Subgroups — C₃×#22472 #10641079

Order 768.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	#22472	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
21	C₃×#529	—	2	4	no	—
22	C₃×#529	—	2	4	no	—
23	C₂×C₃×#126	C₄	1	1	yes	characteristic
24	C₂×C₃×#126	C₄	1	1	yes	characteristic
25	C₂×C₃×#125	C₄	1	1	yes	characteristic
26	C₂×C₃×#124	C₄	1	1	yes	characteristic
27	C₂×C₃×#123	C₄	1	1	yes	characteristic
28	C₂×C₃×#123	C₄	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
30	C₂×C₃×#121	C₄	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₃×#436	—	2	4	no	—
39	C₃×#435	—	2	4	no	—
40	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×#97	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
52	C₃×#336	C₂²	1	1	yes	characteristic
53	C₃×#336	C₂²	1	1	yes	characteristic
54	C₃×#336	C₂²	1	1	yes	characteristic
55	C₃×#336	C₂²	1	1	yes	characteristic
56	C₃×#336	C₂²	1	1	yes	characteristic
57	C₃×#336	C₂²	1	1	yes	characteristic
58	C₃×#336	C₂²	1	1	yes	characteristic
59	C₃×#336	C₂²	1	1	yes	characteristic
60	C₃×#336	C₂²	1	1	yes	characteristic
61	C₃×#336	C₂²	1	1	yes	characteristic
62	C₃×#336	C₂²	1	1	yes	characteristic
63	C₃×#336	C₂²	1	1	yes	characteristic
64	C₂×#529	C₂×C₃	1	1	yes	characteristic
65	C₂×#436	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#435	C₂×C₃	1	1	yes	characteristic, complemented
67	#1985	C₂×C₃	1	1	yes	characteristic, complemented
68	#1984	C₂×C₃	1	1	yes	characteristic, complemented
69	#1870	C₂×C₃	1	1	yes	characteristic, complemented
70	#1870	C₂×C₃	1	1	yes	characteristic, complemented
71	#1870	C₂×C₃	1	1	yes	characteristic, complemented
72	#1869	C₂×C₃	1	1	yes	characteristic, complemented
73	#1818	C₂×C₃	1	1	yes	characteristic, complemented
74	#1817	C₂×C₃	1	1	yes	characteristic, complemented
75	#1798	C₂×C₃	1	1	yes	characteristic, complemented
76	#1750	C₂×C₃	1	1	yes	characteristic, complemented
77	#1729	C₂×C₃	1	1	yes	characteristic, complemented
78	#1728	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×M₁₆	—	2	2	no	—
89	C₂×C₃×M₁₆	—	2	2	no	—
90	C₂×C₃×M₁₆	—	2	2	no	—
91	C₂×C₃×M₁₆	—	2	2	no	—
92	C₂×C₃×M₁₆	—	2	2	no	—
93	C₂×C₃×M₁₆	—	2	2	no	—
94	C₂×C₃×M₁₆	—	4	1	no	—
95	C₂×C₃×M₁₆	—	4	1	no	—
96	C₂×C₃×M₁₆	—	4	1	no	—
97	C₂²×C₃×C₈	—	2	2	no	—
98	C₂²×C₃×C₈	—	2	2	no	—
99	C₂²×C₃×C₈	—	4	1	no	—
100	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
108	C₃×#126	—	2	4	no	—
109	C₃×#126	—	2	4	no	—
110	C₃×#125	—	2	4	no	—
111	C₃×#124	—	2	4	no	—
112	C₃×#123	—	2	4	no	—
113	C₃×#123	—	2	4	no	—
114	C₃×C₂²⋊Q₈	—	2	4	no	—
115	C₃×#121	—	2	4	no	—
116	C₃×C₄×Q₈	—	2	2	no	—
117	C₃×C₄×Q₈	—	2	2	no	—
118	C₃×C₄×D₄	—	2	2	no	—
119	C₃×C₄×D₄	—	2	2	no	—
120	C₃×C₄×D₄	—	2	2	no	—
121	C₃×C₄×D₄	—	2	2	no	—
122	C₃×C₄×D₄	D₄	1	4	yes	—
123	C₃×C₄×D₄	D₄	1	4	yes	—
124	C₃×#117	—	2	2	no	—
125	C₃×#117	—	2	2	no	—
126	C₃×#117	—	2	2	no	—
127	C₃×#117	—	2	2	no	—
128	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
139	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
142	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
145	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄²	—	2	2	no	—
149	C₂×C₃×C₄²	—	2	2	no	—
150	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
156	C₃×C₄⋊C₈	—	2	2	no	—
157	C₃×C₄⋊C₈	—	2	2	no	—
158	C₃×C₂²⋊C₈	—	2	2	no	—
159	C₃×C₂²⋊C₈	—	2	2	no	—
160	C₃×C₂²⋊C₈	—	2	2	no	—
161	C₃×C₂²⋊C₈	—	2	2	no	—
162	C₃×C₂²⋊C₈	—	2	2	no	—
163	C₃×C₂²⋊C₈	—	2	2	no	—
164	C₃×C₂²⋊C₈	—	4	1	no	—
165	C₃×C₂²⋊C₈	—	4	1	no	—
166	C₃×#97	—	2	2	no	—
167	C₃×C₄×C₈	—	2	2	no	—
168	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
169	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
170	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
172	#529	—	2	4	no	—
173	#529	—	2	4	no	—
174	C₂×#126	C₃×C₄	1	1	yes	characteristic
175	C₂×#126	C₃×C₄	1	1	yes	characteristic
176	C₂×#125	C₃×C₄	1	1	yes	characteristic
177	C₂×#124	C₃×C₄	1	1	yes	characteristic
178	C₂×#123	C₃×C₄	1	1	yes	characteristic
179	C₂×#123	C₃×C₄	1	1	yes	characteristic
180	C₂×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
181	C₂×#121	C₃×C₄	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
185	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
186	C₂×#117	C₂²×C₃	1	1	yes	characteristic
187	C₂×#117	C₂²×C₃	1	1	yes	characteristic
188	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
189	#436	—	2	4	no	—
190	#435	—	2	4	no	—
191	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
193	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
194	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
195	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
196	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
201	C₂×#97	C₂²×C₃	1	1	yes	characteristic
202	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
203	#336	C₂²×C₃	1	1	yes	characteristic
204	#336	C₂²×C₃	1	1	yes	characteristic
205	#336	C₂²×C₃	1	1	yes	characteristic
206	#336	C₂²×C₃	1	1	yes	characteristic
207	#336	C₂²×C₃	1	1	yes	characteristic
208	#336	C₂²×C₃	1	1	yes	characteristic
209	#336	C₂²×C₃	1	1	yes	characteristic
210	#336	C₂²×C₃	1	1	yes	characteristic
211	#336	C₂²×C₃	1	1	yes	characteristic
212	#336	C₂²×C₃	1	1	yes	characteristic
213	#336	C₂²×C₃	1	1	yes	characteristic
214	#336	C₂²×C₃	1	1	yes	characteristic
215	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
216	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
217	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×Q₈	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	4	1	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	—	2	2	no	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	—	4	1	no	—
225	C₂×C₃×D₄	—	4	1	no	—
226	C₂×C₃×D₄	—	4	1	no	—
227	C₂×C₃×D₄	—	4	1	no	—
228	C₂×C₃×D₄	—	4	1	no	—
229	C₂×C₃×D₄	C₂²⋊C₄	1	4	yes	—
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	—	2	1	no	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	4	1	no	—
248	C₂²×C₃×C₄	—	4	1	no	—
249	C₂²×C₃×C₄	—	4	1	no	—
250	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
262	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
263	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
264	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
265	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
266	C₃×M₁₆	—	4	4	no	—
267	C₃×M₁₆	—	4	4	no	—
268	C₃×M₁₆	—	4	4	no	—
269	C₂×C₃×C₈	—	2	1	no	—
270	C₂×C₃×C₈	—	2	1	no	—
271	C₂×C₃×C₈	—	2	1	no	—
272	C₂×C₃×C₈	—	2	1	no	—
273	C₂×C₃×C₈	—	2	1	no	—
274	C₂×C₃×C₈	—	2	1	no	—
275	C₂×C₃×C₈	—	2	1	no	—
276	C₂×C₃×C₈	—	2	1	no	—
277	C₂×C₃×C₈	—	2	1	no	—
278	C₂×C₃×C₈	—	2	1	no	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	2	1	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	2	1	no	—
285	C₂×C₃×C₈	—	2	1	no	—
286	C₂×C₃×C₈	—	2	1	no	—
287	C₂×C₃×C₈	—	2	1	no	—
288	C₂×C₃×C₈	—	2	1	no	—
289	C₂×C₃×C₈	—	2	1	no	—
290	C₂×C₃×C₈	—	2	1	no	—
291	C₂×C₃×C₈	—	4	4	no	—
292	C₂×C₃×C₈	#41	1	2	yes	—
293	C₂×C₃×C₈	#41	1	2	yes	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	2	no	—
296	C₃×C₄⋊C₄	—	2	2	no	—
297	C₃×C₄⋊C₄	—	2	2	no	—
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	2	no	—
300	C₃×C₄⋊C₄	—	2	2	no	—
301	C₃×C₄⋊C₄	—	2	2	no	—
302	C₃×C₄⋊C₄	—	2	2	no	—
303	C₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	C₃×C₂²⋊C₄	—	2	2	no	—
306	C₃×C₂²⋊C₄	—	2	2	no	—
307	C₃×C₂²⋊C₄	—	2	2	no	—
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×C₂²⋊C₄	—	2	2	no	—
311	C₃×C₂²⋊C₄	—	2	2	no	—
312	C₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
313	C₃×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
314	C₃×C₄²	—	2	2	no	—
315	C₃×C₄²	—	2	2	no	—
316	C₃×C₄²	—	2	1	no	—
317	C₃×C₄²	—	2	1	no	—
318	C₃×C₄²	—	2	1	no	—
319	C₃×C₄²	—	2	1	no	—
320	C₃×C₄²	—	2	1	no	—
321	C₃×C₄²	—	2	1	no	—
322	C₃×C₄²	C₂×D₄	1	2	yes	—
323	C₃×C₄²	C₂×D₄	1	2	yes	—
324	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
325	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
326	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
327	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
328	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
329	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	4	1	no	—
340	C₂×M₁₆	—	4	1	no	—
341	C₂×M₁₆	—	4	1	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	4	1	no	—
345	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
353	#126	—	2	4	no	—
354	#126	—	2	4	no	—
355	#125	—	2	4	no	—
356	#124	—	2	4	no	—
357	#123	—	2	4	no	—
358	#123	—	2	4	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	#121	—	2	4	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	C₃×D₄	1	4	yes	—
368	C₄×D₄	C₃×D₄	1	4	yes	—
369	#117	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
396	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
401	C₄⋊C₈	—	2	2	no	—
402	C₄⋊C₈	—	2	2	no	—
403	C₂²⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	C₂²⋊C₈	—	2	2	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	C₂²⋊C₈	—	2	2	no	—
409	C₂²⋊C₈	—	4	1	no	—
410	C₂²⋊C₈	—	4	1	no	—
411	#97	—	2	2	no	—
412	C₄×C₈	—	2	2	no	—
413	C₂³×C₃	—	2	1	no	—
414	C₂³×C₃	—	2	1	no	—
415	C₂³×C₃	—	2	1	no	—
416	C₂³×C₃	—	2	1	no	—
417	C₂³×C₃	—	2	1	no	—
418	C₂³×C₃	—	2	1	no	—
419	C₂³×C₃	—	2	1	no	—
420	C₂³×C₃	—	2	1	no	—
421	C₂³×C₃	—	2	1	no	—
422	C₂³×C₃	—	2	1	no	—
423	C₂³×C₃	—	2	1	no	—
424	C₂³×C₃	—	2	1	no	—
425	C₂³×C₃	—	2	1	no	—
426	C₂³×C₃	—	2	1	no	—
427	C₂³×C₃	—	2	1	no	—
428	C₂³×C₃	—	2	1	no	—
429	C₂³×C₃	—	2	1	no	—
430	C₂³×C₃	—	2	1	no	—
431	C₂³×C₃	—	2	1	no	—
432	C₂³×C₃	C₂×C₂²⋊C₄	1	2	yes	—
433	C₂³×C₃	C₂×C₂²⋊C₄	1	2	yes	—
434	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
435	C₃×Q₈	—	4	4	no	—
436	C₃×D₄	—	4	4	no	—
437	C₃×D₄	—	4	4	no	—
438	C₃×D₄	—	4	4	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	4	4	no	—
476	C₂×C₃×C₄	—	4	4	no	—
477	C₂×C₃×C₄	—	4	1	no	—
478	C₂×C₃×C₄	—	4	1	no	—
479	C₂×C₃×C₄	—	4	1	no	—
480	C₂×C₃×C₄	—	4	1	no	—
481	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
482	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
483	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
484	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	2	yes	—
485	C₂×C₃×C₄	#131	1	2	yes	—
486	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
490	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
491	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
492	C₃×C₈	—	2	2	no	—
493	C₃×C₈	—	2	2	no	—
494	C₃×C₈	—	4	1	no	—
495	C₃×C₈	—	4	1	no	—
496	C₃×C₈	—	4	1	no	—
497	C₃×C₈	—	4	1	no	—
498	C₃×C₈	—	4	1	no	—
499	C₃×C₈	—	4	1	no	—
500	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
501	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
502	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	4	1	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	—	4	1	no	—
513	C₂×D₄	—	4	1	no	—
514	C₂×D₄	C₃×C₂²⋊C₄	1	4	yes	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	1	no	—
535	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
547	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
548	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
549	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
551	M₁₆	—	4	4	no	—
552	M₁₆	—	4	4	no	—
553	M₁₆	—	4	4	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	4	4	no	—
577	C₂×C₈	C₃×#41	1	2	yes	—
578	C₂×C₈	C₃×#41	1	2	yes	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	C₃×C₂²⋊C₄	1	4	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	C₃×C₂²⋊C₄	1	4	yes	—
598	C₂²⋊C₄	C₃×C₂²⋊C₄	1	4	yes	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	C₂×C₃×D₄	1	2	yes	—
608	C₄²	C₂×C₃×D₄	1	2	yes	—
609	C₂²×C₃	—	2	2	no	—
610	C₂²×C₃	—	2	2	no	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	2	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	1	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	1	no	—
629	C₂²×C₃	—	4	1	no	—
630	C₂²×C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
631	C₂²×C₃	C₄×#41	1	1	yes	characteristic
632	C₂²×C₃	#520	1	1	yes	characteristic
633	C₂²×C₃	C₂×#131	1	1	yes	characteristic
634	C₂²×C₃	#568	1	1	yes	characteristic
635	C₂²×C₃	#568	1	1	yes	characteristic
636	C₂²×C₃	#568	1	1	yes	characteristic
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	2	2	no	—
639	C₃×C₄	—	2	2	no	—
640	C₃×C₄	—	2	2	no	—
641	C₃×C₄	—	2	2	no	—
642	C₃×C₄	—	4	1	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	#546	1	1	yes	characteristic
649	C₃×C₄	#546	1	1	yes	characteristic
650	C₃×C₄	#547	1	1	yes	characteristic
651	C₃×C₄	#547	1	1	yes	characteristic
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	C₂×C₃×C₂²⋊C₄	1	2	yes	—
672	C₂³	C₂×C₃×C₂²⋊C₄	1	2	yes	—
673	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
674	Q₈	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	2	yes	—
721	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	2	yes	—
722	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	2	yes	—
723	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	2	yes	—
724	C₂×C₄	C₃×#131	1	2	yes	—
725	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
726	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
727	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
728	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
729	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	4	1	no	—
734	C₈	—	4	1	no	—
735	C₈	—	4	1	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₂×C₃	—	4	2	no	—
740	C₂×C₃	—	4	2	no	—
741	C₂×C₃	—	8	1	no	—
742	C₂×C₃	#2339	1	1	yes	characteristic
743	C₂×C₃	#2879	1	1	yes	characteristic
744	C₂×C₃	#2880	1	1	yes	characteristic
745	C₂×C₃	#2967	1	1	yes	characteristic
746	C₂×C₃	#2969	1	1	yes	characteristic
747	C₂×C₃	#2993	1	1	yes	characteristic
748	C₂×C₃	#2995	1	1	yes	characteristic
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
771	C₂²	C₃×C₄×#41	1	1	yes	characteristic
772	C₂²	C₃×#520	1	1	yes	characteristic
773	C₂²	C₂×C₃×#131	1	1	yes	characteristic
774	C₂²	C₃×#568	1	1	yes	characteristic
775	C₂²	C₃×#568	1	1	yes	characteristic
776	C₂²	C₃×#568	1	1	yes	characteristic
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	C₃×#546	1	1	yes	characteristic
789	C₄	C₃×#546	1	1	yes	characteristic
790	C₄	C₃×#547	1	1	yes	characteristic
791	C₄	C₃×#547	1	1	yes	characteristic
792	C₃	#22472	1	1	yes	characteristic, direct product factor, Sylow
793	C₂	—	4	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	1	no	—
796	C₂	C₃×#2339	1	1	yes	characteristic
797	C₂	C₃×#2879	1	1	yes	characteristic
798	C₂	C₃×#2880	1	1	yes	characteristic
799	C₂	C₃×#2967	1	1	yes	characteristic
800	C₂	C₃×#2969	1	1	yes	characteristic
801	C₂	C₃×#2993	1	1	yes	characteristic
802	C₂	C₃×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂³	C₂³×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂×C₃×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#436	C₂	semidirect
3. C₂×C₃×#435	C₂	semidirect
4. C₃×#1985	C₂	semidirect
5. C₃×#1984	C₂	semidirect
6. C₃×#1870	C₂	semidirect
7. C₃×#1870	C₂	semidirect
8. C₃×#1870	C₂	semidirect
9. C₃×#1869	C₂	semidirect
10. C₃×#1818	C₂	semidirect
11. C₃×#1817	C₂	semidirect
12. C₃×#1798	C₂	semidirect
13. C₃×#1750	C₂	semidirect
14. C₃×#1729	C₂	semidirect
15. C₃×#1728	C₂	semidirect
16. #22472	C₃	direct (N × H)
65. C₂×#436	C₂×C₃	semidirect
66. C₂×#435	C₂×C₃	semidirect
67. #1985	C₂×C₃	semidirect
68. #1984	C₂×C₃	semidirect
69. #1870	C₂×C₃	semidirect
70. #1870	C₂×C₃	semidirect
71. #1870	C₂×C₃	semidirect
72. #1869	C₂×C₃	semidirect
73. #1818	C₂×C₃	semidirect
74. #1817	C₂×C₃	semidirect
75. #1798	C₂×C₃	semidirect
76. #1750	C₂×C₃	semidirect
77. #1729	C₂×C₃	semidirect
78. #1728	C₂×C₃	semidirect
792. C₃	#22472	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×#529	2
C₂×C₃×#436	2
C₂×C₃×#435	2
C₃×#1985	2
C₃×#1984	2
C₃×#1870	2
C₃×#1869	2
C₃×#1818	2
C₃×#1817	2
C₃×#1798	2
C₃×#1750	2
C₃×#1729	2
C₃×#1728	2
#22472	3

Subgroups — C3×#22472 #10641079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22472 #10641079