Subgroups — C₃×#37647 #10656254

Order 768.

3130 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2681	C₂	1	2	yes	maximal, complemented
7	C₃×#2680	C₂	1	2	yes	maximal, complemented
8	C₃×#2674	C₂	1	2	yes	maximal, complemented
9	C₃×#2672	C₂	1	2	yes	maximal, complemented
10	C₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2614	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2472	C₂	1	2	yes	maximal, complemented
15	C₃×#2449	C₂	1	2	yes	maximal, complemented
16	C₃×#2440	C₂	1	2	yes	maximal, complemented
17	C₃×#2437	C₂	1	2	yes	maximal, complemented
18	C₃×#2413	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2412	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2405	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
24	#37647	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
29	C₃×#546	—	2	8	no	—
30	C₃×#536	—	2	8	no	—
31	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₃×#124	C₂²	1	2	yes	complemented
34	C₂×C₃×#123	—	2	8	no	—
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×#123	C₂²	1	1	yes	characteristic
38	C₂×C₃×#123	C₂²	1	2	yes	—
39	C₂×C₃×#123	C₂²	1	2	yes	—
40	C₂×C₃×#123	C₂²	1	1	yes	characteristic
41	C₂×C₃×#123	C₂²	1	1	yes	characteristic
42	C₂×C₃×#123	C₂²	1	1	yes	characteristic
43	C₂×C₃×#123	C₂²	1	1	yes	characteristic
44	C₂×C₃×#123	C₂²	1	1	yes	characteristic
45	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₂²⋊Q₈	—	2	8	no	—
49	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
53	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₃×#121	C₂²	1	1	yes	characteristic
57	C₂×C₃×#121	C₂²	1	1	yes	characteristic
58	C₂×C₃×#121	C₂²	1	1	yes	characteristic
59	C₂×C₃×#120	C₂²	1	1	yes	characteristic
60	C₂×C₃×#120	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
65	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
72	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
73	C₃×#399	C₂²	1	2	yes	complemented
74	C₃×#399	C₂²	1	2	yes	complemented
75	C₃×#398	C₂²	1	2	yes	complemented
76	C₃×#398	C₂²	1	2	yes	complemented
77	C₃×#398	C₂²	1	2	yes	complemented
78	C₃×#397	C₂²	1	2	yes	complemented
79	C₃×#397	C₂²	1	2	yes	complemented
80	C₃×#396	C₂²	1	2	yes	complemented
81	C₃×#396	C₂²	1	2	yes	complemented
82	C₃×#396	C₂²	1	2	yes	complemented
83	C₃×#395	C₂²	1	2	yes	complemented
84	C₃×#395	C₂²	1	2	yes	complemented
85	C₃×#395	C₂²	1	2	yes	complemented
86	C₃×#394	C₂²	1	2	yes	—
87	C₃×#394	C₂²	1	2	yes	—
88	C₃×#394	C₂²	1	2	yes	complemented
89	C₃×#394	C₂²	1	2	yes	complemented
90	C₃×#394	C₂²	1	2	yes	complemented
91	C₃×#393	C₂²	1	2	yes	complemented
92	C₃×#393	C₂²	1	2	yes	complemented
93	C₃×#390	C₂²	1	2	yes	complemented
94	C₃×#389	C₂²	1	2	yes	complemented
95	C₃×#389	C₂²	1	2	yes	complemented
96	C₃×#389	C₂²	1	2	yes	complemented
97	C₃×#388	C₂²	1	2	yes	complemented
98	C₃×#388	C₂²	1	2	yes	complemented
99	C₃×#388	C₂²	1	2	yes	complemented
100	C₃×#388	C₂²	1	2	yes	complemented
101	C₃×#387	C₂²	1	2	yes	complemented
102	C₃×#386	C₂²	1	1	yes	characteristic
103	C₃×#386	C₂²	1	1	yes	characteristic
104	C₃×#386	C₂²	1	2	yes	—
105	C₃×#386	C₂²	1	2	yes	—
106	C₃×#386	C₂²	1	1	yes	characteristic, complemented
107	C₃×#386	C₂²	1	2	yes	complemented
108	C₃×#385	C₂²	1	2	yes	—
109	C₃×#385	C₂²	1	2	yes	—
110	C₃×#385	C₂²	1	2	yes	—
111	C₃×#385	C₂²	1	2	yes	complemented
112	C₃×#385	C₂²	1	2	yes	complemented
113	C₃×#385	C₂²	1	1	yes	characteristic, complemented
114	C₃×#385	C₂²	1	2	yes	complemented
115	C₃×#385	C₂²	1	2	yes	complemented
116	C₃×#384	C₂²	1	2	yes	complemented
117	C₃×#381	C₂²	1	1	yes	characteristic, complemented
118	C₃×#381	C₂²	1	1	yes	characteristic, complemented
119	C₃×#381	C₂²	1	1	yes	characteristic, complemented
120	C₃×#381	C₂²	1	1	yes	characteristic, complemented
121	C₃×#380	C₂²	1	2	yes	—
122	C₃×#380	C₂²	1	1	yes	characteristic, complemented
123	C₃×#380	C₂²	1	2	yes	complemented
124	C₃×#379	C₂²	1	2	yes	—
125	C₃×#379	C₂²	1	1	yes	characteristic
126	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
127	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	C₂×#546	C₂×C₃	1	1	yes	characteristic
129	C₂×#536	C₂×C₃	1	1	yes	characteristic, complemented
130	C₂²×#123	C₂×C₃	1	1	yes	characteristic, complemented
131	C₂²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
132	#2849	C₂×C₃	1	1	yes	characteristic, complemented
133	#2681	C₂×C₃	1	2	yes	complemented
134	#2680	C₂×C₃	1	2	yes	complemented
135	#2674	C₂×C₃	1	2	yes	complemented
136	#2672	C₂×C₃	1	2	yes	complemented
137	#2618	C₂×C₃	1	1	yes	characteristic, complemented
138	#2614	C₂×C₃	1	1	yes	characteristic, complemented
139	#2501	C₂×C₃	1	1	yes	characteristic, complemented
140	#2486	C₂×C₃	1	1	yes	characteristic, complemented
141	#2472	C₂×C₃	1	2	yes	complemented
142	#2449	C₂×C₃	1	2	yes	complemented
143	#2440	C₂×C₃	1	2	yes	complemented
144	#2437	C₂×C₃	1	2	yes	complemented
145	#2413	C₂×C₃	1	1	yes	characteristic, complemented
146	#2412	C₂×C₃	1	1	yes	characteristic, complemented
147	#2406	C₂×C₃	1	1	yes	characteristic, complemented
148	#2405	C₂×C₃	1	1	yes	characteristic, complemented
149	#2342	C₂×C₃	1	1	yes	characteristic, complemented
150	#2322	C₂×C₃	1	1	yes	characteristic, complemented
151	C₂⁵×C₃	C₂³	1	1	yes	characteristic
152	C₂⁵×C₃	C₂³	1	1	yes	characteristic
153	C₂×C₃×#41	—	2	4	no	—
154	C₂×C₃×#41	—	2	4	no	—
155	C₂×C₃×#41	—	4	2	no	—
156	C₂²×C₃×Q₈	—	2	4	no	—
157	C₂²×C₃×Q₈	—	2	4	no	—
158	C₂²×C₃×Q₈	—	4	2	no	—
159	C₂²×C₃×Q₈	C₂³	1	2	yes	—
160	C₂²×C₃×Q₈	C₂³	1	2	yes	—
161	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
162	C₂²×C₃×D₄	—	2	4	no	—
163	C₂²×C₃×D₄	—	2	4	no	—
164	C₂²×C₃×D₄	—	4	2	no	—
165	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
171	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
172	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
174	C₂³×C₃×C₄	—	2	4	no	—
175	C₂³×C₃×C₄	—	2	4	no	—
176	C₂³×C₃×C₄	—	4	2	no	—
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	C₂³×C₃×C₄	C₂³	1	2	yes	—
181	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
182	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
183	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₃×C₄	C₂³	1	2	yes	—
185	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
186	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
188	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
189	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄⋊Q₈	—	2	8	no	—
191	C₃×#124	—	2	4	no	—
192	C₃×#124	—	2	8	no	—
193	C₃×#123	—	2	4	no	—
194	C₃×#123	—	2	4	no	—
195	C₃×#123	—	2	4	no	—
196	C₃×#123	—	2	4	no	—
197	C₃×#123	—	2	4	no	—
198	C₃×#123	—	2	8	no	—
199	C₃×#123	—	2	8	no	—
200	C₃×#123	—	2	4	no	—
201	C₃×#123	—	2	4	no	—
202	C₃×#123	—	2	4	no	—
203	C₃×#123	—	4	2	no	—
204	C₃×#123	—	4	2	no	—
205	C₃×#123	D₄	1	8	yes	complemented
206	C₃×C₂²⋊Q₈	—	2	8	no	—
207	C₃×C₂²⋊Q₈	—	2	8	no	—
208	C₃×C₂²⋊Q₈	—	2	8	no	—
209	C₃×C₂²⋊Q₈	—	2	8	no	—
210	C₃×C₂²⋊Q₈	—	2	8	no	—
211	C₃×C₂²⋊Q₈	—	2	4	no	—
212	C₃×C₂²⋊Q₈	—	2	8	no	—
213	C₃×#121	—	2	4	no	—
214	C₃×#121	—	2	4	no	—
215	C₃×#121	—	2	4	no	—
216	C₃×#120	—	2	4	no	—
217	C₃×#120	—	2	4	no	—
218	C₃×C₄×D₄	—	2	4	no	—
219	C₃×C₄×D₄	—	2	4	no	—
220	C₃×#117	—	2	4	no	—
221	C₂×C₃×C₄⋊C₄	—	2	4	no	—
222	C₂×C₃×C₄⋊C₄	—	2	4	no	—
223	C₂×C₃×C₄⋊C₄	—	2	4	no	—
224	C₂×C₃×C₄⋊C₄	—	2	8	no	—
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	1	yes	characteristic
228	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₃×C₂²⋊C₄	D₄	1	8	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
257	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
260	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
263	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
264	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
266	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
275	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₃×C₄²	C₂³	1	2	yes	—
286	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
287	C₂×C₃×C₄²	C₂³	1	2	yes	—
288	C₃×#95	C₂³	1	2	yes	—
289	C₃×#95	C₂³	1	2	yes	—
290	C₃×#95	C₂³	1	2	yes	—
291	C₃×#95	C₂³	1	2	yes	—
292	C₃×#95	C₂³	1	2	yes	—
293	C₃×#95	C₂³	1	2	yes	—
294	C₃×#95	C₂³	1	2	yes	—
295	C₃×#95	C₂³	1	2	yes	—
296	C₃×#95	C₂³	1	2	yes	—
297	C₃×#95	C₂³	1	2	yes	—
298	C₃×#95	C₂³	1	2	yes	—
299	C₃×#95	C₂³	1	2	yes	—
300	C₃×#95	C₂³	1	2	yes	—
301	C₃×#95	C₂³	1	2	yes	—
302	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
303	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
306	#546	—	2	8	no	—
307	#536	—	2	8	no	—
308	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
309	C₂×#124	C₂²×C₃	1	1	yes	characteristic
310	C₂×#124	C₂²×C₃	1	2	yes	complemented
311	C₂×#123	—	2	8	no	—
312	C₂×#123	C₂²×C₃	1	1	yes	characteristic
313	C₂×#123	C₂²×C₃	1	1	yes	characteristic
314	C₂×#123	C₂²×C₃	1	1	yes	characteristic
315	C₂×#123	C₂²×C₃	1	1	yes	characteristic
316	C₂×#123	C₂²×C₃	1	1	yes	characteristic
317	C₂×#123	C₂²×C₃	1	2	yes	—
318	C₂×#123	C₂²×C₃	1	2	yes	—
319	C₂×#123	C₂²×C₃	1	1	yes	characteristic
320	C₂×#123	C₂²×C₃	1	1	yes	characteristic
321	C₂×#123	C₂²×C₃	1	1	yes	characteristic
322	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
325	C₂×C₂²⋊Q₈	—	2	8	no	—
326	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
327	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
328	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
330	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
331	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
332	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
333	C₂×#121	C₂²×C₃	1	1	yes	characteristic
334	C₂×#121	C₂²×C₃	1	1	yes	characteristic
335	C₂×#121	C₂²×C₃	1	1	yes	characteristic
336	C₂×#120	C₂²×C₃	1	1	yes	characteristic
337	C₂×#120	C₂²×C₃	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
340	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
341	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
343	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
344	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
345	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	#399	C₂²×C₃	1	2	yes	complemented
351	#399	C₂²×C₃	1	2	yes	complemented
352	#398	C₂²×C₃	1	2	yes	complemented
353	#398	C₂²×C₃	1	2	yes	complemented
354	#398	C₂²×C₃	1	2	yes	complemented
355	#397	C₂²×C₃	1	2	yes	complemented
356	#397	C₂²×C₃	1	2	yes	complemented
357	#396	C₂²×C₃	1	2	yes	complemented
358	#396	C₂²×C₃	1	2	yes	complemented
359	#396	C₂²×C₃	1	2	yes	complemented
360	#395	C₂²×C₃	1	2	yes	complemented
361	#395	C₂²×C₃	1	2	yes	complemented
362	#395	C₂²×C₃	1	2	yes	complemented
363	#394	C₂²×C₃	1	2	yes	—
364	#394	C₂²×C₃	1	2	yes	—
365	#394	C₂²×C₃	1	2	yes	complemented
366	#394	C₂²×C₃	1	2	yes	complemented
367	#394	C₂²×C₃	1	2	yes	complemented
368	#393	C₂²×C₃	1	2	yes	complemented
369	#393	C₂²×C₃	1	2	yes	complemented
370	#390	C₂²×C₃	1	2	yes	complemented
371	#389	C₂²×C₃	1	2	yes	complemented
372	#389	C₂²×C₃	1	2	yes	complemented
373	#389	C₂²×C₃	1	2	yes	complemented
374	#388	C₂²×C₃	1	2	yes	complemented
375	#388	C₂²×C₃	1	2	yes	complemented
376	#388	C₂²×C₃	1	2	yes	complemented
377	#388	C₂²×C₃	1	2	yes	complemented
378	#387	C₂²×C₃	1	2	yes	complemented
379	#386	C₂²×C₃	1	1	yes	characteristic
380	#386	C₂²×C₃	1	2	yes	—
381	#386	C₂²×C₃	1	1	yes	characteristic
382	#386	C₂²×C₃	1	2	yes	—
383	#386	C₂²×C₃	1	2	yes	complemented
384	#386	C₂²×C₃	1	1	yes	characteristic, complemented
385	#385	C₂²×C₃	1	2	yes	—
386	#385	C₂²×C₃	1	2	yes	—
387	#385	C₂²×C₃	1	2	yes	—
388	#385	C₂²×C₃	1	1	yes	characteristic, complemented
389	#385	C₂²×C₃	1	2	yes	complemented
390	#385	C₂²×C₃	1	2	yes	complemented
391	#385	C₂²×C₃	1	2	yes	complemented
392	#385	C₂²×C₃	1	2	yes	complemented
393	#384	C₂²×C₃	1	2	yes	complemented
394	#381	C₂²×C₃	1	1	yes	characteristic, complemented
395	#381	C₂²×C₃	1	1	yes	characteristic, complemented
396	#381	C₂²×C₃	1	1	yes	characteristic, complemented
397	#381	C₂²×C₃	1	1	yes	characteristic, complemented
398	#380	C₂²×C₃	1	2	yes	—
399	#380	C₂²×C₃	1	1	yes	characteristic, complemented
400	#380	C₂²×C₃	1	2	yes	complemented
401	#379	C₂²×C₃	1	1	yes	characteristic
402	#379	C₂²×C₃	1	2	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
405	C₂⁴×C₃	—	2	2	no	—
406	C₂⁴×C₃	—	2	2	no	—
407	C₂⁴×C₃	—	2	4	no	—
408	C₂⁴×C₃	—	2	2	no	—
409	C₂⁴×C₃	—	2	2	no	—
410	C₂⁴×C₃	—	2	4	no	—
411	C₂⁴×C₃	—	4	2	no	—
412	C₂⁴×C₃	—	4	2	no	—
413	C₂⁴×C₃	—	4	1	no	—
414	C₂⁴×C₃	C₂×D₄	1	4	yes	—
415	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
416	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
417	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
418	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
419	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
420	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
421	C₃×#41	—	4	16	no	—
422	C₂×C₃×Q₈	—	2	4	no	—
423	C₂×C₃×Q₈	—	2	4	no	—
424	C₂×C₃×Q₈	—	2	4	no	—
425	C₂×C₃×Q₈	—	2	2	no	—
426	C₂×C₃×Q₈	—	2	4	no	—
427	C₂×C₃×Q₈	—	2	2	no	—
428	C₂×C₃×Q₈	—	4	2	no	—
429	C₂×C₃×Q₈	—	4	2	no	—
430	C₂×C₃×Q₈	—	4	1	no	—
431	C₂×C₃×Q₈	—	4	16	no	—
432	C₂×C₃×D₄	—	2	2	no	—
433	C₂×C₃×D₄	—	2	2	no	—
434	C₂×C₃×D₄	—	2	2	no	—
435	C₂×C₃×D₄	—	2	2	no	—
436	C₂×C₃×D₄	—	2	2	no	—
437	C₂×C₃×D₄	—	2	2	no	—
438	C₂×C₃×D₄	—	2	2	no	—
439	C₂×C₃×D₄	—	2	2	no	—
440	C₂×C₃×D₄	—	2	2	no	—
441	C₂×C₃×D₄	—	2	2	no	—
442	C₂×C₃×D₄	—	2	2	no	—
443	C₂×C₃×D₄	—	2	2	no	—
444	C₂×C₃×D₄	—	2	2	no	—
445	C₂×C₃×D₄	—	2	4	no	—
446	C₂×C₃×D₄	—	2	2	no	—
447	C₂×C₃×D₄	—	2	2	no	—
448	C₂×C₃×D₄	—	2	2	no	—
449	C₂×C₃×D₄	—	2	2	no	—
450	C₂×C₃×D₄	—	4	1	no	—
451	C₂×C₃×D₄	—	4	1	no	—
452	C₂×C₃×D₄	—	4	1	no	—
453	C₂×C₃×D₄	—	4	2	no	—
454	C₂×C₃×D₄	—	4	2	no	—
455	C₂×C₃×D₄	—	4	16	no	—
456	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
457	C₂²×C₃×C₄	—	2	2	no	—
458	C₂²×C₃×C₄	—	2	2	no	—
459	C₂²×C₃×C₄	—	2	2	no	—
460	C₂²×C₃×C₄	—	2	2	no	—
461	C₂²×C₃×C₄	—	2	2	no	—
462	C₂²×C₃×C₄	—	2	2	no	—
463	C₂²×C₃×C₄	—	2	2	no	—
464	C₂²×C₃×C₄	—	2	2	no	—
465	C₂²×C₃×C₄	—	2	4	no	—
466	C₂²×C₃×C₄	—	2	4	no	—
467	C₂²×C₃×C₄	—	2	2	no	—
468	C₂²×C₃×C₄	—	2	2	no	—
469	C₂²×C₃×C₄	—	2	2	no	—
470	C₂²×C₃×C₄	—	2	2	no	—
471	C₂²×C₃×C₄	—	2	2	no	—
472	C₂²×C₃×C₄	—	2	4	no	—
473	C₂²×C₃×C₄	—	2	4	no	—
474	C₂²×C₃×C₄	—	2	4	no	—
475	C₂²×C₃×C₄	—	2	2	no	—
476	C₂²×C₃×C₄	—	2	2	no	—
477	C₂²×C₃×C₄	—	2	2	no	—
478	C₂²×C₃×C₄	—	2	2	no	—
479	C₂²×C₃×C₄	—	2	4	no	—
480	C₂²×C₃×C₄	—	2	2	no	—
481	C₂²×C₃×C₄	—	4	2	no	—
482	C₂²×C₃×C₄	—	4	2	no	—
483	C₂²×C₃×C₄	—	4	2	no	—
484	C₂²×C₃×C₄	—	4	2	no	—
485	C₂²×C₃×C₄	—	4	2	no	—
486	C₂²×C₃×C₄	—	4	1	no	—
487	C₂²×C₃×C₄	—	4	1	no	—
488	C₂²×C₃×C₄	—	4	1	no	—
489	C₂²×C₃×C₄	—	4	2	no	—
490	C₂²×C₃×C₄	—	4	16	no	—
491	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
492	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
493	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
494	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
496	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
497	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
498	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
499	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
500	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
501	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
502	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
503	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
504	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
505	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
506	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
507	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
508	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
510	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
511	C₃×C₄⋊C₄	—	2	4	no	—
512	C₃×C₄⋊C₄	—	2	4	no	—
513	C₃×C₄⋊C₄	—	2	4	no	—
514	C₃×C₄⋊C₄	—	2	4	no	—
515	C₃×C₄⋊C₄	—	2	4	no	—
516	C₃×C₄⋊C₄	—	2	4	no	—
517	C₃×C₄⋊C₄	—	2	4	no	—
518	C₃×C₄⋊C₄	—	2	4	no	—
519	C₃×C₄⋊C₄	—	2	4	no	—
520	C₃×C₄⋊C₄	—	2	4	no	—
521	C₃×C₄⋊C₄	—	2	2	no	—
522	C₃×C₄⋊C₄	—	2	2	no	—
523	C₃×C₄⋊C₄	—	2	2	no	—
524	C₃×C₄⋊C₄	—	2	2	no	—
525	C₃×C₄⋊C₄	—	2	4	no	—
526	C₃×C₄⋊C₄	—	2	4	no	—
527	C₃×C₄⋊C₄	—	2	4	no	—
528	C₃×C₄⋊C₄	—	4	2	no	—
529	C₃×C₄⋊C₄	—	4	2	no	—
530	C₃×C₄⋊C₄	—	4	2	no	—
531	C₃×C₄⋊C₄	—	4	2	no	—
532	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
533	C₃×C₂²⋊C₄	—	2	2	no	—
534	C₃×C₂²⋊C₄	—	2	4	no	—
535	C₃×C₂²⋊C₄	—	2	4	no	—
536	C₃×C₂²⋊C₄	—	2	2	no	—
537	C₃×C₂²⋊C₄	—	2	4	no	—
538	C₃×C₂²⋊C₄	—	2	2	no	—
539	C₃×C₂²⋊C₄	—	2	2	no	—
540	C₃×C₂²⋊C₄	—	2	2	no	—
541	C₃×C₂²⋊C₄	—	2	4	no	—
542	C₃×C₂²⋊C₄	—	2	2	no	—
543	C₃×C₂²⋊C₄	—	2	4	no	—
544	C₃×C₂²⋊C₄	—	2	2	no	—
545	C₃×C₂²⋊C₄	—	2	2	no	—
546	C₃×C₂²⋊C₄	—	2	4	no	—
547	C₃×C₂²⋊C₄	—	2	4	no	—
548	C₃×C₂²⋊C₄	—	2	4	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	2	no	—
551	C₃×C₂²⋊C₄	—	2	2	no	—
552	C₃×C₂²⋊C₄	—	2	4	no	—
553	C₃×C₂²⋊C₄	—	2	4	no	—
554	C₃×C₂²⋊C₄	—	4	2	no	—
555	C₃×C₂²⋊C₄	—	4	2	no	—
556	C₃×C₂²⋊C₄	—	4	2	no	—
557	C₃×C₂²⋊C₄	—	4	2	no	—
558	C₃×C₂²⋊C₄	—	4	2	no	—
559	C₃×C₂²⋊C₄	—	4	2	no	—
560	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
561	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
562	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
563	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
564	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
565	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
566	C₃×C₄²	—	2	4	no	—
567	C₃×C₄²	—	2	2	no	—
568	C₃×C₄²	—	4	2	no	—
569	C₂⁵	C₂³×C₃	1	1	yes	characteristic
570	C₂⁵	C₂³×C₃	1	1	yes	characteristic
571	C₂×#41	—	2	4	no	—
572	C₂×#41	—	2	4	no	—
573	C₂×#41	—	4	2	no	—
574	C₂²×Q₈	—	2	4	no	—
575	C₂²×Q₈	—	2	4	no	—
576	C₂²×Q₈	—	4	2	no	—
577	C₂²×Q₈	C₂³×C₃	1	2	yes	—
578	C₂²×Q₈	C₂³×C₃	1	2	yes	—
579	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
580	C₂²×D₄	—	2	4	no	—
581	C₂²×D₄	—	2	4	no	—
582	C₂²×D₄	—	4	2	no	—
583	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
584	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
590	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
592	C₂³×C₄	—	2	4	no	—
593	C₂³×C₄	—	2	4	no	—
594	C₂³×C₄	—	4	2	no	—
595	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₃	1	2	yes	—
598	C₂³×C₄	C₂³×C₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
608	C₄⋊Q₈	—	2	8	no	—
609	#124	—	2	4	no	—
610	#124	—	2	8	no	—
611	#123	—	2	4	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	4	no	—
615	#123	—	2	4	no	—
616	#123	—	2	8	no	—
617	#123	—	2	8	no	—
618	#123	—	2	4	no	—
619	#123	—	2	4	no	—
620	#123	—	2	4	no	—
621	#123	—	4	2	no	—
622	#123	—	4	2	no	—
623	#123	C₃×D₄	1	8	yes	complemented
624	C₂²⋊Q₈	—	2	8	no	—
625	C₂²⋊Q₈	—	2	8	no	—
626	C₂²⋊Q₈	—	2	8	no	—
627	C₂²⋊Q₈	—	2	8	no	—
628	C₂²⋊Q₈	—	2	8	no	—
629	C₂²⋊Q₈	—	2	4	no	—
630	C₂²⋊Q₈	—	2	8	no	—
631	#121	—	2	4	no	—
632	#121	—	2	4	no	—
633	#121	—	2	4	no	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	C₄×D₄	—	2	4	no	—
637	C₄×D₄	—	2	4	no	—
638	#117	—	2	4	no	—
639	C₂×C₄⋊C₄	—	2	4	no	—
640	C₂×C₄⋊C₄	—	2	4	no	—
641	C₂×C₄⋊C₄	—	2	4	no	—
642	C₂×C₄⋊C₄	—	2	8	no	—
643	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
665	C₂×C₂²⋊C₄	—	2	4	no	—
666	C₂×C₂²⋊C₄	—	2	4	no	—
667	C₂×C₂²⋊C₄	—	2	8	no	—
668	C₂×C₂²⋊C₄	—	2	4	no	—
669	C₂×C₂²⋊C₄	C₃×D₄	1	8	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
703	C₂×C₄²	C₂³×C₃	1	2	yes	—
704	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₃	1	2	yes	—
706	#95	C₂³×C₃	1	2	yes	—
707	#95	C₂³×C₃	1	2	yes	—
708	#95	C₂³×C₃	1	2	yes	—
709	#95	C₂³×C₃	1	2	yes	—
710	#95	C₂³×C₃	1	2	yes	—
711	#95	C₂³×C₃	1	2	yes	—
712	#95	C₂³×C₃	1	2	yes	—
713	#95	C₂³×C₃	1	2	yes	—
714	#95	C₂³×C₃	1	2	yes	—
715	#95	C₂³×C₃	1	2	yes	—
716	#95	C₂³×C₃	1	2	yes	—
717	#95	C₂³×C₃	1	2	yes	—
718	#95	C₂³×C₃	1	2	yes	—
719	#95	C₂³×C₃	1	2	yes	—
720	C₂³×C₃	—	2	1	no	—
721	C₂³×C₃	—	2	1	no	—
722	C₂³×C₃	—	2	2	no	—
723	C₂³×C₃	—	2	2	no	—
724	C₂³×C₃	—	2	2	no	—
725	C₂³×C₃	—	2	8	no	—
726	C₂³×C₃	—	2	8	no	—
727	C₂³×C₃	—	2	1	no	—
728	C₂³×C₃	—	2	1	no	—
729	C₂³×C₃	—	2	1	no	—
730	C₂³×C₃	—	2	1	no	—
731	C₂³×C₃	—	2	2	no	—
732	C₂³×C₃	—	2	2	no	—
733	C₂³×C₃	—	2	2	no	—
734	C₂³×C₃	—	2	2	no	—
735	C₂³×C₃	—	2	1	no	—
736	C₂³×C₃	—	2	1	no	—
737	C₂³×C₃	—	2	1	no	—
738	C₂³×C₃	—	2	1	no	—
739	C₂³×C₃	—	2	1	no	—
740	C₂³×C₃	—	2	1	no	—
741	C₂³×C₃	—	2	2	no	—
742	C₂³×C₃	—	2	2	no	—
743	C₂³×C₃	—	2	2	no	—
744	C₂³×C₃	—	2	2	no	—
745	C₂³×C₃	—	4	4	no	—
746	C₂³×C₃	—	4	8	no	—
747	C₂³×C₃	—	4	8	no	—
748	C₂³×C₃	—	4	4	no	—
749	C₂³×C₃	—	4	8	no	—
750	C₂³×C₃	—	4	4	no	—
751	C₂³×C₃	—	8	2	no	—
752	C₂³×C₃	—	8	4	no	—
753	C₂³×C₃	C₂²×D₄	1	2	yes	—
754	C₂³×C₃	C₂²×D₄	1	2	yes	—
755	C₂³×C₃	C₂²×D₄	1	2	yes	—
756	C₂³×C₃	C₂²×D₄	1	2	yes	—
757	C₂³×C₃	C₂²×D₄	1	2	yes	—
758	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
759	C₂³×C₃	2₋¹⁺⁴	1	4	yes	—
760	C₂³×C₃	C₂⁵	1	1	yes	characteristic
761	C₃×Q₈	—	4	8	no	—
762	C₃×Q₈	—	4	8	no	—
763	C₃×Q₈	—	4	4	no	—
764	C₃×D₄	—	2	8	no	—
765	C₃×D₄	—	4	4	no	—
766	C₃×D₄	—	4	4	no	—
767	C₃×D₄	—	4	4	no	—
768	C₃×D₄	—	4	4	no	—
769	C₃×D₄	—	4	4	no	—
770	C₃×D₄	—	4	4	no	—
771	C₃×D₄	—	8	2	no	—
772	C₃×D₄	—	8	2	no	—
773	C₂×C₃×C₄	—	2	8	no	—
774	C₂×C₃×C₄	—	2	8	no	—
775	C₂×C₃×C₄	—	2	1	no	—
776	C₂×C₃×C₄	—	2	1	no	—
777	C₂×C₃×C₄	—	2	2	no	—
778	C₂×C₃×C₄	—	2	1	no	—
779	C₂×C₃×C₄	—	2	2	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	1	no	—
782	C₂×C₃×C₄	—	2	1	no	—
783	C₂×C₃×C₄	—	2	2	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	2	no	—
786	C₂×C₃×C₄	—	2	2	no	—
787	C₂×C₃×C₄	—	2	1	no	—
788	C₂×C₃×C₄	—	2	2	no	—
789	C₂×C₃×C₄	—	2	2	no	—
790	C₂×C₃×C₄	—	2	1	no	—
791	C₂×C₃×C₄	—	2	1	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	2	no	—
794	C₂×C₃×C₄	—	2	2	no	—
795	C₂×C₃×C₄	—	2	2	no	—
796	C₂×C₃×C₄	—	2	1	no	—
797	C₂×C₃×C₄	—	2	2	no	—
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	2	no	—
802	C₂×C₃×C₄	—	2	2	no	—
803	C₂×C₃×C₄	—	2	1	no	—
804	C₂×C₃×C₄	—	2	1	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	2	no	—
807	C₂×C₃×C₄	—	2	2	no	—
808	C₂×C₃×C₄	—	2	2	no	—
809	C₂×C₃×C₄	—	2	2	no	—
810	C₂×C₃×C₄	—	2	2	no	—
811	C₂×C₃×C₄	—	2	2	no	—
812	C₂×C₃×C₄	—	2	2	no	—
813	C₂×C₃×C₄	—	2	2	no	—
814	C₂×C₃×C₄	—	2	2	no	—
815	C₂×C₃×C₄	—	4	4	no	—
816	C₂×C₃×C₄	—	4	4	no	—
817	C₂×C₃×C₄	—	4	8	no	—
818	C₂×C₃×C₄	—	4	8	no	—
819	C₂×C₃×C₄	—	4	8	no	—
820	C₂×C₃×C₄	—	4	4	no	—
821	C₂×C₃×C₄	—	4	4	no	—
822	C₂×C₃×C₄	—	4	4	no	—
823	C₂×C₃×C₄	—	4	4	no	—
824	C₂×C₃×C₄	—	4	4	no	—
825	C₂×C₃×C₄	—	8	2	no	—
826	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
827	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
828	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
829	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
830	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
831	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
832	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
833	C₂⁴	—	2	2	no	—
834	C₂⁴	—	2	2	no	—
835	C₂⁴	—	2	4	no	—
836	C₂⁴	—	2	2	no	—
837	C₂⁴	—	2	2	no	—
838	C₂⁴	—	2	4	no	—
839	C₂⁴	—	4	2	no	—
840	C₂⁴	—	4	1	no	—
841	C₂⁴	—	4	2	no	—
842	C₂⁴	C₂×C₃×D₄	1	4	yes	—
843	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
844	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
845	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
846	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
848	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
849	#41	—	4	16	no	—
850	C₂×Q₈	—	2	4	no	—
851	C₂×Q₈	—	2	4	no	—
852	C₂×Q₈	—	2	4	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	4	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	4	2	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	—	4	1	no	—
859	C₂×Q₈	—	4	16	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	4	1	no	—
879	C₂×D₄	—	4	1	no	—
880	C₂×D₄	—	4	1	no	—
881	C₂×D₄	—	4	2	no	—
882	C₂×D₄	—	4	2	no	—
883	C₂×D₄	—	4	16	no	—
884	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	2	4	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	1	no	—
912	C₂²×C₄	—	4	1	no	—
913	C₂²×C₄	—	4	1	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	16	no	—
919	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
920	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
921	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
922	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
927	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	2	4	no	—
941	C₄⋊C₄	—	2	4	no	—
942	C₄⋊C₄	—	2	4	no	—
943	C₄⋊C₄	—	2	4	no	—
944	C₄⋊C₄	—	2	4	no	—
945	C₄⋊C₄	—	2	4	no	—
946	C₄⋊C₄	—	2	4	no	—
947	C₄⋊C₄	—	2	4	no	—
948	C₄⋊C₄	—	2	4	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	4	no	—
954	C₄⋊C₄	—	2	4	no	—
955	C₄⋊C₄	—	2	4	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	4	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
989	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
990	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
991	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
992	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
993	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
994	C₄²	—	2	4	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	4	2	no	—
997	C₂²×C₃	—	2	2	no	—
998	C₂²×C₃	—	2	2	no	—
999	C₂²×C₃	—	2	2	no	—
1000	C₂²×C₃	—	2	2	no	—
1001	C₂²×C₃	—	2	4	no	—
1002	C₂²×C₃	—	2	4	no	—
1003	C₂²×C₃	—	2	4	no	—
1004	C₂²×C₃	—	2	4	no	—
1005	C₂²×C₃	—	2	2	no	—
1006	C₂²×C₃	—	2	2	no	—
1007	C₂²×C₃	—	2	2	no	—
1008	C₂²×C₃	—	2	2	no	—
1009	C₂²×C₃	—	2	4	no	—
1010	C₂²×C₃	—	4	16	no	—
1011	C₂²×C₃	—	4	1	no	—
1012	C₂²×C₃	—	4	1	no	—
1013	C₂²×C₃	—	4	2	no	—
1014	C₂²×C₃	—	4	2	no	—
1015	C₂²×C₃	—	4	2	no	—
1016	C₂²×C₃	—	4	1	no	—
1017	C₂²×C₃	—	4	1	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	1	no	—
1020	C₂²×C₃	—	4	1	no	—
1021	C₂²×C₃	—	4	1	no	—
1022	C₂²×C₃	—	4	2	no	—
1023	C₂²×C₃	—	4	2	no	—
1024	C₂²×C₃	—	4	2	no	—
1025	C₂²×C₃	—	4	2	no	—
1026	C₂²×C₃	—	8	8	no	—
1027	C₂²×C₃	#536	1	4	yes	complemented
1028	C₂²×C₃	D₄²	1	4	yes	—
1029	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1030	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1031	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
1033	C₂²×C₃	#585	1	2	yes	—
1034	C₃×C₄	—	2	4	no	—
1035	C₃×C₄	—	2	2	no	—
1036	C₃×C₄	—	2	2	no	—
1037	C₃×C₄	—	2	2	no	—
1038	C₃×C₄	—	2	2	no	—
1039	C₃×C₄	—	2	2	no	—
1040	C₃×C₄	—	2	4	no	—
1041	C₃×C₄	—	4	1	no	—
1042	C₃×C₄	—	4	2	no	—
1043	C₃×C₄	—	4	1	no	—
1044	C₃×C₄	—	4	1	no	—
1045	C₃×C₄	—	4	2	no	—
1046	C₃×C₄	—	4	2	no	—
1047	C₃×C₄	—	4	1	no	—
1048	C₃×C₄	—	4	2	no	—
1049	C₃×C₄	—	4	2	no	—
1050	C₃×C₄	—	4	2	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	8	no	—
1065	C₂³	—	2	8	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	2	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	4	4	no	—
1077	C₂³	—	4	8	no	—
1078	C₂³	—	4	8	no	—
1079	C₂³	—	4	4	no	—
1080	C₂³	—	4	8	no	—
1081	C₂³	—	4	4	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	4	no	—
1084	C₂³	C₂²×C₃×D₄	1	2	yes	—
1085	C₂³	C₂²×C₃×D₄	1	2	yes	—
1086	C₂³	C₂²×C₃×D₄	1	2	yes	—
1087	C₂³	C₂²×C₃×D₄	1	2	yes	—
1088	C₂³	C₂²×C₃×D₄	1	2	yes	—
1089	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1090	C₂³	C₃×2₋¹⁺⁴	1	4	yes	—
1091	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1092	Q₈	—	4	8	no	—
1093	Q₈	—	4	8	no	—
1094	Q₈	—	4	4	no	—
1095	D₄	—	2	8	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	4	4	no	—
1100	D₄	—	4	4	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	8	no	—
1117	C₂×C₄	—	2	8	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	4	4	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	8	no	—
1149	C₂×C₄	—	4	8	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	8	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1158	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1159	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1160	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1161	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1162	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1163	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1164	C₂×C₃	—	2	4	no	—
1165	C₂×C₃	—	2	4	no	—
1166	C₂×C₃	—	4	2	no	—
1167	C₂×C₃	—	4	2	no	—
1168	C₂×C₃	—	8	1	no	—
1169	C₂×C₃	—	8	1	no	—
1170	C₂×C₃	C₂×#536	1	1	yes	characteristic
1171	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
1172	C₂×C₃	#3485	1	1	yes	characteristic
1173	C₂×C₃	#3489	1	2	yes	—
1174	C₂×C₃	#3535	1	2	yes	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	4	no	—
1180	C₂²	—	2	4	no	—
1181	C₂²	—	2	4	no	—
1182	C₂²	—	2	4	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	4	no	—
1188	C₂²	—	4	16	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	2	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	4	2	no	—
1204	C₂²	—	8	8	no	—
1205	C₂²	C₃×#536	1	4	yes	complemented
1206	C₂²	C₃×D₄²	1	4	yes	—
1207	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1208	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1209	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1210	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
1211	C₂²	C₃×#585	1	2	yes	—
1212	C₄	—	2	4	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	2	4	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	2	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	2	no	—
1228	C₄	—	4	2	no	—
1229	C₃	#37647	1	1	yes	characteristic, direct product factor, Sylow
1230	C₂	—	2	4	no	—
1231	C₂	—	2	4	no	—
1232	C₂	—	4	2	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	8	1	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×C₃×#536	1	1	yes	characteristic
1237	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
1238	C₂	C₃×#3485	1	1	yes	characteristic
1239	C₂	C₃×#3489	1	2	yes	—
1240	C₂	C₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	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
2. C₂×C₃×#536	C₂	semidirect
3. C₂²×C₃×#123	C₂	semidirect
4. C₂²×C₃×C₂²⋊Q₈	C₂	semidirect
5. C₃×#2849	C₂	semidirect
6. C₃×#2681	C₂	semidirect
7. C₃×#2680	C₂	semidirect
8. C₃×#2674	C₂	semidirect
9. C₃×#2672	C₂	semidirect
10. C₃×#2618	C₂	semidirect
11. C₃×#2614	C₂	semidirect
12. C₃×#2501	C₂	semidirect
13. C₃×#2486	C₂	semidirect
14. C₃×#2472	C₂	semidirect
15. C₃×#2449	C₂	semidirect
16. C₃×#2440	C₂	semidirect
17. C₃×#2437	C₂	semidirect
18. C₃×#2413	C₂	semidirect
19. C₃×#2412	C₂	semidirect
20. C₃×#2406	C₂	semidirect
21. C₃×#2405	C₂	semidirect
22. C₃×#2342	C₂	semidirect
23. C₃×#2322	C₂	semidirect
24. #37647	C₃	direct (N × H)
26. C₂³×C₃×Q₈	C₂²	semidirect
31. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
45. C₂×C₃×#123	C₂²	semidirect
46. C₂×C₃×#123	C₂²	semidirect
47. C₂×C₃×#123	C₂²	semidirect
52. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₃×#117	C₂²	semidirect
65. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
66. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
67. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
73. C₃×#399	C₂²	semidirect
74. C₃×#399	C₂²	semidirect
75. C₃×#398	C₂²	semidirect
76. C₃×#398	C₂²	semidirect
77. C₃×#398	C₂²	semidirect
78. C₃×#397	C₂²	semidirect
79. C₃×#397	C₂²	semidirect
80. C₃×#396	C₂²	semidirect
81. C₃×#396	C₂²	semidirect
82. C₃×#396	C₂²	semidirect
83. C₃×#395	C₂²	semidirect
84. C₃×#395	C₂²	semidirect
85. C₃×#395	C₂²	semidirect
88. C₃×#394	C₂²	semidirect
89. C₃×#394	C₂²	semidirect
90. C₃×#394	C₂²	semidirect
91. C₃×#393	C₂²	semidirect
92. C₃×#393	C₂²	semidirect
93. C₃×#390	C₂²	semidirect
94. C₃×#389	C₂²	semidirect
95. C₃×#389	C₂²	semidirect
96. C₃×#389	C₂²	semidirect
97. C₃×#388	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#388	C₂²	semidirect
100. C₃×#388	C₂²	semidirect
101. C₃×#387	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
111. C₃×#385	C₂²	semidirect
112. C₃×#385	C₂²	semidirect
113. C₃×#385	C₂²	semidirect
114. C₃×#385	C₂²	semidirect
115. C₃×#385	C₂²	semidirect
116. C₃×#384	C₂²	semidirect
117. C₃×#381	C₂²	semidirect
118. C₃×#381	C₂²	semidirect
119. C₃×#381	C₂²	semidirect
120. C₃×#381	C₂²	semidirect
122. C₃×#380	C₂²	semidirect
123. C₃×#380	C₂²	semidirect
127. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
129. C₂×#536	C₂×C₃	semidirect
130. C₂²×#123	C₂×C₃	semidirect
131. C₂²×C₂²⋊Q₈	C₂×C₃	semidirect
132. #2849	C₂×C₃	semidirect
133. #2681	C₂×C₃	semidirect
134. #2680	C₂×C₃	semidirect
135. #2674	C₂×C₃	semidirect
136. #2672	C₂×C₃	semidirect
137. #2618	C₂×C₃	semidirect
138. #2614	C₂×C₃	semidirect
139. #2501	C₂×C₃	semidirect
140. #2486	C₂×C₃	semidirect
141. #2472	C₂×C₃	semidirect
142. #2449	C₂×C₃	semidirect
143. #2440	C₂×C₃	semidirect
144. #2437	C₂×C₃	semidirect
145. #2413	C₂×C₃	semidirect
146. #2412	C₂×C₃	semidirect
147. #2406	C₂×C₃	semidirect
148. #2405	C₂×C₃	semidirect
149. #2342	C₂×C₃	semidirect
150. #2322	C₂×C₃	semidirect
205. C₃×#123	D₄	semidirect
303. C₂³×Q₈	C₂²×C₃	semidirect
308. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
310. C₂×#124	C₂²×C₃	semidirect
322. C₂×#123	C₂²×C₃	semidirect
323. C₂×#123	C₂²×C₃	semidirect
324. C₂×#123	C₂²×C₃	semidirect
329. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
330. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
331. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
332. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
340. C₂×#117	C₂²×C₃	semidirect
342. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
343. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
344. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
350. #399	C₂²×C₃	semidirect
351. #399	C₂²×C₃	semidirect
352. #398	C₂²×C₃	semidirect
353. #398	C₂²×C₃	semidirect
354. #398	C₂²×C₃	semidirect
355. #397	C₂²×C₃	semidirect
356. #397	C₂²×C₃	semidirect
357. #396	C₂²×C₃	semidirect
358. #396	C₂²×C₃	semidirect
359. #396	C₂²×C₃	semidirect
360. #395	C₂²×C₃	semidirect
361. #395	C₂²×C₃	semidirect
362. #395	C₂²×C₃	semidirect
365. #394	C₂²×C₃	semidirect
366. #394	C₂²×C₃	semidirect
367. #394	C₂²×C₃	semidirect
368. #393	C₂²×C₃	semidirect
369. #393	C₂²×C₃	semidirect
370. #390	C₂²×C₃	semidirect
371. #389	C₂²×C₃	semidirect
372. #389	C₂²×C₃	semidirect
373. #389	C₂²×C₃	semidirect
374. #388	C₂²×C₃	semidirect
375. #388	C₂²×C₃	semidirect
376. #388	C₂²×C₃	semidirect
377. #388	C₂²×C₃	semidirect
378. #387	C₂²×C₃	semidirect
383. #386	C₂²×C₃	semidirect
384. #386	C₂²×C₃	semidirect
388. #385	C₂²×C₃	semidirect
389. #385	C₂²×C₃	semidirect
390. #385	C₂²×C₃	semidirect
391. #385	C₂²×C₃	semidirect
392. #385	C₂²×C₃	semidirect
393. #384	C₂²×C₃	semidirect
394. #381	C₂²×C₃	semidirect
395. #381	C₂²×C₃	semidirect
396. #381	C₂²×C₃	semidirect
397. #381	C₂²×C₃	semidirect
399. #380	C₂²×C₃	semidirect
400. #380	C₂²×C₃	semidirect
404. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
623. #123	C₃×D₄	semidirect
1027. C₂²×C₃	#536	semidirect
1205. C₂²	C₃×#536	semidirect
1229. C₃	#37647	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×#546	2
C₂×C₃×#536	2
C₂²×C₃×#123	2
C₂²×C₃×C₂²⋊Q₈	2
C₃×#2849	2
C₃×#2681	2
C₃×#2680	2
C₃×#2674	2
C₃×#2672	2
C₃×#2618	2
C₃×#2614	2
C₃×#2501	2
C₃×#2486	2
C₃×#2472	2
C₃×#2449	2
C₃×#2440	2
C₃×#2437	2
C₃×#2413	2
C₃×#2412	2
C₃×#2406	2
C₃×#2405	2
C₃×#2342	2
C₃×#2322	2
#37647	3

Subgroups — C3×#37647 #10656254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37647 #10656254