Subgroups — C₃×#10589756 #13153013

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3697	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×(C₂×D₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63458	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63457	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63456	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63455	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#63446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#63444	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#63444	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×#5654	—	3	1	no	maximal
17	#10589756	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	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#611	C₂²	1	1	yes	characteristic
23	C₂×C₃×#611	C₂²	1	1	yes	characteristic
24	C₂×C₃×#611	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#611	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
27	C₃×D₄×D₉	—	2	4	no	—
28	C₃×#3697	—	2	4	no	—
29	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
31	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic, complemented
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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₉×C₂²⋊C₄	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×(C₂×D₉)⋊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×D₃×D₄	—	3	1	no	—
56	C₂×C₃×#235	—	3	1	no	—
57	C₃²×#123	D₃	1	1	yes	characteristic
58	C₃×#939	—	3	1	no	—
59	C₂×C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
60	C₃×#896	—	3	1	no	—
61	C₃×#895	—	3	1	no	—
62	C₃×#894	—	3	1	no	—
63	C₃×#893	—	3	1	no	—
64	C₃×#885	—	3	1	no	—
65	C₃×#884	—	3	1	no	—
66	C₃×#882	—	3	1	no	—
67	C₃×#882	—	3	1	no	—
68	C₃×#67⋊C₄	—	3	1	no	—
69	C₃×D₃×C₂²⋊C₄	—	3	1	no	—
70	C₂×D₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
72	C₉×#123	—	2	1	no	—
73	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
74	#63501	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	#63458	C₂×C₃	1	1	yes	characteristic, complemented
77	#63457	C₂×C₃	1	1	yes	characteristic, complemented
78	#63456	C₂×C₃	1	1	yes	characteristic, complemented
79	#63455	C₂×C₃	1	1	yes	characteristic, complemented
80	#63447	C₂×C₃	1	1	yes	characteristic, complemented
81	#63446	C₂×C₃	1	1	yes	characteristic, complemented
82	#63444	C₂×C₃	1	1	yes	characteristic, complemented
83	#63444	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	C₂²×C₃×D₉	—	2	2	no	—
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	—	4	1	no	—
93	C₂²×C₃×D₉	—	4	1	no	—
94	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
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	C₂×C₃×C₄×C₉	—	2	2	no	—
100	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
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	C₃×#611	—	2	2	no	—
106	C₃×#611	—	2	2	no	—
107	C₃×#611	—	4	1	no	—
108	C₃×#611	D₄	1	4	yes	complemented
109	C₂×C₃×Dic₉	—	4	1	no	—
110	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
111	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
112	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
113	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
114	C₃×D₃₆	—	2	2	no	—
115	C₃×D₃₆	—	2	2	no	—
116	C₃×D₃₆	—	2	2	no	—
117	C₃×D₃₆	—	4	1	no	—
118	C₃×C₄×D₉	—	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	#5654	—	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	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
129	C₂×C₃×#67	—	3	1	no	—
130	C₂×C₃×#67	—	3	1	no	—
131	C₂×C₃×#67	—	3	1	no	—
132	C₂×C₃×#67	—	3	1	no	—
133	C₂²×C₃×Dic₃	—	3	1	no	—
134	C₃×D₃×D₄	—	6	4	no	—
135	C₃×#235	—	6	4	no	—
136	C₂×C₃×D₁₂	—	3	1	no	—
137	C₂×C₃×D₁₂	—	3	1	no	—
138	C₂×C₃×D₁₂	—	3	1	no	—
139	C₂×C₃×D₁₂	—	3	1	no	—
140	C₂×C₃×C₄×D₃	—	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×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
149	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
151	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
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×(C₂×D₃)⋊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	C₂²×C₃	1	1	yes	characteristic
166	C₂²×C₄×C₉	—	2	1	no	—
167	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×#611	C₂²×C₃	1	1	yes	characteristic
169	C₂×#611	C₂²×C₃	1	1	yes	characteristic
170	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
173	D₄×D₉	—	2	4	no	—
174	#3697	—	2	4	no	—
175	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
176	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
177	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₉×C₄⋊C₄	—	2	1	no	—
185	C₉×C₄⋊C₄	—	2	1	no	—
186	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
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	—	2	1	no	—
191	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₉×C₂²⋊C₄	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	(C₂×D₉)⋊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	C₂×D₄	1	2	yes	—
212	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
213	C₂×C₃×D₉	—	2	1	no	—
214	C₂×C₃×D₉	—	2	1	no	—
215	C₂×C₃×D₉	—	2	1	no	—
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×C₄×C₉	—	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×D₃×D₄	—	3	1	no	—
239	C₂×#235	—	3	1	no	—
240	C₃×#124	—	9	1	no	—
241	C₃×#123	—	2	1	no	—
242	C₃×#123	—	9	1	no	—
243	C₃×#123	D₉	1	1	yes	characteristic, complemented
244	C₃×#123	C₃×D₃	1	1	yes	characteristic
245	C₃×C₂²⋊Q₈	—	9	1	no	—
246	C₃×#121	—	9	1	no	—
247	C₃×#121	—	9	1	no	—
248	C₃×#121	—	9	1	no	—
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	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
257	#896	—	3	1	no	—
258	#895	—	3	1	no	—
259	#894	—	3	1	no	—
260	#893	—	3	1	no	—
261	#885	—	3	1	no	—
262	#884	—	3	1	no	—
263	#882	—	3	1	no	—
264	#882	—	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	C₂²×C₃×D₃	—	3	1	no	—
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	C₂×C₃²×C₄	—	2	2	no	—
281	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
282	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
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	C₃×#67	—	3	4	no	—
287	C₃×#67	—	6	2	no	—
288	C₃×#67	—	6	2	no	—
289	C₃×#67	—	12	1	no	—
290	C₂×C₃×Dic₃	—	3	1	no	—
291	C₂×C₃×Dic₃	—	3	1	no	—
292	C₂×C₃×Dic₃	—	3	1	no	—
293	C₂×C₃×Dic₃	—	3	1	no	—
294	C₂×C₃×Dic₃	—	12	1	no	—
295	C₃×D₁₂	—	6	2	no	—
296	C₃×D₁₂	—	6	2	no	—
297	C₃×D₁₂	—	6	2	no	—
298	C₃×D₁₂	—	12	1	no	—
299	C₃×C₄×D₃	—	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	C₂³×C₃	1	1	yes	characteristic
307	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
308	C₂²×D₉	—	2	2	no	—
309	C₂²×D₉	—	2	2	no	—
310	C₂²×D₉	—	2	2	no	—
311	C₂²×D₉	—	2	2	no	—
312	C₂²×D₉	—	4	1	no	—
313	C₂²×D₉	—	4	1	no	—
314	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
315	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
316	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
317	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
318	D₄×C₉	—	2	2	no	—
319	D₄×C₉	—	4	2	no	—
320	C₂×C₄×C₉	—	2	2	no	—
321	C₂×C₄×C₉	—	2	1	no	—
322	C₂×C₄×C₉	—	2	1	no	—
323	C₂×C₄×C₉	—	2	1	no	—
324	C₂×C₄×C₉	—	2	1	no	—
325	C₂×C₄×C₉	—	2	1	no	—
326	C₂×C₄×C₉	—	4	2	no	—
327	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
330	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
331	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
332	#611	—	2	2	no	—
333	#611	—	2	2	no	—
334	#611	—	4	1	no	—
335	#611	C₃×D₄	1	4	yes	complemented
336	C₂×Dic₉	—	4	1	no	—
337	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
338	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
339	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
340	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
341	D₃₆	—	2	2	no	—
342	D₃₆	—	2	2	no	—
343	D₃₆	—	2	2	no	—
344	D₃₆	—	4	1	no	—
345	C₄×D₉	—	2	2	no	—
346	C₄×D₉	—	2	2	no	—
347	C₄×D₉	—	2	2	no	—
348	C₄×D₉	—	4	1	no	—
349	Dic₁₈	—	2	2	no	—
350	#546	—	9	1	no	Sylow
351	C₂×C₃×C₉	—	2	2	no	—
352	C₂×C₃×C₉	—	4	1	no	—
353	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
355	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
356	C₃×D₉	—	2	2	no	—
357	C₃×D₉	—	2	2	no	—
358	C₃×D₉	—	4	1	no	—
359	C₃×D₉	—	4	1	no	—
360	C₂⁴×C₃	—	9	1	no	—
361	C₂⁴×C₃	—	9	1	no	—
362	C₂³×D₃	—	3	1	no	—
363	C₂³×D₃	—	3	1	no	—
364	C₃×#41	—	18	4	no	—
365	C₂×C₃×Q₈	—	9	1	no	—
366	C₂×C₃×D₄	—	2	1	no	—
367	C₂×C₃×D₄	—	9	1	no	—
368	C₂×C₃×D₄	—	9	1	no	—
369	C₂×C₃×D₄	—	9	1	no	—
370	C₂×C₃×D₄	—	9	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	—	18	4	no	—
376	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
377	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
378	C₂²×C₃×C₄	—	2	1	no	—
379	C₂²×C₃×C₄	—	9	1	no	—
380	C₂²×C₃×C₄	—	9	1	no	—
381	C₂²×C₃×C₄	—	9	1	no	—
382	C₂²×C₃×C₄	—	9	1	no	—
383	C₂²×C₃×C₄	—	9	1	no	—
384	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic, complemented
385	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₂×#67	—	3	1	no	—
387	C₂×#67	—	3	1	no	—
388	C₂×#67	—	3	1	no	—
389	C₂×#67	—	3	1	no	—
390	C₂²×Dic₃	—	3	1	no	—
391	D₃×D₄	—	6	4	no	—
392	#235	—	6	4	no	—
393	C₂×D₁₂	—	3	1	no	—
394	C₂×D₁₂	—	3	1	no	—
395	C₂×D₁₂	—	3	1	no	—
396	C₂×D₁₂	—	3	1	no	—
397	C₂×C₄×D₃	—	3	1	no	—
398	C₂×C₄×D₃	—	3	1	no	—
399	C₂×C₄×D₃	—	3	1	no	—
400	C₂×C₄×D₃	—	3	1	no	—
401	C₂×Dic₆	—	3	1	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	—	9	1	no	—
405	C₃×C₄⋊C₄	—	9	1	no	—
406	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
407	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
408	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
409	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	9	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	C₂×D₉	1	1	yes	characteristic, complemented
423	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
424	C₃×C₂²⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
425	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
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	(C₂×D₃)⋊C₄	—	3	1	no	—
431	(C₂×D₃)⋊C₄	—	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	Dic₃⋊C₄	—	3	1	no	—
439	Dic₃⋊C₄	—	3	1	no	—
440	C₄×Dic₃	—	3	1	no	—
441	C₂²×C₃²	—	2	1	no	—
442	C₂²×C₃²	—	2	1	no	—
443	C₂²×C₃²	—	2	1	no	—
444	C₂²×C₃²	—	2	1	no	—
445	C₂²×C₃²	—	2	1	no	—
446	C₂²×C₃²	D₃×D₄	1	2	yes	—
447	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
448	C₂×C₃×D₃	—	3	2	no	—
449	C₂×C₃×D₃	—	3	2	no	—
450	C₂×C₃×D₃	—	6	1	no	—
451	C₂×C₃×D₃	—	6	1	no	—
452	C₂×C₃×D₃	—	6	1	no	—
453	C₂×C₃×D₃	—	6	1	no	—
454	C₂×C₃×D₃	—	6	1	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	—	12	4	no	—
461	C₂×C₃×D₃	—	12	4	no	—
462	C₃²×C₄	—	2	1	no	—
463	C₃²×C₄	—	2	1	no	—
464	C₃²×C₄	—	2	1	no	—
465	C₃²×C₄	—	2	1	no	—
466	C₃²×C₄	—	2	1	no	—
467	C₃×Dic₃	—	3	2	no	—
468	C₃×Dic₃	—	6	1	no	—
469	C₃×Dic₃	—	6	1	no	—
470	C₃×Dic₃	—	6	1	no	—
471	C₂²×C₉	—	2	1	no	—
472	C₂²×C₉	—	2	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	2	no	—
478	C₂²×C₉	—	4	1	no	—
479	C₂²×C₉	—	4	1	no	—
480	C₂²×C₉	—	4	1	no	—
481	C₂²×C₉	—	4	1	no	—
482	C₂²×C₉	—	4	1	no	—
483	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
484	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
485	C₂×D₉	—	2	1	no	—
486	C₂×D₉	—	2	1	no	—
487	C₂×D₉	—	2	1	no	—
488	C₂×D₉	—	2	1	no	—
489	C₂×D₉	—	2	1	no	—
490	C₂×D₉	—	2	1	no	—
491	C₂×D₉	—	2	1	no	—
492	C₂×D₉	—	2	1	no	—
493	C₂×D₉	—	2	1	no	—
494	C₂×D₉	—	2	1	no	—
495	C₂×D₉	—	4	4	no	—
496	C₂×D₉	—	4	4	no	—
497	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
498	C₂×D₉	C₃×#41	1	2	yes	complemented
499	C₄×C₉	—	2	1	no	—
500	C₄×C₉	—	2	1	no	—
501	C₄×C₉	—	2	1	no	—
502	C₄×C₉	—	2	1	no	—
503	C₄×C₉	—	2	1	no	—
504	C₄×C₉	—	4	1	no	—
505	C₄×C₉	—	4	1	no	—
506	C₄×C₉	—	4	1	no	—
507	C₄×C₉	—	4	1	no	—
508	C₄×C₉	—	4	1	no	—
509	Dic₉	—	2	1	no	—
510	Dic₉	—	2	1	no	—
511	Dic₉	—	2	1	no	—
512	Dic₉	C₂×C₃×D₄	1	2	yes	—
513	C₂×#41	—	9	1	no	—
514	C₂²×D₄	—	9	1	no	—
515	#124	—	9	1	no	—
516	#123	—	9	1	no	—
517	#123	C₃×D₉	1	1	yes	characteristic, complemented
518	C₂²⋊Q₈	—	9	1	no	—
519	#121	—	9	1	no	—
520	#121	—	9	1	no	—
521	#121	—	9	1	no	—
522	#120	—	9	1	no	—
523	#120	—	9	1	no	—
524	C₄×D₄	—	9	1	no	—
525	C₄×D₄	—	9	1	no	—
526	C₂×C₂²⋊C₄	—	9	1	no	—
527	C₂×C₂²⋊C₄	—	9	1	no	—
528	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	9	1	no	—
532	C₂³×C₃	—	9	1	no	—
533	C₂³×C₃	—	9	1	no	—
534	C₂³×C₃	—	9	1	no	—
535	C₂³×C₃	—	18	2	no	—
536	C₂³×C₃	—	18	2	no	—
537	C₂³×C₃	—	18	2	no	—
538	C₂³×C₃	—	18	2	no	—
539	C₂³×C₃	—	36	1	no	—
540	C₂³×C₃	—	36	1	no	—
541	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
542	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
543	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
544	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
545	C₂²×D₃	—	3	1	no	—
546	C₂²×D₃	—	3	1	no	—
547	C₂²×D₃	—	3	1	no	—
548	C₂²×D₃	—	3	1	no	—
549	C₂²×D₃	—	6	2	no	—
550	C₂²×D₃	—	6	2	no	—
551	C₂²×D₃	—	6	2	no	—
552	C₂²×D₃	—	6	2	no	—
553	C₂²×D₃	—	12	1	no	—
554	C₂²×D₃	—	12	1	no	—
555	C₃×Q₈	—	18	2	no	—
556	C₃×D₄	—	2	2	no	—
557	C₃×D₄	—	2	2	no	—
558	C₃×D₄	—	4	2	no	—
559	C₃×D₄	—	9	4	no	—
560	C₃×D₄	—	18	2	no	—
561	C₃×D₄	—	18	2	no	—
562	C₃×D₄	—	18	2	no	—
563	C₃×D₄	—	18	2	no	—
564	C₃×D₄	—	18	2	no	—
565	C₃×D₄	—	36	1	no	—
566	C₃×D₄	—	36	1	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	4	2	no	—
575	C₂×C₃×C₄	—	9	1	no	—
576	C₂×C₃×C₄	—	9	1	no	—
577	C₂×C₃×C₄	—	9	1	no	—
578	C₂×C₃×C₄	—	9	1	no	—
579	C₂×C₃×C₄	—	18	2	no	—
580	C₂×C₃×C₄	—	18	2	no	—
581	C₂×C₃×C₄	—	18	2	no	—
582	C₂×C₃×C₄	—	36	1	no	—
583	C₂×C₃×C₄	—	36	1	no	—
584	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
590	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
591	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
592	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
594	#67	—	3	4	no	—
595	#67	—	6	2	no	—
596	#67	—	6	2	no	—
597	#67	—	12	1	no	—
598	C₂×Dic₃	—	3	1	no	—
599	C₂×Dic₃	—	3	1	no	—
600	C₂×Dic₃	—	3	1	no	—
601	C₂×Dic₃	—	3	1	no	—
602	C₂×Dic₃	—	12	1	no	—
603	D₁₂	—	6	2	no	—
604	D₁₂	—	6	2	no	—
605	D₁₂	—	6	2	no	—
606	D₁₂	—	12	1	no	—
607	C₄×D₃	—	6	2	no	—
608	C₄×D₃	—	6	2	no	—
609	C₄×D₃	—	6	2	no	—
610	C₄×D₃	—	12	1	no	—
611	Dic₆	—	6	2	no	—
612	C₂×C₃²	—	2	2	no	—
613	C₂×C₃²	—	4	1	no	—
614	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
615	C₂×C₃²	D₃×#41	1	1	yes	characteristic
616	C₂×C₃²	#1009	1	1	yes	characteristic
617	C₃×D₃	—	6	2	no	—
618	C₃×D₃	—	6	2	no	—
619	C₃×D₃	—	12	1	no	—
620	C₃×D₃	—	12	1	no	—
621	C₂×C₉	—	2	2	no	—
622	C₂×C₉	—	2	1	no	—
623	C₂×C₉	—	2	1	no	—
624	C₂×C₉	—	2	1	no	—
625	C₂×C₉	—	4	2	no	—
626	C₂×C₉	—	4	1	no	—
627	C₂×C₉	—	8	1	no	—
628	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
629	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
630	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
631	D₉	—	2	2	no	—
632	D₉	—	2	2	no	—
633	D₉	—	4	1	no	—
634	D₉	—	4	1	no	—
635	C₂⁴	—	9	1	no	—
636	C₂⁴	—	9	1	no	—
637	#41	—	18	4	no	—
638	C₂×Q₈	—	9	1	no	—
639	C₂×D₄	—	9	1	no	—
640	C₂×D₄	—	9	1	no	—
641	C₂×D₄	—	9	1	no	—
642	C₂×D₄	—	9	1	no	—
643	C₂×D₄	—	9	1	no	—
644	C₂×D₄	—	9	1	no	—
645	C₂×D₄	—	9	1	no	—
646	C₂×D₄	—	9	1	no	—
647	C₂×D₄	—	18	4	no	—
648	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
649	C₂²×C₄	—	9	1	no	—
650	C₂²×C₄	—	9	1	no	—
651	C₂²×C₄	—	9	1	no	—
652	C₂²×C₄	—	9	1	no	—
653	C₂²×C₄	—	9	1	no	—
654	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
655	C₄⋊C₄	—	9	1	no	—
656	C₄⋊C₄	—	9	1	no	—
657	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
658	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
659	C₂²⋊C₄	—	9	1	no	—
660	C₂²⋊C₄	—	9	1	no	—
661	C₂²⋊C₄	—	9	1	no	—
662	C₂²⋊C₄	—	9	1	no	—
663	C₂²⋊C₄	—	9	1	no	—
664	C₂²⋊C₄	—	9	1	no	—
665	C₂²⋊C₄	—	9	1	no	—
666	C₂²⋊C₄	—	9	1	no	—
667	C₂²⋊C₄	—	9	1	no	—
668	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
669	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
670	C₂²⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
671	C₄²	—	9	1	no	—
672	C₂²×C₃	—	2	1	no	—
673	C₂²×C₃	—	2	1	no	—
674	C₂²×C₃	—	2	1	no	—
675	C₂²×C₃	—	2	1	no	—
676	C₂²×C₃	—	2	1	no	—
677	C₂²×C₃	—	2	1	no	—
678	C₂²×C₃	—	2	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	2	no	—
684	C₂²×C₃	—	4	1	no	—
685	C₂²×C₃	—	4	1	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	9	2	no	—
690	C₂²×C₃	—	9	2	no	—
691	C₂²×C₃	—	18	1	no	—
692	C₂²×C₃	—	18	1	no	—
693	C₂²×C₃	—	18	1	no	—
694	C₂²×C₃	—	18	1	no	—
695	C₂²×C₃	—	18	1	no	—
696	C₂²×C₃	—	18	1	no	—
697	C₂²×C₃	—	18	1	no	—
698	C₂²×C₃	—	18	1	no	—
699	C₂²×C₃	—	18	1	no	—
700	C₂²×C₃	—	18	1	no	—
701	C₂²×C₃	—	36	4	no	—
702	C₂²×C₃	—	36	4	no	—
703	C₂²×C₃	D₄×D₉	1	2	yes	—
704	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
705	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
706	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
707	C₂×D₃	—	3	2	no	—
708	C₂×D₃	—	3	2	no	—
709	C₂×D₃	—	6	1	no	—
710	C₂×D₃	—	6	1	no	—
711	C₂×D₃	—	6	1	no	—
712	C₂×D₃	—	6	1	no	—
713	C₂×D₃	—	6	1	no	—
714	C₂×D₃	—	6	1	no	—
715	C₂×D₃	—	6	1	no	—
716	C₂×D₃	—	6	1	no	—
717	C₂×D₃	—	6	1	no	—
718	C₂×D₃	—	6	1	no	—
719	C₂×D₃	—	12	4	no	—
720	C₂×D₃	—	12	4	no	—
721	C₃×C₄	—	2	1	no	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	—	2	1	no	—
727	C₃×C₄	—	2	1	no	—
728	C₃×C₄	—	2	1	no	—
729	C₃×C₄	—	2	1	no	—
730	C₃×C₄	—	2	1	no	—
731	C₃×C₄	—	4	1	no	—
732	C₃×C₄	—	4	1	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	9	2	no	—
737	C₃×C₄	—	18	1	no	—
738	C₃×C₄	—	18	1	no	—
739	C₃×C₄	—	18	1	no	—
740	Dic₃	—	3	2	no	—
741	Dic₃	—	6	1	no	—
742	Dic₃	—	6	1	no	—
743	Dic₃	—	6	1	no	—
744	C₃²	#5654	1	1	yes	characteristic
745	C₉	—	2	1	no	—
746	C₉	C₃×#546	1	1	yes	characteristic, complemented
747	C₂³	—	9	1	no	—
748	C₂³	—	9	1	no	—
749	C₂³	—	9	1	no	—
750	C₂³	—	9	1	no	—
751	C₂³	—	18	2	no	—
752	C₂³	—	18	2	no	—
753	C₂³	—	18	2	no	—
754	C₂³	—	18	2	no	—
755	C₂³	—	36	1	no	—
756	C₂³	—	36	1	no	—
757	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
758	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
759	Q₈	—	18	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	9	4	no	—
762	D₄	—	18	2	no	—
763	D₄	—	18	2	no	—
764	D₄	—	18	2	no	—
765	D₄	—	18	2	no	—
766	D₄	—	18	2	no	—
767	D₄	—	36	1	no	—
768	D₄	—	36	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	9	1	no	—
771	C₂×C₄	—	9	1	no	—
772	C₂×C₄	—	9	1	no	—
773	C₂×C₄	—	9	1	no	—
774	C₂×C₄	—	18	2	no	—
775	C₂×C₄	—	18	2	no	—
776	C₂×C₄	—	18	2	no	—
777	C₂×C₄	—	36	1	no	—
778	C₂×C₄	—	36	1	no	—
779	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
782	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
783	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
784	C₂×C₃	—	2	2	no	—
785	C₂×C₃	—	2	2	no	—
786	C₂×C₃	—	2	1	no	—
787	C₂×C₃	—	2	1	no	—
788	C₂×C₃	—	2	1	no	—
789	C₂×C₃	—	4	2	no	—
790	C₂×C₃	—	4	1	no	—
791	C₂×C₃	—	4	1	no	—
792	C₂×C₃	—	8	1	no	—
793	C₂×C₃	—	18	2	no	—
794	C₂×C₃	—	18	2	no	—
795	C₂×C₃	—	36	1	no	—
796	C₂×C₃	—	36	1	no	—
797	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
798	C₂×C₃	#41×D₉	1	1	yes	characteristic
799	C₂×C₃	#63715	1	1	yes	characteristic
800	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
801	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
802	C₂×C₃	C₃×#1009	1	1	yes	characteristic
803	D₃	—	6	2	no	—
804	D₃	—	6	2	no	—
805	D₃	—	12	1	no	—
806	D₃	—	12	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	9	2	no	—
813	C₂²	—	9	2	no	—
814	C₂²	—	18	1	no	—
815	C₂²	—	18	1	no	—
816	C₂²	—	18	1	no	—
817	C₂²	—	18	1	no	—
818	C₂²	—	18	1	no	—
819	C₂²	—	18	1	no	—
820	C₂²	—	18	1	no	—
821	C₂²	—	18	1	no	—
822	C₂²	—	18	1	no	—
823	C₂²	—	18	1	no	—
824	C₂²	—	36	4	no	—
825	C₂²	—	36	4	no	—
826	C₂²	C₃×D₄×D₉	1	2	yes	—
827	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	9	2	no	—
834	C₄	—	18	1	no	—
835	C₄	—	18	1	no	—
836	C₄	—	18	1	no	—
837	C₃	—	2	1	no	—
838	C₃	#10589756	1	1	yes	characteristic, direct product factor
839	C₃	C₃×#5654	1	1	yes	characteristic
840	C₂	—	2	2	no	—
841	C₂	—	4	1	no	—
842	C₂	—	18	2	no	—
843	C₂	—	18	2	no	—
844	C₂	—	36	1	no	—
845	C₂	—	36	1	no	—
846	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
847	C₂	C₃×#41×D₉	1	1	yes	characteristic
848	C₂	C₃×#63715	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×#123	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#123	D₉
hypocenter	C₉	C₃×#546
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₉	C₂	semidirect
2. C₂×C₃×#3697	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₃×#63501	C₂	semidirect
5. C₂×C₃×(C₂×D₉)⋊C₄	C₂	semidirect
6. C₃×#63458	C₂	semidirect
7. C₃×#63457	C₂	semidirect
8. C₃×#63456	C₂	semidirect
9. C₃×#63455	C₂	semidirect
10. C₃×#63447	C₂	semidirect
11. C₃×#63446	C₂	semidirect
12. C₃×#63444	C₂	semidirect
13. C₃×#63444	C₂	semidirect
14. C₃×#611⋊C₄	C₂	semidirect
15. C₃×C₂²⋊C₄×D₉	C₂	semidirect
17. #10589756	C₃	direct (N × H)
21. C₂²×C₃×C₄×C₉	C₂²	semidirect
24. C₂×C₃×#611	C₂²	semidirect
25. C₂×C₃×#611	C₂²	semidirect
26. C₂²×C₃×Dic₉	C₂²	semidirect
31. C₂×C₃×D₃₆	C₂²	semidirect
32. C₂×C₃×D₃₆	C₂²	semidirect
34. C₂×C₃×C₄×D₉	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×C₄⋊C₄	C₂²	semidirect
40. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
41. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
42. C₃×C₉×C₂²⋊C₄	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×(C₂×D₉)⋊C₄	C₂²	semidirect
52. C₃×Dic₉⋊C₄	C₂²	semidirect
53. C₃×Dic₉⋊C₄	C₂²	semidirect
54. C₃×C₄×Dic₉	C₂²	semidirect
70. C₂×D₄×D₉	C₂×C₃	semidirect
71. C₂×#3697	C₂×C₃	semidirect
73. C₉×#123	C₂×C₃	semidirect
74. #63501	C₂×C₃	semidirect
75. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
76. #63458	C₂×C₃	semidirect
77. #63457	C₂×C₃	semidirect
78. #63456	C₂×C₃	semidirect
79. #63455	C₂×C₃	semidirect
80. #63447	C₂×C₃	semidirect
81. #63446	C₂×C₃	semidirect
82. #63444	C₂×C₃	semidirect
83. #63444	C₂×C₃	semidirect
84. #611⋊C₄	C₂×C₃	semidirect
85. C₂²⋊C₄×D₉	C₂×C₃	semidirect
108. C₃×#611	D₄	semidirect
167. C₂²×C₄×C₉	C₂²×C₃	semidirect
170. C₂×#611	C₂²×C₃	semidirect
171. C₂×#611	C₂²×C₃	semidirect
172. C₂²×Dic₉	C₂²×C₃	semidirect
177. C₂×D₃₆	C₂²×C₃	semidirect
178. C₂×D₃₆	C₂²×C₃	semidirect
180. C₂×C₄×D₉	C₂²×C₃	semidirect
181. C₂×C₄×D₉	C₂²×C₃	semidirect
182. C₂×C₄×D₉	C₂²×C₃	semidirect
183. C₂×Dic₁₈	C₂²×C₃	semidirect
186. C₉×C₄⋊C₄	C₂²×C₃	semidirect
187. C₉×C₄⋊C₄	C₂²×C₃	semidirect
191. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
192. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
193. C₉×C₂²⋊C₄	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. (C₂×D₉)⋊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
243. C₃×#123	D₉	semidirect
335. #611	C₃×D₄	semidirect
384. C₂²×C₃×C₄	C₂×D₉	semidirect
406. C₃×C₄⋊C₄	C₂×D₉	semidirect
407. C₃×C₄⋊C₄	C₂×D₉	semidirect
422. C₃×C₂²⋊C₄	C₂×D₉	semidirect
423. C₃×C₂²⋊C₄	C₂×D₉	semidirect
424. C₃×C₂²⋊C₄	C₂×D₉	semidirect
498. C₂×D₉	C₃×#41	semidirect
517. #123	C₃×D₉	semidirect
528. C₃×C₉	#546	semidirect
654. C₂²×C₄	C₂×C₃×D₉	semidirect
657. C₄⋊C₄	C₂×C₃×D₉	semidirect
658. C₄⋊C₄	C₂×C₃×D₉	semidirect
668. C₂²⋊C₄	C₂×C₃×D₉	semidirect
669. C₂²⋊C₄	C₂×C₃×D₉	semidirect
670. C₂²⋊C₄	C₂×C₃×D₉	semidirect
746. C₉	C₃×#546	semidirect
838. C₃	#10589756	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×D₄×D₉	2
C₂×C₃×#3697	2
C₃×C₉×#123	2
C₃×#63501	2
C₂×C₃×(C₂×D₉)⋊C₄	2
C₃×#63458	2
C₃×#63457	2
C₃×#63456	2
C₃×#63455	2
C₃×#63447	2
C₃×#63446	2
C₃×#63444	2
C₃×#611⋊C₄	2
C₃×C₂²⋊C₄×D₉	2
C₃×#5654	3
#10589756	3

Subgroups — C3×#10589756 #13153013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589756 #13153013