Subgroups — C₃×#86036 #11901967

Order 1152.

2485 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5828	C₂	1	2	yes	maximal, complemented
3	C₃×#5791	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5660	C₂	1	2	yes	maximal, complemented
6	C₃×#5657	C₂	1	2	yes	maximal, complemented
7	C₃×#5645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5638	C₂	1	2	yes	maximal, complemented
9	C₃×#5634	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5613	C₂	1	2	yes	maximal, complemented
11	C₃×#5605	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5602	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5593	C₂	1	2	yes	maximal, complemented
14	C₃×#5589	C₂	1	2	yes	maximal, complemented
15	C₃×#5557	C₂	1	2	yes	maximal, complemented
16	C₃×#5547	C₂	1	2	yes	maximal, complemented
17	C₃×C₄×D₃×D₄	C₂	1	2	yes	maximal, complemented
18	C₃×#5538	C₂	1	2	yes	maximal, complemented
19	C₃×#5528	C₂	1	2	yes	maximal, complemented
20	C₃×#3459	—	3	1	no	maximal
21	#86036	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
26	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
29	C₃²×#123	C₂²	1	2	yes	complemented
30	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#121	C₂²	1	1	yes	characteristic
33	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#120	C₂²	1	2	yes	complemented
35	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
36	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
37	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
38	C₃×#953	C₂²	1	2	yes	complemented
39	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
40	C₃×#946	C₂²	1	2	yes	complemented
41	C₃×#946	C₂²	1	2	yes	complemented
42	C₃×#939	C₂²	1	2	yes	—
43	C₃×#939	C₂²	1	2	yes	complemented
44	C₃×#938	C₂²	1	2	yes	—
45	C₃×#938	C₂²	1	2	yes	—
46	C₃×#938	C₂²	1	2	yes	complemented
47	C₃×#937	C₂²	1	2	yes	complemented
48	C₃×#937	C₂²	1	2	yes	complemented
49	C₃×#937	C₂²	1	2	yes	complemented
50	C₃×#936	C₂²	1	2	yes	complemented
51	C₃×#935	C₂²	1	2	yes	complemented
52	C₃×#935	C₂²	1	2	yes	complemented
53	C₃×#935	C₂²	1	2	yes	complemented
54	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
55	C₃×#930	C₂²	1	1	yes	characteristic
56	C₃×#930	C₂²	1	1	yes	characteristic, complemented
57	C₃×#929	C₂²	1	2	yes	complemented
58	C₃×C₄×#67	C₂²	1	2	yes	complemented
59	C₃×C₄×#67	C₂²	1	2	yes	complemented
60	C₃×C₄×#67	C₂²	1	2	yes	complemented
61	C₃×C₄×#67	C₂²	1	2	yes	complemented
62	C₃×C₄×#67	C₂²	1	2	yes	complemented
63	C₃×C₄×#67	C₂²	1	2	yes	complemented
64	C₃×C₄×#67	C₂²	1	2	yes	complemented
65	C₃×C₄×#67	C₂²	1	2	yes	complemented
66	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
67	C₃×#926	C₂²	1	1	yes	characteristic, complemented
68	C₃×#926	C₂²	1	2	yes	complemented
69	C₃×#924	C₂²	1	1	yes	characteristic, complemented
70	C₃×#924	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
73	C₃×#898	C₂²	1	2	yes	complemented
74	C₃×#898	C₂²	1	2	yes	complemented
75	C₃×#897	C₂²	1	2	yes	complemented
76	C₃×#896	C₂²	1	2	yes	complemented
77	C₃×#896	C₂²	1	2	yes	complemented
78	C₃×#894	C₂²	1	2	yes	complemented
79	C₃×#894	C₂²	1	2	yes	complemented
80	C₃×#893	C₂²	1	2	yes	complemented
81	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×#890	C₂²	1	2	yes	complemented
83	C₃×#889	C₂²	1	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#886	C₂²	1	2	yes	complemented
86	C₃×#885	C₂²	1	2	yes	complemented
87	C₃×#885	C₂²	1	2	yes	complemented
88	C₃×#884	C₂²	1	2	yes	—
89	C₃×#884	C₂²	1	2	yes	—
90	C₃×#883	C₂²	1	2	yes	complemented
91	C₃×#883	C₂²	1	2	yes	complemented
92	C₃×#883	C₂²	1	2	yes	complemented
93	C₃×#883	C₂²	1	2	yes	complemented
94	C₃×#882	C₂²	1	2	yes	complemented
95	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
96	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
97	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	C₃×#879	C₂²	1	2	yes	complemented
100	C₃×#879	C₂²	1	2	yes	complemented
101	C₃×#879	C₂²	1	2	yes	complemented
102	C₃×#879	C₂²	1	2	yes	complemented
103	C₃×#878	C₂²	1	2	yes	complemented
104	C₃×#878	C₂²	1	2	yes	complemented
105	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
106	C₃×#872	C₂²	1	2	yes	complemented
107	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
108	C₃×C₄×Dic₆	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	1	no	—
113	C₃×#539	—	3	1	no	—
114	C₃×#538	—	3	2	no	—
115	C₃×#538	—	3	2	no	—
116	C₃×#538	—	3	2	no	—
117	C₃×#534	—	3	1	no	—
118	C₃×#534	—	3	2	no	—
119	C₃×#529	—	3	2	no	—
120	C₃×#529	—	3	2	no	—
121	C₃×#529	—	3	2	no	—
122	C₃×#525	—	2	1	no	—
123	C₃×#525	—	3	2	no	—
124	C₃×#525	—	3	1	no	—
125	C₃×#525	—	3	2	no	—
126	C₃×#525	D₃	1	1	yes	characteristic, complemented
127	C₃×#525	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂×C₃×C₄×D₄	—	3	1	no	—
129	C₂×C₃×C₄×D₄	—	3	2	no	—
130	#5828	C₂×C₃	1	2	yes	complemented
131	#5791	C₂×C₃	1	1	yes	characteristic, complemented
132	C₂×C₄×#67	C₂×C₃	1	1	yes	characteristic, complemented
133	#5660	C₂×C₃	1	2	yes	complemented
134	#5657	C₂×C₃	1	2	yes	complemented
135	#5645	C₂×C₃	1	1	yes	characteristic, complemented
136	#5638	C₂×C₃	1	2	yes	complemented
137	#5634	C₂×C₃	1	1	yes	characteristic, complemented
138	#5613	C₂×C₃	1	2	yes	complemented
139	#5605	C₂×C₃	1	1	yes	characteristic, complemented
140	#5602	C₂×C₃	1	1	yes	characteristic, complemented
141	#5593	C₂×C₃	1	2	yes	complemented
142	#5589	C₂×C₃	1	2	yes	complemented
143	#5557	C₂×C₃	1	2	yes	complemented
144	#5547	C₂×C₃	1	2	yes	complemented
145	C₄×D₃×D₄	C₂×C₃	1	2	yes	complemented
146	#5538	C₂×C₃	1	2	yes	complemented
147	#5528	C₂×C₃	1	2	yes	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	C₃²×#41	—	4	2	no	—
152	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃²×D₄	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
155	C₂×C₃²×D₄	C₂³	1	2	yes	—
156	C₂×C₃²×D₄	C₂³	1	2	yes	—
157	C₂²×C₃²×C₄	—	4	2	no	—
158	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃²×C₄	C₂³	1	2	yes	—
160	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
162	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
165	C₂×C₃×#67	—	2	4	no	—
166	C₂×C₃×#67	C₂³	1	2	yes	—
167	C₂×C₃×#67	C₂³	1	2	yes	—
168	C₂×C₃×#67	C₂³	1	2	yes	—
169	C₂×C₃×#67	C₂³	1	2	yes	—
170	C₂×C₃×#67	C₂³	1	2	yes	—
171	C₂×C₃×#67	C₂³	1	2	yes	—
172	C₂×C₃×#67	C₂³	1	2	yes	—
173	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
174	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
175	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
176	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
177	C₃×D₃×D₄	—	2	8	no	—
178	C₃×#235	—	4	2	no	—
179	C₂×C₃×D₁₂	C₂³	1	2	yes	—
180	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄×D₃	—	4	2	no	—
182	C₂×C₃×C₄×D₃	—	4	4	no	—
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×C₄×D₃	C₂³	1	2	yes	—
188	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
190	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
191	C₂×C₃×Dic₆	C₂³	1	2	yes	—
192	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃²×C₄²	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×#217	C₂³	1	2	yes	—
209	C₃×#217	C₂³	1	2	yes	—
210	C₃×#217	C₂³	1	2	yes	—
211	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
230	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₃×C₄×Dic₃	C₂³	1	2	yes	—
238	C₃×C₄×Dic₃	C₂³	1	2	yes	—
239	C₃×C₄×Dic₃	C₂³	1	2	yes	—
240	C₃×C₄×Dic₃	C₂³	1	2	yes	—
241	C₃×C₄×Dic₃	C₂³	1	2	yes	—
242	#3459	—	3	1	no	Sylow
243	C₂×C₃×#41	—	2	1	no	—
244	C₂×C₃×#41	—	3	1	no	—
245	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
246	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₂²×C₃×D₄	—	3	1	no	—
248	C₂²×C₃×D₄	—	3	2	no	—
249	C₂³×C₃×C₄	—	2	1	no	—
250	C₂³×C₃×C₄	—	3	1	no	—
251	C₂³×C₃×C₄	—	3	2	no	—
252	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
253	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
254	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
255	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
256	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
258	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
259	C₃×#126	—	3	2	no	—
260	C₃×#126	—	3	2	no	—
261	C₃×#126	—	3	2	no	—
262	C₃×#126	—	3	2	no	—
263	C₃×#126	—	3	2	no	—
264	C₃×#126	—	3	2	no	—
265	C₃×#125	—	3	2	no	—
266	C₃×#125	—	3	2	no	—
267	C₃×#125	—	3	2	no	—
268	C₃×#124	—	3	2	no	—
269	C₃×#124	—	3	2	no	—
270	C₃×#124	—	3	2	no	—
271	C₃×#123	—	2	2	no	—
272	C₃×#123	—	3	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	C₂×D₃	1	2	yes	complemented
284	C₃×#123	C₂²×C₃	1	2	yes	complemented
285	C₃×C₂²⋊Q₈	—	2	1	no	—
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	1	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	C₂×D₃	1	1	yes	characteristic, complemented
298	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
300	C₃×#121	—	2	1	no	—
301	C₃×#121	—	2	1	no	—
302	C₃×#121	—	3	2	no	—
303	C₃×#121	—	3	2	no	—
304	C₃×#121	—	3	2	no	—
305	C₃×#121	—	3	2	no	—
306	C₃×#121	—	3	2	no	—
307	C₃×#121	—	3	1	no	—
308	C₃×#121	—	3	1	no	—
309	C₃×#121	—	3	2	no	—
310	C₃×#121	—	3	2	no	—
311	C₃×#121	C₂×D₃	1	1	yes	characteristic
312	C₃×#121	C₂×D₃	1	1	yes	characteristic, complemented
313	C₃×#121	C₂²×C₃	1	1	yes	characteristic
314	C₃×#121	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₃×#120	—	2	2	no	—
316	C₃×#120	—	3	2	no	—
317	C₃×#120	—	3	2	no	—
318	C₃×#120	—	3	2	no	—
319	C₃×#120	—	3	2	no	—
320	C₃×#120	—	3	2	no	—
321	C₃×#120	C₂×D₃	1	2	yes	complemented
322	C₃×#120	C₂²×C₃	1	2	yes	complemented
323	C₃×C₄×Q₈	—	3	2	no	—
324	C₃×C₄×D₄	—	2	2	no	—
325	C₃×C₄×D₄	—	2	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	2	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	—	3	2	no	—
339	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
340	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
341	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
342	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
343	C₃×#117	—	2	1	no	—
344	C₃×#117	—	3	2	no	—
345	C₃×#117	—	3	1	no	—
346	C₃×#117	—	3	2	no	—
347	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
348	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₂×C₃×C₄⋊C₄	—	3	1	no	—
350	C₂×C₃×C₄⋊C₄	—	3	2	no	—
351	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
352	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
353	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
354	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
355	C₂×C₃×C₄²	—	3	1	no	—
356	C₂×C₃×C₄²	—	3	2	no	—
357	#953	C₂²×C₃	1	2	yes	complemented
358	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
359	#946	C₂²×C₃	1	2	yes	complemented
360	#946	C₂²×C₃	1	2	yes	complemented
361	#939	C₂²×C₃	1	2	yes	—
362	#939	C₂²×C₃	1	2	yes	complemented
363	#938	C₂²×C₃	1	2	yes	—
364	#938	C₂²×C₃	1	2	yes	—
365	#938	C₂²×C₃	1	2	yes	complemented
366	#937	C₂²×C₃	1	2	yes	complemented
367	#937	C₂²×C₃	1	2	yes	complemented
368	#937	C₂²×C₃	1	2	yes	complemented
369	#936	C₂²×C₃	1	2	yes	complemented
370	#935	C₂²×C₃	1	2	yes	complemented
371	#935	C₂²×C₃	1	2	yes	complemented
372	#935	C₂²×C₃	1	2	yes	complemented
373	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
374	#930	C₂²×C₃	1	1	yes	characteristic
375	#930	C₂²×C₃	1	1	yes	characteristic, complemented
376	#929	C₂²×C₃	1	2	yes	complemented
377	C₄×#67	C₂²×C₃	1	2	yes	complemented
378	C₄×#67	C₂²×C₃	1	2	yes	complemented
379	C₄×#67	C₂²×C₃	1	2	yes	complemented
380	C₄×#67	C₂²×C₃	1	2	yes	complemented
381	C₄×#67	C₂²×C₃	1	2	yes	complemented
382	C₄×#67	C₂²×C₃	1	2	yes	complemented
383	C₄×#67	C₂²×C₃	1	2	yes	complemented
384	C₄×#67	C₂²×C₃	1	2	yes	complemented
385	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
386	#926	C₂²×C₃	1	1	yes	characteristic, complemented
387	#926	C₂²×C₃	1	2	yes	complemented
388	#924	C₂²×C₃	1	1	yes	characteristic, complemented
389	#924	C₂²×C₃	1	1	yes	characteristic, complemented
390	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
391	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
392	#898	C₂²×C₃	1	2	yes	complemented
393	#898	C₂²×C₃	1	2	yes	complemented
394	#897	C₂²×C₃	1	2	yes	complemented
395	#896	C₂²×C₃	1	2	yes	complemented
396	#896	C₂²×C₃	1	2	yes	complemented
397	#894	C₂²×C₃	1	2	yes	complemented
398	#894	C₂²×C₃	1	2	yes	complemented
399	#893	C₂²×C₃	1	2	yes	complemented
400	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
401	#890	C₂²×C₃	1	2	yes	complemented
402	#889	C₂²×C₃	1	2	yes	complemented
403	#889	C₂²×C₃	1	2	yes	complemented
404	#886	C₂²×C₃	1	2	yes	complemented
405	#885	C₂²×C₃	1	2	yes	complemented
406	#885	C₂²×C₃	1	2	yes	complemented
407	#884	C₂²×C₃	1	2	yes	—
408	#884	C₂²×C₃	1	2	yes	—
409	#883	C₂²×C₃	1	2	yes	complemented
410	#883	C₂²×C₃	1	2	yes	complemented
411	#883	C₂²×C₃	1	2	yes	complemented
412	#883	C₂²×C₃	1	2	yes	complemented
413	#882	C₂²×C₃	1	2	yes	complemented
414	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
415	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
416	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
417	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
418	#879	C₂²×C₃	1	2	yes	complemented
419	#879	C₂²×C₃	1	2	yes	complemented
420	#879	C₂²×C₃	1	2	yes	complemented
421	#879	C₂²×C₃	1	2	yes	complemented
422	#878	C₂²×C₃	1	2	yes	complemented
423	#878	C₂²×C₃	1	2	yes	complemented
424	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
425	#872	C₂²×C₃	1	2	yes	complemented
426	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
427	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
428	C₂³×C₃²	—	2	2	no	—
429	C₂³×C₃²	—	4	1	no	—
430	C₂³×C₃²	—	4	1	no	—
431	C₂³×C₃²	C₂⁴	1	2	yes	—
432	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
433	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
434	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×D₃	—	2	4	no	—
436	C₂²×C₃×D₃	—	4	1	no	—
437	C₂²×C₃×D₃	—	4	2	no	—
438	C₂²×C₃×D₃	—	4	1	no	—
439	C₂²×C₃×D₃	—	4	2	no	—
440	C₂²×C₃×D₃	#41	1	4	yes	complemented
441	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
442	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
443	C₃²×Q₈	—	4	1	no	—
444	C₃²×D₄	—	2	4	no	—
445	C₃²×D₄	—	4	2	no	—
446	C₃²×D₄	—	4	1	no	—
447	C₃²×D₄	—	4	2	no	—
448	C₂×C₃²×C₄	—	2	2	no	—
449	C₂×C₃²×C₄	—	2	2	no	—
450	C₂×C₃²×C₄	—	2	4	no	—
451	C₂×C₃²×C₄	—	2	2	no	—
452	C₂×C₃²×C₄	—	4	1	no	—
453	C₂×C₃²×C₄	—	4	1	no	—
454	C₂×C₃²×C₄	—	4	1	no	—
455	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
456	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
457	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
458	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
459	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
460	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
461	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
462	C₃×#67	—	2	4	no	—
463	C₃×#67	—	2	4	no	—
464	C₃×#67	—	2	4	no	—
465	C₃×#67	—	2	4	no	—
466	C₃×#67	—	4	2	no	—
467	C₃×#67	—	4	2	no	—
468	C₃×#67	—	4	2	no	—
469	C₂×C₃×Dic₃	—	2	2	no	—
470	C₂×C₃×Dic₃	—	4	2	no	—
471	C₂×C₃×Dic₃	—	4	1	no	—
472	C₂×C₃×Dic₃	—	4	1	no	—
473	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
474	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
475	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
476	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
477	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
478	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
479	C₃×D₁₂	—	2	4	no	—
480	C₃×D₁₂	—	4	1	no	—
481	C₃×C₄×D₃	—	2	4	no	—
482	C₃×C₄×D₃	—	2	4	no	—
483	C₃×C₄×D₃	—	2	4	no	—
484	C₃×C₄×D₃	—	4	2	no	—
485	C₃×C₄×D₃	—	4	2	no	—
486	C₃×C₄×D₃	—	4	2	no	—
487	C₃×C₄×D₃	—	4	2	no	—
488	C₃×Dic₆	—	4	2	no	—
489	C₃×Dic₆	—	4	1	no	—
490	#543	—	3	1	no	—
491	#539	—	3	2	no	—
492	#539	—	3	2	no	—
493	#539	—	3	1	no	—
494	#539	—	3	1	no	—
495	#538	—	3	2	no	—
496	#538	—	3	2	no	—
497	#538	—	3	2	no	—
498	#534	—	3	1	no	—
499	#534	—	3	2	no	—
500	#529	—	3	2	no	—
501	#529	—	3	2	no	—
502	#529	—	3	2	no	—
503	#525	—	3	2	no	—
504	#525	—	3	1	no	—
505	#525	—	3	2	no	—
506	#525	C₃×D₃	1	1	yes	characteristic, complemented
507	C₂×C₄×D₄	—	3	1	no	—
508	C₂×C₄×D₄	—	3	2	no	—
509	C₂⁴×C₃	—	2	1	no	—
510	C₂⁴×C₃	—	3	1	no	—
511	C₂⁴×C₃	—	3	2	no	—
512	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
513	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
514	C₂³×D₃	C₂³×C₃	1	2	yes	—
515	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
516	C₃×#41	—	4	2	no	—
517	C₃×#41	—	4	2	no	—
518	C₃×#41	—	4	4	no	—
519	C₃×#41	—	12	2	no	—
520	C₂×C₃×Q₈	—	2	1	no	—
521	C₂×C₃×Q₈	—	3	2	no	—
522	C₂×C₃×Q₈	—	3	1	no	—
523	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
524	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₃×D₄	—	2	2	no	—
526	C₂×C₃×D₄	—	2	2	no	—
527	C₂×C₃×D₄	—	2	2	no	—
528	C₂×C₃×D₄	—	2	1	no	—
529	C₂×C₃×D₄	—	3	2	no	—
530	C₂×C₃×D₄	—	3	2	no	—
531	C₂×C₃×D₄	—	3	2	no	—
532	C₂×C₃×D₄	—	3	2	no	—
533	C₂×C₃×D₄	—	3	2	no	—
534	C₂×C₃×D₄	—	3	2	no	—
535	C₂×C₃×D₄	—	3	2	no	—
536	C₂×C₃×D₄	—	3	2	no	—
537	C₂×C₃×D₄	—	3	1	no	—
538	C₂×C₃×D₄	—	6	8	no	—
539	C₂×C₃×D₄	—	6	4	no	—
540	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
541	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
542	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
543	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
544	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
545	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
547	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
548	C₂²×C₃×C₄	—	2	1	no	—
549	C₂²×C₃×C₄	—	2	1	no	—
550	C₂²×C₃×C₄	—	2	1	no	—
551	C₂²×C₃×C₄	—	2	2	no	—
552	C₂²×C₃×C₄	—	2	1	no	—
553	C₂²×C₃×C₄	—	2	1	no	—
554	C₂²×C₃×C₄	—	2	1	no	—
555	C₂²×C₃×C₄	—	3	1	no	—
556	C₂²×C₃×C₄	—	3	1	no	—
557	C₂²×C₃×C₄	—	3	1	no	—
558	C₂²×C₃×C₄	—	3	2	no	—
559	C₂²×C₃×C₄	—	3	2	no	—
560	C₂²×C₃×C₄	—	3	2	no	—
561	C₂²×C₃×C₄	—	3	2	no	—
562	C₂²×C₃×C₄	—	3	2	no	—
563	C₂²×C₃×C₄	—	3	2	no	—
564	C₂²×C₃×C₄	—	3	2	no	—
565	C₂²×C₃×C₄	—	3	2	no	—
566	C₂²×C₃×C₄	—	4	2	no	—
567	C₂²×C₃×C₄	—	4	2	no	—
568	C₂²×C₃×C₄	—	4	4	no	—
569	C₂²×C₃×C₄	—	12	2	no	—
570	C₂²×C₃×C₄	—	12	4	no	—
571	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
572	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
573	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
574	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
575	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
576	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
577	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
578	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
580	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
583	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
584	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
585	C₂×#67	—	2	4	no	—
586	C₂×#67	C₂³×C₃	1	2	yes	—
587	C₂×#67	C₂³×C₃	1	2	yes	—
588	C₂×#67	C₂³×C₃	1	2	yes	—
589	C₂×#67	C₂³×C₃	1	2	yes	—
590	C₂×#67	C₂³×C₃	1	2	yes	—
591	C₂×#67	C₂³×C₃	1	2	yes	—
592	C₂×#67	C₂³×C₃	1	2	yes	—
593	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
594	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
595	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
596	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
597	D₃×D₄	—	2	8	no	—
598	#235	—	4	2	no	—
599	C₂×D₁₂	C₂³×C₃	1	2	yes	—
600	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₄×D₃	—	4	2	no	—
602	C₂×C₄×D₃	—	4	4	no	—
603	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
604	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
605	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
606	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
607	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
608	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
609	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
610	C₂×Dic₆	C₂³×C₃	1	2	yes	—
611	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
612	C₃×C₄⋊C₄	—	2	1	no	—
613	C₃×C₄⋊C₄	—	2	1	no	—
614	C₃×C₄⋊C₄	—	2	2	no	—
615	C₃×C₄⋊C₄	—	2	2	no	—
616	C₃×C₄⋊C₄	—	3	2	no	—
617	C₃×C₄⋊C₄	—	3	2	no	—
618	C₃×C₄⋊C₄	—	3	2	no	—
619	C₃×C₄⋊C₄	—	3	2	no	—
620	C₃×C₄⋊C₄	—	3	2	no	—
621	C₃×C₄⋊C₄	—	3	2	no	—
622	C₃×C₄⋊C₄	—	3	2	no	—
623	C₃×C₄⋊C₄	—	3	2	no	—
624	C₃×C₄⋊C₄	—	3	2	no	—
625	C₃×C₄⋊C₄	—	3	2	no	—
626	C₃×C₄⋊C₄	—	3	2	no	—
627	C₃×C₄⋊C₄	—	3	2	no	—
628	C₃×C₄⋊C₄	—	3	1	no	—
629	C₃×C₄⋊C₄	—	3	2	no	—
630	C₃×C₄⋊C₄	—	3	1	no	—
631	C₃×C₄⋊C₄	—	3	2	no	—
632	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
633	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
634	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
635	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
636	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
637	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
638	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
639	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
640	C₃×C₂²⋊C₄	—	2	2	no	—
641	C₃×C₂²⋊C₄	—	2	2	no	—
642	C₃×C₂²⋊C₄	—	2	2	no	—
643	C₃×C₂²⋊C₄	—	2	2	no	—
644	C₃×C₂²⋊C₄	—	2	2	no	—
645	C₃×C₂²⋊C₄	—	3	2	no	—
646	C₃×C₂²⋊C₄	—	3	2	no	—
647	C₃×C₂²⋊C₄	—	3	2	no	—
648	C₃×C₂²⋊C₄	—	3	2	no	—
649	C₃×C₂²⋊C₄	—	3	2	no	—
650	C₃×C₂²⋊C₄	—	3	2	no	—
651	C₃×C₂²⋊C₄	—	3	2	no	—
652	C₃×C₂²⋊C₄	—	3	2	no	—
653	C₃×C₂²⋊C₄	—	3	2	no	—
654	C₃×C₂²⋊C₄	—	3	2	no	—
655	C₃×C₂²⋊C₄	—	3	2	no	—
656	C₃×C₂²⋊C₄	—	3	2	no	—
657	C₃×C₂²⋊C₄	—	3	2	no	—
658	C₃×C₂²⋊C₄	—	3	2	no	—
659	C₃×C₂²⋊C₄	—	3	2	no	—
660	C₃×C₂²⋊C₄	—	3	2	no	—
661	C₃×C₂²⋊C₄	—	3	2	no	—
662	C₃×C₂²⋊C₄	—	3	2	no	—
663	C₃×C₂²⋊C₄	—	3	2	no	—
664	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
665	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
666	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
667	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
668	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
669	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
670	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
671	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
672	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
673	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
674	C₃×C₄²	—	2	2	no	—
675	C₃×C₄²	—	3	2	no	—
676	C₃×C₄²	—	3	2	no	—
677	C₃×C₄²	—	3	2	no	—
678	C₃×C₄²	—	3	2	no	—
679	C₃×C₄²	—	3	2	no	—
680	C₃×C₄²	C₂²×D₃	1	2	yes	—
681	C₃×C₄²	C₂³×C₃	1	2	yes	—
682	#217	C₂³×C₃	1	2	yes	—
683	#217	C₂³×C₃	1	2	yes	—
684	#217	C₂³×C₃	1	2	yes	—
685	#217	C₂³×C₃	1	2	yes	—
686	#217	C₂³×C₃	1	2	yes	—
687	#217	C₂³×C₃	1	2	yes	—
688	#217	C₂³×C₃	1	2	yes	—
689	#217	C₂³×C₃	1	2	yes	—
690	#217	C₂³×C₃	1	2	yes	—
691	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
692	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
693	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
694	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
695	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
696	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
697	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
698	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
699	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
700	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
701	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
702	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
703	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
704	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
705	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
706	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
707	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
708	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
709	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
710	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
711	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
712	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
713	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
714	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
715	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
716	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
717	C₄×Dic₃	C₂³×C₃	1	2	yes	—
718	C₄×Dic₃	C₂³×C₃	1	2	yes	—
719	C₄×Dic₃	C₂³×C₃	1	2	yes	—
720	C₄×Dic₃	C₂³×C₃	1	2	yes	—
721	C₄×Dic₃	C₂³×C₃	1	2	yes	—
722	C₂²×C₃²	—	2	1	no	—
723	C₂²×C₃²	—	2	1	no	—
724	C₂²×C₃²	—	2	1	no	—
725	C₂²×C₃²	—	2	1	no	—
726	C₂²×C₃²	—	2	1	no	—
727	C₂²×C₃²	—	2	1	no	—
728	C₂²×C₃²	—	2	2	no	—
729	C₂²×C₃²	—	2	2	no	—
730	C₂²×C₃²	—	2	1	no	—
731	C₂²×C₃²	—	2	1	no	—
732	C₂²×C₃²	—	2	2	no	—
733	C₂²×C₃²	—	4	4	no	—
734	C₂²×C₃²	C₂×#41	1	2	yes	—
735	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
736	C₂×C₃×D₃	—	2	2	no	—
737	C₂×C₃×D₃	—	2	2	no	—
738	C₂×C₃×D₃	—	2	2	no	—
739	C₂×C₃×D₃	—	2	2	no	—
740	C₂×C₃×D₃	—	2	2	no	—
741	C₂×C₃×D₃	—	4	4	no	—
742	C₂×C₃×D₃	—	4	8	no	—
743	C₂×C₃×D₃	C₂×#41	1	4	yes	—
744	C₃²×C₄	—	2	1	no	—
745	C₃²×C₄	—	2	2	no	—
746	C₃²×C₄	—	2	1	no	—
747	C₃²×C₄	—	2	1	no	—
748	C₃²×C₄	—	2	2	no	—
749	C₃²×C₄	—	2	2	no	—
750	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
751	C₃×Dic₃	—	2	2	no	—
752	C₃×Dic₃	—	2	2	no	—
753	C₃×Dic₃	—	2	2	no	—
754	C₃×Dic₃	—	2	2	no	—
755	C₃×Dic₃	—	2	2	no	—
756	C₃×Dic₃	—	2	2	no	—
757	C₂×#41	—	3	1	no	—
758	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
759	C₂²×D₄	—	3	1	no	—
760	C₂²×D₄	—	3	2	no	—
761	C₂³×C₄	—	3	1	no	—
762	C₂³×C₄	—	3	2	no	—
763	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
764	#126	—	3	2	no	—
765	#126	—	3	2	no	—
766	#126	—	3	2	no	—
767	#126	—	3	2	no	—
768	#126	—	3	2	no	—
769	#126	—	3	2	no	—
770	#125	—	3	2	no	—
771	#125	—	3	2	no	—
772	#125	—	3	2	no	—
773	#124	—	3	2	no	—
774	#124	—	3	2	no	—
775	#124	—	3	2	no	—
776	#123	—	3	2	no	—
777	#123	—	3	2	no	—
778	#123	—	3	2	no	—
779	#123	—	3	2	no	—
780	#123	—	3	2	no	—
781	#123	—	3	2	no	—
782	#123	—	3	2	no	—
783	#123	—	3	2	no	—
784	#123	—	3	2	no	—
785	#123	—	3	2	no	—
786	#123	—	3	2	no	—
787	#123	C₂×C₃×D₃	1	2	yes	complemented
788	C₂²⋊Q₈	—	3	2	no	—
789	C₂²⋊Q₈	—	3	2	no	—
790	C₂²⋊Q₈	—	3	1	no	—
791	C₂²⋊Q₈	—	3	1	no	—
792	C₂²⋊Q₈	—	3	2	no	—
793	C₂²⋊Q₈	—	3	2	no	—
794	C₂²⋊Q₈	—	3	2	no	—
795	C₂²⋊Q₈	—	3	2	no	—
796	C₂²⋊Q₈	—	3	2	no	—
797	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
798	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
799	#121	—	3	2	no	—
800	#121	—	3	2	no	—
801	#121	—	3	2	no	—
802	#121	—	3	2	no	—
803	#121	—	3	2	no	—
804	#121	—	3	1	no	—
805	#121	—	3	1	no	—
806	#121	—	3	2	no	—
807	#121	—	3	2	no	—
808	#121	C₂×C₃×D₃	1	1	yes	characteristic
809	#121	C₂×C₃×D₃	1	1	yes	characteristic, complemented
810	#120	—	3	2	no	—
811	#120	—	3	2	no	—
812	#120	—	3	2	no	—
813	#120	—	3	2	no	—
814	#120	—	3	2	no	—
815	#120	C₂×C₃×D₃	1	2	yes	complemented
816	C₄×Q₈	—	3	2	no	—
817	C₄×D₄	—	3	2	no	—
818	C₄×D₄	—	3	2	no	—
819	C₄×D₄	—	3	2	no	—
820	C₄×D₄	—	3	2	no	—
821	C₄×D₄	—	3	2	no	—
822	C₄×D₄	—	3	2	no	—
823	C₄×D₄	—	3	2	no	—
824	C₄×D₄	—	3	2	no	—
825	C₄×D₄	—	3	2	no	—
826	C₄×D₄	—	3	2	no	—
827	C₄×D₄	—	3	2	no	—
828	C₄×D₄	—	3	2	no	—
829	C₄×D₄	—	3	2	no	—
830	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
831	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
832	#117	—	3	2	no	—
833	#117	—	3	1	no	—
834	#117	—	3	2	no	—
835	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
836	C₂×C₄⋊C₄	—	3	1	no	—
837	C₂×C₄⋊C₄	—	3	2	no	—
838	C₂×C₂²⋊C₄	—	3	1	no	—
839	C₂×C₂²⋊C₄	—	3	1	no	—
840	C₂×C₂²⋊C₄	—	3	2	no	—
841	C₂×C₂²⋊C₄	—	3	2	no	—
842	C₂×C₄²	—	3	1	no	—
843	C₂×C₄²	—	3	2	no	—
844	C₂³×C₃	—	2	2	no	—
845	C₂³×C₃	—	2	2	no	—
846	C₂³×C₃	—	2	1	no	—
847	C₂³×C₃	—	2	1	no	—
848	C₂³×C₃	—	2	1	no	—
849	C₂³×C₃	—	2	2	no	—
850	C₂³×C₃	—	3	2	no	—
851	C₂³×C₃	—	3	4	no	—
852	C₂³×C₃	—	3	2	no	—
853	C₂³×C₃	—	4	2	no	—
854	C₂³×C₃	—	4	1	no	—
855	C₂³×C₃	—	4	1	no	—
856	C₂³×C₃	—	4	1	no	—
857	C₂³×C₃	—	4	1	no	—
858	C₂³×C₃	—	4	2	no	—
859	C₂³×C₃	—	4	2	no	—
860	C₂³×C₃	—	6	4	no	—
861	C₂³×C₃	—	12	1	no	—
862	C₂³×C₃	—	12	2	no	—
863	C₂³×C₃	—	12	1	no	—
864	C₂³×C₃	—	12	2	no	—
865	C₂³×C₃	C₂³×D₃	1	2	yes	—
866	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
867	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
868	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
869	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
870	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
871	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
872	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
873	C₂²×D₃	—	2	4	no	—
874	C₂²×D₃	—	4	1	no	—
875	C₂²×D₃	—	4	2	no	—
876	C₂²×D₃	—	4	1	no	—
877	C₂²×D₃	—	4	2	no	—
878	C₂²×D₃	C₃×#41	1	4	yes	complemented
879	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
880	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
881	C₃×Q₈	—	4	1	no	—
882	C₃×Q₈	—	4	1	no	—
883	C₃×Q₈	—	4	2	no	—
884	C₃×Q₈	—	12	2	no	—
885	C₃×Q₈	—	12	1	no	—
886	C₃×D₄	—	2	4	no	—
887	C₃×D₄	—	2	4	no	—
888	C₃×D₄	—	4	4	no	—
889	C₃×D₄	—	4	2	no	—
890	C₃×D₄	—	4	1	no	—
891	C₃×D₄	—	4	2	no	—
892	C₃×D₄	—	4	2	no	—
893	C₃×D₄	—	4	2	no	—
894	C₃×D₄	—	4	1	no	—
895	C₃×D₄	—	4	2	no	—
896	C₃×D₄	—	4	4	no	—
897	C₃×D₄	—	4	4	no	—
898	C₃×D₄	—	6	4	no	—
899	C₃×D₄	—	6	4	no	—
900	C₃×D₄	—	6	4	no	—
901	C₃×D₄	—	6	4	no	—
902	C₃×D₄	—	6	4	no	—
903	C₃×D₄	—	12	1	no	—
904	C₃×D₄	—	12	2	no	—
905	C₃×D₄	—	12	2	no	—
906	C₃×D₄	—	12	2	no	—
907	C₂×C₃×C₄	—	2	4	no	—
908	C₂×C₃×C₄	—	2	2	no	—
909	C₂×C₃×C₄	—	2	2	no	—
910	C₂×C₃×C₄	—	2	2	no	—
911	C₂×C₃×C₄	—	2	4	no	—
912	C₂×C₃×C₄	—	2	2	no	—
913	C₂×C₃×C₄	—	2	4	no	—
914	C₂×C₃×C₄	—	2	2	no	—
915	C₂×C₃×C₄	—	2	2	no	—
916	C₂×C₃×C₄	—	2	1	no	—
917	C₂×C₃×C₄	—	2	1	no	—
918	C₂×C₃×C₄	—	2	2	no	—
919	C₂×C₃×C₄	—	2	2	no	—
920	C₂×C₃×C₄	—	2	1	no	—
921	C₂×C₃×C₄	—	2	1	no	—
922	C₂×C₃×C₄	—	2	2	no	—
923	C₂×C₃×C₄	—	3	2	no	—
924	C₂×C₃×C₄	—	3	2	no	—
925	C₂×C₃×C₄	—	3	2	no	—
926	C₂×C₃×C₄	—	3	2	no	—
927	C₂×C₃×C₄	—	3	2	no	—
928	C₂×C₃×C₄	—	3	2	no	—
929	C₂×C₃×C₄	—	4	2	no	—
930	C₂×C₃×C₄	—	4	2	no	—
931	C₂×C₃×C₄	—	4	4	no	—
932	C₂×C₃×C₄	—	4	1	no	—
933	C₂×C₃×C₄	—	4	1	no	—
934	C₂×C₃×C₄	—	4	1	no	—
935	C₂×C₃×C₄	—	4	1	no	—
936	C₂×C₃×C₄	—	4	1	no	—
937	C₂×C₃×C₄	—	4	1	no	—
938	C₂×C₃×C₄	—	4	2	no	—
939	C₂×C₃×C₄	—	4	2	no	—
940	C₂×C₃×C₄	—	4	2	no	—
941	C₂×C₃×C₄	—	6	4	no	—
942	C₂×C₃×C₄	—	6	2	no	—
943	C₂×C₃×C₄	—	6	4	no	—
944	C₂×C₃×C₄	—	6	4	no	—
945	C₂×C₃×C₄	—	12	2	no	—
946	C₂×C₃×C₄	—	12	2	no	—
947	C₂×C₃×C₄	—	12	2	no	—
948	C₂×C₃×C₄	—	12	2	no	—
949	C₂×C₃×C₄	—	12	1	no	—
950	C₂×C₃×C₄	—	12	1	no	—
951	C₂×C₃×C₄	—	12	2	no	—
952	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
953	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
954	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
955	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
956	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
957	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
958	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
959	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
960	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
961	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
962	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
963	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
964	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
965	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
966	#67	—	2	4	no	—
967	#67	—	2	4	no	—
968	#67	—	2	4	no	—
969	#67	—	2	4	no	—
970	#67	—	4	2	no	—
971	#67	—	4	2	no	—
972	#67	—	4	2	no	—
973	C₂×Dic₃	—	2	2	no	—
974	C₂×Dic₃	—	4	2	no	—
975	C₂×Dic₃	—	4	1	no	—
976	C₂×Dic₃	—	4	1	no	—
977	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
978	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
979	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
980	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
981	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
982	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
983	D₁₂	—	2	4	no	—
984	D₁₂	—	4	1	no	—
985	C₄×D₃	—	2	4	no	—
986	C₄×D₃	—	2	4	no	—
987	C₄×D₃	—	2	4	no	—
988	C₄×D₃	—	4	2	no	—
989	C₄×D₃	—	4	2	no	—
990	C₄×D₃	—	4	2	no	—
991	C₄×D₃	—	4	2	no	—
992	Dic₆	—	4	2	no	—
993	Dic₆	—	4	1	no	—
994	C₂×C₃²	—	2	2	no	—
995	C₂×C₃²	—	4	1	no	—
996	C₂×C₃²	—	4	1	no	—
997	C₂×C₃²	—	4	2	no	—
998	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
999	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1000	C₂×C₃²	#585	1	1	yes	characteristic
1001	C₃×D₃	—	2	4	no	—
1002	C₃×D₃	—	4	2	no	—
1003	C₂⁴	—	3	1	no	—
1004	C₂⁴	—	3	2	no	—
1005	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
1006	#41	—	4	2	no	—
1007	#41	—	12	2	no	—
1008	C₂×Q₈	—	3	2	no	—
1009	C₂×Q₈	—	3	1	no	—
1010	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1011	C₂×D₄	—	3	2	no	—
1012	C₂×D₄	—	3	2	no	—
1013	C₂×D₄	—	3	2	no	—
1014	C₂×D₄	—	3	2	no	—
1015	C₂×D₄	—	3	2	no	—
1016	C₂×D₄	—	3	2	no	—
1017	C₂×D₄	—	3	2	no	—
1018	C₂×D₄	—	3	2	no	—
1019	C₂×D₄	—	3	1	no	—
1020	C₂×D₄	—	6	8	no	—
1021	C₂×D₄	—	6	4	no	—
1022	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1023	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1024	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1025	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1026	C₂²×C₄	—	3	1	no	—
1027	C₂²×C₄	—	3	1	no	—
1028	C₂²×C₄	—	3	1	no	—
1029	C₂²×C₄	—	3	2	no	—
1030	C₂²×C₄	—	3	2	no	—
1031	C₂²×C₄	—	3	2	no	—
1032	C₂²×C₄	—	3	2	no	—
1033	C₂²×C₄	—	3	2	no	—
1034	C₂²×C₄	—	3	2	no	—
1035	C₂²×C₄	—	3	2	no	—
1036	C₂²×C₄	—	3	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	12	2	no	—
1039	C₂²×C₄	—	12	4	no	—
1040	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1042	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1047	C₄⋊C₄	—	3	2	no	—
1048	C₄⋊C₄	—	3	2	no	—
1049	C₄⋊C₄	—	3	2	no	—
1050	C₄⋊C₄	—	3	2	no	—
1051	C₄⋊C₄	—	3	2	no	—
1052	C₄⋊C₄	—	3	2	no	—
1053	C₄⋊C₄	—	3	2	no	—
1054	C₄⋊C₄	—	3	1	no	—
1055	C₄⋊C₄	—	3	2	no	—
1056	C₄⋊C₄	—	3	2	no	—
1057	C₄⋊C₄	—	3	1	no	—
1058	C₄⋊C₄	—	3	2	no	—
1059	C₄⋊C₄	—	3	2	no	—
1060	C₄⋊C₄	—	3	2	no	—
1061	C₄⋊C₄	—	3	2	no	—
1062	C₄⋊C₄	—	3	2	no	—
1063	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1064	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1067	C₂²⋊C₄	—	3	2	no	—
1068	C₂²⋊C₄	—	3	2	no	—
1069	C₂²⋊C₄	—	3	2	no	—
1070	C₂²⋊C₄	—	3	2	no	—
1071	C₂²⋊C₄	—	3	2	no	—
1072	C₂²⋊C₄	—	3	2	no	—
1073	C₂²⋊C₄	—	3	2	no	—
1074	C₂²⋊C₄	—	3	2	no	—
1075	C₂²⋊C₄	—	3	2	no	—
1076	C₂²⋊C₄	—	3	2	no	—
1077	C₂²⋊C₄	—	3	2	no	—
1078	C₂²⋊C₄	—	3	2	no	—
1079	C₂²⋊C₄	—	3	2	no	—
1080	C₂²⋊C₄	—	3	2	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	—	3	2	no	—
1086	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1087	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1088	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1089	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1090	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1091	C₄²	—	3	2	no	—
1092	C₄²	—	3	2	no	—
1093	C₄²	—	3	2	no	—
1094	C₄²	—	3	2	no	—
1095	C₄²	—	3	2	no	—
1096	C₄²	C₂²×C₃×D₃	1	2	yes	—
1097	C₂²×C₃	—	2	1	no	—
1098	C₂²×C₃	—	2	1	no	—
1099	C₂²×C₃	—	2	1	no	—
1100	C₂²×C₃	—	2	1	no	—
1101	C₂²×C₃	—	2	2	no	—
1102	C₂²×C₃	—	2	2	no	—
1103	C₂²×C₃	—	2	1	no	—
1104	C₂²×C₃	—	2	1	no	—
1105	C₂²×C₃	—	2	2	no	—
1106	C₂²×C₃	—	2	2	no	—
1107	C₂²×C₃	—	2	1	no	—
1108	C₂²×C₃	—	2	1	no	—
1109	C₂²×C₃	—	2	1	no	—
1110	C₂²×C₃	—	2	2	no	—
1111	C₂²×C₃	—	2	1	no	—
1112	C₂²×C₃	—	2	1	no	—
1113	C₂²×C₃	—	2	1	no	—
1114	C₂²×C₃	—	2	2	no	—
1115	C₂²×C₃	—	2	2	no	—
1116	C₂²×C₃	—	2	1	no	—
1117	C₂²×C₃	—	2	1	no	—
1118	C₂²×C₃	—	2	1	no	—
1119	C₂²×C₃	—	2	2	no	—
1120	C₂²×C₃	—	2	1	no	—
1121	C₂²×C₃	—	2	2	no	—
1122	C₂²×C₃	—	2	1	no	—
1123	C₂²×C₃	—	3	4	no	—
1124	C₂²×C₃	—	4	1	no	—
1125	C₂²×C₃	—	4	1	no	—
1126	C₂²×C₃	—	4	1	no	—
1127	C₂²×C₃	—	4	1	no	—
1128	C₂²×C₃	—	4	1	no	—
1129	C₂²×C₃	—	4	1	no	—
1130	C₂²×C₃	—	4	2	no	—
1131	C₂²×C₃	—	4	2	no	—
1132	C₂²×C₃	—	4	2	no	—
1133	C₂²×C₃	—	4	4	no	—
1134	C₂²×C₃	—	4	4	no	—
1135	C₂²×C₃	—	4	8	no	—
1136	C₂²×C₃	—	6	2	no	—
1137	C₂²×C₃	—	6	2	no	—
1138	C₂²×C₃	—	6	2	no	—
1139	C₂²×C₃	—	6	2	no	—
1140	C₂²×C₃	—	6	2	no	—
1141	C₂²×C₃	—	12	4	no	—
1142	C₂²×C₃	—	12	8	no	—
1143	C₂²×C₃	D₃×#41	1	2	yes	—
1144	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
1145	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1146	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1147	C₂×D₃	—	2	2	no	—
1148	C₂×D₃	—	2	2	no	—
1149	C₂×D₃	—	2	2	no	—
1150	C₂×D₃	—	2	2	no	—
1151	C₂×D₃	—	2	2	no	—
1152	C₂×D₃	—	4	4	no	—
1153	C₂×D₃	—	4	8	no	—
1154	C₂×D₃	C₂×C₃×#41	1	4	yes	—
1155	C₃×C₄	—	2	2	no	—
1156	C₃×C₄	—	2	1	no	—
1157	C₃×C₄	—	2	1	no	—
1158	C₃×C₄	—	2	1	no	—
1159	C₃×C₄	—	2	2	no	—
1160	C₃×C₄	—	2	2	no	—
1161	C₃×C₄	—	2	2	no	—
1162	C₃×C₄	—	2	2	no	—
1163	C₃×C₄	—	2	1	no	—
1164	C₃×C₄	—	2	1	no	—
1165	C₃×C₄	—	2	2	no	—
1166	C₃×C₄	—	2	1	no	—
1167	C₃×C₄	—	2	2	no	—
1168	C₃×C₄	—	2	2	no	—
1169	C₃×C₄	—	4	1	no	—
1170	C₃×C₄	—	4	1	no	—
1171	C₃×C₄	—	4	2	no	—
1172	C₃×C₄	—	4	2	no	—
1173	C₃×C₄	—	4	2	no	—
1174	C₃×C₄	—	6	2	no	—
1175	C₃×C₄	—	6	2	no	—
1176	C₃×C₄	—	6	2	no	—
1177	C₃×C₄	—	6	2	no	—
1178	C₃×C₄	—	6	2	no	—
1179	C₃×C₄	—	6	2	no	—
1180	C₃×C₄	#1004	1	2	yes	—
1181	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1182	Dic₃	—	2	2	no	—
1183	Dic₃	—	2	2	no	—
1184	Dic₃	—	2	2	no	—
1185	Dic₃	—	2	2	no	—
1186	Dic₃	—	2	2	no	—
1187	Dic₃	—	2	2	no	—
1188	C₃²	#3459	1	1	yes	characteristic, complemented, Sylow
1189	C₂³	—	2	2	no	—
1190	C₂³	—	3	2	no	—
1191	C₂³	—	3	4	no	—
1192	C₂³	—	3	2	no	—
1193	C₂³	—	4	1	no	—
1194	C₂³	—	4	1	no	—
1195	C₂³	—	6	4	no	—
1196	C₂³	—	12	1	no	—
1197	C₂³	—	12	2	no	—
1198	C₂³	—	12	1	no	—
1199	C₂³	—	12	2	no	—
1200	C₂³	C₂³×C₃×D₃	1	2	yes	—
1201	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1202	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1203	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1204	Q₈	—	4	1	no	—
1205	Q₈	—	12	1	no	—
1206	Q₈	—	12	2	no	—
1207	D₄	—	2	4	no	—
1208	D₄	—	4	1	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	6	4	no	—
1212	D₄	—	6	4	no	—
1213	D₄	—	6	4	no	—
1214	D₄	—	6	4	no	—
1215	D₄	—	6	4	no	—
1216	D₄	—	12	1	no	—
1217	D₄	—	12	2	no	—
1218	D₄	—	12	2	no	—
1219	D₄	—	12	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	4	no	—
1224	C₂×C₄	—	3	2	no	—
1225	C₂×C₄	—	3	2	no	—
1226	C₂×C₄	—	3	2	no	—
1227	C₂×C₄	—	3	2	no	—
1228	C₂×C₄	—	3	2	no	—
1229	C₂×C₄	—	3	2	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	1	no	—
1232	C₂×C₄	—	4	1	no	—
1233	C₂×C₄	—	6	4	no	—
1234	C₂×C₄	—	6	2	no	—
1235	C₂×C₄	—	6	4	no	—
1236	C₂×C₄	—	6	4	no	—
1237	C₂×C₄	—	12	2	no	—
1238	C₂×C₄	—	12	2	no	—
1239	C₂×C₄	—	12	2	no	—
1240	C₂×C₄	—	12	2	no	—
1241	C₂×C₄	—	12	1	no	—
1242	C₂×C₄	—	12	2	no	—
1243	C₂×C₄	—	12	1	no	—
1244	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1245	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1246	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1247	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1248	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1249	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1250	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1251	C₂×C₃	—	2	2	no	—
1252	C₂×C₃	—	2	2	no	—
1253	C₂×C₃	—	2	1	no	—
1254	C₂×C₃	—	2	1	no	—
1255	C₂×C₃	—	2	1	no	—
1256	C₂×C₃	—	4	2	no	—
1257	C₂×C₃	—	4	2	no	—
1258	C₂×C₃	—	4	2	no	—
1259	C₂×C₃	—	4	1	no	—
1260	C₂×C₃	—	4	1	no	—
1261	C₂×C₃	—	4	2	no	—
1262	C₂×C₃	—	4	2	no	—
1263	C₂×C₃	—	4	1	no	—
1264	C₂×C₃	—	4	1	no	—
1265	C₂×C₃	—	6	4	no	—
1266	C₂×C₃	—	8	2	no	—
1267	C₂×C₃	—	12	2	no	—
1268	C₂×C₃	C₂×#1004	1	1	yes	characteristic
1269	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
1270	C₂×C₃	#5964	1	1	yes	characteristic
1271	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1272	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1273	C₂×C₃	C₃×#585	1	1	yes	characteristic
1274	D₃	—	2	4	no	—
1275	D₃	—	4	2	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	1	no	—
1278	C₂²	—	2	1	no	—
1279	C₂²	—	2	1	no	—
1280	C₂²	—	2	2	no	—
1281	C₂²	—	2	2	no	—
1282	C₂²	—	2	1	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	1	no	—
1285	C₂²	—	2	2	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	3	4	no	—
1288	C₂²	—	4	4	no	—
1289	C₂²	—	6	2	no	—
1290	C₂²	—	6	2	no	—
1291	C₂²	—	6	2	no	—
1292	C₂²	—	6	2	no	—
1293	C₂²	—	6	2	no	—
1294	C₂²	—	12	4	no	—
1295	C₂²	—	12	8	no	—
1296	C₂²	C₃×D₃×#41	1	2	yes	—
1297	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1298	C₄	—	2	1	no	—
1299	C₄	—	2	1	no	—
1300	C₄	—	2	1	no	—
1301	C₄	—	2	2	no	—
1302	C₄	—	2	2	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	6	2	no	—
1305	C₄	—	6	2	no	—
1306	C₄	—	6	2	no	—
1307	C₄	—	6	2	no	—
1308	C₄	—	6	2	no	—
1309	C₄	—	6	2	no	—
1310	C₄	C₃×#1004	1	2	yes	—
1311	C₃	—	2	1	no	—
1312	C₃	#86036	1	1	yes	characteristic, direct product factor
1313	C₃	C₃×#3459	1	1	yes	characteristic, complemented
1314	C₂	—	2	2	no	—
1315	C₂	—	4	1	no	—
1316	C₂	—	4	1	no	—
1317	C₂	—	4	2	no	—
1318	C₂	—	6	4	no	—
1319	C₂	—	12	2	no	—
1320	C₂	C₂×C₃×#1004	1	1	yes	characteristic
1321	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
1322	C₂	C₃×#5964	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×#525	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#525	D₃
hypocenter	C₃	C₃×#3459
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
1. C₃²×#525	C₂	semidirect
2. C₃×#5828	C₂	semidirect
3. C₃×#5791	C₂	semidirect
4. C₂×C₃×C₄×#67	C₂	semidirect
5. C₃×#5660	C₂	semidirect
6. C₃×#5657	C₂	semidirect
7. C₃×#5645	C₂	semidirect
8. C₃×#5638	C₂	semidirect
9. C₃×#5634	C₂	semidirect
10. C₃×#5613	C₂	semidirect
11. C₃×#5605	C₂	semidirect
12. C₃×#5602	C₂	semidirect
13. C₃×#5593	C₂	semidirect
14. C₃×#5589	C₂	semidirect
15. C₃×#5557	C₂	semidirect
16. C₃×#5547	C₂	semidirect
17. C₃×C₄×D₃×D₄	C₂	semidirect
18. C₃×#5538	C₂	semidirect
19. C₃×#5528	C₂	semidirect
21. #86036	C₃	direct (N × H)
22. C₂×C₃²×#41	C₂²	semidirect
23. C₂³×C₃²×C₄	C₂²	semidirect
26. C₂×C₃×#235	C₂²	semidirect
28. C₂²×C₃×C₄×D₃	C₂²	semidirect
29. C₃²×#123	C₂²	semidirect
30. C₃²×C₂²⋊Q₈	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. C₃²×C₄×D₄	C₂²	semidirect
37. C₃²×#117	C₂²	semidirect
38. C₃×#953	C₂²	semidirect
39. C₂×C₃×#217	C₂²	semidirect
40. C₃×#946	C₂²	semidirect
41. C₃×#946	C₂²	semidirect
43. C₃×#939	C₂²	semidirect
46. C₃×#938	C₂²	semidirect
47. C₃×#937	C₂²	semidirect
48. C₃×#937	C₂²	semidirect
49. C₃×#937	C₂²	semidirect
50. C₃×#936	C₂²	semidirect
51. C₃×#935	C₂²	semidirect
52. C₃×#935	C₂²	semidirect
53. C₃×#935	C₂²	semidirect
54. C₃×D₄×Dic₃	C₂²	semidirect
56. C₃×#930	C₂²	semidirect
57. C₃×#929	C₂²	semidirect
58. C₃×C₄×#67	C₂²	semidirect
59. C₃×C₄×#67	C₂²	semidirect
60. C₃×C₄×#67	C₂²	semidirect
61. C₃×C₄×#67	C₂²	semidirect
62. C₃×C₄×#67	C₂²	semidirect
63. C₃×C₄×#67	C₂²	semidirect
64. C₃×C₄×#67	C₂²	semidirect
65. C₃×C₄×#67	C₂²	semidirect
67. C₃×#926	C₂²	semidirect
68. C₃×#926	C₂²	semidirect
69. C₃×#924	C₂²	semidirect
70. C₃×#924	C₂²	semidirect
71. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
72. C₂×C₃×C₄×Dic₃	C₂²	semidirect
73. C₃×#898	C₂²	semidirect
74. C₃×#898	C₂²	semidirect
75. C₃×#897	C₂²	semidirect
76. C₃×#896	C₂²	semidirect
77. C₃×#896	C₂²	semidirect
78. C₃×#894	C₂²	semidirect
79. C₃×#894	C₂²	semidirect
80. C₃×#893	C₂²	semidirect
81. C₃×D₃×C₄⋊C₄	C₂²	semidirect
82. C₃×#890	C₂²	semidirect
83. C₃×#889	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#886	C₂²	semidirect
86. C₃×#885	C₂²	semidirect
87. C₃×#885	C₂²	semidirect
90. C₃×#883	C₂²	semidirect
91. C₃×#883	C₂²	semidirect
92. C₃×#883	C₂²	semidirect
93. C₃×#883	C₂²	semidirect
94. C₃×#882	C₂²	semidirect
95. C₃×#67⋊C₄	C₂²	semidirect
96. C₃×#67⋊C₄	C₂²	semidirect
98. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
99. C₃×#879	C₂²	semidirect
100. C₃×#879	C₂²	semidirect
101. C₃×#879	C₂²	semidirect
102. C₃×#879	C₂²	semidirect
103. C₃×#878	C₂²	semidirect
104. C₃×#878	C₂²	semidirect
105. C₃×C₄×D₁₂	C₂²	semidirect
106. C₃×#872	C₂²	semidirect
107. C₃×C₄²×D₃	C₂²	semidirect
108. C₃×C₄×Dic₆	C₂²	semidirect
126. C₃×#525	D₃	semidirect
127. C₃×#525	C₂×C₃	semidirect
130. #5828	C₂×C₃	semidirect
131. #5791	C₂×C₃	semidirect
132. C₂×C₄×#67	C₂×C₃	semidirect
133. #5660	C₂×C₃	semidirect
134. #5657	C₂×C₃	semidirect
135. #5645	C₂×C₃	semidirect
136. #5638	C₂×C₃	semidirect
137. #5634	C₂×C₃	semidirect
138. #5613	C₂×C₃	semidirect
139. #5605	C₂×C₃	semidirect
140. #5602	C₂×C₃	semidirect
141. #5593	C₂×C₃	semidirect
142. #5589	C₂×C₃	semidirect
143. #5557	C₂×C₃	semidirect
144. #5547	C₂×C₃	semidirect
145. C₄×D₃×D₄	C₂×C₃	semidirect
146. #5538	C₂×C₃	semidirect
147. #5528	C₂×C₃	semidirect
245. C₂×C₃×#41	C₂×D₃	semidirect
246. C₂×C₃×#41	C₂²×C₃	semidirect
252. C₂³×C₃×C₄	C₂×D₃	semidirect
253. C₂³×C₃×C₄	C₂²×C₃	semidirect
256. C₂×#235	C₂²×C₃	semidirect
258. C₂²×C₄×D₃	C₂²×C₃	semidirect
283. C₃×#123	C₂×D₃	semidirect
284. C₃×#123	C₂²×C₃	semidirect
296. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
297. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
298. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
299. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
312. C₃×#121	C₂×D₃	semidirect
314. C₃×#121	C₂²×C₃	semidirect
321. C₃×#120	C₂×D₃	semidirect
322. C₃×#120	C₂²×C₃	semidirect
339. C₃×C₄×D₄	C₂×D₃	semidirect
340. C₃×C₄×D₄	C₂×D₃	semidirect
341. C₃×C₄×D₄	C₂²×C₃	semidirect
342. C₃×C₄×D₄	C₂²×C₃	semidirect
347. C₃×#117	C₂×D₃	semidirect
348. C₃×#117	C₂²×C₃	semidirect
357. #953	C₂²×C₃	semidirect
358. C₂×#217	C₂²×C₃	semidirect
359. #946	C₂²×C₃	semidirect
360. #946	C₂²×C₃	semidirect
362. #939	C₂²×C₃	semidirect
365. #938	C₂²×C₃	semidirect
366. #937	C₂²×C₃	semidirect
367. #937	C₂²×C₃	semidirect
368. #937	C₂²×C₃	semidirect
369. #936	C₂²×C₃	semidirect
370. #935	C₂²×C₃	semidirect
371. #935	C₂²×C₃	semidirect
372. #935	C₂²×C₃	semidirect
373. D₄×Dic₃	C₂²×C₃	semidirect
375. #930	C₂²×C₃	semidirect
376. #929	C₂²×C₃	semidirect
377. C₄×#67	C₂²×C₃	semidirect
378. C₄×#67	C₂²×C₃	semidirect
379. C₄×#67	C₂²×C₃	semidirect
380. C₄×#67	C₂²×C₃	semidirect
381. C₄×#67	C₂²×C₃	semidirect
382. C₄×#67	C₂²×C₃	semidirect
383. C₄×#67	C₂²×C₃	semidirect
384. C₄×#67	C₂²×C₃	semidirect
386. #926	C₂²×C₃	semidirect
387. #926	C₂²×C₃	semidirect
388. #924	C₂²×C₃	semidirect
389. #924	C₂²×C₃	semidirect
390. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
391. C₂×C₄×Dic₃	C₂²×C₃	semidirect
392. #898	C₂²×C₃	semidirect
393. #898	C₂²×C₃	semidirect
394. #897	C₂²×C₃	semidirect
395. #896	C₂²×C₃	semidirect
396. #896	C₂²×C₃	semidirect
397. #894	C₂²×C₃	semidirect
398. #894	C₂²×C₃	semidirect
399. #893	C₂²×C₃	semidirect
400. D₃×C₄⋊C₄	C₂²×C₃	semidirect
401. #890	C₂²×C₃	semidirect
402. #889	C₂²×C₃	semidirect
403. #889	C₂²×C₃	semidirect
404. #886	C₂²×C₃	semidirect
405. #885	C₂²×C₃	semidirect
406. #885	C₂²×C₃	semidirect
409. #883	C₂²×C₃	semidirect
410. #883	C₂²×C₃	semidirect
411. #883	C₂²×C₃	semidirect
412. #883	C₂²×C₃	semidirect
413. #882	C₂²×C₃	semidirect
414. #67⋊C₄	C₂²×C₃	semidirect
415. #67⋊C₄	C₂²×C₃	semidirect
417. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
418. #879	C₂²×C₃	semidirect
419. #879	C₂²×C₃	semidirect
420. #879	C₂²×C₃	semidirect
421. #879	C₂²×C₃	semidirect
422. #878	C₂²×C₃	semidirect
423. #878	C₂²×C₃	semidirect
424. C₄×D₁₂	C₂²×C₃	semidirect
425. #872	C₂²×C₃	semidirect
426. C₄²×D₃	C₂²×C₃	semidirect
427. C₄×Dic₆	C₂²×C₃	semidirect
440. C₂²×C₃×D₃	#41	semidirect
506. #525	C₃×D₃	semidirect
758. C₂×#41	C₂×C₃×D₃	semidirect
763. C₂³×C₄	C₂×C₃×D₃	semidirect
787. #123	C₂×C₃×D₃	semidirect
797. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
798. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
809. #121	C₂×C₃×D₃	semidirect
815. #120	C₂×C₃×D₃	semidirect
830. C₄×D₄	C₂×C₃×D₃	semidirect
831. C₄×D₄	C₂×C₃×D₃	semidirect
835. #117	C₂×C₃×D₃	semidirect
878. C₂²×D₃	C₃×#41	semidirect
1188. C₃²	#3459	semidirect
1312. C₃	#86036	direct (N × H)
1313. 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×#525	2
C₃×#5828	2
C₃×#5791	2
C₂×C₃×C₄×#67	2
C₃×#5660	2
C₃×#5657	2
C₃×#5645	2
C₃×#5638	2
C₃×#5634	2
C₃×#5613	2
C₃×#5605	2
C₃×#5602	2
C₃×#5593	2
C₃×#5589	2
C₃×#5557	2
C₃×#5547	2
C₃×C₄×D₃×D₄	2
C₃×#5538	2
C₃×#5528	2
C₃×#3459	3
#86036	3

Subgroups — C3×#86036 #11901967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86036 #11901967