Subgroups — C₃×#35870 #10654477

Order 768.

1508 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2655	C₂	1	2	yes	maximal
2	C₃×#2642	C₂	1	1	yes	maximal, characteristic
3	C₃×#2590	C₂	1	2	yes	maximal
4	C₃×#2585	C₂	1	2	yes	maximal
5	C₃×#2565	C₂	1	1	yes	maximal, characteristic
6	C₃×#2546	C₂	1	1	yes	maximal, characteristic
7	C₃×#2533	C₂	1	2	yes	maximal
8	C₃×#2533	C₂	1	2	yes	maximal
9	C₃×#2528	C₂	1	2	yes	maximal
10	C₃×#2524	C₂	1	2	yes	maximal
11	C₃×#2514	C₂	1	1	yes	maximal, characteristic
12	C₃×#2511	C₂	1	1	yes	maximal, characteristic
13	C₃×#2446	C₂	1	1	yes	maximal, characteristic
14	C₃×#2446	C₂	1	1	yes	maximal, characteristic
15	C₃×#2402	C₂	1	1	yes	maximal, characteristic
16	C₃×#2402	C₂	1	2	yes	maximal
17	C₃×#2370	C₂	1	1	yes	maximal, characteristic
18	C₃×#2365	C₂	1	1	yes	maximal, characteristic
19	C₃×#2365	C₂	1	1	yes	maximal, characteristic
20	C₃×#2365	C₂	1	1	yes	maximal, characteristic
21	C₃×#2356	C₂	1	1	yes	maximal, characteristic
22	C₃×#2355	C₂	1	1	yes	maximal, characteristic
23	C₃×#2276	C₂	1	1	yes	maximal, characteristic
24	#35870	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#125	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×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₃×#401	C₂²	1	2	yes	—
35	C₃×#400	C₂²	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
46	C₃×#400	C₂²	1	1	yes	characteristic
47	C₃×#400	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
52	C₃×#398	C₂²	1	2	yes	—
53	C₃×#398	C₂²	1	2	yes	—
54	C₃×#398	C₂²	1	1	yes	characteristic
55	C₃×#398	C₂²	1	2	yes	—
56	C₃×#398	C₂²	1	1	yes	characteristic
57	C₃×#398	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×#391	C₂²	1	1	yes	characteristic
65	C₃×#391	C₂²	1	1	yes	characteristic
66	C₃×#391	C₂²	1	1	yes	characteristic
67	C₃×#391	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	1	yes	characteristic
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	2	yes	—
74	C₃×#389	C₂²	1	2	yes	—
75	C₃×#389	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	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×#383	C₂²	1	2	yes	—
99	C₃×#383	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	1	yes	characteristic
101	C₃×#382	C₂²	1	2	yes	—
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	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
108	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
109	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₄⋊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	#2655	C₂×C₃	1	2	yes	—
125	#2642	C₂×C₃	1	1	yes	characteristic
126	#2590	C₂×C₃	1	2	yes	—
127	#2585	C₂×C₃	1	2	yes	—
128	#2565	C₂×C₃	1	1	yes	characteristic
129	#2546	C₂×C₃	1	1	yes	characteristic
130	#2533	C₂×C₃	1	2	yes	—
131	#2533	C₂×C₃	1	2	yes	—
132	#2528	C₂×C₃	1	2	yes	—
133	#2524	C₂×C₃	1	2	yes	—
134	#2514	C₂×C₃	1	1	yes	characteristic
135	#2511	C₂×C₃	1	1	yes	characteristic
136	#2446	C₂×C₃	1	1	yes	characteristic
137	#2446	C₂×C₃	1	1	yes	characteristic
138	#2402	C₂×C₃	1	2	yes	—
139	#2402	C₂×C₃	1	1	yes	characteristic
140	#2370	C₂×C₃	1	1	yes	characteristic
141	#2365	C₂×C₃	1	1	yes	characteristic
142	#2365	C₂×C₃	1	1	yes	characteristic
143	#2365	C₂×C₃	1	1	yes	characteristic
144	#2356	C₂×C₃	1	1	yes	characteristic
145	#2355	C₂×C₃	1	1	yes	characteristic
146	#2276	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	C₃×C₄⋊Q₈	—	2	4	no	—
151	C₃×C₄⋊Q₈	—	2	4	no	—
152	C₃×C₄⋊Q₈	—	2	4	no	—
153	C₃×#125	—	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×C₄×Q₈	—	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	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	2	yes	—
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	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	2	yes	—
203	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄²	C₂³	1	2	yes	—
206	C₂×C₃×C₄²	C₂³	1	2	yes	—
207	C₂×C₃×C₄²	C₂³	1	2	yes	—
208	C₂×C₃×C₄²	C₂³	1	2	yes	—
209	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
210	C₃×#95	C₂³	1	1	yes	characteristic
211	C₃×#95	C₂³	1	1	yes	characteristic
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
221	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
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	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	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
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×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
258	C₂×#125	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×C₄×Q₈	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	1	yes	characteristic
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	2	yes	—
275	#400	C₂²×C₃	1	1	yes	characteristic
276	#400	C₂²×C₃	1	1	yes	characteristic
277	#400	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	1	yes	characteristic
281	#398	C₂²×C₃	1	2	yes	—
282	#398	C₂²×C₃	1	1	yes	characteristic
283	#398	C₂²×C₃	1	2	yes	—
284	#398	C₂²×C₃	1	2	yes	—
285	#398	C₂²×C₃	1	2	yes	—
286	#398	C₂²×C₃	1	1	yes	characteristic
287	#398	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	#391	C₂²×C₃	1	1	yes	characteristic
295	#391	C₂²×C₃	1	1	yes	characteristic
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#389	C₂²×C₃	1	2	yes	—
299	#389	C₂²×C₃	1	2	yes	—
300	#389	C₂²×C₃	1	2	yes	—
301	#389	C₂²×C₃	1	2	yes	—
302	#389	C₂²×C₃	1	2	yes	—
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	1	yes	characteristic
305	#389	C₂²×C₃	1	2	yes	—
306	#387	C₂²×C₃	1	2	yes	—
307	#387	C₂²×C₃	1	2	yes	—
308	#387	C₂²×C₃	1	2	yes	—
309	#387	C₂²×C₃	1	2	yes	—
310	#387	C₂²×C₃	1	2	yes	—
311	#387	C₂²×C₃	1	2	yes	—
312	#387	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	#387	C₂²×C₃	1	2	yes	—
327	#384	C₂²×C₃	1	1	yes	characteristic
328	#383	C₂²×C₃	1	2	yes	—
329	#383	C₂²×C₃	1	2	yes	—
330	#382	C₂²×C₃	1	1	yes	characteristic
331	#382	C₂²×C₃	1	2	yes	—
332	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
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	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	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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	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	C₂×C₃×Q₈	—	2	2	no	—
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	#41	1	4	yes	—
363	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
372	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	4	no	—
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	2	no	—
391	C₃×C₄⋊C₄	—	2	4	no	—
392	C₃×C₄⋊C₄	—	2	4	no	—
393	C₃×C₄⋊C₄	—	2	4	no	—
394	C₃×C₄⋊C₄	—	2	4	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	4	no	—
400	C₃×C₄⋊C₄	—	2	4	no	—
401	C₃×C₄⋊C₄	—	2	4	no	—
402	C₃×C₄⋊C₄	—	2	4	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	2	2	no	—
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	2	2	no	—
410	C₃×C₄⋊C₄	—	2	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	4	no	—
413	C₃×C₄⋊C₄	—	2	4	no	—
414	C₃×C₄⋊C₄	—	4	1	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	1	no	—
419	C₃×C₄⋊C₄	#41	1	4	yes	—
420	C₃×C₄²	—	2	2	no	—
421	C₃×C₄²	—	2	4	no	—
422	C₃×C₄²	—	2	4	no	—
423	C₃×C₄²	—	2	4	no	—
424	C₃×C₄²	—	2	4	no	—
425	C₃×C₄²	—	2	2	no	—
426	C₃×C₄²	—	2	2	no	—
427	C₃×C₄²	—	2	2	no	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	2	2	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	4	no	—
432	C₃×C₄²	—	4	2	no	—
433	C₃×C₄²	—	4	2	no	—
434	C₃×C₄²	—	4	2	no	—
435	C₃×C₄²	—	4	2	no	—
436	C₃×C₄²	#41	1	4	yes	—
437	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
440	C₄⋊Q₈	—	2	4	no	—
441	C₄⋊Q₈	—	2	4	no	—
442	C₄⋊Q₈	—	2	4	no	—
443	#125	—	2	4	no	—
444	C₄×Q₈	—	2	4	no	—
445	C₄×Q₈	—	2	4	no	—
446	C₄×Q₈	—	2	4	no	—
447	C₄×Q₈	—	2	4	no	—
448	C₄×Q₈	—	2	4	no	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₃	1	2	yes	—
484	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₃	1	2	yes	—
490	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₃	1	2	yes	—
496	C₂×C₄²	C₂³×C₃	1	2	yes	—
497	C₂×C₄²	C₂³×C₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
500	#95	C₂³×C₃	1	1	yes	characteristic
501	#95	C₂³×C₃	1	1	yes	characteristic
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	2	yes	—
504	#95	C₂³×C₃	1	1	yes	characteristic
505	#95	C₂³×C₃	1	1	yes	characteristic
506	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
512	#95	C₂³×C₃	1	2	yes	—
513	#95	C₂³×C₃	1	1	yes	characteristic
514	#95	C₂³×C₃	1	1	yes	characteristic
515	#95	C₂³×C₃	1	2	yes	—
516	#95	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
521	#95	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
527	#95	C₂³×C₃	1	1	yes	characteristic
528	#95	C₂³×C₃	1	1	yes	characteristic
529	#95	C₂³×C₃	1	1	yes	characteristic
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	C₂³×C₃	C₂⁵	1	1	yes	characteristic
546	C₃×Q₈	—	2	8	no	—
547	C₃×Q₈	—	4	4	no	—
548	C₃×Q₈	—	4	4	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	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	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	2	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	2	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	2	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	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	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	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	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	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	C₂×#41	1	4	yes	—
609	C₂×C₃×C₄	C₂×#41	1	2	yes	—
610	C₂×C₃×C₄	C₂×#41	1	4	yes	—
611	C₂×C₃×C₄	C₂×#41	1	2	yes	—
612	C₂×C₃×C₄	C₂×#41	1	2	yes	—
613	C₂×C₃×C₄	C₂×#41	1	2	yes	—
614	C₂×C₃×C₄	C₂×#41	1	2	yes	—
615	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
616	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
617	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	C₃×#41	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
640	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	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	—	2	2	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	—	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	1	no	—
683	C₄⋊C₄	C₃×#41	1	4	yes	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	C₃×#41	1	4	yes	—
701	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
702	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
703	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
704	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
706	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²×C₃	#585	1	1	yes	characteristic
708	C₃×C₄	—	2	4	no	—
709	C₃×C₄	—	2	2	no	—
710	C₃×C₄	—	2	2	no	—
711	C₃×C₄	—	2	4	no	—
712	C₃×C₄	—	2	2	no	—
713	C₃×C₄	—	2	2	no	—
714	C₃×C₄	—	2	2	no	—
715	C₃×C₄	—	4	2	no	—
716	C₃×C₄	—	4	2	no	—
717	C₃×C₄	—	4	2	no	—
718	C₃×C₄	—	4	2	no	—
719	C₃×C₄	—	4	2	no	—
720	C₃×C₄	—	4	1	no	—
721	C₃×C₄	—	4	1	no	—
722	C₃×C₄	—	4	1	no	—
723	C₃×C₄	—	4	2	no	—
724	C₃×C₄	—	4	1	no	—
725	C₃×C₄	—	4	1	no	—
726	C₃×C₄	—	4	1	no	—
727	C₃×C₄	—	4	1	no	—
728	C₃×C₄	—	4	1	no	—
729	C₃×C₄	—	4	1	no	—
730	C₃×C₄	#529	1	4	yes	—
731	C₂³	C₂⁵×C₃	1	1	yes	characteristic
732	Q₈	—	2	8	no	—
733	Q₈	—	4	4	no	—
734	Q₈	—	4	4	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	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	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	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	2	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	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	C₂×C₃×#41	1	4	yes	—
795	C₂×C₄	C₂×C₃×#41	1	2	yes	—
796	C₂×C₄	C₂×C₃×#41	1	4	yes	—
797	C₂×C₄	C₂×C₃×#41	1	2	yes	—
798	C₂×C₄	C₂×C₃×#41	1	2	yes	—
799	C₂×C₄	C₂×C₃×#41	1	2	yes	—
800	C₂×C₄	C₂×C₃×#41	1	2	yes	—
801	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
802	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
803	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₃	C₂×#529	1	1	yes	characteristic
805	C₂×C₃	#3507	1	1	yes	characteristic
806	C₂×C₃	#3509	1	1	yes	characteristic
807	C₂×C₃	#3515	1	1	yes	characteristic
808	C₂×C₃	#3516	1	1	yes	characteristic
809	C₂×C₃	#3523	1	1	yes	characteristic
810	C₂×C₃	#3523	1	1	yes	characteristic
811	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
812	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
813	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
814	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
815	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
816	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
817	C₂²	C₃×#585	1	1	yes	characteristic
818	C₄	—	2	4	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	C₃×#529	1	4	yes	—
841	C₃	#35870	1	1	yes	characteristic, direct product factor, Sylow
842	C₂	C₂×C₃×#529	1	1	yes	characteristic
843	C₂	C₃×#3507	1	1	yes	characteristic
844	C₂	C₃×#3509	1	1	yes	characteristic
845	C₂	C₃×#3515	1	1	yes	characteristic
846	C₂	C₃×#3516	1	1	yes	characteristic
847	C₂	C₃×#3523	1	1	yes	characteristic
848	C₂	C₃×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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
24. #35870	C₃	direct (N × H)
841. C₃	#35870	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×#2655	2
C₃×#2642	2
C₃×#2590	2
C₃×#2585	2
C₃×#2565	2
C₃×#2546	2
C₃×#2533	2
C₃×#2528	2
C₃×#2524	2
C₃×#2514	2
C₃×#2511	2
C₃×#2446	2
C₃×#2402	2
C₃×#2370	2
C₃×#2365	2
C₃×#2356	2
C₃×#2355	2
C₃×#2276	2
#35870	3

Subgroups — C3×#35870 #10654477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35870 #10654477