Subgroups — C₃×#34521 #10653128

Order 768.

2008 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#563	C₂	1	1	yes	maximal, characteristic
2	C₃×#2383	C₂	1	2	yes	maximal, complemented
3	C₃×#2381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₃×#2372	C₂	1	1	yes	maximal, characteristic
6	C₃×#2371	C₂	1	2	yes	maximal, complemented
7	C₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2368	C₂	1	2	yes	maximal, complemented
9	C₃×#2362	C₂	1	2	yes	maximal, complemented
10	C₃×#2359	C₂	1	2	yes	maximal
11	C₃×#2335	C₂	1	2	yes	maximal
12	C₃×#2334	C₂	1	2	yes	maximal, complemented
13	C₃×#2330	C₂	1	2	yes	maximal, complemented
14	C₃×#2329	C₂	1	2	yes	maximal, complemented
15	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2326	C₂	1	1	yes	maximal, characteristic
17	C₃×#2323	C₂	1	2	yes	maximal, complemented
18	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#126	C₂	1	2	yes	maximal, complemented
20	#34521	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#563	C₄	1	16	yes	complemented
22	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×#126	C₂²	1	2	yes	—
25	C₂×C₃×#126	C₂²	1	2	yes	—
26	C₂×C₃×#125	C₂²	1	2	yes	—
27	C₂×C₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	2	yes	—
37	C₃×#391	C₂²	1	1	yes	characteristic
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	1	yes	characteristic
40	C₃×#391	C₂²	1	1	yes	characteristic
41	C₃×#391	C₂²	1	1	yes	characteristic
42	C₃×#391	C₂²	1	1	yes	characteristic
43	C₃×#390	C₂²	1	1	yes	characteristic
44	C₃×#389	C₂²	1	2	yes	—
45	C₃×#389	C₂²	1	2	yes	—
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	2	yes	—
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#388	C₂²	1	2	yes	—
53	C₃×#388	C₂²	1	2	yes	—
54	C₃×#388	C₂²	1	2	yes	—
55	C₃×#388	C₂²	1	2	yes	—
56	C₃×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
63	C₃×#387	C₂²	1	2	yes	—
64	C₃×#387	C₂²	1	2	yes	—
65	C₃×#387	C₂²	1	2	yes	—
66	C₃×#387	C₂²	1	2	yes	—
67	C₃×#387	C₂²	1	2	yes	—
68	C₃×#387	C₂²	1	2	yes	—
69	C₃×#387	C₂²	1	2	yes	—
70	C₃×#387	C₂²	1	2	yes	—
71	C₃×#387	C₂²	1	2	yes	—
72	C₃×#387	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#386	C₂²	1	2	yes	—
79	C₃×#385	C₂²	1	2	yes	—
80	C₃×#385	C₂²	1	2	yes	—
81	C₃×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#384	C₂²	1	1	yes	characteristic
85	C₃×#384	C₂²	1	1	yes	characteristic
86	C₃×#383	C₂²	1	2	yes	—
87	C₃×#382	C₂²	1	1	yes	characteristic
88	C₃×#380	C₂²	1	2	yes	—
89	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
90	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
91	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
92	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
93	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
94	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
95	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
96	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
97	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
98	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
104	C₃×#376	C₂²	1	1	yes	characteristic
105	C₃×#376	C₂²	1	2	yes	—
106	C₃×#376	C₂²	1	1	yes	characteristic
107	C₂×C₃×#95	C₂²	1	2	yes	—
108	C₃×C₄³	C₂²	1	1	yes	characteristic
109	C₂×#563	C₂×C₃	1	1	yes	characteristic
110	#2383	C₂×C₃	1	2	yes	complemented
111	#2381	C₂×C₃	1	1	yes	characteristic, complemented
112	#2373	C₂×C₃	1	2	yes	complemented
113	#2372	C₂×C₃	1	1	yes	characteristic
114	#2371	C₂×C₃	1	2	yes	complemented
115	#2369	C₂×C₃	1	1	yes	characteristic, complemented
116	#2368	C₂×C₃	1	2	yes	complemented
117	#2362	C₂×C₃	1	2	yes	complemented
118	#2359	C₂×C₃	1	2	yes	—
119	#2335	C₂×C₃	1	2	yes	—
120	#2334	C₂×C₃	1	2	yes	complemented
121	#2330	C₂×C₃	1	2	yes	complemented
122	#2329	C₂×C₃	1	2	yes	complemented
123	#2327	C₂×C₃	1	1	yes	characteristic, complemented
124	#2326	C₂×C₃	1	1	yes	characteristic
125	#2323	C₂×C₃	1	2	yes	complemented
126	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
127	C₄×#126	C₂×C₃	1	2	yes	complemented
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×D₄	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	2	yes	—
135	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
136	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
137	C₃×#126	C₂×C₄	1	16	yes	complemented
138	C₃×#126	C₂×C₄	1	16	yes	complemented
139	C₃×#125	C₂×C₄	1	16	yes	complemented
140	C₃×#124	C₂×C₄	1	8	yes	—
141	C₃×#123	C₂×C₄	1	16	yes	—
142	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
143	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
144	C₃×C₄×Q₈	—	4	2	no	—
145	C₃×C₄×Q₈	—	4	2	no	—
146	C₃×C₄×Q₈	—	4	2	no	—
147	C₃×C₄×D₄	—	4	2	no	—
148	C₃×#117	—	4	4	no	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	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	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×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	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	2	yes	—
185	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄²	C₂³	1	2	yes	—
192	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	2	yes	—
198	C₂×C₃×C₄²	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	C₂³	1	2	yes	—
200	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	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	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	#563	C₃×C₄	1	16	yes	complemented
230	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
232	C₂×#126	C₂²×C₃	1	2	yes	—
233	C₂×#126	C₂²×C₃	1	2	yes	—
234	C₂×#125	C₂²×C₃	1	2	yes	—
235	C₂×#124	C₂²×C₃	1	1	yes	characteristic
236	C₂×#123	C₂²×C₃	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
238	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
243	C₂×#117	C₂²×C₃	1	2	yes	—
244	#391	C₂²×C₃	1	1	yes	characteristic
245	#391	C₂²×C₃	1	1	yes	characteristic
246	#391	C₂²×C₃	1	2	yes	—
247	#391	C₂²×C₃	1	1	yes	characteristic
248	#391	C₂²×C₃	1	1	yes	characteristic
249	#391	C₂²×C₃	1	1	yes	characteristic
250	#391	C₂²×C₃	1	2	yes	—
251	#390	C₂²×C₃	1	1	yes	characteristic
252	#389	C₂²×C₃	1	2	yes	—
253	#389	C₂²×C₃	1	2	yes	—
254	#389	C₂²×C₃	1	2	yes	—
255	#389	C₂²×C₃	1	2	yes	—
256	#389	C₂²×C₃	1	2	yes	—
257	#389	C₂²×C₃	1	2	yes	—
258	#389	C₂²×C₃	1	2	yes	—
259	#389	C₂²×C₃	1	2	yes	—
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	—
269	#388	C₂²×C₃	1	2	yes	—
270	#387	C₂²×C₃	1	2	yes	—
271	#387	C₂²×C₃	1	2	yes	—
272	#387	C₂²×C₃	1	2	yes	—
273	#387	C₂²×C₃	1	2	yes	—
274	#387	C₂²×C₃	1	2	yes	—
275	#387	C₂²×C₃	1	2	yes	—
276	#387	C₂²×C₃	1	2	yes	—
277	#387	C₂²×C₃	1	2	yes	—
278	#387	C₂²×C₃	1	2	yes	—
279	#387	C₂²×C₃	1	2	yes	—
280	#387	C₂²×C₃	1	2	yes	—
281	#387	C₂²×C₃	1	2	yes	—
282	#387	C₂²×C₃	1	2	yes	—
283	#387	C₂²×C₃	1	2	yes	—
284	#387	C₂²×C₃	1	2	yes	—
285	#387	C₂²×C₃	1	2	yes	—
286	#386	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	2	yes	—
288	#385	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	2	yes	—
291	#385	C₂²×C₃	1	2	yes	—
292	#384	C₂²×C₃	1	1	yes	characteristic
293	#384	C₂²×C₃	1	1	yes	characteristic
294	#383	C₂²×C₃	1	2	yes	—
295	#382	C₂²×C₃	1	1	yes	characteristic
296	#380	C₂²×C₃	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
303	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
305	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
308	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
312	#376	C₂²×C₃	1	1	yes	characteristic
313	#376	C₂²×C₃	1	1	yes	characteristic
314	#376	C₂²×C₃	1	2	yes	—
315	C₂×#95	C₂²×C₃	1	2	yes	—
316	C₄³	C₂²×C₃	1	1	yes	characteristic
317	C₂⁴×C₃	C₂⁴	1	2	yes	—
318	C₂×C₃×Q₈	—	4	1	no	—
319	C₂×C₃×Q₈	—	4	1	no	—
320	C₂×C₃×Q₈	—	4	1	no	—
321	C₂×C₃×Q₈	—	4	1	no	—
322	C₂×C₃×Q₈	—	4	1	no	—
323	C₂×C₃×Q₈	—	4	1	no	—
324	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
325	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
326	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
327	C₂×C₃×D₄	—	4	1	no	—
328	C₂×C₃×D₄	—	4	1	no	—
329	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
330	C₂²×C₃×C₄	—	2	4	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	2	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	C₂²×C₄	1	8	yes	—
339	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
340	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
349	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
350	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	4	no	—
358	C₃×C₄⋊C₄	—	2	4	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	1	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	1	no	—
369	C₃×C₄⋊C₄	—	4	1	no	—
370	C₃×C₄⋊C₄	—	4	1	no	—
371	C₃×C₄⋊C₄	—	4	1	no	—
372	C₃×C₄⋊C₄	—	4	1	no	—
373	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
374	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
375	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
376	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
377	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
378	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
379	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
380	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	4	2	no	—
384	C₃×C₂²⋊C₄	—	4	2	no	—
385	C₃×C₂²⋊C₄	—	4	2	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
388	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
389	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
390	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
391	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
392	C₃×C₄²	—	2	4	no	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	2	no	—
395	C₃×C₄²	—	2	2	no	—
396	C₃×C₄²	—	2	4	no	—
397	C₃×C₄²	—	2	4	no	—
398	C₃×C₄²	—	4	2	no	—
399	C₃×C₄²	—	4	2	no	—
400	C₃×C₄²	—	4	1	no	—
401	C₃×C₄²	—	4	2	no	—
402	C₃×C₄²	—	4	2	no	—
403	C₃×C₄²	—	4	2	no	—
404	C₃×C₄²	—	4	1	no	—
405	C₃×C₄²	—	4	1	no	—
406	C₃×C₄²	—	4	2	no	—
407	C₃×C₄²	—	4	2	no	—
408	C₃×C₄²	C₂²×C₄	1	4	yes	—
409	C₃×C₄²	C₂²×C₄	1	4	yes	—
410	C₃×C₄²	C₂²×C₄	1	4	yes	—
411	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₃	1	2	yes	—
416	C₂³×C₄	C₂³×C₃	1	2	yes	—
417	C₂³×C₄	C₂³×C₃	1	2	yes	—
418	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
419	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
420	#126	C₂×C₃×C₄	1	16	yes	complemented
421	#126	C₂×C₃×C₄	1	16	yes	complemented
422	#125	C₂×C₃×C₄	1	16	yes	complemented
423	#124	C₂×C₃×C₄	1	8	yes	—
424	#123	C₂×C₃×C₄	1	16	yes	—
425	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
426	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
427	C₄×Q₈	—	4	2	no	—
428	C₄×Q₈	—	4	2	no	—
429	C₄×Q₈	—	4	2	no	—
430	C₄×D₄	—	4	2	no	—
431	#117	—	4	4	no	—
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	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₄⋊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	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
470	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
476	C₂×C₄²	C₂³×C₃	1	2	yes	—
477	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₃	1	2	yes	—
481	C₂×C₄²	C₂³×C₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₃	1	2	yes	—
483	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄²	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	#95	C₂³×C₃	1	2	yes	—
505	#95	C₂³×C₃	1	2	yes	—
506	#95	C₂³×C₃	1	2	yes	—
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	2	yes	—
510	#95	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	2	yes	—
512	C₂³×C₃	—	2	2	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	2	no	—
518	C₂³×C₃	C₂³×C₄	1	4	yes	—
519	C₂³×C₃	C₂⁵	1	1	yes	characteristic
520	C₃×Q₈	—	4	4	no	—
521	C₃×Q₈	—	4	4	no	—
522	C₃×Q₈	—	4	4	no	—
523	C₃×D₄	—	4	4	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	2	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	2	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	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	2	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	2	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	—	4	8	no	—
565	C₂×C₃×C₄	—	8	4	no	—
566	C₂×C₃×C₄	—	8	4	no	—
567	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
568	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
569	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
570	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
571	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
572	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
573	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
574	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
575	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
576	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
577	C₂⁴	C₂⁴×C₃	1	2	yes	—
578	C₂×Q₈	—	4	1	no	—
579	C₂×Q₈	—	4	1	no	—
580	C₂×Q₈	—	4	1	no	—
581	C₂×Q₈	—	4	1	no	—
582	C₂×Q₈	—	4	1	no	—
583	C₂×Q₈	—	4	1	no	—
584	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
585	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
586	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃	1	2	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	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	1	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	1	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
634	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
635	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
636	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
637	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
638	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
639	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
640	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
648	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
649	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
650	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
651	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	2	no	—
660	C₄²	—	4	2	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	1	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	2	no	—
665	C₄²	—	4	2	no	—
666	C₄²	—	4	1	no	—
667	C₄²	—	4	1	no	—
668	C₄²	C₂²×C₃×C₄	1	4	yes	—
669	C₄²	C₂²×C₃×C₄	1	4	yes	—
670	C₄²	C₂²×C₃×C₄	1	4	yes	—
671	C₂²×C₃	—	2	4	no	—
672	C₂²×C₃	—	2	4	no	—
673	C₂²×C₃	—	2	4	no	—
674	C₂²×C₃	—	4	2	no	—
675	C₂²×C₃	—	4	2	no	—
676	C₂²×C₃	—	4	2	no	—
677	C₂²×C₃	—	4	2	no	—
678	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
679	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
681	C₂²×C₃	#585	1	1	yes	characteristic
682	C₂²×C₃	#585	1	2	yes	—
683	C₃×C₄	—	2	4	no	—
684	C₃×C₄	—	2	4	no	—
685	C₃×C₄	—	2	2	no	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	—	2	4	no	—
689	C₃×C₄	—	2	4	no	—
690	C₃×C₄	—	2	4	no	—
691	C₃×C₄	—	2	2	no	—
692	C₃×C₄	—	2	4	no	—
693	C₃×C₄	—	4	2	no	—
694	C₃×C₄	—	4	1	no	—
695	C₃×C₄	—	4	2	no	—
696	C₃×C₄	—	4	1	no	—
697	C₃×C₄	—	4	2	no	—
698	C₃×C₄	—	4	1	no	—
699	C₃×C₄	—	4	2	no	—
700	C₃×C₄	—	4	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	C₂³×C₃×C₄	1	4	yes	—
708	C₂³	C₂⁵×C₃	1	1	yes	characteristic
709	Q₈	—	4	4	no	—
710	Q₈	—	4	4	no	—
711	Q₈	—	4	4	no	—
712	D₄	—	4	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	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	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	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	2	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	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
757	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
758	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
759	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
760	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
761	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
762	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
763	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
764	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
766	C₂×C₃	—	4	4	no	—
767	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂×C₃	C₄×2₋¹⁺⁴	1	2	yes	—
769	C₂×C₃	#3544	1	1	yes	characteristic
770	C₂×C₃	#3551	1	1	yes	characteristic
771	C₂×C₃	#3564	1	2	yes	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
780	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
781	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
782	C₂²	C₃×#585	1	1	yes	characteristic
783	C₂²	C₃×#585	1	2	yes	—
784	C₄	—	2	4	no	—
785	C₄	—	2	4	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	4	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₃	#34521	1	1	yes	characteristic, direct product factor, Sylow
803	C₂	—	4	4	no	—
804	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂	C₃×C₄×2₋¹⁺⁴	1	2	yes	—
806	C₂	C₃×#3544	1	1	yes	characteristic
807	C₂	C₃×#3551	1	1	yes	characteristic
808	C₂	C₃×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2383	C₂	semidirect
3. C₃×#2381	C₂	semidirect
4. C₃×#2373	C₂	semidirect
6. C₃×#2371	C₂	semidirect
7. C₃×#2369	C₂	semidirect
8. C₃×#2368	C₂	semidirect
9. C₃×#2362	C₂	semidirect
12. C₃×#2334	C₂	semidirect
13. C₃×#2330	C₂	semidirect
14. C₃×#2329	C₂	semidirect
15. C₃×#2327	C₂	semidirect
17. C₃×#2323	C₂	semidirect
18. C₃×C₄×C₄⋊Q₈	C₂	semidirect
19. C₃×C₄×#126	C₂	semidirect
20. #34521	C₃	direct (N × H)
21. C₃×#563	C₄	semidirect
110. #2383	C₂×C₃	semidirect
111. #2381	C₂×C₃	semidirect
112. #2373	C₂×C₃	semidirect
114. #2371	C₂×C₃	semidirect
115. #2369	C₂×C₃	semidirect
116. #2368	C₂×C₃	semidirect
117. #2362	C₂×C₃	semidirect
120. #2334	C₂×C₃	semidirect
121. #2330	C₂×C₃	semidirect
122. #2329	C₂×C₃	semidirect
123. #2327	C₂×C₃	semidirect
125. #2323	C₂×C₃	semidirect
126. C₄×C₄⋊Q₈	C₂×C₃	semidirect
127. C₄×#126	C₂×C₃	semidirect
135. C₃×C₄⋊Q₈	C₂×C₄	semidirect
136. C₃×C₄⋊Q₈	C₂×C₄	semidirect
137. C₃×#126	C₂×C₄	semidirect
138. C₃×#126	C₂×C₄	semidirect
139. C₃×#125	C₂×C₄	semidirect
142. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
143. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
229. #563	C₃×C₄	semidirect
418. C₄⋊Q₈	C₂×C₃×C₄	semidirect
419. C₄⋊Q₈	C₂×C₃×C₄	semidirect
420. #126	C₂×C₃×C₄	semidirect
421. #126	C₂×C₃×C₄	semidirect
422. #125	C₂×C₃×C₄	semidirect
425. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
426. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
802. C₃	#34521	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×#563	2
C₃×#2383	2
C₃×#2381	2
C₃×#2373	2
C₃×#2372	2
C₃×#2371	2
C₃×#2369	2
C₃×#2368	2
C₃×#2362	2
C₃×#2359	2
C₃×#2335	2
C₃×#2334	2
C₃×#2330	2
C₃×#2329	2
C₃×#2327	2
C₃×#2326	2
C₃×#2323	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#126	2
#34521	3

Subgroups — C3×#34521 #10653128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34521 #10653128