Subgroups — C₃×#86523 #11901745

Order 1152.

2188 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5733	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5707	C₂	1	2	yes	maximal, complemented
5	C₃×#5706	C₂	1	2	yes	maximal, complemented
6	C₃×#5682	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5680	C₂	1	2	yes	maximal, complemented
8	C₃×#5678	C₂	1	2	yes	maximal, complemented
9	C₃×#5668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5657	C₂	1	2	yes	maximal, complemented
11	C₃×#5649	C₂	1	2	yes	maximal, complemented
12	C₃×#5638	C₂	1	2	yes	maximal, complemented
13	C₃×#5627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5625	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5624	C₂	1	2	yes	maximal, complemented
16	C₃×#5619	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5606	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5583	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5562	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3455	—	3	1	no	maximal
25	#86523	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×#239	C₂²	1	1	yes	characteristic
27	C₂×C₃×#237	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
29	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#126	C₂²	1	2	yes	complemented
31	C₃²×#124	C₂²	1	2	yes	—
32	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#123	C₂²	1	2	yes	—
34	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	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, complemented
39	C₃²×#117	C₂²	1	1	yes	characteristic
40	C₃×#947	C₂²	1	2	yes	—
41	C₃×#946	C₂²	1	1	yes	characteristic
42	C₃×#946	C₂²	1	2	yes	—
43	C₃×#946	C₂²	1	2	yes	complemented
44	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
46	C₃×#944	C₂²	1	1	yes	characteristic, complemented
47	C₃×#940	C₂²	1	1	yes	characteristic, complemented
48	C₃×#939	C₂²	1	2	yes	—
49	C₃×#938	C₂²	1	1	yes	characteristic
50	C₃×#938	C₂²	1	2	yes	—
51	C₃×#937	C₂²	1	2	yes	—
52	C₃×D₄×Dic₃	C₂²	1	2	yes	—
53	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₃×#930	C₂²	1	1	yes	characteristic
55	C₃×#930	C₂²	1	2	yes	—
56	C₃×#929	C₂²	1	2	yes	complemented
57	C₃×C₄×#67	C₂²	1	2	yes	—
58	C₃×#926	C₂²	1	1	yes	characteristic
59	C₃×#924	C₂²	1	1	yes	characteristic
60	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
61	C₃×#898	C₂²	1	2	yes	—
62	C₃×#898	C₂²	1	2	yes	complemented
63	C₃×#898	C₂²	1	2	yes	complemented
64	C₃×#897	C₂²	1	1	yes	characteristic
65	C₃×#897	C₂²	1	2	yes	—
66	C₃×#896	C₂²	1	2	yes	complemented
67	C₃×#895	C₂²	1	1	yes	characteristic
68	C₃×#894	C₂²	1	2	yes	—
69	C₃×#894	C₂²	1	2	yes	—
70	C₃×#893	C₂²	1	2	yes	—
71	C₃×#893	C₂²	1	2	yes	—
72	C₃×#893	C₂²	1	1	yes	characteristic, complemented
73	C₃×#892	C₂²	1	1	yes	characteristic
74	C₃×#892	C₂²	1	1	yes	characteristic
75	C₃×#892	C₂²	1	1	yes	characteristic
76	C₃×#892	C₂²	1	1	yes	characteristic
77	C₃×#892	C₂²	1	2	yes	complemented
78	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#887	C₂²	1	1	yes	characteristic, complemented
86	C₃×#887	C₂²	1	2	yes	complemented
87	C₃×#886	C₂²	1	2	yes	—
88	C₃×#886	C₂²	1	2	yes	complemented
89	C₃×#885	C₂²	1	2	yes	—
90	C₃×#885	C₂²	1	2	yes	—
91	C₃×#884	C₂²	1	2	yes	—
92	C₃×#884	C₂²	1	2	yes	—
93	C₃×#884	C₂²	1	2	yes	—
94	C₃×#883	C₂²	1	2	yes	—
95	C₃×#883	C₂²	1	2	yes	—
96	C₃×#883	C₂²	1	2	yes	complemented
97	C₃×#883	C₂²	1	2	yes	complemented
98	C₃×#882	C₂²	1	2	yes	—
99	C₃×#67⋊C₄	C₂²	1	2	yes	—
100	C₃×#67⋊C₄	C₂²	1	2	yes	—
101	C₃×#67⋊C₄	C₂²	1	2	yes	—
102	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
103	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
104	C₃×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×#879	C₂²	1	2	yes	—
107	C₃×#879	C₂²	1	2	yes	—
108	C₃×#879	C₂²	1	2	yes	complemented
109	C₃×#878	C₂²	1	2	yes	complemented
110	C₃×#877	C₂²	1	1	yes	characteristic
111	C₃×#877	C₂²	1	1	yes	characteristic
112	C₃×#877	C₂²	1	2	yes	complemented
113	C₃×#876	C₂²	1	2	yes	—
114	C₃×#875	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×D₁₂	C₂²	1	2	yes	—
116	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
117	C₃×#872	C₂²	1	1	yes	characteristic
118	C₃×#872	C₂²	1	1	yes	characteristic
119	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
121	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
122	C₃×#870	C₂²	1	2	yes	complemented
123	C₃×#869	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#542	—	2	1	no	—
126	C₃×#542	—	3	1	no	—
127	C₃×#542	—	3	1	no	—
128	C₃×#542	—	3	1	no	—
129	C₃×#542	D₃	1	1	yes	characteristic, complemented
130	C₃×#542	C₂×C₃	1	1	yes	characteristic, complemented
131	C₃×#541	—	3	1	no	—
132	C₃×#541	—	3	1	no	—
133	C₃×#540	—	3	1	no	—
134	C₃×#540	—	3	1	no	—
135	C₃×#539	—	3	2	no	—
136	C₃×#539	—	3	2	no	—
137	C₃×#538	—	3	2	no	—
138	C₃×#538	—	3	2	no	—
139	C₃×#533	—	3	1	no	—
140	C₃×#532	—	3	1	no	—
141	C₃×#529	—	3	2	no	—
142	C₃×#529	—	3	2	no	—
143	C₃×#529	—	3	2	no	—
144	C₃×#529	—	3	2	no	—
145	C₃×#525	—	3	1	no	—
146	C₃×#525	—	3	1	no	—
147	C₃×C₄×#41	—	3	1	no	—
148	C₃×C₄×#41	—	3	1	no	—
149	C₂×C₃×#117	—	3	1	no	—
150	#5733	C₂×C₃	1	1	yes	characteristic, complemented
151	#5728	C₂×C₃	1	1	yes	characteristic, complemented
152	#5707	C₂×C₃	1	2	yes	complemented
153	#5706	C₂×C₃	1	2	yes	complemented
154	#5682	C₂×C₃	1	1	yes	characteristic, complemented
155	#5680	C₂×C₃	1	2	yes	complemented
156	#5678	C₂×C₃	1	2	yes	complemented
157	#5668	C₂×C₃	1	1	yes	characteristic, complemented
158	#5657	C₂×C₃	1	2	yes	complemented
159	#5649	C₂×C₃	1	2	yes	complemented
160	#5638	C₂×C₃	1	2	yes	complemented
161	#5627	C₂×C₃	1	1	yes	characteristic, complemented
162	#5625	C₂×C₃	1	1	yes	characteristic, complemented
163	#5624	C₂×C₃	1	2	yes	complemented
164	#5619	C₂×C₃	1	1	yes	characteristic, complemented
165	#5606	C₂×C₃	1	1	yes	characteristic, complemented
166	#5583	C₂×C₃	1	1	yes	characteristic, complemented
167	C₄×#239	C₂×C₃	1	1	yes	characteristic, complemented
168	#5562	C₂×C₃	1	1	yes	characteristic, complemented
169	C₄×#237	C₂×C₃	1	1	yes	characteristic, complemented
170	#5534	C₂×C₃	1	1	yes	characteristic, complemented
171	D₃×#117	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
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	C₂×C₃²×D₄	C₂³	1	2	yes	—
177	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃²×C₄	C₂³	1	2	yes	—
179	C₂×C₃×#67	C₂³	1	2	yes	—
180	C₂×C₃×#67	C₂³	1	2	yes	—
181	C₂×C₃×#67	C₂³	1	2	yes	—
182	C₂×C₃×#67	C₂³	1	2	yes	—
183	C₂×C₃×#67	C₂³	1	2	yes	—
184	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
185	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
186	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
187	C₃×#239	—	2	4	no	—
188	C₃×#237	—	2	4	no	—
189	C₂×C₃×D₁₂	C₂³	1	2	yes	—
190	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
191	C₂×C₃×D₁₂	C₂³	1	2	yes	—
192	C₂×C₃×C₄×D₃	—	2	4	no	—
193	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
201	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
202	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
203	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
204	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
205	C₂×C₃×Dic₆	C₂³	1	2	yes	—
206	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₃²×C₂²⋊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×C₄²	C₂³	1	1	yes	characteristic
221	C₃²×C₄²	C₂³	1	1	yes	characteristic
222	C₃²×C₄²	C₂³	1	2	yes	—
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	2	yes	—
227	C₃×#217	C₂³	1	2	yes	—
228	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
229	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
230	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
231	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄⋊Dic₃	C₂³	1	2	yes	—
243	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
244	C₃×C₄⋊Dic₃	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	1	yes	characteristic
248	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
249	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
250	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
251	C₃×Dic₃⋊C₄	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	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	2	yes	—
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×C₄×Dic₃	C₂³	1	1	yes	characteristic
264	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
265	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
266	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
267	C₃×C₄×Dic₃	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	2	yes	—
269	C₃×C₄×Dic₃	C₂³	1	2	yes	—
270	C₃×C₄×Dic₃	C₂³	1	2	yes	—
271	C₃×C₄×Dic₃	C₂³	1	2	yes	—
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	#3455	—	3	1	no	Sylow
275	C₂×C₃×#41	—	3	1	no	—
276	C₂×C₃×#41	—	3	1	no	—
277	C₂³×C₃×C₄	—	3	1	no	—
278	C₂×#239	C₂²×C₃	1	1	yes	characteristic
279	C₂×#237	C₂²×C₃	1	1	yes	characteristic
280	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
281	C₃×C₄⋊Q₈	—	2	1	no	—
282	C₃×C₄⋊Q₈	—	3	1	no	—
283	C₃×C₄⋊Q₈	—	3	1	no	—
284	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
285	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₃×#127	—	3	1	no	—
287	C₃×#126	—	2	2	no	—
288	C₃×#126	—	3	2	no	—
289	C₃×#126	—	3	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	—	3	2	no	—
298	C₃×#125	—	3	2	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	1	no	—
301	C₃×#125	—	3	1	no	—
302	C₃×#125	—	3	2	no	—
303	C₃×#124	—	2	2	no	—
304	C₃×#124	—	2	1	no	—
305	C₃×#124	—	3	2	no	—
306	C₃×#124	—	3	2	no	—
307	C₃×#124	—	3	2	no	—
308	C₃×#124	—	3	1	no	—
309	C₃×#124	C₂×D₃	1	2	yes	—
310	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
311	C₃×#124	C₂²×C₃	1	2	yes	—
312	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₃×#123	—	2	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	—	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	C₂×D₃	1	2	yes	—
324	C₃×#123	C₂²×C₃	1	2	yes	—
325	C₃×C₂²⋊Q₈	—	2	1	no	—
326	C₃×C₂²⋊Q₈	—	2	2	no	—
327	C₃×C₂²⋊Q₈	—	3	1	no	—
328	C₃×C₂²⋊Q₈	—	3	2	no	—
329	C₃×C₂²⋊Q₈	—	3	2	no	—
330	C₃×C₂²⋊Q₈	—	3	1	no	—
331	C₃×C₂²⋊Q₈	—	3	2	no	—
332	C₃×C₂²⋊Q₈	—	3	1	no	—
333	C₃×C₂²⋊Q₈	—	3	2	no	—
334	C₃×C₂²⋊Q₈	—	3	2	no	—
335	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
336	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
337	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
338	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
339	C₃×#121	—	2	1	no	—
340	C₃×#121	—	3	1	no	—
341	C₃×#121	—	3	2	no	—
342	C₃×#121	—	3	2	no	—
343	C₃×#121	—	3	1	no	—
344	C₃×#121	—	3	2	no	—
345	C₃×#121	—	3	1	no	—
346	C₃×#121	—	3	2	no	—
347	C₃×#121	—	3	2	no	—
348	C₃×#121	—	3	2	no	—
349	C₃×#121	C₂×D₃	1	1	yes	characteristic
350	C₃×#121	C₂²×C₃	1	1	yes	characteristic
351	C₃×#120	—	3	2	no	—
352	C₃×#120	—	3	2	no	—
353	C₃×C₄×Q₈	—	2	1	no	—
354	C₃×C₄×Q₈	—	3	1	no	—
355	C₃×C₄×Q₈	—	3	2	no	—
356	C₃×C₄×Q₈	—	3	1	no	—
357	C₃×C₄×Q₈	—	3	2	no	—
358	C₃×C₄×Q₈	—	3	1	no	—
359	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
360	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
361	C₃×C₄×D₄	—	2	1	no	—
362	C₃×C₄×D₄	—	3	2	no	—
363	C₃×C₄×D₄	—	3	1	no	—
364	C₃×C₄×D₄	—	3	2	no	—
365	C₃×C₄×D₄	—	3	2	no	—
366	C₃×C₄×D₄	—	3	2	no	—
367	C₃×C₄×D₄	—	3	1	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	2	no	—
373	C₃×C₄×D₄	—	3	2	no	—
374	C₃×C₄×D₄	—	3	1	no	—
375	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
376	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
377	C₃×#117	—	2	1	no	—
378	C₃×#117	—	3	1	no	—
379	C₃×#117	—	3	1	no	—
380	C₃×#117	—	3	1	no	—
381	C₃×#117	—	3	1	no	—
382	C₃×#117	—	3	1	no	—
383	C₃×#117	—	3	2	no	—
384	C₃×#117	—	3	1	no	—
385	C₃×#117	—	3	1	no	—
386	C₃×#117	—	3	2	no	—
387	C₃×#117	—	3	1	no	—
388	C₃×#117	—	3	1	no	—
389	C₃×#117	C₂×D₃	1	1	yes	characteristic
390	C₃×#117	C₂²×C₃	1	1	yes	characteristic
391	C₂×C₃×C₄⋊C₄	—	3	1	no	—
392	C₂×C₃×C₄⋊C₄	—	3	1	no	—
393	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
394	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
395	C₂×C₃×C₄²	—	3	2	no	—
396	C₂×C₃×C₄²	—	3	1	no	—
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	—	3	2	no	—
399	#947	C₂²×C₃	1	2	yes	—
400	#946	C₂²×C₃	1	2	yes	—
401	#946	C₂²×C₃	1	1	yes	characteristic
402	#946	C₂²×C₃	1	2	yes	complemented
403	Q₈×Dic₃	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	#940	C₂²×C₃	1	1	yes	characteristic, complemented
407	#939	C₂²×C₃	1	2	yes	—
408	#938	C₂²×C₃	1	2	yes	—
409	#938	C₂²×C₃	1	1	yes	characteristic
410	#937	C₂²×C₃	1	2	yes	—
411	D₄×Dic₃	C₂²×C₃	1	2	yes	—
412	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
413	#930	C₂²×C₃	1	2	yes	—
414	#930	C₂²×C₃	1	1	yes	characteristic
415	#929	C₂²×C₃	1	2	yes	complemented
416	C₄×#67	C₂²×C₃	1	2	yes	—
417	#926	C₂²×C₃	1	1	yes	characteristic
418	#924	C₂²×C₃	1	1	yes	characteristic
419	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
420	#898	C₂²×C₃	1	2	yes	—
421	#898	C₂²×C₃	1	2	yes	complemented
422	#898	C₂²×C₃	1	2	yes	complemented
423	#897	C₂²×C₃	1	2	yes	—
424	#897	C₂²×C₃	1	1	yes	characteristic
425	#896	C₂²×C₃	1	2	yes	complemented
426	#895	C₂²×C₃	1	1	yes	characteristic
427	#894	C₂²×C₃	1	2	yes	—
428	#894	C₂²×C₃	1	2	yes	—
429	#893	C₂²×C₃	1	2	yes	—
430	#893	C₂²×C₃	1	2	yes	—
431	#893	C₂²×C₃	1	1	yes	characteristic, complemented
432	#892	C₂²×C₃	1	1	yes	characteristic
433	#892	C₂²×C₃	1	1	yes	characteristic
434	#892	C₂²×C₃	1	1	yes	characteristic
435	#892	C₂²×C₃	1	1	yes	characteristic
436	#892	C₂²×C₃	1	2	yes	complemented
437	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
438	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	complemented
444	#887	C₂²×C₃	1	2	yes	complemented
445	#887	C₂²×C₃	1	1	yes	characteristic, complemented
446	#886	C₂²×C₃	1	2	yes	—
447	#886	C₂²×C₃	1	2	yes	complemented
448	#885	C₂²×C₃	1	2	yes	—
449	#885	C₂²×C₃	1	2	yes	—
450	#884	C₂²×C₃	1	2	yes	—
451	#884	C₂²×C₃	1	2	yes	—
452	#884	C₂²×C₃	1	2	yes	—
453	#883	C₂²×C₃	1	2	yes	—
454	#883	C₂²×C₃	1	2	yes	—
455	#883	C₂²×C₃	1	2	yes	complemented
456	#883	C₂²×C₃	1	2	yes	complemented
457	#882	C₂²×C₃	1	2	yes	—
458	#67⋊C₄	C₂²×C₃	1	2	yes	—
459	#67⋊C₄	C₂²×C₃	1	2	yes	—
460	#67⋊C₄	C₂²×C₃	1	2	yes	—
461	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
462	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
463	D₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
464	D₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
465	#879	C₂²×C₃	1	2	yes	—
466	#879	C₂²×C₃	1	2	yes	—
467	#879	C₂²×C₃	1	2	yes	complemented
468	#878	C₂²×C₃	1	2	yes	complemented
469	#877	C₂²×C₃	1	1	yes	characteristic
470	#877	C₂²×C₃	1	1	yes	characteristic
471	#877	C₂²×C₃	1	2	yes	complemented
472	#876	C₂²×C₃	1	2	yes	—
473	#875	C₂²×C₃	1	1	yes	characteristic, complemented
474	C₄×D₁₂	C₂²×C₃	1	2	yes	—
475	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
476	#872	C₂²×C₃	1	1	yes	characteristic
477	#872	C₂²×C₃	1	1	yes	characteristic
478	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
479	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
480	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
481	#870	C₂²×C₃	1	2	yes	complemented
482	#869	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
485	C₂³×C₃²	C₂⁴	1	2	yes	—
486	C₂²×C₃×D₃	—	2	2	no	—
487	C₂²×C₃×D₃	—	4	1	no	—
488	C₂²×C₃×D₃	—	4	1	no	—
489	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
490	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
491	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
492	C₃²×Q₈	—	2	2	no	—
493	C₃²×Q₈	—	4	2	no	—
494	C₃²×D₄	—	2	2	no	—
495	C₃²×D₄	—	4	2	no	—
496	C₂×C₃²×C₄	—	2	2	no	—
497	C₂×C₃²×C₄	—	4	2	no	—
498	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
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	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₃×#67	—	2	4	no	—
508	C₃×#67	—	4	2	no	—
509	C₃×#67	—	4	2	no	—
510	C₃×#67	—	4	2	no	—
511	C₃×#67	—	4	2	no	—
512	C₂×C₃×Dic₃	—	2	2	no	—
513	C₂×C₃×Dic₃	—	2	4	no	—
514	C₂×C₃×Dic₃	—	4	2	no	—
515	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
521	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
522	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₃×D₁₂	—	2	4	no	—
525	C₃×D₁₂	—	2	2	no	—
526	C₃×D₁₂	—	4	2	no	—
527	C₃×C₄×D₃	—	2	2	no	—
528	C₃×C₄×D₃	—	2	2	no	—
529	C₃×C₄×D₃	—	2	2	no	—
530	C₃×C₄×D₃	—	2	4	no	—
531	C₃×C₄×D₃	—	4	2	no	—
532	C₃×C₄×D₃	—	4	1	no	—
533	C₃×C₄×D₃	—	4	2	no	—
534	C₃×C₄×D₃	—	4	1	no	—
535	C₃×C₄×D₃	—	4	1	no	—
536	C₃×C₄×D₃	—	4	1	no	—
537	C₃×C₄×D₃	#41	1	4	yes	—
538	C₃×Dic₆	—	2	2	no	—
539	C₃×Dic₆	—	4	2	no	—
540	#542	—	3	1	no	—
541	#542	—	3	1	no	—
542	#542	—	3	1	no	—
543	#542	C₃×D₃	1	1	yes	characteristic, complemented
544	#541	—	3	1	no	—
545	#541	—	3	1	no	—
546	#540	—	3	1	no	—
547	#540	—	3	1	no	—
548	#539	—	3	2	no	—
549	#539	—	3	2	no	—
550	#538	—	3	2	no	—
551	#538	—	3	2	no	—
552	#533	—	3	1	no	—
553	#532	—	3	1	no	—
554	#529	—	3	2	no	—
555	#529	—	3	2	no	—
556	#529	—	3	2	no	—
557	#529	—	3	2	no	—
558	#525	—	3	1	no	—
559	#525	—	3	1	no	—
560	C₄×#41	—	3	1	no	—
561	C₄×#41	—	3	1	no	—
562	C₂×#117	—	3	1	no	—
563	C₂⁴×C₃	—	3	1	no	—
564	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
565	C₃×#41	—	6	4	no	—
566	C₃×#41	—	6	4	no	—
567	C₂×C₃×Q₈	—	2	1	no	—
568	C₂×C₃×Q₈	—	2	2	no	—
569	C₂×C₃×Q₈	—	3	1	no	—
570	C₂×C₃×Q₈	—	3	2	no	—
571	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
572	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
573	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
575	C₂×C₃×D₄	—	2	1	no	—
576	C₂×C₃×D₄	—	2	2	no	—
577	C₂×C₃×D₄	—	3	2	no	—
578	C₂×C₃×D₄	—	3	2	no	—
579	C₂×C₃×D₄	—	3	2	no	—
580	C₂×C₃×D₄	—	3	2	no	—
581	C₂×C₃×D₄	—	3	2	no	—
582	C₂×C₃×D₄	—	3	2	no	—
583	C₂×C₃×D₄	—	3	1	no	—
584	C₂×C₃×D₄	—	3	2	no	—
585	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
586	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
587	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
589	C₂²×C₃×C₄	—	2	1	no	—
590	C₂²×C₃×C₄	—	2	2	no	—
591	C₂²×C₃×C₄	—	3	1	no	—
592	C₂²×C₃×C₄	—	3	2	no	—
593	C₂²×C₃×C₄	—	3	1	no	—
594	C₂²×C₃×C₄	—	3	2	no	—
595	C₂²×C₃×C₄	—	3	2	no	—
596	C₂²×C₃×C₄	—	3	1	no	—
597	C₂²×C₃×C₄	—	3	1	no	—
598	C₂²×C₃×C₄	—	3	1	no	—
599	C₂²×C₃×C₄	—	3	1	no	—
600	C₂²×C₃×C₄	—	3	1	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	—	6	4	no	—
606	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
607	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
608	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
609	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
610	C₂×#67	C₂³×C₃	1	2	yes	—
611	C₂×#67	C₂³×C₃	1	2	yes	—
612	C₂×#67	C₂³×C₃	1	2	yes	—
613	C₂×#67	C₂³×C₃	1	2	yes	—
614	C₂×#67	C₂³×C₃	1	2	yes	—
615	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
616	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
617	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
618	#239	—	2	4	no	—
619	#237	—	2	4	no	—
620	C₂×D₁₂	C₂³×C₃	1	2	yes	—
621	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
622	C₂×D₁₂	C₂³×C₃	1	2	yes	—
623	C₂×C₄×D₃	—	2	4	no	—
624	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
625	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
626	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
627	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
631	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
632	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
633	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
634	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
635	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
636	C₂×Dic₆	C₂³×C₃	1	2	yes	—
637	C₃×C₄⋊C₄	—	2	1	no	—
638	C₃×C₄⋊C₄	—	2	1	no	—
639	C₃×C₄⋊C₄	—	2	1	no	—
640	C₃×C₄⋊C₄	—	2	1	no	—
641	C₃×C₄⋊C₄	—	2	2	no	—
642	C₃×C₄⋊C₄	—	2	2	no	—
643	C₃×C₄⋊C₄	—	2	2	no	—
644	C₃×C₄⋊C₄	—	3	1	no	—
645	C₃×C₄⋊C₄	—	3	1	no	—
646	C₃×C₄⋊C₄	—	3	1	no	—
647	C₃×C₄⋊C₄	—	3	1	no	—
648	C₃×C₄⋊C₄	—	3	2	no	—
649	C₃×C₄⋊C₄	—	3	2	no	—
650	C₃×C₄⋊C₄	—	3	2	no	—
651	C₃×C₄⋊C₄	—	3	2	no	—
652	C₃×C₄⋊C₄	—	3	2	no	—
653	C₃×C₄⋊C₄	—	3	2	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	1	no	—
659	C₃×C₄⋊C₄	—	3	1	no	—
660	C₃×C₄⋊C₄	—	3	2	no	—
661	C₃×C₄⋊C₄	—	3	2	no	—
662	C₃×C₄⋊C₄	—	3	2	no	—
663	C₃×C₄⋊C₄	—	3	2	no	—
664	C₃×C₄⋊C₄	—	3	2	no	—
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	1	yes	characteristic
668	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
669	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
670	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
671	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
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×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
677	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
678	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
679	C₃×C₂²⋊C₄	—	2	1	no	—
680	C₃×C₂²⋊C₄	—	2	1	no	—
681	C₃×C₂²⋊C₄	—	2	2	no	—
682	C₃×C₂²⋊C₄	—	2	2	no	—
683	C₃×C₂²⋊C₄	—	2	2	no	—
684	C₃×C₂²⋊C₄	—	2	2	no	—
685	C₃×C₂²⋊C₄	—	2	2	no	—
686	C₃×C₂²⋊C₄	—	3	1	no	—
687	C₃×C₂²⋊C₄	—	3	1	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	1	no	—
692	C₃×C₂²⋊C₄	—	3	1	no	—
693	C₃×C₂²⋊C₄	—	3	1	no	—
694	C₃×C₂²⋊C₄	—	3	1	no	—
695	C₃×C₂²⋊C₄	—	3	2	no	—
696	C₃×C₂²⋊C₄	—	3	2	no	—
697	C₃×C₂²⋊C₄	—	3	2	no	—
698	C₃×C₂²⋊C₄	—	3	2	no	—
699	C₃×C₂²⋊C₄	—	3	2	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	2	no	—
704	C₃×C₂²⋊C₄	—	3	2	no	—
705	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
706	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	2	yes	—
710	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
711	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
717	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
718	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
719	C₃×C₄²	—	2	1	no	—
720	C₃×C₄²	—	2	1	no	—
721	C₃×C₄²	—	2	2	no	—
722	C₃×C₄²	—	3	1	no	—
723	C₃×C₄²	—	3	1	no	—
724	C₃×C₄²	—	3	2	no	—
725	C₃×C₄²	—	3	2	no	—
726	C₃×C₄²	—	3	1	no	—
727	C₃×C₄²	—	3	1	no	—
728	C₃×C₄²	—	3	1	no	—
729	C₃×C₄²	—	3	1	no	—
730	C₃×C₄²	—	3	2	no	—
731	C₃×C₄²	—	3	2	no	—
732	C₃×C₄²	—	3	2	no	—
733	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
734	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
735	C₃×C₄²	C₂²×D₃	1	2	yes	—
736	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
737	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
738	C₃×C₄²	C₂³×C₃	1	2	yes	—
739	#217	C₂³×C₃	1	1	yes	characteristic
740	#217	C₂³×C₃	1	1	yes	characteristic
741	#217	C₂³×C₃	1	2	yes	—
742	#217	C₂³×C₃	1	2	yes	—
743	#217	C₂³×C₃	1	2	yes	—
744	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
745	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
746	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
747	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
748	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
760	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
761	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
762	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
763	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
764	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
765	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
766	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
767	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
778	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
779	C₄×Dic₃	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	1	yes	characteristic
784	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
785	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₃	1	2	yes	—
787	C₄×Dic₃	C₂³×C₃	1	2	yes	—
788	C₄×Dic₃	C₂³×C₃	1	2	yes	—
789	C₄×Dic₃	C₂³×C₃	1	2	yes	—
790	C₂²×C₃²	—	2	2	no	—
791	C₂²×C₃²	—	2	1	no	—
792	C₂²×C₃²	—	2	2	no	—
793	C₂²×C₃²	—	2	1	no	—
794	C₂²×C₃²	—	2	2	no	—
795	C₂²×C₃²	—	2	1	no	—
796	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
797	C₂×C₃×D₃	—	2	1	no	—
798	C₂×C₃×D₃	—	2	1	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	2	no	—
803	C₂×C₃×D₃	—	2	1	no	—
804	C₂×C₃×D₃	—	2	1	no	—
805	C₂×C₃×D₃	—	4	4	no	—
806	C₂×C₃×D₃	C₂×#41	1	2	yes	—
807	C₃²×C₄	—	2	1	no	—
808	C₃²×C₄	—	2	2	no	—
809	C₃²×C₄	—	2	1	no	—
810	C₃²×C₄	—	2	1	no	—
811	C₃²×C₄	—	2	1	no	—
812	C₃²×C₄	—	2	2	no	—
813	C₃²×C₄	—	2	1	no	—
814	C₃²×C₄	—	2	2	no	—
815	C₃²×C₄	C₂×#41	1	2	yes	—
816	C₃×Dic₃	—	2	2	no	—
817	C₃×Dic₃	—	2	1	no	—
818	C₃×Dic₃	—	2	2	no	—
819	C₃×Dic₃	—	2	2	no	—
820	C₃×Dic₃	—	2	1	no	—
821	C₃×Dic₃	—	2	1	no	—
822	C₃×Dic₃	—	2	1	no	—
823	C₃×Dic₃	—	2	1	no	—
824	C₃×Dic₃	C₂×#41	1	2	yes	—
825	C₂×#41	—	3	1	no	—
826	C₂×#41	—	3	1	no	—
827	C₂³×C₄	—	3	1	no	—
828	C₄⋊Q₈	—	3	1	no	—
829	C₄⋊Q₈	—	3	1	no	—
830	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
831	#127	—	3	1	no	—
832	#126	—	3	2	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	—	3	2	no	—
839	#126	C₂×C₃×D₃	1	2	yes	complemented
840	#125	—	3	2	no	—
841	#125	—	3	2	no	—
842	#125	—	3	2	no	—
843	#125	—	3	1	no	—
844	#125	—	3	1	no	—
845	#125	—	3	2	no	—
846	#124	—	3	2	no	—
847	#124	—	3	2	no	—
848	#124	—	3	2	no	—
849	#124	—	3	1	no	—
850	#124	C₂×C₃×D₃	1	2	yes	—
851	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
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	2	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	#123	C₂×C₃×D₃	1	2	yes	—
862	C₂²⋊Q₈	—	3	1	no	—
863	C₂²⋊Q₈	—	3	2	no	—
864	C₂²⋊Q₈	—	3	2	no	—
865	C₂²⋊Q₈	—	3	1	no	—
866	C₂²⋊Q₈	—	3	1	no	—
867	C₂²⋊Q₈	—	3	2	no	—
868	C₂²⋊Q₈	—	3	2	no	—
869	C₂²⋊Q₈	—	3	2	no	—
870	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
871	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
872	#121	—	3	1	no	—
873	#121	—	3	2	no	—
874	#121	—	3	2	no	—
875	#121	—	3	1	no	—
876	#121	—	3	2	no	—
877	#121	—	3	1	no	—
878	#121	—	3	2	no	—
879	#121	—	3	2	no	—
880	#121	—	3	2	no	—
881	#121	C₂×C₃×D₃	1	1	yes	characteristic
882	#120	—	3	2	no	—
883	#120	—	3	2	no	—
884	C₄×Q₈	—	3	1	no	—
885	C₄×Q₈	—	3	2	no	—
886	C₄×Q₈	—	3	1	no	—
887	C₄×Q₈	—	3	2	no	—
888	C₄×Q₈	—	3	1	no	—
889	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
890	C₄×D₄	—	3	1	no	—
891	C₄×D₄	—	3	2	no	—
892	C₄×D₄	—	3	2	no	—
893	C₄×D₄	—	3	2	no	—
894	C₄×D₄	—	3	1	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	2	no	—
901	C₄×D₄	—	3	2	no	—
902	C₄×D₄	—	3	1	no	—
903	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
904	#117	—	3	1	no	—
905	#117	—	3	1	no	—
906	#117	—	3	1	no	—
907	#117	—	3	1	no	—
908	#117	—	3	1	no	—
909	#117	—	3	2	no	—
910	#117	—	3	1	no	—
911	#117	—	3	1	no	—
912	#117	—	3	2	no	—
913	#117	—	3	1	no	—
914	#117	—	3	1	no	—
915	#117	C₂×C₃×D₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	—	3	1	no	—
917	C₂×C₄⋊C₄	—	3	1	no	—
918	C₂×C₂²⋊C₄	—	3	1	no	—
919	C₂×C₂²⋊C₄	—	3	1	no	—
920	C₂×C₄²	—	3	2	no	—
921	C₂×C₄²	—	3	1	no	—
922	C₂×C₄²	—	3	1	no	—
923	C₂×C₄²	—	3	2	no	—
924	C₂³×C₃	—	2	1	no	—
925	C₂³×C₃	—	2	2	no	—
926	C₂³×C₃	—	3	1	no	—
927	C₂³×C₃	—	3	1	no	—
928	C₂³×C₃	—	3	2	no	—
929	C₂³×C₃	—	6	2	no	—
930	C₂³×C₃	—	12	1	no	—
931	C₂³×C₃	—	12	1	no	—
932	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
933	C₂³×C₃	C₂³×D₃	1	2	yes	—
934	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
935	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
936	C₂²×D₃	—	2	2	no	—
937	C₂²×D₃	—	4	1	no	—
938	C₂²×D₃	—	4	1	no	—
939	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
940	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
941	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
942	C₃×Q₈	—	2	2	no	—
943	C₃×Q₈	—	2	2	no	—
944	C₃×Q₈	—	4	2	no	—
945	C₃×Q₈	—	4	2	no	—
946	C₃×Q₈	—	4	2	no	—
947	C₃×Q₈	—	6	2	no	—
948	C₃×Q₈	—	8	2	no	—
949	C₃×Q₈	—	12	2	no	—
950	C₃×D₄	—	2	2	no	—
951	C₃×D₄	—	2	2	no	—
952	C₃×D₄	—	4	2	no	—
953	C₃×D₄	—	4	2	no	—
954	C₃×D₄	—	4	2	no	—
955	C₃×D₄	—	6	4	no	—
956	C₃×D₄	—	6	4	no	—
957	C₃×D₄	—	6	2	no	—
958	C₃×D₄	—	8	2	no	—
959	C₃×D₄	—	12	2	no	—
960	C₃×D₄	—	12	2	no	—
961	C₃×D₄	—	12	2	no	—
962	C₃×D₄	—	12	2	no	—
963	C₃×D₄	—	12	2	no	—
964	C₂×C₃×C₄	—	2	2	no	—
965	C₂×C₃×C₄	—	2	2	no	—
966	C₂×C₃×C₄	—	2	1	no	—
967	C₂×C₃×C₄	—	2	1	no	—
968	C₂×C₃×C₄	—	2	1	no	—
969	C₂×C₃×C₄	—	2	2	no	—
970	C₂×C₃×C₄	—	2	1	no	—
971	C₂×C₃×C₄	—	2	1	no	—
972	C₂×C₃×C₄	—	2	2	no	—
973	C₂×C₃×C₄	—	2	1	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	3	1	no	—
976	C₂×C₃×C₄	—	3	4	no	—
977	C₂×C₃×C₄	—	3	1	no	—
978	C₂×C₃×C₄	—	3	1	no	—
979	C₂×C₃×C₄	—	3	2	no	—
980	C₂×C₃×C₄	—	3	2	no	—
981	C₂×C₃×C₄	—	3	2	no	—
982	C₂×C₃×C₄	—	3	1	no	—
983	C₂×C₃×C₄	—	3	1	no	—
984	C₂×C₃×C₄	—	3	1	no	—
985	C₂×C₃×C₄	—	4	2	no	—
986	C₂×C₃×C₄	—	4	2	no	—
987	C₂×C₃×C₄	—	4	2	no	—
988	C₂×C₃×C₄	—	6	2	no	—
989	C₂×C₃×C₄	—	6	4	no	—
990	C₂×C₃×C₄	—	6	2	no	—
991	C₂×C₃×C₄	—	6	2	no	—
992	C₂×C₃×C₄	—	6	4	no	—
993	C₂×C₃×C₄	—	6	2	no	—
994	C₂×C₃×C₄	—	8	2	no	—
995	C₂×C₃×C₄	—	12	1	no	—
996	C₂×C₃×C₄	—	12	2	no	—
997	C₂×C₃×C₄	—	12	1	no	—
998	C₂×C₃×C₄	—	12	1	no	—
999	C₂×C₃×C₄	—	12	2	no	—
1000	C₂×C₃×C₄	—	12	1	no	—
1001	C₂×C₃×C₄	—	12	2	no	—
1002	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1003	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1004	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1005	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1006	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1007	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1008	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1009	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1010	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1011	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1012	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1013	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1014	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1017	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1019	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1020	#67	—	2	4	no	—
1021	#67	—	4	2	no	—
1022	#67	—	4	2	no	—
1023	#67	—	4	2	no	—
1024	#67	—	4	2	no	—
1025	C₂×Dic₃	—	2	2	no	—
1026	C₂×Dic₃	—	2	4	no	—
1027	C₂×Dic₃	—	4	2	no	—
1028	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1029	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1030	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1031	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1032	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1033	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1034	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1035	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1036	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1037	D₁₂	—	2	4	no	—
1038	D₁₂	—	2	2	no	—
1039	D₁₂	—	4	2	no	—
1040	C₄×D₃	—	2	2	no	—
1041	C₄×D₃	—	2	2	no	—
1042	C₄×D₃	—	2	2	no	—
1043	C₄×D₃	—	2	4	no	—
1044	C₄×D₃	—	4	2	no	—
1045	C₄×D₃	—	4	1	no	—
1046	C₄×D₃	—	4	2	no	—
1047	C₄×D₃	—	4	1	no	—
1048	C₄×D₃	—	4	1	no	—
1049	C₄×D₃	—	4	1	no	—
1050	C₄×D₃	C₃×#41	1	4	yes	—
1051	Dic₆	—	2	2	no	—
1052	Dic₆	—	4	2	no	—
1053	C₂×C₃²	—	4	1	no	—
1054	C₂×C₃²	—	4	2	no	—
1055	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1056	C₂×C₃²	#585	1	1	yes	characteristic
1057	C₂×C₃²	#585	1	1	yes	characteristic
1058	C₃×D₃	—	2	2	no	—
1059	C₃×D₃	—	4	2	no	—
1060	C₃×D₃	—	4	1	no	—
1061	C₂⁴	—	3	1	no	—
1062	#41	—	6	4	no	—
1063	#41	—	6	4	no	—
1064	C₂×Q₈	—	3	1	no	—
1065	C₂×Q₈	—	3	2	no	—
1066	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1067	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
1068	C₂×D₄	—	3	2	no	—
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	3	2	no	—
1071	C₂×D₄	—	3	2	no	—
1072	C₂×D₄	—	3	2	no	—
1073	C₂×D₄	—	3	2	no	—
1074	C₂×D₄	—	3	1	no	—
1075	C₂×D₄	—	3	2	no	—
1076	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1077	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1078	C₂²×C₄	—	3	1	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	2	no	—
1082	C₂²×C₄	—	3	2	no	—
1083	C₂²×C₄	—	3	1	no	—
1084	C₂²×C₄	—	3	1	no	—
1085	C₂²×C₄	—	3	1	no	—
1086	C₂²×C₄	—	3	1	no	—
1087	C₂²×C₄	—	3	1	no	—
1088	C₂²×C₄	—	3	1	no	—
1089	C₂²×C₄	—	3	1	no	—
1090	C₂²×C₄	—	3	2	no	—
1091	C₂²×C₄	—	3	2	no	—
1092	C₂²×C₄	—	6	4	no	—
1093	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1094	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1095	C₄⋊C₄	—	3	1	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	1	no	—
1101	C₄⋊C₄	—	3	1	no	—
1102	C₄⋊C₄	—	3	1	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	2	no	—
1106	C₄⋊C₄	—	3	2	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	2	no	—
1109	C₄⋊C₄	—	3	2	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	2	no	—
1113	C₄⋊C₄	—	3	2	no	—
1114	C₄⋊C₄	—	3	2	no	—
1115	C₄⋊C₄	—	3	2	no	—
1116	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1119	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1120	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1121	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1122	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	1	no	—
1125	C₂²⋊C₄	—	3	2	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	1	no	—
1129	C₂²⋊C₄	—	3	1	no	—
1130	C₂²⋊C₄	—	3	1	no	—
1131	C₂²⋊C₄	—	3	1	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	2	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	2	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	2	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	—	3	2	no	—
1142	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1143	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1145	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1146	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1147	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1148	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1149	C₄²	—	3	1	no	—
1150	C₄²	—	3	1	no	—
1151	C₄²	—	3	2	no	—
1152	C₄²	—	3	2	no	—
1153	C₄²	—	3	1	no	—
1154	C₄²	—	3	1	no	—
1155	C₄²	—	3	1	no	—
1156	C₄²	—	3	1	no	—
1157	C₄²	—	3	2	no	—
1158	C₄²	—	3	2	no	—
1159	C₄²	—	3	2	no	—
1160	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1161	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1162	C₄²	C₂²×C₃×D₃	1	2	yes	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	2	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	—	2	2	no	—
1168	C₂²×C₃	—	2	1	no	—
1169	C₂²×C₃	—	2	2	no	—
1170	C₂²×C₃	—	2	1	no	—
1171	C₂²×C₃	—	2	2	no	—
1172	C₂²×C₃	—	2	1	no	—
1173	C₂²×C₃	—	2	2	no	—
1174	C₂²×C₃	—	2	1	no	—
1175	C₂²×C₃	—	2	1	no	—
1176	C₂²×C₃	—	3	2	no	—
1177	C₂²×C₃	—	4	1	no	—
1178	C₂²×C₃	—	4	2	no	—
1179	C₂²×C₃	—	4	2	no	—
1180	C₂²×C₃	—	4	1	no	—
1181	C₂²×C₃	—	4	2	no	—
1182	C₂²×C₃	—	4	1	no	—
1183	C₂²×C₃	—	6	1	no	—
1184	C₂²×C₃	—	6	1	no	—
1185	C₂²×C₃	—	6	1	no	—
1186	C₂²×C₃	—	6	2	no	—
1187	C₂²×C₃	—	6	2	no	—
1188	C₂²×C₃	—	6	1	no	—
1189	C₂²×C₃	—	6	2	no	—
1190	C₂²×C₃	—	6	1	no	—
1191	C₂²×C₃	—	12	4	no	—
1192	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1193	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1194	C₂×D₃	—	2	1	no	—
1195	C₂×D₃	—	2	1	no	—
1196	C₂×D₃	—	2	1	no	—
1197	C₂×D₃	—	2	2	no	—
1198	C₂×D₃	—	2	2	no	—
1199	C₂×D₃	—	2	2	no	—
1200	C₂×D₃	—	2	1	no	—
1201	C₂×D₃	—	2	1	no	—
1202	C₂×D₃	—	4	4	no	—
1203	C₂×D₃	C₂×C₃×#41	1	2	yes	—
1204	C₃×C₄	—	2	1	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	1	no	—
1207	C₃×C₄	—	2	2	no	—
1208	C₃×C₄	—	2	2	no	—
1209	C₃×C₄	—	2	1	no	—
1210	C₃×C₄	—	2	1	no	—
1211	C₃×C₄	—	2	1	no	—
1212	C₃×C₄	—	2	1	no	—
1213	C₃×C₄	—	2	2	no	—
1214	C₃×C₄	—	2	1	no	—
1215	C₃×C₄	—	2	1	no	—
1216	C₃×C₄	—	2	1	no	—
1217	C₃×C₄	—	2	2	no	—
1218	C₃×C₄	—	2	1	no	—
1219	C₃×C₄	—	2	2	no	—
1220	C₃×C₄	—	2	2	no	—
1221	C₃×C₄	—	3	2	no	—
1222	C₃×C₄	—	4	1	no	—
1223	C₃×C₄	—	4	1	no	—
1224	C₃×C₄	—	4	2	no	—
1225	C₃×C₄	—	4	2	no	—
1226	C₃×C₄	—	4	2	no	—
1227	C₃×C₄	—	4	1	no	—
1228	C₃×C₄	—	4	1	no	—
1229	C₃×C₄	—	4	1	no	—
1230	C₃×C₄	—	6	1	no	—
1231	C₃×C₄	—	6	2	no	—
1232	C₃×C₄	—	6	1	no	—
1233	C₃×C₄	—	6	1	no	—
1234	C₃×C₄	—	6	1	no	—
1235	C₃×C₄	—	6	1	no	—
1236	C₃×C₄	—	6	2	no	—
1237	C₃×C₄	—	6	2	no	—
1238	C₃×C₄	D₃×#41	1	2	yes	—
1239	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1240	Dic₃	—	2	2	no	—
1241	Dic₃	—	2	1	no	—
1242	Dic₃	—	2	2	no	—
1243	Dic₃	—	2	2	no	—
1244	Dic₃	—	2	1	no	—
1245	Dic₃	—	2	1	no	—
1246	Dic₃	—	2	1	no	—
1247	Dic₃	—	2	1	no	—
1248	Dic₃	C₂×C₃×#41	1	2	yes	—
1249	C₃²	#3455	1	1	yes	characteristic, complemented, Sylow
1250	C₂³	—	3	1	no	—
1251	C₂³	—	3	1	no	—
1252	C₂³	—	3	2	no	—
1253	C₂³	—	6	2	no	—
1254	C₂³	—	12	1	no	—
1255	C₂³	—	12	1	no	—
1256	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1257	C₂³	C₂³×C₃×D₃	1	2	yes	—
1258	Q₈	—	2	2	no	—
1259	Q₈	—	4	2	no	—
1260	Q₈	—	6	2	no	—
1261	Q₈	—	12	2	no	—
1262	D₄	—	2	2	no	—
1263	D₄	—	4	2	no	—
1264	D₄	—	6	4	no	—
1265	D₄	—	6	4	no	—
1266	D₄	—	6	2	no	—
1267	D₄	—	12	2	no	—
1268	D₄	—	12	2	no	—
1269	D₄	—	12	2	no	—
1270	D₄	—	12	2	no	—
1271	D₄	—	12	2	no	—
1272	C₂×C₄	—	2	2	no	—
1273	C₂×C₄	—	3	1	no	—
1274	C₂×C₄	—	3	4	no	—
1275	C₂×C₄	—	3	1	no	—
1276	C₂×C₄	—	3	1	no	—
1277	C₂×C₄	—	3	2	no	—
1278	C₂×C₄	—	3	2	no	—
1279	C₂×C₄	—	3	2	no	—
1280	C₂×C₄	—	3	1	no	—
1281	C₂×C₄	—	3	1	no	—
1282	C₂×C₄	—	3	1	no	—
1283	C₂×C₄	—	4	2	no	—
1284	C₂×C₄	—	6	2	no	—
1285	C₂×C₄	—	6	4	no	—
1286	C₂×C₄	—	6	2	no	—
1287	C₂×C₄	—	6	2	no	—
1288	C₂×C₄	—	6	4	no	—
1289	C₂×C₄	—	6	2	no	—
1290	C₂×C₄	—	12	1	no	—
1291	C₂×C₄	—	12	2	no	—
1292	C₂×C₄	—	12	1	no	—
1293	C₂×C₄	—	12	1	no	—
1294	C₂×C₄	—	12	2	no	—
1295	C₂×C₄	—	12	1	no	—
1296	C₂×C₄	—	12	2	no	—
1297	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1298	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1299	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1300	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1301	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1302	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1303	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1304	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1305	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1306	C₂×C₃	—	2	1	no	—
1307	C₂×C₃	—	2	1	no	—
1308	C₂×C₃	—	2	1	no	—
1309	C₂×C₃	—	4	1	no	—
1310	C₂×C₃	—	4	2	no	—
1311	C₂×C₃	—	4	1	no	—
1312	C₂×C₃	—	4	2	no	—
1313	C₂×C₃	—	6	2	no	—
1314	C₂×C₃	—	8	1	no	—
1315	C₂×C₃	—	8	2	no	—
1316	C₂×C₃	—	12	1	no	—
1317	C₂×C₃	—	12	2	no	—
1318	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1319	C₂×C₃	#5966	1	1	yes	characteristic
1320	C₂×C₃	#5968	1	1	yes	characteristic
1321	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1322	C₂×C₃	C₃×#585	1	1	yes	characteristic
1323	C₂×C₃	C₃×#585	1	1	yes	characteristic
1324	D₃	—	2	2	no	—
1325	D₃	—	4	1	no	—
1326	D₃	—	4	2	no	—
1327	C₂²	—	2	1	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	1	no	—
1331	C₂²	—	2	2	no	—
1332	C₂²	—	2	1	no	—
1333	C₂²	—	3	2	no	—
1334	C₂²	—	6	1	no	—
1335	C₂²	—	6	1	no	—
1336	C₂²	—	6	1	no	—
1337	C₂²	—	6	2	no	—
1338	C₂²	—	6	2	no	—
1339	C₂²	—	6	1	no	—
1340	C₂²	—	6	2	no	—
1341	C₂²	—	6	1	no	—
1342	C₂²	—	12	4	no	—
1343	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1344	C₄	—	2	1	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	1	no	—
1350	C₄	—	2	1	no	—
1351	C₄	—	2	1	no	—
1352	C₄	—	3	2	no	—
1353	C₄	—	6	1	no	—
1354	C₄	—	6	2	no	—
1355	C₄	—	6	1	no	—
1356	C₄	—	6	1	no	—
1357	C₄	—	6	1	no	—
1358	C₄	—	6	1	no	—
1359	C₄	—	6	2	no	—
1360	C₄	—	6	2	no	—
1361	C₄	C₃×D₃×#41	1	2	yes	—
1362	C₃	—	2	1	no	—
1363	C₃	#86523	1	1	yes	characteristic, direct product factor
1364	C₃	C₃×#3455	1	1	yes	characteristic, complemented
1365	C₂	—	4	1	no	—
1366	C₂	—	4	2	no	—
1367	C₂	—	6	2	no	—
1368	C₂	—	12	1	no	—
1369	C₂	—	12	2	no	—
1370	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1371	C₂	C₃×#5966	1	1	yes	characteristic
1372	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×#542	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#542	D₃
hypocenter	C₃	C₃×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#542

Complements

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

N	H ≅ G/N	type
1. C₃²×#542	C₂	semidirect
2. C₃×#5733	C₂	semidirect
3. C₃×#5728	C₂	semidirect
4. C₃×#5707	C₂	semidirect
5. C₃×#5706	C₂	semidirect
6. C₃×#5682	C₂	semidirect
7. C₃×#5680	C₂	semidirect
8. C₃×#5678	C₂	semidirect
9. C₃×#5668	C₂	semidirect
10. C₃×#5657	C₂	semidirect
11. C₃×#5649	C₂	semidirect
12. C₃×#5638	C₂	semidirect
13. C₃×#5627	C₂	semidirect
14. C₃×#5625	C₂	semidirect
15. C₃×#5624	C₂	semidirect
16. C₃×#5619	C₂	semidirect
17. C₃×#5606	C₂	semidirect
18. C₃×#5583	C₂	semidirect
19. C₃×C₄×#239	C₂	semidirect
20. C₃×#5562	C₂	semidirect
21. C₃×C₄×#237	C₂	semidirect
22. C₃×#5534	C₂	semidirect
23. C₃×D₃×#117	C₂	semidirect
25. #86523	C₃	direct (N × H)
29. C₃²×C₄⋊Q₈	C₂²	semidirect
30. C₃²×#126	C₂²	semidirect
32. C₃²×#124	C₂²	semidirect
35. C₃²×C₂²⋊Q₈	C₂²	semidirect
37. C₃²×C₄×Q₈	C₂²	semidirect
38. C₃²×C₄×D₄	C₂²	semidirect
43. C₃×#946	C₂²	semidirect
44. C₃×Q₈×Dic₃	C₂²	semidirect
45. C₃×Q₈×Dic₃	C₂²	semidirect
46. C₃×#944	C₂²	semidirect
47. C₃×#940	C₂²	semidirect
53. C₃×D₄×Dic₃	C₂²	semidirect
56. C₃×#929	C₂²	semidirect
60. C₂×C₃×C₄×Dic₃	C₂²	semidirect
62. C₃×#898	C₂²	semidirect
63. C₃×#898	C₂²	semidirect
66. C₃×#896	C₂²	semidirect
72. C₃×#893	C₂²	semidirect
77. C₃×#892	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
88. C₃×#886	C₂²	semidirect
96. C₃×#883	C₂²	semidirect
97. C₃×#883	C₂²	semidirect
102. C₃×#67⋊C₄	C₂²	semidirect
103. C₃×#67⋊C₄	C₂²	semidirect
108. C₃×#879	C₂²	semidirect
109. C₃×#878	C₂²	semidirect
112. C₃×#877	C₂²	semidirect
114. C₃×#875	C₂²	semidirect
116. C₃×C₄×D₁₂	C₂²	semidirect
121. C₃×C₄²×D₃	C₂²	semidirect
122. C₃×#870	C₂²	semidirect
123. C₃×#869	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
129. C₃×#542	D₃	semidirect
130. C₃×#542	C₂×C₃	semidirect
150. #5733	C₂×C₃	semidirect
151. #5728	C₂×C₃	semidirect
152. #5707	C₂×C₃	semidirect
153. #5706	C₂×C₃	semidirect
154. #5682	C₂×C₃	semidirect
155. #5680	C₂×C₃	semidirect
156. #5678	C₂×C₃	semidirect
157. #5668	C₂×C₃	semidirect
158. #5657	C₂×C₃	semidirect
159. #5649	C₂×C₃	semidirect
160. #5638	C₂×C₃	semidirect
161. #5627	C₂×C₃	semidirect
162. #5625	C₂×C₃	semidirect
163. #5624	C₂×C₃	semidirect
164. #5619	C₂×C₃	semidirect
165. #5606	C₂×C₃	semidirect
166. #5583	C₂×C₃	semidirect
167. C₄×#239	C₂×C₃	semidirect
168. #5562	C₂×C₃	semidirect
169. C₄×#237	C₂×C₃	semidirect
170. #5534	C₂×C₃	semidirect
171. D₃×#117	C₂×C₃	semidirect
284. C₃×C₄⋊Q₈	C₂×D₃	semidirect
285. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
295. C₃×#126	C₂×D₃	semidirect
296. C₃×#126	C₂²×C₃	semidirect
310. C₃×#124	C₂×D₃	semidirect
312. C₃×#124	C₂²×C₃	semidirect
336. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
338. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
359. C₃×C₄×Q₈	C₂×D₃	semidirect
360. C₃×C₄×Q₈	C₂²×C₃	semidirect
375. C₃×C₄×D₄	C₂×D₃	semidirect
376. C₃×C₄×D₄	C₂²×C₃	semidirect
402. #946	C₂²×C₃	semidirect
403. Q₈×Dic₃	C₂²×C₃	semidirect
404. Q₈×Dic₃	C₂²×C₃	semidirect
405. #944	C₂²×C₃	semidirect
406. #940	C₂²×C₃	semidirect
412. D₄×Dic₃	C₂²×C₃	semidirect
415. #929	C₂²×C₃	semidirect
419. C₂×C₄×Dic₃	C₂²×C₃	semidirect
421. #898	C₂²×C₃	semidirect
422. #898	C₂²×C₃	semidirect
425. #896	C₂²×C₃	semidirect
431. #893	C₂²×C₃	semidirect
436. #892	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
447. #886	C₂²×C₃	semidirect
455. #883	C₂²×C₃	semidirect
456. #883	C₂²×C₃	semidirect
461. #67⋊C₄	C₂²×C₃	semidirect
462. #67⋊C₄	C₂²×C₃	semidirect
467. #879	C₂²×C₃	semidirect
468. #878	C₂²×C₃	semidirect
471. #877	C₂²×C₃	semidirect
473. #875	C₂²×C₃	semidirect
475. C₄×D₁₂	C₂²×C₃	semidirect
480. C₄²×D₃	C₂²×C₃	semidirect
481. #870	C₂²×C₃	semidirect
482. #869	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
543. #542	C₃×D₃	semidirect
830. C₄⋊Q₈	C₂×C₃×D₃	semidirect
839. #126	C₂×C₃×D₃	semidirect
851. #124	C₂×C₃×D₃	semidirect
871. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
889. C₄×Q₈	C₂×C₃×D₃	semidirect
903. C₄×D₄	C₂×C₃×D₃	semidirect
1249. C₃²	#3455	semidirect
1363. C₃	#86523	direct (N × H)
1364. C₃	C₃×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#542	2
C₃×#5733	2
C₃×#5728	2
C₃×#5707	2
C₃×#5706	2
C₃×#5682	2
C₃×#5680	2
C₃×#5678	2
C₃×#5668	2
C₃×#5657	2
C₃×#5649	2
C₃×#5638	2
C₃×#5627	2
C₃×#5625	2
C₃×#5624	2
C₃×#5619	2
C₃×#5606	2
C₃×#5583	2
C₃×C₄×#239	2
C₃×#5562	2
C₃×C₄×#237	2
C₃×#5534	2
C₃×D₃×#117	2
C₃×#3455	3
#86523	3

Subgroups — C3×#86523 #11901745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86523 #11901745