Subgroups — C₃×#36184 #10654791

Order 768.

2302 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#553	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2553	C₂	1	4	yes	maximal, complemented
9	C₃×#2519	C₂	1	4	yes	maximal, complemented
10	C₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2500	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2499	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2425	C₂	1	4	yes	maximal, complemented
15	C₃×#2359	C₂	1	4	yes	maximal, complemented
16	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
20	#36184	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#553	—	2	8	no	—
22	C₃×#552	—	2	8	no	—
23	C₂×C₃×#126	C₂²	1	2	yes	—
24	C₂×C₃×#126	C₂²	1	2	yes	—
25	C₂×C₃×#125	C₂²	1	2	yes	—
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×#123	C₂²	1	2	yes	—
31	C₂×C₃×#123	C₂²	1	4	yes	—
32	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×#121	C₂²	1	2	yes	—
35	C₂×C₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃×#117	C₂²	1	2	yes	—
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
49	C₃×#399	C₂²	1	4	yes	—
50	C₃×#398	C₂²	1	4	yes	—
51	C₃×#398	C₂²	1	4	yes	—
52	C₃×#397	C₂²	1	4	yes	—
53	C₃×#396	C₂²	1	4	yes	—
54	C₃×#394	C₂²	1	4	yes	—
55	C₃×#391	C₂²	1	1	yes	characteristic
56	C₃×#391	C₂²	1	1	yes	characteristic
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#390	C₂²	1	1	yes	characteristic
59	C₃×#390	C₂²	1	1	yes	characteristic
60	C₃×#390	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	4	yes	—
62	C₃×#389	C₂²	1	4	yes	—
63	C₃×#388	C₂²	1	4	yes	—
64	C₃×#388	C₂²	1	4	yes	—
65	C₃×#388	C₂²	1	4	yes	—
66	C₃×#388	C₂²	1	4	yes	—
67	C₃×#387	C₂²	1	4	yes	—
68	C₃×#387	C₂²	1	4	yes	—
69	C₃×#386	C₂²	1	4	yes	—
70	C₃×#386	C₂²	1	4	yes	—
71	C₃×#385	C₂²	1	4	yes	—
72	C₃×#385	C₂²	1	4	yes	—
73	C₃×#384	C₂²	1	1	yes	characteristic
74	C₃×#384	C₂²	1	1	yes	characteristic
75	C₃×#384	C₂²	1	1	yes	characteristic
76	C₃×#384	C₂²	1	1	yes	characteristic
77	C₃×#382	C₂²	1	1	yes	characteristic
78	C₃×#382	C₂²	1	1	yes	characteristic
79	C₃×#382	C₂²	1	4	yes	—
80	C₃×#382	C₂²	1	1	yes	characteristic
81	C₃×#382	C₂²	1	1	yes	characteristic
82	C₃×#382	C₂²	1	1	yes	characteristic
83	C₃×#380	C₂²	1	4	yes	—
84	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
85	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
86	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
87	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
89	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
90	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
91	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
92	C₂×C₃×#95	C₂²	1	4	yes	—
93	C₃×C₄³	C₂²	1	1	yes	characteristic
94	C₂×#553	C₂×C₃	1	1	yes	characteristic
95	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
96	#2859	C₂×C₃	1	1	yes	characteristic, complemented
97	#2850	C₂×C₃	1	1	yes	characteristic, complemented
98	#2850	C₂×C₃	1	1	yes	characteristic, complemented
99	#2566	C₂×C₃	1	1	yes	characteristic, complemented
100	#2565	C₂×C₃	1	1	yes	characteristic, complemented
101	#2553	C₂×C₃	1	4	yes	complemented
102	#2519	C₂×C₃	1	4	yes	complemented
103	#2502	C₂×C₃	1	1	yes	characteristic, complemented
104	#2501	C₂×C₃	1	1	yes	characteristic, complemented
105	#2500	C₂×C₃	1	1	yes	characteristic, complemented
106	#2499	C₂×C₃	1	1	yes	characteristic, complemented
107	#2425	C₂×C₃	1	4	yes	complemented
108	#2359	C₂×C₃	1	4	yes	complemented
109	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
110	#2285	C₂×C₃	1	1	yes	characteristic, complemented
111	C₂×#382	C₂×C₃	1	1	yes	characteristic, complemented
112	C₄²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
114	C₂²×C₃×D₄	C₂³	1	2	yes	—
115	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃×D₄	C₂³	1	2	yes	—
118	C₂³×C₃×C₄	C₂³	1	2	yes	—
119	C₂³×C₃×C₄	C₂³	1	2	yes	—
120	C₂³×C₃×C₄	C₂³	1	2	yes	—
121	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂³	1	2	yes	—
124	C₂³×C₃×C₄	C₂³	1	2	yes	—
125	C₃×#126	—	2	8	no	—
126	C₃×#126	—	2	8	no	—
127	C₃×#125	—	2	8	no	—
128	C₃×#125	—	2	4	no	—
129	C₃×#125	—	2	4	no	—
130	C₃×#124	—	2	4	no	—
131	C₃×#123	—	2	8	no	—
132	C₃×#123	—	2	8	no	—
133	C₃×#123	—	2	16	no	—
134	C₃×C₂²⋊Q₈	—	2	4	no	—
135	C₃×C₂²⋊Q₈	—	2	4	no	—
136	C₃×#121	—	2	8	no	—
137	C₃×#121	—	2	4	no	—
138	C₃×#121	—	2	4	no	—
139	C₃×C₄×Q₈	—	2	4	no	—
140	C₃×C₄×D₄	—	2	8	no	—
141	C₃×C₄×D₄	—	2	8	no	—
142	C₃×C₄×D₄	—	2	4	no	—
143	C₃×C₄×D₄	D₄	1	8	yes	—
144	C₃×#117	—	2	4	no	—
145	C₃×#117	—	2	4	no	—
146	C₃×#117	—	2	8	no	—
147	C₂×C₃×C₄⋊C₄	—	2	4	no	—
148	C₂×C₃×C₄⋊C₄	—	2	4	no	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	4	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	4	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄²	—	2	4	no	—
186	C₂×C₃×C₄²	—	2	4	no	—
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
193	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
199	C₃×#95	C₂³	1	4	yes	—
200	C₃×#95	C₂³	1	4	yes	—
201	C₃×#95	C₂³	1	4	yes	—
202	C₃×#95	C₂³	1	4	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	4	yes	—
207	C₃×#95	C₂³	1	4	yes	—
208	C₃×#95	C₂³	1	4	yes	—
209	C₃×#95	C₂³	1	4	yes	—
210	#553	—	2	8	no	—
211	#552	—	2	8	no	—
212	C₂×#126	C₂²×C₃	1	2	yes	—
213	C₂×#126	C₂²×C₃	1	2	yes	—
214	C₂×#125	C₂²×C₃	1	1	yes	characteristic
215	C₂×#125	C₂²×C₃	1	1	yes	characteristic
216	C₂×#125	C₂²×C₃	1	2	yes	—
217	C₂×#124	C₂²×C₃	1	1	yes	characteristic
218	C₂×#123	C₂²×C₃	1	4	yes	—
219	C₂×#123	C₂²×C₃	1	2	yes	—
220	C₂×#123	C₂²×C₃	1	2	yes	—
221	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
223	C₂×#121	C₂²×C₃	1	1	yes	characteristic
224	C₂×#121	C₂²×C₃	1	1	yes	characteristic
225	C₂×#121	C₂²×C₃	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
230	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
231	C₂×#117	C₂²×C₃	1	2	yes	—
232	C₂×#117	C₂²×C₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
238	#399	C₂²×C₃	1	4	yes	—
239	#398	C₂²×C₃	1	4	yes	—
240	#398	C₂²×C₃	1	4	yes	—
241	#397	C₂²×C₃	1	4	yes	—
242	#396	C₂²×C₃	1	4	yes	—
243	#394	C₂²×C₃	1	4	yes	—
244	#391	C₂²×C₃	1	1	yes	characteristic
245	#391	C₂²×C₃	1	1	yes	characteristic
246	#391	C₂²×C₃	1	1	yes	characteristic
247	#390	C₂²×C₃	1	1	yes	characteristic
248	#390	C₂²×C₃	1	1	yes	characteristic
249	#390	C₂²×C₃	1	1	yes	characteristic
250	#389	C₂²×C₃	1	4	yes	—
251	#389	C₂²×C₃	1	4	yes	—
252	#388	C₂²×C₃	1	4	yes	—
253	#388	C₂²×C₃	1	4	yes	—
254	#388	C₂²×C₃	1	4	yes	—
255	#388	C₂²×C₃	1	4	yes	—
256	#387	C₂²×C₃	1	4	yes	—
257	#387	C₂²×C₃	1	4	yes	—
258	#386	C₂²×C₃	1	4	yes	—
259	#386	C₂²×C₃	1	4	yes	—
260	#385	C₂²×C₃	1	4	yes	—
261	#385	C₂²×C₃	1	4	yes	—
262	#384	C₂²×C₃	1	1	yes	characteristic
263	#384	C₂²×C₃	1	1	yes	characteristic
264	#384	C₂²×C₃	1	1	yes	characteristic
265	#384	C₂²×C₃	1	1	yes	characteristic
266	#382	C₂²×C₃	1	1	yes	characteristic
267	#382	C₂²×C₃	1	1	yes	characteristic
268	#382	C₂²×C₃	1	1	yes	characteristic
269	#382	C₂²×C₃	1	1	yes	characteristic
270	#382	C₂²×C₃	1	4	yes	—
271	#382	C₂²×C₃	1	1	yes	characteristic
272	#380	C₂²×C₃	1	4	yes	—
273	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
275	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
276	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
281	C₂×#95	C₂²×C₃	1	4	yes	—
282	C₄³	C₂²×C₃	1	1	yes	characteristic
283	C₂⁴×C₃	C₂⁴	1	2	yes	—
284	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
286	C₂×C₃×Q₈	—	2	2	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	2	2	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	4	no	—
291	C₂×C₃×D₄	—	2	8	no	—
292	C₂×C₃×D₄	—	2	4	no	—
293	C₂×C₃×D₄	—	2	2	no	—
294	C₂×C₃×D₄	—	2	2	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	4	4	no	—
297	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
298	C₂²×C₃×C₄	—	2	2	no	—
299	C₂²×C₃×C₄	—	2	2	no	—
300	C₂²×C₃×C₄	—	2	2	no	—
301	C₂²×C₃×C₄	—	2	2	no	—
302	C₂²×C₃×C₄	—	2	4	no	—
303	C₂²×C₃×C₄	—	2	4	no	—
304	C₂²×C₃×C₄	—	2	8	no	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	4	no	—
310	C₂²×C₃×C₄	—	4	2	no	—
311	C₂²×C₃×C₄	—	4	2	no	—
312	C₂²×C₃×C₄	—	4	4	no	—
313	C₂²×C₃×C₄	—	4	4	no	—
314	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
315	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
319	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
320	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
321	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
322	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
323	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
324	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
329	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
330	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
331	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
332	C₃×C₄⋊C₄	—	2	2	no	—
333	C₃×C₄⋊C₄	—	2	2	no	—
334	C₃×C₄⋊C₄	—	2	2	no	—
335	C₃×C₄⋊C₄	—	2	2	no	—
336	C₃×C₄⋊C₄	—	2	4	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	2	4	no	—
343	C₃×C₄⋊C₄	—	2	4	no	—
344	C₃×C₄⋊C₄	—	2	4	no	—
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	4	no	—
348	C₃×C₄⋊C₄	—	2	8	no	—
349	C₃×C₄⋊C₄	—	2	8	no	—
350	C₃×C₄⋊C₄	—	4	4	no	—
351	C₃×C₄⋊C₄	—	4	4	no	—
352	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	4	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	4	no	—
360	C₃×C₂²⋊C₄	—	2	4	no	—
361	C₃×C₂²⋊C₄	—	2	8	no	—
362	C₃×C₂²⋊C₄	—	2	8	no	—
363	C₃×C₂²⋊C₄	—	2	8	no	—
364	C₃×C₂²⋊C₄	—	4	4	no	—
365	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
366	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
367	C₃×C₂²⋊C₄	#41	1	8	yes	—
368	C₃×C₄²	—	2	4	no	—
369	C₃×C₄²	—	2	4	no	—
370	C₃×C₄²	—	2	4	no	—
371	C₃×C₄²	—	2	4	no	—
372	C₃×C₄²	—	2	2	no	—
373	C₃×C₄²	—	2	4	no	—
374	C₃×C₄²	—	2	2	no	—
375	C₃×C₄²	—	2	4	no	—
376	C₃×C₄²	—	2	2	no	—
377	C₃×C₄²	—	4	2	no	—
378	C₃×C₄²	C₂×D₄	1	4	yes	—
379	C₃×C₄²	#41	1	4	yes	—
380	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
381	C₂²×D₄	C₂³×C₃	1	2	yes	—
382	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₃	1	2	yes	—
386	C₂³×C₄	C₂³×C₃	1	2	yes	—
387	C₂³×C₄	C₂³×C₃	1	2	yes	—
388	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₃	1	2	yes	—
392	#126	—	2	8	no	—
393	#126	—	2	8	no	—
394	#125	—	2	8	no	—
395	#125	—	2	4	no	—
396	#125	—	2	4	no	—
397	#124	—	2	4	no	—
398	#123	—	2	8	no	—
399	#123	—	2	8	no	—
400	#123	—	2	16	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	#121	—	2	8	no	—
404	#121	—	2	4	no	—
405	#121	—	2	4	no	—
406	C₄×Q₈	—	2	4	no	—
407	C₄×D₄	—	2	8	no	—
408	C₄×D₄	—	2	8	no	—
409	C₄×D₄	—	2	4	no	—
410	C₄×D₄	C₃×D₄	1	8	yes	—
411	#117	—	2	4	no	—
412	#117	—	2	4	no	—
413	#117	—	2	8	no	—
414	C₂×C₄⋊C₄	—	2	4	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₄²	—	2	4	no	—
453	C₂×C₄²	—	2	4	no	—
454	C₂×C₄²	C₂³×C₃	1	2	yes	—
455	C₂×C₄²	C₂³×C₃	1	2	yes	—
456	C₂×C₄²	C₂³×C₃	1	2	yes	—
457	C₂×C₄²	C₂³×C₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₃	1	2	yes	—
464	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
466	#95	C₂³×C₃	1	4	yes	—
467	#95	C₂³×C₃	1	4	yes	—
468	#95	C₂³×C₃	1	4	yes	—
469	#95	C₂³×C₃	1	4	yes	—
470	#95	C₂³×C₃	1	2	yes	—
471	#95	C₂³×C₃	1	2	yes	—
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	4	yes	—
474	#95	C₂³×C₃	1	4	yes	—
475	#95	C₂³×C₃	1	4	yes	—
476	#95	C₂³×C₃	1	4	yes	—
477	C₂³×C₃	—	2	1	no	—
478	C₂³×C₃	—	2	1	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	1	no	—
482	C₂³×C₃	—	2	1	no	—
483	C₂³×C₃	—	2	2	no	—
484	C₂³×C₃	—	2	2	no	—
485	C₂³×C₃	—	2	4	no	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	2	4	no	—
489	C₂³×C₃	C₂²×D₄	1	2	yes	—
490	C₂³×C₃	C₂²×D₄	1	2	yes	—
491	C₂³×C₃	C₂×#41	1	4	yes	—
492	C₂³×C₃	C₂⁵	1	1	yes	characteristic
493	C₃×Q₈	—	4	4	no	—
494	C₃×D₄	—	2	8	no	—
495	C₃×D₄	—	4	8	no	—
496	C₃×D₄	—	4	4	no	—
497	C₃×D₄	—	8	4	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	2	no	—
510	C₂×C₃×C₄	—	2	8	no	—
511	C₂×C₃×C₄	—	2	8	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	2	no	—
517	C₂×C₃×C₄	—	2	2	no	—
518	C₂×C₃×C₄	—	2	2	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	4	no	—
522	C₂×C₃×C₄	—	2	4	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	4	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	4	no	—
528	C₂×C₃×C₄	—	2	4	no	—
529	C₂×C₃×C₄	—	2	4	no	—
530	C₂×C₃×C₄	—	4	8	no	—
531	C₂×C₃×C₄	—	4	8	no	—
532	C₂×C₃×C₄	—	4	8	no	—
533	C₂×C₃×C₄	—	8	4	no	—
534	C₂×C₃×C₄	—	8	4	no	—
535	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
536	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
537	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
538	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
539	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
540	C₂×C₃×C₄	C₂×#41	1	4	yes	—
541	C₂×C₃×C₄	C₂×#41	1	4	yes	—
542	C₂×C₃×C₄	C₂×#41	1	4	yes	—
543	C₂×C₃×C₄	C₂×#41	1	2	yes	—
544	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
545	C₂⁴	C₂⁴×C₃	1	2	yes	—
546	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
547	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
577	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
628	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
629	C₂²⋊C₄	C₃×#41	1	8	yes	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	4	2	no	—
640	C₄²	C₂×C₃×D₄	1	4	yes	—
641	C₄²	C₃×#41	1	4	yes	—
642	C₂²×C₃	—	2	2	no	—
643	C₂²×C₃	—	2	4	no	—
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	4	no	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	4	2	no	—
650	C₂²×C₃	—	4	2	no	—
651	C₂²×C₃	—	4	2	no	—
652	C₂²×C₃	—	4	2	no	—
653	C₂²×C₃	—	4	4	no	—
654	C₂²×C₃	—	4	2	no	—
655	C₂²×C₃	—	4	4	no	—
656	C₂²×C₃	#532	1	4	yes	—
657	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
658	C₂²×C₃	C₂²×#41	1	2	yes	—
659	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
660	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
661	C₂²×C₃	#585	1	2	yes	—
662	C₃×C₄	—	2	2	no	—
663	C₃×C₄	—	2	2	no	—
664	C₃×C₄	—	2	2	no	—
665	C₃×C₄	—	2	4	no	—
666	C₃×C₄	—	2	4	no	—
667	C₃×C₄	—	2	2	no	—
668	C₃×C₄	—	2	4	no	—
669	C₃×C₄	—	4	2	no	—
670	C₃×C₄	—	4	2	no	—
671	C₃×C₄	—	4	2	no	—
672	C₃×C₄	—	4	2	no	—
673	C₃×C₄	—	4	2	no	—
674	C₃×C₄	—	4	2	no	—
675	C₃×C₄	—	4	2	no	—
676	C₃×C₄	—	4	2	no	—
677	C₃×C₄	#547	1	4	yes	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	C₂²×C₃×D₄	1	2	yes	—
691	C₂³	C₂²×C₃×D₄	1	2	yes	—
692	C₂³	C₂×C₃×#41	1	4	yes	—
693	C₂³	C₂⁵×C₃	1	1	yes	characteristic
694	Q₈	—	4	4	no	—
695	D₄	—	2	8	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	4	no	—
698	D₄	—	8	4	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	4	8	no	—
733	C₂×C₄	—	4	8	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
737	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
738	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
739	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
740	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
741	C₂×C₄	C₂×C₃×#41	1	4	yes	—
742	C₂×C₄	C₂×C₃×#41	1	4	yes	—
743	C₂×C₄	C₂×C₃×#41	1	4	yes	—
744	C₂×C₄	C₂×C₃×#41	1	2	yes	—
745	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
746	C₂×C₃	—	2	4	no	—
747	C₂×C₃	—	4	2	no	—
748	C₂×C₃	—	8	2	no	—
749	C₂×C₃	C₂×#532	1	1	yes	characteristic
750	C₂×C₃	C₂×#547	1	1	yes	characteristic
751	C₂×C₃	#3475	1	2	yes	—
752	C₂×C₃	#3500	1	1	yes	characteristic
753	C₂×C₃	#3515	1	2	yes	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	4	no	—
768	C₂²	C₃×#532	1	4	yes	—
769	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
770	C₂²	C₂²×C₃×#41	1	2	yes	—
771	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
772	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
773	C₂²	C₃×#585	1	2	yes	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	4	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	4	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₃×#547	1	4	yes	—
790	C₃	#36184	1	1	yes	characteristic, direct product factor, Sylow
791	C₂	—	2	4	no	—
792	C₂	—	4	2	no	—
793	C₂	—	8	2	no	—
794	C₂	C₂×C₃×#532	1	1	yes	characteristic
795	C₂	C₂×C₃×#547	1	1	yes	characteristic
796	C₂	C₃×#3475	1	2	yes	—
797	C₂	C₃×#3500	1	1	yes	characteristic
798	C₂	C₃×#3515	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#553	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#552	C₂	semidirect
3. C₃×#2859	C₂	semidirect
4. C₃×#2850	C₂	semidirect
5. C₃×#2850	C₂	semidirect
6. C₃×#2566	C₂	semidirect
7. C₃×#2565	C₂	semidirect
8. C₃×#2553	C₂	semidirect
9. C₃×#2519	C₂	semidirect
10. C₃×#2502	C₂	semidirect
11. C₃×#2501	C₂	semidirect
12. C₃×#2500	C₂	semidirect
13. C₃×#2499	C₂	semidirect
14. C₃×#2425	C₂	semidirect
15. C₃×#2359	C₂	semidirect
16. C₃×C₄×#124	C₂	semidirect
17. C₃×#2285	C₂	semidirect
18. C₂×C₃×#382	C₂	semidirect
19. C₃×C₄²×D₄	C₂	semidirect
20. #36184	C₃	direct (N × H)
95. C₂×#552	C₂×C₃	semidirect
96. #2859	C₂×C₃	semidirect
97. #2850	C₂×C₃	semidirect
98. #2850	C₂×C₃	semidirect
99. #2566	C₂×C₃	semidirect
100. #2565	C₂×C₃	semidirect
101. #2553	C₂×C₃	semidirect
102. #2519	C₂×C₃	semidirect
103. #2502	C₂×C₃	semidirect
104. #2501	C₂×C₃	semidirect
105. #2500	C₂×C₃	semidirect
106. #2499	C₂×C₃	semidirect
107. #2425	C₂×C₃	semidirect
108. #2359	C₂×C₃	semidirect
109. C₄×#124	C₂×C₃	semidirect
110. #2285	C₂×C₃	semidirect
111. C₂×#382	C₂×C₃	semidirect
112. C₄²×D₄	C₂×C₃	semidirect
790. C₃	#36184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#553	2
C₂×C₃×#552	2
C₃×#2859	2
C₃×#2850	2
C₃×#2566	2
C₃×#2565	2
C₃×#2553	2
C₃×#2519	2
C₃×#2502	2
C₃×#2501	2
C₃×#2500	2
C₃×#2499	2
C₃×#2425	2
C₃×#2359	2
C₃×C₄×#124	2
C₃×#2285	2
C₂×C₃×#382	2
C₃×C₄²×D₄	2
#36184	3

Subgroups — C3×#36184 #10654791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36184 #10654791