Subgroups — C₃×#10589712 #13152813

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3699	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63499	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×(C₂×D₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63458	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63456	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#611⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₂²⋊C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5610	—	3	1	no	maximal
17	#10589712	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
19	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#611	C₂²	1	1	yes	characteristic
25	C₂×C₃×#611	C₂²	1	1	yes	characteristic
26	C₂×C₃×#611	C₂²	1	1	yes	characteristic
27	C₂×C₃×#611	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#611	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
31	C₃×#3699	—	2	4	no	—
32	C₃×D₄×D₉	—	2	4	no	—
33	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3676	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3676	C₂²	1	1	yes	characteristic, complemented
43	C₃×#3676	C₂²	1	1	yes	characteristic, complemented
44	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
45	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
46	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic
47	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#237	—	3	1	no	—
56	C₂×C₃×D₃×D₄	—	3	1	no	—
57	C₃²×#121	D₃	1	1	yes	characteristic
58	C₃×#939	—	3	1	no	—
59	C₃×#937	—	3	1	no	—
60	C₃×#937	—	3	1	no	—
61	C₃×#935	—	3	1	no	—
62	C₃×C₄×#67	—	3	1	no	—
63	C₂×C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
64	C₃×#896	—	3	1	no	—
65	C₃×#894	—	3	1	no	—
66	C₃×#885	—	3	1	no	—
67	C₃×#884	—	3	1	no	—
68	C₃×#67⋊C₄	—	3	1	no	—
69	C₃×D₃×C₂²⋊C₄	—	3	1	no	—
70	C₂×#3699	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×D₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
72	C₉×#121	—	2	1	no	—
73	C₉×#121	C₂×C₃	1	1	yes	characteristic, complemented
74	#63501	C₂×C₃	1	1	yes	characteristic, complemented
75	#63499	C₂×C₃	1	1	yes	characteristic, complemented
76	#63499	C₂×C₃	1	1	yes	characteristic, complemented
77	#63497	C₂×C₃	1	1	yes	characteristic, complemented
78	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
80	#63458	C₂×C₃	1	1	yes	characteristic, complemented
81	#63456	C₂×C₃	1	1	yes	characteristic, complemented
82	#63447	C₂×C₃	1	1	yes	characteristic, complemented
83	#63446	C₂×C₃	1	1	yes	characteristic, complemented
84	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂²⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₃×D₉	—	2	2	no	—
90	C₂²×C₃×D₉	—	2	2	no	—
91	C₂²×C₃×D₉	—	2	2	no	—
92	C₂²×C₃×D₉	—	2	2	no	—
93	C₂²×C₃×D₉	—	4	1	no	—
94	C₂²×C₃×D₉	—	4	1	no	—
95	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
96	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
97	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
98	C₃×D₄×C₉	—	2	2	no	—
99	C₃×D₄×C₉	—	2	2	no	—
100	C₃×D₄×C₉	—	4	1	no	—
101	C₂×C₃×C₄×C₉	—	4	1	no	—
102	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
106	C₃×#611	—	2	2	no	—
107	C₃×#611	—	2	2	no	—
108	C₃×#611	—	2	2	no	—
109	C₃×#611	—	4	1	no	—
110	C₃×#611	D₄	1	4	yes	complemented
111	C₂×C₃×Dic₉	—	2	2	no	—
112	C₂×C₃×Dic₉	—	2	2	no	—
113	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
114	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
115	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
116	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
117	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
118	C₃×D₃₆	—	2	2	no	—
119	C₃×C₄×D₉	—	2	2	no	—
120	C₃×C₄×D₉	—	2	2	no	—
121	C₃×C₄×D₉	—	4	1	no	—
122	C₃×Dic₁₈	—	2	2	no	—
123	C₃×#546	—	9	1	no	—
124	#5610	—	3	1	no	—
125	C₂³×C₃×D₃	—	3	1	no	—
126	C₂³×C₃×D₃	—	3	1	no	—
127	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
128	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
131	C₂×C₃×#67	—	3	1	no	—
132	C₂×C₃×#67	—	3	1	no	—
133	C₂×C₃×#67	—	3	1	no	—
134	C₂×C₃×#67	—	3	1	no	—
135	C₂×C₃×#67	—	3	1	no	—
136	C₂²×C₃×Dic₃	—	3	1	no	—
137	C₂²×C₃×Dic₃	—	3	1	no	—
138	C₃×#237	—	6	4	no	—
139	C₃×D₃×D₄	—	6	4	no	—
140	C₂×C₃×D₁₂	—	3	1	no	—
141	C₂×C₃×C₄×D₃	—	3	1	no	—
142	C₂×C₃×C₄×D₃	—	3	1	no	—
143	C₂×C₃×C₄×D₃	—	3	1	no	—
144	C₂×C₃×Dic₆	—	3	1	no	—
145	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
146	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
147	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
148	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
149	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₃×#217	—	3	1	no	—
151	C₃×#217	—	3	1	no	—
152	C₃×#217	—	3	1	no	—
153	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
154	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
155	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
156	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
157	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
158	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
159	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
160	C₃×Dic₃⋊C₄	—	3	1	no	—
161	C₃×Dic₃⋊C₄	—	3	1	no	—
162	C₃×Dic₃⋊C₄	—	3	1	no	—
163	C₃×C₄×Dic₃	—	3	1	no	—
164	C₂×D₄×C₉	—	2	1	no	—
165	C₂×D₄×C₉	—	2	1	no	—
166	C₂×D₄×C₉	—	2	1	no	—
167	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
168	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂²×C₄×C₉	—	2	1	no	—
171	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂×#611	C₂²×C₃	1	1	yes	characteristic
173	C₂×#611	C₂²×C₃	1	1	yes	characteristic
174	C₂×#611	C₂²×C₃	1	1	yes	characteristic
175	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
179	#3699	—	2	4	no	—
180	D₄×D₉	—	2	4	no	—
181	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₉×C₄⋊C₄	—	2	1	no	—
187	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₉×C₂²⋊C₄	—	2	1	no	—
189	C₉×C₂²⋊C₄	—	2	1	no	—
190	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
194	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
195	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
196	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
198	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
199	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
200	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
202	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
203	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
204	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
206	C₂²×C₃×C₉	—	2	1	no	—
207	C₂²×C₃×C₉	—	2	1	no	—
208	C₂²×C₃×C₉	—	2	1	no	—
209	C₂²×C₃×C₉	—	2	1	no	—
210	C₂²×C₃×C₉	—	2	1	no	—
211	C₂²×C₃×C₉	—	2	1	no	—
212	C₂²×C₃×C₉	—	2	1	no	—
213	C₂²×C₃×C₉	—	2	1	no	—
214	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
215	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
216	C₂×C₃×D₉	—	2	1	no	—
217	C₂×C₃×D₉	—	2	1	no	—
218	C₂×C₃×D₉	—	2	1	no	—
219	C₂×C₃×D₉	—	2	1	no	—
220	C₂×C₃×D₉	—	2	1	no	—
221	C₂×C₃×D₉	—	2	1	no	—
222	C₂×C₃×D₉	—	2	1	no	—
223	C₂×C₃×D₉	—	4	4	no	—
224	C₂×C₃×D₉	—	4	4	no	—
225	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
226	C₂×C₃×D₉	#41	1	2	yes	complemented
227	C₃×C₄×C₉	—	2	1	no	—
228	C₃×C₄×C₉	—	2	1	no	—
229	C₃×C₄×C₉	—	2	1	no	—
230	C₃×C₄×C₉	—	2	1	no	—
231	C₃×Dic₉	—	2	1	no	—
232	C₃×Dic₉	—	2	1	no	—
233	C₃×Dic₉	—	2	1	no	—
234	C₃×Dic₉	—	2	1	no	—
235	C₃×Dic₉	C₂×D₄	1	2	yes	—
236	C₂×C₃×#41	—	9	1	no	—
237	C₂²×C₃×D₄	—	9	1	no	—
238	C₂×#237	—	3	1	no	—
239	C₂×D₃×D₄	—	3	1	no	—
240	C₃×#124	—	9	1	no	—
241	C₃×#123	—	9	1	no	—
242	C₃×#123	—	9	1	no	—
243	C₃×C₂²⋊Q₈	—	9	1	no	—
244	C₃×#121	—	2	1	no	—
245	C₃×#121	—	9	1	no	—
246	C₃×#121	—	9	1	no	—
247	C₃×#121	D₉	1	1	yes	characteristic, complemented
248	C₃×#121	C₃×D₃	1	1	yes	characteristic
249	C₃×#120	—	9	1	no	—
250	C₃×#120	—	9	1	no	—
251	C₃×C₄×D₄	—	9	1	no	—
252	C₃×C₄×D₄	—	9	1	no	—
253	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
254	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
255	#939	—	3	1	no	—
256	#937	—	3	1	no	—
257	#937	—	3	1	no	—
258	#935	—	3	1	no	—
259	C₄×#67	—	3	1	no	—
260	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
261	#896	—	3	1	no	—
262	#894	—	3	1	no	—
263	#885	—	3	1	no	—
264	#884	—	3	1	no	—
265	#67⋊C₄	—	3	1	no	—
266	D₃×C₂²⋊C₄	—	3	1	no	—
267	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
268	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
269	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
270	C₂²×C₃×D₃	—	3	1	no	—
271	C₂²×C₃×D₃	—	3	1	no	—
272	C₂²×C₃×D₃	—	3	1	no	—
273	C₂²×C₃×D₃	—	6	2	no	—
274	C₂²×C₃×D₃	—	6	2	no	—
275	C₂²×C₃×D₃	—	6	2	no	—
276	C₂²×C₃×D₃	—	6	2	no	—
277	C₂²×C₃×D₃	—	12	1	no	—
278	C₂²×C₃×D₃	—	12	1	no	—
279	C₃²×D₄	—	2	2	no	—
280	C₃²×D₄	—	2	2	no	—
281	C₃²×D₄	—	4	1	no	—
282	C₂×C₃²×C₄	—	4	1	no	—
283	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
285	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
286	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
287	C₃×#67	—	3	4	no	—
288	C₃×#67	—	6	2	no	—
289	C₃×#67	—	6	2	no	—
290	C₃×#67	—	6	2	no	—
291	C₃×#67	—	12	1	no	—
292	C₂×C₃×Dic₃	—	3	1	no	—
293	C₂×C₃×Dic₃	—	3	1	no	—
294	C₂×C₃×Dic₃	—	3	1	no	—
295	C₂×C₃×Dic₃	—	3	1	no	—
296	C₂×C₃×Dic₃	—	3	1	no	—
297	C₂×C₃×Dic₃	—	6	2	no	—
298	C₂×C₃×Dic₃	—	6	2	no	—
299	C₃×D₁₂	—	6	2	no	—
300	C₃×C₄×D₃	—	6	2	no	—
301	C₃×C₄×D₃	—	6	2	no	—
302	C₃×C₄×D₃	—	12	1	no	—
303	C₃×Dic₆	—	6	2	no	—
304	C₂³×C₉	—	2	1	no	—
305	C₂³×C₉	—	2	1	no	—
306	C₂³×C₉	—	2	1	no	—
307	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
308	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
309	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
310	C₂²×D₉	—	2	2	no	—
311	C₂²×D₉	—	2	2	no	—
312	C₂²×D₉	—	2	2	no	—
313	C₂²×D₉	—	2	2	no	—
314	C₂²×D₉	—	4	1	no	—
315	C₂²×D₉	—	4	1	no	—
316	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
317	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
318	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
319	D₄×C₉	—	2	2	no	—
320	D₄×C₉	—	2	2	no	—
321	D₄×C₉	—	4	2	no	—
322	D₄×C₉	—	4	2	no	—
323	D₄×C₉	—	4	1	no	—
324	D₄×C₉	—	4	2	no	—
325	C₂×C₄×C₉	—	2	1	no	—
326	C₂×C₄×C₉	—	2	1	no	—
327	C₂×C₄×C₉	—	2	1	no	—
328	C₂×C₄×C₉	—	2	1	no	—
329	C₂×C₄×C₉	—	4	1	no	—
330	C₂×C₄×C₉	—	4	2	no	—
331	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
332	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
334	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
335	#611	—	2	2	no	—
336	#611	—	2	2	no	—
337	#611	—	2	2	no	—
338	#611	—	4	1	no	—
339	#611	C₃×D₄	1	4	yes	complemented
340	C₂×Dic₉	—	2	2	no	—
341	C₂×Dic₉	—	2	2	no	—
342	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
343	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
344	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
345	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
346	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
347	D₃₆	—	2	2	no	—
348	C₄×D₉	—	2	2	no	—
349	C₄×D₉	—	2	2	no	—
350	C₄×D₉	—	4	1	no	—
351	Dic₁₈	—	2	2	no	—
352	#546	—	9	1	no	Sylow
353	C₂×C₃×C₉	—	2	2	no	—
354	C₂×C₃×C₉	—	4	1	no	—
355	C₂×C₃×C₉	—	4	1	no	—
356	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
358	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
359	C₃×D₉	—	2	2	no	—
360	C₃×D₉	—	2	2	no	—
361	C₃×D₉	—	4	1	no	—
362	C₂⁴×C₃	—	9	1	no	—
363	C₂⁴×C₃	—	9	1	no	—
364	C₂³×D₃	—	3	1	no	—
365	C₂³×D₃	—	3	1	no	—
366	C₃×#41	—	18	4	no	—
367	C₂×C₃×Q₈	—	9	1	no	—
368	C₂×C₃×D₄	—	2	1	no	—
369	C₂×C₃×D₄	—	2	1	no	—
370	C₂×C₃×D₄	—	2	1	no	—
371	C₂×C₃×D₄	—	9	1	no	—
372	C₂×C₃×D₄	—	9	1	no	—
373	C₂×C₃×D₄	—	9	1	no	—
374	C₂×C₃×D₄	—	9	1	no	—
375	C₂×C₃×D₄	—	9	1	no	—
376	C₂×C₃×D₄	—	9	1	no	—
377	C₂×C₃×D₄	—	18	4	no	—
378	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
379	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic, complemented
380	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic, complemented
381	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
383	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
384	C₂²×C₃×C₄	—	2	1	no	—
385	C₂²×C₃×C₄	—	9	1	no	—
386	C₂²×C₃×C₄	—	9	1	no	—
387	C₂²×C₃×C₄	—	9	1	no	—
388	C₂²×C₃×C₄	—	9	1	no	—
389	C₂²×C₃×C₄	—	9	1	no	—
390	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic, complemented
391	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
392	C₂×#67	—	3	1	no	—
393	C₂×#67	—	3	1	no	—
394	C₂×#67	—	3	1	no	—
395	C₂×#67	—	3	1	no	—
396	C₂×#67	—	3	1	no	—
397	C₂²×Dic₃	—	3	1	no	—
398	C₂²×Dic₃	—	3	1	no	—
399	#237	—	6	4	no	—
400	D₃×D₄	—	6	4	no	—
401	C₂×D₁₂	—	3	1	no	—
402	C₂×C₄×D₃	—	3	1	no	—
403	C₂×C₄×D₃	—	3	1	no	—
404	C₂×C₄×D₃	—	3	1	no	—
405	C₂×Dic₆	—	3	1	no	—
406	C₃×C₄⋊C₄	—	2	1	no	—
407	C₃×C₄⋊C₄	—	9	1	no	—
408	C₃×C₄⋊C₄	—	9	1	no	—
409	C₃×C₄⋊C₄	—	9	1	no	—
410	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
411	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	9	1	no	—
415	C₃×C₂²⋊C₄	—	9	1	no	—
416	C₃×C₂²⋊C₄	—	9	1	no	—
417	C₃×C₂²⋊C₄	—	9	1	no	—
418	C₃×C₂²⋊C₄	—	9	1	no	—
419	C₃×C₂²⋊C₄	—	9	1	no	—
420	C₃×C₂²⋊C₄	—	9	1	no	—
421	C₃×C₂²⋊C₄	—	9	1	no	—
422	C₃×C₂²⋊C₄	—	9	1	no	—
423	C₃×C₂²⋊C₄	—	9	1	no	—
424	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
425	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
426	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
428	C₃×C₄²	—	9	1	no	—
429	#217	—	3	1	no	—
430	#217	—	3	1	no	—
431	#217	—	3	1	no	—
432	(C₂×D₃)⋊C₄	—	3	1	no	—
433	(C₂×D₃)⋊C₄	—	3	1	no	—
434	(C₂×D₃)⋊C₄	—	3	1	no	—
435	(C₂×D₃)⋊C₄	—	3	1	no	—
436	(C₂×D₃)⋊C₄	—	3	1	no	—
437	(C₂×D₃)⋊C₄	—	3	1	no	—
438	(C₂×D₃)⋊C₄	—	3	1	no	—
439	Dic₃⋊C₄	—	3	1	no	—
440	Dic₃⋊C₄	—	3	1	no	—
441	Dic₃⋊C₄	—	3	1	no	—
442	C₄×Dic₃	—	3	1	no	—
443	C₂²×C₃²	—	2	1	no	—
444	C₂²×C₃²	—	2	1	no	—
445	C₂²×C₃²	—	2	1	no	—
446	C₂²×C₃²	—	2	1	no	—
447	C₂²×C₃²	—	2	1	no	—
448	C₂²×C₃²	—	2	1	no	—
449	C₂²×C₃²	—	2	1	no	—
450	C₂²×C₃²	—	2	1	no	—
451	C₂²×C₃²	D₃×D₄	1	2	yes	—
452	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
453	C₂×C₃×D₃	—	3	2	no	—
454	C₂×C₃×D₃	—	3	2	no	—
455	C₂×C₃×D₃	—	6	1	no	—
456	C₂×C₃×D₃	—	6	1	no	—
457	C₂×C₃×D₃	—	6	1	no	—
458	C₂×C₃×D₃	—	6	1	no	—
459	C₂×C₃×D₃	—	6	1	no	—
460	C₂×C₃×D₃	—	6	1	no	—
461	C₂×C₃×D₃	—	6	1	no	—
462	C₂×C₃×D₃	—	12	4	no	—
463	C₂×C₃×D₃	—	12	4	no	—
464	C₃²×C₄	—	2	1	no	—
465	C₃²×C₄	—	2	1	no	—
466	C₃²×C₄	—	2	1	no	—
467	C₃²×C₄	—	2	1	no	—
468	C₃×Dic₃	—	3	2	no	—
469	C₃×Dic₃	—	6	1	no	—
470	C₃×Dic₃	—	6	1	no	—
471	C₃×Dic₃	—	6	1	no	—
472	C₃×Dic₃	—	6	1	no	—
473	C₂²×C₉	—	2	1	no	—
474	C₂²×C₉	—	2	1	no	—
475	C₂²×C₉	—	2	1	no	—
476	C₂²×C₉	—	2	1	no	—
477	C₂²×C₉	—	2	1	no	—
478	C₂²×C₉	—	2	1	no	—
479	C₂²×C₉	—	2	1	no	—
480	C₂²×C₉	—	2	1	no	—
481	C₂²×C₉	—	2	1	no	—
482	C₂²×C₉	—	2	2	no	—
483	C₂²×C₉	—	4	1	no	—
484	C₂²×C₉	—	4	1	no	—
485	C₂²×C₉	—	4	1	no	—
486	C₂²×C₉	—	4	1	no	—
487	C₂²×C₉	—	4	1	no	—
488	C₂²×C₉	—	4	1	no	—
489	C₂²×C₉	—	4	1	no	—
490	C₂²×C₉	—	4	1	no	—
491	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
492	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
493	C₂×D₉	—	2	1	no	—
494	C₂×D₉	—	2	1	no	—
495	C₂×D₉	—	2	1	no	—
496	C₂×D₉	—	2	1	no	—
497	C₂×D₉	—	2	1	no	—
498	C₂×D₉	—	2	1	no	—
499	C₂×D₉	—	2	1	no	—
500	C₂×D₉	—	4	4	no	—
501	C₂×D₉	—	4	4	no	—
502	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
503	C₂×D₉	C₃×#41	1	2	yes	complemented
504	C₄×C₉	—	2	2	no	—
505	C₄×C₉	—	2	1	no	—
506	C₄×C₉	—	2	1	no	—
507	C₄×C₉	—	2	1	no	—
508	C₄×C₉	—	2	1	no	—
509	C₄×C₉	—	4	1	no	—
510	C₄×C₉	—	4	1	no	—
511	C₄×C₉	—	4	1	no	—
512	Dic₉	—	2	1	no	—
513	Dic₉	—	2	1	no	—
514	Dic₉	—	2	1	no	—
515	Dic₉	—	2	1	no	—
516	Dic₉	C₂×C₃×D₄	1	2	yes	—
517	C₂×#41	—	9	1	no	—
518	C₂²×D₄	—	9	1	no	—
519	#124	—	9	1	no	—
520	#123	—	9	1	no	—
521	#123	—	9	1	no	—
522	C₂²⋊Q₈	—	9	1	no	—
523	#121	—	9	1	no	—
524	#121	—	9	1	no	—
525	#121	C₃×D₉	1	1	yes	characteristic, complemented
526	#120	—	9	1	no	—
527	#120	—	9	1	no	—
528	C₄×D₄	—	9	1	no	—
529	C₄×D₄	—	9	1	no	—
530	C₂×C₂²⋊C₄	—	9	1	no	—
531	C₂×C₂²⋊C₄	—	9	1	no	—
532	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
533	C₂³×C₃	—	2	1	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	—	2	1	no	—
536	C₂³×C₃	—	9	1	no	—
537	C₂³×C₃	—	9	1	no	—
538	C₂³×C₃	—	9	1	no	—
539	C₂³×C₃	—	18	2	no	—
540	C₂³×C₃	—	18	2	no	—
541	C₂³×C₃	—	18	2	no	—
542	C₂³×C₃	—	18	2	no	—
543	C₂³×C₃	—	36	1	no	—
544	C₂³×C₃	—	36	1	no	—
545	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
546	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
547	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
548	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
549	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
550	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
551	C₂²×D₃	—	3	1	no	—
552	C₂²×D₃	—	3	1	no	—
553	C₂²×D₃	—	3	1	no	—
554	C₂²×D₃	—	6	2	no	—
555	C₂²×D₃	—	6	2	no	—
556	C₂²×D₃	—	6	2	no	—
557	C₂²×D₃	—	6	2	no	—
558	C₂²×D₃	—	12	1	no	—
559	C₂²×D₃	—	12	1	no	—
560	C₃×Q₈	—	18	2	no	—
561	C₃×D₄	—	2	2	no	—
562	C₃×D₄	—	2	2	no	—
563	C₃×D₄	—	2	2	no	—
564	C₃×D₄	—	2	2	no	—
565	C₃×D₄	—	4	2	no	—
566	C₃×D₄	—	4	2	no	—
567	C₃×D₄	—	4	1	no	—
568	C₃×D₄	—	4	1	no	—
569	C₃×D₄	—	4	2	no	—
570	C₃×D₄	—	9	4	no	—
571	C₃×D₄	—	18	2	no	—
572	C₃×D₄	—	18	2	no	—
573	C₃×D₄	—	18	2	no	—
574	C₃×D₄	—	18	2	no	—
575	C₃×D₄	—	36	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	4	1	no	—
581	C₂×C₃×C₄	—	4	1	no	—
582	C₂×C₃×C₄	—	4	2	no	—
583	C₂×C₃×C₄	—	9	1	no	—
584	C₂×C₃×C₄	—	9	1	no	—
585	C₂×C₃×C₄	—	9	1	no	—
586	C₂×C₃×C₄	—	9	1	no	—
587	C₂×C₃×C₄	—	9	1	no	—
588	C₂×C₃×C₄	—	18	2	no	—
589	C₂×C₃×C₄	—	18	2	no	—
590	C₂×C₃×C₄	—	18	2	no	—
591	C₂×C₃×C₄	—	18	2	no	—
592	C₂×C₃×C₄	—	36	1	no	—
593	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
594	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
596	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
597	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
598	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
600	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
601	#67	—	3	4	no	—
602	#67	—	6	2	no	—
603	#67	—	6	2	no	—
604	#67	—	6	2	no	—
605	#67	—	12	1	no	—
606	C₂×Dic₃	—	3	1	no	—
607	C₂×Dic₃	—	3	1	no	—
608	C₂×Dic₃	—	3	1	no	—
609	C₂×Dic₃	—	3	1	no	—
610	C₂×Dic₃	—	3	1	no	—
611	C₂×Dic₃	—	6	2	no	—
612	C₂×Dic₃	—	6	2	no	—
613	D₁₂	—	6	2	no	—
614	C₄×D₃	—	6	2	no	—
615	C₄×D₃	—	6	2	no	—
616	C₄×D₃	—	12	1	no	—
617	Dic₆	—	6	2	no	—
618	C₂×C₃²	—	2	2	no	—
619	C₂×C₃²	—	4	1	no	—
620	C₂×C₃²	—	4	1	no	—
621	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
622	C₂×C₃²	#1004	1	1	yes	characteristic
623	C₂×C₃²	D₃×#41	1	1	yes	characteristic
624	C₃×D₃	—	6	2	no	—
625	C₃×D₃	—	6	2	no	—
626	C₃×D₃	—	12	1	no	—
627	C₂×C₉	—	2	2	no	—
628	C₂×C₉	—	2	1	no	—
629	C₂×C₉	—	2	1	no	—
630	C₂×C₉	—	2	1	no	—
631	C₂×C₉	—	4	2	no	—
632	C₂×C₉	—	4	1	no	—
633	C₂×C₉	—	4	1	no	—
634	C₂×C₉	—	8	1	no	—
635	C₂×C₉	—	8	1	no	—
636	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
637	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
638	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
639	D₉	—	2	2	no	—
640	D₉	—	2	2	no	—
641	D₉	—	4	1	no	—
642	C₂⁴	—	9	1	no	—
643	C₂⁴	—	9	1	no	—
644	#41	—	18	4	no	—
645	C₂×Q₈	—	9	1	no	—
646	C₂×D₄	—	9	1	no	—
647	C₂×D₄	—	9	1	no	—
648	C₂×D₄	—	9	1	no	—
649	C₂×D₄	—	9	1	no	—
650	C₂×D₄	—	9	1	no	—
651	C₂×D₄	—	9	1	no	—
652	C₂×D₄	—	18	4	no	—
653	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
654	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
655	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
656	C₂²×C₄	—	9	1	no	—
657	C₂²×C₄	—	9	1	no	—
658	C₂²×C₄	—	9	1	no	—
659	C₂²×C₄	—	9	1	no	—
660	C₂²×C₄	—	9	1	no	—
661	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
662	C₄⋊C₄	—	9	1	no	—
663	C₄⋊C₄	—	9	1	no	—
664	C₄⋊C₄	—	9	1	no	—
665	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
666	C₂²⋊C₄	—	9	1	no	—
667	C₂²⋊C₄	—	9	1	no	—
668	C₂²⋊C₄	—	9	1	no	—
669	C₂²⋊C₄	—	9	1	no	—
670	C₂²⋊C₄	—	9	1	no	—
671	C₂²⋊C₄	—	9	1	no	—
672	C₂²⋊C₄	—	9	1	no	—
673	C₂²⋊C₄	—	9	1	no	—
674	C₂²⋊C₄	—	9	1	no	—
675	C₂²⋊C₄	—	9	1	no	—
676	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
677	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
678	C₄²	—	9	1	no	—
679	C₂²×C₃	—	2	1	no	—
680	C₂²×C₃	—	2	1	no	—
681	C₂²×C₃	—	2	1	no	—
682	C₂²×C₃	—	2	1	no	—
683	C₂²×C₃	—	2	1	no	—
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	2	1	no	—
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	—	2	1	no	—
692	C₂²×C₃	—	2	1	no	—
693	C₂²×C₃	—	2	1	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	2	1	no	—
696	C₂²×C₃	—	2	2	no	—
697	C₂²×C₃	—	4	1	no	—
698	C₂²×C₃	—	4	1	no	—
699	C₂²×C₃	—	4	1	no	—
700	C₂²×C₃	—	4	1	no	—
701	C₂²×C₃	—	4	1	no	—
702	C₂²×C₃	—	4	1	no	—
703	C₂²×C₃	—	4	1	no	—
704	C₂²×C₃	—	4	1	no	—
705	C₂²×C₃	—	9	2	no	—
706	C₂²×C₃	—	9	2	no	—
707	C₂²×C₃	—	18	1	no	—
708	C₂²×C₃	—	18	1	no	—
709	C₂²×C₃	—	18	1	no	—
710	C₂²×C₃	—	18	1	no	—
711	C₂²×C₃	—	18	1	no	—
712	C₂²×C₃	—	18	1	no	—
713	C₂²×C₃	—	18	1	no	—
714	C₂²×C₃	—	36	4	no	—
715	C₂²×C₃	—	36	4	no	—
716	C₂²×C₃	D₄×D₉	1	2	yes	—
717	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
718	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
719	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
720	C₂×D₃	—	3	2	no	—
721	C₂×D₃	—	3	2	no	—
722	C₂×D₃	—	6	1	no	—
723	C₂×D₃	—	6	1	no	—
724	C₂×D₃	—	6	1	no	—
725	C₂×D₃	—	6	1	no	—
726	C₂×D₃	—	6	1	no	—
727	C₂×D₃	—	6	1	no	—
728	C₂×D₃	—	6	1	no	—
729	C₂×D₃	—	12	4	no	—
730	C₂×D₃	—	12	4	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	1	no	—
733	C₃×C₄	—	2	1	no	—
734	C₃×C₄	—	2	1	no	—
735	C₃×C₄	—	2	1	no	—
736	C₃×C₄	—	2	1	no	—
737	C₃×C₄	—	2	1	no	—
738	C₃×C₄	—	2	1	no	—
739	C₃×C₄	—	2	1	no	—
740	C₃×C₄	—	4	1	no	—
741	C₃×C₄	—	4	1	no	—
742	C₃×C₄	—	4	1	no	—
743	C₃×C₄	—	9	2	no	—
744	C₃×C₄	—	18	1	no	—
745	C₃×C₄	—	18	1	no	—
746	C₃×C₄	—	18	1	no	—
747	C₃×C₄	—	18	1	no	—
748	Dic₃	—	3	2	no	—
749	Dic₃	—	6	1	no	—
750	Dic₃	—	6	1	no	—
751	Dic₃	—	6	1	no	—
752	Dic₃	—	6	1	no	—
753	C₃²	#5610	1	1	yes	characteristic
754	C₉	—	2	1	no	—
755	C₉	C₃×#546	1	1	yes	characteristic, complemented
756	C₂³	—	9	1	no	—
757	C₂³	—	9	1	no	—
758	C₂³	—	9	1	no	—
759	C₂³	—	18	2	no	—
760	C₂³	—	18	2	no	—
761	C₂³	—	18	2	no	—
762	C₂³	—	18	2	no	—
763	C₂³	—	36	1	no	—
764	C₂³	—	36	1	no	—
765	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
766	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
767	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
768	Q₈	—	18	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	1	no	—
772	D₄	—	9	4	no	—
773	D₄	—	18	2	no	—
774	D₄	—	18	2	no	—
775	D₄	—	18	2	no	—
776	D₄	—	18	2	no	—
777	D₄	—	36	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	9	1	no	—
780	C₂×C₄	—	9	1	no	—
781	C₂×C₄	—	9	1	no	—
782	C₂×C₄	—	9	1	no	—
783	C₂×C₄	—	9	1	no	—
784	C₂×C₄	—	18	2	no	—
785	C₂×C₄	—	18	2	no	—
786	C₂×C₄	—	18	2	no	—
787	C₂×C₄	—	18	2	no	—
788	C₂×C₄	—	36	1	no	—
789	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
790	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
791	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
792	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
793	C₂×C₃	—	2	2	no	—
794	C₂×C₃	—	2	2	no	—
795	C₂×C₃	—	2	1	no	—
796	C₂×C₃	—	2	1	no	—
797	C₂×C₃	—	2	1	no	—
798	C₂×C₃	—	4	2	no	—
799	C₂×C₃	—	4	1	no	—
800	C₂×C₃	—	4	1	no	—
801	C₂×C₃	—	4	1	no	—
802	C₂×C₃	—	4	1	no	—
803	C₂×C₃	—	8	1	no	—
804	C₂×C₃	—	8	1	no	—
805	C₂×C₃	—	18	2	no	—
806	C₂×C₃	—	18	2	no	—
807	C₂×C₃	—	36	1	no	—
808	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
809	C₂×C₃	#63710	1	1	yes	characteristic
810	C₂×C₃	#41×D₉	1	1	yes	characteristic
811	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
812	C₂×C₃	C₃×#1004	1	1	yes	characteristic
813	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
814	D₃	—	6	2	no	—
815	D₃	—	6	2	no	—
816	D₃	—	12	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	9	2	no	—
826	C₂²	—	9	2	no	—
827	C₂²	—	18	1	no	—
828	C₂²	—	18	1	no	—
829	C₂²	—	18	1	no	—
830	C₂²	—	18	1	no	—
831	C₂²	—	18	1	no	—
832	C₂²	—	18	1	no	—
833	C₂²	—	18	1	no	—
834	C₂²	—	36	4	no	—
835	C₂²	—	36	4	no	—
836	C₂²	C₃×D₄×D₉	1	2	yes	—
837	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	9	2	no	—
843	C₄	—	18	1	no	—
844	C₄	—	18	1	no	—
845	C₄	—	18	1	no	—
846	C₄	—	18	1	no	—
847	C₃	—	2	1	no	—
848	C₃	#10589712	1	1	yes	characteristic, direct product factor
849	C₃	C₃×#5610	1	1	yes	characteristic
850	C₂	—	2	2	no	—
851	C₂	—	4	1	no	—
852	C₂	—	4	1	no	—
853	C₂	—	18	2	no	—
854	C₂	—	18	2	no	—
855	C₂	—	36	1	no	—
856	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
857	C₂	C₃×#63710	1	1	yes	characteristic
858	C₂	C₃×#41×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#121	D₉
hypocenter	C₉	C₃×#546
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3699	C₂	semidirect
2. C₂×C₃×D₄×D₉	C₂	semidirect
3. C₃×C₉×#121	C₂	semidirect
4. C₃×#63501	C₂	semidirect
5. C₃×#63499	C₂	semidirect
6. C₃×#63499	C₂	semidirect
7. C₃×#63497	C₂	semidirect
8. C₃×C₄×#611	C₂	semidirect
9. C₂×C₃×(C₂×D₉)⋊C₄	C₂	semidirect
10. C₃×#63458	C₂	semidirect
11. C₃×#63456	C₂	semidirect
12. C₃×#63447	C₂	semidirect
13. C₃×#63446	C₂	semidirect
14. C₃×#611⋊C₄	C₂	semidirect
15. C₃×C₂²⋊C₄×D₉	C₂	semidirect
17. #10589712	C₃	direct (N × H)
21. C₂×C₃×D₄×C₉	C₂²	semidirect
22. C₂×C₃×D₄×C₉	C₂²	semidirect
23. C₂²×C₃×C₄×C₉	C₂²	semidirect
27. C₂×C₃×#611	C₂²	semidirect
28. C₂×C₃×#611	C₂²	semidirect
29. C₂²×C₃×Dic₉	C₂²	semidirect
30. C₂²×C₃×Dic₉	C₂²	semidirect
35. C₂×C₃×C₄×D₉	C₂²	semidirect
36. C₂×C₃×C₄×D₉	C₂²	semidirect
37. C₂×C₃×Dic₁₈	C₂²	semidirect
38. C₃×C₉×C₄⋊C₄	C₂²	semidirect
39. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
41. C₃×#3676	C₂²	semidirect
42. C₃×#3676	C₂²	semidirect
43. C₃×#3676	C₂²	semidirect
47. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
48. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
49. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
50. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
51. C₃×Dic₉⋊C₄	C₂²	semidirect
52. C₃×Dic₉⋊C₄	C₂²	semidirect
53. C₃×Dic₉⋊C₄	C₂²	semidirect
54. C₃×C₄×Dic₉	C₂²	semidirect
70. C₂×#3699	C₂×C₃	semidirect
71. C₂×D₄×D₉	C₂×C₃	semidirect
73. C₉×#121	C₂×C₃	semidirect
74. #63501	C₂×C₃	semidirect
75. #63499	C₂×C₃	semidirect
76. #63499	C₂×C₃	semidirect
77. #63497	C₂×C₃	semidirect
78. C₄×#611	C₂×C₃	semidirect
79. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
80. #63458	C₂×C₃	semidirect
81. #63456	C₂×C₃	semidirect
82. #63447	C₂×C₃	semidirect
83. #63446	C₂×C₃	semidirect
84. #611⋊C₄	C₂×C₃	semidirect
85. C₂²⋊C₄×D₉	C₂×C₃	semidirect
110. C₃×#611	D₄	semidirect
168. C₂×D₄×C₉	C₂²×C₃	semidirect
169. C₂×D₄×C₉	C₂²×C₃	semidirect
171. C₂²×C₄×C₉	C₂²×C₃	semidirect
175. C₂×#611	C₂²×C₃	semidirect
176. C₂×#611	C₂²×C₃	semidirect
177. C₂²×Dic₉	C₂²×C₃	semidirect
178. C₂²×Dic₉	C₂²×C₃	semidirect
183. C₂×C₄×D₉	C₂²×C₃	semidirect
184. C₂×C₄×D₉	C₂²×C₃	semidirect
185. C₂×Dic₁₈	C₂²×C₃	semidirect
187. C₉×C₄⋊C₄	C₂²×C₃	semidirect
190. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
191. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
192. #3676	C₂²×C₃	semidirect
193. #3676	C₂²×C₃	semidirect
194. #3676	C₂²×C₃	semidirect
198. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
199. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
200. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
201. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
202. Dic₉⋊C₄	C₂²×C₃	semidirect
203. Dic₉⋊C₄	C₂²×C₃	semidirect
204. Dic₉⋊C₄	C₂²×C₃	semidirect
205. C₄×Dic₉	C₂²×C₃	semidirect
226. C₂×C₃×D₉	#41	semidirect
247. C₃×#121	D₉	semidirect
339. #611	C₃×D₄	semidirect
379. C₂×C₃×D₄	C₂×D₉	semidirect
380. C₂×C₃×D₄	C₂×D₉	semidirect
390. C₂²×C₃×C₄	C₂×D₉	semidirect
410. C₃×C₄⋊C₄	C₂×D₉	semidirect
424. C₃×C₂²⋊C₄	C₂×D₉	semidirect
425. C₃×C₂²⋊C₄	C₂×D₉	semidirect
503. C₂×D₉	C₃×#41	semidirect
525. #121	C₃×D₉	semidirect
532. C₃×C₉	#546	semidirect
654. C₂×D₄	C₂×C₃×D₉	semidirect
655. C₂×D₄	C₂×C₃×D₉	semidirect
661. C₂²×C₄	C₂×C₃×D₉	semidirect
665. C₄⋊C₄	C₂×C₃×D₉	semidirect
676. C₂²⋊C₄	C₂×C₃×D₉	semidirect
677. C₂²⋊C₄	C₂×C₃×D₉	semidirect
755. C₉	C₃×#546	semidirect
848. C₃	#10589712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3699	2
C₂×C₃×D₄×D₉	2
C₃×C₉×#121	2
C₃×#63501	2
C₃×#63499	2
C₃×#63497	2
C₃×C₄×#611	2
C₂×C₃×(C₂×D₉)⋊C₄	2
C₃×#63458	2
C₃×#63456	2
C₃×#63447	2
C₃×#63446	2
C₃×#611⋊C₄	2
C₃×C₂²⋊C₄×D₉	2
C₃×#5610	3
#10589712	3

Subgroups — C3×#10589712 #13152813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589712 #13152813