Subgroups — C₃×#37658 #10656265

Order 768.

3366 conjugacy classes of subgroups.

The subgroup lattice has 1402 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, complemented
2	C₂×C₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2679	C₂	1	2	yes	maximal, complemented
7	C₃×#2678	C₂	1	2	yes	maximal, complemented
8	C₃×#2672	C₂	1	2	yes	maximal, complemented
9	C₃×#2669	C₂	1	2	yes	maximal, complemented
10	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2461	C₂	1	2	yes	maximal, complemented
15	C₃×#2445	C₂	1	2	yes	maximal, complemented
16	C₃×#2424	C₂	1	2	yes	maximal, complemented
17	C₃×#2418	C₂	1	2	yes	maximal, complemented
18	C₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
24	#37658	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×#546	—	2	8	no	—
30	C₃×#535	—	2	8	no	—
31	C₂×C₃×#127	C₂²	1	2	yes	—
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#124	C₂²	1	2	yes	complemented
34	C₃×#525	—	2	8	no	—
35	C₃×#525	—	2	8	no	—
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×#123	C₂²	1	2	yes	complemented
38	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#123	C₂²	1	2	yes	complemented
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₃×#121	C₂²	1	1	yes	characteristic
49	C₂×C₃×#121	C₂²	1	1	yes	characteristic
50	C₂×C₃×#121	C₂²	1	2	yes	—
51	C₂×C₃×#121	C₂²	1	1	yes	characteristic
52	C₂×C₃×#121	C₂²	1	1	yes	characteristic
53	C₂×C₃×#121	C₂²	1	1	yes	characteristic
54	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×#121	C₂²	1	2	yes	complemented
57	C₂×C₃×#120	C₂²	1	1	yes	characteristic
58	C₂×C₃×#120	C₂²	1	2	yes	—
59	C₂×C₃×#120	C₂²	1	2	yes	—
60	C₂×C₃×#120	C₂²	1	2	yes	—
61	C₂×C₃×#120	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#120	C₂²	1	2	yes	complemented
63	C₂×C₃×#120	C₂²	1	2	yes	complemented
64	C₂×C₃×#120	C₂²	1	2	yes	complemented
65	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
67	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
69	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
70	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
75	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
76	C₃×#399	C₂²	1	2	yes	complemented
77	C₃×#397	C₂²	1	2	yes	complemented
78	C₃×#396	C₂²	1	2	yes	complemented
79	C₃×#396	C₂²	1	2	yes	complemented
80	C₃×#395	C₂²	1	2	yes	complemented
81	C₃×#394	C₂²	1	2	yes	—
82	C₃×#394	C₂²	1	2	yes	—
83	C₃×#394	C₂²	1	2	yes	complemented
84	C₃×#394	C₂²	1	2	yes	complemented
85	C₃×#394	C₂²	1	2	yes	complemented
86	C₃×#394	C₂²	1	2	yes	complemented
87	C₃×#394	C₂²	1	2	yes	complemented
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×#394	C₂²	1	2	yes	complemented
92	C₃×#392	C₂²	1	2	yes	—
93	C₃×#392	C₂²	1	2	yes	complemented
94	C₃×#392	C₂²	1	2	yes	complemented
95	C₃×#392	C₂²	1	2	yes	complemented
96	C₃×#391	C₂²	1	1	yes	characteristic, complemented
97	C₃×#390	C₂²	1	2	yes	—
98	C₃×#390	C₂²	1	1	yes	characteristic, complemented
99	C₃×#390	C₂²	1	1	yes	characteristic, complemented
100	C₃×#390	C₂²	1	2	yes	complemented
101	C₃×#390	C₂²	1	2	yes	complemented
102	C₃×#390	C₂²	1	2	yes	complemented
103	C₃×#390	C₂²	1	2	yes	complemented
104	C₃×#389	C₂²	1	1	yes	characteristic, complemented
105	C₃×#389	C₂²	1	2	yes	complemented
106	C₃×#388	C₂²	1	2	yes	complemented
107	C₃×#388	C₂²	1	2	yes	complemented
108	C₃×#388	C₂²	1	2	yes	complemented
109	C₃×#388	C₂²	1	2	yes	complemented
110	C₃×#388	C₂²	1	2	yes	complemented
111	C₃×#386	C₂²	1	2	yes	complemented
112	C₃×#386	C₂²	1	2	yes	complemented
113	C₃×#386	C₂²	1	2	yes	complemented
114	C₃×#386	C₂²	1	2	yes	complemented
115	C₃×#386	C₂²	1	2	yes	complemented
116	C₃×#385	C₂²	1	2	yes	complemented
117	C₃×#385	C₂²	1	2	yes	complemented
118	C₃×#384	C₂²	1	1	yes	characteristic, complemented
119	C₃×#380	C₂²	1	1	yes	characteristic, complemented
120	C₃×#380	C₂²	1	1	yes	characteristic, complemented
121	C₃×#380	C₂²	1	1	yes	characteristic, complemented
122	C₃×#380	C₂²	1	1	yes	characteristic, complemented
123	C₃×#380	C₂²	1	1	yes	characteristic, complemented
124	C₃×#380	C₂²	1	2	yes	complemented
125	C₃×#379	C₂²	1	2	yes	complemented
126	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
127	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
129	C₂×#535	C₂×C₃	1	1	yes	characteristic, complemented
130	C₂×#525	C₂×C₃	1	1	yes	characteristic, complemented
131	C₂×#525	C₂×C₃	1	1	yes	characteristic, complemented
132	#2847	C₂×C₃	1	1	yes	characteristic, complemented
133	#2679	C₂×C₃	1	2	yes	complemented
134	#2678	C₂×C₃	1	2	yes	complemented
135	#2672	C₂×C₃	1	2	yes	complemented
136	#2669	C₂×C₃	1	2	yes	complemented
137	#2620	C₂×C₃	1	1	yes	characteristic, complemented
138	#2616	C₂×C₃	1	1	yes	characteristic, complemented
139	#2540	C₂×C₃	1	1	yes	characteristic, complemented
140	#2537	C₂×C₃	1	1	yes	characteristic, complemented
141	#2461	C₂×C₃	1	2	yes	complemented
142	#2445	C₂×C₃	1	2	yes	complemented
143	#2424	C₂×C₃	1	2	yes	complemented
144	#2418	C₂×C₃	1	2	yes	complemented
145	#2415	C₂×C₃	1	1	yes	characteristic, complemented
146	#2414	C₂×C₃	1	1	yes	characteristic, complemented
147	#2408	C₂×C₃	1	1	yes	characteristic, complemented
148	#2407	C₂×C₃	1	1	yes	characteristic, complemented
149	#2354	C₂×C₃	1	1	yes	characteristic, complemented
150	#2324	C₂×C₃	1	1	yes	characteristic, complemented
151	C₂⁵×C₃	C₂³	1	1	yes	characteristic
152	C₂⁵×C₃	C₂³	1	2	yes	—
153	C₂×C₃×#41	—	2	4	no	—
154	C₂×C₃×#41	—	2	4	no	—
155	C₂×C₃×#41	—	2	4	no	—
156	C₂×C₃×#41	—	2	4	no	—
157	C₂×C₃×#41	—	4	2	no	—
158	C₂×C₃×#41	—	4	2	no	—
159	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
160	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
161	C₂²×C₃×D₄	—	2	4	no	—
162	C₂²×C₃×D₄	—	2	4	no	—
163	C₂²×C₃×D₄	—	4	2	no	—
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂²×C₃×D₄	C₂³	1	2	yes	—
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	2	yes	—
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	C₂²×C₃×D₄	C₂³	1	2	yes	—
175	C₂²×C₃×D₄	C₂³	1	2	yes	—
176	C₂²×C₃×D₄	C₂³	1	2	yes	—
177	C₂²×C₃×D₄	C₂³	1	2	yes	—
178	C₂²×C₃×D₄	C₂³	1	2	yes	—
179	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
180	C₂²×C₃×D₄	C₂³	1	2	yes	—
181	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
182	C₂³×C₃×C₄	—	2	4	no	—
183	C₂³×C₃×C₄	—	2	4	no	—
184	C₂³×C₃×C₄	—	4	2	no	—
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	C₂³×C₃×C₄	C₂³	1	2	yes	—
191	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
192	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
193	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
194	C₂³×C₃×C₄	C₂³	1	2	yes	—
195	C₃×#127	—	2	8	no	—
196	C₃×#124	—	2	8	no	—
197	C₃×#124	—	2	4	no	—
198	C₃×#123	—	2	4	no	—
199	C₃×#123	—	2	8	no	—
200	C₃×#123	—	2	4	no	—
201	C₃×#123	—	2	8	no	—
202	C₃×C₂²⋊Q₈	—	2	4	no	—
203	C₃×C₂²⋊Q₈	—	2	4	no	—
204	C₃×C₂²⋊Q₈	—	2	4	no	—
205	C₃×C₂²⋊Q₈	—	2	4	no	—
206	C₃×C₂²⋊Q₈	—	2	4	no	—
207	C₃×C₂²⋊Q₈	—	4	2	no	—
208	C₃×#121	—	2	4	no	—
209	C₃×#121	—	2	4	no	—
210	C₃×#121	—	2	4	no	—
211	C₃×#121	—	2	4	no	—
212	C₃×#121	—	2	4	no	—
213	C₃×#121	—	2	4	no	—
214	C₃×#121	—	2	4	no	—
215	C₃×#121	—	2	8	no	—
216	C₃×#121	—	4	4	no	—
217	C₃×#121	—	4	2	no	—
218	C₃×#121	D₄	1	8	yes	complemented
219	C₃×#120	—	2	4	no	—
220	C₃×#120	—	2	8	no	—
221	C₃×#120	—	2	8	no	—
222	C₃×#120	—	2	8	no	—
223	C₃×#120	—	2	4	no	—
224	C₃×#120	—	2	8	no	—
225	C₃×#120	—	4	4	no	—
226	C₃×#120	—	4	4	no	—
227	C₃×C₄×D₄	—	2	8	no	—
228	C₃×C₄×D₄	—	2	4	no	—
229	C₃×C₄×D₄	—	2	4	no	—
230	C₃×C₄×D₄	—	2	8	no	—
231	C₃×C₄×D₄	—	2	4	no	—
232	C₃×C₄×D₄	—	2	4	no	—
233	C₃×C₄×D₄	D₄	1	8	yes	complemented
234	C₃×#117	—	2	4	no	—
235	C₃×#117	—	2	4	no	—
236	C₃×#117	—	2	4	no	—
237	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
241	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
256	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
262	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
270	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
278	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
282	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
284	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
285	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₃×C₄²	C₂³	1	2	yes	—
292	C₂×C₃×C₄²	C₂³	1	2	yes	—
293	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
294	C₂×C₃×C₄²	C₂³	1	2	yes	—
295	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
303	C₃×#95	C₂³	1	2	yes	—
304	C₃×#95	C₂³	1	2	yes	—
305	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
307	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
309	#546	—	2	8	no	—
310	#535	—	2	8	no	—
311	C₂×#127	C₂²×C₃	1	2	yes	—
312	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂×#124	C₂²×C₃	1	2	yes	complemented
314	#525	—	2	8	no	—
315	#525	—	2	8	no	—
316	C₂×#123	C₂²×C₃	1	1	yes	characteristic
317	C₂×#123	C₂²×C₃	1	2	yes	complemented
318	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
319	C₂×#123	C₂²×C₃	1	2	yes	complemented
320	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
321	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
325	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₂×#121	C₂²×C₃	1	1	yes	characteristic
327	C₂×#121	C₂²×C₃	1	1	yes	characteristic
328	C₂×#121	C₂²×C₃	1	1	yes	characteristic
329	C₂×#121	C₂²×C₃	1	1	yes	characteristic
330	C₂×#121	C₂²×C₃	1	1	yes	characteristic
331	C₂×#121	C₂²×C₃	1	2	yes	—
332	C₂×#121	C₂²×C₃	1	1	yes	characteristic
333	C₂×#121	C₂²×C₃	1	1	yes	characteristic
334	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
335	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
336	C₂×#121	C₂²×C₃	1	2	yes	complemented
337	C₂×#120	C₂²×C₃	1	1	yes	characteristic
338	C₂×#120	C₂²×C₃	1	2	yes	—
339	C₂×#120	C₂²×C₃	1	2	yes	—
340	C₂×#120	C₂²×C₃	1	2	yes	—
341	C₂×#120	C₂²×C₃	1	1	yes	characteristic, complemented
342	C₂×#120	C₂²×C₃	1	2	yes	complemented
343	C₂×#120	C₂²×C₃	1	2	yes	complemented
344	C₂×#120	C₂²×C₃	1	2	yes	complemented
345	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
348	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
350	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
351	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
352	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
353	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
354	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
355	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
356	#399	C₂²×C₃	1	2	yes	complemented
357	#397	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	#394	C₂²×C₃	1	2	yes	—
362	#394	C₂²×C₃	1	2	yes	—
363	#394	C₂²×C₃	1	2	yes	complemented
364	#394	C₂²×C₃	1	2	yes	complemented
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	#394	C₂²×C₃	1	2	yes	complemented
369	#394	C₂²×C₃	1	2	yes	complemented
370	#394	C₂²×C₃	1	2	yes	complemented
371	#394	C₂²×C₃	1	2	yes	complemented
372	#392	C₂²×C₃	1	2	yes	—
373	#392	C₂²×C₃	1	2	yes	complemented
374	#392	C₂²×C₃	1	2	yes	complemented
375	#392	C₂²×C₃	1	2	yes	complemented
376	#391	C₂²×C₃	1	1	yes	characteristic, complemented
377	#390	C₂²×C₃	1	2	yes	—
378	#390	C₂²×C₃	1	1	yes	characteristic, complemented
379	#390	C₂²×C₃	1	2	yes	complemented
380	#390	C₂²×C₃	1	1	yes	characteristic, complemented
381	#390	C₂²×C₃	1	2	yes	complemented
382	#390	C₂²×C₃	1	2	yes	complemented
383	#390	C₂²×C₃	1	2	yes	complemented
384	#389	C₂²×C₃	1	1	yes	characteristic, complemented
385	#389	C₂²×C₃	1	2	yes	complemented
386	#388	C₂²×C₃	1	2	yes	complemented
387	#388	C₂²×C₃	1	2	yes	complemented
388	#388	C₂²×C₃	1	2	yes	complemented
389	#388	C₂²×C₃	1	2	yes	complemented
390	#388	C₂²×C₃	1	2	yes	complemented
391	#386	C₂²×C₃	1	2	yes	complemented
392	#386	C₂²×C₃	1	2	yes	complemented
393	#386	C₂²×C₃	1	2	yes	complemented
394	#386	C₂²×C₃	1	2	yes	complemented
395	#386	C₂²×C₃	1	2	yes	complemented
396	#385	C₂²×C₃	1	2	yes	complemented
397	#385	C₂²×C₃	1	2	yes	complemented
398	#384	C₂²×C₃	1	1	yes	characteristic, complemented
399	#380	C₂²×C₃	1	1	yes	characteristic, complemented
400	#380	C₂²×C₃	1	1	yes	characteristic, complemented
401	#380	C₂²×C₃	1	1	yes	characteristic, complemented
402	#380	C₂²×C₃	1	1	yes	characteristic, complemented
403	#380	C₂²×C₃	1	1	yes	characteristic, complemented
404	#380	C₂²×C₃	1	2	yes	complemented
405	#379	C₂²×C₃	1	2	yes	complemented
406	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
407	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
408	C₂⁴×C₃	—	2	2	no	—
409	C₂⁴×C₃	—	2	2	no	—
410	C₂⁴×C₃	—	2	2	no	—
411	C₂⁴×C₃	—	2	4	no	—
412	C₂⁴×C₃	—	2	4	no	—
413	C₂⁴×C₃	—	4	1	no	—
414	C₂⁴×C₃	—	4	1	no	—
415	C₂⁴×C₃	—	4	1	no	—
416	C₂⁴×C₃	—	4	1	no	—
417	C₂⁴×C₃	—	4	2	no	—
418	C₂⁴×C₃	—	4	2	no	—
419	C₂⁴×C₃	—	4	2	no	—
420	C₂⁴×C₃	—	4	2	no	—
421	C₂⁴×C₃	—	4	2	no	—
422	C₂⁴×C₃	C₂⁴	1	2	yes	—
423	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
424	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
425	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
426	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
427	C₂⁴×C₃	C₂⁴	1	2	yes	—
428	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
429	C₃×#41	—	4	16	no	—
430	C₃×#41	—	4	16	no	—
431	C₂×C₃×Q₈	—	2	2	no	—
432	C₂×C₃×Q₈	—	2	2	no	—
433	C₂×C₃×Q₈	—	2	2	no	—
434	C₂×C₃×Q₈	—	2	2	no	—
435	C₂×C₃×Q₈	—	2	2	no	—
436	C₂×C₃×Q₈	—	4	1	no	—
437	C₂×C₃×D₄	—	2	2	no	—
438	C₂×C₃×D₄	—	2	4	no	—
439	C₂×C₃×D₄	—	2	2	no	—
440	C₂×C₃×D₄	—	2	2	no	—
441	C₂×C₃×D₄	—	2	4	no	—
442	C₂×C₃×D₄	—	2	2	no	—
443	C₂×C₃×D₄	—	2	4	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	4	no	—
449	C₂×C₃×D₄	—	2	2	no	—
450	C₂×C₃×D₄	—	2	4	no	—
451	C₂×C₃×D₄	—	2	4	no	—
452	C₂×C₃×D₄	—	2	4	no	—
453	C₂×C₃×D₄	—	2	4	no	—
454	C₂×C₃×D₄	—	2	2	no	—
455	C₂×C₃×D₄	—	2	2	no	—
456	C₂×C₃×D₄	—	2	2	no	—
457	C₂×C₃×D₄	—	2	2	no	—
458	C₂×C₃×D₄	—	2	2	no	—
459	C₂×C₃×D₄	—	2	4	no	—
460	C₂×C₃×D₄	—	2	2	no	—
461	C₂×C₃×D₄	—	2	4	no	—
462	C₂×C₃×D₄	—	2	2	no	—
463	C₂×C₃×D₄	—	2	2	no	—
464	C₂×C₃×D₄	—	4	16	no	—
465	C₂×C₃×D₄	—	4	2	no	—
466	C₂×C₃×D₄	—	4	1	no	—
467	C₂×C₃×D₄	—	4	2	no	—
468	C₂×C₃×D₄	—	4	1	no	—
469	C₂×C₃×D₄	—	4	2	no	—
470	C₂×C₃×D₄	—	4	1	no	—
471	C₂×C₃×D₄	—	4	1	no	—
472	C₂×C₃×D₄	—	4	1	no	—
473	C₂×C₃×D₄	—	4	2	no	—
474	C₂×C₃×D₄	—	4	1	no	—
475	C₂×C₃×D₄	—	4	1	no	—
476	C₂×C₃×D₄	—	4	1	no	—
477	C₂×C₃×D₄	—	4	2	no	—
478	C₂×C₃×D₄	—	4	1	no	—
479	C₂×C₃×D₄	—	4	2	no	—
480	C₂×C₃×D₄	—	4	2	no	—
481	C₂×C₃×D₄	—	4	2	no	—
482	C₂×C₃×D₄	—	4	2	no	—
483	C₂×C₃×D₄	—	4	2	no	—
484	C₂×C₃×D₄	—	4	2	no	—
485	C₂×C₃×D₄	—	4	2	no	—
486	C₂×C₃×D₄	—	4	2	no	—
487	C₂×C₃×D₄	—	4	2	no	—
488	C₂×C₃×D₄	—	4	2	no	—
489	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
490	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
491	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
492	C₂²×C₃×C₄	—	2	2	no	—
493	C₂²×C₃×C₄	—	2	2	no	—
494	C₂²×C₃×C₄	—	2	2	no	—
495	C₂²×C₃×C₄	—	2	2	no	—
496	C₂²×C₃×C₄	—	2	2	no	—
497	C₂²×C₃×C₄	—	2	2	no	—
498	C₂²×C₃×C₄	—	2	2	no	—
499	C₂²×C₃×C₄	—	2	4	no	—
500	C₂²×C₃×C₄	—	2	2	no	—
501	C₂²×C₃×C₄	—	2	4	no	—
502	C₂²×C₃×C₄	—	2	2	no	—
503	C₂²×C₃×C₄	—	2	2	no	—
504	C₂²×C₃×C₄	—	2	2	no	—
505	C₂²×C₃×C₄	—	2	2	no	—
506	C₂²×C₃×C₄	—	2	2	no	—
507	C₂²×C₃×C₄	—	2	2	no	—
508	C₂²×C₃×C₄	—	2	2	no	—
509	C₂²×C₃×C₄	—	2	2	no	—
510	C₂²×C₃×C₄	—	2	2	no	—
511	C₂²×C₃×C₄	—	2	2	no	—
512	C₂²×C₃×C₄	—	2	4	no	—
513	C₂²×C₃×C₄	—	4	1	no	—
514	C₂²×C₃×C₄	—	4	1	no	—
515	C₂²×C₃×C₄	—	4	1	no	—
516	C₂²×C₃×C₄	—	4	2	no	—
517	C₂²×C₃×C₄	—	4	16	no	—
518	C₂²×C₃×C₄	—	4	2	no	—
519	C₂²×C₃×C₄	—	4	2	no	—
520	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
521	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
522	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
523	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
524	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
525	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
526	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
527	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
528	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
529	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
530	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
531	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
532	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
533	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
534	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
535	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
536	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
537	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
538	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
539	C₃×C₄⋊C₄	—	2	2	no	—
540	C₃×C₄⋊C₄	—	2	2	no	—
541	C₃×C₄⋊C₄	—	2	2	no	—
542	C₃×C₄⋊C₄	—	2	2	no	—
543	C₃×C₄⋊C₄	—	2	2	no	—
544	C₃×C₄⋊C₄	—	2	2	no	—
545	C₃×C₄⋊C₄	—	2	2	no	—
546	C₃×C₄⋊C₄	—	2	4	no	—
547	C₃×C₄⋊C₄	—	2	4	no	—
548	C₃×C₄⋊C₄	—	2	2	no	—
549	C₃×C₄⋊C₄	—	2	4	no	—
550	C₃×C₄⋊C₄	—	2	2	no	—
551	C₃×C₄⋊C₄	—	4	2	no	—
552	C₃×C₄⋊C₄	—	4	2	no	—
553	C₃×C₄⋊C₄	—	4	2	no	—
554	C₃×C₄⋊C₄	—	4	2	no	—
555	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
556	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
557	C₃×C₂²⋊C₄	—	2	4	no	—
558	C₃×C₂²⋊C₄	—	2	4	no	—
559	C₃×C₂²⋊C₄	—	2	2	no	—
560	C₃×C₂²⋊C₄	—	2	2	no	—
561	C₃×C₂²⋊C₄	—	2	4	no	—
562	C₃×C₂²⋊C₄	—	2	4	no	—
563	C₃×C₂²⋊C₄	—	2	4	no	—
564	C₃×C₂²⋊C₄	—	2	4	no	—
565	C₃×C₂²⋊C₄	—	2	4	no	—
566	C₃×C₂²⋊C₄	—	2	4	no	—
567	C₃×C₂²⋊C₄	—	2	4	no	—
568	C₃×C₂²⋊C₄	—	2	2	no	—
569	C₃×C₂²⋊C₄	—	2	2	no	—
570	C₃×C₂²⋊C₄	—	2	2	no	—
571	C₃×C₂²⋊C₄	—	2	4	no	—
572	C₃×C₂²⋊C₄	—	2	2	no	—
573	C₃×C₂²⋊C₄	—	2	4	no	—
574	C₃×C₂²⋊C₄	—	2	2	no	—
575	C₃×C₂²⋊C₄	—	2	2	no	—
576	C₃×C₂²⋊C₄	—	2	4	no	—
577	C₃×C₂²⋊C₄	—	2	4	no	—
578	C₃×C₂²⋊C₄	—	2	4	no	—
579	C₃×C₂²⋊C₄	—	4	2	no	—
580	C₃×C₂²⋊C₄	—	4	2	no	—
581	C₃×C₂²⋊C₄	—	4	2	no	—
582	C₃×C₂²⋊C₄	—	4	2	no	—
583	C₃×C₂²⋊C₄	—	4	2	no	—
584	C₃×C₂²⋊C₄	—	4	2	no	—
585	C₃×C₂²⋊C₄	—	4	2	no	—
586	C₃×C₂²⋊C₄	—	4	2	no	—
587	C₃×C₂²⋊C₄	—	4	2	no	—
588	C₃×C₂²⋊C₄	—	4	2	no	—
589	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
590	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
591	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
592	C₃×C₄²	—	2	4	no	—
593	C₃×C₄²	—	2	2	no	—
594	C₃×C₄²	—	2	4	no	—
595	C₃×C₄²	—	4	2	no	—
596	C₃×C₄²	C₂×D₄	1	4	yes	—
597	C₂⁵	C₂³×C₃	1	1	yes	characteristic
598	C₂⁵	C₂³×C₃	1	2	yes	—
599	C₂×#41	—	2	4	no	—
600	C₂×#41	—	2	4	no	—
601	C₂×#41	—	2	4	no	—
602	C₂×#41	—	2	4	no	—
603	C₂×#41	—	4	2	no	—
604	C₂×#41	—	4	2	no	—
605	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
606	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
607	C₂²×D₄	—	2	4	no	—
608	C₂²×D₄	—	2	4	no	—
609	C₂²×D₄	—	4	2	no	—
610	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
612	C₂²×D₄	C₂³×C₃	1	2	yes	—
613	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
614	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
615	C₂²×D₄	C₂³×C₃	1	2	yes	—
616	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₃	1	2	yes	—
619	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₃	1	2	yes	—
622	C₂²×D₄	C₂³×C₃	1	2	yes	—
623	C₂²×D₄	C₂³×C₃	1	2	yes	—
624	C₂²×D₄	C₂³×C₃	1	2	yes	—
625	C₂²×D₄	C₂³×C₃	1	2	yes	—
626	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₃	1	2	yes	—
628	C₂³×C₄	—	2	4	no	—
629	C₂³×C₄	—	2	4	no	—
630	C₂³×C₄	—	4	2	no	—
631	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₃	1	2	yes	—
634	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₃	1	2	yes	—
641	#127	—	2	8	no	—
642	#124	—	2	8	no	—
643	#124	—	2	4	no	—
644	#123	—	2	4	no	—
645	#123	—	2	8	no	—
646	#123	—	2	4	no	—
647	#123	—	2	8	no	—
648	C₂²⋊Q₈	—	2	4	no	—
649	C₂²⋊Q₈	—	2	4	no	—
650	C₂²⋊Q₈	—	2	4	no	—
651	C₂²⋊Q₈	—	2	4	no	—
652	C₂²⋊Q₈	—	2	4	no	—
653	C₂²⋊Q₈	—	4	2	no	—
654	#121	—	2	4	no	—
655	#121	—	2	4	no	—
656	#121	—	2	4	no	—
657	#121	—	2	4	no	—
658	#121	—	2	4	no	—
659	#121	—	2	4	no	—
660	#121	—	2	4	no	—
661	#121	—	2	8	no	—
662	#121	—	4	4	no	—
663	#121	—	4	2	no	—
664	#121	C₃×D₄	1	8	yes	complemented
665	#120	—	2	4	no	—
666	#120	—	2	8	no	—
667	#120	—	2	8	no	—
668	#120	—	2	8	no	—
669	#120	—	2	4	no	—
670	#120	—	2	8	no	—
671	#120	—	4	4	no	—
672	#120	—	4	4	no	—
673	C₄×D₄	—	2	8	no	—
674	C₄×D₄	—	2	4	no	—
675	C₄×D₄	—	2	4	no	—
676	C₄×D₄	—	2	8	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	2	4	no	—
679	C₄×D₄	C₃×D₄	1	8	yes	complemented
680	#117	—	2	4	no	—
681	#117	—	2	4	no	—
682	#117	—	2	4	no	—
683	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	—	2	8	no	—
702	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
737	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₃	1	2	yes	—
739	C₂×C₄²	C₂³×C₃	1	2	yes	—
740	C₂×C₄²	C₂³×C₃	1	2	yes	—
741	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
742	#95	C₂³×C₃	1	2	yes	—
743	#95	C₂³×C₃	1	2	yes	—
744	#95	C₂³×C₃	1	2	yes	—
745	#95	C₂³×C₃	1	2	yes	—
746	#95	C₂³×C₃	1	2	yes	—
747	#95	C₂³×C₃	1	2	yes	—
748	#95	C₂³×C₃	1	2	yes	—
749	#95	C₂³×C₃	1	2	yes	—
750	#95	C₂³×C₃	1	2	yes	—
751	C₂³×C₃	—	2	1	no	—
752	C₂³×C₃	—	2	1	no	—
753	C₂³×C₃	—	2	1	no	—
754	C₂³×C₃	—	2	1	no	—
755	C₂³×C₃	—	2	1	no	—
756	C₂³×C₃	—	2	2	no	—
757	C₂³×C₃	—	2	1	no	—
758	C₂³×C₃	—	2	1	no	—
759	C₂³×C₃	—	2	1	no	—
760	C₂³×C₃	—	2	2	no	—
761	C₂³×C₃	—	2	1	no	—
762	C₂³×C₃	—	2	1	no	—
763	C₂³×C₃	—	2	1	no	—
764	C₂³×C₃	—	2	1	no	—
765	C₂³×C₃	—	2	2	no	—
766	C₂³×C₃	—	2	2	no	—
767	C₂³×C₃	—	2	2	no	—
768	C₂³×C₃	—	2	1	no	—
769	C₂³×C₃	—	2	1	no	—
770	C₂³×C₃	—	2	1	no	—
771	C₂³×C₃	—	2	1	no	—
772	C₂³×C₃	—	2	1	no	—
773	C₂³×C₃	—	2	1	no	—
774	C₂³×C₃	—	2	2	no	—
775	C₂³×C₃	—	2	1	no	—
776	C₂³×C₃	—	2	1	no	—
777	C₂³×C₃	—	2	1	no	—
778	C₂³×C₃	—	2	1	no	—
779	C₂³×C₃	—	2	1	no	—
780	C₂³×C₃	—	2	1	no	—
781	C₂³×C₃	—	2	2	no	—
782	C₂³×C₃	—	2	1	no	—
783	C₂³×C₃	—	2	2	no	—
784	C₂³×C₃	—	2	1	no	—
785	C₂³×C₃	—	2	1	no	—
786	C₂³×C₃	—	2	1	no	—
787	C₂³×C₃	—	2	2	no	—
788	C₂³×C₃	—	2	2	no	—
789	C₂³×C₃	—	2	2	no	—
790	C₂³×C₃	—	2	1	no	—
791	C₂³×C₃	—	2	1	no	—
792	C₂³×C₃	—	2	1	no	—
793	C₂³×C₃	—	2	2	no	—
794	C₂³×C₃	—	2	2	no	—
795	C₂³×C₃	—	4	4	no	—
796	C₂³×C₃	—	4	4	no	—
797	C₂³×C₃	—	4	4	no	—
798	C₂³×C₃	—	4	8	no	—
799	C₂³×C₃	—	4	4	no	—
800	C₂³×C₃	—	4	4	no	—
801	C₂³×C₃	—	4	4	no	—
802	C₂³×C₃	—	4	8	no	—
803	C₂³×C₃	—	4	4	no	—
804	C₂³×C₃	—	8	4	no	—
805	C₂³×C₃	—	8	4	no	—
806	C₂³×C₃	—	8	4	no	—
807	C₂³×C₃	—	8	4	no	—
808	C₂³×C₃	—	8	4	no	—
809	C₂³×C₃	C₂²×D₄	1	2	yes	—
810	C₂³×C₃	C₂²×D₄	1	4	yes	—
811	C₂³×C₃	C₂²×D₄	1	2	yes	—
812	C₂³×C₃	C₂²×D₄	1	2	yes	—
813	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
814	C₂³×C₃	C₂⁵	1	1	yes	characteristic
815	C₃×Q₈	—	4	4	no	—
816	C₃×Q₈	—	4	4	no	—
817	C₃×D₄	—	2	8	no	—
818	C₃×D₄	—	4	4	no	—
819	C₃×D₄	—	4	8	no	—
820	C₃×D₄	—	4	4	no	—
821	C₃×D₄	—	4	8	no	—
822	C₃×D₄	—	4	4	no	—
823	C₃×D₄	—	4	4	no	—
824	C₃×D₄	—	4	8	no	—
825	C₃×D₄	—	4	4	no	—
826	C₃×D₄	—	4	4	no	—
827	C₃×D₄	—	4	8	no	—
828	C₃×D₄	—	4	4	no	—
829	C₃×D₄	—	4	4	no	—
830	C₃×D₄	—	8	4	no	—
831	C₃×D₄	—	8	4	no	—
832	C₃×D₄	—	8	4	no	—
833	C₃×D₄	—	8	4	no	—
834	C₃×D₄	—	8	4	no	—
835	C₂×C₃×C₄	—	2	1	no	—
836	C₂×C₃×C₄	—	2	1	no	—
837	C₂×C₃×C₄	—	2	1	no	—
838	C₂×C₃×C₄	—	2	1	no	—
839	C₂×C₃×C₄	—	2	1	no	—
840	C₂×C₃×C₄	—	2	1	no	—
841	C₂×C₃×C₄	—	2	1	no	—
842	C₂×C₃×C₄	—	2	1	no	—
843	C₂×C₃×C₄	—	2	2	no	—
844	C₂×C₃×C₄	—	2	1	no	—
845	C₂×C₃×C₄	—	2	2	no	—
846	C₂×C₃×C₄	—	2	1	no	—
847	C₂×C₃×C₄	—	2	8	no	—
848	C₂×C₃×C₄	—	2	8	no	—
849	C₂×C₃×C₄	—	2	8	no	—
850	C₂×C₃×C₄	—	2	1	no	—
851	C₂×C₃×C₄	—	2	1	no	—
852	C₂×C₃×C₄	—	2	2	no	—
853	C₂×C₃×C₄	—	2	2	no	—
854	C₂×C₃×C₄	—	2	1	no	—
855	C₂×C₃×C₄	—	2	2	no	—
856	C₂×C₃×C₄	—	2	2	no	—
857	C₂×C₃×C₄	—	2	1	no	—
858	C₂×C₃×C₄	—	2	1	no	—
859	C₂×C₃×C₄	—	2	1	no	—
860	C₂×C₃×C₄	—	2	2	no	—
861	C₂×C₃×C₄	—	2	2	no	—
862	C₂×C₃×C₄	—	2	2	no	—
863	C₂×C₃×C₄	—	2	1	no	—
864	C₂×C₃×C₄	—	2	2	no	—
865	C₂×C₃×C₄	—	2	2	no	—
866	C₂×C₃×C₄	—	2	2	no	—
867	C₂×C₃×C₄	—	2	1	no	—
868	C₂×C₃×C₄	—	2	2	no	—
869	C₂×C₃×C₄	—	2	1	no	—
870	C₂×C₃×C₄	—	2	2	no	—
871	C₂×C₃×C₄	—	2	1	no	—
872	C₂×C₃×C₄	—	2	1	no	—
873	C₂×C₃×C₄	—	2	2	no	—
874	C₂×C₃×C₄	—	2	1	no	—
875	C₂×C₃×C₄	—	2	2	no	—
876	C₂×C₃×C₄	—	2	2	no	—
877	C₂×C₃×C₄	—	4	4	no	—
878	C₂×C₃×C₄	—	4	4	no	—
879	C₂×C₃×C₄	—	4	4	no	—
880	C₂×C₃×C₄	—	4	8	no	—
881	C₂×C₃×C₄	—	4	4	no	—
882	C₂×C₃×C₄	—	4	4	no	—
883	C₂×C₃×C₄	—	8	4	no	—
884	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
885	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
886	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
887	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
888	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
889	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
890	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
891	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
892	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
893	C₂⁴	—	2	2	no	—
894	C₂⁴	—	2	2	no	—
895	C₂⁴	—	2	2	no	—
896	C₂⁴	—	2	4	no	—
897	C₂⁴	—	2	4	no	—
898	C₂⁴	—	4	1	no	—
899	C₂⁴	—	4	1	no	—
900	C₂⁴	—	4	1	no	—
901	C₂⁴	—	4	1	no	—
902	C₂⁴	—	4	2	no	—
903	C₂⁴	—	4	2	no	—
904	C₂⁴	—	4	2	no	—
905	C₂⁴	—	4	2	no	—
906	C₂⁴	—	4	2	no	—
907	C₂⁴	C₂⁴×C₃	1	2	yes	—
908	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
909	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
910	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
911	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
912	C₂⁴	C₂⁴×C₃	1	2	yes	—
913	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
914	#41	—	4	16	no	—
915	#41	—	4	16	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	2	2	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	4	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	4	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	4	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	4	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	4	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	4	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	4	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	4	16	no	—
950	C₂×D₄	—	4	2	no	—
951	C₂×D₄	—	4	1	no	—
952	C₂×D₄	—	4	1	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	4	1	no	—
955	C₂×D₄	—	4	1	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	4	1	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	1	no	—
960	C₂×D₄	—	4	1	no	—
961	C₂×D₄	—	4	1	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	1	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	2	no	—
966	C₂×D₄	—	4	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	4	2	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
975	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
976	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	4	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	4	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	4	no	—
998	C₂²×C₄	—	4	1	no	—
999	C₂²×C₄	—	4	1	no	—
1000	C₂²×C₄	—	4	1	no	—
1001	C₂²×C₄	—	4	2	no	—
1002	C₂²×C₄	—	4	16	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	4	2	no	—
1005	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
1006	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
1007	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
1008	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1011	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
1018	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	4	no	—
1032	C₄⋊C₄	—	2	4	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	4	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	4	2	no	—
1037	C₄⋊C₄	—	4	2	no	—
1038	C₄⋊C₄	—	4	2	no	—
1039	C₄⋊C₄	—	4	2	no	—
1040	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
1041	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
1042	C₂²⋊C₄	—	2	4	no	—
1043	C₂²⋊C₄	—	2	4	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	4	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	2	4	no	—
1050	C₂²⋊C₄	—	2	4	no	—
1051	C₂²⋊C₄	—	2	4	no	—
1052	C₂²⋊C₄	—	2	4	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	4	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	4	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	4	no	—
1062	C₂²⋊C₄	—	2	4	no	—
1063	C₂²⋊C₄	—	2	4	no	—
1064	C₂²⋊C₄	—	4	2	no	—
1065	C₂²⋊C₄	—	4	2	no	—
1066	C₂²⋊C₄	—	4	2	no	—
1067	C₂²⋊C₄	—	4	2	no	—
1068	C₂²⋊C₄	—	4	2	no	—
1069	C₂²⋊C₄	—	4	2	no	—
1070	C₂²⋊C₄	—	4	2	no	—
1071	C₂²⋊C₄	—	4	2	no	—
1072	C₂²⋊C₄	—	4	2	no	—
1073	C₂²⋊C₄	—	4	2	no	—
1074	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1075	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
1076	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1077	C₄²	—	2	4	no	—
1078	C₄²	—	2	2	no	—
1079	C₄²	—	2	4	no	—
1080	C₄²	—	4	2	no	—
1081	C₄²	C₂×C₃×D₄	1	4	yes	—
1082	C₂²×C₃	—	2	2	no	—
1083	C₂²×C₃	—	2	2	no	—
1084	C₂²×C₃	—	2	2	no	—
1085	C₂²×C₃	—	2	2	no	—
1086	C₂²×C₃	—	2	2	no	—
1087	C₂²×C₃	—	2	4	no	—
1088	C₂²×C₃	—	2	2	no	—
1089	C₂²×C₃	—	2	4	no	—
1090	C₂²×C₃	—	2	2	no	—
1091	C₂²×C₃	—	2	2	no	—
1092	C₂²×C₃	—	2	4	no	—
1093	C₂²×C₃	—	2	2	no	—
1094	C₂²×C₃	—	2	2	no	—
1095	C₂²×C₃	—	2	2	no	—
1096	C₂²×C₃	—	2	2	no	—
1097	C₂²×C₃	—	4	16	no	—
1098	C₂²×C₃	—	4	1	no	—
1099	C₂²×C₃	—	4	1	no	—
1100	C₂²×C₃	—	4	2	no	—
1101	C₂²×C₃	—	4	1	no	—
1102	C₂²×C₃	—	4	1	no	—
1103	C₂²×C₃	—	4	1	no	—
1104	C₂²×C₃	—	4	1	no	—
1105	C₂²×C₃	—	4	2	no	—
1106	C₂²×C₃	—	4	1	no	—
1107	C₂²×C₃	—	4	1	no	—
1108	C₂²×C₃	—	4	1	no	—
1109	C₂²×C₃	—	4	1	no	—
1110	C₂²×C₃	—	4	1	no	—
1111	C₂²×C₃	—	4	1	no	—
1112	C₂²×C₃	—	4	2	no	—
1113	C₂²×C₃	—	4	1	no	—
1114	C₂²×C₃	—	4	1	no	—
1115	C₂²×C₃	—	4	1	no	—
1116	C₂²×C₃	—	4	2	no	—
1117	C₂²×C₃	—	4	1	no	—
1118	C₂²×C₃	—	4	1	no	—
1119	C₂²×C₃	—	4	2	no	—
1120	C₂²×C₃	—	4	1	no	—
1121	C₂²×C₃	—	4	2	no	—
1122	C₂²×C₃	—	4	1	no	—
1123	C₂²×C₃	—	4	2	no	—
1124	C₂²×C₃	—	4	1	no	—
1125	C₂²×C₃	—	4	1	no	—
1126	C₂²×C₃	—	4	2	no	—
1127	C₂²×C₃	—	4	2	no	—
1128	C₂²×C₃	—	4	1	no	—
1129	C₂²×C₃	—	4	2	no	—
1130	C₂²×C₃	—	4	2	no	—
1131	C₂²×C₃	—	4	1	no	—
1132	C₂²×C₃	—	8	16	no	—
1133	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1134	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1135	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1136	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1137	C₂²×C₃	#585	1	1	yes	characteristic
1138	C₂²×C₃	#585	1	1	yes	characteristic
1139	C₂²×C₃	#585	1	1	yes	characteristic
1140	C₃×C₄	—	2	2	no	—
1141	C₃×C₄	—	2	2	no	—
1142	C₃×C₄	—	2	2	no	—
1143	C₃×C₄	—	2	2	no	—
1144	C₃×C₄	—	2	4	no	—
1145	C₃×C₄	—	2	2	no	—
1146	C₃×C₄	—	4	1	no	—
1147	C₃×C₄	—	4	1	no	—
1148	C₃×C₄	—	4	1	no	—
1149	C₃×C₄	—	4	2	no	—
1150	C₃×C₄	—	4	2	no	—
1151	C₃×C₄	—	4	1	no	—
1152	C₃×C₄	—	4	2	no	—
1153	C₃×C₄	—	4	2	no	—
1154	C₃×C₄	—	4	2	no	—
1155	C₃×C₄	D₄²	1	4	yes	—
1156	C₂³	—	2	1	no	—
1157	C₂³	—	2	1	no	—
1158	C₂³	—	2	1	no	—
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	1	no	—
1161	C₂³	—	2	2	no	—
1162	C₂³	—	2	1	no	—
1163	C₂³	—	2	1	no	—
1164	C₂³	—	2	1	no	—
1165	C₂³	—	2	2	no	—
1166	C₂³	—	2	1	no	—
1167	C₂³	—	2	1	no	—
1168	C₂³	—	2	1	no	—
1169	C₂³	—	2	1	no	—
1170	C₂³	—	2	2	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	2	1	no	—
1174	C₂³	—	2	1	no	—
1175	C₂³	—	2	1	no	—
1176	C₂³	—	2	1	no	—
1177	C₂³	—	2	1	no	—
1178	C₂³	—	2	1	no	—
1179	C₂³	—	2	2	no	—
1180	C₂³	—	2	1	no	—
1181	C₂³	—	2	1	no	—
1182	C₂³	—	2	1	no	—
1183	C₂³	—	2	1	no	—
1184	C₂³	—	2	1	no	—
1185	C₂³	—	2	1	no	—
1186	C₂³	—	2	2	no	—
1187	C₂³	—	2	1	no	—
1188	C₂³	—	2	2	no	—
1189	C₂³	—	2	1	no	—
1190	C₂³	—	2	1	no	—
1191	C₂³	—	2	1	no	—
1192	C₂³	—	2	2	no	—
1193	C₂³	—	2	2	no	—
1194	C₂³	—	2	2	no	—
1195	C₂³	—	2	1	no	—
1196	C₂³	—	2	1	no	—
1197	C₂³	—	2	1	no	—
1198	C₂³	—	2	2	no	—
1199	C₂³	—	2	2	no	—
1200	C₂³	—	4	4	no	—
1201	C₂³	—	4	4	no	—
1202	C₂³	—	4	4	no	—
1203	C₂³	—	4	8	no	—
1204	C₂³	—	4	4	no	—
1205	C₂³	—	4	4	no	—
1206	C₂³	—	4	4	no	—
1207	C₂³	—	4	8	no	—
1208	C₂³	—	4	4	no	—
1209	C₂³	—	8	4	no	—
1210	C₂³	—	8	4	no	—
1211	C₂³	—	8	4	no	—
1212	C₂³	—	8	4	no	—
1213	C₂³	—	8	4	no	—
1214	C₂³	C₂²×C₃×D₄	1	2	yes	—
1215	C₂³	C₂²×C₃×D₄	1	4	yes	—
1216	C₂³	C₂²×C₃×D₄	1	2	yes	—
1217	C₂³	C₂²×C₃×D₄	1	2	yes	—
1218	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1219	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1220	Q₈	—	4	4	no	—
1221	Q₈	—	4	4	no	—
1222	D₄	—	2	8	no	—
1223	D₄	—	4	4	no	—
1224	D₄	—	4	8	no	—
1225	D₄	—	4	8	no	—
1226	D₄	—	4	4	no	—
1227	D₄	—	4	4	no	—
1228	D₄	—	4	4	no	—
1229	D₄	—	4	4	no	—
1230	D₄	—	4	8	no	—
1231	D₄	—	4	8	no	—
1232	D₄	—	4	4	no	—
1233	D₄	—	4	4	no	—
1234	D₄	—	4	4	no	—
1235	D₄	—	8	4	no	—
1236	D₄	—	8	4	no	—
1237	D₄	—	8	4	no	—
1238	D₄	—	8	4	no	—
1239	D₄	—	8	4	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	8	no	—
1253	C₂×C₄	—	2	8	no	—
1254	C₂×C₄	—	2	8	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	2	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	2	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	2	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	2	no	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	2	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	2	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	2	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	2	no	—
1281	C₂×C₄	—	2	2	no	—
1282	C₂×C₄	—	4	4	no	—
1283	C₂×C₄	—	4	4	no	—
1284	C₂×C₄	—	4	4	no	—
1285	C₂×C₄	—	4	8	no	—
1286	C₂×C₄	—	4	4	no	—
1287	C₂×C₄	—	4	4	no	—
1288	C₂×C₄	—	8	4	no	—
1289	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1290	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1291	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1292	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1293	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1294	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1295	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1296	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1297	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1298	C₂×C₃	—	4	2	no	—
1299	C₂×C₃	—	4	2	no	—
1300	C₂×C₃	—	4	2	no	—
1301	C₂×C₃	—	4	4	no	—
1302	C₂×C₃	—	4	2	no	—
1303	C₂×C₃	—	8	1	no	—
1304	C₂×C₃	—	8	2	no	—
1305	C₂×C₃	#3449	1	1	yes	characteristic
1306	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
1307	C₂×C₃	#3485	1	1	yes	characteristic
1308	C₂×C₃	#3488	1	1	yes	characteristic
1309	C₂×C₃	#3488	1	1	yes	characteristic
1310	C₂×C₃	#3540	1	1	yes	characteristic
1311	C₂×C₃	#3542	1	1	yes	characteristic
1312	C₂²	—	2	2	no	—
1313	C₂²	—	2	2	no	—
1314	C₂²	—	2	2	no	—
1315	C₂²	—	2	2	no	—
1316	C₂²	—	2	2	no	—
1317	C₂²	—	2	4	no	—
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	4	no	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	4	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	2	2	no	—
1326	C₂²	—	2	2	no	—
1327	C₂²	—	4	16	no	—
1328	C₂²	—	4	1	no	—
1329	C₂²	—	4	1	no	—
1330	C₂²	—	4	2	no	—
1331	C₂²	—	4	1	no	—
1332	C₂²	—	4	1	no	—
1333	C₂²	—	4	1	no	—
1334	C₂²	—	4	1	no	—
1335	C₂²	—	4	2	no	—
1336	C₂²	—	4	1	no	—
1337	C₂²	—	4	1	no	—
1338	C₂²	—	4	1	no	—
1339	C₂²	—	4	1	no	—
1340	C₂²	—	4	1	no	—
1341	C₂²	—	4	1	no	—
1342	C₂²	—	4	1	no	—
1343	C₂²	—	4	2	no	—
1344	C₂²	—	4	1	no	—
1345	C₂²	—	4	1	no	—
1346	C₂²	—	4	1	no	—
1347	C₂²	—	4	2	no	—
1348	C₂²	—	4	1	no	—
1349	C₂²	—	4	2	no	—
1350	C₂²	—	4	1	no	—
1351	C₂²	—	4	2	no	—
1352	C₂²	—	4	1	no	—
1353	C₂²	—	4	2	no	—
1354	C₂²	—	4	1	no	—
1355	C₂²	—	4	1	no	—
1356	C₂²	—	4	2	no	—
1357	C₂²	—	4	2	no	—
1358	C₂²	—	4	2	no	—
1359	C₂²	—	4	1	no	—
1360	C₂²	—	4	2	no	—
1361	C₂²	—	4	1	no	—
1362	C₂²	—	8	16	no	—
1363	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1364	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1365	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1366	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1367	C₂²	C₃×#585	1	1	yes	characteristic
1368	C₂²	C₃×#585	1	1	yes	characteristic
1369	C₂²	C₃×#585	1	1	yes	characteristic
1370	C₄	—	2	2	no	—
1371	C₄	—	2	2	no	—
1372	C₄	—	2	2	no	—
1373	C₄	—	2	2	no	—
1374	C₄	—	2	4	no	—
1375	C₄	—	2	2	no	—
1376	C₄	—	4	1	no	—
1377	C₄	—	4	1	no	—
1378	C₄	—	4	1	no	—
1379	C₄	—	4	2	no	—
1380	C₄	—	4	2	no	—
1381	C₄	—	4	1	no	—
1382	C₄	—	4	2	no	—
1383	C₄	—	4	2	no	—
1384	C₄	—	4	2	no	—
1385	C₄	C₃×D₄²	1	4	yes	—
1386	C₃	#37658	1	1	yes	characteristic, direct product factor, Sylow
1387	C₂	—	4	2	no	—
1388	C₂	—	4	2	no	—
1389	C₂	—	4	2	no	—
1390	C₂	—	4	2	no	—
1391	C₂	—	4	4	no	—
1392	C₂	—	8	2	no	—
1393	C₂	—	8	1	no	—
1394	C₂	C₃×#3449	1	1	yes	characteristic
1395	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
1396	C₂	C₃×#3485	1	1	yes	characteristic
1397	C₂	C₃×#3488	1	1	yes	characteristic
1398	C₂	C₃×#3488	1	1	yes	characteristic
1399	C₂	C₃×#3540	1	1	yes	characteristic
1400	C₂	C₃×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#546	C₂	semidirect
2. C₂×C₃×#535	C₂	semidirect
3. C₂×C₃×#525	C₂	semidirect
4. C₂×C₃×#525	C₂	semidirect
5. C₃×#2847	C₂	semidirect
6. C₃×#2679	C₂	semidirect
7. C₃×#2678	C₂	semidirect
8. C₃×#2672	C₂	semidirect
9. C₃×#2669	C₂	semidirect
10. C₃×#2620	C₂	semidirect
11. C₃×#2616	C₂	semidirect
12. C₃×#2540	C₂	semidirect
13. C₃×#2537	C₂	semidirect
14. C₃×#2461	C₂	semidirect
15. C₃×#2445	C₂	semidirect
16. C₃×#2424	C₂	semidirect
17. C₃×#2418	C₂	semidirect
18. C₃×#2415	C₂	semidirect
19. C₃×#2414	C₂	semidirect
20. C₃×#2408	C₂	semidirect
21. C₃×#2407	C₂	semidirect
22. C₃×#2354	C₂	semidirect
23. C₃×#2324	C₂	semidirect
24. #37658	C₃	direct (N × H)
27. C₂³×C₃×D₄	C₂²	semidirect
28. C₂⁴×C₃×C₄	C₂²	semidirect
32. C₂×C₃×#124	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
37. C₂×C₃×#123	C₂²	semidirect
38. C₂×C₃×#123	C₂²	semidirect
39. C₂×C₃×#123	C₂²	semidirect
40. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₃×#121	C₂²	semidirect
55. C₂×C₃×#121	C₂²	semidirect
56. C₂×C₃×#121	C₂²	semidirect
61. C₂×C₃×#120	C₂²	semidirect
62. C₂×C₃×#120	C₂²	semidirect
63. C₂×C₃×#120	C₂²	semidirect
64. C₂×C₃×#120	C₂²	semidirect
67. C₂×C₃×C₄×D₄	C₂²	semidirect
68. C₂×C₃×C₄×D₄	C₂²	semidirect
69. C₂×C₃×C₄×D₄	C₂²	semidirect
70. C₂×C₃×C₄×D₄	C₂²	semidirect
71. C₂×C₃×C₄×D₄	C₂²	semidirect
72. C₂×C₃×#117	C₂²	semidirect
73. C₂×C₃×#117	C₂²	semidirect
74. C₂×C₃×#117	C₂²	semidirect
75. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
76. C₃×#399	C₂²	semidirect
77. C₃×#397	C₂²	semidirect
78. C₃×#396	C₂²	semidirect
79. C₃×#396	C₂²	semidirect
80. C₃×#395	C₂²	semidirect
83. C₃×#394	C₂²	semidirect
84. C₃×#394	C₂²	semidirect
85. C₃×#394	C₂²	semidirect
86. C₃×#394	C₂²	semidirect
87. C₃×#394	C₂²	semidirect
88. C₃×#394	C₂²	semidirect
89. C₃×#394	C₂²	semidirect
90. C₃×#394	C₂²	semidirect
91. C₃×#394	C₂²	semidirect
93. C₃×#392	C₂²	semidirect
94. C₃×#392	C₂²	semidirect
95. C₃×#392	C₂²	semidirect
96. C₃×#391	C₂²	semidirect
98. C₃×#390	C₂²	semidirect
99. C₃×#390	C₂²	semidirect
100. C₃×#390	C₂²	semidirect
101. C₃×#390	C₂²	semidirect
102. C₃×#390	C₂²	semidirect
103. C₃×#390	C₂²	semidirect
104. C₃×#389	C₂²	semidirect
105. C₃×#389	C₂²	semidirect
106. C₃×#388	C₂²	semidirect
107. C₃×#388	C₂²	semidirect
108. C₃×#388	C₂²	semidirect
109. C₃×#388	C₂²	semidirect
110. C₃×#388	C₂²	semidirect
111. C₃×#386	C₂²	semidirect
112. C₃×#386	C₂²	semidirect
113. C₃×#386	C₂²	semidirect
114. C₃×#386	C₂²	semidirect
115. C₃×#386	C₂²	semidirect
116. C₃×#385	C₂²	semidirect
117. C₃×#385	C₂²	semidirect
118. C₃×#384	C₂²	semidirect
119. C₃×#380	C₂²	semidirect
120. C₃×#380	C₂²	semidirect
121. C₃×#380	C₂²	semidirect
122. C₃×#380	C₂²	semidirect
123. C₃×#380	C₂²	semidirect
124. C₃×#380	C₂²	semidirect
125. C₃×#379	C₂²	semidirect
126. C₃×C₄×C₄⋊C₄	C₂²	semidirect
127. C₃×C₄×C₄⋊C₄	C₂²	semidirect
128. C₂×#546	C₂×C₃	semidirect
129. C₂×#535	C₂×C₃	semidirect
130. C₂×#525	C₂×C₃	semidirect
131. C₂×#525	C₂×C₃	semidirect
132. #2847	C₂×C₃	semidirect
133. #2679	C₂×C₃	semidirect
134. #2678	C₂×C₃	semidirect
135. #2672	C₂×C₃	semidirect
136. #2669	C₂×C₃	semidirect
137. #2620	C₂×C₃	semidirect
138. #2616	C₂×C₃	semidirect
139. #2540	C₂×C₃	semidirect
140. #2537	C₂×C₃	semidirect
141. #2461	C₂×C₃	semidirect
142. #2445	C₂×C₃	semidirect
143. #2424	C₂×C₃	semidirect
144. #2418	C₂×C₃	semidirect
145. #2415	C₂×C₃	semidirect
146. #2414	C₂×C₃	semidirect
147. #2408	C₂×C₃	semidirect
148. #2407	C₂×C₃	semidirect
149. #2354	C₂×C₃	semidirect
150. #2324	C₂×C₃	semidirect
218. C₃×#121	D₄	semidirect
233. C₃×C₄×D₄	D₄	semidirect
307. C₂³×D₄	C₂²×C₃	semidirect
308. C₂⁴×C₄	C₂²×C₃	semidirect
312. C₂×#124	C₂²×C₃	semidirect
313. C₂×#124	C₂²×C₃	semidirect
317. C₂×#123	C₂²×C₃	semidirect
318. C₂×#123	C₂²×C₃	semidirect
319. C₂×#123	C₂²×C₃	semidirect
320. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
321. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
322. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
323. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
324. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
334. C₂×#121	C₂²×C₃	semidirect
335. C₂×#121	C₂²×C₃	semidirect
336. C₂×#121	C₂²×C₃	semidirect
341. C₂×#120	C₂²×C₃	semidirect
342. C₂×#120	C₂²×C₃	semidirect
343. C₂×#120	C₂²×C₃	semidirect
344. C₂×#120	C₂²×C₃	semidirect
347. C₂×C₄×D₄	C₂²×C₃	semidirect
348. C₂×C₄×D₄	C₂²×C₃	semidirect
349. C₂×C₄×D₄	C₂²×C₃	semidirect
350. C₂×C₄×D₄	C₂²×C₃	semidirect
351. C₂×C₄×D₄	C₂²×C₃	semidirect
352. C₂×#117	C₂²×C₃	semidirect
353. C₂×#117	C₂²×C₃	semidirect
354. C₂×#117	C₂²×C₃	semidirect
355. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
356. #399	C₂²×C₃	semidirect
357. #397	C₂²×C₃	semidirect
358. #396	C₂²×C₃	semidirect
359. #396	C₂²×C₃	semidirect
360. #395	C₂²×C₃	semidirect
363. #394	C₂²×C₃	semidirect
364. #394	C₂²×C₃	semidirect
365. #394	C₂²×C₃	semidirect
366. #394	C₂²×C₃	semidirect
367. #394	C₂²×C₃	semidirect
368. #394	C₂²×C₃	semidirect
369. #394	C₂²×C₃	semidirect
370. #394	C₂²×C₃	semidirect
371. #394	C₂²×C₃	semidirect
373. #392	C₂²×C₃	semidirect
374. #392	C₂²×C₃	semidirect
375. #392	C₂²×C₃	semidirect
376. #391	C₂²×C₃	semidirect
378. #390	C₂²×C₃	semidirect
379. #390	C₂²×C₃	semidirect
380. #390	C₂²×C₃	semidirect
381. #390	C₂²×C₃	semidirect
382. #390	C₂²×C₃	semidirect
383. #390	C₂²×C₃	semidirect
384. #389	C₂²×C₃	semidirect
385. #389	C₂²×C₃	semidirect
386. #388	C₂²×C₃	semidirect
387. #388	C₂²×C₃	semidirect
388. #388	C₂²×C₃	semidirect
389. #388	C₂²×C₃	semidirect
390. #388	C₂²×C₃	semidirect
391. #386	C₂²×C₃	semidirect
392. #386	C₂²×C₃	semidirect
393. #386	C₂²×C₃	semidirect
394. #386	C₂²×C₃	semidirect
395. #386	C₂²×C₃	semidirect
396. #385	C₂²×C₃	semidirect
397. #385	C₂²×C₃	semidirect
398. #384	C₂²×C₃	semidirect
399. #380	C₂²×C₃	semidirect
400. #380	C₂²×C₃	semidirect
401. #380	C₂²×C₃	semidirect
402. #380	C₂²×C₃	semidirect
403. #380	C₂²×C₃	semidirect
404. #380	C₂²×C₃	semidirect
405. #379	C₂²×C₃	semidirect
406. C₄×C₄⋊C₄	C₂²×C₃	semidirect
407. C₄×C₄⋊C₄	C₂²×C₃	semidirect
664. #121	C₃×D₄	semidirect
679. C₄×D₄	C₃×D₄	semidirect
1386. C₃	#37658	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×#535	2
C₂×C₃×#525	2
C₃×#2847	2
C₃×#2679	2
C₃×#2678	2
C₃×#2672	2
C₃×#2669	2
C₃×#2620	2
C₃×#2616	2
C₃×#2540	2
C₃×#2537	2
C₃×#2461	2
C₃×#2445	2
C₃×#2424	2
C₃×#2418	2
C₃×#2415	2
C₃×#2414	2
C₃×#2408	2
C₃×#2407	2
C₃×#2354	2
C₃×#2324	2
#37658	3

Subgroups — C3×#37658 #10656265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37658 #10656265