Subgroups — C₃×#35851 #10654458

Order 768.

1816 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2667	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2652	C₂	1	2	yes	maximal, complemented
3	C₃×#2578	C₂	1	2	yes	maximal, complemented
4	C₃×#2575	C₂	1	2	yes	maximal, complemented
5	C₃×#2553	C₂	1	2	yes	maximal, complemented
6	C₃×#2534	C₂	1	1	yes	maximal, characteristic
7	C₃×#2522	C₂	1	2	yes	maximal, complemented
8	C₃×#2495	C₂	1	2	yes	maximal, complemented
9	C₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2480	C₂	1	2	yes	maximal, complemented
11	C₃×#2470	C₂	1	2	yes	maximal, complemented
12	C₃×#2418	C₂	1	2	yes	maximal
13	C₃×#2395	C₂	1	2	yes	maximal, complemented
14	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2373	C₂	1	2	yes	maximal, complemented
16	C₃×#2359	C₂	1	2	yes	maximal, complemented
17	C₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2273	C₂	1	1	yes	maximal, characteristic, complemented
20	#35851	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#126	C₂²	1	2	yes	—
22	C₂×C₃×#123	C₂²	1	2	yes	—
23	C₂×C₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₃×#120	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
27	C₂×C₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃×#117	C₂²	1	2	yes	complemented
29	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×#400	C₂²	1	1	yes	characteristic, complemented
32	C₃×#400	C₂²	1	2	yes	complemented
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
35	C₃×#399	C₂²	1	2	yes	—
36	C₃×#399	C₂²	1	2	yes	—
37	C₃×#399	C₂²	1	1	yes	characteristic, complemented
38	C₃×#398	C₂²	1	2	yes	complemented
39	C₃×#398	C₂²	1	1	yes	characteristic, complemented
40	C₃×#398	C₂²	1	2	yes	complemented
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#397	C₂²	1	2	yes	—
43	C₃×#397	C₂²	1	2	yes	—
44	C₃×#397	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	1	yes	characteristic, complemented
47	C₃×#397	C₂²	1	2	yes	complemented
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#396	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×#389	C₂²	1	2	yes	complemented
54	C₃×#389	C₂²	1	2	yes	complemented
55	C₃×#389	C₂²	1	2	yes	complemented
56	C₃×#389	C₂²	1	2	yes	complemented
57	C₃×#388	C₂²	1	2	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	2	yes	—
61	C₃×#388	C₂²	1	2	yes	—
62	C₃×#388	C₂²	1	2	yes	—
63	C₃×#388	C₂²	1	2	yes	—
64	C₃×#388	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	complemented
66	C₃×#387	C₂²	1	2	yes	complemented
67	C₃×#387	C₂²	1	2	yes	complemented
68	C₃×#387	C₂²	1	2	yes	complemented
69	C₃×#387	C₂²	1	2	yes	complemented
70	C₃×#387	C₂²	1	2	yes	complemented
71	C₃×#387	C₂²	1	2	yes	complemented
72	C₃×#387	C₂²	1	2	yes	complemented
73	C₃×#386	C₂²	1	2	yes	—
74	C₃×#386	C₂²	1	2	yes	—
75	C₃×#386	C₂²	1	2	yes	—
76	C₃×#385	C₂²	1	2	yes	—
77	C₃×#385	C₂²	1	2	yes	—
78	C₃×#385	C₂²	1	2	yes	—
79	C₃×#385	C₂²	1	2	yes	—
80	C₃×#385	C₂²	1	2	yes	complemented
81	C₃×#383	C₂²	1	1	yes	characteristic, complemented
82	C₃×#383	C₂²	1	2	yes	complemented
83	C₃×#382	C₂²	1	2	yes	complemented
84	C₃×#381	C₂²	1	1	yes	characteristic
85	C₃×#381	C₂²	1	1	yes	characteristic
86	C₃×#380	C₂²	1	1	yes	characteristic
87	C₃×#380	C₂²	1	2	yes	—
88	C₃×#380	C₂²	1	2	yes	—
89	C₃×#380	C₂²	1	1	yes	characteristic, complemented
90	C₃×#379	C₂²	1	2	yes	—
91	C₃×#379	C₂²	1	1	yes	characteristic
92	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
93	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
94	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×#376	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
108	#2667	C₂×C₃	1	1	yes	characteristic, complemented
109	#2652	C₂×C₃	1	2	yes	complemented
110	#2578	C₂×C₃	1	2	yes	complemented
111	#2575	C₂×C₃	1	2	yes	complemented
112	#2553	C₂×C₃	1	2	yes	complemented
113	#2534	C₂×C₃	1	1	yes	characteristic
114	#2522	C₂×C₃	1	2	yes	complemented
115	#2495	C₂×C₃	1	2	yes	complemented
116	#2482	C₂×C₃	1	1	yes	characteristic, complemented
117	#2480	C₂×C₃	1	2	yes	complemented
118	#2470	C₂×C₃	1	2	yes	complemented
119	#2418	C₂×C₃	1	2	yes	—
120	#2395	C₂×C₃	1	1	yes	characteristic, complemented
121	#2395	C₂×C₃	1	2	yes	complemented
122	#2373	C₂×C₃	1	2	yes	complemented
123	#2359	C₂×C₃	1	2	yes	complemented
124	#2353	C₂×C₃	1	1	yes	characteristic, complemented
125	#2347	C₂×C₃	1	1	yes	characteristic, complemented
126	#2273	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₃×D₄	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	2	yes	—
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	2	yes	—
133	C₂³×C₃×C₄	C₂³	1	2	yes	—
134	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₃×#126	—	2	8	no	—
137	C₃×#123	—	2	8	no	—
138	C₃×#123	—	4	2	no	—
139	C₃×#120	—	4	2	no	—
140	C₃×C₄×D₄	—	2	4	no	—
141	C₃×C₄×D₄	—	4	4	no	—
142	C₃×#117	—	2	4	no	—
143	C₃×#117	—	4	4	no	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
163	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	2	yes	—
191	C₂×C₃×C₄²	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	C₂³	1	2	yes	—
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	1	yes	characteristic
197	C₃×#95	C₂³	1	1	yes	characteristic
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	1	yes	characteristic
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	1	yes	characteristic
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	1	yes	characteristic
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	1	yes	characteristic
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
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	C₂×#126	C₂²×C₃	1	2	yes	—
225	C₂×#123	C₂²×C₃	1	2	yes	—
226	C₂×#123	C₂²×C₃	1	1	yes	characteristic
227	C₂×#120	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
230	C₂×#117	C₂²×C₃	1	1	yes	characteristic
231	C₂×#117	C₂²×C₃	1	2	yes	complemented
232	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
234	#400	C₂²×C₃	1	2	yes	complemented
235	#400	C₂²×C₃	1	2	yes	complemented
236	#400	C₂²×C₃	1	1	yes	characteristic, complemented
237	#400	C₂²×C₃	1	2	yes	complemented
238	#399	C₂²×C₃	1	2	yes	—
239	#399	C₂²×C₃	1	2	yes	—
240	#399	C₂²×C₃	1	1	yes	characteristic, complemented
241	#398	C₂²×C₃	1	2	yes	complemented
242	#398	C₂²×C₃	1	1	yes	characteristic, complemented
243	#398	C₂²×C₃	1	2	yes	complemented
244	#397	C₂²×C₃	1	2	yes	—
245	#397	C₂²×C₃	1	2	yes	—
246	#397	C₂²×C₃	1	2	yes	—
247	#397	C₂²×C₃	1	2	yes	—
248	#397	C₂²×C₃	1	2	yes	—
249	#397	C₂²×C₃	1	2	yes	complemented
250	#397	C₂²×C₃	1	1	yes	characteristic, complemented
251	#396	C₂²×C₃	1	2	yes	—
252	#396	C₂²×C₃	1	2	yes	—
253	#394	C₂²×C₃	1	2	yes	—
254	#394	C₂²×C₃	1	2	yes	—
255	#394	C₂²×C₃	1	2	yes	—
256	#389	C₂²×C₃	1	2	yes	complemented
257	#389	C₂²×C₃	1	2	yes	complemented
258	#389	C₂²×C₃	1	2	yes	complemented
259	#389	C₂²×C₃	1	2	yes	complemented
260	#388	C₂²×C₃	1	2	yes	—
261	#388	C₂²×C₃	1	2	yes	—
262	#388	C₂²×C₃	1	2	yes	—
263	#388	C₂²×C₃	1	2	yes	—
264	#388	C₂²×C₃	1	2	yes	—
265	#388	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	complemented
269	#387	C₂²×C₃	1	2	yes	complemented
270	#387	C₂²×C₃	1	2	yes	complemented
271	#387	C₂²×C₃	1	2	yes	complemented
272	#387	C₂²×C₃	1	2	yes	complemented
273	#387	C₂²×C₃	1	2	yes	complemented
274	#387	C₂²×C₃	1	2	yes	complemented
275	#387	C₂²×C₃	1	2	yes	complemented
276	#386	C₂²×C₃	1	2	yes	—
277	#386	C₂²×C₃	1	2	yes	—
278	#386	C₂²×C₃	1	2	yes	—
279	#385	C₂²×C₃	1	2	yes	—
280	#385	C₂²×C₃	1	2	yes	—
281	#385	C₂²×C₃	1	2	yes	—
282	#385	C₂²×C₃	1	2	yes	—
283	#385	C₂²×C₃	1	2	yes	complemented
284	#383	C₂²×C₃	1	2	yes	complemented
285	#383	C₂²×C₃	1	1	yes	characteristic, complemented
286	#382	C₂²×C₃	1	2	yes	complemented
287	#381	C₂²×C₃	1	1	yes	characteristic
288	#381	C₂²×C₃	1	1	yes	characteristic
289	#380	C₂²×C₃	1	1	yes	characteristic
290	#380	C₂²×C₃	1	2	yes	—
291	#380	C₂²×C₃	1	2	yes	—
292	#380	C₂²×C₃	1	1	yes	characteristic, complemented
293	#379	C₂²×C₃	1	2	yes	—
294	#379	C₂²×C₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
296	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
297	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
298	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
299	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
300	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
306	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
308	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
309	#376	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
311	C₂⁴×C₃	—	2	2	no	—
312	C₂⁴×C₃	—	2	4	no	—
313	C₂⁴×C₃	—	4	2	no	—
314	C₂⁴×C₃	—	4	1	no	—
315	C₂⁴×C₃	—	4	1	no	—
316	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
317	C₂⁴×C₃	C₂⁴	1	2	yes	—
318	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₃×D₄	—	2	2	no	—
320	C₂×C₃×D₄	—	2	4	no	—
321	C₂×C₃×D₄	—	2	4	no	—
322	C₂×C₃×D₄	—	2	2	no	—
323	C₂×C₃×D₄	—	4	1	no	—
324	C₂×C₃×D₄	—	4	2	no	—
325	C₂²×C₃×C₄	—	2	4	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	2	4	no	—
328	C₂²×C₃×C₄	—	2	4	no	—
329	C₂²×C₃×C₄	—	2	4	no	—
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	4	2	no	—
332	C₂²×C₃×C₄	—	4	2	no	—
333	C₂²×C₃×C₄	—	4	2	no	—
334	C₂²×C₃×C₄	—	4	1	no	—
335	C₂²×C₃×C₄	—	4	2	no	—
336	C₂²×C₃×C₄	—	4	2	no	—
337	C₂²×C₃×C₄	—	4	2	no	—
338	C₂²×C₃×C₄	—	4	2	no	—
339	C₂²×C₃×C₄	—	4	1	no	—
340	C₂²×C₃×C₄	#41	1	4	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
350	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
357	C₃×C₄⋊C₄	—	2	2	no	—
358	C₃×C₄⋊C₄	—	2	2	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	—	2	4	no	—
364	C₃×C₄⋊C₄	—	2	4	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	2	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	2	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₂²⋊C₄	—	2	4	no	—
376	C₃×C₂²⋊C₄	—	2	4	no	—
377	C₃×C₂²⋊C₄	—	2	2	no	—
378	C₃×C₂²⋊C₄	—	2	4	no	—
379	C₃×C₂²⋊C₄	—	2	4	no	—
380	C₃×C₂²⋊C₄	—	2	4	no	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	4	no	—
385	C₃×C₂²⋊C₄	—	2	4	no	—
386	C₃×C₂²⋊C₄	—	2	4	no	—
387	C₃×C₂²⋊C₄	—	2	2	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₂²⋊C₄	—	4	2	no	—
391	C₃×C₂²⋊C₄	—	4	2	no	—
392	C₃×C₂²⋊C₄	—	4	2	no	—
393	C₃×C₂²⋊C₄	—	4	2	no	—
394	C₃×C₂²⋊C₄	—	4	1	no	—
395	C₃×C₂²⋊C₄	—	4	2	no	—
396	C₃×C₂²⋊C₄	—	4	1	no	—
397	C₃×C₂²⋊C₄	#41	1	8	yes	—
398	C₃×C₄²	—	2	4	no	—
399	C₃×C₄²	—	2	2	no	—
400	C₃×C₄²	—	2	4	no	—
401	C₃×C₄²	—	4	2	no	—
402	C₃×C₄²	—	4	2	no	—
403	C₃×C₄²	—	4	2	no	—
404	C₃×C₄²	—	4	2	no	—
405	C₃×C₄²	—	4	2	no	—
406	C₃×C₄²	—	4	2	no	—
407	C₂⁵	C₂³×C₃	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₃	1	2	yes	—
410	C₂³×C₄	C₂³×C₃	1	2	yes	—
411	C₂³×C₄	C₂³×C₃	1	2	yes	—
412	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₃	1	2	yes	—
414	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
416	#126	—	2	8	no	—
417	#123	—	2	8	no	—
418	#123	—	4	2	no	—
419	#120	—	4	2	no	—
420	C₄×D₄	—	2	4	no	—
421	C₄×D₄	—	4	4	no	—
422	#117	—	2	4	no	—
423	#117	—	4	4	no	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₂²⋊C₄	—	2	8	no	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₃	1	2	yes	—
470	C₂×C₄²	C₂³×C₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₃	1	2	yes	—
474	C₂×C₄²	C₂³×C₃	1	2	yes	—
475	C₂×C₄²	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	1	yes	characteristic
477	#95	C₂³×C₃	1	1	yes	characteristic
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	1	yes	characteristic
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	1	yes	characteristic
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	1	yes	characteristic
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	1	yes	characteristic
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	2	yes	—
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	2	yes	—
504	C₂³×C₃	—	2	8	no	—
505	C₂³×C₃	—	2	2	no	—
506	C₂³×C₃	—	2	2	no	—
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	2	no	—
509	C₂³×C₃	—	2	2	no	—
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	2	2	no	—
512	C₂³×C₃	—	2	1	no	—
513	C₂³×C₃	—	2	2	no	—
514	C₂³×C₃	—	2	2	no	—
515	C₂³×C₃	—	2	2	no	—
516	C₂³×C₃	—	2	2	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	8	2	no	—
520	C₂³×C₃	—	8	2	no	—
521	C₂³×C₃	—	8	4	no	—
522	C₂³×C₃	—	8	4	no	—
523	C₂³×C₃	C₂×#41	1	4	yes	—
524	C₂³×C₃	C₂×#41	1	2	yes	—
525	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
526	C₂³×C₃	C₂⁵	1	1	yes	characteristic
527	C₃×D₄	—	4	4	no	—
528	C₃×D₄	—	4	8	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	4	4	no	—
570	C₂×C₃×C₄	—	4	8	no	—
571	C₂×C₃×C₄	—	8	2	no	—
572	C₂×C₃×C₄	—	8	4	no	—
573	C₂×C₃×C₄	—	8	4	no	—
574	C₂×C₃×C₄	—	8	2	no	—
575	C₂×C₃×C₄	C₂×#41	1	2	yes	—
576	C₂×C₃×C₄	C₂×#41	1	4	yes	—
577	C₂×C₃×C₄	C₂×#41	1	2	yes	—
578	C₂×C₃×C₄	C₂×#41	1	4	yes	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	—	2	4	no	—
581	C₂⁴	—	4	1	no	—
582	C₂⁴	—	4	2	no	—
583	C₂⁴	—	4	1	no	—
584	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
585	C₂⁴	C₂⁴×C₃	1	2	yes	—
586	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	4	2	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	C₃×#41	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	C₃×#41	1	8	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	4	2	no	—
670	C₄²	—	4	2	no	—
671	C₄²	—	4	2	no	—
672	C₄²	—	4	2	no	—
673	C₄²	—	4	2	no	—
674	C₄²	—	4	2	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	2	4	no	—
677	C₂²×C₃	—	2	2	no	—
678	C₂²×C₃	—	2	2	no	—
679	C₂²×C₃	—	2	2	no	—
680	C₂²×C₃	—	2	4	no	—
681	C₂²×C₃	—	2	4	no	—
682	C₂²×C₃	—	2	4	no	—
683	C₂²×C₃	—	4	1	no	—
684	C₂²×C₃	—	4	1	no	—
685	C₂²×C₃	—	4	2	no	—
686	C₂²×C₃	—	4	2	no	—
687	C₂²×C₃	—	4	2	no	—
688	C₂²×C₃	—	4	2	no	—
689	C₂²×C₃	—	4	2	no	—
690	C₂²×C₃	—	4	2	no	—
691	C₂²×C₃	—	4	2	no	—
692	C₂²×C₃	—	8	8	no	—
693	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
694	C₂²×C₃	C₂²×#41	1	2	yes	—
695	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₃	#585	1	2	yes	—
697	C₂²×C₃	#585	1	1	yes	characteristic
698	C₃×C₄	—	2	2	no	—
699	C₃×C₄	—	2	2	no	—
700	C₃×C₄	—	2	4	no	—
701	C₃×C₄	—	2	4	no	—
702	C₃×C₄	—	4	1	no	—
703	C₃×C₄	—	4	2	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	2	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	1	no	—
708	C₃×C₄	—	4	2	no	—
709	C₃×C₄	—	4	2	no	—
710	C₃×C₄	—	4	2	no	—
711	C₃×C₄	—	4	2	no	—
712	C₃×C₄	—	4	2	no	—
713	C₃×C₄	—	4	2	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	8	2	no	—
730	C₂³	—	8	2	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₂×C₃×#41	1	4	yes	—
734	C₂³	C₂×C₃×#41	1	2	yes	—
735	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
736	C₂³	C₂⁵×C₃	1	1	yes	characteristic
737	D₄	—	4	4	no	—
738	D₄	—	4	8	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	8	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	C₂×C₃×#41	1	2	yes	—
786	C₂×C₄	C₂×C₃×#41	1	4	yes	—
787	C₂×C₄	C₂×C₃×#41	1	2	yes	—
788	C₂×C₄	C₂×C₃×#41	1	4	yes	—
789	C₂×C₃	—	4	2	no	—
790	C₂×C₃	—	4	2	no	—
791	C₂×C₃	—	4	4	no	—
792	C₂×C₃	#3444	1	1	yes	characteristic
793	C₂×C₃	#3491	1	1	yes	characteristic
794	C₂×C₃	#3494	1	1	yes	characteristic
795	C₂×C₃	#3513	1	2	yes	—
796	C₂×C₃	#3521	1	2	yes	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	8	8	no	—
815	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
816	C₂²	C₂²×C₃×#41	1	2	yes	—
817	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
818	C₂²	C₃×#585	1	2	yes	—
819	C₂²	C₃×#585	1	1	yes	characteristic
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₃	#35851	1	1	yes	characteristic, direct product factor, Sylow
837	C₂	—	4	2	no	—
838	C₂	—	4	4	no	—
839	C₂	—	4	2	no	—
840	C₂	C₃×#3444	1	1	yes	characteristic
841	C₂	C₃×#3491	1	1	yes	characteristic
842	C₂	C₃×#3494	1	1	yes	characteristic
843	C₂	C₃×#3513	1	2	yes	—
844	C₂	C₃×#3521	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	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×#2667	C₂	semidirect
2. C₃×#2652	C₂	semidirect
3. C₃×#2578	C₂	semidirect
4. C₃×#2575	C₂	semidirect
5. C₃×#2553	C₂	semidirect
7. C₃×#2522	C₂	semidirect
8. C₃×#2495	C₂	semidirect
9. C₃×#2482	C₂	semidirect
10. C₃×#2480	C₂	semidirect
11. C₃×#2470	C₂	semidirect
13. C₃×#2395	C₂	semidirect
14. C₃×#2395	C₂	semidirect
15. C₃×#2373	C₂	semidirect
16. C₃×#2359	C₂	semidirect
17. C₃×#2353	C₂	semidirect
18. C₃×#2347	C₂	semidirect
19. C₃×#2273	C₂	semidirect
20. #35851	C₃	direct (N × H)
28. C₂×C₃×#117	C₂²	semidirect
31. C₃×#400	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
37. C₃×#399	C₂²	semidirect
38. C₃×#398	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#397	C₂²	semidirect
53. C₃×#389	C₂²	semidirect
54. C₃×#389	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
66. C₃×#387	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
68. C₃×#387	C₂²	semidirect
69. C₃×#387	C₂²	semidirect
70. C₃×#387	C₂²	semidirect
71. C₃×#387	C₂²	semidirect
72. C₃×#387	C₂²	semidirect
80. C₃×#385	C₂²	semidirect
81. C₃×#383	C₂²	semidirect
82. C₃×#383	C₂²	semidirect
83. C₃×#382	C₂²	semidirect
89. C₃×#380	C₂²	semidirect
92. C₃×C₄×C₄⋊C₄	C₂²	semidirect
93. C₃×C₄×C₄⋊C₄	C₂²	semidirect
94. C₃×C₄×C₄⋊C₄	C₂²	semidirect
95. C₃×C₄×C₄⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×#376	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2667	C₂×C₃	semidirect
109. #2652	C₂×C₃	semidirect
110. #2578	C₂×C₃	semidirect
111. #2575	C₂×C₃	semidirect
112. #2553	C₂×C₃	semidirect
114. #2522	C₂×C₃	semidirect
115. #2495	C₂×C₃	semidirect
116. #2482	C₂×C₃	semidirect
117. #2480	C₂×C₃	semidirect
118. #2470	C₂×C₃	semidirect
120. #2395	C₂×C₃	semidirect
121. #2395	C₂×C₃	semidirect
122. #2373	C₂×C₃	semidirect
123. #2359	C₂×C₃	semidirect
124. #2353	C₂×C₃	semidirect
125. #2347	C₂×C₃	semidirect
126. #2273	C₂×C₃	semidirect
231. C₂×#117	C₂²×C₃	semidirect
234. #400	C₂²×C₃	semidirect
235. #400	C₂²×C₃	semidirect
236. #400	C₂²×C₃	semidirect
237. #400	C₂²×C₃	semidirect
240. #399	C₂²×C₃	semidirect
241. #398	C₂²×C₃	semidirect
242. #398	C₂²×C₃	semidirect
243. #398	C₂²×C₃	semidirect
249. #397	C₂²×C₃	semidirect
250. #397	C₂²×C₃	semidirect
256. #389	C₂²×C₃	semidirect
257. #389	C₂²×C₃	semidirect
258. #389	C₂²×C₃	semidirect
259. #389	C₂²×C₃	semidirect
268. #388	C₂²×C₃	semidirect
269. #387	C₂²×C₃	semidirect
270. #387	C₂²×C₃	semidirect
271. #387	C₂²×C₃	semidirect
272. #387	C₂²×C₃	semidirect
273. #387	C₂²×C₃	semidirect
274. #387	C₂²×C₃	semidirect
275. #387	C₂²×C₃	semidirect
283. #385	C₂²×C₃	semidirect
284. #383	C₂²×C₃	semidirect
285. #383	C₂²×C₃	semidirect
286. #382	C₂²×C₃	semidirect
292. #380	C₂²×C₃	semidirect
295. C₄×C₄⋊C₄	C₂²×C₃	semidirect
296. C₄×C₄⋊C₄	C₂²×C₃	semidirect
297. C₄×C₄⋊C₄	C₂²×C₃	semidirect
298. C₄×C₄⋊C₄	C₂²×C₃	semidirect
307. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
308. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
309. #376	C₂²×C₃	semidirect
310. C₂×#95	C₂²×C₃	semidirect
836. C₃	#35851	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×#2667	2
C₃×#2652	2
C₃×#2578	2
C₃×#2575	2
C₃×#2553	2
C₃×#2534	2
C₃×#2522	2
C₃×#2495	2
C₃×#2482	2
C₃×#2480	2
C₃×#2470	2
C₃×#2418	2
C₃×#2395	2
C₃×#2373	2
C₃×#2359	2
C₃×#2353	2
C₃×#2347	2
C₃×#2273	2
#35851	3

Subgroups — C3×#35851 #10654458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35851 #10654458