Subgroups — C₃×#35899 #10654506

Order 768.

1536 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2654	C₂	1	2	yes	maximal
2	C₃×#2645	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2596	C₂	1	2	yes	maximal
4	C₃×#2594	C₂	1	2	yes	maximal
5	C₃×#2529	C₂	1	2	yes	maximal
6	C₃×#2528	C₂	1	2	yes	maximal, complemented
7	C₃×#2528	C₂	1	2	yes	maximal, complemented
8	C₃×#2508	C₂	1	2	yes	maximal, complemented
9	C₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2489	C₂	1	1	yes	maximal, characteristic
11	C₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2429	C₂	1	1	yes	maximal, characteristic
14	C₃×#2423	C₂	1	1	yes	maximal, characteristic
15	C₃×#2402	C₂	1	2	yes	maximal, complemented
16	C₃×#2401	C₂	1	1	yes	maximal, characteristic
17	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2362	C₂	1	1	yes	maximal, characteristic
20	C₃×#2362	C₂	1	1	yes	maximal, characteristic
21	C₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2346	C₂	1	1	yes	maximal, characteristic
23	C₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
24	#35899	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	C₂²	1	1	yes	characteristic
34	C₃×#401	C₂²	1	2	yes	—
35	C₃×#401	C₂²	1	1	yes	characteristic
36	C₃×#400	C₂²	1	2	yes	—
37	C₃×#400	C₂²	1	2	yes	—
38	C₃×#400	C₂²	1	2	yes	—
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	1	yes	characteristic
41	C₃×#400	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	1	yes	characteristic
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#399	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#398	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	2	yes	—
51	C₃×#398	C₂²	1	2	yes	—
52	C₃×#397	C₂²	1	1	yes	characteristic
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	1	yes	characteristic
55	C₃×#397	C₂²	1	1	yes	characteristic
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	1	yes	characteristic
61	C₃×#391	C₂²	1	1	yes	characteristic
62	C₃×#391	C₂²	1	1	yes	characteristic
63	C₃×#391	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	2	yes	—
67	C₃×#389	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	1	yes	characteristic
71	C₃×#389	C₂²	1	2	yes	—
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	2	yes	—
74	C₃×#389	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#388	C₂²	1	2	yes	—
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#387	C₂²	1	2	yes	—
95	C₃×#387	C₂²	1	2	yes	—
96	C₃×#387	C₂²	1	2	yes	—
97	C₃×#384	C₂²	1	1	yes	characteristic
98	C₃×#382	C₂²	1	2	yes	—
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	1	yes	characteristic
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	2	yes	—
123	C₃×#376	C₂²	1	2	yes	—
124	#2654	C₂×C₃	1	2	yes	—
125	#2645	C₂×C₃	1	1	yes	characteristic, complemented
126	#2596	C₂×C₃	1	2	yes	—
127	#2594	C₂×C₃	1	2	yes	—
128	#2529	C₂×C₃	1	2	yes	—
129	#2528	C₂×C₃	1	2	yes	complemented
130	#2528	C₂×C₃	1	2	yes	complemented
131	#2508	C₂×C₃	1	2	yes	complemented
132	#2507	C₂×C₃	1	1	yes	characteristic, complemented
133	#2489	C₂×C₃	1	1	yes	characteristic
134	#2453	C₂×C₃	1	1	yes	characteristic, complemented
135	#2446	C₂×C₃	1	1	yes	characteristic, complemented
136	#2429	C₂×C₃	1	1	yes	characteristic
137	#2423	C₂×C₃	1	1	yes	characteristic
138	#2402	C₂×C₃	1	2	yes	complemented
139	#2401	C₂×C₃	1	1	yes	characteristic
140	#2370	C₂×C₃	1	1	yes	characteristic, complemented
141	#2365	C₂×C₃	1	1	yes	characteristic, complemented
142	#2362	C₂×C₃	1	1	yes	characteristic
143	#2362	C₂×C₃	1	1	yes	characteristic
144	#2355	C₂×C₃	1	1	yes	characteristic, complemented
145	#2346	C₂×C₃	1	1	yes	characteristic
146	#2276	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
150	C₃×C₄⋊Q₈	—	2	4	no	—
151	C₃×#125	—	2	4	no	—
152	C₃×C₂²⋊Q₈	—	2	4	no	—
153	C₃×C₂²⋊Q₈	—	2	4	no	—
154	C₃×C₄×Q₈	—	2	4	no	—
155	C₃×C₄×Q₈	—	2	4	no	—
156	C₃×C₄×Q₈	—	2	4	no	—
157	C₃×C₄×Q₈	—	2	4	no	—
158	C₃×#117	—	2	4	no	—
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	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	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂³	1	2	yes	—
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₂×C₃×C₄²	C₂³	1	2	yes	—
205	C₂×C₃×C₄²	C₂³	1	2	yes	—
206	C₂×C₃×C₄²	C₂³	1	2	yes	—
207	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄²	C₂³	1	2	yes	—
211	C₂×C₃×C₄²	C₂³	1	2	yes	—
212	C₂×C₃×C₄²	C₂³	1	2	yes	—
213	C₂×C₃×C₄²	C₂³	1	2	yes	—
214	C₂×C₃×C₄²	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	1	yes	characteristic
216	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
221	C₃×#95	C₂³	1	1	yes	characteristic
222	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
227	C₃×#95	C₂³	1	1	yes	characteristic
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₂×#125	C₂²×C₃	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
263	C₂×#117	C₂²×C₃	1	1	yes	characteristic
264	#401	C₂²×C₃	1	2	yes	—
265	#401	C₂²×C₃	1	1	yes	characteristic
266	#400	C₂²×C₃	1	2	yes	—
267	#400	C₂²×C₃	1	2	yes	—
268	#400	C₂²×C₃	1	2	yes	—
269	#400	C₂²×C₃	1	2	yes	—
270	#400	C₂²×C₃	1	2	yes	—
271	#400	C₂²×C₃	1	1	yes	characteristic
272	#400	C₂²×C₃	1	1	yes	characteristic
273	#400	C₂²×C₃	1	1	yes	characteristic
274	#400	C₂²×C₃	1	2	yes	—
275	#399	C₂²×C₃	1	2	yes	—
276	#398	C₂²×C₃	1	2	yes	—
277	#398	C₂²×C₃	1	2	yes	—
278	#398	C₂²×C₃	1	2	yes	—
279	#398	C₂²×C₃	1	2	yes	—
280	#398	C₂²×C₃	1	2	yes	—
281	#398	C₂²×C₃	1	2	yes	—
282	#397	C₂²×C₃	1	1	yes	characteristic
283	#397	C₂²×C₃	1	1	yes	characteristic
284	#397	C₂²×C₃	1	1	yes	characteristic
285	#397	C₂²×C₃	1	2	yes	—
286	#396	C₂²×C₃	1	2	yes	—
287	#396	C₂²×C₃	1	1	yes	characteristic
288	#391	C₂²×C₃	1	1	yes	characteristic
289	#391	C₂²×C₃	1	1	yes	characteristic
290	#391	C₂²×C₃	1	1	yes	characteristic
291	#391	C₂²×C₃	1	1	yes	characteristic
292	#391	C₂²×C₃	1	1	yes	characteristic
293	#391	C₂²×C₃	1	1	yes	characteristic
294	#389	C₂²×C₃	1	2	yes	—
295	#389	C₂²×C₃	1	2	yes	—
296	#389	C₂²×C₃	1	1	yes	characteristic
297	#389	C₂²×C₃	1	1	yes	characteristic
298	#389	C₂²×C₃	1	1	yes	characteristic
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	1	yes	characteristic
301	#389	C₂²×C₃	1	2	yes	—
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	2	yes	—
304	#389	C₂²×C₃	1	2	yes	—
305	#388	C₂²×C₃	1	2	yes	—
306	#388	C₂²×C₃	1	2	yes	—
307	#388	C₂²×C₃	1	2	yes	—
308	#388	C₂²×C₃	1	2	yes	—
309	#388	C₂²×C₃	1	2	yes	—
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#387	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#387	C₂²×C₃	1	2	yes	—
323	#387	C₂²×C₃	1	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#384	C₂²×C₃	1	1	yes	characteristic
328	#382	C₂²×C₃	1	2	yes	—
329	#382	C₂²×C₃	1	2	yes	—
330	#382	C₂²×C₃	1	2	yes	—
331	#380	C₂²×C₃	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
333	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
335	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
336	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	#376	C₂²×C₃	1	2	yes	—
352	#376	C₂²×C₃	1	1	yes	characteristic
353	#376	C₂²×C₃	1	2	yes	—
354	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₃×Q₈	—	2	2	no	—
356	C₂×C₃×Q₈	—	2	2	no	—
357	C₂×C₃×Q₈	—	2	2	no	—
358	C₂×C₃×Q₈	—	2	2	no	—
359	C₂×C₃×Q₈	—	2	2	no	—
360	C₂×C₃×Q₈	#41	1	4	yes	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	2	no	—
363	C₂²×C₃×C₄	—	2	2	no	—
364	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₃×C₄⋊C₄	—	2	2	no	—
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₄⋊C₄	—	2	4	no	—
390	C₃×C₄⋊C₄	—	2	2	no	—
391	C₃×C₄⋊C₄	—	2	4	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	2	4	no	—
394	C₃×C₄⋊C₄	—	2	4	no	—
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	2	2	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	4	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	4	no	—
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	4	2	no	—
406	C₃×C₄⋊C₄	—	4	1	no	—
407	C₃×C₄⋊C₄	—	4	2	no	—
408	C₃×C₄⋊C₄	—	4	2	no	—
409	C₃×C₄⋊C₄	—	4	2	no	—
410	C₃×C₄⋊C₄	—	4	1	no	—
411	C₃×C₄⋊C₄	—	4	2	no	—
412	C₃×C₄⋊C₄	—	4	2	no	—
413	C₃×C₄⋊C₄	—	4	2	no	—
414	C₃×C₄⋊C₄	#41	1	4	yes	—
415	C₃×C₄⋊C₄	#41	1	4	yes	—
416	C₃×C₂²⋊C₄	—	2	4	no	—
417	C₃×C₂²⋊C₄	—	2	4	no	—
418	C₃×C₂²⋊C₄	—	2	4	no	—
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₂²⋊C₄	—	2	2	no	—
421	C₃×C₂²⋊C₄	—	4	1	no	—
422	C₃×C₂²⋊C₄	—	4	1	no	—
423	C₃×C₂²⋊C₄	—	4	1	no	—
424	C₃×C₂²⋊C₄	—	4	1	no	—
425	C₃×C₂²⋊C₄	—	4	2	no	—
426	C₃×C₄²	—	2	4	no	—
427	C₃×C₄²	—	2	2	no	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	2	4	no	—
430	C₃×C₄²	—	2	4	no	—
431	C₃×C₄²	—	2	4	no	—
432	C₃×C₄²	—	2	2	no	—
433	C₃×C₄²	—	2	2	no	—
434	C₃×C₄²	—	2	2	no	—
435	C₃×C₄²	—	2	2	no	—
436	C₃×C₄²	—	2	2	no	—
437	C₃×C₄²	—	2	4	no	—
438	C₃×C₄²	—	4	2	no	—
439	C₃×C₄²	—	4	2	no	—
440	C₃×C₄²	—	4	2	no	—
441	C₃×C₄²	—	4	2	no	—
442	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
445	C₄⋊Q₈	—	2	4	no	—
446	#125	—	2	4	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	2	4	no	—
451	C₄×Q₈	—	2	4	no	—
452	C₄×Q₈	—	2	4	no	—
453	#117	—	2	4	no	—
454	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄²	C₂³×C₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₃	1	2	yes	—
500	C₂×C₄²	C₂³×C₃	1	2	yes	—
501	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₃	1	2	yes	—
503	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₃	1	2	yes	—
506	C₂×C₄²	C₂³×C₃	1	2	yes	—
507	C₂×C₄²	C₂³×C₃	1	2	yes	—
508	C₂×C₄²	C₂³×C₃	1	2	yes	—
509	C₂×C₄²	C₂³×C₃	1	2	yes	—
510	#95	C₂³×C₃	1	1	yes	characteristic
511	#95	C₂³×C₃	1	1	yes	characteristic
512	#95	C₂³×C₃	1	2	yes	—
513	#95	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	2	yes	—
515	#95	C₂³×C₃	1	1	yes	characteristic
516	#95	C₂³×C₃	1	1	yes	characteristic
517	#95	C₂³×C₃	1	1	yes	characteristic
518	#95	C₂³×C₃	1	2	yes	—
519	#95	C₂³×C₃	1	2	yes	—
520	#95	C₂³×C₃	1	2	yes	—
521	#95	C₂³×C₃	1	1	yes	characteristic
522	#95	C₂³×C₃	1	1	yes	characteristic
523	#95	C₂³×C₃	1	1	yes	characteristic
524	#95	C₂³×C₃	1	1	yes	characteristic
525	#95	C₂³×C₃	1	1	yes	characteristic
526	#95	C₂³×C₃	1	1	yes	characteristic
527	#95	C₂³×C₃	1	2	yes	—
528	#95	C₂³×C₃	1	2	yes	—
529	#95	C₂³×C₃	1	1	yes	characteristic
530	#95	C₂³×C₃	1	1	yes	characteristic
531	#95	C₂³×C₃	1	2	yes	—
532	#95	C₂³×C₃	1	2	yes	—
533	#95	C₂³×C₃	1	2	yes	—
534	#95	C₂³×C₃	1	1	yes	characteristic
535	#95	C₂³×C₃	1	1	yes	characteristic
536	#95	C₂³×C₃	1	1	yes	characteristic
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	2	yes	—
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	2	yes	—
548	#95	C₂³×C₃	1	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
550	C₂³×C₃	—	2	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	2	1	no	—
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	—	2	1	no	—
557	C₂³×C₃	C₂⁵	1	1	yes	characteristic
558	C₃×Q₈	—	2	8	no	—
559	C₃×Q₈	—	4	4	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	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	1	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	4	4	no	—
619	C₂×C₃×C₄	C₂×#41	1	4	yes	—
620	C₂×C₃×C₄	C₂×#41	1	4	yes	—
621	C₂×C₃×C₄	C₂×#41	1	4	yes	—
622	C₂×C₃×C₄	C₂×#41	1	2	yes	—
623	C₂×C₃×C₄	C₂×#41	1	2	yes	—
624	C₂×C₃×C₄	C₂×#41	1	2	yes	—
625	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
626	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
627	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	C₃×#41	1	4	yes	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	C₃×#41	1	4	yes	—
688	C₄⋊C₄	C₃×#41	1	4	yes	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	4	1	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	4	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₂²×C₃	—	4	1	no	—
716	C₂²×C₃	—	4	1	no	—
717	C₂²×C₃	—	4	1	no	—
718	C₂²×C₃	—	4	1	no	—
719	C₂²×C₃	—	4	1	no	—
720	C₂²×C₃	—	4	1	no	—
721	C₂²×C₃	—	4	1	no	—
722	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
723	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
724	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
725	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
726	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
727	C₂²×C₃	#585	1	1	yes	characteristic
728	C₂²×C₃	#585	1	1	yes	characteristic
729	C₃×C₄	—	2	4	no	—
730	C₃×C₄	—	2	4	no	—
731	C₃×C₄	—	2	4	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	2	2	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	2	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	1	no	—
738	C₃×C₄	—	4	1	no	—
739	C₃×C₄	—	4	1	no	—
740	C₃×C₄	—	4	1	no	—
741	C₃×C₄	—	4	2	no	—
742	C₃×C₄	—	4	1	no	—
743	C₃×C₄	—	4	1	no	—
744	C₃×C₄	—	4	2	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	—	4	1	no	—
747	C₃×C₄	—	4	2	no	—
748	C₃×C₄	—	4	1	no	—
749	C₃×C₄	—	4	2	no	—
750	C₃×C₄	#529	1	4	yes	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	C₂⁵×C₃	1	1	yes	characteristic
759	Q₈	—	2	8	no	—
760	Q₈	—	4	4	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	C₂×C₃×#41	1	4	yes	—
821	C₂×C₄	C₂×C₃×#41	1	4	yes	—
822	C₂×C₄	C₂×C₃×#41	1	4	yes	—
823	C₂×C₄	C₂×C₃×#41	1	2	yes	—
824	C₂×C₄	C₂×C₃×#41	1	2	yes	—
825	C₂×C₄	C₂×C₃×#41	1	2	yes	—
826	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
827	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
828	C₂×C₃	—	8	1	no	—
829	C₂×C₃	C₂×#529	1	1	yes	characteristic
830	C₂×C₃	#3515	1	1	yes	characteristic
831	C₂×C₃	#3515	1	1	yes	characteristic
832	C₂×C₃	#3516	1	1	yes	characteristic
833	C₂×C₃	#3518	1	1	yes	characteristic
834	C₂×C₃	#3523	1	1	yes	characteristic
835	C₂×C₃	#3524	1	1	yes	characteristic
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
844	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
845	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
846	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
847	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
848	C₂²	C₃×#585	1	1	yes	characteristic
849	C₂²	C₃×#585	1	1	yes	characteristic
850	C₄	—	2	4	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	2	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	C₃×#529	1	4	yes	—
872	C₃	#35899	1	1	yes	characteristic, direct product factor, Sylow
873	C₂	—	8	1	no	—
874	C₂	C₂×C₃×#529	1	1	yes	characteristic
875	C₂	C₃×#3515	1	1	yes	characteristic
876	C₂	C₃×#3515	1	1	yes	characteristic
877	C₂	C₃×#3516	1	1	yes	characteristic
878	C₂	C₃×#3518	1	1	yes	characteristic
879	C₂	C₃×#3523	1	1	yes	characteristic
880	C₂	C₃×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁴×C₃	C₂⁴
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. C₃×#2645	C₂	semidirect
6. C₃×#2528	C₂	semidirect
7. C₃×#2528	C₂	semidirect
8. C₃×#2508	C₂	semidirect
9. C₃×#2507	C₂	semidirect
11. C₃×#2453	C₂	semidirect
12. C₃×#2446	C₂	semidirect
15. C₃×#2402	C₂	semidirect
17. C₃×#2370	C₂	semidirect
18. C₃×#2365	C₂	semidirect
21. C₃×#2355	C₂	semidirect
23. C₃×#2276	C₂	semidirect
24. #35899	C₃	direct (N × H)
125. #2645	C₂×C₃	semidirect
129. #2528	C₂×C₃	semidirect
130. #2528	C₂×C₃	semidirect
131. #2508	C₂×C₃	semidirect
132. #2507	C₂×C₃	semidirect
134. #2453	C₂×C₃	semidirect
135. #2446	C₂×C₃	semidirect
138. #2402	C₂×C₃	semidirect
140. #2370	C₂×C₃	semidirect
141. #2365	C₂×C₃	semidirect
144. #2355	C₂×C₃	semidirect
146. #2276	C₂×C₃	semidirect
872. C₃	#35899	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×#2654	2
C₃×#2645	2
C₃×#2596	2
C₃×#2594	2
C₃×#2529	2
C₃×#2528	2
C₃×#2508	2
C₃×#2507	2
C₃×#2489	2
C₃×#2453	2
C₃×#2446	2
C₃×#2429	2
C₃×#2423	2
C₃×#2402	2
C₃×#2401	2
C₃×#2370	2
C₃×#2365	2
C₃×#2362	2
C₃×#2355	2
C₃×#2346	2
C₃×#2276	2
#35899	3

Subgroups — C3×#35899 #10654506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35899 #10654506