Subgroups — C₃×#86041 #11904588

Order 1152.

3481 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5833	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5654	C₂	1	4	yes	maximal, complemented
7	C₃×#5629	C₂	1	2	yes	maximal, complemented
8	C₃×#5627	C₂	1	2	yes	maximal, complemented
9	C₃×#5607	C₂	1	2	yes	maximal, complemented
10	C₃×D₃×#121	C₂	1	2	yes	maximal, complemented
11	C₃×#5590	C₂	1	4	yes	maximal, complemented
12	C₃×#5553	C₂	1	2	yes	maximal, complemented
13	C₃×#5552	C₂	1	2	yes	maximal, complemented
14	C₃×#5550	C₂	1	2	yes	maximal, complemented
15	C₃×D₄×D₁₂	C₂	1	2	yes	maximal, complemented
16	C₃×#5525	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5523	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3488	—	3	1	no	maximal
19	#86041	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×#67	C₂²	1	2	yes	complemented
23	C₂²×C₃×#67	C₂²	1	2	yes	complemented
24	C₃×#1009	—	2	8	no	—
25	C₂×C₃×#239	C₂²	1	2	yes	complemented
26	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
27	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
28	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
29	C₂×C₃×#235	—	2	8	no	—
30	C₂×C₃×#235	C₂²	1	1	yes	characteristic
31	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#235	C₂²	1	2	yes	complemented
34	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#235	C₂²	1	2	yes	complemented
36	C₂×C₃×#235	C₂²	1	2	yes	complemented
37	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
40	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
41	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
42	C₃²×#123	C₂²	1	2	yes	complemented
43	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
46	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
47	C₃²×#120	C₂²	1	2	yes	complemented
48	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
49	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
50	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
51	C₃×#946	C₂²	1	2	yes	complemented
52	C₃×#940	C₂²	1	4	yes	complemented
53	C₃×#939	C₂²	1	4	yes	complemented
54	C₃×#939	C₂²	1	4	yes	complemented
55	C₃×#938	C₂²	1	2	yes	complemented
56	C₃×#937	C₂²	1	4	yes	complemented
57	C₃×#930	C₂²	1	2	yes	complemented
58	C₃×#930	C₂²	1	2	yes	complemented
59	C₃×#930	C₂²	1	2	yes	complemented
60	C₃×#930	C₂²	1	2	yes	complemented
61	C₃×#930	C₂²	1	2	yes	complemented
62	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
63	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
64	C₃×#924	C₂²	1	2	yes	complemented
65	C₃×#896	C₂²	1	4	yes	complemented
66	C₃×#895	C₂²	1	2	yes	complemented
67	C₃×#895	C₂²	1	2	yes	complemented
68	C₃×#895	C₂²	1	4	yes	complemented
69	C₃×#894	C₂²	1	4	yes	complemented
70	C₃×#893	C₂²	1	4	yes	complemented
71	C₃×#892	C₂²	1	2	yes	complemented
72	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₃×#885	C₂²	1	4	yes	complemented
74	C₃×#884	C₂²	1	4	yes	complemented
75	C₃×#884	C₂²	1	4	yes	complemented
76	C₃×#884	C₂²	1	4	yes	complemented
77	C₃×#882	C₂²	1	4	yes	complemented
78	C₃×#882	C₂²	1	4	yes	complemented
79	C₃×#882	C₂²	1	4	yes	complemented
80	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
81	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
82	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₃×#875	C₂²	1	2	yes	complemented
84	C₃×#874	C₂²	1	2	yes	complemented
85	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
86	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
87	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
88	C₂²×C₃×#41	—	3	1	no	—
89	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂²×#235	C₂×C₃	1	1	yes	characteristic, complemented
91	C₃×#550	—	3	2	no	—
92	C₃×#548	—	3	2	no	—
93	C₃×#546	—	3	4	no	—
94	C₃×#546	—	3	2	no	—
95	C₃×D₄²	—	3	4	no	—
96	C₃×D₄²	—	3	2	no	—
97	C₃×#537	—	3	1	no	—
98	C₃×#537	—	3	2	no	—
99	C₃×#535	—	3	2	no	—
100	C₃×#535	—	3	1	no	—
101	C₃×#525	—	2	1	no	—
102	C₃×#525	—	3	2	no	—
103	C₃×#525	D₃	1	1	yes	characteristic, complemented
104	C₃×#525	C₂×C₃	1	1	yes	characteristic, complemented
105	C₂×C₃×#121	—	3	1	no	—
106	C₂×C₃×#121	—	3	2	no	—
107	C₃×#520	—	3	1	no	—
108	#5833	C₂×C₃	1	1	yes	characteristic, complemented
109	C₂×#930	C₂×C₃	1	1	yes	characteristic, complemented
110	#5654	C₂×C₃	1	4	yes	complemented
111	#5629	C₂×C₃	1	2	yes	complemented
112	#5627	C₂×C₃	1	2	yes	complemented
113	#5607	C₂×C₃	1	2	yes	complemented
114	D₃×#121	C₂×C₃	1	2	yes	complemented
115	#5590	C₂×C₃	1	4	yes	complemented
116	#5553	C₂×C₃	1	2	yes	complemented
117	#5552	C₂×C₃	1	2	yes	complemented
118	#5550	C₂×C₃	1	2	yes	complemented
119	D₄×D₁₂	C₂×C₃	1	2	yes	complemented
120	#5525	C₂×C₃	1	1	yes	characteristic, complemented
121	#5523	C₂×C₃	1	1	yes	characteristic, complemented
122	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
123	C₂³×C₃×D₃	C₂³	1	2	yes	—
124	C₂³×C₃×D₃	C₂³	1	4	yes	—
125	C₂³×C₃×D₃	C₂³	1	2	yes	—
126	C₃²×#41	—	2	4	no	—
127	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₃²×D₄	C₂³	1	2	yes	—
130	C₂×C₃²×D₄	C₂³	1	2	yes	—
131	C₂×C₃²×D₄	C₂³	1	2	yes	—
132	C₂²×C₃²×C₄	—	2	4	no	—
133	C₂²×C₃²×C₄	C₂³	1	2	yes	—
134	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
135	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
136	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
137	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
138	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×#67	—	2	8	no	—
141	C₂×C₃×#67	—	4	4	no	—
142	C₂×C₃×#67	C₂³	1	4	yes	—
143	C₂×C₃×#67	C₂³	1	2	yes	—
144	C₂×C₃×#67	C₂³	1	2	yes	—
145	C₂×C₃×#67	C₂³	1	2	yes	—
146	C₂×C₃×#67	C₂³	1	4	yes	—
147	C₂×C₃×#67	C₂³	1	4	yes	—
148	C₂×C₃×#67	C₂³	1	4	yes	—
149	C₂×C₃×#67	C₂³	1	2	yes	—
150	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
151	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
152	C₃×#239	—	2	8	no	—
153	C₃×D₃×D₄	—	2	16	no	—
154	C₃×D₃×D₄	—	2	8	no	—
155	C₃×D₃×D₄	—	4	8	no	—
156	C₃×#235	—	2	4	no	—
157	C₃×#235	—	2	8	no	—
158	C₃×#235	—	2	4	no	—
159	C₃×#235	—	2	8	no	—
160	C₃×#235	—	2	4	no	—
161	C₃×#235	—	2	8	no	—
162	C₃×#235	D₄	1	8	yes	complemented
163	C₂×C₃×D₁₂	—	2	4	no	—
164	C₂×C₃×D₁₂	—	2	4	no	—
165	C₂×C₃×D₁₂	—	2	8	no	—
166	C₂×C₃×D₁₂	C₂³	1	2	yes	—
167	C₂×C₃×D₁₂	C₂³	1	4	yes	—
168	C₂×C₃×D₁₂	C₂³	1	2	yes	—
169	C₂×C₃×D₁₂	C₂³	1	2	yes	—
170	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×C₃×D₁₂	C₂³	1	4	yes	—
172	C₂×C₃×D₁₂	C₂³	1	4	yes	—
173	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄×D₃	—	2	8	no	—
175	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
176	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
177	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
179	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
180	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₃×Dic₆	—	2	4	no	—
182	C₂×C₃×Dic₆	C₂³	1	2	yes	—
183	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
185	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₂²⋊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×C₄²	C₂³	1	2	yes	—
195	C₃×#217	C₂³	1	4	yes	—
196	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
197	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
198	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
199	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
200	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
201	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
202	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
203	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
204	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
205	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
206	C₃×C₄×Dic₃	C₂³	1	4	yes	—
207	#3488	—	3	1	no	Sylow
208	C₃×H(5,𝔽₂)	—	6	8	no	—
209	C₂×C₃×#41	—	2	1	no	—
210	C₂×C₃×#41	—	3	2	no	—
211	C₂×C₃×#41	—	3	1	no	—
212	C₂×C₃×#41	—	3	2	no	—
213	C₂×C₃×#41	—	3	1	no	—
214	C₂×C₃×#41	—	3	1	no	—
215	C₂×C₃×#41	—	3	2	no	—
216	C₂×C₃×#41	—	3	1	no	—
217	C₂×C₃×#41	—	3	2	no	—
218	C₂×C₃×#41	—	6	8	no	—
219	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
220	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₂²×C₃×Q₈	—	3	1	no	—
222	C₂²×C₃×D₄	—	3	2	no	—
223	C₂²×C₃×D₄	—	3	2	no	—
224	C₂²×C₃×D₄	—	3	2	no	—
225	C₂²×C₃×D₄	—	3	4	no	—
226	C₂²×C₃×D₄	—	3	4	no	—
227	C₂²×C₃×D₄	—	3	1	no	—
228	C₂²×C₃×D₄	—	3	1	no	—
229	C₂²×C₃×D₄	—	3	2	no	—
230	C₂³×C₃×C₄	—	2	1	no	—
231	C₂³×C₃×C₄	—	3	2	no	—
232	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
233	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
234	C₂²×#67	C₂²×C₃	1	2	yes	complemented
235	C₂²×#67	C₂²×C₃	1	2	yes	complemented
236	#1009	—	2	8	no	—
237	C₂×#239	C₂²×C₃	1	2	yes	complemented
238	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
239	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
240	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
241	C₂×#235	—	2	8	no	—
242	C₂×#235	C₂²×C₃	1	1	yes	characteristic
243	C₂×#235	C₂²×C₃	1	2	yes	complemented
244	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
245	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
246	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₂×#235	C₂²×C₃	1	2	yes	complemented
248	C₂×#235	C₂²×C₃	1	2	yes	complemented
249	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
251	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
252	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
253	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
254	C₃×#127	—	3	4	no	—
255	C₃×#127	—	3	2	no	—
256	C₃×#124	—	3	4	no	—
257	C₃×#124	—	3	2	no	—
258	C₃×#123	—	2	2	no	—
259	C₃×#123	—	3	4	no	—
260	C₃×#123	C₂×D₃	1	2	yes	complemented
261	C₃×#123	C₂²×C₃	1	2	yes	complemented
262	C₃×C₂²⋊Q₈	—	2	1	no	—
263	C₃×C₂²⋊Q₈	—	2	1	no	—
264	C₃×C₂²⋊Q₈	—	3	2	no	—
265	C₃×C₂²⋊Q₈	—	3	2	no	—
266	C₃×C₂²⋊Q₈	—	3	4	no	—
267	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
268	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
269	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
270	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
271	C₃×#121	—	2	1	no	—
272	C₃×#121	—	2	1	no	—
273	C₃×#121	—	3	2	no	—
274	C₃×#121	—	3	4	no	—
275	C₃×#121	—	3	4	no	—
276	C₃×#121	—	3	2	no	—
277	C₃×#121	—	3	2	no	—
278	C₃×#121	—	3	2	no	—
279	C₃×#121	—	3	2	no	—
280	C₃×#121	—	3	2	no	—
281	C₃×#121	—	3	2	no	—
282	C₃×#121	—	3	2	no	—
283	C₃×#121	—	3	4	no	—
284	C₃×#121	—	3	4	no	—
285	C₃×#121	—	3	4	no	—
286	C₃×#121	—	3	4	no	—
287	C₃×#121	C₂×D₃	1	1	yes	characteristic, complemented
288	C₃×#121	C₂×D₃	1	1	yes	characteristic, complemented
289	C₃×#121	C₂²×C₃	1	1	yes	characteristic, complemented
290	C₃×#121	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₃×#120	—	2	2	no	—
292	C₃×#120	—	3	4	no	—
293	C₃×#120	—	3	4	no	—
294	C₃×#120	—	3	4	no	—
295	C₃×#120	—	3	4	no	—
296	C₃×#120	C₂×D₃	1	2	yes	complemented
297	C₃×#120	C₂²×C₃	1	2	yes	complemented
298	C₃×C₄×Q₈	—	3	2	no	—
299	C₃×C₄×D₄	—	2	2	no	—
300	C₃×C₄×D₄	—	2	2	no	—
301	C₃×C₄×D₄	—	3	4	no	—
302	C₃×C₄×D₄	—	3	4	no	—
303	C₃×C₄×D₄	—	3	4	no	—
304	C₃×C₄×D₄	—	3	2	no	—
305	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
306	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
307	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
308	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
309	C₃×#117	—	2	1	no	—
310	C₃×#117	—	3	2	no	—
311	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
312	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
313	C₂×C₃×C₄⋊C₄	—	3	1	no	—
314	C₂×C₃×C₄⋊C₄	—	3	2	no	—
315	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
316	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
317	#946	C₂²×C₃	1	2	yes	complemented
318	#940	C₂²×C₃	1	4	yes	complemented
319	#939	C₂²×C₃	1	4	yes	complemented
320	#939	C₂²×C₃	1	4	yes	complemented
321	#938	C₂²×C₃	1	2	yes	complemented
322	#937	C₂²×C₃	1	4	yes	complemented
323	#930	C₂²×C₃	1	2	yes	complemented
324	#930	C₂²×C₃	1	2	yes	complemented
325	#930	C₂²×C₃	1	2	yes	complemented
326	#930	C₂²×C₃	1	2	yes	complemented
327	#930	C₂²×C₃	1	2	yes	complemented
328	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
329	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
330	#924	C₂²×C₃	1	2	yes	complemented
331	#896	C₂²×C₃	1	4	yes	complemented
332	#895	C₂²×C₃	1	4	yes	complemented
333	#895	C₂²×C₃	1	2	yes	complemented
334	#895	C₂²×C₃	1	2	yes	complemented
335	#894	C₂²×C₃	1	4	yes	complemented
336	#893	C₂²×C₃	1	4	yes	complemented
337	#892	C₂²×C₃	1	2	yes	complemented
338	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
339	#885	C₂²×C₃	1	4	yes	complemented
340	#884	C₂²×C₃	1	4	yes	complemented
341	#884	C₂²×C₃	1	4	yes	complemented
342	#884	C₂²×C₃	1	4	yes	complemented
343	#882	C₂²×C₃	1	4	yes	complemented
344	#882	C₂²×C₃	1	4	yes	complemented
345	#882	C₂²×C₃	1	4	yes	complemented
346	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
347	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
348	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
349	#875	C₂²×C₃	1	2	yes	complemented
350	#874	C₂²×C₃	1	2	yes	complemented
351	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
352	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
353	C₂³×C₃²	—	2	2	no	—
354	C₂³×C₃²	—	2	2	no	—
355	C₂³×C₃²	—	4	1	no	—
356	C₂³×C₃²	C₂⁴	1	2	yes	—
357	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
359	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
360	C₂²×C₃×D₃	—	2	4	no	—
361	C₂²×C₃×D₃	—	2	4	no	—
362	C₂²×C₃×D₃	—	2	4	no	—
363	C₂²×C₃×D₃	—	2	8	no	—
364	C₂²×C₃×D₃	—	4	2	no	—
365	C₂²×C₃×D₃	—	4	4	no	—
366	C₂²×C₃×D₃	—	4	2	no	—
367	C₂²×C₃×D₃	—	4	4	no	—
368	C₂²×C₃×D₃	—	4	2	no	—
369	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
370	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
371	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
372	C₃²×Q₈	—	2	2	no	—
373	C₃²×D₄	—	2	4	no	—
374	C₃²×D₄	—	2	4	no	—
375	C₃²×D₄	—	2	2	no	—
376	C₃²×D₄	—	4	2	no	—
377	C₂×C₃²×C₄	—	2	2	no	—
378	C₂×C₃²×C₄	—	2	2	no	—
379	C₂×C₃²×C₄	—	2	2	no	—
380	C₂×C₃²×C₄	—	2	4	no	—
381	C₂×C₃²×C₄	—	2	2	no	—
382	C₂×C₃²×C₄	—	2	2	no	—
383	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
384	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
385	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
386	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
387	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
388	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
391	C₃×#67	—	2	4	no	—
392	C₃×#67	—	2	8	no	—
393	C₃×#67	—	2	4	no	—
394	C₃×#67	—	2	4	no	—
395	C₃×#67	—	2	8	no	—
396	C₃×#67	—	4	4	no	—
397	C₃×#67	—	4	4	no	—
398	C₃×#67	C₂×D₄	1	8	yes	complemented
399	C₂×C₃×Dic₃	—	2	4	no	—
400	C₂×C₃×Dic₃	—	4	2	no	—
401	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
402	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
403	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
404	C₃×D₁₂	—	2	4	no	—
405	C₃×D₁₂	—	2	8	no	—
406	C₃×D₁₂	—	2	4	no	—
407	C₃×D₁₂	—	2	2	no	—
408	C₃×D₁₂	—	2	4	no	—
409	C₃×D₁₂	—	4	4	no	—
410	C₃×D₁₂	—	4	4	no	—
411	C₃×D₁₂	C₂×D₄	1	4	yes	complemented
412	C₃×C₄×D₃	—	2	4	no	—
413	C₃×C₄×D₃	—	2	4	no	—
414	C₃×C₄×D₃	—	2	4	no	—
415	C₃×C₄×D₃	—	2	8	no	—
416	C₃×C₄×D₃	—	4	4	no	—
417	C₃×C₄×D₃	C₂×D₄	1	8	yes	complemented
418	C₃×Dic₆	—	2	2	no	—
419	C₃×Dic₆	—	2	4	no	—
420	C₃×Dic₆	C₂×D₄	1	4	yes	complemented
421	C₂×H(5,𝔽₂)	—	3	1	no	—
422	C₂²×#41	—	3	1	no	—
423	#550	—	3	2	no	—
424	#548	—	3	2	no	—
425	#546	—	3	4	no	—
426	#546	—	3	2	no	—
427	D₄²	—	3	4	no	—
428	D₄²	—	3	2	no	—
429	#537	—	3	1	no	—
430	#537	—	3	2	no	—
431	#535	—	3	2	no	—
432	#535	—	3	1	no	—
433	#525	—	3	2	no	—
434	#525	C₃×D₃	1	1	yes	characteristic, complemented
435	C₂×#121	—	3	1	no	—
436	C₂×#121	—	3	2	no	—
437	#520	—	3	1	no	—
438	C₂⁴×C₃	—	2	1	no	—
439	C₂⁴×C₃	—	3	2	no	—
440	C₂⁴×C₃	—	3	4	no	—
441	C₂⁴×C₃	—	3	2	no	—
442	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
443	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
444	C₂³×D₃	C₂³×C₃	1	2	yes	—
445	C₂³×D₃	C₂³×C₃	1	4	yes	—
446	C₂³×D₃	C₂³×C₃	1	2	yes	—
447	C₃×#41	—	2	4	no	—
448	C₃×#41	—	2	4	no	—
449	C₃×#41	—	3	8	no	—
450	C₃×#41	—	4	4	no	—
451	C₃×#41	—	6	8	no	—
452	C₃×#41	—	6	8	no	—
453	C₃×#41	—	6	4	no	—
454	C₃×#41	—	6	4	no	—
455	C₃×#41	—	6	8	no	—
456	C₃×#41	—	6	8	no	—
457	C₃×#41	—	6	4	no	—
458	C₂×C₃×Q₈	—	2	1	no	—
459	C₂×C₃×Q₈	—	3	1	no	—
460	C₂×C₃×Q₈	—	3	2	no	—
461	C₂×C₃×Q₈	—	3	1	no	—
462	C₂×C₃×Q₈	—	6	4	no	—
463	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
464	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₃×D₄	—	2	2	no	—
466	C₂×C₃×D₄	—	2	2	no	—
467	C₂×C₃×D₄	—	2	2	no	—
468	C₂×C₃×D₄	—	2	1	no	—
469	C₂×C₃×D₄	—	3	2	no	—
470	C₂×C₃×D₄	—	3	4	no	—
471	C₂×C₃×D₄	—	3	2	no	—
472	C₂×C₃×D₄	—	3	2	no	—
473	C₂×C₃×D₄	—	3	4	no	—
474	C₂×C₃×D₄	—	3	2	no	—
475	C₂×C₃×D₄	—	3	4	no	—
476	C₂×C₃×D₄	—	3	4	no	—
477	C₂×C₃×D₄	—	3	1	no	—
478	C₂×C₃×D₄	—	3	2	no	—
479	C₂×C₃×D₄	—	3	4	no	—
480	C₂×C₃×D₄	—	3	2	no	—
481	C₂×C₃×D₄	—	3	2	no	—
482	C₂×C₃×D₄	—	3	1	no	—
483	C₂×C₃×D₄	—	3	4	no	—
484	C₂×C₃×D₄	—	3	4	no	—
485	C₂×C₃×D₄	—	6	4	no	—
486	C₂×C₃×D₄	—	6	8	no	—
487	C₂×C₃×D₄	—	6	8	no	—
488	C₂×C₃×D₄	—	6	16	no	—
489	C₂×C₃×D₄	—	6	8	no	—
490	C₂×C₃×D₄	—	6	4	no	—
491	C₂×C₃×D₄	—	12	8	no	—
492	C₂×C₃×D₄	—	12	4	no	—
493	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
494	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
495	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
496	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
497	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
499	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
500	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
501	C₂²×C₃×C₄	—	2	4	no	—
502	C₂²×C₃×C₄	—	2	4	no	—
503	C₂²×C₃×C₄	—	2	1	no	—
504	C₂²×C₃×C₄	—	2	1	no	—
505	C₂²×C₃×C₄	—	2	1	no	—
506	C₂²×C₃×C₄	—	2	2	no	—
507	C₂²×C₃×C₄	—	2	1	no	—
508	C₂²×C₃×C₄	—	2	1	no	—
509	C₂²×C₃×C₄	—	2	1	no	—
510	C₂²×C₃×C₄	—	3	2	no	—
511	C₂²×C₃×C₄	—	3	2	no	—
512	C₂²×C₃×C₄	—	3	2	no	—
513	C₂²×C₃×C₄	—	3	2	no	—
514	C₂²×C₃×C₄	—	3	2	no	—
515	C₂²×C₃×C₄	—	3	4	no	—
516	C₂²×C₃×C₄	—	3	2	no	—
517	C₂²×C₃×C₄	—	3	4	no	—
518	C₂²×C₃×C₄	—	4	4	no	—
519	C₂²×C₃×C₄	—	6	8	no	—
520	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
521	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
522	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
523	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
524	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
525	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
526	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
527	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
528	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×#67	—	2	8	no	—
535	C₂×#67	—	4	4	no	—
536	C₂×#67	C₂³×C₃	1	4	yes	—
537	C₂×#67	C₂³×C₃	1	2	yes	—
538	C₂×#67	C₂³×C₃	1	2	yes	—
539	C₂×#67	C₂³×C₃	1	2	yes	—
540	C₂×#67	C₂³×C₃	1	4	yes	—
541	C₂×#67	C₂³×C₃	1	4	yes	—
542	C₂×#67	C₂³×C₃	1	4	yes	—
543	C₂×#67	C₂³×C₃	1	2	yes	—
544	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
545	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
546	#239	—	2	8	no	—
547	D₃×D₄	—	2	16	no	—
548	D₃×D₄	—	2	8	no	—
549	D₃×D₄	—	4	8	no	—
550	#235	—	2	4	no	—
551	#235	—	2	8	no	—
552	#235	—	2	4	no	—
553	#235	—	2	8	no	—
554	#235	—	2	4	no	—
555	#235	—	2	8	no	—
556	#235	C₃×D₄	1	8	yes	complemented
557	C₂×D₁₂	—	2	4	no	—
558	C₂×D₁₂	—	2	4	no	—
559	C₂×D₁₂	—	2	8	no	—
560	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
561	C₂×D₁₂	C₂³×C₃	1	2	yes	—
562	C₂×D₁₂	C₂³×C₃	1	2	yes	—
563	C₂×D₁₂	C₂³×C₃	1	4	yes	—
564	C₂×D₁₂	C₂³×C₃	1	2	yes	—
565	C₂×D₁₂	C₂³×C₃	1	4	yes	—
566	C₂×D₁₂	C₂³×C₃	1	4	yes	—
567	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄×D₃	—	2	8	no	—
569	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
570	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
571	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
572	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
573	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
574	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
575	C₂×Dic₆	—	2	4	no	—
576	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
577	C₂×Dic₆	C₂³×C₃	1	2	yes	—
578	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
579	C₃×C₄⋊C₄	—	2	1	no	—
580	C₃×C₄⋊C₄	—	2	1	no	—
581	C₃×C₄⋊C₄	—	2	2	no	—
582	C₃×C₄⋊C₄	—	2	2	no	—
583	C₃×C₄⋊C₄	—	3	4	no	—
584	C₃×C₄⋊C₄	—	3	4	no	—
585	C₃×C₄⋊C₄	—	3	2	no	—
586	C₃×C₄⋊C₄	—	3	2	no	—
587	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
588	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
589	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
590	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
591	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
593	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
594	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
595	C₃×C₂²⋊C₄	—	2	2	no	—
596	C₃×C₂²⋊C₄	—	2	2	no	—
597	C₃×C₂²⋊C₄	—	2	2	no	—
598	C₃×C₂²⋊C₄	—	2	2	no	—
599	C₃×C₂²⋊C₄	—	2	2	no	—
600	C₃×C₂²⋊C₄	—	3	4	no	—
601	C₃×C₂²⋊C₄	—	3	4	no	—
602	C₃×C₂²⋊C₄	—	3	4	no	—
603	C₃×C₂²⋊C₄	—	3	4	no	—
604	C₃×C₂²⋊C₄	—	3	4	no	—
605	C₃×C₂²⋊C₄	—	3	4	no	—
606	C₃×C₂²⋊C₄	—	3	4	no	—
607	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
608	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
609	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
610	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
611	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
612	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
614	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₃×C₄²	—	2	2	no	—
618	C₃×C₄²	—	3	4	no	—
619	C₃×C₄²	C₂²×D₃	1	2	yes	—
620	C₃×C₄²	C₂³×C₃	1	2	yes	—
621	#217	C₂³×C₃	1	4	yes	—
622	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
623	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
624	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
625	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
626	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
627	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
628	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
629	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
630	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
631	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
632	C₄×Dic₃	C₂³×C₃	1	4	yes	—
633	C₂²×C₃²	—	2	1	no	—
634	C₂²×C₃²	—	2	1	no	—
635	C₂²×C₃²	—	2	1	no	—
636	C₂²×C₃²	—	2	1	no	—
637	C₂²×C₃²	—	2	1	no	—
638	C₂²×C₃²	—	2	1	no	—
639	C₂²×C₃²	—	2	2	no	—
640	C₂²×C₃²	—	2	1	no	—
641	C₂²×C₃²	—	2	2	no	—
642	C₂²×C₃²	—	2	2	no	—
643	C₂²×C₃²	—	4	4	no	—
644	C₂²×C₃²	C₂²×D₄	1	2	yes	—
645	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	complemented
646	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
647	C₂×C₃×D₃	—	2	2	no	—
648	C₂×C₃×D₃	—	2	2	no	—
649	C₂×C₃×D₃	—	2	2	no	—
650	C₂×C₃×D₃	—	2	4	no	—
651	C₂×C₃×D₃	—	2	2	no	—
652	C₂×C₃×D₃	—	2	4	no	—
653	C₂×C₃×D₃	—	2	2	no	—
654	C₂×C₃×D₃	—	2	4	no	—
655	C₂×C₃×D₃	—	4	8	no	—
656	C₂×C₃×D₃	—	8	8	no	—
657	C₂×C₃×D₃	—	8	4	no	—
658	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
659	C₃²×C₄	—	2	1	no	—
660	C₃²×C₄	—	2	1	no	—
661	C₃²×C₄	—	2	2	no	—
662	C₃²×C₄	—	2	2	no	—
663	C₃²×C₄	—	2	2	no	—
664	C₃²×C₄	C₂²×D₄	1	2	yes	—
665	C₃²×C₄	C₂²×D₄	1	2	yes	—
666	C₃×Dic₃	—	2	2	no	—
667	C₃×Dic₃	—	2	4	no	—
668	C₃×Dic₃	C₂²×D₄	1	4	yes	—
669	H(5,𝔽₂)	—	6	8	no	—
670	C₂×#41	—	3	2	no	—
671	C₂×#41	—	3	1	no	—
672	C₂×#41	—	3	2	no	—
673	C₂×#41	—	3	1	no	—
674	C₂×#41	—	3	1	no	—
675	C₂×#41	—	3	2	no	—
676	C₂×#41	—	3	2	no	—
677	C₂×#41	—	3	1	no	—
678	C₂×#41	—	6	8	no	—
679	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
680	C₂²×Q₈	—	3	1	no	—
681	C₂²×D₄	—	3	2	no	—
682	C₂²×D₄	—	3	2	no	—
683	C₂²×D₄	—	3	2	no	—
684	C₂²×D₄	—	3	4	no	—
685	C₂²×D₄	—	3	4	no	—
686	C₂²×D₄	—	3	1	no	—
687	C₂²×D₄	—	3	1	no	—
688	C₂²×D₄	—	3	2	no	—
689	C₂³×C₄	—	3	2	no	—
690	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
691	#127	—	3	4	no	—
692	#127	—	3	2	no	—
693	#124	—	3	4	no	—
694	#124	—	3	2	no	—
695	#123	—	3	4	no	—
696	#123	C₂×C₃×D₃	1	2	yes	complemented
697	C₂²⋊Q₈	—	3	2	no	—
698	C₂²⋊Q₈	—	3	2	no	—
699	C₂²⋊Q₈	—	3	4	no	—
700	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
701	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
702	#121	—	3	2	no	—
703	#121	—	3	4	no	—
704	#121	—	3	4	no	—
705	#121	—	3	2	no	—
706	#121	—	3	2	no	—
707	#121	—	3	2	no	—
708	#121	—	3	2	no	—
709	#121	—	3	2	no	—
710	#121	—	3	2	no	—
711	#121	—	3	2	no	—
712	#121	—	3	4	no	—
713	#121	—	3	4	no	—
714	#121	—	3	4	no	—
715	#121	—	3	4	no	—
716	#121	C₂×C₃×D₃	1	1	yes	characteristic, complemented
717	#121	C₂×C₃×D₃	1	1	yes	characteristic, complemented
718	#120	—	3	4	no	—
719	#120	—	3	4	no	—
720	#120	—	3	4	no	—
721	#120	—	3	4	no	—
722	#120	C₂×C₃×D₃	1	2	yes	complemented
723	C₄×Q₈	—	3	2	no	—
724	C₄×D₄	—	3	4	no	—
725	C₄×D₄	—	3	4	no	—
726	C₄×D₄	—	3	4	no	—
727	C₄×D₄	—	3	2	no	—
728	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
729	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
730	#117	—	3	2	no	—
731	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
732	C₂×C₄⋊C₄	—	3	1	no	—
733	C₂×C₄⋊C₄	—	3	2	no	—
734	C₂×C₂²⋊C₄	—	3	2	no	—
735	C₂×C₂²⋊C₄	—	3	4	no	—
736	C₂³×C₃	—	2	2	no	—
737	C₂³×C₃	—	2	2	no	—
738	C₂³×C₃	—	2	2	no	—
739	C₂³×C₃	—	2	2	no	—
740	C₂³×C₃	—	2	1	no	—
741	C₂³×C₃	—	2	1	no	—
742	C₂³×C₃	—	2	1	no	—
743	C₂³×C₃	—	2	2	no	—
744	C₂³×C₃	—	3	2	no	—
745	C₂³×C₃	—	3	4	no	—
746	C₂³×C₃	—	3	2	no	—
747	C₂³×C₃	—	4	2	no	—
748	C₂³×C₃	—	4	2	no	—
749	C₂³×C₃	—	4	1	no	—
750	C₂³×C₃	—	4	1	no	—
751	C₂³×C₃	—	4	2	no	—
752	C₂³×C₃	—	6	4	no	—
753	C₂³×C₃	—	6	8	no	—
754	C₂³×C₃	—	6	4	no	—
755	C₂³×C₃	—	6	4	no	—
756	C₂³×C₃	—	12	2	no	—
757	C₂³×C₃	—	12	2	no	—
758	C₂³×C₃	—	12	4	no	—
759	C₂³×C₃	—	12	2	no	—
760	C₂³×C₃	—	12	4	no	—
761	C₂³×C₃	C₂³×D₃	1	2	yes	—
762	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
763	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
764	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
765	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
766	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
767	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
768	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
769	C₂²×D₃	—	2	4	no	—
770	C₂²×D₃	—	2	4	no	—
771	C₂²×D₃	—	2	4	no	—
772	C₂²×D₃	—	2	8	no	—
773	C₂²×D₃	—	4	2	no	—
774	C₂²×D₃	—	4	4	no	—
775	C₂²×D₃	—	4	2	no	—
776	C₂²×D₃	—	4	4	no	—
777	C₂²×D₃	—	4	2	no	—
778	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
779	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
780	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
781	C₃×Q₈	—	2	2	no	—
782	C₃×Q₈	—	2	2	no	—
783	C₃×Q₈	—	3	4	no	—
784	C₃×Q₈	—	4	2	no	—
785	C₃×Q₈	—	6	4	no	—
786	C₃×Q₈	—	6	2	no	—
787	C₃×D₄	—	2	4	no	—
788	C₃×D₄	—	2	4	no	—
789	C₃×D₄	—	2	4	no	—
790	C₃×D₄	—	2	4	no	—
791	C₃×D₄	—	2	2	no	—
792	C₃×D₄	—	2	2	no	—
793	C₃×D₄	—	3	8	no	—
794	C₃×D₄	—	3	4	no	—
795	C₃×D₄	—	4	2	no	—
796	C₃×D₄	—	4	4	no	—
797	C₃×D₄	—	4	4	no	—
798	C₃×D₄	—	4	2	no	—
799	C₃×D₄	—	4	2	no	—
800	C₃×D₄	—	4	4	no	—
801	C₃×D₄	—	6	8	no	—
802	C₃×D₄	—	6	4	no	—
803	C₃×D₄	—	6	8	no	—
804	C₃×D₄	—	6	4	no	—
805	C₃×D₄	—	6	4	no	—
806	C₃×D₄	—	6	4	no	—
807	C₃×D₄	—	6	8	no	—
808	C₃×D₄	—	6	4	no	—
809	C₃×D₄	—	6	4	no	—
810	C₃×D₄	—	6	2	no	—
811	C₃×D₄	—	12	4	no	—
812	C₃×D₄	—	12	4	no	—
813	C₃×D₄	—	12	4	no	—
814	C₃×D₄	—	12	4	no	—
815	C₂×C₃×C₄	—	2	2	no	—
816	C₂×C₃×C₄	—	2	2	no	—
817	C₂×C₃×C₄	—	2	2	no	—
818	C₂×C₃×C₄	—	2	2	no	—
819	C₂×C₃×C₄	—	2	2	no	—
820	C₂×C₃×C₄	—	2	2	no	—
821	C₂×C₃×C₄	—	2	4	no	—
822	C₂×C₃×C₄	—	2	2	no	—
823	C₂×C₃×C₄	—	2	2	no	—
824	C₂×C₃×C₄	—	2	4	no	—
825	C₂×C₃×C₄	—	2	2	no	—
826	C₂×C₃×C₄	—	2	2	no	—
827	C₂×C₃×C₄	—	2	1	no	—
828	C₂×C₃×C₄	—	2	1	no	—
829	C₂×C₃×C₄	—	2	2	no	—
830	C₂×C₃×C₄	—	2	2	no	—
831	C₂×C₃×C₄	—	2	1	no	—
832	C₂×C₃×C₄	—	2	1	no	—
833	C₂×C₃×C₄	—	2	2	no	—
834	C₂×C₃×C₄	—	2	4	no	—
835	C₂×C₃×C₄	—	3	2	no	—
836	C₂×C₃×C₄	—	3	8	no	—
837	C₂×C₃×C₄	—	3	4	no	—
838	C₂×C₃×C₄	—	3	2	no	—
839	C₂×C₃×C₄	—	4	2	no	—
840	C₂×C₃×C₄	—	4	2	no	—
841	C₂×C₃×C₄	—	4	2	no	—
842	C₂×C₃×C₄	—	4	2	no	—
843	C₂×C₃×C₄	—	4	4	no	—
844	C₂×C₃×C₄	—	4	2	no	—
845	C₂×C₃×C₄	—	6	4	no	—
846	C₂×C₃×C₄	—	6	8	no	—
847	C₂×C₃×C₄	—	6	4	no	—
848	C₂×C₃×C₄	—	6	4	no	—
849	C₂×C₃×C₄	—	6	4	no	—
850	C₂×C₃×C₄	—	12	4	no	—
851	C₂×C₃×C₄	—	12	2	no	—
852	C₂×C₃×C₄	D₃×D₄	1	4	yes	complemented
853	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
854	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
855	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
856	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
857	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
858	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
859	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
860	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
861	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
862	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
863	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
864	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
865	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
866	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
867	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
868	#67	—	2	4	no	—
869	#67	—	2	8	no	—
870	#67	—	2	4	no	—
871	#67	—	2	4	no	—
872	#67	—	2	8	no	—
873	#67	—	4	4	no	—
874	#67	—	4	4	no	—
875	#67	C₂×C₃×D₄	1	8	yes	complemented
876	C₂×Dic₃	—	2	4	no	—
877	C₂×Dic₃	—	4	2	no	—
878	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
879	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
880	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
881	D₁₂	—	2	4	no	—
882	D₁₂	—	2	8	no	—
883	D₁₂	—	2	4	no	—
884	D₁₂	—	2	2	no	—
885	D₁₂	—	2	4	no	—
886	D₁₂	—	4	4	no	—
887	D₁₂	—	4	4	no	—
888	D₁₂	C₂×C₃×D₄	1	4	yes	complemented
889	C₄×D₃	—	2	4	no	—
890	C₄×D₃	—	2	4	no	—
891	C₄×D₃	—	2	4	no	—
892	C₄×D₃	—	2	8	no	—
893	C₄×D₃	—	4	4	no	—
894	C₄×D₃	C₂×C₃×D₄	1	8	yes	complemented
895	Dic₆	—	2	2	no	—
896	Dic₆	—	2	4	no	—
897	Dic₆	C₂×C₃×D₄	1	4	yes	complemented
898	C₂×C₃²	—	2	2	no	—
899	C₂×C₃²	—	2	2	no	—
900	C₂×C₃²	—	4	1	no	—
901	C₂×C₃²	—	4	2	no	—
902	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
903	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
904	C₂×C₃²	#585	1	1	yes	characteristic
905	C₃×D₃	—	2	4	no	—
906	C₃×D₃	—	4	2	no	—
907	C₃×D₃	—	4	4	no	—
908	C₂⁴	—	3	2	no	—
909	C₂⁴	—	3	4	no	—
910	C₂⁴	—	3	2	no	—
911	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
912	#41	—	2	4	no	—
913	#41	—	3	8	no	—
914	#41	—	6	8	no	—
915	#41	—	6	8	no	—
916	#41	—	6	4	no	—
917	#41	—	6	4	no	—
918	#41	—	6	8	no	—
919	#41	—	6	8	no	—
920	#41	—	6	4	no	—
921	C₂×Q₈	—	3	1	no	—
922	C₂×Q₈	—	3	2	no	—
923	C₂×Q₈	—	3	1	no	—
924	C₂×Q₈	—	6	4	no	—
925	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
926	C₂×D₄	—	3	2	no	—
927	C₂×D₄	—	3	4	no	—
928	C₂×D₄	—	3	2	no	—
929	C₂×D₄	—	3	2	no	—
930	C₂×D₄	—	3	4	no	—
931	C₂×D₄	—	3	2	no	—
932	C₂×D₄	—	3	4	no	—
933	C₂×D₄	—	3	4	no	—
934	C₂×D₄	—	3	1	no	—
935	C₂×D₄	—	3	2	no	—
936	C₂×D₄	—	3	4	no	—
937	C₂×D₄	—	3	2	no	—
938	C₂×D₄	—	3	2	no	—
939	C₂×D₄	—	3	1	no	—
940	C₂×D₄	—	3	4	no	—
941	C₂×D₄	—	3	4	no	—
942	C₂×D₄	—	6	4	no	—
943	C₂×D₄	—	6	8	no	—
944	C₂×D₄	—	6	8	no	—
945	C₂×D₄	—	6	16	no	—
946	C₂×D₄	—	6	8	no	—
947	C₂×D₄	—	6	4	no	—
948	C₂×D₄	—	12	8	no	—
949	C₂×D₄	—	12	4	no	—
950	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
951	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
952	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
953	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
954	C₂²×C₄	—	2	4	no	—
955	C₂²×C₄	—	3	2	no	—
956	C₂²×C₄	—	3	2	no	—
957	C₂²×C₄	—	3	2	no	—
958	C₂²×C₄	—	3	2	no	—
959	C₂²×C₄	—	3	2	no	—
960	C₂²×C₄	—	3	4	no	—
961	C₂²×C₄	—	3	2	no	—
962	C₂²×C₄	—	3	4	no	—
963	C₂²×C₄	—	6	8	no	—
964	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
965	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
966	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
967	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
968	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
969	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
970	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
971	C₄⋊C₄	—	3	2	no	—
972	C₄⋊C₄	—	3	4	no	—
973	C₄⋊C₄	—	3	2	no	—
974	C₄⋊C₄	—	3	4	no	—
975	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
978	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
979	C₂²⋊C₄	—	3	4	no	—
980	C₂²⋊C₄	—	3	4	no	—
981	C₂²⋊C₄	—	3	4	no	—
982	C₂²⋊C₄	—	3	4	no	—
983	C₂²⋊C₄	—	3	4	no	—
984	C₂²⋊C₄	—	3	4	no	—
985	C₂²⋊C₄	—	3	4	no	—
986	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
987	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
988	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
989	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
990	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
991	C₄²	—	3	4	no	—
992	C₄²	C₂²×C₃×D₃	1	2	yes	—
993	C₂²×C₃	—	2	1	no	—
994	C₂²×C₃	—	2	1	no	—
995	C₂²×C₃	—	2	1	no	—
996	C₂²×C₃	—	2	1	no	—
997	C₂²×C₃	—	2	1	no	—
998	C₂²×C₃	—	2	1	no	—
999	C₂²×C₃	—	2	1	no	—
1000	C₂²×C₃	—	2	1	no	—
1001	C₂²×C₃	—	2	2	no	—
1002	C₂²×C₃	—	2	1	no	—
1003	C₂²×C₃	—	2	2	no	—
1004	C₂²×C₃	—	2	2	no	—
1005	C₂²×C₃	—	2	1	no	—
1006	C₂²×C₃	—	2	1	no	—
1007	C₂²×C₃	—	2	2	no	—
1008	C₂²×C₃	—	2	1	no	—
1009	C₂²×C₃	—	2	2	no	—
1010	C₂²×C₃	—	2	1	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	1	no	—
1013	C₂²×C₃	—	2	2	no	—
1014	C₂²×C₃	—	2	2	no	—
1015	C₂²×C₃	—	2	2	no	—
1016	C₂²×C₃	—	2	1	no	—
1017	C₂²×C₃	—	3	4	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	1	no	—
1020	C₂²×C₃	—	4	1	no	—
1021	C₂²×C₃	—	4	1	no	—
1022	C₂²×C₃	—	4	1	no	—
1023	C₂²×C₃	—	4	1	no	—
1024	C₂²×C₃	—	4	2	no	—
1025	C₂²×C₃	—	4	2	no	—
1026	C₂²×C₃	—	4	2	no	—
1027	C₂²×C₃	—	4	4	no	—
1028	C₂²×C₃	—	4	4	no	—
1029	C₂²×C₃	—	4	8	no	—
1030	C₂²×C₃	—	6	2	no	—
1031	C₂²×C₃	—	6	2	no	—
1032	C₂²×C₃	—	6	2	no	—
1033	C₂²×C₃	—	6	4	no	—
1034	C₂²×C₃	—	6	4	no	—
1035	C₂²×C₃	—	6	2	no	—
1036	C₂²×C₃	—	6	2	no	—
1037	C₂²×C₃	—	6	4	no	—
1038	C₂²×C₃	—	12	8	no	—
1039	C₂²×C₃	—	24	4	no	—
1040	C₂²×C₃	—	24	8	no	—
1041	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
1042	C₂²×C₃	#1009	1	2	yes	complemented
1043	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
1044	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	complemented
1045	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1046	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1047	C₂×D₃	—	2	2	no	—
1048	C₂×D₃	—	2	2	no	—
1049	C₂×D₃	—	2	2	no	—
1050	C₂×D₃	—	2	4	no	—
1051	C₂×D₃	—	2	2	no	—
1052	C₂×D₃	—	2	4	no	—
1053	C₂×D₃	—	2	2	no	—
1054	C₂×D₃	—	2	4	no	—
1055	C₂×D₃	—	4	8	no	—
1056	C₂×D₃	—	8	8	no	—
1057	C₂×D₃	—	8	4	no	—
1058	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
1059	C₃×C₄	—	2	1	no	—
1060	C₃×C₄	—	2	1	no	—
1061	C₃×C₄	—	2	2	no	—
1062	C₃×C₄	—	2	2	no	—
1063	C₃×C₄	—	2	2	no	—
1064	C₃×C₄	—	2	1	no	—
1065	C₃×C₄	—	2	1	no	—
1066	C₃×C₄	—	2	2	no	—
1067	C₃×C₄	—	2	2	no	—
1068	C₃×C₄	—	2	2	no	—
1069	C₃×C₄	—	2	2	no	—
1070	C₃×C₄	—	2	2	no	—
1071	C₃×C₄	—	3	4	no	—
1072	C₃×C₄	—	4	1	no	—
1073	C₃×C₄	—	4	1	no	—
1074	C₃×C₄	—	4	2	no	—
1075	C₃×C₄	—	4	2	no	—
1076	C₃×C₄	—	4	2	no	—
1077	C₃×C₄	—	6	2	no	—
1078	C₃×C₄	—	6	4	no	—
1079	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
1080	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
1081	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
1082	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
1083	Dic₃	—	2	2	no	—
1084	Dic₃	—	2	4	no	—
1085	Dic₃	C₂²×C₃×D₄	1	4	yes	—
1086	C₃²	#3488	1	1	yes	characteristic, complemented, Sylow
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	3	2	no	—
1090	C₂³	—	3	4	no	—
1091	C₂³	—	3	2	no	—
1092	C₂³	—	4	1	no	—
1093	C₂³	—	6	4	no	—
1094	C₂³	—	6	8	no	—
1095	C₂³	—	6	4	no	—
1096	C₂³	—	6	4	no	—
1097	C₂³	—	12	2	no	—
1098	C₂³	—	12	2	no	—
1099	C₂³	—	12	4	no	—
1100	C₂³	—	12	2	no	—
1101	C₂³	—	12	4	no	—
1102	C₂³	C₂³×C₃×D₃	1	2	yes	—
1103	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1104	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1105	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1106	Q₈	—	2	2	no	—
1107	Q₈	—	3	4	no	—
1108	Q₈	—	6	4	no	—
1109	Q₈	—	6	2	no	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	4	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	3	8	no	—
1114	D₄	—	3	4	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	6	8	no	—
1117	D₄	—	6	4	no	—
1118	D₄	—	6	8	no	—
1119	D₄	—	6	4	no	—
1120	D₄	—	6	4	no	—
1121	D₄	—	6	4	no	—
1122	D₄	—	6	8	no	—
1123	D₄	—	6	4	no	—
1124	D₄	—	6	4	no	—
1125	D₄	—	6	2	no	—
1126	D₄	—	12	4	no	—
1127	D₄	—	12	4	no	—
1128	D₄	—	12	4	no	—
1129	D₄	—	12	4	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	3	2	no	—
1137	C₂×C₄	—	3	8	no	—
1138	C₂×C₄	—	3	4	no	—
1139	C₂×C₄	—	3	2	no	—
1140	C₂×C₄	—	6	4	no	—
1141	C₂×C₄	—	6	8	no	—
1142	C₂×C₄	—	6	4	no	—
1143	C₂×C₄	—	6	4	no	—
1144	C₂×C₄	—	6	4	no	—
1145	C₂×C₄	—	12	4	no	—
1146	C₂×C₄	—	12	2	no	—
1147	C₂×C₄	C₃×D₃×D₄	1	4	yes	complemented
1148	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1149	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1150	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1151	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1152	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1153	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1154	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1155	C₂×C₃	—	2	2	no	—
1156	C₂×C₃	—	2	2	no	—
1157	C₂×C₃	—	2	2	no	—
1158	C₂×C₃	—	2	2	no	—
1159	C₂×C₃	—	2	1	no	—
1160	C₂×C₃	—	2	1	no	—
1161	C₂×C₃	—	2	1	no	—
1162	C₂×C₃	—	4	2	no	—
1163	C₂×C₃	—	4	2	no	—
1164	C₂×C₃	—	4	2	no	—
1165	C₂×C₃	—	4	1	no	—
1166	C₂×C₃	—	4	2	no	—
1167	C₂×C₃	—	4	2	no	—
1168	C₂×C₃	—	4	1	no	—
1169	C₂×C₃	—	6	4	no	—
1170	C₂×C₃	—	8	2	no	—
1171	C₂×C₃	—	12	2	no	—
1172	C₂×C₃	—	12	4	no	—
1173	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
1174	C₂×C₃	C₂×#1009	1	1	yes	characteristic
1175	C₂×C₃	#5964	1	1	yes	characteristic
1176	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
1177	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1178	C₂×C₃	C₃×#585	1	1	yes	characteristic
1179	D₃	—	2	4	no	—
1180	D₃	—	4	2	no	—
1181	D₃	—	4	4	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	3	4	no	—
1193	C₂²	—	4	4	no	—
1194	C₂²	—	6	2	no	—
1195	C₂²	—	6	2	no	—
1196	C₂²	—	6	2	no	—
1197	C₂²	—	6	4	no	—
1198	C₂²	—	6	4	no	—
1199	C₂²	—	6	2	no	—
1200	C₂²	—	6	2	no	—
1201	C₂²	—	6	4	no	—
1202	C₂²	—	12	8	no	—
1203	C₂²	—	24	4	no	—
1204	C₂²	—	24	8	no	—
1205	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
1206	C₂²	C₃×#1009	1	2	yes	complemented
1207	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	2	no	—
1213	C₄	—	3	4	no	—
1214	C₄	—	6	2	no	—
1215	C₄	—	6	4	no	—
1216	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
1217	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
1218	C₃	—	2	1	no	—
1219	C₃	#86041	1	1	yes	characteristic, direct product factor
1220	C₃	C₃×#3488	1	1	yes	characteristic, complemented
1221	C₂	—	2	2	no	—
1222	C₂	—	2	2	no	—
1223	C₂	—	4	1	no	—
1224	C₂	—	4	2	no	—
1225	C₂	—	6	4	no	—
1226	C₂	—	12	2	no	—
1227	C₂	—	12	4	no	—
1228	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
1229	C₂	C₂×C₃×#1009	1	1	yes	characteristic
1230	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	C₃²×#525	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#525	D₃
hypocenter	C₃	C₃×#3488
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1009	C₂	semidirect
2. C₂²×C₃×#235	C₂	semidirect
3. C₃²×#525	C₂	semidirect
4. C₃×#5833	C₂	semidirect
5. C₂×C₃×#930	C₂	semidirect
6. C₃×#5654	C₂	semidirect
7. C₃×#5629	C₂	semidirect
8. C₃×#5627	C₂	semidirect
9. C₃×#5607	C₂	semidirect
10. C₃×D₃×#121	C₂	semidirect
11. C₃×#5590	C₂	semidirect
12. C₃×#5553	C₂	semidirect
13. C₃×#5552	C₂	semidirect
14. C₃×#5550	C₂	semidirect
15. C₃×D₄×D₁₂	C₂	semidirect
16. C₃×#5525	C₂	semidirect
17. C₃×#5523	C₂	semidirect
19. #86041	C₃	direct (N × H)
20. C₂×C₃²×#41	C₂²	semidirect
21. C₂³×C₃²×C₄	C₂²	semidirect
22. C₂²×C₃×#67	C₂²	semidirect
23. C₂²×C₃×#67	C₂²	semidirect
25. C₂×C₃×#239	C₂²	semidirect
26. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂×C₃×D₃×D₄	C₂²	semidirect
28. C₂×C₃×D₃×D₄	C₂²	semidirect
31. C₂×C₃×#235	C₂²	semidirect
32. C₂×C₃×#235	C₂²	semidirect
33. C₂×C₃×#235	C₂²	semidirect
34. C₂×C₃×#235	C₂²	semidirect
35. C₂×C₃×#235	C₂²	semidirect
36. C₂×C₃×#235	C₂²	semidirect
37. C₂²×C₃×D₁₂	C₂²	semidirect
38. C₂²×C₃×D₁₂	C₂²	semidirect
39. C₂²×C₃×D₁₂	C₂²	semidirect
40. C₂²×C₃×C₄×D₃	C₂²	semidirect
41. C₂²×C₃×Dic₆	C₂²	semidirect
42. C₃²×#123	C₂²	semidirect
43. C₃²×C₂²⋊Q₈	C₂²	semidirect
44. C₃²×C₂²⋊Q₈	C₂²	semidirect
45. C₃²×#121	C₂²	semidirect
46. C₃²×#121	C₂²	semidirect
47. C₃²×#120	C₂²	semidirect
48. C₃²×C₄×D₄	C₂²	semidirect
49. C₃²×C₄×D₄	C₂²	semidirect
50. C₃²×#117	C₂²	semidirect
51. C₃×#946	C₂²	semidirect
52. C₃×#940	C₂²	semidirect
53. C₃×#939	C₂²	semidirect
54. C₃×#939	C₂²	semidirect
55. C₃×#938	C₂²	semidirect
56. C₃×#937	C₂²	semidirect
57. C₃×#930	C₂²	semidirect
58. C₃×#930	C₂²	semidirect
59. C₃×#930	C₂²	semidirect
60. C₃×#930	C₂²	semidirect
61. C₃×#930	C₂²	semidirect
62. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
63. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
64. C₃×#924	C₂²	semidirect
65. C₃×#896	C₂²	semidirect
66. C₃×#895	C₂²	semidirect
67. C₃×#895	C₂²	semidirect
68. C₃×#895	C₂²	semidirect
69. C₃×#894	C₂²	semidirect
70. C₃×#893	C₂²	semidirect
71. C₃×#892	C₂²	semidirect
72. C₃×D₃×C₄⋊C₄	C₂²	semidirect
73. C₃×#885	C₂²	semidirect
74. C₃×#884	C₂²	semidirect
75. C₃×#884	C₂²	semidirect
76. C₃×#884	C₂²	semidirect
77. C₃×#882	C₂²	semidirect
78. C₃×#882	C₂²	semidirect
79. C₃×#882	C₂²	semidirect
80. C₃×#67⋊C₄	C₂²	semidirect
81. C₃×#67⋊C₄	C₂²	semidirect
82. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
83. C₃×#875	C₂²	semidirect
84. C₃×#874	C₂²	semidirect
85. C₃×C₄×D₁₂	C₂²	semidirect
86. C₃×C₄×Dic₆	C₂²	semidirect
89. C₂×#1009	C₂×C₃	semidirect
90. C₂²×#235	C₂×C₃	semidirect
103. C₃×#525	D₃	semidirect
104. C₃×#525	C₂×C₃	semidirect
108. #5833	C₂×C₃	semidirect
109. C₂×#930	C₂×C₃	semidirect
110. #5654	C₂×C₃	semidirect
111. #5629	C₂×C₃	semidirect
112. #5627	C₂×C₃	semidirect
113. #5607	C₂×C₃	semidirect
114. D₃×#121	C₂×C₃	semidirect
115. #5590	C₂×C₃	semidirect
116. #5553	C₂×C₃	semidirect
117. #5552	C₂×C₃	semidirect
118. #5550	C₂×C₃	semidirect
119. D₄×D₁₂	C₂×C₃	semidirect
120. #5525	C₂×C₃	semidirect
121. #5523	C₂×C₃	semidirect
162. C₃×#235	D₄	semidirect
219. C₂×C₃×#41	C₂×D₃	semidirect
220. C₂×C₃×#41	C₂²×C₃	semidirect
232. C₂³×C₃×C₄	C₂×D₃	semidirect
233. C₂³×C₃×C₄	C₂²×C₃	semidirect
234. C₂²×#67	C₂²×C₃	semidirect
235. C₂²×#67	C₂²×C₃	semidirect
237. C₂×#239	C₂²×C₃	semidirect
238. C₂×D₃×D₄	C₂²×C₃	semidirect
239. C₂×D₃×D₄	C₂²×C₃	semidirect
240. C₂×D₃×D₄	C₂²×C₃	semidirect
243. C₂×#235	C₂²×C₃	semidirect
244. C₂×#235	C₂²×C₃	semidirect
245. C₂×#235	C₂²×C₃	semidirect
246. C₂×#235	C₂²×C₃	semidirect
247. C₂×#235	C₂²×C₃	semidirect
248. C₂×#235	C₂²×C₃	semidirect
249. C₂²×D₁₂	C₂²×C₃	semidirect
250. C₂²×D₁₂	C₂²×C₃	semidirect
251. C₂²×D₁₂	C₂²×C₃	semidirect
252. C₂²×C₄×D₃	C₂²×C₃	semidirect
253. C₂²×Dic₆	C₂²×C₃	semidirect
260. C₃×#123	C₂×D₃	semidirect
261. C₃×#123	C₂²×C₃	semidirect
267. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
268. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
269. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
270. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
287. C₃×#121	C₂×D₃	semidirect
288. C₃×#121	C₂×D₃	semidirect
289. C₃×#121	C₂²×C₃	semidirect
290. C₃×#121	C₂²×C₃	semidirect
296. C₃×#120	C₂×D₃	semidirect
297. C₃×#120	C₂²×C₃	semidirect
305. C₃×C₄×D₄	C₂×D₃	semidirect
306. C₃×C₄×D₄	C₂×D₃	semidirect
307. C₃×C₄×D₄	C₂²×C₃	semidirect
308. C₃×C₄×D₄	C₂²×C₃	semidirect
311. C₃×#117	C₂×D₃	semidirect
312. C₃×#117	C₂²×C₃	semidirect
317. #946	C₂²×C₃	semidirect
318. #940	C₂²×C₃	semidirect
319. #939	C₂²×C₃	semidirect
320. #939	C₂²×C₃	semidirect
321. #938	C₂²×C₃	semidirect
322. #937	C₂²×C₃	semidirect
323. #930	C₂²×C₃	semidirect
324. #930	C₂²×C₃	semidirect
325. #930	C₂²×C₃	semidirect
326. #930	C₂²×C₃	semidirect
327. #930	C₂²×C₃	semidirect
328. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
329. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
330. #924	C₂²×C₃	semidirect
331. #896	C₂²×C₃	semidirect
332. #895	C₂²×C₃	semidirect
333. #895	C₂²×C₃	semidirect
334. #895	C₂²×C₃	semidirect
335. #894	C₂²×C₃	semidirect
336. #893	C₂²×C₃	semidirect
337. #892	C₂²×C₃	semidirect
338. D₃×C₄⋊C₄	C₂²×C₃	semidirect
339. #885	C₂²×C₃	semidirect
340. #884	C₂²×C₃	semidirect
341. #884	C₂²×C₃	semidirect
342. #884	C₂²×C₃	semidirect
343. #882	C₂²×C₃	semidirect
344. #882	C₂²×C₃	semidirect
345. #882	C₂²×C₃	semidirect
346. #67⋊C₄	C₂²×C₃	semidirect
347. #67⋊C₄	C₂²×C₃	semidirect
348. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
349. #875	C₂²×C₃	semidirect
350. #874	C₂²×C₃	semidirect
351. C₄×D₁₂	C₂²×C₃	semidirect
352. C₄×Dic₆	C₂²×C₃	semidirect
383. C₂×C₃²×C₄	C₂×D₄	semidirect
398. C₃×#67	C₂×D₄	semidirect
411. C₃×D₁₂	C₂×D₄	semidirect
417. C₃×C₄×D₃	C₂×D₄	semidirect
420. C₃×Dic₆	C₂×D₄	semidirect
434. #525	C₃×D₃	semidirect
556. #235	C₃×D₄	semidirect
645. C₂²×C₃²	H(5,𝔽₂)	semidirect
679. C₂×#41	C₂×C₃×D₃	semidirect
690. C₂³×C₄	C₂×C₃×D₃	semidirect
696. #123	C₂×C₃×D₃	semidirect
700. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
701. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
716. #121	C₂×C₃×D₃	semidirect
717. #121	C₂×C₃×D₃	semidirect
722. #120	C₂×C₃×D₃	semidirect
728. C₄×D₄	C₂×C₃×D₃	semidirect
729. C₄×D₄	C₂×C₃×D₃	semidirect
731. #117	C₂×C₃×D₃	semidirect
852. C₂×C₃×C₄	D₃×D₄	semidirect
853. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
875. #67	C₂×C₃×D₄	semidirect
888. D₁₂	C₂×C₃×D₄	semidirect
894. C₄×D₃	C₂×C₃×D₄	semidirect
897. Dic₆	C₂×C₃×D₄	semidirect
1042. C₂²×C₃	#1009	semidirect
1044. C₂²×C₃	C₃×H(5,𝔽₂)	semidirect
1086. C₃²	#3488	semidirect
1147. C₂×C₄	C₃×D₃×D₄	semidirect
1206. C₂²	C₃×#1009	semidirect
1219. C₃	#86041	direct (N × H)
1220. C₃	C₃×#3488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1009	2
C₂²×C₃×#235	2
C₃²×#525	2
C₃×#5833	2
C₂×C₃×#930	2
C₃×#5654	2
C₃×#5629	2
C₃×#5627	2
C₃×#5607	2
C₃×D₃×#121	2
C₃×#5590	2
C₃×#5553	2
C₃×#5552	2
C₃×#5550	2
C₃×D₄×D₁₂	2
C₃×#5525	2
C₃×#5523	2
C₃×#3488	3
#86041	3

Subgroups — C3×#86041 #11904588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86041 #11904588