Subgroups — C₃×#42474 #10661081

Order 768.

2996 conjugacy classes of subgroups.

The subgroup lattice has 1286 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×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2812	C₂	1	2	yes	maximal, complemented
4	C₃×#2701	C₂	1	2	yes	maximal, complemented
5	C₃×#2697	C₂	1	2	yes	maximal, complemented
6	C₃×#2682	C₂	1	2	yes	maximal, complemented
7	C₃×#2678	C₂	1	2	yes	maximal, complemented
8	C₃×#2622	C₂	1	2	yes	maximal, complemented
9	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2613	C₂	1	2	yes	maximal, complemented
11	C₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2405	C₂	1	2	yes	maximal, complemented
22	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
24	#42474	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂³×C₃×D₄	C₂²	1	2	yes	—
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
29	C₃×#546	—	2	8	no	—
30	C₃×D₄²	—	2	8	no	—
31	C₂×C₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#123	C₂²	1	2	yes	complemented
35	C₂×C₃×#123	C₂²	1	2	yes	complemented
36	C₂×C₃×#123	C₂²	1	2	yes	complemented
37	C₂×C₃×#123	C₂²	1	2	yes	complemented
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₃×#121	C₂²	1	2	yes	—
44	C₂×C₃×#121	C₂²	1	2	yes	complemented
45	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#120	C₂²	1	2	yes	—
47	C₂×C₃×#120	C₂²	1	2	yes	—
48	C₂×C₃×#120	C₂²	1	2	yes	complemented
49	C₂×C₃×#120	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
58	C₃×#398	C₂²	1	1	yes	characteristic, complemented
59	C₃×#397	C₂²	1	1	yes	characteristic, complemented
60	C₃×#397	C₂²	1	2	yes	complemented
61	C₃×#397	C₂²	1	2	yes	complemented
62	C₃×#397	C₂²	1	2	yes	complemented
63	C₃×#397	C₂²	1	2	yes	complemented
64	C₃×#397	C₂²	1	2	yes	complemented
65	C₃×#396	C₂²	1	2	yes	complemented
66	C₃×#396	C₂²	1	2	yes	complemented
67	C₃×#396	C₂²	1	1	yes	characteristic, complemented
68	C₃×#396	C₂²	1	1	yes	characteristic, complemented
69	C₃×#394	C₂²	1	1	yes	characteristic
70	C₃×#394	C₂²	1	2	yes	—
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×#394	C₂²	1	2	yes	complemented
75	C₃×#394	C₂²	1	2	yes	complemented
76	C₃×#394	C₂²	1	1	yes	characteristic, complemented
77	C₃×#394	C₂²	1	1	yes	characteristic, complemented
78	C₃×#394	C₂²	1	2	yes	complemented
79	C₃×#394	C₂²	1	2	yes	complemented
80	C₃×#394	C₂²	1	2	yes	complemented
81	C₃×#394	C₂²	1	2	yes	complemented
82	C₃×#394	C₂²	1	2	yes	complemented
83	C₃×#394	C₂²	1	2	yes	complemented
84	C₃×#392	C₂²	1	1	yes	characteristic
85	C₃×#392	C₂²	1	2	yes	complemented
86	C₃×#392	C₂²	1	2	yes	complemented
87	C₃×#392	C₂²	1	2	yes	complemented
88	C₃×#392	C₂²	1	2	yes	complemented
89	C₃×#392	C₂²	1	2	yes	complemented
90	C₃×#391	C₂²	1	1	yes	characteristic, complemented
91	C₃×#391	C₂²	1	1	yes	characteristic, complemented
92	C₃×#390	C₂²	1	1	yes	characteristic
93	C₃×#390	C₂²	1	1	yes	characteristic
94	C₃×#390	C₂²	1	1	yes	characteristic, complemented
95	C₃×#390	C₂²	1	1	yes	characteristic, complemented
96	C₃×#390	C₂²	1	2	yes	complemented
97	C₃×#390	C₂²	1	1	yes	characteristic, complemented
98	C₃×#390	C₂²	1	1	yes	characteristic, complemented
99	C₃×#390	C₂²	1	2	yes	complemented
100	C₃×#390	C₂²	1	2	yes	complemented
101	C₃×#389	C₂²	1	1	yes	characteristic, complemented
102	C₃×#389	C₂²	1	1	yes	characteristic, complemented
103	C₃×#389	C₂²	1	2	yes	complemented
104	C₃×#388	C₂²	1	2	yes	complemented
105	C₃×#388	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×#386	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	2	yes	complemented
113	C₃×#385	C₂²	1	2	yes	complemented
114	C₃×#384	C₂²	1	1	yes	characteristic, complemented
115	C₃×#381	C₂²	1	2	yes	complemented
116	C₃×#380	C₂²	1	1	yes	characteristic, complemented
117	C₃×#380	C₂²	1	1	yes	characteristic, complemented
118	C₃×#379	C₂²	1	2	yes	complemented
119	C₃×#379	C₂²	1	2	yes	complemented
120	C₃×#379	C₂²	1	2	yes	complemented
121	C₃×#379	C₂²	1	2	yes	complemented
122	C₃×#379	C₂²	1	2	yes	complemented
123	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
126	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
128	#2812	C₂×C₃	1	2	yes	complemented
129	#2701	C₂×C₃	1	2	yes	complemented
130	#2697	C₂×C₃	1	2	yes	complemented
131	#2682	C₂×C₃	1	2	yes	complemented
132	#2678	C₂×C₃	1	2	yes	complemented
133	#2622	C₂×C₃	1	2	yes	complemented
134	#2620	C₂×C₃	1	1	yes	characteristic, complemented
135	#2613	C₂×C₃	1	2	yes	complemented
136	#2447	C₂×C₃	1	1	yes	characteristic, complemented
137	#2445	C₂×C₃	1	1	yes	characteristic, complemented
138	#2435	C₂×C₃	1	1	yes	characteristic, complemented
139	#2431	C₂×C₃	1	1	yes	characteristic, complemented
140	#2422	C₂×C₃	1	1	yes	characteristic, complemented
141	#2422	C₂×C₃	1	1	yes	characteristic, complemented
142	#2415	C₂×C₃	1	1	yes	characteristic, complemented
143	#2414	C₂×C₃	1	1	yes	characteristic, complemented
144	#2408	C₂×C₃	1	1	yes	characteristic, complemented
145	#2407	C₂×C₃	1	1	yes	characteristic, complemented
146	#2405	C₂×C₃	1	2	yes	complemented
147	#2392	C₂×C₃	1	1	yes	characteristic, complemented
148	#2309	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	2	yes	—
150	C₂⁵×C₃	C₂³	1	2	yes	—
151	C₂×C₃×#41	—	2	4	no	—
152	C₂×C₃×#41	—	4	2	no	—
153	C₂×C₃×#41	—	4	2	no	—
154	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	—	2	8	no	—
156	C₂²×C₃×D₄	—	2	4	no	—
157	C₂²×C₃×D₄	—	4	2	no	—
158	C₂²×C₃×D₄	—	4	2	no	—
159	C₂²×C₃×D₄	—	4	2	no	—
160	C₂²×C₃×D₄	—	4	2	no	—
161	C₂²×C₃×D₄	—	4	4	no	—
162	C₂²×C₃×D₄	—	4	4	no	—
163	C₂²×C₃×D₄	D₄	1	8	yes	complemented
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	2	yes	—
171	C₂²×C₃×D₄	C₂³	1	2	yes	—
172	C₂²×C₃×D₄	C₂³	1	2	yes	—
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	C₂²×C₃×D₄	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	2	yes	—
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	C₃×#127	—	2	4	no	—
186	C₃×#124	—	2	4	no	—
187	C₃×#124	—	4	2	no	—
188	C₃×#123	—	2	8	no	—
189	C₃×#123	—	4	4	no	—
190	C₃×#123	—	4	4	no	—
191	C₃×#123	—	4	4	no	—
192	C₃×C₂²⋊Q₈	—	2	4	no	—
193	C₃×C₂²⋊Q₈	—	4	2	no	—
194	C₃×#121	—	2	4	no	—
195	C₃×#121	—	2	8	no	—
196	C₃×#121	—	2	4	no	—
197	C₃×#121	—	2	8	no	—
198	C₃×#121	—	2	4	no	—
199	C₃×#121	—	4	2	no	—
200	C₃×#120	—	2	8	no	—
201	C₃×#120	—	2	8	no	—
202	C₃×#120	—	2	8	no	—
203	C₃×#120	—	4	4	no	—
204	C₃×C₄×D₄	—	2	4	no	—
205	C₃×C₄×D₄	—	2	4	no	—
206	C₃×C₄×D₄	—	2	4	no	—
207	C₃×C₄×D₄	—	2	4	no	—
208	C₃×C₄×D₄	—	4	2	no	—
209	C₃×#117	—	4	2	no	—
210	C₃×#117	—	4	2	no	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	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	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×C₄²	C₂³	1	1	yes	characteristic
269	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
270	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
271	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
272	C₂×C₃×C₄²	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	1	yes	characteristic
274	C₃×#95	C₂³	1	1	yes	characteristic
275	C₃×#95	C₂³	1	1	yes	characteristic
276	C₃×#95	C₂³	1	1	yes	characteristic
277	C₃×#95	C₂³	1	1	yes	characteristic
278	C₃×#95	C₂³	1	1	yes	characteristic
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₃×#95	C₂³	1	2	yes	—
283	C₃×#95	C₂³	1	2	yes	—
284	C₃×#95	C₂³	1	2	yes	—
285	C₃×#95	C₂³	1	2	yes	—
286	C₃×#95	C₂³	1	2	yes	—
287	C₂²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₂³×D₄	C₂²×C₃	1	2	yes	—
289	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
290	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
291	#546	—	2	8	no	—
292	D₄²	—	2	8	no	—
293	C₂×#127	C₂²×C₃	1	1	yes	characteristic
294	C₂×#124	C₂²×C₃	1	1	yes	characteristic
295	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×#123	C₂²×C₃	1	2	yes	complemented
297	C₂×#123	C₂²×C₃	1	2	yes	complemented
298	C₂×#123	C₂²×C₃	1	2	yes	complemented
299	C₂×#123	C₂²×C₃	1	2	yes	complemented
300	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₂×#121	C₂²×C₃	1	1	yes	characteristic
303	C₂×#121	C₂²×C₃	1	1	yes	characteristic
304	C₂×#121	C₂²×C₃	1	1	yes	characteristic
305	C₂×#121	C₂²×C₃	1	2	yes	—
306	C₂×#121	C₂²×C₃	1	2	yes	complemented
307	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₂×#120	C₂²×C₃	1	2	yes	—
309	C₂×#120	C₂²×C₃	1	2	yes	—
310	C₂×#120	C₂²×C₃	1	2	yes	complemented
311	C₂×#120	C₂²×C₃	1	2	yes	complemented
312	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
317	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
318	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
319	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
320	#398	C₂²×C₃	1	1	yes	characteristic, complemented
321	#397	C₂²×C₃	1	1	yes	characteristic, complemented
322	#397	C₂²×C₃	1	2	yes	complemented
323	#397	C₂²×C₃	1	2	yes	complemented
324	#397	C₂²×C₃	1	2	yes	complemented
325	#397	C₂²×C₃	1	2	yes	complemented
326	#397	C₂²×C₃	1	2	yes	complemented
327	#396	C₂²×C₃	1	2	yes	complemented
328	#396	C₂²×C₃	1	2	yes	complemented
329	#396	C₂²×C₃	1	1	yes	characteristic, complemented
330	#396	C₂²×C₃	1	1	yes	characteristic, complemented
331	#394	C₂²×C₃	1	2	yes	—
332	#394	C₂²×C₃	1	1	yes	characteristic
333	#394	C₂²×C₃	1	2	yes	complemented
334	#394	C₂²×C₃	1	2	yes	complemented
335	#394	C₂²×C₃	1	2	yes	complemented
336	#394	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	#394	C₂²×C₃	1	1	yes	characteristic, complemented
341	#394	C₂²×C₃	1	1	yes	characteristic, complemented
342	#394	C₂²×C₃	1	2	yes	complemented
343	#394	C₂²×C₃	1	2	yes	complemented
344	#394	C₂²×C₃	1	2	yes	complemented
345	#394	C₂²×C₃	1	2	yes	complemented
346	#392	C₂²×C₃	1	1	yes	characteristic
347	#392	C₂²×C₃	1	2	yes	complemented
348	#392	C₂²×C₃	1	2	yes	complemented
349	#392	C₂²×C₃	1	2	yes	complemented
350	#392	C₂²×C₃	1	2	yes	complemented
351	#392	C₂²×C₃	1	2	yes	complemented
352	#391	C₂²×C₃	1	1	yes	characteristic, complemented
353	#391	C₂²×C₃	1	1	yes	characteristic, complemented
354	#390	C₂²×C₃	1	1	yes	characteristic
355	#390	C₂²×C₃	1	1	yes	characteristic
356	#390	C₂²×C₃	1	1	yes	characteristic, complemented
357	#390	C₂²×C₃	1	1	yes	characteristic, complemented
358	#390	C₂²×C₃	1	2	yes	complemented
359	#390	C₂²×C₃	1	2	yes	complemented
360	#390	C₂²×C₃	1	1	yes	characteristic, complemented
361	#390	C₂²×C₃	1	2	yes	complemented
362	#390	C₂²×C₃	1	1	yes	characteristic, complemented
363	#389	C₂²×C₃	1	1	yes	characteristic, complemented
364	#389	C₂²×C₃	1	1	yes	characteristic, complemented
365	#389	C₂²×C₃	1	2	yes	complemented
366	#388	C₂²×C₃	1	2	yes	complemented
367	#388	C₂²×C₃	1	2	yes	complemented
368	#386	C₂²×C₃	1	2	yes	complemented
369	#386	C₂²×C₃	1	2	yes	complemented
370	#386	C₂²×C₃	1	2	yes	complemented
371	#386	C₂²×C₃	1	2	yes	complemented
372	#385	C₂²×C₃	1	2	yes	complemented
373	#385	C₂²×C₃	1	2	yes	complemented
374	#385	C₂²×C₃	1	2	yes	complemented
375	#385	C₂²×C₃	1	2	yes	complemented
376	#384	C₂²×C₃	1	1	yes	characteristic, complemented
377	#381	C₂²×C₃	1	2	yes	complemented
378	#380	C₂²×C₃	1	1	yes	characteristic, complemented
379	#380	C₂²×C₃	1	1	yes	characteristic, complemented
380	#379	C₂²×C₃	1	2	yes	complemented
381	#379	C₂²×C₃	1	2	yes	complemented
382	#379	C₂²×C₃	1	2	yes	complemented
383	#379	C₂²×C₃	1	2	yes	complemented
384	#379	C₂²×C₃	1	2	yes	complemented
385	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
386	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
387	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
388	C₂⁴×C₃	—	2	4	no	—
389	C₂⁴×C₃	—	2	4	no	—
390	C₂⁴×C₃	—	4	2	no	—
391	C₂⁴×C₃	—	4	2	no	—
392	C₂⁴×C₃	—	4	2	no	—
393	C₂⁴×C₃	—	4	2	no	—
394	C₂⁴×C₃	—	4	2	no	—
395	C₂⁴×C₃	—	4	2	no	—
396	C₂⁴×C₃	—	4	2	no	—
397	C₂⁴×C₃	—	4	2	no	—
398	C₂⁴×C₃	—	4	2	no	—
399	C₂⁴×C₃	—	4	2	no	—
400	C₂⁴×C₃	—	4	2	no	—
401	C₂⁴×C₃	C₂×D₄	1	8	yes	—
402	C₂⁴×C₃	C₂⁴	1	2	yes	—
403	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
404	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
405	C₂⁴×C₃	C₂⁴	1	2	yes	—
406	C₂⁴×C₃	C₂⁴	1	2	yes	—
407	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
408	C₃×#41	—	4	16	no	—
409	C₂×C₃×Q₈	—	2	2	no	—
410	C₂×C₃×Q₈	—	2	2	no	—
411	C₂×C₃×Q₈	—	2	2	no	—
412	C₂×C₃×D₄	—	2	2	no	—
413	C₂×C₃×D₄	—	2	2	no	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	4	no	—
416	C₂×C₃×D₄	—	2	4	no	—
417	C₂×C₃×D₄	—	2	4	no	—
418	C₂×C₃×D₄	—	2	4	no	—
419	C₂×C₃×D₄	—	2	4	no	—
420	C₂×C₃×D₄	—	2	2	no	—
421	C₂×C₃×D₄	—	2	4	no	—
422	C₂×C₃×D₄	—	2	4	no	—
423	C₂×C₃×D₄	—	2	4	no	—
424	C₂×C₃×D₄	—	2	2	no	—
425	C₂×C₃×D₄	—	2	2	no	—
426	C₂×C₃×D₄	—	2	2	no	—
427	C₂×C₃×D₄	—	2	2	no	—
428	C₂×C₃×D₄	—	2	2	no	—
429	C₂×C₃×D₄	—	2	2	no	—
430	C₂×C₃×D₄	—	2	2	no	—
431	C₂×C₃×D₄	—	2	4	no	—
432	C₂×C₃×D₄	—	2	2	no	—
433	C₂×C₃×D₄	—	4	16	no	—
434	C₂×C₃×D₄	—	4	1	no	—
435	C₂×C₃×D₄	—	4	2	no	—
436	C₂×C₃×D₄	—	4	2	no	—
437	C₂×C₃×D₄	—	4	2	no	—
438	C₂×C₃×D₄	—	4	2	no	—
439	C₂×C₃×D₄	—	4	2	no	—
440	C₂×C₃×D₄	—	4	2	no	—
441	C₂×C₃×D₄	—	4	2	no	—
442	C₂×C₃×D₄	—	4	2	no	—
443	C₂×C₃×D₄	—	4	1	no	—
444	C₂×C₃×D₄	—	4	1	no	—
445	C₂×C₃×D₄	—	4	1	no	—
446	C₂×C₃×D₄	—	4	2	no	—
447	C₂×C₃×D₄	—	4	2	no	—
448	C₂×C₃×D₄	—	4	2	no	—
449	C₂×C₃×D₄	—	4	2	no	—
450	C₂×C₃×D₄	—	4	2	no	—
451	C₂×C₃×D₄	—	4	2	no	—
452	C₂×C₃×D₄	—	4	2	no	—
453	C₂×C₃×D₄	—	4	2	no	—
454	C₂×C₃×D₄	—	4	2	no	—
455	C₂×C₃×D₄	—	4	32	no	—
456	C₂×C₃×D₄	—	4	16	no	—
457	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
458	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
459	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
460	C₂²×C₃×C₄	—	2	2	no	—
461	C₂²×C₃×C₄	—	2	2	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	—	2	2	no	—
467	C₂²×C₃×C₄	—	2	2	no	—
468	C₂²×C₃×C₄	—	2	2	no	—
469	C₂²×C₃×C₄	—	2	2	no	—
470	C₂²×C₃×C₄	—	2	2	no	—
471	C₂²×C₃×C₄	—	2	4	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	2	no	—
477	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
488	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
489	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
490	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	C₃×C₄⋊C₄	—	2	2	no	—
496	C₃×C₄⋊C₄	—	2	2	no	—
497	C₃×C₄⋊C₄	—	2	2	no	—
498	C₃×C₄⋊C₄	—	2	2	no	—
499	C₃×C₄⋊C₄	—	2	4	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	4	no	—
504	C₃×C₄⋊C₄	—	4	1	no	—
505	C₃×C₄⋊C₄	—	4	1	no	—
506	C₃×C₄⋊C₄	—	4	1	no	—
507	C₃×C₄⋊C₄	—	4	1	no	—
508	C₃×C₄⋊C₄	—	4	2	no	—
509	C₃×C₄⋊C₄	—	4	2	no	—
510	C₃×C₄⋊C₄	—	4	2	no	—
511	C₃×C₄⋊C₄	—	4	2	no	—
512	C₃×C₂²⋊C₄	—	2	2	no	—
513	C₃×C₂²⋊C₄	—	2	4	no	—
514	C₃×C₂²⋊C₄	—	2	4	no	—
515	C₃×C₂²⋊C₄	—	2	4	no	—
516	C₃×C₂²⋊C₄	—	2	4	no	—
517	C₃×C₂²⋊C₄	—	2	2	no	—
518	C₃×C₂²⋊C₄	—	2	4	no	—
519	C₃×C₂²⋊C₄	—	2	4	no	—
520	C₃×C₂²⋊C₄	—	2	4	no	—
521	C₃×C₂²⋊C₄	—	2	4	no	—
522	C₃×C₂²⋊C₄	—	2	2	no	—
523	C₃×C₂²⋊C₄	—	2	2	no	—
524	C₃×C₂²⋊C₄	—	2	2	no	—
525	C₃×C₂²⋊C₄	—	2	4	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	4	2	no	—
528	C₃×C₂²⋊C₄	—	4	2	no	—
529	C₃×C₂²⋊C₄	—	4	2	no	—
530	C₃×C₂²⋊C₄	—	4	2	no	—
531	C₃×C₂²⋊C₄	—	4	1	no	—
532	C₃×C₂²⋊C₄	—	4	1	no	—
533	C₃×C₂²⋊C₄	—	4	2	no	—
534	C₃×C₂²⋊C₄	—	4	1	no	—
535	C₃×C₂²⋊C₄	—	4	1	no	—
536	C₃×C₂²⋊C₄	—	4	2	no	—
537	C₃×C₂²⋊C₄	—	4	1	no	—
538	C₃×C₂²⋊C₄	—	4	1	no	—
539	C₃×C₂²⋊C₄	—	4	2	no	—
540	C₃×C₂²⋊C₄	—	4	2	no	—
541	C₃×C₂²⋊C₄	—	4	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	—	4	2	no	—
551	C₃×C₄²	—	2	2	no	—
552	C₃×C₄²	—	2	2	no	—
553	C₃×C₄²	—	2	2	no	—
554	C₃×C₄²	—	2	2	no	—
555	C₃×C₄²	—	4	2	no	—
556	C₂⁵	C₂³×C₃	1	2	yes	—
557	C₂⁵	C₂³×C₃	1	2	yes	—
558	C₂×#41	—	2	4	no	—
559	C₂×#41	—	4	2	no	—
560	C₂×#41	—	4	2	no	—
561	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
562	C₂²×D₄	—	2	8	no	—
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	4	2	no	—
565	C₂²×D₄	—	4	2	no	—
566	C₂²×D₄	—	4	2	no	—
567	C₂²×D₄	—	4	2	no	—
568	C₂²×D₄	—	4	4	no	—
569	C₂²×D₄	—	4	4	no	—
570	C₂²×D₄	C₃×D₄	1	8	yes	complemented
571	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₃	1	2	yes	—
574	C₂²×D₄	C₂³×C₃	1	2	yes	—
575	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
576	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₃	1	2	yes	—
580	C₂²×D₄	C₂³×C₃	1	2	yes	—
581	C₂²×D₄	C₂³×C₃	1	2	yes	—
582	C₂²×D₄	C₂³×C₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₃	1	2	yes	—
585	C₂²×D₄	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	2	yes	—
591	C₂³×C₄	C₂³×C₃	1	2	yes	—
592	#127	—	2	4	no	—
593	#124	—	2	4	no	—
594	#124	—	4	2	no	—
595	#123	—	2	8	no	—
596	#123	—	4	4	no	—
597	#123	—	4	4	no	—
598	#123	—	4	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	4	2	no	—
601	#121	—	2	4	no	—
602	#121	—	2	8	no	—
603	#121	—	2	4	no	—
604	#121	—	2	8	no	—
605	#121	—	2	4	no	—
606	#121	—	4	2	no	—
607	#120	—	2	8	no	—
608	#120	—	2	8	no	—
609	#120	—	2	8	no	—
610	#120	—	4	4	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	4	2	no	—
616	#117	—	4	2	no	—
617	#117	—	4	2	no	—
618	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	—	2	8	no	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₃	1	2	yes	—
680	#95	C₂³×C₃	1	1	yes	characteristic
681	#95	C₂³×C₃	1	1	yes	characteristic
682	#95	C₂³×C₃	1	1	yes	characteristic
683	#95	C₂³×C₃	1	1	yes	characteristic
684	#95	C₂³×C₃	1	1	yes	characteristic
685	#95	C₂³×C₃	1	1	yes	characteristic
686	#95	C₂³×C₃	1	2	yes	—
687	#95	C₂³×C₃	1	2	yes	—
688	#95	C₂³×C₃	1	2	yes	—
689	#95	C₂³×C₃	1	2	yes	—
690	#95	C₂³×C₃	1	2	yes	—
691	#95	C₂³×C₃	1	2	yes	—
692	#95	C₂³×C₃	1	2	yes	—
693	#95	C₂³×C₃	1	2	yes	—
694	C₂³×C₃	—	2	1	no	—
695	C₂³×C₃	—	2	1	no	—
696	C₂³×C₃	—	2	1	no	—
697	C₂³×C₃	—	2	1	no	—
698	C₂³×C₃	—	2	2	no	—
699	C₂³×C₃	—	2	1	no	—
700	C₂³×C₃	—	2	2	no	—
701	C₂³×C₃	—	2	2	no	—
702	C₂³×C₃	—	2	2	no	—
703	C₂³×C₃	—	2	2	no	—
704	C₂³×C₃	—	2	2	no	—
705	C₂³×C₃	—	2	2	no	—
706	C₂³×C₃	—	2	2	no	—
707	C₂³×C₃	—	2	1	no	—
708	C₂³×C₃	—	2	1	no	—
709	C₂³×C₃	—	2	1	no	—
710	C₂³×C₃	—	2	2	no	—
711	C₂³×C₃	—	2	2	no	—
712	C₂³×C₃	—	2	2	no	—
713	C₂³×C₃	—	2	2	no	—
714	C₂³×C₃	—	2	1	no	—
715	C₂³×C₃	—	2	1	no	—
716	C₂³×C₃	—	2	1	no	—
717	C₂³×C₃	—	2	1	no	—
718	C₂³×C₃	—	2	1	no	—
719	C₂³×C₃	—	2	2	no	—
720	C₂³×C₃	—	2	1	no	—
721	C₂³×C₃	—	2	2	no	—
722	C₂³×C₃	—	2	2	no	—
723	C₂³×C₃	—	2	1	no	—
724	C₂³×C₃	—	2	2	no	—
725	C₂³×C₃	—	2	2	no	—
726	C₂³×C₃	—	2	1	no	—
727	C₂³×C₃	—	2	1	no	—
728	C₂³×C₃	—	2	1	no	—
729	C₂³×C₃	—	2	2	no	—
730	C₂³×C₃	—	2	1	no	—
731	C₂³×C₃	—	2	2	no	—
732	C₂³×C₃	—	4	8	no	—
733	C₂³×C₃	—	4	8	no	—
734	C₂³×C₃	—	4	8	no	—
735	C₂³×C₃	—	4	8	no	—
736	C₂³×C₃	—	4	8	no	—
737	C₂³×C₃	—	8	4	no	—
738	C₂³×C₃	—	8	4	no	—
739	C₂³×C₃	—	8	4	no	—
740	C₂³×C₃	—	8	4	no	—
741	C₂³×C₃	—	8	4	no	—
742	C₂³×C₃	—	8	4	no	—
743	C₂³×C₃	—	8	4	no	—
744	C₂³×C₃	—	8	4	no	—
745	C₂³×C₃	—	8	4	no	—
746	C₂³×C₃	C₂²×D₄	1	4	yes	—
747	C₂³×C₃	C₂²×D₄	1	2	yes	—
748	C₂³×C₃	C₂²×D₄	1	4	yes	—
749	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
750	C₂³×C₃	C₂⁵	1	1	yes	characteristic
751	C₃×Q₈	—	4	4	no	—
752	C₃×D₄	—	2	8	no	—
753	C₃×D₄	—	2	8	no	—
754	C₃×D₄	—	2	8	no	—
755	C₃×D₄	—	4	8	no	—
756	C₃×D₄	—	4	8	no	—
757	C₃×D₄	—	4	8	no	—
758	C₃×D₄	—	4	4	no	—
759	C₃×D₄	—	4	4	no	—
760	C₃×D₄	—	4	8	no	—
761	C₃×D₄	—	4	8	no	—
762	C₃×D₄	—	4	8	no	—
763	C₃×D₄	—	4	4	no	—
764	C₃×D₄	—	8	4	no	—
765	C₃×D₄	—	8	4	no	—
766	C₃×D₄	—	8	4	no	—
767	C₂×C₃×C₄	—	2	1	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	1	no	—
770	C₂×C₃×C₄	—	2	1	no	—
771	C₂×C₃×C₄	—	2	8	no	—
772	C₂×C₃×C₄	—	2	1	no	—
773	C₂×C₃×C₄	—	2	1	no	—
774	C₂×C₃×C₄	—	2	1	no	—
775	C₂×C₃×C₄	—	2	2	no	—
776	C₂×C₃×C₄	—	2	1	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	2	no	—
779	C₂×C₃×C₄	—	2	2	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	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	1	no	—
791	C₂×C₃×C₄	—	2	1	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	1	no	—
794	C₂×C₃×C₄	—	2	1	no	—
795	C₂×C₃×C₄	—	2	1	no	—
796	C₂×C₃×C₄	—	2	2	no	—
797	C₂×C₃×C₄	—	2	2	no	—
798	C₂×C₃×C₄	—	2	1	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	2	no	—
802	C₂×C₃×C₄	—	2	1	no	—
803	C₂×C₃×C₄	—	2	2	no	—
804	C₂×C₃×C₄	—	2	1	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	1	no	—
807	C₂×C₃×C₄	—	2	1	no	—
808	C₂×C₃×C₄	—	2	1	no	—
809	C₂×C₃×C₄	—	2	1	no	—
810	C₂×C₃×C₄	—	2	2	no	—
811	C₂×C₃×C₄	—	2	1	no	—
812	C₂×C₃×C₄	—	2	1	no	—
813	C₂×C₃×C₄	—	2	1	no	—
814	C₂×C₃×C₄	—	4	8	no	—
815	C₂×C₃×C₄	—	4	8	no	—
816	C₂×C₃×C₄	—	4	4	no	—
817	C₂×C₃×C₄	—	4	4	no	—
818	C₂×C₃×C₄	—	8	4	no	—
819	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
820	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
821	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
822	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
823	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
824	C₂⁴	—	2	4	no	—
825	C₂⁴	—	2	4	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	—	4	2	no	—
831	C₂⁴	—	4	2	no	—
832	C₂⁴	—	4	2	no	—
833	C₂⁴	—	4	2	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	—	4	2	no	—
837	C₂⁴	C₂×C₃×D₄	1	8	yes	—
838	C₂⁴	C₂⁴×C₃	1	2	yes	—
839	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
840	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
841	C₂⁴	C₂⁴×C₃	1	2	yes	—
842	C₂⁴	C₂⁴×C₃	1	2	yes	—
843	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
844	#41	—	4	16	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	4	no	—
852	C₂×D₄	—	2	4	no	—
853	C₂×D₄	—	2	4	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	4	16	no	—
870	C₂×D₄	—	4	1	no	—
871	C₂×D₄	—	4	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	4	2	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	—	4	2	no	—
880	C₂×D₄	—	4	2	no	—
881	C₂×D₄	—	4	1	no	—
882	C₂×D₄	—	4	1	no	—
883	C₂×D₄	—	4	1	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	32	no	—
892	C₂×D₄	—	4	16	no	—
893	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
894	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
895	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
914	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	4	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	4	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	1	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	4	1	no	—
964	C₂²⋊C₄	—	4	1	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	1	no	—
967	C₂²⋊C₄	—	4	1	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	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	1	no	—
985	C₂²⋊C₄	—	4	1	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	4	2	no	—
992	C₂²×C₃	—	2	2	no	—
993	C₂²×C₃	—	2	4	no	—
994	C₂²×C₃	—	2	4	no	—
995	C₂²×C₃	—	2	4	no	—
996	C₂²×C₃	—	2	4	no	—
997	C₂²×C₃	—	2	2	no	—
998	C₂²×C₃	—	2	2	no	—
999	C₂²×C₃	—	2	2	no	—
1000	C₂²×C₃	—	2	4	no	—
1001	C₂²×C₃	—	2	4	no	—
1002	C₂²×C₃	—	2	2	no	—
1003	C₂²×C₃	—	2	2	no	—
1004	C₂²×C₃	—	4	1	no	—
1005	C₂²×C₃	—	4	1	no	—
1006	C₂²×C₃	—	4	2	no	—
1007	C₂²×C₃	—	4	1	no	—
1008	C₂²×C₃	—	4	2	no	—
1009	C₂²×C₃	—	4	2	no	—
1010	C₂²×C₃	—	4	2	no	—
1011	C₂²×C₃	—	4	1	no	—
1012	C₂²×C₃	—	4	1	no	—
1013	C₂²×C₃	—	4	1	no	—
1014	C₂²×C₃	—	4	2	no	—
1015	C₂²×C₃	—	4	2	no	—
1016	C₂²×C₃	—	4	1	no	—
1017	C₂²×C₃	—	4	2	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	2	no	—
1020	C₂²×C₃	—	4	1	no	—
1021	C₂²×C₃	—	4	2	no	—
1022	C₂²×C₃	—	4	2	no	—
1023	C₂²×C₃	—	4	1	no	—
1024	C₂²×C₃	—	4	1	no	—
1025	C₂²×C₃	—	4	2	no	—
1026	C₂²×C₃	—	4	1	no	—
1027	C₂²×C₃	—	4	2	no	—
1028	C₂²×C₃	—	4	1	no	—
1029	C₂²×C₃	—	4	1	no	—
1030	C₂²×C₃	—	4	2	no	—
1031	C₂²×C₃	—	4	2	no	—
1032	C₂²×C₃	—	4	1	no	—
1033	C₂²×C₃	—	4	2	no	—
1034	C₂²×C₃	—	8	16	no	—
1035	C₂²×C₃	—	8	16	no	—
1036	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1037	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1039	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1040	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1041	C₂²×C₃	#585	1	1	yes	characteristic
1042	C₂²×C₃	#585	1	1	yes	characteristic
1043	C₃×C₄	—	2	2	no	—
1044	C₃×C₄	—	2	2	no	—
1045	C₃×C₄	—	4	1	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	2	no	—
1051	C₃×C₄	—	4	1	no	—
1052	C₃×C₄	—	4	1	no	—
1053	C₃×C₄	—	4	1	no	—
1054	C₃×C₄	—	4	1	no	—
1055	C₃×C₄	—	4	1	no	—
1056	C₃×C₄	—	4	1	no	—
1057	C₃×C₄	—	4	2	no	—
1058	C₃×C₄	—	4	2	no	—
1059	C₃×C₄	#534	1	4	yes	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	2	no	—
1068	C₂³	—	2	2	no	—
1069	C₂³	—	2	2	no	—
1070	C₂³	—	2	2	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	2	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	1	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	2	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	—	8	4	no	—
1104	C₂³	—	8	4	no	—
1105	C₂³	—	8	4	no	—
1106	C₂³	—	8	4	no	—
1107	C₂³	—	8	4	no	—
1108	C₂³	—	8	4	no	—
1109	C₂³	—	8	4	no	—
1110	C₂³	—	8	4	no	—
1111	C₂³	—	8	4	no	—
1112	C₂³	C₂²×C₃×D₄	1	4	yes	—
1113	C₂³	C₂²×C₃×D₄	1	2	yes	—
1114	C₂³	C₂²×C₃×D₄	1	4	yes	—
1115	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1116	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1117	Q₈	—	4	4	no	—
1118	D₄	—	2	8	no	—
1119	D₄	—	2	8	no	—
1120	D₄	—	2	8	no	—
1121	D₄	—	4	8	no	—
1122	D₄	—	4	8	no	—
1123	D₄	—	4	8	no	—
1124	D₄	—	4	8	no	—
1125	D₄	—	4	8	no	—
1126	D₄	—	4	8	no	—
1127	D₄	—	4	4	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	4	no	—
1130	D₄	—	8	4	no	—
1131	D₄	—	8	4	no	—
1132	D₄	—	8	4	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	8	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	4	8	no	—
1181	C₂×C₄	—	4	8	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	8	4	no	—
1185	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1186	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1187	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1188	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1189	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1190	C₂×C₃	—	4	4	no	—
1191	C₂×C₃	—	4	2	no	—
1192	C₂×C₃	—	4	4	no	—
1193	C₂×C₃	—	4	2	no	—
1194	C₂×C₃	—	8	1	no	—
1195	C₂×C₃	—	8	2	no	—
1196	C₂×C₃	C₂×#534	1	1	yes	characteristic
1197	C₂×C₃	#3484	1	1	yes	characteristic
1198	C₂×C₃	#3485	1	1	yes	characteristic
1199	C₂×C₃	#3542	1	1	yes	characteristic
1200	C₂×C₃	#3546	1	1	yes	characteristic
1201	C₂×C₃	#3546	1	1	yes	characteristic
1202	C₂×C₃	#3558	1	1	yes	characteristic
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	4	no	—
1205	C₂²	—	2	4	no	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	2	4	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	4	no	—
1212	C₂²	—	2	4	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	2	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	8	16	no	—
1246	C₂²	—	8	16	no	—
1247	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1248	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1249	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1250	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1251	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1252	C₂²	C₃×#585	1	1	yes	characteristic
1253	C₂²	C₃×#585	1	1	yes	characteristic
1254	C₄	—	2	2	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	2	no	—
1259	C₄	—	4	2	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	2	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	1	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	2	no	—
1269	C₄	—	4	2	no	—
1270	C₄	C₃×#534	1	4	yes	—
1271	C₃	#42474	1	1	yes	characteristic, direct product factor, Sylow
1272	C₂	—	4	2	no	—
1273	C₂	—	4	4	no	—
1274	C₂	—	4	2	no	—
1275	C₂	—	4	4	no	—
1276	C₂	—	8	2	no	—
1277	C₂	—	8	1	no	—
1278	C₂	C₂×C₃×#534	1	1	yes	characteristic
1279	C₂	C₃×#3484	1	1	yes	characteristic
1280	C₂	C₃×#3485	1	1	yes	characteristic
1281	C₂	C₃×#3542	1	1	yes	characteristic
1282	C₂	C₃×#3546	1	1	yes	characteristic
1283	C₂	C₃×#3546	1	1	yes	characteristic
1284	C₂	C₃×#3558	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×D₄²	C₂	semidirect
3. C₃×#2812	C₂	semidirect
4. C₃×#2701	C₂	semidirect
5. C₃×#2697	C₂	semidirect
6. C₃×#2682	C₂	semidirect
7. C₃×#2678	C₂	semidirect
8. C₃×#2622	C₂	semidirect
9. C₃×#2620	C₂	semidirect
10. C₃×#2613	C₂	semidirect
11. C₃×#2447	C₂	semidirect
12. C₃×#2445	C₂	semidirect
13. C₃×#2435	C₂	semidirect
14. C₃×#2431	C₂	semidirect
15. C₃×#2422	C₂	semidirect
16. C₃×#2422	C₂	semidirect
17. C₃×#2415	C₂	semidirect
18. C₃×#2414	C₂	semidirect
19. C₃×#2408	C₂	semidirect
20. C₃×#2407	C₂	semidirect
21. C₃×#2405	C₂	semidirect
22. C₃×#2392	C₂	semidirect
23. C₃×#2309	C₂	semidirect
24. #42474	C₃	direct (N × H)
25. C₂²×C₃×#41	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
34. C₂×C₃×#123	C₂²	semidirect
35. C₂×C₃×#123	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
37. C₂×C₃×#123	C₂²	semidirect
38. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃×#121	C₂²	semidirect
45. C₂×C₃×#121	C₂²	semidirect
48. C₂×C₃×#120	C₂²	semidirect
49. C₂×C₃×#120	C₂²	semidirect
52. C₂×C₃×C₄×D₄	C₂²	semidirect
53. C₂×C₃×C₄×D₄	C₂²	semidirect
54. C₂×C₃×C₄×D₄	C₂²	semidirect
55. C₂×C₃×#117	C₂²	semidirect
56. C₂×C₃×#117	C₂²	semidirect
57. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
58. C₃×#398	C₂²	semidirect
59. C₃×#397	C₂²	semidirect
60. C₃×#397	C₂²	semidirect
61. C₃×#397	C₂²	semidirect
62. C₃×#397	C₂²	semidirect
63. C₃×#397	C₂²	semidirect
64. C₃×#397	C₂²	semidirect
65. C₃×#396	C₂²	semidirect
66. C₃×#396	C₂²	semidirect
67. C₃×#396	C₂²	semidirect
68. C₃×#396	C₂²	semidirect
71. C₃×#394	C₂²	semidirect
72. C₃×#394	C₂²	semidirect
73. C₃×#394	C₂²	semidirect
74. C₃×#394	C₂²	semidirect
75. C₃×#394	C₂²	semidirect
76. C₃×#394	C₂²	semidirect
77. C₃×#394	C₂²	semidirect
78. C₃×#394	C₂²	semidirect
79. C₃×#394	C₂²	semidirect
80. C₃×#394	C₂²	semidirect
81. C₃×#394	C₂²	semidirect
82. C₃×#394	C₂²	semidirect
83. C₃×#394	C₂²	semidirect
85. C₃×#392	C₂²	semidirect
86. C₃×#392	C₂²	semidirect
87. C₃×#392	C₂²	semidirect
88. C₃×#392	C₂²	semidirect
89. C₃×#392	C₂²	semidirect
90. C₃×#391	C₂²	semidirect
91. C₃×#391	C₂²	semidirect
94. C₃×#390	C₂²	semidirect
95. C₃×#390	C₂²	semidirect
96. C₃×#390	C₂²	semidirect
97. C₃×#390	C₂²	semidirect
98. C₃×#390	C₂²	semidirect
99. C₃×#390	C₂²	semidirect
100. C₃×#390	C₂²	semidirect
101. C₃×#389	C₂²	semidirect
102. C₃×#389	C₂²	semidirect
103. C₃×#389	C₂²	semidirect
104. C₃×#388	C₂²	semidirect
105. C₃×#388	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
108. C₃×#386	C₂²	semidirect
109. C₃×#386	C₂²	semidirect
110. C₃×#385	C₂²	semidirect
111. C₃×#385	C₂²	semidirect
112. C₃×#385	C₂²	semidirect
113. C₃×#385	C₂²	semidirect
114. C₃×#384	C₂²	semidirect
115. C₃×#381	C₂²	semidirect
116. C₃×#380	C₂²	semidirect
117. C₃×#380	C₂²	semidirect
118. C₃×#379	C₂²	semidirect
119. C₃×#379	C₂²	semidirect
120. C₃×#379	C₂²	semidirect
121. C₃×#379	C₂²	semidirect
122. C₃×#379	C₂²	semidirect
123. C₃×C₄×C₄⋊C₄	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
126. C₂×#546	C₂×C₃	semidirect
127. C₂×D₄²	C₂×C₃	semidirect
128. #2812	C₂×C₃	semidirect
129. #2701	C₂×C₃	semidirect
130. #2697	C₂×C₃	semidirect
131. #2682	C₂×C₃	semidirect
132. #2678	C₂×C₃	semidirect
133. #2622	C₂×C₃	semidirect
134. #2620	C₂×C₃	semidirect
135. #2613	C₂×C₃	semidirect
136. #2447	C₂×C₃	semidirect
137. #2445	C₂×C₃	semidirect
138. #2435	C₂×C₃	semidirect
139. #2431	C₂×C₃	semidirect
140. #2422	C₂×C₃	semidirect
141. #2422	C₂×C₃	semidirect
142. #2415	C₂×C₃	semidirect
143. #2414	C₂×C₃	semidirect
144. #2408	C₂×C₃	semidirect
145. #2407	C₂×C₃	semidirect
146. #2405	C₂×C₃	semidirect
147. #2392	C₂×C₃	semidirect
148. #2309	C₂×C₃	semidirect
163. C₂²×C₃×D₄	D₄	semidirect
287. C₂²×#41	C₂²×C₃	semidirect
295. C₂×#124	C₂²×C₃	semidirect
296. C₂×#123	C₂²×C₃	semidirect
297. C₂×#123	C₂²×C₃	semidirect
298. C₂×#123	C₂²×C₃	semidirect
299. C₂×#123	C₂²×C₃	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
301. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
306. C₂×#121	C₂²×C₃	semidirect
307. C₂×#121	C₂²×C₃	semidirect
310. C₂×#120	C₂²×C₃	semidirect
311. C₂×#120	C₂²×C₃	semidirect
314. C₂×C₄×D₄	C₂²×C₃	semidirect
315. C₂×C₄×D₄	C₂²×C₃	semidirect
316. C₂×C₄×D₄	C₂²×C₃	semidirect
317. C₂×#117	C₂²×C₃	semidirect
318. C₂×#117	C₂²×C₃	semidirect
319. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
320. #398	C₂²×C₃	semidirect
321. #397	C₂²×C₃	semidirect
322. #397	C₂²×C₃	semidirect
323. #397	C₂²×C₃	semidirect
324. #397	C₂²×C₃	semidirect
325. #397	C₂²×C₃	semidirect
326. #397	C₂²×C₃	semidirect
327. #396	C₂²×C₃	semidirect
328. #396	C₂²×C₃	semidirect
329. #396	C₂²×C₃	semidirect
330. #396	C₂²×C₃	semidirect
333. #394	C₂²×C₃	semidirect
334. #394	C₂²×C₃	semidirect
335. #394	C₂²×C₃	semidirect
336. #394	C₂²×C₃	semidirect
337. #394	C₂²×C₃	semidirect
338. #394	C₂²×C₃	semidirect
339. #394	C₂²×C₃	semidirect
340. #394	C₂²×C₃	semidirect
341. #394	C₂²×C₃	semidirect
342. #394	C₂²×C₃	semidirect
343. #394	C₂²×C₃	semidirect
344. #394	C₂²×C₃	semidirect
345. #394	C₂²×C₃	semidirect
347. #392	C₂²×C₃	semidirect
348. #392	C₂²×C₃	semidirect
349. #392	C₂²×C₃	semidirect
350. #392	C₂²×C₃	semidirect
351. #392	C₂²×C₃	semidirect
352. #391	C₂²×C₃	semidirect
353. #391	C₂²×C₃	semidirect
356. #390	C₂²×C₃	semidirect
357. #390	C₂²×C₃	semidirect
358. #390	C₂²×C₃	semidirect
359. #390	C₂²×C₃	semidirect
360. #390	C₂²×C₃	semidirect
361. #390	C₂²×C₃	semidirect
362. #390	C₂²×C₃	semidirect
363. #389	C₂²×C₃	semidirect
364. #389	C₂²×C₃	semidirect
365. #389	C₂²×C₃	semidirect
366. #388	C₂²×C₃	semidirect
367. #388	C₂²×C₃	semidirect
368. #386	C₂²×C₃	semidirect
369. #386	C₂²×C₃	semidirect
370. #386	C₂²×C₃	semidirect
371. #386	C₂²×C₃	semidirect
372. #385	C₂²×C₃	semidirect
373. #385	C₂²×C₃	semidirect
374. #385	C₂²×C₃	semidirect
375. #385	C₂²×C₃	semidirect
376. #384	C₂²×C₃	semidirect
377. #381	C₂²×C₃	semidirect
378. #380	C₂²×C₃	semidirect
379. #380	C₂²×C₃	semidirect
380. #379	C₂²×C₃	semidirect
381. #379	C₂²×C₃	semidirect
382. #379	C₂²×C₃	semidirect
383. #379	C₂²×C₃	semidirect
384. #379	C₂²×C₃	semidirect
385. C₄×C₄⋊C₄	C₂²×C₃	semidirect
386. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
387. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
570. C₂²×D₄	C₃×D₄	semidirect
1271. C₃	#42474	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×D₄²	2
C₃×#2812	2
C₃×#2701	2
C₃×#2697	2
C₃×#2682	2
C₃×#2678	2
C₃×#2622	2
C₃×#2620	2
C₃×#2613	2
C₃×#2447	2
C₃×#2445	2
C₃×#2435	2
C₃×#2431	2
C₃×#2422	2
C₃×#2415	2
C₃×#2414	2
C₃×#2408	2
C₃×#2407	2
C₃×#2405	2
C₃×#2392	2
C₃×#2309	2
#42474	3

Subgroups — C3×#42474 #10661081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42474 #10661081