Subgroups — C₃×#42938 #10661545

Order 768.

1462 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2839	C₂	1	2	yes	maximal, complemented
2	C₃×#2745	C₂	1	2	yes	maximal
3	C₃×#2744	C₂	1	2	yes	maximal
4	C₃×#2739	C₂	1	2	yes	maximal
5	C₃×#2738	C₂	1	2	yes	maximal
6	C₃×#2666	C₂	1	2	yes	maximal, complemented
7	C₃×#2655	C₂	1	2	yes	maximal, complemented
8	C₃×#2621	C₂	1	1	yes	maximal, characteristic
9	C₃×#2585	C₂	1	2	yes	maximal, complemented
10	C₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2503	C₂	1	1	yes	maximal, characteristic
17	C₃×#2502	C₂	1	1	yes	maximal, characteristic
18	C₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2396	C₂	1	1	yes	maximal, characteristic
21	C₃×#2362	C₂	1	1	yes	maximal, characteristic
22	C₃×#2362	C₂	1	1	yes	maximal, characteristic
23	C₃×#2316	C₂	1	1	yes	maximal, characteristic
24	#42938	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×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×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×#401	C₂²	1	2	yes	—
35	C₃×#400	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	2	yes	—
41	C₃×#400	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#400	C₂²	1	2	yes	—
46	C₃×#400	C₂²	1	2	yes	—
47	C₃×#399	C₂²	1	1	yes	characteristic
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#398	C₂²	1	2	yes	—
50	C₃×#398	C₂²	1	1	yes	characteristic
51	C₃×#398	C₂²	1	1	yes	characteristic
52	C₃×#398	C₂²	1	2	yes	—
53	C₃×#398	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	2	yes	—
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#398	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#397	C₂²	1	2	yes	—
60	C₃×#397	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	1	yes	characteristic
62	C₃×#396	C₂²	1	1	yes	characteristic
63	C₃×#395	C₂²	1	1	yes	characteristic
64	C₃×#395	C₂²	1	2	yes	—
65	C₃×#393	C₂²	1	1	yes	characteristic
66	C₃×#391	C₂²	1	1	yes	characteristic
67	C₃×#391	C₂²	1	1	yes	characteristic
68	C₃×#391	C₂²	1	1	yes	characteristic
69	C₃×#391	C₂²	1	1	yes	characteristic
70	C₃×#391	C₂²	1	2	yes	—
71	C₃×#391	C₂²	1	1	yes	characteristic
72	C₃×#391	C₂²	1	1	yes	characteristic
73	C₃×#391	C₂²	1	1	yes	characteristic
74	C₃×#391	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	1	yes	characteristic
76	C₃×#389	C₂²	1	1	yes	characteristic
77	C₃×#389	C₂²	1	2	yes	—
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	1	yes	characteristic
80	C₃×#389	C₂²	1	2	yes	—
81	C₃×#389	C₂²	1	2	yes	—
82	C₃×#389	C₂²	1	1	yes	characteristic
83	C₃×#389	C₂²	1	1	yes	characteristic
84	C₃×#389	C₂²	1	2	yes	—
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	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×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	2	yes	—
99	C₃×#387	C₂²	1	2	yes	—
100	C₃×#387	C₂²	1	2	yes	—
101	C₃×#387	C₂²	1	2	yes	—
102	C₃×#385	C₂²	1	2	yes	—
103	C₃×#385	C₂²	1	2	yes	—
104	C₃×#384	C₂²	1	1	yes	characteristic
105	C₃×#384	C₂²	1	1	yes	characteristic
106	C₃×#383	C₂²	1	2	yes	—
107	C₃×#382	C₂²	1	1	yes	characteristic
108	C₃×#382	C₂²	1	2	yes	—
109	C₃×#382	C₂²	1	1	yes	characteristic
110	C₃×#382	C₂²	1	1	yes	characteristic
111	C₃×#381	C₂²	1	2	yes	—
112	C₃×#381	C₂²	1	2	yes	—
113	C₃×#380	C₂²	1	2	yes	—
114	C₃×#380	C₂²	1	2	yes	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	#2839	C₂×C₃	1	2	yes	complemented
125	#2745	C₂×C₃	1	2	yes	—
126	#2744	C₂×C₃	1	2	yes	—
127	#2739	C₂×C₃	1	2	yes	—
128	#2738	C₂×C₃	1	2	yes	—
129	#2666	C₂×C₃	1	2	yes	complemented
130	#2655	C₂×C₃	1	2	yes	complemented
131	#2621	C₂×C₃	1	1	yes	characteristic
132	#2585	C₂×C₃	1	2	yes	complemented
133	#2582	C₂×C₃	1	1	yes	characteristic, complemented
134	#2581	C₂×C₃	1	1	yes	characteristic, complemented
135	#2571	C₂×C₃	1	1	yes	characteristic, complemented
136	#2570	C₂×C₃	1	1	yes	characteristic, complemented
137	#2514	C₂×C₃	1	1	yes	characteristic, complemented
138	#2511	C₂×C₃	1	1	yes	characteristic, complemented
139	#2503	C₂×C₃	1	1	yes	characteristic
140	#2502	C₂×C₃	1	1	yes	characteristic
141	#2446	C₂×C₃	1	1	yes	characteristic, complemented
142	#2446	C₂×C₃	1	1	yes	characteristic, complemented
143	#2396	C₂×C₃	1	1	yes	characteristic
144	#2362	C₂×C₃	1	1	yes	characteristic
145	#2362	C₂×C₃	1	1	yes	characteristic
146	#2316	C₂×C₃	1	1	yes	characteristic
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₃×C₄⋊Q₈	—	4	2	no	—
153	C₃×C₂²⋊Q₈	—	2	4	no	—
154	C₃×C₂²⋊Q₈	—	2	4	no	—
155	C₃×C₄×Q₈	—	4	2	no	—
156	C₃×C₄×Q₈	—	4	2	no	—
157	C₃×C₄×Q₈	—	4	2	no	—
158	C₃×#117	—	4	2	no	—
159	C₃×#117	—	4	2	no	—
160	C₂×C₃×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊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	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄²	C₂³	1	2	yes	—
209	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
218	C₃×#95	C₂³	1	1	yes	characteristic
219	C₃×#95	C₂³	1	1	yes	characteristic
220	C₃×#95	C₂³	1	1	yes	characteristic
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	1	yes	characteristic
224	C₃×#95	C₂³	1	1	yes	characteristic
225	C₃×#95	C₂³	1	1	yes	characteristic
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
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×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
258	C₂×C₄×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×#117	C₂²×C₃	1	1	yes	characteristic
262	C₂×#117	C₂²×C₃	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
264	#401	C₂²×C₃	1	2	yes	—
265	#400	C₂²×C₃	1	2	yes	—
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	2	yes	—
272	#400	C₂²×C₃	1	2	yes	—
273	#400	C₂²×C₃	1	2	yes	—
274	#400	C₂²×C₃	1	1	yes	characteristic
275	#400	C₂²×C₃	1	2	yes	—
276	#400	C₂²×C₃	1	2	yes	—
277	#399	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
282	#398	C₂²×C₃	1	2	yes	—
283	#398	C₂²×C₃	1	2	yes	—
284	#398	C₂²×C₃	1	2	yes	—
285	#398	C₂²×C₃	1	1	yes	characteristic
286	#398	C₂²×C₃	1	2	yes	—
287	#398	C₂²×C₃	1	2	yes	—
288	#398	C₂²×C₃	1	2	yes	—
289	#397	C₂²×C₃	1	2	yes	—
290	#397	C₂²×C₃	1	2	yes	—
291	#396	C₂²×C₃	1	1	yes	characteristic
292	#396	C₂²×C₃	1	1	yes	characteristic
293	#395	C₂²×C₃	1	2	yes	—
294	#395	C₂²×C₃	1	1	yes	characteristic
295	#393	C₂²×C₃	1	1	yes	characteristic
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#391	C₂²×C₃	1	1	yes	characteristic
299	#391	C₂²×C₃	1	2	yes	—
300	#391	C₂²×C₃	1	1	yes	characteristic
301	#391	C₂²×C₃	1	1	yes	characteristic
302	#391	C₂²×C₃	1	1	yes	characteristic
303	#391	C₂²×C₃	1	1	yes	characteristic
304	#391	C₂²×C₃	1	1	yes	characteristic
305	#389	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	1	yes	characteristic
309	#389	C₂²×C₃	1	2	yes	—
310	#389	C₂²×C₃	1	1	yes	characteristic
311	#389	C₂²×C₃	1	1	yes	characteristic
312	#389	C₂²×C₃	1	2	yes	—
313	#389	C₂²×C₃	1	2	yes	—
314	#389	C₂²×C₃	1	2	yes	—
315	#388	C₂²×C₃	1	2	yes	—
316	#388	C₂²×C₃	1	2	yes	—
317	#388	C₂²×C₃	1	2	yes	—
318	#388	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	#387	C₂²×C₃	1	2	yes	—
328	#387	C₂²×C₃	1	2	yes	—
329	#387	C₂²×C₃	1	2	yes	—
330	#387	C₂²×C₃	1	2	yes	—
331	#387	C₂²×C₃	1	2	yes	—
332	#385	C₂²×C₃	1	2	yes	—
333	#385	C₂²×C₃	1	2	yes	—
334	#384	C₂²×C₃	1	1	yes	characteristic
335	#384	C₂²×C₃	1	1	yes	characteristic
336	#383	C₂²×C₃	1	2	yes	—
337	#382	C₂²×C₃	1	1	yes	characteristic
338	#382	C₂²×C₃	1	1	yes	characteristic
339	#382	C₂²×C₃	1	1	yes	characteristic
340	#382	C₂²×C₃	1	2	yes	—
341	#381	C₂²×C₃	1	2	yes	—
342	#381	C₂²×C₃	1	2	yes	—
343	#380	C₂²×C₃	1	2	yes	—
344	#380	C₂²×C₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	—	2	2	no	—
361	C₂×C₃×Q₈	—	2	2	no	—
362	C₂×C₃×Q₈	—	4	1	no	—
363	C₂×C₃×Q₈	—	4	1	no	—
364	C₂²×C₃×C₄	—	2	2	no	—
365	C₂²×C₃×C₄	—	2	2	no	—
366	C₂²×C₃×C₄	—	2	4	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	#41	1	4	yes	—
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	1	yes	characteristic
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
384	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₃×C₄⋊C₄	—	2	4	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	2	2	no	—
396	C₃×C₄⋊C₄	—	2	2	no	—
397	C₃×C₄⋊C₄	—	2	4	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	4	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	2	no	—
411	C₃×C₄⋊C₄	—	4	1	no	—
412	C₃×C₄⋊C₄	—	4	1	no	—
413	C₃×C₄⋊C₄	—	4	2	no	—
414	C₃×C₄⋊C₄	—	4	2	no	—
415	C₃×C₄⋊C₄	—	4	2	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	—	4	1	no	—
418	C₃×C₄⋊C₄	—	4	1	no	—
419	C₃×C₄⋊C₄	—	4	1	no	—
420	C₃×C₄⋊C₄	—	4	1	no	—
421	C₃×C₄⋊C₄	—	4	1	no	—
422	C₃×C₄⋊C₄	—	4	2	no	—
423	C₃×C₄⋊C₄	—	4	2	no	—
424	C₃×C₄⋊C₄	—	4	2	no	—
425	C₃×C₄⋊C₄	—	4	2	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	2	no	—
430	C₃×C₂²⋊C₄	—	4	1	no	—
431	C₃×C₂²⋊C₄	—	4	1	no	—
432	C₃×C₂²⋊C₄	—	4	1	no	—
433	C₃×C₂²⋊C₄	—	4	1	no	—
434	C₃×C₂²⋊C₄	—	4	2	no	—
435	C₃×C₄²	—	2	2	no	—
436	C₃×C₄²	—	2	2	no	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	2	2	no	—
440	C₃×C₄²	—	2	4	no	—
441	C₃×C₄²	—	2	2	no	—
442	C₃×C₄²	—	4	2	no	—
443	C₃×C₄²	—	4	2	no	—
444	C₃×C₄²	—	4	2	no	—
445	C₃×C₄²	—	4	2	no	—
446	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
448	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₃	1	2	yes	—
451	C₄⋊Q₈	—	4	2	no	—
452	C₂²⋊Q₈	—	2	4	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₄×Q₈	—	4	2	no	—
455	C₄×Q₈	—	4	2	no	—
456	C₄×Q₈	—	4	2	no	—
457	#117	—	4	2	no	—
458	#117	—	4	2	no	—
459	C₂×C₄⋊C₄	—	2	4	no	—
460	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₃	1	2	yes	—
510	C₂×C₄²	C₂³×C₃	1	2	yes	—
511	C₂×C₄²	C₂³×C₃	1	2	yes	—
512	C₂×C₄²	C₂³×C₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
519	#95	C₂³×C₃	1	1	yes	characteristic
520	#95	C₂³×C₃	1	2	yes	—
521	#95	C₂³×C₃	1	2	yes	—
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	2	yes	—
526	#95	C₂³×C₃	1	2	yes	—
527	#95	C₂³×C₃	1	1	yes	characteristic
528	#95	C₂³×C₃	1	2	yes	—
529	#95	C₂³×C₃	1	2	yes	—
530	#95	C₂³×C₃	1	2	yes	—
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	2	yes	—
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
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	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	2	yes	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	—	2	1	no	—
557	C₂³×C₃	—	2	1	no	—
558	C₂³×C₃	—	2	1	no	—
559	C₂³×C₃	—	2	1	no	—
560	C₂³×C₃	C₂×#41	1	2	yes	—
561	C₂³×C₃	C₂⁵	1	1	yes	characteristic
562	C₃×Q₈	—	4	4	no	—
563	C₃×Q₈	—	4	4	no	—
564	C₃×Q₈	—	4	4	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	8	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	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	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	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	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	1	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	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	8	4	no	—
627	C₂×C₃×C₄	C₂×#41	1	2	yes	—
628	C₂×C₃×C₄	C₂×#41	1	2	yes	—
629	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
630	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
631	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
632	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
633	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	C₃×#41	1	4	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	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	4	1	no	—
710	C₂²⋊C₄	—	4	1	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	4	2	no	—
722	C₄²	—	4	2	no	—
723	C₄²	—	4	2	no	—
724	C₄²	—	4	2	no	—
725	C₂²×C₃	—	2	2	no	—
726	C₂²×C₃	—	2	2	no	—
727	C₂²×C₃	—	2	2	no	—
728	C₂²×C₃	—	4	1	no	—
729	C₂²×C₃	—	4	1	no	—
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
733	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
735	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
737	C₂²×C₃	#585	1	1	yes	characteristic
738	C₂²×C₃	#585	1	1	yes	characteristic
739	C₃×C₄	—	2	2	no	—
740	C₃×C₄	—	2	2	no	—
741	C₃×C₄	—	2	2	no	—
742	C₃×C₄	—	4	2	no	—
743	C₃×C₄	—	4	2	no	—
744	C₃×C₄	—	4	2	no	—
745	C₃×C₄	—	4	2	no	—
746	C₃×C₄	—	4	2	no	—
747	C₃×C₄	—	4	2	no	—
748	C₃×C₄	—	4	1	no	—
749	C₃×C₄	—	4	2	no	—
750	C₃×C₄	—	4	1	no	—
751	C₃×C₄	—	4	1	no	—
752	C₃×C₄	—	4	1	no	—
753	C₃×C₄	—	4	1	no	—
754	C₃×C₄	—	4	1	no	—
755	C₃×C₄	—	4	1	no	—
756	C₃×C₄	—	4	2	no	—
757	C₃×C₄	—	4	1	no	—
758	C₃×C₄	—	4	1	no	—
759	C₃×C₄	—	4	1	no	—
760	C₃×C₄	#539	1	4	yes	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	C₂×C₃×#41	1	2	yes	—
768	C₂³	C₂⁵×C₃	1	1	yes	characteristic
769	Q₈	—	4	4	no	—
770	Q₈	—	4	4	no	—
771	Q₈	—	4	4	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	8	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	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	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	8	4	no	—
834	C₂×C₄	C₂×C₃×#41	1	2	yes	—
835	C₂×C₄	C₂×C₃×#41	1	2	yes	—
836	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
837	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
838	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
839	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
840	C₂×C₃	—	4	2	no	—
841	C₂×C₃	C₂×#539	1	1	yes	characteristic
842	C₂×C₃	#3509	1	1	yes	characteristic
843	C₂×C₃	#3510	1	1	yes	characteristic
844	C₂×C₃	#3541	1	1	yes	characteristic
845	C₂×C₃	#3547	1	1	yes	characteristic
846	C₂×C₃	#3555	1	1	yes	characteristic
847	C₂×C₃	#3563	1	1	yes	characteristic
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
856	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
857	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
858	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
860	C₂²	C₃×#585	1	1	yes	characteristic
861	C₂²	C₃×#585	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	C₃×#539	1	4	yes	—
884	C₃	#42938	1	1	yes	characteristic, direct product factor, Sylow
885	C₂	—	4	2	no	—
886	C₂	C₂×C₃×#539	1	1	yes	characteristic
887	C₂	C₃×#3509	1	1	yes	characteristic
888	C₂	C₃×#3510	1	1	yes	characteristic
889	C₂	C₃×#3541	1	1	yes	characteristic
890	C₂	C₃×#3547	1	1	yes	characteristic
891	C₂	C₃×#3555	1	1	yes	characteristic
892	C₂	C₃×#3563	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
1. C₃×#2839	C₂	semidirect
6. C₃×#2666	C₂	semidirect
7. C₃×#2655	C₂	semidirect
9. C₃×#2585	C₂	semidirect
10. C₃×#2582	C₂	semidirect
11. C₃×#2581	C₂	semidirect
12. C₃×#2571	C₂	semidirect
13. C₃×#2570	C₂	semidirect
14. C₃×#2514	C₂	semidirect
15. C₃×#2511	C₂	semidirect
18. C₃×#2446	C₂	semidirect
19. C₃×#2446	C₂	semidirect
24. #42938	C₃	direct (N × H)
124. #2839	C₂×C₃	semidirect
129. #2666	C₂×C₃	semidirect
130. #2655	C₂×C₃	semidirect
132. #2585	C₂×C₃	semidirect
133. #2582	C₂×C₃	semidirect
134. #2581	C₂×C₃	semidirect
135. #2571	C₂×C₃	semidirect
136. #2570	C₂×C₃	semidirect
137. #2514	C₂×C₃	semidirect
138. #2511	C₂×C₃	semidirect
141. #2446	C₂×C₃	semidirect
142. #2446	C₂×C₃	semidirect
884. C₃	#42938	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×#2839	2
C₃×#2745	2
C₃×#2744	2
C₃×#2739	2
C₃×#2738	2
C₃×#2666	2
C₃×#2655	2
C₃×#2621	2
C₃×#2585	2
C₃×#2582	2
C₃×#2581	2
C₃×#2571	2
C₃×#2570	2
C₃×#2514	2
C₃×#2511	2
C₃×#2503	2
C₃×#2502	2
C₃×#2446	2
C₃×#2396	2
C₃×#2362	2
C₃×#2316	2
#42938	3

Subgroups — C3×#42938 #10661545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42938 #10661545