Subgroups — C₃×#86388 #11901979

Order 1152.

2445 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5707	C₂	1	2	yes	maximal, complemented
3	C₃×#5706	C₂	1	2	yes	maximal, complemented
4	C₃×#5680	C₂	1	2	yes	maximal, complemented
5	C₃×#5678	C₂	1	2	yes	maximal, complemented
6	C₃×#5660	C₂	1	2	yes	maximal, complemented
7	C₃×#5656	C₂	1	2	yes	maximal, complemented
8	C₃×#5634	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5624	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5613	C₂	1	2	yes	maximal, complemented
11	C₃×#5606	C₂	1	2	yes	maximal, complemented
12	C₃×#5605	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5600	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5589	C₂	1	2	yes	maximal, complemented
15	C₃×#5586	C₂	1	2	yes	maximal, complemented
16	C₃×#5564	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×D₃×D₄	C₂	1	2	yes	maximal, complemented
18	C₃×#5494	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3459	—	3	1	no	maximal
21	#86388	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#237	C₂²	1	2	yes	complemented
25	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
26	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
28	C₃²×#126	C₂²	1	2	yes	complemented
29	C₃²×#124	C₂²	1	2	yes	complemented
30	C₃²×#123	C₂²	1	2	yes	complemented
31	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#121	C₂²	1	1	yes	characteristic
33	C₃²×#121	C₂²	1	2	yes	complemented
34	C₃²×#120	C₂²	1	2	yes	complemented
35	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
36	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₃×#953	C₂²	1	2	yes	complemented
38	C₃×#947	C₂²	1	1	yes	characteristic, complemented
39	C₃×#946	C₂²	1	2	yes	complemented
40	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₃×#939	C₂²	1	2	yes	—
42	C₃×#939	C₂²	1	2	yes	complemented
43	C₃×#938	C₂²	1	2	yes	—
44	C₃×#938	C₂²	1	2	yes	—
45	C₃×#937	C₂²	1	2	yes	complemented
46	C₃×#937	C₂²	1	2	yes	complemented
47	C₃×#937	C₂²	1	2	yes	complemented
48	C₃×#936	C₂²	1	1	yes	characteristic, complemented
49	C₃×#935	C₂²	1	2	yes	complemented
50	C₃×#935	C₂²	1	2	yes	complemented
51	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
52	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
53	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	C₃×#930	C₂²	1	1	yes	characteristic
55	C₃×#929	C₂²	1	2	yes	complemented
56	C₃×C₄×#67	C₂²	1	2	yes	complemented
57	C₃×C₄×#67	C₂²	1	2	yes	complemented
58	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
59	C₃×#924	C₂²	1	1	yes	characteristic, complemented
60	C₃×#924	C₂²	1	2	yes	complemented
61	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
63	C₃×#898	C₂²	1	2	yes	complemented
64	C₃×#897	C₂²	1	2	yes	complemented
65	C₃×#896	C₂²	1	2	yes	complemented
66	C₃×#896	C₂²	1	2	yes	complemented
67	C₃×#896	C₂²	1	2	yes	complemented
68	C₃×#894	C₂²	1	2	yes	complemented
69	C₃×#893	C₂²	1	2	yes	complemented
70	C₃×#893	C₂²	1	1	yes	characteristic, complemented
71	C₃×#892	C₂²	1	2	yes	complemented
72	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₃×#890	C₂²	1	1	yes	characteristic, complemented
74	C₃×#890	C₂²	1	1	yes	characteristic, complemented
75	C₃×#889	C₂²	1	2	yes	complemented
76	C₃×#887	C₂²	1	1	yes	characteristic, complemented
77	C₃×#886	C₂²	1	2	yes	complemented
78	C₃×#886	C₂²	1	2	yes	complemented
79	C₃×#885	C₂²	1	2	yes	complemented
80	C₃×#884	C₂²	1	2	yes	—
81	C₃×#884	C₂²	1	2	yes	—
82	C₃×#884	C₂²	1	2	yes	complemented
83	C₃×#883	C₂²	1	2	yes	complemented
84	C₃×#883	C₂²	1	2	yes	complemented
85	C₃×#883	C₂²	1	2	yes	complemented
86	C₃×#883	C₂²	1	2	yes	complemented
87	C₃×#883	C₂²	1	2	yes	complemented
88	C₃×#882	C₂²	1	2	yes	complemented
89	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
90	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
91	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
92	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
93	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
94	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
95	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
96	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	C₃×#879	C₂²	1	2	yes	complemented
99	C₃×#879	C₂²	1	2	yes	complemented
100	C₃×#879	C₂²	1	2	yes	complemented
101	C₃×#878	C₂²	1	2	yes	complemented
102	C₃×#878	C₂²	1	2	yes	complemented
103	C₃×#877	C₂²	1	2	yes	complemented
104	C₃×#877	C₂²	1	2	yes	complemented
105	C₃×#876	C₂²	1	2	yes	complemented
106	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
107	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
108	C₃×#870	C₂²	1	2	yes	complemented
109	C₃×#543	—	3	1	no	—
110	C₃×#539	—	3	2	no	—
111	C₃×#539	—	3	2	no	—
112	C₃×#539	—	3	2	no	—
113	C₃×#538	—	2	1	no	—
114	C₃×#538	—	3	2	no	—
115	C₃×#538	—	3	2	no	—
116	C₃×#538	—	3	1	no	—
117	C₃×#538	D₃	1	1	yes	characteristic, complemented
118	C₃×#538	C₂×C₃	1	1	yes	characteristic, complemented
119	C₃×#534	—	3	1	no	—
120	C₃×#534	—	3	2	no	—
121	C₃×#529	—	3	2	no	—
122	C₃×#529	—	3	2	no	—
123	C₃×#529	—	3	1	no	—
124	C₃×#529	—	3	1	no	—
125	C₃×#525	—	3	2	no	—
126	C₃×#525	—	3	2	no	—
127	C₃×#525	—	3	2	no	—
128	C₂×C₃×C₄×D₄	—	3	2	no	—
129	C₂×C₃×C₄×D₄	—	3	1	no	—
130	#5707	C₂×C₃	1	2	yes	complemented
131	#5706	C₂×C₃	1	2	yes	complemented
132	#5680	C₂×C₃	1	2	yes	complemented
133	#5678	C₂×C₃	1	2	yes	complemented
134	#5660	C₂×C₃	1	2	yes	complemented
135	#5656	C₂×C₃	1	2	yes	complemented
136	#5634	C₂×C₃	1	1	yes	characteristic, complemented
137	#5624	C₂×C₃	1	1	yes	characteristic, complemented
138	#5613	C₂×C₃	1	2	yes	complemented
139	#5606	C₂×C₃	1	2	yes	complemented
140	#5605	C₂×C₃	1	1	yes	characteristic, complemented
141	#5600	C₂×C₃	1	1	yes	characteristic, complemented
142	#5589	C₂×C₃	1	2	yes	complemented
143	#5586	C₂×C₃	1	2	yes	complemented
144	#5564	C₂×C₃	1	2	yes	complemented
145	C₄×D₃×D₄	C₂×C₃	1	2	yes	complemented
146	#5494	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#67⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₃	C₂³	1	2	yes	—
150	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
151	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃²×D₄	C₂³	1	2	yes	—
153	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃²×D₄	C₂³	1	2	yes	—
155	C₂×C₃²×D₄	C₂³	1	2	yes	—
156	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃²×C₄	C₂³	1	2	yes	—
159	C₂×C₃×#67	—	2	4	no	—
160	C₂×C₃×#67	C₂³	1	2	yes	—
161	C₂×C₃×#67	C₂³	1	2	yes	—
162	C₂×C₃×#67	C₂³	1	2	yes	—
163	C₂×C₃×#67	C₂³	1	2	yes	—
164	C₂×C₃×#67	C₂³	1	2	yes	—
165	C₂×C₃×#67	C₂³	1	2	yes	—
166	C₂×C₃×#67	C₂³	1	2	yes	—
167	C₂²×C₃×Dic₃	—	4	2	no	—
168	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
169	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
170	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
172	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
173	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
174	C₃×#237	—	4	4	no	—
175	C₃×D₃×D₄	—	2	8	no	—
176	C₂×C₃×D₁₂	C₂³	1	2	yes	—
177	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄×D₃	—	4	2	no	—
179	C₂×C₃×C₄×D₃	—	4	4	no	—
180	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
182	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
184	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₃×Dic₆	C₂³	1	2	yes	—
188	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
189	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃²×C₄²	C₂³	1	2	yes	—
201	C₃×#217	C₂³	1	2	yes	—
202	C₃×#217	C₂³	1	2	yes	—
203	C₃×#217	C₂³	1	2	yes	—
204	C₃×#217	C₂³	1	2	yes	—
205	C₃×#217	C₂³	1	2	yes	—
206	C₃×#217	C₂³	1	2	yes	—
207	C₃×#217	C₂³	1	2	yes	—
208	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
225	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
226	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
227	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
230	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
235	C₃×C₄×Dic₃	C₂³	1	2	yes	—
236	C₃×C₄×Dic₃	C₂³	1	2	yes	—
237	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
238	C₃×C₄×Dic₃	C₂³	1	2	yes	—
239	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
240	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
241	#3459	—	3	1	no	Sylow
242	C₂×C₃×#41	—	3	2	no	—
243	C₂²×C₃×D₄	—	3	1	no	—
244	C₂²×C₃×D₄	—	3	2	no	—
245	C₂³×C₃×C₄	—	3	1	no	—
246	C₂³×C₃×C₄	—	3	1	no	—
247	C₂³×C₃×C₄	—	3	2	no	—
248	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
249	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₂×#237	C₂²×C₃	1	2	yes	complemented
251	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
252	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
254	C₃×#126	—	2	2	no	—
255	C₃×#126	—	3	2	no	—
256	C₃×#126	—	3	2	no	—
257	C₃×#126	—	3	2	no	—
258	C₃×#126	—	3	2	no	—
259	C₃×#126	—	3	2	no	—
260	C₃×#126	C₂×D₃	1	2	yes	complemented
261	C₃×#126	C₂²×C₃	1	2	yes	complemented
262	C₃×#125	—	3	2	no	—
263	C₃×#125	—	3	1	no	—
264	C₃×#125	—	3	1	no	—
265	C₃×#125	—	3	2	no	—
266	C₃×#124	—	2	2	no	—
267	C₃×#124	—	3	1	no	—
268	C₃×#124	—	3	1	no	—
269	C₃×#124	—	3	2	no	—
270	C₃×#124	C₂×D₃	1	2	yes	complemented
271	C₃×#124	C₂²×C₃	1	2	yes	complemented
272	C₃×#123	—	2	2	no	—
273	C₃×#123	—	3	2	no	—
274	C₃×#123	—	3	2	no	—
275	C₃×#123	—	3	2	no	—
276	C₃×#123	—	3	2	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	—	3	2	no	—
279	C₃×#123	—	3	2	no	—
280	C₃×#123	—	3	2	no	—
281	C₃×#123	—	3	2	no	—
282	C₃×#123	—	3	2	no	—
283	C₃×#123	—	3	2	no	—
284	C₃×#123	C₂×D₃	1	2	yes	complemented
285	C₃×#123	C₂²×C₃	1	2	yes	complemented
286	C₃×C₂²⋊Q₈	—	2	1	no	—
287	C₃×C₂²⋊Q₈	—	3	2	no	—
288	C₃×C₂²⋊Q₈	—	3	2	no	—
289	C₃×C₂²⋊Q₈	—	3	1	no	—
290	C₃×C₂²⋊Q₈	—	3	2	no	—
291	C₃×C₂²⋊Q₈	—	3	2	no	—
292	C₃×C₂²⋊Q₈	—	3	2	no	—
293	C₃×C₂²⋊Q₈	—	3	2	no	—
294	C₃×C₂²⋊Q₈	—	3	2	no	—
295	C₃×C₂²⋊Q₈	—	3	2	no	—
296	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
297	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₃×#121	—	2	1	no	—
299	C₃×#121	—	2	2	no	—
300	C₃×#121	—	3	2	no	—
301	C₃×#121	—	3	2	no	—
302	C₃×#121	—	3	2	no	—
303	C₃×#121	—	3	2	no	—
304	C₃×#121	—	3	1	no	—
305	C₃×#121	—	3	2	no	—
306	C₃×#121	—	3	2	no	—
307	C₃×#121	—	3	2	no	—
308	C₃×#121	C₂×D₃	1	1	yes	characteristic
309	C₃×#121	C₂×D₃	1	2	yes	complemented
310	C₃×#121	C₂²×C₃	1	1	yes	characteristic
311	C₃×#121	C₂²×C₃	1	2	yes	complemented
312	C₃×#120	—	2	2	no	—
313	C₃×#120	—	3	2	no	—
314	C₃×#120	—	3	2	no	—
315	C₃×#120	—	3	2	no	—
316	C₃×#120	—	3	2	no	—
317	C₃×#120	—	3	2	no	—
318	C₃×#120	C₂×D₃	1	2	yes	complemented
319	C₃×#120	C₂²×C₃	1	2	yes	complemented
320	C₃×C₄×Q₈	—	3	1	no	—
321	C₃×C₄×Q₈	—	3	1	no	—
322	C₃×C₄×D₄	—	2	2	no	—
323	C₃×C₄×D₄	—	3	2	no	—
324	C₃×C₄×D₄	—	3	1	no	—
325	C₃×C₄×D₄	—	3	2	no	—
326	C₃×C₄×D₄	—	3	2	no	—
327	C₃×C₄×D₄	—	3	2	no	—
328	C₃×C₄×D₄	—	3	2	no	—
329	C₃×C₄×D₄	—	3	1	no	—
330	C₃×C₄×D₄	—	3	2	no	—
331	C₃×C₄×D₄	—	3	2	no	—
332	C₃×C₄×D₄	—	3	2	no	—
333	C₃×C₄×D₄	—	3	2	no	—
334	C₃×C₄×D₄	—	3	2	no	—
335	C₃×C₄×D₄	—	3	2	no	—
336	C₃×C₄×D₄	—	3	2	no	—
337	C₃×C₄×D₄	—	3	2	no	—
338	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
339	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
340	C₃×#117	—	3	2	no	—
341	C₃×#117	—	3	2	no	—
342	C₃×#117	—	3	2	no	—
343	C₂×C₃×C₄⋊C₄	—	3	1	no	—
344	C₂×C₃×C₄⋊C₄	—	3	2	no	—
345	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
347	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
350	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
351	C₂×C₃×C₄²	—	3	1	no	—
352	C₂×C₃×C₄²	—	3	2	no	—
353	#953	C₂²×C₃	1	2	yes	complemented
354	#947	C₂²×C₃	1	1	yes	characteristic, complemented
355	#946	C₂²×C₃	1	2	yes	complemented
356	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
357	#939	C₂²×C₃	1	2	yes	—
358	#939	C₂²×C₃	1	2	yes	complemented
359	#938	C₂²×C₃	1	2	yes	—
360	#938	C₂²×C₃	1	2	yes	—
361	#937	C₂²×C₃	1	2	yes	complemented
362	#937	C₂²×C₃	1	2	yes	complemented
363	#937	C₂²×C₃	1	2	yes	complemented
364	#936	C₂²×C₃	1	1	yes	characteristic, complemented
365	#935	C₂²×C₃	1	2	yes	complemented
366	#935	C₂²×C₃	1	2	yes	complemented
367	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
368	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
369	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
370	#930	C₂²×C₃	1	1	yes	characteristic
371	#929	C₂²×C₃	1	2	yes	complemented
372	C₄×#67	C₂²×C₃	1	2	yes	complemented
373	C₄×#67	C₂²×C₃	1	2	yes	complemented
374	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	#924	C₂²×C₃	1	1	yes	characteristic, complemented
376	#924	C₂²×C₃	1	2	yes	complemented
377	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
378	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
379	#898	C₂²×C₃	1	2	yes	complemented
380	#897	C₂²×C₃	1	2	yes	complemented
381	#896	C₂²×C₃	1	2	yes	complemented
382	#896	C₂²×C₃	1	2	yes	complemented
383	#896	C₂²×C₃	1	2	yes	complemented
384	#894	C₂²×C₃	1	2	yes	complemented
385	#893	C₂²×C₃	1	1	yes	characteristic, complemented
386	#893	C₂²×C₃	1	2	yes	complemented
387	#892	C₂²×C₃	1	2	yes	complemented
388	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
389	#890	C₂²×C₃	1	1	yes	characteristic, complemented
390	#890	C₂²×C₃	1	1	yes	characteristic, complemented
391	#889	C₂²×C₃	1	2	yes	complemented
392	#887	C₂²×C₃	1	1	yes	characteristic, complemented
393	#886	C₂²×C₃	1	2	yes	complemented
394	#886	C₂²×C₃	1	2	yes	complemented
395	#885	C₂²×C₃	1	2	yes	complemented
396	#884	C₂²×C₃	1	2	yes	—
397	#884	C₂²×C₃	1	2	yes	—
398	#884	C₂²×C₃	1	2	yes	complemented
399	#883	C₂²×C₃	1	2	yes	complemented
400	#883	C₂²×C₃	1	2	yes	complemented
401	#883	C₂²×C₃	1	2	yes	complemented
402	#883	C₂²×C₃	1	2	yes	complemented
403	#883	C₂²×C₃	1	2	yes	complemented
404	#882	C₂²×C₃	1	2	yes	complemented
405	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
406	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
407	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
408	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
409	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
410	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
411	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
412	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
413	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
414	#879	C₂²×C₃	1	2	yes	complemented
415	#879	C₂²×C₃	1	2	yes	complemented
416	#879	C₂²×C₃	1	2	yes	complemented
417	#878	C₂²×C₃	1	2	yes	complemented
418	#878	C₂²×C₃	1	2	yes	complemented
419	#877	C₂²×C₃	1	2	yes	complemented
420	#877	C₂²×C₃	1	2	yes	complemented
421	#876	C₂²×C₃	1	2	yes	complemented
422	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
423	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
424	#870	C₂²×C₃	1	2	yes	complemented
425	C₂³×C₃²	—	2	2	no	—
426	C₂³×C₃²	—	4	1	no	—
427	C₂³×C₃²	—	4	1	no	—
428	C₂³×C₃²	C₂⁴	1	2	yes	—
429	C₂³×C₃²	C₂⁴	1	2	yes	—
430	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
431	C₂²×C₃×D₃	—	2	4	no	—
432	C₂²×C₃×D₃	—	4	1	no	—
433	C₂²×C₃×D₃	—	4	2	no	—
434	C₂²×C₃×D₃	—	4	1	no	—
435	C₂²×C₃×D₃	—	4	2	no	—
436	C₂²×C₃×D₃	#41	1	4	yes	complemented
437	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
438	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
439	C₃²×Q₈	—	4	1	no	—
440	C₃²×D₄	—	2	4	no	—
441	C₃²×D₄	—	4	2	no	—
442	C₃²×D₄	—	4	1	no	—
443	C₃²×D₄	—	4	2	no	—
444	C₂×C₃²×C₄	—	4	2	no	—
445	C₂×C₃²×C₄	—	4	1	no	—
446	C₂×C₃²×C₄	—	4	1	no	—
447	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
448	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
449	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
450	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
451	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
452	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
453	C₃×#67	—	2	4	no	—
454	C₃×#67	—	2	4	no	—
455	C₃×#67	—	2	4	no	—
456	C₃×#67	—	2	4	no	—
457	C₃×#67	—	4	2	no	—
458	C₃×#67	—	4	2	no	—
459	C₃×#67	—	4	2	no	—
460	C₂×C₃×Dic₃	—	2	2	no	—
461	C₂×C₃×Dic₃	—	2	4	no	—
462	C₂×C₃×Dic₃	—	2	2	no	—
463	C₂×C₃×Dic₃	—	2	4	no	—
464	C₂×C₃×Dic₃	—	4	1	no	—
465	C₂×C₃×Dic₃	—	4	2	no	—
466	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
467	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
468	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
469	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
470	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
471	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
472	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
473	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
474	C₃×D₁₂	—	2	4	no	—
475	C₃×D₁₂	—	4	1	no	—
476	C₃×C₄×D₃	—	2	4	no	—
477	C₃×C₄×D₃	—	2	4	no	—
478	C₃×C₄×D₃	—	2	4	no	—
479	C₃×C₄×D₃	—	4	2	no	—
480	C₃×C₄×D₃	—	4	2	no	—
481	C₃×C₄×D₃	—	4	2	no	—
482	C₃×C₄×D₃	—	4	2	no	—
483	C₃×Dic₆	—	4	1	no	—
484	C₃×Dic₆	—	4	2	no	—
485	#543	—	3	1	no	—
486	#539	—	3	2	no	—
487	#539	—	3	2	no	—
488	#539	—	3	2	no	—
489	#538	—	3	2	no	—
490	#538	—	3	2	no	—
491	#538	—	3	1	no	—
492	#538	C₃×D₃	1	1	yes	characteristic, complemented
493	#534	—	3	1	no	—
494	#534	—	3	2	no	—
495	#529	—	3	2	no	—
496	#529	—	3	2	no	—
497	#529	—	3	1	no	—
498	#529	—	3	1	no	—
499	#525	—	3	2	no	—
500	#525	—	3	2	no	—
501	#525	—	3	2	no	—
502	C₂×C₄×D₄	—	3	2	no	—
503	C₂×C₄×D₄	—	3	1	no	—
504	C₂⁴×C₃	—	2	1	no	—
505	C₂⁴×C₃	—	3	1	no	—
506	C₂⁴×C₃	—	3	2	no	—
507	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
508	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
509	C₂³×D₃	C₂³×C₃	1	2	yes	—
510	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
511	C₃×#41	—	12	4	no	—
512	C₂×C₃×Q₈	—	2	1	no	—
513	C₂×C₃×Q₈	—	3	1	no	—
514	C₂×C₃×Q₈	—	3	2	no	—
515	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
516	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₃×D₄	—	2	2	no	—
518	C₂×C₃×D₄	—	2	2	no	—
519	C₂×C₃×D₄	—	2	2	no	—
520	C₂×C₃×D₄	—	2	1	no	—
521	C₂×C₃×D₄	—	3	2	no	—
522	C₂×C₃×D₄	—	3	2	no	—
523	C₂×C₃×D₄	—	3	2	no	—
524	C₂×C₃×D₄	—	3	2	no	—
525	C₂×C₃×D₄	—	3	2	no	—
526	C₂×C₃×D₄	—	3	2	no	—
527	C₂×C₃×D₄	—	3	2	no	—
528	C₂×C₃×D₄	—	3	2	no	—
529	C₂×C₃×D₄	—	3	1	no	—
530	C₂×C₃×D₄	—	6	8	no	—
531	C₂×C₃×D₄	—	6	4	no	—
532	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
533	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
534	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
535	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
536	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
537	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
539	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
540	C₂²×C₃×C₄	—	2	1	no	—
541	C₂²×C₃×C₄	—	2	1	no	—
542	C₂²×C₃×C₄	—	2	2	no	—
543	C₂²×C₃×C₄	—	3	1	no	—
544	C₂²×C₃×C₄	—	3	1	no	—
545	C₂²×C₃×C₄	—	3	2	no	—
546	C₂²×C₃×C₄	—	3	2	no	—
547	C₂²×C₃×C₄	—	3	1	no	—
548	C₂²×C₃×C₄	—	3	2	no	—
549	C₂²×C₃×C₄	—	3	2	no	—
550	C₂²×C₃×C₄	—	3	2	no	—
551	C₂²×C₃×C₄	—	3	2	no	—
552	C₂²×C₃×C₄	—	3	2	no	—
553	C₂²×C₃×C₄	—	3	2	no	—
554	C₂²×C₃×C₄	—	3	2	no	—
555	C₂²×C₃×C₄	—	3	2	no	—
556	C₂²×C₃×C₄	—	12	2	no	—
557	C₂²×C₃×C₄	—	12	4	no	—
558	C₂²×C₃×C₄	—	12	2	no	—
559	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
560	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
561	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
562	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
565	C₂×#67	—	2	4	no	—
566	C₂×#67	C₂³×C₃	1	2	yes	—
567	C₂×#67	C₂³×C₃	1	2	yes	—
568	C₂×#67	C₂³×C₃	1	2	yes	—
569	C₂×#67	C₂³×C₃	1	2	yes	—
570	C₂×#67	C₂³×C₃	1	2	yes	—
571	C₂×#67	C₂³×C₃	1	2	yes	—
572	C₂×#67	C₂³×C₃	1	2	yes	—
573	C₂²×Dic₃	—	4	2	no	—
574	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
575	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
576	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
577	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
578	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
579	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
580	#237	—	4	4	no	—
581	D₃×D₄	—	2	8	no	—
582	C₂×D₁₂	C₂³×C₃	1	2	yes	—
583	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₄×D₃	—	4	2	no	—
585	C₂×C₄×D₃	—	4	4	no	—
586	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
587	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
588	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
589	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
590	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
591	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
592	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
593	C₂×Dic₆	C₂³×C₃	1	2	yes	—
594	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
595	C₃×C₄⋊C₄	—	2	2	no	—
596	C₃×C₄⋊C₄	—	2	2	no	—
597	C₃×C₄⋊C₄	—	2	1	no	—
598	C₃×C₄⋊C₄	—	2	1	no	—
599	C₃×C₄⋊C₄	—	3	2	no	—
600	C₃×C₄⋊C₄	—	3	2	no	—
601	C₃×C₄⋊C₄	—	3	2	no	—
602	C₃×C₄⋊C₄	—	3	2	no	—
603	C₃×C₄⋊C₄	—	3	2	no	—
604	C₃×C₄⋊C₄	—	3	2	no	—
605	C₃×C₄⋊C₄	—	3	2	no	—
606	C₃×C₄⋊C₄	—	3	2	no	—
607	C₃×C₄⋊C₄	—	3	2	no	—
608	C₃×C₄⋊C₄	—	3	2	no	—
609	C₃×C₄⋊C₄	—	3	2	no	—
610	C₃×C₄⋊C₄	—	3	2	no	—
611	C₃×C₄⋊C₄	—	3	1	no	—
612	C₃×C₄⋊C₄	—	3	2	no	—
613	C₃×C₄⋊C₄	—	3	1	no	—
614	C₃×C₄⋊C₄	—	3	2	no	—
615	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
616	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
617	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
618	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
619	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
620	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
621	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
622	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
623	C₃×C₂²⋊C₄	—	2	2	no	—
624	C₃×C₂²⋊C₄	—	2	2	no	—
625	C₃×C₂²⋊C₄	—	2	2	no	—
626	C₃×C₂²⋊C₄	—	2	2	no	—
627	C₃×C₂²⋊C₄	—	2	2	no	—
628	C₃×C₂²⋊C₄	—	2	2	no	—
629	C₃×C₂²⋊C₄	—	2	2	no	—
630	C₃×C₂²⋊C₄	—	3	2	no	—
631	C₃×C₂²⋊C₄	—	3	2	no	—
632	C₃×C₂²⋊C₄	—	3	2	no	—
633	C₃×C₂²⋊C₄	—	3	2	no	—
634	C₃×C₂²⋊C₄	—	3	2	no	—
635	C₃×C₂²⋊C₄	—	3	2	no	—
636	C₃×C₂²⋊C₄	—	3	2	no	—
637	C₃×C₂²⋊C₄	—	3	2	no	—
638	C₃×C₂²⋊C₄	—	3	2	no	—
639	C₃×C₂²⋊C₄	—	3	2	no	—
640	C₃×C₂²⋊C₄	—	3	2	no	—
641	C₃×C₂²⋊C₄	—	3	2	no	—
642	C₃×C₂²⋊C₄	—	3	2	no	—
643	C₃×C₂²⋊C₄	—	3	2	no	—
644	C₃×C₂²⋊C₄	—	3	2	no	—
645	C₃×C₂²⋊C₄	—	3	2	no	—
646	C₃×C₂²⋊C₄	—	3	2	no	—
647	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
648	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
649	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
650	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
651	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
652	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
653	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
654	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
655	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
656	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
657	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
658	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
659	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
660	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
661	C₃×C₄²	—	2	2	no	—
662	C₃×C₄²	—	3	2	no	—
663	C₃×C₄²	—	3	1	no	—
664	C₃×C₄²	—	3	1	no	—
665	C₃×C₄²	—	3	2	no	—
666	C₃×C₄²	—	3	2	no	—
667	C₃×C₄²	—	3	1	no	—
668	C₃×C₄²	—	3	1	no	—
669	C₃×C₄²	C₂²×D₃	1	2	yes	—
670	C₃×C₄²	C₂³×C₃	1	2	yes	—
671	#217	C₂³×C₃	1	2	yes	—
672	#217	C₂³×C₃	1	2	yes	—
673	#217	C₂³×C₃	1	2	yes	—
674	#217	C₂³×C₃	1	2	yes	—
675	#217	C₂³×C₃	1	2	yes	—
676	#217	C₂³×C₃	1	2	yes	—
677	#217	C₂³×C₃	1	2	yes	—
678	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
679	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
680	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
681	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
682	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
683	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
684	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
685	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
686	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
687	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
688	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
689	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
690	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
691	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
692	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
693	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
694	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
695	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
696	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
697	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
698	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
699	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
700	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
701	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
702	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
703	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
704	C₄×Dic₃	C₂³×C₃	1	2	yes	—
705	C₄×Dic₃	C₂³×C₃	1	2	yes	—
706	C₄×Dic₃	C₂³×C₃	1	2	yes	—
707	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
708	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
709	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
710	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
711	C₂²×C₃²	—	2	1	no	—
712	C₂²×C₃²	—	2	1	no	—
713	C₂²×C₃²	—	2	2	no	—
714	C₂²×C₃²	—	2	2	no	—
715	C₂²×C₃²	—	2	2	no	—
716	C₂²×C₃²	—	2	2	no	—
717	C₂²×C₃²	—	2	2	no	—
718	C₂²×C₃²	—	2	2	no	—
719	C₂²×C₃²	—	4	4	no	—
720	C₂²×C₃²	C₂×#41	1	2	yes	—
721	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
722	C₂×C₃×D₃	—	2	2	no	—
723	C₂×C₃×D₃	—	2	2	no	—
724	C₂×C₃×D₃	—	2	2	no	—
725	C₂×C₃×D₃	—	2	2	no	—
726	C₂×C₃×D₃	—	2	2	no	—
727	C₂×C₃×D₃	—	4	4	no	—
728	C₂×C₃×D₃	—	4	8	no	—
729	C₂×C₃×D₃	C₂×#41	1	4	yes	—
730	C₃²×C₄	—	2	2	no	—
731	C₃²×C₄	—	2	2	no	—
732	C₃²×C₄	—	2	2	no	—
733	C₃²×C₄	—	2	1	no	—
734	C₃²×C₄	—	2	2	no	—
735	C₃²×C₄	—	2	1	no	—
736	C₃×Dic₃	—	2	2	no	—
737	C₃×Dic₃	—	2	1	no	—
738	C₃×Dic₃	—	2	1	no	—
739	C₃×Dic₃	—	2	2	no	—
740	C₃×Dic₃	—	2	2	no	—
741	C₃×Dic₃	—	2	1	no	—
742	C₃×Dic₃	—	2	2	no	—
743	C₃×Dic₃	H(5,𝔽₂)	1	2	yes	—
744	C₂×#41	—	3	2	no	—
745	C₂²×D₄	—	3	1	no	—
746	C₂²×D₄	—	3	2	no	—
747	C₂³×C₄	—	3	1	no	—
748	C₂³×C₄	—	3	1	no	—
749	C₂³×C₄	—	3	2	no	—
750	#126	—	3	2	no	—
751	#126	—	3	2	no	—
752	#126	—	3	2	no	—
753	#126	—	3	2	no	—
754	#126	—	3	2	no	—
755	#126	C₂×C₃×D₃	1	2	yes	complemented
756	#125	—	3	2	no	—
757	#125	—	3	1	no	—
758	#125	—	3	1	no	—
759	#125	—	3	2	no	—
760	#124	—	3	1	no	—
761	#124	—	3	1	no	—
762	#124	—	3	2	no	—
763	#124	C₂×C₃×D₃	1	2	yes	complemented
764	#123	—	3	2	no	—
765	#123	—	3	2	no	—
766	#123	—	3	2	no	—
767	#123	—	3	2	no	—
768	#123	—	3	2	no	—
769	#123	—	3	2	no	—
770	#123	—	3	2	no	—
771	#123	—	3	2	no	—
772	#123	—	3	2	no	—
773	#123	—	3	2	no	—
774	#123	—	3	2	no	—
775	#123	C₂×C₃×D₃	1	2	yes	complemented
776	C₂²⋊Q₈	—	3	2	no	—
777	C₂²⋊Q₈	—	3	2	no	—
778	C₂²⋊Q₈	—	3	1	no	—
779	C₂²⋊Q₈	—	3	2	no	—
780	C₂²⋊Q₈	—	3	2	no	—
781	C₂²⋊Q₈	—	3	2	no	—
782	C₂²⋊Q₈	—	3	2	no	—
783	C₂²⋊Q₈	—	3	2	no	—
784	C₂²⋊Q₈	—	3	2	no	—
785	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
786	#121	—	3	2	no	—
787	#121	—	3	2	no	—
788	#121	—	3	2	no	—
789	#121	—	3	2	no	—
790	#121	—	3	1	no	—
791	#121	—	3	2	no	—
792	#121	—	3	2	no	—
793	#121	—	3	2	no	—
794	#121	C₂×C₃×D₃	1	1	yes	characteristic
795	#121	C₂×C₃×D₃	1	2	yes	complemented
796	#120	—	3	2	no	—
797	#120	—	3	2	no	—
798	#120	—	3	2	no	—
799	#120	—	3	2	no	—
800	#120	—	3	2	no	—
801	#120	C₂×C₃×D₃	1	2	yes	complemented
802	C₄×Q₈	—	3	1	no	—
803	C₄×Q₈	—	3	1	no	—
804	C₄×D₄	—	3	2	no	—
805	C₄×D₄	—	3	1	no	—
806	C₄×D₄	—	3	2	no	—
807	C₄×D₄	—	3	2	no	—
808	C₄×D₄	—	3	2	no	—
809	C₄×D₄	—	3	2	no	—
810	C₄×D₄	—	3	1	no	—
811	C₄×D₄	—	3	2	no	—
812	C₄×D₄	—	3	2	no	—
813	C₄×D₄	—	3	2	no	—
814	C₄×D₄	—	3	2	no	—
815	C₄×D₄	—	3	2	no	—
816	C₄×D₄	—	3	2	no	—
817	C₄×D₄	—	3	2	no	—
818	C₄×D₄	—	3	2	no	—
819	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
820	#117	—	3	2	no	—
821	#117	—	3	2	no	—
822	#117	—	3	2	no	—
823	C₂×C₄⋊C₄	—	3	1	no	—
824	C₂×C₄⋊C₄	—	3	2	no	—
825	C₂×C₂²⋊C₄	—	3	1	no	—
826	C₂×C₂²⋊C₄	—	3	2	no	—
827	C₂×C₂²⋊C₄	—	3	2	no	—
828	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
829	C₂×C₄²	—	3	1	no	—
830	C₂×C₄²	—	3	2	no	—
831	C₂³×C₃	—	2	2	no	—
832	C₂³×C₃	—	2	2	no	—
833	C₂³×C₃	—	2	1	no	—
834	C₂³×C₃	—	2	2	no	—
835	C₂³×C₃	—	2	2	no	—
836	C₂³×C₃	—	3	2	no	—
837	C₂³×C₃	—	3	4	no	—
838	C₂³×C₃	—	3	2	no	—
839	C₂³×C₃	—	4	2	no	—
840	C₂³×C₃	—	4	1	no	—
841	C₂³×C₃	—	4	1	no	—
842	C₂³×C₃	—	4	1	no	—
843	C₂³×C₃	—	4	1	no	—
844	C₂³×C₃	—	6	4	no	—
845	C₂³×C₃	—	8	1	no	—
846	C₂³×C₃	—	8	1	no	—
847	C₂³×C₃	—	12	1	no	—
848	C₂³×C₃	—	12	2	no	—
849	C₂³×C₃	—	12	1	no	—
850	C₂³×C₃	—	12	2	no	—
851	C₂³×C₃	C₂³×D₃	1	2	yes	—
852	C₂³×C₃	C₂³×D₃	1	2	yes	—
853	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
854	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
855	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
856	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
857	C₂²×D₃	—	2	4	no	—
858	C₂²×D₃	—	4	1	no	—
859	C₂²×D₃	—	4	2	no	—
860	C₂²×D₃	—	4	1	no	—
861	C₂²×D₃	—	4	2	no	—
862	C₂²×D₃	C₃×#41	1	4	yes	complemented
863	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
864	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
865	C₃×Q₈	—	4	1	no	—
866	C₃×Q₈	—	4	1	no	—
867	C₃×Q₈	—	8	1	no	—
868	C₃×Q₈	—	12	1	no	—
869	C₃×Q₈	—	12	2	no	—
870	C₃×D₄	—	2	4	no	—
871	C₃×D₄	—	2	4	no	—
872	C₃×D₄	—	4	4	no	—
873	C₃×D₄	—	4	2	no	—
874	C₃×D₄	—	4	1	no	—
875	C₃×D₄	—	4	2	no	—
876	C₃×D₄	—	4	2	no	—
877	C₃×D₄	—	4	1	no	—
878	C₃×D₄	—	4	2	no	—
879	C₃×D₄	—	6	4	no	—
880	C₃×D₄	—	6	4	no	—
881	C₃×D₄	—	6	4	no	—
882	C₃×D₄	—	6	4	no	—
883	C₃×D₄	—	6	4	no	—
884	C₃×D₄	—	8	2	no	—
885	C₃×D₄	—	8	1	no	—
886	C₃×D₄	—	8	2	no	—
887	C₃×D₄	—	12	1	no	—
888	C₃×D₄	—	12	2	no	—
889	C₃×D₄	—	12	2	no	—
890	C₃×D₄	—	12	2	no	—
891	C₂×C₃×C₄	—	2	2	no	—
892	C₂×C₃×C₄	—	2	2	no	—
893	C₂×C₃×C₄	—	2	2	no	—
894	C₂×C₃×C₄	—	2	1	no	—
895	C₂×C₃×C₄	—	2	1	no	—
896	C₂×C₃×C₄	—	2	2	no	—
897	C₂×C₃×C₄	—	3	1	no	—
898	C₂×C₃×C₄	—	3	2	no	—
899	C₂×C₃×C₄	—	3	1	no	—
900	C₂×C₃×C₄	—	3	1	no	—
901	C₂×C₃×C₄	—	3	2	no	—
902	C₂×C₃×C₄	—	3	1	no	—
903	C₂×C₃×C₄	—	3	2	no	—
904	C₂×C₃×C₄	—	3	2	no	—
905	C₂×C₃×C₄	—	4	2	no	—
906	C₂×C₃×C₄	—	4	1	no	—
907	C₂×C₃×C₄	—	4	1	no	—
908	C₂×C₃×C₄	—	4	2	no	—
909	C₂×C₃×C₄	—	4	1	no	—
910	C₂×C₃×C₄	—	4	1	no	—
911	C₂×C₃×C₄	—	6	4	no	—
912	C₂×C₃×C₄	—	6	4	no	—
913	C₂×C₃×C₄	—	6	4	no	—
914	C₂×C₃×C₄	—	6	2	no	—
915	C₂×C₃×C₄	—	6	4	no	—
916	C₂×C₃×C₄	—	6	4	no	—
917	C₂×C₃×C₄	—	6	2	no	—
918	C₂×C₃×C₄	—	8	1	no	—
919	C₂×C₃×C₄	—	8	2	no	—
920	C₂×C₃×C₄	—	8	1	no	—
921	C₂×C₃×C₄	—	12	2	no	—
922	C₂×C₃×C₄	—	12	2	no	—
923	C₂×C₃×C₄	—	12	2	no	—
924	C₂×C₃×C₄	—	12	2	no	—
925	C₂×C₃×C₄	—	12	2	no	—
926	C₂×C₃×C₄	—	12	1	no	—
927	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
928	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
929	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
930	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
931	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
932	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
933	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
934	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
935	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
936	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
937	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
938	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
939	#67	—	2	4	no	—
940	#67	—	2	4	no	—
941	#67	—	2	4	no	—
942	#67	—	2	4	no	—
943	#67	—	4	2	no	—
944	#67	—	4	2	no	—
945	#67	—	4	2	no	—
946	C₂×Dic₃	—	2	2	no	—
947	C₂×Dic₃	—	2	4	no	—
948	C₂×Dic₃	—	2	2	no	—
949	C₂×Dic₃	—	2	4	no	—
950	C₂×Dic₃	—	4	1	no	—
951	C₂×Dic₃	—	4	2	no	—
952	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
953	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
954	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
955	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
956	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
957	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
958	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
959	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
960	D₁₂	—	2	4	no	—
961	D₁₂	—	4	1	no	—
962	C₄×D₃	—	2	4	no	—
963	C₄×D₃	—	2	4	no	—
964	C₄×D₃	—	2	4	no	—
965	C₄×D₃	—	4	2	no	—
966	C₄×D₃	—	4	2	no	—
967	C₄×D₃	—	4	2	no	—
968	C₄×D₃	—	4	2	no	—
969	Dic₆	—	4	1	no	—
970	Dic₆	—	4	2	no	—
971	C₂×C₃²	—	2	2	no	—
972	C₂×C₃²	—	4	2	no	—
973	C₂×C₃²	—	4	2	no	—
974	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
975	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂×C₃²	#585	1	1	yes	characteristic
977	C₃×D₃	—	2	4	no	—
978	C₃×D₃	—	4	2	no	—
979	C₂⁴	—	3	1	no	—
980	C₂⁴	—	3	2	no	—
981	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
982	#41	—	12	4	no	—
983	C₂×Q₈	—	3	1	no	—
984	C₂×Q₈	—	3	2	no	—
985	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
986	C₂×D₄	—	3	2	no	—
987	C₂×D₄	—	3	2	no	—
988	C₂×D₄	—	3	2	no	—
989	C₂×D₄	—	3	2	no	—
990	C₂×D₄	—	3	2	no	—
991	C₂×D₄	—	3	2	no	—
992	C₂×D₄	—	3	2	no	—
993	C₂×D₄	—	3	2	no	—
994	C₂×D₄	—	3	1	no	—
995	C₂×D₄	—	6	8	no	—
996	C₂×D₄	—	6	4	no	—
997	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
998	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
999	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1000	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1001	C₂²×C₄	—	3	1	no	—
1002	C₂²×C₄	—	3	1	no	—
1003	C₂²×C₄	—	3	2	no	—
1004	C₂²×C₄	—	3	2	no	—
1005	C₂²×C₄	—	3	1	no	—
1006	C₂²×C₄	—	3	2	no	—
1007	C₂²×C₄	—	3	2	no	—
1008	C₂²×C₄	—	3	2	no	—
1009	C₂²×C₄	—	3	2	no	—
1010	C₂²×C₄	—	3	2	no	—
1011	C₂²×C₄	—	3	2	no	—
1012	C₂²×C₄	—	3	2	no	—
1013	C₂²×C₄	—	3	2	no	—
1014	C₂²×C₄	—	12	2	no	—
1015	C₂²×C₄	—	12	4	no	—
1016	C₂²×C₄	—	12	2	no	—
1017	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1020	C₄⋊C₄	—	3	2	no	—
1021	C₄⋊C₄	—	3	2	no	—
1022	C₄⋊C₄	—	3	2	no	—
1023	C₄⋊C₄	—	3	2	no	—
1024	C₄⋊C₄	—	3	2	no	—
1025	C₄⋊C₄	—	3	2	no	—
1026	C₄⋊C₄	—	3	2	no	—
1027	C₄⋊C₄	—	3	2	no	—
1028	C₄⋊C₄	—	3	2	no	—
1029	C₄⋊C₄	—	3	2	no	—
1030	C₄⋊C₄	—	3	2	no	—
1031	C₄⋊C₄	—	3	1	no	—
1032	C₄⋊C₄	—	3	2	no	—
1033	C₄⋊C₄	—	3	2	no	—
1034	C₄⋊C₄	—	3	1	no	—
1035	C₄⋊C₄	—	3	2	no	—
1036	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1037	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1038	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1040	C₂²⋊C₄	—	3	2	no	—
1041	C₂²⋊C₄	—	3	2	no	—
1042	C₂²⋊C₄	—	3	2	no	—
1043	C₂²⋊C₄	—	3	2	no	—
1044	C₂²⋊C₄	—	3	2	no	—
1045	C₂²⋊C₄	—	3	2	no	—
1046	C₂²⋊C₄	—	3	2	no	—
1047	C₂²⋊C₄	—	3	2	no	—
1048	C₂²⋊C₄	—	3	2	no	—
1049	C₂²⋊C₄	—	3	2	no	—
1050	C₂²⋊C₄	—	3	2	no	—
1051	C₂²⋊C₄	—	3	2	no	—
1052	C₂²⋊C₄	—	3	2	no	—
1053	C₂²⋊C₄	—	3	2	no	—
1054	C₂²⋊C₄	—	3	2	no	—
1055	C₂²⋊C₄	—	3	2	no	—
1056	C₂²⋊C₄	—	3	2	no	—
1057	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1058	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1059	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1060	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1061	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1062	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1063	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1064	C₄²	—	3	2	no	—
1065	C₄²	—	3	1	no	—
1066	C₄²	—	3	1	no	—
1067	C₄²	—	3	2	no	—
1068	C₄²	—	3	2	no	—
1069	C₄²	—	3	1	no	—
1070	C₄²	—	3	1	no	—
1071	C₄²	C₂²×C₃×D₃	1	2	yes	—
1072	C₂²×C₃	—	2	1	no	—
1073	C₂²×C₃	—	2	1	no	—
1074	C₂²×C₃	—	2	1	no	—
1075	C₂²×C₃	—	2	1	no	—
1076	C₂²×C₃	—	2	2	no	—
1077	C₂²×C₃	—	2	2	no	—
1078	C₂²×C₃	—	2	2	no	—
1079	C₂²×C₃	—	2	2	no	—
1080	C₂²×C₃	—	2	2	no	—
1081	C₂²×C₃	—	2	2	no	—
1082	C₂²×C₃	—	2	2	no	—
1083	C₂²×C₃	—	2	2	no	—
1084	C₂²×C₃	—	2	2	no	—
1085	C₂²×C₃	—	2	2	no	—
1086	C₂²×C₃	—	2	2	no	—
1087	C₂²×C₃	—	2	2	no	—
1088	C₂²×C₃	—	2	2	no	—
1089	C₂²×C₃	—	2	1	no	—
1090	C₂²×C₃	—	3	4	no	—
1091	C₂²×C₃	—	4	1	no	—
1092	C₂²×C₃	—	4	1	no	—
1093	C₂²×C₃	—	4	2	no	—
1094	C₂²×C₃	—	4	2	no	—
1095	C₂²×C₃	—	4	2	no	—
1096	C₂²×C₃	—	4	2	no	—
1097	C₂²×C₃	—	4	2	no	—
1098	C₂²×C₃	—	4	2	no	—
1099	C₂²×C₃	—	4	4	no	—
1100	C₂²×C₃	—	4	4	no	—
1101	C₂²×C₃	—	6	2	no	—
1102	C₂²×C₃	—	6	2	no	—
1103	C₂²×C₃	—	6	2	no	—
1104	C₂²×C₃	—	6	2	no	—
1105	C₂²×C₃	—	6	2	no	—
1106	C₂²×C₃	—	8	4	no	—
1107	C₂²×C₃	—	12	4	no	—
1108	C₂²×C₃	—	12	8	no	—
1109	C₂²×C₃	D₃×#41	1	2	yes	—
1110	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
1111	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1112	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1113	C₂×D₃	—	2	2	no	—
1114	C₂×D₃	—	2	2	no	—
1115	C₂×D₃	—	2	2	no	—
1116	C₂×D₃	—	2	2	no	—
1117	C₂×D₃	—	2	2	no	—
1118	C₂×D₃	—	4	4	no	—
1119	C₂×D₃	—	4	8	no	—
1120	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1121	C₃×C₄	—	2	2	no	—
1122	C₃×C₄	—	2	2	no	—
1123	C₃×C₄	—	2	2	no	—
1124	C₃×C₄	—	2	1	no	—
1125	C₃×C₄	—	2	1	no	—
1126	C₃×C₄	—	2	2	no	—
1127	C₃×C₄	—	2	2	no	—
1128	C₃×C₄	—	2	2	no	—
1129	C₃×C₄	—	2	2	no	—
1130	C₃×C₄	—	2	1	no	—
1131	C₃×C₄	—	2	2	no	—
1132	C₃×C₄	—	2	1	no	—
1133	C₃×C₄	—	3	2	no	—
1134	C₃×C₄	—	4	2	no	—
1135	C₃×C₄	—	4	2	no	—
1136	C₃×C₄	—	4	1	no	—
1137	C₃×C₄	—	4	1	no	—
1138	C₃×C₄	—	4	2	no	—
1139	C₃×C₄	—	4	2	no	—
1140	C₃×C₄	—	6	2	no	—
1141	C₃×C₄	—	6	1	no	—
1142	C₃×C₄	—	6	1	no	—
1143	C₃×C₄	—	6	1	no	—
1144	C₃×C₄	—	6	2	no	—
1145	C₃×C₄	—	6	2	no	—
1146	C₃×C₄	—	6	2	no	—
1147	Dic₃	—	2	2	no	—
1148	Dic₃	—	2	1	no	—
1149	Dic₃	—	2	1	no	—
1150	Dic₃	—	2	2	no	—
1151	Dic₃	—	2	2	no	—
1152	Dic₃	—	2	1	no	—
1153	Dic₃	—	2	2	no	—
1154	Dic₃	C₃×H(5,𝔽₂)	1	2	yes	—
1155	C₃²	#3459	1	1	yes	characteristic, complemented, Sylow
1156	C₂³	—	2	2	no	—
1157	C₂³	—	3	2	no	—
1158	C₂³	—	3	4	no	—
1159	C₂³	—	3	2	no	—
1160	C₂³	—	4	1	no	—
1161	C₂³	—	4	1	no	—
1162	C₂³	—	6	4	no	—
1163	C₂³	—	12	1	no	—
1164	C₂³	—	12	2	no	—
1165	C₂³	—	12	1	no	—
1166	C₂³	—	12	2	no	—
1167	C₂³	C₂³×C₃×D₃	1	2	yes	—
1168	C₂³	C₂³×C₃×D₃	1	2	yes	—
1169	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1170	Q₈	—	4	1	no	—
1171	Q₈	—	12	2	no	—
1172	Q₈	—	12	1	no	—
1173	D₄	—	2	4	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	1	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	6	4	no	—
1178	D₄	—	6	4	no	—
1179	D₄	—	6	4	no	—
1180	D₄	—	6	4	no	—
1181	D₄	—	6	4	no	—
1182	D₄	—	12	1	no	—
1183	D₄	—	12	2	no	—
1184	D₄	—	12	2	no	—
1185	D₄	—	12	2	no	—
1186	C₂×C₄	—	3	1	no	—
1187	C₂×C₄	—	3	2	no	—
1188	C₂×C₄	—	3	1	no	—
1189	C₂×C₄	—	3	2	no	—
1190	C₂×C₄	—	3	1	no	—
1191	C₂×C₄	—	3	1	no	—
1192	C₂×C₄	—	3	2	no	—
1193	C₂×C₄	—	3	2	no	—
1194	C₂×C₄	—	4	1	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	6	4	no	—
1198	C₂×C₄	—	6	4	no	—
1199	C₂×C₄	—	6	4	no	—
1200	C₂×C₄	—	6	2	no	—
1201	C₂×C₄	—	6	4	no	—
1202	C₂×C₄	—	6	4	no	—
1203	C₂×C₄	—	6	2	no	—
1204	C₂×C₄	—	12	2	no	—
1205	C₂×C₄	—	12	2	no	—
1206	C₂×C₄	—	12	2	no	—
1207	C₂×C₄	—	12	2	no	—
1208	C₂×C₄	—	12	2	no	—
1209	C₂×C₄	—	12	1	no	—
1210	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1211	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1212	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1213	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1214	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1215	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1216	C₂×C₃	—	2	2	no	—
1217	C₂×C₃	—	2	2	no	—
1218	C₂×C₃	—	2	1	no	—
1219	C₂×C₃	—	2	1	no	—
1220	C₂×C₃	—	2	1	no	—
1221	C₂×C₃	—	4	2	no	—
1222	C₂×C₃	—	4	2	no	—
1223	C₂×C₃	—	4	2	no	—
1224	C₂×C₃	—	4	2	no	—
1225	C₂×C₃	—	4	2	no	—
1226	C₂×C₃	—	6	4	no	—
1227	C₂×C₃	—	8	2	no	—
1228	C₂×C₃	—	8	2	no	—
1229	C₂×C₃	—	12	2	no	—
1230	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1231	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1232	C₂×C₃	#5966	1	1	yes	characteristic
1233	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1234	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1235	C₂×C₃	C₃×#585	1	1	yes	characteristic
1236	D₃	—	2	4	no	—
1237	D₃	—	4	2	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	2	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	3	4	no	—
1247	C₂²	—	4	4	no	—
1248	C₂²	—	6	2	no	—
1249	C₂²	—	6	2	no	—
1250	C₂²	—	6	2	no	—
1251	C₂²	—	6	2	no	—
1252	C₂²	—	6	2	no	—
1253	C₂²	—	12	4	no	—
1254	C₂²	—	12	8	no	—
1255	C₂²	C₃×D₃×#41	1	2	yes	—
1256	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1257	C₄	—	2	2	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	2	no	—
1263	C₄	—	3	2	no	—
1264	C₄	—	6	2	no	—
1265	C₄	—	6	1	no	—
1266	C₄	—	6	1	no	—
1267	C₄	—	6	1	no	—
1268	C₄	—	6	2	no	—
1269	C₄	—	6	2	no	—
1270	C₄	—	6	2	no	—
1271	C₃	—	2	1	no	—
1272	C₃	#86388	1	1	yes	characteristic, direct product factor
1273	C₃	C₃×#3459	1	1	yes	characteristic, complemented
1274	C₂	—	2	2	no	—
1275	C₂	—	4	2	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	6	4	no	—
1278	C₂	—	12	2	no	—
1279	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1280	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1281	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×#538	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#538	D₃
hypocenter	C₃	C₃×#3459
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#538

Complements

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

N	H ≅ G/N	type
1. C₃²×#538	C₂	semidirect
2. C₃×#5707	C₂	semidirect
3. C₃×#5706	C₂	semidirect
4. C₃×#5680	C₂	semidirect
5. C₃×#5678	C₂	semidirect
6. C₃×#5660	C₂	semidirect
7. C₃×#5656	C₂	semidirect
8. C₃×#5634	C₂	semidirect
9. C₃×#5624	C₂	semidirect
10. C₃×#5613	C₂	semidirect
11. C₃×#5606	C₂	semidirect
12. C₃×#5605	C₂	semidirect
13. C₃×#5600	C₂	semidirect
14. C₃×#5589	C₂	semidirect
15. C₃×#5586	C₂	semidirect
16. C₃×#5564	C₂	semidirect
17. C₃×C₄×D₃×D₄	C₂	semidirect
18. C₃×#5494	C₂	semidirect
19. C₂×C₃×#67⋊C₄	C₂	semidirect
21. #86388	C₃	direct (N × H)
23. C₂³×C₃×Dic₃	C₂²	semidirect
24. C₂×C₃×#237	C₂²	semidirect
27. C₂²×C₃×C₄×D₃	C₂²	semidirect
28. C₃²×#126	C₂²	semidirect
29. C₃²×#124	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×C₂²⋊Q₈	C₂²	semidirect
33. C₃²×#121	C₂²	semidirect
34. C₃²×#120	C₂²	semidirect
35. C₃²×C₄×D₄	C₂²	semidirect
36. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
37. C₃×#953	C₂²	semidirect
38. C₃×#947	C₂²	semidirect
39. C₃×#946	C₂²	semidirect
40. C₃×Q₈×Dic₃	C₂²	semidirect
42. C₃×#939	C₂²	semidirect
45. C₃×#937	C₂²	semidirect
46. C₃×#937	C₂²	semidirect
47. C₃×#937	C₂²	semidirect
48. C₃×#936	C₂²	semidirect
49. C₃×#935	C₂²	semidirect
50. C₃×#935	C₂²	semidirect
51. C₃×D₄×Dic₃	C₂²	semidirect
52. C₃×D₄×Dic₃	C₂²	semidirect
53. C₃×D₄×Dic₃	C₂²	semidirect
55. C₃×#929	C₂²	semidirect
56. C₃×C₄×#67	C₂²	semidirect
57. C₃×C₄×#67	C₂²	semidirect
59. C₃×#924	C₂²	semidirect
60. C₃×#924	C₂²	semidirect
61. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
62. C₂×C₃×C₄×Dic₃	C₂²	semidirect
63. C₃×#898	C₂²	semidirect
64. C₃×#897	C₂²	semidirect
65. C₃×#896	C₂²	semidirect
66. C₃×#896	C₂²	semidirect
67. C₃×#896	C₂²	semidirect
68. C₃×#894	C₂²	semidirect
69. C₃×#893	C₂²	semidirect
70. C₃×#893	C₂²	semidirect
71. C₃×#892	C₂²	semidirect
72. C₃×D₃×C₄⋊C₄	C₂²	semidirect
73. C₃×#890	C₂²	semidirect
74. C₃×#890	C₂²	semidirect
75. C₃×#889	C₂²	semidirect
76. C₃×#887	C₂²	semidirect
77. C₃×#886	C₂²	semidirect
78. C₃×#886	C₂²	semidirect
79. C₃×#885	C₂²	semidirect
82. C₃×#884	C₂²	semidirect
83. C₃×#883	C₂²	semidirect
84. C₃×#883	C₂²	semidirect
85. C₃×#883	C₂²	semidirect
86. C₃×#883	C₂²	semidirect
87. C₃×#883	C₂²	semidirect
88. C₃×#882	C₂²	semidirect
89. C₃×#67⋊C₄	C₂²	semidirect
90. C₃×#67⋊C₄	C₂²	semidirect
91. C₃×#67⋊C₄	C₂²	semidirect
92. C₃×#67⋊C₄	C₂²	semidirect
93. C₃×#67⋊C₄	C₂²	semidirect
94. C₃×#67⋊C₄	C₂²	semidirect
95. C₃×#67⋊C₄	C₂²	semidirect
97. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
98. C₃×#879	C₂²	semidirect
99. C₃×#879	C₂²	semidirect
100. C₃×#879	C₂²	semidirect
101. C₃×#878	C₂²	semidirect
102. C₃×#878	C₂²	semidirect
103. C₃×#877	C₂²	semidirect
104. C₃×#877	C₂²	semidirect
105. C₃×#876	C₂²	semidirect
106. C₃×C₄×D₁₂	C₂²	semidirect
107. C₃×C₄²×D₃	C₂²	semidirect
108. C₃×#870	C₂²	semidirect
117. C₃×#538	D₃	semidirect
118. C₃×#538	C₂×C₃	semidirect
130. #5707	C₂×C₃	semidirect
131. #5706	C₂×C₃	semidirect
132. #5680	C₂×C₃	semidirect
133. #5678	C₂×C₃	semidirect
134. #5660	C₂×C₃	semidirect
135. #5656	C₂×C₃	semidirect
136. #5634	C₂×C₃	semidirect
137. #5624	C₂×C₃	semidirect
138. #5613	C₂×C₃	semidirect
139. #5606	C₂×C₃	semidirect
140. #5605	C₂×C₃	semidirect
141. #5600	C₂×C₃	semidirect
142. #5589	C₂×C₃	semidirect
143. #5586	C₂×C₃	semidirect
144. #5564	C₂×C₃	semidirect
145. C₄×D₃×D₄	C₂×C₃	semidirect
146. #5494	C₂×C₃	semidirect
147. C₂×#67⋊C₄	C₂×C₃	semidirect
249. C₂³×Dic₃	C₂²×C₃	semidirect
250. C₂×#237	C₂²×C₃	semidirect
253. C₂²×C₄×D₃	C₂²×C₃	semidirect
260. C₃×#126	C₂×D₃	semidirect
261. C₃×#126	C₂²×C₃	semidirect
270. C₃×#124	C₂×D₃	semidirect
271. C₃×#124	C₂²×C₃	semidirect
284. C₃×#123	C₂×D₃	semidirect
285. C₃×#123	C₂²×C₃	semidirect
296. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
297. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
309. C₃×#121	C₂×D₃	semidirect
311. C₃×#121	C₂²×C₃	semidirect
318. C₃×#120	C₂×D₃	semidirect
319. C₃×#120	C₂²×C₃	semidirect
338. C₃×C₄×D₄	C₂×D₃	semidirect
339. C₃×C₄×D₄	C₂²×C₃	semidirect
349. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
350. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
353. #953	C₂²×C₃	semidirect
354. #947	C₂²×C₃	semidirect
355. #946	C₂²×C₃	semidirect
356. Q₈×Dic₃	C₂²×C₃	semidirect
358. #939	C₂²×C₃	semidirect
361. #937	C₂²×C₃	semidirect
362. #937	C₂²×C₃	semidirect
363. #937	C₂²×C₃	semidirect
364. #936	C₂²×C₃	semidirect
365. #935	C₂²×C₃	semidirect
366. #935	C₂²×C₃	semidirect
367. D₄×Dic₃	C₂²×C₃	semidirect
368. D₄×Dic₃	C₂²×C₃	semidirect
369. D₄×Dic₃	C₂²×C₃	semidirect
371. #929	C₂²×C₃	semidirect
372. C₄×#67	C₂²×C₃	semidirect
373. C₄×#67	C₂²×C₃	semidirect
375. #924	C₂²×C₃	semidirect
376. #924	C₂²×C₃	semidirect
377. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
378. C₂×C₄×Dic₃	C₂²×C₃	semidirect
379. #898	C₂²×C₃	semidirect
380. #897	C₂²×C₃	semidirect
381. #896	C₂²×C₃	semidirect
382. #896	C₂²×C₃	semidirect
383. #896	C₂²×C₃	semidirect
384. #894	C₂²×C₃	semidirect
385. #893	C₂²×C₃	semidirect
386. #893	C₂²×C₃	semidirect
387. #892	C₂²×C₃	semidirect
388. D₃×C₄⋊C₄	C₂²×C₃	semidirect
389. #890	C₂²×C₃	semidirect
390. #890	C₂²×C₃	semidirect
391. #889	C₂²×C₃	semidirect
392. #887	C₂²×C₃	semidirect
393. #886	C₂²×C₃	semidirect
394. #886	C₂²×C₃	semidirect
395. #885	C₂²×C₃	semidirect
398. #884	C₂²×C₃	semidirect
399. #883	C₂²×C₃	semidirect
400. #883	C₂²×C₃	semidirect
401. #883	C₂²×C₃	semidirect
402. #883	C₂²×C₃	semidirect
403. #883	C₂²×C₃	semidirect
404. #882	C₂²×C₃	semidirect
405. #67⋊C₄	C₂²×C₃	semidirect
406. #67⋊C₄	C₂²×C₃	semidirect
407. #67⋊C₄	C₂²×C₃	semidirect
408. #67⋊C₄	C₂²×C₃	semidirect
409. #67⋊C₄	C₂²×C₃	semidirect
410. #67⋊C₄	C₂²×C₃	semidirect
411. #67⋊C₄	C₂²×C₃	semidirect
413. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
414. #879	C₂²×C₃	semidirect
415. #879	C₂²×C₃	semidirect
416. #879	C₂²×C₃	semidirect
417. #878	C₂²×C₃	semidirect
418. #878	C₂²×C₃	semidirect
419. #877	C₂²×C₃	semidirect
420. #877	C₂²×C₃	semidirect
421. #876	C₂²×C₃	semidirect
422. C₄×D₁₂	C₂²×C₃	semidirect
423. C₄²×D₃	C₂²×C₃	semidirect
424. #870	C₂²×C₃	semidirect
436. C₂²×C₃×D₃	#41	semidirect
492. #538	C₃×D₃	semidirect
755. #126	C₂×C₃×D₃	semidirect
763. #124	C₂×C₃×D₃	semidirect
775. #123	C₂×C₃×D₃	semidirect
785. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
795. #121	C₂×C₃×D₃	semidirect
801. #120	C₂×C₃×D₃	semidirect
819. C₄×D₄	C₂×C₃×D₃	semidirect
828. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
862. C₂²×D₃	C₃×#41	semidirect
1155. C₃²	#3459	semidirect
1272. C₃	#86388	direct (N × H)
1273. C₃	C₃×#3459	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#538	2
C₃×#5707	2
C₃×#5706	2
C₃×#5680	2
C₃×#5678	2
C₃×#5660	2
C₃×#5656	2
C₃×#5634	2
C₃×#5624	2
C₃×#5613	2
C₃×#5606	2
C₃×#5605	2
C₃×#5600	2
C₃×#5589	2
C₃×#5586	2
C₃×#5564	2
C₃×C₄×D₃×D₄	2
C₃×#5494	2
C₂×C₃×#67⋊C₄	2
C₃×#3459	3
#86388	3

Subgroups — C3×#86388 #11901979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86388 #11901979