Subgroups — C₃×#37654 #10656261

Order 768.

3250 conjugacy classes of subgroups.

The subgroup lattice has 1300 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×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2680	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×#2671	C₂	1	2	yes	maximal, complemented
10	C₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2613	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2464	C₂	1	2	yes	maximal, complemented
15	C₃×#2455	C₂	1	2	yes	maximal, complemented
16	C₃×#2422	C₂	1	2	yes	maximal, complemented
17	C₃×#2418	C₂	1	2	yes	maximal, complemented
18	C₃×#2413	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2412	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2405	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
24	#37654	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×#546	—	2	8	no	—
30	C₃×#534	—	2	8	no	—
31	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₃×#525	—	2	8	no	—
33	C₂×C₃×#123	—	2	8	no	—
34	C₂×C₃×#123	C₂²	1	2	yes	—
35	C₂×C₃×#123	C₂²	1	2	yes	—
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×#123	C₂²	1	1	yes	characteristic
38	C₂×C₃×#123	C₂²	1	1	yes	characteristic
39	C₂×C₃×#123	C₂²	1	2	yes	—
40	C₂×C₃×#123	C₂²	1	1	yes	characteristic
41	C₂×C₃×#123	C₂²	1	1	yes	characteristic
42	C₂×C₃×#123	C₂²	1	2	yes	complemented
43	C₂×C₃×#123	C₂²	1	2	yes	complemented
44	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#121	C₂²	1	1	yes	characteristic
50	C₂×C₃×#121	C₂²	1	2	yes	—
51	C₂×C₃×#121	C₂²	1	2	yes	—
52	C₂×C₃×#121	C₂²	1	2	yes	complemented
53	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#120	C₂²	1	1	yes	characteristic
56	C₂×C₃×#120	C₂²	1	2	yes	—
57	C₂×C₃×#120	C₂²	1	1	yes	characteristic
58	C₂×C₃×#120	C₂²	1	1	yes	characteristic
59	C₂×C₃×#120	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×#120	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
63	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
64	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₃×#399	C₂²	1	2	yes	complemented
74	C₃×#399	C₂²	1	2	yes	complemented
75	C₃×#398	C₂²	1	2	yes	complemented
76	C₃×#398	C₂²	1	2	yes	complemented
77	C₃×#397	C₂²	1	2	yes	complemented
78	C₃×#397	C₂²	1	2	yes	complemented
79	C₃×#397	C₂²	1	2	yes	complemented
80	C₃×#396	C₂²	1	2	yes	complemented
81	C₃×#395	C₂²	1	2	yes	complemented
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×#392	C₂²	1	2	yes	—
91	C₃×#392	C₂²	1	2	yes	complemented
92	C₃×#392	C₂²	1	2	yes	complemented
93	C₃×#390	C₂²	1	2	yes	complemented
94	C₃×#390	C₂²	1	2	yes	complemented
95	C₃×#389	C₂²	1	2	yes	complemented
96	C₃×#389	C₂²	1	2	yes	complemented
97	C₃×#388	C₂²	1	2	yes	complemented
98	C₃×#388	C₂²	1	2	yes	complemented
99	C₃×#388	C₂²	1	2	yes	complemented
100	C₃×#388	C₂²	1	2	yes	complemented
101	C₃×#388	C₂²	1	2	yes	complemented
102	C₃×#386	C₂²	1	1	yes	characteristic
103	C₃×#386	C₂²	1	1	yes	characteristic
104	C₃×#386	C₂²	1	1	yes	characteristic, complemented
105	C₃×#386	C₂²	1	2	yes	complemented
106	C₃×#386	C₂²	1	2	yes	complemented
107	C₃×#386	C₂²	1	2	yes	complemented
108	C₃×#386	C₂²	1	2	yes	complemented
109	C₃×#385	C₂²	1	2	yes	complemented
110	C₃×#385	C₂²	1	2	yes	complemented
111	C₃×#385	C₂²	1	2	yes	complemented
112	C₃×#385	C₂²	1	1	yes	characteristic, complemented
113	C₃×#385	C₂²	1	2	yes	complemented
114	C₃×#385	C₂²	1	2	yes	complemented
115	C₃×#385	C₂²	1	2	yes	complemented
116	C₃×#384	C₂²	1	2	yes	complemented
117	C₃×#381	C₂²	1	1	yes	characteristic, complemented
118	C₃×#381	C₂²	1	1	yes	characteristic, complemented
119	C₃×#381	C₂²	1	1	yes	characteristic, complemented
120	C₃×#380	C₂²	1	1	yes	characteristic, complemented
121	C₃×#380	C₂²	1	2	yes	complemented
122	C₃×#380	C₂²	1	2	yes	complemented
123	C₃×#379	C₂²	1	1	yes	characteristic
124	C₃×#379	C₂²	1	2	yes	complemented
125	C₃×#379	C₂²	1	1	yes	characteristic, complemented
126	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
127	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
129	C₂×#534	C₂×C₃	1	1	yes	characteristic, complemented
130	C₂×#525	C₂×C₃	1	1	yes	characteristic, complemented
131	C₂²×#123	C₂×C₃	1	1	yes	characteristic, complemented
132	#2849	C₂×C₃	1	1	yes	characteristic, complemented
133	#2680	C₂×C₃	1	2	yes	complemented
134	#2678	C₂×C₃	1	2	yes	complemented
135	#2672	C₂×C₃	1	2	yes	complemented
136	#2671	C₂×C₃	1	2	yes	complemented
137	#2617	C₂×C₃	1	1	yes	characteristic, complemented
138	#2613	C₂×C₃	1	1	yes	characteristic, complemented
139	#2501	C₂×C₃	1	1	yes	characteristic, complemented
140	#2486	C₂×C₃	1	1	yes	characteristic, complemented
141	#2464	C₂×C₃	1	2	yes	complemented
142	#2455	C₂×C₃	1	2	yes	complemented
143	#2422	C₂×C₃	1	2	yes	complemented
144	#2418	C₂×C₃	1	2	yes	complemented
145	#2413	C₂×C₃	1	1	yes	characteristic, complemented
146	#2412	C₂×C₃	1	1	yes	characteristic, complemented
147	#2406	C₂×C₃	1	1	yes	characteristic, complemented
148	#2405	C₂×C₃	1	1	yes	characteristic, complemented
149	#2342	C₂×C₃	1	1	yes	characteristic, complemented
150	#2321	C₂×C₃	1	1	yes	characteristic, complemented
151	C₂⁵×C₃	C₂³	1	1	yes	characteristic
152	C₂⁵×C₃	C₂³	1	1	yes	characteristic
153	C₂⁵×C₃	C₂³	1	1	yes	characteristic
154	C₂×C₃×#41	—	2	4	no	—
155	C₂×C₃×#41	—	2	4	no	—
156	C₂×C₃×#41	—	4	2	no	—
157	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	—	2	4	no	—
159	C₂²×C₃×D₄	—	2	4	no	—
160	C₂²×C₃×D₄	—	2	4	no	—
161	C₂²×C₃×D₄	—	2	4	no	—
162	C₂²×C₃×D₄	—	4	2	no	—
163	C₂²×C₃×D₄	—	4	2	no	—
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃×D₄	C₂³	1	2	yes	—
167	C₂²×C₃×D₄	C₂³	1	2	yes	—
168	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
171	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
172	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂³	1	2	yes	—
174	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
175	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃×D₄	C₂³	1	2	yes	—
177	C₂²×C₃×D₄	C₂³	1	2	yes	—
178	C₂³×C₃×C₄	—	2	4	no	—
179	C₂³×C₃×C₄	—	2	4	no	—
180	C₂³×C₃×C₄	—	4	2	no	—
181	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
182	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
183	C₂³×C₃×C₄	C₂³	1	2	yes	—
184	C₂³×C₃×C₄	C₂³	1	2	yes	—
185	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
186	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
188	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
189	C₂³×C₃×C₄	C₂³	1	2	yes	—
190	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
191	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
192	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
193	C₃×#124	—	2	4	no	—
194	C₃×#123	—	2	4	no	—
195	C₃×#123	—	2	4	no	—
196	C₃×#123	—	2	4	no	—
197	C₃×#123	—	2	8	no	—
198	C₃×#123	—	2	8	no	—
199	C₃×#123	—	2	8	no	—
200	C₃×#123	—	2	8	no	—
201	C₃×#123	—	2	8	no	—
202	C₃×#123	—	2	4	no	—
203	C₃×#123	—	2	4	no	—
204	C₃×#123	—	2	4	no	—
205	C₃×#123	—	4	2	no	—
206	C₃×#123	—	4	2	no	—
207	C₃×C₂²⋊Q₈	—	2	8	no	—
208	C₃×C₂²⋊Q₈	—	2	4	no	—
209	C₃×#121	—	2	8	no	—
210	C₃×#121	—	2	8	no	—
211	C₃×#121	—	2	4	no	—
212	C₃×#121	—	2	8	no	—
213	C₃×#121	—	2	4	no	—
214	C₃×#121	—	2	4	no	—
215	C₃×#120	—	2	4	no	—
216	C₃×#120	—	2	4	no	—
217	C₃×#120	—	2	4	no	—
218	C₃×#120	—	2	8	no	—
219	C₃×#120	—	2	4	no	—
220	C₃×#120	D₄	1	8	yes	complemented
221	C₃×C₄×D₄	—	2	8	no	—
222	C₃×C₄×D₄	—	2	4	no	—
223	C₃×C₄×D₄	—	2	8	no	—
224	C₃×C₄×D₄	—	2	4	no	—
225	C₃×#117	—	2	4	no	—
226	C₂×C₃×C₄⋊C₄	—	2	4	no	—
227	C₂×C₃×C₄⋊C₄	—	2	4	no	—
228	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₃×C₂²⋊C₄	D₄	1	8	yes	complemented
250	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	C₂³	1	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	1	yes	characteristic
261	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
263	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
264	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
273	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
275	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₃×C₄²	C₂³	1	2	yes	—
288	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₃×C₄²	C₂³	1	2	yes	—
290	C₃×#95	C₂³	1	2	yes	—
291	C₃×#95	C₂³	1	2	yes	—
292	C₃×#95	C₂³	1	2	yes	—
293	C₃×#95	C₂³	1	2	yes	—
294	C₃×#95	C₂³	1	2	yes	—
295	C₃×#95	C₂³	1	2	yes	—
296	C₃×#95	C₂³	1	2	yes	—
297	C₃×#95	C₂³	1	2	yes	—
298	C₃×#95	C₂³	1	2	yes	—
299	C₃×#95	C₂³	1	2	yes	—
300	C₃×#95	C₂³	1	2	yes	—
301	C₃×#95	C₂³	1	2	yes	—
302	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
303	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
304	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
306	#546	—	2	8	no	—
307	#534	—	2	8	no	—
308	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
309	#525	—	2	8	no	—
310	C₂×#123	—	2	8	no	—
311	C₂×#123	C₂²×C₃	1	1	yes	characteristic
312	C₂×#123	C₂²×C₃	1	1	yes	characteristic
313	C₂×#123	C₂²×C₃	1	1	yes	characteristic
314	C₂×#123	C₂²×C₃	1	2	yes	—
315	C₂×#123	C₂²×C₃	1	2	yes	—
316	C₂×#123	C₂²×C₃	1	1	yes	characteristic
317	C₂×#123	C₂²×C₃	1	2	yes	—
318	C₂×#123	C₂²×C₃	1	1	yes	characteristic
319	C₂×#123	C₂²×C₃	1	2	yes	complemented
320	C₂×#123	C₂²×C₃	1	2	yes	complemented
321	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	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	2	yes	—
328	C₂×#121	C₂²×C₃	1	2	yes	—
329	C₂×#121	C₂²×C₃	1	2	yes	complemented
330	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
331	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
332	C₂×#120	C₂²×C₃	1	1	yes	characteristic
333	C₂×#120	C₂²×C₃	1	1	yes	characteristic
334	C₂×#120	C₂²×C₃	1	2	yes	—
335	C₂×#120	C₂²×C₃	1	1	yes	characteristic
336	C₂×#120	C₂²×C₃	1	1	yes	characteristic, complemented
337	C₂×#120	C₂²×C₃	1	1	yes	characteristic, complemented
338	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
340	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
341	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
342	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
343	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
344	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
345	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
350	#399	C₂²×C₃	1	2	yes	complemented
351	#399	C₂²×C₃	1	2	yes	complemented
352	#398	C₂²×C₃	1	2	yes	complemented
353	#398	C₂²×C₃	1	2	yes	complemented
354	#397	C₂²×C₃	1	2	yes	complemented
355	#397	C₂²×C₃	1	2	yes	complemented
356	#397	C₂²×C₃	1	2	yes	complemented
357	#396	C₂²×C₃	1	2	yes	complemented
358	#395	C₂²×C₃	1	2	yes	complemented
359	#394	C₂²×C₃	1	2	yes	—
360	#394	C₂²×C₃	1	2	yes	complemented
361	#394	C₂²×C₃	1	2	yes	complemented
362	#394	C₂²×C₃	1	2	yes	complemented
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	#392	C₂²×C₃	1	2	yes	—
368	#392	C₂²×C₃	1	2	yes	complemented
369	#392	C₂²×C₃	1	2	yes	complemented
370	#390	C₂²×C₃	1	2	yes	complemented
371	#390	C₂²×C₃	1	2	yes	complemented
372	#389	C₂²×C₃	1	2	yes	complemented
373	#389	C₂²×C₃	1	2	yes	complemented
374	#388	C₂²×C₃	1	2	yes	complemented
375	#388	C₂²×C₃	1	2	yes	complemented
376	#388	C₂²×C₃	1	2	yes	complemented
377	#388	C₂²×C₃	1	2	yes	complemented
378	#388	C₂²×C₃	1	2	yes	complemented
379	#386	C₂²×C₃	1	1	yes	characteristic
380	#386	C₂²×C₃	1	1	yes	characteristic
381	#386	C₂²×C₃	1	2	yes	complemented
382	#386	C₂²×C₃	1	2	yes	complemented
383	#386	C₂²×C₃	1	2	yes	complemented
384	#386	C₂²×C₃	1	1	yes	characteristic, complemented
385	#386	C₂²×C₃	1	2	yes	complemented
386	#385	C₂²×C₃	1	1	yes	characteristic, complemented
387	#385	C₂²×C₃	1	2	yes	complemented
388	#385	C₂²×C₃	1	2	yes	complemented
389	#385	C₂²×C₃	1	2	yes	complemented
390	#385	C₂²×C₃	1	2	yes	complemented
391	#385	C₂²×C₃	1	2	yes	complemented
392	#385	C₂²×C₃	1	2	yes	complemented
393	#384	C₂²×C₃	1	2	yes	complemented
394	#381	C₂²×C₃	1	1	yes	characteristic, complemented
395	#381	C₂²×C₃	1	1	yes	characteristic, complemented
396	#381	C₂²×C₃	1	1	yes	characteristic, complemented
397	#380	C₂²×C₃	1	1	yes	characteristic, complemented
398	#380	C₂²×C₃	1	2	yes	complemented
399	#380	C₂²×C₃	1	2	yes	complemented
400	#379	C₂²×C₃	1	1	yes	characteristic
401	#379	C₂²×C₃	1	1	yes	characteristic, complemented
402	#379	C₂²×C₃	1	2	yes	complemented
403	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
404	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
405	C₂⁴×C₃	—	2	2	no	—
406	C₂⁴×C₃	—	2	2	no	—
407	C₂⁴×C₃	—	2	2	no	—
408	C₂⁴×C₃	—	2	2	no	—
409	C₂⁴×C₃	—	2	2	no	—
410	C₂⁴×C₃	—	2	2	no	—
411	C₂⁴×C₃	—	4	2	no	—
412	C₂⁴×C₃	—	4	2	no	—
413	C₂⁴×C₃	—	4	2	no	—
414	C₂⁴×C₃	—	4	2	no	—
415	C₂⁴×C₃	—	4	2	no	—
416	C₂⁴×C₃	—	4	1	no	—
417	C₂⁴×C₃	—	4	2	no	—
418	C₂⁴×C₃	C₂×D₄	1	4	yes	—
419	C₂⁴×C₃	C₂×D₄	1	4	yes	—
420	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
421	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
422	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
423	C₂⁴×C₃	C₂⁴	1	2	yes	—
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	C₃×#41	—	4	16	no	—
428	C₂×C₃×Q₈	—	2	2	no	—
429	C₂×C₃×Q₈	—	2	2	no	—
430	C₂×C₃×Q₈	—	4	1	no	—
431	C₂×C₃×D₄	—	2	2	no	—
432	C₂×C₃×D₄	—	2	2	no	—
433	C₂×C₃×D₄	—	2	2	no	—
434	C₂×C₃×D₄	—	2	4	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	2	no	—
439	C₂×C₃×D₄	—	2	2	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	2	no	—
444	C₂×C₃×D₄	—	2	2	no	—
445	C₂×C₃×D₄	—	2	4	no	—
446	C₂×C₃×D₄	—	2	4	no	—
447	C₂×C₃×D₄	—	2	2	no	—
448	C₂×C₃×D₄	—	2	2	no	—
449	C₂×C₃×D₄	—	2	4	no	—
450	C₂×C₃×D₄	—	2	2	no	—
451	C₂×C₃×D₄	—	2	2	no	—
452	C₂×C₃×D₄	—	2	2	no	—
453	C₂×C₃×D₄	—	2	2	no	—
454	C₂×C₃×D₄	—	4	1	no	—
455	C₂×C₃×D₄	—	4	2	no	—
456	C₂×C₃×D₄	—	4	2	no	—
457	C₂×C₃×D₄	—	4	1	no	—
458	C₂×C₃×D₄	—	4	2	no	—
459	C₂×C₃×D₄	—	4	2	no	—
460	C₂×C₃×D₄	—	4	2	no	—
461	C₂×C₃×D₄	—	4	2	no	—
462	C₂×C₃×D₄	—	4	2	no	—
463	C₂×C₃×D₄	—	4	1	no	—
464	C₂×C₃×D₄	—	4	2	no	—
465	C₂×C₃×D₄	—	4	2	no	—
466	C₂×C₃×D₄	—	4	2	no	—
467	C₂×C₃×D₄	—	4	2	no	—
468	C₂×C₃×D₄	—	4	16	no	—
469	C₂×C₃×D₄	—	4	16	no	—
470	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
471	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
472	C₂²×C₃×C₄	—	2	2	no	—
473	C₂²×C₃×C₄	—	2	2	no	—
474	C₂²×C₃×C₄	—	2	2	no	—
475	C₂²×C₃×C₄	—	2	2	no	—
476	C₂²×C₃×C₄	—	2	2	no	—
477	C₂²×C₃×C₄	—	2	4	no	—
478	C₂²×C₃×C₄	—	2	2	no	—
479	C₂²×C₃×C₄	—	2	2	no	—
480	C₂²×C₃×C₄	—	2	4	no	—
481	C₂²×C₃×C₄	—	2	2	no	—
482	C₂²×C₃×C₄	—	2	2	no	—
483	C₂²×C₃×C₄	—	2	2	no	—
484	C₂²×C₃×C₄	—	2	2	no	—
485	C₂²×C₃×C₄	—	2	2	no	—
486	C₂²×C₃×C₄	—	2	2	no	—
487	C₂²×C₃×C₄	—	2	2	no	—
488	C₂²×C₃×C₄	—	2	4	no	—
489	C₂²×C₃×C₄	—	2	4	no	—
490	C₂²×C₃×C₄	—	2	2	no	—
491	C₂²×C₃×C₄	—	2	2	no	—
492	C₂²×C₃×C₄	—	2	4	no	—
493	C₂²×C₃×C₄	—	4	2	no	—
494	C₂²×C₃×C₄	—	4	2	no	—
495	C₂²×C₃×C₄	—	4	2	no	—
496	C₂²×C₃×C₄	—	4	2	no	—
497	C₂²×C₃×C₄	—	4	1	no	—
498	C₂²×C₃×C₄	—	4	1	no	—
499	C₂²×C₃×C₄	—	4	1	no	—
500	C₂²×C₃×C₄	—	4	2	no	—
501	C₂²×C₃×C₄	—	4	2	no	—
502	C₂²×C₃×C₄	—	4	2	no	—
503	C₂²×C₃×C₄	—	4	16	no	—
504	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
505	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
506	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
507	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
508	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
509	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
510	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
511	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
512	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
513	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
514	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
515	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
516	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
517	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
518	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
519	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
520	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
521	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
522	C₃×C₄⋊C₄	—	2	4	no	—
523	C₃×C₄⋊C₄	—	2	4	no	—
524	C₃×C₄⋊C₄	—	2	4	no	—
525	C₃×C₄⋊C₄	—	2	4	no	—
526	C₃×C₄⋊C₄	—	2	4	no	—
527	C₃×C₄⋊C₄	—	2	2	no	—
528	C₃×C₄⋊C₄	—	2	4	no	—
529	C₃×C₄⋊C₄	—	2	4	no	—
530	C₃×C₄⋊C₄	—	2	2	no	—
531	C₃×C₄⋊C₄	—	2	2	no	—
532	C₃×C₄⋊C₄	—	2	2	no	—
533	C₃×C₄⋊C₄	—	2	4	no	—
534	C₃×C₄⋊C₄	—	2	4	no	—
535	C₃×C₄⋊C₄	—	4	2	no	—
536	C₃×C₄⋊C₄	—	4	2	no	—
537	C₃×C₄⋊C₄	—	4	2	no	—
538	C₃×C₄⋊C₄	—	4	2	no	—
539	C₃×C₂²⋊C₄	—	2	2	no	—
540	C₃×C₂²⋊C₄	—	2	2	no	—
541	C₃×C₂²⋊C₄	—	2	4	no	—
542	C₃×C₂²⋊C₄	—	2	4	no	—
543	C₃×C₂²⋊C₄	—	2	2	no	—
544	C₃×C₂²⋊C₄	—	2	4	no	—
545	C₃×C₂²⋊C₄	—	2	2	no	—
546	C₃×C₂²⋊C₄	—	2	4	no	—
547	C₃×C₂²⋊C₄	—	2	4	no	—
548	C₃×C₂²⋊C₄	—	2	4	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	2	no	—
551	C₃×C₂²⋊C₄	—	2	4	no	—
552	C₃×C₂²⋊C₄	—	2	2	no	—
553	C₃×C₂²⋊C₄	—	2	2	no	—
554	C₃×C₂²⋊C₄	—	2	4	no	—
555	C₃×C₂²⋊C₄	—	2	4	no	—
556	C₃×C₂²⋊C₄	—	2	2	no	—
557	C₃×C₂²⋊C₄	—	2	2	no	—
558	C₃×C₂²⋊C₄	—	2	4	no	—
559	C₃×C₂²⋊C₄	—	2	4	no	—
560	C₃×C₂²⋊C₄	—	2	2	no	—
561	C₃×C₂²⋊C₄	—	4	2	no	—
562	C₃×C₂²⋊C₄	—	4	2	no	—
563	C₃×C₂²⋊C₄	—	4	2	no	—
564	C₃×C₂²⋊C₄	—	4	2	no	—
565	C₃×C₂²⋊C₄	—	4	2	no	—
566	C₃×C₂²⋊C₄	—	4	2	no	—
567	C₃×C₂²⋊C₄	—	4	2	no	—
568	C₃×C₂²⋊C₄	—	4	2	no	—
569	C₃×C₂²⋊C₄	—	4	2	no	—
570	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
571	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
572	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
573	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
574	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
575	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
576	C₃×C₄²	—	2	4	no	—
577	C₃×C₄²	—	2	2	no	—
578	C₃×C₄²	—	4	2	no	—
579	C₂⁵	C₂³×C₃	1	1	yes	characteristic
580	C₂⁵	C₂³×C₃	1	1	yes	characteristic
581	C₂⁵	C₂³×C₃	1	1	yes	characteristic
582	C₂×#41	—	2	4	no	—
583	C₂×#41	—	2	4	no	—
584	C₂×#41	—	4	2	no	—
585	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
586	C₂²×D₄	—	2	4	no	—
587	C₂²×D₄	—	2	4	no	—
588	C₂²×D₄	—	2	4	no	—
589	C₂²×D₄	—	2	4	no	—
590	C₂²×D₄	—	4	2	no	—
591	C₂²×D₄	—	4	2	no	—
592	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₃	1	2	yes	—
595	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₃	1	2	yes	—
599	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₃	1	2	yes	—
606	C₂³×C₄	—	2	4	no	—
607	C₂³×C₄	—	2	4	no	—
608	C₂³×C₄	—	4	2	no	—
609	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₃	1	2	yes	—
616	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₃	1	2	yes	—
619	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
621	#124	—	2	4	no	—
622	#123	—	2	4	no	—
623	#123	—	2	4	no	—
624	#123	—	2	4	no	—
625	#123	—	2	8	no	—
626	#123	—	2	8	no	—
627	#123	—	2	8	no	—
628	#123	—	2	8	no	—
629	#123	—	2	8	no	—
630	#123	—	2	4	no	—
631	#123	—	2	4	no	—
632	#123	—	2	4	no	—
633	#123	—	4	2	no	—
634	#123	—	4	2	no	—
635	C₂²⋊Q₈	—	2	8	no	—
636	C₂²⋊Q₈	—	2	4	no	—
637	#121	—	2	8	no	—
638	#121	—	2	8	no	—
639	#121	—	2	4	no	—
640	#121	—	2	8	no	—
641	#121	—	2	4	no	—
642	#121	—	2	4	no	—
643	#120	—	2	4	no	—
644	#120	—	2	4	no	—
645	#120	—	2	4	no	—
646	#120	—	2	8	no	—
647	#120	—	2	4	no	—
648	#120	C₃×D₄	1	8	yes	complemented
649	C₄×D₄	—	2	8	no	—
650	C₄×D₄	—	2	4	no	—
651	C₄×D₄	—	2	8	no	—
652	C₄×D₄	—	2	4	no	—
653	#117	—	2	4	no	—
654	C₂×C₄⋊C₄	—	2	4	no	—
655	C₂×C₄⋊C₄	—	2	4	no	—
656	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
673	C₂×C₂²⋊C₄	—	2	4	no	—
674	C₂×C₂²⋊C₄	—	2	4	no	—
675	C₂×C₂²⋊C₄	—	2	4	no	—
676	C₂×C₂²⋊C₄	—	2	4	no	—
677	C₂×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
678	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₂×C₄²	C₂³×C₃	1	2	yes	—
716	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₃	1	2	yes	—
718	#95	C₂³×C₃	1	2	yes	—
719	#95	C₂³×C₃	1	2	yes	—
720	#95	C₂³×C₃	1	2	yes	—
721	#95	C₂³×C₃	1	2	yes	—
722	#95	C₂³×C₃	1	2	yes	—
723	#95	C₂³×C₃	1	2	yes	—
724	#95	C₂³×C₃	1	2	yes	—
725	#95	C₂³×C₃	1	2	yes	—
726	#95	C₂³×C₃	1	2	yes	—
727	#95	C₂³×C₃	1	2	yes	—
728	#95	C₂³×C₃	1	2	yes	—
729	#95	C₂³×C₃	1	2	yes	—
730	C₂³×C₃	—	2	2	no	—
731	C₂³×C₃	—	2	2	no	—
732	C₂³×C₃	—	2	8	no	—
733	C₂³×C₃	—	2	2	no	—
734	C₂³×C₃	—	2	1	no	—
735	C₂³×C₃	—	2	1	no	—
736	C₂³×C₃	—	2	1	no	—
737	C₂³×C₃	—	2	2	no	—
738	C₂³×C₃	—	2	1	no	—
739	C₂³×C₃	—	2	1	no	—
740	C₂³×C₃	—	2	1	no	—
741	C₂³×C₃	—	2	2	no	—
742	C₂³×C₃	—	2	2	no	—
743	C₂³×C₃	—	2	2	no	—
744	C₂³×C₃	—	2	2	no	—
745	C₂³×C₃	—	2	2	no	—
746	C₂³×C₃	—	2	2	no	—
747	C₂³×C₃	—	2	2	no	—
748	C₂³×C₃	—	2	2	no	—
749	C₂³×C₃	—	2	2	no	—
750	C₂³×C₃	—	2	2	no	—
751	C₂³×C₃	—	2	8	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	1	no	—
757	C₂³×C₃	—	2	1	no	—
758	C₂³×C₃	—	2	2	no	—
759	C₂³×C₃	—	2	2	no	—
760	C₂³×C₃	—	2	2	no	—
761	C₂³×C₃	—	2	2	no	—
762	C₂³×C₃	—	4	8	no	—
763	C₂³×C₃	—	4	4	no	—
764	C₂³×C₃	—	4	4	no	—
765	C₂³×C₃	—	4	4	no	—
766	C₂³×C₃	—	4	4	no	—
767	C₂³×C₃	—	4	4	no	—
768	C₂³×C₃	—	4	8	no	—
769	C₂³×C₃	—	4	4	no	—
770	C₂³×C₃	—	8	4	no	—
771	C₂³×C₃	—	8	4	no	—
772	C₂³×C₃	—	8	4	no	—
773	C₂³×C₃	—	8	2	no	—
774	C₂³×C₃	—	8	4	no	—
775	C₂³×C₃	C₂²×D₄	1	2	yes	—
776	C₂³×C₃	C₂²×D₄	1	2	yes	—
777	C₂³×C₃	C₂²×D₄	1	2	yes	—
778	C₂³×C₃	C₂²×D₄	1	4	yes	—
779	C₂³×C₃	C₂²×D₄	1	2	yes	—
780	C₂³×C₃	C₂²×D₄	1	2	yes	—
781	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
782	C₂³×C₃	C₂⁵	1	1	yes	characteristic
783	C₃×Q₈	—	4	4	no	—
784	C₃×D₄	—	2	8	no	—
785	C₃×D₄	—	4	8	no	—
786	C₃×D₄	—	4	4	no	—
787	C₃×D₄	—	4	4	no	—
788	C₃×D₄	—	4	8	no	—
789	C₃×D₄	—	4	8	no	—
790	C₃×D₄	—	4	4	no	—
791	C₃×D₄	—	4	4	no	—
792	C₃×D₄	—	4	8	no	—
793	C₃×D₄	—	4	4	no	—
794	C₃×D₄	—	4	4	no	—
795	C₃×D₄	—	8	2	no	—
796	C₃×D₄	—	8	2	no	—
797	C₃×D₄	—	8	4	no	—
798	C₂×C₃×C₄	—	2	8	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	1	no	—
801	C₂×C₃×C₄	—	2	1	no	—
802	C₂×C₃×C₄	—	2	1	no	—
803	C₂×C₃×C₄	—	2	1	no	—
804	C₂×C₃×C₄	—	2	1	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	2	no	—
807	C₂×C₃×C₄	—	2	2	no	—
808	C₂×C₃×C₄	—	2	2	no	—
809	C₂×C₃×C₄	—	2	1	no	—
810	C₂×C₃×C₄	—	2	2	no	—
811	C₂×C₃×C₄	—	2	2	no	—
812	C₂×C₃×C₄	—	2	2	no	—
813	C₂×C₃×C₄	—	2	1	no	—
814	C₂×C₃×C₄	—	2	1	no	—
815	C₂×C₃×C₄	—	2	2	no	—
816	C₂×C₃×C₄	—	2	2	no	—
817	C₂×C₃×C₄	—	2	1	no	—
818	C₂×C₃×C₄	—	2	2	no	—
819	C₂×C₃×C₄	—	2	1	no	—
820	C₂×C₃×C₄	—	2	1	no	—
821	C₂×C₃×C₄	—	2	2	no	—
822	C₂×C₃×C₄	—	2	2	no	—
823	C₂×C₃×C₄	—	2	2	no	—
824	C₂×C₃×C₄	—	2	2	no	—
825	C₂×C₃×C₄	—	2	1	no	—
826	C₂×C₃×C₄	—	2	1	no	—
827	C₂×C₃×C₄	—	2	2	no	—
828	C₂×C₃×C₄	—	2	2	no	—
829	C₂×C₃×C₄	—	2	2	no	—
830	C₂×C₃×C₄	—	2	2	no	—
831	C₂×C₃×C₄	—	2	2	no	—
832	C₂×C₃×C₄	—	2	2	no	—
833	C₂×C₃×C₄	—	2	2	no	—
834	C₂×C₃×C₄	—	2	2	no	—
835	C₂×C₃×C₄	—	2	2	no	—
836	C₂×C₃×C₄	—	2	2	no	—
837	C₂×C₃×C₄	—	4	4	no	—
838	C₂×C₃×C₄	—	4	4	no	—
839	C₂×C₃×C₄	—	4	8	no	—
840	C₂×C₃×C₄	—	4	8	no	—
841	C₂×C₃×C₄	—	4	4	no	—
842	C₂×C₃×C₄	—	4	4	no	—
843	C₂×C₃×C₄	—	4	4	no	—
844	C₂×C₃×C₄	—	4	4	no	—
845	C₂×C₃×C₄	—	4	4	no	—
846	C₂×C₃×C₄	—	8	2	no	—
847	C₂×C₃×C₄	—	8	4	no	—
848	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
849	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
850	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
851	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
852	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
853	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
854	C₂⁴	—	2	2	no	—
855	C₂⁴	—	2	2	no	—
856	C₂⁴	—	2	2	no	—
857	C₂⁴	—	2	2	no	—
858	C₂⁴	—	2	2	no	—
859	C₂⁴	—	2	2	no	—
860	C₂⁴	—	4	2	no	—
861	C₂⁴	—	4	2	no	—
862	C₂⁴	—	4	1	no	—
863	C₂⁴	—	4	2	no	—
864	C₂⁴	—	4	2	no	—
865	C₂⁴	—	4	2	no	—
866	C₂⁴	—	4	2	no	—
867	C₂⁴	C₂×C₃×D₄	1	4	yes	—
868	C₂⁴	C₂×C₃×D₄	1	4	yes	—
869	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
870	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
871	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
872	C₂⁴	C₂⁴×C₃	1	2	yes	—
873	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
874	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
875	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
876	#41	—	4	16	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	4	1	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	4	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	4	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	4	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	1	no	—
907	C₂×D₄	—	4	1	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	16	no	—
918	C₂×D₄	—	4	16	no	—
919	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
920	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	4	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	4	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	4	no	—
938	C₂²×C₄	—	2	4	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	4	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	1	no	—
945	C₂²×C₄	—	4	1	no	—
946	C₂²×C₄	—	4	1	no	—
947	C₂²×C₄	—	4	2	no	—
948	C₂²×C₄	—	4	2	no	—
949	C₂²×C₄	—	4	2	no	—
950	C₂²×C₄	—	4	2	no	—
951	C₂²×C₄	—	4	2	no	—
952	C₂²×C₄	—	4	16	no	—
953	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
954	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
955	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
958	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
960	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
967	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
968	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
971	C₄⋊C₄	—	2	4	no	—
972	C₄⋊C₄	—	2	4	no	—
973	C₄⋊C₄	—	2	4	no	—
974	C₄⋊C₄	—	2	4	no	—
975	C₄⋊C₄	—	2	4	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	4	no	—
978	C₄⋊C₄	—	2	4	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	4	no	—
983	C₄⋊C₄	—	2	4	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	4	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	4	no	—
996	C₂²⋊C₄	—	2	4	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	4	no	—
1004	C₂²⋊C₄	—	2	4	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	4	no	—
1008	C₂²⋊C₄	—	2	4	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1020	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1021	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1022	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1023	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1024	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
1025	C₄²	—	2	4	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	4	2	no	—
1028	C₂²×C₃	—	2	2	no	—
1029	C₂²×C₃	—	2	2	no	—
1030	C₂²×C₃	—	2	4	no	—
1031	C₂²×C₃	—	2	4	no	—
1032	C₂²×C₃	—	2	2	no	—
1033	C₂²×C₃	—	2	2	no	—
1034	C₂²×C₃	—	2	4	no	—
1035	C₂²×C₃	—	2	2	no	—
1036	C₂²×C₃	—	2	2	no	—
1037	C₂²×C₃	—	2	2	no	—
1038	C₂²×C₃	—	2	4	no	—
1039	C₂²×C₃	—	2	4	no	—
1040	C₂²×C₃	—	2	4	no	—
1041	C₂²×C₃	—	2	2	no	—
1042	C₂²×C₃	—	2	2	no	—
1043	C₂²×C₃	—	4	16	no	—
1044	C₂²×C₃	—	4	2	no	—
1045	C₂²×C₃	—	4	1	no	—
1046	C₂²×C₃	—	4	1	no	—
1047	C₂²×C₃	—	4	2	no	—
1048	C₂²×C₃	—	4	2	no	—
1049	C₂²×C₃	—	4	2	no	—
1050	C₂²×C₃	—	4	2	no	—
1051	C₂²×C₃	—	4	2	no	—
1052	C₂²×C₃	—	4	2	no	—
1053	C₂²×C₃	—	4	2	no	—
1054	C₂²×C₃	—	4	2	no	—
1055	C₂²×C₃	—	4	1	no	—
1056	C₂²×C₃	—	4	1	no	—
1057	C₂²×C₃	—	4	1	no	—
1058	C₂²×C₃	—	4	1	no	—
1059	C₂²×C₃	—	4	2	no	—
1060	C₂²×C₃	—	4	1	no	—
1061	C₂²×C₃	—	4	1	no	—
1062	C₂²×C₃	—	4	2	no	—
1063	C₂²×C₃	—	4	2	no	—
1064	C₂²×C₃	—	4	2	no	—
1065	C₂²×C₃	—	8	8	no	—
1066	C₂²×C₃	—	8	8	no	—
1067	C₂²×C₃	D₄²	1	4	yes	—
1068	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1069	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1070	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1071	C₂²×C₃	#585	1	2	yes	—
1072	C₂²×C₃	#585	1	2	yes	—
1073	C₃×C₄	—	2	2	no	—
1074	C₃×C₄	—	2	2	no	—
1075	C₃×C₄	—	2	2	no	—
1076	C₃×C₄	—	2	2	no	—
1077	C₃×C₄	—	2	2	no	—
1078	C₃×C₄	—	2	4	no	—
1079	C₃×C₄	—	4	2	no	—
1080	C₃×C₄	—	4	1	no	—
1081	C₃×C₄	—	4	2	no	—
1082	C₃×C₄	—	4	1	no	—
1083	C₃×C₄	—	4	2	no	—
1084	C₃×C₄	—	4	1	no	—
1085	C₃×C₄	—	4	1	no	—
1086	C₃×C₄	—	4	2	no	—
1087	C₃×C₄	—	4	2	no	—
1088	C₃×C₄	—	4	2	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	2	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	2	1	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	8	no	—
1110	C₂³	—	2	8	no	—
1111	C₂³	—	2	1	no	—
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	1	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	4	8	no	—
1122	C₂³	—	4	4	no	—
1123	C₂³	—	4	4	no	—
1124	C₂³	—	4	4	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	4	no	—
1127	C₂³	—	4	8	no	—
1128	C₂³	—	4	4	no	—
1129	C₂³	—	8	4	no	—
1130	C₂³	—	8	4	no	—
1131	C₂³	—	8	4	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	—	8	4	no	—
1134	C₂³	C₂²×C₃×D₄	1	2	yes	—
1135	C₂³	C₂²×C₃×D₄	1	2	yes	—
1136	C₂³	C₂²×C₃×D₄	1	2	yes	—
1137	C₂³	C₂²×C₃×D₄	1	4	yes	—
1138	C₂³	C₂²×C₃×D₄	1	2	yes	—
1139	C₂³	C₂²×C₃×D₄	1	2	yes	—
1140	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1141	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1142	Q₈	—	4	4	no	—
1143	D₄	—	2	8	no	—
1144	D₄	—	4	8	no	—
1145	D₄	—	4	4	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	8	no	—
1148	D₄	—	4	8	no	—
1149	D₄	—	4	4	no	—
1150	D₄	—	4	4	no	—
1151	D₄	—	4	8	no	—
1152	D₄	—	4	4	no	—
1153	D₄	—	4	4	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	2	no	—
1156	D₄	—	8	4	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	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	—	2	2	no	—
1167	C₂×C₄	—	2	8	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	4	4	no	—
1197	C₂×C₄	—	4	4	no	—
1198	C₂×C₄	—	4	8	no	—
1199	C₂×C₄	—	4	8	no	—
1200	C₂×C₄	—	4	4	no	—
1201	C₂×C₄	—	4	4	no	—
1202	C₂×C₄	—	4	4	no	—
1203	C₂×C₄	—	4	4	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	8	2	no	—
1206	C₂×C₄	—	8	4	no	—
1207	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1208	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1209	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1210	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1211	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1212	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1213	C₂×C₃	—	2	4	no	—
1214	C₂×C₃	—	4	4	no	—
1215	C₂×C₃	—	4	2	no	—
1216	C₂×C₃	—	4	2	no	—
1217	C₂×C₃	—	4	2	no	—
1218	C₂×C₃	—	8	1	no	—
1219	C₂×C₃	—	8	1	no	—
1220	C₂×C₃	#3449	1	1	yes	characteristic
1221	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
1222	C₂×C₃	#3485	1	1	yes	characteristic
1223	C₂×C₃	#3485	1	2	yes	—
1224	C₂×C₃	#3533	1	2	yes	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	2	4	no	—
1229	C₂²	—	2	2	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	2	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	2	no	—
1235	C₂²	—	2	4	no	—
1236	C₂²	—	2	4	no	—
1237	C₂²	—	2	4	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	4	16	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	2	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	2	no	—
1261	C₂²	—	4	2	no	—
1262	C₂²	—	8	8	no	—
1263	C₂²	—	8	8	no	—
1264	C₂²	C₃×D₄²	1	4	yes	—
1265	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1266	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1267	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1268	C₂²	C₃×#585	1	2	yes	—
1269	C₂²	C₃×#585	1	2	yes	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	4	no	—
1276	C₄	—	4	2	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	2	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	—	4	2	no	—
1284	C₄	—	4	2	no	—
1285	C₄	—	4	2	no	—
1286	C₃	#37654	1	1	yes	characteristic, direct product factor, Sylow
1287	C₂	—	2	4	no	—
1288	C₂	—	4	4	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	2	no	—
1291	C₂	—	4	2	no	—
1292	C₂	—	8	1	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₃×#3449	1	1	yes	characteristic
1295	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
1296	C₂	C₃×#3485	1	1	yes	characteristic
1297	C₂	C₃×#3485	1	2	yes	—
1298	C₂	C₃×#3533	1	2	yes	—

	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×#534	C₂	semidirect
3. C₂×C₃×#525	C₂	semidirect
4. C₂²×C₃×#123	C₂	semidirect
5. C₃×#2849	C₂	semidirect
6. C₃×#2680	C₂	semidirect
7. C₃×#2678	C₂	semidirect
8. C₃×#2672	C₂	semidirect
9. C₃×#2671	C₂	semidirect
10. C₃×#2617	C₂	semidirect
11. C₃×#2613	C₂	semidirect
12. C₃×#2501	C₂	semidirect
13. C₃×#2486	C₂	semidirect
14. C₃×#2464	C₂	semidirect
15. C₃×#2455	C₂	semidirect
16. C₃×#2422	C₂	semidirect
17. C₃×#2418	C₂	semidirect
18. C₃×#2413	C₂	semidirect
19. C₃×#2412	C₂	semidirect
20. C₃×#2406	C₂	semidirect
21. C₃×#2405	C₂	semidirect
22. C₃×#2342	C₂	semidirect
23. C₃×#2321	C₂	semidirect
24. #37654	C₃	direct (N × H)
28. C₂⁴×C₃×C₄	C₂²	semidirect
31. C₂×C₃×#124	C₂²	semidirect
42. C₂×C₃×#123	C₂²	semidirect
43. C₂×C₃×#123	C₂²	semidirect
44. C₂×C₃×#123	C₂²	semidirect
45. C₂×C₃×#123	C₂²	semidirect
46. C₂×C₃×#123	C₂²	semidirect
47. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₃×#121	C₂²	semidirect
53. C₂×C₃×#121	C₂²	semidirect
54. C₂×C₃×#121	C₂²	semidirect
59. C₂×C₃×#120	C₂²	semidirect
60. C₂×C₃×#120	C₂²	semidirect
62. C₂×C₃×C₄×D₄	C₂²	semidirect
63. C₂×C₃×C₄×D₄	C₂²	semidirect
64. C₂×C₃×C₄×D₄	C₂²	semidirect
65. C₂×C₃×#117	C₂²	semidirect
66. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
67. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
71. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
72. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
73. C₃×#399	C₂²	semidirect
74. C₃×#399	C₂²	semidirect
75. C₃×#398	C₂²	semidirect
76. C₃×#398	C₂²	semidirect
77. C₃×#397	C₂²	semidirect
78. C₃×#397	C₂²	semidirect
79. C₃×#397	C₂²	semidirect
80. C₃×#396	C₂²	semidirect
81. 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
91. C₃×#392	C₂²	semidirect
92. C₃×#392	C₂²	semidirect
93. C₃×#390	C₂²	semidirect
94. C₃×#390	C₂²	semidirect
95. C₃×#389	C₂²	semidirect
96. C₃×#389	C₂²	semidirect
97. C₃×#388	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#388	C₂²	semidirect
100. C₃×#388	C₂²	semidirect
101. C₃×#388	C₂²	semidirect
104. C₃×#386	C₂²	semidirect
105. C₃×#386	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
108. C₃×#386	C₂²	semidirect
109. C₃×#385	C₂²	semidirect
110. C₃×#385	C₂²	semidirect
111. C₃×#385	C₂²	semidirect
112. C₃×#385	C₂²	semidirect
113. C₃×#385	C₂²	semidirect
114. C₃×#385	C₂²	semidirect
115. C₃×#385	C₂²	semidirect
116. C₃×#384	C₂²	semidirect
117. C₃×#381	C₂²	semidirect
118. C₃×#381	C₂²	semidirect
119. C₃×#381	C₂²	semidirect
120. C₃×#380	C₂²	semidirect
121. C₃×#380	C₂²	semidirect
122. C₃×#380	C₂²	semidirect
124. C₃×#379	C₂²	semidirect
125. C₃×#379	C₂²	semidirect
126. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
127. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
128. C₂×#546	C₂×C₃	semidirect
129. C₂×#534	C₂×C₃	semidirect
130. C₂×#525	C₂×C₃	semidirect
131. C₂²×#123	C₂×C₃	semidirect
132. #2849	C₂×C₃	semidirect
133. #2680	C₂×C₃	semidirect
134. #2678	C₂×C₃	semidirect
135. #2672	C₂×C₃	semidirect
136. #2671	C₂×C₃	semidirect
137. #2617	C₂×C₃	semidirect
138. #2613	C₂×C₃	semidirect
139. #2501	C₂×C₃	semidirect
140. #2486	C₂×C₃	semidirect
141. #2464	C₂×C₃	semidirect
142. #2455	C₂×C₃	semidirect
143. #2422	C₂×C₃	semidirect
144. #2418	C₂×C₃	semidirect
145. #2413	C₂×C₃	semidirect
146. #2412	C₂×C₃	semidirect
147. #2406	C₂×C₃	semidirect
148. #2405	C₂×C₃	semidirect
149. #2342	C₂×C₃	semidirect
150. #2321	C₂×C₃	semidirect
220. C₃×#120	D₄	semidirect
249. C₂×C₃×C₂²⋊C₄	D₄	semidirect
305. C₂⁴×C₄	C₂²×C₃	semidirect
308. C₂×#124	C₂²×C₃	semidirect
319. C₂×#123	C₂²×C₃	semidirect
320. C₂×#123	C₂²×C₃	semidirect
321. C₂×#123	C₂²×C₃	semidirect
322. C₂×#123	C₂²×C₃	semidirect
323. C₂×#123	C₂²×C₃	semidirect
324. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
329. C₂×#121	C₂²×C₃	semidirect
330. C₂×#121	C₂²×C₃	semidirect
331. C₂×#121	C₂²×C₃	semidirect
336. C₂×#120	C₂²×C₃	semidirect
337. C₂×#120	C₂²×C₃	semidirect
339. C₂×C₄×D₄	C₂²×C₃	semidirect
340. C₂×C₄×D₄	C₂²×C₃	semidirect
341. C₂×C₄×D₄	C₂²×C₃	semidirect
342. C₂×#117	C₂²×C₃	semidirect
343. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
344. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
348. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
349. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
350. #399	C₂²×C₃	semidirect
351. #399	C₂²×C₃	semidirect
352. #398	C₂²×C₃	semidirect
353. #398	C₂²×C₃	semidirect
354. #397	C₂²×C₃	semidirect
355. #397	C₂²×C₃	semidirect
356. #397	C₂²×C₃	semidirect
357. #396	C₂²×C₃	semidirect
358. #395	C₂²×C₃	semidirect
360. #394	C₂²×C₃	semidirect
361. #394	C₂²×C₃	semidirect
362. #394	C₂²×C₃	semidirect
363. #394	C₂²×C₃	semidirect
364. #394	C₂²×C₃	semidirect
365. #394	C₂²×C₃	semidirect
366. #394	C₂²×C₃	semidirect
368. #392	C₂²×C₃	semidirect
369. #392	C₂²×C₃	semidirect
370. #390	C₂²×C₃	semidirect
371. #390	C₂²×C₃	semidirect
372. #389	C₂²×C₃	semidirect
373. #389	C₂²×C₃	semidirect
374. #388	C₂²×C₃	semidirect
375. #388	C₂²×C₃	semidirect
376. #388	C₂²×C₃	semidirect
377. #388	C₂²×C₃	semidirect
378. #388	C₂²×C₃	semidirect
381. #386	C₂²×C₃	semidirect
382. #386	C₂²×C₃	semidirect
383. #386	C₂²×C₃	semidirect
384. #386	C₂²×C₃	semidirect
385. #386	C₂²×C₃	semidirect
386. #385	C₂²×C₃	semidirect
387. #385	C₂²×C₃	semidirect
388. #385	C₂²×C₃	semidirect
389. #385	C₂²×C₃	semidirect
390. #385	C₂²×C₃	semidirect
391. #385	C₂²×C₃	semidirect
392. #385	C₂²×C₃	semidirect
393. #384	C₂²×C₃	semidirect
394. #381	C₂²×C₃	semidirect
395. #381	C₂²×C₃	semidirect
396. #381	C₂²×C₃	semidirect
397. #380	C₂²×C₃	semidirect
398. #380	C₂²×C₃	semidirect
399. #380	C₂²×C₃	semidirect
401. #379	C₂²×C₃	semidirect
402. #379	C₂²×C₃	semidirect
403. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
404. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
648. #120	C₃×D₄	semidirect
677. C₂×C₂²⋊C₄	C₃×D₄	semidirect
1286. C₃	#37654	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×#534	2
C₂×C₃×#525	2
C₂²×C₃×#123	2
C₃×#2849	2
C₃×#2680	2
C₃×#2678	2
C₃×#2672	2
C₃×#2671	2
C₃×#2617	2
C₃×#2613	2
C₃×#2501	2
C₃×#2486	2
C₃×#2464	2
C₃×#2455	2
C₃×#2422	2
C₃×#2418	2
C₃×#2413	2
C₃×#2412	2
C₃×#2406	2
C₃×#2405	2
C₃×#2342	2
C₃×#2321	2
#37654	3

Subgroups — C3×#37654 #10656261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37654 #10656261