Subgroups — C₃×#40613 #10659220

Order 768.

1778 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2841	C₂	1	2	yes	maximal, complemented
2	C₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2768	C₂	1	2	yes	maximal, complemented
5	C₃×#2742	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2720	C₂	1	2	yes	maximal, complemented
7	C₃×#2677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2667	C₂	1	2	yes	maximal, complemented
9	C₃×#2628	C₂	1	2	yes	maximal, complemented
10	C₃×#2626	C₂	1	1	yes	maximal, characteristic
11	C₃×#2583	C₂	1	2	yes	maximal, complemented
12	C₃×#2505	C₂	1	2	yes	maximal, complemented
13	C₃×#2473	C₂	1	2	yes	maximal, complemented
14	C₃×#2441	C₂	1	2	yes	maximal, complemented
15	C₃×#2440	C₂	1	2	yes	maximal, complemented
16	C₃×#2437	C₂	1	2	yes	maximal
17	C₂×C₃×#399	C₂	1	1	yes	maximal, characteristic
18	C₃×#2342	C₂	1	2	yes	maximal
19	C₃×#2315	C₂	1	1	yes	maximal, characteristic
20	#40613	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₃×#125	C₂²	1	2	yes	complemented
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×#117	C₂²	1	2	yes	—
27	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#400	C₂²	1	2	yes	complemented
37	C₃×#399	C₂²	1	1	yes	characteristic
38	C₃×#399	C₂²	1	1	yes	characteristic
39	C₃×#399	C₂²	1	2	yes	—
40	C₃×#399	C₂²	1	2	yes	—
41	C₃×#399	C₂²	1	1	yes	characteristic
42	C₃×#399	C₂²	1	1	yes	characteristic
43	C₃×#399	C₂²	1	2	yes	—
44	C₃×#399	C₂²	1	1	yes	characteristic
45	C₃×#399	C₂²	1	1	yes	characteristic
46	C₃×#398	C₂²	1	2	yes	complemented
47	C₃×#398	C₂²	1	2	yes	complemented
48	C₃×#398	C₂²	1	2	yes	complemented
49	C₃×#398	C₂²	1	2	yes	complemented
50	C₃×#398	C₂²	1	2	yes	complemented
51	C₃×#398	C₂²	1	2	yes	complemented
52	C₃×#398	C₂²	1	2	yes	complemented
53	C₃×#398	C₂²	1	2	yes	complemented
54	C₃×#396	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#396	C₂²	1	2	yes	—
57	C₃×#396	C₂²	1	2	yes	—
58	C₃×#395	C₂²	1	2	yes	complemented
59	C₃×#395	C₂²	1	2	yes	complemented
60	C₃×#395	C₂²	1	2	yes	complemented
61	C₃×#395	C₂²	1	2	yes	complemented
62	C₃×#393	C₂²	1	1	yes	characteristic
63	C₃×#393	C₂²	1	1	yes	characteristic
64	C₃×#393	C₂²	1	2	yes	—
65	C₃×#389	C₂²	1	2	yes	complemented
66	C₃×#389	C₂²	1	2	yes	complemented
67	C₃×#389	C₂²	1	2	yes	complemented
68	C₃×#389	C₂²	1	2	yes	complemented
69	C₃×#389	C₂²	1	2	yes	complemented
70	C₃×#389	C₂²	1	2	yes	complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#389	C₂²	1	2	yes	complemented
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×#385	C₂²	1	2	yes	—
82	C₃×#385	C₂²	1	1	yes	characteristic
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	1	yes	characteristic
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	1	yes	characteristic
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	1	yes	characteristic
94	C₃×#384	C₂²	1	2	yes	complemented
95	C₃×#382	C₂²	1	2	yes	complemented
96	C₃×#381	C₂²	1	2	yes	—
97	C₃×#380	C₂²	1	1	yes	characteristic
98	C₃×#380	C₂²	1	2	yes	—
99	C₃×#380	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#379	C₂²	1	2	yes	—
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂×C₃×#95	C₂²	1	1	yes	characteristic
108	#2841	C₂×C₃	1	2	yes	complemented
109	#2807	C₂×C₃	1	1	yes	characteristic, complemented
110	#2807	C₂×C₃	1	1	yes	characteristic, complemented
111	#2768	C₂×C₃	1	2	yes	complemented
112	#2742	C₂×C₃	1	1	yes	characteristic, complemented
113	#2720	C₂×C₃	1	2	yes	complemented
114	#2677	C₂×C₃	1	1	yes	characteristic, complemented
115	#2667	C₂×C₃	1	2	yes	complemented
116	#2628	C₂×C₃	1	2	yes	complemented
117	#2626	C₂×C₃	1	1	yes	characteristic
118	#2583	C₂×C₃	1	2	yes	complemented
119	#2505	C₂×C₃	1	2	yes	complemented
120	#2473	C₂×C₃	1	2	yes	complemented
121	#2441	C₂×C₃	1	2	yes	complemented
122	#2440	C₂×C₃	1	2	yes	complemented
123	#2437	C₂×C₃	1	2	yes	—
124	C₂×#399	C₂×C₃	1	1	yes	characteristic
125	#2342	C₂×C₃	1	2	yes	—
126	#2315	C₂×C₃	1	1	yes	characteristic
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂³×C₃×C₄	C₂³	1	2	yes	—
131	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	2	yes	—
133	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
134	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₂³×C₃×C₄	C₂³	1	2	yes	—
137	C₃×C₄⋊Q₈	—	4	4	no	—
138	C₃×#125	—	4	4	no	—
139	C₃×C₂²⋊Q₈	—	4	4	no	—
140	C₃×C₂²⋊Q₈	—	4	2	no	—
141	C₃×C₂²⋊Q₈	—	4	4	no	—
142	C₃×#117	—	4	4	no	—
143	C₂×C₃×C₄⋊C₄	—	4	4	no	—
144	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	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×C₂²⋊C₄	—	4	4	no	—
175	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
176	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
177	C₂×C₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
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	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	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	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	1	yes	characteristic
203	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
218	C₃×#95	C₂³	1	1	yes	characteristic
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
227	C₂×#125	C₂²×C₃	1	2	yes	complemented
228	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
229	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
231	C₂×#117	C₂²×C₃	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
236	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
238	#400	C₂²×C₃	1	2	yes	complemented
239	#400	C₂²×C₃	1	2	yes	complemented
240	#400	C₂²×C₃	1	2	yes	complemented
241	#400	C₂²×C₃	1	2	yes	complemented
242	#399	C₂²×C₃	1	1	yes	characteristic
243	#399	C₂²×C₃	1	1	yes	characteristic
244	#399	C₂²×C₃	1	1	yes	characteristic
245	#399	C₂²×C₃	1	2	yes	—
246	#399	C₂²×C₃	1	2	yes	—
247	#399	C₂²×C₃	1	1	yes	characteristic
248	#399	C₂²×C₃	1	1	yes	characteristic
249	#399	C₂²×C₃	1	2	yes	—
250	#399	C₂²×C₃	1	1	yes	characteristic
251	#398	C₂²×C₃	1	2	yes	complemented
252	#398	C₂²×C₃	1	2	yes	complemented
253	#398	C₂²×C₃	1	2	yes	complemented
254	#398	C₂²×C₃	1	2	yes	complemented
255	#398	C₂²×C₃	1	2	yes	complemented
256	#398	C₂²×C₃	1	2	yes	complemented
257	#398	C₂²×C₃	1	2	yes	complemented
258	#398	C₂²×C₃	1	2	yes	complemented
259	#396	C₂²×C₃	1	2	yes	—
260	#396	C₂²×C₃	1	2	yes	—
261	#396	C₂²×C₃	1	2	yes	—
262	#396	C₂²×C₃	1	2	yes	—
263	#395	C₂²×C₃	1	2	yes	complemented
264	#395	C₂²×C₃	1	2	yes	complemented
265	#395	C₂²×C₃	1	2	yes	complemented
266	#395	C₂²×C₃	1	2	yes	complemented
267	#393	C₂²×C₃	1	2	yes	—
268	#393	C₂²×C₃	1	1	yes	characteristic
269	#393	C₂²×C₃	1	1	yes	characteristic
270	#389	C₂²×C₃	1	2	yes	complemented
271	#389	C₂²×C₃	1	2	yes	complemented
272	#389	C₂²×C₃	1	2	yes	complemented
273	#389	C₂²×C₃	1	2	yes	complemented
274	#389	C₂²×C₃	1	2	yes	complemented
275	#389	C₂²×C₃	1	2	yes	complemented
276	#389	C₂²×C₃	1	2	yes	complemented
277	#389	C₂²×C₃	1	2	yes	complemented
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	—
281	#388	C₂²×C₃	1	2	yes	—
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#387	C₂²×C₃	1	2	yes	complemented
286	#385	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	1	yes	characteristic
288	#385	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	1	yes	characteristic
290	#385	C₂²×C₃	1	1	yes	characteristic
291	#385	C₂²×C₃	1	1	yes	characteristic
292	#385	C₂²×C₃	1	2	yes	—
293	#385	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	2	yes	—
296	#385	C₂²×C₃	1	2	yes	—
297	#385	C₂²×C₃	1	2	yes	—
298	#385	C₂²×C₃	1	2	yes	—
299	#384	C₂²×C₃	1	2	yes	complemented
300	#382	C₂²×C₃	1	2	yes	complemented
301	#381	C₂²×C₃	1	2	yes	—
302	#380	C₂²×C₃	1	2	yes	—
303	#380	C₂²×C₃	1	2	yes	—
304	#380	C₂²×C₃	1	2	yes	—
305	#380	C₂²×C₃	1	1	yes	characteristic
306	#380	C₂²×C₃	1	2	yes	—
307	#380	C₂²×C₃	1	2	yes	—
308	#379	C₂²×C₃	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
312	C₂×#95	C₂²×C₃	1	1	yes	characteristic
313	C₂⁴×C₃	—	2	2	no	—
314	C₂⁴×C₃	—	2	2	no	—
315	C₂⁴×C₃	—	4	2	no	—
316	C₂⁴×C₃	—	4	2	no	—
317	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
318	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
319	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
321	C₂×C₃×Q₈	—	4	2	no	—
322	C₂×C₃×Q₈	—	4	2	no	—
323	C₂×C₃×Q₈	—	4	1	no	—
324	C₂×C₃×Q₈	—	4	2	no	—
325	C₂×C₃×Q₈	—	4	2	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	2	4	no	—
328	C₂²×C₃×C₄	—	2	2	no	—
329	C₂²×C₃×C₄	—	2	4	no	—
330	C₂²×C₃×C₄	—	2	4	no	—
331	C₂²×C₃×C₄	—	4	2	no	—
332	C₂²×C₃×C₄	—	4	2	no	—
333	C₂²×C₃×C₄	—	4	2	no	—
334	C₂²×C₃×C₄	—	4	2	no	—
335	C₂²×C₃×C₄	—	4	2	no	—
336	C₂²×C₃×C₄	—	4	1	no	—
337	C₂²×C₃×C₄	—	4	1	no	—
338	C₂²×C₃×C₄	—	4	2	no	—
339	C₂²×C₃×C₄	—	4	2	no	—
340	C₂²×C₃×C₄	—	4	2	no	—
341	C₂²×C₃×C₄	—	4	2	no	—
342	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
343	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
344	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
345	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
346	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
350	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
359	C₃×C₄⋊C₄	—	2	4	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	—	2	4	no	—
364	C₃×C₄⋊C₄	—	4	2	no	—
365	C₃×C₄⋊C₄	—	4	2	no	—
366	C₃×C₄⋊C₄	—	4	1	no	—
367	C₃×C₄⋊C₄	—	4	2	no	—
368	C₃×C₄⋊C₄	—	4	1	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₄⋊C₄	—	4	2	no	—
377	C₃×C₄⋊C₄	—	4	2	no	—
378	C₃×C₄⋊C₄	—	4	2	no	—
379	C₃×C₄⋊C₄	—	4	2	no	—
380	C₃×C₄⋊C₄	—	4	2	no	—
381	C₃×C₄⋊C₄	—	4	1	no	—
382	C₃×C₄⋊C₄	—	4	2	no	—
383	C₃×C₄⋊C₄	—	4	2	no	—
384	C₃×C₄⋊C₄	—	4	2	no	—
385	C₃×C₄⋊C₄	—	4	2	no	—
386	C₃×C₄⋊C₄	—	4	2	no	—
387	C₃×C₄⋊C₄	—	4	2	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	4	no	—
390	C₃×C₂²⋊C₄	—	2	4	no	—
391	C₃×C₂²⋊C₄	—	2	4	no	—
392	C₃×C₂²⋊C₄	—	2	4	no	—
393	C₃×C₂²⋊C₄	—	4	2	no	—
394	C₃×C₂²⋊C₄	—	4	2	no	—
395	C₃×C₂²⋊C₄	—	4	2	no	—
396	C₃×C₂²⋊C₄	—	4	1	no	—
397	C₃×C₂²⋊C₄	—	4	1	no	—
398	C₃×C₂²⋊C₄	—	4	1	no	—
399	C₃×C₂²⋊C₄	—	4	1	no	—
400	C₃×C₂²⋊C₄	—	4	2	no	—
401	C₃×C₂²⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	4	2	no	—
403	C₃×C₂²⋊C₄	—	4	2	no	—
404	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
405	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
406	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
407	C₃×C₄²	—	2	4	no	—
408	C₃×C₄²	—	4	2	no	—
409	C₃×C₄²	—	4	2	no	—
410	C₃×C₄²	—	4	2	no	—
411	C₂⁵	C₂³×C₃	1	1	yes	characteristic
412	C₂²×Q₈	C₂³×C₃	1	2	yes	—
413	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₃	1	2	yes	—
415	C₂³×C₄	C₂³×C₃	1	2	yes	—
416	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₃	1	2	yes	—
421	C₄⋊Q₈	—	4	4	no	—
422	#125	—	4	4	no	—
423	C₂²⋊Q₈	—	4	4	no	—
424	C₂²⋊Q₈	—	4	2	no	—
425	C₂²⋊Q₈	—	4	4	no	—
426	#117	—	4	4	no	—
427	C₂×C₄⋊C₄	—	4	4	no	—
428	C₂×C₄⋊C₄	—	4	2	no	—
429	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₂×C₂²⋊C₄	—	4	4	no	—
459	C₂×C₂²⋊C₄	—	4	2	no	—
460	C₂×C₂²⋊C₄	—	4	2	no	—
461	C₂×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
462	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₃	1	2	yes	—
483	C₂×C₄²	C₂³×C₃	1	2	yes	—
484	C₂×C₄²	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	1	yes	characteristic
487	#95	C₂³×C₃	1	1	yes	characteristic
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	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	2	yes	—
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	1	yes	characteristic
502	#95	C₂³×C₃	1	1	yes	characteristic
503	#95	C₂³×C₃	1	2	yes	—
504	#95	C₂³×C₃	1	2	yes	—
505	#95	C₂³×C₃	1	2	yes	—
506	#95	C₂³×C₃	1	2	yes	—
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	2	yes	—
510	C₂³×C₃	—	2	2	no	—
511	C₂³×C₃	—	2	2	no	—
512	C₂³×C₃	—	2	2	no	—
513	C₂³×C₃	—	2	2	no	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	—	2	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	2	2	no	—
520	C₂³×C₃	—	2	8	no	—
521	C₂³×C₃	—	4	8	no	—
522	C₂³×C₃	—	8	2	no	—
523	C₂³×C₃	—	8	4	no	—
524	C₂³×C₃	—	8	2	no	—
525	C₂³×C₃	C₂²×Q₈	1	2	yes	—
526	C₂³×C₃	C₂²×Q₈	1	2	yes	—
527	C₂³×C₃	C₂²×Q₈	1	2	yes	—
528	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
529	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
530	C₂³×C₃	C₂⁵	1	1	yes	characteristic
531	C₃×Q₈	—	8	4	no	—
532	C₃×Q₈	—	8	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	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	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	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	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	4	8	no	—
575	C₂×C₃×C₄	—	4	8	no	—
576	C₂×C₃×C₄	—	4	4	no	—
577	C₂×C₃×C₄	—	8	2	no	—
578	C₂×C₃×C₄	—	8	4	no	—
579	C₂×C₃×C₄	—	8	2	no	—
580	C₂×C₃×C₄	—	8	2	no	—
581	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
582	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
583	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
589	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
590	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
591	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	2	no	—
594	C₂×Q₈	—	4	1	no	—
595	C₂×Q₈	—	4	2	no	—
596	C₂×Q₈	—	4	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	4	2	no	—
603	C₂²×C₄	—	4	2	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
614	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	1	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	1	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	1	no	—
668	C₂²⋊C₄	—	4	1	no	—
669	C₂²⋊C₄	—	4	1	no	—
670	C₂²⋊C₄	—	4	1	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
676	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
677	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
678	C₄²	—	2	4	no	—
679	C₄²	—	4	2	no	—
680	C₄²	—	4	2	no	—
681	C₄²	—	4	2	no	—
682	C₂²×C₃	—	2	4	no	—
683	C₂²×C₃	—	2	2	no	—
684	C₂²×C₃	—	2	4	no	—
685	C₂²×C₃	—	2	2	no	—
686	C₂²×C₃	—	2	2	no	—
687	C₂²×C₃	—	2	2	no	—
688	C₂²×C₃	—	2	4	no	—
689	C₂²×C₃	—	2	4	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	—	4	1	no	—
692	C₂²×C₃	—	4	2	no	—
693	C₂²×C₃	—	4	2	no	—
694	C₂²×C₃	—	4	1	no	—
695	C₂²×C₃	—	4	1	no	—
696	C₂²×C₃	—	8	8	no	—
697	C₂²×C₃	#544	1	4	yes	—
698	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
699	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
701	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
702	C₂²×C₃	#585	1	2	yes	—
703	C₃×C₄	—	2	4	no	—
704	C₃×C₄	—	2	4	no	—
705	C₃×C₄	—	2	4	no	—
706	C₃×C₄	—	4	2	no	—
707	C₃×C₄	—	4	1	no	—
708	C₃×C₄	—	4	1	no	—
709	C₃×C₄	—	4	2	no	—
710	C₃×C₄	—	4	2	no	—
711	C₃×C₄	—	4	2	no	—
712	C₃×C₄	—	4	2	no	—
713	C₃×C₄	—	4	2	no	—
714	C₃×C₄	—	4	1	no	—
715	C₃×C₄	—	4	2	no	—
716	C₃×C₄	—	4	2	no	—
717	C₃×C₄	—	4	1	no	—
718	C₃×C₄	—	4	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	4	8	no	—
731	C₂³	—	8	2	no	—
732	C₂³	—	8	4	no	—
733	C₂³	—	8	2	no	—
734	C₂³	C₂²×C₃×Q₈	1	2	yes	—
735	C₂³	C₂²×C₃×Q₈	1	2	yes	—
736	C₂³	C₂²×C₃×Q₈	1	2	yes	—
737	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
738	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
739	C₂³	C₂⁵×C₃	1	1	yes	characteristic
740	Q₈	—	8	4	no	—
741	Q₈	—	8	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	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	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	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	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	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
791	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
792	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
793	C₂×C₃	—	2	4	no	—
794	C₂×C₃	—	4	2	no	—
795	C₂×C₃	—	4	2	no	—
796	C₂×C₃	C₂×#544	1	1	yes	characteristic
797	C₂×C₃	#3501	1	2	yes	—
798	C₂×C₃	#3533	1	1	yes	characteristic
799	C₂×C₃	#3535	1	2	yes	—
800	C₂×C₃	#3543	1	1	yes	characteristic
801	C₂²	—	2	4	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	8	8	no	—
816	C₂²	C₃×#544	1	4	yes	—
817	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
818	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
819	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
820	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
821	C₂²	C₃×#585	1	2	yes	—
822	C₄	—	2	4	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₃	#40613	1	1	yes	characteristic, direct product factor, Sylow
839	C₂	—	2	4	no	—
840	C₂	—	4	2	no	—
841	C₂	—	4	2	no	—
842	C₂	C₂×C₃×#544	1	1	yes	characteristic
843	C₂	C₃×#3501	1	2	yes	—
844	C₂	C₃×#3533	1	1	yes	characteristic
845	C₂	C₃×#3535	1	2	yes	—
846	C₂	C₃×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	C₂³
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×#2841	C₂	semidirect
2. C₃×#2807	C₂	semidirect
3. C₃×#2807	C₂	semidirect
4. C₃×#2768	C₂	semidirect
5. C₃×#2742	C₂	semidirect
6. C₃×#2720	C₂	semidirect
7. C₃×#2677	C₂	semidirect
8. C₃×#2667	C₂	semidirect
9. C₃×#2628	C₂	semidirect
11. C₃×#2583	C₂	semidirect
12. C₃×#2505	C₂	semidirect
13. C₃×#2473	C₂	semidirect
14. C₃×#2441	C₂	semidirect
15. C₃×#2440	C₂	semidirect
20. #40613	C₃	direct (N × H)
21. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₃×#125	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
49. C₃×#398	C₂²	semidirect
50. C₃×#398	C₂²	semidirect
51. C₃×#398	C₂²	semidirect
52. C₃×#398	C₂²	semidirect
53. C₃×#398	C₂²	semidirect
58. C₃×#395	C₂²	semidirect
59. C₃×#395	C₂²	semidirect
60. C₃×#395	C₂²	semidirect
61. C₃×#395	C₂²	semidirect
65. C₃×#389	C₂²	semidirect
66. C₃×#389	C₂²	semidirect
67. C₃×#389	C₂²	semidirect
68. C₃×#389	C₂²	semidirect
69. C₃×#389	C₂²	semidirect
70. C₃×#389	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
80. C₃×#387	C₂²	semidirect
94. C₃×#384	C₂²	semidirect
95. C₃×#382	C₂²	semidirect
108. #2841	C₂×C₃	semidirect
109. #2807	C₂×C₃	semidirect
110. #2807	C₂×C₃	semidirect
111. #2768	C₂×C₃	semidirect
112. #2742	C₂×C₃	semidirect
113. #2720	C₂×C₃	semidirect
114. #2677	C₂×C₃	semidirect
115. #2667	C₂×C₃	semidirect
116. #2628	C₂×C₃	semidirect
118. #2583	C₂×C₃	semidirect
119. #2505	C₂×C₃	semidirect
120. #2473	C₂×C₃	semidirect
121. #2441	C₂×C₃	semidirect
122. #2440	C₂×C₃	semidirect
177. C₂×C₃×C₂²⋊C₄	Q₈	semidirect
226. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
227. C₂×#125	C₂²×C₃	semidirect
238. #400	C₂²×C₃	semidirect
239. #400	C₂²×C₃	semidirect
240. #400	C₂²×C₃	semidirect
241. #400	C₂²×C₃	semidirect
251. #398	C₂²×C₃	semidirect
252. #398	C₂²×C₃	semidirect
253. #398	C₂²×C₃	semidirect
254. #398	C₂²×C₃	semidirect
255. #398	C₂²×C₃	semidirect
256. #398	C₂²×C₃	semidirect
257. #398	C₂²×C₃	semidirect
258. #398	C₂²×C₃	semidirect
263. #395	C₂²×C₃	semidirect
264. #395	C₂²×C₃	semidirect
265. #395	C₂²×C₃	semidirect
266. #395	C₂²×C₃	semidirect
270. #389	C₂²×C₃	semidirect
271. #389	C₂²×C₃	semidirect
272. #389	C₂²×C₃	semidirect
273. #389	C₂²×C₃	semidirect
274. #389	C₂²×C₃	semidirect
275. #389	C₂²×C₃	semidirect
276. #389	C₂²×C₃	semidirect
277. #389	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
285. #387	C₂²×C₃	semidirect
299. #384	C₂²×C₃	semidirect
300. #382	C₂²×C₃	semidirect
461. C₂×C₂²⋊C₄	C₃×Q₈	semidirect
838. C₃	#40613	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×#2841	2
C₃×#2807	2
C₃×#2768	2
C₃×#2742	2
C₃×#2720	2
C₃×#2677	2
C₃×#2667	2
C₃×#2628	2
C₃×#2626	2
C₃×#2583	2
C₃×#2505	2
C₃×#2473	2
C₃×#2441	2
C₃×#2440	2
C₃×#2437	2
C₂×C₃×#399	2
C₃×#2342	2
C₃×#2315	2
#40613	3

Subgroups — C3×#40613 #10659220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40613 #10659220