₃×#2672	C₂	semidirect
12. C₃×#2670	C₂	semidirect
13. C₃×#2669	C₂	semidirect
14. C₃×#2662	C₂	semidirect
15. C₃×#2602	C₂	semidirect
16. C₃×#2539	C₂	semidirect
17. C₃×#2414	C₂	semidirect
18. C₃×#2411	C₂	semidirect
19. C₃×#2293	C₂	semidirect
20. #37132	C₃	direct (N × H)
22. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃×#126	C₂²	semidirect
25. C₂×C₃×#126	C₂²	semidirect
27. C₂×C₃×#124	C₂²	semidirect
28. C₂×C₃×#124	C₂²	semidirect
31. C₂×C₃×#123	C₂²	semidirect
32. C₂×C₃×#123	C₂²	semidirect
33. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₃×#121	C₂²	semidirect
41. C₂×C₃×#120	C₂²	semidirect
42. C₂×C₃×#120	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
45. C₂×C₃×#117	C₂²	semidirect
46. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
47. C₃×#399	C₂²	semidirect
48. C₃×#399	C₂²	semidirect
49. C₃×#397	C₂²	semidirect
50. C₃×#396	C₂²	semidirect
51. C₃×#396	C₂²	semidirect
52. C₃×#396	C₂²	semidirect
53. C₃×#396	C₂²	semidirect
54. C₃×#395	C₂²	semidirect
60. C₃×#394	C₂²	semidirect
61. C₃×#394	C₂²	semidirect
62. C₃×#394	C₂²	semidirect
63. C₃×#394	C₂²	semidirect
64. C₃×#393	C₂²	semidirect
70. C₃×#392	C₂²	semidirect
79. C₃×#390	C₂²	semidirect
80. C₃×#390	C₂²	semidirect
81. C₃×#390	C₂²	semidirect
82. C₃×#390	C₂²	semidirect
83. C₃×#390	C₂²	semidirect
84. C₃×#390	C₂²	semidirect
85. C₃×#389	C₂²	semidirect
86. C₃×#389	C₂²	semidirect
87. C₃×#389	C₂²	semidirect
88. C₃×#389	C₂²	semidirect
89. C₃×#389	C₂²	semidirect
90. C₃×#389	C₂²	semidirect
91. C₃×#388	C₂²	semidirect
92. C₃×#388	C₂²	semidirect
93. C₃×#388	C₂²	semidirect
94. C₃×#388	C₂²	semidirect
95. C₃×#388	C₂²	semidirect
96. C₃×#388	C₂²	semidirect
97. C₃×#388	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#387	C₂²	semidirect
101. C₃×#386	C₂²	semidirect
102. C₃×#385	C₂²	semidirect
103. C₃×#385	C₂²	semidirect
104. C₃×#380	C₂²	semidirect
105. C₃×#379	C₂²	semidirect
106. C₃×C₄×C₄⋊C₄	C₂²	semidirect
107. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
108. C₃×C₄³	C₂²	semidirect
109. C₂×#538	C₂×C₃	semidirect
110. #2860	C₂×C₃	semidirect
111. #2858	C₂×C₃	semidirect
112. #2727	C₂×C₃	semidirect
113. #2705	C₂×C₃	semidirect
114. #2682	C₂×C₃	semidirect
115. #2682	C₂×C₃	semidirect
116. #2679	C₂×C₃	semidirect
117. #2678	C₂×C₃	semidirect
118. #2674	C₂×C₃	semidirect
119. #2672	C₂×C₃	semidirect
120. #2670	C₂×C₃	semidirect
121. #2669	C₂×C₃	semidirect
122. #2662	C₂×C₃	semidirect
123. #2602	C₂×C₃	semidirect
124. #2539	C₂×C₃	semidirect
125. #2414	C₂×C₃	semidirect
126. #2411	C₂×C₃	semidirect
127. #2293	C₂×C₃	semidirect
168. C₃×C₄×D₄	D₄	semidirect
241. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
243. C₂×#126	C₂²×C₃	semidirect
244. C₂×#126	C₂²×C₃	semidirect
246. C₂×#124	C₂²×C₃	semidirect
247. C₂×#124	C₂²×C₃	semidirect
250. C₂×#123	C₂²×C₃	semidirect
251. C₂×#123	C₂²×C₃	semidirect
252. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
256. C₂×#121	C₂²×C₃	semidirect
260. C₂×#120	C₂²×C₃	semidirect
261. C₂×#120	C₂²×C₃	semidirect
263. C₂×C₄×D₄	C₂²×C₃	semidirect
264. C₂×#117	C₂²×C₃	semidirect
265. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
266. #399	C₂²×C₃	semidirect
267. #399	C₂²×C₃	semidirect
268. #397	C₂²×C₃	semidirect
269. #396	C₂²×C₃	semidirect
270. #396	C₂²×C₃	semidirect
271. #396	C₂²×C₃	semidirect
272. #396	C₂²×C₃	semidirect
273. #395	C₂²×C₃	semidirect
279. #394	C₂²×C₃	semidirect
280. #394	C₂²×C₃	semidirect
281. #394	C₂²×C₃	semidirect
282. #394	C₂²×C₃	semidirect
283. #393	C₂²×C₃	semidirect
289. #392	C₂²×C₃	semidirect
298. #390	C₂²×C₃	semidirect
299. #390	C₂²×C₃	semidirect
300. #390	C₂²×C₃	semidirect
301. #390	C₂²×C₃	semidirect
302. #390	C₂²×C₃	semidirect
303. #390	C₂²×C₃	semidirect
304. #389	C₂²×C₃	semidirect
305. #389	C₂²×C₃	semidirect
306. #389	C₂²×C₃	semidirect
307. #389	C₂²×C₃	semidirect
308. #389	C₂²×C₃	semidirect
309. #389	C₂²×C₃	semidirect
310. #388	C₂²×C₃	semidirect
311. #388	C₂²×C₃	semidirect
312. #388	C₂²×C₃	semidirect
313. #388	C₂²×C₃	semidirect
314. #388	C₂²×C₃	semidirect
315. #388	C₂²×C₃	semidirect
316. #388	C₂²×C₃	semidirect
317. #388	C₂²×C₃	semidirect
318. #387	C₂²×C₃	semidirect
320. #386	C₂²×C₃	semidirect
321. #385	C₂²×C₃	semidirect
322. #385	C₂²×C₃	semidirect
323. #380	C₂²×C₃	semidirect
324. #379	C₂²×C₃	semidirect
325. C₄×C₄⋊C₄	C₂²×C₃	semidirect
326. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
327. C₄³	C₂²×C₃	semidirect
504. C₄×D₄	C₃×D₄	semidirect
1021. C₃	#37132	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#538	2
C₃×#2860	2
C₃×#2858	2
C₃×#2727	2
C₃×#2705	2
C₃×#2682	2
C₃×#2679	2
C₃×#2678	2
C₃×#2674	2
C₃×#2672	2
C₃×#2670	2
C₃×#2669	2
C₃×#2662	2
C₃×#2602	2
C₃×#2539	2
C₃×#2414	2
C₃×#2411	2
C₃×#2293	2
#37132	3

Subgroups — C3×#37132 #10655739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37132 #10655739