Subgroups — C₃×#86276 #11903481

Order 1152.

2375 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5732	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5730	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5726	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5695	C₂	1	2	yes	maximal, complemented
7	C₃×#5694	C₂	1	2	yes	maximal, complemented
8	C₃×#5642	C₂	1	2	yes	maximal, complemented
9	C₃×#5637	C₂	1	4	yes	maximal, complemented
10	C₃×#5630	C₂	1	2	yes	maximal, complemented
11	C₃×#5580	C₂	1	4	yes	maximal, complemented
12	C₃×#5580	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#239	C₂	1	2	yes	maximal, complemented
14	C₃×#5524	C₂	1	2	yes	maximal, complemented
15	C₃×D₃×#117	C₂	1	2	yes	maximal, complemented
16	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3475	—	3	1	no	maximal
19	#86276	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×#239	C₂²	1	2	yes	—
21	C₂×C₃×#235	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#125	C₂²	1	2	yes	complemented
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
30	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
31	C₃²×#117	C₂²	1	2	yes	—
32	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
33	C₃×#947	C₂²	1	2	yes	—
34	C₃×#947	C₂²	1	4	yes	complemented
35	C₃×#946	C₂²	1	4	yes	complemented
36	C₃×#946	C₂²	1	2	yes	complemented
37	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
38	C₃×C₄×#67	C₂²	1	2	yes	—
39	C₃×C₄×#67	C₂²	1	2	yes	—
40	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
41	C₃×#926	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
43	C₃×#898	C₂²	1	4	yes	complemented
44	C₃×#898	C₂²	1	4	yes	complemented
45	C₃×#898	C₂²	1	4	yes	complemented
46	C₃×#897	C₂²	1	2	yes	complemented
47	C₃×#897	C₂²	1	2	yes	complemented
48	C₃×#895	C₂²	1	4	yes	—
49	C₃×#895	C₂²	1	2	yes	—
50	C₃×#895	C₂²	1	2	yes	complemented
51	C₃×#895	C₂²	1	2	yes	complemented
52	C₃×#894	C₂²	1	4	yes	—
53	C₃×#894	C₂²	1	4	yes	complemented
54	C₃×#894	C₂²	1	4	yes	complemented
55	C₃×#893	C₂²	1	2	yes	—
56	C₃×#893	C₂²	1	4	yes	complemented
57	C₃×#892	C₂²	1	2	yes	complemented
58	C₃×#892	C₂²	1	2	yes	complemented
59	C₃×#892	C₂²	1	4	yes	complemented
60	C₃×#892	C₂²	1	2	yes	complemented
61	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
62	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₃×#890	C₂²	1	4	yes	complemented
64	C₃×#890	C₂²	1	2	yes	complemented
65	C₃×#886	C₂²	1	4	yes	—
66	C₃×#882	C₂²	1	4	yes	—
67	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₃×#877	C₂²	1	4	yes	—
69	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
70	C₃×C₄×D₁₂	C₂²	1	2	yes	—
71	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
72	C₃×C₄×D₁₂	C₂²	1	2	yes	—
73	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
74	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
75	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
76	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
77	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
78	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
79	C₃×#872	C₂²	1	4	yes	complemented
80	C₃×#872	C₂²	1	2	yes	complemented
81	C₃×C₄²×D₃	C₂²	1	4	yes	complemented
82	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
85	C₃×#556	—	3	1	no	—
86	C₃×#555	—	3	1	no	—
87	C₃×#554	—	3	1	no	—
88	C₃×#553	—	3	2	no	—
89	C₃×#552	—	3	2	no	—
90	C₃×#552	—	3	2	no	—
91	C₃×#551	—	3	4	no	—
92	C₃×#547	—	3	1	no	—
93	C₃×#546	—	3	2	no	—
94	C₃×#533	—	2	1	no	—
95	C₃×#533	D₃	1	1	yes	characteristic, complemented
96	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
97	C₃×#529	—	3	4	no	—
98	C₃×#529	—	3	2	no	—
99	C₃×#525	—	3	2	no	—
100	C₃×C₄×#41	—	3	2	no	—
101	C₃×C₄×#41	—	3	1	no	—
102	C₂×C₃×C₄×D₄	—	3	1	no	—
103	C₂×C₃×#117	—	3	2	no	—
104	#5734	C₂×C₃	1	1	yes	characteristic, complemented
105	#5732	C₂×C₃	1	1	yes	characteristic, complemented
106	#5730	C₂×C₃	1	1	yes	characteristic, complemented
107	#5726	C₂×C₃	1	1	yes	characteristic, complemented
108	#5695	C₂×C₃	1	2	yes	complemented
109	#5694	C₂×C₃	1	2	yes	complemented
110	#5642	C₂×C₃	1	2	yes	complemented
111	#5637	C₂×C₃	1	4	yes	complemented
112	#5630	C₂×C₃	1	2	yes	complemented
113	#5580	C₂×C₃	1	4	yes	complemented
114	#5580	C₂×C₃	1	2	yes	complemented
115	C₄×#239	C₂×C₃	1	2	yes	complemented
116	#5524	C₂×C₃	1	2	yes	complemented
117	D₃×#117	C₂×C₃	1	2	yes	complemented
118	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
119	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₂×C₃²×Q₈	C₂³	1	2	yes	—
122	C₂×C₃²×Q₈	C₂³	1	2	yes	—
123	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
124	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
126	C₂×C₃×#67	C₂³	1	2	yes	—
127	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
128	C₃×#239	—	2	8	no	—
129	C₃×#235	—	2	4	no	—
130	C₂×C₃×D₁₂	—	2	4	no	—
131	C₂×C₃×D₁₂	C₂³	1	4	yes	—
132	C₂×C₃×D₁₂	C₂³	1	2	yes	—
133	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
134	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
135	C₂×C₃×D₁₂	C₂³	1	4	yes	—
136	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄×D₃	—	2	8	no	—
138	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
139	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
140	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
141	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
145	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
146	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
147	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
153	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃²×C₄²	C₂³	1	1	yes	characteristic
156	C₃²×C₄²	C₂³	1	1	yes	characteristic
157	C₃²×C₄²	C₂³	1	1	yes	characteristic
158	C₃²×C₄²	C₂³	1	1	yes	characteristic
159	C₃²×C₄²	C₂³	1	4	yes	—
160	C₃×#217	C₂³	1	2	yes	—
161	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
166	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
167	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
168	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
169	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
170	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
171	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
172	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
174	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
175	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
176	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
177	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
180	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
183	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
184	C₃×C₄×Dic₃	C₂³	1	4	yes	—
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	2	yes	—
187	C₃×C₄×Dic₃	C₂³	1	2	yes	—
188	C₃×C₄×Dic₃	C₂³	1	2	yes	—
189	#3475	—	3	1	no	Sylow
190	C₂×C₃×#41	—	3	2	no	—
191	C₂×C₃×#41	—	3	1	no	—
192	C₂²×C₃×D₄	—	3	1	no	—
193	C₂³×C₃×C₄	—	3	2	no	—
194	C₂×#239	C₂²×C₃	1	2	yes	—
195	C₂×#235	C₂²×C₃	1	1	yes	characteristic
196	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
197	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
198	C₃×C₄⋊Q₈	—	2	1	no	—
199	C₃×C₄⋊Q₈	—	2	1	no	—
200	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
201	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
202	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₃×#126	—	3	4	no	—
205	C₃×#126	—	3	4	no	—
206	C₃×#126	—	3	4	no	—
207	C₃×#125	—	2	2	no	—
208	C₃×#125	—	3	4	no	—
209	C₃×#125	—	3	2	no	—
210	C₃×#125	C₂×D₃	1	2	yes	complemented
211	C₃×#125	C₂²×C₃	1	2	yes	complemented
212	C₃×#124	—	3	2	no	—
213	C₃×#124	—	3	4	no	—
214	C₃×#123	—	3	4	no	—
215	C₃×#123	—	3	4	no	—
216	C₃×#123	—	3	4	no	—
217	C₃×#123	—	3	4	no	—
218	C₃×C₂²⋊Q₈	—	2	2	no	—
219	C₃×C₂²⋊Q₈	—	2	2	no	—
220	C₃×C₂²⋊Q₈	—	3	2	no	—
221	C₃×C₂²⋊Q₈	—	3	4	no	—
222	C₃×C₂²⋊Q₈	—	3	2	no	—
223	C₃×C₂²⋊Q₈	—	3	2	no	—
224	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
225	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
226	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
227	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
228	C₃×#121	—	3	4	no	—
229	C₃×#121	—	3	2	no	—
230	C₃×#121	—	3	2	no	—
231	C₃×#121	—	3	2	no	—
232	C₃×#120	—	3	4	no	—
233	C₃×C₄×Q₈	—	2	2	no	—
234	C₃×C₄×Q₈	—	2	2	no	—
235	C₃×C₄×Q₈	—	3	2	no	—
236	C₃×C₄×Q₈	—	3	1	no	—
237	C₃×C₄×Q₈	—	3	1	no	—
238	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
239	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
240	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
241	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
242	C₃×C₄×D₄	—	3	2	no	—
243	C₃×C₄×D₄	—	3	2	no	—
244	C₃×C₄×D₄	—	3	2	no	—
245	C₃×C₄×D₄	—	3	4	no	—
246	C₃×C₄×D₄	—	3	1	no	—
247	C₃×C₄×D₄	—	3	1	no	—
248	C₃×C₄×D₄	—	3	2	no	—
249	C₃×C₄×D₄	—	3	1	no	—
250	C₃×C₄×D₄	—	3	2	no	—
251	C₃×C₄×D₄	—	3	1	no	—
252	C₃×C₄×D₄	—	3	4	no	—
253	C₃×C₄×D₄	—	3	1	no	—
254	C₃×C₄×D₄	—	3	1	no	—
255	C₃×C₄×D₄	—	3	4	no	—
256	C₃×#117	—	2	2	no	—
257	C₃×#117	—	3	1	no	—
258	C₃×#117	—	3	2	no	—
259	C₃×#117	—	3	2	no	—
260	C₃×#117	—	3	4	no	—
261	C₃×#117	—	3	2	no	—
262	C₃×#117	—	3	4	no	—
263	C₃×#117	—	3	4	no	—
264	C₃×#117	—	3	2	no	—
265	C₃×#117	C₂×D₃	1	2	yes	—
266	C₃×#117	C₂²×C₃	1	2	yes	—
267	C₂×C₃×C₄⋊C₄	—	3	1	no	—
268	C₂×C₃×C₄⋊C₄	—	3	2	no	—
269	C₂×C₃×C₄⋊C₄	—	3	2	no	—
270	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
272	C₂×C₃×C₄²	—	2	1	no	—
273	C₂×C₃×C₄²	—	3	4	no	—
274	C₂×C₃×C₄²	—	3	2	no	—
275	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
276	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
277	#947	C₂²×C₃	1	2	yes	—
278	#947	C₂²×C₃	1	4	yes	complemented
279	#946	C₂²×C₃	1	4	yes	complemented
280	#946	C₂²×C₃	1	2	yes	complemented
281	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
282	C₄×#67	C₂²×C₃	1	2	yes	—
283	C₄×#67	C₂²×C₃	1	2	yes	—
284	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
285	#926	C₂²×C₃	1	1	yes	characteristic
286	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
287	#898	C₂²×C₃	1	4	yes	complemented
288	#898	C₂²×C₃	1	4	yes	complemented
289	#898	C₂²×C₃	1	4	yes	complemented
290	#897	C₂²×C₃	1	2	yes	complemented
291	#897	C₂²×C₃	1	2	yes	complemented
292	#895	C₂²×C₃	1	4	yes	—
293	#895	C₂²×C₃	1	2	yes	—
294	#895	C₂²×C₃	1	2	yes	complemented
295	#895	C₂²×C₃	1	2	yes	complemented
296	#894	C₂²×C₃	1	4	yes	—
297	#894	C₂²×C₃	1	4	yes	complemented
298	#894	C₂²×C₃	1	4	yes	complemented
299	#893	C₂²×C₃	1	2	yes	—
300	#893	C₂²×C₃	1	4	yes	complemented
301	#892	C₂²×C₃	1	4	yes	complemented
302	#892	C₂²×C₃	1	2	yes	complemented
303	#892	C₂²×C₃	1	2	yes	complemented
304	#892	C₂²×C₃	1	2	yes	complemented
305	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
306	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
307	#890	C₂²×C₃	1	4	yes	complemented
308	#890	C₂²×C₃	1	2	yes	complemented
309	#886	C₂²×C₃	1	4	yes	—
310	#882	C₂²×C₃	1	4	yes	—
311	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
312	#877	C₂²×C₃	1	4	yes	—
313	C₄×D₁₂	C₂²×C₃	1	2	yes	—
314	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
315	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
316	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
317	C₄×D₁₂	C₂²×C₃	1	2	yes	—
318	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
319	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
320	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
321	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
322	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
323	#872	C₂²×C₃	1	2	yes	complemented
324	#872	C₂²×C₃	1	4	yes	complemented
325	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
326	C₄²×D₃	C₂²×C₃	1	4	yes	complemented
327	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
329	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×D₃	—	2	4	no	—
331	C₂²×C₃×D₃	—	2	4	no	—
332	C₂²×C₃×D₃	—	4	2	no	—
333	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
334	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
335	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
336	C₃²×Q₈	—	2	4	no	—
337	C₃²×Q₈	—	4	2	no	—
338	C₂×C₃²×C₄	—	2	2	no	—
339	C₂×C₃²×C₄	—	4	1	no	—
340	C₂×C₃²×C₄	#41	1	4	yes	complemented
341	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
342	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
344	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
345	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
346	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
347	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
348	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
349	C₃×#67	—	2	4	no	—
350	C₂×C₃×Dic₃	—	2	4	no	—
351	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
353	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
354	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
355	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
356	C₃×D₁₂	—	2	4	no	—
357	C₃×D₁₂	—	2	8	no	—
358	C₃×D₁₂	—	2	2	no	—
359	C₃×D₁₂	—	2	2	no	—
360	C₃×D₁₂	—	4	4	no	—
361	C₃×D₁₂	#41	1	4	yes	complemented
362	C₃×C₄×D₃	—	2	8	no	—
363	C₃×C₄×D₃	—	2	4	no	—
364	C₃×C₄×D₃	—	2	4	no	—
365	C₃×C₄×D₃	—	2	4	no	—
366	C₃×C₄×D₃	—	2	4	no	—
367	C₃×C₄×D₃	—	2	4	no	—
368	C₃×C₄×D₃	—	2	4	no	—
369	C₃×C₄×D₃	—	4	2	no	—
370	C₃×C₄×D₃	—	4	4	no	—
371	C₃×Dic₆	—	2	2	no	—
372	#556	—	3	1	no	—
373	#555	—	3	1	no	—
374	#554	—	3	1	no	—
375	#553	—	3	2	no	—
376	#552	—	3	2	no	—
377	#552	—	3	2	no	—
378	#551	—	3	4	no	—
379	#547	—	3	1	no	—
380	#546	—	3	2	no	—
381	#533	C₃×D₃	1	1	yes	characteristic, complemented
382	#529	—	3	4	no	—
383	#529	—	3	2	no	—
384	#525	—	3	2	no	—
385	C₄×#41	—	3	2	no	—
386	C₄×#41	—	3	1	no	—
387	C₂×C₄×D₄	—	3	1	no	—
388	C₂×#117	—	3	2	no	—
389	C₂⁴×C₃	—	3	2	no	—
390	C₂³×D₃	C₂³×C₃	1	2	yes	—
391	C₃×#41	—	6	8	no	—
392	C₃×#41	—	6	4	no	—
393	C₂×C₃×Q₈	—	2	2	no	—
394	C₂×C₃×Q₈	—	2	2	no	—
395	C₂×C₃×Q₈	—	3	1	no	—
396	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
397	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
398	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
399	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
400	C₂×C₃×D₄	—	3	2	no	—
401	C₂×C₃×D₄	—	3	1	no	—
402	C₂×C₃×D₄	—	3	4	no	—
403	C₂×C₃×D₄	—	3	1	no	—
404	C₂×C₃×D₄	—	3	2	no	—
405	C₂×C₃×D₄	—	3	1	no	—
406	C₂×C₃×D₄	—	3	4	no	—
407	C₂×C₃×D₄	—	6	4	no	—
408	C₂²×C₃×C₄	—	2	1	no	—
409	C₂²×C₃×C₄	—	2	1	no	—
410	C₂²×C₃×C₄	—	2	1	no	—
411	C₂²×C₃×C₄	—	3	2	no	—
412	C₂²×C₃×C₄	—	3	4	no	—
413	C₂²×C₃×C₄	—	3	2	no	—
414	C₂²×C₃×C₄	—	3	2	no	—
415	C₂²×C₃×C₄	—	3	2	no	—
416	C₂²×C₃×C₄	—	3	2	no	—
417	C₂²×C₃×C₄	—	3	2	no	—
418	C₂²×C₃×C₄	—	3	2	no	—
419	C₂²×C₃×C₄	—	3	4	no	—
420	C₂²×C₃×C₄	—	3	2	no	—
421	C₂²×C₃×C₄	—	6	8	no	—
422	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
428	C₂×#67	C₂³×C₃	1	2	yes	—
429	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
430	#239	—	2	8	no	—
431	#235	—	2	4	no	—
432	C₂×D₁₂	—	2	4	no	—
433	C₂×D₁₂	C₂³×C₃	1	2	yes	—
434	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
435	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
436	C₂×D₁₂	C₂³×C₃	1	4	yes	—
437	C₂×D₁₂	C₂³×C₃	1	4	yes	—
438	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
439	C₂×C₄×D₃	—	2	8	no	—
440	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
441	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
442	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
443	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
444	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
445	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
446	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
447	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
448	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
449	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	4	no	—
453	C₃×C₄⋊C₄	—	2	4	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	2	no	—
456	C₃×C₄⋊C₄	—	3	4	no	—
457	C₃×C₄⋊C₄	—	3	4	no	—
458	C₃×C₄⋊C₄	—	3	2	no	—
459	C₃×C₄⋊C₄	—	3	2	no	—
460	C₃×C₄⋊C₄	—	3	1	no	—
461	C₃×C₄⋊C₄	—	3	1	no	—
462	C₃×C₄⋊C₄	—	3	1	no	—
463	C₃×C₄⋊C₄	—	3	1	no	—
464	C₃×C₄⋊C₄	—	3	2	no	—
465	C₃×C₄⋊C₄	—	3	4	no	—
466	C₃×C₄⋊C₄	—	3	4	no	—
467	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
468	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
469	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
470	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
471	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
472	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
473	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
474	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
475	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
478	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₃×C₂²⋊C₄	—	2	4	no	—
480	C₃×C₂²⋊C₄	—	3	2	no	—
481	C₃×C₂²⋊C₄	—	3	2	no	—
482	C₃×C₂²⋊C₄	—	3	4	no	—
483	C₃×C₂²⋊C₄	—	3	4	no	—
484	C₃×C₂²⋊C₄	—	3	2	no	—
485	C₃×C₂²⋊C₄	—	3	2	no	—
486	C₃×C₂²⋊C₄	—	3	2	no	—
487	C₃×C₂²⋊C₄	—	3	4	no	—
488	C₃×C₂²⋊C₄	—	3	2	no	—
489	C₃×C₂²⋊C₄	—	3	4	no	—
490	C₃×C₂²⋊C₄	—	3	2	no	—
491	C₃×C₂²⋊C₄	—	3	4	no	—
492	C₃×C₂²⋊C₄	—	3	4	no	—
493	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
494	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
495	C₃×C₄²	—	2	1	no	—
496	C₃×C₄²	—	2	1	no	—
497	C₃×C₄²	—	2	1	no	—
498	C₃×C₄²	—	2	1	no	—
499	C₃×C₄²	—	2	4	no	—
500	C₃×C₄²	—	3	4	no	—
501	C₃×C₄²	—	3	4	no	—
502	C₃×C₄²	—	3	2	no	—
503	C₃×C₄²	—	3	2	no	—
504	C₃×C₄²	—	3	2	no	—
505	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
506	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
507	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
508	C₃×C₄²	C₂²×D₃	1	4	yes	—
509	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
510	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
511	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
512	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
513	C₃×C₄²	C₂³×C₃	1	4	yes	—
514	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
515	#217	C₂³×C₃	1	2	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
523	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
524	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
525	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
526	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
527	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
528	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
529	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
530	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
531	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
532	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
533	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
534	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
536	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
537	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
538	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
539	C₄×Dic₃	C₂³×C₃	1	2	yes	—
540	C₄×Dic₃	C₂³×C₃	1	2	yes	—
541	C₄×Dic₃	C₂³×C₃	1	2	yes	—
542	C₄×Dic₃	C₂³×C₃	1	4	yes	—
543	C₄×Dic₃	C₂³×C₃	1	4	yes	—
544	C₂²×C₃²	—	2	1	no	—
545	C₂²×C₃²	—	2	1	no	—
546	C₂²×C₃²	C₂×#41	1	2	yes	—
547	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
548	C₂×C₃×D₃	—	2	2	no	—
549	C₂×C₃×D₃	—	2	2	no	—
550	C₂×C₃×D₃	—	2	2	no	—
551	C₂×C₃×D₃	—	2	2	no	—
552	C₂×C₃×D₃	—	2	2	no	—
553	C₂×C₃×D₃	—	2	2	no	—
554	C₂×C₃×D₃	—	2	2	no	—
555	C₂×C₃×D₃	—	2	2	no	—
556	C₂×C₃×D₃	—	4	8	no	—
557	C₂×C₃×D₃	C₂×#41	1	4	yes	—
558	C₃²×C₄	—	2	1	no	—
559	C₃²×C₄	—	2	4	no	—
560	C₃²×C₄	—	2	1	no	—
561	C₃²×C₄	—	2	1	no	—
562	C₃²×C₄	—	2	4	no	—
563	C₃²×C₄	C₂×#41	1	2	yes	—
564	C₃²×C₄	C₂×#41	1	2	yes	—
565	C₃²×C₄	C₂×#41	1	2	yes	—
566	C₃×Dic₃	—	2	2	no	—
567	C₃×Dic₃	—	2	2	no	—
568	C₃×Dic₃	—	2	2	no	—
569	C₃×Dic₃	—	2	2	no	—
570	C₃×Dic₃	—	2	2	no	—
571	C₂×#41	—	3	2	no	—
572	C₂×#41	—	3	1	no	—
573	C₂²×D₄	—	3	1	no	—
574	C₂³×C₄	—	3	2	no	—
575	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
576	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
577	#126	—	3	4	no	—
578	#126	—	3	4	no	—
579	#126	—	3	4	no	—
580	#125	—	3	4	no	—
581	#125	—	3	2	no	—
582	#125	C₂×C₃×D₃	1	2	yes	complemented
583	#124	—	3	2	no	—
584	#124	—	3	4	no	—
585	#123	—	3	4	no	—
586	#123	—	3	4	no	—
587	#123	—	3	4	no	—
588	#123	—	3	4	no	—
589	C₂²⋊Q₈	—	3	2	no	—
590	C₂²⋊Q₈	—	3	4	no	—
591	C₂²⋊Q₈	—	3	2	no	—
592	C₂²⋊Q₈	—	3	2	no	—
593	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
594	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
595	#121	—	3	2	no	—
596	#121	—	3	2	no	—
597	#121	—	3	4	no	—
598	#121	—	3	2	no	—
599	#120	—	3	4	no	—
600	C₄×Q₈	—	3	2	no	—
601	C₄×Q₈	—	3	1	no	—
602	C₄×Q₈	—	3	1	no	—
603	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
604	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
605	C₄×D₄	—	3	2	no	—
606	C₄×D₄	—	3	2	no	—
607	C₄×D₄	—	3	2	no	—
608	C₄×D₄	—	3	4	no	—
609	C₄×D₄	—	3	1	no	—
610	C₄×D₄	—	3	1	no	—
611	C₄×D₄	—	3	2	no	—
612	C₄×D₄	—	3	1	no	—
613	C₄×D₄	—	3	2	no	—
614	C₄×D₄	—	3	1	no	—
615	C₄×D₄	—	3	4	no	—
616	C₄×D₄	—	3	1	no	—
617	C₄×D₄	—	3	1	no	—
618	C₄×D₄	—	3	4	no	—
619	#117	—	3	1	no	—
620	#117	—	3	2	no	—
621	#117	—	3	2	no	—
622	#117	—	3	4	no	—
623	#117	—	3	2	no	—
624	#117	—	3	4	no	—
625	#117	—	3	4	no	—
626	#117	—	3	2	no	—
627	#117	C₂×C₃×D₃	1	2	yes	—
628	C₂×C₄⋊C₄	—	3	1	no	—
629	C₂×C₄⋊C₄	—	3	2	no	—
630	C₂×C₄⋊C₄	—	3	2	no	—
631	C₂×C₂²⋊C₄	—	3	2	no	—
632	C₂×C₂²⋊C₄	—	3	4	no	—
633	C₂×C₄²	—	3	4	no	—
634	C₂×C₄²	—	3	2	no	—
635	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	3	2	no	—
638	C₂³×C₃	—	3	2	no	—
639	C₂³×C₃	—	3	2	no	—
640	C₂³×C₃	—	6	4	no	—
641	C₂³×C₃	—	6	4	no	—
642	C₂³×C₃	—	12	2	no	—
643	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
644	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
645	C₂²×D₃	—	2	4	no	—
646	C₂²×D₃	—	2	4	no	—
647	C₂²×D₃	—	4	2	no	—
648	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
649	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
650	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
651	C₃×Q₈	—	2	4	no	—
652	C₃×Q₈	—	2	4	no	—
653	C₃×Q₈	—	4	4	no	—
654	C₃×Q₈	—	4	2	no	—
655	C₃×Q₈	—	4	2	no	—
656	C₃×Q₈	—	4	4	no	—
657	C₃×Q₈	—	6	2	no	—
658	C₃×D₄	—	3	4	no	—
659	C₃×D₄	—	6	4	no	—
660	C₃×D₄	—	6	8	no	—
661	C₃×D₄	—	6	4	no	—
662	C₃×D₄	—	6	2	no	—
663	C₃×D₄	—	6	2	no	—
664	C₃×D₄	—	12	4	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	4	no	—
674	C₂×C₃×C₄	—	2	4	no	—
675	C₂×C₃×C₄	—	2	4	no	—
676	C₂×C₃×C₄	—	3	2	no	—
677	C₂×C₃×C₄	—	3	2	no	—
678	C₂×C₃×C₄	—	3	2	no	—
679	C₂×C₃×C₄	—	3	2	no	—
680	C₂×C₃×C₄	—	3	2	no	—
681	C₂×C₃×C₄	—	4	2	no	—
682	C₂×C₃×C₄	—	4	1	no	—
683	C₂×C₃×C₄	—	4	1	no	—
684	C₂×C₃×C₄	—	4	2	no	—
685	C₂×C₃×C₄	—	6	8	no	—
686	C₂×C₃×C₄	—	6	4	no	—
687	C₂×C₃×C₄	—	6	4	no	—
688	C₂×C₃×C₄	—	6	4	no	—
689	C₂×C₃×C₄	—	6	4	no	—
690	C₂×C₃×C₄	—	6	4	no	—
691	C₂×C₃×C₄	—	6	4	no	—
692	C₂×C₃×C₄	—	6	4	no	—
693	C₂×C₃×C₄	—	12	2	no	—
694	C₂×C₃×C₄	—	12	4	no	—
695	C₂×C₃×C₄	#239	1	4	yes	complemented
696	C₂×C₃×C₄	C₃×#41	1	4	yes	complemented
697	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
698	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
699	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
700	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
701	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
702	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
703	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
705	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
707	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
708	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	#67	—	2	4	no	—
714	C₂×Dic₃	—	2	4	no	—
715	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
716	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
717	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
718	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
719	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
720	D₁₂	—	2	4	no	—
721	D₁₂	—	2	8	no	—
722	D₁₂	—	2	2	no	—
723	D₁₂	—	2	2	no	—
724	D₁₂	—	4	4	no	—
725	D₁₂	C₃×#41	1	4	yes	complemented
726	C₄×D₃	—	2	8	no	—
727	C₄×D₃	—	2	4	no	—
728	C₄×D₃	—	2	4	no	—
729	C₄×D₃	—	2	4	no	—
730	C₄×D₃	—	2	4	no	—
731	C₄×D₃	—	2	4	no	—
732	C₄×D₃	—	2	4	no	—
733	C₄×D₃	—	4	2	no	—
734	C₄×D₃	—	4	4	no	—
735	Dic₆	—	2	2	no	—
736	C₂×C₃²	—	2	2	no	—
737	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
738	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
739	C₂×C₃²	#585	1	1	yes	characteristic
740	C₃×D₃	—	2	4	no	—
741	C₃×D₃	—	4	2	no	—
742	C₃×D₃	—	4	2	no	—
743	C₂⁴	—	3	2	no	—
744	#41	—	6	8	no	—
745	#41	—	6	4	no	—
746	C₂×Q₈	—	3	1	no	—
747	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
748	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
749	C₂×D₄	—	3	2	no	—
750	C₂×D₄	—	3	1	no	—
751	C₂×D₄	—	3	4	no	—
752	C₂×D₄	—	3	1	no	—
753	C₂×D₄	—	3	2	no	—
754	C₂×D₄	—	3	1	no	—
755	C₂×D₄	—	3	4	no	—
756	C₂×D₄	—	6	4	no	—
757	C₂²×C₄	—	3	2	no	—
758	C₂²×C₄	—	3	2	no	—
759	C₂²×C₄	—	3	4	no	—
760	C₂²×C₄	—	3	2	no	—
761	C₂²×C₄	—	3	2	no	—
762	C₂²×C₄	—	3	2	no	—
763	C₂²×C₄	—	3	2	no	—
764	C₂²×C₄	—	3	2	no	—
765	C₂²×C₄	—	3	4	no	—
766	C₂²×C₄	—	3	2	no	—
767	C₂²×C₄	—	6	8	no	—
768	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
769	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
770	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
771	C₄⋊C₄	—	3	1	no	—
772	C₄⋊C₄	—	3	1	no	—
773	C₄⋊C₄	—	3	1	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	4	no	—
776	C₄⋊C₄	—	3	1	no	—
777	C₄⋊C₄	—	3	2	no	—
778	C₄⋊C₄	—	3	2	no	—
779	C₄⋊C₄	—	3	4	no	—
780	C₄⋊C₄	—	3	2	no	—
781	C₄⋊C₄	—	3	4	no	—
782	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
783	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
784	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
785	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
786	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
787	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
788	C₂²⋊C₄	—	3	2	no	—
789	C₂²⋊C₄	—	3	2	no	—
790	C₂²⋊C₄	—	3	4	no	—
791	C₂²⋊C₄	—	3	4	no	—
792	C₂²⋊C₄	—	3	2	no	—
793	C₂²⋊C₄	—	3	2	no	—
794	C₂²⋊C₄	—	3	2	no	—
795	C₂²⋊C₄	—	3	4	no	—
796	C₂²⋊C₄	—	3	2	no	—
797	C₂²⋊C₄	—	3	4	no	—
798	C₂²⋊C₄	—	3	2	no	—
799	C₂²⋊C₄	—	3	4	no	—
800	C₂²⋊C₄	—	3	4	no	—
801	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
802	C₄²	—	3	2	no	—
803	C₄²	—	3	4	no	—
804	C₄²	—	3	4	no	—
805	C₄²	—	3	2	no	—
806	C₄²	—	3	2	no	—
807	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
808	C₄²	C₂²×C₃×D₃	1	4	yes	—
809	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
810	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
811	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
812	C₂²×C₃	—	2	1	no	—
813	C₂²×C₃	—	2	1	no	—
814	C₂²×C₃	—	2	1	no	—
815	C₂²×C₃	—	2	1	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	1	no	—
818	C₂²×C₃	—	3	4	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	—	4	1	no	—
821	C₂²×C₃	—	6	2	no	—
822	C₂²×C₃	—	6	2	no	—
823	C₂²×C₃	—	6	2	no	—
824	C₂²×C₃	—	6	2	no	—
825	C₂²×C₃	—	6	2	no	—
826	C₂²×C₃	—	6	2	no	—
827	C₂²×C₃	—	6	2	no	—
828	C₂²×C₃	—	6	2	no	—
829	C₂²×C₃	—	12	8	no	—
830	C₂²×C₃	C₂×#239	1	2	yes	—
831	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
832	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
833	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
834	C₂×D₃	—	2	2	no	—
835	C₂×D₃	—	2	2	no	—
836	C₂×D₃	—	2	2	no	—
837	C₂×D₃	—	2	2	no	—
838	C₂×D₃	—	2	2	no	—
839	C₂×D₃	—	2	2	no	—
840	C₂×D₃	—	2	2	no	—
841	C₂×D₃	—	2	2	no	—
842	C₂×D₃	—	4	8	no	—
843	C₂×D₃	C₂×C₃×#41	1	4	yes	—
844	C₃×C₄	—	2	2	no	—
845	C₃×C₄	—	2	1	no	—
846	C₃×C₄	—	2	4	no	—
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	1	no	—
849	C₃×C₄	—	2	4	no	—
850	C₃×C₄	—	2	4	no	—
851	C₃×C₄	—	2	1	no	—
852	C₃×C₄	—	2	1	no	—
853	C₃×C₄	—	2	4	no	—
854	C₃×C₄	—	2	1	no	—
855	C₃×C₄	—	2	2	no	—
856	C₃×C₄	—	2	2	no	—
857	C₃×C₄	—	2	2	no	—
858	C₃×C₄	—	4	1	no	—
859	C₃×C₄	—	4	1	no	—
860	C₃×C₄	—	4	4	no	—
861	C₃×C₄	—	4	4	no	—
862	C₃×C₄	—	6	2	no	—
863	C₃×C₄	—	6	2	no	—
864	C₃×C₄	—	6	2	no	—
865	C₃×C₄	—	6	2	no	—
866	C₃×C₄	—	6	2	no	—
867	C₃×C₄	C₂×#239	1	2	yes	—
868	C₃×C₄	C₂×#239	1	2	yes	—
869	C₃×C₄	D₃×#41	1	2	yes	—
870	C₃×C₄	C₂×C₃×#41	1	2	yes	—
871	C₃×C₄	C₂×C₃×#41	1	2	yes	—
872	C₃×C₄	C₂×C₃×#41	1	2	yes	—
873	Dic₃	—	2	2	no	—
874	Dic₃	—	2	2	no	—
875	Dic₃	—	2	2	no	—
876	Dic₃	—	2	2	no	—
877	Dic₃	—	2	2	no	—
878	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
879	C₂³	—	3	2	no	—
880	C₂³	—	3	2	no	—
881	C₂³	—	3	2	no	—
882	C₂³	—	6	4	no	—
883	C₂³	—	6	4	no	—
884	C₂³	—	12	2	no	—
885	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
886	Q₈	—	2	4	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	6	2	no	—
889	D₄	—	3	4	no	—
890	D₄	—	6	4	no	—
891	D₄	—	6	8	no	—
892	D₄	—	6	4	no	—
893	D₄	—	6	2	no	—
894	D₄	—	6	2	no	—
895	D₄	—	12	4	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	3	2	no	—
898	C₂×C₄	—	3	2	no	—
899	C₂×C₄	—	3	2	no	—
900	C₂×C₄	—	3	2	no	—
901	C₂×C₄	—	3	2	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	6	8	no	—
904	C₂×C₄	—	6	4	no	—
905	C₂×C₄	—	6	4	no	—
906	C₂×C₄	—	6	4	no	—
907	C₂×C₄	—	6	4	no	—
908	C₂×C₄	—	6	4	no	—
909	C₂×C₄	—	6	4	no	—
910	C₂×C₄	—	6	4	no	—
911	C₂×C₄	—	12	2	no	—
912	C₂×C₄	—	12	4	no	—
913	C₂×C₄	C₃×#239	1	4	yes	complemented
914	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
915	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
916	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
917	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
918	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
919	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
920	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
921	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
922	C₂×C₃	—	2	2	no	—
923	C₂×C₃	—	2	2	no	—
924	C₂×C₃	—	2	1	no	—
925	C₂×C₃	—	2	1	no	—
926	C₂×C₃	—	2	1	no	—
927	C₂×C₃	—	4	2	no	—
928	C₂×C₃	—	6	4	no	—
929	C₂×C₃	—	12	2	no	—
930	C₂×C₃	—	12	2	no	—
931	C₂×C₃	C₂²×#239	1	1	yes	characteristic
932	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
933	C₂×C₃	#5964	1	1	yes	characteristic
934	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
935	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
936	C₂×C₃	C₃×#585	1	1	yes	characteristic
937	D₃	—	2	4	no	—
938	D₃	—	4	2	no	—
939	D₃	—	4	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	3	4	no	—
943	C₂²	—	6	2	no	—
944	C₂²	—	6	2	no	—
945	C₂²	—	6	2	no	—
946	C₂²	—	6	2	no	—
947	C₂²	—	6	2	no	—
948	C₂²	—	6	2	no	—
949	C₂²	—	6	2	no	—
950	C₂²	—	6	2	no	—
951	C₂²	—	12	8	no	—
952	C₂²	C₂×C₃×#239	1	2	yes	—
953	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
954	C₄	—	2	1	no	—
955	C₄	—	2	4	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	4	no	—
959	C₄	—	6	2	no	—
960	C₄	—	6	2	no	—
961	C₄	—	6	2	no	—
962	C₄	—	6	2	no	—
963	C₄	—	6	2	no	—
964	C₄	C₂×C₃×#239	1	2	yes	—
965	C₄	C₂×C₃×#239	1	2	yes	—
966	C₄	C₃×D₃×#41	1	2	yes	—
967	C₃	—	2	1	no	—
968	C₃	#86276	1	1	yes	characteristic, direct product factor
969	C₃	C₃×#3475	1	1	yes	characteristic, complemented
970	C₂	—	2	2	no	—
971	C₂	—	6	4	no	—
972	C₂	—	12	2	no	—
973	C₂	—	12	2	no	—
974	C₂	C₂²×C₃×#239	1	1	yes	characteristic
975	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
976	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×#533	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
2. C₃×#5734	C₂	semidirect
3. C₃×#5732	C₂	semidirect
4. C₃×#5730	C₂	semidirect
5. C₃×#5726	C₂	semidirect
6. C₃×#5695	C₂	semidirect
7. C₃×#5694	C₂	semidirect
8. C₃×#5642	C₂	semidirect
9. C₃×#5637	C₂	semidirect
10. C₃×#5630	C₂	semidirect
11. C₃×#5580	C₂	semidirect
12. C₃×#5580	C₂	semidirect
13. C₃×C₄×#239	C₂	semidirect
14. C₃×#5524	C₂	semidirect
15. C₃×D₃×#117	C₂	semidirect
16. C₃×C₄×#235	C₂	semidirect
17. C₂×C₃×C₄×D₁₂	C₂	semidirect
19. #86276	C₃	direct (N × H)
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×C₄⋊Q₈	C₂²	semidirect
26. C₃²×#125	C₂²	semidirect
29. C₃²×C₄×Q₈	C₂²	semidirect
30. C₃²×C₄×Q₈	C₂²	semidirect
34. C₃×#947	C₂²	semidirect
35. C₃×#946	C₂²	semidirect
36. C₃×#946	C₂²	semidirect
37. C₃×Q₈×Dic₃	C₂²	semidirect
43. C₃×#898	C₂²	semidirect
44. C₃×#898	C₂²	semidirect
45. C₃×#898	C₂²	semidirect
46. C₃×#897	C₂²	semidirect
47. C₃×#897	C₂²	semidirect
50. C₃×#895	C₂²	semidirect
51. C₃×#895	C₂²	semidirect
53. C₃×#894	C₂²	semidirect
54. C₃×#894	C₂²	semidirect
56. C₃×#893	C₂²	semidirect
57. C₃×#892	C₂²	semidirect
58. C₃×#892	C₂²	semidirect
59. C₃×#892	C₂²	semidirect
60. C₃×#892	C₂²	semidirect
61. C₃×D₃×C₄⋊C₄	C₂²	semidirect
62. C₃×D₃×C₄⋊C₄	C₂²	semidirect
63. C₃×#890	C₂²	semidirect
64. C₃×#890	C₂²	semidirect
75. C₃×C₄×D₁₂	C₂²	semidirect
76. C₃×C₄×D₁₂	C₂²	semidirect
77. C₃×C₄×D₁₂	C₂²	semidirect
78. C₃×C₄×D₁₂	C₂²	semidirect
79. C₃×#872	C₂²	semidirect
80. C₃×#872	C₂²	semidirect
81. C₃×C₄²×D₃	C₂²	semidirect
82. C₃×C₄²×D₃	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
95. C₃×#533	D₃	semidirect
96. C₃×#533	C₂×C₃	semidirect
104. #5734	C₂×C₃	semidirect
105. #5732	C₂×C₃	semidirect
106. #5730	C₂×C₃	semidirect
107. #5726	C₂×C₃	semidirect
108. #5695	C₂×C₃	semidirect
109. #5694	C₂×C₃	semidirect
110. #5642	C₂×C₃	semidirect
111. #5637	C₂×C₃	semidirect
112. #5630	C₂×C₃	semidirect
113. #5580	C₂×C₃	semidirect
114. #5580	C₂×C₃	semidirect
115. C₄×#239	C₂×C₃	semidirect
116. #5524	C₂×C₃	semidirect
117. D₃×#117	C₂×C₃	semidirect
118. C₄×#235	C₂×C₃	semidirect
119. C₂×C₄×D₁₂	C₂×C₃	semidirect
200. C₃×C₄⋊Q₈	C₂×D₃	semidirect
201. C₃×C₄⋊Q₈	C₂×D₃	semidirect
202. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
203. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
210. C₃×#125	C₂×D₃	semidirect
211. C₃×#125	C₂²×C₃	semidirect
238. C₃×C₄×Q₈	C₂×D₃	semidirect
239. C₃×C₄×Q₈	C₂×D₃	semidirect
240. C₃×C₄×Q₈	C₂²×C₃	semidirect
241. C₃×C₄×Q₈	C₂²×C₃	semidirect
278. #947	C₂²×C₃	semidirect
279. #946	C₂²×C₃	semidirect
280. #946	C₂²×C₃	semidirect
281. Q₈×Dic₃	C₂²×C₃	semidirect
287. #898	C₂²×C₃	semidirect
288. #898	C₂²×C₃	semidirect
289. #898	C₂²×C₃	semidirect
290. #897	C₂²×C₃	semidirect
291. #897	C₂²×C₃	semidirect
294. #895	C₂²×C₃	semidirect
295. #895	C₂²×C₃	semidirect
297. #894	C₂²×C₃	semidirect
298. #894	C₂²×C₃	semidirect
300. #893	C₂²×C₃	semidirect
301. #892	C₂²×C₃	semidirect
302. #892	C₂²×C₃	semidirect
303. #892	C₂²×C₃	semidirect
304. #892	C₂²×C₃	semidirect
305. D₃×C₄⋊C₄	C₂²×C₃	semidirect
306. D₃×C₄⋊C₄	C₂²×C₃	semidirect
307. #890	C₂²×C₃	semidirect
308. #890	C₂²×C₃	semidirect
319. C₄×D₁₂	C₂²×C₃	semidirect
320. C₄×D₁₂	C₂²×C₃	semidirect
321. C₄×D₁₂	C₂²×C₃	semidirect
322. C₄×D₁₂	C₂²×C₃	semidirect
323. #872	C₂²×C₃	semidirect
324. #872	C₂²×C₃	semidirect
325. C₄²×D₃	C₂²×C₃	semidirect
326. C₄²×D₃	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
328. C₄×Dic₆	C₂²×C₃	semidirect
340. C₂×C₃²×C₄	#41	semidirect
361. C₃×D₁₂	#41	semidirect
381. #533	C₃×D₃	semidirect
575. C₄⋊Q₈	C₂×C₃×D₃	semidirect
576. C₄⋊Q₈	C₂×C₃×D₃	semidirect
582. #125	C₂×C₃×D₃	semidirect
603. C₄×Q₈	C₂×C₃×D₃	semidirect
604. C₄×Q₈	C₂×C₃×D₃	semidirect
695. C₂×C₃×C₄	#239	semidirect
696. C₂×C₃×C₄	C₃×#41	semidirect
725. D₁₂	C₃×#41	semidirect
878. C₃²	#3475	semidirect
913. C₂×C₄	C₃×#239	semidirect
968. C₃	#86276	direct (N × H)
969. C₃	C₃×#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃×#5734	2
C₃×#5732	2
C₃×#5730	2
C₃×#5726	2
C₃×#5695	2
C₃×#5694	2
C₃×#5642	2
C₃×#5637	2
C₃×#5630	2
C₃×#5580	2
C₃×C₄×#239	2
C₃×#5524	2
C₃×D₃×#117	2
C₃×C₄×#235	2
C₂×C₃×C₄×D₁₂	2
C₃×#3475	3
#86276	3

Subgroups — C3×#86276 #11903481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86276 #11903481