Subgroups — C₃×#36156 #10654763

Order 768.

2844 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2480	C₂	1	2	yes	maximal, complemented
11	C₃×#2473	C₂	1	2	yes	maximal, complemented
12	C₃×#2468	C₂	1	2	yes	maximal, complemented
13	C₃×#2460	C₂	1	2	yes	maximal, complemented
14	C₃×#2419	C₂	1	2	yes	maximal, complemented
15	C₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2405	C₂	1	2	yes	maximal
18	C₃×#2359	C₂	1	2	yes	maximal, complemented
19	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2342	C₂	1	2	yes	maximal, complemented
21	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
24	#36156	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
27	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
28	C₃×#552	—	2	8	no	—
29	C₂×C₃×#126	C₂²	1	2	yes	complemented
30	C₂×C₃×#125	C₂²	1	2	yes	complemented
31	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#123	C₂²	1	2	yes	—
33	C₂×C₃×#123	C₂²	1	2	yes	—
34	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₄×D₄	—	2	8	no	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×#117	C₂²	1	2	yes	complemented
51	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
59	C₃×#400	C₂²	1	2	yes	complemented
60	C₃×#398	C₂²	1	2	yes	complemented
61	C₃×#398	C₂²	1	2	yes	complemented
62	C₃×#398	C₂²	1	2	yes	complemented
63	C₃×#397	C₂²	1	2	yes	complemented
64	C₃×#397	C₂²	1	2	yes	complemented
65	C₃×#397	C₂²	1	2	yes	complemented
66	C₃×#396	C₂²	1	2	yes	complemented
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	—
71	C₃×#391	C₂²	1	1	yes	characteristic, complemented
72	C₃×#389	C₂²	1	2	yes	complemented
73	C₃×#389	C₂²	1	1	yes	characteristic, complemented
74	C₃×#389	C₂²	1	1	yes	characteristic, complemented
75	C₃×#389	C₂²	1	1	yes	characteristic, complemented
76	C₃×#388	C₂²	1	2	yes	complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	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×#387	C₂²	1	2	yes	complemented
87	C₃×#387	C₂²	1	2	yes	complemented
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
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	2	yes	—
95	C₃×#385	C₂²	1	2	yes	complemented
96	C₃×#385	C₂²	1	2	yes	complemented
97	C₃×#385	C₂²	1	2	yes	complemented
98	C₃×#385	C₂²	1	2	yes	complemented
99	C₃×#382	C₂²	1	1	yes	characteristic, complemented
100	C₃×#381	C₂²	1	2	yes	complemented
101	C₃×#381	C₂²	1	2	yes	complemented
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	C₂²	1	1	yes	characteristic, complemented
107	C₃×#380	C₂²	1	2	yes	complemented
108	C₃×#380	C₂²	1	1	yes	characteristic, complemented
109	C₃×#380	C₂²	1	2	yes	complemented
110	C₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₃×#380	C₂²	1	1	yes	characteristic, complemented
112	C₃×#380	C₂²	1	1	yes	characteristic, complemented
113	C₃×#380	C₂²	1	1	yes	characteristic, complemented
114	C₃×#380	C₂²	1	1	yes	characteristic, complemented
115	C₃×#380	C₂²	1	1	yes	characteristic, complemented
116	C₃×#379	C₂²	1	2	yes	—
117	C₃×#379	C₂²	1	2	yes	—
118	C₃×#379	C₂²	1	2	yes	—
119	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
125	C₂×C₃×#95	C₂²	1	2	yes	complemented
126	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
128	#2851	C₂×C₃	1	1	yes	characteristic, complemented
129	#2848	C₂×C₃	1	1	yes	characteristic, complemented
130	#2848	C₂×C₃	1	1	yes	characteristic, complemented
131	#2562	C₂×C₃	1	1	yes	characteristic, complemented
132	#2536	C₂×C₃	1	1	yes	characteristic, complemented
133	#2486	C₂×C₃	1	1	yes	characteristic, complemented
134	#2485	C₂×C₃	1	1	yes	characteristic, complemented
135	#2480	C₂×C₃	1	2	yes	complemented
136	#2473	C₂×C₃	1	2	yes	complemented
137	#2468	C₂×C₃	1	2	yes	complemented
138	#2460	C₂×C₃	1	2	yes	complemented
139	#2419	C₂×C₃	1	2	yes	complemented
140	#2417	C₂×C₃	1	1	yes	characteristic, complemented
141	#2415	C₂×C₃	1	1	yes	characteristic, complemented
142	#2405	C₂×C₃	1	2	yes	—
143	#2359	C₂×C₃	1	2	yes	complemented
144	#2352	C₂×C₃	1	1	yes	characteristic, complemented
145	#2342	C₂×C₃	1	2	yes	complemented
146	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
147	#2280	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×#380	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	1	yes	characteristic
150	C₂⁵×C₃	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	—	2	4	no	—
153	C₂²×C₃×D₄	—	2	4	no	—
154	C₂²×C₃×D₄	—	2	4	no	—
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	—	2	4	no	—
160	C₂³×C₃×C₄	—	2	4	no	—
161	C₂³×C₃×C₄	—	2	4	no	—
162	C₂³×C₃×C₄	—	2	4	no	—
163	C₂³×C₃×C₄	—	4	2	no	—
164	C₂³×C₃×C₄	—	4	2	no	—
165	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
174	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
176	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
179	C₂³×C₃×C₄	C₂³	1	2	yes	—
180	C₃×#126	—	2	8	no	—
181	C₃×#125	—	2	8	no	—
182	C₃×#125	—	2	4	no	—
183	C₃×#123	—	2	8	no	—
184	C₃×#123	—	2	8	no	—
185	C₃×C₂²⋊Q₈	—	2	4	no	—
186	C₃×C₂²⋊Q₈	—	2	4	no	—
187	C₃×C₂²⋊Q₈	—	2	4	no	—
188	C₃×C₂²⋊Q₈	—	4	2	no	—
189	C₃×C₂²⋊Q₈	—	4	2	no	—
190	C₃×C₄×Q₈	—	2	4	no	—
191	C₃×C₄×D₄	—	2	4	no	—
192	C₃×C₄×D₄	—	2	4	no	—
193	C₃×C₄×D₄	—	2	4	no	—
194	C₃×C₄×D₄	—	2	4	no	—
195	C₃×C₄×D₄	—	2	4	no	—
196	C₃×C₄×D₄	—	2	4	no	—
197	C₃×C₄×D₄	—	2	4	no	—
198	C₃×C₄×D₄	D₄	1	8	yes	—
199	C₃×#117	—	2	4	no	—
200	C₃×#117	—	2	8	no	—
201	C₃×#117	—	4	2	no	—
202	C₂×C₃×C₄⋊C₄	—	2	4	no	—
203	C₂×C₃×C₄⋊C₄	—	2	4	no	—
204	C₂×C₃×C₄⋊C₄	—	4	2	no	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
230	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
256	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₄²	—	2	4	no	—
259	C₂×C₃×C₄²	C₂³	1	2	yes	—
260	C₂×C₃×C₄²	C₂³	1	2	yes	—
261	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
263	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
264	C₂×C₃×C₄²	C₂³	1	2	yes	—
265	C₂×C₃×C₄²	C₂³	1	2	yes	—
266	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₃×#95	C₂³	1	2	yes	—
283	C₃×#95	C₂³	1	2	yes	—
284	C₃×#95	C₂³	1	2	yes	—
285	C₃×#95	C₂³	1	2	yes	—
286	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
288	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
289	#552	—	2	8	no	—
290	C₂×#126	C₂²×C₃	1	2	yes	complemented
291	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₂×#125	C₂²×C₃	1	2	yes	complemented
293	C₂×#123	C₂²×C₃	1	2	yes	—
294	C₂×#123	C₂²×C₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
296	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
300	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂×C₄×D₄	—	2	8	no	—
302	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
310	C₂×#117	C₂²×C₃	1	2	yes	complemented
311	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
314	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
318	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
319	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
320	#400	C₂²×C₃	1	2	yes	complemented
321	#398	C₂²×C₃	1	2	yes	complemented
322	#398	C₂²×C₃	1	2	yes	complemented
323	#398	C₂²×C₃	1	2	yes	complemented
324	#397	C₂²×C₃	1	2	yes	complemented
325	#397	C₂²×C₃	1	2	yes	complemented
326	#397	C₂²×C₃	1	2	yes	complemented
327	#396	C₂²×C₃	1	2	yes	complemented
328	#394	C₂²×C₃	1	2	yes	—
329	#394	C₂²×C₃	1	2	yes	—
330	#394	C₂²×C₃	1	2	yes	—
331	#394	C₂²×C₃	1	2	yes	—
332	#391	C₂²×C₃	1	1	yes	characteristic, complemented
333	#389	C₂²×C₃	1	1	yes	characteristic, complemented
334	#389	C₂²×C₃	1	1	yes	characteristic, complemented
335	#389	C₂²×C₃	1	2	yes	complemented
336	#389	C₂²×C₃	1	1	yes	characteristic, complemented
337	#388	C₂²×C₃	1	2	yes	complemented
338	#388	C₂²×C₃	1	2	yes	complemented
339	#388	C₂²×C₃	1	2	yes	complemented
340	#388	C₂²×C₃	1	2	yes	complemented
341	#388	C₂²×C₃	1	2	yes	complemented
342	#388	C₂²×C₃	1	2	yes	complemented
343	#388	C₂²×C₃	1	2	yes	complemented
344	#387	C₂²×C₃	1	2	yes	complemented
345	#387	C₂²×C₃	1	2	yes	complemented
346	#387	C₂²×C₃	1	2	yes	complemented
347	#387	C₂²×C₃	1	2	yes	complemented
348	#387	C₂²×C₃	1	2	yes	complemented
349	#386	C₂²×C₃	1	2	yes	—
350	#386	C₂²×C₃	1	2	yes	—
351	#385	C₂²×C₃	1	2	yes	—
352	#385	C₂²×C₃	1	2	yes	—
353	#385	C₂²×C₃	1	2	yes	—
354	#385	C₂²×C₃	1	2	yes	—
355	#385	C₂²×C₃	1	2	yes	—
356	#385	C₂²×C₃	1	2	yes	complemented
357	#385	C₂²×C₃	1	2	yes	complemented
358	#385	C₂²×C₃	1	2	yes	complemented
359	#385	C₂²×C₃	1	2	yes	complemented
360	#382	C₂²×C₃	1	1	yes	characteristic, complemented
361	#381	C₂²×C₃	1	2	yes	complemented
362	#381	C₂²×C₃	1	2	yes	complemented
363	#380	C₂²×C₃	1	1	yes	characteristic
364	#380	C₂²×C₃	1	1	yes	characteristic
365	#380	C₂²×C₃	1	2	yes	—
366	#380	C₂²×C₃	1	1	yes	characteristic
367	#380	C₂²×C₃	1	1	yes	characteristic, complemented
368	#380	C₂²×C₃	1	1	yes	characteristic, complemented
369	#380	C₂²×C₃	1	1	yes	characteristic, complemented
370	#380	C₂²×C₃	1	1	yes	characteristic, complemented
371	#380	C₂²×C₃	1	1	yes	characteristic, complemented
372	#380	C₂²×C₃	1	1	yes	characteristic, complemented
373	#380	C₂²×C₃	1	2	yes	complemented
374	#380	C₂²×C₃	1	2	yes	complemented
375	#380	C₂²×C₃	1	1	yes	characteristic, complemented
376	#380	C₂²×C₃	1	1	yes	characteristic, complemented
377	#379	C₂²×C₃	1	2	yes	—
378	#379	C₂²×C₃	1	2	yes	—
379	#379	C₂²×C₃	1	2	yes	—
380	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
381	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
382	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
384	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
385	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
386	C₂×#95	C₂²×C₃	1	2	yes	complemented
387	C₂⁴×C₃	—	2	2	no	—
388	C₂⁴×C₃	—	2	2	no	—
389	C₂⁴×C₃	—	2	2	no	—
390	C₂⁴×C₃	—	2	2	no	—
391	C₂⁴×C₃	—	2	2	no	—
392	C₂⁴×C₃	—	2	2	no	—
393	C₂⁴×C₃	—	2	2	no	—
394	C₂⁴×C₃	—	2	2	no	—
395	C₂⁴×C₃	—	2	2	no	—
396	C₂⁴×C₃	—	4	1	no	—
397	C₂⁴×C₃	—	4	1	no	—
398	C₂⁴×C₃	—	4	1	no	—
399	C₂⁴×C₃	—	4	1	no	—
400	C₂⁴×C₃	#41	1	4	yes	—
401	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
402	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
403	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
404	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
405	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₃×Q₈	—	2	2	no	—
407	C₂×C₃×Q₈	—	2	2	no	—
408	C₂×C₃×Q₈	—	2	2	no	—
409	C₂×C₃×D₄	—	2	32	no	—
410	C₂×C₃×D₄	—	2	2	no	—
411	C₂×C₃×D₄	—	2	2	no	—
412	C₂×C₃×D₄	—	2	2	no	—
413	C₂×C₃×D₄	—	2	2	no	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
421	C₂×C₃×D₄	#41	1	4	yes	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	2	no	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	2	2	no	—
426	C₂²×C₃×C₄	—	2	2	no	—
427	C₂²×C₃×C₄	—	2	2	no	—
428	C₂²×C₃×C₄	—	2	2	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	—	2	2	no	—
431	C₂²×C₃×C₄	—	2	4	no	—
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	4	no	—
435	C₂²×C₃×C₄	—	2	4	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	4	no	—
440	C₂²×C₃×C₄	—	2	2	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	2	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	2	2	no	—
449	C₂²×C₃×C₄	—	2	2	no	—
450	C₂²×C₃×C₄	—	2	2	no	—
451	C₂²×C₃×C₄	—	2	2	no	—
452	C₂²×C₃×C₄	—	2	2	no	—
453	C₂²×C₃×C₄	—	2	2	no	—
454	C₂²×C₃×C₄	—	2	2	no	—
455	C₂²×C₃×C₄	—	4	1	no	—
456	C₂²×C₃×C₄	—	4	1	no	—
457	C₂²×C₃×C₄	—	4	1	no	—
458	C₂²×C₃×C₄	—	4	1	no	—
459	C₂²×C₃×C₄	—	4	1	no	—
460	C₂²×C₃×C₄	—	4	1	no	—
461	C₂²×C₃×C₄	—	4	1	no	—
462	C₂²×C₃×C₄	—	4	16	no	—
463	C₂²×C₃×C₄	—	4	16	no	—
464	C₂²×C₃×C₄	—	4	2	no	—
465	C₂²×C₃×C₄	—	4	2	no	—
466	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
467	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
468	C₂²×C₃×C₄	#41	1	4	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
471	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
473	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
474	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
477	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
478	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
479	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
480	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
481	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
482	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
484	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
485	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
486	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	—	2	2	no	—
489	C₃×C₄⋊C₄	—	2	2	no	—
490	C₃×C₄⋊C₄	—	2	2	no	—
491	C₃×C₄⋊C₄	—	2	2	no	—
492	C₃×C₄⋊C₄	—	2	4	no	—
493	C₃×C₄⋊C₄	—	2	2	no	—
494	C₃×C₄⋊C₄	—	2	4	no	—
495	C₃×C₄⋊C₄	—	2	4	no	—
496	C₃×C₄⋊C₄	—	2	4	no	—
497	C₃×C₄⋊C₄	—	2	4	no	—
498	C₃×C₄⋊C₄	—	2	4	no	—
499	C₃×C₄⋊C₄	—	2	2	no	—
500	C₃×C₄⋊C₄	—	2	4	no	—
501	C₃×C₄⋊C₄	—	2	4	no	—
502	C₃×C₄⋊C₄	—	2	4	no	—
503	C₃×C₄⋊C₄	—	2	2	no	—
504	C₃×C₄⋊C₄	—	2	2	no	—
505	C₃×C₄⋊C₄	—	2	2	no	—
506	C₃×C₄⋊C₄	—	4	2	no	—
507	C₃×C₄⋊C₄	—	4	2	no	—
508	C₃×C₄⋊C₄	—	4	2	no	—
509	C₃×C₄⋊C₄	—	4	2	no	—
510	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
511	C₃×C₂²⋊C₄	—	2	2	no	—
512	C₃×C₂²⋊C₄	—	2	2	no	—
513	C₃×C₂²⋊C₄	—	2	4	no	—
514	C₃×C₂²⋊C₄	—	2	4	no	—
515	C₃×C₂²⋊C₄	—	2	4	no	—
516	C₃×C₂²⋊C₄	—	2	4	no	—
517	C₃×C₂²⋊C₄	—	2	4	no	—
518	C₃×C₂²⋊C₄	—	2	4	no	—
519	C₃×C₂²⋊C₄	—	2	4	no	—
520	C₃×C₂²⋊C₄	—	2	4	no	—
521	C₃×C₂²⋊C₄	—	2	4	no	—
522	C₃×C₂²⋊C₄	—	2	4	no	—
523	C₃×C₂²⋊C₄	—	2	4	no	—
524	C₃×C₂²⋊C₄	—	2	4	no	—
525	C₃×C₂²⋊C₄	—	2	2	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	2	2	no	—
528	C₃×C₂²⋊C₄	—	2	2	no	—
529	C₃×C₂²⋊C₄	—	4	2	no	—
530	C₃×C₂²⋊C₄	—	4	2	no	—
531	C₃×C₂²⋊C₄	—	4	2	no	—
532	C₃×C₂²⋊C₄	—	4	2	no	—
533	C₃×C₂²⋊C₄	—	4	2	no	—
534	C₃×C₂²⋊C₄	—	4	2	no	—
535	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
536	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
537	C₃×C₄²	—	2	2	no	—
538	C₃×C₄²	—	2	2	no	—
539	C₃×C₄²	—	2	2	no	—
540	C₃×C₄²	—	2	4	no	—
541	C₃×C₄²	—	2	4	no	—
542	C₃×C₄²	—	4	2	no	—
543	C₃×C₄²	—	4	2	no	—
544	C₃×C₄²	C₂×D₄	1	4	yes	—
545	C₂⁵	C₂³×C₃	1	1	yes	characteristic
546	C₂⁵	C₂³×C₃	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
548	C₂²×D₄	—	2	4	no	—
549	C₂²×D₄	—	2	4	no	—
550	C₂²×D₄	—	2	4	no	—
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
555	C₂³×C₄	—	2	4	no	—
556	C₂³×C₄	—	2	4	no	—
557	C₂³×C₄	—	2	4	no	—
558	C₂³×C₄	—	2	4	no	—
559	C₂³×C₄	—	4	2	no	—
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	C₂³×C₃	1	2	yes	—
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₃	1	2	yes	—
576	#126	—	2	8	no	—
577	#125	—	2	8	no	—
578	#125	—	2	4	no	—
579	#123	—	2	8	no	—
580	#123	—	2	8	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	—	4	2	no	—
585	C₂²⋊Q₈	—	4	2	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	C₃×D₄	1	8	yes	—
595	#117	—	2	4	no	—
596	#117	—	2	8	no	—
597	#117	—	4	2	no	—
598	C₂×C₄⋊C₄	—	2	4	no	—
599	C₂×C₄⋊C₄	—	2	4	no	—
600	C₂×C₄⋊C₄	—	4	2	no	—
601	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	—	2	8	no	—
626	C₂×C₂²⋊C₄	—	2	4	no	—
627	C₂×C₂²⋊C₄	—	2	4	no	—
628	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₄²	—	2	4	no	—
655	C₂×C₄²	C₂³×C₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
663	#95	C₂³×C₃	1	2	yes	—
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	2	yes	—
666	#95	C₂³×C₃	1	2	yes	—
667	#95	C₂³×C₃	1	2	yes	—
668	#95	C₂³×C₃	1	2	yes	—
669	#95	C₂³×C₃	1	2	yes	—
670	#95	C₂³×C₃	1	2	yes	—
671	#95	C₂³×C₃	1	2	yes	—
672	#95	C₂³×C₃	1	2	yes	—
673	#95	C₂³×C₃	1	2	yes	—
674	#95	C₂³×C₃	1	2	yes	—
675	#95	C₂³×C₃	1	2	yes	—
676	#95	C₂³×C₃	1	2	yes	—
677	#95	C₂³×C₃	1	2	yes	—
678	#95	C₂³×C₃	1	2	yes	—
679	#95	C₂³×C₃	1	2	yes	—
680	#95	C₂³×C₃	1	2	yes	—
681	#95	C₂³×C₃	1	2	yes	—
682	C₂³×C₃	—	2	1	no	—
683	C₂³×C₃	—	2	1	no	—
684	C₂³×C₃	—	2	1	no	—
685	C₂³×C₃	—	2	1	no	—
686	C₂³×C₃	—	2	1	no	—
687	C₂³×C₃	—	2	1	no	—
688	C₂³×C₃	—	2	1	no	—
689	C₂³×C₃	—	2	1	no	—
690	C₂³×C₃	—	2	8	no	—
691	C₂³×C₃	—	2	8	no	—
692	C₂³×C₃	—	2	8	no	—
693	C₂³×C₃	—	2	1	no	—
694	C₂³×C₃	—	2	1	no	—
695	C₂³×C₃	—	2	1	no	—
696	C₂³×C₃	—	2	1	no	—
697	C₂³×C₃	—	2	1	no	—
698	C₂³×C₃	—	2	1	no	—
699	C₂³×C₃	—	2	1	no	—
700	C₂³×C₃	—	2	1	no	—
701	C₂³×C₃	—	2	1	no	—
702	C₂³×C₃	—	2	1	no	—
703	C₂³×C₃	—	2	1	no	—
704	C₂³×C₃	—	2	1	no	—
705	C₂³×C₃	—	2	1	no	—
706	C₂³×C₃	—	2	1	no	—
707	C₂³×C₃	—	2	1	no	—
708	C₂³×C₃	—	2	1	no	—
709	C₂³×C₃	—	2	1	no	—
710	C₂³×C₃	—	2	1	no	—
711	C₂³×C₃	—	4	4	no	—
712	C₂³×C₃	—	4	4	no	—
713	C₂³×C₃	—	4	4	no	—
714	C₂³×C₃	—	4	4	no	—
715	C₂³×C₃	—	4	4	no	—
716	C₂³×C₃	—	4	4	no	—
717	C₂³×C₃	—	4	4	no	—
718	C₂³×C₃	—	4	4	no	—
719	C₂³×C₃	—	4	4	no	—
720	C₂³×C₃	—	4	4	no	—
721	C₂³×C₃	—	4	4	no	—
722	C₂³×C₃	C₂²×D₄	1	2	yes	—
723	C₂³×C₃	C₂²×D₄	1	2	yes	—
724	C₂³×C₃	C₂×#41	1	2	yes	—
725	C₂³×C₃	C₂×#41	1	2	yes	—
726	C₂³×C₃	C₂×#41	1	2	yes	—
727	C₂³×C₃	C₂×#41	1	2	yes	—
728	C₂³×C₃	C₂×#41	1	2	yes	—
729	C₂³×C₃	C₂×#41	1	2	yes	—
730	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
731	C₂³×C₃	C₂⁵	1	1	yes	characteristic
732	C₃×Q₈	—	4	4	no	—
733	C₃×D₄	—	2	8	no	—
734	C₃×D₄	—	2	8	no	—
735	C₃×D₄	—	2	8	no	—
736	C₃×D₄	—	2	8	no	—
737	C₂×C₃×C₄	—	2	8	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	1	no	—
740	C₂×C₃×C₄	—	2	1	no	—
741	C₂×C₃×C₄	—	2	1	no	—
742	C₂×C₃×C₄	—	2	1	no	—
743	C₂×C₃×C₄	—	2	1	no	—
744	C₂×C₃×C₄	—	2	1	no	—
745	C₂×C₃×C₄	—	2	1	no	—
746	C₂×C₃×C₄	—	2	1	no	—
747	C₂×C₃×C₄	—	2	1	no	—
748	C₂×C₃×C₄	—	2	1	no	—
749	C₂×C₃×C₄	—	2	1	no	—
750	C₂×C₃×C₄	—	2	8	no	—
751	C₂×C₃×C₄	—	2	8	no	—
752	C₂×C₃×C₄	—	2	8	no	—
753	C₂×C₃×C₄	—	2	1	no	—
754	C₂×C₃×C₄	—	2	2	no	—
755	C₂×C₃×C₄	—	2	2	no	—
756	C₂×C₃×C₄	—	2	2	no	—
757	C₂×C₃×C₄	—	2	1	no	—
758	C₂×C₃×C₄	—	2	1	no	—
759	C₂×C₃×C₄	—	2	2	no	—
760	C₂×C₃×C₄	—	2	2	no	—
761	C₂×C₃×C₄	—	2	2	no	—
762	C₂×C₃×C₄	—	2	2	no	—
763	C₂×C₃×C₄	—	2	2	no	—
764	C₂×C₃×C₄	—	2	2	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	2	no	—
768	C₂×C₃×C₄	—	2	2	no	—
769	C₂×C₃×C₄	—	2	2	no	—
770	C₂×C₃×C₄	—	2	1	no	—
771	C₂×C₃×C₄	—	2	1	no	—
772	C₂×C₃×C₄	—	2	2	no	—
773	C₂×C₃×C₄	—	2	2	no	—
774	C₂×C₃×C₄	—	2	2	no	—
775	C₂×C₃×C₄	—	2	2	no	—
776	C₂×C₃×C₄	—	2	1	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	2	no	—
779	C₂×C₃×C₄	—	2	2	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	2	no	—
782	C₂×C₃×C₄	—	2	2	no	—
783	C₂×C₃×C₄	—	2	2	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	1	no	—
786	C₂×C₃×C₄	—	4	4	no	—
787	C₂×C₃×C₄	—	4	4	no	—
788	C₂×C₃×C₄	—	4	4	no	—
789	C₂×C₃×C₄	—	4	4	no	—
790	C₂×C₃×C₄	—	4	4	no	—
791	C₂×C₃×C₄	—	4	4	no	—
792	C₂×C₃×C₄	—	4	4	no	—
793	C₂×C₃×C₄	—	4	8	no	—
794	C₂×C₃×C₄	—	4	4	no	—
795	C₂×C₃×C₄	—	4	4	no	—
796	C₂×C₃×C₄	—	8	4	no	—
797	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
798	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
799	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
800	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
801	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
802	C₂×C₃×C₄	C₂×#41	1	2	yes	—
803	C₂×C₃×C₄	C₂×#41	1	2	yes	—
804	C₂×C₃×C₄	C₂×#41	1	2	yes	—
805	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
806	C₂⁴	—	2	2	no	—
807	C₂⁴	—	2	2	no	—
808	C₂⁴	—	2	2	no	—
809	C₂⁴	—	2	2	no	—
810	C₂⁴	—	2	2	no	—
811	C₂⁴	—	2	2	no	—
812	C₂⁴	—	2	2	no	—
813	C₂⁴	—	2	2	no	—
814	C₂⁴	—	2	2	no	—
815	C₂⁴	—	4	1	no	—
816	C₂⁴	—	4	1	no	—
817	C₂⁴	—	4	1	no	—
818	C₂⁴	—	4	1	no	—
819	C₂⁴	C₃×#41	1	4	yes	—
820	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
821	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
822	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
823	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
824	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
825	C₂×Q₈	—	2	2	no	—
826	C₂×Q₈	—	2	2	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×D₄	—	2	32	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
840	C₂×D₄	C₃×#41	1	4	yes	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	1	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	16	no	—
882	C₂²×C₄	—	4	16	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
886	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
887	C₂²×C₄	C₃×#41	1	4	yes	—
888	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	4	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	4	no	—
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
955	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	4	no	—
960	C₄²	—	2	4	no	—
961	C₄²	—	4	2	no	—
962	C₄²	—	4	2	no	—
963	C₄²	C₂×C₃×D₄	1	4	yes	—
964	C₂²×C₃	—	2	2	no	—
965	C₂²×C₃	—	2	2	no	—
966	C₂²×C₃	—	2	2	no	—
967	C₂²×C₃	—	2	2	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	2	2	no	—
970	C₂²×C₃	—	2	2	no	—
971	C₂²×C₃	—	2	2	no	—
972	C₂²×C₃	—	2	2	no	—
973	C₂²×C₃	—	2	2	no	—
974	C₂²×C₃	—	2	2	no	—
975	C₂²×C₃	—	2	2	no	—
976	C₂²×C₃	—	2	2	no	—
977	C₂²×C₃	—	2	2	no	—
978	C₂²×C₃	—	2	2	no	—
979	C₂²×C₃	—	2	2	no	—
980	C₂²×C₃	—	2	2	no	—
981	C₂²×C₃	—	2	2	no	—
982	C₂²×C₃	—	2	2	no	—
983	C₂²×C₃	—	2	2	no	—
984	C₂²×C₃	—	2	2	no	—
985	C₂²×C₃	—	4	16	no	—
986	C₂²×C₃	—	4	16	no	—
987	C₂²×C₃	—	4	1	no	—
988	C₂²×C₃	—	4	1	no	—
989	C₂²×C₃	—	4	1	no	—
990	C₂²×C₃	—	4	1	no	—
991	C₂²×C₃	—	4	1	no	—
992	C₂²×C₃	—	4	1	no	—
993	C₂²×C₃	—	4	1	no	—
994	C₂²×C₃	—	4	1	no	—
995	C₂²×C₃	—	4	1	no	—
996	C₂²×C₃	—	4	1	no	—
997	C₂²×C₃	—	4	1	no	—
998	C₂²×C₃	—	4	1	no	—
999	C₂²×C₃	#525	1	4	yes	—
1000	C₂²×C₃	#552	1	4	yes	complemented
1001	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1002	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1003	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1004	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1005	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1006	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1007	C₂²×C₃	#585	1	1	yes	characteristic
1008	C₃×C₄	—	2	2	no	—
1009	C₃×C₄	—	2	2	no	—
1010	C₃×C₄	—	2	2	no	—
1011	C₃×C₄	—	2	2	no	—
1012	C₃×C₄	—	2	2	no	—
1013	C₃×C₄	—	2	2	no	—
1014	C₃×C₄	—	4	2	no	—
1015	C₃×C₄	—	4	2	no	—
1016	C₃×C₄	—	4	1	no	—
1017	C₃×C₄	—	4	1	no	—
1018	C₃×C₄	—	4	2	no	—
1019	C₃×C₄	—	4	2	no	—
1020	C₃×C₄	—	4	2	no	—
1021	C₃×C₄	—	4	1	no	—
1022	C₃×C₄	—	4	2	no	—
1023	C₃×C₄	—	4	2	no	—
1024	C₃×C₄	—	4	2	no	—
1025	C₃×C₄	#546	1	4	yes	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	8	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	8	no	—
1054	C₂³	—	2	8	no	—
1055	C₂³	—	4	4	no	—
1056	C₂³	—	4	4	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	4	4	no	—
1060	C₂³	—	4	4	no	—
1061	C₂³	—	4	4	no	—
1062	C₂³	—	4	4	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	C₂²×C₃×D₄	1	2	yes	—
1067	C₂³	C₂²×C₃×D₄	1	2	yes	—
1068	C₂³	C₂×C₃×#41	1	2	yes	—
1069	C₂³	C₂×C₃×#41	1	2	yes	—
1070	C₂³	C₂×C₃×#41	1	2	yes	—
1071	C₂³	C₂×C₃×#41	1	2	yes	—
1072	C₂³	C₂×C₃×#41	1	2	yes	—
1073	C₂³	C₂×C₃×#41	1	2	yes	—
1074	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
1075	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1076	Q₈	—	4	4	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	8	no	—
1079	D₄	—	2	8	no	—
1080	D₄	—	2	8	no	—
1081	C₂×C₄	—	2	8	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	8	no	—
1095	C₂×C₄	—	2	8	no	—
1096	C₂×C₄	—	2	8	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	8	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	4	no	—
1140	C₂×C₄	—	8	4	no	—
1141	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1142	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1143	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1144	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1145	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1146	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1147	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1148	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1149	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1150	C₂×C₃	—	2	4	no	—
1151	C₂×C₃	—	2	4	no	—
1152	C₂×C₃	—	4	2	no	—
1153	C₂×C₃	—	4	2	no	—
1154	C₂×C₃	—	4	2	no	—
1155	C₂×C₃	C₂×#525	1	1	yes	characteristic
1156	C₂×C₃	C₂×#546	1	1	yes	characteristic
1157	C₂×C₃	C₂×#552	1	1	yes	characteristic
1158	C₂×C₃	#3475	1	1	yes	characteristic
1159	C₂×C₃	#3489	1	1	yes	characteristic
1160	C₂×C₃	#3505	1	1	yes	characteristic
1161	C₂×C₃	#3520	1	1	yes	characteristic
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	4	16	no	—
1184	C₂²	—	4	16	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	C₃×#525	1	4	yes	—
1198	C₂²	C₃×#552	1	4	yes	complemented
1199	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1200	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1201	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1202	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1203	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1204	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1205	C₂²	C₃×#585	1	1	yes	characteristic
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	C₃×#546	1	4	yes	—
1224	C₃	#36156	1	1	yes	characteristic, direct product factor, Sylow
1225	C₂	—	2	4	no	—
1226	C₂	—	2	4	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	4	2	no	—
1229	C₂	—	4	2	no	—
1230	C₂	C₂×C₃×#525	1	1	yes	characteristic
1231	C₂	C₂×C₃×#546	1	1	yes	characteristic
1232	C₂	C₂×C₃×#552	1	1	yes	characteristic
1233	C₂	C₃×#3475	1	1	yes	characteristic
1234	C₂	C₃×#3489	1	1	yes	characteristic
1235	C₂	C₃×#3505	1	1	yes	characteristic
1236	C₂	C₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	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. C₂×C₃×#552	C₂	semidirect
3. C₃×#2851	C₂	semidirect
4. C₃×#2848	C₂	semidirect
5. C₃×#2848	C₂	semidirect
6. C₃×#2562	C₂	semidirect
7. C₃×#2536	C₂	semidirect
8. C₃×#2486	C₂	semidirect
9. C₃×#2485	C₂	semidirect
10. C₃×#2480	C₂	semidirect
11. C₃×#2473	C₂	semidirect
12. C₃×#2468	C₂	semidirect
13. C₃×#2460	C₂	semidirect
14. C₃×#2419	C₂	semidirect
15. C₃×#2417	C₂	semidirect
16. C₃×#2415	C₂	semidirect
18. C₃×#2359	C₂	semidirect
19. C₃×#2352	C₂	semidirect
20. C₃×#2342	C₂	semidirect
21. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
22. C₃×#2280	C₂	semidirect
23. C₂×C₃×#380	C₂	semidirect
24. #36156	C₃	direct (N × H)
29. C₂×C₃×#126	C₂²	semidirect
30. C₂×C₃×#125	C₂²	semidirect
31. C₂×C₃×#125	C₂²	semidirect
35. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₄×Q₈	C₂²	semidirect
49. C₂×C₃×#117	C₂²	semidirect
50. C₂×C₃×#117	C₂²	semidirect
51. C₂×C₃×#117	C₂²	semidirect
53. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
54. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
59. C₃×#400	C₂²	semidirect
60. C₃×#398	C₂²	semidirect
61. C₃×#398	C₂²	semidirect
62. C₃×#398	C₂²	semidirect
63. C₃×#397	C₂²	semidirect
64. C₃×#397	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#396	C₂²	semidirect
71. C₃×#391	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#389	C₂²	semidirect
74. C₃×#389	C₂²	semidirect
75. C₃×#389	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	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
86. C₃×#387	C₂²	semidirect
87. C₃×#387	C₂²	semidirect
95. C₃×#385	C₂²	semidirect
96. C₃×#385	C₂²	semidirect
97. C₃×#385	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
99. C₃×#382	C₂²	semidirect
100. C₃×#381	C₂²	semidirect
101. C₃×#381	C₂²	semidirect
106. C₃×#380	C₂²	semidirect
107. C₃×#380	C₂²	semidirect
108. C₃×#380	C₂²	semidirect
109. C₃×#380	C₂²	semidirect
110. C₃×#380	C₂²	semidirect
111. C₃×#380	C₂²	semidirect
112. C₃×#380	C₂²	semidirect
113. C₃×#380	C₂²	semidirect
114. C₃×#380	C₂²	semidirect
115. C₃×#380	C₂²	semidirect
119. C₃×C₄×C₄⋊C₄	C₂²	semidirect
120. C₃×C₄×C₄⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₂×C₃×#95	C₂²	semidirect
126. C₂×#552	C₂×C₃	semidirect
128. #2851	C₂×C₃	semidirect
129. #2848	C₂×C₃	semidirect
130. #2848	C₂×C₃	semidirect
131. #2562	C₂×C₃	semidirect
132. #2536	C₂×C₃	semidirect
133. #2486	C₂×C₃	semidirect
134. #2485	C₂×C₃	semidirect
135. #2480	C₂×C₃	semidirect
136. #2473	C₂×C₃	semidirect
137. #2468	C₂×C₃	semidirect
138. #2460	C₂×C₃	semidirect
139. #2419	C₂×C₃	semidirect
140. #2417	C₂×C₃	semidirect
141. #2415	C₂×C₃	semidirect
143. #2359	C₂×C₃	semidirect
144. #2352	C₂×C₃	semidirect
145. #2342	C₂×C₃	semidirect
146. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
147. #2280	C₂×C₃	semidirect
148. C₂×#380	C₂×C₃	semidirect
290. C₂×#126	C₂²×C₃	semidirect
291. C₂×#125	C₂²×C₃	semidirect
292. C₂×#125	C₂²×C₃	semidirect
296. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
297. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
298. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
299. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
300. C₂×C₄×Q₈	C₂²×C₃	semidirect
310. C₂×#117	C₂²×C₃	semidirect
311. C₂×#117	C₂²×C₃	semidirect
312. C₂×#117	C₂²×C₃	semidirect
314. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
315. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
320. #400	C₂²×C₃	semidirect
321. #398	C₂²×C₃	semidirect
322. #398	C₂²×C₃	semidirect
323. #398	C₂²×C₃	semidirect
324. #397	C₂²×C₃	semidirect
325. #397	C₂²×C₃	semidirect
326. #397	C₂²×C₃	semidirect
327. #396	C₂²×C₃	semidirect
332. #391	C₂²×C₃	semidirect
333. #389	C₂²×C₃	semidirect
334. #389	C₂²×C₃	semidirect
335. #389	C₂²×C₃	semidirect
336. #389	C₂²×C₃	semidirect
337. #388	C₂²×C₃	semidirect
338. #388	C₂²×C₃	semidirect
339. #388	C₂²×C₃	semidirect
340. #388	C₂²×C₃	semidirect
341. #388	C₂²×C₃	semidirect
342. #388	C₂²×C₃	semidirect
343. #388	C₂²×C₃	semidirect
344. #387	C₂²×C₃	semidirect
345. #387	C₂²×C₃	semidirect
346. #387	C₂²×C₃	semidirect
347. #387	C₂²×C₃	semidirect
348. #387	C₂²×C₃	semidirect
356. #385	C₂²×C₃	semidirect
357. #385	C₂²×C₃	semidirect
358. #385	C₂²×C₃	semidirect
359. #385	C₂²×C₃	semidirect
360. #382	C₂²×C₃	semidirect
361. #381	C₂²×C₃	semidirect
362. #381	C₂²×C₃	semidirect
367. #380	C₂²×C₃	semidirect
368. #380	C₂²×C₃	semidirect
369. #380	C₂²×C₃	semidirect
370. #380	C₂²×C₃	semidirect
371. #380	C₂²×C₃	semidirect
372. #380	C₂²×C₃	semidirect
373. #380	C₂²×C₃	semidirect
374. #380	C₂²×C₃	semidirect
375. #380	C₂²×C₃	semidirect
376. #380	C₂²×C₃	semidirect
380. C₄×C₄⋊C₄	C₂²×C₃	semidirect
381. C₄×C₄⋊C₄	C₂²×C₃	semidirect
384. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
385. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
386. C₂×#95	C₂²×C₃	semidirect
1000. C₂²×C₃	#552	semidirect
1198. C₂²	C₃×#552	semidirect
1224. C₃	#36156	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×#552	2
C₂²×C₃×C₄×D₄	2
C₃×#2851	2
C₃×#2848	2
C₃×#2562	2
C₃×#2536	2
C₃×#2486	2
C₃×#2485	2
C₃×#2480	2
C₃×#2473	2
C₃×#2468	2
C₃×#2460	2
C₃×#2419	2
C₃×#2417	2
C₃×#2415	2
C₃×#2405	2
C₃×#2359	2
C₃×#2352	2
C₃×#2342	2
C₃×C₄×C₂²⋊Q₈	2
C₃×#2280	2
C₂×C₃×#380	2
#36156	3

Subgroups — C3×#36156 #10654763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36156 #10654763