Subgroups — C₃×#86890 #11909394

Order 1152.

2203 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5708	C₂	1	2	yes	maximal, complemented
3	C₃×D₃×#126	C₂	1	2	yes	maximal, complemented
4	C₃×#5698	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5660	C₂	1	2	yes	maximal, complemented
7	C₃×#5658	C₂	1	2	yes	maximal, complemented
8	C₃×#5614	C₂	1	2	yes	maximal, complemented
9	C₃×#5613	C₂	1	2	yes	maximal, complemented
10	C₃×#5612	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5612	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5603	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5600	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5557	C₂	1	2	yes	maximal, complemented
15	C₃×#5556	C₂	1	2	yes	maximal, complemented
16	C₃×#5551	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5545	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#5542	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#5533	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#5522	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#5513	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#5504	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3521	—	3	1	no	maximal
25	#86890	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×#235	C₂²	1	1	yes	characteristic
28	C₂×C₃×#235	C₂²	1	1	yes	characteristic
29	C₃²×#126	C₂²	1	2	yes	complemented
30	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#123	C₂²	1	2	yes	complemented
32	C₃²×#121	C₂²	1	1	yes	characteristic
33	C₃²×#121	C₂²	1	1	yes	characteristic
34	C₃²×#121	C₂²	1	2	yes	complemented
35	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
38	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×#939	C₂²	1	1	yes	characteristic
41	C₃×#938	C₂²	1	2	yes	—
42	C₃×#938	C₂²	1	2	yes	—
43	C₃×#938	C₂²	1	2	yes	complemented
44	C₃×#937	C₂²	1	2	yes	—
45	C₃×#937	C₂²	1	2	yes	—
46	C₃×#936	C₂²	1	1	yes	characteristic
47	C₃×#936	C₂²	1	1	yes	characteristic
48	C₃×#936	C₂²	1	2	yes	complemented
49	C₃×#935	C₂²	1	1	yes	characteristic, complemented
50	C₃×#935	C₂²	1	2	yes	complemented
51	C₃×#935	C₂²	1	2	yes	complemented
52	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
53	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
54	C₃×#929	C₂²	1	2	yes	—
55	C₃×C₄×#67	C₂²	1	1	yes	characteristic
56	C₃×C₄×#67	C₂²	1	1	yes	characteristic
57	C₃×C₄×#67	C₂²	1	2	yes	—
58	C₃×C₄×#67	C₂²	1	2	yes	complemented
59	C₃×C₄×#67	C₂²	1	2	yes	complemented
60	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
61	C₃×#926	C₂²	1	1	yes	characteristic, complemented
62	C₃×#926	C₂²	1	2	yes	complemented
63	C₃×#926	C₂²	1	2	yes	complemented
64	C₃×#924	C₂²	1	1	yes	characteristic, complemented
65	C₃×#924	C₂²	1	1	yes	characteristic, complemented
66	C₃×#924	C₂²	1	2	yes	complemented
67	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
68	C₃×#898	C₂²	1	2	yes	—
69	C₃×#898	C₂²	1	1	yes	characteristic
70	C₃×#898	C₂²	1	2	yes	—
71	C₃×#898	C₂²	1	2	yes	—
72	C₃×#897	C₂²	1	1	yes	characteristic
73	C₃×#897	C₂²	1	1	yes	characteristic
74	C₃×#897	C₂²	1	2	yes	complemented
75	C₃×#896	C₂²	1	2	yes	complemented
76	C₃×#896	C₂²	1	2	yes	complemented
77	C₃×#893	C₂²	1	1	yes	characteristic
78	C₃×#893	C₂²	1	1	yes	characteristic
79	C₃×#893	C₂²	1	1	yes	characteristic
80	C₃×#892	C₂²	1	1	yes	characteristic
81	C₃×#892	C₂²	1	2	yes	complemented
82	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
84	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₃×#890	C₂²	1	1	yes	characteristic, complemented
86	C₃×#890	C₂²	1	2	yes	complemented
87	C₃×#890	C₂²	1	2	yes	complemented
88	C₃×#889	C₂²	1	2	yes	complemented
89	C₃×#889	C₂²	1	1	yes	characteristic, complemented
90	C₃×#888	C₂²	1	1	yes	characteristic, complemented
91	C₃×#887	C₂²	1	1	yes	characteristic, complemented
92	C₃×#887	C₂²	1	1	yes	characteristic, complemented
93	C₃×#887	C₂²	1	1	yes	characteristic, complemented
94	C₃×#887	C₂²	1	1	yes	characteristic, complemented
95	C₃×#886	C₂²	1	1	yes	characteristic
96	C₃×#885	C₂²	1	2	yes	—
97	C₃×#885	C₂²	1	1	yes	characteristic
98	C₃×#883	C₂²	1	2	yes	—
99	C₃×#883	C₂²	1	2	yes	—
100	C₃×#883	C₂²	1	2	yes	complemented
101	C₃×#883	C₂²	1	2	yes	complemented
102	C₃×#67⋊C₄	C₂²	1	2	yes	—
103	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
104	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
105	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₃×#879	C₂²	1	2	yes	complemented
109	C₃×#879	C₂²	1	1	yes	characteristic, complemented
110	C₃×#879	C₂²	1	2	yes	complemented
111	C₃×#879	C₂²	1	2	yes	complemented
112	C₃×#879	C₂²	1	2	yes	complemented
113	C₃×#879	C₂²	1	2	yes	complemented
114	C₃×#878	C₂²	1	1	yes	characteristic, complemented
115	C₃×#878	C₂²	1	2	yes	complemented
116	C₃×#877	C₂²	1	2	yes	complemented
117	C₃×#876	C₂²	1	2	yes	—
118	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
119	C₃×#872	C₂²	1	1	yes	characteristic
120	C₃×#872	C₂²	1	2	yes	complemented
121	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
122	C₃×#869	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×#556	—	3	1	no	—
126	C₃×#556	—	3	1	no	—
127	C₃×#554	—	3	1	no	—
128	C₃×#553	—	2	1	no	—
129	C₃×#553	—	3	2	no	—
130	C₃×#553	D₃	1	1	yes	characteristic, complemented
131	C₃×#553	C₂×C₃	1	1	yes	characteristic, complemented
132	C₃×#552	—	3	2	no	—
133	C₃×#552	—	3	1	no	—
134	C₃×#551	—	3	2	no	—
135	C₃×#551	—	3	2	no	—
136	C₃×#547	—	3	1	no	—
137	C₃×#546	—	3	1	no	—
138	C₃×#546	—	3	1	no	—
139	C₃×#542	—	3	1	no	—
140	C₃×#541	—	3	1	no	—
141	C₃×#539	—	3	2	no	—
142	C₃×#538	—	3	2	no	—
143	C₃×#529	—	3	1	no	—
144	C₃×#529	—	3	1	no	—
145	C₃×#529	—	3	2	no	—
146	C₂×C₃×#126	—	3	2	no	—
147	C₃×#520	—	3	1	no	—
148	C₃×#518	—	3	1	no	—
149	C₃×C₄×#41	—	3	1	no	—
150	#5708	C₂×C₃	1	2	yes	complemented
151	D₃×#126	C₂×C₃	1	2	yes	complemented
152	#5698	C₂×C₃	1	1	yes	characteristic, complemented
153	#5690	C₂×C₃	1	1	yes	characteristic, complemented
154	#5660	C₂×C₃	1	2	yes	complemented
155	#5658	C₂×C₃	1	2	yes	complemented
156	#5614	C₂×C₃	1	2	yes	complemented
157	#5613	C₂×C₃	1	2	yes	complemented
158	#5612	C₂×C₃	1	1	yes	characteristic, complemented
159	#5612	C₂×C₃	1	1	yes	characteristic, complemented
160	#5603	C₂×C₃	1	1	yes	characteristic, complemented
161	#5600	C₂×C₃	1	1	yes	characteristic, complemented
162	#5557	C₂×C₃	1	2	yes	complemented
163	#5556	C₂×C₃	1	2	yes	complemented
164	#5551	C₂×C₃	1	1	yes	characteristic, complemented
165	#5545	C₂×C₃	1	1	yes	characteristic, complemented
166	#5542	C₂×C₃	1	1	yes	characteristic, complemented
167	#5538	C₂×C₃	1	1	yes	characteristic, complemented
168	#5533	C₂×C₃	1	1	yes	characteristic, complemented
169	#5522	C₂×C₃	1	1	yes	characteristic, complemented
170	#5513	C₂×C₃	1	1	yes	characteristic, complemented
171	#5504	C₂×C₃	1	1	yes	characteristic, complemented
172	C₂³×C₃×D₃	C₂³	1	2	yes	—
173	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
174	C₂×C₃²×D₄	C₂³	1	2	yes	—
175	C₂×C₃²×D₄	C₂³	1	2	yes	—
176	C₂×C₃²×D₄	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	C₂²×C₃²×C₄	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	1	yes	characteristic
185	C₂×C₃×#67	C₂³	1	1	yes	characteristic
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	C₃×D₃×D₄	—	2	4	no	—
190	C₃×#235	—	2	4	no	—
191	C₃×#235	—	2	4	no	—
192	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
194	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
197	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
198	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
201	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
202	C₂×C₃×Dic₆	C₂³	1	2	yes	—
203	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
204	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₃²×C₄²	C₂³	1	2	yes	—
218	C₃²×C₄²	C₂³	1	1	yes	characteristic
219	C₃×#217	C₂³	1	2	yes	—
220	C₃×#217	C₂³	1	1	yes	characteristic
221	C₃×#217	C₂³	1	2	yes	—
222	C₃×#217	C₂³	1	2	yes	—
223	C₃×#217	C₂³	1	2	yes	—
224	C₃×#217	C₂³	1	2	yes	—
225	C₃×#217	C₂³	1	2	yes	—
226	C₃×#217	C₂³	1	1	yes	characteristic
227	C₃×#217	C₂³	1	1	yes	characteristic
228	C₃×#217	C₂³	1	2	yes	—
229	C₃×#217	C₂³	1	1	yes	characteristic
230	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
231	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
232	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
233	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
235	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
241	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
242	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
243	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
244	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
245	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
246	C₃×C₄⋊Dic₃	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×Dic₃⋊C₄	C₂³	1	2	yes	—
251	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
252	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
253	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
259	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
260	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
261	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
263	C₃×Dic₃⋊C₄	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	2	yes	—
269	C₃×C₄×Dic₃	C₂³	1	2	yes	—
270	C₃×C₄×Dic₃	C₂³	1	2	yes	—
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	#3521	—	3	1	no	Sylow
275	C₂×C₃×#41	—	3	1	no	—
276	C₂×C₃×#41	—	3	1	no	—
277	C₂²×C₃×D₄	—	3	1	no	—
278	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
279	C₂×#235	C₂²×C₃	1	1	yes	characteristic
280	C₂×#235	C₂²×C₃	1	1	yes	characteristic
281	C₃×C₄⋊Q₈	—	3	1	no	—
282	C₃×C₄⋊Q₈	—	3	1	no	—
283	C₃×#126	—	2	2	no	—
284	C₃×#126	—	3	1	no	—
285	C₃×#126	—	3	2	no	—
286	C₃×#126	—	3	2	no	—
287	C₃×#126	—	3	2	no	—
288	C₃×#126	—	3	2	no	—
289	C₃×#126	—	3	2	no	—
290	C₃×#126	—	3	2	no	—
291	C₃×#126	—	3	1	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	2	no	—
295	C₃×#126	C₂×D₃	1	2	yes	complemented
296	C₃×#126	C₂²×C₃	1	2	yes	complemented
297	C₃×#125	—	2	1	no	—
298	C₃×#125	—	3	1	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	2	no	—
301	C₃×#125	—	3	1	no	—
302	C₃×#125	—	3	2	no	—
303	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
304	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₃×#124	—	3	1	no	—
306	C₃×#124	—	3	1	no	—
307	C₃×#124	—	3	2	no	—
308	C₃×#124	—	3	1	no	—
309	C₃×#124	—	3	2	no	—
310	C₃×#123	—	2	2	no	—
311	C₃×#123	—	3	2	no	—
312	C₃×#123	—	3	1	no	—
313	C₃×#123	—	3	2	no	—
314	C₃×#123	—	3	2	no	—
315	C₃×#123	—	3	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×#123	—	3	2	no	—
318	C₃×#123	—	3	2	no	—
319	C₃×#123	—	3	1	no	—
320	C₃×#123	C₂×D₃	1	2	yes	complemented
321	C₃×#123	C₂²×C₃	1	2	yes	complemented
322	C₃×C₂²⋊Q₈	—	3	1	no	—
323	C₃×C₂²⋊Q₈	—	3	2	no	—
324	C₃×C₂²⋊Q₈	—	3	1	no	—
325	C₃×C₂²⋊Q₈	—	3	2	no	—
326	C₃×C₂²⋊Q₈	—	3	2	no	—
327	C₃×C₂²⋊Q₈	—	3	1	no	—
328	C₃×C₂²⋊Q₈	—	3	1	no	—
329	C₃×C₂²⋊Q₈	—	3	2	no	—
330	C₃×C₂²⋊Q₈	—	3	1	no	—
331	C₃×C₂²⋊Q₈	—	3	2	no	—
332	C₃×#121	—	2	1	no	—
333	C₃×#121	—	2	1	no	—
334	C₃×#121	—	2	2	no	—
335	C₃×#121	—	3	2	no	—
336	C₃×#121	—	3	2	no	—
337	C₃×#121	—	3	2	no	—
338	C₃×#121	—	3	1	no	—
339	C₃×#121	C₂×D₃	1	1	yes	characteristic
340	C₃×#121	C₂×D₃	1	1	yes	characteristic
341	C₃×#121	C₂×D₃	1	2	yes	complemented
342	C₃×#121	C₂²×C₃	1	1	yes	characteristic
343	C₃×#121	C₂²×C₃	1	1	yes	characteristic
344	C₃×#121	C₂²×C₃	1	2	yes	complemented
345	C₃×#120	—	3	2	no	—
346	C₃×#120	—	3	2	no	—
347	C₃×C₄×Q₈	—	3	1	no	—
348	C₃×C₄×Q₈	—	3	1	no	—
349	C₃×C₄×Q₈	—	3	1	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×D₄	—	2	1	no	—
354	C₃×C₄×D₄	—	2	1	no	—
355	C₃×C₄×D₄	—	2	2	no	—
356	C₃×C₄×D₄	—	3	1	no	—
357	C₃×C₄×D₄	—	3	2	no	—
358	C₃×C₄×D₄	—	3	2	no	—
359	C₃×C₄×D₄	—	3	1	no	—
360	C₃×C₄×D₄	—	3	1	no	—
361	C₃×C₄×D₄	—	3	2	no	—
362	C₃×C₄×D₄	—	3	2	no	—
363	C₃×C₄×D₄	—	3	1	no	—
364	C₃×C₄×D₄	—	3	1	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	1	no	—
370	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
371	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
372	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
373	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
374	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
375	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
376	C₃×#117	—	2	1	no	—
377	C₃×#117	—	3	1	no	—
378	C₃×#117	—	3	2	no	—
379	C₃×#117	—	3	2	no	—
380	C₃×#117	—	3	1	no	—
381	C₃×#117	—	3	2	no	—
382	C₃×#117	—	3	2	no	—
383	C₃×#117	—	3	2	no	—
384	C₃×#117	—	3	1	no	—
385	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
386	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
387	C₂×C₃×C₄⋊C₄	—	2	1	no	—
388	C₂×C₃×C₄⋊C₄	—	3	2	no	—
389	C₂×C₃×C₄⋊C₄	—	3	2	no	—
390	C₂×C₃×C₄⋊C₄	—	3	2	no	—
391	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
392	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
393	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
394	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
395	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
396	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
397	C₂×C₃×C₄²	—	3	1	no	—
398	C₂×C₃×C₄²	—	3	2	no	—
399	#939	C₂²×C₃	1	1	yes	characteristic
400	#938	C₂²×C₃	1	2	yes	—
401	#938	C₂²×C₃	1	2	yes	—
402	#938	C₂²×C₃	1	2	yes	complemented
403	#937	C₂²×C₃	1	2	yes	—
404	#937	C₂²×C₃	1	2	yes	—
405	#936	C₂²×C₃	1	1	yes	characteristic
406	#936	C₂²×C₃	1	1	yes	characteristic
407	#936	C₂²×C₃	1	2	yes	complemented
408	#935	C₂²×C₃	1	2	yes	complemented
409	#935	C₂²×C₃	1	1	yes	characteristic, complemented
410	#935	C₂²×C₃	1	2	yes	complemented
411	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
412	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
413	#929	C₂²×C₃	1	2	yes	—
414	C₄×#67	C₂²×C₃	1	2	yes	—
415	C₄×#67	C₂²×C₃	1	1	yes	characteristic
416	C₄×#67	C₂²×C₃	1	1	yes	characteristic
417	C₄×#67	C₂²×C₃	1	2	yes	complemented
418	C₄×#67	C₂²×C₃	1	2	yes	complemented
419	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
420	#926	C₂²×C₃	1	2	yes	complemented
421	#926	C₂²×C₃	1	1	yes	characteristic, complemented
422	#926	C₂²×C₃	1	2	yes	complemented
423	#924	C₂²×C₃	1	2	yes	complemented
424	#924	C₂²×C₃	1	1	yes	characteristic, complemented
425	#924	C₂²×C₃	1	1	yes	characteristic, complemented
426	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
427	#898	C₂²×C₃	1	2	yes	—
428	#898	C₂²×C₃	1	2	yes	—
429	#898	C₂²×C₃	1	2	yes	—
430	#898	C₂²×C₃	1	1	yes	characteristic
431	#897	C₂²×C₃	1	1	yes	characteristic
432	#897	C₂²×C₃	1	1	yes	characteristic
433	#897	C₂²×C₃	1	2	yes	complemented
434	#896	C₂²×C₃	1	2	yes	complemented
435	#896	C₂²×C₃	1	2	yes	complemented
436	#893	C₂²×C₃	1	1	yes	characteristic
437	#893	C₂²×C₃	1	1	yes	characteristic
438	#893	C₂²×C₃	1	1	yes	characteristic
439	#892	C₂²×C₃	1	1	yes	characteristic
440	#892	C₂²×C₃	1	2	yes	complemented
441	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
442	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
443	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
444	#890	C₂²×C₃	1	2	yes	complemented
445	#890	C₂²×C₃	1	1	yes	characteristic, complemented
446	#890	C₂²×C₃	1	2	yes	complemented
447	#889	C₂²×C₃	1	2	yes	complemented
448	#889	C₂²×C₃	1	1	yes	characteristic, complemented
449	#888	C₂²×C₃	1	1	yes	characteristic, complemented
450	#887	C₂²×C₃	1	1	yes	characteristic, complemented
451	#887	C₂²×C₃	1	1	yes	characteristic, complemented
452	#887	C₂²×C₃	1	1	yes	characteristic, complemented
453	#887	C₂²×C₃	1	1	yes	characteristic, complemented
454	#886	C₂²×C₃	1	1	yes	characteristic
455	#885	C₂²×C₃	1	2	yes	—
456	#885	C₂²×C₃	1	1	yes	characteristic
457	#883	C₂²×C₃	1	2	yes	—
458	#883	C₂²×C₃	1	2	yes	—
459	#883	C₂²×C₃	1	2	yes	complemented
460	#883	C₂²×C₃	1	2	yes	complemented
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	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
465	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
466	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
467	#879	C₂²×C₃	1	2	yes	complemented
468	#879	C₂²×C₃	1	2	yes	complemented
469	#879	C₂²×C₃	1	2	yes	complemented
470	#879	C₂²×C₃	1	2	yes	complemented
471	#879	C₂²×C₃	1	2	yes	complemented
472	#879	C₂²×C₃	1	1	yes	characteristic, complemented
473	#878	C₂²×C₃	1	2	yes	complemented
474	#878	C₂²×C₃	1	1	yes	characteristic, complemented
475	#877	C₂²×C₃	1	2	yes	complemented
476	#876	C₂²×C₃	1	2	yes	—
477	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
478	#872	C₂²×C₃	1	1	yes	characteristic
479	#872	C₂²×C₃	1	2	yes	complemented
480	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
481	#869	C₂²×C₃	1	1	yes	characteristic, complemented
482	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
484	C₂³×C₃²	C₂⁴	1	2	yes	—
485	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
486	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
487	C₂²×C₃×D₃	—	2	4	no	—
488	C₂²×C₃×D₃	—	4	2	no	—
489	C₂²×C₃×D₃	—	4	2	no	—
490	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
491	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
492	C₃²×D₄	—	2	2	no	—
493	C₃²×D₄	—	4	2	no	—
494	C₃²×D₄	—	4	1	no	—
495	C₃²×D₄	—	4	2	no	—
496	C₂×C₃²×C₄	—	2	2	no	—
497	C₂×C₃²×C₄	—	2	2	no	—
498	C₂×C₃²×C₄	—	4	2	no	—
499	C₂×C₃²×C₄	—	4	2	no	—
500	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
501	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
503	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
507	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
508	C₃×#67	—	2	4	no	—
509	C₃×#67	—	2	4	no	—
510	C₃×#67	—	2	4	no	—
511	C₃×#67	—	4	1	no	—
512	C₃×#67	—	4	1	no	—
513	C₂×C₃×Dic₃	—	4	2	no	—
514	C₂×C₃×Dic₃	—	4	1	no	—
515	C₂×C₃×Dic₃	—	4	1	no	—
516	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
517	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
518	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
519	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
520	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
521	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
522	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
523	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
524	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
525	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
526	C₃×D₁₂	#41	1	4	yes	—
527	C₃×C₄×D₃	—	2	4	no	—
528	C₃×C₄×D₃	—	2	4	no	—
529	C₃×C₄×D₃	—	2	2	no	—
530	C₃×C₄×D₃	—	4	2	no	—
531	C₃×C₄×D₃	—	4	2	no	—
532	C₃×C₄×D₃	—	4	2	no	—
533	C₃×C₄×D₃	—	4	2	no	—
534	C₃×Dic₆	—	2	2	no	—
535	C₃×Dic₆	—	2	2	no	—
536	C₃×Dic₆	—	4	2	no	—
537	C₃×Dic₆	—	4	1	no	—
538	#556	—	3	1	no	—
539	#556	—	3	1	no	—
540	#554	—	3	1	no	—
541	#553	—	3	2	no	—
542	#553	C₃×D₃	1	1	yes	characteristic, complemented
543	#552	—	3	2	no	—
544	#552	—	3	1	no	—
545	#551	—	3	2	no	—
546	#551	—	3	2	no	—
547	#547	—	3	1	no	—
548	#546	—	3	1	no	—
549	#546	—	3	1	no	—
550	#542	—	3	1	no	—
551	#541	—	3	1	no	—
552	#539	—	3	2	no	—
553	#538	—	3	2	no	—
554	#529	—	3	1	no	—
555	#529	—	3	1	no	—
556	#529	—	3	2	no	—
557	C₂×#126	—	3	2	no	—
558	#520	—	3	1	no	—
559	#518	—	3	1	no	—
560	C₄×#41	—	3	1	no	—
561	C₂⁴×C₃	—	3	2	no	—
562	C₂³×D₃	C₂³×C₃	1	2	yes	—
563	C₃×#41	—	6	4	no	—
564	C₃×#41	—	6	4	no	—
565	C₂×C₃×Q₈	—	3	1	no	—
566	C₂×C₃×Q₈	—	3	1	no	—
567	C₂×C₃×Q₈	—	3	1	no	—
568	C₂×C₃×Q₈	—	3	2	no	—
569	C₂×C₃×D₄	—	2	1	no	—
570	C₂×C₃×D₄	—	2	2	no	—
571	C₂×C₃×D₄	—	2	1	no	—
572	C₂×C₃×D₄	—	2	2	no	—
573	C₂×C₃×D₄	—	3	2	no	—
574	C₂×C₃×D₄	—	3	2	no	—
575	C₂×C₃×D₄	—	3	2	no	—
576	C₂×C₃×D₄	—	3	1	no	—
577	C₂×C₃×D₄	—	3	1	no	—
578	C₂×C₃×D₄	—	3	1	no	—
579	C₂×C₃×D₄	—	6	4	no	—
580	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
581	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
582	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
583	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
584	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
586	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
587	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂²×C₃×C₄	—	2	1	no	—
589	C₂²×C₃×C₄	—	2	1	no	—
590	C₂²×C₃×C₄	—	2	2	no	—
591	C₂²×C₃×C₄	—	2	2	no	—
592	C₂²×C₃×C₄	—	3	1	no	—
593	C₂²×C₃×C₄	—	3	1	no	—
594	C₂²×C₃×C₄	—	3	2	no	—
595	C₂²×C₃×C₄	—	3	2	no	—
596	C₂²×C₃×C₄	—	3	2	no	—
597	C₂²×C₃×C₄	—	3	1	no	—
598	C₂²×C₃×C₄	—	3	2	no	—
599	C₂²×C₃×C₄	—	3	2	no	—
600	C₂²×C₃×C₄	—	3	2	no	—
601	C₂²×C₃×C₄	—	3	2	no	—
602	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
603	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
604	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
605	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
606	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
608	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
609	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
610	C₂×#67	C₂³×C₃	1	2	yes	—
611	C₂×#67	C₂³×C₃	1	2	yes	—
612	C₂×#67	C₂³×C₃	1	2	yes	—
613	C₂×#67	C₂³×C₃	1	1	yes	characteristic
614	C₂×#67	C₂³×C₃	1	1	yes	characteristic
615	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
616	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
617	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
618	D₃×D₄	—	2	4	no	—
619	#235	—	2	4	no	—
620	#235	—	2	4	no	—
621	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
623	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
625	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
626	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
627	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
628	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
629	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
630	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
631	C₂×Dic₆	C₂³×C₃	1	2	yes	—
632	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
633	C₃×C₄⋊C₄	—	2	1	no	—
634	C₃×C₄⋊C₄	—	2	1	no	—
635	C₃×C₄⋊C₄	—	2	2	no	—
636	C₃×C₄⋊C₄	—	2	1	no	—
637	C₃×C₄⋊C₄	—	2	2	no	—
638	C₃×C₄⋊C₄	—	2	1	no	—
639	C₃×C₄⋊C₄	—	2	2	no	—
640	C₃×C₄⋊C₄	—	3	1	no	—
641	C₃×C₄⋊C₄	—	3	2	no	—
642	C₃×C₄⋊C₄	—	3	2	no	—
643	C₃×C₄⋊C₄	—	3	2	no	—
644	C₃×C₄⋊C₄	—	3	2	no	—
645	C₃×C₄⋊C₄	—	3	2	no	—
646	C₃×C₄⋊C₄	—	3	1	no	—
647	C₃×C₄⋊C₄	—	3	1	no	—
648	C₃×C₄⋊C₄	—	3	2	no	—
649	C₃×C₄⋊C₄	—	3	2	no	—
650	C₃×C₄⋊C₄	—	3	2	no	—
651	C₃×C₄⋊C₄	—	3	1	no	—
652	C₃×C₄⋊C₄	—	3	1	no	—
653	C₃×C₄⋊C₄	—	3	1	no	—
654	C₃×C₄⋊C₄	—	3	1	no	—
655	C₃×C₄⋊C₄	—	3	2	no	—
656	C₃×C₄⋊C₄	—	3	2	no	—
657	C₃×C₄⋊C₄	—	3	1	no	—
658	C₃×C₄⋊C₄	—	3	1	no	—
659	C₃×C₄⋊C₄	—	3	1	no	—
660	C₃×C₄⋊C₄	—	3	2	no	—
661	C₃×C₄⋊C₄	—	3	2	no	—
662	C₃×C₄⋊C₄	—	3	2	no	—
663	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
664	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
665	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
666	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
667	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
668	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
669	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
670	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
671	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
672	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
673	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
674	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
675	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
676	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
677	C₃×C₂²⋊C₄	—	2	2	no	—
678	C₃×C₂²⋊C₄	—	2	1	no	—
679	C₃×C₂²⋊C₄	—	2	2	no	—
680	C₃×C₂²⋊C₄	—	2	2	no	—
681	C₃×C₂²⋊C₄	—	2	1	no	—
682	C₃×C₂²⋊C₄	—	2	2	no	—
683	C₃×C₂²⋊C₄	—	3	2	no	—
684	C₃×C₂²⋊C₄	—	3	2	no	—
685	C₃×C₂²⋊C₄	—	3	2	no	—
686	C₃×C₂²⋊C₄	—	3	1	no	—
687	C₃×C₂²⋊C₄	—	3	1	no	—
688	C₃×C₂²⋊C₄	—	3	1	no	—
689	C₃×C₂²⋊C₄	—	3	2	no	—
690	C₃×C₂²⋊C₄	—	3	2	no	—
691	C₃×C₂²⋊C₄	—	3	2	no	—
692	C₃×C₂²⋊C₄	—	3	1	no	—
693	C₃×C₂²⋊C₄	—	3	2	no	—
694	C₃×C₂²⋊C₄	—	3	1	no	—
695	C₃×C₂²⋊C₄	—	3	1	no	—
696	C₃×C₂²⋊C₄	—	3	2	no	—
697	C₃×C₂²⋊C₄	—	3	1	no	—
698	C₃×C₂²⋊C₄	—	3	1	no	—
699	C₃×C₂²⋊C₄	—	3	2	no	—
700	C₃×C₂²⋊C₄	—	3	2	no	—
701	C₃×C₂²⋊C₄	—	3	2	no	—
702	C₃×C₂²⋊C₄	—	3	2	no	—
703	C₃×C₂²⋊C₄	—	3	2	no	—
704	C₃×C₂²⋊C₄	—	3	2	no	—
705	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
706	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
707	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
708	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
709	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
710	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
711	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
713	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
714	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
716	C₃×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
717	C₃×C₄²	—	2	2	no	—
718	C₃×C₄²	—	2	1	no	—
719	C₃×C₄²	—	3	1	no	—
720	C₃×C₄²	—	3	1	no	—
721	C₃×C₄²	—	3	1	no	—
722	C₃×C₄²	—	3	2	no	—
723	C₃×C₄²	—	3	1	no	—
724	C₃×C₄²	—	3	2	no	—
725	C₃×C₄²	—	3	2	no	—
726	C₃×C₄²	—	3	2	no	—
727	C₃×C₄²	—	3	2	no	—
728	C₃×C₄²	—	3	1	no	—
729	C₃×C₄²	C₂²×D₃	1	2	yes	—
730	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
731	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
732	C₃×C₄²	C₂³×C₃	1	2	yes	—
733	#217	C₂³×C₃	1	2	yes	—
734	#217	C₂³×C₃	1	1	yes	characteristic
735	#217	C₂³×C₃	1	2	yes	—
736	#217	C₂³×C₃	1	2	yes	—
737	#217	C₂³×C₃	1	2	yes	—
738	#217	C₂³×C₃	1	2	yes	—
739	#217	C₂³×C₃	1	2	yes	—
740	#217	C₂³×C₃	1	1	yes	characteristic
741	#217	C₂³×C₃	1	1	yes	characteristic
742	#217	C₂³×C₃	1	2	yes	—
743	#217	C₂³×C₃	1	1	yes	characteristic
744	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
745	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
746	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
747	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
748	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
750	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
751	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
752	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
754	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
755	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
756	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
757	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
758	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
759	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
760	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
761	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
762	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
763	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
764	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
765	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
766	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
767	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
768	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
769	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
770	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
771	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
772	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
773	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
776	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
778	C₄×Dic₃	C₂³×C₃	1	2	yes	—
779	C₄×Dic₃	C₂³×C₃	1	2	yes	—
780	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
781	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
782	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
783	C₄×Dic₃	C₂³×C₃	1	2	yes	—
784	C₄×Dic₃	C₂³×C₃	1	2	yes	—
785	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
787	C₄×Dic₃	C₂³×C₃	1	2	yes	—
788	C₂²×C₃²	—	2	1	no	—
789	C₂²×C₃²	—	2	1	no	—
790	C₂²×C₃²	—	2	1	no	—
791	C₂²×C₃²	—	2	2	no	—
792	C₂²×C₃²	—	2	1	no	—
793	C₂²×C₃²	—	2	1	no	—
794	C₂²×C₃²	—	2	2	no	—
795	C₂²×C₃²	—	2	1	no	—
796	C₂²×C₃²	—	2	2	no	—
797	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
798	C₂×C₃×D₃	—	2	2	no	—
799	C₂×C₃×D₃	—	2	2	no	—
800	C₂×C₃×D₃	—	2	1	no	—
801	C₂×C₃×D₃	—	2	1	no	—
802	C₂×C₃×D₃	—	2	1	no	—
803	C₂×C₃×D₃	—	8	4	no	—
804	C₂×C₃×D₃	C₂×#41	1	4	yes	—
805	C₃²×C₄	—	2	1	no	—
806	C₃²×C₄	—	2	1	no	—
807	C₃²×C₄	—	2	2	no	—
808	C₃²×C₄	—	2	1	no	—
809	C₃²×C₄	—	2	1	no	—
810	C₃²×C₄	—	2	2	no	—
811	C₃²×C₄	—	2	2	no	—
812	C₃²×C₄	C₂×#41	1	2	yes	—
813	C₃×Dic₃	—	2	2	no	—
814	C₃×Dic₃	—	2	2	no	—
815	C₃×Dic₃	—	2	1	no	—
816	C₃×Dic₃	—	2	1	no	—
817	C₃×Dic₃	—	2	1	no	—
818	C₃×Dic₃	—	2	2	no	—
819	C₃×Dic₃	—	2	1	no	—
820	C₃×Dic₃	—	2	1	no	—
821	C₃×Dic₃	—	2	1	no	—
822	C₃×Dic₃	—	2	1	no	—
823	C₂×#41	—	3	1	no	—
824	C₂×#41	—	3	1	no	—
825	C₂²×D₄	—	3	1	no	—
826	C₄⋊Q₈	—	3	1	no	—
827	C₄⋊Q₈	—	3	1	no	—
828	#126	—	3	1	no	—
829	#126	—	3	2	no	—
830	#126	—	3	2	no	—
831	#126	—	3	2	no	—
832	#126	—	3	2	no	—
833	#126	—	3	2	no	—
834	#126	—	3	2	no	—
835	#126	—	3	1	no	—
836	#126	—	3	2	no	—
837	#126	—	3	2	no	—
838	#126	—	3	2	no	—
839	#126	C₂×C₃×D₃	1	2	yes	complemented
840	#125	—	3	2	no	—
841	#125	—	3	1	no	—
842	#125	—	3	1	no	—
843	#125	—	3	2	no	—
844	#125	—	3	2	no	—
845	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
846	#124	—	3	2	no	—
847	#124	—	3	1	no	—
848	#124	—	3	1	no	—
849	#124	—	3	1	no	—
850	#124	—	3	2	no	—
851	#123	—	3	2	no	—
852	#123	—	3	1	no	—
853	#123	—	3	2	no	—
854	#123	—	3	2	no	—
855	#123	—	3	2	no	—
856	#123	—	3	2	no	—
857	#123	—	3	1	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	C₂×C₃×D₃	1	2	yes	complemented
861	C₂²⋊Q₈	—	3	1	no	—
862	C₂²⋊Q₈	—	3	2	no	—
863	C₂²⋊Q₈	—	3	1	no	—
864	C₂²⋊Q₈	—	3	2	no	—
865	C₂²⋊Q₈	—	3	2	no	—
866	C₂²⋊Q₈	—	3	2	no	—
867	C₂²⋊Q₈	—	3	1	no	—
868	C₂²⋊Q₈	—	3	1	no	—
869	C₂²⋊Q₈	—	3	1	no	—
870	C₂²⋊Q₈	—	3	2	no	—
871	#121	—	3	1	no	—
872	#121	—	3	2	no	—
873	#121	—	3	2	no	—
874	#121	—	3	2	no	—
875	#121	C₂×C₃×D₃	1	1	yes	characteristic
876	#121	C₂×C₃×D₃	1	1	yes	characteristic
877	#121	C₂×C₃×D₃	1	2	yes	complemented
878	#120	—	3	2	no	—
879	#120	—	3	2	no	—
880	C₄×Q₈	—	3	1	no	—
881	C₄×Q₈	—	3	1	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	1	no	—
884	C₄×Q₈	—	3	2	no	—
885	C₄×Q₈	—	3	1	no	—
886	C₄×D₄	—	3	1	no	—
887	C₄×D₄	—	3	2	no	—
888	C₄×D₄	—	3	2	no	—
889	C₄×D₄	—	3	2	no	—
890	C₄×D₄	—	3	2	no	—
891	C₄×D₄	—	3	1	no	—
892	C₄×D₄	—	3	1	no	—
893	C₄×D₄	—	3	1	no	—
894	C₄×D₄	—	3	1	no	—
895	C₄×D₄	—	3	1	no	—
896	C₄×D₄	—	3	2	no	—
897	C₄×D₄	—	3	2	no	—
898	C₄×D₄	—	3	2	no	—
899	C₄×D₄	—	3	1	no	—
900	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
901	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
902	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
903	#117	—	3	1	no	—
904	#117	—	3	2	no	—
905	#117	—	3	2	no	—
906	#117	—	3	1	no	—
907	#117	—	3	2	no	—
908	#117	—	3	2	no	—
909	#117	—	3	2	no	—
910	#117	—	3	1	no	—
911	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
912	C₂×C₄⋊C₄	—	3	2	no	—
913	C₂×C₄⋊C₄	—	3	2	no	—
914	C₂×C₄⋊C₄	—	3	2	no	—
915	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
916	C₂×C₂²⋊C₄	—	3	2	no	—
917	C₂×C₂²⋊C₄	—	3	2	no	—
918	C₂×C₂²⋊C₄	—	3	2	no	—
919	C₂×C₂²⋊C₄	—	3	2	no	—
920	C₂×C₄²	—	3	1	no	—
921	C₂×C₄²	—	3	2	no	—
922	C₂³×C₃	—	2	1	no	—
923	C₂³×C₃	—	2	2	no	—
924	C₂³×C₃	—	2	1	no	—
925	C₂³×C₃	—	3	2	no	—
926	C₂³×C₃	—	3	1	no	—
927	C₂³×C₃	—	6	4	no	—
928	C₂³×C₃	—	12	2	no	—
929	C₂³×C₃	—	12	2	no	—
930	C₂³×C₃	C₂³×D₃	1	2	yes	—
931	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
932	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
933	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
934	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
935	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
936	C₂²×D₃	—	2	4	no	—
937	C₂²×D₃	—	4	2	no	—
938	C₂²×D₃	—	4	2	no	—
939	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
940	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
941	C₃×Q₈	—	6	2	no	—
942	C₃×Q₈	—	6	2	no	—
943	C₃×Q₈	—	12	2	no	—
944	C₃×Q₈	—	12	1	no	—
945	C₃×D₄	—	2	2	no	—
946	C₃×D₄	—	2	2	no	—
947	C₃×D₄	—	3	4	no	—
948	C₃×D₄	—	4	2	no	—
949	C₃×D₄	—	4	1	no	—
950	C₃×D₄	—	4	2	no	—
951	C₃×D₄	—	4	2	no	—
952	C₃×D₄	—	4	2	no	—
953	C₃×D₄	—	4	1	no	—
954	C₃×D₄	—	4	2	no	—
955	C₃×D₄	—	4	2	no	—
956	C₃×D₄	—	4	4	no	—
957	C₃×D₄	—	6	4	no	—
958	C₃×D₄	—	6	4	no	—
959	C₃×D₄	—	6	4	no	—
960	C₃×D₄	—	8	2	no	—
961	C₃×D₄	—	12	1	no	—
962	C₃×D₄	—	12	1	no	—
963	C₂×C₃×C₄	—	2	2	no	—
964	C₂×C₃×C₄	—	2	2	no	—
965	C₂×C₃×C₄	—	2	2	no	—
966	C₂×C₃×C₄	—	2	2	no	—
967	C₂×C₃×C₄	—	2	1	no	—
968	C₂×C₃×C₄	—	2	1	no	—
969	C₂×C₃×C₄	—	2	2	no	—
970	C₂×C₃×C₄	—	2	1	no	—
971	C₂×C₃×C₄	—	2	2	no	—
972	C₂×C₃×C₄	—	2	1	no	—
973	C₂×C₃×C₄	—	2	1	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	3	1	no	—
976	C₂×C₃×C₄	—	3	1	no	—
977	C₂×C₃×C₄	—	3	1	no	—
978	C₂×C₃×C₄	—	3	1	no	—
979	C₂×C₃×C₄	—	3	2	no	—
980	C₂×C₃×C₄	—	3	2	no	—
981	C₂×C₃×C₄	—	3	1	no	—
982	C₂×C₃×C₄	—	3	1	no	—
983	C₂×C₃×C₄	—	3	2	no	—
984	C₂×C₃×C₄	—	3	1	no	—
985	C₂×C₃×C₄	—	4	2	no	—
986	C₂×C₃×C₄	—	4	2	no	—
987	C₂×C₃×C₄	—	4	2	no	—
988	C₂×C₃×C₄	—	4	2	no	—
989	C₂×C₃×C₄	—	4	2	no	—
990	C₂×C₃×C₄	—	4	2	no	—
991	C₂×C₃×C₄	—	6	4	no	—
992	C₂×C₃×C₄	—	6	4	no	—
993	C₂×C₃×C₄	—	6	2	no	—
994	C₂×C₃×C₄	—	8	2	no	—
995	C₂×C₃×C₄	—	8	2	no	—
996	C₂×C₃×C₄	—	12	2	no	—
997	C₂×C₃×C₄	—	12	2	no	—
998	C₂×C₃×C₄	—	12	2	no	—
999	C₂×C₃×C₄	—	12	2	no	—
1000	C₂×C₃×C₄	—	12	1	no	—
1001	C₂×C₃×C₄	—	12	2	no	—
1002	C₂×C₃×C₄	—	12	1	no	—
1003	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1004	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1005	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1006	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1007	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1008	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1009	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1010	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1011	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1012	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1013	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1014	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1015	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1017	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1019	#67	—	2	4	no	—
1020	#67	—	2	4	no	—
1021	#67	—	2	4	no	—
1022	#67	—	4	1	no	—
1023	#67	—	4	1	no	—
1024	C₂×Dic₃	—	4	2	no	—
1025	C₂×Dic₃	—	4	1	no	—
1026	C₂×Dic₃	—	4	1	no	—
1027	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1028	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1029	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1030	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1031	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1032	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1033	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1034	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1035	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1036	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1037	D₁₂	C₃×#41	1	4	yes	—
1038	C₄×D₃	—	2	4	no	—
1039	C₄×D₃	—	2	4	no	—
1040	C₄×D₃	—	2	2	no	—
1041	C₄×D₃	—	4	2	no	—
1042	C₄×D₃	—	4	2	no	—
1043	C₄×D₃	—	4	2	no	—
1044	C₄×D₃	—	4	2	no	—
1045	Dic₆	—	2	2	no	—
1046	Dic₆	—	2	2	no	—
1047	Dic₆	—	4	2	no	—
1048	Dic₆	—	4	1	no	—
1049	C₂×C₃²	—	4	1	no	—
1050	C₂×C₃²	—	4	2	no	—
1051	C₂×C₃²	—	4	1	no	—
1052	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1053	C₂×C₃²	#585	1	1	yes	characteristic
1054	C₂×C₃²	#585	1	1	yes	characteristic
1055	C₃×D₃	—	2	4	no	—
1056	C₃×D₃	—	4	1	no	—
1057	C₂⁴	—	3	2	no	—
1058	#41	—	6	4	no	—
1059	#41	—	6	4	no	—
1060	C₂×Q₈	—	3	1	no	—
1061	C₂×Q₈	—	3	1	no	—
1062	C₂×Q₈	—	3	1	no	—
1063	C₂×Q₈	—	3	2	no	—
1064	C₂×D₄	—	3	2	no	—
1065	C₂×D₄	—	3	2	no	—
1066	C₂×D₄	—	3	2	no	—
1067	C₂×D₄	—	3	1	no	—
1068	C₂×D₄	—	3	1	no	—
1069	C₂×D₄	—	3	1	no	—
1070	C₂×D₄	—	6	4	no	—
1071	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1072	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1073	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1074	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1075	C₂²×C₄	—	3	1	no	—
1076	C₂²×C₄	—	3	1	no	—
1077	C₂²×C₄	—	3	2	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	2	no	—
1082	C₂²×C₄	—	3	2	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1086	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1087	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1088	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1089	C₄⋊C₄	—	3	1	no	—
1090	C₄⋊C₄	—	3	1	no	—
1091	C₄⋊C₄	—	3	2	no	—
1092	C₄⋊C₄	—	3	2	no	—
1093	C₄⋊C₄	—	3	2	no	—
1094	C₄⋊C₄	—	3	2	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	2	no	—
1098	C₄⋊C₄	—	3	1	no	—
1099	C₄⋊C₄	—	3	1	no	—
1100	C₄⋊C₄	—	3	1	no	—
1101	C₄⋊C₄	—	3	1	no	—
1102	C₄⋊C₄	—	3	1	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	2	no	—
1106	C₄⋊C₄	—	3	2	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	1	no	—
1109	C₄⋊C₄	—	3	1	no	—
1110	C₄⋊C₄	—	3	1	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1114	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1115	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1119	C₂²⋊C₄	—	3	2	no	—
1120	C₂²⋊C₄	—	3	2	no	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	1	no	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	1	no	—
1125	C₂²⋊C₄	—	3	2	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	1	no	—
1129	C₂²⋊C₄	—	3	2	no	—
1130	C₂²⋊C₄	—	3	1	no	—
1131	C₂²⋊C₄	—	3	1	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	1	no	—
1134	C₂²⋊C₄	—	3	1	no	—
1135	C₂²⋊C₄	—	3	2	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	2	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1142	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1143	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1144	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1145	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1147	C₄²	—	3	1	no	—
1148	C₄²	—	3	1	no	—
1149	C₄²	—	3	1	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	1	no	—
1152	C₄²	—	3	2	no	—
1153	C₄²	—	3	2	no	—
1154	C₄²	—	3	2	no	—
1155	C₄²	—	3	2	no	—
1156	C₄²	—	3	1	no	—
1157	C₄²	C₂²×C₃×D₃	1	2	yes	—
1158	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1159	C₂²×C₃	—	2	2	no	—
1160	C₂²×C₃	—	2	1	no	—
1161	C₂²×C₃	—	2	1	no	—
1162	C₂²×C₃	—	2	2	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	1	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	—	2	2	no	—
1168	C₂²×C₃	—	2	1	no	—
1169	C₂²×C₃	—	2	1	no	—
1170	C₂²×C₃	—	2	1	no	—
1171	C₂²×C₃	—	2	2	no	—
1172	C₂²×C₃	—	2	1	no	—
1173	C₂²×C₃	—	2	1	no	—
1174	C₂²×C₃	—	2	2	no	—
1175	C₂²×C₃	—	2	1	no	—
1176	C₂²×C₃	—	2	2	no	—
1177	C₂²×C₃	—	2	1	no	—
1178	C₂²×C₃	—	2	1	no	—
1179	C₂²×C₃	—	3	4	no	—
1180	C₂²×C₃	—	4	1	no	—
1181	C₂²×C₃	—	4	1	no	—
1182	C₂²×C₃	—	4	1	no	—
1183	C₂²×C₃	—	4	2	no	—
1184	C₂²×C₃	—	4	2	no	—
1185	C₂²×C₃	—	4	1	no	—
1186	C₂²×C₃	—	4	2	no	—
1187	C₂²×C₃	—	4	1	no	—
1188	C₂²×C₃	—	6	2	no	—
1189	C₂²×C₃	—	6	2	no	—
1190	C₂²×C₃	—	6	1	no	—
1191	C₂²×C₃	—	6	1	no	—
1192	C₂²×C₃	—	6	1	no	—
1193	C₂²×C₃	—	24	4	no	—
1194	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1195	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1196	C₂×D₃	—	2	2	no	—
1197	C₂×D₃	—	2	2	no	—
1198	C₂×D₃	—	2	1	no	—
1199	C₂×D₃	—	2	1	no	—
1200	C₂×D₃	—	2	1	no	—
1201	C₂×D₃	—	8	4	no	—
1202	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	1	no	—
1205	C₃×C₄	—	2	1	no	—
1206	C₃×C₄	—	2	2	no	—
1207	C₃×C₄	—	2	2	no	—
1208	C₃×C₄	—	2	1	no	—
1209	C₃×C₄	—	2	2	no	—
1210	C₃×C₄	—	2	1	no	—
1211	C₃×C₄	—	2	1	no	—
1212	C₃×C₄	—	2	2	no	—
1213	C₃×C₄	—	2	1	no	—
1214	C₃×C₄	—	2	1	no	—
1215	C₃×C₄	—	2	2	no	—
1216	C₃×C₄	—	2	2	no	—
1217	C₃×C₄	—	2	2	no	—
1218	C₃×C₄	—	4	1	no	—
1219	C₃×C₄	—	4	1	no	—
1220	C₃×C₄	—	4	2	no	—
1221	C₃×C₄	—	4	1	no	—
1222	C₃×C₄	—	4	2	no	—
1223	C₃×C₄	—	4	1	no	—
1224	C₃×C₄	—	4	2	no	—
1225	C₃×C₄	—	6	1	no	—
1226	C₃×C₄	—	6	2	no	—
1227	C₃×C₄	—	6	2	no	—
1228	C₃×C₄	—	6	1	no	—
1229	C₃×C₄	—	6	1	no	—
1230	C₃×C₄	—	6	2	no	—
1231	C₃×C₄	—	6	1	no	—
1232	C₃×C₄	—	6	1	no	—
1233	C₃×C₄	—	6	1	no	—
1234	C₃×C₄	—	6	1	no	—
1235	C₃×C₄	D₃×#41	1	2	yes	—
1236	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1237	Dic₃	—	2	2	no	—
1238	Dic₃	—	2	2	no	—
1239	Dic₃	—	2	1	no	—
1240	Dic₃	—	2	1	no	—
1241	Dic₃	—	2	1	no	—
1242	Dic₃	—	2	2	no	—
1243	Dic₃	—	2	1	no	—
1244	Dic₃	—	2	1	no	—
1245	Dic₃	—	2	1	no	—
1246	Dic₃	—	2	1	no	—
1247	C₃²	#3521	1	1	yes	characteristic, complemented, Sylow
1248	C₂³	—	3	2	no	—
1249	C₂³	—	3	1	no	—
1250	C₂³	—	6	4	no	—
1251	C₂³	—	12	2	no	—
1252	C₂³	—	12	2	no	—
1253	C₂³	C₂³×C₃×D₃	1	2	yes	—
1254	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1255	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1256	Q₈	—	6	2	no	—
1257	Q₈	—	6	2	no	—
1258	Q₈	—	12	2	no	—
1259	Q₈	—	12	1	no	—
1260	D₄	—	2	2	no	—
1261	D₄	—	3	4	no	—
1262	D₄	—	4	1	no	—
1263	D₄	—	4	2	no	—
1264	D₄	—	4	2	no	—
1265	D₄	—	6	4	no	—
1266	D₄	—	6	4	no	—
1267	D₄	—	6	4	no	—
1268	D₄	—	12	1	no	—
1269	D₄	—	12	1	no	—
1270	C₂×C₄	—	2	2	no	—
1271	C₂×C₄	—	2	2	no	—
1272	C₂×C₄	—	3	1	no	—
1273	C₂×C₄	—	3	1	no	—
1274	C₂×C₄	—	3	1	no	—
1275	C₂×C₄	—	3	1	no	—
1276	C₂×C₄	—	3	2	no	—
1277	C₂×C₄	—	3	2	no	—
1278	C₂×C₄	—	3	1	no	—
1279	C₂×C₄	—	3	1	no	—
1280	C₂×C₄	—	3	2	no	—
1281	C₂×C₄	—	3	1	no	—
1282	C₂×C₄	—	4	2	no	—
1283	C₂×C₄	—	4	2	no	—
1284	C₂×C₄	—	6	4	no	—
1285	C₂×C₄	—	6	4	no	—
1286	C₂×C₄	—	6	2	no	—
1287	C₂×C₄	—	12	2	no	—
1288	C₂×C₄	—	12	2	no	—
1289	C₂×C₄	—	12	2	no	—
1290	C₂×C₄	—	12	2	no	—
1291	C₂×C₄	—	12	1	no	—
1292	C₂×C₄	—	12	2	no	—
1293	C₂×C₄	—	12	1	no	—
1294	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1295	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1296	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1297	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1298	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1299	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1300	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1301	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1302	C₂×C₃	—	2	1	no	—
1303	C₂×C₃	—	2	1	no	—
1304	C₂×C₃	—	2	1	no	—
1305	C₂×C₃	—	4	2	no	—
1306	C₂×C₃	—	4	2	no	—
1307	C₂×C₃	—	4	1	no	—
1308	C₂×C₃	—	4	1	no	—
1309	C₂×C₃	—	4	2	no	—
1310	C₂×C₃	—	4	1	no	—
1311	C₂×C₃	—	4	1	no	—
1312	C₂×C₃	—	6	4	no	—
1313	C₂×C₃	—	8	2	no	—
1314	C₂×C₃	—	8	1	no	—
1315	C₂×C₃	—	12	1	no	—
1316	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1317	C₂×C₃	#5964	1	1	yes	characteristic
1318	C₂×C₃	#5966	1	1	yes	characteristic
1319	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1320	C₂×C₃	C₃×#585	1	1	yes	characteristic
1321	C₂×C₃	C₃×#585	1	1	yes	characteristic
1322	D₃	—	2	4	no	—
1323	D₃	—	4	1	no	—
1324	C₂²	—	2	1	no	—
1325	C₂²	—	2	1	no	—
1326	C₂²	—	2	2	no	—
1327	C₂²	—	2	1	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	1	no	—
1330	C₂²	—	2	1	no	—
1331	C₂²	—	2	2	no	—
1332	C₂²	—	2	1	no	—
1333	C₂²	—	3	4	no	—
1334	C₂²	—	6	2	no	—
1335	C₂²	—	6	2	no	—
1336	C₂²	—	6	1	no	—
1337	C₂²	—	6	1	no	—
1338	C₂²	—	6	1	no	—
1339	C₂²	—	24	4	no	—
1340	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1341	C₄	—	2	1	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	6	1	no	—
1349	C₄	—	6	2	no	—
1350	C₄	—	6	2	no	—
1351	C₄	—	6	1	no	—
1352	C₄	—	6	1	no	—
1353	C₄	—	6	2	no	—
1354	C₄	—	6	1	no	—
1355	C₄	—	6	1	no	—
1356	C₄	—	6	1	no	—
1357	C₄	—	6	1	no	—
1358	C₄	C₃×D₃×#41	1	2	yes	—
1359	C₃	—	2	1	no	—
1360	C₃	#86890	1	1	yes	characteristic, direct product factor
1361	C₃	C₃×#3521	1	1	yes	characteristic, complemented
1362	C₂	—	4	2	no	—
1363	C₂	—	4	1	no	—
1364	C₂	—	4	1	no	—
1365	C₂	—	6	4	no	—
1366	C₂	—	12	1	no	—
1367	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1368	C₂	C₃×#5964	1	1	yes	characteristic
1369	C₂	C₃×#5966	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×#553	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#553	D₃
hypocenter	C₃	C₃×#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#553

Complements

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

N	H ≅ G/N	type
1. C₃²×#553	C₂	semidirect
2. C₃×#5708	C₂	semidirect
3. C₃×D₃×#126	C₂	semidirect
4. C₃×#5698	C₂	semidirect
5. C₃×#5690	C₂	semidirect
6. C₃×#5660	C₂	semidirect
7. C₃×#5658	C₂	semidirect
8. C₃×#5614	C₂	semidirect
9. C₃×#5613	C₂	semidirect
10. C₃×#5612	C₂	semidirect
11. C₃×#5612	C₂	semidirect
12. C₃×#5603	C₂	semidirect
13. C₃×#5600	C₂	semidirect
14. C₃×#5557	C₂	semidirect
15. C₃×#5556	C₂	semidirect
16. C₃×#5551	C₂	semidirect
17. C₃×#5545	C₂	semidirect
18. C₃×#5542	C₂	semidirect
19. C₃×#5538	C₂	semidirect
20. C₃×#5533	C₂	semidirect
21. C₃×#5522	C₂	semidirect
22. C₃×#5513	C₂	semidirect
23. C₃×#5504	C₂	semidirect
25. #86890	C₃	direct (N × H)
29. C₃²×#126	C₂²	semidirect
30. C₃²×#125	C₂²	semidirect
31. C₃²×#123	C₂²	semidirect
34. C₃²×#121	C₂²	semidirect
36. C₃²×C₄×D₄	C₂²	semidirect
37. C₃²×C₄×D₄	C₂²	semidirect
38. C₃²×#117	C₂²	semidirect
39. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
43. C₃×#938	C₂²	semidirect
48. C₃×#936	C₂²	semidirect
49. C₃×#935	C₂²	semidirect
50. C₃×#935	C₂²	semidirect
51. C₃×#935	C₂²	semidirect
53. C₃×D₄×Dic₃	C₂²	semidirect
58. C₃×C₄×#67	C₂²	semidirect
59. C₃×C₄×#67	C₂²	semidirect
61. C₃×#926	C₂²	semidirect
62. C₃×#926	C₂²	semidirect
63. C₃×#926	C₂²	semidirect
64. C₃×#924	C₂²	semidirect
65. C₃×#924	C₂²	semidirect
66. C₃×#924	C₂²	semidirect
67. C₂×C₃×C₄×Dic₃	C₂²	semidirect
74. C₃×#897	C₂²	semidirect
75. C₃×#896	C₂²	semidirect
76. C₃×#896	C₂²	semidirect
81. C₃×#892	C₂²	semidirect
82. C₃×D₃×C₄⋊C₄	C₂²	semidirect
83. C₃×D₃×C₄⋊C₄	C₂²	semidirect
84. C₃×D₃×C₄⋊C₄	C₂²	semidirect
85. C₃×#890	C₂²	semidirect
86. C₃×#890	C₂²	semidirect
87. C₃×#890	C₂²	semidirect
88. C₃×#889	C₂²	semidirect
89. C₃×#889	C₂²	semidirect
90. C₃×#888	C₂²	semidirect
91. C₃×#887	C₂²	semidirect
92. C₃×#887	C₂²	semidirect
93. C₃×#887	C₂²	semidirect
94. C₃×#887	C₂²	semidirect
100. C₃×#883	C₂²	semidirect
101. C₃×#883	C₂²	semidirect
103. C₃×#67⋊C₄	C₂²	semidirect
104. C₃×#67⋊C₄	C₂²	semidirect
108. C₃×#879	C₂²	semidirect
109. C₃×#879	C₂²	semidirect
110. C₃×#879	C₂²	semidirect
111. C₃×#879	C₂²	semidirect
112. C₃×#879	C₂²	semidirect
113. C₃×#879	C₂²	semidirect
114. C₃×#878	C₂²	semidirect
115. C₃×#878	C₂²	semidirect
116. C₃×#877	C₂²	semidirect
120. C₃×#872	C₂²	semidirect
121. C₃×C₄²×D₃	C₂²	semidirect
122. C₃×#869	C₂²	semidirect
123. C₃×C₄×Dic₆	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
130. C₃×#553	D₃	semidirect
131. C₃×#553	C₂×C₃	semidirect
150. #5708	C₂×C₃	semidirect
151. D₃×#126	C₂×C₃	semidirect
152. #5698	C₂×C₃	semidirect
153. #5690	C₂×C₃	semidirect
154. #5660	C₂×C₃	semidirect
155. #5658	C₂×C₃	semidirect
156. #5614	C₂×C₃	semidirect
157. #5613	C₂×C₃	semidirect
158. #5612	C₂×C₃	semidirect
159. #5612	C₂×C₃	semidirect
160. #5603	C₂×C₃	semidirect
161. #5600	C₂×C₃	semidirect
162. #5557	C₂×C₃	semidirect
163. #5556	C₂×C₃	semidirect
164. #5551	C₂×C₃	semidirect
165. #5545	C₂×C₃	semidirect
166. #5542	C₂×C₃	semidirect
167. #5538	C₂×C₃	semidirect
168. #5533	C₂×C₃	semidirect
169. #5522	C₂×C₃	semidirect
170. #5513	C₂×C₃	semidirect
171. #5504	C₂×C₃	semidirect
295. C₃×#126	C₂×D₃	semidirect
296. C₃×#126	C₂²×C₃	semidirect
303. C₃×#125	C₂×D₃	semidirect
304. C₃×#125	C₂²×C₃	semidirect
320. C₃×#123	C₂×D₃	semidirect
321. C₃×#123	C₂²×C₃	semidirect
341. C₃×#121	C₂×D₃	semidirect
344. C₃×#121	C₂²×C₃	semidirect
371. C₃×C₄×D₄	C₂×D₃	semidirect
372. C₃×C₄×D₄	C₂×D₃	semidirect
374. C₃×C₄×D₄	C₂²×C₃	semidirect
375. C₃×C₄×D₄	C₂²×C₃	semidirect
385. C₃×#117	C₂×D₃	semidirect
386. C₃×#117	C₂²×C₃	semidirect
391. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
392. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
402. #938	C₂²×C₃	semidirect
407. #936	C₂²×C₃	semidirect
408. #935	C₂²×C₃	semidirect
409. #935	C₂²×C₃	semidirect
410. #935	C₂²×C₃	semidirect
412. D₄×Dic₃	C₂²×C₃	semidirect
417. C₄×#67	C₂²×C₃	semidirect
418. C₄×#67	C₂²×C₃	semidirect
420. #926	C₂²×C₃	semidirect
421. #926	C₂²×C₃	semidirect
422. #926	C₂²×C₃	semidirect
423. #924	C₂²×C₃	semidirect
424. #924	C₂²×C₃	semidirect
425. #924	C₂²×C₃	semidirect
426. C₂×C₄×Dic₃	C₂²×C₃	semidirect
433. #897	C₂²×C₃	semidirect
434. #896	C₂²×C₃	semidirect
435. #896	C₂²×C₃	semidirect
440. #892	C₂²×C₃	semidirect
441. D₃×C₄⋊C₄	C₂²×C₃	semidirect
442. D₃×C₄⋊C₄	C₂²×C₃	semidirect
443. D₃×C₄⋊C₄	C₂²×C₃	semidirect
444. #890	C₂²×C₃	semidirect
445. #890	C₂²×C₃	semidirect
446. #890	C₂²×C₃	semidirect
447. #889	C₂²×C₃	semidirect
448. #889	C₂²×C₃	semidirect
449. #888	C₂²×C₃	semidirect
450. #887	C₂²×C₃	semidirect
451. #887	C₂²×C₃	semidirect
452. #887	C₂²×C₃	semidirect
453. #887	C₂²×C₃	semidirect
459. #883	C₂²×C₃	semidirect
460. #883	C₂²×C₃	semidirect
462. #67⋊C₄	C₂²×C₃	semidirect
463. #67⋊C₄	C₂²×C₃	semidirect
467. #879	C₂²×C₃	semidirect
468. #879	C₂²×C₃	semidirect
469. #879	C₂²×C₃	semidirect
470. #879	C₂²×C₃	semidirect
471. #879	C₂²×C₃	semidirect
472. #879	C₂²×C₃	semidirect
473. #878	C₂²×C₃	semidirect
474. #878	C₂²×C₃	semidirect
475. #877	C₂²×C₃	semidirect
479. #872	C₂²×C₃	semidirect
480. C₄²×D₃	C₂²×C₃	semidirect
481. #869	C₂²×C₃	semidirect
482. C₄×Dic₆	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
542. #553	C₃×D₃	semidirect
839. #126	C₂×C₃×D₃	semidirect
845. #125	C₂×C₃×D₃	semidirect
860. #123	C₂×C₃×D₃	semidirect
877. #121	C₂×C₃×D₃	semidirect
901. C₄×D₄	C₂×C₃×D₃	semidirect
902. C₄×D₄	C₂×C₃×D₃	semidirect
911. #117	C₂×C₃×D₃	semidirect
915. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
1247. C₃²	#3521	semidirect
1360. C₃	#86890	direct (N × H)
1361. C₃	C₃×#3521	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#553	2
C₃×#5708	2
C₃×D₃×#126	2
C₃×#5698	2
C₃×#5690	2
C₃×#5660	2
C₃×#5658	2
C₃×#5614	2
C₃×#5613	2
C₃×#5612	2
C₃×#5603	2
C₃×#5600	2
C₃×#5557	2
C₃×#5556	2
C₃×#5551	2
C₃×#5545	2
C₃×#5542	2
C₃×#5538	2
C₃×#5533	2
C₃×#5522	2
C₃×#5513	2
C₃×#5504	2
C₃×#3521	3
#86890	3

Subgroups — C3×#86890 #11909394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86890 #11909394