Subgroups — C₃×#35007 #10653614

Order 768.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#538	C₂	1	2	yes	maximal, complemented
2	C₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2662	C₂	1	2	yes	maximal, complemented
7	C₃×#2661	C₂	1	2	yes	maximal, complemented
8	C₃×#2555	C₂	1	2	yes	maximal, complemented
9	C₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2472	C₂	1	2	yes	maximal, complemented
13	C₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2424	C₂	1	2	yes	maximal, complemented
18	C₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2321	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×C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	#35007	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₃×#538	—	2	16	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₃×#126	C₂²	1	2	yes	complemented
31	C₂×C₃×#126	C₂²	1	2	yes	complemented
32	C₂×C₃×#124	C₂²	1	2	yes	complemented
33	C₂×C₃×#124	C₂²	1	2	yes	complemented
34	C₂×C₃×#124	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×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×#121	C₂²	1	2	yes	—
39	C₂×C₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	2	yes	complemented
43	C₂×C₃×#121	C₂²	1	2	yes	complemented
44	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#121	C₂²	1	2	yes	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	—
49	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
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
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
58	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
59	C₃×#398	C₂²	1	2	yes	complemented
60	C₃×#397	C₂²	1	2	yes	complemented
61	C₃×#396	C₂²	1	2	yes	complemented
62	C₃×#396	C₂²	1	2	yes	complemented
63	C₃×#395	C₂²	1	2	yes	complemented
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	complemented
66	C₃×#394	C₂²	1	2	yes	complemented
67	C₃×#394	C₂²	1	2	yes	complemented
68	C₃×#394	C₂²	1	2	yes	complemented
69	C₃×#394	C₂²	1	2	yes	complemented
70	C₃×#393	C₂²	1	2	yes	complemented
71	C₃×#392	C₂²	1	2	yes	—
72	C₃×#392	C₂²	1	2	yes	—
73	C₃×#392	C₂²	1	2	yes	—
74	C₃×#392	C₂²	1	2	yes	complemented
75	C₃×#390	C₂²	1	2	yes	—
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#390	C₂²	1	1	yes	characteristic
78	C₃×#390	C₂²	1	1	yes	characteristic
79	C₃×#390	C₂²	1	1	yes	characteristic
80	C₃×#390	C₂²	1	1	yes	characteristic
81	C₃×#390	C₂²	1	1	yes	characteristic
82	C₃×#390	C₂²	1	2	yes	—
83	C₃×#390	C₂²	1	1	yes	characteristic
84	C₃×#390	C₂²	1	1	yes	characteristic
85	C₃×#390	C₂²	1	2	yes	complemented
86	C₃×#390	C₂²	1	2	yes	complemented
87	C₃×#390	C₂²	1	1	yes	characteristic, complemented
88	C₃×#390	C₂²	1	2	yes	complemented
89	C₃×#390	C₂²	1	2	yes	complemented
90	C₃×#390	C₂²	1	1	yes	characteristic, complemented
91	C₃×#389	C₂²	1	1	yes	characteristic, complemented
92	C₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₃×#389	C₂²	1	1	yes	characteristic, complemented
95	C₃×#388	C₂²	1	2	yes	complemented
96	C₃×#388	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×#388	C₂²	1	2	yes	complemented
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	—
109	C₃×#384	C₂²	1	1	yes	characteristic, complemented
110	C₃×#380	C₂²	1	1	yes	characteristic
111	C₃×#380	C₂²	1	1	yes	characteristic, complemented
112	C₃×#379	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, 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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
125	C₂×#538	C₂×C₃	1	2	yes	complemented
126	#2860	C₂×C₃	1	1	yes	characteristic, complemented
127	#2858	C₂×C₃	1	1	yes	characteristic, complemented
128	#2856	C₂×C₃	1	1	yes	characteristic, complemented
129	#2854	C₂×C₃	1	1	yes	characteristic, complemented
130	#2662	C₂×C₃	1	2	yes	complemented
131	#2661	C₂×C₃	1	2	yes	complemented
132	#2555	C₂×C₃	1	2	yes	complemented
133	#2554	C₂×C₃	1	2	yes	complemented
134	#2512	C₂×C₃	1	1	yes	characteristic, complemented
135	#2491	C₂×C₃	1	1	yes	characteristic, complemented
136	#2472	C₂×C₃	1	2	yes	complemented
137	#2445	C₂×C₃	1	1	yes	characteristic, complemented
138	#2440	C₂×C₃	1	1	yes	characteristic, complemented
139	#2433	C₂×C₃	1	1	yes	characteristic, complemented
140	#2428	C₂×C₃	1	1	yes	characteristic, complemented
141	#2424	C₂×C₃	1	2	yes	complemented
142	#2416	C₂×C₃	1	1	yes	characteristic, complemented
143	#2408	C₂×C₃	1	1	yes	characteristic, complemented
144	#2321	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	C₄²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁵×C₃	C₂³	1	2	yes	—
149	C₂²×C₃×Q₈	C₂³	1	2	yes	—
150	C₂²×C₃×D₄	—	2	4	no	—
151	C₂²×C₃×D₄	—	4	2	no	—
152	C₂²×C₃×D₄	—	4	2	no	—
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	2	yes	—
163	C₂²×C₃×D₄	C₂³	1	2	yes	—
164	C₂²×C₃×D₄	C₂³	1	2	yes	—
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	2	yes	—
171	C₂³×C₃×C₄	C₂³	1	2	yes	—
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊Q₈	—	4	2	no	—
175	C₃×#127	—	4	2	no	—
176	C₃×#127	—	4	2	no	—
177	C₃×#126	—	2	8	no	—
178	C₃×#126	—	2	8	no	—
179	C₃×#124	—	2	8	no	—
180	C₃×#124	—	2	8	no	—
181	C₃×#124	—	4	4	no	—
182	C₃×#123	—	2	8	no	—
183	C₃×#123	—	2	8	no	—
184	C₃×C₂²⋊Q₈	—	2	8	no	—
185	C₃×#121	—	2	8	no	—
186	C₃×#121	—	2	8	no	—
187	C₃×#121	—	2	4	no	—
188	C₃×#121	—	2	8	no	—
189	C₃×#121	—	4	4	no	—
190	C₃×#121	—	4	2	no	—
191	C₃×#121	—	4	2	no	—
192	C₃×#121	—	4	2	no	—
193	C₃×#120	—	2	8	no	—
194	C₃×#120	—	2	8	no	—
195	C₃×#120	—	2	8	no	—
196	C₃×C₄×D₄	—	2	8	no	—
197	C₃×C₄×D₄	—	2	4	no	—
198	C₃×C₄×D₄	—	2	4	no	—
199	C₃×C₄×D₄	—	4	2	no	—
200	C₃×C₄×D₄	D₄	1	8	yes	complemented
201	C₂×C₃×C₄⋊C₄	—	4	2	no	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
219	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
253	C₂×C₃×C₄²	—	4	2	no	—
254	C₂×C₃×C₄²	—	4	2	no	—
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
258	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
259	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
260	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
261	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₄²	C₂³	1	2	yes	—
263	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
264	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
265	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
266	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
267	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
268	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
269	C₃×#95	C₂³	1	1	yes	characteristic
270	C₃×#95	C₂³	1	1	yes	characteristic
271	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
283	#538	—	2	16	no	—
284	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₂×#127	C₂²×C₃	1	1	yes	characteristic
286	C₂×#127	C₂²×C₃	1	1	yes	characteristic
287	C₂×#126	C₂²×C₃	1	2	yes	complemented
288	C₂×#126	C₂²×C₃	1	2	yes	complemented
289	C₂×#124	C₂²×C₃	1	2	yes	complemented
290	C₂×#124	C₂²×C₃	1	2	yes	complemented
291	C₂×#124	C₂²×C₃	1	2	yes	complemented
292	C₂×#123	C₂²×C₃	1	2	yes	complemented
293	C₂×#123	C₂²×C₃	1	2	yes	complemented
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
295	C₂×#121	C₂²×C₃	1	2	yes	—
296	C₂×#121	C₂²×C₃	1	1	yes	characteristic
297	C₂×#121	C₂²×C₃	1	1	yes	characteristic
298	C₂×#121	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	2	yes	complemented
300	C₂×#121	C₂²×C₃	1	2	yes	complemented
301	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₂×#121	C₂²×C₃	1	2	yes	complemented
303	C₂×#120	C₂²×C₃	1	2	yes	—
304	C₂×#120	C₂²×C₃	1	2	yes	—
305	C₂×#120	C₂²×C₃	1	2	yes	—
306	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
307	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
311	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
314	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
316	#398	C₂²×C₃	1	2	yes	complemented
317	#397	C₂²×C₃	1	2	yes	complemented
318	#396	C₂²×C₃	1	2	yes	complemented
319	#396	C₂²×C₃	1	2	yes	complemented
320	#395	C₂²×C₃	1	2	yes	complemented
321	#394	C₂²×C₃	1	2	yes	—
322	#394	C₂²×C₃	1	2	yes	complemented
323	#394	C₂²×C₃	1	2	yes	complemented
324	#394	C₂²×C₃	1	2	yes	complemented
325	#394	C₂²×C₃	1	2	yes	complemented
326	#394	C₂²×C₃	1	2	yes	complemented
327	#393	C₂²×C₃	1	2	yes	complemented
328	#392	C₂²×C₃	1	2	yes	—
329	#392	C₂²×C₃	1	2	yes	—
330	#392	C₂²×C₃	1	2	yes	—
331	#392	C₂²×C₃	1	2	yes	complemented
332	#390	C₂²×C₃	1	1	yes	characteristic
333	#390	C₂²×C₃	1	1	yes	characteristic
334	#390	C₂²×C₃	1	1	yes	characteristic
335	#390	C₂²×C₃	1	1	yes	characteristic
336	#390	C₂²×C₃	1	1	yes	characteristic
337	#390	C₂²×C₃	1	1	yes	characteristic
338	#390	C₂²×C₃	1	2	yes	—
339	#390	C₂²×C₃	1	1	yes	characteristic
340	#390	C₂²×C₃	1	1	yes	characteristic
341	#390	C₂²×C₃	1	2	yes	—
342	#390	C₂²×C₃	1	2	yes	complemented
343	#390	C₂²×C₃	1	2	yes	complemented
344	#390	C₂²×C₃	1	1	yes	characteristic, complemented
345	#390	C₂²×C₃	1	2	yes	complemented
346	#390	C₂²×C₃	1	1	yes	characteristic, complemented
347	#390	C₂²×C₃	1	2	yes	complemented
348	#389	C₂²×C₃	1	1	yes	characteristic, complemented
349	#389	C₂²×C₃	1	1	yes	characteristic, complemented
350	#389	C₂²×C₃	1	1	yes	characteristic, complemented
351	#389	C₂²×C₃	1	1	yes	characteristic, complemented
352	#388	C₂²×C₃	1	2	yes	complemented
353	#388	C₂²×C₃	1	2	yes	complemented
354	#388	C₂²×C₃	1	2	yes	complemented
355	#388	C₂²×C₃	1	2	yes	complemented
356	#388	C₂²×C₃	1	2	yes	complemented
357	#388	C₂²×C₃	1	2	yes	complemented
358	#388	C₂²×C₃	1	2	yes	complemented
359	#388	C₂²×C₃	1	2	yes	complemented
360	#386	C₂²×C₃	1	2	yes	—
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	2	yes	complemented
363	#386	C₂²×C₃	1	2	yes	complemented
364	#386	C₂²×C₃	1	2	yes	complemented
365	#385	C₂²×C₃	1	2	yes	—
366	#384	C₂²×C₃	1	1	yes	characteristic, complemented
367	#380	C₂²×C₃	1	1	yes	characteristic
368	#380	C₂²×C₃	1	1	yes	characteristic, complemented
369	#379	C₂²×C₃	1	2	yes	—
370	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
371	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
372	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
376	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
378	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
379	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
380	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
381	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
382	C₂⁴×C₃	—	2	4	no	—
383	C₂⁴×C₃	—	2	4	no	—
384	C₂⁴×C₃	—	2	4	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	C₂⁴	1	2	yes	—
390	C₂⁴×C₃	C₂⁴	1	2	yes	—
391	C₂⁴×C₃	C₂⁴	1	2	yes	—
392	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
393	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×Q₈	—	2	4	no	—
395	C₂×C₃×Q₈	—	4	2	no	—
396	C₂×C₃×Q₈	—	4	2	no	—
397	C₂×C₃×D₄	—	2	2	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	2	4	no	—
400	C₂×C₃×D₄	—	2	4	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	2	4	no	—
403	C₂×C₃×D₄	—	2	4	no	—
404	C₂×C₃×D₄	—	2	4	no	—
405	C₂×C₃×D₄	—	2	4	no	—
406	C₂×C₃×D₄	—	2	4	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	2	4	no	—
409	C₂×C₃×D₄	—	2	2	no	—
410	C₂×C₃×D₄	—	2	2	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	2	no	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	4	2	no	—
420	C₂×C₃×D₄	—	4	2	no	—
421	C₂×C₃×D₄	—	4	16	no	—
422	C₂×C₃×D₄	—	4	2	no	—
423	C₂×C₃×D₄	—	4	2	no	—
424	C₂×C₃×D₄	—	4	2	no	—
425	C₂×C₃×D₄	—	4	2	no	—
426	C₂×C₃×D₄	—	4	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	2	no	—
430	C₂×C₃×D₄	—	4	2	no	—
431	C₂×C₃×D₄	—	4	2	no	—
432	C₂×C₃×D₄	—	4	2	no	—
433	C₂×C₃×D₄	—	4	2	no	—
434	C₂×C₃×D₄	—	4	2	no	—
435	C₂×C₃×D₄	—	4	2	no	—
436	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
437	C₂²×C₃×C₄	—	2	2	no	—
438	C₂²×C₃×C₄	—	2	2	no	—
439	C₂²×C₃×C₄	—	2	2	no	—
440	C₂²×C₃×C₄	—	2	4	no	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	2	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	4	no	—
448	C₂²×C₃×C₄	—	4	1	no	—
449	C₂²×C₃×C₄	—	4	1	no	—
450	C₂²×C₃×C₄	—	4	1	no	—
451	C₂²×C₃×C₄	—	4	1	no	—
452	C₂²×C₃×C₄	—	4	1	no	—
453	C₂²×C₃×C₄	—	4	1	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	C₂×D₄	1	4	yes	—
459	C₂²×C₃×C₄	C₂×D₄	1	4	yes	complemented
460	C₂²×C₃×C₄	#41	1	4	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	2	yes	—
466	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
477	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₃×C₄⋊C₄	—	2	4	no	—
480	C₃×C₄⋊C₄	—	2	4	no	—
481	C₃×C₄⋊C₄	—	2	4	no	—
482	C₃×C₄⋊C₄	—	2	4	no	—
483	C₃×C₄⋊C₄	—	2	4	no	—
484	C₃×C₄⋊C₄	—	2	2	no	—
485	C₃×C₄⋊C₄	—	2	2	no	—
486	C₃×C₄⋊C₄	—	2	2	no	—
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	—	2	2	no	—
489	C₃×C₄⋊C₄	—	2	2	no	—
490	C₃×C₄⋊C₄	—	2	2	no	—
491	C₃×C₄⋊C₄	—	4	2	no	—
492	C₃×C₄⋊C₄	—	4	2	no	—
493	C₃×C₄⋊C₄	—	4	2	no	—
494	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
495	C₃×C₂²⋊C₄	—	2	4	no	—
496	C₃×C₂²⋊C₄	—	2	4	no	—
497	C₃×C₂²⋊C₄	—	2	2	no	—
498	C₃×C₂²⋊C₄	—	2	4	no	—
499	C₃×C₂²⋊C₄	—	2	4	no	—
500	C₃×C₂²⋊C₄	—	2	4	no	—
501	C₃×C₂²⋊C₄	—	2	4	no	—
502	C₃×C₂²⋊C₄	—	2	4	no	—
503	C₃×C₂²⋊C₄	—	2	4	no	—
504	C₃×C₂²⋊C₄	—	2	4	no	—
505	C₃×C₂²⋊C₄	—	2	4	no	—
506	C₃×C₂²⋊C₄	—	2	4	no	—
507	C₃×C₂²⋊C₄	—	2	4	no	—
508	C₃×C₂²⋊C₄	—	2	2	no	—
509	C₃×C₂²⋊C₄	—	2	2	no	—
510	C₃×C₂²⋊C₄	—	2	4	no	—
511	C₃×C₂²⋊C₄	—	2	4	no	—
512	C₃×C₂²⋊C₄	—	2	4	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	—	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	—	4	2	no	—
522	C₃×C₂²⋊C₄	—	4	2	no	—
523	C₃×C₂²⋊C₄	—	4	2	no	—
524	C₃×C₂²⋊C₄	—	4	2	no	—
525	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
526	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
527	C₃×C₂²⋊C₄	#41	1	4	yes	—
528	C₃×C₄²	—	2	4	no	—
529	C₃×C₄²	—	2	2	no	—
530	C₃×C₄²	—	2	2	no	—
531	C₃×C₄²	—	2	2	no	—
532	C₃×C₄²	—	2	2	no	—
533	C₃×C₄²	—	2	2	no	—
534	C₃×C₄²	—	2	2	no	—
535	C₃×C₄²	—	2	2	no	—
536	C₃×C₄²	—	4	1	no	—
537	C₃×C₄²	—	4	1	no	—
538	C₃×C₄²	—	4	1	no	—
539	C₃×C₄²	—	4	1	no	—
540	C₃×C₄²	—	4	1	no	—
541	C₃×C₄²	C₂×D₄	1	4	yes	complemented
542	C₂⁵	C₂³×C₃	1	2	yes	—
543	C₂²×Q₈	C₂³×C₃	1	2	yes	—
544	C₂²×D₄	—	2	4	no	—
545	C₂²×D₄	—	4	2	no	—
546	C₂²×D₄	—	4	2	no	—
547	C₂²×D₄	C₂³×C₃	1	2	yes	—
548	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₃	1	2	yes	—
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	C₂²×D₄	C₂³×C₃	1	2	yes	—
559	C₂²×D₄	C₂³×C₃	1	2	yes	—
560	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₃	1	2	yes	—
565	C₂³×C₄	C₂³×C₃	1	2	yes	—
566	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
568	C₄⋊Q₈	—	4	2	no	—
569	#127	—	4	2	no	—
570	#127	—	4	2	no	—
571	#126	—	2	8	no	—
572	#126	—	2	8	no	—
573	#124	—	2	8	no	—
574	#124	—	2	8	no	—
575	#124	—	4	4	no	—
576	#123	—	2	8	no	—
577	#123	—	2	8	no	—
578	C₂²⋊Q₈	—	2	8	no	—
579	#121	—	2	8	no	—
580	#121	—	2	8	no	—
581	#121	—	2	4	no	—
582	#121	—	2	8	no	—
583	#121	—	4	4	no	—
584	#121	—	4	2	no	—
585	#121	—	4	2	no	—
586	#121	—	4	2	no	—
587	#120	—	2	8	no	—
588	#120	—	2	8	no	—
589	#120	—	2	8	no	—
590	C₄×D₄	—	2	8	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	4	2	no	—
594	C₄×D₄	C₃×D₄	1	8	yes	complemented
595	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	8	no	—
613	C₂×C₂²⋊C₄	—	4	4	no	—
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	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄²	—	4	2	no	—
648	C₂×C₄²	—	4	2	no	—
649	C₂×C₄²	C₂³×C₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
663	#95	C₂³×C₃	1	1	yes	characteristic
664	#95	C₂³×C₃	1	1	yes	characteristic
665	#95	C₂³×C₃	1	1	yes	characteristic
666	#95	C₂³×C₃	1	1	yes	characteristic
667	#95	C₂³×C₃	1	1	yes	characteristic
668	#95	C₂³×C₃	1	1	yes	characteristic
669	#95	C₂³×C₃	1	2	yes	—
670	#95	C₂³×C₃	1	2	yes	—
671	#95	C₂³×C₃	1	2	yes	—
672	#95	C₂³×C₃	1	2	yes	—
673	#95	C₂³×C₃	1	2	yes	—
674	#95	C₂³×C₃	1	2	yes	—
675	#95	C₂³×C₃	1	2	yes	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	1	no	—
679	C₂³×C₃	—	2	1	no	—
680	C₂³×C₃	—	2	1	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	—	2	1	no	—
683	C₂³×C₃	—	2	1	no	—
684	C₂³×C₃	—	2	1	no	—
685	C₂³×C₃	—	2	1	no	—
686	C₂³×C₃	—	2	2	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	2	no	—
690	C₂³×C₃	—	2	2	no	—
691	C₂³×C₃	—	2	2	no	—
692	C₂³×C₃	—	2	2	no	—
693	C₂³×C₃	—	2	2	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	2	no	—
696	C₂³×C₃	—	2	2	no	—
697	C₂³×C₃	—	2	2	no	—
698	C₂³×C₃	—	2	2	no	—
699	C₂³×C₃	—	2	2	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	—	4	8	no	—
708	C₂³×C₃	—	4	8	no	—
709	C₂³×C₃	—	4	8	no	—
710	C₂³×C₃	—	8	4	no	—
711	C₂³×C₃	—	8	4	no	—
712	C₂³×C₃	—	8	4	no	—
713	C₂³×C₃	—	8	4	no	—
714	C₂³×C₃	C₂²×D₄	1	2	yes	—
715	C₂³×C₃	C₂²×D₄	1	2	yes	—
716	C₂³×C₃	C₂×#41	1	2	yes	—
717	C₂³×C₃	C₂×#41	1	2	yes	—
718	C₂³×C₃	C₂⁵	1	1	yes	characteristic
719	C₃×Q₈	—	8	4	no	—
720	C₃×D₄	—	2	8	no	—
721	C₃×D₄	—	4	8	no	—
722	C₃×D₄	—	4	8	no	—
723	C₃×D₄	—	4	4	no	—
724	C₃×D₄	—	4	4	no	—
725	C₃×D₄	—	4	4	no	—
726	C₃×D₄	—	8	4	no	—
727	C₃×D₄	—	8	4	no	—
728	C₃×D₄	—	8	4	no	—
729	C₃×D₄	—	8	4	no	—
730	C₃×D₄	—	8	4	no	—
731	C₃×D₄	—	8	4	no	—
732	C₃×D₄	—	8	4	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	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	1	no	—
741	C₂×C₃×C₄	—	2	1	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	1	no	—
751	C₂×C₃×C₄	—	2	8	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	2	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	1	no	—
761	C₂×C₃×C₄	—	2	2	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	2	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	1	no	—
770	C₂×C₃×C₄	—	2	2	no	—
771	C₂×C₃×C₄	—	2	2	no	—
772	C₂×C₃×C₄	—	2	2	no	—
773	C₂×C₃×C₄	—	2	2	no	—
774	C₂×C₃×C₄	—	2	1	no	—
775	C₂×C₃×C₄	—	2	2	no	—
776	C₂×C₃×C₄	—	4	4	no	—
777	C₂×C₃×C₄	—	4	4	no	—
778	C₂×C₃×C₄	—	4	4	no	—
779	C₂×C₃×C₄	—	4	4	no	—
780	C₂×C₃×C₄	—	4	4	no	—
781	C₂×C₃×C₄	—	8	4	no	—
782	C₂×C₃×C₄	—	8	4	no	—
783	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
784	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
785	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
786	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
787	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
788	C₂×C₃×C₄	C₂×#41	1	2	yes	—
789	C₂×C₃×C₄	C₂×#41	1	2	yes	—
790	C₂×C₃×C₄	C₂×#41	1	2	yes	—
791	C₂×C₃×C₄	C₂×#41	1	2	yes	—
792	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
793	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
794	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
795	C₂⁴	—	2	4	no	—
796	C₂⁴	—	2	4	no	—
797	C₂⁴	—	2	4	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	—	4	2	no	—
801	C₂⁴	—	4	2	no	—
802	C₂⁴	C₂⁴×C₃	1	2	yes	—
803	C₂⁴	C₂⁴×C₃	1	2	yes	—
804	C₂⁴	C₂⁴×C₃	1	2	yes	—
805	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
806	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
807	C₂×Q₈	—	2	4	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	16	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	4	1	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	1	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	1	no	—
866	C₂²×C₄	—	4	1	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	C₂×C₃×D₄	1	4	yes	—
872	C₂²×C₄	C₂×C₃×D₄	1	4	yes	complemented
873	C₂²×C₄	C₃×#41	1	4	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	2	yes	—
879	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	4	2	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
908	C₂²⋊C₄	—	2	4	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	4	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	4	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	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
939	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
940	C₂²⋊C₄	C₃×#41	1	4	yes	—
941	C₄²	—	2	4	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	4	1	no	—
950	C₄²	—	4	1	no	—
951	C₄²	—	4	1	no	—
952	C₄²	—	4	1	no	—
953	C₄²	—	4	1	no	—
954	C₄²	C₂×C₃×D₄	1	4	yes	complemented
955	C₂²×C₃	—	2	2	no	—
956	C₂²×C₃	—	2	2	no	—
957	C₂²×C₃	—	2	2	no	—
958	C₂²×C₃	—	2	2	no	—
959	C₂²×C₃	—	2	2	no	—
960	C₂²×C₃	—	2	2	no	—
961	C₂²×C₃	—	2	2	no	—
962	C₂²×C₃	—	2	2	no	—
963	C₂²×C₃	—	2	2	no	—
964	C₂²×C₃	—	4	1	no	—
965	C₂²×C₃	—	4	1	no	—
966	C₂²×C₃	—	4	1	no	—
967	C₂²×C₃	—	4	1	no	—
968	C₂²×C₃	—	4	2	no	—
969	C₂²×C₃	—	4	2	no	—
970	C₂²×C₃	—	4	2	no	—
971	C₂²×C₃	—	4	2	no	—
972	C₂²×C₃	—	4	2	no	—
973	C₂²×C₃	—	4	2	no	—
974	C₂²×C₃	—	4	2	no	—
975	C₂²×C₃	—	4	2	no	—
976	C₂²×C₃	—	4	2	no	—
977	C₂²×C₃	—	4	2	no	—
978	C₂²×C₃	—	4	2	no	—
979	C₂²×C₃	—	4	2	no	—
980	C₂²×C₃	—	4	2	no	—
981	C₂²×C₃	—	4	2	no	—
982	C₂²×C₃	—	4	2	no	—
983	C₂²×C₃	—	4	2	no	—
984	C₂²×C₃	—	4	2	no	—
985	C₂²×C₃	—	4	2	no	—
986	C₂²×C₃	—	4	2	no	—
987	C₂²×C₃	—	4	2	no	—
988	C₂²×C₃	—	4	2	no	—
989	C₂²×C₃	—	8	16	no	—
990	C₂²×C₃	#532	1	4	yes	—
991	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
992	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
993	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
994	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
995	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
996	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
997	C₂²×C₃	#585	1	1	yes	characteristic
998	C₃×C₄	—	2	2	no	—
999	C₃×C₄	—	2	2	no	—
1000	C₃×C₄	—	2	2	no	—
1001	C₃×C₄	—	2	2	no	—
1002	C₃×C₄	—	2	2	no	—
1003	C₃×C₄	—	2	2	no	—
1004	C₃×C₄	—	2	2	no	—
1005	C₃×C₄	—	2	2	no	—
1006	C₃×C₄	—	2	2	no	—
1007	C₃×C₄	—	4	2	no	—
1008	C₃×C₄	—	4	1	no	—
1009	C₃×C₄	—	4	1	no	—
1010	C₃×C₄	—	4	2	no	—
1011	C₃×C₄	—	4	2	no	—
1012	C₃×C₄	—	4	2	no	—
1013	C₃×C₄	—	4	2	no	—
1014	C₃×C₄	—	4	1	no	—
1015	C₃×C₄	#538	1	4	yes	complemented
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	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	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	4	8	no	—
1048	C₂³	—	4	8	no	—
1049	C₂³	—	4	8	no	—
1050	C₂³	—	8	4	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	—	8	4	no	—
1053	C₂³	—	8	4	no	—
1054	C₂³	C₂²×C₃×D₄	1	2	yes	—
1055	C₂³	C₂²×C₃×D₄	1	2	yes	—
1056	C₂³	C₂×C₃×#41	1	2	yes	—
1057	C₂³	C₂×C₃×#41	1	2	yes	—
1058	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1059	Q₈	—	8	4	no	—
1060	D₄	—	2	8	no	—
1061	D₄	—	4	8	no	—
1062	D₄	—	4	8	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	8	4	no	—
1067	D₄	—	8	4	no	—
1068	D₄	—	8	4	no	—
1069	D₄	—	8	4	no	—
1070	D₄	—	8	4	no	—
1071	D₄	—	8	4	no	—
1072	D₄	—	8	4	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	1	no	—
1078	C₂×C₄	—	2	1	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	1	no	—
1085	C₂×C₄	—	2	1	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	8	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	4	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	4	no	—
1121	C₂×C₄	—	8	4	no	—
1122	C₂×C₄	—	8	4	no	—
1123	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1124	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1125	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1126	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1127	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1128	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1129	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1130	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1131	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1132	C₂×C₄	C₃×H(5,𝔽₂)	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×C₃	—	2	4	no	—
1136	C₂×C₃	—	4	2	no	—
1137	C₂×C₃	—	8	2	no	—
1138	C₂×C₃	—	8	2	no	—
1139	C₂×C₃	—	8	2	no	—
1140	C₂×C₃	C₂×#532	1	1	yes	characteristic
1141	C₂×C₃	C₂×#538	1	1	yes	characteristic
1142	C₂×C₃	#3460	1	1	yes	characteristic
1143	C₂×C₃	#3496	1	1	yes	characteristic
1144	C₂×C₃	#3498	1	1	yes	characteristic
1145	C₂×C₃	#3514	1	1	yes	characteristic
1146	C₂×C₃	#3519	1	1	yes	characteristic
1147	C₂²	—	2	2	no	—
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	2	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	8	16	no	—
1182	C₂²	C₃×#532	1	4	yes	—
1183	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1184	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1185	C₂²	C₂²×C₃×#41	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	C₃×#585	1	1	yes	characteristic
1190	C₄	—	2	2	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	C₃×#538	1	4	yes	complemented
1208	C₃	#35007	1	1	yes	characteristic, direct product factor, Sylow
1209	C₂	—	2	4	no	—
1210	C₂	—	4	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₂×C₃×#532	1	1	yes	characteristic
1215	C₂	C₂×C₃×#538	1	1	yes	characteristic
1216	C₂	C₃×#3460	1	1	yes	characteristic
1217	C₂	C₃×#3496	1	1	yes	characteristic
1218	C₂	C₃×#3498	1	1	yes	characteristic
1219	C₂	C₃×#3514	1	1	yes	characteristic
1220	C₂	C₃×#3519	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×#538	C₂	semidirect
2. C₃×#2860	C₂	semidirect
3. C₃×#2858	C₂	semidirect
4. C₃×#2856	C₂	semidirect
5. C₃×#2854	C₂	semidirect
6. C₃×#2662	C₂	semidirect
7. C₃×#2661	C₂	semidirect
8. C₃×#2555	C₂	semidirect
9. C₃×#2554	C₂	semidirect
10. C₃×#2512	C₂	semidirect
11. C₃×#2491	C₂	semidirect
12. C₃×#2472	C₂	semidirect
13. C₃×#2445	C₂	semidirect
14. C₃×#2440	C₂	semidirect
15. C₃×#2433	C₂	semidirect
16. C₃×#2428	C₂	semidirect
17. C₃×#2424	C₂	semidirect
18. C₃×#2416	C₂	semidirect
19. C₃×#2408	C₂	semidirect
20. C₃×#2321	C₂	semidirect
21. C₃×C₄×#121	C₂	semidirect
22. C₂×C₃×#390	C₂	semidirect
23. C₃×C₄²×D₄	C₂	semidirect
24. #35007	C₃	direct (N × H)
27. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×#126	C₂²	semidirect
31. C₂×C₃×#126	C₂²	semidirect
32. C₂×C₃×#124	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
34. C₂×C₃×#124	C₂²	semidirect
35. C₂×C₃×#123	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
42. C₂×C₃×#121	C₂²	semidirect
43. C₂×C₃×#121	C₂²	semidirect
44. C₂×C₃×#121	C₂²	semidirect
45. C₂×C₃×#121	C₂²	semidirect
53. C₂×C₃×C₄×D₄	C₂²	semidirect
58. C₂²×C₃×C₄²	C₂²	semidirect
59. C₃×#398	C₂²	semidirect
60. C₃×#397	C₂²	semidirect
61. C₃×#396	C₂²	semidirect
62. C₃×#396	C₂²	semidirect
63. C₃×#395	C₂²	semidirect
65. C₃×#394	C₂²	semidirect
66. C₃×#394	C₂²	semidirect
67. C₃×#394	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#393	C₂²	semidirect
74. C₃×#392	C₂²	semidirect
85. C₃×#390	C₂²	semidirect
86. C₃×#390	C₂²	semidirect
87. C₃×#390	C₂²	semidirect
88. C₃×#390	C₂²	semidirect
89. C₃×#390	C₂²	semidirect
90. C₃×#390	C₂²	semidirect
91. C₃×#389	C₂²	semidirect
92. C₃×#389	C₂²	semidirect
93. C₃×#389	C₂²	semidirect
94. C₃×#389	C₂²	semidirect
95. C₃×#388	C₂²	semidirect
96. C₃×#388	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
102. C₃×#388	C₂²	semidirect
105. C₃×#386	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
109. C₃×#384	C₂²	semidirect
111. C₃×#380	C₂²	semidirect
113. C₃×C₄×C₄⋊C₄	C₂²	semidirect
114. C₃×C₄×C₄⋊C₄	C₂²	semidirect
115. C₃×C₄×C₄⋊C₄	C₂²	semidirect
116. C₃×C₄×C₄⋊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×C₄³	C₂²	semidirect
125. C₂×#538	C₂×C₃	semidirect
126. #2860	C₂×C₃	semidirect
127. #2858	C₂×C₃	semidirect
128. #2856	C₂×C₃	semidirect
129. #2854	C₂×C₃	semidirect
130. #2662	C₂×C₃	semidirect
131. #2661	C₂×C₃	semidirect
132. #2555	C₂×C₃	semidirect
133. #2554	C₂×C₃	semidirect
134. #2512	C₂×C₃	semidirect
135. #2491	C₂×C₃	semidirect
136. #2472	C₂×C₃	semidirect
137. #2445	C₂×C₃	semidirect
138. #2440	C₂×C₃	semidirect
139. #2433	C₂×C₃	semidirect
140. #2428	C₂×C₃	semidirect
141. #2424	C₂×C₃	semidirect
142. #2416	C₂×C₃	semidirect
143. #2408	C₂×C₃	semidirect
144. #2321	C₂×C₃	semidirect
145. C₄×#121	C₂×C₃	semidirect
146. C₂×#390	C₂×C₃	semidirect
147. C₄²×D₄	C₂×C₃	semidirect
200. C₃×C₄×D₄	D₄	semidirect
284. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
287. C₂×#126	C₂²×C₃	semidirect
288. C₂×#126	C₂²×C₃	semidirect
289. C₂×#124	C₂²×C₃	semidirect
290. C₂×#124	C₂²×C₃	semidirect
291. C₂×#124	C₂²×C₃	semidirect
292. C₂×#123	C₂²×C₃	semidirect
293. C₂×#123	C₂²×C₃	semidirect
299. C₂×#121	C₂²×C₃	semidirect
300. C₂×#121	C₂²×C₃	semidirect
301. C₂×#121	C₂²×C₃	semidirect
302. C₂×#121	C₂²×C₃	semidirect
310. C₂×C₄×D₄	C₂²×C₃	semidirect
315. C₂²×C₄²	C₂²×C₃	semidirect
316. #398	C₂²×C₃	semidirect
317. #397	C₂²×C₃	semidirect
318. #396	C₂²×C₃	semidirect
319. #396	C₂²×C₃	semidirect
320. #395	C₂²×C₃	semidirect
322. #394	C₂²×C₃	semidirect
323. #394	C₂²×C₃	semidirect
324. #394	C₂²×C₃	semidirect
325. #394	C₂²×C₃	semidirect
326. #394	C₂²×C₃	semidirect
327. #393	C₂²×C₃	semidirect
331. #392	C₂²×C₃	semidirect
342. #390	C₂²×C₃	semidirect
343. #390	C₂²×C₃	semidirect
344. #390	C₂²×C₃	semidirect
345. #390	C₂²×C₃	semidirect
346. #390	C₂²×C₃	semidirect
347. #390	C₂²×C₃	semidirect
348. #389	C₂²×C₃	semidirect
349. #389	C₂²×C₃	semidirect
350. #389	C₂²×C₃	semidirect
351. #389	C₂²×C₃	semidirect
352. #388	C₂²×C₃	semidirect
353. #388	C₂²×C₃	semidirect
354. #388	C₂²×C₃	semidirect
355. #388	C₂²×C₃	semidirect
356. #388	C₂²×C₃	semidirect
357. #388	C₂²×C₃	semidirect
358. #388	C₂²×C₃	semidirect
359. #388	C₂²×C₃	semidirect
362. #386	C₂²×C₃	semidirect
363. #386	C₂²×C₃	semidirect
364. #386	C₂²×C₃	semidirect
366. #384	C₂²×C₃	semidirect
368. #380	C₂²×C₃	semidirect
370. C₄×C₄⋊C₄	C₂²×C₃	semidirect
371. C₄×C₄⋊C₄	C₂²×C₃	semidirect
372. C₄×C₄⋊C₄	C₂²×C₃	semidirect
373. C₄×C₄⋊C₄	C₂²×C₃	semidirect
377. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
378. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
379. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
380. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
381. C₄³	C₂²×C₃	semidirect
459. C₂²×C₃×C₄	C₂×D₄	semidirect
494. C₃×C₄⋊C₄	C₂×D₄	semidirect
526. C₃×C₂²⋊C₄	C₂×D₄	semidirect
541. C₃×C₄²	C₂×D₄	semidirect
594. C₄×D₄	C₃×D₄	semidirect
872. C₂²×C₄	C₂×C₃×D₄	semidirect
907. C₄⋊C₄	C₂×C₃×D₄	semidirect
939. C₂²⋊C₄	C₂×C₃×D₄	semidirect
954. C₄²	C₂×C₃×D₄	semidirect
1015. C₃×C₄	#538	semidirect
1207. C₄	C₃×#538	semidirect
1208. C₃	#35007	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×#538	2
C₃×#2860	2
C₃×#2858	2
C₃×#2856	2
C₃×#2854	2
C₃×#2662	2
C₃×#2661	2
C₃×#2555	2
C₃×#2554	2
C₃×#2512	2
C₃×#2491	2
C₃×#2472	2
C₃×#2445	2
C₃×#2440	2
C₃×#2433	2
C₃×#2428	2
C₃×#2424	2
C₃×#2416	2
C₃×#2408	2
C₃×#2321	2
C₃×C₄×#121	2
C₂×C₃×#390	2
C₃×C₄²×D₄	2
#35007	3

Subgroups — C3×#35007 #10653614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35007 #10653614