Subgroups — C₃×#86675 #11903469

Order 1152.

2410 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5829	C₂	1	2	yes	maximal, complemented
3	C₃×Dic₃×#41	C₂	1	2	yes	maximal, complemented
4	C₃×#5732	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5658	C₂	1	4	yes	maximal, complemented
7	C₃×#5649	C₂	1	4	yes	maximal, complemented
8	C₃×#5639	C₂	1	2	yes	maximal, complemented
9	C₃×#5624	C₂	1	2	yes	maximal, complemented
10	C₃×#5618	C₂	1	2	yes	maximal, complemented
11	C₃×#5606	C₂	1	2	yes	maximal, complemented
12	C₃×#5563	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5513	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#892	C₂	1	2	yes	maximal, complemented
18	C₃×#3475	—	3	1	no	maximal
19	#86675	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃²×#41	C₂²	1	2	yes	—
21	C₂×C₃×#237	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₃×D₄	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×#123	C₂²	1	4	yes	complemented
26	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃²×#121	C₂²	1	2	yes	complemented
28	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₃×#947	C₂²	1	2	yes	—
32	C₃×#946	C₂²	1	2	yes	—
33	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
34	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
35	C₃×#939	C₂²	1	4	yes	—
36	C₃×#938	C₂²	1	2	yes	complemented
37	C₃×#937	C₂²	1	4	yes	—
38	C₃×D₄×Dic₃	C₂²	1	2	yes	—
39	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
40	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
42	C₃×D₄×Dic₃	C₂²	1	4	yes	complemented
43	C₃×#930	C₂²	1	2	yes	—
44	C₃×#929	C₂²	1	4	yes	—
45	C₃×C₄×#67	C₂²	1	2	yes	—
46	C₃×C₄×#67	C₂²	1	2	yes	—
47	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
48	C₃×#926	C₂²	1	4	yes	complemented
49	C₃×#926	C₂²	1	2	yes	complemented
50	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
51	C₃×#924	C₂²	1	2	yes	complemented
52	C₂×C₃×C₄×Dic₃	C₂²	1	4	yes	complemented
53	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
54	C₃×#898	C₂²	1	4	yes	complemented
55	C₃×#898	C₂²	1	4	yes	complemented
56	C₃×#897	C₂²	1	2	yes	—
57	C₃×#897	C₂²	1	2	yes	complemented
58	C₃×#893	C₂²	1	1	yes	characteristic
59	C₃×#892	C₂²	1	1	yes	characteristic
60	C₃×#892	C₂²	1	2	yes	—
61	C₃×#892	C₂²	1	4	yes	—
62	C₃×#892	C₂²	1	2	yes	complemented
63	C₃×#892	C₂²	1	2	yes	complemented
64	C₃×#892	C₂²	1	4	yes	complemented
65	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₃×#890	C₂²	1	2	yes	complemented
67	C₃×#890	C₂²	1	2	yes	complemented
68	C₃×#889	C₂²	1	4	yes	complemented
69	C₃×#887	C₂²	1	1	yes	characteristic, complemented
70	C₃×#887	C₂²	1	2	yes	complemented
71	C₃×#886	C₂²	1	4	yes	complemented
72	C₃×#885	C₂²	1	4	yes	complemented
73	C₃×#883	C₂²	1	4	yes	—
74	C₃×#67⋊C₄	C₂²	1	2	yes	—
75	C₃×#67⋊C₄	C₂²	1	2	yes	—
76	C₃×#67⋊C₄	C₂²	1	4	yes	complemented
77	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₃×#879	C₂²	1	4	yes	complemented
79	C₃×#878	C₂²	1	4	yes	complemented
80	C₃×#877	C₂²	1	2	yes	complemented
81	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
82	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
83	C₃×#869	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	—	2	1	no	—
93	C₃×#547	D₃	1	1	yes	characteristic, complemented
94	C₃×#547	C₂×C₃	1	1	yes	characteristic, complemented
95	C₃×#546	—	3	2	no	—
96	C₃×#533	—	3	1	no	—
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	#5829	C₂×C₃	1	2	yes	complemented
105	Dic₃×#41	C₂×C₃	1	2	yes	complemented
106	#5732	C₂×C₃	1	1	yes	characteristic, complemented
107	#5728	C₂×C₃	1	1	yes	characteristic, complemented
108	#5658	C₂×C₃	1	4	yes	complemented
109	#5649	C₂×C₃	1	4	yes	complemented
110	#5639	C₂×C₃	1	2	yes	complemented
111	#5624	C₂×C₃	1	2	yes	complemented
112	#5618	C₂×C₃	1	2	yes	complemented
113	#5606	C₂×C₃	1	2	yes	complemented
114	#5563	C₂×C₃	1	1	yes	characteristic, complemented
115	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
116	#5543	C₂×C₃	1	1	yes	characteristic, complemented
117	C₄×#237	C₂×C₃	1	1	yes	characteristic, complemented
118	#5513	C₂×C₃	1	2	yes	complemented
119	C₂×#892	C₂×C₃	1	2	yes	complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₃²×#41	—	2	8	no	—
122	C₂×C₃²×Q₈	C₂³	1	2	yes	—
123	C₂×C₃²×D₄	C₂³	1	4	yes	—
124	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
125	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃²×C₄	C₂³	1	4	yes	—
127	C₂²×C₃²×C₄	C₂³	1	2	yes	—
128	C₂²×C₃²×C₄	C₂³	1	2	yes	—
129	C₂×C₃×#67	C₂³	1	2	yes	—
130	C₂×C₃×#67	C₂³	1	2	yes	—
131	C₂×C₃×#67	C₂³	1	4	yes	—
132	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
133	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
134	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
135	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
136	C₃×#237	—	2	4	no	—
137	C₃×D₃×D₄	—	2	4	no	—
138	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄×D₃	—	2	8	no	—
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	1	yes	characteristic
143	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
146	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
147	C₂×C₃×Dic₆	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
151	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₄²	C₂³	1	1	yes	characteristic
157	C₃×#217	C₂³	1	2	yes	—
158	C₃×#217	C₂³	1	4	yes	—
159	C₃×#217	C₂³	1	4	yes	—
160	C₃×#217	C₂³	1	2	yes	—
161	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	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	4	yes	—
168	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
169	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
170	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
171	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
172	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
175	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
180	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
181	C₃×C₄×Dic₃	C₂³	1	2	yes	—
182	C₃×C₄×Dic₃	C₂³	1	4	yes	—
183	C₃×C₄×Dic₃	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	1	yes	characteristic
187	C₃×C₄×Dic₃	C₂³	1	2	yes	—
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	#3475	—	3	1	no	Sylow
190	C₂×C₃×#41	—	2	2	no	—
191	C₂×C₃×#41	—	3	1	no	—
192	C₂×C₃×#41	C₂×D₃	1	2	yes	—
193	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
194	C₂²×C₃×D₄	—	3	1	no	—
195	C₂³×C₃×C₄	—	3	2	no	—
196	C₂×#237	C₂²×C₃	1	1	yes	characteristic
197	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
198	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
199	C₃×C₄⋊Q₈	—	2	1	no	—
200	C₃×C₄⋊Q₈	—	3	1	no	—
201	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
202	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₃×#126	—	3	4	no	—
204	C₃×#126	—	3	4	no	—
205	C₃×#126	—	3	4	no	—
206	C₃×#125	—	3	4	no	—
207	C₃×#125	—	3	2	no	—
208	C₃×#125	—	3	2	no	—
209	C₃×#124	—	3	2	no	—
210	C₃×#124	—	3	4	no	—
211	C₃×#123	—	2	4	no	—
212	C₃×#123	—	3	4	no	—
213	C₃×#123	—	3	4	no	—
214	C₃×#123	—	3	4	no	—
215	C₃×#123	C₂×D₃	1	4	yes	complemented
216	C₃×#123	C₂²×C₃	1	4	yes	complemented
217	C₃×C₂²⋊Q₈	—	2	2	no	—
218	C₃×C₂²⋊Q₈	—	3	2	no	—
219	C₃×C₂²⋊Q₈	—	3	2	no	—
220	C₃×C₂²⋊Q₈	—	3	2	no	—
221	C₃×C₂²⋊Q₈	—	3	2	no	—
222	C₃×C₂²⋊Q₈	—	3	4	no	—
223	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
224	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
225	C₃×#121	—	2	2	no	—
226	C₃×#121	—	3	2	no	—
227	C₃×#121	—	3	4	no	—
228	C₃×#121	—	3	2	no	—
229	C₃×#121	C₂×D₃	1	2	yes	complemented
230	C₃×#121	C₂²×C₃	1	2	yes	complemented
231	C₃×#120	—	3	4	no	—
232	C₃×C₄×Q₈	—	3	2	no	—
233	C₃×C₄×Q₈	—	3	2	no	—
234	C₃×C₄×Q₈	—	3	1	no	—
235	C₃×C₄×Q₈	—	3	2	no	—
236	C₃×C₄×Q₈	—	3	1	no	—
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	—	2	1	no	—
239	C₃×C₄×D₄	—	3	1	no	—
240	C₃×C₄×D₄	—	3	2	no	—
241	C₃×C₄×D₄	—	3	4	no	—
242	C₃×C₄×D₄	—	3	4	no	—
243	C₃×C₄×D₄	—	3	1	no	—
244	C₃×C₄×D₄	—	3	2	no	—
245	C₃×C₄×D₄	—	3	2	no	—
246	C₃×C₄×D₄	—	3	1	no	—
247	C₃×C₄×D₄	—	3	2	no	—
248	C₃×C₄×D₄	—	3	2	no	—
249	C₃×C₄×D₄	—	3	4	no	—
250	C₃×C₄×D₄	—	3	1	no	—
251	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
252	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
253	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
254	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₃×#117	—	3	4	no	—
256	C₃×#117	—	3	2	no	—
257	C₃×#117	—	3	1	no	—
258	C₃×#117	—	3	2	no	—
259	C₃×#117	—	3	4	no	—
260	C₃×#117	—	3	4	no	—
261	C₃×#117	—	3	2	no	—
262	C₃×#117	—	3	2	no	—
263	C₃×#117	—	3	2	no	—
264	C₂×C₃×C₄⋊C₄	—	2	2	no	—
265	C₂×C₃×C₄⋊C₄	—	3	2	no	—
266	C₂×C₃×C₄⋊C₄	—	3	1	no	—
267	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
268	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
269	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
270	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
271	C₂×C₃×C₄²	—	3	4	no	—
272	C₂×C₃×C₄²	—	3	2	no	—
273	C₂×C₃×C₄²	—	3	1	no	—
274	#947	C₂²×C₃	1	2	yes	—
275	#946	C₂²×C₃	1	2	yes	—
276	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
277	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
278	#939	C₂²×C₃	1	4	yes	—
279	#938	C₂²×C₃	1	2	yes	complemented
280	#937	C₂²×C₃	1	4	yes	—
281	D₄×Dic₃	C₂²×C₃	1	2	yes	—
282	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
283	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
284	D₄×Dic₃	C₂²×C₃	1	4	yes	complemented
285	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
286	#930	C₂²×C₃	1	2	yes	—
287	#929	C₂²×C₃	1	4	yes	—
288	C₄×#67	C₂²×C₃	1	2	yes	—
289	C₄×#67	C₂²×C₃	1	2	yes	—
290	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
291	#926	C₂²×C₃	1	2	yes	complemented
292	#926	C₂²×C₃	1	4	yes	complemented
293	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
294	#924	C₂²×C₃	1	2	yes	complemented
295	C₂×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
296	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
297	#898	C₂²×C₃	1	4	yes	complemented
298	#898	C₂²×C₃	1	4	yes	complemented
299	#897	C₂²×C₃	1	2	yes	—
300	#897	C₂²×C₃	1	2	yes	complemented
301	#893	C₂²×C₃	1	1	yes	characteristic
302	#892	C₂²×C₃	1	4	yes	—
303	#892	C₂²×C₃	1	2	yes	—
304	#892	C₂²×C₃	1	1	yes	characteristic
305	#892	C₂²×C₃	1	4	yes	complemented
306	#892	C₂²×C₃	1	2	yes	complemented
307	#892	C₂²×C₃	1	2	yes	complemented
308	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
309	#890	C₂²×C₃	1	2	yes	complemented
310	#890	C₂²×C₃	1	2	yes	complemented
311	#889	C₂²×C₃	1	4	yes	complemented
312	#887	C₂²×C₃	1	2	yes	complemented
313	#887	C₂²×C₃	1	1	yes	characteristic, complemented
314	#886	C₂²×C₃	1	4	yes	complemented
315	#885	C₂²×C₃	1	4	yes	complemented
316	#883	C₂²×C₃	1	4	yes	—
317	#67⋊C₄	C₂²×C₃	1	2	yes	—
318	#67⋊C₄	C₂²×C₃	1	2	yes	—
319	#67⋊C₄	C₂²×C₃	1	4	yes	complemented
320	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
321	#879	C₂²×C₃	1	4	yes	complemented
322	#878	C₂²×C₃	1	4	yes	complemented
323	#877	C₂²×C₃	1	2	yes	complemented
324	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
325	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
326	#869	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₂³×C₃²	C₂⁴	1	2	yes	—
329	C₂³×C₃²	C₂⁴	1	2	yes	—
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	1	yes	characteristic
335	C₃²×Q₈	—	2	4	no	—
336	C₃²×D₄	—	2	8	no	—
337	C₃²×D₄	—	2	2	no	—
338	C₃²×D₄	#41	1	4	yes	complemented
339	C₂×C₃²×C₄	—	2	8	no	—
340	C₂×C₃²×C₄	—	2	4	no	—
341	C₂×C₃²×C₄	—	2	4	no	—
342	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
344	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
345	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
346	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
347	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
348	C₃×#67	—	2	4	no	—
349	C₃×#67	—	2	4	no	—
350	C₃×#67	—	4	4	no	—
351	C₂×C₃×Dic₃	—	2	4	no	—
352	C₂×C₃×Dic₃	—	2	4	no	—
353	C₂×C₃×Dic₃	—	4	4	no	—
354	C₂×C₃×Dic₃	—	4	2	no	—
355	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
356	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
357	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
360	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
361	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
362	C₃×D₁₂	—	2	2	no	—
363	C₃×C₄×D₃	—	2	4	no	—
364	C₃×C₄×D₃	—	2	4	no	—
365	C₃×C₄×D₃	—	2	2	no	—
366	C₃×C₄×D₃	—	2	4	no	—
367	C₃×C₄×D₃	—	4	1	no	—
368	C₃×C₄×D₃	#41	1	4	yes	complemented
369	C₃×Dic₆	—	2	2	no	—
370	C₃×Dic₆	—	4	2	no	—
371	#556	—	3	1	no	—
372	#555	—	3	1	no	—
373	#554	—	3	1	no	—
374	#553	—	3	2	no	—
375	#552	—	3	2	no	—
376	#552	—	3	2	no	—
377	#551	—	3	4	no	—
378	#547	C₃×D₃	1	1	yes	characteristic, complemented
379	#546	—	3	2	no	—
380	#533	—	3	1	no	—
381	#529	—	3	4	no	—
382	#529	—	3	2	no	—
383	#525	—	3	2	no	—
384	C₄×#41	—	3	2	no	—
385	C₄×#41	—	3	1	no	—
386	C₂×C₄×D₄	—	3	1	no	—
387	C₂×#117	—	3	2	no	—
388	C₂⁴×C₃	—	3	2	no	—
389	C₂³×D₃	C₂³×C₃	1	2	yes	—
390	C₃×#41	—	2	8	no	—
391	C₃×#41	—	2	8	no	—
392	C₃×#41	—	4	8	no	—
393	C₃×#41	—	6	4	no	—
394	C₂×C₃×Q₈	—	2	2	no	—
395	C₂×C₃×Q₈	—	3	1	no	—
396	C₂×C₃×Q₈	—	3	2	no	—
397	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
398	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
399	C₂×C₃×D₄	—	2	1	no	—
400	C₂×C₃×D₄	—	2	1	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	3	2	no	—
403	C₂×C₃×D₄	—	3	2	no	—
404	C₂×C₃×D₄	—	3	4	no	—
405	C₂×C₃×D₄	—	3	1	no	—
406	C₂×C₃×D₄	—	6	4	no	—
407	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
408	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
409	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
410	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
411	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
412	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	4	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	—	3	1	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	—	3	1	no	—
422	C₂²×C₃×C₄	—	3	2	no	—
423	C₂²×C₃×C₄	—	3	2	no	—
424	C₂²×C₃×C₄	—	3	2	no	—
425	C₂²×C₃×C₄	—	3	1	no	—
426	C₂²×C₃×C₄	—	6	8	no	—
427	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
428	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
429	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
430	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
431	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
432	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
433	C₂×#67	C₂³×C₃	1	2	yes	—
434	C₂×#67	C₂³×C₃	1	2	yes	—
435	C₂×#67	C₂³×C₃	1	4	yes	—
436	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
437	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
438	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
439	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
440	#237	—	2	4	no	—
441	D₃×D₄	—	2	4	no	—
442	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
443	C₂×C₄×D₃	—	2	8	no	—
444	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
449	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
450	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
451	C₂×Dic₆	C₂³×C₃	1	2	yes	—
452	C₃×C₄⋊C₄	—	2	1	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	2	4	no	—
455	C₃×C₄⋊C₄	—	2	1	no	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₄⋊C₄	—	3	2	no	—
458	C₃×C₄⋊C₄	—	3	2	no	—
459	C₃×C₄⋊C₄	—	3	2	no	—
460	C₃×C₄⋊C₄	—	3	4	no	—
461	C₃×C₄⋊C₄	—	3	4	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	2	no	—
467	C₃×C₄⋊C₄	—	3	4	no	—
468	C₃×C₄⋊C₄	—	3	4	no	—
469	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
472	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
473	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
474	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
477	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
478	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₃×C₂²⋊C₄	—	2	2	no	—
480	C₃×C₂²⋊C₄	—	2	2	no	—
481	C₃×C₂²⋊C₄	—	2	4	no	—
482	C₃×C₂²⋊C₄	—	3	2	no	—
483	C₃×C₂²⋊C₄	—	3	4	no	—
484	C₃×C₂²⋊C₄	—	3	2	no	—
485	C₃×C₂²⋊C₄	—	3	4	no	—
486	C₃×C₂²⋊C₄	—	3	2	no	—
487	C₃×C₂²⋊C₄	—	3	4	no	—
488	C₃×C₂²⋊C₄	—	3	4	no	—
489	C₃×C₂²⋊C₄	—	3	4	no	—
490	C₃×C₂²⋊C₄	—	3	2	no	—
491	C₃×C₂²⋊C₄	—	3	2	no	—
492	C₃×C₂²⋊C₄	—	3	4	no	—
493	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
494	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
495	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
496	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
499	C₃×C₄²	—	2	1	no	—
500	C₃×C₄²	—	3	2	no	—
501	C₃×C₄²	—	3	1	no	—
502	C₃×C₄²	—	3	4	no	—
503	C₃×C₄²	—	3	4	no	—
504	C₃×C₄²	—	3	1	no	—
505	C₃×C₄²	—	3	4	no	—
506	C₃×C₄²	—	3	2	no	—
507	C₃×C₄²	—	3	1	no	—
508	C₃×C₄²	—	3	2	no	—
509	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
510	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
511	#217	C₂³×C₃	1	2	yes	—
512	#217	C₂³×C₃	1	4	yes	—
513	#217	C₂³×C₃	1	4	yes	—
514	#217	C₂³×C₃	1	2	yes	—
515	(C₂×D₃)⋊C₄	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	4	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
522	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
523	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
524	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
525	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
526	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
527	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
528	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
529	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
530	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
531	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
532	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
533	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
534	C₄×Dic₃	C₂³×C₃	1	2	yes	—
535	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
536	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
537	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₄×Dic₃	C₂³×C₃	1	2	yes	—
539	C₄×Dic₃	C₂³×C₃	1	4	yes	—
540	C₄×Dic₃	C₂³×C₃	1	2	yes	—
541	C₄×Dic₃	C₂³×C₃	1	4	yes	—
542	C₄×Dic₃	C₂³×C₃	1	4	yes	—
543	C₂²×C₃²	—	2	2	no	—
544	C₂²×C₃²	—	2	2	no	—
545	C₂²×C₃²	—	2	2	no	—
546	C₂²×C₃²	—	2	2	no	—
547	C₂²×C₃²	—	2	2	no	—
548	C₂²×C₃²	C₂×#41	1	4	yes	—
549	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
550	C₂×C₃×D₃	—	2	1	no	—
551	C₂×C₃×D₃	—	2	1	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	—	4	8	no	—
556	C₂×C₃×D₃	C₂×#41	1	2	yes	—
557	C₃²×C₄	—	2	2	no	—
558	C₃²×C₄	—	2	2	no	—
559	C₃²×C₄	—	2	4	no	—
560	C₃²×C₄	—	2	1	no	—
561	C₃²×C₄	C₂×#41	1	2	yes	—
562	C₃²×C₄	C₂×#41	1	2	yes	—
563	C₃×Dic₃	—	2	2	no	—
564	C₃×Dic₃	—	2	2	no	—
565	C₃×Dic₃	—	2	1	no	—
566	C₃×Dic₃	—	2	4	no	—
567	C₃×Dic₃	—	2	1	no	—
568	C₃×Dic₃	—	2	2	no	—
569	C₃×Dic₃	C₂×#41	1	2	yes	—
570	C₂×#41	—	3	1	no	—
571	C₂×#41	C₂×C₃×D₃	1	2	yes	—
572	C₂²×D₄	—	3	1	no	—
573	C₂³×C₄	—	3	2	no	—
574	C₄⋊Q₈	—	3	1	no	—
575	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
576	#126	—	3	4	no	—
577	#126	—	3	4	no	—
578	#126	—	3	4	no	—
579	#125	—	3	4	no	—
580	#125	—	3	2	no	—
581	#125	—	3	2	no	—
582	#124	—	3	2	no	—
583	#124	—	3	4	no	—
584	#123	—	3	4	no	—
585	#123	—	3	4	no	—
586	#123	—	3	4	no	—
587	#123	C₂×C₃×D₃	1	4	yes	complemented
588	C₂²⋊Q₈	—	3	2	no	—
589	C₂²⋊Q₈	—	3	2	no	—
590	C₂²⋊Q₈	—	3	2	no	—
591	C₂²⋊Q₈	—	3	2	no	—
592	C₂²⋊Q₈	—	3	4	no	—
593	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
594	#121	—	3	2	no	—
595	#121	—	3	4	no	—
596	#121	—	3	2	no	—
597	#121	C₂×C₃×D₃	1	2	yes	complemented
598	#120	—	3	4	no	—
599	C₄×Q₈	—	3	2	no	—
600	C₄×Q₈	—	3	2	no	—
601	C₄×Q₈	—	3	1	no	—
602	C₄×Q₈	—	3	2	no	—
603	C₄×Q₈	—	3	1	no	—
604	C₄×D₄	—	3	1	no	—
605	C₄×D₄	—	3	4	no	—
606	C₄×D₄	—	3	2	no	—
607	C₄×D₄	—	3	4	no	—
608	C₄×D₄	—	3	1	no	—
609	C₄×D₄	—	3	2	no	—
610	C₄×D₄	—	3	2	no	—
611	C₄×D₄	—	3	1	no	—
612	C₄×D₄	—	3	2	no	—
613	C₄×D₄	—	3	2	no	—
614	C₄×D₄	—	3	4	no	—
615	C₄×D₄	—	3	1	no	—
616	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
617	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
618	#117	—	3	4	no	—
619	#117	—	3	2	no	—
620	#117	—	3	1	no	—
621	#117	—	3	2	no	—
622	#117	—	3	4	no	—
623	#117	—	3	4	no	—
624	#117	—	3	2	no	—
625	#117	—	3	2	no	—
626	#117	—	3	2	no	—
627	C₂×C₄⋊C₄	—	3	2	no	—
628	C₂×C₄⋊C₄	—	3	1	no	—
629	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
630	C₂×C₂²⋊C₄	—	3	4	no	—
631	C₂×C₂²⋊C₄	—	3	2	no	—
632	C₂×C₄²	—	3	4	no	—
633	C₂×C₄²	—	3	2	no	—
634	C₂×C₄²	—	3	1	no	—
635	C₂³×C₃	—	2	2	no	—
636	C₂³×C₃	—	2	2	no	—
637	C₂³×C₃	—	3	1	no	—
638	C₂³×C₃	—	3	2	no	—
639	C₂³×C₃	—	6	4	no	—
640	C₂³×C₃	—	6	4	no	—
641	C₂³×C₃	—	12	2	no	—
642	C₂³×C₃	C₂³×D₃	1	2	yes	—
643	C₂³×C₃	C₂³×D₃	1	2	yes	—
644	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
645	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
646	C₂²×D₃	—	2	4	no	—
647	C₂²×D₃	—	2	4	no	—
648	C₂²×D₃	—	4	2	no	—
649	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
650	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
651	C₃×Q₈	—	2	4	no	—
652	C₃×Q₈	—	2	4	no	—
653	C₃×Q₈	—	4	4	no	—
654	C₃×Q₈	—	6	2	no	—
655	C₃×Q₈	—	12	2	no	—
656	C₃×D₄	—	2	8	no	—
657	C₃×D₄	—	2	8	no	—
658	C₃×D₄	—	2	2	no	—
659	C₃×D₄	—	2	2	no	—
660	C₃×D₄	—	2	4	no	—
661	C₃×D₄	—	4	2	no	—
662	C₃×D₄	—	4	8	no	—
663	C₃×D₄	—	6	4	no	—
664	C₃×D₄	—	6	4	no	—
665	C₃×D₄	—	6	2	no	—
666	C₃×D₄	—	12	4	no	—
667	C₃×D₄	#237	1	4	yes	complemented
668	C₃×D₄	C₃×#41	1	4	yes	complemented
669	C₂×C₃×C₄	—	2	8	no	—
670	C₂×C₃×C₄	—	2	8	no	—
671	C₂×C₃×C₄	—	2	4	no	—
672	C₂×C₃×C₄	—	2	4	no	—
673	C₂×C₃×C₄	—	2	4	no	—
674	C₂×C₃×C₄	—	2	4	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	4	no	—
681	C₂×C₃×C₄	—	3	1	no	—
682	C₂×C₃×C₄	—	3	4	no	—
683	C₂×C₃×C₄	—	3	2	no	—
684	C₂×C₃×C₄	—	3	2	no	—
685	C₂×C₃×C₄	—	3	1	no	—
686	C₂×C₃×C₄	—	3	2	no	—
687	C₂×C₃×C₄	—	3	4	no	—
688	C₂×C₃×C₄	—	3	1	no	—
689	C₂×C₃×C₄	—	4	4	no	—
690	C₂×C₃×C₄	—	4	4	no	—
691	C₂×C₃×C₄	—	4	8	no	—
692	C₂×C₃×C₄	—	6	4	no	—
693	C₂×C₃×C₄	—	6	4	no	—
694	C₂×C₃×C₄	—	6	4	no	—
695	C₂×C₃×C₄	—	6	4	no	—
696	C₂×C₃×C₄	—	6	2	no	—
697	C₂×C₃×C₄	—	6	4	no	—
698	C₂×C₃×C₄	—	12	1	no	—
699	C₂×C₃×C₄	—	12	2	no	—
700	C₂×C₃×C₄	—	12	4	no	—
701	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
702	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
703	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
705	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
706	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
707	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
708	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
709	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
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	#67	—	2	4	no	—
715	#67	—	4	4	no	—
716	C₂×Dic₃	—	2	4	no	—
717	C₂×Dic₃	—	2	4	no	—
718	C₂×Dic₃	—	4	4	no	—
719	C₂×Dic₃	—	4	2	no	—
720	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
721	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
722	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
723	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
724	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
725	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
726	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
727	D₁₂	—	2	2	no	—
728	C₄×D₃	—	2	4	no	—
729	C₄×D₃	—	2	4	no	—
730	C₄×D₃	—	2	2	no	—
731	C₄×D₃	—	2	4	no	—
732	C₄×D₃	—	4	1	no	—
733	C₄×D₃	C₃×#41	1	4	yes	complemented
734	Dic₆	—	2	2	no	—
735	Dic₆	—	4	2	no	—
736	C₂×C₃²	—	2	4	no	—
737	C₂×C₃²	—	4	2	no	—
738	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
739	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
740	C₂×C₃²	#585	1	1	yes	characteristic
741	C₃×D₃	—	2	2	no	—
742	C₃×D₃	—	4	2	no	—
743	C₂⁴	—	3	2	no	—
744	#41	—	2	8	no	—
745	#41	—	6	4	no	—
746	C₂×Q₈	—	3	1	no	—
747	C₂×Q₈	—	3	2	no	—
748	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
749	C₂×D₄	—	3	2	no	—
750	C₂×D₄	—	3	2	no	—
751	C₂×D₄	—	3	4	no	—
752	C₂×D₄	—	3	1	no	—
753	C₂×D₄	—	6	4	no	—
754	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
755	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
756	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
757	C₂²×C₄	—	3	1	no	—
758	C₂²×C₄	—	3	2	no	—
759	C₂²×C₄	—	3	2	no	—
760	C₂²×C₄	—	3	4	no	—
761	C₂²×C₄	—	3	2	no	—
762	C₂²×C₄	—	3	1	no	—
763	C₂²×C₄	—	3	2	no	—
764	C₂²×C₄	—	3	2	no	—
765	C₂²×C₄	—	3	2	no	—
766	C₂²×C₄	—	3	1	no	—
767	C₂²×C₄	—	6	8	no	—
768	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
769	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
770	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
771	C₄⋊C₄	—	3	1	no	—
772	C₄⋊C₄	—	3	1	no	—
773	C₄⋊C₄	—	3	2	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	2	no	—
776	C₄⋊C₄	—	3	2	no	—
777	C₄⋊C₄	—	3	2	no	—
778	C₄⋊C₄	—	3	4	no	—
779	C₄⋊C₄	—	3	4	no	—
780	C₄⋊C₄	—	3	2	no	—
781	C₄⋊C₄	—	3	4	no	—
782	C₄⋊C₄	—	3	4	no	—
783	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×C₃×D₃	1	2	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	4	no	—
790	C₂²⋊C₄	—	3	2	no	—
791	C₂²⋊C₄	—	3	4	no	—
792	C₂²⋊C₄	—	3	2	no	—
793	C₂²⋊C₄	—	3	4	no	—
794	C₂²⋊C₄	—	3	4	no	—
795	C₂²⋊C₄	—	3	4	no	—
796	C₂²⋊C₄	—	3	2	no	—
797	C₂²⋊C₄	—	3	2	no	—
798	C₂²⋊C₄	—	3	4	no	—
799	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
800	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
801	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
802	C₄²	—	3	2	no	—
803	C₄²	—	3	1	no	—
804	C₄²	—	3	4	no	—
805	C₄²	—	3	4	no	—
806	C₄²	—	3	1	no	—
807	C₄²	—	3	4	no	—
808	C₄²	—	3	2	no	—
809	C₄²	—	3	1	no	—
810	C₄²	—	3	2	no	—
811	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
812	C₂²×C₃	—	2	2	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	2	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	2	4	no	—
823	C₂²×C₃	—	2	1	no	—
824	C₂²×C₃	—	3	2	no	—
825	C₂²×C₃	—	4	2	no	—
826	C₂²×C₃	—	4	2	no	—
827	C₂²×C₃	—	4	2	no	—
828	C₂²×C₃	—	4	2	no	—
829	C₂²×C₃	—	4	2	no	—
830	C₂²×C₃	—	6	1	no	—
831	C₂²×C₃	—	6	1	no	—
832	C₂²×C₃	—	6	2	no	—
833	C₂²×C₃	—	6	2	no	—
834	C₂²×C₃	—	6	2	no	—
835	C₂²×C₃	—	12	8	no	—
836	C₂²×C₃	C₂×#237	1	4	yes	—
837	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
838	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
839	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
840	C₂×D₃	—	2	1	no	—
841	C₂×D₃	—	2	1	no	—
842	C₂×D₃	—	2	2	no	—
843	C₂×D₃	—	2	2	no	—
844	C₂×D₃	—	2	2	no	—
845	C₂×D₃	—	4	8	no	—
846	C₂×D₃	C₂×C₃×#41	1	2	yes	—
847	C₃×C₄	—	2	2	no	—
848	C₃×C₄	—	2	4	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	1	no	—
851	C₃×C₄	—	2	2	no	—
852	C₃×C₄	—	2	2	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	—	3	2	no	—
858	C₃×C₄	—	4	2	no	—
859	C₃×C₄	—	4	4	no	—
860	C₃×C₄	—	4	2	no	—
861	C₃×C₄	—	4	1	no	—
862	C₃×C₄	—	6	1	no	—
863	C₃×C₄	—	6	2	no	—
864	C₃×C₄	—	6	2	no	—
865	C₃×C₄	—	6	1	no	—
866	C₃×C₄	—	6	2	no	—
867	C₃×C₄	—	6	4	no	—
868	C₃×C₄	C₂×#237	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	Dic₃	—	2	2	no	—
873	Dic₃	—	2	2	no	—
874	Dic₃	—	2	1	no	—
875	Dic₃	—	2	4	no	—
876	Dic₃	—	2	1	no	—
877	Dic₃	—	2	2	no	—
878	Dic₃	C₂×C₃×#41	1	2	yes	—
879	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
880	C₂³	—	3	1	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	2	yes	—
886	C₂³	C₂³×C₃×D₃	1	2	yes	—
887	Q₈	—	2	4	no	—
888	Q₈	—	6	2	no	—
889	Q₈	—	12	2	no	—
890	D₄	—	2	8	no	—
891	D₄	—	2	2	no	—
892	D₄	—	6	4	no	—
893	D₄	—	6	4	no	—
894	D₄	—	6	2	no	—
895	D₄	—	12	4	no	—
896	D₄	C₃×#237	1	4	yes	complemented
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	4	no	—
900	C₂×C₄	—	3	1	no	—
901	C₂×C₄	—	3	4	no	—
902	C₂×C₄	—	3	2	no	—
903	C₂×C₄	—	3	2	no	—
904	C₂×C₄	—	3	1	no	—
905	C₂×C₄	—	3	2	no	—
906	C₂×C₄	—	3	4	no	—
907	C₂×C₄	—	3	1	no	—
908	C₂×C₄	—	6	4	no	—
909	C₂×C₄	—	6	4	no	—
910	C₂×C₄	—	6	4	no	—
911	C₂×C₄	—	6	4	no	—
912	C₂×C₄	—	6	2	no	—
913	C₂×C₄	—	6	4	no	—
914	C₂×C₄	—	12	1	no	—
915	C₂×C₄	—	12	2	no	—
916	C₂×C₄	—	12	4	no	—
917	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
918	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
919	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
920	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
921	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
922	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
923	C₂×C₃	—	2	4	no	—
924	C₂×C₃	—	2	4	no	—
925	C₂×C₃	—	2	1	no	—
926	C₂×C₃	—	2	1	no	—
927	C₂×C₃	—	2	1	no	—
928	C₂×C₃	—	4	4	no	—
929	C₂×C₃	—	4	2	no	—
930	C₂×C₃	—	4	2	no	—
931	C₂×C₃	—	6	2	no	—
932	C₂×C₃	—	8	2	no	—
933	C₂×C₃	—	12	2	no	—
934	C₂×C₃	C₂²×#237	1	1	yes	characteristic
935	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
936	C₂×C₃	#5968	1	1	yes	characteristic
937	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
938	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
939	C₂×C₃	C₃×#585	1	1	yes	characteristic
940	D₃	—	2	2	no	—
941	D₃	—	4	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	3	2	no	—
948	C₂²	—	6	1	no	—
949	C₂²	—	6	1	no	—
950	C₂²	—	6	2	no	—
951	C₂²	—	6	2	no	—
952	C₂²	—	6	2	no	—
953	C₂²	—	12	8	no	—
954	C₂²	C₂×C₃×#237	1	4	yes	—
955	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	4	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	1	no	—
960	C₄	—	3	2	no	—
961	C₄	—	6	1	no	—
962	C₄	—	6	2	no	—
963	C₄	—	6	2	no	—
964	C₄	—	6	1	no	—
965	C₄	—	6	2	no	—
966	C₄	—	6	4	no	—
967	C₄	C₂×C₃×#237	1	2	yes	—
968	C₄	C₃×D₃×#41	1	2	yes	—
969	C₃	—	2	1	no	—
970	C₃	#86675	1	1	yes	characteristic, direct product factor
971	C₃	C₃×#3475	1	1	yes	characteristic, complemented
972	C₂	—	2	4	no	—
973	C₂	—	4	2	no	—
974	C₂	—	6	2	no	—
975	C₂	—	12	2	no	—
976	C₂	C₂²×C₃×#237	1	1	yes	characteristic
977	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
978	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×#547	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#547	D₃
hypocenter	C₃	C₃×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#547

Complements

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

N	H ≅ G/N	type
1. C₃²×#547	C₂	semidirect
2. C₃×#5829	C₂	semidirect
3. C₃×Dic₃×#41	C₂	semidirect
4. C₃×#5732	C₂	semidirect
5. C₃×#5728	C₂	semidirect
6. C₃×#5658	C₂	semidirect
7. C₃×#5649	C₂	semidirect
8. C₃×#5639	C₂	semidirect
9. C₃×#5624	C₂	semidirect
10. C₃×#5618	C₂	semidirect
11. C₃×#5606	C₂	semidirect
12. C₃×#5563	C₂	semidirect
13. C₃×C₄×D₃×D₄	C₂	semidirect
14. C₃×#5543	C₂	semidirect
15. C₃×C₄×#237	C₂	semidirect
16. C₃×#5513	C₂	semidirect
17. C₂×C₃×#892	C₂	semidirect
19. #86675	C₃	direct (N × H)
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×#123	C₂²	semidirect
26. C₃²×C₂²⋊Q₈	C₂²	semidirect
27. C₃²×#121	C₂²	semidirect
29. C₃²×C₄×D₄	C₂²	semidirect
30. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
33. C₃×Q₈×Dic₃	C₂²	semidirect
34. C₃×Q₈×Dic₃	C₂²	semidirect
36. C₃×#938	C₂²	semidirect
40. C₃×D₄×Dic₃	C₂²	semidirect
41. C₃×D₄×Dic₃	C₂²	semidirect
42. C₃×D₄×Dic₃	C₂²	semidirect
48. C₃×#926	C₂²	semidirect
49. C₃×#926	C₂²	semidirect
50. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
51. C₃×#924	C₂²	semidirect
52. C₂×C₃×C₄×Dic₃	C₂²	semidirect
53. C₂×C₃×C₄×Dic₃	C₂²	semidirect
54. C₃×#898	C₂²	semidirect
55. C₃×#898	C₂²	semidirect
57. C₃×#897	C₂²	semidirect
62. C₃×#892	C₂²	semidirect
63. C₃×#892	C₂²	semidirect
64. C₃×#892	C₂²	semidirect
66. C₃×#890	C₂²	semidirect
67. C₃×#890	C₂²	semidirect
68. C₃×#889	C₂²	semidirect
69. C₃×#887	C₂²	semidirect
70. C₃×#887	C₂²	semidirect
71. C₃×#886	C₂²	semidirect
72. C₃×#885	C₂²	semidirect
76. C₃×#67⋊C₄	C₂²	semidirect
78. C₃×#879	C₂²	semidirect
79. C₃×#878	C₂²	semidirect
80. C₃×#877	C₂²	semidirect
83. C₃×#869	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
93. C₃×#547	D₃	semidirect
94. C₃×#547	C₂×C₃	semidirect
104. #5829	C₂×C₃	semidirect
105. Dic₃×#41	C₂×C₃	semidirect
106. #5732	C₂×C₃	semidirect
107. #5728	C₂×C₃	semidirect
108. #5658	C₂×C₃	semidirect
109. #5649	C₂×C₃	semidirect
110. #5639	C₂×C₃	semidirect
111. #5624	C₂×C₃	semidirect
112. #5618	C₂×C₃	semidirect
113. #5606	C₂×C₃	semidirect
114. #5563	C₂×C₃	semidirect
115. C₄×D₃×D₄	C₂×C₃	semidirect
116. #5543	C₂×C₃	semidirect
117. C₄×#237	C₂×C₃	semidirect
118. #5513	C₂×C₃	semidirect
119. C₂×#892	C₂×C₃	semidirect
201. C₃×C₄⋊Q₈	C₂×D₃	semidirect
202. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
215. C₃×#123	C₂×D₃	semidirect
216. C₃×#123	C₂²×C₃	semidirect
223. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
224. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
229. C₃×#121	C₂×D₃	semidirect
230. C₃×#121	C₂²×C₃	semidirect
252. C₃×C₄×D₄	C₂×D₃	semidirect
254. C₃×C₄×D₄	C₂²×C₃	semidirect
267. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
268. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
276. Q₈×Dic₃	C₂²×C₃	semidirect
277. Q₈×Dic₃	C₂²×C₃	semidirect
279. #938	C₂²×C₃	semidirect
283. D₄×Dic₃	C₂²×C₃	semidirect
284. D₄×Dic₃	C₂²×C₃	semidirect
285. D₄×Dic₃	C₂²×C₃	semidirect
291. #926	C₂²×C₃	semidirect
292. #926	C₂²×C₃	semidirect
293. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
294. #924	C₂²×C₃	semidirect
295. C₂×C₄×Dic₃	C₂²×C₃	semidirect
296. C₂×C₄×Dic₃	C₂²×C₃	semidirect
297. #898	C₂²×C₃	semidirect
298. #898	C₂²×C₃	semidirect
300. #897	C₂²×C₃	semidirect
305. #892	C₂²×C₃	semidirect
306. #892	C₂²×C₃	semidirect
307. #892	C₂²×C₃	semidirect
309. #890	C₂²×C₃	semidirect
310. #890	C₂²×C₃	semidirect
311. #889	C₂²×C₃	semidirect
312. #887	C₂²×C₃	semidirect
313. #887	C₂²×C₃	semidirect
314. #886	C₂²×C₃	semidirect
315. #885	C₂²×C₃	semidirect
319. #67⋊C₄	C₂²×C₃	semidirect
321. #879	C₂²×C₃	semidirect
322. #878	C₂²×C₃	semidirect
323. #877	C₂²×C₃	semidirect
326. #869	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
338. C₃²×D₄	#41	semidirect
368. C₃×C₄×D₃	#41	semidirect
378. #547	C₃×D₃	semidirect
575. C₄⋊Q₈	C₂×C₃×D₃	semidirect
587. #123	C₂×C₃×D₃	semidirect
593. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
597. #121	C₂×C₃×D₃	semidirect
617. C₄×D₄	C₂×C₃×D₃	semidirect
629. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
667. C₃×D₄	#237	semidirect
668. C₃×D₄	C₃×#41	semidirect
733. C₄×D₃	C₃×#41	semidirect
879. C₃²	#3475	semidirect
896. D₄	C₃×#237	semidirect
970. C₃	#86675	direct (N × H)
971. 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×#547	2
C₃×#5829	2
C₃×Dic₃×#41	2
C₃×#5732	2
C₃×#5728	2
C₃×#5658	2
C₃×#5649	2
C₃×#5639	2
C₃×#5624	2
C₃×#5618	2
C₃×#5606	2
C₃×#5563	2
C₃×C₄×D₃×D₄	2
C₃×#5543	2
C₃×C₄×#237	2
C₃×#5513	2
C₂×C₃×#892	2
C₃×#3475	3
#86675	3

Subgroups — C3×#86675 #11903469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86675 #11903469