Subgroups — C₃×#87081 #11910639

Order 1152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#560	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5715	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5713	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5710	C₂	1	2	yes	maximal, complemented
5	C₃×#5708	C₂	1	2	yes	maximal, complemented
6	C₃×#5665	C₂	1	2	yes	maximal, complemented
7	C₃×#5659	C₂	1	2	yes	maximal, complemented
8	C₃×D₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5651	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5621	C₂	1	2	yes	maximal, complemented
11	C₃×#5618	C₂	1	2	yes	maximal, complemented
12	C₃×#5615	C₂	1	2	yes	maximal, complemented
13	C₃×#5613	C₂	1	2	yes	maximal, complemented
14	C₃×#5611	C₂	1	2	yes	maximal, complemented
15	C₃×#5606	C₂	1	2	yes	maximal, complemented
16	C₃×#5593	C₂	1	2	yes	maximal, complemented
17	C₃×#5591	C₂	1	2	yes	maximal, complemented
18	C₃×#5589	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5587	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3533	—	3	1	no	maximal
21	#87081	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂×C₃×#237	C₂²	1	2	yes	—
24	C₂×C₃×#237	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₃²×#127	C₂²	1	1	yes	characteristic
28	C₃²×#126	C₂²	1	2	yes	complemented
29	C₃²×#123	C₂²	1	1	yes	characteristic
30	C₃²×#123	C₂²	1	2	yes	complemented
31	C₃²×#121	C₂²	1	2	yes	complemented
32	C₃²×#121	C₂²	1	2	yes	complemented
33	C₃²×#121	C₂²	1	2	yes	complemented
34	C₃²×#120	C₂²	1	1	yes	characteristic
35	C₃²×#120	C₂²	1	2	yes	complemented
36	C₃×#953	C₂²	1	1	yes	characteristic
37	C₂×C₃×#217	C₂²	1	2	yes	complemented
38	C₃×#940	C₂²	1	1	yes	characteristic, complemented
39	C₃×#939	C₂²	1	2	yes	—
40	C₃×#939	C₂²	1	2	yes	complemented
41	C₃×#939	C₂²	1	2	yes	complemented
42	C₃×#939	C₂²	1	2	yes	complemented
43	C₃×#939	C₂²	1	2	yes	complemented
44	C₃×#938	C₂²	1	2	yes	—
45	C₃×#938	C₂²	1	2	yes	—
46	C₃×#938	C₂²	1	2	yes	complemented
47	C₃×#937	C₂²	1	2	yes	—
48	C₃×#937	C₂²	1	2	yes	—
49	C₃×#937	C₂²	1	2	yes	complemented
50	C₃×#936	C₂²	1	1	yes	characteristic
51	C₃×#936	C₂²	1	2	yes	complemented
52	C₃×#936	C₂²	1	2	yes	complemented
53	C₃×#935	C₂²	1	1	yes	characteristic
54	C₃×#935	C₂²	1	1	yes	characteristic
55	C₃×#935	C₂²	1	2	yes	complemented
56	C₃×#935	C₂²	1	2	yes	complemented
57	C₃×#935	C₂²	1	2	yes	complemented
58	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
59	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
60	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
61	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
62	C₃×#929	C₂²	1	2	yes	complemented
63	C₃×#929	C₂²	1	1	yes	characteristic, complemented
64	C₃×C₄×#67	C₂²	1	2	yes	complemented
65	C₃×C₄×#67	C₂²	1	2	yes	complemented
66	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
67	C₃×#924	C₂²	1	2	yes	complemented
68	C₃×#898	C₂²	1	2	yes	complemented
69	C₃×#897	C₂²	1	2	yes	complemented
70	C₃×#896	C₂²	1	2	yes	complemented
71	C₃×#896	C₂²	1	2	yes	complemented
72	C₃×#894	C₂²	1	2	yes	complemented
73	C₃×#892	C₂²	1	2	yes	complemented
74	C₃×#892	C₂²	1	2	yes	complemented
75	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
76	C₃×#890	C₂²	1	2	yes	complemented
77	C₃×#889	C₂²	1	2	yes	complemented
78	C₃×#889	C₂²	1	2	yes	complemented
79	C₃×#888	C₂²	1	2	yes	complemented
80	C₃×#886	C₂²	1	1	yes	characteristic
81	C₃×#886	C₂²	1	2	yes	complemented
82	C₃×#886	C₂²	1	1	yes	characteristic, complemented
83	C₃×#885	C₂²	1	2	yes	complemented
84	C₃×#885	C₂²	1	2	yes	complemented
85	C₃×#884	C₂²	1	2	yes	—
86	C₃×#883	C₂²	1	2	yes	—
87	C₃×#883	C₂²	1	2	yes	—
88	C₃×#883	C₂²	1	2	yes	—
89	C₃×#883	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	complemented
91	C₃×#67⋊C₄	C₂²	1	2	yes	—
92	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
93	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
94	C₃×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
95	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₃×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	C₃×#879	C₂²	1	2	yes	complemented
98	C₃×#879	C₂²	1	2	yes	complemented
99	C₃×#879	C₂²	1	2	yes	complemented
100	C₃×#879	C₂²	1	2	yes	complemented
101	C₃×#878	C₂²	1	2	yes	complemented
102	C₃×#878	C₂²	1	2	yes	complemented
103	C₃×#878	C₂²	1	2	yes	complemented
104	C₃×#878	C₂²	1	2	yes	complemented
105	C₃×#877	C₂²	1	2	yes	complemented
106	C₃×#875	C₂²	1	1	yes	characteristic, complemented
107	C₃×#872	C₂²	1	1	yes	characteristic, complemented
108	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
109	C₃×#563	—	3	1	no	—
110	C₃×#562	—	3	2	no	—
111	C₃×#560	—	2	1	no	—
112	C₃×#560	D₃	1	1	yes	characteristic, complemented
113	C₃×#560	C₂×C₃	1	1	yes	characteristic, complemented
114	C₃×#559	—	3	1	no	—
115	C₃×#553	—	3	2	no	—
116	C₃×#552	—	3	2	no	—
117	C₃×#551	—	3	2	no	—
118	C₃×#551	—	3	1	no	—
119	C₃×#547	—	3	2	no	—
120	C₃×#546	—	3	2	no	—
121	C₃×#542	—	3	2	no	—
122	C₃×#540	—	3	2	no	—
123	C₃×#539	—	3	2	no	—
124	C₃×#538	—	3	2	no	—
125	C₃×#538	—	3	2	no	—
126	C₃×#535	—	3	1	no	—
127	C₃×#534	—	3	1	no	—
128	C₃×#525	—	3	2	no	—
129	C₂×C₃×#123	—	3	1	no	—
130	#5715	C₂×C₃	1	1	yes	characteristic, complemented
131	#5713	C₂×C₃	1	1	yes	characteristic, complemented
132	#5710	C₂×C₃	1	2	yes	complemented
133	#5708	C₂×C₃	1	2	yes	complemented
134	#5665	C₂×C₃	1	2	yes	complemented
135	#5659	C₂×C₃	1	2	yes	complemented
136	D₃×#123	C₂×C₃	1	1	yes	characteristic, complemented
137	#5651	C₂×C₃	1	1	yes	characteristic, complemented
138	#5621	C₂×C₃	1	2	yes	complemented
139	#5618	C₂×C₃	1	2	yes	complemented
140	#5615	C₂×C₃	1	2	yes	complemented
141	#5613	C₂×C₃	1	2	yes	complemented
142	#5611	C₂×C₃	1	2	yes	complemented
143	#5606	C₂×C₃	1	2	yes	complemented
144	#5593	C₂×C₃	1	2	yes	complemented
145	#5591	C₂×C₃	1	2	yes	complemented
146	#5589	C₂×C₃	1	1	yes	characteristic, complemented
147	#5587	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
150	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
151	C₂×C₃²×D₄	C₂³	1	2	yes	—
152	C₂×C₃²×D₄	C₂³	1	2	yes	—
153	C₂×C₃²×D₄	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	C₂³	1	2	yes	—
155	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
156	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃²×D₄	C₂³	1	2	yes	—
158	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃²×C₄	C₂³	1	2	yes	—
160	C₂×C₃×#67	—	4	2	no	—
161	C₂×C₃×#67	C₂³	1	2	yes	—
162	C₂×C₃×#67	C₂³	1	2	yes	—
163	C₂×C₃×#67	C₂³	1	2	yes	—
164	C₂×C₃×#67	C₂³	1	2	yes	—
165	C₂×C₃×#67	C₂³	1	1	yes	characteristic
166	C₂×C₃×#67	C₂³	1	2	yes	—
167	C₂×C₃×#67	C₂³	1	2	yes	—
168	C₂×C₃×#67	C₂³	1	1	yes	characteristic
169	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
170	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
172	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
173	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
174	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
175	C₃×#237	—	4	4	no	—
176	C₃×#237	—	4	2	no	—
177	C₃×D₃×D₄	—	4	2	no	—
178	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄×D₃	—	4	2	no	—
180	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
184	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₃×Dic₆	C₂³	1	2	yes	—
186	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
187	C₂×C₃×Dic₆	C₂³	1	2	yes	—
188	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃²×C₄²	C₂³	1	1	yes	characteristic
199	C₃×#217	C₂³	1	2	yes	—
200	C₃×#217	C₂³	1	2	yes	—
201	C₃×#217	C₂³	1	2	yes	—
202	C₃×#217	C₂³	1	2	yes	—
203	C₃×#217	C₂³	1	2	yes	—
204	C₃×#217	C₂³	1	1	yes	characteristic
205	C₃×#217	C₂³	1	2	yes	—
206	C₃×#217	C₂³	1	2	yes	—
207	C₃×#217	C₂³	1	2	yes	—
208	C₃×#217	C₂³	1	1	yes	characteristic
209	C₃×#217	C₂³	1	2	yes	—
210	C₃×#217	C₂³	1	2	yes	—
211	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₃×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
221	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
226	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
227	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
230	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
236	C₃×C₄×Dic₃	C₂³	1	2	yes	—
237	C₃×C₄×Dic₃	C₂³	1	2	yes	—
238	C₃×C₄×Dic₃	C₂³	1	2	yes	—
239	C₃×C₄×Dic₃	C₂³	1	2	yes	—
240	#3533	—	3	1	no	Sylow
241	C₂×C₃×#41	—	3	2	no	—
242	C₂×C₃×#41	—	3	1	no	—
243	C₂²×C₃×D₄	—	3	1	no	—
244	C₂²×C₃×D₄	—	3	1	no	—
245	C₂³×C₃×C₄	—	3	1	no	—
246	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
247	C₂×#237	C₂²×C₃	1	2	yes	—
248	C₂×#237	C₂²×C₃	1	1	yes	characteristic, complemented
249	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
250	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
251	C₃×C₄⋊Q₈	—	3	2	no	—
252	C₃×#127	—	2	1	no	—
253	C₃×#127	—	3	1	no	—
254	C₃×#127	C₂×D₃	1	1	yes	characteristic
255	C₃×#127	C₂²×C₃	1	1	yes	characteristic
256	C₃×#126	—	2	2	no	—
257	C₃×#126	—	3	2	no	—
258	C₃×#126	—	3	2	no	—
259	C₃×#126	—	3	2	no	—
260	C₃×#126	—	3	2	no	—
261	C₃×#126	—	3	2	no	—
262	C₃×#126	C₂×D₃	1	2	yes	complemented
263	C₃×#126	C₂²×C₃	1	2	yes	complemented
264	C₃×#125	—	3	2	no	—
265	C₃×#125	—	3	2	no	—
266	C₃×#125	—	3	2	no	—
267	C₃×#124	—	3	2	no	—
268	C₃×#124	—	3	2	no	—
269	C₃×#124	—	3	1	no	—
270	C₃×#124	—	3	2	no	—
271	C₃×#124	—	3	2	no	—
272	C₃×#124	—	3	1	no	—
273	C₃×#123	—	2	1	no	—
274	C₃×#123	—	2	2	no	—
275	C₃×#123	—	3	1	no	—
276	C₃×#123	—	3	1	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	—	3	2	no	—
279	C₃×#123	—	3	2	no	—
280	C₃×#123	—	3	1	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	—	3	2	no	—
287	C₃×#123	—	3	2	no	—
288	C₃×#123	—	3	1	no	—
289	C₃×#123	—	3	1	no	—
290	C₃×#123	—	3	2	no	—
291	C₃×#123	C₂×D₃	1	1	yes	characteristic
292	C₃×#123	C₂×D₃	1	2	yes	complemented
293	C₃×#123	C₂²×C₃	1	1	yes	characteristic
294	C₃×#123	C₂²×C₃	1	2	yes	complemented
295	C₃×C₂²⋊Q₈	—	3	2	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×C₂²⋊Q₈	—	3	2	no	—
302	C₃×C₂²⋊Q₈	—	3	2	no	—
303	C₃×#121	—	2	2	no	—
304	C₃×#121	—	2	2	no	—
305	C₃×#121	—	2	2	no	—
306	C₃×#121	—	3	2	no	—
307	C₃×#121	—	3	2	no	—
308	C₃×#121	—	3	2	no	—
309	C₃×#121	—	3	2	no	—
310	C₃×#121	—	3	2	no	—
311	C₃×#121	—	3	2	no	—
312	C₃×#121	—	3	2	no	—
313	C₃×#121	—	3	2	no	—
314	C₃×#121	—	3	2	no	—
315	C₃×#121	C₂×D₃	1	2	yes	complemented
316	C₃×#121	C₂×D₃	1	2	yes	complemented
317	C₃×#121	C₂×D₃	1	2	yes	complemented
318	C₃×#121	C₂²×C₃	1	2	yes	complemented
319	C₃×#121	C₂²×C₃	1	2	yes	complemented
320	C₃×#121	C₂²×C₃	1	2	yes	complemented
321	C₃×#120	—	2	1	no	—
322	C₃×#120	—	2	2	no	—
323	C₃×#120	—	3	1	no	—
324	C₃×#120	—	3	2	no	—
325	C₃×#120	—	3	2	no	—
326	C₃×#120	—	3	2	no	—
327	C₃×#120	C₂×D₃	1	1	yes	characteristic
328	C₃×#120	C₂×D₃	1	2	yes	complemented
329	C₃×#120	C₂²×C₃	1	1	yes	characteristic
330	C₃×#120	C₂²×C₃	1	2	yes	complemented
331	C₃×C₄×Q₈	—	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×C₄×D₄	—	3	2	no	—
339	C₃×C₄×D₄	—	3	2	no	—
340	C₃×C₄×D₄	—	3	2	no	—
341	C₃×#117	—	3	2	no	—
342	C₃×#117	—	3	2	no	—
343	C₃×#117	—	3	2	no	—
344	C₃×#117	—	3	1	no	—
345	C₂×C₃×C₄⋊C₄	—	3	2	no	—
346	C₂×C₃×C₄⋊C₄	—	3	2	no	—
347	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
350	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
351	#953	C₂²×C₃	1	1	yes	characteristic
352	C₂×#217	C₂²×C₃	1	2	yes	complemented
353	#940	C₂²×C₃	1	1	yes	characteristic, complemented
354	#939	C₂²×C₃	1	2	yes	—
355	#939	C₂²×C₃	1	2	yes	complemented
356	#939	C₂²×C₃	1	2	yes	complemented
357	#939	C₂²×C₃	1	2	yes	complemented
358	#939	C₂²×C₃	1	2	yes	complemented
359	#938	C₂²×C₃	1	2	yes	—
360	#938	C₂²×C₃	1	2	yes	—
361	#938	C₂²×C₃	1	2	yes	complemented
362	#937	C₂²×C₃	1	2	yes	—
363	#937	C₂²×C₃	1	2	yes	—
364	#937	C₂²×C₃	1	2	yes	complemented
365	#936	C₂²×C₃	1	1	yes	characteristic
366	#936	C₂²×C₃	1	2	yes	complemented
367	#936	C₂²×C₃	1	2	yes	complemented
368	#935	C₂²×C₃	1	1	yes	characteristic
369	#935	C₂²×C₃	1	1	yes	characteristic
370	#935	C₂²×C₃	1	2	yes	complemented
371	#935	C₂²×C₃	1	2	yes	complemented
372	#935	C₂²×C₃	1	2	yes	complemented
373	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
374	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
375	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
376	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
377	#929	C₂²×C₃	1	1	yes	characteristic, complemented
378	#929	C₂²×C₃	1	2	yes	complemented
379	C₄×#67	C₂²×C₃	1	2	yes	complemented
380	C₄×#67	C₂²×C₃	1	2	yes	complemented
381	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
382	#924	C₂²×C₃	1	2	yes	complemented
383	#898	C₂²×C₃	1	2	yes	complemented
384	#897	C₂²×C₃	1	2	yes	complemented
385	#896	C₂²×C₃	1	2	yes	complemented
386	#896	C₂²×C₃	1	2	yes	complemented
387	#894	C₂²×C₃	1	2	yes	complemented
388	#892	C₂²×C₃	1	2	yes	complemented
389	#892	C₂²×C₃	1	2	yes	complemented
390	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
391	#890	C₂²×C₃	1	2	yes	complemented
392	#889	C₂²×C₃	1	2	yes	complemented
393	#889	C₂²×C₃	1	2	yes	complemented
394	#888	C₂²×C₃	1	2	yes	complemented
395	#886	C₂²×C₃	1	1	yes	characteristic
396	#886	C₂²×C₃	1	1	yes	characteristic, complemented
397	#886	C₂²×C₃	1	2	yes	complemented
398	#885	C₂²×C₃	1	2	yes	complemented
399	#885	C₂²×C₃	1	2	yes	complemented
400	#884	C₂²×C₃	1	2	yes	—
401	#883	C₂²×C₃	1	2	yes	—
402	#883	C₂²×C₃	1	2	yes	—
403	#883	C₂²×C₃	1	2	yes	—
404	#883	C₂²×C₃	1	2	yes	complemented
405	#883	C₂²×C₃	1	2	yes	complemented
406	#67⋊C₄	C₂²×C₃	1	2	yes	—
407	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
408	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
409	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
410	D₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
411	D₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
412	#879	C₂²×C₃	1	2	yes	complemented
413	#879	C₂²×C₃	1	2	yes	complemented
414	#879	C₂²×C₃	1	2	yes	complemented
415	#879	C₂²×C₃	1	2	yes	complemented
416	#878	C₂²×C₃	1	2	yes	complemented
417	#878	C₂²×C₃	1	2	yes	complemented
418	#878	C₂²×C₃	1	2	yes	complemented
419	#878	C₂²×C₃	1	2	yes	complemented
420	#877	C₂²×C₃	1	2	yes	complemented
421	#875	C₂²×C₃	1	1	yes	characteristic, complemented
422	#872	C₂²×C₃	1	1	yes	characteristic, complemented
423	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
424	C₂³×C₃²	—	4	2	no	—
425	C₂³×C₃²	—	4	1	no	—
426	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
427	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
428	C₂³×C₃²	C₂⁴	1	2	yes	—
429	C₂³×C₃²	C₂⁴	1	2	yes	—
430	C₂²×C₃×D₃	—	2	2	no	—
431	C₂²×C₃×D₃	—	2	2	no	—
432	C₂²×C₃×D₃	—	4	2	no	—
433	C₂²×C₃×D₃	—	4	2	no	—
434	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
437	C₃²×D₄	—	4	1	no	—
438	C₃²×D₄	—	4	2	no	—
439	C₃²×D₄	—	4	1	no	—
440	C₃²×D₄	—	4	2	no	—
441	C₃²×D₄	—	4	2	no	—
442	C₃²×D₄	—	4	2	no	—
443	C₃²×D₄	—	4	2	no	—
444	C₂×C₃²×C₄	—	4	1	no	—
445	C₂×C₃²×C₄	—	4	2	no	—
446	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
447	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
448	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
449	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
450	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
451	C₃×#67	—	2	4	no	—
452	C₃×#67	—	2	4	no	—
453	C₃×#67	—	4	1	no	—
454	C₃×#67	—	4	1	no	—
455	C₃×#67	—	4	2	no	—
456	C₃×#67	—	4	2	no	—
457	C₃×#67	—	4	2	no	—
458	C₃×#67	—	4	2	no	—
459	C₂×C₃×Dic₃	—	4	1	no	—
460	C₂×C₃×Dic₃	—	4	2	no	—
461	C₂×C₃×Dic₃	—	4	2	no	—
462	C₂×C₃×Dic₃	—	4	2	no	—
463	C₂×C₃×Dic₃	—	4	2	no	—
464	C₂×C₃×Dic₃	—	4	1	no	—
465	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
466	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
467	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
468	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
469	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
470	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
471	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
472	C₃×D₁₂	—	4	1	no	—
473	C₃×C₄×D₃	—	2	4	no	—
474	C₃×C₄×D₃	—	2	2	no	—
475	C₃×C₄×D₃	—	4	2	no	—
476	C₃×C₄×D₃	—	4	2	no	—
477	C₃×C₄×D₃	—	4	2	no	—
478	C₃×Dic₆	—	4	2	no	—
479	C₃×Dic₆	—	4	1	no	—
480	C₃×Dic₆	—	4	2	no	—
481	#563	—	3	1	no	—
482	#562	—	3	2	no	—
483	#560	C₃×D₃	1	1	yes	characteristic, complemented
484	#559	—	3	1	no	—
485	#553	—	3	2	no	—
486	#552	—	3	2	no	—
487	#551	—	3	2	no	—
488	#551	—	3	1	no	—
489	#547	—	3	2	no	—
490	#546	—	3	2	no	—
491	#542	—	3	2	no	—
492	#540	—	3	2	no	—
493	#539	—	3	2	no	—
494	#538	—	3	2	no	—
495	#538	—	3	2	no	—
496	#535	—	3	1	no	—
497	#534	—	3	1	no	—
498	#525	—	3	2	no	—
499	C₂×#123	—	3	1	no	—
500	C₂⁴×C₃	—	2	1	no	—
501	C₂⁴×C₃	—	3	1	no	—
502	C₂⁴×C₃	—	3	1	no	—
503	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
504	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
505	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
506	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
507	C₃×#41	—	12	4	no	—
508	C₃×#41	—	12	2	no	—
509	C₂×C₃×Q₈	—	3	2	no	—
510	C₂×C₃×Q₈	—	3	2	no	—
511	C₂×C₃×Q₈	—	3	1	no	—
512	C₂×C₃×D₄	—	2	2	no	—
513	C₂×C₃×D₄	—	2	2	no	—
514	C₂×C₃×D₄	—	2	2	no	—
515	C₂×C₃×D₄	—	2	2	no	—
516	C₂×C₃×D₄	—	2	1	no	—
517	C₂×C₃×D₄	—	2	2	no	—
518	C₂×C₃×D₄	—	2	1	no	—
519	C₂×C₃×D₄	—	3	2	no	—
520	C₂×C₃×D₄	—	3	2	no	—
521	C₂×C₃×D₄	—	3	2	no	—
522	C₂×C₃×D₄	—	3	2	no	—
523	C₂×C₃×D₄	—	3	2	no	—
524	C₂×C₃×D₄	—	3	1	no	—
525	C₂×C₃×D₄	—	3	1	no	—
526	C₂×C₃×D₄	—	3	2	no	—
527	C₂×C₃×D₄	—	3	1	no	—
528	C₂×C₃×D₄	—	12	2	no	—
529	C₂×C₃×D₄	—	12	2	no	—
530	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
531	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
532	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
533	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
534	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
535	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
536	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
537	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
538	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
539	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
540	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
541	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
544	C₂²×C₃×C₄	—	2	2	no	—
545	C₂²×C₃×C₄	—	2	1	no	—
546	C₂²×C₃×C₄	—	3	2	no	—
547	C₂²×C₃×C₄	—	3	2	no	—
548	C₂²×C₃×C₄	—	3	2	no	—
549	C₂²×C₃×C₄	—	3	2	no	—
550	C₂²×C₃×C₄	—	3	1	no	—
551	C₂²×C₃×C₄	—	3	1	no	—
552	C₂²×C₃×C₄	—	3	2	no	—
553	C₂²×C₃×C₄	—	3	1	no	—
554	C₂²×C₃×C₄	—	3	2	no	—
555	C₂²×C₃×C₄	—	3	2	no	—
556	C₂²×C₃×C₄	—	3	2	no	—
557	C₂²×C₃×C₄	—	12	2	no	—
558	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
559	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
560	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
562	C₂×#67	—	4	2	no	—
563	C₂×#67	C₂³×C₃	1	2	yes	—
564	C₂×#67	C₂³×C₃	1	2	yes	—
565	C₂×#67	C₂³×C₃	1	2	yes	—
566	C₂×#67	C₂³×C₃	1	2	yes	—
567	C₂×#67	C₂³×C₃	1	1	yes	characteristic
568	C₂×#67	C₂³×C₃	1	2	yes	—
569	C₂×#67	C₂³×C₃	1	2	yes	—
570	C₂×#67	C₂³×C₃	1	1	yes	characteristic
571	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
572	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
573	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
574	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
575	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
576	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
577	#237	—	4	4	no	—
578	#237	—	4	2	no	—
579	D₃×D₄	—	4	2	no	—
580	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₄×D₃	—	4	2	no	—
582	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
584	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
585	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
586	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
587	C₂×Dic₆	C₂³×C₃	1	2	yes	—
588	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
589	C₂×Dic₆	C₂³×C₃	1	2	yes	—
590	C₃×C₄⋊C₄	—	2	2	no	—
591	C₃×C₄⋊C₄	—	2	2	no	—
592	C₃×C₄⋊C₄	—	2	2	no	—
593	C₃×C₄⋊C₄	—	3	2	no	—
594	C₃×C₄⋊C₄	—	3	2	no	—
595	C₃×C₄⋊C₄	—	3	2	no	—
596	C₃×C₄⋊C₄	—	3	2	no	—
597	C₃×C₄⋊C₄	—	3	2	no	—
598	C₃×C₄⋊C₄	—	3	2	no	—
599	C₃×C₄⋊C₄	—	3	2	no	—
600	C₃×C₄⋊C₄	—	3	2	no	—
601	C₃×C₄⋊C₄	—	3	2	no	—
602	C₃×C₄⋊C₄	—	3	2	no	—
603	C₃×C₄⋊C₄	—	3	2	no	—
604	C₃×C₄⋊C₄	—	3	2	no	—
605	C₃×C₄⋊C₄	—	3	2	no	—
606	C₃×C₄⋊C₄	—	3	2	no	—
607	C₃×C₄⋊C₄	—	3	2	no	—
608	C₃×C₄⋊C₄	—	3	2	no	—
609	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
610	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
611	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
612	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
614	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
615	C₃×C₂²⋊C₄	—	2	2	no	—
616	C₃×C₂²⋊C₄	—	2	2	no	—
617	C₃×C₂²⋊C₄	—	2	2	no	—
618	C₃×C₂²⋊C₄	—	2	1	no	—
619	C₃×C₂²⋊C₄	—	2	2	no	—
620	C₃×C₂²⋊C₄	—	2	1	no	—
621	C₃×C₂²⋊C₄	—	2	2	no	—
622	C₃×C₂²⋊C₄	—	3	2	no	—
623	C₃×C₂²⋊C₄	—	3	2	no	—
624	C₃×C₂²⋊C₄	—	3	2	no	—
625	C₃×C₂²⋊C₄	—	3	1	no	—
626	C₃×C₂²⋊C₄	—	3	2	no	—
627	C₃×C₂²⋊C₄	—	3	1	no	—
628	C₃×C₂²⋊C₄	—	3	2	no	—
629	C₃×C₂²⋊C₄	—	3	2	no	—
630	C₃×C₂²⋊C₄	—	3	2	no	—
631	C₃×C₂²⋊C₄	—	3	2	no	—
632	C₃×C₂²⋊C₄	—	3	2	no	—
633	C₃×C₂²⋊C₄	—	3	2	no	—
634	C₃×C₂²⋊C₄	—	3	2	no	—
635	C₃×C₂²⋊C₄	—	3	2	no	—
636	C₃×C₂²⋊C₄	—	3	2	no	—
637	C₃×C₂²⋊C₄	—	3	2	no	—
638	C₃×C₂²⋊C₄	—	3	2	no	—
639	C₃×C₂²⋊C₄	—	3	2	no	—
640	C₃×C₂²⋊C₄	—	3	2	no	—
641	C₃×C₂²⋊C₄	—	3	2	no	—
642	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
643	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
644	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
645	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
646	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
647	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
648	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
649	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
652	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
653	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
655	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
656	C₃×C₄²	—	2	1	no	—
657	C₃×C₄²	—	3	1	no	—
658	C₃×C₄²	—	3	2	no	—
659	C₃×C₄²	—	3	2	no	—
660	C₃×C₄²	—	3	2	no	—
661	C₃×C₄²	—	3	2	no	—
662	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
663	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
664	#217	C₂³×C₃	1	2	yes	—
665	#217	C₂³×C₃	1	2	yes	—
666	#217	C₂³×C₃	1	2	yes	—
667	#217	C₂³×C₃	1	2	yes	—
668	#217	C₂³×C₃	1	2	yes	—
669	#217	C₂³×C₃	1	1	yes	characteristic
670	#217	C₂³×C₃	1	2	yes	—
671	#217	C₂³×C₃	1	2	yes	—
672	#217	C₂³×C₃	1	2	yes	—
673	#217	C₂³×C₃	1	1	yes	characteristic
674	#217	C₂³×C₃	1	2	yes	—
675	#217	C₂³×C₃	1	2	yes	—
676	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
677	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
678	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
679	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
680	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
681	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
682	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
683	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
684	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
685	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
686	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
687	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
688	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
689	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
690	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
691	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
692	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
693	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
694	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
695	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
696	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
697	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
698	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
699	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
700	C₄×Dic₃	C₂³×C₃	1	2	yes	—
701	C₄×Dic₃	C₂³×C₃	1	2	yes	—
702	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
703	C₄×Dic₃	C₂³×C₃	1	2	yes	—
704	C₄×Dic₃	C₂³×C₃	1	2	yes	—
705	C₂²×C₃²	—	2	2	no	—
706	C₂²×C₃²	—	2	2	no	—
707	C₂²×C₃²	—	2	1	no	—
708	C₂²×C₃²	—	2	1	no	—
709	C₂²×C₃²	—	2	2	no	—
710	C₂²×C₃²	—	2	2	no	—
711	C₂²×C₃²	—	2	2	no	—
712	C₂²×C₃²	—	2	2	no	—
713	C₂²×C₃²	—	2	2	no	—
714	C₂²×C₃²	—	2	2	no	—
715	C₂²×C₃²	—	8	2	no	—
716	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
717	C₂×C₃×D₃	—	2	2	no	—
718	C₂×C₃×D₃	—	2	1	no	—
719	C₂×C₃×D₃	—	2	1	no	—
720	C₂×C₃×D₃	—	2	2	no	—
721	C₂×C₃×D₃	—	2	2	no	—
722	C₂×C₃×D₃	—	4	4	no	—
723	C₂×C₃×D₃	—	8	2	no	—
724	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
725	C₃²×C₄	—	2	2	no	—
726	C₃²×C₄	—	2	1	no	—
727	C₃²×C₄	—	2	2	no	—
728	C₃²×C₄	—	2	2	no	—
729	C₃²×C₄	—	2	2	no	—
730	C₃×Dic₃	—	2	2	no	—
731	C₃×Dic₃	—	2	2	no	—
732	C₃×Dic₃	—	2	2	no	—
733	C₃×Dic₃	—	2	1	no	—
734	C₃×Dic₃	—	2	2	no	—
735	C₃×Dic₃	—	2	2	no	—
736	C₃×Dic₃	—	2	2	no	—
737	C₂×#41	—	3	2	no	—
738	C₂×#41	—	3	1	no	—
739	C₂²×D₄	—	3	1	no	—
740	C₂²×D₄	—	3	1	no	—
741	C₂³×C₄	—	3	1	no	—
742	C₄⋊Q₈	—	3	2	no	—
743	#127	—	3	1	no	—
744	#127	C₂×C₃×D₃	1	1	yes	characteristic
745	#126	—	3	2	no	—
746	#126	—	3	2	no	—
747	#126	—	3	2	no	—
748	#126	—	3	2	no	—
749	#126	—	3	2	no	—
750	#126	C₂×C₃×D₃	1	2	yes	complemented
751	#125	—	3	2	no	—
752	#125	—	3	2	no	—
753	#125	—	3	2	no	—
754	#124	—	3	1	no	—
755	#124	—	3	2	no	—
756	#124	—	3	2	no	—
757	#124	—	3	2	no	—
758	#124	—	3	2	no	—
759	#124	—	3	1	no	—
760	#123	—	3	1	no	—
761	#123	—	3	1	no	—
762	#123	—	3	2	no	—
763	#123	—	3	2	no	—
764	#123	—	3	2	no	—
765	#123	—	3	1	no	—
766	#123	—	3	2	no	—
767	#123	—	3	2	no	—
768	#123	—	3	2	no	—
769	#123	—	3	1	no	—
770	#123	—	3	2	no	—
771	#123	—	3	2	no	—
772	#123	—	3	1	no	—
773	#123	—	3	2	no	—
774	#123	—	3	2	no	—
775	#123	—	3	2	no	—
776	#123	C₂×C₃×D₃	1	1	yes	characteristic
777	#123	C₂×C₃×D₃	1	2	yes	complemented
778	C₂²⋊Q₈	—	3	2	no	—
779	C₂²⋊Q₈	—	3	2	no	—
780	C₂²⋊Q₈	—	3	2	no	—
781	C₂²⋊Q₈	—	3	2	no	—
782	C₂²⋊Q₈	—	3	2	no	—
783	C₂²⋊Q₈	—	3	2	no	—
784	C₂²⋊Q₈	—	3	2	no	—
785	C₂²⋊Q₈	—	3	2	no	—
786	#121	—	3	2	no	—
787	#121	—	3	2	no	—
788	#121	—	3	2	no	—
789	#121	—	3	2	no	—
790	#121	—	3	2	no	—
791	#121	—	3	2	no	—
792	#121	—	3	2	no	—
793	#121	—	3	2	no	—
794	#121	—	3	2	no	—
795	#121	C₂×C₃×D₃	1	2	yes	complemented
796	#121	C₂×C₃×D₃	1	2	yes	complemented
797	#121	C₂×C₃×D₃	1	2	yes	complemented
798	#120	—	3	1	no	—
799	#120	—	3	2	no	—
800	#120	—	3	2	no	—
801	#120	—	3	2	no	—
802	#120	C₂×C₃×D₃	1	1	yes	characteristic
803	#120	C₂×C₃×D₃	1	2	yes	complemented
804	C₄×Q₈	—	3	2	no	—
805	C₄×D₄	—	3	2	no	—
806	C₄×D₄	—	3	2	no	—
807	C₄×D₄	—	3	2	no	—
808	C₄×D₄	—	3	2	no	—
809	C₄×D₄	—	3	2	no	—
810	C₄×D₄	—	3	2	no	—
811	C₄×D₄	—	3	2	no	—
812	C₄×D₄	—	3	2	no	—
813	C₄×D₄	—	3	2	no	—
814	#117	—	3	2	no	—
815	#117	—	3	2	no	—
816	#117	—	3	2	no	—
817	#117	—	3	1	no	—
818	C₂×C₄⋊C₄	—	3	2	no	—
819	C₂×C₄⋊C₄	—	3	2	no	—
820	C₂×C₂²⋊C₄	—	3	2	no	—
821	C₂×C₂²⋊C₄	—	3	1	no	—
822	C₂×C₂²⋊C₄	—	3	2	no	—
823	C₂×C₂²⋊C₄	—	3	1	no	—
824	C₂³×C₃	—	2	1	no	—
825	C₂³×C₃	—	2	2	no	—
826	C₂³×C₃	—	2	1	no	—
827	C₂³×C₃	—	2	2	no	—
828	C₂³×C₃	—	3	1	no	—
829	C₂³×C₃	—	3	1	no	—
830	C₂³×C₃	—	3	1	no	—
831	C₂³×C₃	—	4	1	no	—
832	C₂³×C₃	—	4	1	no	—
833	C₂³×C₃	—	4	2	no	—
834	C₂³×C₃	—	4	2	no	—
835	C₂³×C₃	—	6	2	no	—
836	C₂³×C₃	—	6	2	no	—
837	C₂³×C₃	—	8	1	no	—
838	C₂³×C₃	—	8	2	no	—
839	C₂³×C₃	—	12	2	no	—
840	C₂³×C₃	—	12	2	no	—
841	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
842	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
843	C₂³×C₃	C₂³×D₃	1	2	yes	—
844	C₂³×C₃	C₂³×D₃	1	2	yes	—
845	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
846	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
847	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
848	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
849	C₂²×D₃	—	2	2	no	—
850	C₂²×D₃	—	2	2	no	—
851	C₂²×D₃	—	4	2	no	—
852	C₂²×D₃	—	4	2	no	—
853	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
854	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
855	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
856	C₃×Q₈	—	12	2	no	—
857	C₃×Q₈	—	12	2	no	—
858	C₃×Q₈	—	12	1	no	—
859	C₃×D₄	—	4	1	no	—
860	C₃×D₄	—	4	2	no	—
861	C₃×D₄	—	4	1	no	—
862	C₃×D₄	—	4	1	no	—
863	C₃×D₄	—	4	2	no	—
864	C₃×D₄	—	4	2	no	—
865	C₃×D₄	—	4	2	no	—
866	C₃×D₄	—	4	2	no	—
867	C₃×D₄	—	4	2	no	—
868	C₃×D₄	—	4	1	no	—
869	C₃×D₄	—	4	2	no	—
870	C₃×D₄	—	4	2	no	—
871	C₃×D₄	—	4	2	no	—
872	C₃×D₄	—	4	2	no	—
873	C₃×D₄	—	6	4	no	—
874	C₃×D₄	—	6	4	no	—
875	C₃×D₄	—	8	1	no	—
876	C₃×D₄	—	8	2	no	—
877	C₃×D₄	—	8	1	no	—
878	C₃×D₄	—	8	2	no	—
879	C₃×D₄	—	8	2	no	—
880	C₃×D₄	—	8	2	no	—
881	C₃×D₄	—	8	2	no	—
882	C₃×D₄	—	12	1	no	—
883	C₃×D₄	—	12	2	no	—
884	C₃×D₄	—	12	2	no	—
885	C₃×D₄	—	12	2	no	—
886	C₃×D₄	—	12	1	no	—
887	C₃×D₄	—	12	1	no	—
888	C₃×D₄	—	12	2	no	—
889	C₂×C₃×C₄	—	2	2	no	—
890	C₂×C₃×C₄	—	2	1	no	—
891	C₂×C₃×C₄	—	2	2	no	—
892	C₂×C₃×C₄	—	2	2	no	—
893	C₂×C₃×C₄	—	2	2	no	—
894	C₂×C₃×C₄	—	3	2	no	—
895	C₂×C₃×C₄	—	3	2	no	—
896	C₂×C₃×C₄	—	3	2	no	—
897	C₂×C₃×C₄	—	3	2	no	—
898	C₂×C₃×C₄	—	3	2	no	—
899	C₂×C₃×C₄	—	3	2	no	—
900	C₂×C₃×C₄	—	3	1	no	—
901	C₂×C₃×C₄	—	4	1	no	—
902	C₂×C₃×C₄	—	4	1	no	—
903	C₂×C₃×C₄	—	4	2	no	—
904	C₂×C₃×C₄	—	4	2	no	—
905	C₂×C₃×C₄	—	6	4	no	—
906	C₂×C₃×C₄	—	6	2	no	—
907	C₂×C₃×C₄	—	8	1	no	—
908	C₂×C₃×C₄	—	8	2	no	—
909	C₂×C₃×C₄	—	12	2	no	—
910	C₂×C₃×C₄	—	12	2	no	—
911	C₂×C₃×C₄	—	12	2	no	—
912	C₂×C₃×C₄	—	12	2	no	—
913	C₂×C₃×C₄	—	12	1	no	—
914	C₂×C₃×C₄	—	12	1	no	—
915	C₂×C₃×C₄	—	12	2	no	—
916	C₂×C₃×C₄	—	12	2	no	—
917	C₂×C₃×C₄	—	12	2	no	—
918	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
919	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
920	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
921	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
922	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
923	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
924	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
925	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
926	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
927	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
928	#67	—	2	4	no	—
929	#67	—	2	4	no	—
930	#67	—	4	1	no	—
931	#67	—	4	1	no	—
932	#67	—	4	2	no	—
933	#67	—	4	2	no	—
934	#67	—	4	2	no	—
935	#67	—	4	2	no	—
936	C₂×Dic₃	—	4	1	no	—
937	C₂×Dic₃	—	4	2	no	—
938	C₂×Dic₃	—	4	2	no	—
939	C₂×Dic₃	—	4	2	no	—
940	C₂×Dic₃	—	4	2	no	—
941	C₂×Dic₃	—	4	1	no	—
942	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
943	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
944	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
945	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
946	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
947	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
948	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
949	D₁₂	—	4	1	no	—
950	C₄×D₃	—	2	4	no	—
951	C₄×D₃	—	2	2	no	—
952	C₄×D₃	—	4	2	no	—
953	C₄×D₃	—	4	2	no	—
954	C₄×D₃	—	4	2	no	—
955	Dic₆	—	4	2	no	—
956	Dic₆	—	4	1	no	—
957	Dic₆	—	4	2	no	—
958	C₂×C₃²	—	4	1	no	—
959	C₂×C₃²	—	4	1	no	—
960	C₂×C₃²	—	4	2	no	—
961	C₂×C₃²	—	4	2	no	—
962	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
963	C₂×C₃²	#585	1	2	yes	—
964	C₃×D₃	—	2	2	no	—
965	C₃×D₃	—	4	1	no	—
966	C₃×D₃	—	4	1	no	—
967	C₂⁴	—	3	1	no	—
968	C₂⁴	—	3	1	no	—
969	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
970	#41	—	12	4	no	—
971	#41	—	12	2	no	—
972	C₂×Q₈	—	3	2	no	—
973	C₂×Q₈	—	3	2	no	—
974	C₂×Q₈	—	3	1	no	—
975	C₂×D₄	—	3	2	no	—
976	C₂×D₄	—	3	2	no	—
977	C₂×D₄	—	3	2	no	—
978	C₂×D₄	—	3	2	no	—
979	C₂×D₄	—	3	2	no	—
980	C₂×D₄	—	3	1	no	—
981	C₂×D₄	—	3	1	no	—
982	C₂×D₄	—	3	2	no	—
983	C₂×D₄	—	3	1	no	—
984	C₂×D₄	—	12	2	no	—
985	C₂×D₄	—	12	2	no	—
986	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
987	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
988	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
989	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
990	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
991	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
992	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
993	C₂²×C₄	—	3	2	no	—
994	C₂²×C₄	—	3	2	no	—
995	C₂²×C₄	—	3	2	no	—
996	C₂²×C₄	—	3	2	no	—
997	C₂²×C₄	—	3	1	no	—
998	C₂²×C₄	—	3	1	no	—
999	C₂²×C₄	—	3	2	no	—
1000	C₂²×C₄	—	3	1	no	—
1001	C₂²×C₄	—	3	2	no	—
1002	C₂²×C₄	—	3	2	no	—
1003	C₂²×C₄	—	3	2	no	—
1004	C₂²×C₄	—	12	2	no	—
1005	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1006	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1007	C₄⋊C₄	—	3	2	no	—
1008	C₄⋊C₄	—	3	2	no	—
1009	C₄⋊C₄	—	3	2	no	—
1010	C₄⋊C₄	—	3	2	no	—
1011	C₄⋊C₄	—	3	2	no	—
1012	C₄⋊C₄	—	3	2	no	—
1013	C₄⋊C₄	—	3	2	no	—
1014	C₄⋊C₄	—	3	2	no	—
1015	C₄⋊C₄	—	3	2	no	—
1016	C₄⋊C₄	—	3	2	no	—
1017	C₄⋊C₄	—	3	2	no	—
1018	C₄⋊C₄	—	3	2	no	—
1019	C₄⋊C₄	—	3	2	no	—
1020	C₄⋊C₄	—	3	2	no	—
1021	C₄⋊C₄	—	3	2	no	—
1022	C₄⋊C₄	—	3	2	no	—
1023	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1024	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1025	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1026	C₂²⋊C₄	—	3	2	no	—
1027	C₂²⋊C₄	—	3	2	no	—
1028	C₂²⋊C₄	—	3	2	no	—
1029	C₂²⋊C₄	—	3	1	no	—
1030	C₂²⋊C₄	—	3	2	no	—
1031	C₂²⋊C₄	—	3	1	no	—
1032	C₂²⋊C₄	—	3	2	no	—
1033	C₂²⋊C₄	—	3	2	no	—
1034	C₂²⋊C₄	—	3	2	no	—
1035	C₂²⋊C₄	—	3	2	no	—
1036	C₂²⋊C₄	—	3	2	no	—
1037	C₂²⋊C₄	—	3	2	no	—
1038	C₂²⋊C₄	—	3	2	no	—
1039	C₂²⋊C₄	—	3	2	no	—
1040	C₂²⋊C₄	—	3	2	no	—
1041	C₂²⋊C₄	—	3	2	no	—
1042	C₂²⋊C₄	—	3	2	no	—
1043	C₂²⋊C₄	—	3	2	no	—
1044	C₂²⋊C₄	—	3	2	no	—
1045	C₂²⋊C₄	—	3	2	no	—
1046	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1047	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1048	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1049	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1050	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1051	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1052	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1053	C₄²	—	3	1	no	—
1054	C₄²	—	3	2	no	—
1055	C₄²	—	3	2	no	—
1056	C₄²	—	3	2	no	—
1057	C₄²	—	3	2	no	—
1058	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1059	C₂²×C₃	—	2	1	no	—
1060	C₂²×C₃	—	2	2	no	—
1061	C₂²×C₃	—	2	2	no	—
1062	C₂²×C₃	—	2	1	no	—
1063	C₂²×C₃	—	2	2	no	—
1064	C₂²×C₃	—	2	2	no	—
1065	C₂²×C₃	—	2	2	no	—
1066	C₂²×C₃	—	2	2	no	—
1067	C₂²×C₃	—	2	2	no	—
1068	C₂²×C₃	—	2	2	no	—
1069	C₂²×C₃	—	2	2	no	—
1070	C₂²×C₃	—	2	2	no	—
1071	C₂²×C₃	—	2	1	no	—
1072	C₂²×C₃	—	2	1	no	—
1073	C₂²×C₃	—	2	2	no	—
1074	C₂²×C₃	—	2	2	no	—
1075	C₂²×C₃	—	2	2	no	—
1076	C₂²×C₃	—	2	2	no	—
1077	C₂²×C₃	—	2	2	no	—
1078	C₂²×C₃	—	2	2	no	—
1079	C₂²×C₃	—	2	1	no	—
1080	C₂²×C₃	—	3	2	no	—
1081	C₂²×C₃	—	4	1	no	—
1082	C₂²×C₃	—	4	2	no	—
1083	C₂²×C₃	—	4	2	no	—
1084	C₂²×C₃	—	4	2	no	—
1085	C₂²×C₃	—	4	2	no	—
1086	C₂²×C₃	—	4	2	no	—
1087	C₂²×C₃	—	4	1	no	—
1088	C₂²×C₃	—	4	2	no	—
1089	C₂²×C₃	—	4	2	no	—
1090	C₂²×C₃	—	4	2	no	—
1091	C₂²×C₃	—	6	2	no	—
1092	C₂²×C₃	—	6	1	no	—
1093	C₂²×C₃	—	6	1	no	—
1094	C₂²×C₃	—	6	2	no	—
1095	C₂²×C₃	—	6	2	no	—
1096	C₂²×C₃	—	8	2	no	—
1097	C₂²×C₃	—	8	2	no	—
1098	C₂²×C₃	—	8	4	no	—
1099	C₂²×C₃	—	12	4	no	—
1100	C₂²×C₃	—	24	2	no	—
1101	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1102	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1103	C₂×D₃	—	2	2	no	—
1104	C₂×D₃	—	2	1	no	—
1105	C₂×D₃	—	2	1	no	—
1106	C₂×D₃	—	2	2	no	—
1107	C₂×D₃	—	2	2	no	—
1108	C₂×D₃	—	4	4	no	—
1109	C₂×D₃	—	8	2	no	—
1110	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
1111	C₃×C₄	—	2	2	no	—
1112	C₃×C₄	—	2	1	no	—
1113	C₃×C₄	—	2	2	no	—
1114	C₃×C₄	—	2	2	no	—
1115	C₃×C₄	—	2	2	no	—
1116	C₃×C₄	—	2	2	no	—
1117	C₃×C₄	—	2	1	no	—
1118	C₃×C₄	—	2	2	no	—
1119	C₃×C₄	—	2	2	no	—
1120	C₃×C₄	—	2	2	no	—
1121	C₃×C₄	—	4	2	no	—
1122	C₃×C₄	—	4	2	no	—
1123	C₃×C₄	—	4	2	no	—
1124	C₃×C₄	—	4	1	no	—
1125	C₃×C₄	—	4	2	no	—
1126	C₃×C₄	—	6	2	no	—
1127	C₃×C₄	—	6	1	no	—
1128	C₃×C₄	—	6	2	no	—
1129	C₃×C₄	—	6	2	no	—
1130	C₃×C₄	—	6	2	no	—
1131	C₃×C₄	—	6	2	no	—
1132	C₃×C₄	—	6	2	no	—
1133	Dic₃	—	2	2	no	—
1134	Dic₃	—	2	2	no	—
1135	Dic₃	—	2	2	no	—
1136	Dic₃	—	2	1	no	—
1137	Dic₃	—	2	2	no	—
1138	Dic₃	—	2	2	no	—
1139	Dic₃	—	2	2	no	—
1140	C₃²	#3533	1	1	yes	characteristic, complemented, Sylow
1141	C₂³	—	3	1	no	—
1142	C₂³	—	3	1	no	—
1143	C₂³	—	3	1	no	—
1144	C₂³	—	4	1	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	6	2	no	—
1147	C₂³	—	6	2	no	—
1148	C₂³	—	12	2	no	—
1149	C₂³	—	12	2	no	—
1150	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1151	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1152	C₂³	C₂³×C₃×D₃	1	2	yes	—
1153	C₂³	C₂³×C₃×D₃	1	2	yes	—
1154	Q₈	—	12	2	no	—
1155	Q₈	—	12	1	no	—
1156	Q₈	—	12	2	no	—
1157	D₄	—	4	1	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	1	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	2	no	—
1164	D₄	—	6	4	no	—
1165	D₄	—	6	4	no	—
1166	D₄	—	12	1	no	—
1167	D₄	—	12	1	no	—
1168	D₄	—	12	1	no	—
1169	D₄	—	12	2	no	—
1170	D₄	—	12	2	no	—
1171	D₄	—	12	2	no	—
1172	D₄	—	12	2	no	—
1173	C₂×C₄	—	3	2	no	—
1174	C₂×C₄	—	3	2	no	—
1175	C₂×C₄	—	3	2	no	—
1176	C₂×C₄	—	3	2	no	—
1177	C₂×C₄	—	3	2	no	—
1178	C₂×C₄	—	3	2	no	—
1179	C₂×C₄	—	3	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	6	4	no	—
1183	C₂×C₄	—	6	2	no	—
1184	C₂×C₄	—	12	2	no	—
1185	C₂×C₄	—	12	2	no	—
1186	C₂×C₄	—	12	2	no	—
1187	C₂×C₄	—	12	1	no	—
1188	C₂×C₄	—	12	1	no	—
1189	C₂×C₄	—	12	2	no	—
1190	C₂×C₄	—	12	2	no	—
1191	C₂×C₄	—	12	2	no	—
1192	C₂×C₄	—	12	2	no	—
1193	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1194	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1195	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1196	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1197	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1198	C₂×C₃	—	2	1	no	—
1199	C₂×C₃	—	2	2	no	—
1200	C₂×C₃	—	4	1	no	—
1201	C₂×C₃	—	4	2	no	—
1202	C₂×C₃	—	4	1	no	—
1203	C₂×C₃	—	4	2	no	—
1204	C₂×C₃	—	4	1	no	—
1205	C₂×C₃	—	4	1	no	—
1206	C₂×C₃	—	4	2	no	—
1207	C₂×C₃	—	4	2	no	—
1208	C₂×C₃	—	6	2	no	—
1209	C₂×C₃	—	8	1	no	—
1210	C₂×C₃	—	8	2	no	—
1211	C₂×C₃	—	8	1	no	—
1212	C₂×C₃	—	8	2	no	—
1213	C₂×C₃	—	12	1	no	—
1214	C₂×C₃	—	12	1	no	—
1215	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂×C₃	#5966	1	2	yes	—
1217	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1218	C₂×C₃	C₃×#585	1	2	yes	—
1219	D₃	—	2	2	no	—
1220	D₃	—	4	1	no	—
1221	D₃	—	4	1	no	—
1222	C₂²	—	2	1	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	2	no	—
1228	C₂²	—	2	2	no	—
1229	C₂²	—	2	2	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	2	no	—
1232	C₂²	—	3	2	no	—
1233	C₂²	—	6	2	no	—
1234	C₂²	—	6	1	no	—
1235	C₂²	—	6	1	no	—
1236	C₂²	—	6	2	no	—
1237	C₂²	—	6	2	no	—
1238	C₂²	—	8	2	no	—
1239	C₂²	—	12	4	no	—
1240	C₂²	—	24	2	no	—
1241	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1242	C₄	—	2	2	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	6	2	no	—
1248	C₄	—	6	1	no	—
1249	C₄	—	6	2	no	—
1250	C₄	—	6	2	no	—
1251	C₄	—	6	2	no	—
1252	C₄	—	6	2	no	—
1253	C₄	—	6	2	no	—
1254	C₃	—	2	1	no	—
1255	C₃	#87081	1	1	yes	characteristic, direct product factor
1256	C₃	C₃×#3533	1	1	yes	characteristic, complemented
1257	C₂	—	4	1	no	—
1258	C₂	—	4	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	2	no	—
1261	C₂	—	6	2	no	—
1262	C₂	—	12	1	no	—
1263	C₂	—	12	1	no	—
1264	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1265	C₂	C₃×#5966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#560	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#560	D₃
hypocenter	C₃	C₃×#3533
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#560

Complements

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

N	H ≅ G/N	type
1. C₃²×#560	C₂	semidirect
2. C₃×#5715	C₂	semidirect
3. C₃×#5713	C₂	semidirect
4. C₃×#5710	C₂	semidirect
5. C₃×#5708	C₂	semidirect
6. C₃×#5665	C₂	semidirect
7. C₃×#5659	C₂	semidirect
8. C₃×D₃×#123	C₂	semidirect
9. C₃×#5651	C₂	semidirect
10. C₃×#5621	C₂	semidirect
11. C₃×#5618	C₂	semidirect
12. C₃×#5615	C₂	semidirect
13. C₃×#5613	C₂	semidirect
14. C₃×#5611	C₂	semidirect
15. C₃×#5606	C₂	semidirect
16. C₃×#5593	C₂	semidirect
17. C₃×#5591	C₂	semidirect
18. C₃×#5589	C₂	semidirect
19. C₃×#5587	C₂	semidirect
21. #87081	C₃	direct (N × H)
24. C₂×C₃×#237	C₂²	semidirect
26. C₂²×C₃×C₄×D₃	C₂²	semidirect
28. C₃²×#126	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×#121	C₂²	semidirect
32. C₃²×#121	C₂²	semidirect
33. C₃²×#121	C₂²	semidirect
35. C₃²×#120	C₂²	semidirect
37. C₂×C₃×#217	C₂²	semidirect
38. C₃×#940	C₂²	semidirect
40. C₃×#939	C₂²	semidirect
41. C₃×#939	C₂²	semidirect
42. C₃×#939	C₂²	semidirect
43. C₃×#939	C₂²	semidirect
46. C₃×#938	C₂²	semidirect
49. C₃×#937	C₂²	semidirect
51. C₃×#936	C₂²	semidirect
52. C₃×#936	C₂²	semidirect
55. C₃×#935	C₂²	semidirect
56. C₃×#935	C₂²	semidirect
57. C₃×#935	C₂²	semidirect
58. C₃×D₄×Dic₃	C₂²	semidirect
59. C₃×D₄×Dic₃	C₂²	semidirect
60. C₃×D₄×Dic₃	C₂²	semidirect
61. C₃×D₄×Dic₃	C₂²	semidirect
62. C₃×#929	C₂²	semidirect
63. C₃×#929	C₂²	semidirect
64. C₃×C₄×#67	C₂²	semidirect
65. C₃×C₄×#67	C₂²	semidirect
66. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
67. C₃×#924	C₂²	semidirect
68. C₃×#898	C₂²	semidirect
69. C₃×#897	C₂²	semidirect
70. C₃×#896	C₂²	semidirect
71. C₃×#896	C₂²	semidirect
72. C₃×#894	C₂²	semidirect
73. C₃×#892	C₂²	semidirect
74. C₃×#892	C₂²	semidirect
75. C₃×D₃×C₄⋊C₄	C₂²	semidirect
76. C₃×#890	C₂²	semidirect
77. C₃×#889	C₂²	semidirect
78. C₃×#889	C₂²	semidirect
79. C₃×#888	C₂²	semidirect
81. C₃×#886	C₂²	semidirect
82. C₃×#886	C₂²	semidirect
83. C₃×#885	C₂²	semidirect
84. C₃×#885	C₂²	semidirect
89. C₃×#883	C₂²	semidirect
90. C₃×#883	C₂²	semidirect
92. C₃×#67⋊C₄	C₂²	semidirect
93. C₃×#67⋊C₄	C₂²	semidirect
96. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
97. C₃×#879	C₂²	semidirect
98. C₃×#879	C₂²	semidirect
99. C₃×#879	C₂²	semidirect
100. C₃×#879	C₂²	semidirect
101. C₃×#878	C₂²	semidirect
102. C₃×#878	C₂²	semidirect
103. C₃×#878	C₂²	semidirect
104. C₃×#878	C₂²	semidirect
105. C₃×#877	C₂²	semidirect
106. C₃×#875	C₂²	semidirect
107. C₃×#872	C₂²	semidirect
108. C₃×C₄×Dic₆	C₂²	semidirect
112. C₃×#560	D₃	semidirect
113. C₃×#560	C₂×C₃	semidirect
130. #5715	C₂×C₃	semidirect
131. #5713	C₂×C₃	semidirect
132. #5710	C₂×C₃	semidirect
133. #5708	C₂×C₃	semidirect
134. #5665	C₂×C₃	semidirect
135. #5659	C₂×C₃	semidirect
136. D₃×#123	C₂×C₃	semidirect
137. #5651	C₂×C₃	semidirect
138. #5621	C₂×C₃	semidirect
139. #5618	C₂×C₃	semidirect
140. #5615	C₂×C₃	semidirect
141. #5613	C₂×C₃	semidirect
142. #5611	C₂×C₃	semidirect
143. #5606	C₂×C₃	semidirect
144. #5593	C₂×C₃	semidirect
145. #5591	C₂×C₃	semidirect
146. #5589	C₂×C₃	semidirect
147. #5587	C₂×C₃	semidirect
248. C₂×#237	C₂²×C₃	semidirect
250. C₂²×C₄×D₃	C₂²×C₃	semidirect
262. C₃×#126	C₂×D₃	semidirect
263. C₃×#126	C₂²×C₃	semidirect
292. C₃×#123	C₂×D₃	semidirect
294. C₃×#123	C₂²×C₃	semidirect
315. C₃×#121	C₂×D₃	semidirect
316. C₃×#121	C₂×D₃	semidirect
317. C₃×#121	C₂×D₃	semidirect
318. C₃×#121	C₂²×C₃	semidirect
319. C₃×#121	C₂²×C₃	semidirect
320. C₃×#121	C₂²×C₃	semidirect
328. C₃×#120	C₂×D₃	semidirect
330. C₃×#120	C₂²×C₃	semidirect
352. C₂×#217	C₂²×C₃	semidirect
353. #940	C₂²×C₃	semidirect
355. #939	C₂²×C₃	semidirect
356. #939	C₂²×C₃	semidirect
357. #939	C₂²×C₃	semidirect
358. #939	C₂²×C₃	semidirect
361. #938	C₂²×C₃	semidirect
364. #937	C₂²×C₃	semidirect
366. #936	C₂²×C₃	semidirect
367. #936	C₂²×C₃	semidirect
370. #935	C₂²×C₃	semidirect
371. #935	C₂²×C₃	semidirect
372. #935	C₂²×C₃	semidirect
373. D₄×Dic₃	C₂²×C₃	semidirect
374. D₄×Dic₃	C₂²×C₃	semidirect
375. D₄×Dic₃	C₂²×C₃	semidirect
376. D₄×Dic₃	C₂²×C₃	semidirect
377. #929	C₂²×C₃	semidirect
378. #929	C₂²×C₃	semidirect
379. C₄×#67	C₂²×C₃	semidirect
380. C₄×#67	C₂²×C₃	semidirect
381. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
382. #924	C₂²×C₃	semidirect
383. #898	C₂²×C₃	semidirect
384. #897	C₂²×C₃	semidirect
385. #896	C₂²×C₃	semidirect
386. #896	C₂²×C₃	semidirect
387. #894	C₂²×C₃	semidirect
388. #892	C₂²×C₃	semidirect
389. #892	C₂²×C₃	semidirect
390. D₃×C₄⋊C₄	C₂²×C₃	semidirect
391. #890	C₂²×C₃	semidirect
392. #889	C₂²×C₃	semidirect
393. #889	C₂²×C₃	semidirect
394. #888	C₂²×C₃	semidirect
396. #886	C₂²×C₃	semidirect
397. #886	C₂²×C₃	semidirect
398. #885	C₂²×C₃	semidirect
399. #885	C₂²×C₃	semidirect
404. #883	C₂²×C₃	semidirect
405. #883	C₂²×C₃	semidirect
407. #67⋊C₄	C₂²×C₃	semidirect
408. #67⋊C₄	C₂²×C₃	semidirect
411. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
412. #879	C₂²×C₃	semidirect
413. #879	C₂²×C₃	semidirect
414. #879	C₂²×C₃	semidirect
415. #879	C₂²×C₃	semidirect
416. #878	C₂²×C₃	semidirect
417. #878	C₂²×C₃	semidirect
418. #878	C₂²×C₃	semidirect
419. #878	C₂²×C₃	semidirect
420. #877	C₂²×C₃	semidirect
421. #875	C₂²×C₃	semidirect
422. #872	C₂²×C₃	semidirect
423. C₄×Dic₆	C₂²×C₃	semidirect
483. #560	C₃×D₃	semidirect
750. #126	C₂×C₃×D₃	semidirect
777. #123	C₂×C₃×D₃	semidirect
795. #121	C₂×C₃×D₃	semidirect
796. #121	C₂×C₃×D₃	semidirect
797. #121	C₂×C₃×D₃	semidirect
803. #120	C₂×C₃×D₃	semidirect
1140. C₃²	#3533	semidirect
1255. C₃	#87081	direct (N × H)
1256. C₃	C₃×#3533	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#560	2
C₃×#5715	2
C₃×#5713	2
C₃×#5710	2
C₃×#5708	2
C₃×#5665	2
C₃×#5659	2
C₃×D₃×#123	2
C₃×#5651	2
C₃×#5621	2
C₃×#5618	2
C₃×#5615	2
C₃×#5613	2
C₃×#5611	2
C₃×#5606	2
C₃×#5593	2
C₃×#5591	2
C₃×#5589	2
C₃×#5587	2
C₃×#3533	3
#87081	3

Subgroups — C3×#87081 #11910639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87081 #11910639