Subgroups — C₃×#86119 #11900872

Order 1152.

2541 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5706	C₂	1	2	yes	maximal, complemented
3	C₃×#5706	C₂	1	2	yes	maximal, complemented
4	C₃×#5691	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5688	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5656	C₂	1	2	yes	maximal, complemented
9	C₃×#5649	C₂	1	2	yes	maximal, complemented
10	C₃×#5627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5622	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5606	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5596	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5578	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5548	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5547	C₂	1	2	yes	maximal, complemented
18	C₃×C₄×#237	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5528	C₂	1	2	yes	maximal, complemented
21	C₃×#5522	C₂	1	2	yes	maximal, complemented
22	C₃×#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3444	—	3	1	no	maximal
25	#86119	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×#239	C₂²	1	1	yes	characteristic
27	C₂×C₃×#237	C₂²	1	2	yes	—
28	C₂×C₃×#237	C₂²	1	1	yes	characteristic
29	C₂×C₃×#235	C₂²	1	2	yes	—
30	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
33	C₃²×#126	C₂²	1	2	yes	complemented
34	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#123	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₃²×#121	C₂²	1	1	yes	characteristic
39	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃²×C₄×D₄	C₂²	1	2	yes	—
41	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃²×#117	C₂²	1	2	yes	complemented
43	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
44	C₃×#946	C₂²	1	1	yes	characteristic
45	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₃×#944	C₂²	1	1	yes	characteristic, complemented
47	C₃×#940	C₂²	1	1	yes	characteristic, complemented
48	C₃×#939	C₂²	1	2	yes	—
49	C₃×#938	C₂²	1	1	yes	characteristic
50	C₃×#937	C₂²	1	2	yes	—
51	C₃×D₄×Dic₃	C₂²	1	2	yes	—
52	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃×#930	C₂²	1	1	yes	characteristic
54	C₃×#929	C₂²	1	2	yes	—
55	C₃×C₄×#67	C₂²	1	2	yes	—
56	C₃×C₄×#67	C₂²	1	2	yes	—
57	C₃×C₄×#67	C₂²	1	2	yes	complemented
58	C₃×#924	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
60	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
63	C₃×#898	C₂²	1	2	yes	complemented
64	C₃×#897	C₂²	1	1	yes	characteristic
65	C₃×#896	C₂²	1	2	yes	—
66	C₃×#896	C₂²	1	2	yes	—
67	C₃×#896	C₂²	1	2	yes	—
68	C₃×#895	C₂²	1	1	yes	characteristic
69	C₃×#894	C₂²	1	2	yes	—
70	C₃×#894	C₂²	1	2	yes	—
71	C₃×#893	C₂²	1	2	yes	—
72	C₃×#893	C₂²	1	2	yes	—
73	C₃×#893	C₂²	1	2	yes	—
74	C₃×#893	C₂²	1	1	yes	characteristic, complemented
75	C₃×#892	C₂²	1	1	yes	characteristic
76	C₃×#892	C₂²	1	1	yes	characteristic
77	C₃×#892	C₂²	1	2	yes	complemented
78	C₃×#892	C₂²	1	2	yes	complemented
79	C₃×#889	C₂²	1	2	yes	complemented
80	C₃×#889	C₂²	1	2	yes	complemented
81	C₃×#888	C₂²	1	1	yes	characteristic, complemented
82	C₃×#888	C₂²	1	1	yes	characteristic, complemented
83	C₃×#887	C₂²	1	2	yes	complemented
84	C₃×#887	C₂²	1	2	yes	complemented
85	C₃×#887	C₂²	1	1	yes	characteristic, complemented
86	C₃×#887	C₂²	1	2	yes	complemented
87	C₃×#885	C₂²	1	2	yes	complemented
88	C₃×#885	C₂²	1	2	yes	complemented
89	C₃×#884	C₂²	1	2	yes	—
90	C₃×#884	C₂²	1	2	yes	—
91	C₃×#884	C₂²	1	2	yes	—
92	C₃×#883	C₂²	1	2	yes	—
93	C₃×#883	C₂²	1	2	yes	—
94	C₃×#882	C₂²	1	2	yes	—
95	C₃×#67⋊C₄	C₂²	1	2	yes	—
96	C₃×#67⋊C₄	C₂²	1	2	yes	—
97	C₃×#67⋊C₄	C₂²	1	2	yes	—
98	C₃×#67⋊C₄	C₂²	1	2	yes	—
99	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
100	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
101	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
102	C₃×#879	C₂²	1	2	yes	complemented
103	C₃×#878	C₂²	1	2	yes	—
104	C₃×#877	C₂²	1	2	yes	—
105	C₃×#877	C₂²	1	2	yes	complemented
106	C₃×#877	C₂²	1	2	yes	complemented
107	C₃×#876	C₂²	1	2	yes	complemented
108	C₃×#875	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₄×D₁₂	C₂²	1	2	yes	—
110	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
111	C₃×#872	C₂²	1	2	yes	—
112	C₃×#872	C₂²	1	2	yes	complemented
113	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
114	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
115	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
116	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
117	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
118	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
119	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
120	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
121	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
122	C₃×#870	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#533	—	3	1	no	—
126	C₃×#533	—	3	1	no	—
127	C₃×#533	—	3	1	no	—
128	C₃×#532	—	3	1	no	—
129	C₃×#532	—	3	1	no	—
130	C₃×#532	—	3	1	no	—
131	C₃×#529	—	2	1	no	—
132	C₃×#529	—	3	2	no	—
133	C₃×#529	—	3	2	no	—
134	C₃×#529	—	3	1	no	—
135	C₃×#529	—	3	1	no	—
136	C₃×#529	—	3	2	no	—
137	C₃×#529	—	3	2	no	—
138	C₃×#529	—	3	1	no	—
139	C₃×#529	D₃	1	1	yes	characteristic, complemented
140	C₃×#529	C₂×C₃	1	1	yes	characteristic, complemented
141	C₃×#525	—	3	2	no	—
142	C₃×#525	—	3	1	no	—
143	C₃×#525	—	3	1	no	—
144	C₃×#525	—	3	2	no	—
145	C₃×C₄×#41	—	3	1	no	—
146	C₃×C₄×#41	—	3	2	no	—
147	C₃×C₄×#41	—	3	1	no	—
148	C₃×C₄×#41	—	3	2	no	—
149	C₂²×C₃×C₄²	—	3	1	no	—
150	#5706	C₂×C₃	1	2	yes	complemented
151	#5706	C₂×C₃	1	2	yes	complemented
152	#5691	C₂×C₃	1	1	yes	characteristic, complemented
153	#5688	C₂×C₃	1	1	yes	characteristic, complemented
154	#5680	C₂×C₃	1	1	yes	characteristic, complemented
155	#5668	C₂×C₃	1	1	yes	characteristic, complemented
156	#5656	C₂×C₃	1	2	yes	complemented
157	#5649	C₂×C₃	1	2	yes	complemented
158	#5627	C₂×C₃	1	1	yes	characteristic, complemented
159	#5622	C₂×C₃	1	1	yes	characteristic, complemented
160	#5606	C₂×C₃	1	1	yes	characteristic, complemented
161	#5596	C₂×C₃	1	1	yes	characteristic, complemented
162	#5578	C₂×C₃	1	1	yes	characteristic, complemented
163	C₄×#239	C₂×C₃	1	1	yes	characteristic, complemented
164	#5548	C₂×C₃	1	1	yes	characteristic, complemented
165	#5547	C₂×C₃	1	2	yes	complemented
166	C₄×#237	C₂×C₃	1	1	yes	characteristic, complemented
167	C₄×#237	C₂×C₃	1	2	yes	complemented
168	#5528	C₂×C₃	1	2	yes	complemented
169	#5522	C₂×C₃	1	2	yes	complemented
170	#5479	C₂×C₃	1	1	yes	characteristic, complemented
171	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
174	C₂×C₃²×D₄	C₂³	1	2	yes	—
175	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃²×C₄	C₂³	1	2	yes	—
180	C₂×C₃×#67	C₂³	1	2	yes	—
181	C₂×C₃×#67	C₂³	1	2	yes	—
182	C₂×C₃×#67	C₂³	1	2	yes	—
183	C₂×C₃×#67	C₂³	1	2	yes	—
184	C₂×C₃×#67	C₂³	1	2	yes	—
185	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
186	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
187	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
188	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
189	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
190	C₃×#239	—	2	4	no	—
191	C₃×#237	—	2	8	no	—
192	C₃×#237	—	2	4	no	—
193	C₃×#235	—	2	8	no	—
194	C₂×C₃×D₁₂	C₂³	1	2	yes	—
195	C₂×C₃×D₁₂	C₂³	1	2	yes	—
196	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄×D₃	—	2	4	no	—
198	C₂×C₃×C₄×D₃	—	2	4	no	—
199	C₂×C₃×C₄×D₃	—	2	4	no	—
200	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
204	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
205	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
213	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
215	C₂×C₃×Dic₆	C₂³	1	2	yes	—
216	C₂×C₃×Dic₆	C₂³	1	2	yes	—
217	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
218	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
220	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
221	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
222	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
224	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃²×C₄²	C₂³	1	1	yes	characteristic
230	C₃²×C₄²	C₂³	1	1	yes	characteristic
231	C₃²×C₄²	C₂³	1	1	yes	characteristic
232	C₃²×C₄²	C₂³	1	1	yes	characteristic
233	C₃²×C₄²	C₂³	1	2	yes	—
234	C₃×#217	C₂³	1	2	yes	—
235	C₃×#217	C₂³	1	2	yes	—
236	C₃×#217	C₂³	1	2	yes	—
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
243	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
244	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
245	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
246	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
247	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
248	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
249	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
250	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
251	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
252	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
253	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
256	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
260	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
261	C₃×C₄×Dic₃	C₂³	1	2	yes	—
262	C₃×C₄×Dic₃	C₂³	1	2	yes	—
263	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
264	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
265	C₃×C₄×Dic₃	C₂³	1	2	yes	—
266	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
267	C₃×C₄×Dic₃	C₂³	1	2	yes	—
268	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
269	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
270	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
271	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
275	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
276	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
277	C₃×C₄×Dic₃	C₂³	1	2	yes	—
278	#3444	—	3	1	no	Sylow
279	C₂×C₃×#41	—	3	1	no	—
280	C₂×C₃×#41	—	3	2	no	—
281	C₂×C₃×#41	—	3	1	no	—
282	C₂×C₃×#41	—	3	2	no	—
283	C₂³×C₃×C₄	—	3	1	no	—
284	C₂³×C₃×C₄	—	3	1	no	—
285	C₂³×C₃×C₄	—	3	1	no	—
286	C₂×#239	C₂²×C₃	1	1	yes	characteristic
287	C₂×#237	C₂²×C₃	1	2	yes	—
288	C₂×#237	C₂²×C₃	1	1	yes	characteristic
289	C₂×#235	C₂²×C₃	1	2	yes	—
290	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
291	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
292	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
293	C₃×C₄⋊Q₈	—	3	1	no	—
294	C₃×C₄⋊Q₈	—	3	1	no	—
295	C₃×C₄⋊Q₈	—	3	1	no	—
296	C₃×#127	—	3	1	no	—
297	C₃×#126	—	2	2	no	—
298	C₃×#126	—	3	2	no	—
299	C₃×#126	—	3	2	no	—
300	C₃×#126	—	3	2	no	—
301	C₃×#126	C₂×D₃	1	2	yes	complemented
302	C₃×#126	C₂²×C₃	1	2	yes	complemented
303	C₃×#125	—	2	1	no	—
304	C₃×#125	—	3	2	no	—
305	C₃×#125	—	3	2	no	—
306	C₃×#125	—	3	1	no	—
307	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
308	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₃×#124	—	2	1	no	—
310	C₃×#124	—	3	2	no	—
311	C₃×#124	—	3	2	no	—
312	C₃×#124	—	3	1	no	—
313	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
314	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₃×#123	—	2	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×#123	—	3	2	no	—
318	C₃×#123	—	3	2	no	—
319	C₃×#123	—	3	2	no	—
320	C₃×#123	—	3	2	no	—
321	C₃×#123	C₂×D₃	1	2	yes	—
322	C₃×#123	C₂²×C₃	1	2	yes	—
323	C₃×C₂²⋊Q₈	—	2	1	no	—
324	C₃×C₂²⋊Q₈	—	3	1	no	—
325	C₃×C₂²⋊Q₈	—	3	1	no	—
326	C₃×C₂²⋊Q₈	—	3	2	no	—
327	C₃×C₂²⋊Q₈	—	3	2	no	—
328	C₃×C₂²⋊Q₈	—	3	2	no	—
329	C₃×C₂²⋊Q₈	—	3	1	no	—
330	C₃×C₂²⋊Q₈	—	3	2	no	—
331	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
332	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
333	C₃×#121	—	2	1	no	—
334	C₃×#121	—	3	1	no	—
335	C₃×#121	—	3	2	no	—
336	C₃×#121	—	3	1	no	—
337	C₃×#121	—	3	1	no	—
338	C₃×#121	—	3	2	no	—
339	C₃×#121	—	3	2	no	—
340	C₃×#121	—	3	2	no	—
341	C₃×#121	C₂×D₃	1	1	yes	characteristic
342	C₃×#121	C₂²×C₃	1	1	yes	characteristic
343	C₃×#120	—	3	2	no	—
344	C₃×#120	—	3	2	no	—
345	C₃×C₄×Q₈	—	2	1	no	—
346	C₃×C₄×Q₈	—	3	1	no	—
347	C₃×C₄×Q₈	—	3	2	no	—
348	C₃×C₄×Q₈	—	3	2	no	—
349	C₃×C₄×Q₈	—	3	2	no	—
350	C₃×C₄×Q₈	—	3	1	no	—
351	C₃×C₄×Q₈	—	3	2	no	—
352	C₃×C₄×Q₈	—	3	1	no	—
353	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
354	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
355	C₃×C₄×D₄	—	2	2	no	—
356	C₃×C₄×D₄	—	2	1	no	—
357	C₃×C₄×D₄	—	3	2	no	—
358	C₃×C₄×D₄	—	3	1	no	—
359	C₃×C₄×D₄	—	3	2	no	—
360	C₃×C₄×D₄	—	3	2	no	—
361	C₃×C₄×D₄	—	3	2	no	—
362	C₃×C₄×D₄	—	3	2	no	—
363	C₃×C₄×D₄	—	3	2	no	—
364	C₃×C₄×D₄	—	3	2	no	—
365	C₃×C₄×D₄	—	3	1	no	—
366	C₃×C₄×D₄	—	3	2	no	—
367	C₃×C₄×D₄	—	3	2	no	—
368	C₃×C₄×D₄	—	3	2	no	—
369	C₃×C₄×D₄	—	3	2	no	—
370	C₃×C₄×D₄	—	3	2	no	—
371	C₃×C₄×D₄	—	3	2	no	—
372	C₃×C₄×D₄	—	3	2	no	—
373	C₃×C₄×D₄	—	3	2	no	—
374	C₃×C₄×D₄	—	3	1	no	—
375	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
376	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
377	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
378	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
379	C₃×#117	—	2	2	no	—
380	C₃×#117	—	3	1	no	—
381	C₃×#117	—	3	1	no	—
382	C₃×#117	—	3	2	no	—
383	C₃×#117	—	3	2	no	—
384	C₃×#117	—	3	2	no	—
385	C₃×#117	—	3	2	no	—
386	C₃×#117	—	3	2	no	—
387	C₃×#117	—	3	2	no	—
388	C₃×#117	—	3	2	no	—
389	C₃×#117	C₂×D₃	1	2	yes	complemented
390	C₃×#117	C₂²×C₃	1	2	yes	complemented
391	C₂×C₃×C₄²	—	2	1	no	—
392	C₂×C₃×C₄²	—	3	1	no	—
393	C₂×C₃×C₄²	—	3	1	no	—
394	C₂×C₃×C₄²	—	3	1	no	—
395	C₂×C₃×C₄²	—	3	2	no	—
396	C₂×C₃×C₄²	—	3	1	no	—
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	—	3	1	no	—
399	C₂×C₃×C₄²	—	3	1	no	—
400	C₂×C₃×C₄²	—	3	1	no	—
401	C₂×C₃×C₄²	—	3	1	no	—
402	C₂×C₃×C₄²	—	3	1	no	—
403	C₂×C₃×C₄²	—	3	1	no	—
404	C₂×C₃×C₄²	—	3	2	no	—
405	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
406	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
407	#946	C₂²×C₃	1	1	yes	characteristic
408	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
409	#944	C₂²×C₃	1	1	yes	characteristic, complemented
410	#940	C₂²×C₃	1	1	yes	characteristic, complemented
411	#939	C₂²×C₃	1	2	yes	—
412	#938	C₂²×C₃	1	1	yes	characteristic
413	#937	C₂²×C₃	1	2	yes	—
414	D₄×Dic₃	C₂²×C₃	1	2	yes	—
415	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
416	#930	C₂²×C₃	1	1	yes	characteristic
417	#929	C₂²×C₃	1	2	yes	—
418	C₄×#67	C₂²×C₃	1	2	yes	—
419	C₄×#67	C₂²×C₃	1	2	yes	—
420	C₄×#67	C₂²×C₃	1	2	yes	complemented
421	#924	C₂²×C₃	1	1	yes	characteristic
422	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
423	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
424	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
425	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
426	#898	C₂²×C₃	1	2	yes	complemented
427	#897	C₂²×C₃	1	1	yes	characteristic
428	#896	C₂²×C₃	1	2	yes	—
429	#896	C₂²×C₃	1	2	yes	—
430	#896	C₂²×C₃	1	2	yes	—
431	#895	C₂²×C₃	1	1	yes	characteristic
432	#894	C₂²×C₃	1	2	yes	—
433	#894	C₂²×C₃	1	2	yes	—
434	#893	C₂²×C₃	1	2	yes	—
435	#893	C₂²×C₃	1	2	yes	—
436	#893	C₂²×C₃	1	2	yes	—
437	#893	C₂²×C₃	1	1	yes	characteristic, complemented
438	#892	C₂²×C₃	1	1	yes	characteristic
439	#892	C₂²×C₃	1	1	yes	characteristic
440	#892	C₂²×C₃	1	2	yes	complemented
441	#892	C₂²×C₃	1	2	yes	complemented
442	#889	C₂²×C₃	1	2	yes	complemented
443	#889	C₂²×C₃	1	2	yes	complemented
444	#888	C₂²×C₃	1	1	yes	characteristic, complemented
445	#888	C₂²×C₃	1	1	yes	characteristic, complemented
446	#887	C₂²×C₃	1	2	yes	complemented
447	#887	C₂²×C₃	1	2	yes	complemented
448	#887	C₂²×C₃	1	1	yes	characteristic, complemented
449	#887	C₂²×C₃	1	2	yes	complemented
450	#885	C₂²×C₃	1	2	yes	complemented
451	#885	C₂²×C₃	1	2	yes	complemented
452	#884	C₂²×C₃	1	2	yes	—
453	#884	C₂²×C₃	1	2	yes	—
454	#884	C₂²×C₃	1	2	yes	—
455	#883	C₂²×C₃	1	2	yes	—
456	#883	C₂²×C₃	1	2	yes	—
457	#882	C₂²×C₃	1	2	yes	—
458	#67⋊C₄	C₂²×C₃	1	2	yes	—
459	#67⋊C₄	C₂²×C₃	1	2	yes	—
460	#67⋊C₄	C₂²×C₃	1	2	yes	—
461	#67⋊C₄	C₂²×C₃	1	2	yes	—
462	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
463	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
464	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
465	#879	C₂²×C₃	1	2	yes	complemented
466	#878	C₂²×C₃	1	2	yes	—
467	#877	C₂²×C₃	1	2	yes	—
468	#877	C₂²×C₃	1	2	yes	complemented
469	#877	C₂²×C₃	1	2	yes	complemented
470	#876	C₂²×C₃	1	2	yes	complemented
471	#875	C₂²×C₃	1	1	yes	characteristic, complemented
472	C₄×D₁₂	C₂²×C₃	1	2	yes	—
473	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
474	#872	C₂²×C₃	1	2	yes	—
475	#872	C₂²×C₃	1	2	yes	complemented
476	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
477	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
478	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
479	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
480	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
481	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
482	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
483	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
484	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
485	#870	C₂²×C₃	1	1	yes	characteristic, complemented
486	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
487	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
488	C₂³×C₃²	C₂⁴	1	2	yes	—
489	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
490	C₂²×C₃×D₃	—	2	2	no	—
491	C₂²×C₃×D₃	—	2	2	no	—
492	C₂²×C₃×D₃	—	2	2	no	—
493	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
494	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
495	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
496	C₃²×Q₈	—	2	2	no	—
497	C₃²×D₄	—	2	4	no	—
498	C₃²×D₄	—	2	2	no	—
499	C₂×C₃²×C₄	—	2	2	no	—
500	C₂×C₃²×C₄	—	2	2	no	—
501	C₂×C₃²×C₄	—	2	2	no	—
502	C₂×C₃²×C₄	—	2	4	no	—
503	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
508	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
509	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
510	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
512	C₃×#67	—	2	4	no	—
513	C₃×#67	—	2	4	no	—
514	C₃×#67	—	2	4	no	—
515	C₃×#67	—	2	4	no	—
516	C₃×#67	—	2	4	no	—
517	C₂×C₃×Dic₃	—	2	2	no	—
518	C₂×C₃×Dic₃	—	2	2	no	—
519	C₂×C₃×Dic₃	—	2	4	no	—
520	C₂×C₃×Dic₃	—	2	4	no	—
521	C₂×C₃×Dic₃	#41	1	4	yes	complemented
522	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
525	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
526	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
527	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
528	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
529	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
530	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
531	C₃×D₁₂	—	2	4	no	—
532	C₃×D₁₂	—	2	4	no	—
533	C₃×D₁₂	—	2	2	no	—
534	C₃×C₄×D₃	—	2	2	no	—
535	C₃×C₄×D₃	—	2	2	no	—
536	C₃×C₄×D₃	—	2	2	no	—
537	C₃×C₄×D₃	—	2	2	no	—
538	C₃×C₄×D₃	—	2	4	no	—
539	C₃×C₄×D₃	—	2	2	no	—
540	C₃×C₄×D₃	—	2	2	no	—
541	C₃×C₄×D₃	—	2	2	no	—
542	C₃×C₄×D₃	—	2	2	no	—
543	C₃×C₄×D₃	—	2	2	no	—
544	C₃×C₄×D₃	—	2	2	no	—
545	C₃×C₄×D₃	—	2	4	no	—
546	C₃×C₄×D₃	—	2	4	no	—
547	C₃×C₄×D₃	#41	1	4	yes	complemented
548	C₃×C₄×D₃	#41	1	4	yes	complemented
549	C₃×Dic₆	—	2	2	no	—
550	C₃×Dic₆	—	2	4	no	—
551	C₃×Dic₆	—	2	4	no	—
552	#533	—	3	1	no	—
553	#533	—	3	1	no	—
554	#533	—	3	1	no	—
555	#532	—	3	1	no	—
556	#532	—	3	1	no	—
557	#532	—	3	1	no	—
558	#529	—	3	2	no	—
559	#529	—	3	2	no	—
560	#529	—	3	1	no	—
561	#529	—	3	1	no	—
562	#529	—	3	2	no	—
563	#529	—	3	2	no	—
564	#529	—	3	1	no	—
565	#529	C₃×D₃	1	1	yes	characteristic, complemented
566	#525	—	3	2	no	—
567	#525	—	3	1	no	—
568	#525	—	3	1	no	—
569	#525	—	3	2	no	—
570	C₄×#41	—	3	1	no	—
571	C₄×#41	—	3	2	no	—
572	C₄×#41	—	3	1	no	—
573	C₄×#41	—	3	2	no	—
574	C₂²×C₄²	—	3	1	no	—
575	C₂⁴×C₃	—	3	1	no	—
576	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
577	C₃×#41	—	6	8	no	—
578	C₃×#41	—	6	8	no	—
579	C₃×#41	—	6	4	no	—
580	C₃×#41	—	6	4	no	—
581	C₂×C₃×Q₈	—	2	1	no	—
582	C₂×C₃×Q₈	—	3	2	no	—
583	C₂×C₃×Q₈	—	3	2	no	—
584	C₂×C₃×Q₈	—	3	1	no	—
585	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
586	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₃×D₄	—	2	2	no	—
588	C₂×C₃×D₄	—	2	1	no	—
589	C₂×C₃×D₄	—	3	2	no	—
590	C₂×C₃×D₄	—	3	2	no	—
591	C₂×C₃×D₄	—	3	2	no	—
592	C₂×C₃×D₄	—	3	2	no	—
593	C₂×C₃×D₄	—	3	2	no	—
594	C₂×C₃×D₄	—	3	2	no	—
595	C₂×C₃×D₄	—	3	2	no	—
596	C₂×C₃×D₄	—	3	1	no	—
597	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
598	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
599	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
600	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
601	C₂²×C₃×C₄	—	2	1	no	—
602	C₂²×C₃×C₄	—	2	1	no	—
603	C₂²×C₃×C₄	—	2	1	no	—
604	C₂²×C₃×C₄	—	2	2	no	—
605	C₂²×C₃×C₄	—	3	1	no	—
606	C₂²×C₃×C₄	—	3	1	no	—
607	C₂²×C₃×C₄	—	3	1	no	—
608	C₂²×C₃×C₄	—	3	1	no	—
609	C₂²×C₃×C₄	—	3	1	no	—
610	C₂²×C₃×C₄	—	3	2	no	—
611	C₂²×C₃×C₄	—	3	2	no	—
612	C₂²×C₃×C₄	—	3	1	no	—
613	C₂²×C₃×C₄	—	3	1	no	—
614	C₂²×C₃×C₄	—	3	1	no	—
615	C₂²×C₃×C₄	—	3	1	no	—
616	C₂²×C₃×C₄	—	3	1	no	—
617	C₂²×C₃×C₄	—	3	1	no	—
618	C₂²×C₃×C₄	—	3	1	no	—
619	C₂²×C₃×C₄	—	3	1	no	—
620	C₂²×C₃×C₄	—	3	1	no	—
621	C₂²×C₃×C₄	—	3	2	no	—
622	C₂²×C₃×C₄	—	3	2	no	—
623	C₂²×C₃×C₄	—	3	1	no	—
624	C₂²×C₃×C₄	—	3	2	no	—
625	C₂²×C₃×C₄	—	6	4	no	—
626	C₂²×C₃×C₄	—	6	4	no	—
627	C₂²×C₃×C₄	—	6	4	no	—
628	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
629	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
630	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
631	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
632	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
634	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
636	C₂×#67	C₂³×C₃	1	2	yes	—
637	C₂×#67	C₂³×C₃	1	2	yes	—
638	C₂×#67	C₂³×C₃	1	2	yes	—
639	C₂×#67	C₂³×C₃	1	2	yes	—
640	C₂×#67	C₂³×C₃	1	2	yes	—
641	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
642	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
643	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
644	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
645	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
646	#239	—	2	4	no	—
647	#237	—	2	8	no	—
648	#237	—	2	4	no	—
649	#235	—	2	8	no	—
650	C₂×D₁₂	C₂³×C₃	1	2	yes	—
651	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
652	C₂×D₁₂	C₂³×C₃	1	2	yes	—
653	C₂×C₄×D₃	—	2	4	no	—
654	C₂×C₄×D₃	—	2	4	no	—
655	C₂×C₄×D₃	—	2	4	no	—
656	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
658	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
659	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
660	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
661	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
662	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
663	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
664	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
665	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
666	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
667	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
668	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
669	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
670	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
671	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
672	C₂×Dic₆	C₂³×C₃	1	2	yes	—
673	C₂×Dic₆	C₂³×C₃	1	2	yes	—
674	C₃×C₄⋊C₄	—	2	2	no	—
675	C₃×C₄⋊C₄	—	2	2	no	—
676	C₃×C₄⋊C₄	—	2	1	no	—
677	C₃×C₄⋊C₄	—	2	2	no	—
678	C₃×C₄⋊C₄	—	2	1	no	—
679	C₃×C₄⋊C₄	—	2	2	no	—
680	C₃×C₄⋊C₄	—	3	2	no	—
681	C₃×C₄⋊C₄	—	3	2	no	—
682	C₃×C₄⋊C₄	—	3	2	no	—
683	C₃×C₄⋊C₄	—	3	2	no	—
684	C₃×C₄⋊C₄	—	3	2	no	—
685	C₃×C₄⋊C₄	—	3	2	no	—
686	C₃×C₄⋊C₄	—	3	2	no	—
687	C₃×C₄⋊C₄	—	3	2	no	—
688	C₃×C₄⋊C₄	—	3	2	no	—
689	C₃×C₄⋊C₄	—	3	2	no	—
690	C₃×C₄⋊C₄	—	3	1	no	—
691	C₃×C₄⋊C₄	—	3	1	no	—
692	C₃×C₄⋊C₄	—	3	2	no	—
693	C₃×C₄⋊C₄	—	3	2	no	—
694	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
695	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
696	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
697	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
698	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
699	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
700	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
701	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
702	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
703	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
704	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
705	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
706	C₃×C₂²⋊C₄	—	2	2	no	—
707	C₃×C₂²⋊C₄	—	2	2	no	—
708	C₃×C₂²⋊C₄	—	2	2	no	—
709	C₃×C₂²⋊C₄	—	2	2	no	—
710	C₃×C₂²⋊C₄	—	2	2	no	—
711	C₃×C₂²⋊C₄	—	3	2	no	—
712	C₃×C₂²⋊C₄	—	3	2	no	—
713	C₃×C₂²⋊C₄	—	3	2	no	—
714	C₃×C₂²⋊C₄	—	3	2	no	—
715	C₃×C₂²⋊C₄	—	3	2	no	—
716	C₃×C₂²⋊C₄	—	3	2	no	—
717	C₃×C₂²⋊C₄	—	3	2	no	—
718	C₃×C₂²⋊C₄	—	3	2	no	—
719	C₃×C₂²⋊C₄	—	3	2	no	—
720	C₃×C₂²⋊C₄	—	3	2	no	—
721	C₃×C₂²⋊C₄	—	3	2	no	—
722	C₃×C₂²⋊C₄	—	3	2	no	—
723	C₃×C₂²⋊C₄	—	3	2	no	—
724	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
725	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
726	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
727	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
728	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
729	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
730	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
731	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
732	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
733	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
734	C₃×C₄²	—	2	1	no	—
735	C₃×C₄²	—	2	1	no	—
736	C₃×C₄²	—	2	1	no	—
737	C₃×C₄²	—	2	1	no	—
738	C₃×C₄²	—	2	2	no	—
739	C₃×C₄²	—	3	1	no	—
740	C₃×C₄²	—	3	1	no	—
741	C₃×C₄²	—	3	1	no	—
742	C₃×C₄²	—	3	1	no	—
743	C₃×C₄²	—	3	1	no	—
744	C₃×C₄²	—	3	1	no	—
745	C₃×C₄²	—	3	1	no	—
746	C₃×C₄²	—	3	1	no	—
747	C₃×C₄²	—	3	1	no	—
748	C₃×C₄²	—	3	1	no	—
749	C₃×C₄²	—	3	2	no	—
750	C₃×C₄²	—	3	2	no	—
751	C₃×C₄²	—	3	2	no	—
752	C₃×C₄²	—	3	2	no	—
753	C₃×C₄²	—	3	1	no	—
754	C₃×C₄²	—	3	1	no	—
755	C₃×C₄²	—	3	2	no	—
756	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
757	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
758	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
759	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
760	C₃×C₄²	C₂²×D₃	1	2	yes	—
761	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
762	C₃×C₄²	C₂³×C₃	1	2	yes	—
763	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
764	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
765	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
766	#217	C₂³×C₃	1	2	yes	—
767	#217	C₂³×C₃	1	2	yes	—
768	#217	C₂³×C₃	1	2	yes	—
769	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
770	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
771	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
772	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
773	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
774	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
775	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
776	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
777	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
778	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
779	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
780	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
781	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
782	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
785	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
788	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
789	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
790	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
791	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
792	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
793	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₃	1	2	yes	—
795	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
797	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
798	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
799	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
800	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
801	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
802	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
803	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
804	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
805	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
806	C₄×Dic₃	C₂³×C₃	1	2	yes	—
807	C₄×Dic₃	C₂³×C₃	1	2	yes	—
808	C₄×Dic₃	C₂³×C₃	1	2	yes	—
809	C₄×Dic₃	C₂³×C₃	1	2	yes	—
810	C₂²×C₃²	—	2	1	no	—
811	C₂²×C₃²	—	2	1	no	—
812	C₂²×C₃²	—	2	2	no	—
813	C₂²×C₃²	—	2	2	no	—
814	C₂²×C₃²	—	2	2	no	—
815	C₂²×C₃²	C₂×#41	1	2	yes	—
816	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
817	C₂×C₃×D₃	—	2	8	no	—
818	C₂×C₃×D₃	—	2	1	no	—
819	C₂×C₃×D₃	—	2	1	no	—
820	C₂×C₃×D₃	—	2	1	no	—
821	C₂×C₃×D₃	—	2	1	no	—
822	C₂×C₃×D₃	—	2	2	no	—
823	C₂×C₃×D₃	—	2	2	no	—
824	C₂×C₃×D₃	—	2	2	no	—
825	C₂×C₃×D₃	C₂×#41	1	2	yes	—
826	C₂×C₃×D₃	C₂×#41	1	2	yes	—
827	C₃²×C₄	—	2	2	no	—
828	C₃²×C₄	—	2	2	no	—
829	C₃²×C₄	—	2	1	no	—
830	C₃²×C₄	—	2	1	no	—
831	C₃²×C₄	—	2	1	no	—
832	C₃²×C₄	—	2	1	no	—
833	C₃²×C₄	—	2	2	no	—
834	C₃²×C₄	C₂×#41	1	2	yes	—
835	C₃²×C₄	C₂×#41	1	2	yes	—
836	C₃×Dic₃	—	2	2	no	—
837	C₃×Dic₃	—	2	2	no	—
838	C₃×Dic₃	—	2	2	no	—
839	C₃×Dic₃	—	2	1	no	—
840	C₃×Dic₃	—	2	1	no	—
841	C₃×Dic₃	C₂×#41	1	2	yes	—
842	C₃×Dic₃	C₂×#41	1	2	yes	—
843	C₃×Dic₃	C₂×#41	1	2	yes	—
844	C₃×Dic₃	C₂×#41	1	2	yes	—
845	C₂×#41	—	3	1	no	—
846	C₂×#41	—	3	2	no	—
847	C₂×#41	—	3	1	no	—
848	C₂×#41	—	3	2	no	—
849	C₂³×C₄	—	3	1	no	—
850	C₂³×C₄	—	3	1	no	—
851	C₂³×C₄	—	3	1	no	—
852	C₄⋊Q₈	—	3	1	no	—
853	C₄⋊Q₈	—	3	1	no	—
854	C₄⋊Q₈	—	3	1	no	—
855	#127	—	3	1	no	—
856	#126	—	3	2	no	—
857	#126	—	3	2	no	—
858	#126	—	3	2	no	—
859	#126	C₂×C₃×D₃	1	2	yes	complemented
860	#125	—	3	2	no	—
861	#125	—	3	2	no	—
862	#125	—	3	1	no	—
863	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
864	#124	—	3	2	no	—
865	#124	—	3	2	no	—
866	#124	—	3	1	no	—
867	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
868	#123	—	3	2	no	—
869	#123	—	3	2	no	—
870	#123	—	3	2	no	—
871	#123	—	3	2	no	—
872	#123	—	3	2	no	—
873	#123	C₂×C₃×D₃	1	2	yes	—
874	C₂²⋊Q₈	—	3	1	no	—
875	C₂²⋊Q₈	—	3	1	no	—
876	C₂²⋊Q₈	—	3	2	no	—
877	C₂²⋊Q₈	—	3	2	no	—
878	C₂²⋊Q₈	—	3	2	no	—
879	C₂²⋊Q₈	—	3	1	no	—
880	C₂²⋊Q₈	—	3	2	no	—
881	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
882	#121	—	3	1	no	—
883	#121	—	3	2	no	—
884	#121	—	3	1	no	—
885	#121	—	3	1	no	—
886	#121	—	3	2	no	—
887	#121	—	3	2	no	—
888	#121	—	3	2	no	—
889	#121	C₂×C₃×D₃	1	1	yes	characteristic
890	#120	—	3	2	no	—
891	#120	—	3	2	no	—
892	C₄×Q₈	—	3	1	no	—
893	C₄×Q₈	—	3	2	no	—
894	C₄×Q₈	—	3	2	no	—
895	C₄×Q₈	—	3	2	no	—
896	C₄×Q₈	—	3	1	no	—
897	C₄×Q₈	—	3	2	no	—
898	C₄×Q₈	—	3	1	no	—
899	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
900	C₄×D₄	—	3	2	no	—
901	C₄×D₄	—	3	1	no	—
902	C₄×D₄	—	3	2	no	—
903	C₄×D₄	—	3	2	no	—
904	C₄×D₄	—	3	2	no	—
905	C₄×D₄	—	3	2	no	—
906	C₄×D₄	—	3	2	no	—
907	C₄×D₄	—	3	2	no	—
908	C₄×D₄	—	3	1	no	—
909	C₄×D₄	—	3	2	no	—
910	C₄×D₄	—	3	2	no	—
911	C₄×D₄	—	3	2	no	—
912	C₄×D₄	—	3	2	no	—
913	C₄×D₄	—	3	2	no	—
914	C₄×D₄	—	3	2	no	—
915	C₄×D₄	—	3	2	no	—
916	C₄×D₄	—	3	2	no	—
917	C₄×D₄	—	3	1	no	—
918	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
919	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
920	#117	—	3	1	no	—
921	#117	—	3	1	no	—
922	#117	—	3	2	no	—
923	#117	—	3	2	no	—
924	#117	—	3	2	no	—
925	#117	—	3	2	no	—
926	#117	—	3	2	no	—
927	#117	—	3	2	no	—
928	#117	—	3	2	no	—
929	#117	C₂×C₃×D₃	1	2	yes	complemented
930	C₂×C₄²	—	3	2	no	—
931	C₂×C₄²	—	3	1	no	—
932	C₂×C₄²	—	3	1	no	—
933	C₂×C₄²	—	3	1	no	—
934	C₂×C₄²	—	3	2	no	—
935	C₂×C₄²	—	3	1	no	—
936	C₂×C₄²	—	3	1	no	—
937	C₂×C₄²	—	3	1	no	—
938	C₂×C₄²	—	3	1	no	—
939	C₂×C₄²	—	3	1	no	—
940	C₂×C₄²	—	3	1	no	—
941	C₂×C₄²	—	3	1	no	—
942	C₂×C₄²	—	3	1	no	—
943	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
944	C₂³×C₃	—	2	1	no	—
945	C₂³×C₃	—	2	2	no	—
946	C₂³×C₃	—	3	1	no	—
947	C₂³×C₃	—	3	1	no	—
948	C₂³×C₃	—	3	2	no	—
949	C₂³×C₃	—	6	2	no	—
950	C₂³×C₃	—	6	2	no	—
951	C₂³×C₃	—	6	2	no	—
952	C₂³×C₃	C₂³×D₃	1	2	yes	—
953	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
954	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
955	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
956	C₂²×D₃	—	2	2	no	—
957	C₂²×D₃	—	2	2	no	—
958	C₂²×D₃	—	2	2	no	—
959	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
960	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
961	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
962	C₃×Q₈	—	2	2	no	—
963	C₃×Q₈	—	2	2	no	—
964	C₃×Q₈	—	4	2	no	—
965	C₃×Q₈	—	6	4	no	—
966	C₃×Q₈	—	6	4	no	—
967	C₃×Q₈	—	6	2	no	—
968	C₃×D₄	—	2	4	no	—
969	C₃×D₄	—	2	4	no	—
970	C₃×D₄	—	2	2	no	—
971	C₃×D₄	—	2	2	no	—
972	C₃×D₄	—	4	2	no	—
973	C₃×D₄	—	4	4	no	—
974	C₃×D₄	—	6	4	no	—
975	C₃×D₄	—	6	4	no	—
976	C₃×D₄	—	6	4	no	—
977	C₃×D₄	—	6	4	no	—
978	C₃×D₄	—	6	4	no	—
979	C₃×D₄	—	6	4	no	—
980	C₃×D₄	—	6	4	no	—
981	C₃×D₄	—	6	2	no	—
982	C₂×C₃×C₄	—	2	2	no	—
983	C₂×C₃×C₄	—	2	2	no	—
984	C₂×C₃×C₄	—	2	2	no	—
985	C₂×C₃×C₄	—	2	2	no	—
986	C₂×C₃×C₄	—	2	4	no	—
987	C₂×C₃×C₄	—	2	2	no	—
988	C₂×C₃×C₄	—	2	2	no	—
989	C₂×C₃×C₄	—	2	4	no	—
990	C₂×C₃×C₄	—	2	1	no	—
991	C₂×C₃×C₄	—	2	1	no	—
992	C₂×C₃×C₄	—	2	1	no	—
993	C₂×C₃×C₄	—	2	1	no	—
994	C₂×C₃×C₄	—	2	1	no	—
995	C₂×C₃×C₄	—	2	1	no	—
996	C₂×C₃×C₄	—	2	2	no	—
997	C₂×C₃×C₄	—	2	2	no	—
998	C₂×C₃×C₄	—	2	2	no	—
999	C₂×C₃×C₄	—	3	4	no	—
1000	C₂×C₃×C₄	—	3	1	no	—
1001	C₂×C₃×C₄	—	3	1	no	—
1002	C₂×C₃×C₄	—	3	1	no	—
1003	C₂×C₃×C₄	—	3	1	no	—
1004	C₂×C₃×C₄	—	3	4	no	—
1005	C₂×C₃×C₄	—	3	4	no	—
1006	C₂×C₃×C₄	—	3	1	no	—
1007	C₂×C₃×C₄	—	3	1	no	—
1008	C₂×C₃×C₄	—	3	2	no	—
1009	C₂×C₃×C₄	—	3	2	no	—
1010	C₂×C₃×C₄	—	3	2	no	—
1011	C₂×C₃×C₄	—	4	2	no	—
1012	C₂×C₃×C₄	—	4	2	no	—
1013	C₂×C₃×C₄	—	4	4	no	—
1014	C₂×C₃×C₄	—	4	2	no	—
1015	C₂×C₃×C₄	—	6	2	no	—
1016	C₂×C₃×C₄	—	6	2	no	—
1017	C₂×C₃×C₄	—	6	2	no	—
1018	C₂×C₃×C₄	—	6	2	no	—
1019	C₂×C₃×C₄	—	6	2	no	—
1020	C₂×C₃×C₄	—	6	2	no	—
1021	C₂×C₃×C₄	—	6	4	no	—
1022	C₂×C₃×C₄	—	6	4	no	—
1023	C₂×C₃×C₄	—	6	2	no	—
1024	C₂×C₃×C₄	—	6	2	no	—
1025	C₂×C₃×C₄	—	6	2	no	—
1026	C₂×C₃×C₄	—	6	2	no	—
1027	C₂×C₃×C₄	—	6	4	no	—
1028	C₂×C₃×C₄	—	6	4	no	—
1029	C₂×C₃×C₄	—	6	2	no	—
1030	C₂×C₃×C₄	—	6	2	no	—
1031	C₂×C₃×C₄	—	6	4	no	—
1032	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1033	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1034	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1035	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1036	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1037	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1038	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1039	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1040	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1041	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1042	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1043	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1044	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1045	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1046	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1047	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1048	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1049	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1050	#67	—	2	4	no	—
1051	#67	—	2	4	no	—
1052	#67	—	2	4	no	—
1053	#67	—	2	4	no	—
1054	#67	—	2	4	no	—
1055	C₂×Dic₃	—	2	2	no	—
1056	C₂×Dic₃	—	2	2	no	—
1057	C₂×Dic₃	—	2	4	no	—
1058	C₂×Dic₃	—	2	4	no	—
1059	C₂×Dic₃	C₃×#41	1	4	yes	complemented
1060	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1061	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1062	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1063	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1064	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1065	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1066	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1067	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1068	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1069	D₁₂	—	2	4	no	—
1070	D₁₂	—	2	4	no	—
1071	D₁₂	—	2	2	no	—
1072	C₄×D₃	—	2	2	no	—
1073	C₄×D₃	—	2	2	no	—
1074	C₄×D₃	—	2	2	no	—
1075	C₄×D₃	—	2	2	no	—
1076	C₄×D₃	—	2	4	no	—
1077	C₄×D₃	—	2	2	no	—
1078	C₄×D₃	—	2	2	no	—
1079	C₄×D₃	—	2	2	no	—
1080	C₄×D₃	—	2	2	no	—
1081	C₄×D₃	—	2	2	no	—
1082	C₄×D₃	—	2	2	no	—
1083	C₄×D₃	—	2	4	no	—
1084	C₄×D₃	—	2	4	no	—
1085	C₄×D₃	C₃×#41	1	4	yes	complemented
1086	C₄×D₃	C₃×#41	1	4	yes	complemented
1087	Dic₆	—	2	2	no	—
1088	Dic₆	—	2	4	no	—
1089	Dic₆	—	2	4	no	—
1090	C₂×C₃²	—	2	2	no	—
1091	C₂×C₃²	—	4	2	no	—
1092	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1093	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1094	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1095	C₃×D₃	—	2	2	no	—
1096	C₃×D₃	—	2	2	no	—
1097	C₃×D₃	—	4	2	no	—
1098	C₂⁴	—	3	1	no	—
1099	#41	—	6	8	no	—
1100	#41	—	6	8	no	—
1101	#41	—	6	4	no	—
1102	#41	—	6	4	no	—
1103	C₂×Q₈	—	3	2	no	—
1104	C₂×Q₈	—	3	2	no	—
1105	C₂×Q₈	—	3	1	no	—
1106	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1107	C₂×D₄	—	3	2	no	—
1108	C₂×D₄	—	3	2	no	—
1109	C₂×D₄	—	3	2	no	—
1110	C₂×D₄	—	3	2	no	—
1111	C₂×D₄	—	3	2	no	—
1112	C₂×D₄	—	3	2	no	—
1113	C₂×D₄	—	3	2	no	—
1114	C₂×D₄	—	3	1	no	—
1115	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1116	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1117	C₂²×C₄	—	3	1	no	—
1118	C₂²×C₄	—	3	1	no	—
1119	C₂²×C₄	—	3	1	no	—
1120	C₂²×C₄	—	3	1	no	—
1121	C₂²×C₄	—	3	1	no	—
1122	C₂²×C₄	—	3	2	no	—
1123	C₂²×C₄	—	3	2	no	—
1124	C₂²×C₄	—	3	1	no	—
1125	C₂²×C₄	—	3	1	no	—
1126	C₂²×C₄	—	3	1	no	—
1127	C₂²×C₄	—	3	1	no	—
1128	C₂²×C₄	—	3	1	no	—
1129	C₂²×C₄	—	3	1	no	—
1130	C₂²×C₄	—	3	1	no	—
1131	C₂²×C₄	—	3	1	no	—
1132	C₂²×C₄	—	3	1	no	—
1133	C₂²×C₄	—	3	1	no	—
1134	C₂²×C₄	—	3	2	no	—
1135	C₂²×C₄	—	3	2	no	—
1136	C₂²×C₄	—	3	2	no	—
1137	C₂²×C₄	—	6	4	no	—
1138	C₂²×C₄	—	6	4	no	—
1139	C₂²×C₄	—	6	4	no	—
1140	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1144	C₄⋊C₄	—	3	2	no	—
1145	C₄⋊C₄	—	3	2	no	—
1146	C₄⋊C₄	—	3	2	no	—
1147	C₄⋊C₄	—	3	2	no	—
1148	C₄⋊C₄	—	3	1	no	—
1149	C₄⋊C₄	—	3	1	no	—
1150	C₄⋊C₄	—	3	2	no	—
1151	C₄⋊C₄	—	3	2	no	—
1152	C₄⋊C₄	—	3	2	no	—
1153	C₄⋊C₄	—	3	2	no	—
1154	C₄⋊C₄	—	3	2	no	—
1155	C₄⋊C₄	—	3	2	no	—
1156	C₄⋊C₄	—	3	2	no	—
1157	C₄⋊C₄	—	3	2	no	—
1158	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1159	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1160	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1161	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1162	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1163	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1164	C₂²⋊C₄	—	3	2	no	—
1165	C₂²⋊C₄	—	3	2	no	—
1166	C₂²⋊C₄	—	3	2	no	—
1167	C₂²⋊C₄	—	3	2	no	—
1168	C₂²⋊C₄	—	3	2	no	—
1169	C₂²⋊C₄	—	3	2	no	—
1170	C₂²⋊C₄	—	3	2	no	—
1171	C₂²⋊C₄	—	3	2	no	—
1172	C₂²⋊C₄	—	3	2	no	—
1173	C₂²⋊C₄	—	3	2	no	—
1174	C₂²⋊C₄	—	3	2	no	—
1175	C₂²⋊C₄	—	3	2	no	—
1176	C₂²⋊C₄	—	3	2	no	—
1177	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1178	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1179	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1180	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1181	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1182	C₄²	—	3	1	no	—
1183	C₄²	—	3	1	no	—
1184	C₄²	—	3	1	no	—
1185	C₄²	—	3	1	no	—
1186	C₄²	—	3	1	no	—
1187	C₄²	—	3	1	no	—
1188	C₄²	—	3	1	no	—
1189	C₄²	—	3	1	no	—
1190	C₄²	—	3	1	no	—
1191	C₄²	—	3	1	no	—
1192	C₄²	—	3	1	no	—
1193	C₄²	—	3	1	no	—
1194	C₄²	—	3	2	no	—
1195	C₄²	—	3	2	no	—
1196	C₄²	—	3	2	no	—
1197	C₄²	—	3	2	no	—
1198	C₄²	—	3	2	no	—
1199	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1200	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1201	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1202	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1203	C₄²	C₂²×C₃×D₃	1	2	yes	—
1204	C₂²×C₃	—	2	1	no	—
1205	C₂²×C₃	—	2	1	no	—
1206	C₂²×C₃	—	2	1	no	—
1207	C₂²×C₃	—	2	1	no	—
1208	C₂²×C₃	—	2	2	no	—
1209	C₂²×C₃	—	2	2	no	—
1210	C₂²×C₃	—	2	2	no	—
1211	C₂²×C₃	—	2	2	no	—
1212	C₂²×C₃	—	2	2	no	—
1213	C₂²×C₃	—	2	2	no	—
1214	C₂²×C₃	—	2	2	no	—
1215	C₂²×C₃	—	2	1	no	—
1216	C₂²×C₃	—	3	2	no	—
1217	C₂²×C₃	—	3	2	no	—
1218	C₂²×C₃	—	4	1	no	—
1219	C₂²×C₃	—	4	1	no	—
1220	C₂²×C₃	—	4	2	no	—
1221	C₂²×C₃	—	4	2	no	—
1222	C₂²×C₃	—	4	2	no	—
1223	C₂²×C₃	—	6	8	no	—
1224	C₂²×C₃	—	6	1	no	—
1225	C₂²×C₃	—	6	1	no	—
1226	C₂²×C₃	—	6	1	no	—
1227	C₂²×C₃	—	6	1	no	—
1228	C₂²×C₃	—	6	2	no	—
1229	C₂²×C₃	—	6	2	no	—
1230	C₂²×C₃	—	6	2	no	—
1231	C₂²×C₃	D₃×#41	1	2	yes	—
1232	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
1233	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1234	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1235	C₂×D₃	—	2	8	no	—
1236	C₂×D₃	—	2	1	no	—
1237	C₂×D₃	—	2	1	no	—
1238	C₂×D₃	—	2	1	no	—
1239	C₂×D₃	—	2	1	no	—
1240	C₂×D₃	—	2	2	no	—
1241	C₂×D₃	—	2	2	no	—
1242	C₂×D₃	—	2	2	no	—
1243	C₂×D₃	C₂×C₃×#41	1	2	yes	—
1244	C₂×D₃	C₂×C₃×#41	1	2	yes	—
1245	C₃×C₄	—	2	1	no	—
1246	C₃×C₄	—	2	1	no	—
1247	C₃×C₄	—	2	1	no	—
1248	C₃×C₄	—	2	1	no	—
1249	C₃×C₄	—	2	2	no	—
1250	C₃×C₄	—	2	2	no	—
1251	C₃×C₄	—	2	2	no	—
1252	C₃×C₄	—	2	2	no	—
1253	C₃×C₄	—	2	2	no	—
1254	C₃×C₄	—	2	1	no	—
1255	C₃×C₄	—	2	1	no	—
1256	C₃×C₄	—	2	1	no	—
1257	C₃×C₄	—	2	1	no	—
1258	C₃×C₄	—	2	2	no	—
1259	C₃×C₄	—	2	2	no	—
1260	C₃×C₄	—	2	2	no	—
1261	C₃×C₄	—	3	2	no	—
1262	C₃×C₄	—	3	2	no	—
1263	C₃×C₄	—	3	2	no	—
1264	C₃×C₄	—	3	2	no	—
1265	C₃×C₄	—	4	1	no	—
1266	C₃×C₄	—	4	1	no	—
1267	C₃×C₄	—	4	1	no	—
1268	C₃×C₄	—	4	1	no	—
1269	C₃×C₄	—	4	2	no	—
1270	C₃×C₄	—	4	2	no	—
1271	C₃×C₄	—	4	2	no	—
1272	C₃×C₄	—	6	1	no	—
1273	C₃×C₄	—	6	1	no	—
1274	C₃×C₄	—	6	2	no	—
1275	C₃×C₄	—	6	2	no	—
1276	C₃×C₄	—	6	2	no	—
1277	C₃×C₄	D₃×#41	1	2	yes	—
1278	C₃×C₄	D₃×#41	1	2	yes	—
1279	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1280	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1281	Dic₃	—	2	2	no	—
1282	Dic₃	—	2	2	no	—
1283	Dic₃	—	2	2	no	—
1284	Dic₃	—	2	1	no	—
1285	Dic₃	—	2	1	no	—
1286	Dic₃	C₂×C₃×#41	1	2	yes	—
1287	Dic₃	C₂×C₃×#41	1	2	yes	—
1288	Dic₃	C₂×C₃×#41	1	2	yes	—
1289	Dic₃	C₂×C₃×#41	1	2	yes	—
1290	C₃²	#3444	1	1	yes	characteristic, complemented, Sylow
1291	C₂³	—	3	1	no	—
1292	C₂³	—	3	1	no	—
1293	C₂³	—	3	2	no	—
1294	C₂³	—	6	2	no	—
1295	C₂³	—	6	2	no	—
1296	C₂³	—	6	2	no	—
1297	C₂³	C₂³×C₃×D₃	1	2	yes	—
1298	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1299	Q₈	—	2	2	no	—
1300	Q₈	—	6	4	no	—
1301	Q₈	—	6	4	no	—
1302	Q₈	—	6	2	no	—
1303	D₄	—	2	4	no	—
1304	D₄	—	2	2	no	—
1305	D₄	—	6	4	no	—
1306	D₄	—	6	4	no	—
1307	D₄	—	6	4	no	—
1308	D₄	—	6	4	no	—
1309	D₄	—	6	4	no	—
1310	D₄	—	6	4	no	—
1311	D₄	—	6	4	no	—
1312	D₄	—	6	2	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	2	no	—
1315	C₂×C₄	—	2	2	no	—
1316	C₂×C₄	—	2	4	no	—
1317	C₂×C₄	—	3	4	no	—
1318	C₂×C₄	—	3	1	no	—
1319	C₂×C₄	—	3	1	no	—
1320	C₂×C₄	—	3	1	no	—
1321	C₂×C₄	—	3	1	no	—
1322	C₂×C₄	—	3	4	no	—
1323	C₂×C₄	—	3	4	no	—
1324	C₂×C₄	—	3	1	no	—
1325	C₂×C₄	—	3	1	no	—
1326	C₂×C₄	—	3	2	no	—
1327	C₂×C₄	—	3	2	no	—
1328	C₂×C₄	—	3	2	no	—
1329	C₂×C₄	—	6	2	no	—
1330	C₂×C₄	—	6	2	no	—
1331	C₂×C₄	—	6	2	no	—
1332	C₂×C₄	—	6	2	no	—
1333	C₂×C₄	—	6	2	no	—
1334	C₂×C₄	—	6	2	no	—
1335	C₂×C₄	—	6	4	no	—
1336	C₂×C₄	—	6	4	no	—
1337	C₂×C₄	—	6	2	no	—
1338	C₂×C₄	—	6	2	no	—
1339	C₂×C₄	—	6	2	no	—
1340	C₂×C₄	—	6	2	no	—
1341	C₂×C₄	—	6	4	no	—
1342	C₂×C₄	—	6	4	no	—
1343	C₂×C₄	—	6	2	no	—
1344	C₂×C₄	—	6	2	no	—
1345	C₂×C₄	—	6	4	no	—
1346	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1347	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1348	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1349	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1350	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1351	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1352	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1353	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1354	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1355	C₂×C₃	—	2	2	no	—
1356	C₂×C₃	—	2	2	no	—
1357	C₂×C₃	—	2	1	no	—
1358	C₂×C₃	—	2	1	no	—
1359	C₂×C₃	—	2	1	no	—
1360	C₂×C₃	—	4	2	no	—
1361	C₂×C₃	—	4	2	no	—
1362	C₂×C₃	—	4	2	no	—
1363	C₂×C₃	—	6	2	no	—
1364	C₂×C₃	—	6	2	no	—
1365	C₂×C₃	—	8	2	no	—
1366	C₂×C₃	—	12	2	no	—
1367	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1368	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1369	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1370	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1371	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1372	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1373	D₃	—	2	2	no	—
1374	D₃	—	2	2	no	—
1375	D₃	—	4	2	no	—
1376	C₂²	—	2	1	no	—
1377	C₂²	—	2	1	no	—
1378	C₂²	—	2	2	no	—
1379	C₂²	—	2	2	no	—
1380	C₂²	—	2	2	no	—
1381	C₂²	—	3	2	no	—
1382	C₂²	—	3	2	no	—
1383	C₂²	—	6	8	no	—
1384	C₂²	—	6	1	no	—
1385	C₂²	—	6	1	no	—
1386	C₂²	—	6	1	no	—
1387	C₂²	—	6	1	no	—
1388	C₂²	—	6	2	no	—
1389	C₂²	—	6	2	no	—
1390	C₂²	—	6	2	no	—
1391	C₂²	C₃×D₃×#41	1	2	yes	—
1392	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1393	C₄	—	2	1	no	—
1394	C₄	—	2	1	no	—
1395	C₄	—	2	1	no	—
1396	C₄	—	2	1	no	—
1397	C₄	—	2	2	no	—
1398	C₄	—	2	2	no	—
1399	C₄	—	2	2	no	—
1400	C₄	—	3	2	no	—
1401	C₄	—	3	2	no	—
1402	C₄	—	3	2	no	—
1403	C₄	—	3	2	no	—
1404	C₄	—	6	1	no	—
1405	C₄	—	6	1	no	—
1406	C₄	—	6	2	no	—
1407	C₄	—	6	2	no	—
1408	C₄	—	6	2	no	—
1409	C₄	C₃×D₃×#41	1	2	yes	—
1410	C₄	C₃×D₃×#41	1	2	yes	—
1411	C₃	—	2	1	no	—
1412	C₃	#86119	1	1	yes	characteristic, direct product factor
1413	C₃	C₃×#3444	1	1	yes	characteristic, complemented
1414	C₂	—	2	2	no	—
1415	C₂	—	4	2	no	—
1416	C₂	—	6	2	no	—
1417	C₂	—	6	2	no	—
1418	C₂	—	12	2	no	—
1419	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1420	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1421	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#529	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#529	D₃
hypocenter	C₃	C₃×#3444
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
1. C₃²×#529	C₂	semidirect
2. C₃×#5706	C₂	semidirect
3. C₃×#5706	C₂	semidirect
4. C₃×#5691	C₂	semidirect
5. C₃×#5688	C₂	semidirect
6. C₃×#5680	C₂	semidirect
7. C₃×#5668	C₂	semidirect
8. C₃×#5656	C₂	semidirect
9. C₃×#5649	C₂	semidirect
10. C₃×#5627	C₂	semidirect
11. C₃×#5622	C₂	semidirect
12. C₃×#5606	C₂	semidirect
13. C₃×#5596	C₂	semidirect
14. C₃×#5578	C₂	semidirect
15. C₃×C₄×#239	C₂	semidirect
16. C₃×#5548	C₂	semidirect
17. C₃×#5547	C₂	semidirect
18. C₃×C₄×#237	C₂	semidirect
19. C₃×C₄×#237	C₂	semidirect
20. C₃×#5528	C₂	semidirect
21. C₃×#5522	C₂	semidirect
22. C₃×#5479	C₂	semidirect
23. C₂×C₃×C₄²×D₃	C₂	semidirect
25. #86119	C₃	direct (N × H)
33. C₃²×#126	C₂²	semidirect
34. C₃²×#125	C₂²	semidirect
35. C₃²×#124	C₂²	semidirect
39. C₃²×C₄×Q₈	C₂²	semidirect
41. C₃²×C₄×D₄	C₂²	semidirect
42. C₃²×#117	C₂²	semidirect
45. C₃×Q₈×Dic₃	C₂²	semidirect
46. C₃×#944	C₂²	semidirect
47. C₃×#940	C₂²	semidirect
52. C₃×D₄×Dic₃	C₂²	semidirect
57. C₃×C₄×#67	C₂²	semidirect
62. C₂×C₃×C₄×Dic₃	C₂²	semidirect
63. C₃×#898	C₂²	semidirect
74. C₃×#893	C₂²	semidirect
77. C₃×#892	C₂²	semidirect
78. C₃×#892	C₂²	semidirect
79. C₃×#889	C₂²	semidirect
80. C₃×#889	C₂²	semidirect
81. C₃×#888	C₂²	semidirect
82. C₃×#888	C₂²	semidirect
83. C₃×#887	C₂²	semidirect
84. C₃×#887	C₂²	semidirect
85. C₃×#887	C₂²	semidirect
86. C₃×#887	C₂²	semidirect
87. C₃×#885	C₂²	semidirect
88. C₃×#885	C₂²	semidirect
99. C₃×#67⋊C₄	C₂²	semidirect
100. C₃×#67⋊C₄	C₂²	semidirect
101. C₃×#67⋊C₄	C₂²	semidirect
102. C₃×#879	C₂²	semidirect
105. C₃×#877	C₂²	semidirect
106. C₃×#877	C₂²	semidirect
107. C₃×#876	C₂²	semidirect
108. C₃×#875	C₂²	semidirect
110. C₃×C₄×D₁₂	C₂²	semidirect
112. C₃×#872	C₂²	semidirect
121. C₃×C₄²×D₃	C₂²	semidirect
122. C₃×#870	C₂²	semidirect
123. C₃×C₄×Dic₆	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
139. C₃×#529	D₃	semidirect
140. C₃×#529	C₂×C₃	semidirect
150. #5706	C₂×C₃	semidirect
151. #5706	C₂×C₃	semidirect
152. #5691	C₂×C₃	semidirect
153. #5688	C₂×C₃	semidirect
154. #5680	C₂×C₃	semidirect
155. #5668	C₂×C₃	semidirect
156. #5656	C₂×C₃	semidirect
157. #5649	C₂×C₃	semidirect
158. #5627	C₂×C₃	semidirect
159. #5622	C₂×C₃	semidirect
160. #5606	C₂×C₃	semidirect
161. #5596	C₂×C₃	semidirect
162. #5578	C₂×C₃	semidirect
163. C₄×#239	C₂×C₃	semidirect
164. #5548	C₂×C₃	semidirect
165. #5547	C₂×C₃	semidirect
166. C₄×#237	C₂×C₃	semidirect
167. C₄×#237	C₂×C₃	semidirect
168. #5528	C₂×C₃	semidirect
169. #5522	C₂×C₃	semidirect
170. #5479	C₂×C₃	semidirect
171. C₂×C₄²×D₃	C₂×C₃	semidirect
301. C₃×#126	C₂×D₃	semidirect
302. C₃×#126	C₂²×C₃	semidirect
307. C₃×#125	C₂×D₃	semidirect
308. C₃×#125	C₂²×C₃	semidirect
313. C₃×#124	C₂×D₃	semidirect
314. C₃×#124	C₂²×C₃	semidirect
353. C₃×C₄×Q₈	C₂×D₃	semidirect
354. C₃×C₄×Q₈	C₂²×C₃	semidirect
376. C₃×C₄×D₄	C₂×D₃	semidirect
378. C₃×C₄×D₄	C₂²×C₃	semidirect
389. C₃×#117	C₂×D₃	semidirect
390. C₃×#117	C₂²×C₃	semidirect
408. Q₈×Dic₃	C₂²×C₃	semidirect
409. #944	C₂²×C₃	semidirect
410. #940	C₂²×C₃	semidirect
415. D₄×Dic₃	C₂²×C₃	semidirect
420. C₄×#67	C₂²×C₃	semidirect
425. C₂×C₄×Dic₃	C₂²×C₃	semidirect
426. #898	C₂²×C₃	semidirect
437. #893	C₂²×C₃	semidirect
440. #892	C₂²×C₃	semidirect
441. #892	C₂²×C₃	semidirect
442. #889	C₂²×C₃	semidirect
443. #889	C₂²×C₃	semidirect
444. #888	C₂²×C₃	semidirect
445. #888	C₂²×C₃	semidirect
446. #887	C₂²×C₃	semidirect
447. #887	C₂²×C₃	semidirect
448. #887	C₂²×C₃	semidirect
449. #887	C₂²×C₃	semidirect
450. #885	C₂²×C₃	semidirect
451. #885	C₂²×C₃	semidirect
462. #67⋊C₄	C₂²×C₃	semidirect
463. #67⋊C₄	C₂²×C₃	semidirect
464. #67⋊C₄	C₂²×C₃	semidirect
465. #879	C₂²×C₃	semidirect
468. #877	C₂²×C₃	semidirect
469. #877	C₂²×C₃	semidirect
470. #876	C₂²×C₃	semidirect
471. #875	C₂²×C₃	semidirect
473. C₄×D₁₂	C₂²×C₃	semidirect
475. #872	C₂²×C₃	semidirect
484. C₄²×D₃	C₂²×C₃	semidirect
485. #870	C₂²×C₃	semidirect
486. C₄×Dic₆	C₂²×C₃	semidirect
487. C₄×Dic₆	C₂²×C₃	semidirect
521. C₂×C₃×Dic₃	#41	semidirect
547. C₃×C₄×D₃	#41	semidirect
548. C₃×C₄×D₃	#41	semidirect
565. #529	C₃×D₃	semidirect
859. #126	C₂×C₃×D₃	semidirect
863. #125	C₂×C₃×D₃	semidirect
867. #124	C₂×C₃×D₃	semidirect
899. C₄×Q₈	C₂×C₃×D₃	semidirect
919. C₄×D₄	C₂×C₃×D₃	semidirect
929. #117	C₂×C₃×D₃	semidirect
1059. C₂×Dic₃	C₃×#41	semidirect
1085. C₄×D₃	C₃×#41	semidirect
1086. C₄×D₃	C₃×#41	semidirect
1290. C₃²	#3444	semidirect
1412. C₃	#86119	direct (N × H)
1413. C₃	C₃×#3444	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#529	2
C₃×#5706	2
C₃×#5691	2
C₃×#5688	2
C₃×#5680	2
C₃×#5668	2
C₃×#5656	2
C₃×#5649	2
C₃×#5627	2
C₃×#5622	2
C₃×#5606	2
C₃×#5596	2
C₃×#5578	2
C₃×C₄×#239	2
C₃×#5548	2
C₃×#5547	2
C₃×C₄×#237	2
C₃×#5528	2
C₃×#5522	2
C₃×#5479	2
C₂×C₃×C₄²×D₃	2
C₃×#3444	3
#86119	3

Subgroups — C3×#86119 #11900872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86119 #11900872