Subgroups — C₃×#35734 #10654341

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2655	C₂	1	2	yes	maximal, complemented
2	C₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2576	C₂	1	2	yes	maximal, complemented
4	C₃×#2573	C₂	1	2	yes	maximal, complemented
5	C₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2522	C₂	1	2	yes	maximal, complemented
8	C₃×#2515	C₂	1	2	yes	maximal, complemented
9	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2470	C₂	1	2	yes	maximal, complemented
14	C₃×#2457	C₂	1	2	yes	maximal
15	C₃×#2395	C₂	1	2	yes	maximal, complemented
16	C₃×#2392	C₂	1	1	yes	maximal, characteristic
17	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	#35734	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	C₂²	1	2	yes	—
34	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×#401	C₂²	1	2	yes	—
38	C₃×#400	C₂²	1	2	yes	—
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	2	yes	—
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#399	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	1	yes	characteristic
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	1	yes	characteristic
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#396	C₂²	1	2	yes	—
53	C₃×#396	C₂²	1	2	yes	—
54	C₃×#396	C₂²	1	1	yes	characteristic
55	C₃×#396	C₂²	1	1	yes	characteristic
56	C₃×#394	C₂²	1	1	yes	characteristic
57	C₃×#394	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	1	yes	characteristic
59	C₃×#394	C₂²	1	2	yes	—
60	C₃×#392	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	2	yes	—
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	2	yes	—
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#384	C₂²	1	1	yes	characteristic
92	C₃×#383	C₂²	1	2	yes	—
93	C₃×#382	C₂²	1	1	yes	characteristic
94	C₃×#382	C₂²	1	1	yes	characteristic
95	C₃×#382	C₂²	1	2	yes	—
96	C₃×#381	C₂²	1	2	yes	—
97	C₃×#381	C₂²	1	2	yes	—
98	C₃×#380	C₂²	1	1	yes	characteristic
99	C₃×#380	C₂²	1	1	yes	characteristic
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	1	yes	characteristic
102	C₃×#380	C₂²	1	1	yes	characteristic
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	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	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
124	#2655	C₂×C₃	1	2	yes	complemented
125	#2629	C₂×C₃	1	1	yes	characteristic, complemented
126	#2576	C₂×C₃	1	2	yes	complemented
127	#2573	C₂×C₃	1	2	yes	complemented
128	#2571	C₂×C₃	1	1	yes	characteristic, complemented
129	#2562	C₂×C₃	1	1	yes	characteristic, complemented
130	#2522	C₂×C₃	1	2	yes	complemented
131	#2515	C₂×C₃	1	2	yes	complemented
132	#2495	C₂×C₃	1	1	yes	characteristic, complemented
133	#2494	C₂×C₃	1	1	yes	characteristic, complemented
134	#2487	C₂×C₃	1	1	yes	characteristic, complemented
135	#2486	C₂×C₃	1	1	yes	characteristic, complemented
136	#2470	C₂×C₃	1	2	yes	complemented
137	#2457	C₂×C₃	1	2	yes	—
138	#2395	C₂×C₃	1	2	yes	complemented
139	#2392	C₂×C₃	1	1	yes	characteristic
140	#2370	C₂×C₃	1	1	yes	characteristic, complemented
141	#2352	C₂×C₃	1	1	yes	characteristic, complemented
142	#2352	C₂×C₃	1	1	yes	characteristic, complemented
143	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
144	#2345	C₂×C₃	1	1	yes	characteristic, complemented
145	#2344	C₂×C₃	1	1	yes	characteristic, complemented
146	#2274	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
148	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	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	C₃×#125	—	2	4	no	—
157	C₃×#123	—	4	4	no	—
158	C₃×C₄×D₄	—	2	4	no	—
159	C₃×C₄×D₄	—	2	4	no	—
160	C₃×C₄×D₄	—	2	4	no	—
161	C₃×C₄×D₄	—	4	4	no	—
162	C₃×#117	—	2	4	no	—
163	C₃×#117	—	2	4	no	—
164	C₃×#117	—	4	4	no	—
165	C₂×C₃×C₄⋊C₄	—	2	4	no	—
166	C₂×C₃×C₄⋊C₄	—	2	4	no	—
167	C₂×C₃×C₄⋊C₄	—	2	4	no	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	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×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	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	2	yes	—
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	2	yes	—
223	C₂×C₃×C₄²	C₂³	1	2	yes	—
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
228	C₃×#95	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	2	yes	—
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	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	2	yes	—
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₂×#125	C₂²×C₃	1	1	yes	characteristic
259	C₂×#123	C₂²×C₃	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
264	C₂×#117	C₂²×C₃	1	1	yes	characteristic
265	C₂×#117	C₂²×C₃	1	1	yes	characteristic
266	C₂×#117	C₂²×C₃	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
270	#401	C₂²×C₃	1	2	yes	—
271	#400	C₂²×C₃	1	2	yes	—
272	#400	C₂²×C₃	1	2	yes	—
273	#400	C₂²×C₃	1	2	yes	—
274	#400	C₂²×C₃	1	2	yes	—
275	#400	C₂²×C₃	1	2	yes	—
276	#399	C₂²×C₃	1	2	yes	—
277	#398	C₂²×C₃	1	2	yes	—
278	#398	C₂²×C₃	1	2	yes	—
279	#398	C₂²×C₃	1	1	yes	characteristic
280	#398	C₂²×C₃	1	2	yes	—
281	#397	C₂²×C₃	1	1	yes	characteristic
282	#397	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	2	yes	—
284	#397	C₂²×C₃	1	2	yes	—
285	#396	C₂²×C₃	1	2	yes	—
286	#396	C₂²×C₃	1	2	yes	—
287	#396	C₂²×C₃	1	1	yes	characteristic
288	#396	C₂²×C₃	1	1	yes	characteristic
289	#394	C₂²×C₃	1	2	yes	—
290	#394	C₂²×C₃	1	1	yes	characteristic
291	#394	C₂²×C₃	1	1	yes	characteristic
292	#394	C₂²×C₃	1	1	yes	characteristic
293	#392	C₂²×C₃	1	1	yes	characteristic
294	#389	C₂²×C₃	1	1	yes	characteristic
295	#389	C₂²×C₃	1	1	yes	characteristic
296	#389	C₂²×C₃	1	2	yes	—
297	#389	C₂²×C₃	1	2	yes	—
298	#389	C₂²×C₃	1	1	yes	characteristic
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	2	yes	—
301	#389	C₂²×C₃	1	1	yes	characteristic
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#388	C₂²×C₃	1	2	yes	—
304	#388	C₂²×C₃	1	2	yes	—
305	#388	C₂²×C₃	1	2	yes	—
306	#388	C₂²×C₃	1	2	yes	—
307	#388	C₂²×C₃	1	2	yes	—
308	#388	C₂²×C₃	1	2	yes	—
309	#387	C₂²×C₃	1	2	yes	—
310	#387	C₂²×C₃	1	2	yes	—
311	#387	C₂²×C₃	1	2	yes	—
312	#387	C₂²×C₃	1	2	yes	—
313	#387	C₂²×C₃	1	2	yes	—
314	#387	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#386	C₂²×C₃	1	2	yes	—
319	#386	C₂²×C₃	1	2	yes	—
320	#386	C₂²×C₃	1	2	yes	—
321	#385	C₂²×C₃	1	2	yes	—
322	#385	C₂²×C₃	1	2	yes	—
323	#385	C₂²×C₃	1	2	yes	—
324	#384	C₂²×C₃	1	1	yes	characteristic
325	#383	C₂²×C₃	1	2	yes	—
326	#382	C₂²×C₃	1	2	yes	—
327	#382	C₂²×C₃	1	1	yes	characteristic
328	#382	C₂²×C₃	1	1	yes	characteristic
329	#381	C₂²×C₃	1	2	yes	—
330	#381	C₂²×C₃	1	2	yes	—
331	#380	C₂²×C₃	1	1	yes	characteristic
332	#380	C₂²×C₃	1	1	yes	characteristic
333	#380	C₂²×C₃	1	1	yes	characteristic
334	#380	C₂²×C₃	1	1	yes	characteristic
335	#380	C₂²×C₃	1	2	yes	—
336	#380	C₂²×C₃	1	1	yes	characteristic
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	C₂²×C₃	1	1	yes	characteristic
339	#380	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₃	1	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	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
357	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	2	2	no	—
362	C₂×C₃×D₄	—	2	2	no	—
363	C₂×C₃×D₄	—	2	2	no	—
364	C₂×C₃×D₄	—	2	2	no	—
365	C₂×C₃×D₄	—	2	2	no	—
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	4	1	no	—
368	C₂×C₃×D₄	—	4	1	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	2	2	no	—
371	C₂²×C₃×C₄	—	2	4	no	—
372	C₂²×C₃×C₄	—	2	4	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	4	no	—
381	C₂²×C₃×C₄	—	4	2	no	—
382	C₂²×C₃×C₄	—	4	2	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	—	4	2	no	—
386	C₂²×C₃×C₄	#41	1	4	yes	—
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	2	no	—
413	C₃×C₄⋊C₄	—	2	2	no	—
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	2	2	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	4	no	—
421	C₃×C₄⋊C₄	—	2	4	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	4	1	no	—
425	C₃×C₄⋊C₄	—	4	1	no	—
426	C₃×C₄⋊C₄	—	4	2	no	—
427	C₃×C₄⋊C₄	—	4	2	no	—
428	C₃×C₄⋊C₄	—	4	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	2	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	—	4	2	no	—
434	C₃×C₄⋊C₄	#41	1	4	yes	—
435	C₃×C₂²⋊C₄	—	2	2	no	—
436	C₃×C₂²⋊C₄	—	2	2	no	—
437	C₃×C₂²⋊C₄	—	2	2	no	—
438	C₃×C₂²⋊C₄	—	2	4	no	—
439	C₃×C₂²⋊C₄	—	2	4	no	—
440	C₃×C₂²⋊C₄	—	2	2	no	—
441	C₃×C₂²⋊C₄	—	2	4	no	—
442	C₃×C₂²⋊C₄	—	2	4	no	—
443	C₃×C₂²⋊C₄	—	2	2	no	—
444	C₃×C₂²⋊C₄	—	2	2	no	—
445	C₃×C₂²⋊C₄	—	2	2	no	—
446	C₃×C₂²⋊C₄	—	2	2	no	—
447	C₃×C₂²⋊C₄	—	2	2	no	—
448	C₃×C₂²⋊C₄	—	2	2	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	1	no	—
451	C₃×C₂²⋊C₄	—	4	2	no	—
452	C₃×C₂²⋊C₄	—	4	2	no	—
453	C₃×C₂²⋊C₄	—	4	1	no	—
454	C₃×C₂²⋊C₄	—	4	2	no	—
455	C₃×C₂²⋊C₄	—	4	2	no	—
456	C₃×C₄²	—	2	4	no	—
457	C₃×C₄²	—	2	2	no	—
458	C₃×C₄²	—	2	2	no	—
459	C₃×C₄²	—	2	2	no	—
460	C₃×C₄²	—	4	2	no	—
461	C₃×C₄²	—	4	2	no	—
462	C₃×C₄²	—	4	2	no	—
463	C₃×C₄²	—	4	2	no	—
464	C₃×C₄²	—	4	2	no	—
465	C₃×C₄²	—	4	2	no	—
466	C₃×C₄²	#41	1	4	yes	—
467	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃	1	2	yes	—
475	C₂³×C₄	C₂³×C₃	1	2	yes	—
476	#125	—	2	4	no	—
477	#123	—	4	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	4	4	no	—
482	#117	—	2	4	no	—
483	#117	—	2	4	no	—
484	#117	—	4	4	no	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	—	2	4	no	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₃	1	2	yes	—
543	C₂×C₄²	C₂³×C₃	1	2	yes	—
544	C₂×C₄²	C₂³×C₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	2	yes	—
554	#95	C₂³×C₃	1	2	yes	—
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	2	yes	—
557	#95	C₂³×C₃	1	1	yes	characteristic
558	#95	C₂³×C₃	1	1	yes	characteristic
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	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	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	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	C₂³×C₃	—	2	1	no	—
579	C₂³×C₃	—	2	1	no	—
580	C₂³×C₃	—	2	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	2	1	no	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	—	2	1	no	—
586	C₂³×C₃	—	2	1	no	—
587	C₂³×C₃	—	2	1	no	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	1	no	—
590	C₂³×C₃	—	2	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	1	no	—
594	C₂³×C₃	—	2	1	no	—
595	C₂³×C₃	—	2	1	no	—
596	C₂³×C₃	C₂×#41	1	2	yes	—
597	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
598	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
599	C₂³×C₃	C₂⁵	1	1	yes	characteristic
600	C₃×D₄	—	2	8	no	—
601	C₃×D₄	—	4	4	no	—
602	C₃×D₄	—	4	4	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	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	1	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	8	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	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	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	1	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	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	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	1	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	2	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	1	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	2	1	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	—	4	8	no	—
658	C₂×C₃×C₄	—	4	4	no	—
659	C₂×C₃×C₄	—	4	4	no	—
660	C₂×C₃×C₄	—	8	4	no	—
661	C₂×C₃×C₄	—	8	4	no	—
662	C₂×C₃×C₄	C₂×#41	1	4	yes	—
663	C₂×C₃×C₄	C₂×#41	1	2	yes	—
664	C₂×C₃×C₄	C₂×#41	1	2	yes	—
665	C₂×C₃×C₄	C₂×#41	1	2	yes	—
666	C₂×C₃×C₄	C₂×#41	1	2	yes	—
667	C₂×C₃×C₄	C₂×#41	1	2	yes	—
668	C₂×C₃×C₄	C₂×#41	1	2	yes	—
669	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	1	no	—
680	C₂×D₄	—	4	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	C₃×#41	1	4	yes	—
699	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	C₃×#41	1	4	yes	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	1	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	C₃×#41	1	4	yes	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	2	no	—
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	4	1	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	1	no	—
792	C₂²×C₃	—	4	1	no	—
793	C₂²×C₃	—	4	1	no	—
794	C₂²×C₃	—	4	1	no	—
795	C₂²×C₃	—	4	1	no	—
796	C₂²×C₃	—	4	1	no	—
797	C₂²×C₃	—	4	1	no	—
798	C₂²×C₃	—	4	1	no	—
799	C₂²×C₃	—	4	1	no	—
800	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
801	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
802	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
803	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
804	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
805	C₂²×C₃	#585	1	1	yes	characteristic
806	C₂²×C₃	#585	1	1	yes	characteristic
807	C₃×C₄	—	2	2	no	—
808	C₃×C₄	—	2	2	no	—
809	C₃×C₄	—	2	2	no	—
810	C₃×C₄	—	2	4	no	—
811	C₃×C₄	—	4	1	no	—
812	C₃×C₄	—	4	1	no	—
813	C₃×C₄	—	4	1	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	1	no	—
819	C₃×C₄	—	4	1	no	—
820	C₃×C₄	—	4	1	no	—
821	C₃×C₄	—	4	1	no	—
822	C₃×C₄	—	4	2	no	—
823	C₃×C₄	—	4	2	no	—
824	C₃×C₄	—	4	2	no	—
825	C₃×C₄	—	4	2	no	—
826	C₃×C₄	#529	1	4	yes	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	C₂×C₃×#41	1	2	yes	—
846	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
847	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
848	C₂³	C₂⁵×C₃	1	1	yes	characteristic
849	D₄	—	2	8	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	4	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	8	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	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	2	no	—
873	C₂×C₄	—	2	2	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	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	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	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	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	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	4	8	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	8	4	no	—
910	C₂×C₄	—	8	4	no	—
911	C₂×C₄	C₂×C₃×#41	1	4	yes	—
912	C₂×C₄	C₂×C₃×#41	1	2	yes	—
913	C₂×C₄	C₂×C₃×#41	1	2	yes	—
914	C₂×C₄	C₂×C₃×#41	1	2	yes	—
915	C₂×C₄	C₂×C₃×#41	1	2	yes	—
916	C₂×C₄	C₂×C₃×#41	1	2	yes	—
917	C₂×C₄	C₂×C₃×#41	1	2	yes	—
918	C₂×C₃	—	4	2	no	—
919	C₂×C₃	—	4	2	no	—
920	C₂×C₃	—	4	2	no	—
921	C₂×C₃	C₂×#529	1	1	yes	characteristic
922	C₂×C₃	#3492	1	1	yes	characteristic
923	C₂×C₃	#3494	1	1	yes	characteristic
924	C₂×C₃	#3495	1	1	yes	characteristic
925	C₂×C₃	#3512	1	1	yes	characteristic
926	C₂×C₃	#3513	1	1	yes	characteristic
927	C₂×C₃	#3516	1	1	yes	characteristic
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
950	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
951	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
952	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
954	C₂²	C₃×#585	1	1	yes	characteristic
955	C₂²	C₃×#585	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	C₃×#529	1	4	yes	—
976	C₃	#35734	1	1	yes	characteristic, direct product factor, Sylow
977	C₂	—	4	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	4	2	no	—
980	C₂	C₂×C₃×#529	1	1	yes	characteristic
981	C₂	C₃×#3492	1	1	yes	characteristic
982	C₂	C₃×#3494	1	1	yes	characteristic
983	C₂	C₃×#3495	1	1	yes	characteristic
984	C₂	C₃×#3512	1	1	yes	characteristic
985	C₂	C₃×#3513	1	1	yes	characteristic
986	C₂	C₃×#3516	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#2655	C₂	semidirect
2. C₃×#2629	C₂	semidirect
3. C₃×#2576	C₂	semidirect
4. C₃×#2573	C₂	semidirect
5. C₃×#2571	C₂	semidirect
6. C₃×#2562	C₂	semidirect
7. C₃×#2522	C₂	semidirect
8. C₃×#2515	C₂	semidirect
9. C₃×#2495	C₂	semidirect
10. C₃×#2494	C₂	semidirect
11. C₃×#2487	C₂	semidirect
12. C₃×#2486	C₂	semidirect
13. C₃×#2470	C₂	semidirect
15. C₃×#2395	C₂	semidirect
17. C₃×#2370	C₂	semidirect
18. C₃×#2352	C₂	semidirect
19. C₃×#2352	C₂	semidirect
20. C₃×D₄×C₄⋊C₄	C₂	semidirect
21. C₃×#2345	C₂	semidirect
22. C₃×#2344	C₂	semidirect
23. C₃×#2274	C₂	semidirect
24. #35734	C₃	direct (N × H)
124. #2655	C₂×C₃	semidirect
125. #2629	C₂×C₃	semidirect
126. #2576	C₂×C₃	semidirect
127. #2573	C₂×C₃	semidirect
128. #2571	C₂×C₃	semidirect
129. #2562	C₂×C₃	semidirect
130. #2522	C₂×C₃	semidirect
131. #2515	C₂×C₃	semidirect
132. #2495	C₂×C₃	semidirect
133. #2494	C₂×C₃	semidirect
134. #2487	C₂×C₃	semidirect
135. #2486	C₂×C₃	semidirect
136. #2470	C₂×C₃	semidirect
138. #2395	C₂×C₃	semidirect
140. #2370	C₂×C₃	semidirect
141. #2352	C₂×C₃	semidirect
142. #2352	C₂×C₃	semidirect
143. D₄×C₄⋊C₄	C₂×C₃	semidirect
144. #2345	C₂×C₃	semidirect
145. #2344	C₂×C₃	semidirect
146. #2274	C₂×C₃	semidirect
976. C₃	#35734	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×#2655	2
C₃×#2629	2
C₃×#2576	2
C₃×#2573	2
C₃×#2571	2
C₃×#2562	2
C₃×#2522	2
C₃×#2515	2
C₃×#2495	2
C₃×#2494	2
C₃×#2487	2
C₃×#2486	2
C₃×#2470	2
C₃×#2457	2
C₃×#2395	2
C₃×#2392	2
C₃×#2370	2
C₃×#2352	2
C₃×D₄×C₄⋊C₄	2
C₃×#2345	2
C₃×#2344	2
C₃×#2274	2
#35734	3

Subgroups — C3×#35734 #10654341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35734 #10654341