Subgroups — C₃×#34502 #10653109

Order 768.

2156 conjugacy classes of subgroups.

The subgroup lattice has 876 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	1	yes	maximal, characteristic
2	C₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2375	C₂	1	1	yes	maximal, characteristic
5	C₃×#2374	C₂	1	2	yes	maximal, complemented
6	C₃×#2373	C₂	1	2	yes	maximal, complemented
7	C₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2352	C₂	1	2	yes	maximal, complemented
9	C₃×#2346	C₂	1	2	yes	maximal, complemented
10	C₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₃×#2335	C₂	1	2	yes	maximal, complemented
12	C₃×#2334	C₂	1	2	yes	maximal, complemented
13	C₃×#2323	C₂	1	2	yes	maximal, complemented
14	C₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2321	C₂	1	1	yes	maximal, characteristic
16	C₃×#2319	C₂	1	2	yes	maximal, complemented
17	C₃×#2312	C₂	1	2	yes	maximal, complemented
18	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2298	C₂	1	2	yes	maximal, complemented
20	#34502	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃×#551	C₄	1	16	yes	complemented
22	C₂×C₃×#126	C₂²	1	2	yes	—
23	C₂×C₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₃×#123	C₂²	1	1	yes	characteristic
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×#120	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₂×C₃×#117	C₂²	1	2	yes	—
33	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	2	yes	complemented
37	C₃×#391	C₂²	1	1	yes	characteristic, complemented
38	C₃×#390	C₂²	1	2	yes	—
39	C₃×#390	C₂²	1	1	yes	characteristic
40	C₃×#390	C₂²	1	2	yes	—
41	C₃×#389	C₂²	1	2	yes	complemented
42	C₃×#389	C₂²	1	2	yes	complemented
43	C₃×#389	C₂²	1	2	yes	complemented
44	C₃×#389	C₂²	1	2	yes	complemented
45	C₃×#389	C₂²	1	2	yes	complemented
46	C₃×#388	C₂²	1	2	yes	—
47	C₃×#388	C₂²	1	2	yes	—
48	C₃×#388	C₂²	1	2	yes	—
49	C₃×#388	C₂²	1	2	yes	—
50	C₃×#388	C₂²	1	2	yes	—
51	C₃×#388	C₂²	1	2	yes	—
52	C₃×#388	C₂²	1	2	yes	—
53	C₃×#388	C₂²	1	2	yes	—
54	C₃×#388	C₂²	1	2	yes	—
55	C₃×#388	C₂²	1	2	yes	—
56	C₃×#388	C₂²	1	2	yes	—
57	C₃×#388	C₂²	1	2	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	2	yes	—
60	C₃×#388	C₂²	1	2	yes	—
61	C₃×#388	C₂²	1	2	yes	—
62	C₃×#388	C₂²	1	2	yes	—
63	C₃×#388	C₂²	1	2	yes	complemented
64	C₃×#388	C₂²	1	2	yes	complemented
65	C₃×#388	C₂²	1	2	yes	complemented
66	C₃×#387	C₂²	1	2	yes	complemented
67	C₃×#387	C₂²	1	2	yes	complemented
68	C₃×#387	C₂²	1	2	yes	complemented
69	C₃×#387	C₂²	1	2	yes	complemented
70	C₃×#387	C₂²	1	2	yes	complemented
71	C₃×#387	C₂²	1	2	yes	complemented
72	C₃×#387	C₂²	1	2	yes	complemented
73	C₃×#387	C₂²	1	2	yes	complemented
74	C₃×#386	C₂²	1	1	yes	characteristic
75	C₃×#386	C₂²	1	1	yes	characteristic
76	C₃×#386	C₂²	1	2	yes	—
77	C₃×#386	C₂²	1	2	yes	—
78	C₃×#385	C₂²	1	2	yes	—
79	C₃×#385	C₂²	1	2	yes	—
80	C₃×#385	C₂²	1	1	yes	characteristic
81	C₃×#385	C₂²	1	1	yes	characteristic, complemented
82	C₃×#382	C₂²	1	1	yes	characteristic, complemented
83	C₃×#382	C₂²	1	2	yes	complemented
84	C₃×#381	C₂²	1	2	yes	—
85	C₃×#381	C₂²	1	1	yes	characteristic, complemented
86	C₃×#380	C₂²	1	2	yes	—
87	C₃×#380	C₂²	1	2	yes	—
88	C₃×#380	C₂²	1	2	yes	—
89	C₃×#380	C₂²	1	2	yes	complemented
90	C₃×#379	C₂²	1	2	yes	—
91	C₃×#379	C₂²	1	1	yes	characteristic
92	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
93	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
94	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
99	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×#376	C₂²	1	2	yes	complemented
107	C₃×#376	C₂²	1	2	yes	complemented
108	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
109	C₂×#551	C₂×C₃	1	1	yes	characteristic
110	#2378	C₂×C₃	1	2	yes	complemented
111	#2376	C₂×C₃	1	1	yes	characteristic, complemented
112	#2375	C₂×C₃	1	1	yes	characteristic
113	#2374	C₂×C₃	1	2	yes	complemented
114	#2373	C₂×C₃	1	2	yes	complemented
115	#2372	C₂×C₃	1	1	yes	characteristic, complemented
116	#2352	C₂×C₃	1	2	yes	complemented
117	#2346	C₂×C₃	1	2	yes	complemented
118	#2342	C₂×C₃	1	2	yes	complemented
119	#2335	C₂×C₃	1	2	yes	complemented
120	#2334	C₂×C₃	1	2	yes	complemented
121	#2323	C₂×C₃	1	2	yes	complemented
122	#2322	C₂×C₃	1	1	yes	characteristic, complemented
123	#2321	C₂×C₃	1	1	yes	characteristic
124	#2319	C₂×C₃	1	2	yes	complemented
125	#2312	C₂×C₃	1	2	yes	complemented
126	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
127	#2298	C₂×C₃	1	2	yes	complemented
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
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	C₂³×C₃×C₄	C₂³	1	2	yes	—
138	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₃×#126	C₂×C₄	1	16	yes	complemented
140	C₃×#124	C₂×C₄	1	8	yes	—
141	C₃×#123	C₂×C₄	1	8	yes	—
142	C₃×#123	C₂×C₄	1	16	yes	complemented
143	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
144	C₃×#120	C₂×C₄	1	8	yes	—
145	C₃×C₄×Q₈	—	4	2	no	—
146	C₃×C₄×D₄	—	4	2	no	—
147	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
148	C₃×#117	—	4	4	no	—
149	C₃×#117	C₂×C₄	1	16	yes	complemented
150	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	4	2	no	—
168	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
169	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄²	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₂×C₃×C₄²	C₂³	1	2	yes	—
202	C₂×C₃×C₄²	C₂³	1	2	yes	—
203	C₂×C₃×C₄²	C₂³	1	2	yes	—
204	C₂×C₃×C₄²	C₂³	1	2	yes	—
205	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄²	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	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	2	yes	—
228	C₃×#95	C₂³	1	2	yes	—
229	#551	C₃×C₄	1	16	yes	complemented
230	C₂×#126	C₂²×C₃	1	2	yes	—
231	C₂×#124	C₂²×C₃	1	1	yes	characteristic
232	C₂×#123	C₂²×C₃	1	1	yes	characteristic
233	C₂×#123	C₂²×C₃	1	2	yes	—
234	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
235	C₂×#120	C₂²×C₃	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
237	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
239	C₂×#117	C₂²×C₃	1	2	yes	—
240	C₂×#117	C₂²×C₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
244	#391	C₂²×C₃	1	2	yes	complemented
245	#391	C₂²×C₃	1	1	yes	characteristic, complemented
246	#390	C₂²×C₃	1	2	yes	—
247	#390	C₂²×C₃	1	2	yes	—
248	#390	C₂²×C₃	1	1	yes	characteristic
249	#389	C₂²×C₃	1	2	yes	complemented
250	#389	C₂²×C₃	1	2	yes	complemented
251	#389	C₂²×C₃	1	2	yes	complemented
252	#389	C₂²×C₃	1	2	yes	complemented
253	#389	C₂²×C₃	1	2	yes	complemented
254	#388	C₂²×C₃	1	2	yes	—
255	#388	C₂²×C₃	1	2	yes	—
256	#388	C₂²×C₃	1	2	yes	—
257	#388	C₂²×C₃	1	2	yes	—
258	#388	C₂²×C₃	1	2	yes	—
259	#388	C₂²×C₃	1	2	yes	—
260	#388	C₂²×C₃	1	2	yes	—
261	#388	C₂²×C₃	1	2	yes	—
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	complemented
272	#388	C₂²×C₃	1	2	yes	complemented
273	#388	C₂²×C₃	1	2	yes	complemented
274	#387	C₂²×C₃	1	2	yes	complemented
275	#387	C₂²×C₃	1	2	yes	complemented
276	#387	C₂²×C₃	1	2	yes	complemented
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	1	yes	characteristic
284	#386	C₂²×C₃	1	1	yes	characteristic
285	#386	C₂²×C₃	1	2	yes	—
286	#385	C₂²×C₃	1	1	yes	characteristic
287	#385	C₂²×C₃	1	2	yes	—
288	#385	C₂²×C₃	1	2	yes	—
289	#385	C₂²×C₃	1	1	yes	characteristic, complemented
290	#382	C₂²×C₃	1	2	yes	complemented
291	#382	C₂²×C₃	1	1	yes	characteristic, complemented
292	#381	C₂²×C₃	1	2	yes	—
293	#381	C₂²×C₃	1	1	yes	characteristic, complemented
294	#380	C₂²×C₃	1	2	yes	—
295	#380	C₂²×C₃	1	2	yes	—
296	#380	C₂²×C₃	1	2	yes	—
297	#380	C₂²×C₃	1	2	yes	complemented
298	#379	C₂²×C₃	1	1	yes	characteristic
299	#379	C₂²×C₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
301	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
303	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
304	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
305	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
308	C₄×C₂²⋊C₄	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	1	yes	characteristic, complemented
312	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
313	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
314	#376	C₂²×C₃	1	2	yes	complemented
315	#376	C₂²×C₃	1	2	yes	complemented
316	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
317	C₂⁴×C₃	—	4	2	no	—
318	C₂⁴×C₃	—	4	2	no	—
319	C₂⁴×C₃	—	4	1	no	—
320	C₂⁴×C₃	—	4	1	no	—
321	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
322	C₂⁴×C₃	C₂⁴	1	2	yes	—
323	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₃×Q₈	—	4	1	no	—
326	C₂×C₃×Q₈	—	4	1	no	—
327	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
328	C₂×C₃×D₄	—	4	1	no	—
329	C₂×C₃×D₄	—	4	2	no	—
330	C₂×C₃×D₄	—	4	2	no	—
331	C₂×C₃×D₄	—	4	1	no	—
332	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
333	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	2	no	—
336	C₂²×C₃×C₄	—	4	1	no	—
337	C₂²×C₃×C₄	—	4	2	no	—
338	C₂²×C₃×C₄	—	4	2	no	—
339	C₂²×C₃×C₄	—	4	2	no	—
340	C₂²×C₃×C₄	—	4	1	no	—
341	C₂²×C₃×C₄	—	4	2	no	—
342	C₂²×C₃×C₄	—	4	1	no	—
343	C₂²×C₃×C₄	—	4	1	no	—
344	C₂²×C₃×C₄	—	4	2	no	—
345	C₂²×C₃×C₄	—	4	2	no	—
346	C₂²×C₃×C₄	—	4	2	no	—
347	C₂²×C₃×C₄	—	4	2	no	—
348	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
349	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
350	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
360	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
361	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
362	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
364	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
366	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₃×C₄⋊C₄	—	2	4	no	—
368	C₃×C₄⋊C₄	—	4	2	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	1	no	—
377	C₃×C₄⋊C₄	—	4	2	no	—
378	C₃×C₄⋊C₄	—	4	1	no	—
379	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
380	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
381	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
382	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
383	C₃×C₂²⋊C₄	—	2	4	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	2	no	—
389	C₃×C₂²⋊C₄	—	4	2	no	—
390	C₃×C₂²⋊C₄	—	4	2	no	—
391	C₃×C₂²⋊C₄	—	4	2	no	—
392	C₃×C₂²⋊C₄	—	4	2	no	—
393	C₃×C₂²⋊C₄	—	4	2	no	—
394	C₃×C₂²⋊C₄	—	4	1	no	—
395	C₃×C₂²⋊C₄	—	4	1	no	—
396	C₃×C₂²⋊C₄	—	4	2	no	—
397	C₃×C₂²⋊C₄	—	4	1	no	—
398	C₃×C₂²⋊C₄	—	4	1	no	—
399	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
400	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
401	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
402	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
403	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
404	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
405	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
406	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
407	C₃×C₄²	—	2	4	no	—
408	C₃×C₄²	—	2	2	no	—
409	C₃×C₄²	—	4	2	no	—
410	C₃×C₄²	—	4	2	no	—
411	C₃×C₄²	—	4	2	no	—
412	C₃×C₄²	—	4	2	no	—
413	C₃×C₄²	—	4	2	no	—
414	C₃×C₄²	—	4	2	no	—
415	C₃×C₄²	—	4	2	no	—
416	C₃×C₄²	—	4	2	no	—
417	C₃×C₄²	—	4	1	no	—
418	C₃×C₄²	—	4	2	no	—
419	C₃×C₄²	C₂²×C₄	1	4	yes	—
420	C₃×C₄²	C₂²×C₄	1	8	yes	—
421	C₂⁵	C₂³×C₃	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
424	C₂²×D₄	C₂³×C₃	1	2	yes	—
425	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₃	1	2	yes	—
431	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
432	#126	C₂×C₃×C₄	1	16	yes	complemented
433	#124	C₂×C₃×C₄	1	8	yes	—
434	#123	C₂×C₃×C₄	1	8	yes	—
435	#123	C₂×C₃×C₄	1	16	yes	complemented
436	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
437	#120	C₂×C₃×C₄	1	8	yes	—
438	C₄×Q₈	—	4	2	no	—
439	C₄×D₄	—	4	2	no	—
440	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
441	#117	—	4	4	no	—
442	#117	C₂×C₃×C₄	1	16	yes	complemented
443	C₂×C₄⋊C₄	—	4	2	no	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	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×C₄⋊C₄	C₂³×C₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₂²⋊C₄	—	4	2	no	—
461	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	16	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	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₃	1	2	yes	—
490	C₂×C₄²	C₂³×C₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₃	1	2	yes	—
493	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
499	C₂×C₄²	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
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	#95	C₂³×C₃	1	2	yes	—
511	#95	C₂³×C₃	1	2	yes	—
512	#95	C₂³×C₃	1	2	yes	—
513	#95	C₂³×C₃	1	2	yes	—
514	#95	C₂³×C₃	1	2	yes	—
515	#95	C₂³×C₃	1	2	yes	—
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	2	yes	—
521	#95	C₂³×C₃	1	2	yes	—
522	C₂³×C₃	—	2	2	no	—
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	2	no	—
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	—	2	2	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	2	2	no	—
532	C₂³×C₃	—	2	1	no	—
533	C₂³×C₃	—	2	2	no	—
534	C₂³×C₃	—	2	2	no	—
535	C₂³×C₃	—	2	2	no	—
536	C₂³×C₃	—	4	8	no	—
537	C₂³×C₃	—	4	4	no	—
538	C₂³×C₃	—	8	2	no	—
539	C₂³×C₃	—	8	2	no	—
540	C₂³×C₃	—	8	4	no	—
541	C₂³×C₃	C₂³×C₄	1	2	yes	—
542	C₂³×C₃	C₂³×C₄	1	4	yes	—
543	C₂³×C₃	C₂³×C₄	1	2	yes	—
544	C₂³×C₃	C₂⁵	1	1	yes	characteristic
545	C₃×Q₈	—	4	4	no	—
546	C₃×D₄	—	4	8	no	—
547	C₃×D₄	—	4	4	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	1	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	1	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	1	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	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	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	—	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	—	4	8	no	—
586	C₂×C₃×C₄	—	4	4	no	—
587	C₂×C₃×C₄	—	4	8	no	—
588	C₂×C₃×C₄	—	8	2	no	—
589	C₂×C₃×C₄	—	8	2	no	—
590	C₂×C₃×C₄	—	8	2	no	—
591	C₂×C₃×C₄	—	8	2	no	—
592	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
593	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
594	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
595	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
596	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
597	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
598	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
599	C₂⁴	—	4	1	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	—	4	1	no	—
603	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
604	C₂⁴	C₂⁴×C₃	1	2	yes	—
605	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
615	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	4	1	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	1	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
631	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
632	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	1	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	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
662	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
663	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
664	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	1	no	—
669	C₂²⋊C₄	—	4	1	no	—
670	C₂²⋊C₄	—	4	2	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	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₂²⋊C₄	—	4	1	no	—
681	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
682	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
683	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
684	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
685	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
686	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
687	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
688	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	1	no	—
701	C₄²	C₂²×C₃×C₄	1	4	yes	—
702	C₄²	C₂²×C₃×C₄	1	8	yes	—
703	C₂²×C₃	—	2	4	no	—
704	C₂²×C₃	—	2	4	no	—
705	C₂²×C₃	—	2	4	no	—
706	C₂²×C₃	—	2	4	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	4	no	—
709	C₂²×C₃	—	2	2	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	2	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	no	—
715	C₂²×C₃	—	4	2	no	—
716	C₂²×C₃	—	4	2	no	—
717	C₂²×C₃	—	4	2	no	—
718	C₂²×C₃	—	4	2	no	—
719	C₂²×C₃	—	4	2	no	—
720	C₂²×C₃	—	8	8	no	—
721	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
722	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
723	C₂²×C₃	#585	1	2	yes	—
724	C₂²×C₃	#585	1	2	yes	—
725	C₂²×C₃	#585	1	1	yes	characteristic
726	C₃×C₄	—	2	4	no	—
727	C₃×C₄	—	2	4	no	—
728	C₃×C₄	—	2	4	no	—
729	C₃×C₄	—	2	4	no	—
730	C₃×C₄	—	2	4	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	4	2	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	2	no	—
738	C₃×C₄	—	4	2	no	—
739	C₃×C₄	—	4	2	no	—
740	C₃×C₄	—	4	2	no	—
741	C₃×C₄	—	4	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	8	2	no	—
759	C₂³	—	8	2	no	—
760	C₂³	—	8	4	no	—
761	C₂³	C₂³×C₃×C₄	1	2	yes	—
762	C₂³	C₂³×C₃×C₄	1	4	yes	—
763	C₂³	C₂³×C₃×C₄	1	2	yes	—
764	C₂³	C₂⁵×C₃	1	1	yes	characteristic
765	Q₈	—	4	4	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	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	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	8	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
813	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
814	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
815	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
816	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
817	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
818	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
819	C₂×C₃	—	4	2	no	—
820	C₂×C₃	—	4	4	no	—
821	C₂×C₃	—	4	2	no	—
822	C₂×C₃	#3428	1	2	yes	—
823	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂×C₃	#3545	1	1	yes	characteristic
825	C₂×C₃	#3551	1	1	yes	characteristic
826	C₂×C₃	#3566	1	2	yes	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	8	no	—
845	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
846	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
847	C₂²	C₃×#585	1	2	yes	—
848	C₂²	C₃×#585	1	2	yes	—
849	C₂²	C₃×#585	1	1	yes	characteristic
850	C₄	—	2	4	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₃	#34502	1	1	yes	characteristic, direct product factor, Sylow
867	C₂	—	4	4	no	—
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	C₃×#3428	1	2	yes	—
871	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
872	C₂	C₃×#3545	1	1	yes	characteristic
873	C₂	C₃×#3551	1	1	yes	characteristic
874	C₂	C₃×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×#2378	C₂	semidirect
3. C₃×#2376	C₂	semidirect
5. C₃×#2374	C₂	semidirect
6. C₃×#2373	C₂	semidirect
7. C₃×#2372	C₂	semidirect
8. C₃×#2352	C₂	semidirect
9. C₃×#2346	C₂	semidirect
10. C₃×#2342	C₂	semidirect
11. C₃×#2335	C₂	semidirect
12. C₃×#2334	C₂	semidirect
13. C₃×#2323	C₂	semidirect
14. C₃×#2322	C₂	semidirect
16. C₃×#2319	C₂	semidirect
17. C₃×#2312	C₂	semidirect
18. C₃×C₄×#124	C₂	semidirect
19. C₃×#2298	C₂	semidirect
20. #34502	C₃	direct (N × H)
21. C₃×#551	C₄	semidirect
28. C₂×C₃×C₄×Q₈	C₂²	semidirect
33. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
36. C₃×#391	C₂²	semidirect
37. C₃×#391	C₂²	semidirect
41. C₃×#389	C₂²	semidirect
42. C₃×#389	C₂²	semidirect
43. C₃×#389	C₂²	semidirect
44. C₃×#389	C₂²	semidirect
45. C₃×#389	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#388	C₂²	semidirect
66. C₃×#387	C₂²	semidirect
67. C₃×#387	C₂²	semidirect
68. C₃×#387	C₂²	semidirect
69. C₃×#387	C₂²	semidirect
70. C₃×#387	C₂²	semidirect
71. C₃×#387	C₂²	semidirect
72. C₃×#387	C₂²	semidirect
73. C₃×#387	C₂²	semidirect
81. C₃×#385	C₂²	semidirect
82. C₃×#382	C₂²	semidirect
83. C₃×#382	C₂²	semidirect
85. C₃×#381	C₂²	semidirect
89. C₃×#380	C₂²	semidirect
92. C₃×C₄×C₄⋊C₄	C₂²	semidirect
93. C₃×C₄×C₄⋊C₄	C₂²	semidirect
94. C₃×C₄×C₄⋊C₄	C₂²	semidirect
95. C₃×C₄×C₄⋊C₄	C₂²	semidirect
96. C₃×C₄×C₄⋊C₄	C₂²	semidirect
103. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
104. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
106. C₃×#376	C₂²	semidirect
107. C₃×#376	C₂²	semidirect
108. C₃×C₄³	C₂²	semidirect
110. #2378	C₂×C₃	semidirect
111. #2376	C₂×C₃	semidirect
113. #2374	C₂×C₃	semidirect
114. #2373	C₂×C₃	semidirect
115. #2372	C₂×C₃	semidirect
116. #2352	C₂×C₃	semidirect
117. #2346	C₂×C₃	semidirect
118. #2342	C₂×C₃	semidirect
119. #2335	C₂×C₃	semidirect
120. #2334	C₂×C₃	semidirect
121. #2323	C₂×C₃	semidirect
122. #2322	C₂×C₃	semidirect
124. #2319	C₂×C₃	semidirect
125. #2312	C₂×C₃	semidirect
126. C₄×#124	C₂×C₃	semidirect
127. #2298	C₂×C₃	semidirect
139. C₃×#126	C₂×C₄	semidirect
142. C₃×#123	C₂×C₄	semidirect
143. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
147. C₃×C₄×D₄	C₂×C₄	semidirect
149. C₃×#117	C₂×C₄	semidirect
168. C₂×C₃×C₂²⋊C₄	C₂×C₄	semidirect
229. #551	C₃×C₄	semidirect
236. C₂×C₄×Q₈	C₂²×C₃	semidirect
241. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
244. #391	C₂²×C₃	semidirect
245. #391	C₂²×C₃	semidirect
249. #389	C₂²×C₃	semidirect
250. #389	C₂²×C₃	semidirect
251. #389	C₂²×C₃	semidirect
252. #389	C₂²×C₃	semidirect
253. #389	C₂²×C₃	semidirect
271. #388	C₂²×C₃	semidirect
272. #388	C₂²×C₃	semidirect
273. #388	C₂²×C₃	semidirect
274. #387	C₂²×C₃	semidirect
275. #387	C₂²×C₃	semidirect
276. #387	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
289. #385	C₂²×C₃	semidirect
290. #382	C₂²×C₃	semidirect
291. #382	C₂²×C₃	semidirect
293. #381	C₂²×C₃	semidirect
297. #380	C₂²×C₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
302. C₄×C₄⋊C₄	C₂²×C₃	semidirect
303. C₄×C₄⋊C₄	C₂²×C₃	semidirect
304. C₄×C₄⋊C₄	C₂²×C₃	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
312. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
313. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
314. #376	C₂²×C₃	semidirect
315. #376	C₂²×C₃	semidirect
316. C₄³	C₂²×C₃	semidirect
432. #126	C₂×C₃×C₄	semidirect
435. #123	C₂×C₃×C₄	semidirect
436. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
440. C₄×D₄	C₂×C₃×C₄	semidirect
442. #117	C₂×C₃×C₄	semidirect
461. C₂×C₂²⋊C₄	C₂×C₃×C₄	semidirect
866. C₃	#34502	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×#2378	2
C₃×#2376	2
C₃×#2375	2
C₃×#2374	2
C₃×#2373	2
C₃×#2372	2
C₃×#2352	2
C₃×#2346	2
C₃×#2342	2
C₃×#2335	2
C₃×#2334	2
C₃×#2323	2
C₃×#2322	2
C₃×#2321	2
C₃×#2319	2
C₃×#2312	2
C₃×C₄×#124	2
C₃×#2298	2
#34502	3

Subgroups — C3×#34502 #10653109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34502 #10653109