Subgroups — C₃×#86017 #11910963

Order 1152.

2503 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄×#67	C₂	1	2	yes	maximal, complemented
3	C₃×#5791	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5667	C₂	1	2	yes	maximal, complemented
6	C₃×#5666	C₂	1	2	yes	maximal, complemented
7	C₃×#5665	C₂	1	2	yes	maximal, complemented
8	C₃×#5663	C₂	1	2	yes	maximal, complemented
9	C₃×#5658	C₂	1	2	yes	maximal, complemented
10	C₃×#5657	C₂	1	2	yes	maximal, complemented
11	C₃×#5654	C₂	1	2	yes	maximal, complemented
12	C₃×#5653	C₂	1	2	yes	maximal, complemented
13	C₃×#5515	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5514	C₂	1	2	yes	maximal, complemented
15	C₃×#5510	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5494	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5493	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5490	C₂	1	2	yes	maximal, complemented
19	C₃×#5490	C₂	1	2	yes	maximal, complemented
20	C₃×#3534	—	3	1	no	maximal
21	#86017	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×#67	C₂²	1	2	yes	complemented
25	C₂²×C₃×#67	C₂²	1	2	yes	complemented
26	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
27	C₂×C₃×#235	C₂²	1	2	yes	complemented
28	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#123	C₂²	1	2	yes	complemented
31	C₃²×#123	C₂²	1	2	yes	complemented
32	C₃²×#123	C₂²	1	2	yes	complemented
33	C₃²×#123	C₂²	1	2	yes	complemented
34	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×#953	C₂²	1	2	yes	complemented
40	C₃×#953	C₂²	1	2	yes	complemented
41	C₃×#940	C₂²	1	2	yes	complemented
42	C₃×#939	C₂²	1	2	yes	—
43	C₃×#939	C₂²	1	2	yes	complemented
44	C₃×#938	C₂²	1	2	yes	complemented
45	C₃×#937	C₂²	1	2	yes	—
46	C₃×#937	C₂²	1	2	yes	complemented
47	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
48	C₃×#930	C₂²	1	1	yes	characteristic
49	C₃×#930	C₂²	1	2	yes	complemented
50	C₃×#930	C₂²	1	2	yes	complemented
51	C₃×#930	C₂²	1	1	yes	characteristic, complemented
52	C₃×#930	C₂²	1	1	yes	characteristic, complemented
53	C₃×#930	C₂²	1	2	yes	complemented
54	C₃×#930	C₂²	1	1	yes	characteristic, complemented
55	C₃×#930	C₂²	1	1	yes	characteristic, complemented
56	C₃×#930	C₂²	1	2	yes	complemented
57	C₃×#930	C₂²	1	1	yes	characteristic, complemented
58	C₃×#929	C₂²	1	2	yes	complemented
59	C₃×#929	C₂²	1	2	yes	complemented
60	C₃×C₄×#67	C₂²	1	2	yes	complemented
61	C₃×C₄×#67	C₂²	1	2	yes	complemented
62	C₃×C₄×#67	C₂²	1	2	yes	complemented
63	C₃×C₄×#67	C₂²	1	2	yes	complemented
64	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
65	C₃×#926	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
67	C₃×#924	C₂²	1	1	yes	characteristic, complemented
68	C₃×#924	C₂²	1	1	yes	characteristic, complemented
69	C₃×#898	C₂²	1	2	yes	complemented
70	C₃×#898	C₂²	1	2	yes	complemented
71	C₃×#898	C₂²	1	2	yes	complemented
72	C₃×#897	C₂²	1	2	yes	complemented
73	C₃×#897	C₂²	1	2	yes	complemented
74	C₃×#896	C₂²	1	2	yes	complemented
75	C₃×#895	C₂²	1	2	yes	complemented
76	C₃×#895	C₂²	1	2	yes	complemented
77	C₃×#895	C₂²	1	2	yes	complemented
78	C₃×#894	C₂²	1	2	yes	complemented
79	C₃×#894	C₂²	1	2	yes	complemented
80	C₃×#894	C₂²	1	2	yes	complemented
81	C₃×#893	C₂²	1	2	yes	complemented
82	C₃×#892	C₂²	1	2	yes	complemented
83	C₃×#890	C₂²	1	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#886	C₂²	1	2	yes	complemented
86	C₃×#886	C₂²	1	2	yes	complemented
87	C₃×#885	C₂²	1	2	yes	complemented
88	C₃×#885	C₂²	1	2	yes	complemented
89	C₃×#885	C₂²	1	2	yes	complemented
90	C₃×#884	C₂²	1	2	yes	complemented
91	C₃×#884	C₂²	1	2	yes	complemented
92	C₃×#884	C₂²	1	2	yes	complemented
93	C₃×#884	C₂²	1	2	yes	complemented
94	C₃×#884	C₂²	1	2	yes	complemented
95	C₃×#883	C₂²	1	2	yes	complemented
96	C₃×#883	C₂²	1	2	yes	complemented
97	C₃×#883	C₂²	1	2	yes	complemented
98	C₃×#882	C₂²	1	2	yes	complemented
99	C₃×#882	C₂²	1	2	yes	complemented
100	C₃×#882	C₂²	1	2	yes	complemented
101	C₃×#882	C₂²	1	2	yes	complemented
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	2	yes	complemented
105	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₃×#879	C₂²	1	2	yes	complemented
107	C₃×#878	C₂²	1	2	yes	complemented
108	C₃×#878	C₂²	1	2	yes	complemented
109	C₃×#562	—	3	2	no	—
110	C₃×#560	—	3	2	no	—
111	C₃×#553	—	3	2	no	—
112	C₃×#551	—	3	2	no	—
113	C₃×#546	—	3	2	no	—
114	C₃×#546	—	3	2	no	—
115	C₃×#546	—	3	2	no	—
116	C₃×D₄²	—	3	2	no	—
117	C₃×#540	—	3	2	no	—
118	C₃×#539	—	3	2	no	—
119	C₃×#539	—	3	1	no	—
120	C₃×#538	—	3	2	no	—
121	C₃×#538	—	3	1	no	—
122	C₃×#537	—	3	1	no	—
123	C₃×#534	—	3	2	no	—
124	C₃×#534	—	3	1	no	—
125	C₃×#525	—	3	1	no	—
126	C₂×C₃×#123	—	2	1	no	—
127	C₂×C₃×#123	D₃	1	1	yes	characteristic, complemented
128	C₂×C₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
129	C₂×C₃×#121	—	3	1	no	—
130	D₄×#67	C₂×C₃	1	2	yes	complemented
131	#5791	C₂×C₃	1	1	yes	characteristic, complemented
132	C₂×#930	C₂×C₃	1	1	yes	characteristic, complemented
133	#5667	C₂×C₃	1	2	yes	complemented
134	#5666	C₂×C₃	1	2	yes	complemented
135	#5665	C₂×C₃	1	2	yes	complemented
136	#5663	C₂×C₃	1	2	yes	complemented
137	#5658	C₂×C₃	1	2	yes	complemented
138	#5657	C₂×C₃	1	2	yes	complemented
139	#5654	C₂×C₃	1	2	yes	complemented
140	#5653	C₂×C₃	1	2	yes	complemented
141	#5515	C₂×C₃	1	1	yes	characteristic, complemented
142	#5514	C₂×C₃	1	2	yes	complemented
143	#5510	C₂×C₃	1	1	yes	characteristic, complemented
144	#5494	C₂×C₃	1	1	yes	characteristic, complemented
145	#5493	C₂×C₃	1	1	yes	characteristic, complemented
146	#5490	C₂×C₃	1	2	yes	complemented
147	#5490	C₂×C₃	1	2	yes	complemented
148	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
149	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
150	C₂³×C₃×D₃	C₂³	1	2	yes	—
151	C₂³×C₃×D₃	C₂³	1	2	yes	—
152	C₂×C₃²×D₄	—	4	2	no	—
153	C₂×C₃²×D₄	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	C₂³	1	2	yes	—
155	C₂²×C₃²×C₄	—	4	2	no	—
156	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
160	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×#67	—	4	4	no	—
166	C₂×C₃×#67	—	4	4	no	—
167	C₂×C₃×#67	C₂³	1	2	yes	—
168	C₂×C₃×#67	C₂³	1	2	yes	—
169	C₂×C₃×#67	C₂³	1	2	yes	—
170	C₂×C₃×#67	C₂³	1	2	yes	—
171	C₂×C₃×#67	C₂³	1	2	yes	—
172	C₂×C₃×#67	C₂³	1	2	yes	—
173	C₂×C₃×#67	C₂³	1	2	yes	—
174	C₂×C₃×#67	C₂³	1	2	yes	—
175	C₂×C₃×#67	C₂³	1	2	yes	—
176	C₂×C₃×#67	C₂³	1	2	yes	—
177	C₂×C₃×#67	C₂³	1	2	yes	—
178	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
179	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
180	C₃×D₃×D₄	—	4	4	no	—
181	C₃×#235	—	4	2	no	—
182	C₃×#235	—	4	4	no	—
183	C₂×C₃×D₁₂	—	4	2	no	—
184	C₂×C₃×D₁₂	C₂³	1	2	yes	—
185	C₂×C₃×D₁₂	C₂³	1	2	yes	—
186	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
187	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
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×C₄×D₃	C₂³	1	2	yes	—
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	2	yes	—
195	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
196	C₂×C₃×Dic₆	C₂³	1	2	yes	—
197	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
198	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×#217	C₂³	1	2	yes	—
209	C₃×#217	C₂³	1	2	yes	—
210	C₃×#217	C₂³	1	2	yes	—
211	C₃×#217	C₂³	1	2	yes	—
212	C₃×#217	C₂³	1	2	yes	—
213	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
231	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
232	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₃×C₄×Dic₃	C₂³	1	2	yes	—
241	C₃×C₄×Dic₃	C₂³	1	2	yes	—
242	C₃×C₄×Dic₃	C₂³	1	2	yes	—
243	#3534	—	3	1	no	Sylow
244	C₂×C₃×#41	—	3	1	no	—
245	C₂×C₃×#41	—	3	2	no	—
246	C₂²×C₃×D₄	—	2	1	no	—
247	C₂²×C₃×D₄	—	3	2	no	—
248	C₂²×C₃×D₄	—	3	2	no	—
249	C₂²×C₃×D₄	—	3	2	no	—
250	C₂²×C₃×D₄	—	3	1	no	—
251	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
252	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
253	C₂³×C₃×C₄	—	2	1	no	—
254	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
255	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₂²×#67	C₂²×C₃	1	2	yes	complemented
257	C₂²×#67	C₂²×C₃	1	2	yes	complemented
258	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
259	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₂×#235	C₂²×C₃	1	2	yes	complemented
261	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
262	C₃×#127	—	3	2	no	—
263	C₃×#126	—	3	2	no	—
264	C₃×#126	—	3	2	no	—
265	C₃×#126	—	3	2	no	—
266	C₃×#126	—	3	2	no	—
267	C₃×#125	—	3	2	no	—
268	C₃×#125	—	3	2	no	—
269	C₃×#124	—	3	2	no	—
270	C₃×#124	—	3	2	no	—
271	C₃×#124	—	3	2	no	—
272	C₃×#123	—	2	2	no	—
273	C₃×#123	—	2	2	no	—
274	C₃×#123	—	2	2	no	—
275	C₃×#123	—	2	2	no	—
276	C₃×#123	—	3	2	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	—	3	2	no	—
279	C₃×#123	—	3	2	no	—
280	C₃×#123	—	3	2	no	—
281	C₃×#123	—	3	2	no	—
282	C₃×#123	—	3	2	no	—
283	C₃×#123	—	3	2	no	—
284	C₃×#123	—	3	2	no	—
285	C₃×#123	—	3	2	no	—
286	C₃×#123	C₂×D₃	1	2	yes	complemented
287	C₃×#123	C₂×D₃	1	2	yes	complemented
288	C₃×#123	C₂×D₃	1	2	yes	complemented
289	C₃×#123	C₂×D₃	1	2	yes	complemented
290	C₃×#123	C₂²×C₃	1	2	yes	complemented
291	C₃×#123	C₂²×C₃	1	2	yes	complemented
292	C₃×#123	C₂²×C₃	1	2	yes	complemented
293	C₃×#123	C₂²×C₃	1	2	yes	complemented
294	C₃×C₂²⋊Q₈	—	3	1	no	—
295	C₃×C₂²⋊Q₈	—	3	1	no	—
296	C₃×C₂²⋊Q₈	—	3	2	no	—
297	C₃×C₂²⋊Q₈	—	3	2	no	—
298	C₃×C₂²⋊Q₈	—	3	2	no	—
299	C₃×C₂²⋊Q₈	—	3	2	no	—
300	C₃×C₂²⋊Q₈	—	3	2	no	—
301	C₃×#121	—	3	2	no	—
302	C₃×#121	—	3	2	no	—
303	C₃×#121	—	3	2	no	—
304	C₃×#121	—	3	1	no	—
305	C₃×#121	—	3	2	no	—
306	C₃×#121	—	3	1	no	—
307	C₃×#121	—	3	1	no	—
308	C₃×#121	—	3	1	no	—
309	C₃×#121	—	3	1	no	—
310	C₃×#121	—	3	2	no	—
311	C₃×#121	—	3	1	no	—
312	C₃×#121	—	3	2	no	—
313	C₃×#121	—	3	2	no	—
314	C₃×#121	—	3	2	no	—
315	C₃×#121	—	3	2	no	—
316	C₃×#121	—	3	2	no	—
317	C₃×#121	—	3	2	no	—
318	C₃×#121	—	3	2	no	—
319	C₃×#121	—	3	2	no	—
320	C₃×#121	—	3	2	no	—
321	C₃×#121	—	3	2	no	—
322	C₃×#120	—	3	2	no	—
323	C₃×#120	—	3	2	no	—
324	C₃×#120	—	3	2	no	—
325	C₃×#120	—	3	2	no	—
326	C₃×#120	—	3	2	no	—
327	C₃×#120	—	3	2	no	—
328	C₃×#120	—	3	2	no	—
329	C₃×#120	—	3	2	no	—
330	C₃×C₄×D₄	—	3	2	no	—
331	C₃×C₄×D₄	—	3	2	no	—
332	C₃×C₄×D₄	—	3	2	no	—
333	C₃×C₄×D₄	—	3	2	no	—
334	C₃×C₄×D₄	—	3	2	no	—
335	C₃×C₄×D₄	—	3	2	no	—
336	C₃×C₄×D₄	—	3	2	no	—
337	C₃×C₄×D₄	—	3	2	no	—
338	C₃×#117	—	3	1	no	—
339	C₃×#117	—	3	2	no	—
340	C₂×C₃×C₄⋊C₄	—	2	1	no	—
341	C₂×C₃×C₄⋊C₄	—	2	1	no	—
342	C₂×C₃×C₄⋊C₄	—	3	1	no	—
343	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
344	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
345	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
346	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
347	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
354	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
355	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
356	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
357	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
358	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
359	#953	C₂²×C₃	1	2	yes	complemented
360	#953	C₂²×C₃	1	2	yes	complemented
361	#940	C₂²×C₃	1	2	yes	complemented
362	#939	C₂²×C₃	1	2	yes	—
363	#939	C₂²×C₃	1	2	yes	complemented
364	#938	C₂²×C₃	1	2	yes	complemented
365	#937	C₂²×C₃	1	2	yes	—
366	#937	C₂²×C₃	1	2	yes	complemented
367	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
368	#930	C₂²×C₃	1	1	yes	characteristic
369	#930	C₂²×C₃	1	1	yes	characteristic, complemented
370	#930	C₂²×C₃	1	1	yes	characteristic, complemented
371	#930	C₂²×C₃	1	1	yes	characteristic, complemented
372	#930	C₂²×C₃	1	2	yes	complemented
373	#930	C₂²×C₃	1	2	yes	complemented
374	#930	C₂²×C₃	1	2	yes	complemented
375	#930	C₂²×C₃	1	1	yes	characteristic, complemented
376	#930	C₂²×C₃	1	1	yes	characteristic, complemented
377	#930	C₂²×C₃	1	2	yes	complemented
378	#929	C₂²×C₃	1	2	yes	complemented
379	#929	C₂²×C₃	1	2	yes	complemented
380	C₄×#67	C₂²×C₃	1	2	yes	complemented
381	C₄×#67	C₂²×C₃	1	2	yes	complemented
382	C₄×#67	C₂²×C₃	1	2	yes	complemented
383	C₄×#67	C₂²×C₃	1	2	yes	complemented
384	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
385	#926	C₂²×C₃	1	1	yes	characteristic, complemented
386	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
387	#924	C₂²×C₃	1	1	yes	characteristic, complemented
388	#924	C₂²×C₃	1	1	yes	characteristic, complemented
389	#898	C₂²×C₃	1	2	yes	complemented
390	#898	C₂²×C₃	1	2	yes	complemented
391	#898	C₂²×C₃	1	2	yes	complemented
392	#897	C₂²×C₃	1	2	yes	complemented
393	#897	C₂²×C₃	1	2	yes	complemented
394	#896	C₂²×C₃	1	2	yes	complemented
395	#895	C₂²×C₃	1	2	yes	complemented
396	#895	C₂²×C₃	1	2	yes	complemented
397	#895	C₂²×C₃	1	2	yes	complemented
398	#894	C₂²×C₃	1	2	yes	complemented
399	#894	C₂²×C₃	1	2	yes	complemented
400	#894	C₂²×C₃	1	2	yes	complemented
401	#893	C₂²×C₃	1	2	yes	complemented
402	#892	C₂²×C₃	1	2	yes	complemented
403	#890	C₂²×C₃	1	2	yes	complemented
404	#889	C₂²×C₃	1	2	yes	complemented
405	#886	C₂²×C₃	1	2	yes	complemented
406	#886	C₂²×C₃	1	2	yes	complemented
407	#885	C₂²×C₃	1	2	yes	complemented
408	#885	C₂²×C₃	1	2	yes	complemented
409	#885	C₂²×C₃	1	2	yes	complemented
410	#884	C₂²×C₃	1	2	yes	complemented
411	#884	C₂²×C₃	1	2	yes	complemented
412	#884	C₂²×C₃	1	2	yes	complemented
413	#884	C₂²×C₃	1	2	yes	complemented
414	#884	C₂²×C₃	1	2	yes	complemented
415	#883	C₂²×C₃	1	2	yes	complemented
416	#883	C₂²×C₃	1	2	yes	complemented
417	#883	C₂²×C₃	1	2	yes	complemented
418	#882	C₂²×C₃	1	2	yes	complemented
419	#882	C₂²×C₃	1	2	yes	complemented
420	#882	C₂²×C₃	1	2	yes	complemented
421	#882	C₂²×C₃	1	2	yes	complemented
422	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
423	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
424	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
425	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
426	#879	C₂²×C₃	1	2	yes	complemented
427	#878	C₂²×C₃	1	2	yes	complemented
428	#878	C₂²×C₃	1	2	yes	complemented
429	C₂³×C₃²	—	2	2	no	—
430	C₂³×C₃²	—	2	2	no	—
431	C₂³×C₃²	—	2	2	no	—
432	C₂³×C₃²	—	4	1	no	—
433	C₂³×C₃²	—	4	1	no	—
434	C₂³×C₃²	—	4	1	no	—
435	C₂³×C₃²	C₂⁴	1	2	yes	—
436	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
437	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
438	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
439	C₂²×C₃×D₃	—	2	4	no	—
440	C₂²×C₃×D₃	—	4	2	no	—
441	C₂²×C₃×D₃	—	4	2	no	—
442	C₂²×C₃×D₃	—	4	2	no	—
443	C₂²×C₃×D₃	—	4	2	no	—
444	C₂²×C₃×D₃	—	4	2	no	—
445	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
446	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
447	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
448	C₃²×D₄	—	2	4	no	—
449	C₃²×D₄	—	4	2	no	—
450	C₂×C₃²×C₄	—	2	2	no	—
451	C₂×C₃²×C₄	—	2	2	no	—
452	C₂×C₃²×C₄	—	2	2	no	—
453	C₂×C₃²×C₄	—	4	1	no	—
454	C₂×C₃²×C₄	—	4	1	no	—
455	C₂×C₃²×C₄	—	4	1	no	—
456	C₂×C₃²×C₄	—	4	1	no	—
457	C₂×C₃²×C₄	—	4	1	no	—
458	C₂×C₃²×C₄	—	4	1	no	—
459	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
460	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
461	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
462	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
463	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
464	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
465	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
466	C₃×#67	—	2	4	no	—
467	C₃×#67	—	2	4	no	—
468	C₃×#67	—	2	4	no	—
469	C₃×#67	—	2	4	no	—
470	C₃×#67	—	4	2	no	—
471	C₃×#67	—	4	2	no	—
472	C₃×#67	—	4	2	no	—
473	C₃×#67	—	4	2	no	—
474	C₃×#67	—	4	2	no	—
475	C₃×#67	—	4	2	no	—
476	C₃×#67	—	4	2	no	—
477	C₂×C₃×Dic₃	—	4	2	no	—
478	C₂×C₃×Dic₃	—	4	2	no	—
479	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
480	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
481	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
482	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
483	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
484	C₃×D₁₂	—	4	1	no	—
485	C₃×D₁₂	—	4	2	no	—
486	C₃×D₁₂	—	4	1	no	—
487	C₃×D₁₂	—	4	2	no	—
488	C₃×D₁₂	—	4	2	no	—
489	C₃×D₁₂	—	4	1	no	—
490	C₃×D₁₂	—	4	2	no	—
491	C₃×C₄×D₃	—	4	2	no	—
492	C₃×C₄×D₃	—	4	2	no	—
493	C₃×C₄×D₃	—	4	2	no	—
494	C₃×C₄×D₃	—	4	2	no	—
495	C₃×C₄×D₃	—	4	2	no	—
496	C₃×Dic₆	—	4	1	no	—
497	C₃×Dic₆	—	4	2	no	—
498	#562	—	3	2	no	—
499	#560	—	3	2	no	—
500	#553	—	3	2	no	—
501	#551	—	3	2	no	—
502	#546	—	3	2	no	—
503	#546	—	3	2	no	—
504	#546	—	3	2	no	—
505	D₄²	—	3	2	no	—
506	#540	—	3	2	no	—
507	#539	—	3	2	no	—
508	#539	—	3	1	no	—
509	#538	—	3	2	no	—
510	#538	—	3	1	no	—
511	#537	—	3	1	no	—
512	#534	—	3	2	no	—
513	#534	—	3	1	no	—
514	#525	—	3	1	no	—
515	C₂×#123	C₃×D₃	1	1	yes	characteristic, complemented
516	C₂×#121	—	3	1	no	—
517	C₂⁴×C₃	—	2	1	no	—
518	C₂⁴×C₃	—	2	1	no	—
519	C₂⁴×C₃	—	3	2	no	—
520	C₂⁴×C₃	—	3	2	no	—
521	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
522	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
523	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
524	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
525	C₂³×D₃	C₂³×C₃	1	2	yes	—
526	C₂³×D₃	C₂³×C₃	1	2	yes	—
527	C₃×#41	—	12	2	no	—
528	C₃×#41	—	12	4	no	—
529	C₂×C₃×Q₈	—	3	1	no	—
530	C₂×C₃×Q₈	—	3	2	no	—
531	C₂×C₃×D₄	—	2	2	no	—
532	C₂×C₃×D₄	—	2	2	no	—
533	C₂×C₃×D₄	—	3	2	no	—
534	C₂×C₃×D₄	—	3	2	no	—
535	C₂×C₃×D₄	—	3	2	no	—
536	C₂×C₃×D₄	—	3	2	no	—
537	C₂×C₃×D₄	—	3	2	no	—
538	C₂×C₃×D₄	—	3	2	no	—
539	C₂×C₃×D₄	—	3	2	no	—
540	C₂×C₃×D₄	—	3	2	no	—
541	C₂×C₃×D₄	—	3	2	no	—
542	C₂×C₃×D₄	—	3	2	no	—
543	C₂×C₃×D₄	—	3	2	no	—
544	C₂×C₃×D₄	—	3	2	no	—
545	C₂×C₃×D₄	—	3	1	no	—
546	C₂×C₃×D₄	—	3	2	no	—
547	C₂×C₃×D₄	—	3	1	no	—
548	C₂×C₃×D₄	—	3	2	no	—
549	C₂×C₃×D₄	—	3	1	no	—
550	C₂×C₃×D₄	—	3	2	no	—
551	C₂×C₃×D₄	—	4	2	no	—
552	C₂×C₃×D₄	—	4	2	no	—
553	C₂×C₃×D₄	—	4	4	no	—
554	C₂×C₃×D₄	—	12	2	no	—
555	C₂×C₃×D₄	—	12	4	no	—
556	C₂×C₃×D₄	—	12	4	no	—
557	C₂×C₃×D₄	—	12	4	no	—
558	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
559	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
560	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
561	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
562	C₂²×C₃×C₄	—	2	1	no	—
563	C₂²×C₃×C₄	—	2	1	no	—
564	C₂²×C₃×C₄	—	2	1	no	—
565	C₂²×C₃×C₄	—	2	1	no	—
566	C₂²×C₃×C₄	—	2	1	no	—
567	C₂²×C₃×C₄	—	2	1	no	—
568	C₂²×C₃×C₄	—	2	1	no	—
569	C₂²×C₃×C₄	—	2	1	no	—
570	C₂²×C₃×C₄	—	2	1	no	—
571	C₂²×C₃×C₄	—	3	2	no	—
572	C₂²×C₃×C₄	—	3	2	no	—
573	C₂²×C₃×C₄	—	3	2	no	—
574	C₂²×C₃×C₄	—	3	2	no	—
575	C₂²×C₃×C₄	—	3	2	no	—
576	C₂²×C₃×C₄	—	3	2	no	—
577	C₂²×C₃×C₄	—	3	2	no	—
578	C₂²×C₃×C₄	—	4	2	no	—
579	C₂²×C₃×C₄	—	4	2	no	—
580	C₂²×C₃×C₄	—	4	4	no	—
581	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
582	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
583	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
584	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
585	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
586	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
587	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
588	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
589	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
590	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
591	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
592	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
593	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
594	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×#67	—	4	4	no	—
600	C₂×#67	—	4	4	no	—
601	C₂×#67	C₂³×C₃	1	2	yes	—
602	C₂×#67	C₂³×C₃	1	2	yes	—
603	C₂×#67	C₂³×C₃	1	2	yes	—
604	C₂×#67	C₂³×C₃	1	2	yes	—
605	C₂×#67	C₂³×C₃	1	2	yes	—
606	C₂×#67	C₂³×C₃	1	2	yes	—
607	C₂×#67	C₂³×C₃	1	2	yes	—
608	C₂×#67	C₂³×C₃	1	2	yes	—
609	C₂×#67	C₂³×C₃	1	2	yes	—
610	C₂×#67	C₂³×C₃	1	2	yes	—
611	C₂×#67	C₂³×C₃	1	2	yes	—
612	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
613	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
614	D₃×D₄	—	4	4	no	—
615	#235	—	4	2	no	—
616	#235	—	4	4	no	—
617	C₂×D₁₂	—	4	2	no	—
618	C₂×D₁₂	C₂³×C₃	1	2	yes	—
619	C₂×D₁₂	C₂³×C₃	1	2	yes	—
620	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
621	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
622	C₂×D₁₂	C₂³×C₃	1	2	yes	—
623	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
624	C₂×D₁₂	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×C₄×D₃	C₂³×C₃	1	2	yes	—
629	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
630	C₂×Dic₆	C₂³×C₃	1	2	yes	—
631	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
632	C₃×C₄⋊C₄	—	2	2	no	—
633	C₃×C₄⋊C₄	—	2	2	no	—
634	C₃×C₄⋊C₄	—	2	2	no	—
635	C₃×C₄⋊C₄	—	2	2	no	—
636	C₃×C₄⋊C₄	—	3	2	no	—
637	C₃×C₄⋊C₄	—	3	2	no	—
638	C₃×C₄⋊C₄	—	3	2	no	—
639	C₃×C₄⋊C₄	—	3	2	no	—
640	C₃×C₄⋊C₄	—	3	2	no	—
641	C₃×C₄⋊C₄	—	3	2	no	—
642	C₃×C₄⋊C₄	—	3	1	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	1	no	—
648	C₃×C₄⋊C₄	—	3	2	no	—
649	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
650	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
651	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
652	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
653	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
654	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
655	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
656	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
657	C₃×C₂²⋊C₄	—	2	2	no	—
658	C₃×C₂²⋊C₄	—	2	2	no	—
659	C₃×C₂²⋊C₄	—	2	2	no	—
660	C₃×C₂²⋊C₄	—	2	2	no	—
661	C₃×C₂²⋊C₄	—	2	2	no	—
662	C₃×C₂²⋊C₄	—	2	2	no	—
663	C₃×C₂²⋊C₄	—	3	2	no	—
664	C₃×C₂²⋊C₄	—	3	2	no	—
665	C₃×C₂²⋊C₄	—	3	2	no	—
666	C₃×C₂²⋊C₄	—	3	2	no	—
667	C₃×C₂²⋊C₄	—	3	2	no	—
668	C₃×C₂²⋊C₄	—	3	2	no	—
669	C₃×C₂²⋊C₄	—	3	2	no	—
670	C₃×C₂²⋊C₄	—	3	2	no	—
671	C₃×C₂²⋊C₄	—	3	2	no	—
672	C₃×C₂²⋊C₄	—	3	2	no	—
673	C₃×C₂²⋊C₄	—	3	2	no	—
674	C₃×C₂²⋊C₄	—	3	2	no	—
675	C₃×C₂²⋊C₄	—	3	2	no	—
676	C₃×C₂²⋊C₄	—	3	2	no	—
677	C₃×C₂²⋊C₄	—	3	2	no	—
678	C₃×C₂²⋊C₄	—	3	2	no	—
679	C₃×C₂²⋊C₄	—	3	2	no	—
680	C₃×C₂²⋊C₄	—	3	2	no	—
681	C₃×C₂²⋊C₄	—	3	2	no	—
682	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
683	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
684	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
686	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
687	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
688	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
689	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
690	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
691	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
692	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
693	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
694	C₃×C₄²	—	3	2	no	—
695	C₃×C₄²	—	3	2	no	—
696	C₃×C₄²	—	3	2	no	—
697	#217	C₂³×C₃	1	2	yes	—
698	#217	C₂³×C₃	1	2	yes	—
699	#217	C₂³×C₃	1	2	yes	—
700	#217	C₂³×C₃	1	2	yes	—
701	#217	C₂³×C₃	1	2	yes	—
702	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
703	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
704	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
705	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
706	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
707	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
708	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
709	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
710	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
711	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
712	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
713	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
714	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
715	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
716	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
717	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
718	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
719	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
720	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
721	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
722	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
723	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
724	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
725	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
726	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
727	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
728	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
729	C₄×Dic₃	C₂³×C₃	1	2	yes	—
730	C₄×Dic₃	C₂³×C₃	1	2	yes	—
731	C₄×Dic₃	C₂³×C₃	1	2	yes	—
732	C₂²×C₃²	—	2	1	no	—
733	C₂²×C₃²	—	2	1	no	—
734	C₂²×C₃²	—	2	1	no	—
735	C₂²×C₃²	—	2	1	no	—
736	C₂²×C₃²	—	2	1	no	—
737	C₂²×C₃²	—	2	2	no	—
738	C₂²×C₃²	—	2	1	no	—
739	C₂²×C₃²	—	2	2	no	—
740	C₂²×C₃²	—	2	1	no	—
741	C₂²×C₃²	—	2	2	no	—
742	C₂²×C₃²	—	4	4	no	—
743	C₂²×C₃²	—	8	2	no	—
744	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
745	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
746	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
747	C₂×C₃×D₃	—	2	2	no	—
748	C₂×C₃×D₃	—	2	2	no	—
749	C₂×C₃×D₃	—	2	2	no	—
750	C₂×C₃×D₃	—	2	2	no	—
751	C₂×C₃×D₃	—	2	2	no	—
752	C₂×C₃×D₃	—	2	2	no	—
753	C₂×C₃×D₃	—	2	2	no	—
754	C₂×C₃×D₃	—	2	2	no	—
755	C₂×C₃×D₃	—	2	2	no	—
756	C₂×C₃×D₃	—	8	4	no	—
757	C₂×C₃×D₃	—	8	4	no	—
758	C₃²×C₄	—	2	2	no	—
759	C₃²×C₄	—	2	1	no	—
760	C₃²×C₄	—	2	1	no	—
761	C₃²×C₄	—	2	2	no	—
762	C₃²×C₄	—	2	1	no	—
763	C₃²×C₄	—	2	1	no	—
764	C₃²×C₄	—	2	2	no	—
765	C₃×Dic₃	—	2	2	no	—
766	C₃×Dic₃	—	2	2	no	—
767	C₃×Dic₃	—	2	2	no	—
768	C₃×Dic₃	—	2	2	no	—
769	C₃×Dic₃	—	2	2	no	—
770	C₂×#41	—	3	1	no	—
771	C₂×#41	—	3	2	no	—
772	C₂²×D₄	—	3	2	no	—
773	C₂²×D₄	—	3	2	no	—
774	C₂²×D₄	—	3	2	no	—
775	C₂²×D₄	—	3	1	no	—
776	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
777	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
778	#127	—	3	2	no	—
779	#126	—	3	2	no	—
780	#126	—	3	2	no	—
781	#126	—	3	2	no	—
782	#126	—	3	2	no	—
783	#125	—	3	2	no	—
784	#125	—	3	2	no	—
785	#124	—	3	2	no	—
786	#124	—	3	2	no	—
787	#124	—	3	2	no	—
788	#123	—	3	2	no	—
789	#123	—	3	2	no	—
790	#123	—	3	2	no	—
791	#123	—	3	2	no	—
792	#123	—	3	2	no	—
793	#123	—	3	2	no	—
794	#123	—	3	2	no	—
795	#123	—	3	2	no	—
796	#123	—	3	2	no	—
797	#123	—	3	2	no	—
798	#123	C₂×C₃×D₃	1	2	yes	complemented
799	#123	C₂×C₃×D₃	1	2	yes	complemented
800	#123	C₂×C₃×D₃	1	2	yes	complemented
801	#123	C₂×C₃×D₃	1	2	yes	complemented
802	C₂²⋊Q₈	—	3	1	no	—
803	C₂²⋊Q₈	—	3	1	no	—
804	C₂²⋊Q₈	—	3	2	no	—
805	C₂²⋊Q₈	—	3	2	no	—
806	C₂²⋊Q₈	—	3	2	no	—
807	C₂²⋊Q₈	—	3	2	no	—
808	C₂²⋊Q₈	—	3	2	no	—
809	#121	—	3	2	no	—
810	#121	—	3	2	no	—
811	#121	—	3	2	no	—
812	#121	—	3	1	no	—
813	#121	—	3	1	no	—
814	#121	—	3	1	no	—
815	#121	—	3	1	no	—
816	#121	—	3	2	no	—
817	#121	—	3	2	no	—
818	#121	—	3	1	no	—
819	#121	—	3	1	no	—
820	#121	—	3	2	no	—
821	#121	—	3	2	no	—
822	#121	—	3	2	no	—
823	#121	—	3	2	no	—
824	#121	—	3	2	no	—
825	#121	—	3	2	no	—
826	#121	—	3	2	no	—
827	#121	—	3	2	no	—
828	#121	—	3	2	no	—
829	#121	—	3	2	no	—
830	#120	—	3	2	no	—
831	#120	—	3	2	no	—
832	#120	—	3	2	no	—
833	#120	—	3	2	no	—
834	#120	—	3	2	no	—
835	#120	—	3	2	no	—
836	#120	—	3	2	no	—
837	#120	—	3	2	no	—
838	C₄×D₄	—	3	2	no	—
839	C₄×D₄	—	3	2	no	—
840	C₄×D₄	—	3	2	no	—
841	C₄×D₄	—	3	2	no	—
842	C₄×D₄	—	3	2	no	—
843	C₄×D₄	—	3	2	no	—
844	C₄×D₄	—	3	2	no	—
845	C₄×D₄	—	3	2	no	—
846	#117	—	3	1	no	—
847	#117	—	3	2	no	—
848	C₂×C₄⋊C₄	—	3	1	no	—
849	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
850	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
851	C₂×C₂²⋊C₄	—	3	2	no	—
852	C₂×C₂²⋊C₄	—	3	2	no	—
853	C₂×C₂²⋊C₄	—	3	2	no	—
854	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
855	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
856	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
857	C₂³×C₃	—	2	4	no	—
858	C₂³×C₃	—	2	2	no	—
859	C₂³×C₃	—	2	2	no	—
860	C₂³×C₃	—	2	2	no	—
861	C₂³×C₃	—	2	2	no	—
862	C₂³×C₃	—	2	2	no	—
863	C₂³×C₃	—	2	2	no	—
864	C₂³×C₃	—	2	1	no	—
865	C₂³×C₃	—	2	1	no	—
866	C₂³×C₃	—	2	1	no	—
867	C₂³×C₃	—	2	2	no	—
868	C₂³×C₃	—	3	2	no	—
869	C₂³×C₃	—	3	2	no	—
870	C₂³×C₃	—	3	2	no	—
871	C₂³×C₃	—	4	2	no	—
872	C₂³×C₃	—	4	2	no	—
873	C₂³×C₃	—	4	1	no	—
874	C₂³×C₃	—	4	1	no	—
875	C₂³×C₃	—	4	1	no	—
876	C₂³×C₃	—	4	1	no	—
877	C₂³×C₃	—	4	1	no	—
878	C₂³×C₃	—	4	1	no	—
879	C₂³×C₃	—	4	2	no	—
880	C₂³×C₃	—	4	2	no	—
881	C₂³×C₃	—	4	2	no	—
882	C₂³×C₃	—	6	4	no	—
883	C₂³×C₃	—	12	2	no	—
884	C₂³×C₃	—	12	2	no	—
885	C₂³×C₃	—	12	2	no	—
886	C₂³×C₃	—	12	2	no	—
887	C₂³×C₃	—	12	2	no	—
888	C₂³×C₃	C₂³×D₃	1	2	yes	—
889	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
890	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
891	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
892	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
893	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
894	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
895	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
896	C₂²×D₃	—	2	4	no	—
897	C₂²×D₃	—	4	2	no	—
898	C₂²×D₃	—	4	2	no	—
899	C₂²×D₃	—	4	2	no	—
900	C₂²×D₃	—	4	2	no	—
901	C₂²×D₃	—	4	2	no	—
902	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
903	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
904	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
905	C₃×Q₈	—	12	1	no	—
906	C₃×Q₈	—	12	2	no	—
907	C₃×D₄	—	2	4	no	—
908	C₃×D₄	—	2	4	no	—
909	C₃×D₄	—	4	4	no	—
910	C₃×D₄	—	4	2	no	—
911	C₃×D₄	—	4	2	no	—
912	C₃×D₄	—	4	4	no	—
913	C₃×D₄	—	6	4	no	—
914	C₃×D₄	—	6	4	no	—
915	C₃×D₄	—	6	4	no	—
916	C₃×D₄	—	6	4	no	—
917	C₃×D₄	—	12	2	no	—
918	C₃×D₄	—	12	1	no	—
919	C₃×D₄	—	12	2	no	—
920	C₃×D₄	—	12	1	no	—
921	C₃×D₄	—	12	2	no	—
922	C₃×D₄	—	12	1	no	—
923	C₃×D₄	—	12	2	no	—
924	C₃×D₄	—	12	2	no	—
925	C₃×D₄	—	12	2	no	—
926	C₃×D₄	—	12	2	no	—
927	C₃×D₄	—	12	2	no	—
928	C₃×D₄	—	12	2	no	—
929	C₃×D₄	—	12	2	no	—
930	C₃×D₄	—	12	2	no	—
931	C₂×C₃×C₄	—	2	2	no	—
932	C₂×C₃×C₄	—	2	2	no	—
933	C₂×C₃×C₄	—	2	2	no	—
934	C₂×C₃×C₄	—	2	2	no	—
935	C₂×C₃×C₄	—	2	2	no	—
936	C₂×C₃×C₄	—	2	2	no	—
937	C₂×C₃×C₄	—	2	2	no	—
938	C₂×C₃×C₄	—	2	2	no	—
939	C₂×C₃×C₄	—	2	1	no	—
940	C₂×C₃×C₄	—	2	1	no	—
941	C₂×C₃×C₄	—	2	1	no	—
942	C₂×C₃×C₄	—	2	1	no	—
943	C₂×C₃×C₄	—	2	2	no	—
944	C₂×C₃×C₄	—	3	2	no	—
945	C₂×C₃×C₄	—	3	2	no	—
946	C₂×C₃×C₄	—	3	2	no	—
947	C₂×C₃×C₄	—	3	2	no	—
948	C₂×C₃×C₄	—	3	2	no	—
949	C₂×C₃×C₄	—	4	2	no	—
950	C₂×C₃×C₄	—	4	2	no	—
951	C₂×C₃×C₄	—	4	2	no	—
952	C₂×C₃×C₄	—	4	1	no	—
953	C₂×C₃×C₄	—	4	1	no	—
954	C₂×C₃×C₄	—	4	1	no	—
955	C₂×C₃×C₄	—	4	1	no	—
956	C₂×C₃×C₄	—	4	1	no	—
957	C₂×C₃×C₄	—	4	1	no	—
958	C₂×C₃×C₄	—	4	1	no	—
959	C₂×C₃×C₄	—	4	1	no	—
960	C₂×C₃×C₄	—	4	1	no	—
961	C₂×C₃×C₄	—	4	1	no	—
962	C₂×C₃×C₄	—	4	1	no	—
963	C₂×C₃×C₄	—	4	1	no	—
964	C₂×C₃×C₄	—	4	2	no	—
965	C₂×C₃×C₄	—	4	2	no	—
966	C₂×C₃×C₄	—	4	2	no	—
967	C₂×C₃×C₄	—	4	2	no	—
968	C₂×C₃×C₄	—	4	2	no	—
969	C₂×C₃×C₄	—	4	2	no	—
970	C₂×C₃×C₄	—	12	2	no	—
971	C₂×C₃×C₄	—	12	2	no	—
972	C₂×C₃×C₄	—	12	2	no	—
973	C₂×C₃×C₄	—	12	2	no	—
974	C₂×C₃×C₄	—	12	2	no	—
975	C₂×C₃×C₄	—	12	2	no	—
976	C₂×C₃×C₄	—	12	2	no	—
977	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
978	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
979	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
980	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
981	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
982	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
983	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
984	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
985	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
986	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
987	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
988	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
989	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
990	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
991	#67	—	2	4	no	—
992	#67	—	2	4	no	—
993	#67	—	2	4	no	—
994	#67	—	2	4	no	—
995	#67	—	4	2	no	—
996	#67	—	4	2	no	—
997	#67	—	4	2	no	—
998	#67	—	4	2	no	—
999	#67	—	4	2	no	—
1000	#67	—	4	2	no	—
1001	#67	—	4	2	no	—
1002	C₂×Dic₃	—	4	2	no	—
1003	C₂×Dic₃	—	4	2	no	—
1004	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1005	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1006	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1007	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1008	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1009	D₁₂	—	4	1	no	—
1010	D₁₂	—	4	2	no	—
1011	D₁₂	—	4	1	no	—
1012	D₁₂	—	4	2	no	—
1013	D₁₂	—	4	2	no	—
1014	D₁₂	—	4	1	no	—
1015	D₁₂	—	4	2	no	—
1016	C₄×D₃	—	4	2	no	—
1017	C₄×D₃	—	4	2	no	—
1018	C₄×D₃	—	4	2	no	—
1019	C₄×D₃	—	4	2	no	—
1020	C₄×D₃	—	4	2	no	—
1021	Dic₆	—	4	1	no	—
1022	Dic₆	—	4	2	no	—
1023	C₂×C₃²	—	2	2	no	—
1024	C₂×C₃²	—	2	2	no	—
1025	C₂×C₃²	—	4	1	no	—
1026	C₂×C₃²	—	4	2	no	—
1027	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1028	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1029	C₂×C₃²	#585	1	1	yes	characteristic
1030	C₃×D₃	—	4	2	no	—
1031	C₃×D₃	—	4	2	no	—
1032	C₃×D₃	—	4	2	no	—
1033	C₂⁴	—	3	2	no	—
1034	C₂⁴	—	3	2	no	—
1035	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
1036	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
1037	#41	—	12	2	no	—
1038	#41	—	12	4	no	—
1039	C₂×Q₈	—	3	1	no	—
1040	C₂×Q₈	—	3	2	no	—
1041	C₂×D₄	—	3	2	no	—
1042	C₂×D₄	—	3	2	no	—
1043	C₂×D₄	—	3	2	no	—
1044	C₂×D₄	—	3	2	no	—
1045	C₂×D₄	—	3	2	no	—
1046	C₂×D₄	—	3	2	no	—
1047	C₂×D₄	—	3	2	no	—
1048	C₂×D₄	—	3	2	no	—
1049	C₂×D₄	—	3	2	no	—
1050	C₂×D₄	—	3	2	no	—
1051	C₂×D₄	—	3	2	no	—
1052	C₂×D₄	—	3	2	no	—
1053	C₂×D₄	—	3	1	no	—
1054	C₂×D₄	—	3	2	no	—
1055	C₂×D₄	—	3	1	no	—
1056	C₂×D₄	—	3	2	no	—
1057	C₂×D₄	—	3	1	no	—
1058	C₂×D₄	—	3	2	no	—
1059	C₂×D₄	—	4	2	no	—
1060	C₂×D₄	—	12	2	no	—
1061	C₂×D₄	—	12	4	no	—
1062	C₂×D₄	—	12	4	no	—
1063	C₂×D₄	—	12	4	no	—
1064	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1065	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1066	C₂²×C₄	—	3	2	no	—
1067	C₂²×C₄	—	3	2	no	—
1068	C₂²×C₄	—	3	2	no	—
1069	C₂²×C₄	—	3	2	no	—
1070	C₂²×C₄	—	3	2	no	—
1071	C₂²×C₄	—	3	2	no	—
1072	C₂²×C₄	—	3	2	no	—
1073	C₂²×C₄	—	4	2	no	—
1074	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1075	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1076	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1077	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1078	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1079	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1080	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1081	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1082	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1083	C₄⋊C₄	—	3	1	no	—
1084	C₄⋊C₄	—	3	2	no	—
1085	C₄⋊C₄	—	3	1	no	—
1086	C₄⋊C₄	—	3	1	no	—
1087	C₄⋊C₄	—	3	2	no	—
1088	C₄⋊C₄	—	3	1	no	—
1089	C₄⋊C₄	—	3	2	no	—
1090	C₄⋊C₄	—	3	2	no	—
1091	C₄⋊C₄	—	3	2	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	C₂²×C₃×D₃	1	2	yes	—
1097	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1098	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1099	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1100	C₂²⋊C₄	—	3	2	no	—
1101	C₂²⋊C₄	—	3	2	no	—
1102	C₂²⋊C₄	—	3	2	no	—
1103	C₂²⋊C₄	—	3	2	no	—
1104	C₂²⋊C₄	—	3	2	no	—
1105	C₂²⋊C₄	—	3	2	no	—
1106	C₂²⋊C₄	—	3	2	no	—
1107	C₂²⋊C₄	—	3	2	no	—
1108	C₂²⋊C₄	—	3	2	no	—
1109	C₂²⋊C₄	—	3	2	no	—
1110	C₂²⋊C₄	—	3	2	no	—
1111	C₂²⋊C₄	—	3	2	no	—
1112	C₂²⋊C₄	—	3	2	no	—
1113	C₂²⋊C₄	—	3	2	no	—
1114	C₂²⋊C₄	—	3	2	no	—
1115	C₂²⋊C₄	—	3	2	no	—
1116	C₂²⋊C₄	—	3	2	no	—
1117	C₂²⋊C₄	—	3	2	no	—
1118	C₂²⋊C₄	—	3	2	no	—
1119	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1120	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1121	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1122	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1123	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1124	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1125	C₄²	—	3	2	no	—
1126	C₄²	—	3	2	no	—
1127	C₄²	—	3	2	no	—
1128	C₂²×C₃	—	2	2	no	—
1129	C₂²×C₃	—	2	2	no	—
1130	C₂²×C₃	—	2	1	no	—
1131	C₂²×C₃	—	2	1	no	—
1132	C₂²×C₃	—	2	1	no	—
1133	C₂²×C₃	—	2	1	no	—
1134	C₂²×C₃	—	2	1	no	—
1135	C₂²×C₃	—	2	1	no	—
1136	C₂²×C₃	—	2	1	no	—
1137	C₂²×C₃	—	2	1	no	—
1138	C₂²×C₃	—	2	2	no	—
1139	C₂²×C₃	—	2	1	no	—
1140	C₂²×C₃	—	2	2	no	—
1141	C₂²×C₃	—	2	2	no	—
1142	C₂²×C₃	—	2	1	no	—
1143	C₂²×C₃	—	2	1	no	—
1144	C₂²×C₃	—	2	2	no	—
1145	C₂²×C₃	—	2	2	no	—
1146	C₂²×C₃	—	2	1	no	—
1147	C₂²×C₃	—	2	2	no	—
1148	C₂²×C₃	—	2	1	no	—
1149	C₂²×C₃	—	2	1	no	—
1150	C₂²×C₃	—	2	2	no	—
1151	C₂²×C₃	—	2	2	no	—
1152	C₂²×C₃	—	2	2	no	—
1153	C₂²×C₃	—	2	1	no	—
1154	C₂²×C₃	—	4	1	no	—
1155	C₂²×C₃	—	4	1	no	—
1156	C₂²×C₃	—	4	1	no	—
1157	C₂²×C₃	—	4	1	no	—
1158	C₂²×C₃	—	4	2	no	—
1159	C₂²×C₃	—	4	2	no	—
1160	C₂²×C₃	—	4	2	no	—
1161	C₂²×C₃	—	4	4	no	—
1162	C₂²×C₃	—	4	4	no	—
1163	C₂²×C₃	—	4	8	no	—
1164	C₂²×C₃	—	6	2	no	—
1165	C₂²×C₃	—	6	2	no	—
1166	C₂²×C₃	—	6	2	no	—
1167	C₂²×C₃	—	6	2	no	—
1168	C₂²×C₃	—	6	2	no	—
1169	C₂²×C₃	—	6	2	no	—
1170	C₂²×C₃	—	6	2	no	—
1171	C₂²×C₃	—	6	2	no	—
1172	C₂²×C₃	—	6	2	no	—
1173	C₂²×C₃	—	8	2	no	—
1174	C₂²×C₃	—	8	2	no	—
1175	C₂²×C₃	—	8	4	no	—
1176	C₂²×C₃	—	24	4	no	—
1177	C₂²×C₃	—	24	4	no	—
1178	C₂²×C₃	#1004	1	2	yes	—
1179	C₂²×C₃	#1009	1	2	yes	—
1180	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
1181	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
1182	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1183	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1184	C₂×D₃	—	2	2	no	—
1185	C₂×D₃	—	2	2	no	—
1186	C₂×D₃	—	2	2	no	—
1187	C₂×D₃	—	2	2	no	—
1188	C₂×D₃	—	2	2	no	—
1189	C₂×D₃	—	2	2	no	—
1190	C₂×D₃	—	2	2	no	—
1191	C₂×D₃	—	2	2	no	—
1192	C₂×D₃	—	2	2	no	—
1193	C₂×D₃	—	8	4	no	—
1194	C₂×D₃	—	8	4	no	—
1195	C₃×C₄	—	2	1	no	—
1196	C₃×C₄	—	2	1	no	—
1197	C₃×C₄	—	2	1	no	—
1198	C₃×C₄	—	2	1	no	—
1199	C₃×C₄	—	2	2	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	1	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	1	no	—
1207	C₃×C₄	—	2	1	no	—
1208	C₃×C₄	—	2	2	no	—
1209	C₃×C₄	—	4	1	no	—
1210	C₃×C₄	—	4	1	no	—
1211	C₃×C₄	—	4	1	no	—
1212	C₃×C₄	—	4	1	no	—
1213	C₃×C₄	—	4	2	no	—
1214	C₃×C₄	—	4	2	no	—
1215	C₃×C₄	—	4	2	no	—
1216	C₃×C₄	—	6	2	no	—
1217	C₃×C₄	—	6	2	no	—
1218	C₃×C₄	—	6	2	no	—
1219	C₃×C₄	—	6	2	no	—
1220	C₃×C₄	—	6	2	no	—
1221	Dic₃	—	2	2	no	—
1222	Dic₃	—	2	2	no	—
1223	Dic₃	—	2	2	no	—
1224	Dic₃	—	2	2	no	—
1225	Dic₃	—	2	2	no	—
1226	C₃²	#3534	1	1	yes	characteristic, complemented, Sylow
1227	C₂³	—	2	2	no	—
1228	C₂³	—	2	2	no	—
1229	C₂³	—	2	2	no	—
1230	C₂³	—	3	2	no	—
1231	C₂³	—	3	2	no	—
1232	C₂³	—	3	2	no	—
1233	C₂³	—	4	1	no	—
1234	C₂³	—	4	1	no	—
1235	C₂³	—	4	1	no	—
1236	C₂³	—	6	4	no	—
1237	C₂³	—	12	2	no	—
1238	C₂³	—	12	2	no	—
1239	C₂³	—	12	2	no	—
1240	C₂³	—	12	2	no	—
1241	C₂³	—	12	2	no	—
1242	C₂³	C₂³×C₃×D₃	1	2	yes	—
1243	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1244	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1245	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1246	Q₈	—	12	1	no	—
1247	Q₈	—	12	2	no	—
1248	D₄	—	2	4	no	—
1249	D₄	—	4	2	no	—
1250	D₄	—	6	4	no	—
1251	D₄	—	6	4	no	—
1252	D₄	—	6	4	no	—
1253	D₄	—	6	4	no	—
1254	D₄	—	12	1	no	—
1255	D₄	—	12	2	no	—
1256	D₄	—	12	1	no	—
1257	D₄	—	12	2	no	—
1258	D₄	—	12	1	no	—
1259	D₄	—	12	2	no	—
1260	D₄	—	12	2	no	—
1261	D₄	—	12	2	no	—
1262	D₄	—	12	2	no	—
1263	D₄	—	12	2	no	—
1264	D₄	—	12	2	no	—
1265	D₄	—	12	2	no	—
1266	D₄	—	12	2	no	—
1267	D₄	—	12	2	no	—
1268	C₂×C₄	—	2	2	no	—
1269	C₂×C₄	—	2	2	no	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	3	2	no	—
1272	C₂×C₄	—	3	2	no	—
1273	C₂×C₄	—	3	2	no	—
1274	C₂×C₄	—	3	2	no	—
1275	C₂×C₄	—	3	2	no	—
1276	C₂×C₄	—	4	1	no	—
1277	C₂×C₄	—	4	1	no	—
1278	C₂×C₄	—	4	1	no	—
1279	C₂×C₄	—	4	1	no	—
1280	C₂×C₄	—	4	1	no	—
1281	C₂×C₄	—	4	1	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	2	no	—
1287	C₂×C₄	—	12	2	no	—
1288	C₂×C₄	—	12	2	no	—
1289	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
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	2	yes	—
1294	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1295	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1296	C₂×C₃	—	2	4	no	—
1297	C₂×C₃	—	2	2	no	—
1298	C₂×C₃	—	2	2	no	—
1299	C₂×C₃	—	2	2	no	—
1300	C₂×C₃	—	2	2	no	—
1301	C₂×C₃	—	2	1	no	—
1302	C₂×C₃	—	2	1	no	—
1303	C₂×C₃	—	2	1	no	—
1304	C₂×C₃	—	4	2	no	—
1305	C₂×C₃	—	4	2	no	—
1306	C₂×C₃	—	4	1	no	—
1307	C₂×C₃	—	4	2	no	—
1308	C₂×C₃	—	4	2	no	—
1309	C₂×C₃	—	4	1	no	—
1310	C₂×C₃	—	8	2	no	—
1311	C₂×C₃	—	12	2	no	—
1312	C₂×C₃	—	12	2	no	—
1313	C₂×C₃	—	12	2	no	—
1314	C₂×C₃	C₂×#1004	1	1	yes	characteristic
1315	C₂×C₃	C₂×#1009	1	1	yes	characteristic
1316	C₂×C₃	#5964	1	1	yes	characteristic
1317	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1318	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1319	C₂×C₃	C₃×#585	1	1	yes	characteristic
1320	D₃	—	4	2	no	—
1321	D₃	—	4	2	no	—
1322	D₃	—	4	2	no	—
1323	C₂²	—	2	1	no	—
1324	C₂²	—	2	1	no	—
1325	C₂²	—	2	1	no	—
1326	C₂²	—	2	1	no	—
1327	C₂²	—	2	1	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	2	no	—
1330	C₂²	—	2	1	no	—
1331	C₂²	—	2	1	no	—
1332	C₂²	—	2	2	no	—
1333	C₂²	—	4	4	no	—
1334	C₂²	—	6	2	no	—
1335	C₂²	—	6	2	no	—
1336	C₂²	—	6	2	no	—
1337	C₂²	—	6	2	no	—
1338	C₂²	—	6	2	no	—
1339	C₂²	—	6	2	no	—
1340	C₂²	—	6	2	no	—
1341	C₂²	—	6	2	no	—
1342	C₂²	—	6	2	no	—
1343	C₂²	—	8	2	no	—
1344	C₂²	—	24	4	no	—
1345	C₂²	—	24	4	no	—
1346	C₂²	C₃×#1004	1	2	yes	—
1347	C₂²	C₃×#1009	1	2	yes	—
1348	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1349	C₄	—	2	1	no	—
1350	C₄	—	2	1	no	—
1351	C₄	—	2	1	no	—
1352	C₄	—	2	1	no	—
1353	C₄	—	2	2	no	—
1354	C₄	—	2	2	no	—
1355	C₄	—	2	2	no	—
1356	C₄	—	6	2	no	—
1357	C₄	—	6	2	no	—
1358	C₄	—	6	2	no	—
1359	C₄	—	6	2	no	—
1360	C₄	—	6	2	no	—
1361	C₃	—	2	1	no	—
1362	C₃	#86017	1	1	yes	characteristic, direct product factor
1363	C₃	C₃×#3534	1	1	yes	characteristic, complemented
1364	C₂	—	2	2	no	—
1365	C₂	—	2	2	no	—
1366	C₂	—	4	1	no	—
1367	C₂	—	4	2	no	—
1368	C₂	—	12	2	no	—
1369	C₂	—	12	2	no	—
1370	C₂	—	12	2	no	—
1371	C₂	C₂×C₃×#1004	1	1	yes	characteristic
1372	C₂	C₂×C₃×#1009	1	1	yes	characteristic
1373	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×#123	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₂×C₃×#123	D₃
hypocenter	C₃	C₃×#3534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#123	C₂	semidirect
2. C₃×D₄×#67	C₂	semidirect
3. C₃×#5791	C₂	semidirect
4. C₂×C₃×#930	C₂	semidirect
5. C₃×#5667	C₂	semidirect
6. C₃×#5666	C₂	semidirect
7. C₃×#5665	C₂	semidirect
8. C₃×#5663	C₂	semidirect
9. C₃×#5658	C₂	semidirect
10. C₃×#5657	C₂	semidirect
11. C₃×#5654	C₂	semidirect
12. C₃×#5653	C₂	semidirect
13. C₃×#5515	C₂	semidirect
14. C₃×#5514	C₂	semidirect
15. C₃×#5510	C₂	semidirect
16. C₃×#5494	C₂	semidirect
17. C₃×#5493	C₂	semidirect
18. C₃×#5490	C₂	semidirect
19. C₃×#5490	C₂	semidirect
21. #86017	C₃	direct (N × H)
23. C₂³×C₃²×C₄	C₂²	semidirect
24. C₂²×C₃×#67	C₂²	semidirect
25. C₂²×C₃×#67	C₂²	semidirect
26. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂×C₃×#235	C₂²	semidirect
28. C₂×C₃×#235	C₂²	semidirect
29. C₂²×C₃×D₁₂	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×#123	C₂²	semidirect
32. C₃²×#123	C₂²	semidirect
33. C₃²×#123	C₂²	semidirect
34. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
36. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
39. C₃×#953	C₂²	semidirect
40. C₃×#953	C₂²	semidirect
41. C₃×#940	C₂²	semidirect
43. C₃×#939	C₂²	semidirect
44. C₃×#938	C₂²	semidirect
46. C₃×#937	C₂²	semidirect
47. C₃×D₄×Dic₃	C₂²	semidirect
49. C₃×#930	C₂²	semidirect
50. C₃×#930	C₂²	semidirect
51. C₃×#930	C₂²	semidirect
52. C₃×#930	C₂²	semidirect
53. C₃×#930	C₂²	semidirect
54. C₃×#930	C₂²	semidirect
55. C₃×#930	C₂²	semidirect
56. C₃×#930	C₂²	semidirect
57. C₃×#930	C₂²	semidirect
58. C₃×#929	C₂²	semidirect
59. C₃×#929	C₂²	semidirect
60. C₃×C₄×#67	C₂²	semidirect
61. C₃×C₄×#67	C₂²	semidirect
62. C₃×C₄×#67	C₂²	semidirect
63. C₃×C₄×#67	C₂²	semidirect
64. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
65. C₃×#926	C₂²	semidirect
66. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
67. C₃×#924	C₂²	semidirect
68. C₃×#924	C₂²	semidirect
69. C₃×#898	C₂²	semidirect
70. C₃×#898	C₂²	semidirect
71. C₃×#898	C₂²	semidirect
72. C₃×#897	C₂²	semidirect
73. C₃×#897	C₂²	semidirect
74. C₃×#896	C₂²	semidirect
75. C₃×#895	C₂²	semidirect
76. C₃×#895	C₂²	semidirect
77. C₃×#895	C₂²	semidirect
78. C₃×#894	C₂²	semidirect
79. C₃×#894	C₂²	semidirect
80. C₃×#894	C₂²	semidirect
81. C₃×#893	C₂²	semidirect
82. C₃×#892	C₂²	semidirect
83. C₃×#890	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#886	C₂²	semidirect
86. C₃×#886	C₂²	semidirect
87. C₃×#885	C₂²	semidirect
88. C₃×#885	C₂²	semidirect
89. C₃×#885	C₂²	semidirect
90. C₃×#884	C₂²	semidirect
91. C₃×#884	C₂²	semidirect
92. C₃×#884	C₂²	semidirect
93. C₃×#884	C₂²	semidirect
94. C₃×#884	C₂²	semidirect
95. C₃×#883	C₂²	semidirect
96. C₃×#883	C₂²	semidirect
97. C₃×#883	C₂²	semidirect
98. C₃×#882	C₂²	semidirect
99. C₃×#882	C₂²	semidirect
100. C₃×#882	C₂²	semidirect
101. C₃×#882	C₂²	semidirect
102. C₃×#67⋊C₄	C₂²	semidirect
103. C₃×#67⋊C₄	C₂²	semidirect
104. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
105. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
106. C₃×#879	C₂²	semidirect
107. C₃×#878	C₂²	semidirect
108. C₃×#878	C₂²	semidirect
127. C₂×C₃×#123	D₃	semidirect
128. C₂×C₃×#123	C₂×C₃	semidirect
130. D₄×#67	C₂×C₃	semidirect
131. #5791	C₂×C₃	semidirect
132. C₂×#930	C₂×C₃	semidirect
133. #5667	C₂×C₃	semidirect
134. #5666	C₂×C₃	semidirect
135. #5665	C₂×C₃	semidirect
136. #5663	C₂×C₃	semidirect
137. #5658	C₂×C₃	semidirect
138. #5657	C₂×C₃	semidirect
139. #5654	C₂×C₃	semidirect
140. #5653	C₂×C₃	semidirect
141. #5515	C₂×C₃	semidirect
142. #5514	C₂×C₃	semidirect
143. #5510	C₂×C₃	semidirect
144. #5494	C₂×C₃	semidirect
145. #5493	C₂×C₃	semidirect
146. #5490	C₂×C₃	semidirect
147. #5490	C₂×C₃	semidirect
254. C₂³×C₃×C₄	C₂×D₃	semidirect
255. C₂³×C₃×C₄	C₂²×C₃	semidirect
256. C₂²×#67	C₂²×C₃	semidirect
257. C₂²×#67	C₂²×C₃	semidirect
258. C₂×D₃×D₄	C₂²×C₃	semidirect
259. C₂×#235	C₂²×C₃	semidirect
260. C₂×#235	C₂²×C₃	semidirect
261. C₂²×D₁₂	C₂²×C₃	semidirect
286. C₃×#123	C₂×D₃	semidirect
287. C₃×#123	C₂×D₃	semidirect
288. C₃×#123	C₂×D₃	semidirect
289. C₃×#123	C₂×D₃	semidirect
290. C₃×#123	C₂²×C₃	semidirect
291. C₃×#123	C₂²×C₃	semidirect
292. C₃×#123	C₂²×C₃	semidirect
293. C₃×#123	C₂²×C₃	semidirect
343. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
344. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
345. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
346. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
353. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
354. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
355. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
356. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
357. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
358. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
359. #953	C₂²×C₃	semidirect
360. #953	C₂²×C₃	semidirect
361. #940	C₂²×C₃	semidirect
363. #939	C₂²×C₃	semidirect
364. #938	C₂²×C₃	semidirect
366. #937	C₂²×C₃	semidirect
367. D₄×Dic₃	C₂²×C₃	semidirect
369. #930	C₂²×C₃	semidirect
370. #930	C₂²×C₃	semidirect
371. #930	C₂²×C₃	semidirect
372. #930	C₂²×C₃	semidirect
373. #930	C₂²×C₃	semidirect
374. #930	C₂²×C₃	semidirect
375. #930	C₂²×C₃	semidirect
376. #930	C₂²×C₃	semidirect
377. #930	C₂²×C₃	semidirect
378. #929	C₂²×C₃	semidirect
379. #929	C₂²×C₃	semidirect
380. C₄×#67	C₂²×C₃	semidirect
381. C₄×#67	C₂²×C₃	semidirect
382. C₄×#67	C₂²×C₃	semidirect
383. C₄×#67	C₂²×C₃	semidirect
384. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
385. #926	C₂²×C₃	semidirect
386. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
387. #924	C₂²×C₃	semidirect
388. #924	C₂²×C₃	semidirect
389. #898	C₂²×C₃	semidirect
390. #898	C₂²×C₃	semidirect
391. #898	C₂²×C₃	semidirect
392. #897	C₂²×C₃	semidirect
393. #897	C₂²×C₃	semidirect
394. #896	C₂²×C₃	semidirect
395. #895	C₂²×C₃	semidirect
396. #895	C₂²×C₃	semidirect
397. #895	C₂²×C₃	semidirect
398. #894	C₂²×C₃	semidirect
399. #894	C₂²×C₃	semidirect
400. #894	C₂²×C₃	semidirect
401. #893	C₂²×C₃	semidirect
402. #892	C₂²×C₃	semidirect
403. #890	C₂²×C₃	semidirect
404. #889	C₂²×C₃	semidirect
405. #886	C₂²×C₃	semidirect
406. #886	C₂²×C₃	semidirect
407. #885	C₂²×C₃	semidirect
408. #885	C₂²×C₃	semidirect
409. #885	C₂²×C₃	semidirect
410. #884	C₂²×C₃	semidirect
411. #884	C₂²×C₃	semidirect
412. #884	C₂²×C₃	semidirect
413. #884	C₂²×C₃	semidirect
414. #884	C₂²×C₃	semidirect
415. #883	C₂²×C₃	semidirect
416. #883	C₂²×C₃	semidirect
417. #883	C₂²×C₃	semidirect
418. #882	C₂²×C₃	semidirect
419. #882	C₂²×C₃	semidirect
420. #882	C₂²×C₃	semidirect
421. #882	C₂²×C₃	semidirect
422. #67⋊C₄	C₂²×C₃	semidirect
423. #67⋊C₄	C₂²×C₃	semidirect
424. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
425. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
426. #879	C₂²×C₃	semidirect
427. #878	C₂²×C₃	semidirect
428. #878	C₂²×C₃	semidirect
515. C₂×#123	C₃×D₃	semidirect
777. C₂³×C₄	C₂×C₃×D₃	semidirect
798. #123	C₂×C₃×D₃	semidirect
799. #123	C₂×C₃×D₃	semidirect
800. #123	C₂×C₃×D₃	semidirect
801. #123	C₂×C₃×D₃	semidirect
849. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
850. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
854. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
855. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
856. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
1226. C₃²	#3534	semidirect
1362. C₃	#86017	direct (N × H)
1363. C₃	C₃×#3534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#123	2
C₃×D₄×#67	2
C₃×#5791	2
C₂×C₃×#930	2
C₃×#5667	2
C₃×#5666	2
C₃×#5665	2
C₃×#5663	2
C₃×#5658	2
C₃×#5657	2
C₃×#5654	2
C₃×#5653	2
C₃×#5515	2
C₃×#5514	2
C₃×#5510	2
C₃×#5494	2
C₃×#5493	2
C₃×#5490	2
C₃×#3534	3
#86017	3

Subgroups — C3×#86017 #11910963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86017 #11910963