Subgroups — C₃×#36158 #10654765

Order 768.

4084 conjugacy classes of subgroups.

The subgroup lattice has 1266 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, complemented
2	C₂³×C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2846	C₂	1	1	yes	maximal, characteristic
6	C₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2534	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2480	C₂	1	2	yes	maximal, complemented
11	C₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₃×#2472	C₂	1	2	yes	maximal, complemented
13	C₃×#2437	C₂	1	2	yes	maximal, complemented
14	C₃×#2418	C₂	1	2	yes	maximal, complemented
15	C₃×#2412	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2412	C₂	1	2	yes	maximal, complemented
17	C₃×#2411	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2358	C₂	1	2	yes	maximal, complemented
19	C₃×#2342	C₂	1	2	yes	maximal, complemented
20	C₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#120	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
24	#36158	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂⁶×C₃	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×#551	—	2	8	no	—
29	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#123	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	2	yes	complemented
39	C₂×C₃×#120	C₂²	1	1	yes	characteristic
40	C₂×C₃×#120	C₂²	1	2	yes	—
41	C₂×C₃×#120	C₂²	1	1	yes	characteristic
42	C₂×C₃×#120	C₂²	1	1	yes	characteristic
43	C₂×C₃×#120	C₂²	1	2	yes	—
44	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
47	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₃×C₂²⋊C₄	—	2	8	no	—
51	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
61	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
63	C₃×#399	C₂²	1	2	yes	complemented
64	C₃×#397	C₂²	1	2	yes	complemented
65	C₃×#397	C₂²	1	2	yes	complemented
66	C₃×#397	C₂²	1	2	yes	complemented
67	C₃×#397	C₂²	1	2	yes	complemented
68	C₃×#397	C₂²	1	2	yes	complemented
69	C₃×#396	C₂²	1	2	yes	complemented
70	C₃×#396	C₂²	1	2	yes	complemented
71	C₃×#394	C₂²	1	2	yes	complemented
72	C₃×#394	C₂²	1	2	yes	complemented
73	C₃×#394	C₂²	1	2	yes	complemented
74	C₃×#393	C₂²	1	2	yes	complemented
75	C₃×#390	C₂²	1	2	yes	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×#388	C₂²	1	2	yes	complemented
84	C₃×#386	C₂²	1	2	yes	complemented
85	C₃×#386	C₂²	1	1	yes	characteristic, complemented
86	C₃×#386	C₂²	1	2	yes	complemented
87	C₃×#386	C₂²	1	2	yes	complemented
88	C₃×#386	C₂²	1	2	yes	complemented
89	C₃×#386	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	1	yes	characteristic, complemented
91	C₃×#385	C₂²	1	2	yes	complemented
92	C₃×#385	C₂²	1	1	yes	characteristic, complemented
93	C₃×#385	C₂²	1	2	yes	complemented
94	C₃×#385	C₂²	1	2	yes	complemented
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×#385	C₂²	1	1	yes	characteristic, complemented
100	C₃×#381	C₂²	1	2	yes	complemented
101	C₃×#381	C₂²	1	1	yes	characteristic, complemented
102	C₃×#381	C₂²	1	1	yes	characteristic, complemented
103	C₃×#381	C₂²	1	1	yes	characteristic, complemented
104	C₃×#381	C₂²	1	1	yes	characteristic, complemented
105	C₃×#380	C₂²	1	2	yes	complemented
106	C₃×#380	C₂²	1	2	yes	complemented
107	C₃×#380	C₂²	1	2	yes	complemented
108	C₃×#380	C₂²	1	2	yes	complemented
109	C₃×#380	C₂²	1	1	yes	characteristic, complemented
110	C₃×#379	C₂²	1	1	yes	characteristic
111	C₃×#379	C₂²	1	2	yes	—
112	C₃×#379	C₂²	1	2	yes	—
113	C₃×#379	C₂²	1	2	yes	—
114	C₃×#379	C₂²	1	2	yes	—
115	C₃×#379	C₂²	1	1	yes	characteristic
116	C₃×#379	C₂²	1	1	yes	characteristic
117	C₃×#379	C₂²	1	1	yes	characteristic
118	C₃×#379	C₂²	1	1	yes	characteristic
119	C₃×#379	C₂²	1	1	yes	characteristic
120	C₃×#379	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
126	C₂×#551	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂³×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
128	#2849	C₂×C₃	1	1	yes	characteristic, complemented
129	#2848	C₂×C₃	1	1	yes	characteristic, complemented
130	#2846	C₂×C₃	1	1	yes	characteristic
131	#2561	C₂×C₃	1	1	yes	characteristic, complemented
132	#2534	C₂×C₃	1	1	yes	characteristic, complemented
133	#2483	C₂×C₃	1	1	yes	characteristic, complemented
134	#2482	C₂×C₃	1	1	yes	characteristic, complemented
135	#2480	C₂×C₃	1	2	yes	complemented
136	#2480	C₂×C₃	1	2	yes	complemented
137	#2472	C₂×C₃	1	2	yes	complemented
138	#2437	C₂×C₃	1	2	yes	complemented
139	#2418	C₂×C₃	1	2	yes	complemented
140	#2412	C₂×C₃	1	2	yes	complemented
141	#2412	C₂×C₃	1	1	yes	characteristic, complemented
142	#2411	C₂×C₃	1	1	yes	characteristic, complemented
143	#2358	C₂×C₃	1	2	yes	complemented
144	#2342	C₂×C₃	1	2	yes	complemented
145	#2342	C₂×C₃	1	1	yes	characteristic, complemented
146	C₄×#120	C₂×C₃	1	1	yes	characteristic, complemented
147	#2280	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×#379	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	—	2	4	no	—
150	C₂⁵×C₃	—	2	8	no	—
151	C₂⁵×C₃	—	2	4	no	—
152	C₂⁵×C₃	—	4	4	no	—
153	C₂⁵×C₃	—	4	2	no	—
154	C₂⁵×C₃	C₂³	1	1	yes	characteristic
155	C₂⁵×C₃	C₂³	1	2	yes	—
156	C₂⁵×C₃	C₂³	1	1	yes	characteristic
157	C₂⁵×C₃	C₂³	1	1	yes	characteristic
158	C₂⁵×C₃	C₂³	1	2	yes	—
159	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic, complemented
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂³	1	2	yes	—
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	—	2	4	no	—
166	C₂³×C₃×C₄	—	2	4	no	—
167	C₂³×C₃×C₄	—	2	4	no	—
168	C₂³×C₃×C₄	—	4	2	no	—
169	C₂³×C₃×C₄	—	4	4	no	—
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	2	yes	—
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	2	yes	—
175	C₂³×C₃×C₄	C₂³	1	2	yes	—
176	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂³	1	2	yes	—
179	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
180	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic, complemented
182	C₃×#126	—	2	4	no	—
183	C₃×#126	—	2	4	no	—
184	C₃×#124	—	2	4	no	—
185	C₃×#123	—	2	4	no	—
186	C₃×#123	—	2	4	no	—
187	C₃×#123	—	2	4	no	—
188	C₃×#123	—	4	2	no	—
189	C₃×C₂²⋊Q₈	—	2	4	no	—
190	C₃×C₂²⋊Q₈	—	2	4	no	—
191	C₃×C₂²⋊Q₈	—	4	4	no	—
192	C₃×#120	—	2	4	no	—
193	C₃×#120	—	2	4	no	—
194	C₃×#120	—	2	8	no	—
195	C₃×#120	—	4	2	no	—
196	C₃×#120	—	4	4	no	—
197	C₃×C₄×D₄	—	2	4	no	—
198	C₃×C₄×D₄	—	2	4	no	—
199	C₃×C₄×D₄	—	4	4	no	—
200	C₃×#117	—	2	4	no	—
201	C₃×#117	—	2	4	no	—
202	C₃×#117	—	4	2	no	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	complemented
217	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
219	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
220	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
221	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
222	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
223	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
225	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
226	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
227	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
228	C₂×C₃×C₂²⋊C₄	D₄	1	8	yes	complemented
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
257	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
259	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
260	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
261	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
262	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
263	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
268	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
269	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
270	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
271	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
272	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic, complemented
273	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic, complemented
274	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic, complemented
275	C₂×C₃×C₄²	C₂³	1	2	yes	complemented
276	C₂×C₃×C₄²	C₂³	1	2	yes	complemented
277	C₃×#95	C₂³	1	2	yes	complemented
278	C₃×#95	C₂³	1	2	yes	complemented
279	C₃×#95	C₂³	1	2	yes	complemented
280	C₃×#95	C₂³	1	2	yes	complemented
281	C₃×#95	C₂³	1	2	yes	complemented
282	C₃×#95	C₂³	1	2	yes	complemented
283	C₃×#95	C₂³	1	2	yes	complemented
284	C₃×#95	C₂³	1	2	yes	complemented
285	C₃×#95	C₂³	1	2	yes	complemented
286	C₃×#95	C₂³	1	2	yes	complemented
287	C₃×#95	C₂³	1	2	yes	complemented
288	C₃×#95	C₂³	1	2	yes	complemented
289	C₃×#95	C₂³	1	2	yes	complemented
290	C₃×#95	C₂³	1	2	yes	complemented
291	C₂⁶	C₂²×C₃	1	1	yes	characteristic
292	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
293	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
294	#551	—	2	8	no	—
295	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
300	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
305	C₂×#120	C₂²×C₃	1	1	yes	characteristic
306	C₂×#120	C₂²×C₃	1	2	yes	—
307	C₂×#120	C₂²×C₃	1	1	yes	characteristic
308	C₂×#120	C₂²×C₃	1	1	yes	characteristic
309	C₂×#120	C₂²×C₃	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
311	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
312	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
313	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₂²×C₂²⋊C₄	—	2	8	no	—
317	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
324	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
325	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
328	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
329	#399	C₂²×C₃	1	2	yes	complemented
330	#397	C₂²×C₃	1	2	yes	complemented
331	#397	C₂²×C₃	1	2	yes	complemented
332	#397	C₂²×C₃	1	2	yes	complemented
333	#397	C₂²×C₃	1	2	yes	complemented
334	#397	C₂²×C₃	1	2	yes	complemented
335	#396	C₂²×C₃	1	2	yes	complemented
336	#396	C₂²×C₃	1	2	yes	complemented
337	#394	C₂²×C₃	1	2	yes	complemented
338	#394	C₂²×C₃	1	2	yes	complemented
339	#394	C₂²×C₃	1	2	yes	complemented
340	#393	C₂²×C₃	1	2	yes	complemented
341	#390	C₂²×C₃	1	2	yes	complemented
342	#388	C₂²×C₃	1	2	yes	complemented
343	#388	C₂²×C₃	1	2	yes	complemented
344	#388	C₂²×C₃	1	2	yes	complemented
345	#388	C₂²×C₃	1	2	yes	complemented
346	#388	C₂²×C₃	1	2	yes	complemented
347	#388	C₂²×C₃	1	2	yes	complemented
348	#388	C₂²×C₃	1	2	yes	complemented
349	#388	C₂²×C₃	1	2	yes	complemented
350	#386	C₂²×C₃	1	2	yes	complemented
351	#386	C₂²×C₃	1	2	yes	complemented
352	#386	C₂²×C₃	1	2	yes	complemented
353	#386	C₂²×C₃	1	2	yes	complemented
354	#386	C₂²×C₃	1	1	yes	characteristic, complemented
355	#386	C₂²×C₃	1	2	yes	complemented
356	#385	C₂²×C₃	1	2	yes	complemented
357	#385	C₂²×C₃	1	2	yes	complemented
358	#385	C₂²×C₃	1	1	yes	characteristic, complemented
359	#385	C₂²×C₃	1	1	yes	characteristic, complemented
360	#385	C₂²×C₃	1	2	yes	complemented
361	#385	C₂²×C₃	1	2	yes	complemented
362	#385	C₂²×C₃	1	2	yes	complemented
363	#385	C₂²×C₃	1	2	yes	complemented
364	#385	C₂²×C₃	1	2	yes	complemented
365	#385	C₂²×C₃	1	1	yes	characteristic, complemented
366	#381	C₂²×C₃	1	1	yes	characteristic, complemented
367	#381	C₂²×C₃	1	1	yes	characteristic, complemented
368	#381	C₂²×C₃	1	1	yes	characteristic, complemented
369	#381	C₂²×C₃	1	2	yes	complemented
370	#381	C₂²×C₃	1	1	yes	characteristic, complemented
371	#380	C₂²×C₃	1	1	yes	characteristic, complemented
372	#380	C₂²×C₃	1	2	yes	complemented
373	#380	C₂²×C₃	1	2	yes	complemented
374	#380	C₂²×C₃	1	2	yes	complemented
375	#380	C₂²×C₃	1	2	yes	complemented
376	#379	C₂²×C₃	1	1	yes	characteristic
377	#379	C₂²×C₃	1	1	yes	characteristic
378	#379	C₂²×C₃	1	1	yes	characteristic
379	#379	C₂²×C₃	1	2	yes	—
380	#379	C₂²×C₃	1	1	yes	characteristic
381	#379	C₂²×C₃	1	2	yes	—
382	#379	C₂²×C₃	1	1	yes	characteristic
383	#379	C₂²×C₃	1	2	yes	—
384	#379	C₂²×C₃	1	2	yes	—
385	#379	C₂²×C₃	1	1	yes	characteristic
386	#379	C₂²×C₃	1	1	yes	characteristic
387	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
388	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
389	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
390	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
391	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
392	C₂⁴×C₃	—	2	2	no	—
393	C₂⁴×C₃	—	2	4	no	—
394	C₂⁴×C₃	—	2	4	no	—
395	C₂⁴×C₃	—	2	2	no	—
396	C₂⁴×C₃	—	2	32	no	—
397	C₂⁴×C₃	—	2	4	no	—
398	C₂⁴×C₃	—	2	4	no	—
399	C₂⁴×C₃	—	2	2	no	—
400	C₂⁴×C₃	—	2	4	no	—
401	C₂⁴×C₃	—	2	4	no	—
402	C₂⁴×C₃	—	2	4	no	—
403	C₂⁴×C₃	—	2	4	no	—
404	C₂⁴×C₃	—	2	2	no	—
405	C₂⁴×C₃	—	2	4	no	—
406	C₂⁴×C₃	—	2	4	no	—
407	C₂⁴×C₃	—	2	2	no	—
408	C₂⁴×C₃	—	2	4	no	—
409	C₂⁴×C₃	—	2	2	no	—
410	C₂⁴×C₃	—	2	4	no	—
411	C₂⁴×C₃	—	2	2	no	—
412	C₂⁴×C₃	—	2	4	no	—
413	C₂⁴×C₃	—	4	2	no	—
414	C₂⁴×C₃	—	4	2	no	—
415	C₂⁴×C₃	—	4	2	no	—
416	C₂⁴×C₃	—	4	2	no	—
417	C₂⁴×C₃	—	4	2	no	—
418	C₂⁴×C₃	—	4	2	no	—
419	C₂⁴×C₃	—	4	16	no	—
420	C₂⁴×C₃	—	4	32	no	—
421	C₂⁴×C₃	—	4	16	no	—
422	C₂⁴×C₃	—	4	32	no	—
423	C₂⁴×C₃	C₂×D₄	1	4	yes	—
424	C₂⁴×C₃	#41	1	4	yes	—
425	C₂⁴×C₃	#41	1	8	yes	—
426	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
427	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
428	C₂⁴×C₃	C₂⁴	1	2	yes	—
429	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
430	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
431	C₂⁴×C₃	C₂⁴	1	2	yes	—
432	C₂×C₃×Q₈	—	2	2	no	—
433	C₂×C₃×Q₈	—	4	2	no	—
434	C₂×C₃×D₄	—	2	2	no	—
435	C₂×C₃×D₄	—	2	2	no	—
436	C₂×C₃×D₄	—	2	4	no	—
437	C₂×C₃×D₄	—	2	2	no	—
438	C₂×C₃×D₄	—	2	4	no	—
439	C₂×C₃×D₄	—	2	4	no	—
440	C₂×C₃×D₄	—	2	4	no	—
441	C₂×C₃×D₄	—	2	2	no	—
442	C₂×C₃×D₄	—	2	2	no	—
443	C₂×C₃×D₄	—	2	4	no	—
444	C₂×C₃×D₄	—	4	2	no	—
445	C₂×C₃×D₄	—	4	2	no	—
446	C₂×C₃×D₄	—	4	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	4	no	—
453	C₂²×C₃×C₄	—	2	4	no	—
454	C₂²×C₃×C₄	—	2	4	no	—
455	C₂²×C₃×C₄	—	2	2	no	—
456	C₂²×C₃×C₄	—	2	4	no	—
457	C₂²×C₃×C₄	—	2	4	no	—
458	C₂²×C₃×C₄	—	2	2	no	—
459	C₂²×C₃×C₄	—	2	2	no	—
460	C₂²×C₃×C₄	—	2	4	no	—
461	C₂²×C₃×C₄	—	2	4	no	—
462	C₂²×C₃×C₄	—	2	4	no	—
463	C₂²×C₃×C₄	—	2	4	no	—
464	C₂²×C₃×C₄	—	2	4	no	—
465	C₂²×C₃×C₄	—	2	2	no	—
466	C₂²×C₃×C₄	—	4	2	no	—
467	C₂²×C₃×C₄	—	4	2	no	—
468	C₂²×C₃×C₄	—	4	2	no	—
469	C₂²×C₃×C₄	—	4	2	no	—
470	C₂²×C₃×C₄	—	4	2	no	—
471	C₂²×C₃×C₄	—	4	2	no	—
472	C₂²×C₃×C₄	—	4	2	no	—
473	C₂²×C₃×C₄	—	4	2	no	—
474	C₂²×C₃×C₄	—	4	2	no	—
475	C₂²×C₃×C₄	—	4	2	no	—
476	C₂²×C₃×C₄	—	4	16	no	—
477	C₂²×C₃×C₄	—	4	16	no	—
478	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
479	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
480	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
481	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
484	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
485	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
486	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
487	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
488	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
489	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
490	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
492	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
493	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
494	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
497	C₃×C₄⋊C₄	—	2	2	no	—
498	C₃×C₄⋊C₄	—	2	2	no	—
499	C₃×C₄⋊C₄	—	2	2	no	—
500	C₃×C₄⋊C₄	—	2	2	no	—
501	C₃×C₄⋊C₄	—	2	2	no	—
502	C₃×C₄⋊C₄	—	2	2	no	—
503	C₃×C₄⋊C₄	—	2	2	no	—
504	C₃×C₄⋊C₄	—	2	2	no	—
505	C₃×C₄⋊C₄	—	4	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	—	4	2	no	—
511	C₃×C₂²⋊C₄	—	2	4	no	—
512	C₃×C₂²⋊C₄	—	2	4	no	—
513	C₃×C₂²⋊C₄	—	2	2	no	—
514	C₃×C₂²⋊C₄	—	2	2	no	—
515	C₃×C₂²⋊C₄	—	2	2	no	—
516	C₃×C₂²⋊C₄	—	2	2	no	—
517	C₃×C₂²⋊C₄	—	2	2	no	—
518	C₃×C₂²⋊C₄	—	2	2	no	—
519	C₃×C₂²⋊C₄	—	2	2	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	4	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	2	4	no	—
528	C₃×C₂²⋊C₄	—	2	4	no	—
529	C₃×C₂²⋊C₄	—	2	2	no	—
530	C₃×C₂²⋊C₄	—	2	4	no	—
531	C₃×C₂²⋊C₄	—	2	4	no	—
532	C₃×C₂²⋊C₄	—	2	2	no	—
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	4	no	—
537	C₃×C₂²⋊C₄	—	2	4	no	—
538	C₃×C₂²⋊C₄	—	2	4	no	—
539	C₃×C₂²⋊C₄	—	2	2	no	—
540	C₃×C₂²⋊C₄	—	2	2	no	—
541	C₃×C₂²⋊C₄	—	2	2	no	—
542	C₃×C₂²⋊C₄	—	4	2	no	—
543	C₃×C₂²⋊C₄	—	4	2	no	—
544	C₃×C₂²⋊C₄	—	4	2	no	—
545	C₃×C₂²⋊C₄	—	4	2	no	—
546	C₃×C₂²⋊C₄	—	4	2	no	—
547	C₃×C₂²⋊C₄	—	4	2	no	—
548	C₃×C₂²⋊C₄	—	4	2	no	—
549	C₃×C₂²⋊C₄	—	4	2	no	—
550	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
551	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
552	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
553	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
554	C₃×C₄²	—	2	2	no	—
555	C₃×C₄²	—	2	2	no	—
556	C₃×C₄²	—	2	2	no	—
557	C₃×C₄²	—	4	2	no	—
558	C₃×C₄²	—	4	2	no	—
559	C₂⁵	—	2	4	no	—
560	C₂⁵	—	2	8	no	—
561	C₂⁵	—	2	4	no	—
562	C₂⁵	—	4	4	no	—
563	C₂⁵	—	4	2	no	—
564	C₂⁵	C₂³×C₃	1	1	yes	characteristic
565	C₂⁵	C₂³×C₃	1	2	yes	—
566	C₂⁵	C₂³×C₃	1	1	yes	characteristic
567	C₂⁵	C₂³×C₃	1	1	yes	characteristic
568	C₂⁵	C₂³×C₃	1	2	yes	—
569	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
570	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₃	1	2	yes	—
575	C₂³×C₄	—	2	4	no	—
576	C₂³×C₄	—	2	4	no	—
577	C₂³×C₄	—	2	4	no	—
578	C₂³×C₄	—	4	2	no	—
579	C₂³×C₄	—	4	4	no	—
580	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₃	1	2	yes	—
584	C₂³×C₄	C₂³×C₃	1	2	yes	—
585	C₂³×C₄	C₂³×C₃	1	2	yes	—
586	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₃	1	2	yes	—
589	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic, complemented
592	#126	—	2	4	no	—
593	#126	—	2	4	no	—
594	#124	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	4	no	—
598	#123	—	4	2	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	4	4	no	—
602	#120	—	2	4	no	—
603	#120	—	2	4	no	—
604	#120	—	2	8	no	—
605	#120	—	4	2	no	—
606	#120	—	4	4	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	4	no	—
609	C₄×D₄	—	4	4	no	—
610	#117	—	2	4	no	—
611	#117	—	2	4	no	—
612	#117	—	4	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
614	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
615	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
616	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
617	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
618	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
619	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
620	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
621	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
622	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
623	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
624	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
625	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
626	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
627	C₂×C₂²⋊C₄	—	2	4	no	—
628	C₂×C₂²⋊C₄	—	2	4	no	—
629	C₂×C₂²⋊C₄	—	2	8	no	—
630	C₂×C₂²⋊C₄	—	2	4	no	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₂²⋊C₄	—	2	8	no	—
633	C₂×C₂²⋊C₄	—	2	8	no	—
634	C₂×C₂²⋊C₄	—	2	8	no	—
635	C₂×C₂²⋊C₄	—	2	8	no	—
636	C₂×C₂²⋊C₄	—	4	2	no	—
637	C₂×C₂²⋊C₄	—	4	4	no	—
638	C₂×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
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	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
678	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
679	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
680	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
681	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
682	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic, complemented
683	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic, complemented
684	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic, complemented
685	C₂×C₄²	C₂³×C₃	1	2	yes	complemented
686	C₂×C₄²	C₂³×C₃	1	2	yes	complemented
687	#95	C₂³×C₃	1	2	yes	complemented
688	#95	C₂³×C₃	1	2	yes	complemented
689	#95	C₂³×C₃	1	2	yes	complemented
690	#95	C₂³×C₃	1	2	yes	complemented
691	#95	C₂³×C₃	1	2	yes	complemented
692	#95	C₂³×C₃	1	2	yes	complemented
693	#95	C₂³×C₃	1	2	yes	complemented
694	#95	C₂³×C₃	1	2	yes	complemented
695	#95	C₂³×C₃	1	2	yes	complemented
696	#95	C₂³×C₃	1	2	yes	complemented
697	#95	C₂³×C₃	1	2	yes	complemented
698	#95	C₂³×C₃	1	2	yes	complemented
699	#95	C₂³×C₃	1	2	yes	complemented
700	#95	C₂³×C₃	1	2	yes	complemented
701	C₂³×C₃	—	2	8	no	—
702	C₂³×C₃	—	2	8	no	—
703	C₂³×C₃	—	2	16	no	—
704	C₂³×C₃	—	2	8	no	—
705	C₂³×C₃	—	2	16	no	—
706	C₂³×C₃	—	2	2	no	—
707	C₂³×C₃	—	2	2	no	—
708	C₂³×C₃	—	2	2	no	—
709	C₂³×C₃	—	2	1	no	—
710	C₂³×C₃	—	2	2	no	—
711	C₂³×C₃	—	2	1	no	—
712	C₂³×C₃	—	2	2	no	—
713	C₂³×C₃	—	2	2	no	—
714	C₂³×C₃	—	2	2	no	—
715	C₂³×C₃	—	2	8	no	—
716	C₂³×C₃	—	2	16	no	—
717	C₂³×C₃	—	2	8	no	—
718	C₂³×C₃	—	2	16	no	—
719	C₂³×C₃	—	2	8	no	—
720	C₂³×C₃	—	2	16	no	—
721	C₂³×C₃	—	2	2	no	—
722	C₂³×C₃	—	2	2	no	—
723	C₂³×C₃	—	2	2	no	—
724	C₂³×C₃	—	2	1	no	—
725	C₂³×C₃	—	2	2	no	—
726	C₂³×C₃	—	2	1	no	—
727	C₂³×C₃	—	2	2	no	—
728	C₂³×C₃	—	2	2	no	—
729	C₂³×C₃	—	2	2	no	—
730	C₂³×C₃	—	2	2	no	—
731	C₂³×C₃	—	2	1	no	—
732	C₂³×C₃	—	2	2	no	—
733	C₂³×C₃	—	2	1	no	—
734	C₂³×C₃	—	2	1	no	—
735	C₂³×C₃	—	2	2	no	—
736	C₂³×C₃	—	4	4	no	—
737	C₂³×C₃	—	4	8	no	—
738	C₂³×C₃	—	4	8	no	—
739	C₂³×C₃	—	4	8	no	—
740	C₂³×C₃	—	4	8	no	—
741	C₂³×C₃	—	4	8	no	—
742	C₂³×C₃	—	4	8	no	—
743	C₂³×C₃	—	4	8	no	—
744	C₂³×C₃	—	4	8	no	—
745	C₂³×C₃	—	4	8	no	—
746	C₂³×C₃	—	4	8	no	—
747	C₂³×C₃	—	4	8	no	—
748	C₂³×C₃	—	4	8	no	—
749	C₂³×C₃	—	4	8	no	—
750	C₂³×C₃	—	4	128	no	—
751	C₂³×C₃	—	4	4	no	—
752	C₂³×C₃	—	4	8	no	—
753	C₂³×C₃	—	4	4	no	—
754	C₂³×C₃	—	4	8	no	—
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	C₂×#41	1	4	yes	—
759	C₂³×C₃	C₂×#41	1	4	yes	—
760	C₂³×C₃	C₂×#41	1	2	yes	—
761	C₂³×C₃	C₂×#41	1	4	yes	—
762	C₂³×C₃	C₂×#41	1	4	yes	—
763	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
764	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
765	C₂³×C₃	C₂⁵	1	1	yes	characteristic
766	C₃×Q₈	—	8	2	no	—
767	C₃×D₄	—	4	4	no	—
768	C₃×D₄	—	4	4	no	—
769	C₃×D₄	—	4	8	no	—
770	C₃×D₄	—	8	2	no	—
771	C₃×D₄	—	8	4	no	—
772	C₂×C₃×C₄	—	2	8	no	—
773	C₂×C₃×C₄	—	2	1	no	—
774	C₂×C₃×C₄	—	2	1	no	—
775	C₂×C₃×C₄	—	2	1	no	—
776	C₂×C₃×C₄	—	2	2	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	2	no	—
779	C₂×C₃×C₄	—	2	1	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	1	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	2	no	—
786	C₂×C₃×C₄	—	2	1	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	2	no	—
791	C₂×C₃×C₄	—	2	2	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	1	no	—
794	C₂×C₃×C₄	—	2	2	no	—
795	C₂×C₃×C₄	—	2	2	no	—
796	C₂×C₃×C₄	—	2	2	no	—
797	C₂×C₃×C₄	—	2	2	no	—
798	C₂×C₃×C₄	—	2	2	no	—
799	C₂×C₃×C₄	—	2	2	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	2	no	—
804	C₂×C₃×C₄	—	2	2	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	1	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	—	4	4	no	—
813	C₂×C₃×C₄	—	4	8	no	—
814	C₂×C₃×C₄	—	4	8	no	—
815	C₂×C₃×C₄	—	4	8	no	—
816	C₂×C₃×C₄	—	4	8	no	—
817	C₂×C₃×C₄	—	4	4	no	—
818	C₂×C₃×C₄	—	4	4	no	—
819	C₂×C₃×C₄	—	4	4	no	—
820	C₂×C₃×C₄	—	8	2	no	—
821	C₂×C₃×C₄	—	8	2	no	—
822	C₂×C₃×C₄	—	8	4	no	—
823	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
824	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
825	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
826	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
827	C₂⁴	—	2	2	no	—
828	C₂⁴	—	2	4	no	—
829	C₂⁴	—	2	4	no	—
830	C₂⁴	—	2	2	no	—
831	C₂⁴	—	2	32	no	—
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	2	2	no	—
835	C₂⁴	—	2	4	no	—
836	C₂⁴	—	2	4	no	—
837	C₂⁴	—	2	4	no	—
838	C₂⁴	—	2	4	no	—
839	C₂⁴	—	2	2	no	—
840	C₂⁴	—	2	4	no	—
841	C₂⁴	—	2	4	no	—
842	C₂⁴	—	2	2	no	—
843	C₂⁴	—	2	4	no	—
844	C₂⁴	—	2	2	no	—
845	C₂⁴	—	2	4	no	—
846	C₂⁴	—	2	2	no	—
847	C₂⁴	—	2	4	no	—
848	C₂⁴	—	4	2	no	—
849	C₂⁴	—	4	2	no	—
850	C₂⁴	—	4	2	no	—
851	C₂⁴	—	4	2	no	—
852	C₂⁴	—	4	2	no	—
853	C₂⁴	—	4	2	no	—
854	C₂⁴	—	4	16	no	—
855	C₂⁴	—	4	32	no	—
856	C₂⁴	—	4	16	no	—
857	C₂⁴	—	4	32	no	—
858	C₂⁴	C₂×C₃×D₄	1	4	yes	—
859	C₂⁴	C₃×#41	1	4	yes	—
860	C₂⁴	C₃×#41	1	8	yes	—
861	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
862	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
863	C₂⁴	C₂⁴×C₃	1	2	yes	—
864	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
865	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
866	C₂⁴	C₂⁴×C₃	1	2	yes	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	4	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	4	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	—	4	2	no	—
881	C₂×D₄	—	4	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	2	4	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	4	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	4	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	—	4	2	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	16	no	—
912	C₂²×C₄	—	4	16	no	—
913	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
914	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
915	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
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	4	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
986	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
987	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
988	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	4	2	no	—
993	C₄²	—	4	2	no	—
994	C₂²×C₃	—	2	32	no	—
995	C₂²×C₃	—	2	2	no	—
996	C₂²×C₃	—	2	4	no	—
997	C₂²×C₃	—	2	4	no	—
998	C₂²×C₃	—	2	2	no	—
999	C₂²×C₃	—	2	4	no	—
1000	C₂²×C₃	—	2	4	no	—
1001	C₂²×C₃	—	2	4	no	—
1002	C₂²×C₃	—	2	2	no	—
1003	C₂²×C₃	—	2	4	no	—
1004	C₂²×C₃	—	2	2	no	—
1005	C₂²×C₃	—	2	4	no	—
1006	C₂²×C₃	—	2	4	no	—
1007	C₂²×C₃	—	2	4	no	—
1008	C₂²×C₃	—	2	4	no	—
1009	C₂²×C₃	—	2	2	no	—
1010	C₂²×C₃	—	2	4	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	4	no	—
1013	C₂²×C₃	—	2	2	no	—
1014	C₂²×C₃	—	2	4	no	—
1015	C₂²×C₃	—	4	16	no	—
1016	C₂²×C₃	—	4	32	no	—
1017	C₂²×C₃	—	4	16	no	—
1018	C₂²×C₃	—	4	32	no	—
1019	C₂²×C₃	—	4	2	no	—
1020	C₂²×C₃	—	4	2	no	—
1021	C₂²×C₃	—	4	2	no	—
1022	C₂²×C₃	—	4	2	no	—
1023	C₂²×C₃	—	4	2	no	—
1024	C₂²×C₃	—	4	2	no	—
1025	C₂²×C₃	—	4	1	no	—
1026	C₂²×C₃	—	4	1	no	—
1027	C₂²×C₃	—	4	2	no	—
1028	C₂²×C₃	—	4	1	no	—
1029	C₂²×C₃	—	4	2	no	—
1030	C₂²×C₃	#525	1	4	yes	—
1031	C₂²×C₃	#546	1	4	yes	—
1032	C₂²×C₃	#551	1	8	yes	complemented
1033	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1034	C₂²×C₃	C₂²×#41	1	2	yes	—
1035	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
1036	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1037	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
1038	C₃×C₄	—	2	2	no	—
1039	C₃×C₄	—	2	2	no	—
1040	C₃×C₄	—	2	2	no	—
1041	C₃×C₄	—	2	2	no	—
1042	C₃×C₄	—	4	1	no	—
1043	C₃×C₄	—	4	1	no	—
1044	C₃×C₄	—	4	1	no	—
1045	C₃×C₄	—	4	2	no	—
1046	C₃×C₄	—	4	1	no	—
1047	C₃×C₄	—	4	2	no	—
1048	C₃×C₄	—	4	2	no	—
1049	C₃×C₄	—	4	1	no	—
1050	C₃×C₄	—	4	1	no	—
1051	C₃×C₄	—	4	1	no	—
1052	C₃×C₄	—	4	2	no	—
1053	C₃×C₄	—	4	2	no	—
1054	C₃×C₄	—	4	2	no	—
1055	C₂³	—	2	8	no	—
1056	C₂³	—	2	8	no	—
1057	C₂³	—	2	16	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	8	no	—
1068	C₂³	—	2	16	no	—
1069	C₂³	—	2	8	no	—
1070	C₂³	—	2	16	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	2	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	2	no	—
1081	C₂³	—	2	8	no	—
1082	C₂³	—	2	16	no	—
1083	C₂³	—	2	8	no	—
1084	C₂³	—	2	16	no	—
1085	C₂³	—	2	1	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	4	4	no	—
1091	C₂³	—	4	8	no	—
1092	C₂³	—	4	8	no	—
1093	C₂³	—	4	8	no	—
1094	C₂³	—	4	8	no	—
1095	C₂³	—	4	8	no	—
1096	C₂³	—	4	8	no	—
1097	C₂³	—	4	8	no	—
1098	C₂³	—	4	8	no	—
1099	C₂³	—	4	8	no	—
1100	C₂³	—	4	8	no	—
1101	C₂³	—	4	8	no	—
1102	C₂³	—	4	8	no	—
1103	C₂³	—	4	8	no	—
1104	C₂³	—	4	128	no	—
1105	C₂³	—	4	4	no	—
1106	C₂³	—	4	8	no	—
1107	C₂³	—	4	4	no	—
1108	C₂³	—	4	8	no	—
1109	C₂³	C₂²×C₃×D₄	1	2	yes	—
1110	C₂³	C₂²×C₃×D₄	1	2	yes	—
1111	C₂³	C₂²×C₃×D₄	1	2	yes	—
1112	C₂³	C₂×C₃×#41	1	4	yes	—
1113	C₂³	C₂×C₃×#41	1	4	yes	—
1114	C₂³	C₂×C₃×#41	1	2	yes	—
1115	C₂³	C₂×C₃×#41	1	4	yes	—
1116	C₂³	C₂×C₃×#41	1	4	yes	—
1117	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1118	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1119	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1120	Q₈	—	8	2	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	8	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	4	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	8	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	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	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	8	no	—
1168	C₂×C₄	—	4	8	no	—
1169	C₂×C₄	—	4	8	no	—
1170	C₂×C₄	—	4	8	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	4	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	4	no	—
1177	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1178	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1179	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1180	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1181	C₂×C₃	—	2	4	no	—
1182	C₂×C₃	—	2	8	no	—
1183	C₂×C₃	—	2	4	no	—
1184	C₂×C₃	—	4	2	no	—
1185	C₂×C₃	—	4	4	no	—
1186	C₂×C₃	—	8	1	no	—
1187	C₂×C₃	C₂×#525	1	1	yes	characteristic
1188	C₂×C₃	C₂×#546	1	1	yes	characteristic
1189	C₂×C₃	C₂×#551	1	2	yes	—
1190	C₂×C₃	#3484	1	1	yes	characteristic
1191	C₂×C₃	#3490	1	2	yes	—
1192	C₂²	—	2	32	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	4	no	—
1195	C₂²	—	2	4	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	4	no	—
1198	C₂²	—	2	4	no	—
1199	C₂²	—	2	4	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	4	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	4	no	—
1204	C₂²	—	2	4	no	—
1205	C₂²	—	2	4	no	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	4	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	4	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	4	no	—
1213	C₂²	—	4	16	no	—
1214	C₂²	—	4	32	no	—
1215	C₂²	—	4	16	no	—
1216	C₂²	—	4	32	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	C₃×#525	1	4	yes	—
1229	C₂²	C₃×#546	1	4	yes	—
1230	C₂²	C₃×#551	1	8	yes	complemented
1231	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1232	C₂²	C₂²×C₃×#41	1	2	yes	—
1233	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1234	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1235	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	2	2	no	—
1239	C₄	—	2	2	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	2	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	2	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	2	no	—
1252	C₄	—	4	2	no	—
1253	C₃	#36158	1	1	yes	characteristic, direct product factor, Sylow
1254	C₂	—	2	4	no	—
1255	C₂	—	2	8	no	—
1256	C₂	—	2	4	no	—
1257	C₂	—	4	2	no	—
1258	C₂	—	4	4	no	—
1259	C₂	—	8	1	no	—
1260	C₂	C₂×C₃×#525	1	1	yes	characteristic
1261	C₂	C₂×C₃×#546	1	1	yes	characteristic
1262	C₂	C₂×C₃×#551	1	2	yes	—
1263	C₂	C₃×#3484	1	1	yes	characteristic
1264	C₂	C₃×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2846	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#551	C₂	semidirect
2. C₂³×C₃×C₂²⋊C₄	C₂	semidirect
3. C₃×#2849	C₂	semidirect
4. C₃×#2848	C₂	semidirect
6. C₃×#2561	C₂	semidirect
7. C₃×#2534	C₂	semidirect
8. C₃×#2483	C₂	semidirect
9. C₃×#2482	C₂	semidirect
10. C₃×#2480	C₂	semidirect
11. C₃×#2480	C₂	semidirect
12. C₃×#2472	C₂	semidirect
13. C₃×#2437	C₂	semidirect
14. C₃×#2418	C₂	semidirect
15. C₃×#2412	C₂	semidirect
16. C₃×#2412	C₂	semidirect
17. C₃×#2411	C₂	semidirect
18. C₃×#2358	C₂	semidirect
19. C₃×#2342	C₂	semidirect
20. C₃×#2342	C₂	semidirect
21. C₃×C₄×#120	C₂	semidirect
22. C₃×#2280	C₂	semidirect
23. C₂×C₃×#379	C₂	semidirect
24. #36158	C₃	direct (N × H)
29. C₂×C₃×#126	C₂²	semidirect
30. C₂×C₃×#126	C₂²	semidirect
31. C₂×C₃×#124	C₂²	semidirect
32. C₂×C₃×#123	C₂²	semidirect
33. C₂×C₃×#123	C₂²	semidirect
34. C₂×C₃×#123	C₂²	semidirect
35. C₂×C₃×#123	C₂²	semidirect
36. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃×C₄×D₄	C₂²	semidirect
45. C₂×C₃×C₄×D₄	C₂²	semidirect
46. C₂×C₃×C₄×D₄	C₂²	semidirect
47. C₂×C₃×#117	C₂²	semidirect
48. C₂×C₃×#117	C₂²	semidirect
49. C₂×C₃×#117	C₂²	semidirect
63. C₃×#399	C₂²	semidirect
64. C₃×#397	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#397	C₂²	semidirect
67. C₃×#397	C₂²	semidirect
68. C₃×#397	C₂²	semidirect
69. C₃×#396	C₂²	semidirect
70. C₃×#396	C₂²	semidirect
71. C₃×#394	C₂²	semidirect
72. C₃×#394	C₂²	semidirect
73. C₃×#394	C₂²	semidirect
74. C₃×#393	C₂²	semidirect
75. C₃×#390	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×#388	C₂²	semidirect
84. C₃×#386	C₂²	semidirect
85. C₃×#386	C₂²	semidirect
86. C₃×#386	C₂²	semidirect
87. C₃×#386	C₂²	semidirect
88. C₃×#386	C₂²	semidirect
89. C₃×#386	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#385	C₂²	semidirect
92. C₃×#385	C₂²	semidirect
93. C₃×#385	C₂²	semidirect
94. C₃×#385	C₂²	semidirect
95. C₃×#385	C₂²	semidirect
96. C₃×#385	C₂²	semidirect
97. C₃×#385	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
99. C₃×#385	C₂²	semidirect
100. C₃×#381	C₂²	semidirect
101. C₃×#381	C₂²	semidirect
102. C₃×#381	C₂²	semidirect
103. C₃×#381	C₂²	semidirect
104. C₃×#381	C₂²	semidirect
105. C₃×#380	C₂²	semidirect
106. C₃×#380	C₂²	semidirect
107. C₃×#380	C₂²	semidirect
108. C₃×#380	C₂²	semidirect
109. C₃×#380	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
126. C₂×#551	C₂×C₃	semidirect
127. C₂³×C₂²⋊C₄	C₂×C₃	semidirect
128. #2849	C₂×C₃	semidirect
129. #2848	C₂×C₃	semidirect
131. #2561	C₂×C₃	semidirect
132. #2534	C₂×C₃	semidirect
133. #2483	C₂×C₃	semidirect
134. #2482	C₂×C₃	semidirect
135. #2480	C₂×C₃	semidirect
136. #2480	C₂×C₃	semidirect
137. #2472	C₂×C₃	semidirect
138. #2437	C₂×C₃	semidirect
139. #2418	C₂×C₃	semidirect
140. #2412	C₂×C₃	semidirect
141. #2412	C₂×C₃	semidirect
142. #2411	C₂×C₃	semidirect
143. #2358	C₂×C₃	semidirect
144. #2342	C₂×C₃	semidirect
145. #2342	C₂×C₃	semidirect
146. C₄×#120	C₂×C₃	semidirect
147. #2280	C₂×C₃	semidirect
148. C₂×#379	C₂×C₃	semidirect
159. C₂²×C₃×Q₈	C₂³	semidirect
181. C₂³×C₃×C₄	C₂³	semidirect
203. C₂×C₃×C₄⋊C₄	C₂³	semidirect
204. C₂×C₃×C₄⋊C₄	C₂³	semidirect
205. C₂×C₃×C₄⋊C₄	C₂³	semidirect
206. C₂×C₃×C₄⋊C₄	C₂³	semidirect
207. C₂×C₃×C₄⋊C₄	C₂³	semidirect
208. C₂×C₃×C₄⋊C₄	C₂³	semidirect
209. C₂×C₃×C₄⋊C₄	C₂³	semidirect
210. C₂×C₃×C₄⋊C₄	C₂³	semidirect
211. C₂×C₃×C₄⋊C₄	C₂³	semidirect
212. C₂×C₃×C₄⋊C₄	C₂³	semidirect
213. C₂×C₃×C₄⋊C₄	C₂³	semidirect
214. C₂×C₃×C₄⋊C₄	C₂³	semidirect
215. C₂×C₃×C₄⋊C₄	C₂³	semidirect
216. C₂×C₃×C₄⋊C₄	C₂³	semidirect
228. C₂×C₃×C₂²⋊C₄	D₄	semidirect
267. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
268. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
269. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
270. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
271. C₂×C₃×C₂²⋊C₄	C₂³	semidirect
272. C₂×C₃×C₄²	C₂³	semidirect
273. C₂×C₃×C₄²	C₂³	semidirect
274. C₂×C₃×C₄²	C₂³	semidirect
275. C₂×C₃×C₄²	C₂³	semidirect
276. C₂×C₃×C₄²	C₂³	semidirect
277. C₃×#95	C₂³	semidirect
278. C₃×#95	C₂³	semidirect
279. C₃×#95	C₂³	semidirect
280. C₃×#95	C₂³	semidirect
281. C₃×#95	C₂³	semidirect
282. C₃×#95	C₂³	semidirect
283. C₃×#95	C₂³	semidirect
284. C₃×#95	C₂³	semidirect
285. C₃×#95	C₂³	semidirect
286. C₃×#95	C₂³	semidirect
287. C₃×#95	C₂³	semidirect
288. C₃×#95	C₂³	semidirect
289. C₃×#95	C₂³	semidirect
290. C₃×#95	C₂³	semidirect
295. C₂×#126	C₂²×C₃	semidirect
296. C₂×#126	C₂²×C₃	semidirect
297. C₂×#124	C₂²×C₃	semidirect
298. C₂×#123	C₂²×C₃	semidirect
299. C₂×#123	C₂²×C₃	semidirect
300. C₂×#123	C₂²×C₃	semidirect
301. C₂×#123	C₂²×C₃	semidirect
302. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
303. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
304. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
310. C₂×C₄×D₄	C₂²×C₃	semidirect
311. C₂×C₄×D₄	C₂²×C₃	semidirect
312. C₂×C₄×D₄	C₂²×C₃	semidirect
313. C₂×#117	C₂²×C₃	semidirect
314. C₂×#117	C₂²×C₃	semidirect
315. C₂×#117	C₂²×C₃	semidirect
329. #399	C₂²×C₃	semidirect
330. #397	C₂²×C₃	semidirect
331. #397	C₂²×C₃	semidirect
332. #397	C₂²×C₃	semidirect
333. #397	C₂²×C₃	semidirect
334. #397	C₂²×C₃	semidirect
335. #396	C₂²×C₃	semidirect
336. #396	C₂²×C₃	semidirect
337. #394	C₂²×C₃	semidirect
338. #394	C₂²×C₃	semidirect
339. #394	C₂²×C₃	semidirect
340. #393	C₂²×C₃	semidirect
341. #390	C₂²×C₃	semidirect
342. #388	C₂²×C₃	semidirect
343. #388	C₂²×C₃	semidirect
344. #388	C₂²×C₃	semidirect
345. #388	C₂²×C₃	semidirect
346. #388	C₂²×C₃	semidirect
347. #388	C₂²×C₃	semidirect
348. #388	C₂²×C₃	semidirect
349. #388	C₂²×C₃	semidirect
350. #386	C₂²×C₃	semidirect
351. #386	C₂²×C₃	semidirect
352. #386	C₂²×C₃	semidirect
353. #386	C₂²×C₃	semidirect
354. #386	C₂²×C₃	semidirect
355. #386	C₂²×C₃	semidirect
356. #385	C₂²×C₃	semidirect
357. #385	C₂²×C₃	semidirect
358. #385	C₂²×C₃	semidirect
359. #385	C₂²×C₃	semidirect
360. #385	C₂²×C₃	semidirect
361. #385	C₂²×C₃	semidirect
362. #385	C₂²×C₃	semidirect
363. #385	C₂²×C₃	semidirect
364. #385	C₂²×C₃	semidirect
365. #385	C₂²×C₃	semidirect
366. #381	C₂²×C₃	semidirect
367. #381	C₂²×C₃	semidirect
368. #381	C₂²×C₃	semidirect
369. #381	C₂²×C₃	semidirect
370. #381	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
387. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
388. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
389. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
390. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
391. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
569. C₂²×Q₈	C₂³×C₃	semidirect
591. C₂³×C₄	C₂³×C₃	semidirect
613. C₂×C₄⋊C₄	C₂³×C₃	semidirect
614. C₂×C₄⋊C₄	C₂³×C₃	semidirect
615. C₂×C₄⋊C₄	C₂³×C₃	semidirect
616. C₂×C₄⋊C₄	C₂³×C₃	semidirect
617. C₂×C₄⋊C₄	C₂³×C₃	semidirect
618. C₂×C₄⋊C₄	C₂³×C₃	semidirect
619. C₂×C₄⋊C₄	C₂³×C₃	semidirect
620. C₂×C₄⋊C₄	C₂³×C₃	semidirect
621. C₂×C₄⋊C₄	C₂³×C₃	semidirect
622. C₂×C₄⋊C₄	C₂³×C₃	semidirect
623. C₂×C₄⋊C₄	C₂³×C₃	semidirect
624. C₂×C₄⋊C₄	C₂³×C₃	semidirect
625. C₂×C₄⋊C₄	C₂³×C₃	semidirect
626. C₂×C₄⋊C₄	C₂³×C₃	semidirect
638. C₂×C₂²⋊C₄	C₃×D₄	semidirect
677. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
678. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
679. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
680. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
681. C₂×C₂²⋊C₄	C₂³×C₃	semidirect
682. C₂×C₄²	C₂³×C₃	semidirect
683. C₂×C₄²	C₂³×C₃	semidirect
684. C₂×C₄²	C₂³×C₃	semidirect
685. C₂×C₄²	C₂³×C₃	semidirect
686. C₂×C₄²	C₂³×C₃	semidirect
687. #95	C₂³×C₃	semidirect
688. #95	C₂³×C₃	semidirect
689. #95	C₂³×C₃	semidirect
690. #95	C₂³×C₃	semidirect
691. #95	C₂³×C₃	semidirect
692. #95	C₂³×C₃	semidirect
693. #95	C₂³×C₃	semidirect
694. #95	C₂³×C₃	semidirect
695. #95	C₂³×C₃	semidirect
696. #95	C₂³×C₃	semidirect
697. #95	C₂³×C₃	semidirect
698. #95	C₂³×C₃	semidirect
699. #95	C₂³×C₃	semidirect
700. #95	C₂³×C₃	semidirect
1032. C₂²×C₃	#551	semidirect
1230. C₂²	C₃×#551	semidirect
1253. C₃	#36158	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
C₂³×C₃×C₂²⋊C₄	2
C₃×#2849	2
C₃×#2848	2
C₃×#2846	2
C₃×#2561	2
C₃×#2534	2
C₃×#2483	2
C₃×#2482	2
C₃×#2480	2
C₃×#2472	2
C₃×#2437	2
C₃×#2418	2
C₃×#2412	2
C₃×#2411	2
C₃×#2358	2
C₃×#2342	2
C₃×C₄×#120	2
C₃×#2280	2
C₂×C₃×#379	2
#36158	3

Subgroups — C3×#36158 #10654765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36158 #10654765