Subgroups — C₃×#86991 #11909424

Order 1152.

2190 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5730	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5709	C₂	1	2	yes	maximal, complemented
5	C₃×#5707	C₂	1	2	yes	maximal, complemented
6	C₃×#5705	C₂	1	2	yes	maximal, complemented
7	C₃×D₃×#126	C₂	1	2	yes	maximal, complemented
8	C₃×#5679	C₂	1	2	yes	maximal, complemented
9	C₃×#5678	C₂	1	2	yes	maximal, complemented
10	C₃×#5631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5630	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5581	C₂	1	2	yes	maximal, complemented
15	C₃×#5580	C₂	1	2	yes	maximal, complemented
16	C₃×#5574	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5568	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5550	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5530	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#5529	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5522	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#5521	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3521	—	3	1	no	maximal
25	#86991	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×#239	C₂²	1	1	yes	characteristic
27	C₂×C₃×#235	C₂²	1	1	yes	characteristic
28	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
29	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#126	C₂²	1	2	yes	—
31	C₃²×#126	C₂²	1	2	yes	complemented
32	C₃²×#124	C₂²	1	2	yes	—
33	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
37	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃²×#117	C₂²	1	1	yes	characteristic
39	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
40	C₃×#947	C₂²	1	1	yes	characteristic
41	C₃×#947	C₂²	1	2	yes	complemented
42	C₃×#946	C₂²	1	2	yes	complemented
43	C₃×#946	C₂²	1	2	yes	complemented
44	C₃×#946	C₂²	1	2	yes	complemented
45	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₃×#944	C₂²	1	1	yes	characteristic, complemented
47	C₃×#939	C₂²	1	1	yes	characteristic
48	C₃×#937	C₂²	1	2	yes	—
49	C₃×#935	C₂²	1	1	yes	characteristic
50	C₃×#930	C₂²	1	1	yes	characteristic
51	C₃×C₄×#67	C₂²	1	1	yes	characteristic
52	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
53	C₃×#926	C₂²	1	1	yes	characteristic
54	C₃×#924	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₃×#898	C₂²	1	1	yes	characteristic, complemented
57	C₃×#898	C₂²	1	2	yes	complemented
58	C₃×#898	C₂²	1	2	yes	complemented
59	C₃×#898	C₂²	1	2	yes	complemented
60	C₃×#897	C₂²	1	1	yes	characteristic, complemented
61	C₃×#897	C₂²	1	2	yes	complemented
62	C₃×#896	C₂²	1	2	yes	complemented
63	C₃×#895	C₂²	1	1	yes	characteristic
64	C₃×#895	C₂²	1	2	yes	—
65	C₃×#894	C₂²	1	2	yes	—
66	C₃×#894	C₂²	1	2	yes	—
67	C₃×#894	C₂²	1	2	yes	complemented
68	C₃×#894	C₂²	1	2	yes	complemented
69	C₃×#893	C₂²	1	1	yes	characteristic
70	C₃×#893	C₂²	1	1	yes	characteristic
71	C₃×#893	C₂²	1	1	yes	characteristic
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	complemented
76	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
77	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₃×#890	C₂²	1	1	yes	characteristic, complemented
81	C₃×#890	C₂²	1	1	yes	characteristic, complemented
82	C₃×#890	C₂²	1	2	yes	complemented
83	C₃×#889	C₂²	1	1	yes	characteristic, complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#887	C₂²	1	1	yes	characteristic, complemented
86	C₃×#887	C₂²	1	1	yes	characteristic, complemented
87	C₃×#886	C₂²	1	1	yes	characteristic, complemented
88	C₃×#886	C₂²	1	2	yes	complemented
89	C₃×#885	C₂²	1	1	yes	characteristic
90	C₃×#884	C₂²	1	2	yes	—
91	C₃×#884	C₂²	1	2	yes	complemented
92	C₃×#884	C₂²	1	2	yes	complemented
93	C₃×#883	C₂²	1	2	yes	—
94	C₃×#883	C₂²	1	2	yes	complemented
95	C₃×#883	C₂²	1	2	yes	complemented
96	C₃×#882	C₂²	1	2	yes	—
97	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
98	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
99	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
100	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₃×#879	C₂²	1	2	yes	—
105	C₃×#879	C₂²	1	1	yes	characteristic
106	C₃×#879	C₂²	1	2	yes	—
107	C₃×#879	C₂²	1	2	yes	—
108	C₃×#878	C₂²	1	1	yes	characteristic, complemented
109	C₃×#876	C₂²	1	2	yes	complemented
110	C₃×#876	C₂²	1	2	yes	complemented
111	C₃×#875	C₂²	1	1	yes	characteristic
112	C₃×C₄×D₁₂	C₂²	1	2	yes	—
113	C₃×C₄×D₁₂	C₂²	1	2	yes	—
114	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
115	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
116	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
117	C₃×#872	C₂²	1	2	yes	complemented
118	C₃×#872	C₂²	1	2	yes	complemented
119	C₃×#872	C₂²	1	1	yes	characteristic, complemented
120	C₃×#872	C₂²	1	2	yes	complemented
121	C₃×#872	C₂²	1	2	yes	complemented
122	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
123	C₃×#870	C₂²	1	2	yes	complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#556	—	2	1	no	—
126	C₃×#556	—	3	1	no	—
127	C₃×#556	D₃	1	1	yes	characteristic, complemented
128	C₃×#556	C₂×C₃	1	1	yes	characteristic, complemented
129	C₃×#554	—	3	1	no	—
130	C₃×#553	—	3	2	no	—
131	C₃×#553	—	3	1	no	—
132	C₃×#552	—	3	2	no	—
133	C₃×#552	—	3	1	no	—
134	C₃×#551	—	3	2	no	—
135	C₃×#551	—	3	2	no	—
136	C₃×#547	—	3	1	no	—
137	C₃×#546	—	3	1	no	—
138	C₃×#546	—	3	1	no	—
139	C₃×#542	—	3	1	no	—
140	C₃×#541	—	3	1	no	—
141	C₃×#539	—	3	2	no	—
142	C₃×#538	—	3	2	no	—
143	C₃×#529	—	3	1	no	—
144	C₃×#529	—	3	2	no	—
145	C₃×#529	—	3	1	no	—
146	C₂×C₃×#126	—	3	2	no	—
147	C₃×#520	—	3	1	no	—
148	C₃×#518	—	3	1	no	—
149	C₃×C₄×#41	—	3	1	no	—
150	#5733	C₂×C₃	1	1	yes	characteristic, complemented
151	#5730	C₂×C₃	1	1	yes	characteristic, complemented
152	#5709	C₂×C₃	1	2	yes	complemented
153	#5707	C₂×C₃	1	2	yes	complemented
154	#5705	C₂×C₃	1	2	yes	complemented
155	D₃×#126	C₂×C₃	1	2	yes	complemented
156	#5679	C₂×C₃	1	2	yes	complemented
157	#5678	C₂×C₃	1	2	yes	complemented
158	#5631	C₂×C₃	1	1	yes	characteristic, complemented
159	#5630	C₂×C₃	1	1	yes	characteristic, complemented
160	#5625	C₂×C₃	1	1	yes	characteristic, complemented
161	#5624	C₂×C₃	1	1	yes	characteristic, complemented
162	#5581	C₂×C₃	1	2	yes	complemented
163	#5580	C₂×C₃	1	2	yes	complemented
164	#5574	C₂×C₃	1	1	yes	characteristic, complemented
165	#5568	C₂×C₃	1	1	yes	characteristic, complemented
166	#5550	C₂×C₃	1	1	yes	characteristic, complemented
167	#5538	C₂×C₃	1	1	yes	characteristic, complemented
168	#5530	C₂×C₃	1	1	yes	characteristic, complemented
169	#5529	C₂×C₃	1	1	yes	characteristic, complemented
170	#5522	C₂×C₃	1	1	yes	characteristic, complemented
171	#5521	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×Q₈	C₂³	1	2	yes	—
175	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×#67	C₂³	1	2	yes	—
179	C₂×C₃×#67	C₂³	1	2	yes	—
180	C₂×C₃×#67	C₂³	1	1	yes	characteristic
181	C₂×C₃×#67	C₂³	1	1	yes	characteristic
182	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
183	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
184	C₃×#239	—	2	4	no	—
185	C₃×#235	—	2	4	no	—
186	C₂×C₃×D₁₂	—	2	4	no	—
187	C₂×C₃×D₁₂	C₂³	1	2	yes	—
188	C₂×C₃×D₁₂	C₂³	1	2	yes	—
189	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
190	C₂×C₃×D₁₂	C₂³	1	2	yes	—
191	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
193	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
194	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
201	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
202	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
203	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
204	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
212	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃²×C₄²	C₂³	1	2	yes	—
219	C₃²×C₄²	C₂³	1	2	yes	—
220	C₃²×C₄²	C₂³	1	1	yes	characteristic
221	C₃²×C₄²	C₂³	1	2	yes	—
222	C₃×#217	C₂³	1	1	yes	characteristic
223	C₃×#217	C₂³	1	1	yes	characteristic
224	C₃×#217	C₂³	1	1	yes	characteristic
225	C₃×#217	C₂³	1	2	yes	—
226	C₃×#217	C₂³	1	1	yes	characteristic
227	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
233	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
243	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
244	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
245	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
246	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
247	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
248	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
249	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
250	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
251	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
252	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
253	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
260	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
262	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
263	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
264	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
265	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	#3521	—	3	1	no	Sylow
275	C₂×C₃×#41	—	3	1	no	—
276	C₂×C₃×#41	—	3	1	no	—
277	C₂²×C₃×D₄	—	3	1	no	—
278	C₂×#239	C₂²×C₃	1	1	yes	characteristic
279	C₂×#235	C₂²×C₃	1	1	yes	characteristic
280	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
281	C₃×C₄⋊Q₈	—	2	1	no	—
282	C₃×C₄⋊Q₈	—	3	1	no	—
283	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
284	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₃×#126	—	2	2	no	—
286	C₃×#126	—	2	2	no	—
287	C₃×#126	—	3	2	no	—
288	C₃×#126	—	3	2	no	—
289	C₃×#126	—	3	2	no	—
290	C₃×#126	—	3	1	no	—
291	C₃×#126	—	3	1	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	2	no	—
295	C₃×#126	—	3	2	no	—
296	C₃×#126	—	3	2	no	—
297	C₃×#126	C₂×D₃	1	2	yes	—
298	C₃×#126	C₂×D₃	1	2	yes	complemented
299	C₃×#126	C₂²×C₃	1	2	yes	—
300	C₃×#126	C₂²×C₃	1	2	yes	complemented
301	C₃×#125	—	3	1	no	—
302	C₃×#125	—	3	2	no	—
303	C₃×#125	—	3	2	no	—
304	C₃×#125	—	3	1	no	—
305	C₃×#125	—	3	1	no	—
306	C₃×#125	—	3	2	no	—
307	C₃×#124	—	2	2	no	—
308	C₃×#124	—	3	1	no	—
309	C₃×#124	—	3	2	no	—
310	C₃×#124	—	3	1	no	—
311	C₃×#124	—	3	1	no	—
312	C₃×#124	C₂×D₃	1	2	yes	—
313	C₃×#124	C₂²×C₃	1	2	yes	—
314	C₃×#123	—	3	1	no	—
315	C₃×#123	—	3	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×#123	—	3	2	no	—
318	C₃×#123	—	3	2	no	—
319	C₃×#123	—	3	2	no	—
320	C₃×#123	—	3	2	no	—
321	C₃×#123	—	3	2	no	—
322	C₃×#123	—	3	2	no	—
323	C₃×#123	—	3	1	no	—
324	C₃×C₂²⋊Q₈	—	2	1	no	—
325	C₃×C₂²⋊Q₈	—	2	1	no	—
326	C₃×C₂²⋊Q₈	—	3	2	no	—
327	C₃×C₂²⋊Q₈	—	3	2	no	—
328	C₃×C₂²⋊Q₈	—	3	2	no	—
329	C₃×C₂²⋊Q₈	—	3	1	no	—
330	C₃×C₂²⋊Q₈	—	3	2	no	—
331	C₃×C₂²⋊Q₈	—	3	2	no	—
332	C₃×C₂²⋊Q₈	—	3	1	no	—
333	C₃×C₂²⋊Q₈	—	3	1	no	—
334	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
335	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
336	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
337	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
338	C₃×#121	—	3	1	no	—
339	C₃×#121	—	3	1	no	—
340	C₃×#121	—	3	2	no	—
341	C₃×#121	—	3	1	no	—
342	C₃×#121	—	3	2	no	—
343	C₃×#121	—	3	2	no	—
344	C₃×#121	—	3	2	no	—
345	C₃×#120	—	3	2	no	—
346	C₃×#120	—	3	2	no	—
347	C₃×C₄×Q₈	—	2	1	no	—
348	C₃×C₄×Q₈	—	2	2	no	—
349	C₃×C₄×Q₈	—	3	1	no	—
350	C₃×C₄×Q₈	—	3	1	no	—
351	C₃×C₄×Q₈	—	3	1	no	—
352	C₃×C₄×Q₈	—	3	1	no	—
353	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
354	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
355	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
356	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
357	C₃×C₄×D₄	—	2	1	no	—
358	C₃×C₄×D₄	—	3	1	no	—
359	C₃×C₄×D₄	—	3	1	no	—
360	C₃×C₄×D₄	—	3	1	no	—
361	C₃×C₄×D₄	—	3	1	no	—
362	C₃×C₄×D₄	—	3	1	no	—
363	C₃×C₄×D₄	—	3	1	no	—
364	C₃×C₄×D₄	—	3	1	no	—
365	C₃×C₄×D₄	—	3	2	no	—
366	C₃×C₄×D₄	—	3	2	no	—
367	C₃×C₄×D₄	—	3	2	no	—
368	C₃×C₄×D₄	—	3	2	no	—
369	C₃×C₄×D₄	—	3	2	no	—
370	C₃×C₄×D₄	—	3	2	no	—
371	C₃×C₄×D₄	—	3	2	no	—
372	C₃×C₄×D₄	—	3	1	no	—
373	C₃×C₄×D₄	—	3	2	no	—
374	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
375	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
376	C₃×#117	—	2	1	no	—
377	C₃×#117	—	2	1	no	—
378	C₃×#117	—	3	1	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	2	no	—
385	C₃×#117	C₂×D₃	1	1	yes	characteristic
386	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
387	C₃×#117	C₂²×C₃	1	1	yes	characteristic
388	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
389	C₂×C₃×C₄⋊C₄	—	3	2	no	—
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×C₂²⋊C₄	—	3	2	no	—
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	—	3	2	no	—
399	#947	C₂²×C₃	1	1	yes	characteristic
400	#947	C₂²×C₃	1	2	yes	complemented
401	#946	C₂²×C₃	1	2	yes	complemented
402	#946	C₂²×C₃	1	2	yes	complemented
403	#946	C₂²×C₃	1	2	yes	complemented
404	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
405	#944	C₂²×C₃	1	1	yes	characteristic, complemented
406	#939	C₂²×C₃	1	1	yes	characteristic
407	#937	C₂²×C₃	1	2	yes	—
408	#935	C₂²×C₃	1	1	yes	characteristic
409	#930	C₂²×C₃	1	1	yes	characteristic
410	C₄×#67	C₂²×C₃	1	1	yes	characteristic
411	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
412	#926	C₂²×C₃	1	1	yes	characteristic
413	#924	C₂²×C₃	1	1	yes	characteristic
414	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
415	#898	C₂²×C₃	1	2	yes	complemented
416	#898	C₂²×C₃	1	2	yes	complemented
417	#898	C₂²×C₃	1	2	yes	complemented
418	#898	C₂²×C₃	1	1	yes	characteristic, complemented
419	#897	C₂²×C₃	1	2	yes	complemented
420	#897	C₂²×C₃	1	1	yes	characteristic, complemented
421	#896	C₂²×C₃	1	2	yes	complemented
422	#895	C₂²×C₃	1	2	yes	—
423	#895	C₂²×C₃	1	1	yes	characteristic
424	#894	C₂²×C₃	1	2	yes	—
425	#894	C₂²×C₃	1	2	yes	—
426	#894	C₂²×C₃	1	2	yes	complemented
427	#894	C₂²×C₃	1	2	yes	complemented
428	#893	C₂²×C₃	1	1	yes	characteristic
429	#893	C₂²×C₃	1	1	yes	characteristic
430	#893	C₂²×C₃	1	1	yes	characteristic
431	#893	C₂²×C₃	1	1	yes	characteristic
432	#893	C₂²×C₃	1	1	yes	characteristic
433	#893	C₂²×C₃	1	2	yes	complemented
434	#892	C₂²×C₃	1	2	yes	complemented
435	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
436	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
437	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
438	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
439	#890	C₂²×C₃	1	2	yes	complemented
440	#890	C₂²×C₃	1	1	yes	characteristic, complemented
441	#890	C₂²×C₃	1	1	yes	characteristic, complemented
442	#889	C₂²×C₃	1	2	yes	complemented
443	#889	C₂²×C₃	1	1	yes	characteristic, complemented
444	#887	C₂²×C₃	1	1	yes	characteristic, complemented
445	#887	C₂²×C₃	1	1	yes	characteristic, complemented
446	#886	C₂²×C₃	1	2	yes	complemented
447	#886	C₂²×C₃	1	1	yes	characteristic, complemented
448	#885	C₂²×C₃	1	1	yes	characteristic
449	#884	C₂²×C₃	1	2	yes	—
450	#884	C₂²×C₃	1	2	yes	complemented
451	#884	C₂²×C₃	1	2	yes	complemented
452	#883	C₂²×C₃	1	2	yes	—
453	#883	C₂²×C₃	1	2	yes	complemented
454	#883	C₂²×C₃	1	2	yes	complemented
455	#882	C₂²×C₃	1	2	yes	—
456	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
457	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
458	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
459	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
460	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
461	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
462	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
463	#879	C₂²×C₃	1	2	yes	—
464	#879	C₂²×C₃	1	2	yes	—
465	#879	C₂²×C₃	1	2	yes	—
466	#879	C₂²×C₃	1	1	yes	characteristic
467	#878	C₂²×C₃	1	1	yes	characteristic, complemented
468	#876	C₂²×C₃	1	2	yes	complemented
469	#876	C₂²×C₃	1	2	yes	complemented
470	#875	C₂²×C₃	1	1	yes	characteristic
471	C₄×D₁₂	C₂²×C₃	1	2	yes	—
472	C₄×D₁₂	C₂²×C₃	1	2	yes	—
473	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
474	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
475	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
476	#872	C₂²×C₃	1	2	yes	complemented
477	#872	C₂²×C₃	1	2	yes	complemented
478	#872	C₂²×C₃	1	2	yes	complemented
479	#872	C₂²×C₃	1	2	yes	complemented
480	#872	C₂²×C₃	1	1	yes	characteristic, complemented
481	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
482	#870	C₂²×C₃	1	2	yes	complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
485	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
486	C₂²×C₃×D₃	—	2	4	no	—
487	C₂²×C₃×D₃	—	4	2	no	—
488	C₂²×C₃×D₃	—	4	2	no	—
489	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
490	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
492	C₃²×Q₈	—	2	2	no	—
493	C₃²×Q₈	—	4	2	no	—
494	C₃²×D₄	—	4	1	no	—
495	C₂×C₃²×C₄	—	2	2	no	—
496	C₂×C₃²×C₄	—	2	2	no	—
497	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
498	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
499	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
500	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
501	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
503	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₃×#67	—	2	4	no	—
507	C₃×#67	—	4	1	no	—
508	C₃×#67	—	4	2	no	—
509	C₃×#67	—	4	1	no	—
510	C₂×C₃×Dic₃	—	4	1	no	—
511	C₂×C₃×Dic₃	—	4	1	no	—
512	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
513	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
514	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
515	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
516	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
517	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
518	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
519	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
520	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
521	C₃×D₁₂	—	2	4	no	—
522	C₃×D₁₂	—	2	4	no	—
523	C₃×D₁₂	—	2	2	no	—
524	C₃×D₁₂	—	4	2	no	—
525	C₃×D₁₂	#41	1	4	yes	—
526	C₃×C₄×D₃	—	2	4	no	—
527	C₃×C₄×D₃	—	2	4	no	—
528	C₃×C₄×D₃	—	2	2	no	—
529	C₃×C₄×D₃	—	4	2	no	—
530	C₃×C₄×D₃	—	4	2	no	—
531	C₃×C₄×D₃	—	4	2	no	—
532	C₃×C₄×D₃	—	4	2	no	—
533	C₃×C₄×D₃	—	4	2	no	—
534	C₃×C₄×D₃	—	4	2	no	—
535	C₃×C₄×D₃	—	4	2	no	—
536	C₃×Dic₆	—	2	2	no	—
537	C₃×Dic₆	—	4	1	no	—
538	#556	—	3	1	no	—
539	#556	C₃×D₃	1	1	yes	characteristic, complemented
540	#554	—	3	1	no	—
541	#553	—	3	2	no	—
542	#553	—	3	1	no	—
543	#552	—	3	2	no	—
544	#552	—	3	1	no	—
545	#551	—	3	2	no	—
546	#551	—	3	2	no	—
547	#547	—	3	1	no	—
548	#546	—	3	1	no	—
549	#546	—	3	1	no	—
550	#542	—	3	1	no	—
551	#541	—	3	1	no	—
552	#539	—	3	2	no	—
553	#538	—	3	2	no	—
554	#529	—	3	1	no	—
555	#529	—	3	2	no	—
556	#529	—	3	1	no	—
557	C₂×#126	—	3	2	no	—
558	#520	—	3	1	no	—
559	#518	—	3	1	no	—
560	C₄×#41	—	3	1	no	—
561	C₂⁴×C₃	—	3	2	no	—
562	C₂³×D₃	C₂³×C₃	1	2	yes	—
563	C₃×#41	—	6	4	no	—
564	C₃×#41	—	6	4	no	—
565	C₂×C₃×Q₈	—	2	1	no	—
566	C₂×C₃×Q₈	—	2	2	no	—
567	C₂×C₃×Q₈	—	3	1	no	—
568	C₂×C₃×Q₈	—	3	1	no	—
569	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
570	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
571	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
573	C₂×C₃×D₄	—	2	1	no	—
574	C₂×C₃×D₄	—	3	2	no	—
575	C₂×C₃×D₄	—	3	1	no	—
576	C₂×C₃×D₄	—	3	2	no	—
577	C₂×C₃×D₄	—	3	1	no	—
578	C₂×C₃×D₄	—	3	1	no	—
579	C₂×C₃×D₄	—	3	2	no	—
580	C₂×C₃×D₄	—	3	2	no	—
581	C₂×C₃×D₄	—	3	1	no	—
582	C₂×C₃×D₄	—	3	2	no	—
583	C₂×C₃×D₄	—	6	4	no	—
584	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
585	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
586	C₂²×C₃×C₄	—	2	1	no	—
587	C₂²×C₃×C₄	—	2	1	no	—
588	C₂²×C₃×C₄	—	3	1	no	—
589	C₂²×C₃×C₄	—	3	1	no	—
590	C₂²×C₃×C₄	—	3	2	no	—
591	C₂²×C₃×C₄	—	3	2	no	—
592	C₂²×C₃×C₄	—	3	1	no	—
593	C₂²×C₃×C₄	—	3	2	no	—
594	C₂²×C₃×C₄	—	3	2	no	—
595	C₂²×C₃×C₄	—	3	2	no	—
596	C₂²×C₃×C₄	—	3	2	no	—
597	C₂²×C₃×C₄	—	3	2	no	—
598	C₂²×C₃×C₄	—	3	2	no	—
599	C₂²×C₃×C₄	—	3	2	no	—
600	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
601	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
602	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×#67	C₂³×C₃	1	2	yes	—
605	C₂×#67	C₂³×C₃	1	2	yes	—
606	C₂×#67	C₂³×C₃	1	1	yes	characteristic
607	C₂×#67	C₂³×C₃	1	1	yes	characteristic
608	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
609	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
610	#239	—	2	4	no	—
611	#235	—	2	4	no	—
612	C₂×D₁₂	—	2	4	no	—
613	C₂×D₁₂	C₂³×C₃	1	2	yes	—
614	C₂×D₁₂	C₂³×C₃	1	2	yes	—
615	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
616	C₂×D₁₂	C₂³×C₃	1	2	yes	—
617	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
619	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
620	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
622	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
623	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
624	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
625	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
626	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
627	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
628	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
629	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
630	C₃×C₄⋊C₄	—	2	1	no	—
631	C₃×C₄⋊C₄	—	2	1	no	—
632	C₃×C₄⋊C₄	—	2	1	no	—
633	C₃×C₄⋊C₄	—	2	1	no	—
634	C₃×C₄⋊C₄	—	2	2	no	—
635	C₃×C₄⋊C₄	—	2	2	no	—
636	C₃×C₄⋊C₄	—	2	2	no	—
637	C₃×C₄⋊C₄	—	2	2	no	—
638	C₃×C₄⋊C₄	—	3	1	no	—
639	C₃×C₄⋊C₄	—	3	2	no	—
640	C₃×C₄⋊C₄	—	3	1	no	—
641	C₃×C₄⋊C₄	—	3	2	no	—
642	C₃×C₄⋊C₄	—	3	2	no	—
643	C₃×C₄⋊C₄	—	3	2	no	—
644	C₃×C₄⋊C₄	—	3	1	no	—
645	C₃×C₄⋊C₄	—	3	1	no	—
646	C₃×C₄⋊C₄	—	3	2	no	—
647	C₃×C₄⋊C₄	—	3	2	no	—
648	C₃×C₄⋊C₄	—	3	2	no	—
649	C₃×C₄⋊C₄	—	3	2	no	—
650	C₃×C₄⋊C₄	—	3	1	no	—
651	C₃×C₄⋊C₄	—	3	1	no	—
652	C₃×C₄⋊C₄	—	3	1	no	—
653	C₃×C₄⋊C₄	—	3	1	no	—
654	C₃×C₄⋊C₄	—	3	2	no	—
655	C₃×C₄⋊C₄	—	3	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	C₂²×D₃	1	2	yes	—
661	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
662	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
663	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
664	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
665	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
666	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
667	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
668	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
669	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
670	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
671	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
672	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
673	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
674	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
675	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
676	C₃×C₂²⋊C₄	—	2	2	no	—
677	C₃×C₂²⋊C₄	—	2	2	no	—
678	C₃×C₂²⋊C₄	—	2	1	no	—
679	C₃×C₂²⋊C₄	—	2	1	no	—
680	C₃×C₂²⋊C₄	—	2	2	no	—
681	C₃×C₂²⋊C₄	—	2	2	no	—
682	C₃×C₂²⋊C₄	—	3	1	no	—
683	C₃×C₂²⋊C₄	—	3	1	no	—
684	C₃×C₂²⋊C₄	—	3	1	no	—
685	C₃×C₂²⋊C₄	—	3	2	no	—
686	C₃×C₂²⋊C₄	—	3	1	no	—
687	C₃×C₂²⋊C₄	—	3	2	no	—
688	C₃×C₂²⋊C₄	—	3	2	no	—
689	C₃×C₂²⋊C₄	—	3	2	no	—
690	C₃×C₂²⋊C₄	—	3	2	no	—
691	C₃×C₂²⋊C₄	—	3	2	no	—
692	C₃×C₂²⋊C₄	—	3	2	no	—
693	C₃×C₂²⋊C₄	—	3	2	no	—
694	C₃×C₂²⋊C₄	—	3	2	no	—
695	C₃×C₂²⋊C₄	—	3	1	no	—
696	C₃×C₂²⋊C₄	—	3	2	no	—
697	C₃×C₂²⋊C₄	—	3	2	no	—
698	C₃×C₂²⋊C₄	—	3	1	no	—
699	C₃×C₂²⋊C₄	—	3	1	no	—
700	C₃×C₂²⋊C₄	—	3	2	no	—
701	C₃×C₂²⋊C₄	—	3	2	no	—
702	C₃×C₂²⋊C₄	—	3	2	no	—
703	C₃×C₂²⋊C₄	—	3	1	no	—
704	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
705	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
707	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
708	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
709	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
710	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
711	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
713	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
714	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
716	C₃×C₄²	—	2	2	no	—
717	C₃×C₄²	—	2	2	no	—
718	C₃×C₄²	—	2	1	no	—
719	C₃×C₄²	—	2	2	no	—
720	C₃×C₄²	—	3	1	no	—
721	C₃×C₄²	—	3	1	no	—
722	C₃×C₄²	—	3	1	no	—
723	C₃×C₄²	—	3	2	no	—
724	C₃×C₄²	—	3	1	no	—
725	C₃×C₄²	—	3	2	no	—
726	C₃×C₄²	—	3	2	no	—
727	C₃×C₄²	—	3	1	no	—
728	C₃×C₄²	C₂²×D₃	1	2	yes	—
729	C₃×C₄²	C₂²×D₃	1	2	yes	—
730	C₃×C₄²	C₂²×D₃	1	2	yes	—
731	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
732	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
733	C₃×C₄²	C₂³×C₃	1	2	yes	—
734	C₃×C₄²	C₂³×C₃	1	2	yes	—
735	C₃×C₄²	C₂³×C₃	1	2	yes	—
736	#217	C₂³×C₃	1	1	yes	characteristic
737	#217	C₂³×C₃	1	1	yes	characteristic
738	#217	C₂³×C₃	1	1	yes	characteristic
739	#217	C₂³×C₃	1	2	yes	—
740	#217	C₂³×C₃	1	1	yes	characteristic
741	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
742	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
743	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
744	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
745	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
746	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
747	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
748	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
750	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
751	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
752	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
753	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
754	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
758	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
759	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
760	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
761	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
762	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
763	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
764	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
765	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
766	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
767	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
768	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
769	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
770	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
771	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
772	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
773	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
774	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
776	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
777	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
778	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
780	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
781	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
782	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
783	C₄×Dic₃	C₂³×C₃	1	2	yes	—
784	C₄×Dic₃	C₂³×C₃	1	2	yes	—
785	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₃	1	2	yes	—
787	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
788	C₂²×C₃²	—	2	1	no	—
789	C₂²×C₃²	—	2	1	no	—
790	C₂²×C₃²	—	2	1	no	—
791	C₂²×C₃²	—	2	1	no	—
792	C₂²×C₃²	—	2	1	no	—
793	C₂²×C₃²	—	2	1	no	—
794	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
795	C₂×C₃×D₃	—	2	2	no	—
796	C₂×C₃×D₃	—	2	2	no	—
797	C₂×C₃×D₃	—	2	1	no	—
798	C₂×C₃×D₃	—	2	2	no	—
799	C₂×C₃×D₃	—	2	1	no	—
800	C₂×C₃×D₃	—	2	2	no	—
801	C₂×C₃×D₃	—	2	2	no	—
802	C₂×C₃×D₃	—	2	1	no	—
803	C₂×C₃×D₃	—	8	4	no	—
804	C₂×C₃×D₃	C₂×#41	1	4	yes	—
805	C₃²×C₄	—	2	1	no	—
806	C₃²×C₄	—	2	1	no	—
807	C₃²×C₄	—	2	2	no	—
808	C₃²×C₄	—	2	1	no	—
809	C₃²×C₄	—	2	1	no	—
810	C₃²×C₄	—	2	2	no	—
811	C₃²×C₄	—	2	2	no	—
812	C₃²×C₄	—	2	2	no	—
813	C₃²×C₄	C₂×#41	1	2	yes	—
814	C₃×Dic₃	—	2	2	no	—
815	C₃×Dic₃	—	2	1	no	—
816	C₃×Dic₃	—	2	1	no	—
817	C₃×Dic₃	—	2	1	no	—
818	C₃×Dic₃	—	2	1	no	—
819	C₃×Dic₃	—	2	1	no	—
820	C₃×Dic₃	—	2	1	no	—
821	C₃×Dic₃	—	2	1	no	—
822	C₃×Dic₃	—	2	2	no	—
823	C₂×#41	—	3	1	no	—
824	C₂×#41	—	3	1	no	—
825	C₂²×D₄	—	3	1	no	—
826	C₄⋊Q₈	—	3	1	no	—
827	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
828	#126	—	3	2	no	—
829	#126	—	3	2	no	—
830	#126	—	3	2	no	—
831	#126	—	3	1	no	—
832	#126	—	3	1	no	—
833	#126	—	3	2	no	—
834	#126	—	3	2	no	—
835	#126	—	3	2	no	—
836	#126	—	3	2	no	—
837	#126	—	3	2	no	—
838	#126	C₂×C₃×D₃	1	2	yes	—
839	#126	C₂×C₃×D₃	1	2	yes	complemented
840	#125	—	3	2	no	—
841	#125	—	3	1	no	—
842	#125	—	3	1	no	—
843	#125	—	3	2	no	—
844	#125	—	3	1	no	—
845	#125	—	3	2	no	—
846	#124	—	3	2	no	—
847	#124	—	3	1	no	—
848	#124	—	3	1	no	—
849	#124	—	3	1	no	—
850	#124	C₂×C₃×D₃	1	2	yes	—
851	#123	—	3	1	no	—
852	#123	—	3	2	no	—
853	#123	—	3	2	no	—
854	#123	—	3	2	no	—
855	#123	—	3	2	no	—
856	#123	—	3	2	no	—
857	#123	—	3	1	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	C₂²⋊Q₈	—	3	2	no	—
862	C₂²⋊Q₈	—	3	2	no	—
863	C₂²⋊Q₈	—	3	2	no	—
864	C₂²⋊Q₈	—	3	1	no	—
865	C₂²⋊Q₈	—	3	2	no	—
866	C₂²⋊Q₈	—	3	2	no	—
867	C₂²⋊Q₈	—	3	1	no	—
868	C₂²⋊Q₈	—	3	1	no	—
869	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
871	#121	—	3	1	no	—
872	#121	—	3	1	no	—
873	#121	—	3	2	no	—
874	#121	—	3	1	no	—
875	#121	—	3	2	no	—
876	#121	—	3	2	no	—
877	#121	—	3	2	no	—
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	C₂×C₃×D₃	1	1	yes	characteristic, complemented
885	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
886	C₄×D₄	—	3	1	no	—
887	C₄×D₄	—	3	1	no	—
888	C₄×D₄	—	3	1	no	—
889	C₄×D₄	—	3	1	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	2	no	—
895	C₄×D₄	—	3	2	no	—
896	C₄×D₄	—	3	2	no	—
897	C₄×D₄	—	3	2	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	C₂×C₃×D₃	1	1	yes	characteristic
903	#117	—	3	1	no	—
904	#117	—	3	2	no	—
905	#117	—	3	2	no	—
906	#117	—	3	1	no	—
907	#117	—	3	2	no	—
908	#117	—	3	2	no	—
909	#117	—	3	2	no	—
910	#117	C₂×C₃×D₃	1	1	yes	characteristic
911	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
912	C₂×C₄⋊C₄	—	3	2	no	—
913	C₂×C₄⋊C₄	—	3	1	no	—
914	C₂×C₄⋊C₄	—	3	2	no	—
915	C₂×C₄⋊C₄	—	3	2	no	—
916	C₂×C₂²⋊C₄	—	3	2	no	—
917	C₂×C₂²⋊C₄	—	3	2	no	—
918	C₂×C₂²⋊C₄	—	3	2	no	—
919	C₂×C₂²⋊C₄	—	3	2	no	—
920	C₂×C₄²	—	3	1	no	—
921	C₂×C₄²	—	3	2	no	—
922	C₂³×C₃	—	2	1	no	—
923	C₂³×C₃	—	2	1	no	—
924	C₂³×C₃	—	3	2	no	—
925	C₂³×C₃	—	3	2	no	—
926	C₂³×C₃	—	3	1	no	—
927	C₂³×C₃	—	6	4	no	—
928	C₂³×C₃	—	12	2	no	—
929	C₂³×C₃	—	12	2	no	—
930	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
931	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
932	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
933	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
934	C₂²×D₃	—	2	4	no	—
935	C₂²×D₃	—	4	2	no	—
936	C₂²×D₃	—	4	2	no	—
937	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
938	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
939	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
940	C₃×Q₈	—	2	2	no	—
941	C₃×Q₈	—	2	2	no	—
942	C₃×Q₈	—	4	2	no	—
943	C₃×Q₈	—	4	2	no	—
944	C₃×Q₈	—	4	2	no	—
945	C₃×Q₈	—	4	4	no	—
946	C₃×Q₈	—	6	2	no	—
947	C₃×Q₈	—	12	1	no	—
948	C₃×D₄	—	3	4	no	—
949	C₃×D₄	—	4	1	no	—
950	C₃×D₄	—	4	1	no	—
951	C₃×D₄	—	4	2	no	—
952	C₃×D₄	—	6	4	no	—
953	C₃×D₄	—	6	4	no	—
954	C₃×D₄	—	6	4	no	—
955	C₃×D₄	—	6	2	no	—
956	C₃×D₄	—	12	2	no	—
957	C₃×D₄	—	12	1	no	—
958	C₃×D₄	—	12	2	no	—
959	C₃×D₄	—	12	1	no	—
960	C₂×C₃×C₄	—	2	2	no	—
961	C₂×C₃×C₄	—	2	2	no	—
962	C₂×C₃×C₄	—	2	2	no	—
963	C₂×C₃×C₄	—	2	2	no	—
964	C₂×C₃×C₄	—	2	1	no	—
965	C₂×C₃×C₄	—	2	1	no	—
966	C₂×C₃×C₄	—	2	2	no	—
967	C₂×C₃×C₄	—	2	1	no	—
968	C₂×C₃×C₄	—	2	1	no	—
969	C₂×C₃×C₄	—	2	1	no	—
970	C₂×C₃×C₄	—	2	2	no	—
971	C₂×C₃×C₄	—	2	2	no	—
972	C₂×C₃×C₄	—	2	2	no	—
973	C₂×C₃×C₄	—	3	1	no	—
974	C₂×C₃×C₄	—	3	1	no	—
975	C₂×C₃×C₄	—	3	1	no	—
976	C₂×C₃×C₄	—	3	2	no	—
977	C₂×C₃×C₄	—	3	1	no	—
978	C₂×C₃×C₄	—	3	1	no	—
979	C₂×C₃×C₄	—	3	1	no	—
980	C₂×C₃×C₄	—	3	2	no	—
981	C₂×C₃×C₄	—	3	1	no	—
982	C₂×C₃×C₄	—	4	2	no	—
983	C₂×C₃×C₄	—	4	2	no	—
984	C₂×C₃×C₄	—	6	4	no	—
985	C₂×C₃×C₄	—	6	4	no	—
986	C₂×C₃×C₄	—	6	2	no	—
987	C₂×C₃×C₄	—	12	2	no	—
988	C₂×C₃×C₄	—	12	2	no	—
989	C₂×C₃×C₄	—	12	2	no	—
990	C₂×C₃×C₄	—	12	2	no	—
991	C₂×C₃×C₄	—	12	2	no	—
992	C₂×C₃×C₄	—	12	2	no	—
993	C₂×C₃×C₄	—	12	2	no	—
994	C₂×C₃×C₄	—	12	1	no	—
995	C₂×C₃×C₄	—	12	1	no	—
996	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
997	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
998	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
999	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1000	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1001	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1002	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1003	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1004	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1005	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1006	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1007	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1008	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1009	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1010	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1011	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1012	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1013	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1014	#67	—	2	4	no	—
1015	#67	—	4	1	no	—
1016	#67	—	4	2	no	—
1017	#67	—	4	1	no	—
1018	C₂×Dic₃	—	4	1	no	—
1019	C₂×Dic₃	—	4	1	no	—
1020	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1021	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1022	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1023	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1024	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1025	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1026	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1027	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1028	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1029	D₁₂	—	2	4	no	—
1030	D₁₂	—	2	4	no	—
1031	D₁₂	—	2	2	no	—
1032	D₁₂	—	4	2	no	—
1033	D₁₂	C₃×#41	1	4	yes	—
1034	C₄×D₃	—	2	4	no	—
1035	C₄×D₃	—	2	4	no	—
1036	C₄×D₃	—	2	2	no	—
1037	C₄×D₃	—	4	2	no	—
1038	C₄×D₃	—	4	2	no	—
1039	C₄×D₃	—	4	2	no	—
1040	C₄×D₃	—	4	2	no	—
1041	C₄×D₃	—	4	2	no	—
1042	C₄×D₃	—	4	2	no	—
1043	C₄×D₃	—	4	2	no	—
1044	Dic₆	—	2	2	no	—
1045	Dic₆	—	4	1	no	—
1046	C₂×C₃²	—	4	1	no	—
1047	C₂×C₃²	—	4	1	no	—
1048	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1049	C₂×C₃²	#585	1	1	yes	characteristic
1050	C₂×C₃²	#585	1	1	yes	characteristic
1051	C₃×D₃	—	2	4	no	—
1052	C₃×D₃	—	4	1	no	—
1053	C₃×D₃	—	4	2	no	—
1054	C₂⁴	—	3	2	no	—
1055	#41	—	6	4	no	—
1056	#41	—	6	4	no	—
1057	C₂×Q₈	—	3	1	no	—
1058	C₂×Q₈	—	3	1	no	—
1059	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1060	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
1061	C₂×D₄	—	3	2	no	—
1062	C₂×D₄	—	3	1	no	—
1063	C₂×D₄	—	3	2	no	—
1064	C₂×D₄	—	3	1	no	—
1065	C₂×D₄	—	3	1	no	—
1066	C₂×D₄	—	3	2	no	—
1067	C₂×D₄	—	3	2	no	—
1068	C₂×D₄	—	3	1	no	—
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	6	4	no	—
1071	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1072	C₂²×C₄	—	3	1	no	—
1073	C₂²×C₄	—	3	1	no	—
1074	C₂²×C₄	—	3	2	no	—
1075	C₂²×C₄	—	3	2	no	—
1076	C₂²×C₄	—	3	1	no	—
1077	C₂²×C₄	—	3	2	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	2	no	—
1081	C₂²×C₄	—	3	2	no	—
1082	C₂²×C₄	—	3	2	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1085	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1086	C₄⋊C₄	—	3	1	no	—
1087	C₄⋊C₄	—	3	2	no	—
1088	C₄⋊C₄	—	3	1	no	—
1089	C₄⋊C₄	—	3	1	no	—
1090	C₄⋊C₄	—	3	2	no	—
1091	C₄⋊C₄	—	3	1	no	—
1092	C₄⋊C₄	—	3	2	no	—
1093	C₄⋊C₄	—	3	2	no	—
1094	C₄⋊C₄	—	3	2	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	1	no	—
1097	C₄⋊C₄	—	3	1	no	—
1098	C₄⋊C₄	—	3	1	no	—
1099	C₄⋊C₄	—	3	1	no	—
1100	C₄⋊C₄	—	3	2	no	—
1101	C₄⋊C₄	—	3	2	no	—
1102	C₄⋊C₄	—	3	2	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	2	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	1	no	—
1108	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1109	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1111	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1112	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1114	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1116	C₂²⋊C₄	—	3	1	no	—
1117	C₂²⋊C₄	—	3	1	no	—
1118	C₂²⋊C₄	—	3	1	no	—
1119	C₂²⋊C₄	—	3	2	no	—
1120	C₂²⋊C₄	—	3	1	no	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	2	no	—
1123	C₂²⋊C₄	—	3	2	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	2	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	1	no	—
1130	C₂²⋊C₄	—	3	2	no	—
1131	C₂²⋊C₄	—	3	2	no	—
1132	C₂²⋊C₄	—	3	1	no	—
1133	C₂²⋊C₄	—	3	1	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	2	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	1	no	—
1138	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1139	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1140	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1141	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1142	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1143	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1144	C₄²	—	3	1	no	—
1145	C₄²	—	3	1	no	—
1146	C₄²	—	3	1	no	—
1147	C₄²	—	3	2	no	—
1148	C₄²	—	3	1	no	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	1	no	—
1152	C₄²	C₂²×C₃×D₃	1	2	yes	—
1153	C₄²	C₂²×C₃×D₃	1	2	yes	—
1154	C₄²	C₂²×C₃×D₃	1	2	yes	—
1155	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1156	C₂²×C₃	—	2	1	no	—
1157	C₂²×C₃	—	2	1	no	—
1158	C₂²×C₃	—	2	1	no	—
1159	C₂²×C₃	—	2	1	no	—
1160	C₂²×C₃	—	2	1	no	—
1161	C₂²×C₃	—	2	1	no	—
1162	C₂²×C₃	—	2	1	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	1	no	—
1165	C₂²×C₃	—	2	1	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	—	2	1	no	—
1168	C₂²×C₃	—	2	1	no	—
1169	C₂²×C₃	—	3	4	no	—
1170	C₂²×C₃	—	4	1	no	—
1171	C₂²×C₃	—	4	1	no	—
1172	C₂²×C₃	—	4	1	no	—
1173	C₂²×C₃	—	4	1	no	—
1174	C₂²×C₃	—	4	1	no	—
1175	C₂²×C₃	—	4	1	no	—
1176	C₂²×C₃	—	6	2	no	—
1177	C₂²×C₃	—	6	2	no	—
1178	C₂²×C₃	—	6	1	no	—
1179	C₂²×C₃	—	6	2	no	—
1180	C₂²×C₃	—	6	2	no	—
1181	C₂²×C₃	—	6	1	no	—
1182	C₂²×C₃	—	6	1	no	—
1183	C₂²×C₃	—	6	2	no	—
1184	C₂²×C₃	—	24	4	no	—
1185	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1186	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1187	C₂×D₃	—	2	2	no	—
1188	C₂×D₃	—	2	2	no	—
1189	C₂×D₃	—	2	1	no	—
1190	C₂×D₃	—	2	2	no	—
1191	C₂×D₃	—	2	1	no	—
1192	C₂×D₃	—	2	2	no	—
1193	C₂×D₃	—	2	2	no	—
1194	C₂×D₃	—	2	1	no	—
1195	C₂×D₃	—	8	4	no	—
1196	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1197	C₃×C₄	—	2	2	no	—
1198	C₃×C₄	—	2	1	no	—
1199	C₃×C₄	—	2	1	no	—
1200	C₃×C₄	—	2	2	no	—
1201	C₃×C₄	—	2	2	no	—
1202	C₃×C₄	—	2	2	no	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	2	no	—
1205	C₃×C₄	—	2	1	no	—
1206	C₃×C₄	—	2	1	no	—
1207	C₃×C₄	—	2	2	no	—
1208	C₃×C₄	—	2	1	no	—
1209	C₃×C₄	—	2	1	no	—
1210	C₃×C₄	—	2	2	no	—
1211	C₃×C₄	—	2	2	no	—
1212	C₃×C₄	—	2	2	no	—
1213	C₃×C₄	—	2	1	no	—
1214	C₃×C₄	—	2	2	no	—
1215	C₃×C₄	—	4	1	no	—
1216	C₃×C₄	—	4	1	no	—
1217	C₃×C₄	—	4	2	no	—
1218	C₃×C₄	—	4	2	no	—
1219	C₃×C₄	—	4	2	no	—
1220	C₃×C₄	—	4	2	no	—
1221	C₃×C₄	—	4	1	no	—
1222	C₃×C₄	—	6	1	no	—
1223	C₃×C₄	—	6	2	no	—
1224	C₃×C₄	—	6	1	no	—
1225	C₃×C₄	—	6	1	no	—
1226	C₃×C₄	—	6	1	no	—
1227	C₃×C₄	—	6	1	no	—
1228	C₃×C₄	—	6	2	no	—
1229	C₃×C₄	—	6	1	no	—
1230	C₃×C₄	—	6	1	no	—
1231	C₃×C₄	D₃×#41	1	2	yes	—
1232	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1233	Dic₃	—	2	2	no	—
1234	Dic₃	—	2	1	no	—
1235	Dic₃	—	2	1	no	—
1236	Dic₃	—	2	1	no	—
1237	Dic₃	—	2	1	no	—
1238	Dic₃	—	2	1	no	—
1239	Dic₃	—	2	1	no	—
1240	Dic₃	—	2	1	no	—
1241	Dic₃	—	2	2	no	—
1242	C₃²	#3521	1	1	yes	characteristic, complemented, Sylow
1243	C₂³	—	3	2	no	—
1244	C₂³	—	3	2	no	—
1245	C₂³	—	3	1	no	—
1246	C₂³	—	6	4	no	—
1247	C₂³	—	12	2	no	—
1248	C₂³	—	12	2	no	—
1249	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1250	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1251	Q₈	—	2	2	no	—
1252	Q₈	—	4	2	no	—
1253	Q₈	—	6	2	no	—
1254	Q₈	—	12	1	no	—
1255	D₄	—	3	4	no	—
1256	D₄	—	4	1	no	—
1257	D₄	—	6	4	no	—
1258	D₄	—	6	4	no	—
1259	D₄	—	6	4	no	—
1260	D₄	—	6	2	no	—
1261	D₄	—	12	2	no	—
1262	D₄	—	12	1	no	—
1263	D₄	—	12	2	no	—
1264	D₄	—	12	1	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	3	1	no	—
1268	C₂×C₄	—	3	1	no	—
1269	C₂×C₄	—	3	1	no	—
1270	C₂×C₄	—	3	2	no	—
1271	C₂×C₄	—	3	1	no	—
1272	C₂×C₄	—	3	1	no	—
1273	C₂×C₄	—	3	1	no	—
1274	C₂×C₄	—	3	2	no	—
1275	C₂×C₄	—	3	1	no	—
1276	C₂×C₄	—	6	4	no	—
1277	C₂×C₄	—	6	4	no	—
1278	C₂×C₄	—	6	2	no	—
1279	C₂×C₄	—	12	2	no	—
1280	C₂×C₄	—	12	2	no	—
1281	C₂×C₄	—	12	2	no	—
1282	C₂×C₄	—	12	2	no	—
1283	C₂×C₄	—	12	2	no	—
1284	C₂×C₄	—	12	2	no	—
1285	C₂×C₄	—	12	2	no	—
1286	C₂×C₄	—	12	1	no	—
1287	C₂×C₄	—	12	1	no	—
1288	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1289	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1290	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1291	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1292	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1293	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1294	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1295	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1296	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1297	C₂×C₃	—	2	1	no	—
1298	C₂×C₃	—	2	1	no	—
1299	C₂×C₃	—	2	1	no	—
1300	C₂×C₃	—	4	1	no	—
1301	C₂×C₃	—	4	1	no	—
1302	C₂×C₃	—	4	1	no	—
1303	C₂×C₃	—	4	1	no	—
1304	C₂×C₃	—	6	4	no	—
1305	C₂×C₃	—	8	1	no	—
1306	C₂×C₃	—	8	1	no	—
1307	C₂×C₃	—	12	2	no	—
1308	C₂×C₃	—	12	1	no	—
1309	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1310	C₂×C₃	#5964	1	1	yes	characteristic
1311	C₂×C₃	#5968	1	1	yes	characteristic
1312	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1313	C₂×C₃	C₃×#585	1	1	yes	characteristic
1314	C₂×C₃	C₃×#585	1	1	yes	characteristic
1315	D₃	—	2	4	no	—
1316	D₃	—	4	2	no	—
1317	D₃	—	4	1	no	—
1318	C₂²	—	2	1	no	—
1319	C₂²	—	2	1	no	—
1320	C₂²	—	2	1	no	—
1321	C₂²	—	2	1	no	—
1322	C₂²	—	2	1	no	—
1323	C₂²	—	2	1	no	—
1324	C₂²	—	3	4	no	—
1325	C₂²	—	6	2	no	—
1326	C₂²	—	6	2	no	—
1327	C₂²	—	6	1	no	—
1328	C₂²	—	6	2	no	—
1329	C₂²	—	6	2	no	—
1330	C₂²	—	6	1	no	—
1331	C₂²	—	6	1	no	—
1332	C₂²	—	6	2	no	—
1333	C₂²	—	24	4	no	—
1334	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1335	C₄	—	2	1	no	—
1336	C₄	—	2	1	no	—
1337	C₄	—	2	2	no	—
1338	C₄	—	2	2	no	—
1339	C₄	—	2	2	no	—
1340	C₄	—	2	1	no	—
1341	C₄	—	2	2	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	6	1	no	—
1344	C₄	—	6	2	no	—
1345	C₄	—	6	1	no	—
1346	C₄	—	6	1	no	—
1347	C₄	—	6	1	no	—
1348	C₄	—	6	1	no	—
1349	C₄	—	6	2	no	—
1350	C₄	—	6	1	no	—
1351	C₄	—	6	1	no	—
1352	C₄	C₃×D₃×#41	1	2	yes	—
1353	C₃	—	2	1	no	—
1354	C₃	#86991	1	1	yes	characteristic, direct product factor
1355	C₃	C₃×#3521	1	1	yes	characteristic, complemented
1356	C₂	—	4	1	no	—
1357	C₂	—	4	1	no	—
1358	C₂	—	6	4	no	—
1359	C₂	—	12	2	no	—
1360	C₂	—	12	1	no	—
1361	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1362	C₂	C₃×#5964	1	1	yes	characteristic
1363	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#556	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#556	D₃
hypocenter	C₃	C₃×#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃²×#556	C₂	semidirect
2. C₃×#5733	C₂	semidirect
3. C₃×#5730	C₂	semidirect
4. C₃×#5709	C₂	semidirect
5. C₃×#5707	C₂	semidirect
6. C₃×#5705	C₂	semidirect
7. C₃×D₃×#126	C₂	semidirect
8. C₃×#5679	C₂	semidirect
9. C₃×#5678	C₂	semidirect
10. C₃×#5631	C₂	semidirect
11. C₃×#5630	C₂	semidirect
12. C₃×#5625	C₂	semidirect
13. C₃×#5624	C₂	semidirect
14. C₃×#5581	C₂	semidirect
15. C₃×#5580	C₂	semidirect
16. C₃×#5574	C₂	semidirect
17. C₃×#5568	C₂	semidirect
18. C₃×#5550	C₂	semidirect
19. C₃×#5538	C₂	semidirect
20. C₃×#5530	C₂	semidirect
21. C₃×#5529	C₂	semidirect
22. C₃×#5522	C₂	semidirect
23. C₃×#5521	C₂	semidirect
25. #86991	C₃	direct (N × H)
29. C₃²×C₄⋊Q₈	C₂²	semidirect
31. C₃²×#126	C₂²	semidirect
34. C₃²×C₂²⋊Q₈	C₂²	semidirect
35. C₃²×C₄×Q₈	C₂²	semidirect
36. C₃²×C₄×Q₈	C₂²	semidirect
39. C₃²×#117	C₂²	semidirect
41. C₃×#947	C₂²	semidirect
42. C₃×#946	C₂²	semidirect
43. C₃×#946	C₂²	semidirect
44. C₃×#946	C₂²	semidirect
45. C₃×Q₈×Dic₃	C₂²	semidirect
46. C₃×#944	C₂²	semidirect
52. C₃×C₄×#67	C₂²	semidirect
55. C₂×C₃×C₄×Dic₃	C₂²	semidirect
56. C₃×#898	C₂²	semidirect
57. C₃×#898	C₂²	semidirect
58. C₃×#898	C₂²	semidirect
59. C₃×#898	C₂²	semidirect
60. C₃×#897	C₂²	semidirect
61. C₃×#897	C₂²	semidirect
62. C₃×#896	C₂²	semidirect
67. C₃×#894	C₂²	semidirect
68. C₃×#894	C₂²	semidirect
74. C₃×#893	C₂²	semidirect
75. C₃×#892	C₂²	semidirect
76. C₃×D₃×C₄⋊C₄	C₂²	semidirect
77. C₃×D₃×C₄⋊C₄	C₂²	semidirect
78. C₃×D₃×C₄⋊C₄	C₂²	semidirect
79. C₃×D₃×C₄⋊C₄	C₂²	semidirect
80. C₃×#890	C₂²	semidirect
81. C₃×#890	C₂²	semidirect
82. C₃×#890	C₂²	semidirect
83. C₃×#889	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#887	C₂²	semidirect
86. C₃×#887	C₂²	semidirect
87. C₃×#886	C₂²	semidirect
88. C₃×#886	C₂²	semidirect
91. C₃×#884	C₂²	semidirect
92. C₃×#884	C₂²	semidirect
94. C₃×#883	C₂²	semidirect
95. C₃×#883	C₂²	semidirect
97. C₃×#67⋊C₄	C₂²	semidirect
98. C₃×#67⋊C₄	C₂²	semidirect
99. C₃×#67⋊C₄	C₂²	semidirect
108. C₃×#878	C₂²	semidirect
109. C₃×#876	C₂²	semidirect
110. C₃×#876	C₂²	semidirect
115. C₃×C₄×D₁₂	C₂²	semidirect
116. C₃×C₄×D₁₂	C₂²	semidirect
117. C₃×#872	C₂²	semidirect
118. C₃×#872	C₂²	semidirect
119. C₃×#872	C₂²	semidirect
120. C₃×#872	C₂²	semidirect
121. C₃×#872	C₂²	semidirect
122. C₃×C₄²×D₃	C₂²	semidirect
123. C₃×#870	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
127. C₃×#556	D₃	semidirect
128. C₃×#556	C₂×C₃	semidirect
150. #5733	C₂×C₃	semidirect
151. #5730	C₂×C₃	semidirect
152. #5709	C₂×C₃	semidirect
153. #5707	C₂×C₃	semidirect
154. #5705	C₂×C₃	semidirect
155. D₃×#126	C₂×C₃	semidirect
156. #5679	C₂×C₃	semidirect
157. #5678	C₂×C₃	semidirect
158. #5631	C₂×C₃	semidirect
159. #5630	C₂×C₃	semidirect
160. #5625	C₂×C₃	semidirect
161. #5624	C₂×C₃	semidirect
162. #5581	C₂×C₃	semidirect
163. #5580	C₂×C₃	semidirect
164. #5574	C₂×C₃	semidirect
165. #5568	C₂×C₃	semidirect
166. #5550	C₂×C₃	semidirect
167. #5538	C₂×C₃	semidirect
168. #5530	C₂×C₃	semidirect
169. #5529	C₂×C₃	semidirect
170. #5522	C₂×C₃	semidirect
171. #5521	C₂×C₃	semidirect
283. C₃×C₄⋊Q₈	C₂×D₃	semidirect
284. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
298. C₃×#126	C₂×D₃	semidirect
300. C₃×#126	C₂²×C₃	semidirect
335. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
337. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
353. C₃×C₄×Q₈	C₂×D₃	semidirect
354. C₃×C₄×Q₈	C₂×D₃	semidirect
355. C₃×C₄×Q₈	C₂²×C₃	semidirect
356. C₃×C₄×Q₈	C₂²×C₃	semidirect
386. C₃×#117	C₂×D₃	semidirect
388. C₃×#117	C₂²×C₃	semidirect
400. #947	C₂²×C₃	semidirect
401. #946	C₂²×C₃	semidirect
402. #946	C₂²×C₃	semidirect
403. #946	C₂²×C₃	semidirect
404. Q₈×Dic₃	C₂²×C₃	semidirect
405. #944	C₂²×C₃	semidirect
411. C₄×#67	C₂²×C₃	semidirect
414. C₂×C₄×Dic₃	C₂²×C₃	semidirect
415. #898	C₂²×C₃	semidirect
416. #898	C₂²×C₃	semidirect
417. #898	C₂²×C₃	semidirect
418. #898	C₂²×C₃	semidirect
419. #897	C₂²×C₃	semidirect
420. #897	C₂²×C₃	semidirect
421. #896	C₂²×C₃	semidirect
426. #894	C₂²×C₃	semidirect
427. #894	C₂²×C₃	semidirect
433. #893	C₂²×C₃	semidirect
434. #892	C₂²×C₃	semidirect
435. D₃×C₄⋊C₄	C₂²×C₃	semidirect
436. D₃×C₄⋊C₄	C₂²×C₃	semidirect
437. D₃×C₄⋊C₄	C₂²×C₃	semidirect
438. D₃×C₄⋊C₄	C₂²×C₃	semidirect
439. #890	C₂²×C₃	semidirect
440. #890	C₂²×C₃	semidirect
441. #890	C₂²×C₃	semidirect
442. #889	C₂²×C₃	semidirect
443. #889	C₂²×C₃	semidirect
444. #887	C₂²×C₃	semidirect
445. #887	C₂²×C₃	semidirect
446. #886	C₂²×C₃	semidirect
447. #886	C₂²×C₃	semidirect
450. #884	C₂²×C₃	semidirect
451. #884	C₂²×C₃	semidirect
453. #883	C₂²×C₃	semidirect
454. #883	C₂²×C₃	semidirect
456. #67⋊C₄	C₂²×C₃	semidirect
457. #67⋊C₄	C₂²×C₃	semidirect
458. #67⋊C₄	C₂²×C₃	semidirect
467. #878	C₂²×C₃	semidirect
468. #876	C₂²×C₃	semidirect
469. #876	C₂²×C₃	semidirect
474. C₄×D₁₂	C₂²×C₃	semidirect
475. C₄×D₁₂	C₂²×C₃	semidirect
476. #872	C₂²×C₃	semidirect
477. #872	C₂²×C₃	semidirect
478. #872	C₂²×C₃	semidirect
479. #872	C₂²×C₃	semidirect
480. #872	C₂²×C₃	semidirect
481. C₄²×D₃	C₂²×C₃	semidirect
482. #870	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
539. #556	C₃×D₃	semidirect
827. C₄⋊Q₈	C₂×C₃×D₃	semidirect
839. #126	C₂×C₃×D₃	semidirect
870. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
884. C₄×Q₈	C₂×C₃×D₃	semidirect
885. C₄×Q₈	C₂×C₃×D₃	semidirect
911. #117	C₂×C₃×D₃	semidirect
1242. C₃²	#3521	semidirect
1354. C₃	#86991	direct (N × H)
1355. C₃	C₃×#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#556	2
C₃×#5733	2
C₃×#5730	2
C₃×#5709	2
C₃×#5707	2
C₃×#5705	2
C₃×D₃×#126	2
C₃×#5679	2
C₃×#5678	2
C₃×#5631	2
C₃×#5630	2
C₃×#5625	2
C₃×#5624	2
C₃×#5581	2
C₃×#5580	2
C₃×#5574	2
C₃×#5568	2
C₃×#5550	2
C₃×#5538	2
C₃×#5530	2
C₃×#5529	2
C₃×#5522	2
C₃×#5521	2
C₃×#3521	3
#86991	3

Subgroups — C3×#86991 #11909424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86991 #11909424