Subgroups — C₃×#41436 #10660043

Order 768.

1600 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2838	C₂	1	2	yes	maximal, complemented
2	C₃×#2745	C₂	1	2	yes	maximal, complemented
3	C₃×#2735	C₂	1	2	yes	maximal, complemented
4	C₃×#2695	C₂	1	2	yes	maximal, complemented
5	C₃×#2684	C₂	1	2	yes	maximal
6	C₃×#2665	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2654	C₂	1	2	yes	maximal, complemented
8	C₃×#2649	C₂	1	2	yes	maximal, complemented
9	C₃×#2534	C₂	1	1	yes	maximal, characteristic
10	C₃×#2532	C₂	1	2	yes	maximal, complemented
11	C₃×#2525	C₂	1	2	yes	maximal, complemented
12	C₃×#2521	C₂	1	2	yes	maximal, complemented
13	C₃×#2521	C₂	1	2	yes	maximal, complemented
14	C₃×#2510	C₂	1	2	yes	maximal, complemented
15	C₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2353	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
20	#41436	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₃×#124	C₂²	1	2	yes	—
23	C₂×C₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₃×#120	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×#401	C₂²	1	2	yes	complemented
29	C₃×#400	C₂²	1	2	yes	complemented
30	C₃×#400	C₂²	1	2	yes	complemented
31	C₃×#400	C₂²	1	1	yes	characteristic, complemented
32	C₃×#400	C₂²	1	2	yes	complemented
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#399	C₂²	1	2	yes	—
35	C₃×#399	C₂²	1	2	yes	—
36	C₃×#399	C₂²	1	1	yes	characteristic, complemented
37	C₃×#398	C₂²	1	1	yes	characteristic, complemented
38	C₃×#398	C₂²	1	2	yes	complemented
39	C₃×#398	C₂²	1	2	yes	complemented
40	C₃×#397	C₂²	1	2	yes	—
41	C₃×#397	C₂²	1	2	yes	—
42	C₃×#397	C₂²	1	2	yes	—
43	C₃×#397	C₂²	1	2	yes	—
44	C₃×#397	C₂²	1	2	yes	—
45	C₃×#397	C₂²	1	2	yes	—
46	C₃×#397	C₂²	1	2	yes	complemented
47	C₃×#397	C₂²	1	1	yes	characteristic, complemented
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#396	C₂²	1	2	yes	—
50	C₃×#396	C₂²	1	2	yes	—
51	C₃×#395	C₂²	1	2	yes	complemented
52	C₃×#395	C₂²	1	2	yes	complemented
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#394	C₂²	1	2	yes	—
56	C₃×#393	C₂²	1	2	yes	—
57	C₃×#393	C₂²	1	2	yes	—
58	C₃×#391	C₂²	1	2	yes	complemented
59	C₃×#391	C₂²	1	2	yes	complemented
60	C₃×#389	C₂²	1	2	yes	complemented
61	C₃×#389	C₂²	1	2	yes	complemented
62	C₃×#388	C₂²	1	2	yes	—
63	C₃×#388	C₂²	1	2	yes	—
64	C₃×#388	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#387	C₂²	1	2	yes	complemented
79	C₃×#387	C₂²	1	2	yes	complemented
80	C₃×#387	C₂²	1	2	yes	complemented
81	C₃×#387	C₂²	1	2	yes	complemented
82	C₃×#386	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#386	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	complemented
88	C₃×#383	C₂²	1	2	yes	complemented
89	C₃×#383	C₂²	1	1	yes	characteristic, complemented
90	C₃×#381	C₂²	1	1	yes	characteristic
91	C₃×#381	C₂²	1	1	yes	characteristic
92	C₃×#380	C₂²	1	1	yes	characteristic
93	C₃×#380	C₂²	1	2	yes	—
94	C₃×#380	C₂²	1	2	yes	complemented
95	C₃×#380	C₂²	1	1	yes	characteristic, complemented
96	C₃×#379	C₂²	1	2	yes	—
97	C₃×#379	C₂²	1	2	yes	—
98	C₃×#379	C₂²	1	1	yes	characteristic
99	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
100	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
101	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×#376	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
108	#2838	C₂×C₃	1	2	yes	complemented
109	#2745	C₂×C₃	1	2	yes	complemented
110	#2735	C₂×C₃	1	2	yes	complemented
111	#2695	C₂×C₃	1	2	yes	complemented
112	#2684	C₂×C₃	1	2	yes	—
113	#2665	C₂×C₃	1	1	yes	characteristic, complemented
114	#2654	C₂×C₃	1	2	yes	complemented
115	#2649	C₂×C₃	1	2	yes	complemented
116	#2534	C₂×C₃	1	1	yes	characteristic
117	#2532	C₂×C₃	1	2	yes	complemented
118	#2525	C₂×C₃	1	2	yes	complemented
119	#2521	C₂×C₃	1	2	yes	complemented
120	#2521	C₂×C₃	1	2	yes	complemented
121	#2510	C₂×C₃	1	2	yes	complemented
122	#2482	C₂×C₃	1	1	yes	characteristic, complemented
123	#2395	C₂×C₃	1	1	yes	characteristic, complemented
124	#2353	C₂×C₃	1	1	yes	characteristic, complemented
125	#2347	C₂×C₃	1	1	yes	characteristic, complemented
126	#2312	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	2	yes	—
129	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
133	C₂³×C₃×C₄	C₂³	1	2	yes	—
134	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
135	C₃×#126	—	4	4	no	—
136	C₃×#124	—	4	4	no	—
137	C₃×#123	—	4	2	no	—
138	C₃×#120	—	4	2	no	—
139	C₃×C₄×D₄	—	2	4	no	—
140	C₃×#117	—	2	4	no	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄²	C₂³	1	2	yes	—
186	C₂×C₃×C₄²	C₂³	1	2	yes	—
187	C₂×C₃×C₄²	C₂³	1	2	yes	—
188	C₂×C₃×C₄²	C₂³	1	2	yes	—
189	C₂×C₃×C₄²	C₂³	1	2	yes	—
190	C₂×C₃×C₄²	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	1	yes	characteristic
192	C₃×#95	C₂³	1	1	yes	characteristic
193	C₃×#95	C₂³	1	2	yes	—
194	C₃×#95	C₂³	1	1	yes	characteristic
195	C₃×#95	C₂³	1	2	yes	—
196	C₃×#95	C₂³	1	1	yes	characteristic
197	C₃×#95	C₂³	1	1	yes	characteristic
198	C₃×#95	C₂³	1	1	yes	characteristic
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	2	yes	—
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	2	yes	—
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₂×#126	C₂²×C₃	1	2	yes	complemented
222	C₂×#124	C₂²×C₃	1	2	yes	—
223	C₂×#123	C₂²×C₃	1	1	yes	characteristic
224	C₂×#120	C₂²×C₃	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
226	C₂×#117	C₂²×C₃	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	#401	C₂²×C₃	1	2	yes	complemented
229	#400	C₂²×C₃	1	1	yes	characteristic, complemented
230	#400	C₂²×C₃	1	2	yes	complemented
231	#400	C₂²×C₃	1	2	yes	complemented
232	#400	C₂²×C₃	1	2	yes	complemented
233	#400	C₂²×C₃	1	2	yes	complemented
234	#399	C₂²×C₃	1	2	yes	—
235	#399	C₂²×C₃	1	2	yes	—
236	#399	C₂²×C₃	1	1	yes	characteristic, complemented
237	#398	C₂²×C₃	1	2	yes	complemented
238	#398	C₂²×C₃	1	1	yes	characteristic, complemented
239	#398	C₂²×C₃	1	2	yes	complemented
240	#397	C₂²×C₃	1	2	yes	—
241	#397	C₂²×C₃	1	2	yes	—
242	#397	C₂²×C₃	1	2	yes	—
243	#397	C₂²×C₃	1	2	yes	—
244	#397	C₂²×C₃	1	2	yes	—
245	#397	C₂²×C₃	1	2	yes	—
246	#397	C₂²×C₃	1	2	yes	complemented
247	#397	C₂²×C₃	1	1	yes	characteristic, complemented
248	#396	C₂²×C₃	1	2	yes	—
249	#396	C₂²×C₃	1	2	yes	—
250	#396	C₂²×C₃	1	2	yes	—
251	#395	C₂²×C₃	1	2	yes	complemented
252	#395	C₂²×C₃	1	2	yes	complemented
253	#394	C₂²×C₃	1	2	yes	—
254	#394	C₂²×C₃	1	2	yes	—
255	#394	C₂²×C₃	1	2	yes	—
256	#393	C₂²×C₃	1	2	yes	—
257	#393	C₂²×C₃	1	2	yes	—
258	#391	C₂²×C₃	1	2	yes	complemented
259	#391	C₂²×C₃	1	2	yes	complemented
260	#389	C₂²×C₃	1	2	yes	complemented
261	#389	C₂²×C₃	1	2	yes	complemented
262	#388	C₂²×C₃	1	2	yes	—
263	#388	C₂²×C₃	1	2	yes	—
264	#388	C₂²×C₃	1	2	yes	—
265	#388	C₂²×C₃	1	2	yes	—
266	#388	C₂²×C₃	1	2	yes	—
267	#388	C₂²×C₃	1	2	yes	—
268	#388	C₂²×C₃	1	2	yes	—
269	#388	C₂²×C₃	1	2	yes	—
270	#388	C₂²×C₃	1	2	yes	—
271	#388	C₂²×C₃	1	2	yes	—
272	#388	C₂²×C₃	1	2	yes	—
273	#388	C₂²×C₃	1	2	yes	—
274	#388	C₂²×C₃	1	2	yes	—
275	#388	C₂²×C₃	1	2	yes	—
276	#388	C₂²×C₃	1	2	yes	—
277	#387	C₂²×C₃	1	2	yes	complemented
278	#387	C₂²×C₃	1	2	yes	complemented
279	#387	C₂²×C₃	1	2	yes	complemented
280	#387	C₂²×C₃	1	2	yes	complemented
281	#387	C₂²×C₃	1	2	yes	complemented
282	#386	C₂²×C₃	1	2	yes	—
283	#386	C₂²×C₃	1	2	yes	—
284	#386	C₂²×C₃	1	2	yes	—
285	#386	C₂²×C₃	1	2	yes	—
286	#385	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	2	yes	complemented
288	#383	C₂²×C₃	1	2	yes	complemented
289	#383	C₂²×C₃	1	1	yes	characteristic, complemented
290	#381	C₂²×C₃	1	1	yes	characteristic
291	#381	C₂²×C₃	1	1	yes	characteristic
292	#380	C₂²×C₃	1	2	yes	—
293	#380	C₂²×C₃	1	1	yes	characteristic
294	#380	C₂²×C₃	1	1	yes	characteristic, complemented
295	#380	C₂²×C₃	1	2	yes	complemented
296	#379	C₂²×C₃	1	2	yes	—
297	#379	C₂²×C₃	1	2	yes	—
298	#379	C₂²×C₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
302	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
305	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
306	#376	C₂²×C₃	1	1	yes	characteristic, complemented
307	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₂⁴×C₃	—	2	2	no	—
309	C₂⁴×C₃	—	4	2	no	—
310	C₂⁴×C₃	—	4	2	no	—
311	C₂⁴×C₃	—	4	1	no	—
312	C₂⁴×C₃	—	4	1	no	—
313	C₂⁴×C₃	C₂⁴	1	2	yes	—
314	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
315	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₃×Q₈	—	4	2	no	—
317	C₂×C₃×Q₈	—	4	2	no	—
318	C₂×C₃×Q₈	—	4	2	no	—
319	C₂×C₃×D₄	—	2	2	no	—
320	C₂×C₃×D₄	—	2	2	no	—
321	C₂×C₃×D₄	—	2	4	no	—
322	C₂×C₃×D₄	—	4	1	no	—
323	C₂×C₃×D₄	—	4	2	no	—
324	C₂×C₃×D₄	—	4	2	no	—
325	C₂²×C₃×C₄	—	2	2	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	4	2	no	—
328	C₂²×C₃×C₄	—	4	1	no	—
329	C₂²×C₃×C₄	—	4	2	no	—
330	C₂²×C₃×C₄	—	4	2	no	—
331	C₂²×C₃×C₄	—	4	2	no	—
332	C₂²×C₃×C₄	—	4	2	no	—
333	C₂²×C₃×C₄	—	4	1	no	—
334	C₂²×C₃×C₄	#41	1	4	yes	—
335	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
336	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
337	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
339	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
342	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
343	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
348	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
349	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	2	2	no	—
354	C₃×C₄⋊C₄	—	4	2	no	—
355	C₃×C₄⋊C₄	—	4	2	no	—
356	C₃×C₄⋊C₄	—	4	2	no	—
357	C₃×C₄⋊C₄	—	4	2	no	—
358	C₃×C₄⋊C₄	—	4	2	no	—
359	C₃×C₄⋊C₄	—	4	2	no	—
360	C₃×C₄⋊C₄	—	4	2	no	—
361	C₃×C₄⋊C₄	—	4	2	no	—
362	C₃×C₄⋊C₄	—	4	2	no	—
363	C₃×C₄⋊C₄	—	4	2	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	2	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₂²⋊C₄	—	2	4	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₃×C₂²⋊C₄	—	2	4	no	—
371	C₃×C₂²⋊C₄	—	2	4	no	—
372	C₃×C₂²⋊C₄	—	2	4	no	—
373	C₃×C₂²⋊C₄	—	2	4	no	—
374	C₃×C₂²⋊C₄	—	2	4	no	—
375	C₃×C₂²⋊C₄	—	2	2	no	—
376	C₃×C₂²⋊C₄	—	4	2	no	—
377	C₃×C₂²⋊C₄	—	4	2	no	—
378	C₃×C₂²⋊C₄	—	4	2	no	—
379	C₃×C₂²⋊C₄	—	4	2	no	—
380	C₃×C₂²⋊C₄	—	4	2	no	—
381	C₃×C₂²⋊C₄	—	4	2	no	—
382	C₃×C₂²⋊C₄	—	4	2	no	—
383	C₃×C₂²⋊C₄	—	4	2	no	—
384	C₃×C₂²⋊C₄	—	4	2	no	—
385	C₃×C₂²⋊C₄	—	4	2	no	—
386	C₃×C₂²⋊C₄	—	4	2	no	—
387	C₃×C₂²⋊C₄	—	4	2	no	—
388	C₃×C₂²⋊C₄	—	4	1	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₂²⋊C₄	—	4	1	no	—
391	C₃×C₂²⋊C₄	—	4	2	no	—
392	C₃×C₂²⋊C₄	—	4	2	no	—
393	C₃×C₄²	—	2	4	no	—
394	C₃×C₄²	—	2	2	no	—
395	C₃×C₄²	—	4	2	no	—
396	C₃×C₄²	—	4	2	no	—
397	C₃×C₄²	—	4	2	no	—
398	C₃×C₄²	—	4	2	no	—
399	C₃×C₄²	—	4	2	no	—
400	C₂⁵	C₂³×C₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₃	1	2	yes	—
402	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
403	C₂²×D₄	C₂³×C₃	1	2	yes	—
404	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₃	1	2	yes	—
407	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
408	#126	—	4	4	no	—
409	#124	—	4	4	no	—
410	#123	—	4	2	no	—
411	#120	—	4	2	no	—
412	C₄×D₄	—	2	4	no	—
413	#117	—	2	4	no	—
414	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₂²⋊C₄	—	2	4	no	—
432	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
457	C₂×C₄²	C₂³×C₃	1	2	yes	—
458	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₃	1	2	yes	—
463	C₂×C₄²	C₂³×C₃	1	2	yes	—
464	#95	C₂³×C₃	1	1	yes	characteristic
465	#95	C₂³×C₃	1	1	yes	characteristic
466	#95	C₂³×C₃	1	2	yes	—
467	#95	C₂³×C₃	1	1	yes	characteristic
468	#95	C₂³×C₃	1	2	yes	—
469	#95	C₂³×C₃	1	1	yes	characteristic
470	#95	C₂³×C₃	1	1	yes	characteristic
471	#95	C₂³×C₃	1	1	yes	characteristic
472	#95	C₂³×C₃	1	2	yes	—
473	#95	C₂³×C₃	1	2	yes	—
474	#95	C₂³×C₃	1	2	yes	—
475	#95	C₂³×C₃	1	2	yes	—
476	#95	C₂³×C₃	1	2	yes	—
477	#95	C₂³×C₃	1	2	yes	—
478	#95	C₂³×C₃	1	2	yes	—
479	#95	C₂³×C₃	1	2	yes	—
480	#95	C₂³×C₃	1	2	yes	—
481	#95	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	2	yes	—
483	#95	C₂³×C₃	1	2	yes	—
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	2	yes	—
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	C₂³×C₃	—	2	1	no	—
495	C₂³×C₃	—	2	1	no	—
496	C₂³×C₃	—	2	2	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	2	no	—
499	C₂³×C₃	—	2	1	no	—
500	C₂³×C₃	—	2	2	no	—
501	C₂³×C₃	—	2	1	no	—
502	C₂³×C₃	—	2	2	no	—
503	C₂³×C₃	—	2	2	no	—
504	C₂³×C₃	—	2	2	no	—
505	C₂³×C₃	—	2	2	no	—
506	C₂³×C₃	—	2	2	no	—
507	C₂³×C₃	—	2	2	no	—
508	C₂³×C₃	—	2	2	no	—
509	C₂³×C₃	—	4	4	no	—
510	C₂³×C₃	—	8	2	no	—
511	C₂³×C₃	—	8	2	no	—
512	C₂³×C₃	—	8	4	no	—
513	C₂³×C₃	—	8	4	no	—
514	C₂³×C₃	C₂×#41	1	2	yes	—
515	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
516	C₂³×C₃	C₂⁵	1	1	yes	characteristic
517	C₃×Q₈	—	8	4	no	—
518	C₃×D₄	—	4	4	no	—
519	C₃×D₄	—	8	4	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	2	no	—
553	C₂×C₃×C₄	—	2	2	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	4	4	no	—
563	C₂×C₃×C₄	—	8	2	no	—
564	C₂×C₃×C₄	—	8	2	no	—
565	C₂×C₃×C₄	—	8	4	no	—
566	C₂×C₃×C₄	C₂×#41	1	2	yes	—
567	C₂×C₃×C₄	C₂×#41	1	2	yes	—
568	C₂⁴	—	2	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	4	1	no	—
571	C₂⁴	—	4	2	no	—
572	C₂⁴	—	4	1	no	—
573	C₂⁴	C₂⁴×C₃	1	2	yes	—
574	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
575	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	C₃×#41	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	1	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	1	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	4	2	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₄²	—	4	2	no	—
659	C₄²	—	4	2	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	2	2	no	—
662	C₂²×C₃	—	2	2	no	—
663	C₂²×C₃	—	2	2	no	—
664	C₂²×C₃	—	2	4	no	—
665	C₂²×C₃	—	4	1	no	—
666	C₂²×C₃	—	4	1	no	—
667	C₂²×C₃	—	4	2	no	—
668	C₂²×C₃	—	4	2	no	—
669	C₂²×C₃	—	4	2	no	—
670	C₂²×C₃	—	4	2	no	—
671	C₂²×C₃	—	4	2	no	—
672	C₂²×C₃	—	4	2	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	—	4	2	no	—
675	C₂²×C₃	—	4	2	no	—
676	C₂²×C₃	—	4	2	no	—
677	C₂²×C₃	—	8	8	no	—
678	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
679	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂²×C₃	#585	1	2	yes	—
681	C₂²×C₃	#585	1	2	yes	—
682	C₂²×C₃	#585	1	1	yes	characteristic
683	C₃×C₄	—	2	2	no	—
684	C₃×C₄	—	2	2	no	—
685	C₃×C₄	—	4	1	no	—
686	C₃×C₄	—	4	2	no	—
687	C₃×C₄	—	4	1	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	—	4	2	no	—
690	C₃×C₄	—	4	1	no	—
691	C₃×C₄	—	4	2	no	—
692	C₃×C₄	—	4	2	no	—
693	C₃×C₄	—	4	2	no	—
694	C₃×C₄	—	4	2	no	—
695	C₃×C₄	—	4	2	no	—
696	C₃×C₄	—	4	2	no	—
697	C₃×C₄	—	4	2	no	—
698	C₃×C₄	—	4	2	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	8	2	no	—
716	C₂³	—	8	2	no	—
717	C₂³	—	8	4	no	—
718	C₂³	—	8	4	no	—
719	C₂³	C₂×C₃×#41	1	2	yes	—
720	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
721	C₂³	C₂⁵×C₃	1	1	yes	characteristic
722	Q₈	—	8	4	no	—
723	D₄	—	4	4	no	—
724	D₄	—	8	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	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	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	8	2	no	—
769	C₂×C₄	—	8	2	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	C₂×C₃×#41	1	2	yes	—
772	C₂×C₄	C₂×C₃×#41	1	2	yes	—
773	C₂×C₃	—	4	2	no	—
774	C₂×C₃	—	4	2	no	—
775	C₂×C₃	—	8	2	no	—
776	C₂×C₃	#3455	1	1	yes	characteristic
777	C₂×C₃	#3491	1	1	yes	characteristic
778	C₂×C₃	#3494	1	1	yes	characteristic
779	C₂×C₃	#3560	1	2	yes	—
780	C₂×C₃	#3568	1	2	yes	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	8	no	—
799	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
800	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂²	C₃×#585	1	2	yes	—
802	C₂²	C₃×#585	1	2	yes	—
803	C₂²	C₃×#585	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₃	#41436	1	1	yes	characteristic, direct product factor, Sylow
821	C₂	—	4	2	no	—
822	C₂	—	4	2	no	—
823	C₂	—	8	2	no	—
824	C₂	C₃×#3455	1	1	yes	characteristic
825	C₂	C₃×#3491	1	1	yes	characteristic
826	C₂	C₃×#3494	1	1	yes	characteristic
827	C₂	C₃×#3560	1	2	yes	—
828	C₂	C₃×#3568	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	C₂²
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×#2838	C₂	semidirect
2. C₃×#2745	C₂	semidirect
3. C₃×#2735	C₂	semidirect
4. C₃×#2695	C₂	semidirect
6. C₃×#2665	C₂	semidirect
7. C₃×#2654	C₂	semidirect
8. C₃×#2649	C₂	semidirect
10. C₃×#2532	C₂	semidirect
11. C₃×#2525	C₂	semidirect
12. C₃×#2521	C₂	semidirect
13. C₃×#2521	C₂	semidirect
14. C₃×#2510	C₂	semidirect
15. C₃×#2482	C₂	semidirect
16. C₃×#2395	C₂	semidirect
17. C₃×#2353	C₂	semidirect
18. C₃×#2347	C₂	semidirect
19. C₃×#2312	C₂	semidirect
20. #41436	C₃	direct (N × H)
21. C₂×C₃×#126	C₂²	semidirect
28. C₃×#401	C₂²	semidirect
29. C₃×#400	C₂²	semidirect
30. C₃×#400	C₂²	semidirect
31. C₃×#400	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
36. C₃×#399	C₂²	semidirect
37. C₃×#398	C₂²	semidirect
38. C₃×#398	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
46. C₃×#397	C₂²	semidirect
47. C₃×#397	C₂²	semidirect
51. C₃×#395	C₂²	semidirect
52. C₃×#395	C₂²	semidirect
58. C₃×#391	C₂²	semidirect
59. C₃×#391	C₂²	semidirect
60. C₃×#389	C₂²	semidirect
61. C₃×#389	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
80. C₃×#387	C₂²	semidirect
81. C₃×#387	C₂²	semidirect
87. C₃×#385	C₂²	semidirect
88. C₃×#383	C₂²	semidirect
89. C₃×#383	C₂²	semidirect
94. C₃×#380	C₂²	semidirect
95. C₃×#380	C₂²	semidirect
99. C₃×C₄×C₄⋊C₄	C₂²	semidirect
100. C₃×C₄×C₄⋊C₄	C₂²	semidirect
101. C₃×C₄×C₄⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×#376	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. #2838	C₂×C₃	semidirect
109. #2745	C₂×C₃	semidirect
110. #2735	C₂×C₃	semidirect
111. #2695	C₂×C₃	semidirect
113. #2665	C₂×C₃	semidirect
114. #2654	C₂×C₃	semidirect
115. #2649	C₂×C₃	semidirect
117. #2532	C₂×C₃	semidirect
118. #2525	C₂×C₃	semidirect
119. #2521	C₂×C₃	semidirect
120. #2521	C₂×C₃	semidirect
121. #2510	C₂×C₃	semidirect
122. #2482	C₂×C₃	semidirect
123. #2395	C₂×C₃	semidirect
124. #2353	C₂×C₃	semidirect
125. #2347	C₂×C₃	semidirect
126. #2312	C₂×C₃	semidirect
221. C₂×#126	C₂²×C₃	semidirect
228. #401	C₂²×C₃	semidirect
229. #400	C₂²×C₃	semidirect
230. #400	C₂²×C₃	semidirect
231. #400	C₂²×C₃	semidirect
232. #400	C₂²×C₃	semidirect
233. #400	C₂²×C₃	semidirect
236. #399	C₂²×C₃	semidirect
237. #398	C₂²×C₃	semidirect
238. #398	C₂²×C₃	semidirect
239. #398	C₂²×C₃	semidirect
246. #397	C₂²×C₃	semidirect
247. #397	C₂²×C₃	semidirect
251. #395	C₂²×C₃	semidirect
252. #395	C₂²×C₃	semidirect
258. #391	C₂²×C₃	semidirect
259. #391	C₂²×C₃	semidirect
260. #389	C₂²×C₃	semidirect
261. #389	C₂²×C₃	semidirect
277. #387	C₂²×C₃	semidirect
278. #387	C₂²×C₃	semidirect
279. #387	C₂²×C₃	semidirect
280. #387	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
287. #385	C₂²×C₃	semidirect
288. #383	C₂²×C₃	semidirect
289. #383	C₂²×C₃	semidirect
294. #380	C₂²×C₃	semidirect
295. #380	C₂²×C₃	semidirect
299. C₄×C₄⋊C₄	C₂²×C₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
304. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
305. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
306. #376	C₂²×C₃	semidirect
307. C₂×#95	C₂²×C₃	semidirect
820. C₃	#41436	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×#2838	2
C₃×#2745	2
C₃×#2735	2
C₃×#2695	2
C₃×#2684	2
C₃×#2665	2
C₃×#2654	2
C₃×#2649	2
C₃×#2534	2
C₃×#2532	2
C₃×#2525	2
C₃×#2521	2
C₃×#2510	2
C₃×#2482	2
C₃×#2395	2
C₃×#2353	2
C₃×#2347	2
C₃×#2312	2
#41436	3

Subgroups — C3×#41436 #10660043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41436 #10660043