Subgroups — C₃×#85859 #11904944

Order 1152.

2273 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5804	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5564	C₂	1	4	yes	maximal, complemented
5	C₃×#5556	C₂	1	4	yes	maximal, complemented
6	C₃×#5541	C₂	1	4	yes	maximal, complemented
7	C₃×#5538	C₂	1	4	yes	maximal, complemented
8	C₃×#5531	C₂	1	4	yes	maximal, complemented
9	C₃×#5495	C₂	1	4	yes	maximal, complemented
10	C₂×C₃×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5483	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3491	—	3	1	no	maximal
15	#85859	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
19	C₃²×C₄×D₄	C₂²	1	4	yes	—
20	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
21	C₃²×#117	C₂²	1	2	yes	complemented
22	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃×#953	C₂²	1	2	yes	—
26	C₂×C₃×#217	C₂²	1	1	yes	characteristic
27	C₂×C₃×#217	C₂²	1	1	yes	characteristic
28	C₂×C₃×#217	C₂²	1	2	yes	complemented
29	C₃×#939	C₂²	1	4	yes	—
30	C₃×#937	C₂²	1	2	yes	—
31	C₃×#935	C₂²	1	4	yes	—
32	C₃×#935	C₂²	1	2	yes	—
33	C₃×#935	C₂²	1	2	yes	complemented
34	C₃×#935	C₂²	1	2	yes	complemented
35	C₃×#929	C₂²	1	2	yes	—
36	C₃×#929	C₂²	1	4	yes	complemented
37	C₃×C₄×#67	C₂²	1	4	yes	complemented
38	C₃×C₄×#67	C₂²	1	4	yes	complemented
39	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
40	C₃×#926	C₂²	1	4	yes	complemented
41	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
42	C₃×#924	C₂²	1	4	yes	complemented
43	C₃×#924	C₂²	1	4	yes	complemented
44	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	complemented
47	C₃×#898	C₂²	1	4	yes	complemented
48	C₃×#896	C₂²	1	4	yes	complemented
49	C₃×#889	C₂²	1	4	yes	complemented
50	C₃×#889	C₂²	1	4	yes	complemented
51	C₃×#886	C₂²	1	4	yes	—
52	C₃×#886	C₂²	1	2	yes	complemented
53	C₃×#886	C₂²	1	2	yes	complemented
54	C₃×#885	C₂²	1	4	yes	complemented
55	C₃×#883	C₂²	1	4	yes	complemented
56	C₃×#67⋊C₄	C₂²	1	4	yes	—
57	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
58	C₃×#879	C₂²	1	4	yes	complemented
59	C₃×#879	C₂²	1	4	yes	complemented
60	C₃×#878	C₂²	1	4	yes	complemented
61	C₃×#878	C₂²	1	4	yes	complemented
62	C₃×#877	C₂²	1	4	yes	complemented
63	C₃×#877	C₂²	1	2	yes	complemented
64	C₃×#877	C₂²	1	4	yes	complemented
65	C₃×#876	C₂²	1	4	yes	complemented
66	C₃×#872	C₂²	1	4	yes	complemented
67	C₃×#870	C₂²	1	4	yes	complemented
68	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
69	C₃×#552	—	3	4	no	—
70	C₃×#552	—	3	4	no	—
71	C₃×#551	—	3	4	no	—
72	C₃×#551	—	3	4	no	—
73	C₃×#543	—	3	1	no	—
74	C₃×#539	—	3	4	no	—
75	C₃×#534	—	3	1	no	—
76	C₃×#529	—	3	4	no	—
77	C₂×C₃×#123	—	3	1	no	—
78	C₂×C₃×#123	—	3	1	no	—
79	C₃×#518	—	2	1	no	—
80	C₃×#518	—	3	1	no	—
81	C₃×#518	D₃	1	1	yes	characteristic, complemented
82	C₃×#518	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#117	—	3	1	no	—
84	#5804	C₂×C₃	1	1	yes	characteristic
85	C₂×#935	C₂×C₃	1	1	yes	characteristic, complemented
86	#5564	C₂×C₃	1	4	yes	complemented
87	#5556	C₂×C₃	1	4	yes	complemented
88	#5541	C₂×C₃	1	4	yes	complemented
89	#5538	C₂×C₃	1	4	yes	complemented
90	#5531	C₂×C₃	1	4	yes	complemented
91	#5495	C₂×C₃	1	4	yes	complemented
92	C₂×#886	C₂×C₃	1	1	yes	characteristic, complemented
93	#5486	C₂×C₃	1	1	yes	characteristic, complemented
94	#5483	C₂×C₃	1	1	yes	characteristic, complemented
95	C₂×#877	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
97	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
98	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₃²×D₄	—	2	4	no	—
100	C₂×C₃²×D₄	C₂³	1	2	yes	—
101	C₂×C₃²×D₄	C₂³	1	2	yes	—
102	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
103	C₂²×C₃²×C₄	C₂³	1	2	yes	—
104	C₂²×C₃²×C₄	C₂³	1	2	yes	—
105	C₂²×C₃²×C₄	C₂³	1	4	yes	—
106	C₂×C₃×#67	—	2	4	no	—
107	C₂×C₃×#67	C₂³	1	2	yes	—
108	C₂×C₃×#67	C₂³	1	2	yes	—
109	C₂×C₃×#67	C₂³	1	4	yes	—
110	C₂²×C₃×Dic₃	—	2	4	no	—
111	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
112	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
113	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
114	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
115	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
116	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
117	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
118	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
119	C₂×C₃×Dic₆	C₂³	1	4	yes	—
120	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃²×C₄²	C₂³	1	4	yes	—
127	C₃×#217	C₂³	1	2	yes	—
128	C₃×#217	C₂³	1	2	yes	—
129	C₃×#217	C₂³	1	2	yes	—
130	C₃×#217	C₂³	1	2	yes	—
131	C₃×#217	C₂³	1	4	yes	—
132	C₃×#217	C₂³	1	4	yes	—
133	C₃×#217	C₂³	1	4	yes	—
134	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
139	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
140	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
141	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
147	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₃×C₄×Dic₃	C₂³	1	4	yes	—
150	C₃×C₄×Dic₃	C₂³	1	4	yes	—
151	C₃×C₄×Dic₃	C₂³	1	4	yes	—
152	#3491	—	3	1	no	Sylow
153	C₂²×C₃×D₄	—	2	1	no	—
154	C₂²×C₃×D₄	—	3	1	no	—
155	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
157	C₂³×C₃×C₄	—	3	1	no	—
158	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
159	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
160	C₃×#126	—	3	4	no	—
161	C₃×#126	—	3	4	no	—
162	C₃×#126	—	3	4	no	—
163	C₃×#126	—	3	4	no	—
164	C₃×#125	—	3	4	no	—
165	C₃×#125	—	3	4	no	—
166	C₃×#125	—	3	4	no	—
167	C₃×#124	—	3	4	no	—
168	C₃×#123	—	3	4	no	—
169	C₃×#123	—	3	2	no	—
170	C₃×#123	—	3	2	no	—
171	C₃×#123	—	3	2	no	—
172	C₃×#123	—	3	2	no	—
173	C₃×#123	—	3	4	no	—
174	C₃×#123	—	3	4	no	—
175	C₃×#123	—	3	4	no	—
176	C₃×#123	—	3	2	no	—
177	C₃×#123	—	3	2	no	—
178	C₃×C₂²⋊Q₈	—	3	4	no	—
179	C₃×C₂²⋊Q₈	—	3	4	no	—
180	C₃×C₂²⋊Q₈	—	3	4	no	—
181	C₃×C₂²⋊Q₈	—	3	4	no	—
182	C₃×C₂²⋊Q₈	—	3	4	no	—
183	C₃×#121	—	3	4	no	—
184	C₃×#120	—	3	2	no	—
185	C₃×#120	—	3	2	no	—
186	C₃×C₄×Q₈	—	3	4	no	—
187	C₃×C₄×D₄	—	2	4	no	—
188	C₃×C₄×D₄	—	2	4	no	—
189	C₃×C₄×D₄	—	3	4	no	—
190	C₃×C₄×D₄	—	3	4	no	—
191	C₃×C₄×D₄	—	3	4	no	—
192	C₃×C₄×D₄	C₂×D₃	1	4	yes	—
193	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
194	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
195	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
196	C₃×#117	—	2	2	no	—
197	C₃×#117	—	3	4	no	—
198	C₃×#117	—	3	4	no	—
199	C₃×#117	—	3	4	no	—
200	C₃×#117	—	3	2	no	—
201	C₃×#117	—	3	4	no	—
202	C₃×#117	C₂×D₃	1	2	yes	complemented
203	C₃×#117	C₂²×C₃	1	2	yes	complemented
204	C₂×C₃×C₄⋊C₄	—	3	2	no	—
205	C₂×C₃×C₄⋊C₄	—	3	2	no	—
206	C₂×C₃×C₄⋊C₄	—	3	2	no	—
207	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
208	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
211	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
212	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
213	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
214	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
215	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
218	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
221	C₂×C₃×C₄²	—	3	2	no	—
222	#953	C₂²×C₃	1	2	yes	—
223	C₂×#217	C₂²×C₃	1	1	yes	characteristic
224	C₂×#217	C₂²×C₃	1	1	yes	characteristic
225	C₂×#217	C₂²×C₃	1	2	yes	complemented
226	#939	C₂²×C₃	1	4	yes	—
227	#937	C₂²×C₃	1	2	yes	—
228	#935	C₂²×C₃	1	4	yes	—
229	#935	C₂²×C₃	1	2	yes	—
230	#935	C₂²×C₃	1	2	yes	complemented
231	#935	C₂²×C₃	1	2	yes	complemented
232	#929	C₂²×C₃	1	2	yes	—
233	#929	C₂²×C₃	1	4	yes	complemented
234	C₄×#67	C₂²×C₃	1	4	yes	complemented
235	C₄×#67	C₂²×C₃	1	4	yes	complemented
236	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
237	#926	C₂²×C₃	1	4	yes	complemented
238	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
239	#924	C₂²×C₃	1	4	yes	complemented
240	#924	C₂²×C₃	1	4	yes	complemented
241	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
242	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
243	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	complemented
244	#898	C₂²×C₃	1	4	yes	complemented
245	#896	C₂²×C₃	1	4	yes	complemented
246	#889	C₂²×C₃	1	4	yes	complemented
247	#889	C₂²×C₃	1	4	yes	complemented
248	#886	C₂²×C₃	1	4	yes	—
249	#886	C₂²×C₃	1	2	yes	complemented
250	#886	C₂²×C₃	1	2	yes	complemented
251	#885	C₂²×C₃	1	4	yes	complemented
252	#883	C₂²×C₃	1	4	yes	complemented
253	#67⋊C₄	C₂²×C₃	1	4	yes	—
254	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
255	#879	C₂²×C₃	1	4	yes	complemented
256	#879	C₂²×C₃	1	4	yes	complemented
257	#878	C₂²×C₃	1	4	yes	complemented
258	#878	C₂²×C₃	1	4	yes	complemented
259	#877	C₂²×C₃	1	4	yes	complemented
260	#877	C₂²×C₃	1	4	yes	complemented
261	#877	C₂²×C₃	1	2	yes	complemented
262	#876	C₂²×C₃	1	4	yes	complemented
263	#872	C₂²×C₃	1	4	yes	complemented
264	#870	C₂²×C₃	1	4	yes	complemented
265	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
266	C₂³×C₃²	—	2	2	no	—
267	C₂³×C₃²	—	4	2	no	—
268	C₂³×C₃²	—	4	2	no	—
269	C₂³×C₃²	#41	1	4	yes	—
270	C₂³×C₃²	C₂⁴	1	2	yes	—
271	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
272	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
273	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
274	C₂²×C₃×D₃	—	2	2	no	—
275	C₂²×C₃×D₃	—	4	2	no	—
276	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
277	C₃²×D₄	—	2	4	no	—
278	C₃²×D₄	—	2	4	no	—
279	C₂×C₃²×C₄	—	2	2	no	—
280	C₂×C₃²×C₄	—	4	2	no	—
281	C₂×C₃²×C₄	—	4	4	no	—
282	C₂×C₃²×C₄	—	4	2	no	—
283	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
284	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
285	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
286	C₃×#67	—	2	4	no	—
287	C₃×#67	—	2	4	no	—
288	C₃×#67	—	4	4	no	—
289	C₂×C₃×Dic₃	—	2	4	no	—
290	C₂×C₃×Dic₃	—	2	4	no	—
291	C₂×C₃×Dic₃	—	2	2	no	—
292	C₂×C₃×Dic₃	—	2	2	no	—
293	C₂×C₃×Dic₃	—	2	2	no	—
294	C₂×C₃×Dic₃	—	4	2	no	—
295	C₂×C₃×Dic₃	—	4	2	no	—
296	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
297	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
298	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
299	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
300	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
301	C₃×C₄×D₃	—	4	4	no	—
302	C₃×Dic₆	—	4	4	no	—
303	#552	—	3	4	no	—
304	#552	—	3	4	no	—
305	#551	—	3	4	no	—
306	#551	—	3	4	no	—
307	#543	—	3	1	no	—
308	#539	—	3	4	no	—
309	#534	—	3	1	no	—
310	#529	—	3	4	no	—
311	C₂×#123	—	3	1	no	—
312	C₂×#123	—	3	1	no	—
313	#518	—	3	1	no	—
314	#518	C₃×D₃	1	1	yes	characteristic, complemented
315	C₂×#117	—	3	1	no	—
316	C₂⁴×C₃	—	2	1	no	—
317	C₂⁴×C₃	—	2	1	no	—
318	C₂⁴×C₃	—	3	1	no	—
319	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
320	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
321	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
322	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
323	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
324	C₂×C₃×Q₈	—	3	4	no	—
325	C₂×C₃×D₄	—	2	8	no	—
326	C₂×C₃×D₄	—	2	4	no	—
327	C₂×C₃×D₄	—	2	4	no	—
328	C₂×C₃×D₄	—	2	2	no	—
329	C₂×C₃×D₄	—	2	2	no	—
330	C₂×C₃×D₄	—	3	2	no	—
331	C₂×C₃×D₄	—	3	2	no	—
332	C₂×C₃×D₄	—	3	4	no	—
333	C₂×C₃×D₄	—	6	4	no	—
334	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
335	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
336	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
337	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
338	C₂²×C₃×C₄	—	2	1	no	—
339	C₂²×C₃×C₄	—	2	2	no	—
340	C₂²×C₃×C₄	—	2	2	no	—
341	C₂²×C₃×C₄	—	2	4	no	—
342	C₂²×C₃×C₄	—	3	1	no	—
343	C₂²×C₃×C₄	—	3	2	no	—
344	C₂²×C₃×C₄	—	3	2	no	—
345	C₂²×C₃×C₄	—	3	1	no	—
346	C₂²×C₃×C₄	—	3	1	no	—
347	C₂²×C₃×C₄	—	3	2	no	—
348	C₂²×C₃×C₄	—	3	2	no	—
349	C₂²×C₃×C₄	—	3	4	no	—
350	C₂²×C₃×C₄	—	6	4	no	—
351	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
353	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
354	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
355	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
357	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
358	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
359	C₂×#67	—	2	4	no	—
360	C₂×#67	C₂³×C₃	1	2	yes	—
361	C₂×#67	C₂³×C₃	1	2	yes	—
362	C₂×#67	C₂³×C₃	1	4	yes	—
363	C₂²×Dic₃	—	2	4	no	—
364	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
365	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
366	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
367	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
368	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
369	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
370	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
371	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
372	C₂×Dic₆	C₂³×C₃	1	4	yes	—
373	C₃×C₄⋊C₄	—	2	4	no	—
374	C₃×C₄⋊C₄	—	3	4	no	—
375	C₃×C₄⋊C₄	—	3	4	no	—
376	C₃×C₄⋊C₄	—	3	4	no	—
377	C₃×C₄⋊C₄	—	3	4	no	—
378	C₃×C₄⋊C₄	—	3	4	no	—
379	C₃×C₄⋊C₄	—	3	4	no	—
380	C₃×C₄⋊C₄	—	3	4	no	—
381	C₃×C₄⋊C₄	—	3	4	no	—
382	C₃×C₄⋊C₄	—	3	4	no	—
383	C₃×C₄⋊C₄	—	3	4	no	—
384	C₃×C₄⋊C₄	—	3	4	no	—
385	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
386	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
387	C₃×C₂²⋊C₄	—	2	2	no	—
388	C₃×C₂²⋊C₄	—	2	2	no	—
389	C₃×C₂²⋊C₄	—	2	2	no	—
390	C₃×C₂²⋊C₄	—	2	2	no	—
391	C₃×C₂²⋊C₄	—	2	4	no	—
392	C₃×C₂²⋊C₄	—	3	2	no	—
393	C₃×C₂²⋊C₄	—	3	2	no	—
394	C₃×C₂²⋊C₄	—	3	2	no	—
395	C₃×C₂²⋊C₄	—	3	4	no	—
396	C₃×C₂²⋊C₄	—	3	2	no	—
397	C₃×C₂²⋊C₄	—	3	4	no	—
398	C₃×C₂²⋊C₄	—	3	4	no	—
399	C₃×C₂²⋊C₄	—	3	4	no	—
400	C₃×C₂²⋊C₄	—	3	4	no	—
401	C₃×C₂²⋊C₄	—	3	4	no	—
402	C₃×C₂²⋊C₄	—	3	4	no	—
403	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
404	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
405	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
406	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
407	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
408	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
409	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
410	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
411	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
412	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
413	C₃×C₄²	—	2	4	no	—
414	C₃×C₄²	—	3	4	no	—
415	C₃×C₄²	—	3	4	no	—
416	C₃×C₄²	—	3	4	no	—
417	C₃×C₄²	C₂²×D₃	1	4	yes	—
418	C₃×C₄²	C₂³×C₃	1	4	yes	—
419	#217	C₂³×C₃	1	2	yes	—
420	#217	C₂³×C₃	1	2	yes	—
421	#217	C₂³×C₃	1	2	yes	—
422	#217	C₂³×C₃	1	2	yes	—
423	#217	C₂³×C₃	1	4	yes	—
424	#217	C₂³×C₃	1	4	yes	—
425	#217	C₂³×C₃	1	4	yes	—
426	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
427	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
428	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
429	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
430	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
431	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
432	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
433	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
434	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
435	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
436	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
437	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
438	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
439	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
440	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
441	C₄×Dic₃	C₂³×C₃	1	4	yes	—
442	C₄×Dic₃	C₂³×C₃	1	4	yes	—
443	C₄×Dic₃	C₂³×C₃	1	4	yes	—
444	C₂²×C₃²	—	2	2	no	—
445	C₂²×C₃²	—	2	2	no	—
446	C₂²×C₃²	—	2	2	no	—
447	C₂²×C₃²	—	2	2	no	—
448	C₂²×C₃²	—	2	4	no	—
449	C₂²×C₃²	—	4	4	no	—
450	C₂²×C₃²	—	8	2	no	—
451	C₂²×C₃²	C₂×#41	1	2	yes	—
452	C₂²×C₃²	C₂×#41	1	2	yes	—
453	C₂²×C₃²	C₂×#41	1	2	yes	—
454	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
455	C₂×C₃×D₃	—	2	2	no	—
456	C₂×C₃×D₃	—	2	4	no	—
457	C₂×C₃×D₃	—	8	2	no	—
458	C₃²×C₄	—	2	2	no	—
459	C₃²×C₄	—	2	4	no	—
460	C₃²×C₄	—	2	4	no	—
461	C₃×Dic₃	—	2	2	no	—
462	C₃×Dic₃	—	2	2	no	—
463	C₃×Dic₃	—	2	2	no	—
464	C₃×Dic₃	—	2	4	no	—
465	C₃×Dic₃	—	2	4	no	—
466	C₂²×D₄	—	3	1	no	—
467	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
468	C₂³×C₄	—	3	1	no	—
469	#126	—	3	4	no	—
470	#126	—	3	4	no	—
471	#126	—	3	4	no	—
472	#126	—	3	4	no	—
473	#125	—	3	4	no	—
474	#125	—	3	4	no	—
475	#125	—	3	4	no	—
476	#124	—	3	4	no	—
477	#123	—	3	2	no	—
478	#123	—	3	2	no	—
479	#123	—	3	4	no	—
480	#123	—	3	2	no	—
481	#123	—	3	2	no	—
482	#123	—	3	4	no	—
483	#123	—	3	2	no	—
484	#123	—	3	2	no	—
485	#123	—	3	4	no	—
486	#123	—	3	4	no	—
487	C₂²⋊Q₈	—	3	4	no	—
488	C₂²⋊Q₈	—	3	4	no	—
489	C₂²⋊Q₈	—	3	4	no	—
490	C₂²⋊Q₈	—	3	4	no	—
491	C₂²⋊Q₈	—	3	4	no	—
492	#121	—	3	4	no	—
493	#120	—	3	2	no	—
494	#120	—	3	2	no	—
495	C₄×Q₈	—	3	4	no	—
496	C₄×D₄	—	3	4	no	—
497	C₄×D₄	—	3	4	no	—
498	C₄×D₄	—	3	4	no	—
499	C₄×D₄	C₂×C₃×D₃	1	4	yes	—
500	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
501	#117	—	3	4	no	—
502	#117	—	3	4	no	—
503	#117	—	3	4	no	—
504	#117	—	3	2	no	—
505	#117	—	3	4	no	—
506	#117	C₂×C₃×D₃	1	2	yes	complemented
507	C₂×C₄⋊C₄	—	3	2	no	—
508	C₂×C₄⋊C₄	—	3	2	no	—
509	C₂×C₄⋊C₄	—	3	2	no	—
510	C₂×C₂²⋊C₄	—	3	1	no	—
511	C₂×C₂²⋊C₄	—	3	1	no	—
512	C₂×C₂²⋊C₄	—	3	2	no	—
513	C₂×C₂²⋊C₄	—	3	2	no	—
514	C₂×C₂²⋊C₄	—	3	2	no	—
515	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
518	C₂×C₄²	—	3	2	no	—
519	C₂³×C₃	—	2	4	no	—
520	C₂³×C₃	—	2	2	no	—
521	C₂³×C₃	—	2	2	no	—
522	C₂³×C₃	—	2	1	no	—
523	C₂³×C₃	—	2	2	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	4	no	—
527	C₂³×C₃	—	3	2	no	—
528	C₂³×C₃	—	4	2	no	—
529	C₂³×C₃	—	4	2	no	—
530	C₂³×C₃	—	4	2	no	—
531	C₂³×C₃	—	4	2	no	—
532	C₂³×C₃	—	6	2	no	—
533	C₂³×C₃	—	8	2	no	—
534	C₂³×C₃	—	8	2	no	—
535	C₂³×C₃	—	12	2	no	—
536	C₂³×C₃	#235	1	4	yes	—
537	C₂³×C₃	C₃×#41	1	4	yes	—
538	C₂³×C₃	C₂³×D₃	1	2	yes	—
539	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
540	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
541	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
542	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
543	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
544	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
545	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
546	C₂²×D₃	—	2	2	no	—
547	C₂²×D₃	—	4	2	no	—
548	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
549	C₃×Q₈	—	12	4	no	—
550	C₃×D₄	—	2	8	no	—
551	C₃×D₄	—	2	8	no	—
552	C₃×D₄	—	2	4	no	—
553	C₃×D₄	—	2	4	no	—
554	C₃×D₄	—	2	4	no	—
555	C₃×D₄	—	2	4	no	—
556	C₃×D₄	—	6	4	no	—
557	C₃×D₄	—	6	4	no	—
558	C₃×D₄	—	12	4	no	—
559	C₂×C₃×C₄	—	2	4	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	4	no	—
564	C₂×C₃×C₄	—	2	4	no	—
565	C₂×C₃×C₄	—	3	2	no	—
566	C₂×C₃×C₄	—	3	4	no	—
567	C₂×C₃×C₄	—	3	2	no	—
568	C₂×C₃×C₄	—	3	4	no	—
569	C₂×C₃×C₄	—	3	2	no	—
570	C₂×C₃×C₄	—	4	2	no	—
571	C₂×C₃×C₄	—	4	4	no	—
572	C₂×C₃×C₄	—	4	2	no	—
573	C₂×C₃×C₄	—	4	2	no	—
574	C₂×C₃×C₄	—	4	4	no	—
575	C₂×C₃×C₄	—	4	2	no	—
576	C₂×C₃×C₄	—	6	4	no	—
577	C₂×C₃×C₄	—	6	4	no	—
578	C₂×C₃×C₄	—	6	2	no	—
579	C₂×C₃×C₄	—	6	2	no	—
580	C₂×C₃×C₄	—	6	2	no	—
581	C₂×C₃×C₄	—	8	2	no	—
582	C₂×C₃×C₄	—	8	4	no	—
583	C₂×C₃×C₄	—	8	2	no	—
584	C₂×C₃×C₄	—	12	4	no	—
585	C₂×C₃×C₄	—	12	2	no	—
586	C₂×C₃×C₄	—	12	2	no	—
587	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
588	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
589	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
590	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
591	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
592	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
593	#67	—	2	4	no	—
594	#67	—	2	4	no	—
595	#67	—	4	4	no	—
596	C₂×Dic₃	—	2	4	no	—
597	C₂×Dic₃	—	2	4	no	—
598	C₂×Dic₃	—	2	2	no	—
599	C₂×Dic₃	—	2	2	no	—
600	C₂×Dic₃	—	2	2	no	—
601	C₂×Dic₃	—	4	2	no	—
602	C₂×Dic₃	—	4	2	no	—
603	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
604	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
605	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
606	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
607	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
608	C₄×D₃	—	4	4	no	—
609	Dic₆	—	4	4	no	—
610	C₂×C₃²	—	2	2	no	—
611	C₂×C₃²	—	2	2	no	—
612	C₂×C₃²	—	2	2	no	—
613	C₂×C₃²	—	4	2	no	—
614	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
615	C₂×C₃²	#585	1	2	yes	—
616	C₃×D₃	—	4	2	no	—
617	C₂⁴	—	3	1	no	—
618	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
619	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
620	C₂×Q₈	—	3	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	3	2	no	—
623	C₂×D₄	—	3	2	no	—
624	C₂×D₄	—	3	4	no	—
625	C₂×D₄	—	6	4	no	—
626	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
627	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
628	C₂²×C₄	—	3	1	no	—
629	C₂²×C₄	—	3	2	no	—
630	C₂²×C₄	—	3	2	no	—
631	C₂²×C₄	—	3	1	no	—
632	C₂²×C₄	—	3	1	no	—
633	C₂²×C₄	—	3	2	no	—
634	C₂²×C₄	—	3	2	no	—
635	C₂²×C₄	—	3	4	no	—
636	C₂²×C₄	—	6	4	no	—
637	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
639	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
640	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
641	C₄⋊C₄	—	3	4	no	—
642	C₄⋊C₄	—	3	4	no	—
643	C₄⋊C₄	—	3	4	no	—
644	C₄⋊C₄	—	3	4	no	—
645	C₄⋊C₄	—	3	4	no	—
646	C₄⋊C₄	—	3	4	no	—
647	C₄⋊C₄	—	3	4	no	—
648	C₄⋊C₄	—	3	4	no	—
649	C₄⋊C₄	—	3	4	no	—
650	C₄⋊C₄	—	3	4	no	—
651	C₄⋊C₄	—	3	4	no	—
652	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
653	C₂²⋊C₄	—	3	2	no	—
654	C₂²⋊C₄	—	3	2	no	—
655	C₂²⋊C₄	—	3	2	no	—
656	C₂²⋊C₄	—	3	4	no	—
657	C₂²⋊C₄	—	3	2	no	—
658	C₂²⋊C₄	—	3	4	no	—
659	C₂²⋊C₄	—	3	4	no	—
660	C₂²⋊C₄	—	3	4	no	—
661	C₂²⋊C₄	—	3	4	no	—
662	C₂²⋊C₄	—	3	4	no	—
663	C₂²⋊C₄	—	3	4	no	—
664	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
665	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
666	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
667	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
668	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
669	C₄²	—	3	4	no	—
670	C₄²	—	3	4	no	—
671	C₄²	—	3	4	no	—
672	C₄²	C₂²×C₃×D₃	1	4	yes	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	2	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	2	2	no	—
677	C₂²×C₃	—	2	2	no	—
678	C₂²×C₃	—	2	2	no	—
679	C₂²×C₃	—	2	4	no	—
680	C₂²×C₃	—	2	2	no	—
681	C₂²×C₃	—	2	4	no	—
682	C₂²×C₃	—	2	2	no	—
683	C₂²×C₃	—	2	4	no	—
684	C₂²×C₃	—	2	2	no	—
685	C₂²×C₃	—	2	2	no	—
686	C₂²×C₃	—	2	2	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	4	2	no	—
689	C₂²×C₃	—	4	2	no	—
690	C₂²×C₃	—	4	4	no	—
691	C₂²×C₃	—	4	2	no	—
692	C₂²×C₃	—	4	4	no	—
693	C₂²×C₃	—	4	4	no	—
694	C₂²×C₃	—	6	2	no	—
695	C₂²×C₃	—	6	4	no	—
696	C₂²×C₃	—	8	4	no	—
697	C₂²×C₃	—	8	2	no	—
698	C₂²×C₃	—	8	2	no	—
699	C₂²×C₃	—	8	4	no	—
700	C₂²×C₃	—	24	2	no	—
701	C₂²×C₃	C₂×#235	1	2	yes	—
702	C₂²×C₃	C₂×#235	1	2	yes	—
703	C₂²×C₃	C₂×#235	1	2	yes	—
704	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
705	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
706	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
707	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
708	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
709	C₂×D₃	—	2	2	no	—
710	C₂×D₃	—	2	4	no	—
711	C₂×D₃	—	8	2	no	—
712	C₃×C₄	—	2	4	no	—
713	C₃×C₄	—	2	2	no	—
714	C₃×C₄	—	2	4	no	—
715	C₃×C₄	—	2	4	no	—
716	C₃×C₄	—	2	2	no	—
717	C₃×C₄	—	2	4	no	—
718	C₃×C₄	—	2	4	no	—
719	C₃×C₄	—	4	4	no	—
720	C₃×C₄	—	4	4	no	—
721	C₃×C₄	—	6	2	no	—
722	C₃×C₄	—	6	2	no	—
723	C₃×C₄	—	6	2	no	—
724	C₃×C₄	—	6	4	no	—
725	C₃×C₄	—	6	4	no	—
726	Dic₃	—	2	2	no	—
727	Dic₃	—	2	2	no	—
728	Dic₃	—	2	2	no	—
729	Dic₃	—	2	4	no	—
730	Dic₃	—	2	4	no	—
731	C₃²	#3491	1	1	yes	characteristic, complemented, Sylow
732	C₂³	—	2	2	no	—
733	C₂³	—	3	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	6	2	no	—
737	C₂³	—	12	2	no	—
738	C₂³	C₃×#235	1	4	yes	—
739	C₂³	C₂³×C₃×D₃	1	2	yes	—
740	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
741	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
742	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
743	Q₈	—	12	4	no	—
744	D₄	—	2	4	no	—
745	D₄	—	2	4	no	—
746	D₄	—	6	4	no	—
747	D₄	—	6	4	no	—
748	D₄	—	12	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	3	2	no	—
751	C₂×C₄	—	3	4	no	—
752	C₂×C₄	—	3	2	no	—
753	C₂×C₄	—	3	4	no	—
754	C₂×C₄	—	3	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	6	4	no	—
759	C₂×C₄	—	6	4	no	—
760	C₂×C₄	—	6	2	no	—
761	C₂×C₄	—	6	2	no	—
762	C₂×C₄	—	6	2	no	—
763	C₂×C₄	—	12	4	no	—
764	C₂×C₄	—	12	2	no	—
765	C₂×C₄	—	12	2	no	—
766	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
767	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
768	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	2	2	no	—
771	C₂×C₃	—	2	2	no	—
772	C₂×C₃	—	2	2	no	—
773	C₂×C₃	—	2	2	no	—
774	C₂×C₃	—	2	2	no	—
775	C₂×C₃	—	2	1	no	—
776	C₂×C₃	—	2	2	no	—
777	C₂×C₃	—	4	2	no	—
778	C₂×C₃	—	4	2	no	—
779	C₂×C₃	—	4	2	no	—
780	C₂×C₃	—	4	4	no	—
781	C₂×C₃	—	4	2	no	—
782	C₂×C₃	—	4	2	no	—
783	C₂×C₃	—	12	2	no	—
784	C₂×C₃	C₂²×#235	1	1	yes	characteristic
785	C₂×C₃	#5966	1	2	yes	—
786	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
787	C₂×C₃	C₃×#585	1	2	yes	—
788	D₃	—	4	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	6	2	no	—
796	C₂²	—	6	4	no	—
797	C₂²	—	8	2	no	—
798	C₂²	—	24	2	no	—
799	C₂²	C₂×C₃×#235	1	2	yes	—
800	C₂²	C₂×C₃×#235	1	2	yes	—
801	C₂²	C₂×C₃×#235	1	2	yes	—
802	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
803	C₄	—	2	2	no	—
804	C₄	—	2	4	no	—
805	C₄	—	2	4	no	—
806	C₄	—	6	2	no	—
807	C₄	—	6	2	no	—
808	C₄	—	6	2	no	—
809	C₄	—	6	4	no	—
810	C₄	—	6	4	no	—
811	C₃	—	2	1	no	—
812	C₃	#85859	1	1	yes	characteristic, direct product factor
813	C₃	C₃×#3491	1	1	yes	characteristic, complemented
814	C₂	—	2	2	no	—
815	C₂	—	2	2	no	—
816	C₂	—	2	2	no	—
817	C₂	—	4	2	no	—
818	C₂	—	12	2	no	—
819	C₂	C₂²×C₃×#235	1	1	yes	characteristic
820	C₂	C₃×#5966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#518	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₃×#5804	C₂
hypercenter	C₃×#518	D₃
hypocenter	C₃	C₃×#3491
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#518

Complements

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

N	H ≅ G/N	type
1. C₃²×#518	C₂	semidirect
3. C₂×C₃×#935	C₂	semidirect
4. C₃×#5564	C₂	semidirect
5. C₃×#5556	C₂	semidirect
6. C₃×#5541	C₂	semidirect
7. C₃×#5538	C₂	semidirect
8. C₃×#5531	C₂	semidirect
9. C₃×#5495	C₂	semidirect
10. C₂×C₃×#886	C₂	semidirect
11. C₃×#5486	C₂	semidirect
12. C₃×#5483	C₂	semidirect
13. C₂×C₃×#877	C₂	semidirect
15. #85859	C₃	direct (N × H)
20. C₃²×C₄×D₄	C₂²	semidirect
21. C₃²×#117	C₂²	semidirect
24. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×#217	C₂²	semidirect
33. C₃×#935	C₂²	semidirect
34. C₃×#935	C₂²	semidirect
36. C₃×#929	C₂²	semidirect
37. C₃×C₄×#67	C₂²	semidirect
38. C₃×C₄×#67	C₂²	semidirect
39. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
40. C₃×#926	C₂²	semidirect
41. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
42. C₃×#924	C₂²	semidirect
43. C₃×#924	C₂²	semidirect
44. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
45. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
46. C₂×C₃×C₄×Dic₃	C₂²	semidirect
47. C₃×#898	C₂²	semidirect
48. C₃×#896	C₂²	semidirect
49. C₃×#889	C₂²	semidirect
50. C₃×#889	C₂²	semidirect
52. C₃×#886	C₂²	semidirect
53. C₃×#886	C₂²	semidirect
54. C₃×#885	C₂²	semidirect
55. C₃×#883	C₂²	semidirect
57. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
58. C₃×#879	C₂²	semidirect
59. C₃×#879	C₂²	semidirect
60. C₃×#878	C₂²	semidirect
61. C₃×#878	C₂²	semidirect
62. C₃×#877	C₂²	semidirect
63. C₃×#877	C₂²	semidirect
64. C₃×#877	C₂²	semidirect
65. C₃×#876	C₂²	semidirect
66. C₃×#872	C₂²	semidirect
67. C₃×#870	C₂²	semidirect
68. C₃×C₄×Dic₆	C₂²	semidirect
81. C₃×#518	D₃	semidirect
82. C₃×#518	C₂×C₃	semidirect
85. C₂×#935	C₂×C₃	semidirect
86. #5564	C₂×C₃	semidirect
87. #5556	C₂×C₃	semidirect
88. #5541	C₂×C₃	semidirect
89. #5538	C₂×C₃	semidirect
90. #5531	C₂×C₃	semidirect
91. #5495	C₂×C₃	semidirect
92. C₂×#886	C₂×C₃	semidirect
93. #5486	C₂×C₃	semidirect
94. #5483	C₂×C₃	semidirect
95. C₂×#877	C₂×C₃	semidirect
193. C₃×C₄×D₄	C₂×D₃	semidirect
195. C₃×C₄×D₄	C₂²×C₃	semidirect
202. C₃×#117	C₂×D₃	semidirect
203. C₃×#117	C₂²×C₃	semidirect
217. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
220. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
225. C₂×#217	C₂²×C₃	semidirect
230. #935	C₂²×C₃	semidirect
231. #935	C₂²×C₃	semidirect
233. #929	C₂²×C₃	semidirect
234. C₄×#67	C₂²×C₃	semidirect
235. C₄×#67	C₂²×C₃	semidirect
236. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
237. #926	C₂²×C₃	semidirect
238. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
239. #924	C₂²×C₃	semidirect
240. #924	C₂²×C₃	semidirect
241. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
242. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
243. C₂×C₄×Dic₃	C₂²×C₃	semidirect
244. #898	C₂²×C₃	semidirect
245. #896	C₂²×C₃	semidirect
246. #889	C₂²×C₃	semidirect
247. #889	C₂²×C₃	semidirect
249. #886	C₂²×C₃	semidirect
250. #886	C₂²×C₃	semidirect
251. #885	C₂²×C₃	semidirect
252. #883	C₂²×C₃	semidirect
254. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
255. #879	C₂²×C₃	semidirect
256. #879	C₂²×C₃	semidirect
257. #878	C₂²×C₃	semidirect
258. #878	C₂²×C₃	semidirect
259. #877	C₂²×C₃	semidirect
260. #877	C₂²×C₃	semidirect
261. #877	C₂²×C₃	semidirect
262. #876	C₂²×C₃	semidirect
263. #872	C₂²×C₃	semidirect
264. #870	C₂²×C₃	semidirect
265. C₄×Dic₆	C₂²×C₃	semidirect
314. #518	C₃×D₃	semidirect
500. C₄×D₄	C₂×C₃×D₃	semidirect
506. #117	C₂×C₃×D₃	semidirect
517. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
731. C₃²	#3491	semidirect
812. C₃	#85859	direct (N × H)
813. C₃	C₃×#3491	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#518	2
C₃×#5804	2
C₂×C₃×#935	2
C₃×#5564	2
C₃×#5556	2
C₃×#5541	2
C₃×#5538	2
C₃×#5531	2
C₃×#5495	2
C₂×C₃×#886	2
C₃×#5486	2
C₃×#5483	2
C₂×C₃×#877	2
C₃×#3491	3
#85859	3

Subgroups — C3×#85859 #11904944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85859 #11904944