Subgroups — C₃×#86151 #11903448

Order 1152.

2381 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5708	C₂	1	2	yes	maximal, complemented
3	C₃×#5705	C₂	1	2	yes	maximal, complemented
4	C₃×#5694	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5661	C₂	1	2	yes	maximal, complemented
9	C₃×#5659	C₂	1	2	yes	maximal, complemented
10	C₃×#5639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5616	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5612	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5578	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5557	C₂	1	2	yes	maximal, complemented
17	C₃×#5557	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5547	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5528	C₂	1	2	yes	maximal, complemented
21	C₃×D₃×#117	C₂	1	2	yes	maximal, complemented
22	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3475	—	3	1	no	maximal
25	#86151	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×#239	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×#235	C₂²	1	1	yes	characteristic
29	C₂×C₃×#235	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
31	C₃²×#126	C₂²	1	2	yes	complemented
32	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#124	C₂²	1	1	yes	characteristic
34	C₃²×#123	C₂²	1	2	yes	complemented
35	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#121	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
40	C₃²×#117	C₂²	1	2	yes	complemented
41	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
42	C₃×#946	C₂²	1	1	yes	characteristic
43	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	C₃×#944	C₂²	1	1	yes	characteristic, complemented
45	C₃×#939	C₂²	1	2	yes	complemented
46	C₃×#938	C₂²	1	2	yes	—
47	C₃×#938	C₂²	1	1	yes	characteristic
48	C₃×#937	C₂²	1	2	yes	—
49	C₃×#936	C₂²	1	1	yes	characteristic
50	C₃×#936	C₂²	1	2	yes	complemented
51	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
52	C₃×C₄×#67	C₂²	1	2	yes	—
53	C₃×C₄×#67	C₂²	1	1	yes	characteristic
54	C₃×C₄×#67	C₂²	1	1	yes	characteristic
55	C₃×C₄×#67	C₂²	1	2	yes	complemented
56	C₃×C₄×#67	C₂²	1	2	yes	complemented
57	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₄×#67	C₂²	1	2	yes	complemented
59	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
60	C₃×#926	C₂²	1	2	yes	complemented
61	C₃×#926	C₂²	1	1	yes	characteristic, complemented
62	C₃×#926	C₂²	1	1	yes	characteristic, complemented
63	C₃×#898	C₂²	1	2	yes	complemented
64	C₃×#897	C₂²	1	1	yes	characteristic
65	C₃×#897	C₂²	1	1	yes	characteristic, complemented
66	C₃×#897	C₂²	1	2	yes	complemented
67	C₃×#896	C₂²	1	2	yes	—
68	C₃×#896	C₂²	1	2	yes	complemented
69	C₃×#896	C₂²	1	2	yes	complemented
70	C₃×#894	C₂²	1	2	yes	—
71	C₃×#894	C₂²	1	2	yes	complemented
72	C₃×#893	C₂²	1	1	yes	characteristic
73	C₃×#893	C₂²	1	1	yes	characteristic
74	C₃×#893	C₂²	1	2	yes	complemented
75	C₃×#892	C₂²	1	2	yes	—
76	C₃×#892	C₂²	1	2	yes	—
77	C₃×#892	C₂²	1	1	yes	characteristic, complemented
78	C₃×#892	C₂²	1	2	yes	complemented
79	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×#890	C₂²	1	1	yes	characteristic, complemented
83	C₃×#890	C₂²	1	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#889	C₂²	1	2	yes	complemented
86	C₃×#888	C₂²	1	1	yes	characteristic, complemented
87	C₃×#885	C₂²	1	2	yes	complemented
88	C₃×#884	C₂²	1	2	yes	—
89	C₃×#884	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	—
91	C₃×#883	C₂²	1	2	yes	—
92	C₃×#883	C₂²	1	2	yes	—
93	C₃×#883	C₂²	1	2	yes	complemented
94	C₃×#883	C₂²	1	2	yes	complemented
95	C₃×#882	C₂²	1	2	yes	—
96	C₃×#67⋊C₄	C₂²	1	2	yes	—
97	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₃×#879	C₂²	1	2	yes	complemented
101	C₃×#879	C₂²	1	2	yes	complemented
102	C₃×#879	C₂²	1	2	yes	complemented
103	C₃×#879	C₂²	1	2	yes	complemented
104	C₃×#878	C₂²	1	2	yes	complemented
105	C₃×#877	C₂²	1	2	yes	complemented
106	C₃×#877	C₂²	1	2	yes	complemented
107	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
108	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
109	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
110	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
111	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
112	C₃×#872	C₂²	1	1	yes	characteristic
113	C₃×#872	C₂²	1	2	yes	—
114	C₃×#872	C₂²	1	1	yes	characteristic, complemented
115	C₃×#872	C₂²	1	2	yes	complemented
116	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
117	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
118	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
119	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
120	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
121	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#556	—	3	1	no	—
126	C₃×#555	—	3	1	no	—
127	C₃×#554	—	3	1	no	—
128	C₃×#553	—	3	2	no	—
129	C₃×#552	—	3	2	no	—
130	C₃×#552	—	3	1	no	—
131	C₃×#552	—	3	1	no	—
132	C₃×#551	—	3	2	no	—
133	C₃×#551	—	3	2	no	—
134	C₃×#547	—	3	1	no	—
135	C₃×#546	—	3	1	no	—
136	C₃×#546	—	3	1	no	—
137	C₃×#533	—	3	1	no	—
138	C₃×#529	—	2	1	no	—
139	C₃×#529	—	3	1	no	—
140	C₃×#529	—	3	2	no	—
141	C₃×#529	—	3	2	no	—
142	C₃×#529	D₃	1	1	yes	characteristic, complemented
143	C₃×#529	C₂×C₃	1	1	yes	characteristic, complemented
144	C₃×#525	—	3	2	no	—
145	C₃×C₄×#41	—	3	1	no	—
146	C₃×C₄×#41	—	3	1	no	—
147	C₃×C₄×#41	—	3	1	no	—
148	C₂×C₃×C₄×D₄	—	3	1	no	—
149	C₂×C₃×#117	—	3	2	no	—
150	#5708	C₂×C₃	1	2	yes	complemented
151	#5705	C₂×C₃	1	2	yes	complemented
152	#5694	C₂×C₃	1	1	yes	characteristic, complemented
153	#5690	C₂×C₃	1	1	yes	characteristic, complemented
154	#5676	C₂×C₃	1	1	yes	characteristic, complemented
155	#5671	C₂×C₃	1	1	yes	characteristic, complemented
156	#5661	C₂×C₃	1	2	yes	complemented
157	#5659	C₂×C₃	1	2	yes	complemented
158	#5639	C₂×C₃	1	1	yes	characteristic, complemented
159	#5631	C₂×C₃	1	1	yes	characteristic, complemented
160	#5616	C₂×C₃	1	1	yes	characteristic, complemented
161	#5612	C₂×C₃	1	1	yes	characteristic, complemented
162	#5578	C₂×C₃	1	1	yes	characteristic, complemented
163	C₄×#239	C₂×C₃	1	1	yes	characteristic, complemented
164	#5557	C₂×C₃	1	2	yes	complemented
165	#5557	C₂×C₃	1	1	yes	characteristic, complemented
166	#5547	C₂×C₃	1	2	yes	complemented
167	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
168	#5528	C₂×C₃	1	2	yes	complemented
169	D₃×#117	C₂×C₃	1	2	yes	complemented
170	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
171	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂³×C₃×D₃	C₂³	1	2	yes	—
173	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
174	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
175	C₂×C₃²×D₄	C₂³	1	2	yes	—
176	C₂²×C₃²×C₄	C₂³	1	2	yes	—
177	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×#67	C₂³	1	2	yes	—
181	C₂×C₃×#67	C₂³	1	1	yes	characteristic
182	C₂×C₃×#67	C₂³	1	2	yes	—
183	C₂×C₃×#67	C₂³	1	1	yes	characteristic
184	C₂×C₃×#67	C₂³	1	2	yes	—
185	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
186	C₃×#239	—	2	4	no	—
187	C₃×D₃×D₄	—	2	4	no	—
188	C₃×#235	—	2	4	no	—
189	C₃×#235	—	2	4	no	—
190	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
191	C₂×C₃×D₁₂	C₂³	1	2	yes	—
192	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄×D₃	—	2	8	no	—
194	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
196	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
197	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
198	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
201	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
204	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
205	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
207	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
208	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
209	C₂×C₃×Dic₆	C₂³	1	2	yes	—
210	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
212	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
213	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
216	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃²×C₄²	C₂³	1	1	yes	characteristic
222	C₃²×C₄²	C₂³	1	1	yes	characteristic
223	C₃²×C₄²	C₂³	1	1	yes	characteristic
224	C₃²×C₄²	C₂³	1	1	yes	characteristic
225	C₃²×C₄²	C₂³	1	2	yes	—
226	C₃×#217	C₂³	1	2	yes	—
227	C₃×#217	C₂³	1	2	yes	—
228	C₃×#217	C₂³	1	2	yes	—
229	C₃×#217	C₂³	1	2	yes	—
230	C₃×#217	C₂³	1	1	yes	characteristic
231	C₃×#217	C₂³	1	2	yes	—
232	C₃×#217	C₂³	1	1	yes	characteristic
233	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
243	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
244	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
245	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
246	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
247	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
248	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
249	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
250	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
251	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
252	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
253	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
255	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
256	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
261	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
262	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
263	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
264	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×C₄×Dic₃	C₂³	1	2	yes	—
266	C₃×C₄×Dic₃	C₂³	1	2	yes	—
267	C₃×C₄×Dic₃	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	2	yes	—
269	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
270	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
271	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
275	C₃×C₄×Dic₃	C₂³	1	2	yes	—
276	#3475	—	3	1	no	Sylow
277	C₂×C₃×#41	—	3	1	no	—
278	C₂×C₃×#41	—	3	1	no	—
279	C₂×C₃×#41	—	3	1	no	—
280	C₂²×C₃×D₄	—	3	1	no	—
281	C₂³×C₃×C₄	—	3	2	no	—
282	C₂×#239	C₂²×C₃	1	1	yes	characteristic
283	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
284	C₂×#235	C₂²×C₃	1	1	yes	characteristic
285	C₂×#235	C₂²×C₃	1	1	yes	characteristic
286	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
287	C₃×C₄⋊Q₈	—	3	1	no	—
288	C₃×C₄⋊Q₈	—	3	1	no	—
289	C₃×#126	—	2	2	no	—
290	C₃×#126	—	3	2	no	—
291	C₃×#126	—	3	2	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	2	no	—
295	C₃×#126	C₂×D₃	1	2	yes	complemented
296	C₃×#126	C₂²×C₃	1	2	yes	complemented
297	C₃×#125	—	2	1	no	—
298	C₃×#125	—	3	2	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	2	no	—
301	C₃×#125	—	3	1	no	—
302	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
303	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₃×#124	—	2	1	no	—
305	C₃×#124	—	3	1	no	—
306	C₃×#124	—	3	2	no	—
307	C₃×#124	—	3	2	no	—
308	C₃×#124	C₂×D₃	1	1	yes	characteristic
309	C₃×#124	C₂²×C₃	1	1	yes	characteristic
310	C₃×#123	—	2	2	no	—
311	C₃×#123	—	3	2	no	—
312	C₃×#123	—	3	2	no	—
313	C₃×#123	—	3	2	no	—
314	C₃×#123	—	3	2	no	—
315	C₃×#123	—	3	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×#123	—	3	2	no	—
318	C₃×#123	C₂×D₃	1	2	yes	complemented
319	C₃×#123	C₂²×C₃	1	2	yes	complemented
320	C₃×C₂²⋊Q₈	—	2	1	no	—
321	C₃×C₂²⋊Q₈	—	3	1	no	—
322	C₃×C₂²⋊Q₈	—	3	2	no	—
323	C₃×C₂²⋊Q₈	—	3	2	no	—
324	C₃×C₂²⋊Q₈	—	3	2	no	—
325	C₃×C₂²⋊Q₈	—	3	1	no	—
326	C₃×C₂²⋊Q₈	—	3	1	no	—
327	C₃×C₂²⋊Q₈	—	3	2	no	—
328	C₃×C₂²⋊Q₈	—	3	2	no	—
329	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
330	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
331	C₃×#121	—	2	1	no	—
332	C₃×#121	—	3	2	no	—
333	C₃×#121	—	3	1	no	—
334	C₃×#121	—	3	2	no	—
335	C₃×#121	—	3	2	no	—
336	C₃×#121	—	3	2	no	—
337	C₃×#121	C₂×D₃	1	1	yes	characteristic
338	C₃×#121	C₂²×C₃	1	1	yes	characteristic
339	C₃×#120	—	3	2	no	—
340	C₃×#120	—	3	2	no	—
341	C₃×C₄×Q₈	—	2	1	no	—
342	C₃×C₄×Q₈	—	3	1	no	—
343	C₃×C₄×Q₈	—	3	1	no	—
344	C₃×C₄×Q₈	—	3	1	no	—
345	C₃×C₄×Q₈	—	3	1	no	—
346	C₃×C₄×Q₈	—	3	1	no	—
347	C₃×C₄×Q₈	—	3	2	no	—
348	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
349	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
350	C₃×C₄×D₄	—	2	1	no	—
351	C₃×C₄×D₄	—	2	2	no	—
352	C₃×C₄×D₄	—	3	1	no	—
353	C₃×C₄×D₄	—	3	2	no	—
354	C₃×C₄×D₄	—	3	1	no	—
355	C₃×C₄×D₄	—	3	1	no	—
356	C₃×C₄×D₄	—	3	2	no	—
357	C₃×C₄×D₄	—	3	1	no	—
358	C₃×C₄×D₄	—	3	2	no	—
359	C₃×C₄×D₄	—	3	1	no	—
360	C₃×C₄×D₄	—	3	2	no	—
361	C₃×C₄×D₄	—	3	1	no	—
362	C₃×C₄×D₄	—	3	1	no	—
363	C₃×C₄×D₄	—	3	2	no	—
364	C₃×C₄×D₄	—	3	2	no	—
365	C₃×C₄×D₄	—	3	1	no	—
366	C₃×C₄×D₄	—	3	2	no	—
367	C₃×C₄×D₄	—	3	1	no	—
368	C₃×C₄×D₄	—	3	1	no	—
369	C₃×C₄×D₄	—	3	1	no	—
370	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
371	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
372	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
373	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
374	C₃×#117	—	2	2	no	—
375	C₃×#117	—	3	2	no	—
376	C₃×#117	—	3	1	no	—
377	C₃×#117	—	3	1	no	—
378	C₃×#117	—	3	2	no	—
379	C₃×#117	—	3	2	no	—
380	C₃×#117	—	3	2	no	—
381	C₃×#117	—	3	1	no	—
382	C₃×#117	—	3	2	no	—
383	C₃×#117	—	3	2	no	—
384	C₃×#117	—	3	1	no	—
385	C₃×#117	—	3	2	no	—
386	C₃×#117	—	3	1	no	—
387	C₃×#117	—	3	2	no	—
388	C₃×#117	C₂×D₃	1	2	yes	complemented
389	C₃×#117	C₂²×C₃	1	2	yes	complemented
390	C₂×C₃×C₄⋊C₄	—	3	1	no	—
391	C₂×C₃×C₄⋊C₄	—	3	2	no	—
392	C₂×C₃×C₄⋊C₄	—	3	2	no	—
393	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
394	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
395	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
396	C₂×C₃×C₄²	—	2	1	no	—
397	C₂×C₃×C₄²	—	3	2	no	—
398	C₂×C₃×C₄²	—	3	2	no	—
399	C₂×C₃×C₄²	—	3	1	no	—
400	C₂×C₃×C₄²	—	3	1	no	—
401	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
402	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
403	#946	C₂²×C₃	1	1	yes	characteristic
404	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
405	#944	C₂²×C₃	1	1	yes	characteristic, complemented
406	#939	C₂²×C₃	1	2	yes	complemented
407	#938	C₂²×C₃	1	2	yes	—
408	#938	C₂²×C₃	1	1	yes	characteristic
409	#937	C₂²×C₃	1	2	yes	—
410	#936	C₂²×C₃	1	1	yes	characteristic
411	#936	C₂²×C₃	1	2	yes	complemented
412	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
413	C₄×#67	C₂²×C₃	1	1	yes	characteristic
414	C₄×#67	C₂²×C₃	1	1	yes	characteristic
415	C₄×#67	C₂²×C₃	1	2	yes	—
416	C₄×#67	C₂²×C₃	1	2	yes	complemented
417	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
418	C₄×#67	C₂²×C₃	1	2	yes	complemented
419	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
420	C₄×#67	C₂²×C₃	1	2	yes	complemented
421	#926	C₂²×C₃	1	1	yes	characteristic, complemented
422	#926	C₂²×C₃	1	1	yes	characteristic, complemented
423	#926	C₂²×C₃	1	2	yes	complemented
424	#898	C₂²×C₃	1	2	yes	complemented
425	#897	C₂²×C₃	1	1	yes	characteristic
426	#897	C₂²×C₃	1	2	yes	complemented
427	#897	C₂²×C₃	1	1	yes	characteristic, complemented
428	#896	C₂²×C₃	1	2	yes	—
429	#896	C₂²×C₃	1	2	yes	complemented
430	#896	C₂²×C₃	1	2	yes	complemented
431	#894	C₂²×C₃	1	2	yes	—
432	#894	C₂²×C₃	1	2	yes	complemented
433	#893	C₂²×C₃	1	1	yes	characteristic
434	#893	C₂²×C₃	1	1	yes	characteristic
435	#893	C₂²×C₃	1	2	yes	complemented
436	#892	C₂²×C₃	1	2	yes	—
437	#892	C₂²×C₃	1	2	yes	—
438	#892	C₂²×C₃	1	2	yes	complemented
439	#892	C₂²×C₃	1	1	yes	characteristic, complemented
440	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
441	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
442	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
443	#890	C₂²×C₃	1	1	yes	characteristic, complemented
444	#890	C₂²×C₃	1	2	yes	complemented
445	#889	C₂²×C₃	1	2	yes	complemented
446	#889	C₂²×C₃	1	2	yes	complemented
447	#888	C₂²×C₃	1	1	yes	characteristic, complemented
448	#885	C₂²×C₃	1	2	yes	complemented
449	#884	C₂²×C₃	1	2	yes	—
450	#884	C₂²×C₃	1	2	yes	complemented
451	#883	C₂²×C₃	1	2	yes	—
452	#883	C₂²×C₃	1	2	yes	—
453	#883	C₂²×C₃	1	2	yes	—
454	#883	C₂²×C₃	1	2	yes	complemented
455	#883	C₂²×C₃	1	2	yes	complemented
456	#882	C₂²×C₃	1	2	yes	—
457	#67⋊C₄	C₂²×C₃	1	2	yes	—
458	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
459	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
460	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
461	#879	C₂²×C₃	1	2	yes	complemented
462	#879	C₂²×C₃	1	2	yes	complemented
463	#879	C₂²×C₃	1	2	yes	complemented
464	#879	C₂²×C₃	1	2	yes	complemented
465	#878	C₂²×C₃	1	2	yes	complemented
466	#877	C₂²×C₃	1	2	yes	complemented
467	#877	C₂²×C₃	1	2	yes	complemented
468	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
469	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
470	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
471	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
472	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
473	#872	C₂²×C₃	1	1	yes	characteristic
474	#872	C₂²×C₃	1	2	yes	—
475	#872	C₂²×C₃	1	2	yes	complemented
476	#872	C₂²×C₃	1	1	yes	characteristic, complemented
477	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
478	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
479	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
480	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
481	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
482	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
485	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
486	C₂³×C₃²	C₂⁴	1	2	yes	—
487	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
488	C₂²×C₃×D₃	—	2	4	no	—
489	C₂²×C₃×D₃	—	2	4	no	—
490	C₂²×C₃×D₃	—	4	2	no	—
491	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
492	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
493	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
494	C₃²×Q₈	—	2	2	no	—
495	C₃²×D₄	—	2	2	no	—
496	C₃²×D₄	—	4	2	no	—
497	C₂×C₃²×C₄	—	2	4	no	—
498	C₂×C₃²×C₄	—	2	2	no	—
499	C₂×C₃²×C₄	—	2	2	no	—
500	C₂×C₃²×C₄	—	4	1	no	—
501	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
503	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
504	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
505	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
506	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
508	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
509	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
510	C₃×#67	—	2	2	no	—
511	C₃×#67	—	2	4	no	—
512	C₃×#67	—	2	4	no	—
513	C₃×#67	—	2	2	no	—
514	C₃×#67	—	4	2	no	—
515	C₂×C₃×Dic₃	—	2	4	no	—
516	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
517	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
518	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
519	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
520	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
521	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
522	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
525	C₃×D₁₂	—	2	2	no	—
526	C₃×D₁₂	—	2	4	no	—
527	C₃×D₁₂	#41	1	4	yes	complemented
528	C₃×C₄×D₃	—	2	4	no	—
529	C₃×C₄×D₃	—	2	4	no	—
530	C₃×C₄×D₃	—	2	4	no	—
531	C₃×C₄×D₃	—	2	4	no	—
532	C₃×C₄×D₃	—	2	2	no	—
533	C₃×C₄×D₃	—	2	2	no	—
534	C₃×C₄×D₃	—	2	2	no	—
535	C₃×C₄×D₃	—	2	4	no	—
536	C₃×C₄×D₃	—	4	1	no	—
537	C₃×C₄×D₃	—	4	2	no	—
538	C₃×C₄×D₃	—	4	2	no	—
539	C₃×C₄×D₃	—	4	1	no	—
540	C₃×C₄×D₃	#41	1	4	yes	complemented
541	C₃×Dic₆	—	2	2	no	—
542	C₃×Dic₆	—	2	2	no	—
543	C₃×Dic₆	—	4	2	no	—
544	#556	—	3	1	no	—
545	#555	—	3	1	no	—
546	#554	—	3	1	no	—
547	#553	—	3	2	no	—
548	#552	—	3	2	no	—
549	#552	—	3	1	no	—
550	#552	—	3	1	no	—
551	#551	—	3	2	no	—
552	#551	—	3	2	no	—
553	#547	—	3	1	no	—
554	#546	—	3	1	no	—
555	#546	—	3	1	no	—
556	#533	—	3	1	no	—
557	#529	—	3	1	no	—
558	#529	—	3	2	no	—
559	#529	—	3	2	no	—
560	#529	C₃×D₃	1	1	yes	characteristic, complemented
561	#525	—	3	2	no	—
562	C₄×#41	—	3	1	no	—
563	C₄×#41	—	3	1	no	—
564	C₄×#41	—	3	1	no	—
565	C₂×C₄×D₄	—	3	1	no	—
566	C₂×#117	—	3	2	no	—
567	C₂⁴×C₃	—	3	2	no	—
568	C₂³×D₃	C₂³×C₃	1	2	yes	—
569	C₃×#41	—	6	4	no	—
570	C₃×#41	—	6	4	no	—
571	C₃×#41	—	6	4	no	—
572	C₂×C₃×Q₈	—	2	1	no	—
573	C₂×C₃×Q₈	—	3	1	no	—
574	C₂×C₃×Q₈	—	3	1	no	—
575	C₂×C₃×Q₈	—	3	2	no	—
576	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
577	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₃×D₄	—	2	2	no	—
579	C₂×C₃×D₄	—	2	1	no	—
580	C₂×C₃×D₄	—	3	1	no	—
581	C₂×C₃×D₄	—	3	2	no	—
582	C₂×C₃×D₄	—	3	1	no	—
583	C₂×C₃×D₄	—	3	2	no	—
584	C₂×C₃×D₄	—	3	2	no	—
585	C₂×C₃×D₄	—	3	1	no	—
586	C₂×C₃×D₄	—	3	1	no	—
587	C₂×C₃×D₄	—	3	2	no	—
588	C₂×C₃×D₄	—	6	4	no	—
589	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
590	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
591	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
593	C₂²×C₃×C₄	—	2	1	no	—
594	C₂²×C₃×C₄	—	2	1	no	—
595	C₂²×C₃×C₄	—	2	1	no	—
596	C₂²×C₃×C₄	—	2	2	no	—
597	C₂²×C₃×C₄	—	3	1	no	—
598	C₂²×C₃×C₄	—	3	2	no	—
599	C₂²×C₃×C₄	—	3	2	no	—
600	C₂²×C₃×C₄	—	3	2	no	—
601	C₂²×C₃×C₄	—	3	1	no	—
602	C₂²×C₃×C₄	—	3	1	no	—
603	C₂²×C₃×C₄	—	3	2	no	—
604	C₂²×C₃×C₄	—	3	2	no	—
605	C₂²×C₃×C₄	—	3	2	no	—
606	C₂²×C₃×C₄	—	3	1	no	—
607	C₂²×C₃×C₄	—	3	1	no	—
608	C₂²×C₃×C₄	—	3	2	no	—
609	C₂²×C₃×C₄	—	3	2	no	—
610	C₂²×C₃×C₄	—	3	1	no	—
611	C₂²×C₃×C₄	—	6	8	no	—
612	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
613	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
614	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
615	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
616	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
617	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
618	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
619	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
620	C₂×#67	C₂³×C₃	1	2	yes	—
621	C₂×#67	C₂³×C₃	1	1	yes	characteristic
622	C₂×#67	C₂³×C₃	1	2	yes	—
623	C₂×#67	C₂³×C₃	1	1	yes	characteristic
624	C₂×#67	C₂³×C₃	1	2	yes	—
625	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
626	#239	—	2	4	no	—
627	D₃×D₄	—	2	4	no	—
628	#235	—	2	4	no	—
629	#235	—	2	4	no	—
630	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
631	C₂×D₁₂	C₂³×C₃	1	2	yes	—
632	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₄×D₃	—	2	8	no	—
634	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
635	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
636	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
637	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
638	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
639	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
640	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
641	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
642	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
643	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
644	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
645	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
646	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
647	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
648	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
649	C₂×Dic₆	C₂³×C₃	1	2	yes	—
650	C₃×C₄⋊C₄	—	2	2	no	—
651	C₃×C₄⋊C₄	—	2	2	no	—
652	C₃×C₄⋊C₄	—	2	1	no	—
653	C₃×C₄⋊C₄	—	2	2	no	—
654	C₃×C₄⋊C₄	—	2	1	no	—
655	C₃×C₄⋊C₄	—	2	2	no	—
656	C₃×C₄⋊C₄	—	3	1	no	—
657	C₃×C₄⋊C₄	—	3	1	no	—
658	C₃×C₄⋊C₄	—	3	2	no	—
659	C₃×C₄⋊C₄	—	3	2	no	—
660	C₃×C₄⋊C₄	—	3	2	no	—
661	C₃×C₄⋊C₄	—	3	1	no	—
662	C₃×C₄⋊C₄	—	3	2	no	—
663	C₃×C₄⋊C₄	—	3	2	no	—
664	C₃×C₄⋊C₄	—	3	1	no	—
665	C₃×C₄⋊C₄	—	3	2	no	—
666	C₃×C₄⋊C₄	—	3	2	no	—
667	C₃×C₄⋊C₄	—	3	2	no	—
668	C₃×C₄⋊C₄	—	3	1	no	—
669	C₃×C₄⋊C₄	—	3	2	no	—
670	C₃×C₄⋊C₄	—	3	2	no	—
671	C₃×C₄⋊C₄	—	3	1	no	—
672	C₃×C₄⋊C₄	—	3	1	no	—
673	C₃×C₄⋊C₄	—	3	2	no	—
674	C₃×C₄⋊C₄	—	3	1	no	—
675	C₃×C₄⋊C₄	—	3	2	no	—
676	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
677	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
678	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
679	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
680	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
681	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
682	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
683	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
684	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
685	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
686	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
687	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
688	C₃×C₂²⋊C₄	—	2	2	no	—
689	C₃×C₂²⋊C₄	—	2	2	no	—
690	C₃×C₂²⋊C₄	—	2	2	no	—
691	C₃×C₂²⋊C₄	—	2	2	no	—
692	C₃×C₂²⋊C₄	—	2	2	no	—
693	C₃×C₂²⋊C₄	—	3	2	no	—
694	C₃×C₂²⋊C₄	—	3	2	no	—
695	C₃×C₂²⋊C₄	—	3	2	no	—
696	C₃×C₂²⋊C₄	—	3	1	no	—
697	C₃×C₂²⋊C₄	—	3	2	no	—
698	C₃×C₂²⋊C₄	—	3	1	no	—
699	C₃×C₂²⋊C₄	—	3	2	no	—
700	C₃×C₂²⋊C₄	—	3	1	no	—
701	C₃×C₂²⋊C₄	—	3	1	no	—
702	C₃×C₂²⋊C₄	—	3	2	no	—
703	C₃×C₂²⋊C₄	—	3	2	no	—
704	C₃×C₂²⋊C₄	—	3	2	no	—
705	C₃×C₂²⋊C₄	—	3	2	no	—
706	C₃×C₂²⋊C₄	—	3	2	no	—
707	C₃×C₂²⋊C₄	—	3	2	no	—
708	C₃×C₂²⋊C₄	—	3	1	no	—
709	C₃×C₂²⋊C₄	—	3	2	no	—
710	C₃×C₂²⋊C₄	—	3	1	no	—
711	C₃×C₂²⋊C₄	—	3	2	no	—
712	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
713	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
714	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
716	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
717	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
718	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
719	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
720	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
721	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
722	C₃×C₄²	—	2	1	no	—
723	C₃×C₄²	—	2	1	no	—
724	C₃×C₄²	—	2	1	no	—
725	C₃×C₄²	—	2	1	no	—
726	C₃×C₄²	—	2	2	no	—
727	C₃×C₄²	—	3	2	no	—
728	C₃×C₄²	—	3	2	no	—
729	C₃×C₄²	—	3	2	no	—
730	C₃×C₄²	—	3	2	no	—
731	C₃×C₄²	—	3	1	no	—
732	C₃×C₄²	—	3	1	no	—
733	C₃×C₄²	—	3	1	no	—
734	C₃×C₄²	—	3	1	no	—
735	C₃×C₄²	—	3	1	no	—
736	C₃×C₄²	—	3	1	no	—
737	C₃×C₄²	—	3	2	no	—
738	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
739	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
740	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
741	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
742	C₃×C₄²	C₂²×D₃	1	2	yes	—
743	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
744	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
745	C₃×C₄²	C₂³×C₃	1	2	yes	—
746	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
747	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
748	#217	C₂³×C₃	1	2	yes	—
749	#217	C₂³×C₃	1	2	yes	—
750	#217	C₂³×C₃	1	2	yes	—
751	#217	C₂³×C₃	1	2	yes	—
752	#217	C₂³×C₃	1	1	yes	characteristic
753	#217	C₂³×C₃	1	2	yes	—
754	#217	C₂³×C₃	1	1	yes	characteristic
755	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
756	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
757	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
758	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
759	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
761	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
762	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
763	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
764	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
766	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
767	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
768	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
769	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
770	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
771	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
772	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
773	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
774	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
778	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
779	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
781	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
785	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
787	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
788	C₄×Dic₃	C₂³×C₃	1	2	yes	—
789	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
790	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
791	C₄×Dic₃	C₂³×C₃	1	2	yes	—
792	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
793	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
795	C₄×Dic₃	C₂³×C₃	1	2	yes	—
796	C₄×Dic₃	C₂³×C₃	1	2	yes	—
797	C₄×Dic₃	C₂³×C₃	1	2	yes	—
798	C₂²×C₃²	—	2	1	no	—
799	C₂²×C₃²	—	2	2	no	—
800	C₂²×C₃²	—	2	1	no	—
801	C₂²×C₃²	—	2	1	no	—
802	C₂²×C₃²	—	2	2	no	—
803	C₂²×C₃²	—	2	2	no	—
804	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
805	C₂×C₃×D₃	—	2	2	no	—
806	C₂×C₃×D₃	—	2	1	no	—
807	C₂×C₃×D₃	—	2	2	no	—
808	C₂×C₃×D₃	—	2	1	no	—
809	C₂×C₃×D₃	—	2	1	no	—
810	C₂×C₃×D₃	—	2	1	no	—
811	C₂×C₃×D₃	—	2	1	no	—
812	C₂×C₃×D₃	—	4	8	no	—
813	C₂×C₃×D₃	C₂×#41	1	2	yes	—
814	C₂×C₃×D₃	C₂×#41	1	4	yes	—
815	C₃²×C₄	—	2	1	no	—
816	C₃²×C₄	—	2	1	no	—
817	C₃²×C₄	—	2	2	no	—
818	C₃²×C₄	—	2	2	no	—
819	C₃²×C₄	—	2	2	no	—
820	C₃²×C₄	—	2	1	no	—
821	C₃²×C₄	—	2	1	no	—
822	C₃²×C₄	C₂×#41	1	2	yes	—
823	C₃²×C₄	C₂×#41	1	2	yes	—
824	C₃×Dic₃	—	2	2	no	—
825	C₃×Dic₃	—	2	1	no	—
826	C₃×Dic₃	—	2	1	no	—
827	C₃×Dic₃	—	2	2	no	—
828	C₃×Dic₃	—	2	1	no	—
829	C₃×Dic₃	—	2	1	no	—
830	C₃×Dic₃	—	2	2	no	—
831	C₃×Dic₃	—	2	1	no	—
832	C₃×Dic₃	C₂×#41	1	2	yes	—
833	C₂×#41	—	3	1	no	—
834	C₂×#41	—	3	1	no	—
835	C₂×#41	—	3	1	no	—
836	C₂²×D₄	—	3	1	no	—
837	C₂³×C₄	—	3	2	no	—
838	C₄⋊Q₈	—	3	1	no	—
839	C₄⋊Q₈	—	3	1	no	—
840	#126	—	3	2	no	—
841	#126	—	3	2	no	—
842	#126	—	3	2	no	—
843	#126	—	3	2	no	—
844	#126	—	3	2	no	—
845	#126	C₂×C₃×D₃	1	2	yes	complemented
846	#125	—	3	2	no	—
847	#125	—	3	2	no	—
848	#125	—	3	1	no	—
849	#125	—	3	2	no	—
850	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
851	#124	—	3	1	no	—
852	#124	—	3	2	no	—
853	#124	—	3	2	no	—
854	#124	C₂×C₃×D₃	1	1	yes	characteristic
855	#123	—	3	2	no	—
856	#123	—	3	2	no	—
857	#123	—	3	2	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	#123	—	3	2	no	—
862	#123	C₂×C₃×D₃	1	2	yes	complemented
863	C₂²⋊Q₈	—	3	1	no	—
864	C₂²⋊Q₈	—	3	2	no	—
865	C₂²⋊Q₈	—	3	1	no	—
866	C₂²⋊Q₈	—	3	2	no	—
867	C₂²⋊Q₈	—	3	2	no	—
868	C₂²⋊Q₈	—	3	1	no	—
869	C₂²⋊Q₈	—	3	2	no	—
870	C₂²⋊Q₈	—	3	2	no	—
871	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
872	#121	—	3	2	no	—
873	#121	—	3	2	no	—
874	#121	—	3	1	no	—
875	#121	—	3	2	no	—
876	#121	—	3	2	no	—
877	#121	C₂×C₃×D₃	1	1	yes	characteristic
878	#120	—	3	2	no	—
879	#120	—	3	2	no	—
880	C₄×Q₈	—	3	1	no	—
881	C₄×Q₈	—	3	1	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	1	no	—
884	C₄×Q₈	—	3	1	no	—
885	C₄×Q₈	—	3	2	no	—
886	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
887	C₄×D₄	—	3	1	no	—
888	C₄×D₄	—	3	2	no	—
889	C₄×D₄	—	3	2	no	—
890	C₄×D₄	—	3	1	no	—
891	C₄×D₄	—	3	1	no	—
892	C₄×D₄	—	3	1	no	—
893	C₄×D₄	—	3	2	no	—
894	C₄×D₄	—	3	1	no	—
895	C₄×D₄	—	3	2	no	—
896	C₄×D₄	—	3	1	no	—
897	C₄×D₄	—	3	1	no	—
898	C₄×D₄	—	3	2	no	—
899	C₄×D₄	—	3	2	no	—
900	C₄×D₄	—	3	1	no	—
901	C₄×D₄	—	3	2	no	—
902	C₄×D₄	—	3	1	no	—
903	C₄×D₄	—	3	1	no	—
904	C₄×D₄	—	3	1	no	—
905	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
906	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
907	#117	—	3	2	no	—
908	#117	—	3	1	no	—
909	#117	—	3	1	no	—
910	#117	—	3	2	no	—
911	#117	—	3	2	no	—
912	#117	—	3	2	no	—
913	#117	—	3	1	no	—
914	#117	—	3	2	no	—
915	#117	—	3	2	no	—
916	#117	—	3	1	no	—
917	#117	—	3	2	no	—
918	#117	—	3	1	no	—
919	#117	—	3	2	no	—
920	#117	C₂×C₃×D₃	1	2	yes	complemented
921	C₂×C₄⋊C₄	—	3	2	no	—
922	C₂×C₄⋊C₄	—	3	2	no	—
923	C₂×C₄⋊C₄	—	3	1	no	—
924	C₂×C₂²⋊C₄	—	3	2	no	—
925	C₂×C₂²⋊C₄	—	3	2	no	—
926	C₂×C₂²⋊C₄	—	3	2	no	—
927	C₂×C₄²	—	3	2	no	—
928	C₂×C₄²	—	3	2	no	—
929	C₂×C₄²	—	3	1	no	—
930	C₂×C₄²	—	3	1	no	—
931	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
932	C₂³×C₃	—	2	1	no	—
933	C₂³×C₃	—	2	2	no	—
934	C₂³×C₃	—	3	1	no	—
935	C₂³×C₃	—	3	2	no	—
936	C₂³×C₃	—	3	1	no	—
937	C₂³×C₃	—	6	4	no	—
938	C₂³×C₃	—	6	4	no	—
939	C₂³×C₃	—	12	2	no	—
940	C₂³×C₃	C₂³×D₃	1	2	yes	—
941	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
942	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
943	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
944	C₂²×D₃	—	2	4	no	—
945	C₂²×D₃	—	2	4	no	—
946	C₂²×D₃	—	4	2	no	—
947	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
948	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
949	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
950	C₃×Q₈	—	2	2	no	—
951	C₃×Q₈	—	2	2	no	—
952	C₃×Q₈	—	4	2	no	—
953	C₃×Q₈	—	6	2	no	—
954	C₃×Q₈	—	6	2	no	—
955	C₃×Q₈	—	12	2	no	—
956	C₃×D₄	—	2	2	no	—
957	C₃×D₄	—	2	2	no	—
958	C₃×D₄	—	3	4	no	—
959	C₃×D₄	—	4	2	no	—
960	C₃×D₄	—	4	2	no	—
961	C₃×D₄	—	4	2	no	—
962	C₃×D₄	—	4	4	no	—
963	C₃×D₄	—	6	2	no	—
964	C₃×D₄	—	6	4	no	—
965	C₃×D₄	—	6	2	no	—
966	C₃×D₄	—	6	4	no	—
967	C₃×D₄	—	6	2	no	—
968	C₃×D₄	—	6	4	no	—
969	C₃×D₄	—	12	2	no	—
970	C₂×C₃×C₄	—	2	4	no	—
971	C₂×C₃×C₄	—	2	2	no	—
972	C₂×C₃×C₄	—	2	2	no	—
973	C₂×C₃×C₄	—	2	4	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	2	1	no	—
977	C₂×C₃×C₄	—	2	1	no	—
978	C₂×C₃×C₄	—	2	1	no	—
979	C₂×C₃×C₄	—	2	1	no	—
980	C₂×C₃×C₄	—	2	1	no	—
981	C₂×C₃×C₄	—	2	1	no	—
982	C₂×C₃×C₄	—	2	2	no	—
983	C₂×C₃×C₄	—	2	2	no	—
984	C₂×C₃×C₄	—	2	2	no	—
985	C₂×C₃×C₄	—	3	1	no	—
986	C₂×C₃×C₄	—	3	4	no	—
987	C₂×C₃×C₄	—	3	2	no	—
988	C₂×C₃×C₄	—	3	1	no	—
989	C₂×C₃×C₄	—	3	1	no	—
990	C₂×C₃×C₄	—	3	1	no	—
991	C₂×C₃×C₄	—	3	1	no	—
992	C₂×C₃×C₄	—	3	2	no	—
993	C₂×C₃×C₄	—	3	2	no	—
994	C₂×C₃×C₄	—	3	1	no	—
995	C₂×C₃×C₄	—	4	4	no	—
996	C₂×C₃×C₄	—	4	2	no	—
997	C₂×C₃×C₄	—	4	2	no	—
998	C₂×C₃×C₄	—	4	1	no	—
999	C₂×C₃×C₄	—	4	1	no	—
1000	C₂×C₃×C₄	—	4	2	no	—
1001	C₂×C₃×C₄	—	6	4	no	—
1002	C₂×C₃×C₄	—	6	4	no	—
1003	C₂×C₃×C₄	—	6	4	no	—
1004	C₂×C₃×C₄	—	6	4	no	—
1005	C₂×C₃×C₄	—	6	4	no	—
1006	C₂×C₃×C₄	—	6	4	no	—
1007	C₂×C₃×C₄	—	6	2	no	—
1008	C₂×C₃×C₄	—	6	2	no	—
1009	C₂×C₃×C₄	—	6	2	no	—
1010	C₂×C₃×C₄	—	12	1	no	—
1011	C₂×C₃×C₄	—	12	2	no	—
1012	C₂×C₃×C₄	—	12	1	no	—
1013	C₂×C₃×C₄	—	12	2	no	—
1014	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1017	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1018	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1019	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1020	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1021	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1022	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1023	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1024	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1025	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1026	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1027	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1028	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1029	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1030	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1031	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1032	#67	—	2	2	no	—
1033	#67	—	2	4	no	—
1034	#67	—	2	4	no	—
1035	#67	—	2	2	no	—
1036	#67	—	4	2	no	—
1037	C₂×Dic₃	—	2	4	no	—
1038	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1039	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1040	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1041	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1042	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1043	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1044	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1045	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1046	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1047	D₁₂	—	2	2	no	—
1048	D₁₂	—	2	4	no	—
1049	D₁₂	C₃×#41	1	4	yes	complemented
1050	C₄×D₃	—	2	4	no	—
1051	C₄×D₃	—	2	4	no	—
1052	C₄×D₃	—	2	4	no	—
1053	C₄×D₃	—	2	4	no	—
1054	C₄×D₃	—	2	2	no	—
1055	C₄×D₃	—	2	2	no	—
1056	C₄×D₃	—	2	2	no	—
1057	C₄×D₃	—	2	4	no	—
1058	C₄×D₃	—	4	1	no	—
1059	C₄×D₃	—	4	2	no	—
1060	C₄×D₃	—	4	2	no	—
1061	C₄×D₃	—	4	1	no	—
1062	C₄×D₃	C₃×#41	1	4	yes	complemented
1063	Dic₆	—	2	2	no	—
1064	Dic₆	—	2	2	no	—
1065	Dic₆	—	4	2	no	—
1066	C₂×C₃²	—	4	1	no	—
1067	C₂×C₃²	—	4	2	no	—
1068	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1069	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1070	C₂×C₃²	#585	1	1	yes	characteristic
1071	C₃×D₃	—	2	2	no	—
1072	C₃×D₃	—	2	4	no	—
1073	C₃×D₃	—	4	1	no	—
1074	C₂⁴	—	3	2	no	—
1075	#41	—	6	4	no	—
1076	#41	—	6	4	no	—
1077	#41	—	6	4	no	—
1078	C₂×Q₈	—	3	1	no	—
1079	C₂×Q₈	—	3	1	no	—
1080	C₂×Q₈	—	3	2	no	—
1081	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1082	C₂×D₄	—	3	1	no	—
1083	C₂×D₄	—	3	2	no	—
1084	C₂×D₄	—	3	1	no	—
1085	C₂×D₄	—	3	2	no	—
1086	C₂×D₄	—	3	2	no	—
1087	C₂×D₄	—	3	1	no	—
1088	C₂×D₄	—	3	1	no	—
1089	C₂×D₄	—	3	2	no	—
1090	C₂×D₄	—	6	4	no	—
1091	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1092	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1093	C₂²×C₄	—	3	1	no	—
1094	C₂²×C₄	—	3	2	no	—
1095	C₂²×C₄	—	3	2	no	—
1096	C₂²×C₄	—	3	2	no	—
1097	C₂²×C₄	—	3	2	no	—
1098	C₂²×C₄	—	3	1	no	—
1099	C₂²×C₄	—	3	1	no	—
1100	C₂²×C₄	—	3	1	no	—
1101	C₂²×C₄	—	3	2	no	—
1102	C₂²×C₄	—	3	2	no	—
1103	C₂²×C₄	—	3	1	no	—
1104	C₂²×C₄	—	3	2	no	—
1105	C₂²×C₄	—	3	2	no	—
1106	C₂²×C₄	—	3	1	no	—
1107	C₂²×C₄	—	6	8	no	—
1108	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1111	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1112	C₄⋊C₄	—	3	1	no	—
1113	C₄⋊C₄	—	3	1	no	—
1114	C₄⋊C₄	—	3	1	no	—
1115	C₄⋊C₄	—	3	2	no	—
1116	C₄⋊C₄	—	3	2	no	—
1117	C₄⋊C₄	—	3	2	no	—
1118	C₄⋊C₄	—	3	2	no	—
1119	C₄⋊C₄	—	3	2	no	—
1120	C₄⋊C₄	—	3	1	no	—
1121	C₄⋊C₄	—	3	1	no	—
1122	C₄⋊C₄	—	3	1	no	—
1123	C₄⋊C₄	—	3	2	no	—
1124	C₄⋊C₄	—	3	2	no	—
1125	C₄⋊C₄	—	3	2	no	—
1126	C₄⋊C₄	—	3	1	no	—
1127	C₄⋊C₄	—	3	1	no	—
1128	C₄⋊C₄	—	3	2	no	—
1129	C₄⋊C₄	—	3	2	no	—
1130	C₄⋊C₄	—	3	2	no	—
1131	C₄⋊C₄	—	3	2	no	—
1132	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1133	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1134	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1135	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1136	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1137	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	2	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	—	3	1	no	—
1142	C₂²⋊C₄	—	3	2	no	—
1143	C₂²⋊C₄	—	3	1	no	—
1144	C₂²⋊C₄	—	3	2	no	—
1145	C₂²⋊C₄	—	3	1	no	—
1146	C₂²⋊C₄	—	3	1	no	—
1147	C₂²⋊C₄	—	3	2	no	—
1148	C₂²⋊C₄	—	3	2	no	—
1149	C₂²⋊C₄	—	3	2	no	—
1150	C₂²⋊C₄	—	3	2	no	—
1151	C₂²⋊C₄	—	3	2	no	—
1152	C₂²⋊C₄	—	3	2	no	—
1153	C₂²⋊C₄	—	3	1	no	—
1154	C₂²⋊C₄	—	3	2	no	—
1155	C₂²⋊C₄	—	3	1	no	—
1156	C₂²⋊C₄	—	3	2	no	—
1157	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1158	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1159	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1160	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1161	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1162	C₄²	—	3	1	no	—
1163	C₄²	—	3	2	no	—
1164	C₄²	—	3	2	no	—
1165	C₄²	—	3	1	no	—
1166	C₄²	—	3	2	no	—
1167	C₄²	—	3	2	no	—
1168	C₄²	—	3	2	no	—
1169	C₄²	—	3	1	no	—
1170	C₄²	—	3	1	no	—
1171	C₄²	—	3	1	no	—
1172	C₄²	—	3	1	no	—
1173	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1174	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1175	C₄²	C₂²×C₃×D₃	1	2	yes	—
1176	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1177	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1178	C₂²×C₃	—	2	2	no	—
1179	C₂²×C₃	—	2	2	no	—
1180	C₂²×C₃	—	2	1	no	—
1181	C₂²×C₃	—	2	1	no	—
1182	C₂²×C₃	—	2	2	no	—
1183	C₂²×C₃	—	2	1	no	—
1184	C₂²×C₃	—	2	2	no	—
1185	C₂²×C₃	—	2	2	no	—
1186	C₂²×C₃	—	2	1	no	—
1187	C₂²×C₃	—	2	1	no	—
1188	C₂²×C₃	—	2	2	no	—
1189	C₂²×C₃	—	2	2	no	—
1190	C₂²×C₃	—	2	1	no	—
1191	C₂²×C₃	—	2	1	no	—
1192	C₂²×C₃	—	3	2	no	—
1193	C₂²×C₃	—	3	4	no	—
1194	C₂²×C₃	—	4	1	no	—
1195	C₂²×C₃	—	4	1	no	—
1196	C₂²×C₃	—	4	2	no	—
1197	C₂²×C₃	—	4	2	no	—
1198	C₂²×C₃	—	4	2	no	—
1199	C₂²×C₃	—	6	2	no	—
1200	C₂²×C₃	—	6	1	no	—
1201	C₂²×C₃	—	6	2	no	—
1202	C₂²×C₃	—	6	1	no	—
1203	C₂²×C₃	—	6	1	no	—
1204	C₂²×C₃	—	6	1	no	—
1205	C₂²×C₃	—	6	1	no	—
1206	C₂²×C₃	—	12	8	no	—
1207	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1208	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1209	C₂×D₃	—	2	2	no	—
1210	C₂×D₃	—	2	1	no	—
1211	C₂×D₃	—	2	2	no	—
1212	C₂×D₃	—	2	1	no	—
1213	C₂×D₃	—	2	1	no	—
1214	C₂×D₃	—	2	1	no	—
1215	C₂×D₃	—	2	1	no	—
1216	C₂×D₃	—	4	8	no	—
1217	C₂×D₃	C₂×C₃×#41	1	2	yes	—
1218	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1219	C₃×C₄	—	2	2	no	—
1220	C₃×C₄	—	2	1	no	—
1221	C₃×C₄	—	2	1	no	—
1222	C₃×C₄	—	2	2	no	—
1223	C₃×C₄	—	2	1	no	—
1224	C₃×C₄	—	2	1	no	—
1225	C₃×C₄	—	2	2	no	—
1226	C₃×C₄	—	2	1	no	—
1227	C₃×C₄	—	2	1	no	—
1228	C₃×C₄	—	2	2	no	—
1229	C₃×C₄	—	2	2	no	—
1230	C₃×C₄	—	2	2	no	—
1231	C₃×C₄	—	2	1	no	—
1232	C₃×C₄	—	2	1	no	—
1233	C₃×C₄	—	2	2	no	—
1234	C₃×C₄	—	2	2	no	—
1235	C₃×C₄	—	3	2	no	—
1236	C₃×C₄	—	4	1	no	—
1237	C₃×C₄	—	4	2	no	—
1238	C₃×C₄	—	4	1	no	—
1239	C₃×C₄	—	4	1	no	—
1240	C₃×C₄	—	4	1	no	—
1241	C₃×C₄	—	4	2	no	—
1242	C₃×C₄	—	4	2	no	—
1243	C₃×C₄	—	6	2	no	—
1244	C₃×C₄	—	6	1	no	—
1245	C₃×C₄	—	6	1	no	—
1246	C₃×C₄	—	6	1	no	—
1247	C₃×C₄	—	6	2	no	—
1248	C₃×C₄	—	6	1	no	—
1249	C₃×C₄	—	6	2	no	—
1250	C₃×C₄	—	6	1	no	—
1251	C₃×C₄	D₃×#41	1	2	yes	—
1252	C₃×C₄	D₃×#41	1	2	yes	—
1253	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1254	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1255	Dic₃	—	2	2	no	—
1256	Dic₃	—	2	1	no	—
1257	Dic₃	—	2	1	no	—
1258	Dic₃	—	2	2	no	—
1259	Dic₃	—	2	1	no	—
1260	Dic₃	—	2	1	no	—
1261	Dic₃	—	2	2	no	—
1262	Dic₃	—	2	1	no	—
1263	Dic₃	C₂×C₃×#41	1	2	yes	—
1264	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
1265	C₂³	—	3	1	no	—
1266	C₂³	—	3	2	no	—
1267	C₂³	—	3	1	no	—
1268	C₂³	—	6	4	no	—
1269	C₂³	—	6	4	no	—
1270	C₂³	—	12	2	no	—
1271	C₂³	C₂³×C₃×D₃	1	2	yes	—
1272	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1273	Q₈	—	2	2	no	—
1274	Q₈	—	6	2	no	—
1275	Q₈	—	6	2	no	—
1276	Q₈	—	12	2	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	3	4	no	—
1279	D₄	—	4	2	no	—
1280	D₄	—	6	2	no	—
1281	D₄	—	6	4	no	—
1282	D₄	—	6	2	no	—
1283	D₄	—	6	4	no	—
1284	D₄	—	6	2	no	—
1285	D₄	—	6	4	no	—
1286	D₄	—	12	2	no	—
1287	C₂×C₄	—	2	4	no	—
1288	C₂×C₄	—	2	2	no	—
1289	C₂×C₄	—	2	2	no	—
1290	C₂×C₄	—	3	1	no	—
1291	C₂×C₄	—	3	4	no	—
1292	C₂×C₄	—	3	1	no	—
1293	C₂×C₄	—	3	2	no	—
1294	C₂×C₄	—	3	1	no	—
1295	C₂×C₄	—	3	1	no	—
1296	C₂×C₄	—	3	2	no	—
1297	C₂×C₄	—	3	1	no	—
1298	C₂×C₄	—	3	2	no	—
1299	C₂×C₄	—	3	1	no	—
1300	C₂×C₄	—	4	1	no	—
1301	C₂×C₄	—	6	4	no	—
1302	C₂×C₄	—	6	4	no	—
1303	C₂×C₄	—	6	4	no	—
1304	C₂×C₄	—	6	4	no	—
1305	C₂×C₄	—	6	4	no	—
1306	C₂×C₄	—	6	4	no	—
1307	C₂×C₄	—	6	2	no	—
1308	C₂×C₄	—	6	2	no	—
1309	C₂×C₄	—	6	2	no	—
1310	C₂×C₄	—	12	1	no	—
1311	C₂×C₄	—	12	2	no	—
1312	C₂×C₄	—	12	1	no	—
1313	C₂×C₄	—	12	2	no	—
1314	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1315	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1316	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1317	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1318	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1319	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1320	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1321	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1322	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1323	C₂×C₃	—	2	1	no	—
1324	C₂×C₃	—	2	1	no	—
1325	C₂×C₃	—	2	1	no	—
1326	C₂×C₃	—	4	2	no	—
1327	C₂×C₃	—	4	2	no	—
1328	C₂×C₃	—	4	1	no	—
1329	C₂×C₃	—	4	2	no	—
1330	C₂×C₃	—	4	1	no	—
1331	C₂×C₃	—	6	2	no	—
1332	C₂×C₃	—	6	4	no	—
1333	C₂×C₃	—	8	2	no	—
1334	C₂×C₃	—	12	1	no	—
1335	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1336	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1337	C₂×C₃	#5964	1	1	yes	characteristic
1338	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1339	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1340	C₂×C₃	C₃×#585	1	1	yes	characteristic
1341	D₃	—	2	2	no	—
1342	D₃	—	2	4	no	—
1343	D₃	—	4	1	no	—
1344	C₂²	—	2	2	no	—
1345	C₂²	—	2	1	no	—
1346	C₂²	—	2	1	no	—
1347	C₂²	—	2	2	no	—
1348	C₂²	—	2	1	no	—
1349	C₂²	—	2	2	no	—
1350	C₂²	—	3	2	no	—
1351	C₂²	—	3	4	no	—
1352	C₂²	—	6	2	no	—
1353	C₂²	—	6	1	no	—
1354	C₂²	—	6	2	no	—
1355	C₂²	—	6	1	no	—
1356	C₂²	—	6	1	no	—
1357	C₂²	—	6	1	no	—
1358	C₂²	—	6	1	no	—
1359	C₂²	—	12	8	no	—
1360	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1361	C₄	—	2	2	no	—
1362	C₄	—	2	1	no	—
1363	C₄	—	2	1	no	—
1364	C₄	—	2	2	no	—
1365	C₄	—	2	1	no	—
1366	C₄	—	2	1	no	—
1367	C₄	—	2	2	no	—
1368	C₄	—	3	2	no	—
1369	C₄	—	6	2	no	—
1370	C₄	—	6	1	no	—
1371	C₄	—	6	1	no	—
1372	C₄	—	6	1	no	—
1373	C₄	—	6	2	no	—
1374	C₄	—	6	1	no	—
1375	C₄	—	6	2	no	—
1376	C₄	—	6	1	no	—
1377	C₄	C₃×D₃×#41	1	2	yes	—
1378	C₄	C₃×D₃×#41	1	2	yes	—
1379	C₃	—	2	1	no	—
1380	C₃	#86151	1	1	yes	characteristic, direct product factor
1381	C₃	C₃×#3475	1	1	yes	characteristic, complemented
1382	C₂	—	4	2	no	—
1383	C₂	—	4	1	no	—
1384	C₂	—	6	2	no	—
1385	C₂	—	6	4	no	—
1386	C₂	—	12	1	no	—
1387	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1388	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1389	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#529	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#529	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
1. C₃²×#529	C₂	semidirect
2. C₃×#5708	C₂	semidirect
3. C₃×#5705	C₂	semidirect
4. C₃×#5694	C₂	semidirect
5. C₃×#5690	C₂	semidirect
6. C₃×#5676	C₂	semidirect
7. C₃×#5671	C₂	semidirect
8. C₃×#5661	C₂	semidirect
9. C₃×#5659	C₂	semidirect
10. C₃×#5639	C₂	semidirect
11. C₃×#5631	C₂	semidirect
12. C₃×#5616	C₂	semidirect
13. C₃×#5612	C₂	semidirect
14. C₃×#5578	C₂	semidirect
15. C₃×C₄×#239	C₂	semidirect
16. C₃×#5557	C₂	semidirect
17. C₃×#5557	C₂	semidirect
18. C₃×#5547	C₂	semidirect
19. C₃×C₄×D₃×D₄	C₂	semidirect
20. C₃×#5528	C₂	semidirect
21. C₃×D₃×#117	C₂	semidirect
22. C₃×C₄×#235	C₂	semidirect
23. C₃×C₄×#235	C₂	semidirect
25. #86151	C₃	direct (N × H)
31. C₃²×#126	C₂²	semidirect
32. C₃²×#125	C₂²	semidirect
34. C₃²×#123	C₂²	semidirect
35. C₃²×C₂²⋊Q₈	C₂²	semidirect
37. C₃²×C₄×Q₈	C₂²	semidirect
39. C₃²×C₄×D₄	C₂²	semidirect
40. C₃²×#117	C₂²	semidirect
41. C₂×C₃²×C₄²	C₂²	semidirect
43. C₃×Q₈×Dic₃	C₂²	semidirect
44. C₃×#944	C₂²	semidirect
45. C₃×#939	C₂²	semidirect
50. C₃×#936	C₂²	semidirect
55. C₃×C₄×#67	C₂²	semidirect
56. C₃×C₄×#67	C₂²	semidirect
57. C₃×C₄×#67	C₂²	semidirect
58. C₃×C₄×#67	C₂²	semidirect
59. C₃×C₄×#67	C₂²	semidirect
60. C₃×#926	C₂²	semidirect
61. C₃×#926	C₂²	semidirect
62. C₃×#926	C₂²	semidirect
63. C₃×#898	C₂²	semidirect
65. C₃×#897	C₂²	semidirect
66. C₃×#897	C₂²	semidirect
68. C₃×#896	C₂²	semidirect
69. C₃×#896	C₂²	semidirect
71. C₃×#894	C₂²	semidirect
74. C₃×#893	C₂²	semidirect
77. C₃×#892	C₂²	semidirect
78. C₃×#892	C₂²	semidirect
80. C₃×D₃×C₄⋊C₄	C₂²	semidirect
81. C₃×D₃×C₄⋊C₄	C₂²	semidirect
82. C₃×#890	C₂²	semidirect
83. C₃×#890	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#889	C₂²	semidirect
86. C₃×#888	C₂²	semidirect
87. C₃×#885	C₂²	semidirect
89. C₃×#884	C₂²	semidirect
93. C₃×#883	C₂²	semidirect
94. C₃×#883	C₂²	semidirect
100. C₃×#879	C₂²	semidirect
101. C₃×#879	C₂²	semidirect
102. C₃×#879	C₂²	semidirect
103. C₃×#879	C₂²	semidirect
104. C₃×#878	C₂²	semidirect
105. C₃×#877	C₂²	semidirect
106. C₃×#877	C₂²	semidirect
111. C₃×C₄×D₁₂	C₂²	semidirect
114. C₃×#872	C₂²	semidirect
115. C₃×#872	C₂²	semidirect
117. C₃×C₄²×D₃	C₂²	semidirect
118. C₃×C₄²×D₃	C₂²	semidirect
119. C₃×C₄²×D₃	C₂²	semidirect
120. C₃×C₄×Dic₆	C₂²	semidirect
121. C₃×C₄×Dic₆	C₂²	semidirect
122. C₃×C₄×Dic₆	C₂²	semidirect
123. C₃×C₄×Dic₆	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
142. C₃×#529	D₃	semidirect
143. C₃×#529	C₂×C₃	semidirect
150. #5708	C₂×C₃	semidirect
151. #5705	C₂×C₃	semidirect
152. #5694	C₂×C₃	semidirect
153. #5690	C₂×C₃	semidirect
154. #5676	C₂×C₃	semidirect
155. #5671	C₂×C₃	semidirect
156. #5661	C₂×C₃	semidirect
157. #5659	C₂×C₃	semidirect
158. #5639	C₂×C₃	semidirect
159. #5631	C₂×C₃	semidirect
160. #5616	C₂×C₃	semidirect
161. #5612	C₂×C₃	semidirect
162. #5578	C₂×C₃	semidirect
163. C₄×#239	C₂×C₃	semidirect
164. #5557	C₂×C₃	semidirect
165. #5557	C₂×C₃	semidirect
166. #5547	C₂×C₃	semidirect
167. C₄×D₃×D₄	C₂×C₃	semidirect
168. #5528	C₂×C₃	semidirect
169. D₃×#117	C₂×C₃	semidirect
170. C₄×#235	C₂×C₃	semidirect
171. C₄×#235	C₂×C₃	semidirect
295. C₃×#126	C₂×D₃	semidirect
296. C₃×#126	C₂²×C₃	semidirect
302. C₃×#125	C₂×D₃	semidirect
303. C₃×#125	C₂²×C₃	semidirect
318. C₃×#123	C₂×D₃	semidirect
319. C₃×#123	C₂²×C₃	semidirect
329. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
330. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
348. C₃×C₄×Q₈	C₂×D₃	semidirect
349. C₃×C₄×Q₈	C₂²×C₃	semidirect
371. C₃×C₄×D₄	C₂×D₃	semidirect
373. C₃×C₄×D₄	C₂²×C₃	semidirect
388. C₃×#117	C₂×D₃	semidirect
389. C₃×#117	C₂²×C₃	semidirect
401. C₂×C₃×C₄²	C₂×D₃	semidirect
402. C₂×C₃×C₄²	C₂²×C₃	semidirect
404. Q₈×Dic₃	C₂²×C₃	semidirect
405. #944	C₂²×C₃	semidirect
406. #939	C₂²×C₃	semidirect
411. #936	C₂²×C₃	semidirect
416. C₄×#67	C₂²×C₃	semidirect
417. C₄×#67	C₂²×C₃	semidirect
418. C₄×#67	C₂²×C₃	semidirect
419. C₄×#67	C₂²×C₃	semidirect
420. C₄×#67	C₂²×C₃	semidirect
421. #926	C₂²×C₃	semidirect
422. #926	C₂²×C₃	semidirect
423. #926	C₂²×C₃	semidirect
424. #898	C₂²×C₃	semidirect
426. #897	C₂²×C₃	semidirect
427. #897	C₂²×C₃	semidirect
429. #896	C₂²×C₃	semidirect
430. #896	C₂²×C₃	semidirect
432. #894	C₂²×C₃	semidirect
435. #893	C₂²×C₃	semidirect
438. #892	C₂²×C₃	semidirect
439. #892	C₂²×C₃	semidirect
441. D₃×C₄⋊C₄	C₂²×C₃	semidirect
442. D₃×C₄⋊C₄	C₂²×C₃	semidirect
443. #890	C₂²×C₃	semidirect
444. #890	C₂²×C₃	semidirect
445. #889	C₂²×C₃	semidirect
446. #889	C₂²×C₃	semidirect
447. #888	C₂²×C₃	semidirect
448. #885	C₂²×C₃	semidirect
450. #884	C₂²×C₃	semidirect
454. #883	C₂²×C₃	semidirect
455. #883	C₂²×C₃	semidirect
461. #879	C₂²×C₃	semidirect
462. #879	C₂²×C₃	semidirect
463. #879	C₂²×C₃	semidirect
464. #879	C₂²×C₃	semidirect
465. #878	C₂²×C₃	semidirect
466. #877	C₂²×C₃	semidirect
467. #877	C₂²×C₃	semidirect
472. C₄×D₁₂	C₂²×C₃	semidirect
475. #872	C₂²×C₃	semidirect
476. #872	C₂²×C₃	semidirect
478. C₄²×D₃	C₂²×C₃	semidirect
479. C₄²×D₃	C₂²×C₃	semidirect
480. C₄²×D₃	C₂²×C₃	semidirect
481. C₄×Dic₆	C₂²×C₃	semidirect
482. C₄×Dic₆	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
484. C₄×Dic₆	C₂²×C₃	semidirect
485. C₄×Dic₆	C₂²×C₃	semidirect
527. C₃×D₁₂	#41	semidirect
540. C₃×C₄×D₃	#41	semidirect
560. #529	C₃×D₃	semidirect
845. #126	C₂×C₃×D₃	semidirect
850. #125	C₂×C₃×D₃	semidirect
862. #123	C₂×C₃×D₃	semidirect
871. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
886. C₄×Q₈	C₂×C₃×D₃	semidirect
906. C₄×D₄	C₂×C₃×D₃	semidirect
920. #117	C₂×C₃×D₃	semidirect
931. C₂×C₄²	C₂×C₃×D₃	semidirect
1049. D₁₂	C₃×#41	semidirect
1062. C₄×D₃	C₃×#41	semidirect
1264. C₃²	#3475	semidirect
1380. C₃	#86151	direct (N × H)
1381. C₃	C₃×#3475	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#529	2
C₃×#5708	2
C₃×#5705	2
C₃×#5694	2
C₃×#5690	2
C₃×#5676	2
C₃×#5671	2
C₃×#5661	2
C₃×#5659	2
C₃×#5639	2
C₃×#5631	2
C₃×#5616	2
C₃×#5612	2
C₃×#5578	2
C₃×C₄×#239	2
C₃×#5557	2
C₃×#5547	2
C₃×C₄×D₃×D₄	2
C₃×#5528	2
C₃×D₃×#117	2
C₃×C₄×#235	2
C₃×#3475	3
#86151	3

Subgroups — C3×#86151 #11903448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86151 #11903448