Subgroups — C₃×#87093 #11910352

Order 1152.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5699	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5691	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5684	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5680	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5667	C₂	1	2	yes	maximal, complemented
9	C₃×#5666	C₂	1	2	yes	maximal, complemented
10	C₃×#5656	C₂	1	2	yes	maximal, complemented
11	C₃×#5649	C₂	1	2	yes	maximal, complemented
12	C₃×#5647	C₂	1	2	yes	maximal, complemented
13	C₃×#5646	C₂	1	2	yes	maximal, complemented
14	C₃×#5627	C₂	1	2	yes	maximal, complemented
15	C₃×#5624	C₂	1	2	yes	maximal, complemented
16	C₃×#5620	C₂	1	2	yes	maximal, complemented
17	C₃×#5620	C₂	1	2	yes	maximal, complemented
18	C₃×#5606	C₂	1	2	yes	maximal, complemented
19	C₃×#5596	C₂	1	2	yes	maximal, complemented
20	C₃×#3529	—	3	1	no	maximal
21	#87093	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂×C₃×#239	C₂²	1	1	yes	characteristic
23	C₂×C₃×#237	C₂²	1	2	yes	—
24	C₂×C₃×#237	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	complemented
26	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
27	C₃²×#124	C₂²	1	1	yes	characteristic
28	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
29	C₃²×#123	C₂²	1	2	yes	complemented
30	C₃²×#123	C₂²	1	2	yes	complemented
31	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₃²×#121	C₂²	1	2	yes	—
34	C₃²×#121	C₂²	1	2	yes	complemented
35	C₃×#947	C₂²	1	2	yes	—
36	C₃×#946	C₂²	1	2	yes	complemented
37	C₃×#946	C₂²	1	1	yes	characteristic, complemented
38	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₃×#944	C₂²	1	1	yes	characteristic, complemented
40	C₃×#940	C₂²	1	2	yes	—
41	C₃×#940	C₂²	1	1	yes	characteristic
42	C₃×#939	C₂²	1	2	yes	—
43	C₃×#939	C₂²	1	2	yes	complemented
44	C₃×#939	C₂²	1	2	yes	complemented
45	C₃×#938	C₂²	1	2	yes	—
46	C₃×#938	C₂²	1	1	yes	characteristic
47	C₃×#937	C₂²	1	2	yes	—
48	C₃×#937	C₂²	1	2	yes	complemented
49	C₃×#937	C₂²	1	2	yes	complemented
50	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
51	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
52	C₃×#930	C₂²	1	2	yes	—
53	C₃×#930	C₂²	1	2	yes	—
54	C₃×#930	C₂²	1	2	yes	complemented
55	C₃×#929	C₂²	1	2	yes	—
56	C₃×#929	C₂²	1	2	yes	complemented
57	C₃×#924	C₂²	1	2	yes	complemented
58	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
59	C₃×#898	C₂²	1	2	yes	complemented
60	C₃×#898	C₂²	1	2	yes	complemented
61	C₃×#898	C₂²	1	2	yes	complemented
62	C₃×#898	C₂²	1	2	yes	complemented
63	C₃×#897	C₂²	1	2	yes	complemented
64	C₃×#897	C₂²	1	1	yes	characteristic, complemented
65	C₃×#896	C₂²	1	2	yes	complemented
66	C₃×#896	C₂²	1	2	yes	complemented
67	C₃×#895	C₂²	1	2	yes	—
68	C₃×#895	C₂²	1	1	yes	characteristic
69	C₃×#894	C₂²	1	2	yes	—
70	C₃×#894	C₂²	1	2	yes	complemented
71	C₃×#894	C₂²	1	2	yes	complemented
72	C₃×#893	C₂²	1	2	yes	—
73	C₃×#893	C₂²	1	1	yes	characteristic
74	C₃×#893	C₂²	1	2	yes	complemented
75	C₃×#892	C₂²	1	2	yes	complemented
76	C₃×#892	C₂²	1	2	yes	complemented
77	C₃×#890	C₂²	1	2	yes	complemented
78	C₃×#889	C₂²	1	2	yes	complemented
79	C₃×#888	C₂²	1	2	yes	complemented
80	C₃×#887	C₂²	1	1	yes	characteristic, complemented
81	C₃×#886	C₂²	1	2	yes	complemented
82	C₃×#886	C₂²	1	2	yes	complemented
83	C₃×#885	C₂²	1	2	yes	—
84	C₃×#885	C₂²	1	2	yes	—
85	C₃×#885	C₂²	1	2	yes	complemented
86	C₃×#884	C₂²	1	2	yes	—
87	C₃×#884	C₂²	1	2	yes	—
88	C₃×#884	C₂²	1	2	yes	complemented
89	C₃×#884	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	—
91	C₃×#883	C₂²	1	2	yes	complemented
92	C₃×#883	C₂²	1	2	yes	complemented
93	C₃×#882	C₂²	1	2	yes	—
94	C₃×#882	C₂²	1	2	yes	—
95	C₃×#882	C₂²	1	2	yes	complemented
96	C₃×#67⋊C₄	C₂²	1	2	yes	—
97	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
98	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
99	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
100	C₃×#67⋊C₄	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×#877	C₂²	1	2	yes	complemented
105	C₃×#875	C₂²	1	1	yes	characteristic
106	C₃×#875	C₂²	1	1	yes	characteristic
107	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
108	C₃×#870	C₂²	1	1	yes	characteristic, complemented
109	C₃×#563	—	3	1	no	—
110	C₃×#563	—	3	2	no	—
111	C₃×#562	—	2	1	no	—
112	C₃×#562	—	3	1	no	—
113	C₃×#562	—	3	2	no	—
114	C₃×#562	—	3	2	no	—
115	C₃×#562	D₃	1	1	yes	characteristic, complemented
116	C₃×#562	C₂×C₃	1	1	yes	characteristic, complemented
117	C₃×H(3,𝔽₄)	—	3	1	no	—
118	C₃×#560	—	3	2	no	—
119	C₃×#560	—	3	2	no	—
120	C₃×#560	—	3	2	no	—
121	C₃×#532	—	3	1	no	—
122	C₃×#532	—	3	2	no	—
123	C₃×#529	—	3	1	no	—
124	C₃×#529	—	3	1	no	—
125	C₃×#529	—	3	2	no	—
126	C₃×#529	—	3	2	no	—
127	C₃×#525	—	3	2	no	—
128	C₃×#525	—	3	2	no	—
129	C₃×#525	—	3	2	no	—
130	#5699	C₂×C₃	1	1	yes	characteristic, complemented
131	#5691	C₂×C₃	1	1	yes	characteristic, complemented
132	#5684	C₂×C₃	1	1	yes	characteristic, complemented
133	#5683	C₂×C₃	1	1	yes	characteristic, complemented
134	#5680	C₂×C₃	1	1	yes	characteristic, complemented
135	#5668	C₂×C₃	1	1	yes	characteristic, complemented
136	#5667	C₂×C₃	1	2	yes	complemented
137	#5666	C₂×C₃	1	2	yes	complemented
138	#5656	C₂×C₃	1	2	yes	complemented
139	#5649	C₂×C₃	1	2	yes	complemented
140	#5647	C₂×C₃	1	2	yes	complemented
141	#5646	C₂×C₃	1	2	yes	complemented
142	#5627	C₂×C₃	1	2	yes	complemented
143	#5624	C₂×C₃	1	2	yes	complemented
144	#5620	C₂×C₃	1	2	yes	complemented
145	#5620	C₂×C₃	1	2	yes	complemented
146	#5606	C₂×C₃	1	2	yes	complemented
147	#5596	C₂×C₃	1	2	yes	complemented
148	C₂³×C₃×D₃	C₂³	1	2	yes	—
149	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃²×D₄	C₂³	1	2	yes	—
153	C₂×C₃²×D₄	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃²×C₄	C₂³	1	2	yes	—
156	C₂²×C₃²×C₄	C₂³	1	2	yes	—
157	C₂×C₃×#67	C₂³	1	2	yes	—
158	C₂×C₃×#67	C₂³	1	2	yes	—
159	C₂×C₃×#67	C₂³	1	2	yes	—
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	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
166	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
167	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
168	C₃×#239	—	4	2	no	—
169	C₃×#237	—	4	4	no	—
170	C₃×#237	—	4	2	no	—
171	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
172	C₂×C₃×D₁₂	C₂³	1	2	yes	—
173	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×C₃×D₁₂	C₂³	1	2	yes	—
175	C₂×C₃×D₁₂	C₂³	1	2	yes	—
176	C₂×C₃×C₄×D₃	—	4	4	no	—
177	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
178	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
180	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
185	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
186	C₂×C₃×Dic₆	C₂³	1	2	yes	—
187	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	1	yes	characteristic
200	C₃×#217	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×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
205	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
206	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	C₃×(C₂×D₃)⋊C₄	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	2	yes	—
221	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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×C₄×Dic₃	C₂³	1	1	yes	characteristic
233	C₃×C₄×Dic₃	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	#3529	—	3	1	no	Sylow
240	C₂×C₃×#41	—	3	1	no	—
241	C₂×C₃×#41	—	3	2	no	—
242	C₂×C₃×#41	—	3	1	no	—
243	C₂³×C₃×C₄	—	3	2	no	—
244	C₂×#239	C₂²×C₃	1	1	yes	characteristic
245	C₂×#237	C₂²×C₃	1	2	yes	—
246	C₂×#237	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	complemented
248	C₃×C₄⋊Q₈	—	3	1	no	—
249	C₃×C₄⋊Q₈	—	3	2	no	—
250	C₃×#127	—	3	1	no	—
251	C₃×#127	—	3	2	no	—
252	C₃×#126	—	3	2	no	—
253	C₃×#126	—	3	2	no	—
254	C₃×#126	—	3	2	no	—
255	C₃×#126	—	3	2	no	—
256	C₃×#126	—	3	2	no	—
257	C₃×#126	—	3	2	no	—
258	C₃×#125	—	2	1	no	—
259	C₃×#125	—	3	2	no	—
260	C₃×#125	—	3	2	no	—
261	C₃×#125	—	3	1	no	—
262	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
263	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₃×#124	—	2	1	no	—
265	C₃×#124	—	2	1	no	—
266	C₃×#124	—	3	2	no	—
267	C₃×#124	—	3	2	no	—
268	C₃×#124	—	3	2	no	—
269	C₃×#124	—	3	2	no	—
270	C₃×#124	—	3	1	no	—
271	C₃×#124	—	3	1	no	—
272	C₃×#124	C₂×D₃	1	1	yes	characteristic
273	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
274	C₃×#124	C₂²×C₃	1	1	yes	characteristic
275	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
276	C₃×#123	—	2	2	no	—
277	C₃×#123	—	2	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	—	3	2	no	—
285	C₃×#123	—	3	2	no	—
286	C₃×#123	—	3	2	no	—
287	C₃×#123	—	3	2	no	—
288	C₃×#123	C₂×D₃	1	2	yes	complemented
289	C₃×#123	C₂×D₃	1	2	yes	complemented
290	C₃×#123	C₂²×C₃	1	2	yes	complemented
291	C₃×#123	C₂²×C₃	1	2	yes	complemented
292	C₃×C₂²⋊Q₈	—	2	2	no	—
293	C₃×C₂²⋊Q₈	—	2	2	no	—
294	C₃×C₂²⋊Q₈	—	3	1	no	—
295	C₃×C₂²⋊Q₈	—	3	2	no	—
296	C₃×C₂²⋊Q₈	—	3	2	no	—
297	C₃×C₂²⋊Q₈	—	3	1	no	—
298	C₃×C₂²⋊Q₈	—	3	2	no	—
299	C₃×C₂²⋊Q₈	—	3	2	no	—
300	C₃×C₂²⋊Q₈	—	3	2	no	—
301	C₃×C₂²⋊Q₈	—	3	2	no	—
302	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
303	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
304	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
305	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
306	C₃×#121	—	2	2	no	—
307	C₃×#121	—	2	2	no	—
308	C₃×#121	—	3	1	no	—
309	C₃×#121	—	3	2	no	—
310	C₃×#121	—	3	2	no	—
311	C₃×#121	—	3	2	no	—
312	C₃×#121	—	3	2	no	—
313	C₃×#121	—	3	2	no	—
314	C₃×#121	—	3	2	no	—
315	C₃×#121	—	3	2	no	—
316	C₃×#121	—	3	1	no	—
317	C₃×#121	—	3	2	no	—
318	C₃×#121	—	3	2	no	—
319	C₃×#121	—	3	2	no	—
320	C₃×#121	—	3	2	no	—
321	C₃×#121	—	3	2	no	—
322	C₃×#121	C₂×D₃	1	2	yes	—
323	C₃×#121	C₂×D₃	1	2	yes	complemented
324	C₃×#121	C₂²×C₃	1	2	yes	—
325	C₃×#121	C₂²×C₃	1	2	yes	complemented
326	C₃×#120	—	3	2	no	—
327	C₃×#120	—	3	2	no	—
328	C₃×#120	—	3	2	no	—
329	C₃×#120	—	3	2	no	—
330	C₃×#120	—	3	2	no	—
331	C₃×#120	—	3	2	no	—
332	C₃×C₄×Q₈	—	3	1	no	—
333	C₃×C₄×Q₈	—	3	1	no	—
334	C₃×C₄×D₄	—	3	1	no	—
335	C₃×C₄×D₄	—	3	2	no	—
336	C₃×C₄×D₄	—	3	1	no	—
337	C₃×C₄×D₄	—	3	2	no	—
338	C₃×C₄×D₄	—	3	2	no	—
339	C₃×C₄×D₄	—	3	2	no	—
340	C₃×C₄×D₄	—	3	2	no	—
341	C₃×C₄×D₄	—	3	2	no	—
342	C₃×C₄×D₄	—	3	2	no	—
343	C₃×C₄×D₄	—	3	2	no	—
344	C₃×#117	—	3	2	no	—
345	C₃×#117	—	3	2	no	—
346	C₃×#117	—	3	2	no	—
347	C₂×C₃×C₄²	—	3	2	no	—
348	C₂×C₃×C₄²	—	3	1	no	—
349	#947	C₂²×C₃	1	2	yes	—
350	#946	C₂²×C₃	1	2	yes	complemented
351	#946	C₂²×C₃	1	1	yes	characteristic, complemented
352	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
353	#944	C₂²×C₃	1	1	yes	characteristic, complemented
354	#940	C₂²×C₃	1	2	yes	—
355	#940	C₂²×C₃	1	1	yes	characteristic
356	#939	C₂²×C₃	1	2	yes	—
357	#939	C₂²×C₃	1	2	yes	complemented
358	#939	C₂²×C₃	1	2	yes	complemented
359	#938	C₂²×C₃	1	2	yes	—
360	#938	C₂²×C₃	1	1	yes	characteristic
361	#937	C₂²×C₃	1	2	yes	—
362	#937	C₂²×C₃	1	2	yes	complemented
363	#937	C₂²×C₃	1	2	yes	complemented
364	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
365	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
366	#930	C₂²×C₃	1	2	yes	—
367	#930	C₂²×C₃	1	2	yes	—
368	#930	C₂²×C₃	1	2	yes	complemented
369	#929	C₂²×C₃	1	2	yes	—
370	#929	C₂²×C₃	1	2	yes	complemented
371	#924	C₂²×C₃	1	2	yes	complemented
372	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
373	#898	C₂²×C₃	1	2	yes	complemented
374	#898	C₂²×C₃	1	2	yes	complemented
375	#898	C₂²×C₃	1	2	yes	complemented
376	#898	C₂²×C₃	1	2	yes	complemented
377	#897	C₂²×C₃	1	2	yes	complemented
378	#897	C₂²×C₃	1	1	yes	characteristic, complemented
379	#896	C₂²×C₃	1	2	yes	complemented
380	#896	C₂²×C₃	1	2	yes	complemented
381	#895	C₂²×C₃	1	2	yes	—
382	#895	C₂²×C₃	1	1	yes	characteristic
383	#894	C₂²×C₃	1	2	yes	—
384	#894	C₂²×C₃	1	2	yes	complemented
385	#894	C₂²×C₃	1	2	yes	complemented
386	#893	C₂²×C₃	1	1	yes	characteristic
387	#893	C₂²×C₃	1	2	yes	—
388	#893	C₂²×C₃	1	2	yes	complemented
389	#892	C₂²×C₃	1	2	yes	complemented
390	#892	C₂²×C₃	1	2	yes	complemented
391	#890	C₂²×C₃	1	2	yes	complemented
392	#889	C₂²×C₃	1	2	yes	complemented
393	#888	C₂²×C₃	1	2	yes	complemented
394	#887	C₂²×C₃	1	1	yes	characteristic, complemented
395	#886	C₂²×C₃	1	2	yes	complemented
396	#886	C₂²×C₃	1	2	yes	complemented
397	#885	C₂²×C₃	1	2	yes	—
398	#885	C₂²×C₃	1	2	yes	—
399	#885	C₂²×C₃	1	2	yes	complemented
400	#884	C₂²×C₃	1	2	yes	—
401	#884	C₂²×C₃	1	2	yes	—
402	#884	C₂²×C₃	1	2	yes	complemented
403	#884	C₂²×C₃	1	2	yes	complemented
404	#883	C₂²×C₃	1	2	yes	—
405	#883	C₂²×C₃	1	2	yes	complemented
406	#883	C₂²×C₃	1	2	yes	complemented
407	#882	C₂²×C₃	1	2	yes	—
408	#882	C₂²×C₃	1	2	yes	—
409	#882	C₂²×C₃	1	2	yes	complemented
410	#67⋊C₄	C₂²×C₃	1	2	yes	—
411	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
412	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
413	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
414	#67⋊C₄	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	#877	C₂²×C₃	1	2	yes	complemented
419	#875	C₂²×C₃	1	1	yes	characteristic
420	#875	C₂²×C₃	1	1	yes	characteristic
421	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
422	#870	C₂²×C₃	1	1	yes	characteristic, complemented
423	C₂³×C₃²	C₂⁴	1	2	yes	—
424	C₂³×C₃²	C₂⁴	1	2	yes	—
425	C₂²×C₃×D₃	—	4	2	no	—
426	C₂²×C₃×D₃	—	4	2	no	—
427	C₂²×C₃×D₃	—	4	2	no	—
428	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
429	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
430	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
431	C₃²×Q₈	—	4	1	no	—
432	C₃²×Q₈	—	4	1	no	—
433	C₃²×D₄	—	4	2	no	—
434	C₃²×D₄	—	4	1	no	—
435	C₃²×D₄	—	4	1	no	—
436	C₃²×D₄	—	4	2	no	—
437	C₂×C₃²×C₄	—	4	2	no	—
438	C₂×C₃²×C₄	—	4	2	no	—
439	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
440	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
441	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
442	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
443	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
444	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
445	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
446	C₃×#67	—	4	2	no	—
447	C₃×#67	—	4	2	no	—
448	C₃×#67	—	4	2	no	—
449	C₃×#67	—	4	2	no	—
450	C₃×#67	—	4	2	no	—
451	C₃×#67	—	4	2	no	—
452	C₃×#67	—	4	2	no	—
453	C₃×#67	—	4	2	no	—
454	C₂×C₃×Dic₃	—	2	4	no	—
455	C₂×C₃×Dic₃	—	2	4	no	—
456	C₂×C₃×Dic₃	—	4	2	no	—
457	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
458	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
459	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
460	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
461	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
462	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
463	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
464	C₃×D₁₂	—	4	1	no	—
465	C₃×D₁₂	—	4	2	no	—
466	C₃×D₁₂	—	4	2	no	—
467	C₃×D₁₂	—	4	1	no	—
468	C₃×D₁₂	—	4	2	no	—
469	C₃×C₄×D₃	—	2	4	no	—
470	C₃×C₄×D₃	—	2	4	no	—
471	C₃×C₄×D₃	—	2	2	no	—
472	C₃×C₄×D₃	—	4	2	no	—
473	C₃×C₄×D₃	—	4	2	no	—
474	C₃×C₄×D₃	—	4	1	no	—
475	C₃×C₄×D₃	—	4	1	no	—
476	C₃×Dic₆	—	4	1	no	—
477	C₃×Dic₆	—	4	1	no	—
478	C₃×Dic₆	—	4	2	no	—
479	#563	—	3	1	no	—
480	#563	—	3	2	no	—
481	#562	—	3	1	no	—
482	#562	—	3	2	no	—
483	#562	—	3	2	no	—
484	#562	C₃×D₃	1	1	yes	characteristic, complemented
485	H(3,𝔽₄)	—	3	1	no	—
486	#560	—	3	2	no	—
487	#560	—	3	2	no	—
488	#560	—	3	2	no	—
489	#532	—	3	1	no	—
490	#532	—	3	2	no	—
491	#529	—	3	1	no	—
492	#529	—	3	1	no	—
493	#529	—	3	2	no	—
494	#529	—	3	2	no	—
495	#525	—	3	2	no	—
496	#525	—	3	2	no	—
497	#525	—	3	2	no	—
498	C₂⁴×C₃	—	3	2	no	—
499	C₂³×D₃	C₂³×C₃	1	2	yes	—
500	C₃×#41	—	12	4	no	—
501	C₃×#41	—	12	2	no	—
502	C₃×#41	—	12	2	no	—
503	C₂×C₃×Q₈	—	2	1	no	—
504	C₂×C₃×Q₈	—	2	1	no	—
505	C₂×C₃×Q₈	—	3	1	no	—
506	C₂×C₃×Q₈	—	3	2	no	—
507	C₂×C₃×Q₈	—	3	1	no	—
508	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
509	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
510	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₃×D₄	—	2	2	no	—
513	C₂×C₃×D₄	—	2	2	no	—
514	C₂×C₃×D₄	—	2	1	no	—
515	C₂×C₃×D₄	—	2	1	no	—
516	C₂×C₃×D₄	—	3	2	no	—
517	C₂×C₃×D₄	—	3	2	no	—
518	C₂×C₃×D₄	—	3	2	no	—
519	C₂×C₃×D₄	—	3	2	no	—
520	C₂×C₃×D₄	—	3	2	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	1	no	—
526	C₂×C₃×D₄	—	3	2	no	—
527	C₂×C₃×D₄	—	3	1	no	—
528	C₂×C₃×D₄	—	3	2	no	—
529	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
530	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
531	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
532	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
533	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
535	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
536	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
537	C₂²×C₃×C₄	—	2	2	no	—
538	C₂²×C₃×C₄	—	2	2	no	—
539	C₂²×C₃×C₄	—	3	2	no	—
540	C₂²×C₃×C₄	—	3	2	no	—
541	C₂²×C₃×C₄	—	3	2	no	—
542	C₂²×C₃×C₄	—	3	1	no	—
543	C₂²×C₃×C₄	—	3	2	no	—
544	C₂²×C₃×C₄	—	3	2	no	—
545	C₂²×C₃×C₄	—	3	1	no	—
546	C₂²×C₃×C₄	—	3	1	no	—
547	C₂²×C₃×C₄	—	3	2	no	—
548	C₂²×C₃×C₄	—	3	2	no	—
549	C₂²×C₃×C₄	—	12	4	no	—
550	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
551	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
552	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
553	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
554	C₂×#67	C₂³×C₃	1	2	yes	—
555	C₂×#67	C₂³×C₃	1	2	yes	—
556	C₂×#67	C₂³×C₃	1	2	yes	—
557	C₂×#67	C₂³×C₃	1	2	yes	—
558	C₂×#67	C₂³×C₃	1	2	yes	—
559	C₂×#67	C₂³×C₃	1	2	yes	—
560	C₂×#67	C₂³×C₃	1	2	yes	—
561	C₂×#67	C₂³×C₃	1	2	yes	—
562	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
563	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
564	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
565	#239	—	4	2	no	—
566	#237	—	4	4	no	—
567	#237	—	4	2	no	—
568	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
569	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
570	C₂×D₁₂	C₂³×C₃	1	2	yes	—
571	C₂×D₁₂	C₂³×C₃	1	2	yes	—
572	C₂×D₁₂	C₂³×C₃	1	2	yes	—
573	C₂×C₄×D₃	—	4	4	no	—
574	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
576	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
577	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
580	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
581	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
582	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
583	C₂×Dic₆	C₂³×C₃	1	2	yes	—
584	C₃×C₄⋊C₄	—	2	2	no	—
585	C₃×C₄⋊C₄	—	2	2	no	—
586	C₃×C₄⋊C₄	—	2	2	no	—
587	C₃×C₄⋊C₄	—	2	2	no	—
588	C₃×C₄⋊C₄	—	2	1	no	—
589	C₃×C₄⋊C₄	—	2	1	no	—
590	C₃×C₄⋊C₄	—	3	2	no	—
591	C₃×C₄⋊C₄	—	3	2	no	—
592	C₃×C₄⋊C₄	—	3	2	no	—
593	C₃×C₄⋊C₄	—	3	2	no	—
594	C₃×C₄⋊C₄	—	3	2	no	—
595	C₃×C₄⋊C₄	—	3	2	no	—
596	C₃×C₄⋊C₄	—	3	2	no	—
597	C₃×C₄⋊C₄	—	3	2	no	—
598	C₃×C₄⋊C₄	—	3	2	no	—
599	C₃×C₄⋊C₄	—	3	2	no	—
600	C₃×C₄⋊C₄	—	3	2	no	—
601	C₃×C₄⋊C₄	—	3	1	no	—
602	C₃×C₄⋊C₄	—	3	2	no	—
603	C₃×C₄⋊C₄	—	3	1	no	—
604	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
605	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
606	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
607	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
608	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
609	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
610	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
611	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
612	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
614	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
615	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
616	C₃×C₂²⋊C₄	—	2	2	no	—
617	C₃×C₂²⋊C₄	—	2	2	no	—
618	C₃×C₂²⋊C₄	—	2	2	no	—
619	C₃×C₂²⋊C₄	—	2	2	no	—
620	C₃×C₂²⋊C₄	—	2	2	no	—
621	C₃×C₂²⋊C₄	—	2	2	no	—
622	C₃×C₂²⋊C₄	—	3	2	no	—
623	C₃×C₂²⋊C₄	—	3	2	no	—
624	C₃×C₂²⋊C₄	—	3	2	no	—
625	C₃×C₂²⋊C₄	—	3	2	no	—
626	C₃×C₂²⋊C₄	—	3	2	no	—
627	C₃×C₂²⋊C₄	—	3	2	no	—
628	C₃×C₂²⋊C₄	—	3	2	no	—
629	C₃×C₂²⋊C₄	—	3	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	C₂²×D₃	1	2	yes	—
641	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
642	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
643	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
644	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
645	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
646	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
647	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
652	C₃×C₄²	—	2	1	no	—
653	C₃×C₄²	—	3	2	no	—
654	C₃×C₄²	—	3	2	no	—
655	C₃×C₄²	—	3	1	no	—
656	C₃×C₄²	—	3	1	no	—
657	C₃×C₄²	—	3	2	no	—
658	C₃×C₄²	—	3	1	no	—
659	C₃×C₄²	—	3	2	no	—
660	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
661	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
662	#217	C₂³×C₃	1	2	yes	—
663	#217	C₂³×C₃	1	2	yes	—
664	#217	C₂³×C₃	1	2	yes	—
665	#217	C₂³×C₃	1	2	yes	—
666	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
667	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
668	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
669	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
670	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
671	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
672	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
673	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
674	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
675	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
676	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
677	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
678	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
679	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
680	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
681	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
682	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
683	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
684	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
685	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
686	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
687	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
688	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
689	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
690	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
691	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
692	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
693	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
694	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
695	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
696	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
697	C₄×Dic₃	C₂³×C₃	1	2	yes	—
698	C₄×Dic₃	C₂³×C₃	1	2	yes	—
699	C₄×Dic₃	C₂³×C₃	1	2	yes	—
700	C₄×Dic₃	C₂³×C₃	1	2	yes	—
701	C₂²×C₃²	—	2	2	no	—
702	C₂²×C₃²	—	2	2	no	—
703	C₂²×C₃²	—	2	2	no	—
704	C₂²×C₃²	—	2	2	no	—
705	C₂²×C₃²	—	2	2	no	—
706	C₂²×C₃²	—	2	2	no	—
707	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
708	C₂×C₃×D₃	—	2	2	no	—
709	C₂×C₃×D₃	—	2	2	no	—
710	C₂×C₃×D₃	—	2	1	no	—
711	C₂×C₃×D₃	—	2	1	no	—
712	C₂×C₃×D₃	—	2	1	no	—
713	C₂×C₃×D₃	—	2	2	no	—
714	C₂×C₃×D₃	—	2	2	no	—
715	C₂×C₃×D₃	—	2	2	no	—
716	C₂×C₃×D₃	—	2	2	no	—
717	C₂×C₃×D₃	—	4	8	no	—
718	C₃²×C₄	—	2	2	no	—
719	C₃²×C₄	—	2	1	no	—
720	C₃²×C₄	—	2	2	no	—
721	C₃²×C₄	—	2	1	no	—
722	C₃²×C₄	—	2	1	no	—
723	C₃²×C₄	—	2	2	no	—
724	C₃²×C₄	—	2	2	no	—
725	C₃×Dic₃	—	2	2	no	—
726	C₃×Dic₃	—	2	2	no	—
727	C₃×Dic₃	—	2	2	no	—
728	C₃×Dic₃	—	2	1	no	—
729	C₃×Dic₃	—	2	1	no	—
730	C₃×Dic₃	—	2	2	no	—
731	C₃×Dic₃	H(5,𝔽₂)	1	2	yes	—
732	C₂×#41	—	3	1	no	—
733	C₂×#41	—	3	2	no	—
734	C₂×#41	—	3	1	no	—
735	C₂³×C₄	—	3	2	no	—
736	C₄⋊Q₈	—	3	1	no	—
737	C₄⋊Q₈	—	3	2	no	—
738	#127	—	3	1	no	—
739	#127	—	3	2	no	—
740	#126	—	3	2	no	—
741	#126	—	3	2	no	—
742	#126	—	3	2	no	—
743	#126	—	3	2	no	—
744	#126	—	3	2	no	—
745	#126	—	3	2	no	—
746	#125	—	3	2	no	—
747	#125	—	3	2	no	—
748	#125	—	3	1	no	—
749	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
750	#124	—	3	2	no	—
751	#124	—	3	2	no	—
752	#124	—	3	2	no	—
753	#124	—	3	2	no	—
754	#124	—	3	1	no	—
755	#124	—	3	1	no	—
756	#124	C₂×C₃×D₃	1	1	yes	characteristic
757	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
758	#123	—	3	2	no	—
759	#123	—	3	2	no	—
760	#123	—	3	2	no	—
761	#123	—	3	2	no	—
762	#123	—	3	2	no	—
763	#123	—	3	2	no	—
764	#123	—	3	2	no	—
765	#123	—	3	2	no	—
766	#123	—	3	2	no	—
767	#123	—	3	2	no	—
768	#123	C₂×C₃×D₃	1	2	yes	complemented
769	#123	C₂×C₃×D₃	1	2	yes	complemented
770	C₂²⋊Q₈	—	3	2	no	—
771	C₂²⋊Q₈	—	3	1	no	—
772	C₂²⋊Q₈	—	3	2	no	—
773	C₂²⋊Q₈	—	3	2	no	—
774	C₂²⋊Q₈	—	3	2	no	—
775	C₂²⋊Q₈	—	3	2	no	—
776	C₂²⋊Q₈	—	3	1	no	—
777	C₂²⋊Q₈	—	3	2	no	—
778	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
779	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
780	#121	—	3	2	no	—
781	#121	—	3	1	no	—
782	#121	—	3	2	no	—
783	#121	—	3	2	no	—
784	#121	—	3	2	no	—
785	#121	—	3	2	no	—
786	#121	—	3	2	no	—
787	#121	—	3	2	no	—
788	#121	—	3	2	no	—
789	#121	—	3	1	no	—
790	#121	—	3	2	no	—
791	#121	—	3	2	no	—
792	#121	—	3	2	no	—
793	#121	—	3	2	no	—
794	#121	C₂×C₃×D₃	1	2	yes	—
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	—	3	2	no	—
802	C₄×Q₈	—	3	1	no	—
803	C₄×Q₈	—	3	1	no	—
804	C₄×D₄	—	3	1	no	—
805	C₄×D₄	—	3	2	no	—
806	C₄×D₄	—	3	1	no	—
807	C₄×D₄	—	3	2	no	—
808	C₄×D₄	—	3	2	no	—
809	C₄×D₄	—	3	2	no	—
810	C₄×D₄	—	3	2	no	—
811	C₄×D₄	—	3	2	no	—
812	C₄×D₄	—	3	2	no	—
813	C₄×D₄	—	3	2	no	—
814	#117	—	3	2	no	—
815	#117	—	3	2	no	—
816	#117	—	3	2	no	—
817	C₂×C₄²	—	3	2	no	—
818	C₂×C₄²	—	3	1	no	—
819	C₂³×C₃	—	2	2	no	—
820	C₂³×C₃	—	2	2	no	—
821	C₂³×C₃	—	3	2	no	—
822	C₂³×C₃	—	3	2	no	—
823	C₂³×C₃	—	3	1	no	—
824	C₂³×C₃	—	12	2	no	—
825	C₂³×C₃	—	12	2	no	—
826	C₂³×C₃	—	12	2	no	—
827	C₂³×C₃	C₂³×D₃	1	2	yes	—
828	C₂³×C₃	C₂³×D₃	1	2	yes	—
829	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
830	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
831	C₂²×D₃	—	4	2	no	—
832	C₂²×D₃	—	4	2	no	—
833	C₂²×D₃	—	4	2	no	—
834	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
835	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
836	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
837	C₃×Q₈	—	4	1	no	—
838	C₃×Q₈	—	4	1	no	—
839	C₃×Q₈	—	4	1	no	—
840	C₃×Q₈	—	4	1	no	—
841	C₃×Q₈	—	8	1	no	—
842	C₃×Q₈	—	8	1	no	—
843	C₃×Q₈	—	12	1	no	—
844	C₃×Q₈	—	12	2	no	—
845	C₃×Q₈	—	12	1	no	—
846	C₃×D₄	—	4	2	no	—
847	C₃×D₄	—	4	1	no	—
848	C₃×D₄	—	4	2	no	—
849	C₃×D₄	—	4	1	no	—
850	C₃×D₄	—	4	2	no	—
851	C₃×D₄	—	4	1	no	—
852	C₃×D₄	—	4	1	no	—
853	C₃×D₄	—	4	2	no	—
854	C₃×D₄	—	8	2	no	—
855	C₃×D₄	—	8	1	no	—
856	C₃×D₄	—	8	2	no	—
857	C₃×D₄	—	8	1	no	—
858	C₃×D₄	—	12	2	no	—
859	C₃×D₄	—	12	2	no	—
860	C₃×D₄	—	12	1	no	—
861	C₃×D₄	—	12	2	no	—
862	C₃×D₄	—	12	1	no	—
863	C₃×D₄	—	12	2	no	—
864	C₃×D₄	—	12	2	no	—
865	C₃×D₄	—	12	2	no	—
866	C₃×D₄	—	12	2	no	—
867	C₃×D₄	—	12	2	no	—
868	C₃×D₄	—	12	2	no	—
869	C₃×D₄	—	12	2	no	—
870	C₃×D₄	—	12	2	no	—
871	C₂×C₃×C₄	—	2	1	no	—
872	C₂×C₃×C₄	—	2	1	no	—
873	C₂×C₃×C₄	—	2	1	no	—
874	C₂×C₃×C₄	—	2	2	no	—
875	C₂×C₃×C₄	—	2	2	no	—
876	C₂×C₃×C₄	—	2	2	no	—
877	C₂×C₃×C₄	—	2	2	no	—
878	C₂×C₃×C₄	—	3	1	no	—
879	C₂×C₃×C₄	—	3	2	no	—
880	C₂×C₃×C₄	—	3	1	no	—
881	C₂×C₃×C₄	—	3	2	no	—
882	C₂×C₃×C₄	—	3	1	no	—
883	C₂×C₃×C₄	—	3	2	no	—
884	C₂×C₃×C₄	—	3	2	no	—
885	C₂×C₃×C₄	—	4	2	no	—
886	C₂×C₃×C₄	—	4	2	no	—
887	C₂×C₃×C₄	—	4	2	no	—
888	C₂×C₃×C₄	—	4	2	no	—
889	C₂×C₃×C₄	—	6	4	no	—
890	C₂×C₃×C₄	—	6	4	no	—
891	C₂×C₃×C₄	—	6	2	no	—
892	C₂×C₃×C₄	—	6	4	no	—
893	C₂×C₃×C₄	—	6	4	no	—
894	C₂×C₃×C₄	—	8	2	no	—
895	C₂×C₃×C₄	—	8	2	no	—
896	C₂×C₃×C₄	—	12	1	no	—
897	C₂×C₃×C₄	—	12	1	no	—
898	C₂×C₃×C₄	—	12	2	no	—
899	C₂×C₃×C₄	—	12	2	no	—
900	C₂×C₃×C₄	—	12	2	no	—
901	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
902	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
903	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
904	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
905	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
906	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
907	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
908	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
909	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
910	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
911	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
912	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
913	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
914	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
915	#67	—	4	2	no	—
916	#67	—	4	2	no	—
917	#67	—	4	2	no	—
918	#67	—	4	2	no	—
919	#67	—	4	2	no	—
920	#67	—	4	2	no	—
921	#67	—	4	2	no	—
922	#67	—	4	2	no	—
923	C₂×Dic₃	—	2	4	no	—
924	C₂×Dic₃	—	2	4	no	—
925	C₂×Dic₃	—	4	2	no	—
926	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
927	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
928	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
929	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
930	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
931	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
932	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
933	D₁₂	—	4	1	no	—
934	D₁₂	—	4	2	no	—
935	D₁₂	—	4	2	no	—
936	D₁₂	—	4	1	no	—
937	D₁₂	—	4	2	no	—
938	C₄×D₃	—	2	4	no	—
939	C₄×D₃	—	2	4	no	—
940	C₄×D₃	—	2	2	no	—
941	C₄×D₃	—	4	2	no	—
942	C₄×D₃	—	4	2	no	—
943	C₄×D₃	—	4	1	no	—
944	C₄×D₃	—	4	1	no	—
945	Dic₆	—	4	1	no	—
946	Dic₆	—	4	1	no	—
947	Dic₆	—	4	2	no	—
948	C₂×C₃²	—	4	2	no	—
949	C₂×C₃²	—	4	2	no	—
950	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
951	C₂×C₃²	#585	1	1	yes	characteristic
952	C₂×C₃²	#585	1	1	yes	characteristic
953	C₃×D₃	—	4	1	no	—
954	C₃×D₃	—	4	2	no	—
955	C₃×D₃	—	4	2	no	—
956	C₂⁴	—	3	2	no	—
957	#41	—	12	4	no	—
958	#41	—	12	2	no	—
959	#41	—	12	2	no	—
960	C₂×Q₈	—	3	1	no	—
961	C₂×Q₈	—	3	2	no	—
962	C₂×Q₈	—	3	1	no	—
963	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
964	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
965	C₂×D₄	—	3	2	no	—
966	C₂×D₄	—	3	2	no	—
967	C₂×D₄	—	3	2	no	—
968	C₂×D₄	—	3	2	no	—
969	C₂×D₄	—	3	2	no	—
970	C₂×D₄	—	3	2	no	—
971	C₂×D₄	—	3	2	no	—
972	C₂×D₄	—	3	2	no	—
973	C₂×D₄	—	3	2	no	—
974	C₂×D₄	—	3	1	no	—
975	C₂×D₄	—	3	2	no	—
976	C₂×D₄	—	3	1	no	—
977	C₂×D₄	—	3	2	no	—
978	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
979	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
980	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
981	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
982	C₂²×C₄	—	3	2	no	—
983	C₂²×C₄	—	3	2	no	—
984	C₂²×C₄	—	3	2	no	—
985	C₂²×C₄	—	3	1	no	—
986	C₂²×C₄	—	3	2	no	—
987	C₂²×C₄	—	3	2	no	—
988	C₂²×C₄	—	3	1	no	—
989	C₂²×C₄	—	3	1	no	—
990	C₂²×C₄	—	3	2	no	—
991	C₂²×C₄	—	3	2	no	—
992	C₂²×C₄	—	12	4	no	—
993	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
994	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
995	C₄⋊C₄	—	3	2	no	—
996	C₄⋊C₄	—	3	2	no	—
997	C₄⋊C₄	—	3	2	no	—
998	C₄⋊C₄	—	3	2	no	—
999	C₄⋊C₄	—	3	2	no	—
1000	C₄⋊C₄	—	3	2	no	—
1001	C₄⋊C₄	—	3	2	no	—
1002	C₄⋊C₄	—	3	2	no	—
1003	C₄⋊C₄	—	3	2	no	—
1004	C₄⋊C₄	—	3	2	no	—
1005	C₄⋊C₄	—	3	1	no	—
1006	C₄⋊C₄	—	3	2	no	—
1007	C₄⋊C₄	—	3	2	no	—
1008	C₄⋊C₄	—	3	1	no	—
1009	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1010	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1011	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1012	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1014	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1015	C₂²⋊C₄	—	3	2	no	—
1016	C₂²⋊C₄	—	3	2	no	—
1017	C₂²⋊C₄	—	3	2	no	—
1018	C₂²⋊C₄	—	3	2	no	—
1019	C₂²⋊C₄	—	3	2	no	—
1020	C₂²⋊C₄	—	3	2	no	—
1021	C₂²⋊C₄	—	3	2	no	—
1022	C₂²⋊C₄	—	3	2	no	—
1023	C₂²⋊C₄	—	3	2	no	—
1024	C₂²⋊C₄	—	3	2	no	—
1025	C₂²⋊C₄	—	3	2	no	—
1026	C₂²⋊C₄	—	3	2	no	—
1027	C₂²⋊C₄	—	3	2	no	—
1028	C₂²⋊C₄	—	3	2	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	C₂²×C₃×D₃	1	2	yes	—
1034	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1035	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1036	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1037	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1038	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1039	C₄²	—	3	2	no	—
1040	C₄²	—	3	2	no	—
1041	C₄²	—	3	1	no	—
1042	C₄²	—	3	1	no	—
1043	C₄²	—	3	2	no	—
1044	C₄²	—	3	1	no	—
1045	C₄²	—	3	2	no	—
1046	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1047	C₂²×C₃	—	2	2	no	—
1048	C₂²×C₃	—	2	2	no	—
1049	C₂²×C₃	—	2	2	no	—
1050	C₂²×C₃	—	2	2	no	—
1051	C₂²×C₃	—	2	2	no	—
1052	C₂²×C₃	—	2	2	no	—
1053	C₂²×C₃	—	2	2	no	—
1054	C₂²×C₃	—	2	2	no	—
1055	C₂²×C₃	—	2	2	no	—
1056	C₂²×C₃	—	2	2	no	—
1057	C₂²×C₃	—	2	2	no	—
1058	C₂²×C₃	—	2	2	no	—
1059	C₂²×C₃	—	2	1	no	—
1060	C₂²×C₃	—	4	2	no	—
1061	C₂²×C₃	—	4	2	no	—
1062	C₂²×C₃	—	4	2	no	—
1063	C₂²×C₃	—	4	2	no	—
1064	C₂²×C₃	—	4	2	no	—
1065	C₂²×C₃	—	4	2	no	—
1066	C₂²×C₃	—	6	2	no	—
1067	C₂²×C₃	—	6	2	no	—
1068	C₂²×C₃	—	6	1	no	—
1069	C₂²×C₃	—	6	1	no	—
1070	C₂²×C₃	—	6	2	no	—
1071	C₂²×C₃	—	6	2	no	—
1072	C₂²×C₃	—	6	1	no	—
1073	C₂²×C₃	—	6	2	no	—
1074	C₂²×C₃	—	6	2	no	—
1075	C₂²×C₃	—	12	8	no	—
1076	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1077	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1078	C₂×D₃	—	2	2	no	—
1079	C₂×D₃	—	2	2	no	—
1080	C₂×D₃	—	2	1	no	—
1081	C₂×D₃	—	2	1	no	—
1082	C₂×D₃	—	2	1	no	—
1083	C₂×D₃	—	2	2	no	—
1084	C₂×D₃	—	2	2	no	—
1085	C₂×D₃	—	2	2	no	—
1086	C₂×D₃	—	2	2	no	—
1087	C₂×D₃	—	4	8	no	—
1088	C₃×C₄	—	2	2	no	—
1089	C₃×C₄	—	2	2	no	—
1090	C₃×C₄	—	2	1	no	—
1091	C₃×C₄	—	2	2	no	—
1092	C₃×C₄	—	2	2	no	—
1093	C₃×C₄	—	2	1	no	—
1094	C₃×C₄	—	2	1	no	—
1095	C₃×C₄	—	2	2	no	—
1096	C₃×C₄	—	2	1	no	—
1097	C₃×C₄	—	2	2	no	—
1098	C₃×C₄	—	2	1	no	—
1099	C₃×C₄	—	2	1	no	—
1100	C₃×C₄	—	2	2	no	—
1101	C₃×C₄	—	2	2	no	—
1102	C₃×C₄	—	3	2	no	—
1103	C₃×C₄	—	4	2	no	—
1104	C₃×C₄	—	4	2	no	—
1105	C₃×C₄	—	4	2	no	—
1106	C₃×C₄	—	4	2	no	—
1107	C₃×C₄	—	4	1	no	—
1108	C₃×C₄	—	4	1	no	—
1109	C₃×C₄	—	4	1	no	—
1110	C₃×C₄	—	6	2	no	—
1111	C₃×C₄	—	6	2	no	—
1112	C₃×C₄	—	6	1	no	—
1113	C₃×C₄	—	6	1	no	—
1114	C₃×C₄	—	6	2	no	—
1115	C₃×C₄	—	6	2	no	—
1116	Dic₃	—	2	2	no	—
1117	Dic₃	—	2	2	no	—
1118	Dic₃	—	2	2	no	—
1119	Dic₃	—	2	1	no	—
1120	Dic₃	—	2	1	no	—
1121	Dic₃	—	2	2	no	—
1122	Dic₃	C₃×H(5,𝔽₂)	1	2	yes	—
1123	C₃²	#3529	1	1	yes	characteristic, complemented, Sylow
1124	C₂³	—	3	2	no	—
1125	C₂³	—	3	2	no	—
1126	C₂³	—	3	1	no	—
1127	C₂³	—	12	2	no	—
1128	C₂³	—	12	2	no	—
1129	C₂³	—	12	2	no	—
1130	C₂³	C₂³×C₃×D₃	1	2	yes	—
1131	C₂³	C₂³×C₃×D₃	1	2	yes	—
1132	Q₈	—	4	1	no	—
1133	Q₈	—	4	1	no	—
1134	Q₈	—	12	2	no	—
1135	Q₈	—	12	1	no	—
1136	Q₈	—	12	1	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	1	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	1	no	—
1141	D₄	—	12	2	no	—
1142	D₄	—	12	1	no	—
1143	D₄	—	12	2	no	—
1144	D₄	—	12	2	no	—
1145	D₄	—	12	1	no	—
1146	D₄	—	12	2	no	—
1147	D₄	—	12	2	no	—
1148	D₄	—	12	2	no	—
1149	D₄	—	12	2	no	—
1150	D₄	—	12	2	no	—
1151	D₄	—	12	2	no	—
1152	D₄	—	12	2	no	—
1153	D₄	—	12	2	no	—
1154	C₂×C₄	—	3	1	no	—
1155	C₂×C₄	—	3	2	no	—
1156	C₂×C₄	—	3	1	no	—
1157	C₂×C₄	—	3	2	no	—
1158	C₂×C₄	—	3	1	no	—
1159	C₂×C₄	—	3	2	no	—
1160	C₂×C₄	—	3	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	6	4	no	—
1164	C₂×C₄	—	6	4	no	—
1165	C₂×C₄	—	6	2	no	—
1166	C₂×C₄	—	6	4	no	—
1167	C₂×C₄	—	6	4	no	—
1168	C₂×C₄	—	12	2	no	—
1169	C₂×C₄	—	12	2	no	—
1170	C₂×C₄	—	12	1	no	—
1171	C₂×C₄	—	12	1	no	—
1172	C₂×C₄	—	12	2	no	—
1173	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1174	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1175	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1176	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1177	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1178	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1179	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1180	C₂×C₃	—	2	1	no	—
1181	C₂×C₃	—	2	1	no	—
1182	C₂×C₃	—	2	1	no	—
1183	C₂×C₃	—	4	2	no	—
1184	C₂×C₃	—	4	2	no	—
1185	C₂×C₃	—	4	2	no	—
1186	C₂×C₃	—	4	2	no	—
1187	C₂×C₃	—	8	2	no	—
1188	C₂×C₃	—	8	2	no	—
1189	C₂×C₃	—	12	2	no	—
1190	C₂×C₃	—	12	2	no	—
1191	C₂×C₃	—	12	1	no	—
1192	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1193	C₂×C₃	#5966	1	1	yes	characteristic
1194	C₂×C₃	#5968	1	1	yes	characteristic
1195	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1196	C₂×C₃	C₃×#585	1	1	yes	characteristic
1197	C₂×C₃	C₃×#585	1	1	yes	characteristic
1198	D₃	—	4	2	no	—
1199	D₃	—	4	2	no	—
1200	D₃	—	4	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	6	2	no	—
1208	C₂²	—	6	2	no	—
1209	C₂²	—	6	1	no	—
1210	C₂²	—	6	1	no	—
1211	C₂²	—	6	2	no	—
1212	C₂²	—	6	2	no	—
1213	C₂²	—	6	1	no	—
1214	C₂²	—	6	2	no	—
1215	C₂²	—	6	2	no	—
1216	C₂²	—	12	8	no	—
1217	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	3	2	no	—
1226	C₄	—	6	2	no	—
1227	C₄	—	6	2	no	—
1228	C₄	—	6	1	no	—
1229	C₄	—	6	1	no	—
1230	C₄	—	6	2	no	—
1231	C₄	—	6	2	no	—
1232	C₃	—	2	1	no	—
1233	C₃	#87093	1	1	yes	characteristic, direct product factor
1234	C₃	C₃×#3529	1	1	yes	characteristic, complemented
1235	C₂	—	4	2	no	—
1236	C₂	—	4	2	no	—
1237	C₂	—	12	2	no	—
1238	C₂	—	12	2	no	—
1239	C₂	—	12	1	no	—
1240	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	C₃×#5966	1	1	yes	characteristic
1242	C₂	C₃×#5968	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×#562	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#562	D₃
hypocenter	C₃	C₃×#3529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#562

Complements

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

N	H ≅ G/N	type
1. C₃²×#562	C₂	semidirect
2. C₃×#5699	C₂	semidirect
3. C₃×#5691	C₂	semidirect
4. C₃×#5684	C₂	semidirect
5. C₃×#5683	C₂	semidirect
6. C₃×#5680	C₂	semidirect
7. C₃×#5668	C₂	semidirect
8. C₃×#5667	C₂	semidirect
9. C₃×#5666	C₂	semidirect
10. C₃×#5656	C₂	semidirect
11. C₃×#5649	C₂	semidirect
12. C₃×#5647	C₂	semidirect
13. C₃×#5646	C₂	semidirect
14. C₃×#5627	C₂	semidirect
15. C₃×#5624	C₂	semidirect
16. C₃×#5620	C₂	semidirect
17. C₃×#5620	C₂	semidirect
18. C₃×#5606	C₂	semidirect
19. C₃×#5596	C₂	semidirect
21. #87093	C₃	direct (N × H)
24. C₂×C₃×#237	C₂²	semidirect
25. C₂²×C₃×C₄×D₃	C₂²	semidirect
26. C₃²×#125	C₂²	semidirect
28. C₃²×#124	C₂²	semidirect
29. C₃²×#123	C₂²	semidirect
30. C₃²×#123	C₂²	semidirect
31. C₃²×C₂²⋊Q₈	C₂²	semidirect
32. C₃²×C₂²⋊Q₈	C₂²	semidirect
34. C₃²×#121	C₂²	semidirect
36. C₃×#946	C₂²	semidirect
37. C₃×#946	C₂²	semidirect
38. C₃×Q₈×Dic₃	C₂²	semidirect
39. C₃×#944	C₂²	semidirect
43. C₃×#939	C₂²	semidirect
44. C₃×#939	C₂²	semidirect
48. C₃×#937	C₂²	semidirect
49. C₃×#937	C₂²	semidirect
51. C₃×D₄×Dic₃	C₂²	semidirect
54. C₃×#930	C₂²	semidirect
56. C₃×#929	C₂²	semidirect
57. C₃×#924	C₂²	semidirect
58. C₂×C₃×C₄×Dic₃	C₂²	semidirect
59. C₃×#898	C₂²	semidirect
60. C₃×#898	C₂²	semidirect
61. C₃×#898	C₂²	semidirect
62. C₃×#898	C₂²	semidirect
63. C₃×#897	C₂²	semidirect
64. C₃×#897	C₂²	semidirect
65. C₃×#896	C₂²	semidirect
66. C₃×#896	C₂²	semidirect
70. C₃×#894	C₂²	semidirect
71. C₃×#894	C₂²	semidirect
74. C₃×#893	C₂²	semidirect
75. C₃×#892	C₂²	semidirect
76. C₃×#892	C₂²	semidirect
77. C₃×#890	C₂²	semidirect
78. C₃×#889	C₂²	semidirect
79. C₃×#888	C₂²	semidirect
80. C₃×#887	C₂²	semidirect
81. C₃×#886	C₂²	semidirect
82. C₃×#886	C₂²	semidirect
85. C₃×#885	C₂²	semidirect
88. C₃×#884	C₂²	semidirect
89. C₃×#884	C₂²	semidirect
91. C₃×#883	C₂²	semidirect
92. C₃×#883	C₂²	semidirect
95. C₃×#882	C₂²	semidirect
97. C₃×#67⋊C₄	C₂²	semidirect
98. C₃×#67⋊C₄	C₂²	semidirect
99. C₃×#67⋊C₄	C₂²	semidirect
100. C₃×#67⋊C₄	C₂²	semidirect
101. C₃×#879	C₂²	semidirect
102. C₃×#879	C₂²	semidirect
103. C₃×#878	C₂²	semidirect
104. C₃×#877	C₂²	semidirect
107. C₃×C₄²×D₃	C₂²	semidirect
108. C₃×#870	C₂²	semidirect
115. C₃×#562	D₃	semidirect
116. C₃×#562	C₂×C₃	semidirect
130. #5699	C₂×C₃	semidirect
131. #5691	C₂×C₃	semidirect
132. #5684	C₂×C₃	semidirect
133. #5683	C₂×C₃	semidirect
134. #5680	C₂×C₃	semidirect
135. #5668	C₂×C₃	semidirect
136. #5667	C₂×C₃	semidirect
137. #5666	C₂×C₃	semidirect
138. #5656	C₂×C₃	semidirect
139. #5649	C₂×C₃	semidirect
140. #5647	C₂×C₃	semidirect
141. #5646	C₂×C₃	semidirect
142. #5627	C₂×C₃	semidirect
143. #5624	C₂×C₃	semidirect
144. #5620	C₂×C₃	semidirect
145. #5620	C₂×C₃	semidirect
146. #5606	C₂×C₃	semidirect
147. #5596	C₂×C₃	semidirect
246. C₂×#237	C₂²×C₃	semidirect
247. C₂²×C₄×D₃	C₂²×C₃	semidirect
262. C₃×#125	C₂×D₃	semidirect
263. C₃×#125	C₂²×C₃	semidirect
273. C₃×#124	C₂×D₃	semidirect
275. C₃×#124	C₂²×C₃	semidirect
288. C₃×#123	C₂×D₃	semidirect
289. C₃×#123	C₂×D₃	semidirect
290. C₃×#123	C₂²×C₃	semidirect
291. C₃×#123	C₂²×C₃	semidirect
302. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
303. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
304. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
305. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
323. C₃×#121	C₂×D₃	semidirect
325. C₃×#121	C₂²×C₃	semidirect
350. #946	C₂²×C₃	semidirect
351. #946	C₂²×C₃	semidirect
352. Q₈×Dic₃	C₂²×C₃	semidirect
353. #944	C₂²×C₃	semidirect
357. #939	C₂²×C₃	semidirect
358. #939	C₂²×C₃	semidirect
362. #937	C₂²×C₃	semidirect
363. #937	C₂²×C₃	semidirect
365. D₄×Dic₃	C₂²×C₃	semidirect
368. #930	C₂²×C₃	semidirect
370. #929	C₂²×C₃	semidirect
371. #924	C₂²×C₃	semidirect
372. C₂×C₄×Dic₃	C₂²×C₃	semidirect
373. #898	C₂²×C₃	semidirect
374. #898	C₂²×C₃	semidirect
375. #898	C₂²×C₃	semidirect
376. #898	C₂²×C₃	semidirect
377. #897	C₂²×C₃	semidirect
378. #897	C₂²×C₃	semidirect
379. #896	C₂²×C₃	semidirect
380. #896	C₂²×C₃	semidirect
384. #894	C₂²×C₃	semidirect
385. #894	C₂²×C₃	semidirect
388. #893	C₂²×C₃	semidirect
389. #892	C₂²×C₃	semidirect
390. #892	C₂²×C₃	semidirect
391. #890	C₂²×C₃	semidirect
392. #889	C₂²×C₃	semidirect
393. #888	C₂²×C₃	semidirect
394. #887	C₂²×C₃	semidirect
395. #886	C₂²×C₃	semidirect
396. #886	C₂²×C₃	semidirect
399. #885	C₂²×C₃	semidirect
402. #884	C₂²×C₃	semidirect
403. #884	C₂²×C₃	semidirect
405. #883	C₂²×C₃	semidirect
406. #883	C₂²×C₃	semidirect
409. #882	C₂²×C₃	semidirect
411. #67⋊C₄	C₂²×C₃	semidirect
412. #67⋊C₄	C₂²×C₃	semidirect
413. #67⋊C₄	C₂²×C₃	semidirect
414. #67⋊C₄	C₂²×C₃	semidirect
415. #879	C₂²×C₃	semidirect
416. #879	C₂²×C₃	semidirect
417. #878	C₂²×C₃	semidirect
418. #877	C₂²×C₃	semidirect
421. C₄²×D₃	C₂²×C₃	semidirect
422. #870	C₂²×C₃	semidirect
484. #562	C₃×D₃	semidirect
749. #125	C₂×C₃×D₃	semidirect
757. #124	C₂×C₃×D₃	semidirect
768. #123	C₂×C₃×D₃	semidirect
769. #123	C₂×C₃×D₃	semidirect
778. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
779. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
795. #121	C₂×C₃×D₃	semidirect
1123. C₃²	#3529	semidirect
1233. C₃	#87093	direct (N × H)
1234. C₃	C₃×#3529	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#562	2
C₃×#5699	2
C₃×#5691	2
C₃×#5684	2
C₃×#5683	2
C₃×#5680	2
C₃×#5668	2
C₃×#5667	2
C₃×#5666	2
C₃×#5656	2
C₃×#5649	2
C₃×#5647	2
C₃×#5646	2
C₃×#5627	2
C₃×#5624	2
C₃×#5620	2
C₃×#5606	2
C₃×#5596	2
C₃×#3529	3
#87093	3

Subgroups — C3×#87093 #11910352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87093 #11910352