Subgroups — C₃×#37154 #10655761

Order 768.

2034 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2808	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2757	C₂	1	2	yes	maximal, complemented
5	C₃×#2756	C₂	1	2	yes	maximal, complemented
6	C₃×#2732	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2727	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2685	C₂	1	2	yes	maximal, complemented
9	C₃×#2681	C₂	1	2	yes	maximal, complemented
10	C₃×#2679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2678	C₂	1	2	yes	maximal, complemented
12	C₃×#2668	C₂	1	2	yes	maximal, complemented
13	C₃×#2651	C₂	1	2	yes	maximal, complemented
14	C₃×#2518	C₂	1	2	yes	maximal, complemented
15	C₃×#2472	C₂	1	2	yes	maximal, complemented
16	C₃×#2467	C₂	1	2	yes	maximal, complemented
17	C₃×#2424	C₂	1	2	yes	maximal, complemented
18	C₃×#2321	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	#37154	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₃×#123	C₂²	1	2	yes	complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃×#121	C₂²	1	2	yes	—
28	C₂×C₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₃×#120	C₂²	1	2	yes	—
31	C₂×C₃×#120	C₂²	1	2	yes	—
32	C₂×C₃×#120	C₂²	1	2	yes	—
33	C₂×C₃×#120	C₂²	1	2	yes	complemented
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
36	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
38	C₃×#399	C₂²	1	2	yes	complemented
39	C₃×#399	C₂²	1	2	yes	complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#398	C₂²	1	2	yes	complemented
42	C₃×#397	C₂²	1	2	yes	complemented
43	C₃×#397	C₂²	1	2	yes	complemented
44	C₃×#397	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	2	yes	complemented
46	C₃×#396	C₂²	1	2	yes	complemented
47	C₃×#396	C₂²	1	2	yes	complemented
48	C₃×#396	C₂²	1	2	yes	complemented
49	C₃×#394	C₂²	1	2	yes	—
50	C₃×#394	C₂²	1	2	yes	—
51	C₃×#394	C₂²	1	2	yes	—
52	C₃×#394	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×#394	C₂²	1	2	yes	complemented
58	C₃×#394	C₂²	1	2	yes	complemented
59	C₃×#393	C₂²	1	2	yes	complemented
60	C₃×#392	C₂²	1	2	yes	—
61	C₃×#392	C₂²	1	2	yes	—
62	C₃×#391	C₂²	1	1	yes	characteristic, complemented
63	C₃×#390	C₂²	1	2	yes	—
64	C₃×#390	C₂²	1	2	yes	—
65	C₃×#390	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	2	yes	complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#389	C₂²	1	1	yes	characteristic, complemented
73	C₃×#389	C₂²	1	1	yes	characteristic, complemented
74	C₃×#389	C₂²	1	1	yes	characteristic, complemented
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	2	yes	complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	2	yes	complemented
80	C₃×#388	C₂²	1	2	yes	complemented
81	C₃×#388	C₂²	1	2	yes	complemented
82	C₃×#388	C₂²	1	2	yes	complemented
83	C₃×#388	C₂²	1	2	yes	complemented
84	C₃×#388	C₂²	1	2	yes	complemented
85	C₃×#388	C₂²	1	2	yes	complemented
86	C₃×#388	C₂²	1	2	yes	complemented
87	C₃×#387	C₂²	1	2	yes	complemented
88	C₃×#387	C₂²	1	2	yes	complemented
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×#386	C₂²	1	2	yes	complemented
94	C₃×#386	C₂²	1	2	yes	complemented
95	C₃×#386	C₂²	1	2	yes	complemented
96	C₃×#386	C₂²	1	2	yes	complemented
97	C₃×#385	C₂²	1	2	yes	complemented
98	C₃×#385	C₂²	1	2	yes	complemented
99	C₃×#383	C₂²	1	2	yes	complemented
100	C₃×#382	C₂²	1	1	yes	characteristic, complemented
101	C₃×#380	C₂²	1	1	yes	characteristic, complemented
102	C₃×#380	C₂²	1	1	yes	characteristic, complemented
103	C₃×#379	C₂²	1	2	yes	complemented
104	C₃×#379	C₂²	1	2	yes	complemented
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	#2854	C₂×C₃	1	1	yes	characteristic, complemented
109	#2850	C₂×C₃	1	1	yes	characteristic, complemented
110	#2808	C₂×C₃	1	1	yes	characteristic, complemented
111	#2757	C₂×C₃	1	2	yes	complemented
112	#2756	C₂×C₃	1	2	yes	complemented
113	#2732	C₂×C₃	1	1	yes	characteristic, complemented
114	#2727	C₂×C₃	1	1	yes	characteristic, complemented
115	#2685	C₂×C₃	1	2	yes	complemented
116	#2681	C₂×C₃	1	2	yes	complemented
117	#2679	C₂×C₃	1	1	yes	characteristic, complemented
118	#2678	C₂×C₃	1	2	yes	complemented
119	#2668	C₂×C₃	1	2	yes	complemented
120	#2651	C₂×C₃	1	2	yes	complemented
121	#2518	C₂×C₃	1	2	yes	complemented
122	#2472	C₂×C₃	1	2	yes	complemented
123	#2467	C₂×C₃	1	2	yes	complemented
124	#2424	C₂×C₃	1	2	yes	complemented
125	#2321	C₂×C₃	1	2	yes	complemented
126	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	2	yes	—
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	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	2	yes	—
133	C₂²×C₃×D₄	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₃×D₄	C₂³	1	2	yes	—
137	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₃×#126	—	4	4	no	—
144	C₃×#124	—	4	2	no	—
145	C₃×#123	—	4	4	no	—
146	C₃×C₂²⋊Q₈	—	4	2	no	—
147	C₃×C₂²⋊Q₈	—	4	4	no	—
148	C₃×#121	—	2	4	no	—
149	C₃×#121	—	4	2	no	—
150	C₃×#121	—	4	4	no	—
151	C₃×#121	—	4	2	no	—
152	C₃×#120	—	2	8	no	—
153	C₃×#120	—	4	4	no	—
154	C₃×#120	—	4	4	no	—
155	C₃×#120	—	4	4	no	—
156	C₃×C₄×D₄	—	4	2	no	—
157	C₃×C₄×D₄	—	4	4	no	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	4	4	no	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×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×C₄²	—	4	2	no	—
208	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄²	C₂³	1	2	yes	—
211	C₂×C₃×C₄²	C₂³	1	2	yes	—
212	C₂×C₃×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₂×#126	C₂²×C₃	1	2	yes	complemented
232	C₂×#124	C₂²×C₃	1	1	yes	characteristic
233	C₂×#123	C₂²×C₃	1	2	yes	complemented
234	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
235	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
236	C₂×#121	C₂²×C₃	1	1	yes	characteristic
237	C₂×#121	C₂²×C₃	1	1	yes	characteristic
238	C₂×#121	C₂²×C₃	1	1	yes	characteristic
239	C₂×#121	C₂²×C₃	1	2	yes	—
240	C₂×#120	C₂²×C₃	1	2	yes	—
241	C₂×#120	C₂²×C₃	1	2	yes	—
242	C₂×#120	C₂²×C₃	1	2	yes	—
243	C₂×#120	C₂²×C₃	1	2	yes	complemented
244	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
246	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
247	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
248	#399	C₂²×C₃	1	2	yes	complemented
249	#399	C₂²×C₃	1	2	yes	complemented
250	#398	C₂²×C₃	1	2	yes	complemented
251	#398	C₂²×C₃	1	2	yes	complemented
252	#397	C₂²×C₃	1	2	yes	complemented
253	#397	C₂²×C₃	1	2	yes	complemented
254	#397	C₂²×C₃	1	2	yes	complemented
255	#397	C₂²×C₃	1	2	yes	complemented
256	#396	C₂²×C₃	1	2	yes	complemented
257	#396	C₂²×C₃	1	2	yes	complemented
258	#396	C₂²×C₃	1	2	yes	complemented
259	#394	C₂²×C₃	1	2	yes	—
260	#394	C₂²×C₃	1	2	yes	—
261	#394	C₂²×C₃	1	2	yes	—
262	#394	C₂²×C₃	1	2	yes	—
263	#394	C₂²×C₃	1	2	yes	—
264	#394	C₂²×C₃	1	2	yes	—
265	#394	C₂²×C₃	1	2	yes	—
266	#394	C₂²×C₃	1	2	yes	—
267	#394	C₂²×C₃	1	2	yes	complemented
268	#394	C₂²×C₃	1	2	yes	complemented
269	#393	C₂²×C₃	1	2	yes	complemented
270	#392	C₂²×C₃	1	2	yes	—
271	#392	C₂²×C₃	1	2	yes	—
272	#391	C₂²×C₃	1	1	yes	characteristic, complemented
273	#390	C₂²×C₃	1	2	yes	—
274	#390	C₂²×C₃	1	2	yes	—
275	#390	C₂²×C₃	1	1	yes	characteristic
276	#390	C₂²×C₃	1	1	yes	characteristic
277	#390	C₂²×C₃	1	1	yes	characteristic
278	#390	C₂²×C₃	1	2	yes	—
279	#390	C₂²×C₃	1	1	yes	characteristic
280	#390	C₂²×C₃	1	2	yes	complemented
281	#389	C₂²×C₃	1	1	yes	characteristic, complemented
282	#389	C₂²×C₃	1	1	yes	characteristic, complemented
283	#389	C₂²×C₃	1	2	yes	complemented
284	#389	C₂²×C₃	1	1	yes	characteristic, complemented
285	#388	C₂²×C₃	1	2	yes	complemented
286	#388	C₂²×C₃	1	2	yes	complemented
287	#388	C₂²×C₃	1	2	yes	complemented
288	#388	C₂²×C₃	1	2	yes	complemented
289	#388	C₂²×C₃	1	2	yes	complemented
290	#388	C₂²×C₃	1	2	yes	complemented
291	#388	C₂²×C₃	1	2	yes	complemented
292	#388	C₂²×C₃	1	2	yes	complemented
293	#388	C₂²×C₃	1	2	yes	complemented
294	#388	C₂²×C₃	1	2	yes	complemented
295	#388	C₂²×C₃	1	2	yes	complemented
296	#388	C₂²×C₃	1	2	yes	complemented
297	#387	C₂²×C₃	1	2	yes	complemented
298	#387	C₂²×C₃	1	2	yes	complemented
299	#386	C₂²×C₃	1	2	yes	—
300	#386	C₂²×C₃	1	2	yes	—
301	#386	C₂²×C₃	1	2	yes	—
302	#386	C₂²×C₃	1	2	yes	—
303	#386	C₂²×C₃	1	2	yes	complemented
304	#386	C₂²×C₃	1	2	yes	complemented
305	#386	C₂²×C₃	1	2	yes	complemented
306	#386	C₂²×C₃	1	2	yes	complemented
307	#385	C₂²×C₃	1	2	yes	complemented
308	#385	C₂²×C₃	1	2	yes	complemented
309	#383	C₂²×C₃	1	2	yes	complemented
310	#382	C₂²×C₃	1	1	yes	characteristic, complemented
311	#380	C₂²×C₃	1	1	yes	characteristic, complemented
312	#380	C₂²×C₃	1	1	yes	characteristic, complemented
313	#379	C₂²×C₃	1	2	yes	complemented
314	#379	C₂²×C₃	1	2	yes	complemented
315	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
317	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
318	C₂⁴×C₃	—	2	4	no	—
319	C₂⁴×C₃	—	4	2	no	—
320	C₂⁴×C₃	—	4	2	no	—
321	C₂⁴×C₃	—	4	2	no	—
322	C₂⁴×C₃	—	4	2	no	—
323	C₂⁴×C₃	—	4	2	no	—
324	C₂⁴×C₃	—	4	2	no	—
325	C₂⁴×C₃	C₂⁴	1	2	yes	—
326	C₂⁴×C₃	C₂⁴	1	2	yes	—
327	C₂⁴×C₃	C₂⁴	1	2	yes	—
328	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
329	C₂×C₃×Q₈	—	2	2	no	—
330	C₂×C₃×Q₈	—	4	1	no	—
331	C₂×C₃×Q₈	—	4	1	no	—
332	C₂×C₃×D₄	—	2	4	no	—
333	C₂×C₃×D₄	—	2	4	no	—
334	C₂×C₃×D₄	—	2	4	no	—
335	C₂×C₃×D₄	—	2	4	no	—
336	C₂×C₃×D₄	—	2	4	no	—
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	2	2	no	—
339	C₂×C₃×D₄	—	2	2	no	—
340	C₂×C₃×D₄	—	4	1	no	—
341	C₂×C₃×D₄	—	4	2	no	—
342	C₂×C₃×D₄	—	4	1	no	—
343	C₂×C₃×D₄	—	4	2	no	—
344	C₂×C₃×D₄	—	4	2	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂×C₃×D₄	—	4	2	no	—
347	C₂×C₃×D₄	—	4	1	no	—
348	C₂×C₃×D₄	—	4	1	no	—
349	C₂×C₃×D₄	—	4	2	no	—
350	C₂×C₃×D₄	—	4	2	no	—
351	C₂×C₃×D₄	—	4	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	#41	1	4	yes	—
359	C₂²×C₃×C₄	—	2	2	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	2	no	—
363	C₂²×C₃×C₄	—	2	2	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	4	1	no	—
366	C₂²×C₃×C₄	—	4	1	no	—
367	C₂²×C₃×C₄	—	4	1	no	—
368	C₂²×C₃×C₄	—	4	1	no	—
369	C₂²×C₃×C₄	—	4	2	no	—
370	C₂²×C₃×C₄	—	4	2	no	—
371	C₂²×C₃×C₄	—	4	2	no	—
372	C₂²×C₃×C₄	—	4	2	no	—
373	C₂²×C₃×C₄	—	4	2	no	—
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	4	no	—
391	C₃×C₄⋊C₄	—	2	4	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	4	1	no	—
394	C₃×C₄⋊C₄	—	4	1	no	—
395	C₃×C₄⋊C₄	—	4	2	no	—
396	C₃×C₄⋊C₄	—	4	1	no	—
397	C₃×C₄⋊C₄	—	4	1	no	—
398	C₃×C₄⋊C₄	—	4	1	no	—
399	C₃×C₄⋊C₄	—	4	2	no	—
400	C₃×C₄⋊C₄	—	4	1	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	2	no	—
404	C₃×C₄⋊C₄	—	4	2	no	—
405	C₃×C₄⋊C₄	—	4	2	no	—
406	C₃×C₂²⋊C₄	—	2	4	no	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	4	no	—
410	C₃×C₂²⋊C₄	—	2	4	no	—
411	C₃×C₂²⋊C₄	—	2	4	no	—
412	C₃×C₂²⋊C₄	—	2	4	no	—
413	C₃×C₂²⋊C₄	—	2	4	no	—
414	C₃×C₂²⋊C₄	—	2	4	no	—
415	C₃×C₂²⋊C₄	—	2	4	no	—
416	C₃×C₂²⋊C₄	—	2	4	no	—
417	C₃×C₂²⋊C₄	—	4	2	no	—
418	C₃×C₂²⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	4	2	no	—
420	C₃×C₂²⋊C₄	—	4	2	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	2	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₂²⋊C₄	—	4	2	no	—
426	C₃×C₂²⋊C₄	—	4	2	no	—
427	C₃×C₂²⋊C₄	—	4	2	no	—
428	C₃×C₂²⋊C₄	—	4	2	no	—
429	C₃×C₂²⋊C₄	—	4	2	no	—
430	C₃×C₂²⋊C₄	—	4	2	no	—
431	C₃×C₂²⋊C₄	—	4	2	no	—
432	C₃×C₂²⋊C₄	—	4	2	no	—
433	C₃×C₂²⋊C₄	—	4	2	no	—
434	C₃×C₂²⋊C₄	—	4	2	no	—
435	C₃×C₂²⋊C₄	—	4	2	no	—
436	C₃×C₂²⋊C₄	—	4	2	no	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	4	1	no	—
440	C₃×C₄²	—	4	1	no	—
441	C₃×C₄²	—	4	2	no	—
442	C₃×C₄²	—	4	2	no	—
443	C₃×C₄²	—	4	2	no	—
444	C₂⁵	C₂³×C₃	1	2	yes	—
445	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₃	1	2	yes	—
447	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₃	1	2	yes	—
449	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₃	1	2	yes	—
451	C₂²×D₄	C₂³×C₃	1	2	yes	—
452	C₂²×D₄	C₂³×C₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₃	1	2	yes	—
454	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃	1	2	yes	—
460	#126	—	4	4	no	—
461	#124	—	4	2	no	—
462	#123	—	4	4	no	—
463	C₂²⋊Q₈	—	4	2	no	—
464	C₂²⋊Q₈	—	4	4	no	—
465	#121	—	2	4	no	—
466	#121	—	4	2	no	—
467	#121	—	4	4	no	—
468	#121	—	4	2	no	—
469	#120	—	2	8	no	—
470	#120	—	4	4	no	—
471	#120	—	4	4	no	—
472	#120	—	4	4	no	—
473	C₄×D₄	—	4	2	no	—
474	C₄×D₄	—	4	4	no	—
475	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
492	C₂×C₂²⋊C₄	—	4	4	no	—
493	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×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×C₄²	—	4	2	no	—
525	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	#95	C₂³×C₃	1	2	yes	—
533	#95	C₂³×C₃	1	2	yes	—
534	#95	C₂³×C₃	1	2	yes	—
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	C₂³×C₃	—	2	1	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	2	1	no	—
553	C₂³×C₃	—	2	2	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	1	no	—
558	C₂³×C₃	—	2	1	no	—
559	C₂³×C₃	—	2	2	no	—
560	C₂³×C₃	—	2	2	no	—
561	C₂³×C₃	—	2	2	no	—
562	C₂³×C₃	—	2	2	no	—
563	C₂³×C₃	—	2	2	no	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	2	no	—
567	C₂³×C₃	—	2	2	no	—
568	C₂³×C₃	—	2	2	no	—
569	C₂³×C₃	—	2	2	no	—
570	C₂³×C₃	—	2	2	no	—
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	4	8	no	—
575	C₂³×C₃	—	8	4	no	—
576	C₂³×C₃	—	8	4	no	—
577	C₂³×C₃	—	8	4	no	—
578	C₂³×C₃	—	8	4	no	—
579	C₂³×C₃	—	8	4	no	—
580	C₂³×C₃	—	8	4	no	—
581	C₂³×C₃	C₂×#41	1	4	yes	—
582	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
583	C₂³×C₃	C₂⁵	1	1	yes	characteristic
584	C₃×Q₈	—	8	2	no	—
585	C₃×D₄	—	4	4	no	—
586	C₃×D₄	—	4	8	no	—
587	C₃×D₄	—	8	2	no	—
588	C₃×D₄	—	8	2	no	—
589	C₃×D₄	—	8	4	no	—
590	C₃×D₄	—	8	4	no	—
591	C₃×D₄	—	8	4	no	—
592	C₃×D₄	—	8	4	no	—
593	C₃×D₄	—	8	4	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	4	4	no	—
636	C₂×C₃×C₄	—	4	4	no	—
637	C₂×C₃×C₄	—	4	4	no	—
638	C₂×C₃×C₄	—	8	4	no	—
639	C₂×C₃×C₄	—	8	4	no	—
640	C₂×C₃×C₄	C₂×#41	1	2	yes	—
641	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
642	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
643	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
644	C₂⁴	—	2	4	no	—
645	C₂⁴	—	4	2	no	—
646	C₂⁴	—	4	2	no	—
647	C₂⁴	—	4	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	2	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	C₂⁴×C₃	1	2	yes	—
652	C₂⁴	C₂⁴×C₃	1	2	yes	—
653	C₂⁴	C₂⁴×C₃	1	2	yes	—
654	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	4	1	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	1	no	—
674	C₂×D₄	—	4	1	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	1	no	—
679	C₂×D₄	—	4	1	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	C₃×#41	1	4	yes	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	4	1	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	2	yes	—
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	1	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
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	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	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	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	4	1	no	—
766	C₄²	—	4	1	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₂²×C₃	—	2	4	no	—
771	C₂²×C₃	—	2	4	no	—
772	C₂²×C₃	—	2	2	no	—
773	C₂²×C₃	—	2	4	no	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	2	no	—
776	C₂²×C₃	—	4	1	no	—
777	C₂²×C₃	—	4	1	no	—
778	C₂²×C₃	—	4	1	no	—
779	C₂²×C₃	—	4	2	no	—
780	C₂²×C₃	—	4	2	no	—
781	C₂²×C₃	—	4	2	no	—
782	C₂²×C₃	—	4	1	no	—
783	C₂²×C₃	—	4	2	no	—
784	C₂²×C₃	—	4	2	no	—
785	C₂²×C₃	—	4	2	no	—
786	C₂²×C₃	—	4	2	no	—
787	C₂²×C₃	—	4	2	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	4	2	no	—
790	C₂²×C₃	—	4	2	no	—
791	C₂²×C₃	—	4	2	no	—
792	C₂²×C₃	—	4	2	no	—
793	C₂²×C₃	—	4	2	no	—
794	C₂²×C₃	—	4	2	no	—
795	C₂²×C₃	—	4	2	no	—
796	C₂²×C₃	—	4	2	no	—
797	C₂²×C₃	—	4	2	no	—
798	C₂²×C₃	—	8	16	no	—
799	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
800	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
804	C₂²×C₃	#585	1	1	yes	characteristic
805	C₂²×C₃	#585	1	1	yes	characteristic
806	C₃×C₄	—	2	2	no	—
807	C₃×C₄	—	2	2	no	—
808	C₃×C₄	—	2	2	no	—
809	C₃×C₄	—	2	2	no	—
810	C₃×C₄	—	4	1	no	—
811	C₃×C₄	—	4	2	no	—
812	C₃×C₄	—	4	2	no	—
813	C₃×C₄	—	4	2	no	—
814	C₃×C₄	—	4	2	no	—
815	C₃×C₄	—	4	1	no	—
816	C₃×C₄	—	4	2	no	—
817	C₃×C₄	—	4	2	no	—
818	C₃×C₄	—	4	2	no	—
819	C₃×C₄	—	4	2	no	—
820	C₃×C₄	—	4	2	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	4	8	no	—
848	C₂³	—	8	4	no	—
849	C₂³	—	8	4	no	—
850	C₂³	—	8	4	no	—
851	C₂³	—	8	4	no	—
852	C₂³	—	8	4	no	—
853	C₂³	—	8	4	no	—
854	C₂³	C₂×C₃×#41	1	4	yes	—
855	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
856	C₂³	C₂⁵×C₃	1	1	yes	characteristic
857	Q₈	—	8	2	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	8	no	—
860	D₄	—	8	2	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	4	no	—
863	D₄	—	8	4	no	—
864	D₄	—	8	4	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	8	4	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	C₂×C₃×#41	1	2	yes	—
914	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
915	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
916	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
917	C₂×C₃	—	4	2	no	—
918	C₂×C₃	—	4	4	no	—
919	C₂×C₃	—	8	2	no	—
920	C₂×C₃	—	8	2	no	—
921	C₂×C₃	#3459	1	1	yes	characteristic
922	C₂×C₃	#3514	1	1	yes	characteristic
923	C₂×C₃	#3519	1	1	yes	characteristic
924	C₂×C₃	#3534	1	1	yes	characteristic
925	C₂×C₃	#3537	1	1	yes	characteristic
926	C₂×C₃	#3545	1	1	yes	characteristic
927	C₂×C₃	#3546	1	1	yes	characteristic
928	C₂²	—	2	4	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	8	16	no	—
957	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
958	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
960	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
961	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂²	C₃×#585	1	1	yes	characteristic
963	C₂²	C₃×#585	1	1	yes	characteristic
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₃	#37154	1	1	yes	characteristic, direct product factor, Sylow
980	C₂	—	4	4	no	—
981	C₂	—	4	2	no	—
982	C₂	—	8	2	no	—
983	C₂	—	8	2	no	—
984	C₂	C₃×#3459	1	1	yes	characteristic
985	C₂	C₃×#3514	1	1	yes	characteristic
986	C₂	C₃×#3519	1	1	yes	characteristic
987	C₂	C₃×#3534	1	1	yes	characteristic
988	C₂	C₃×#3537	1	1	yes	characteristic
989	C₂	C₃×#3545	1	1	yes	characteristic
990	C₂	C₃×#3546	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. C₃×#2854	C₂	semidirect
2. C₃×#2850	C₂	semidirect
3. C₃×#2808	C₂	semidirect
4. C₃×#2757	C₂	semidirect
5. C₃×#2756	C₂	semidirect
6. C₃×#2732	C₂	semidirect
7. C₃×#2727	C₂	semidirect
8. C₃×#2685	C₂	semidirect
9. C₃×#2681	C₂	semidirect
10. C₃×#2679	C₂	semidirect
11. C₃×#2678	C₂	semidirect
12. C₃×#2668	C₂	semidirect
13. C₃×#2651	C₂	semidirect
14. C₃×#2518	C₂	semidirect
15. C₃×#2472	C₂	semidirect
16. C₃×#2467	C₂	semidirect
17. C₃×#2424	C₂	semidirect
18. C₃×#2321	C₂	semidirect
19. C₃×C₄×#121	C₂	semidirect
20. #37154	C₃	direct (N × H)
21. C₂×C₃×#126	C₂²	semidirect
23. C₂×C₃×#123	C₂²	semidirect
24. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₃×#120	C₂²	semidirect
35. C₂×C₃×C₄×D₄	C₂²	semidirect
36. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
37. C₂²×C₃×C₄²	C₂²	semidirect
38. C₃×#399	C₂²	semidirect
39. C₃×#399	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
41. C₃×#398	C₂²	semidirect
42. C₃×#397	C₂²	semidirect
43. C₃×#397	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#396	C₂²	semidirect
47. C₃×#396	C₂²	semidirect
48. C₃×#396	C₂²	semidirect
57. C₃×#394	C₂²	semidirect
58. C₃×#394	C₂²	semidirect
59. C₃×#393	C₂²	semidirect
62. C₃×#391	C₂²	semidirect
70. C₃×#390	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#389	C₂²	semidirect
74. C₃×#389	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#388	C₂²	semidirect
82. C₃×#388	C₂²	semidirect
83. C₃×#388	C₂²	semidirect
84. C₃×#388	C₂²	semidirect
85. C₃×#388	C₂²	semidirect
86. C₃×#388	C₂²	semidirect
87. C₃×#387	C₂²	semidirect
88. C₃×#387	C₂²	semidirect
93. C₃×#386	C₂²	semidirect
94. C₃×#386	C₂²	semidirect
95. C₃×#386	C₂²	semidirect
96. C₃×#386	C₂²	semidirect
97. C₃×#385	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
99. C₃×#383	C₂²	semidirect
100. C₃×#382	C₂²	semidirect
101. C₃×#380	C₂²	semidirect
102. C₃×#380	C₂²	semidirect
103. C₃×#379	C₂²	semidirect
104. C₃×#379	C₂²	semidirect
105. C₃×C₄×C₄⋊C₄	C₂²	semidirect
106. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
107. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
108. #2854	C₂×C₃	semidirect
109. #2850	C₂×C₃	semidirect
110. #2808	C₂×C₃	semidirect
111. #2757	C₂×C₃	semidirect
112. #2756	C₂×C₃	semidirect
113. #2732	C₂×C₃	semidirect
114. #2727	C₂×C₃	semidirect
115. #2685	C₂×C₃	semidirect
116. #2681	C₂×C₃	semidirect
117. #2679	C₂×C₃	semidirect
118. #2678	C₂×C₃	semidirect
119. #2668	C₂×C₃	semidirect
120. #2651	C₂×C₃	semidirect
121. #2518	C₂×C₃	semidirect
122. #2472	C₂×C₃	semidirect
123. #2467	C₂×C₃	semidirect
124. #2424	C₂×C₃	semidirect
125. #2321	C₂×C₃	semidirect
126. C₄×#121	C₂×C₃	semidirect
231. C₂×#126	C₂²×C₃	semidirect
233. C₂×#123	C₂²×C₃	semidirect
234. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
235. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
243. C₂×#120	C₂²×C₃	semidirect
245. C₂×C₄×D₄	C₂²×C₃	semidirect
246. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
247. C₂²×C₄²	C₂²×C₃	semidirect
248. #399	C₂²×C₃	semidirect
249. #399	C₂²×C₃	semidirect
250. #398	C₂²×C₃	semidirect
251. #398	C₂²×C₃	semidirect
252. #397	C₂²×C₃	semidirect
253. #397	C₂²×C₃	semidirect
254. #397	C₂²×C₃	semidirect
255. #397	C₂²×C₃	semidirect
256. #396	C₂²×C₃	semidirect
257. #396	C₂²×C₃	semidirect
258. #396	C₂²×C₃	semidirect
267. #394	C₂²×C₃	semidirect
268. #394	C₂²×C₃	semidirect
269. #393	C₂²×C₃	semidirect
272. #391	C₂²×C₃	semidirect
280. #390	C₂²×C₃	semidirect
281. #389	C₂²×C₃	semidirect
282. #389	C₂²×C₃	semidirect
283. #389	C₂²×C₃	semidirect
284. #389	C₂²×C₃	semidirect
285. #388	C₂²×C₃	semidirect
286. #388	C₂²×C₃	semidirect
287. #388	C₂²×C₃	semidirect
288. #388	C₂²×C₃	semidirect
289. #388	C₂²×C₃	semidirect
290. #388	C₂²×C₃	semidirect
291. #388	C₂²×C₃	semidirect
292. #388	C₂²×C₃	semidirect
293. #388	C₂²×C₃	semidirect
294. #388	C₂²×C₃	semidirect
295. #388	C₂²×C₃	semidirect
296. #388	C₂²×C₃	semidirect
297. #387	C₂²×C₃	semidirect
298. #387	C₂²×C₃	semidirect
303. #386	C₂²×C₃	semidirect
304. #386	C₂²×C₃	semidirect
305. #386	C₂²×C₃	semidirect
306. #386	C₂²×C₃	semidirect
307. #385	C₂²×C₃	semidirect
308. #385	C₂²×C₃	semidirect
309. #383	C₂²×C₃	semidirect
310. #382	C₂²×C₃	semidirect
311. #380	C₂²×C₃	semidirect
312. #380	C₂²×C₃	semidirect
313. #379	C₂²×C₃	semidirect
314. #379	C₂²×C₃	semidirect
315. C₄×C₄⋊C₄	C₂²×C₃	semidirect
316. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
317. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
979. C₃	#37154	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×#2854	2
C₃×#2850	2
C₃×#2808	2
C₃×#2757	2
C₃×#2756	2
C₃×#2732	2
C₃×#2727	2
C₃×#2685	2
C₃×#2681	2
C₃×#2679	2
C₃×#2678	2
C₃×#2668	2
C₃×#2651	2
C₃×#2518	2
C₃×#2472	2
C₃×#2467	2
C₃×#2424	2
C₃×#2321	2
C₃×C₄×#121	2
#37154	3

Subgroups — C3×#37154 #10655761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37154 #10655761