Subgroups — C₃×#41405 #10660012

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#551	C₂	1	2	yes	maximal, complemented
2	C₃×#2814	C₂	1	2	yes	maximal, complemented
3	C₃×#2722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2722	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2715	C₂	1	2	yes	maximal, complemented
6	C₃×#2712	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2695	C₂	1	2	yes	maximal, complemented
8	C₃×#2693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2630	C₂	1	2	yes	maximal, complemented
10	C₃×#2625	C₂	1	2	yes	maximal, complemented
11	C₃×#2617	C₂	1	1	yes	maximal, characteristic
12	C₃×#2485	C₂	1	2	yes	maximal, complemented
13	C₃×#2450	C₂	1	2	yes	maximal, complemented
14	C₃×#2438	C₂	1	2	yes	maximal, complemented
15	C₃×#2425	C₂	1	2	yes	maximal, complemented
16	C₃×#2413	C₂	1	2	yes	maximal, complemented
17	C₃×#2412	C₂	1	2	yes	maximal, complemented
18	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
20	#41405	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#551	—	2	16	no	—
22	C₂×C₃×#126	C₂²	1	2	yes	—
23	C₂×C₃×#126	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×#123	C₂²	1	2	yes	—
28	C₂×C₃×#123	C₂²	1	2	yes	—
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#120	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×#117	C₂²	1	2	yes	—
36	C₂×C₃×#117	C₂²	1	2	yes	—
37	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	2	yes	complemented
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#398	C₂²	1	2	yes	complemented
45	C₃×#398	C₂²	1	2	yes	complemented
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×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	1	yes	characteristic
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#397	C₂²	1	2	yes	—
54	C₃×#397	C₂²	1	2	yes	—
55	C₃×#397	C₂²	1	1	yes	characteristic
56	C₃×#397	C₂²	1	2	yes	—
57	C₃×#397	C₂²	1	1	yes	characteristic
58	C₃×#397	C₂²	1	1	yes	characteristic
59	C₃×#397	C₂²	1	1	yes	characteristic
60	C₃×#397	C₂²	1	2	yes	complemented
61	C₃×#396	C₂²	1	2	yes	complemented
62	C₃×#396	C₂²	1	2	yes	complemented
63	C₃×#396	C₂²	1	2	yes	complemented
64	C₃×#396	C₂²	1	2	yes	complemented
65	C₃×#395	C₂²	1	2	yes	complemented
66	C₃×#394	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#394	C₂²	1	2	yes	—
69	C₃×#394	C₂²	1	2	yes	—
70	C₃×#394	C₂²	1	2	yes	complemented
71	C₃×#393	C₂²	1	2	yes	complemented
72	C₃×#392	C₂²	1	1	yes	characteristic
73	C₃×#392	C₂²	1	1	yes	characteristic
74	C₃×#391	C₂²	1	2	yes	complemented
75	C₃×#391	C₂²	1	2	yes	complemented
76	C₃×#389	C₂²	1	2	yes	complemented
77	C₃×#389	C₂²	1	2	yes	complemented
78	C₃×#389	C₂²	1	2	yes	complemented
79	C₃×#389	C₂²	1	2	yes	complemented
80	C₃×#388	C₂²	1	2	yes	complemented
81	C₃×#388	C₂²	1	2	yes	complemented
82	C₃×#388	C₂²	1	2	yes	complemented
83	C₃×#387	C₂²	1	2	yes	complemented
84	C₃×#387	C₂²	1	2	yes	complemented
85	C₃×#387	C₂²	1	2	yes	complemented
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	2	yes	complemented
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	1	yes	characteristic
95	C₃×#385	C₂²	1	1	yes	characteristic
96	C₃×#385	C₂²	1	1	yes	characteristic
97	C₃×#385	C₂²	1	1	yes	characteristic
98	C₃×#385	C₂²	1	2	yes	complemented
99	C₃×#381	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	1	yes	characteristic
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	2	yes	—
105	C₃×#380	C₂²	1	2	yes	complemented
106	C₃×#380	C₂²	1	2	yes	complemented
107	C₂×C₃×#95	C₂²	1	2	yes	—
108	C₂×C₃×#95	C₂²	1	1	yes	characteristic
109	C₂×#551	C₂×C₃	1	2	yes	complemented
110	#2814	C₂×C₃	1	2	yes	complemented
111	#2722	C₂×C₃	1	1	yes	characteristic, complemented
112	#2722	C₂×C₃	1	1	yes	characteristic, complemented
113	#2715	C₂×C₃	1	2	yes	complemented
114	#2712	C₂×C₃	1	1	yes	characteristic, complemented
115	#2695	C₂×C₃	1	2	yes	complemented
116	#2693	C₂×C₃	1	1	yes	characteristic, complemented
117	#2630	C₂×C₃	1	2	yes	complemented
118	#2625	C₂×C₃	1	2	yes	complemented
119	#2617	C₂×C₃	1	1	yes	characteristic
120	#2485	C₂×C₃	1	2	yes	complemented
121	#2450	C₂×C₃	1	2	yes	complemented
122	#2438	C₂×C₃	1	2	yes	complemented
123	#2425	C₂×C₃	1	2	yes	complemented
124	#2413	C₂×C₃	1	2	yes	complemented
125	#2412	C₂×C₃	1	2	yes	complemented
126	C₂×#397	C₂×C₃	1	1	yes	characteristic, complemented
127	#2315	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×D₄	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	2	yes	—
133	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
134	C₂³×C₃×C₄	C₂³	1	2	yes	—
135	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
136	C₂³×C₃×C₄	C₂³	1	2	yes	—
137	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂³	1	2	yes	—
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₃×#126	—	2	8	no	—
143	C₃×#126	—	2	8	no	—
144	C₃×#124	—	2	8	no	—
145	C₃×#123	—	2	8	no	—
146	C₃×#123	—	2	8	no	—
147	C₃×#123	—	2	8	no	—
148	C₃×#123	—	4	4	no	—
149	C₃×C₂²⋊Q₈	—	2	8	no	—
150	C₃×C₂²⋊Q₈	—	2	8	no	—
151	C₃×#121	—	4	2	no	—
152	C₃×#120	—	2	8	no	—
153	C₃×C₄×D₄	—	2	8	no	—
154	C₃×C₄×D₄	—	2	8	no	—
155	C₃×#117	—	2	8	no	—
156	C₃×#117	—	2	8	no	—
157	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
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	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	2	8	no	—
180	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
181	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
182	C₂×C₃×C₂²⋊C₄	D₄	1	8	yes	complemented
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	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	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	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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	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	#551	—	2	16	no	—
236	C₂×#126	C₂²×C₃	1	2	yes	—
237	C₂×#126	C₂²×C₃	1	2	yes	—
238	C₂×#124	C₂²×C₃	1	2	yes	—
239	C₂×#123	C₂²×C₃	1	2	yes	—
240	C₂×#123	C₂²×C₃	1	2	yes	—
241	C₂×#123	C₂²×C₃	1	2	yes	—
242	C₂×#123	C₂²×C₃	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
245	C₂×#121	C₂²×C₃	1	1	yes	characteristic
246	C₂×#120	C₂²×C₃	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
249	C₂×#117	C₂²×C₃	1	2	yes	—
250	C₂×#117	C₂²×C₃	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
256	#400	C₂²×C₃	1	2	yes	complemented
257	#400	C₂²×C₃	1	2	yes	complemented
258	#398	C₂²×C₃	1	2	yes	complemented
259	#398	C₂²×C₃	1	2	yes	complemented
260	#398	C₂²×C₃	1	2	yes	complemented
261	#398	C₂²×C₃	1	2	yes	complemented
262	#398	C₂²×C₃	1	2	yes	complemented
263	#398	C₂²×C₃	1	2	yes	complemented
264	#397	C₂²×C₃	1	1	yes	characteristic
265	#397	C₂²×C₃	1	1	yes	characteristic
266	#397	C₂²×C₃	1	2	yes	—
267	#397	C₂²×C₃	1	2	yes	—
268	#397	C₂²×C₃	1	2	yes	—
269	#397	C₂²×C₃	1	1	yes	characteristic
270	#397	C₂²×C₃	1	2	yes	—
271	#397	C₂²×C₃	1	1	yes	characteristic
272	#397	C₂²×C₃	1	1	yes	characteristic
273	#397	C₂²×C₃	1	1	yes	characteristic
274	#397	C₂²×C₃	1	2	yes	complemented
275	#396	C₂²×C₃	1	2	yes	complemented
276	#396	C₂²×C₃	1	2	yes	complemented
277	#396	C₂²×C₃	1	2	yes	complemented
278	#396	C₂²×C₃	1	2	yes	complemented
279	#395	C₂²×C₃	1	2	yes	complemented
280	#394	C₂²×C₃	1	2	yes	—
281	#394	C₂²×C₃	1	2	yes	—
282	#394	C₂²×C₃	1	2	yes	—
283	#394	C₂²×C₃	1	2	yes	—
284	#394	C₂²×C₃	1	2	yes	complemented
285	#393	C₂²×C₃	1	2	yes	complemented
286	#392	C₂²×C₃	1	1	yes	characteristic
287	#392	C₂²×C₃	1	1	yes	characteristic
288	#391	C₂²×C₃	1	2	yes	complemented
289	#391	C₂²×C₃	1	2	yes	complemented
290	#389	C₂²×C₃	1	2	yes	complemented
291	#389	C₂²×C₃	1	2	yes	complemented
292	#389	C₂²×C₃	1	2	yes	complemented
293	#389	C₂²×C₃	1	2	yes	complemented
294	#388	C₂²×C₃	1	2	yes	complemented
295	#388	C₂²×C₃	1	2	yes	complemented
296	#388	C₂²×C₃	1	2	yes	complemented
297	#387	C₂²×C₃	1	2	yes	complemented
298	#387	C₂²×C₃	1	2	yes	complemented
299	#387	C₂²×C₃	1	2	yes	complemented
300	#386	C₂²×C₃	1	2	yes	—
301	#386	C₂²×C₃	1	2	yes	—
302	#386	C₂²×C₃	1	2	yes	—
303	#386	C₂²×C₃	1	2	yes	—
304	#386	C₂²×C₃	1	2	yes	complemented
305	#385	C₂²×C₃	1	2	yes	—
306	#385	C₂²×C₃	1	2	yes	—
307	#385	C₂²×C₃	1	1	yes	characteristic
308	#385	C₂²×C₃	1	1	yes	characteristic
309	#385	C₂²×C₃	1	1	yes	characteristic
310	#385	C₂²×C₃	1	1	yes	characteristic
311	#385	C₂²×C₃	1	2	yes	—
312	#385	C₂²×C₃	1	2	yes	complemented
313	#381	C₂²×C₃	1	2	yes	—
314	#380	C₂²×C₃	1	2	yes	—
315	#380	C₂²×C₃	1	2	yes	—
316	#380	C₂²×C₃	1	1	yes	characteristic
317	#380	C₂²×C₃	1	2	yes	—
318	#380	C₂²×C₃	1	2	yes	—
319	#380	C₂²×C₃	1	2	yes	complemented
320	#380	C₂²×C₃	1	2	yes	complemented
321	C₂×#95	C₂²×C₃	1	2	yes	—
322	C₂×#95	C₂²×C₃	1	1	yes	characteristic
323	C₂⁴×C₃	—	2	2	no	—
324	C₂⁴×C₃	—	2	2	no	—
325	C₂⁴×C₃	—	4	2	no	—
326	C₂⁴×C₃	—	4	2	no	—
327	C₂⁴×C₃	C₂×D₄	1	4	yes	—
328	C₂⁴×C₃	C₂⁴	1	2	yes	—
329	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
330	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
331	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₃×Q₈	—	2	4	no	—
333	C₂×C₃×Q₈	—	4	2	no	—
334	C₂×C₃×Q₈	—	4	2	no	—
335	C₂×C₃×D₄	—	2	4	no	—
336	C₂×C₃×D₄	—	2	4	no	—
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	2	4	no	—
339	C₂×C₃×D₄	—	2	4	no	—
340	C₂×C₃×D₄	—	4	2	no	—
341	C₂×C₃×D₄	—	4	2	no	—
342	C₂×C₃×D₄	—	4	1	no	—
343	C₂×C₃×D₄	—	4	2	no	—
344	C₂×C₃×D₄	—	4	2	no	—
345	C₂×C₃×D₄	—	4	2	no	—
346	C₂²×C₃×C₄	—	2	4	no	—
347	C₂²×C₃×C₄	—	2	2	no	—
348	C₂²×C₃×C₄	—	2	4	no	—
349	C₂²×C₃×C₄	—	2	4	no	—
350	C₂²×C₃×C₄	—	2	4	no	—
351	C₂²×C₃×C₄	—	2	2	no	—
352	C₂²×C₃×C₄	—	2	4	no	—
353	C₂²×C₃×C₄	—	4	2	no	—
354	C₂²×C₃×C₄	—	4	2	no	—
355	C₂²×C₃×C₄	—	4	2	no	—
356	C₂²×C₃×C₄	—	4	1	no	—
357	C₂²×C₃×C₄	—	4	1	no	—
358	C₂²×C₃×C₄	—	4	2	no	—
359	C₂²×C₃×C₄	—	4	2	no	—
360	C₂²×C₃×C₄	—	4	2	no	—
361	C₂²×C₃×C₄	—	4	2	no	—
362	C₂²×C₃×C₄	—	4	2	no	—
363	C₂²×C₃×C₄	—	4	2	no	—
364	C₂²×C₃×C₄	—	4	2	no	—
365	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
366	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
368	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
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	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
381	C₃×C₄⋊C₄	—	2	4	no	—
382	C₃×C₄⋊C₄	—	2	4	no	—
383	C₃×C₄⋊C₄	—	2	4	no	—
384	C₃×C₄⋊C₄	—	2	4	no	—
385	C₃×C₄⋊C₄	—	2	4	no	—
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	—	4	1	no	—
390	C₃×C₄⋊C₄	—	4	2	no	—
391	C₃×C₄⋊C₄	—	4	1	no	—
392	C₃×C₄⋊C₄	—	4	2	no	—
393	C₃×C₄⋊C₄	—	4	2	no	—
394	C₃×C₄⋊C₄	—	4	2	no	—
395	C₃×C₄⋊C₄	—	4	2	no	—
396	C₃×C₄⋊C₄	—	4	2	no	—
397	C₃×C₄⋊C₄	—	4	2	no	—
398	C₃×C₄⋊C₄	—	4	2	no	—
399	C₃×C₄⋊C₄	—	4	1	no	—
400	C₃×C₄⋊C₄	—	4	2	no	—
401	C₃×C₄⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	2	4	no	—
403	C₃×C₂²⋊C₄	—	2	4	no	—
404	C₃×C₂²⋊C₄	—	2	4	no	—
405	C₃×C₂²⋊C₄	—	2	4	no	—
406	C₃×C₂²⋊C₄	—	2	4	no	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	4	no	—
410	C₃×C₂²⋊C₄	—	2	4	no	—
411	C₃×C₂²⋊C₄	—	2	4	no	—
412	C₃×C₂²⋊C₄	—	2	4	no	—
413	C₃×C₂²⋊C₄	—	4	2	no	—
414	C₃×C₂²⋊C₄	—	4	1	no	—
415	C₃×C₂²⋊C₄	—	4	1	no	—
416	C₃×C₂²⋊C₄	—	4	1	no	—
417	C₃×C₂²⋊C₄	—	4	1	no	—
418	C₃×C₂²⋊C₄	—	4	2	no	—
419	C₃×C₂²⋊C₄	—	4	2	no	—
420	C₃×C₂²⋊C₄	—	4	2	no	—
421	C₃×C₂²⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	4	2	no	—
423	C₃×C₂²⋊C₄	—	4	2	no	—
424	C₃×C₂²⋊C₄	—	4	2	no	—
425	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
426	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
427	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
428	C₃×C₄²	—	2	4	no	—
429	C₃×C₄²	—	2	4	no	—
430	C₃×C₄²	—	2	4	no	—
431	C₂⁵	C₂³×C₃	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₃	1	2	yes	—
433	C₂²×D₄	C₂³×C₃	1	2	yes	—
434	C₂²×D₄	C₂³×C₃	1	2	yes	—
435	C₂²×D₄	C₂³×C₃	1	2	yes	—
436	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₃	1	2	yes	—
438	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃	1	2	yes	—
440	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₃	1	2	yes	—
442	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₃	1	2	yes	—
445	#126	—	2	8	no	—
446	#126	—	2	8	no	—
447	#124	—	2	8	no	—
448	#123	—	2	8	no	—
449	#123	—	2	8	no	—
450	#123	—	2	8	no	—
451	#123	—	4	4	no	—
452	C₂²⋊Q₈	—	2	8	no	—
453	C₂²⋊Q₈	—	2	8	no	—
454	#121	—	4	2	no	—
455	#120	—	2	8	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	8	no	—
458	#117	—	2	8	no	—
459	#117	—	2	8	no	—
460	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₃	1	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	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₂²⋊C₄	—	2	8	no	—
483	C₂×C₂²⋊C₄	—	4	2	no	—
484	C₂×C₂²⋊C₄	—	4	2	no	—
485	C₂×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
486	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₃	1	2	yes	—
514	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	2	yes	—
519	#95	C₂³×C₃	1	2	yes	—
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	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	1	yes	characteristic
531	#95	C₂³×C₃	1	1	yes	characteristic
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	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	2	2	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	1	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	2	no	—
545	C₂³×C₃	—	2	2	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	2	no	—
548	C₂³×C₃	—	2	8	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	2	no	—
553	C₂³×C₃	—	2	2	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	2	2	no	—
556	C₂³×C₃	—	4	8	no	—
557	C₂³×C₃	—	8	2	no	—
558	C₂³×C₃	—	8	2	no	—
559	C₂³×C₃	—	8	4	no	—
560	C₂³×C₃	C₂²×D₄	1	2	yes	—
561	C₂³×C₃	C₂²×D₄	1	2	yes	—
562	C₂³×C₃	C₂²×D₄	1	2	yes	—
563	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
564	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
565	C₂³×C₃	C₂⁵	1	1	yes	characteristic
566	C₃×Q₈	—	8	4	no	—
567	C₃×D₄	—	4	8	no	—
568	C₃×D₄	—	4	8	no	—
569	C₃×D₄	—	8	4	no	—
570	C₃×D₄	—	8	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	—	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	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	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	2	no	—
593	C₂×C₃×C₄	—	2	2	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	2	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	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	4	8	no	—
611	C₂×C₃×C₄	—	4	4	no	—
612	C₂×C₃×C₄	—	4	8	no	—
613	C₂×C₃×C₄	—	8	4	no	—
614	C₂×C₃×C₄	—	8	4	no	—
615	C₂×C₃×C₄	—	8	2	no	—
616	C₂×C₃×C₄	—	8	2	no	—
617	C₂×C₃×C₄	—	8	2	no	—
618	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
619	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	4	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	C₂×C₃×D₄	1	4	yes	—
625	C₂⁴	C₂⁴×C₃	1	2	yes	—
626	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
627	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
628	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	—	4	2	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	1	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
663	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	1	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	4	1	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
723	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
724	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₂²×C₃	—	2	4	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	2	no	—
731	C₂²×C₃	—	2	4	no	—
732	C₂²×C₃	—	2	2	no	—
733	C₂²×C₃	—	2	2	no	—
734	C₂²×C₃	—	2	4	no	—
735	C₂²×C₃	—	2	4	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	—	4	1	no	—
739	C₂²×C₃	—	4	1	no	—
740	C₂²×C₃	—	4	2	no	—
741	C₂²×C₃	—	4	2	no	—
742	C₂²×C₃	—	4	2	no	—
743	C₂²×C₃	—	4	2	no	—
744	C₂²×C₃	—	4	2	no	—
745	C₂²×C₃	—	4	2	no	—
746	C₂²×C₃	—	4	2	no	—
747	C₂²×C₃	—	4	2	no	—
748	C₂²×C₃	—	4	2	no	—
749	C₂²×C₃	—	8	8	no	—
750	C₂²×C₃	#537	1	4	yes	—
751	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
752	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
754	C₂²×C₃	#585	1	2	yes	—
755	C₂²×C₃	#585	1	2	yes	—
756	C₃×C₄	—	2	4	no	—
757	C₃×C₄	—	2	4	no	—
758	C₃×C₄	—	4	2	no	—
759	C₃×C₄	—	4	2	no	—
760	C₃×C₄	—	4	2	no	—
761	C₃×C₄	—	4	2	no	—
762	C₃×C₄	—	4	2	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	4	1	no	—
766	C₃×C₄	—	4	1	no	—
767	C₃×C₄	—	4	2	no	—
768	C₃×C₄	—	4	2	no	—
769	C₃×C₄	—	4	1	no	—
770	C₃×C₄	—	4	1	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	8	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	4	8	no	—
790	C₂³	—	8	2	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	4	no	—
793	C₂³	C₂²×C₃×D₄	1	2	yes	—
794	C₂³	C₂²×C₃×D₄	1	2	yes	—
795	C₂³	C₂²×C₃×D₄	1	2	yes	—
796	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
797	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
798	C₂³	C₂⁵×C₃	1	1	yes	characteristic
799	Q₈	—	8	4	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	8	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	8	4	no	—
847	C₂×C₄	—	8	4	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	—	8	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
852	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
853	C₂×C₃	—	2	4	no	—
854	C₂×C₃	—	4	2	no	—
855	C₂×C₃	—	4	2	no	—
856	C₂×C₃	—	8	2	no	—
857	C₂×C₃	C₂×#537	1	1	yes	characteristic
858	C₂×C₃	#3485	1	2	yes	—
859	C₂×C₃	#3533	1	1	yes	characteristic
860	C₂×C₃	#3545	1	1	yes	characteristic
861	C₂×C₃	#3564	1	2	yes	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	8	8	no	—
884	C₂²	C₃×#537	1	4	yes	—
885	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
886	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂²	C₃×#585	1	2	yes	—
889	C₂²	C₃×#585	1	2	yes	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₃	#41405	1	1	yes	characteristic, direct product factor, Sylow
906	C₂	—	2	4	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	2	no	—
909	C₂	—	8	2	no	—
910	C₂	C₂×C₃×#537	1	1	yes	characteristic
911	C₂	C₃×#3485	1	2	yes	—
912	C₂	C₃×#3533	1	1	yes	characteristic
913	C₂	C₃×#3545	1	1	yes	characteristic
914	C₂	C₃×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2617	C₂
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. C₂×C₃×#551	C₂	semidirect
2. C₃×#2814	C₂	semidirect
3. C₃×#2722	C₂	semidirect
4. C₃×#2722	C₂	semidirect
5. C₃×#2715	C₂	semidirect
6. C₃×#2712	C₂	semidirect
7. C₃×#2695	C₂	semidirect
8. C₃×#2693	C₂	semidirect
9. C₃×#2630	C₂	semidirect
10. C₃×#2625	C₂	semidirect
12. C₃×#2485	C₂	semidirect
13. C₃×#2450	C₂	semidirect
14. C₃×#2438	C₂	semidirect
15. C₃×#2425	C₂	semidirect
16. C₃×#2413	C₂	semidirect
17. C₃×#2412	C₂	semidirect
18. C₂×C₃×#397	C₂	semidirect
19. C₃×#2315	C₂	semidirect
20. #41405	C₃	direct (N × H)
42. C₃×#400	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#398	C₂²	semidirect
45. C₃×#398	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
49. C₃×#398	C₂²	semidirect
60. C₃×#397	C₂²	semidirect
61. C₃×#396	C₂²	semidirect
62. C₃×#396	C₂²	semidirect
63. C₃×#396	C₂²	semidirect
64. C₃×#396	C₂²	semidirect
65. C₃×#395	C₂²	semidirect
70. C₃×#394	C₂²	semidirect
71. C₃×#393	C₂²	semidirect
74. C₃×#391	C₂²	semidirect
75. C₃×#391	C₂²	semidirect
76. C₃×#389	C₂²	semidirect
77. C₃×#389	C₂²	semidirect
78. C₃×#389	C₂²	semidirect
79. C₃×#389	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#388	C₂²	semidirect
82. C₃×#388	C₂²	semidirect
83. C₃×#387	C₂²	semidirect
84. C₃×#387	C₂²	semidirect
85. C₃×#387	C₂²	semidirect
90. C₃×#386	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
105. C₃×#380	C₂²	semidirect
106. C₃×#380	C₂²	semidirect
109. C₂×#551	C₂×C₃	semidirect
110. #2814	C₂×C₃	semidirect
111. #2722	C₂×C₃	semidirect
112. #2722	C₂×C₃	semidirect
113. #2715	C₂×C₃	semidirect
114. #2712	C₂×C₃	semidirect
115. #2695	C₂×C₃	semidirect
116. #2693	C₂×C₃	semidirect
117. #2630	C₂×C₃	semidirect
118. #2625	C₂×C₃	semidirect
120. #2485	C₂×C₃	semidirect
121. #2450	C₂×C₃	semidirect
122. #2438	C₂×C₃	semidirect
123. #2425	C₂×C₃	semidirect
124. #2413	C₂×C₃	semidirect
125. #2412	C₂×C₃	semidirect
126. C₂×#397	C₂×C₃	semidirect
127. #2315	C₂×C₃	semidirect
182. C₂×C₃×C₂²⋊C₄	D₄	semidirect
256. #400	C₂²×C₃	semidirect
257. #400	C₂²×C₃	semidirect
258. #398	C₂²×C₃	semidirect
259. #398	C₂²×C₃	semidirect
260. #398	C₂²×C₃	semidirect
261. #398	C₂²×C₃	semidirect
262. #398	C₂²×C₃	semidirect
263. #398	C₂²×C₃	semidirect
274. #397	C₂²×C₃	semidirect
275. #396	C₂²×C₃	semidirect
276. #396	C₂²×C₃	semidirect
277. #396	C₂²×C₃	semidirect
278. #396	C₂²×C₃	semidirect
279. #395	C₂²×C₃	semidirect
284. #394	C₂²×C₃	semidirect
285. #393	C₂²×C₃	semidirect
288. #391	C₂²×C₃	semidirect
289. #391	C₂²×C₃	semidirect
290. #389	C₂²×C₃	semidirect
291. #389	C₂²×C₃	semidirect
292. #389	C₂²×C₃	semidirect
293. #389	C₂²×C₃	semidirect
294. #388	C₂²×C₃	semidirect
295. #388	C₂²×C₃	semidirect
296. #388	C₂²×C₃	semidirect
297. #387	C₂²×C₃	semidirect
298. #387	C₂²×C₃	semidirect
299. #387	C₂²×C₃	semidirect
304. #386	C₂²×C₃	semidirect
312. #385	C₂²×C₃	semidirect
319. #380	C₂²×C₃	semidirect
320. #380	C₂²×C₃	semidirect
485. C₂×C₂²⋊C₄	C₃×D₄	semidirect
905. C₃	#41405	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#551	2
C₃×#2814	2
C₃×#2722	2
C₃×#2715	2
C₃×#2712	2
C₃×#2695	2
C₃×#2693	2
C₃×#2630	2
C₃×#2625	2
C₃×#2617	2
C₃×#2485	2
C₃×#2450	2
C₃×#2438	2
C₃×#2425	2
C₃×#2413	2
C₃×#2412	2
C₂×C₃×#397	2
C₃×#2315	2
#41405	3

Subgroups — C3×#41405 #10660012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41405 #10660012