Subgroups — C₃×#42461 #10661068

Order 768.

1432 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2836	C₂	1	2	yes	maximal
2	C₃×#2802	C₂	1	2	yes	maximal, complemented
3	C₃×#2772	C₂	1	2	yes	maximal
4	C₃×#2766	C₂	1	2	yes	maximal, complemented
5	C₃×#2725	C₂	1	2	yes	maximal
6	C₃×#2655	C₂	1	2	yes	maximal, complemented
7	C₃×#2634	C₂	1	2	yes	maximal, complemented
8	C₃×#2629	C₂	1	1	yes	maximal, characteristic
9	C₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2497	C₂	1	1	yes	maximal, characteristic
16	C₃×#2496	C₂	1	1	yes	maximal, characteristic
17	C₃×#2495	C₂	1	1	yes	maximal, characteristic
18	C₃×#2494	C₂	1	1	yes	maximal, characteristic
19	C₃×#2469	C₂	1	2	yes	maximal
20	C₃×#2396	C₂	1	1	yes	maximal, characteristic
21	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2314	C₂	1	1	yes	maximal, characteristic
24	#42461	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#126	C₂²	1	2	yes	—
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×#125	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
30	C₂×C₃×#117	C₂²	1	1	yes	characteristic
31	C₃×#401	C₂²	1	2	yes	—
32	C₃×#400	C₂²	1	2	yes	—
33	C₃×#400	C₂²	1	2	yes	—
34	C₃×#400	C₂²	1	2	yes	—
35	C₃×#400	C₂²	1	2	yes	—
36	C₃×#400	C₂²	1	1	yes	characteristic
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×#399	C₂²	1	1	yes	characteristic
42	C₃×#398	C₂²	1	2	yes	—
43	C₃×#398	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	1	yes	characteristic
46	C₃×#398	C₂²	1	1	yes	characteristic
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	2	yes	—
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	1	yes	characteristic
58	C₃×#396	C₂²	1	1	yes	characteristic
59	C₃×#396	C₂²	1	2	yes	—
60	C₃×#395	C₂²	1	1	yes	characteristic
61	C₃×#395	C₂²	1	2	yes	—
62	C₃×#393	C₂²	1	1	yes	characteristic
63	C₃×#389	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	2	yes	—
69	C₃×#389	C₂²	1	2	yes	—
70	C₃×#389	C₂²	1	2	yes	—
71	C₃×#389	C₂²	1	2	yes	—
72	C₃×#389	C₂²	1	2	yes	—
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	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	1	yes	characteristic
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	2	yes	—
80	C₃×#389	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×#388	C₂²	1	2	yes	—
85	C₃×#388	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×#387	C₂²	1	2	yes	—
98	C₃×#387	C₂²	1	2	yes	—
99	C₃×#384	C₂²	1	1	yes	characteristic
100	C₃×#384	C₂²	1	1	yes	characteristic
101	C₃×#384	C₂²	1	1	yes	characteristic
102	C₃×#384	C₂²	1	1	yes	characteristic
103	C₃×#383	C₂²	1	2	yes	—
104	C₃×#382	C₂²	1	1	yes	characteristic
105	C₃×#382	C₂²	1	1	yes	characteristic
106	C₃×#382	C₂²	1	2	yes	—
107	C₃×#382	C₂²	1	1	yes	characteristic
108	C₃×#380	C₂²	1	1	yes	characteristic
109	C₃×#380	C₂²	1	1	yes	characteristic
110	C₃×#380	C₂²	1	1	yes	characteristic
111	C₃×#380	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	#2836	C₂×C₃	1	2	yes	—
125	#2802	C₂×C₃	1	2	yes	complemented
126	#2772	C₂×C₃	1	2	yes	—
127	#2766	C₂×C₃	1	2	yes	complemented
128	#2725	C₂×C₃	1	2	yes	—
129	#2655	C₂×C₃	1	2	yes	complemented
130	#2634	C₂×C₃	1	2	yes	complemented
131	#2629	C₂×C₃	1	1	yes	characteristic
132	#2584	C₂×C₃	1	1	yes	characteristic, complemented
133	#2571	C₂×C₃	1	1	yes	characteristic, complemented
134	#2570	C₂×C₃	1	1	yes	characteristic, complemented
135	#2570	C₂×C₃	1	1	yes	characteristic, complemented
136	#2507	C₂×C₃	1	1	yes	characteristic, complemented
137	#2506	C₂×C₃	1	1	yes	characteristic, complemented
138	#2497	C₂×C₃	1	1	yes	characteristic
139	#2496	C₂×C₃	1	1	yes	characteristic
140	#2495	C₂×C₃	1	1	yes	characteristic
141	#2494	C₂×C₃	1	1	yes	characteristic
142	#2469	C₂×C₃	1	2	yes	—
143	#2396	C₂×C₃	1	1	yes	characteristic
144	#2370	C₂×C₃	1	1	yes	characteristic, complemented
145	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
146	#2314	C₂×C₃	1	1	yes	characteristic
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
149	C₃×#126	—	4	4	no	—
150	C₃×#125	—	2	4	no	—
151	C₃×#125	—	4	4	no	—
152	C₃×C₄×Q₈	—	2	4	no	—
153	C₃×C₄×Q₈	—	4	4	no	—
154	C₃×#117	—	2	4	no	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	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	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
193	C₂×C₃×C₄⋊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	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
209	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	C₂×C₃×C₄²	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	1	yes	characteristic
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	1	yes	characteristic
225	C₃×#95	C₂³	1	1	yes	characteristic
226	C₃×#95	C₂³	1	1	yes	characteristic
227	C₃×#95	C₂³	1	1	yes	characteristic
228	C₃×#95	C₂³	1	2	yes	—
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	C₂×#126	C₂²×C₃	1	2	yes	—
253	C₂×#125	C₂²×C₃	1	1	yes	characteristic
254	C₂×#125	C₂²×C₃	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
257	C₂×#117	C₂²×C₃	1	1	yes	characteristic
258	#401	C₂²×C₃	1	2	yes	—
259	#400	C₂²×C₃	1	2	yes	—
260	#400	C₂²×C₃	1	2	yes	—
261	#400	C₂²×C₃	1	2	yes	—
262	#400	C₂²×C₃	1	2	yes	—
263	#400	C₂²×C₃	1	2	yes	—
264	#400	C₂²×C₃	1	2	yes	—
265	#400	C₂²×C₃	1	1	yes	characteristic
266	#400	C₂²×C₃	1	2	yes	—
267	#400	C₂²×C₃	1	2	yes	—
268	#399	C₂²×C₃	1	1	yes	characteristic
269	#398	C₂²×C₃	1	2	yes	—
270	#398	C₂²×C₃	1	2	yes	—
271	#398	C₂²×C₃	1	2	yes	—
272	#398	C₂²×C₃	1	2	yes	—
273	#398	C₂²×C₃	1	2	yes	—
274	#398	C₂²×C₃	1	2	yes	—
275	#398	C₂²×C₃	1	2	yes	—
276	#398	C₂²×C₃	1	1	yes	characteristic
277	#398	C₂²×C₃	1	1	yes	characteristic
278	#398	C₂²×C₃	1	2	yes	—
279	#397	C₂²×C₃	1	2	yes	—
280	#397	C₂²×C₃	1	2	yes	—
281	#397	C₂²×C₃	1	2	yes	—
282	#396	C₂²×C₃	1	2	yes	—
283	#396	C₂²×C₃	1	2	yes	—
284	#396	C₂²×C₃	1	2	yes	—
285	#396	C₂²×C₃	1	1	yes	characteristic
286	#396	C₂²×C₃	1	1	yes	characteristic
287	#395	C₂²×C₃	1	2	yes	—
288	#395	C₂²×C₃	1	1	yes	characteristic
289	#393	C₂²×C₃	1	1	yes	characteristic
290	#389	C₂²×C₃	1	1	yes	characteristic
291	#389	C₂²×C₃	1	1	yes	characteristic
292	#389	C₂²×C₃	1	1	yes	characteristic
293	#389	C₂²×C₃	1	1	yes	characteristic
294	#389	C₂²×C₃	1	2	yes	—
295	#389	C₂²×C₃	1	1	yes	characteristic
296	#389	C₂²×C₃	1	1	yes	characteristic
297	#389	C₂²×C₃	1	2	yes	—
298	#389	C₂²×C₃	1	2	yes	—
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	2	yes	—
303	#389	C₂²×C₃	1	2	yes	—
304	#389	C₂²×C₃	1	2	yes	—
305	#389	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	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	#387	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	#384	C₂²×C₃	1	1	yes	characteristic
327	#384	C₂²×C₃	1	1	yes	characteristic
328	#384	C₂²×C₃	1	1	yes	characteristic
329	#384	C₂²×C₃	1	1	yes	characteristic
330	#383	C₂²×C₃	1	2	yes	—
331	#382	C₂²×C₃	1	1	yes	characteristic
332	#382	C₂²×C₃	1	1	yes	characteristic
333	#382	C₂²×C₃	1	1	yes	characteristic
334	#382	C₂²×C₃	1	2	yes	—
335	#380	C₂²×C₃	1	1	yes	characteristic
336	#380	C₂²×C₃	1	1	yes	characteristic
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	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	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×Q₈	—	2	2	no	—
353	C₂×C₃×Q₈	—	2	2	no	—
354	C₂×C₃×Q₈	—	2	2	no	—
355	C₂²×C₃×C₄	—	2	2	no	—
356	C₂²×C₃×C₄	—	2	2	no	—
357	C₂²×C₃×C₄	—	2	2	no	—
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
362	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
370	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
371	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₃×C₄⋊C₄	—	2	2	no	—
381	C₃×C₄⋊C₄	—	2	2	no	—
382	C₃×C₄⋊C₄	—	2	2	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	2	no	—
385	C₃×C₄⋊C₄	—	2	4	no	—
386	C₃×C₄⋊C₄	—	2	4	no	—
387	C₃×C₄⋊C₄	—	2	2	no	—
388	C₃×C₄⋊C₄	—	2	2	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	2	no	—
395	C₃×C₄⋊C₄	—	2	2	no	—
396	C₃×C₄⋊C₄	—	2	2	no	—
397	C₃×C₄⋊C₄	—	2	2	no	—
398	C₃×C₄⋊C₄	—	2	2	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	4	1	no	—
401	C₃×C₄⋊C₄	—	4	1	no	—
402	C₃×C₄⋊C₄	—	4	2	no	—
403	C₃×C₄⋊C₄	—	4	2	no	—
404	C₃×C₄⋊C₄	—	4	2	no	—
405	C₃×C₄⋊C₄	—	4	2	no	—
406	C₃×C₄⋊C₄	—	4	2	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	1	no	—
412	C₃×C₄⋊C₄	—	4	2	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	2	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₂²⋊C₄	—	2	2	no	—
421	C₃×C₂²⋊C₄	—	2	2	no	—
422	C₃×C₂²⋊C₄	—	2	2	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₂²⋊C₄	—	4	1	no	—
426	C₃×C₂²⋊C₄	—	4	1	no	—
427	C₃×C₂²⋊C₄	—	4	2	no	—
428	C₃×C₂²⋊C₄	—	4	2	no	—
429	C₃×C₄²	—	2	2	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	2	no	—
432	C₃×C₄²	—	2	4	no	—
433	C₃×C₄²	—	2	2	no	—
434	C₃×C₄²	—	2	2	no	—
435	C₃×C₄²	—	4	2	no	—
436	C₃×C₄²	—	4	2	no	—
437	C₃×C₄²	—	4	2	no	—
438	C₃×C₄²	—	4	2	no	—
439	C₃×C₄²	—	4	2	no	—
440	C₃×C₄²	#41	1	4	yes	—
441	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
443	#126	—	4	4	no	—
444	#125	—	2	4	no	—
445	#125	—	4	4	no	—
446	C₄×Q₈	—	2	4	no	—
447	C₄×Q₈	—	4	4	no	—
448	#117	—	2	4	no	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₃	1	2	yes	—
500	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
510	#95	C₂³×C₃	1	1	yes	characteristic
511	#95	C₂³×C₃	1	1	yes	characteristic
512	#95	C₂³×C₃	1	1	yes	characteristic
513	#95	C₂³×C₃	1	1	yes	characteristic
514	#95	C₂³×C₃	1	1	yes	characteristic
515	#95	C₂³×C₃	1	1	yes	characteristic
516	#95	C₂³×C₃	1	2	yes	—
517	#95	C₂³×C₃	1	2	yes	—
518	#95	C₂³×C₃	1	1	yes	characteristic
519	#95	C₂³×C₃	1	1	yes	characteristic
520	#95	C₂³×C₃	1	1	yes	characteristic
521	#95	C₂³×C₃	1	1	yes	characteristic
522	#95	C₂³×C₃	1	2	yes	—
523	#95	C₂³×C₃	1	2	yes	—
524	#95	C₂³×C₃	1	2	yes	—
525	#95	C₂³×C₃	1	2	yes	—
526	#95	C₂³×C₃	1	2	yes	—
527	#95	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	—	2	1	no	—
547	C₂³×C₃	—	2	1	no	—
548	C₂³×C₃	—	2	1	no	—
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	—	2	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	2	1	no	—
553	C₂³×C₃	C₂⁵	1	1	yes	characteristic
554	C₃×Q₈	—	2	8	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	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	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	1	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	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	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	2	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	2	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	2	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	1	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	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	4	4	no	—
615	C₂×C₃×C₄	C₂×#41	1	2	yes	—
616	C₂×C₃×C₄	C₂×#41	1	2	yes	—
617	C₂×C₃×C₄	C₂×#41	1	2	yes	—
618	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
619	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
620	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
621	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
622	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	2	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	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	1	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	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	1	no	—
699	C₂²⋊C₄	—	4	1	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	4	2	no	—
707	C₄²	—	4	2	no	—
708	C₄²	—	4	2	no	—
709	C₄²	—	4	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	C₃×#41	1	4	yes	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	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	C₂²×#41	1	1	yes	characteristic
720	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
722	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
723	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
724	C₂²×C₃	#585	1	1	yes	characteristic
725	C₂²×C₃	#585	1	1	yes	characteristic
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	2	2	no	—
729	C₃×C₄	—	2	2	no	—
730	C₃×C₄	—	4	1	no	—
731	C₃×C₄	—	4	1	no	—
732	C₃×C₄	—	4	2	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	2	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	4	1	no	—
739	C₃×C₄	—	4	2	no	—
740	C₃×C₄	—	4	1	no	—
741	C₃×C₄	—	4	2	no	—
742	C₃×C₄	—	4	2	no	—
743	C₃×C₄	—	4	2	no	—
744	C₃×C₄	—	4	1	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	—	4	2	no	—
747	C₃×C₄	#541	1	4	yes	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	C₂⁵×C₃	1	1	yes	characteristic
756	Q₈	—	2	8	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	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	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	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	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	C₂×C₃×#41	1	2	yes	—
818	C₂×C₄	C₂×C₃×#41	1	2	yes	—
819	C₂×C₄	C₂×C₃×#41	1	2	yes	—
820	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
821	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
822	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
823	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
824	C₂×C₃	—	8	1	no	—
825	C₂×C₃	C₂×#541	1	1	yes	characteristic
826	C₂×C₃	#3492	1	1	yes	characteristic
827	C₂×C₃	#3512	1	1	yes	characteristic
828	C₂×C₃	#3547	1	1	yes	characteristic
829	C₂×C₃	#3554	1	1	yes	characteristic
830	C₂×C₃	#3555	1	1	yes	characteristic
831	C₂×C₃	#3555	1	1	yes	characteristic
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
840	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
841	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
842	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
843	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂²	C₃×#585	1	1	yes	characteristic
845	C₂²	C₃×#585	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	2	no	—
867	C₄	C₃×#541	1	4	yes	—
868	C₃	#42461	1	1	yes	characteristic, direct product factor, Sylow
869	C₂	—	8	1	no	—
870	C₂	C₂×C₃×#541	1	1	yes	characteristic
871	C₂	C₃×#3492	1	1	yes	characteristic
872	C₂	C₃×#3512	1	1	yes	characteristic
873	C₂	C₃×#3547	1	1	yes	characteristic
874	C₂	C₃×#3554	1	1	yes	characteristic
875	C₂	C₃×#3555	1	1	yes	characteristic
876	C₂	C₃×#3555	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×#2802	C₂	semidirect
4. C₃×#2766	C₂	semidirect
6. C₃×#2655	C₂	semidirect
7. C₃×#2634	C₂	semidirect
9. C₃×#2584	C₂	semidirect
10. C₃×#2571	C₂	semidirect
11. C₃×#2570	C₂	semidirect
12. C₃×#2570	C₂	semidirect
13. C₃×#2507	C₂	semidirect
14. C₃×#2506	C₂	semidirect
21. C₃×#2370	C₂	semidirect
22. C₃×Q₈×C₄⋊C₄	C₂	semidirect
24. #42461	C₃	direct (N × H)
125. #2802	C₂×C₃	semidirect
127. #2766	C₂×C₃	semidirect
129. #2655	C₂×C₃	semidirect
130. #2634	C₂×C₃	semidirect
132. #2584	C₂×C₃	semidirect
133. #2571	C₂×C₃	semidirect
134. #2570	C₂×C₃	semidirect
135. #2570	C₂×C₃	semidirect
136. #2507	C₂×C₃	semidirect
137. #2506	C₂×C₃	semidirect
144. #2370	C₂×C₃	semidirect
145. Q₈×C₄⋊C₄	C₂×C₃	semidirect
868. C₃	#42461	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×#2836	2
C₃×#2802	2
C₃×#2772	2
C₃×#2766	2
C₃×#2725	2
C₃×#2655	2
C₃×#2634	2
C₃×#2629	2
C₃×#2584	2
C₃×#2571	2
C₃×#2570	2
C₃×#2507	2
C₃×#2506	2
C₃×#2497	2
C₃×#2496	2
C₃×#2495	2
C₃×#2494	2
C₃×#2469	2
C₃×#2396	2
C₃×#2370	2
C₃×Q₈×C₄⋊C₄	2
C₃×#2314	2
#42461	3

Subgroups — C3×#42461 #10661068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42461 #10661068