Subgroups — C₃×#34471 #10653078

Order 768.

3112 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₃×#2375	C₂	1	2	yes	maximal, complemented
4	C₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2358	C₂	1	2	yes	maximal, complemented
8	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2333	C₂	1	2	yes	maximal, complemented
14	C₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2308	C₂	1	2	yes	maximal, complemented
21	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#34471	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	2	yes	—
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₃×D₄²	C₄	1	16	yes	complemented
29	C₂×C₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	2	yes	—
33	C₂×C₃×#120	C₂²	1	2	yes	—
34	C₂×C₃×#120	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
42	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
48	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
50	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
51	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
52	C₃×#390	C₂²	1	1	yes	characteristic
53	C₃×#390	C₂²	1	1	yes	characteristic
54	C₃×#390	C₂²	1	1	yes	characteristic
55	C₃×#390	C₂²	1	1	yes	characteristic
56	C₃×#390	C₂²	1	1	yes	characteristic, complemented
57	C₃×#390	C₂²	1	1	yes	characteristic, complemented
58	C₃×#390	C₂²	1	2	yes	complemented
59	C₃×#390	C₂²	1	2	yes	complemented
60	C₃×#390	C₂²	1	2	yes	complemented
61	C₃×#390	C₂²	1	2	yes	complemented
62	C₃×#390	C₂²	1	2	yes	complemented
63	C₃×#390	C₂²	1	2	yes	complemented
64	C₃×#390	C₂²	1	1	yes	characteristic, complemented
65	C₃×#390	C₂²	1	1	yes	characteristic, complemented
66	C₃×#390	C₂²	1	2	yes	complemented
67	C₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₃×#388	C₂²	1	2	yes	complemented
70	C₃×#388	C₂²	1	2	yes	complemented
71	C₃×#388	C₂²	1	1	yes	characteristic, complemented
72	C₃×#388	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	2	yes	complemented
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	1	yes	characteristic, complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	2	yes	complemented
80	C₃×#387	C₂²	1	1	yes	characteristic, complemented
81	C₃×#387	C₂²	1	2	yes	complemented
82	C₃×#387	C₂²	1	1	yes	characteristic, complemented
83	C₃×#386	C₂²	1	1	yes	characteristic
84	C₃×#386	C₂²	1	1	yes	characteristic
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	complemented
87	C₃×#386	C₂²	1	2	yes	complemented
88	C₃×#386	C₂²	1	2	yes	complemented
89	C₃×#386	C₂²	1	2	yes	complemented
90	C₃×#386	C₂²	1	2	yes	complemented
91	C₃×#386	C₂²	1	2	yes	complemented
92	C₃×#386	C₂²	1	2	yes	complemented
93	C₃×#386	C₂²	1	2	yes	complemented
94	C₃×#386	C₂²	1	2	yes	complemented
95	C₃×#386	C₂²	1	2	yes	complemented
96	C₃×#386	C₂²	1	2	yes	complemented
97	C₃×#386	C₂²	1	2	yes	complemented
98	C₃×#386	C₂²	1	2	yes	complemented
99	C₃×#386	C₂²	1	2	yes	complemented
100	C₃×#385	C₂²	1	2	yes	complemented
101	C₃×#385	C₂²	1	2	yes	complemented
102	C₃×#385	C₂²	1	1	yes	characteristic, complemented
103	C₃×#385	C₂²	1	1	yes	characteristic, complemented
104	C₃×#382	C₂²	1	1	yes	characteristic, complemented
105	C₃×#381	C₂²	1	2	yes	complemented
106	C₃×#381	C₂²	1	2	yes	complemented
107	C₃×#380	C₂²	1	2	yes	complemented
108	C₃×#380	C₂²	1	1	yes	characteristic, complemented
109	C₃×#380	C₂²	1	1	yes	characteristic, complemented
110	C₃×#379	C₂²	1	2	yes	complemented
111	C₃×#379	C₂²	1	2	yes	complemented
112	C₃×#379	C₂²	1	2	yes	complemented
113	C₃×#379	C₂²	1	2	yes	complemented
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×#376	C₂²	1	1	yes	characteristic, complemented
125	C₂×D₄²	C₂×C₃	1	1	yes	characteristic
126	#2377	C₂×C₃	1	2	yes	complemented
127	#2375	C₂×C₃	1	2	yes	complemented
128	#2366	C₂×C₃	1	1	yes	characteristic, complemented
129	#2363	C₂×C₃	1	1	yes	characteristic, complemented
130	#2361	C₂×C₃	1	1	yes	characteristic, complemented
131	#2358	C₂×C₃	1	2	yes	complemented
132	#2357	C₂×C₃	1	1	yes	characteristic, complemented
133	#2352	C₂×C₃	1	1	yes	characteristic, complemented
134	D₄×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
135	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
136	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
137	#2333	C₂×C₃	1	2	yes	complemented
138	#2328	C₂×C₃	1	1	yes	characteristic, complemented
139	#2324	C₂×C₃	1	1	yes	characteristic, complemented
140	#2321	C₂×C₃	1	2	yes	complemented
141	#2321	C₂×C₃	1	2	yes	complemented
142	#2319	C₂×C₃	1	1	yes	characteristic, complemented
143	#2309	C₂×C₃	1	1	yes	characteristic, complemented
144	#2308	C₂×C₃	1	2	yes	complemented
145	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#390	C₂×C₃	1	1	yes	characteristic, complemented
147	#2290	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁵×C₃	C₂³	1	2	yes	—
149	C₂⁵×C₃	C₂³	1	2	yes	—
150	C₂²×C₃×D₄	—	4	2	no	—
151	C₂²×C₃×D₄	—	4	2	no	—
152	C₂²×C₃×D₄	—	4	2	no	—
153	C₂²×C₃×D₄	—	4	2	no	—
154	C₂²×C₃×D₄	—	4	4	no	—
155	C₂²×C₃×D₄	—	4	4	no	—
156	C₂²×C₃×D₄	C₂×C₄	1	8	yes	complemented
157	C₂²×C₃×D₄	C₂×C₄	1	8	yes	complemented
158	C₂²×C₃×D₄	C₂×C₄	1	16	yes	complemented
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂³	1	2	yes	—
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂²×C₃×D₄	C₂³	1	2	yes	—
167	C₂²×C₃×D₄	C₂³	1	2	yes	—
168	C₂²×C₃×D₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	2	yes	—
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
175	C₂³×C₃×C₄	C₂³	1	2	yes	—
176	C₂³×C₃×C₄	C₂³	1	2	yes	—
177	C₂³×C₃×C₄	C₂³	1	2	yes	—
178	C₂³×C₃×C₄	C₂³	1	2	yes	—
179	C₃×#127	C₂×C₄	1	8	yes	complemented
180	C₃×#121	C₂×C₄	1	8	yes	complemented
181	C₃×#121	C₂×C₄	1	8	yes	complemented
182	C₃×#121	C₂×C₄	1	16	yes	complemented
183	C₃×#120	C₂×C₄	1	16	yes	complemented
184	C₃×#120	C₂×C₄	1	16	yes	complemented
185	C₃×C₄×D₄	—	4	2	no	—
186	C₃×C₄×D₄	—	4	2	no	—
187	C₃×C₄×D₄	—	4	2	no	—
188	C₃×C₄×D₄	—	4	2	no	—
189	C₃×C₄×D₄	—	4	4	no	—
190	C₃×C₄×D₄	—	4	4	no	—
191	C₃×C₄×D₄	—	4	4	no	—
192	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
193	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
194	C₃×#117	—	4	2	no	—
195	C₃×#117	—	4	2	no	—
196	C₂×C₃×C₄⋊C₄	—	4	2	no	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
211	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
212	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
213	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	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	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₄²	—	4	2	no	—
249	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	2	yes	—
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	2	yes	—
256	C₂×C₃×C₄²	C₂³	1	2	yes	—
257	C₂×C₃×C₄²	C₂³	1	2	yes	—
258	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
259	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	1	yes	characteristic
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	1	yes	characteristic
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	1	yes	characteristic
273	C₃×#95	C₂³	1	1	yes	characteristic
274	C₃×#95	C₂³	1	1	yes	characteristic
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	1	yes	characteristic
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₂³×D₄	C₂²×C₃	1	2	yes	—
280	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
281	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
282	D₄²	C₃×C₄	1	16	yes	complemented
283	C₂×#127	C₂²×C₃	1	1	yes	characteristic
284	C₂×#121	C₂²×C₃	1	1	yes	characteristic
285	C₂×#121	C₂²×C₃	1	2	yes	—
286	C₂×#121	C₂²×C₃	1	1	yes	characteristic
287	C₂×#120	C₂²×C₃	1	2	yes	—
288	C₂×#120	C₂²×C₃	1	2	yes	—
289	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
292	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
293	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
294	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
297	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
300	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
302	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
303	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
304	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
305	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
306	#390	C₂²×C₃	1	1	yes	characteristic
307	#390	C₂²×C₃	1	1	yes	characteristic
308	#390	C₂²×C₃	1	1	yes	characteristic
309	#390	C₂²×C₃	1	1	yes	characteristic
310	#390	C₂²×C₃	1	2	yes	complemented
311	#390	C₂²×C₃	1	1	yes	characteristic, complemented
312	#390	C₂²×C₃	1	2	yes	complemented
313	#390	C₂²×C₃	1	1	yes	characteristic, complemented
314	#390	C₂²×C₃	1	2	yes	complemented
315	#390	C₂²×C₃	1	2	yes	complemented
316	#390	C₂²×C₃	1	2	yes	complemented
317	#390	C₂²×C₃	1	1	yes	characteristic, complemented
318	#390	C₂²×C₃	1	2	yes	complemented
319	#390	C₂²×C₃	1	1	yes	characteristic, complemented
320	#390	C₂²×C₃	1	2	yes	complemented
321	#389	C₂²×C₃	1	1	yes	characteristic, complemented
322	#389	C₂²×C₃	1	1	yes	characteristic, complemented
323	#388	C₂²×C₃	1	2	yes	complemented
324	#388	C₂²×C₃	1	2	yes	complemented
325	#388	C₂²×C₃	1	1	yes	characteristic, complemented
326	#388	C₂²×C₃	1	2	yes	complemented
327	#388	C₂²×C₃	1	2	yes	complemented
328	#388	C₂²×C₃	1	2	yes	complemented
329	#388	C₂²×C₃	1	2	yes	complemented
330	#388	C₂²×C₃	1	2	yes	complemented
331	#388	C₂²×C₃	1	2	yes	complemented
332	#388	C₂²×C₃	1	1	yes	characteristic, complemented
333	#388	C₂²×C₃	1	2	yes	complemented
334	#387	C₂²×C₃	1	1	yes	characteristic, complemented
335	#387	C₂²×C₃	1	2	yes	complemented
336	#387	C₂²×C₃	1	1	yes	characteristic, complemented
337	#386	C₂²×C₃	1	1	yes	characteristic
338	#386	C₂²×C₃	1	2	yes	—
339	#386	C₂²×C₃	1	1	yes	characteristic
340	#386	C₂²×C₃	1	2	yes	complemented
341	#386	C₂²×C₃	1	2	yes	complemented
342	#386	C₂²×C₃	1	2	yes	complemented
343	#386	C₂²×C₃	1	2	yes	complemented
344	#386	C₂²×C₃	1	2	yes	complemented
345	#386	C₂²×C₃	1	2	yes	complemented
346	#386	C₂²×C₃	1	2	yes	complemented
347	#386	C₂²×C₃	1	2	yes	complemented
348	#386	C₂²×C₃	1	2	yes	complemented
349	#386	C₂²×C₃	1	2	yes	complemented
350	#386	C₂²×C₃	1	2	yes	complemented
351	#386	C₂²×C₃	1	2	yes	complemented
352	#386	C₂²×C₃	1	2	yes	complemented
353	#386	C₂²×C₃	1	2	yes	complemented
354	#385	C₂²×C₃	1	1	yes	characteristic, complemented
355	#385	C₂²×C₃	1	2	yes	complemented
356	#385	C₂²×C₃	1	2	yes	complemented
357	#385	C₂²×C₃	1	1	yes	characteristic, complemented
358	#382	C₂²×C₃	1	1	yes	characteristic, complemented
359	#381	C₂²×C₃	1	2	yes	complemented
360	#381	C₂²×C₃	1	2	yes	complemented
361	#380	C₂²×C₃	1	2	yes	complemented
362	#380	C₂²×C₃	1	1	yes	characteristic, complemented
363	#380	C₂²×C₃	1	1	yes	characteristic, complemented
364	#379	C₂²×C₃	1	2	yes	complemented
365	#379	C₂²×C₃	1	2	yes	complemented
366	#379	C₂²×C₃	1	2	yes	complemented
367	#379	C₂²×C₃	1	2	yes	complemented
368	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
369	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
370	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
371	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
372	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
373	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
375	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
376	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
378	#376	C₂²×C₃	1	1	yes	characteristic, complemented
379	C₂⁴×C₃	—	2	4	no	—
380	C₂⁴×C₃	—	2	4	no	—
381	C₂⁴×C₃	—	4	2	no	—
382	C₂⁴×C₃	—	4	2	no	—
383	C₂⁴×C₃	—	4	2	no	—
384	C₂⁴×C₃	—	4	2	no	—
385	C₂⁴×C₃	—	4	2	no	—
386	C₂⁴×C₃	—	4	2	no	—
387	C₂⁴×C₃	—	4	2	no	—
388	C₂⁴×C₃	—	4	2	no	—
389	C₂⁴×C₃	—	4	2	no	—
390	C₂⁴×C₃	—	4	2	no	—
391	C₂⁴×C₃	C₂²×C₄	1	8	yes	—
392	C₂⁴×C₃	C₂²×C₄	1	8	yes	—
393	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
394	C₂⁴×C₃	C₂⁴	1	2	yes	—
395	C₂⁴×C₃	C₂⁴	1	2	yes	—
396	C₂⁴×C₃	C₂⁴	1	2	yes	—
397	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×D₄	—	2	4	no	—
399	C₂×C₃×D₄	—	2	4	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	2	no	—
402	C₂×C₃×D₄	—	2	2	no	—
403	C₂×C₃×D₄	—	2	2	no	—
404	C₂×C₃×D₄	—	2	2	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	4	16	no	—
409	C₂×C₃×D₄	—	4	16	no	—
410	C₂×C₃×D₄	—	4	2	no	—
411	C₂×C₃×D₄	—	4	2	no	—
412	C₂×C₃×D₄	—	4	2	no	—
413	C₂×C₃×D₄	—	4	2	no	—
414	C₂×C₃×D₄	—	4	2	no	—
415	C₂×C₃×D₄	—	4	2	no	—
416	C₂×C₃×D₄	—	4	2	no	—
417	C₂×C₃×D₄	—	4	2	no	—
418	C₂×C₃×D₄	—	4	2	no	—
419	C₂×C₃×D₄	—	4	2	no	—
420	C₂×C₃×D₄	—	4	32	no	—
421	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
422	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
423	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
424	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
425	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
426	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
427	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
428	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
429	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
430	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
431	C₂²×C₃×C₄	—	2	2	no	—
432	C₂²×C₃×C₄	—	2	2	no	—
433	C₂²×C₃×C₄	—	2	2	no	—
434	C₂²×C₃×C₄	—	2	2	no	—
435	C₂²×C₃×C₄	—	2	2	no	—
436	C₂²×C₃×C₄	—	2	2	no	—
437	C₂²×C₃×C₄	—	2	4	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	4	no	—
440	C₂²×C₃×C₄	—	4	1	no	—
441	C₂²×C₃×C₄	—	4	1	no	—
442	C₂²×C₃×C₄	—	4	1	no	—
443	C₂²×C₃×C₄	—	4	2	no	—
444	C₂²×C₃×C₄	—	4	2	no	—
445	C₂²×C₃×C₄	—	4	2	no	—
446	C₂²×C₃×C₄	—	4	2	no	—
447	C₂²×C₃×C₄	—	4	2	no	—
448	C₂²×C₃×C₄	—	4	2	no	—
449	C₂²×C₃×C₄	—	4	2	no	—
450	C₂²×C₃×C₄	—	4	2	no	—
451	C₂²×C₃×C₄	—	4	2	no	—
452	C₂²×C₃×C₄	—	4	2	no	—
453	C₂²×C₃×C₄	—	4	2	no	—
454	C₂²×C₃×C₄	—	4	2	no	—
455	C₂²×C₃×C₄	—	4	2	no	—
456	C₂²×C₃×C₄	—	4	2	no	—
457	C₂²×C₃×C₄	—	4	2	no	—
458	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
459	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
460	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
461	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
464	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
465	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
466	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
467	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
468	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
477	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₃×C₄⋊C₄	—	2	2	no	—
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	2	2	no	—
482	C₃×C₄⋊C₄	—	2	2	no	—
483	C₃×C₄⋊C₄	—	2	2	no	—
484	C₃×C₄⋊C₄	—	4	2	no	—
485	C₃×C₄⋊C₄	—	4	1	no	—
486	C₃×C₄⋊C₄	—	4	1	no	—
487	C₃×C₄⋊C₄	—	4	1	no	—
488	C₃×C₄⋊C₄	—	4	2	no	—
489	C₃×C₄⋊C₄	—	4	2	no	—
490	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
491	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
492	C₃×C₂²⋊C₄	—	2	2	no	—
493	C₃×C₂²⋊C₄	—	2	4	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	2	2	no	—
496	C₃×C₂²⋊C₄	—	2	4	no	—
497	C₃×C₂²⋊C₄	—	2	4	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	2	no	—
500	C₃×C₂²⋊C₄	—	4	2	no	—
501	C₃×C₂²⋊C₄	—	4	2	no	—
502	C₃×C₂²⋊C₄	—	4	2	no	—
503	C₃×C₂²⋊C₄	—	4	2	no	—
504	C₃×C₂²⋊C₄	—	4	2	no	—
505	C₃×C₂²⋊C₄	—	4	2	no	—
506	C₃×C₂²⋊C₄	—	4	2	no	—
507	C₃×C₂²⋊C₄	—	4	2	no	—
508	C₃×C₂²⋊C₄	—	4	2	no	—
509	C₃×C₂²⋊C₄	—	4	2	no	—
510	C₃×C₂²⋊C₄	—	4	1	no	—
511	C₃×C₂²⋊C₄	—	4	1	no	—
512	C₃×C₂²⋊C₄	—	4	1	no	—
513	C₃×C₂²⋊C₄	—	4	2	no	—
514	C₃×C₂²⋊C₄	—	4	2	no	—
515	C₃×C₂²⋊C₄	—	4	2	no	—
516	C₃×C₂²⋊C₄	—	4	2	no	—
517	C₃×C₂²⋊C₄	—	4	2	no	—
518	C₃×C₂²⋊C₄	—	4	2	no	—
519	C₃×C₂²⋊C₄	—	4	2	no	—
520	C₃×C₂²⋊C₄	—	4	2	no	—
521	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
522	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
523	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
524	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
525	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
526	C₃×C₄²	—	2	2	no	—
527	C₃×C₄²	—	2	2	no	—
528	C₃×C₄²	—	2	2	no	—
529	C₃×C₄²	—	2	2	no	—
530	C₃×C₄²	—	4	1	no	—
531	C₃×C₄²	—	4	1	no	—
532	C₃×C₄²	—	4	2	no	—
533	C₃×C₄²	—	4	2	no	—
534	C₃×C₄²	—	4	2	no	—
535	C₃×C₄²	—	4	2	no	—
536	C₃×C₄²	C₂²×C₄	1	4	yes	—
537	C₂⁵	C₂³×C₃	1	2	yes	—
538	C₂⁵	C₂³×C₃	1	2	yes	—
539	C₂²×D₄	—	4	2	no	—
540	C₂²×D₄	—	4	2	no	—
541	C₂²×D₄	—	4	2	no	—
542	C₂²×D₄	—	4	2	no	—
543	C₂²×D₄	—	4	4	no	—
544	C₂²×D₄	—	4	4	no	—
545	C₂²×D₄	C₂×C₃×C₄	1	8	yes	complemented
546	C₂²×D₄	C₂×C₃×C₄	1	8	yes	complemented
547	C₂²×D₄	C₂×C₃×C₄	1	16	yes	complemented
548	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₃	1	2	yes	—
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₃	1	2	yes	—
554	C₂²×D₄	C₂³×C₃	1	2	yes	—
555	C₂²×D₄	C₂³×C₃	1	2	yes	—
556	C₂²×D₄	C₂³×C₃	1	2	yes	—
557	C₂²×D₄	C₂³×C₃	1	2	yes	—
558	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₃	1	2	yes	—
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	2	yes	—
564	C₂³×C₄	C₂³×C₃	1	2	yes	—
565	C₂³×C₄	C₂³×C₃	1	2	yes	—
566	C₂³×C₄	C₂³×C₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₃	1	2	yes	—
568	#127	C₂×C₃×C₄	1	8	yes	complemented
569	#121	C₂×C₃×C₄	1	8	yes	complemented
570	#121	C₂×C₃×C₄	1	8	yes	complemented
571	#121	C₂×C₃×C₄	1	16	yes	complemented
572	#120	C₂×C₃×C₄	1	16	yes	complemented
573	#120	C₂×C₃×C₄	1	16	yes	complemented
574	C₄×D₄	—	4	2	no	—
575	C₄×D₄	—	4	2	no	—
576	C₄×D₄	—	4	2	no	—
577	C₄×D₄	—	4	2	no	—
578	C₄×D₄	—	4	4	no	—
579	C₄×D₄	—	4	4	no	—
580	C₄×D₄	—	4	4	no	—
581	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
582	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
583	#117	—	4	2	no	—
584	#117	—	4	2	no	—
585	C₂×C₄⋊C₄	—	4	2	no	—
586	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	—	4	4	no	—
600	C₂×C₂²⋊C₄	—	4	4	no	—
601	C₂×C₂²⋊C₄	—	4	4	no	—
602	C₂×C₂²⋊C₄	—	4	4	no	—
603	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
637	C₂×C₄²	—	4	2	no	—
638	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₃	1	2	yes	—
643	C₂×C₄²	C₂³×C₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
649	#95	C₂³×C₃	1	1	yes	characteristic
650	#95	C₂³×C₃	1	1	yes	characteristic
651	#95	C₂³×C₃	1	1	yes	characteristic
652	#95	C₂³×C₃	1	1	yes	characteristic
653	#95	C₂³×C₃	1	1	yes	characteristic
654	#95	C₂³×C₃	1	1	yes	characteristic
655	#95	C₂³×C₃	1	2	yes	—
656	#95	C₂³×C₃	1	2	yes	—
657	#95	C₂³×C₃	1	2	yes	—
658	#95	C₂³×C₃	1	2	yes	—
659	#95	C₂³×C₃	1	2	yes	—
660	#95	C₂³×C₃	1	2	yes	—
661	#95	C₂³×C₃	1	1	yes	characteristic
662	#95	C₂³×C₃	1	1	yes	characteristic
663	#95	C₂³×C₃	1	1	yes	characteristic
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	1	yes	characteristic
666	#95	C₂³×C₃	1	2	yes	—
667	#95	C₂³×C₃	1	2	yes	—
668	C₂³×C₃	—	2	1	no	—
669	C₂³×C₃	—	2	1	no	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	—	2	1	no	—
672	C₂³×C₃	—	2	1	no	—
673	C₂³×C₃	—	2	2	no	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	—	2	1	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	2	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	2	2	no	—
680	C₂³×C₃	—	2	2	no	—
681	C₂³×C₃	—	2	2	no	—
682	C₂³×C₃	—	2	2	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	2	2	no	—
685	C₂³×C₃	—	2	2	no	—
686	C₂³×C₃	—	2	2	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	1	no	—
690	C₂³×C₃	—	2	1	no	—
691	C₂³×C₃	—	2	2	no	—
692	C₂³×C₃	—	2	2	no	—
693	C₂³×C₃	—	2	1	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	2	no	—
696	C₂³×C₃	—	2	16	no	—
697	C₂³×C₃	—	4	8	no	—
698	C₂³×C₃	—	4	8	no	—
699	C₂³×C₃	—	4	8	no	—
700	C₂³×C₃	—	4	8	no	—
701	C₂³×C₃	—	4	8	no	—
702	C₂³×C₃	—	8	4	no	—
703	C₂³×C₃	—	8	4	no	—
704	C₂³×C₃	—	8	4	no	—
705	C₂³×C₃	—	8	4	no	—
706	C₂³×C₃	—	8	4	no	—
707	C₂³×C₃	—	8	4	no	—
708	C₂³×C₃	—	8	4	no	—
709	C₂³×C₃	—	8	4	no	—
710	C₂³×C₃	C₂³×C₄	1	2	yes	—
711	C₂³×C₃	C₂³×C₄	1	4	yes	—
712	C₂³×C₃	C₂³×C₄	1	4	yes	—
713	C₂³×C₃	C₂³×C₄	1	4	yes	—
714	C₂³×C₃	C₂³×C₄	1	2	yes	—
715	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
716	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
717	C₂³×C₃	C₂⁵	1	1	yes	characteristic
718	C₃×D₄	—	2	8	no	—
719	C₃×D₄	—	2	16	no	—
720	C₃×D₄	—	2	8	no	—
721	C₃×D₄	—	2	8	no	—
722	C₃×D₄	—	2	8	no	—
723	C₃×D₄	—	4	8	no	—
724	C₃×D₄	—	4	8	no	—
725	C₃×D₄	—	4	8	no	—
726	C₃×D₄	—	4	8	no	—
727	C₃×D₄	—	4	8	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	2	1	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	2	1	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	2	no	—
734	C₂×C₃×C₄	—	2	2	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	1	no	—
740	C₂×C₃×C₄	—	2	8	no	—
741	C₂×C₃×C₄	—	2	8	no	—
742	C₂×C₃×C₄	—	2	1	no	—
743	C₂×C₃×C₄	—	2	1	no	—
744	C₂×C₃×C₄	—	2	1	no	—
745	C₂×C₃×C₄	—	2	1	no	—
746	C₂×C₃×C₄	—	2	1	no	—
747	C₂×C₃×C₄	—	2	1	no	—
748	C₂×C₃×C₄	—	2	1	no	—
749	C₂×C₃×C₄	—	2	1	no	—
750	C₂×C₃×C₄	—	2	2	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	2	no	—
753	C₂×C₃×C₄	—	2	2	no	—
754	C₂×C₃×C₄	—	2	2	no	—
755	C₂×C₃×C₄	—	2	2	no	—
756	C₂×C₃×C₄	—	2	1	no	—
757	C₂×C₃×C₄	—	2	1	no	—
758	C₂×C₃×C₄	—	2	2	no	—
759	C₂×C₃×C₄	—	2	1	no	—
760	C₂×C₃×C₄	—	2	2	no	—
761	C₂×C₃×C₄	—	2	1	no	—
762	C₂×C₃×C₄	—	2	1	no	—
763	C₂×C₃×C₄	—	2	1	no	—
764	C₂×C₃×C₄	—	2	1	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	1	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	2	no	—
770	C₂×C₃×C₄	—	2	1	no	—
771	C₂×C₃×C₄	—	2	1	no	—
772	C₂×C₃×C₄	—	2	2	no	—
773	C₂×C₃×C₄	—	2	1	no	—
774	C₂×C₃×C₄	—	2	1	no	—
775	C₂×C₃×C₄	—	4	8	no	—
776	C₂×C₃×C₄	—	4	4	no	—
777	C₂×C₃×C₄	—	4	4	no	—
778	C₂×C₃×C₄	—	8	4	no	—
779	C₂×C₃×C₄	—	8	4	no	—
780	C₂×C₃×C₄	—	8	4	no	—
781	C₂×C₃×C₄	—	8	4	no	—
782	C₂×C₃×C₄	—	8	4	no	—
783	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
784	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
785	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
786	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
787	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
788	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
789	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
790	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
791	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
792	C₂⁴	—	2	4	no	—
793	C₂⁴	—	2	4	no	—
794	C₂⁴	—	4	2	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	—	4	2	no	—
801	C₂⁴	—	4	2	no	—
802	C₂⁴	—	4	2	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	C₂²×C₃×C₄	1	8	yes	—
805	C₂⁴	C₂²×C₃×C₄	1	8	yes	—
806	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
807	C₂⁴	C₂⁴×C₃	1	2	yes	—
808	C₂⁴	C₂⁴×C₃	1	2	yes	—
809	C₂⁴	C₂⁴×C₃	1	2	yes	—
810	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	4	16	no	—
822	C₂×D₄	—	4	16	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	32	no	—
834	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
835	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
836	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
837	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
838	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
839	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
840	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
841	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
842	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
843	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
872	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
873	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
874	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	1	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	—	4	1	no	—
903	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
904	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	4	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	1	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	1	no	—
934	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
935	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
936	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
937	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
938	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
939	C₄²	—	2	2	no	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	4	1	no	—
944	C₄²	—	4	1	no	—
945	C₄²	—	4	2	no	—
946	C₄²	—	4	2	no	—
947	C₄²	—	4	2	no	—
948	C₄²	—	4	2	no	—
949	C₄²	C₂²×C₃×C₄	1	4	yes	—
950	C₂²×C₃	—	2	2	no	—
951	C₂²×C₃	—	2	2	no	—
952	C₂²×C₃	—	2	2	no	—
953	C₂²×C₃	—	2	2	no	—
954	C₂²×C₃	—	2	2	no	—
955	C₂²×C₃	—	2	2	no	—
956	C₂²×C₃	—	2	2	no	—
957	C₂²×C₃	—	2	4	no	—
958	C₂²×C₃	—	2	2	no	—
959	C₂²×C₃	—	2	4	no	—
960	C₂²×C₃	—	2	4	no	—
961	C₂²×C₃	—	2	4	no	—
962	C₂²×C₃	—	2	4	no	—
963	C₂²×C₃	—	2	4	no	—
964	C₂²×C₃	—	2	4	no	—
965	C₂²×C₃	—	2	4	no	—
966	C₂²×C₃	—	2	2	no	—
967	C₂²×C₃	—	2	4	no	—
968	C₂²×C₃	—	4	2	no	—
969	C₂²×C₃	—	4	2	no	—
970	C₂²×C₃	—	4	1	no	—
971	C₂²×C₃	—	4	2	no	—
972	C₂²×C₃	—	4	2	no	—
973	C₂²×C₃	—	4	2	no	—
974	C₂²×C₃	—	4	1	no	—
975	C₂²×C₃	—	4	2	no	—
976	C₂²×C₃	—	4	2	no	—
977	C₂²×C₃	—	4	2	no	—
978	C₂²×C₃	—	4	1	no	—
979	C₂²×C₃	—	4	2	no	—
980	C₂²×C₃	—	4	2	no	—
981	C₂²×C₃	—	4	2	no	—
982	C₂²×C₃	—	4	1	no	—
983	C₂²×C₃	—	4	2	no	—
984	C₂²×C₃	—	8	16	no	—
985	C₂²×C₃	—	8	16	no	—
986	C₂²×C₃	#518	1	4	yes	—
987	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
988	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
989	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
990	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
991	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
993	C₂²×C₃	#585	1	1	yes	characteristic
994	C₃×C₄	—	2	2	no	—
995	C₃×C₄	—	2	2	no	—
996	C₃×C₄	—	2	2	no	—
997	C₃×C₄	—	2	4	no	—
998	C₃×C₄	—	2	2	no	—
999	C₃×C₄	—	2	2	no	—
1000	C₃×C₄	—	4	1	no	—
1001	C₃×C₄	—	4	1	no	—
1002	C₃×C₄	—	4	2	no	—
1003	C₃×C₄	—	4	1	no	—
1004	C₃×C₄	—	4	1	no	—
1005	C₃×C₄	—	4	1	no	—
1006	C₃×C₄	—	4	2	no	—
1007	C₃×C₄	—	4	1	no	—
1008	C₃×C₄	—	4	2	no	—
1009	C₃×C₄	—	4	2	no	—
1010	C₃×C₄	—	4	1	no	—
1011	C₃×C₄	#518	1	4	yes	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	16	no	—
1041	C₂³	—	4	8	no	—
1042	C₂³	—	4	8	no	—
1043	C₂³	—	4	8	no	—
1044	C₂³	—	4	8	no	—
1045	C₂³	—	4	8	no	—
1046	C₂³	—	8	4	no	—
1047	C₂³	—	8	4	no	—
1048	C₂³	—	8	4	no	—
1049	C₂³	—	8	4	no	—
1050	C₂³	—	8	4	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	—	8	4	no	—
1053	C₂³	—	8	4	no	—
1054	C₂³	C₂³×C₃×C₄	1	2	yes	—
1055	C₂³	C₂³×C₃×C₄	1	4	yes	—
1056	C₂³	C₂³×C₃×C₄	1	4	yes	—
1057	C₂³	C₂³×C₃×C₄	1	4	yes	—
1058	C₂³	C₂³×C₃×C₄	1	2	yes	—
1059	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1060	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1061	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1062	D₄	—	2	8	no	—
1063	D₄	—	2	16	no	—
1064	D₄	—	2	8	no	—
1065	D₄	—	2	8	no	—
1066	D₄	—	2	8	no	—
1067	D₄	—	4	8	no	—
1068	D₄	—	4	8	no	—
1069	D₄	—	4	8	no	—
1070	D₄	—	4	8	no	—
1071	D₄	—	4	8	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	8	no	—
1085	C₂×C₄	—	2	8	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	4	8	no	—
1120	C₂×C₄	—	4	4	no	—
1121	C₂×C₄	—	4	4	no	—
1122	C₂×C₄	—	8	4	no	—
1123	C₂×C₄	—	8	4	no	—
1124	C₂×C₄	—	8	4	no	—
1125	C₂×C₄	—	8	4	no	—
1126	C₂×C₄	—	8	4	no	—
1127	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1128	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1129	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1130	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1131	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
1132	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1133	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1134	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1135	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1136	C₂×C₃	—	2	4	no	—
1137	C₂×C₃	—	4	4	no	—
1138	C₂×C₃	—	4	4	no	—
1139	C₂×C₃	—	4	2	no	—
1140	C₂×C₃	—	4	4	no	—
1141	C₂×C₃	C₂×#518	1	1	yes	characteristic
1142	C₂×C₃	C₂×#518	1	1	yes	characteristic
1143	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1144	C₂×C₃	#3537	1	1	yes	characteristic
1145	C₂×C₃	#3542	1	1	yes	characteristic
1146	C₂×C₃	#3543	1	1	yes	characteristic
1147	C₂×C₃	#3558	1	1	yes	characteristic
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	4	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	4	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	4	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	2	4	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	4	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	4	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	16	no	—
1183	C₂²	—	8	16	no	—
1184	C₂²	C₃×#518	1	4	yes	—
1185	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
1186	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1187	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₂²	C₃×#585	1	1	yes	characteristic
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	4	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	C₃×#518	1	4	yes	—
1210	C₃	#34471	1	1	yes	characteristic, direct product factor, Sylow
1211	C₂	—	2	4	no	—
1212	C₂	—	4	2	no	—
1213	C₂	—	4	4	no	—
1214	C₂	—	4	4	no	—
1215	C₂	—	4	4	no	—
1216	C₂	C₂×C₃×#518	1	1	yes	characteristic
1217	C₂	C₂×C₃×#518	1	1	yes	characteristic
1218	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
1219	C₂	C₃×#3537	1	1	yes	characteristic
1220	C₂	C₃×#3542	1	1	yes	characteristic
1221	C₂	C₃×#3543	1	1	yes	characteristic
1222	C₂	C₃×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×D₄²	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2377	C₂	semidirect
3. C₃×#2375	C₂	semidirect
4. C₃×#2366	C₂	semidirect
5. C₃×#2363	C₂	semidirect
6. C₃×#2361	C₂	semidirect
7. C₃×#2358	C₂	semidirect
8. C₃×#2357	C₂	semidirect
9. C₃×#2352	C₂	semidirect
10. C₃×D₄×C₂²⋊C₄	C₂	semidirect
11. C₃×D₄×C₂²⋊C₄	C₂	semidirect
12. C₃×D₄×C₂²⋊C₄	C₂	semidirect
13. C₃×#2333	C₂	semidirect
14. C₃×#2328	C₂	semidirect
15. C₃×#2324	C₂	semidirect
16. C₃×#2321	C₂	semidirect
17. C₃×#2321	C₂	semidirect
18. C₃×#2319	C₂	semidirect
19. C₃×#2309	C₂	semidirect
20. C₃×#2308	C₂	semidirect
21. C₃×C₄×#121	C₂	semidirect
22. C₂×C₃×#390	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #34471	C₃	direct (N × H)
28. C₃×D₄²	C₄	semidirect
37. C₂×C₃×C₄×D₄	C₂²	semidirect
38. C₂×C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×C₄×D₄	C₂²	semidirect
40. C₂×C₃×C₄×D₄	C₂²	semidirect
41. C₂×C₃×C₄×D₄	C₂²	semidirect
42. C₂×C₃×C₄×D₄	C₂²	semidirect
43. C₂×C₃×C₄×D₄	C₂²	semidirect
44. C₂×C₃×#117	C₂²	semidirect
45. C₂×C₃×#117	C₂²	semidirect
46. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
47. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
48. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
50. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
51. C₂²×C₃×C₄²	C₂²	semidirect
56. C₃×#390	C₂²	semidirect
57. C₃×#390	C₂²	semidirect
58. C₃×#390	C₂²	semidirect
59. C₃×#390	C₂²	semidirect
60. C₃×#390	C₂²	semidirect
61. C₃×#390	C₂²	semidirect
62. C₃×#390	C₂²	semidirect
63. C₃×#390	C₂²	semidirect
64. C₃×#390	C₂²	semidirect
65. C₃×#390	C₂²	semidirect
66. C₃×#390	C₂²	semidirect
67. C₃×#389	C₂²	semidirect
68. C₃×#389	C₂²	semidirect
69. C₃×#388	C₂²	semidirect
70. C₃×#388	C₂²	semidirect
71. C₃×#388	C₂²	semidirect
72. C₃×#388	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#387	C₂²	semidirect
81. C₃×#387	C₂²	semidirect
82. C₃×#387	C₂²	semidirect
86. C₃×#386	C₂²	semidirect
87. C₃×#386	C₂²	semidirect
88. C₃×#386	C₂²	semidirect
89. C₃×#386	C₂²	semidirect
90. C₃×#386	C₂²	semidirect
91. C₃×#386	C₂²	semidirect
92. C₃×#386	C₂²	semidirect
93. C₃×#386	C₂²	semidirect
94. C₃×#386	C₂²	semidirect
95. C₃×#386	C₂²	semidirect
96. C₃×#386	C₂²	semidirect
97. C₃×#386	C₂²	semidirect
98. C₃×#386	C₂²	semidirect
99. C₃×#386	C₂²	semidirect
100. C₃×#385	C₂²	semidirect
101. C₃×#385	C₂²	semidirect
102. C₃×#385	C₂²	semidirect
103. C₃×#385	C₂²	semidirect
104. C₃×#382	C₂²	semidirect
105. C₃×#381	C₂²	semidirect
106. C₃×#381	C₂²	semidirect
107. C₃×#380	C₂²	semidirect
108. C₃×#380	C₂²	semidirect
109. C₃×#380	C₂²	semidirect
110. C₃×#379	C₂²	semidirect
111. C₃×#379	C₂²	semidirect
112. C₃×#379	C₂²	semidirect
113. C₃×#379	C₂²	semidirect
114. C₃×C₄×C₄⋊C₄	C₂²	semidirect
115. C₃×C₄×C₄⋊C₄	C₂²	semidirect
116. C₃×C₄×C₄⋊C₄	C₂²	semidirect
117. C₃×C₄×C₄⋊C₄	C₂²	semidirect
118. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
119. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
120. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×#376	C₂²	semidirect
126. #2377	C₂×C₃	semidirect
127. #2375	C₂×C₃	semidirect
128. #2366	C₂×C₃	semidirect
129. #2363	C₂×C₃	semidirect
130. #2361	C₂×C₃	semidirect
131. #2358	C₂×C₃	semidirect
132. #2357	C₂×C₃	semidirect
133. #2352	C₂×C₃	semidirect
134. D₄×C₂²⋊C₄	C₂×C₃	semidirect
135. D₄×C₂²⋊C₄	C₂×C₃	semidirect
136. D₄×C₂²⋊C₄	C₂×C₃	semidirect
137. #2333	C₂×C₃	semidirect
138. #2328	C₂×C₃	semidirect
139. #2324	C₂×C₃	semidirect
140. #2321	C₂×C₃	semidirect
141. #2321	C₂×C₃	semidirect
142. #2319	C₂×C₃	semidirect
143. #2309	C₂×C₃	semidirect
144. #2308	C₂×C₃	semidirect
145. C₄×#121	C₂×C₃	semidirect
146. C₂×#390	C₂×C₃	semidirect
147. #2290	C₂×C₃	semidirect
156. C₂²×C₃×D₄	C₂×C₄	semidirect
157. C₂²×C₃×D₄	C₂×C₄	semidirect
158. C₂²×C₃×D₄	C₂×C₄	semidirect
179. C₃×#127	C₂×C₄	semidirect
180. C₃×#121	C₂×C₄	semidirect
181. C₃×#121	C₂×C₄	semidirect
182. C₃×#121	C₂×C₄	semidirect
183. C₃×#120	C₂×C₄	semidirect
184. C₃×#120	C₂×C₄	semidirect
192. C₃×C₄×D₄	C₂×C₄	semidirect
193. C₃×C₄×D₄	C₂×C₄	semidirect
282. D₄²	C₃×C₄	semidirect
291. C₂×C₄×D₄	C₂²×C₃	semidirect
292. C₂×C₄×D₄	C₂²×C₃	semidirect
293. C₂×C₄×D₄	C₂²×C₃	semidirect
294. C₂×C₄×D₄	C₂²×C₃	semidirect
295. C₂×C₄×D₄	C₂²×C₃	semidirect
296. C₂×C₄×D₄	C₂²×C₃	semidirect
297. C₂×C₄×D₄	C₂²×C₃	semidirect
298. C₂×#117	C₂²×C₃	semidirect
299. C₂×#117	C₂²×C₃	semidirect
300. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
301. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
302. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
303. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
304. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
305. C₂²×C₄²	C₂²×C₃	semidirect
310. #390	C₂²×C₃	semidirect
311. #390	C₂²×C₃	semidirect
312. #390	C₂²×C₃	semidirect
313. #390	C₂²×C₃	semidirect
314. #390	C₂²×C₃	semidirect
315. #390	C₂²×C₃	semidirect
316. #390	C₂²×C₃	semidirect
317. #390	C₂²×C₃	semidirect
318. #390	C₂²×C₃	semidirect
319. #390	C₂²×C₃	semidirect
320. #390	C₂²×C₃	semidirect
321. #389	C₂²×C₃	semidirect
322. #389	C₂²×C₃	semidirect
323. #388	C₂²×C₃	semidirect
324. #388	C₂²×C₃	semidirect
325. #388	C₂²×C₃	semidirect
326. #388	C₂²×C₃	semidirect
327. #388	C₂²×C₃	semidirect
328. #388	C₂²×C₃	semidirect
329. #388	C₂²×C₃	semidirect
330. #388	C₂²×C₃	semidirect
331. #388	C₂²×C₃	semidirect
332. #388	C₂²×C₃	semidirect
333. #388	C₂²×C₃	semidirect
334. #387	C₂²×C₃	semidirect
335. #387	C₂²×C₃	semidirect
336. #387	C₂²×C₃	semidirect
340. #386	C₂²×C₃	semidirect
341. #386	C₂²×C₃	semidirect
342. #386	C₂²×C₃	semidirect
343. #386	C₂²×C₃	semidirect
344. #386	C₂²×C₃	semidirect
345. #386	C₂²×C₃	semidirect
346. #386	C₂²×C₃	semidirect
347. #386	C₂²×C₃	semidirect
348. #386	C₂²×C₃	semidirect
349. #386	C₂²×C₃	semidirect
350. #386	C₂²×C₃	semidirect
351. #386	C₂²×C₃	semidirect
352. #386	C₂²×C₃	semidirect
353. #386	C₂²×C₃	semidirect
354. #385	C₂²×C₃	semidirect
355. #385	C₂²×C₃	semidirect
356. #385	C₂²×C₃	semidirect
357. #385	C₂²×C₃	semidirect
358. #382	C₂²×C₃	semidirect
359. #381	C₂²×C₃	semidirect
360. #381	C₂²×C₃	semidirect
361. #380	C₂²×C₃	semidirect
362. #380	C₂²×C₃	semidirect
363. #380	C₂²×C₃	semidirect
364. #379	C₂²×C₃	semidirect
365. #379	C₂²×C₃	semidirect
366. #379	C₂²×C₃	semidirect
367. #379	C₂²×C₃	semidirect
368. C₄×C₄⋊C₄	C₂²×C₃	semidirect
369. C₄×C₄⋊C₄	C₂²×C₃	semidirect
370. C₄×C₄⋊C₄	C₂²×C₃	semidirect
371. C₄×C₄⋊C₄	C₂²×C₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
373. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
375. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
377. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
378. #376	C₂²×C₃	semidirect
545. C₂²×D₄	C₂×C₃×C₄	semidirect
546. C₂²×D₄	C₂×C₃×C₄	semidirect
547. C₂²×D₄	C₂×C₃×C₄	semidirect
568. #127	C₂×C₃×C₄	semidirect
569. #121	C₂×C₃×C₄	semidirect
570. #121	C₂×C₃×C₄	semidirect
571. #121	C₂×C₃×C₄	semidirect
572. #120	C₂×C₃×C₄	semidirect
573. #120	C₂×C₃×C₄	semidirect
581. C₄×D₄	C₂×C₃×C₄	semidirect
582. C₄×D₄	C₂×C₃×C₄	semidirect
1210. C₃	#34471	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×D₄²	2
C₃×#2377	2
C₃×#2375	2
C₃×#2366	2
C₃×#2363	2
C₃×#2361	2
C₃×#2358	2
C₃×#2357	2
C₃×#2352	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2333	2
C₃×#2328	2
C₃×#2324	2
C₃×#2321	2
C₃×#2319	2
C₃×#2309	2
C₃×#2308	2
C₃×C₄×#121	2
C₂×C₃×#390	2
C₃×#2290	2
#34471	3

Subgroups — C3×#34471 #10653078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34471 #10653078