Subgroups — #11909419

Order 1152.

1563 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#10589808	C₂	1	2	yes	maximal, complemented
3	D₉×#126	C₂	1	2	yes	maximal, complemented
4	#10589795	C₂	1	2	yes	maximal, complemented
5	#10589781	C₂	1	2	yes	maximal, complemented
6	#10589763	C₂	1	2	yes	maximal, complemented
7	#10589761	C₂	1	2	yes	maximal, complemented
8	#10589740	C₂	1	2	yes	maximal, complemented
9	#10589715	C₂	1	2	yes	maximal, complemented
10	#10589686	C₂	1	1	yes	maximal, characteristic, complemented
11	#10589681	C₂	1	1	yes	maximal, characteristic, complemented
12	#10589667	C₂	1	1	yes	maximal, characteristic, complemented
13	#10589653	C₂	1	1	yes	maximal, characteristic, complemented
14	#10589652	C₂	1	1	yes	maximal, characteristic, complemented
15	#10589652	C₂	1	1	yes	maximal, characteristic, complemented
16	#10589644	C₂	1	1	yes	maximal, characteristic, complemented
17	#10589643	C₂	1	1	yes	maximal, characteristic, complemented
18	#10589636	C₂	1	1	yes	maximal, characteristic, complemented
19	#10589625	C₂	1	1	yes	maximal, characteristic, complemented
20	#10589623	C₂	1	1	yes	maximal, characteristic, complemented
21	#10589620	C₂	1	1	yes	maximal, characteristic, complemented
22	#10589581	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#3697	C₂	1	1	yes	maximal, characteristic, complemented
24	#86170	—	3	1	no	maximal
25	C₂×#3697	C₂²	1	1	yes	characteristic
26	C₂×#3697	C₂²	1	1	yes	characteristic
27	C₂²×D₃₆	C₂²	1	1	yes	characteristic
28	C₉×#126	C₂²	1	1	yes	characteristic
29	C₉×#126	C₂²	1	1	yes	characteristic, complemented
30	C₉×#125	C₂²	1	1	yes	characteristic, complemented
31	C₉×#124	C₂²	1	1	yes	characteristic
32	C₉×#123	C₂²	1	1	yes	characteristic
33	C₉×#123	C₂²	1	1	yes	characteristic, complemented
34	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₉×#121	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
40	C₉×#117	C₂²	1	1	yes	characteristic
41	C₉×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
43	#63508	C₂²	1	2	yes	complemented
44	#63508	C₂²	1	2	yes	complemented
45	#63501	C₂²	1	2	yes	complemented
46	#63500	C₂²	1	2	yes	complemented
47	#63499	C₂²	1	2	yes	—
48	#63499	C₂²	1	2	yes	—
49	#63498	C₂²	1	2	yes	—
50	#63497	C₂²	1	2	yes	—
51	#63492	C₂²	1	1	yes	characteristic
52	#63492	C₂²	1	1	yes	characteristic
53	#63491	C₂²	1	2	yes	complemented
54	C₄×#611	C₂²	1	2	yes	complemented
55	C₄×#611	C₂²	1	2	yes	complemented
56	C₄×#611	C₂²	1	2	yes	complemented
57	#63488	C₂²	1	1	yes	characteristic
58	#63488	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic, complemented
60	#63486	C₂²	1	1	yes	characteristic
61	#63486	C₂²	1	1	yes	characteristic
62	#63486	C₂²	1	1	yes	characteristic, complemented
63	#63486	C₂²	1	1	yes	characteristic, complemented
64	#63460	C₂²	1	2	yes	complemented
65	#63460	C₂²	1	2	yes	complemented
66	#63460	C₂²	1	2	yes	complemented
67	#63460	C₂²	1	2	yes	complemented
68	#63458	C₂²	1	2	yes	complemented
69	#63458	C₂²	1	2	yes	complemented
70	#63458	C₂²	1	2	yes	complemented
71	#63456	C₂²	1	2	yes	—
72	#63456	C₂²	1	2	yes	—
73	#63455	C₂²	1	2	yes	—
74	#63455	C₂²	1	2	yes	—
75	#63454	C₂²	1	2	yes	complemented
76	#63454	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₉	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₉	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₉	C₂²	1	2	yes	complemented
80	#63451	C₂²	1	2	yes	complemented
81	#63451	C₂²	1	2	yes	complemented
82	#63451	C₂²	1	2	yes	complemented
83	#63449	C₂²	1	2	yes	complemented
84	#63447	C₂²	1	2	yes	complemented
85	#63446	C₂²	1	2	yes	—
86	#63446	C₂²	1	2	yes	—
87	#63445	C₂²	1	2	yes	complemented
88	#63445	C₂²	1	2	yes	complemented
89	#63445	C₂²	1	2	yes	complemented
90	#63445	C₂²	1	2	yes	complemented
91	#611⋊C₄	C₂²	1	2	yes	complemented
92	#611⋊C₄	C₂²	1	2	yes	complemented
93	#611⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₉	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₉	C₂²	1	2	yes	—
98	#63441	C₂²	1	2	yes	—
99	#63441	C₂²	1	2	yes	—
100	#63441	C₂²	1	2	yes	—
101	#63441	C₂²	1	2	yes	—
102	#63441	C₂²	1	2	yes	complemented
103	#63439	C₂²	1	2	yes	complemented
104	#63438	C₂²	1	2	yes	complemented
105	#63437	C₂²	1	1	yes	characteristic
106	#63437	C₂²	1	1	yes	characteristic
107	C₄×D₃₆	C₂²	1	1	yes	characteristic
108	C₄×D₃₆	C₂²	1	1	yes	characteristic
109	C₄×D₃₆	C₂²	1	1	yes	characteristic
110	C₄×D₃₆	C₂²	1	1	yes	characteristic
111	C₄×D₃₆	C₂²	1	1	yes	characteristic
112	C₄×D₃₆	C₂²	1	1	yes	characteristic
113	#63434	C₂²	1	2	yes	complemented
114	#63434	C₂²	1	2	yes	complemented
115	C₄²×D₉	C₂²	1	2	yes	complemented
116	#63432	C₂²	1	1	yes	characteristic, complemented
117	#63432	C₂²	1	1	yes	characteristic, complemented
118	#63431	C₂²	1	1	yes	characteristic, complemented
119	#63431	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₁₈	C₂²	1	1	yes	characteristic, complemented
124	C₃×#529	D₃	1	1	yes	characteristic
125	#5706	—	3	2	no	—
126	D₃×#126	—	3	2	no	—
127	#5693	—	3	2	no	—
128	#5679	—	3	2	no	—
129	#5661	—	3	2	no	—
130	#5659	—	3	2	no	—
131	#5638	—	3	2	no	—
132	#5613	—	3	2	no	—
133	#5584	—	3	1	no	—
134	#5579	—	3	1	no	—
135	#5565	—	3	1	no	—
136	#5551	—	3	1	no	—
137	#5550	—	3	1	no	—
138	#5550	—	3	1	no	—
139	#5542	—	3	1	no	—
140	#5541	—	3	1	no	—
141	#5534	—	3	1	no	—
142	#5523	—	3	1	no	—
143	#5521	—	3	1	no	—
144	#5518	—	3	1	no	—
145	#5479	—	3	1	no	—
146	C₄×#235	—	3	1	no	—
147	C₂³×D₉	C₂³	1	2	yes	—
148	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
149	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
150	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
151	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
157	C₂×#611	C₂³	1	2	yes	—
158	C₂×#611	C₂³	1	2	yes	—
159	C₂×#611	C₂³	1	2	yes	—
160	C₂×#611	C₂³	1	2	yes	—
161	C₂²×Dic₉	C₂³	1	2	yes	—
162	#3697	—	2	4	no	—
163	#3697	—	2	4	no	—
164	C₂×D₃₆	—	2	4	no	—
165	C₂×D₃₆	C₂³	1	1	yes	characteristic
166	C₂×D₃₆	C₂³	1	2	yes	—
167	C₂×D₃₆	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₉	C₂³	1	2	yes	—
169	C₂×C₄×D₉	C₂³	1	2	yes	—
170	C₂×C₄×D₉	C₂³	1	2	yes	—
171	C₂×C₄×D₉	C₂³	1	2	yes	—
172	C₂×C₄×D₉	C₂³	1	2	yes	—
173	C₂×C₄×D₉	C₂³	1	2	yes	—
174	C₂×C₄×D₉	C₂³	1	2	yes	—
175	C₂×C₄×D₉	C₂³	1	2	yes	—
176	C₂×Dic₁₈	C₂³	1	1	yes	characteristic
177	C₂×Dic₁₈	C₂³	1	1	yes	characteristic
178	C₂×Dic₁₈	C₂³	1	2	yes	—
179	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₉×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₄²×C₉	C₂³	1	1	yes	characteristic
200	C₄²×C₉	C₂³	1	1	yes	characteristic
201	C₄²×C₉	C₂³	1	1	yes	characteristic
202	C₄²×C₉	C₂³	1	1	yes	characteristic
203	C₄²×C₉	C₂³	1	1	yes	characteristic
204	C₄²×C₉	C₂³	1	1	yes	characteristic
205	#3676	C₂³	1	2	yes	—
206	#3676	C₂³	1	2	yes	—
207	#3676	C₂³	1	2	yes	—
208	#3676	C₂³	1	2	yes	—
209	#3676	C₂³	1	2	yes	—
210	#3676	C₂³	1	2	yes	—
211	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₉)⋊C₄	C₂³	1	2	yes	—
223	C₄⋊Dic₉	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₉	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₉	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₉	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₉	C₂³	1	2	yes	—
228	C₄⋊Dic₉	C₂³	1	2	yes	—
229	C₄⋊Dic₉	C₂³	1	2	yes	—
230	C₄⋊Dic₉	C₂³	1	2	yes	—
231	Dic₉⋊C₄	C₂³	1	2	yes	—
232	Dic₉⋊C₄	C₂³	1	2	yes	—
233	Dic₉⋊C₄	C₂³	1	2	yes	—
234	Dic₉⋊C₄	C₂³	1	2	yes	—
235	Dic₉⋊C₄	C₂³	1	2	yes	—
236	Dic₉⋊C₄	C₂³	1	2	yes	—
237	Dic₉⋊C₄	C₂³	1	2	yes	—
238	Dic₉⋊C₄	C₂³	1	2	yes	—
239	Dic₉⋊C₄	C₂³	1	2	yes	—
240	Dic₉⋊C₄	C₂³	1	2	yes	—
241	Dic₉⋊C₄	C₂³	1	2	yes	—
242	Dic₉⋊C₄	C₂³	1	2	yes	—
243	C₄×Dic₉	C₂³	1	2	yes	—
244	C₄×Dic₉	C₂³	1	2	yes	—
245	C₄×Dic₉	C₂³	1	2	yes	—
246	C₄×Dic₉	C₂³	1	2	yes	—
247	C₄×Dic₉	C₂³	1	2	yes	—
248	C₄×Dic₉	C₂³	1	2	yes	—
249	#3521	—	9	1	no	Sylow
250	C₂×#235	—	3	1	no	—
251	C₂×#235	—	3	1	no	—
252	C₂²×D₁₂	—	3	1	no	—
253	C₃×#126	C₂×D₃	1	1	yes	characteristic
254	C₃×#126	C₂×D₃	1	1	yes	characteristic
255	C₃×#125	C₂×D₃	1	1	yes	characteristic
256	C₃×#124	C₂×D₃	1	1	yes	characteristic
257	C₃×#123	C₂×D₃	1	1	yes	characteristic
258	C₃×#123	C₂×D₃	1	1	yes	characteristic
259	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
260	C₃×#121	C₂×D₃	1	1	yes	characteristic
261	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
262	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
263	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
264	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
265	C₃×#117	C₂×D₃	1	1	yes	characteristic
266	C₃×#117	C₂×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
268	#946	—	3	2	no	—
269	#946	—	3	2	no	—
270	#939	—	3	2	no	—
271	#938	—	3	2	no	—
272	#937	—	3	2	no	—
273	#937	—	3	2	no	—
274	#936	—	3	2	no	—
275	#935	—	3	2	no	—
276	#930	—	3	1	no	—
277	#930	—	3	1	no	—
278	#929	—	3	2	no	—
279	C₄×#67	—	3	2	no	—
280	C₄×#67	—	3	2	no	—
281	C₄×#67	—	3	2	no	—
282	#926	—	3	1	no	—
283	#926	—	3	1	no	—
284	C₂×C₄⋊Dic₃	—	3	1	no	—
285	#924	—	3	1	no	—
286	#924	—	3	1	no	—
287	#924	—	3	1	no	—
288	#924	—	3	1	no	—
289	#898	—	3	2	no	—
290	#898	—	3	2	no	—
291	#898	—	3	2	no	—
292	#898	—	3	2	no	—
293	#896	—	3	2	no	—
294	#896	—	3	2	no	—
295	#896	—	3	2	no	—
296	#894	—	3	2	no	—
297	#894	—	3	2	no	—
298	#893	—	3	2	no	—
299	#893	—	3	2	no	—
300	#892	—	3	2	no	—
301	#892	—	3	2	no	—
302	D₃×C₄⋊C₄	—	3	2	no	—
303	D₃×C₄⋊C₄	—	3	2	no	—
304	D₃×C₄⋊C₄	—	3	2	no	—
305	#889	—	3	2	no	—
306	#889	—	3	2	no	—
307	#889	—	3	2	no	—
308	#887	—	3	2	no	—
309	#885	—	3	2	no	—
310	#884	—	3	2	no	—
311	#884	—	3	2	no	—
312	#883	—	3	2	no	—
313	#883	—	3	2	no	—
314	#883	—	3	2	no	—
315	#883	—	3	2	no	—
316	#67⋊C₄	—	3	2	no	—
317	#67⋊C₄	—	3	2	no	—
318	#67⋊C₄	—	3	2	no	—
319	D₃×C₂²⋊C₄	—	3	2	no	—
320	D₃×C₂²⋊C₄	—	3	2	no	—
321	D₃×C₂²⋊C₄	—	3	2	no	—
322	D₃×C₂²⋊C₄	—	3	2	no	—
323	#879	—	3	2	no	—
324	#879	—	3	2	no	—
325	#879	—	3	2	no	—
326	#879	—	3	2	no	—
327	#879	—	3	2	no	—
328	#877	—	3	2	no	—
329	#876	—	3	2	no	—
330	#875	—	3	1	no	—
331	#875	—	3	1	no	—
332	C₄×D₁₂	—	3	1	no	—
333	C₄×D₁₂	—	3	1	no	—
334	C₄×D₁₂	—	3	1	no	—
335	C₄×D₁₂	—	3	1	no	—
336	C₄×D₁₂	—	3	1	no	—
337	C₄×D₁₂	—	3	1	no	—
338	#872	—	3	2	no	—
339	#872	—	3	2	no	—
340	C₄²×D₃	—	3	2	no	—
341	#870	—	3	1	no	—
342	#870	—	3	1	no	—
343	#869	—	3	1	no	—
344	#869	—	3	1	no	—
345	C₄×Dic₆	—	3	1	no	—
346	C₄×Dic₆	—	3	1	no	—
347	C₄×Dic₆	—	3	1	no	—
348	C₄×Dic₆	—	3	1	no	—
349	C₂³×C₉	C₂⁴	1	1	yes	characteristic
350	C₂³×C₉	C₂⁴	1	1	yes	characteristic
351	C₂³×C₉	C₂⁴	1	1	yes	characteristic
352	C₂²×D₉	—	2	4	no	—
353	C₂²×D₉	—	4	2	no	—
354	C₂²×D₉	—	4	2	no	—
355	C₂²×D₉	C₂⁴	1	2	yes	—
356	C₂²×D₉	C₂⁴	1	2	yes	—
357	Q₈×C₉	—	4	1	no	—
358	D₄×C₉	—	4	1	no	—
359	D₄×C₉	—	4	1	no	—
360	D₄×C₉	—	4	1	no	—
361	C₂×C₄×C₉	—	2	2	no	—
362	C₂×C₄×C₉	—	2	2	no	—
363	C₂×C₄×C₉	—	2	2	no	—
364	C₂×C₄×C₉	—	4	1	no	—
365	C₂×C₄×C₉	—	4	1	no	—
366	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
378	#611	—	2	4	no	—
379	#611	—	2	4	no	—
380	#611	—	4	2	no	—
381	#611	—	4	2	no	—
382	C₂×Dic₉	—	4	2	no	—
383	C₂×Dic₉	C₂⁴	1	2	yes	—
384	C₂×Dic₉	C₂⁴	1	2	yes	—
385	C₂×Dic₉	C₂⁴	1	2	yes	—
386	C₂×Dic₉	C₂⁴	1	2	yes	—
387	C₂×Dic₉	C₂⁴	1	2	yes	—
388	C₂×Dic₉	C₂⁴	1	2	yes	—
389	D₃₆	—	2	4	no	—
390	D₃₆	—	2	2	no	—
391	D₃₆	#41	1	4	yes	—
392	C₄×D₉	—	2	4	no	—
393	C₄×D₉	—	2	4	no	—
394	C₄×D₉	—	4	2	no	—
395	C₄×D₉	—	4	2	no	—
396	C₄×D₉	—	4	2	no	—
397	C₄×D₉	—	4	2	no	—
398	C₄×D₉	—	4	2	no	—
399	C₄×D₉	—	4	2	no	—
400	Dic₁₈	—	2	2	no	—
401	Dic₁₈	—	2	2	no	—
402	Dic₁₈	—	4	2	no	—
403	#556	—	9	1	no	—
404	#556	—	9	1	no	—
405	#554	—	9	1	no	—
406	#553	—	9	2	no	—
407	#553	—	9	1	no	—
408	#552	—	9	2	no	—
409	#552	—	9	1	no	—
410	#551	—	9	2	no	—
411	#551	—	9	2	no	—
412	#547	—	9	1	no	—
413	#546	—	9	1	no	—
414	#546	—	9	1	no	—
415	#542	—	9	1	no	—
416	#541	—	9	1	no	—
417	#539	—	9	2	no	—
418	#538	—	9	2	no	—
419	#529	—	9	2	no	—
420	#529	—	9	1	no	—
421	#529	D₉	1	1	yes	characteristic, complemented
422	C₂×#126	—	9	2	no	—
423	#520	—	9	1	no	—
424	#518	—	9	1	no	—
425	C₄×#41	—	9	1	no	—
426	C₂³×D₃	—	3	2	no	—
427	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
428	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
429	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
436	C₂×#67	—	3	2	no	—
437	C₂×#67	—	3	2	no	—
438	C₂×#67	—	3	2	no	—
439	C₂×#67	—	3	2	no	—
440	C₂²×Dic₃	—	3	2	no	—
441	#235	—	6	4	no	—
442	#235	—	6	4	no	—
443	C₂×D₁₂	—	3	1	no	—
444	C₂×D₁₂	—	3	1	no	—
445	C₂×D₁₂	—	3	2	no	—
446	C₂×D₁₂	—	6	4	no	—
447	C₂×C₄×D₃	—	3	2	no	—
448	C₂×C₄×D₃	—	3	2	no	—
449	C₂×C₄×D₃	—	3	2	no	—
450	C₂×C₄×D₃	—	3	2	no	—
451	C₂×C₄×D₃	—	3	2	no	—
452	C₂×C₄×D₃	—	3	2	no	—
453	C₂×C₄×D₃	—	3	2	no	—
454	C₂×C₄×D₃	—	3	2	no	—
455	C₂×Dic₆	—	3	1	no	—
456	C₂×Dic₆	—	3	1	no	—
457	C₂×Dic₆	—	3	2	no	—
458	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
459	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
461	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
463	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
464	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
465	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
466	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
467	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
468	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₃×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
479	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
480	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
481	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
482	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
483	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
484	#217	—	3	2	no	—
485	#217	—	3	2	no	—
486	#217	—	3	2	no	—
487	#217	—	3	2	no	—
488	#217	—	3	2	no	—
489	#217	—	3	2	no	—
490	(C₂×D₃)⋊C₄	—	3	2	no	—
491	(C₂×D₃)⋊C₄	—	3	2	no	—
492	(C₂×D₃)⋊C₄	—	3	2	no	—
493	(C₂×D₃)⋊C₄	—	3	2	no	—
494	(C₂×D₃)⋊C₄	—	3	2	no	—
495	(C₂×D₃)⋊C₄	—	3	2	no	—
496	(C₂×D₃)⋊C₄	—	3	2	no	—
497	(C₂×D₃)⋊C₄	—	3	2	no	—
498	(C₂×D₃)⋊C₄	—	3	2	no	—
499	(C₂×D₃)⋊C₄	—	3	2	no	—
500	(C₂×D₃)⋊C₄	—	3	2	no	—
501	(C₂×D₃)⋊C₄	—	3	2	no	—
502	C₄⋊Dic₃	—	3	1	no	—
503	C₄⋊Dic₃	—	3	1	no	—
504	C₄⋊Dic₃	—	3	1	no	—
505	C₄⋊Dic₃	—	3	1	no	—
506	C₄⋊Dic₃	—	3	2	no	—
507	C₄⋊Dic₃	—	3	2	no	—
508	C₄⋊Dic₃	—	3	2	no	—
509	C₄⋊Dic₃	—	3	2	no	—
510	Dic₃⋊C₄	—	3	2	no	—
511	Dic₃⋊C₄	—	3	2	no	—
512	Dic₃⋊C₄	—	3	2	no	—
513	Dic₃⋊C₄	—	3	2	no	—
514	Dic₃⋊C₄	—	3	2	no	—
515	Dic₃⋊C₄	—	3	2	no	—
516	Dic₃⋊C₄	—	3	2	no	—
517	Dic₃⋊C₄	—	3	2	no	—
518	Dic₃⋊C₄	—	3	2	no	—
519	Dic₃⋊C₄	—	3	2	no	—
520	Dic₃⋊C₄	—	3	2	no	—
521	Dic₃⋊C₄	—	3	2	no	—
522	C₄×Dic₃	—	3	2	no	—
523	C₄×Dic₃	—	3	2	no	—
524	C₄×Dic₃	—	3	2	no	—
525	C₄×Dic₃	—	3	2	no	—
526	C₄×Dic₃	—	3	2	no	—
527	C₄×Dic₃	—	3	2	no	—
528	C₂²×C₉	—	2	1	no	—
529	C₂²×C₉	—	2	1	no	—
530	C₂²×C₉	—	2	1	no	—
531	C₂²×C₉	—	2	1	no	—
532	C₂²×C₉	—	2	1	no	—
533	C₂²×C₉	—	2	1	no	—
534	C₂²×C₉	—	2	1	no	—
535	C₂²×C₉	—	2	1	no	—
536	C₂²×C₉	—	2	1	no	—
537	C₂²×C₉	C₂⁵	1	1	yes	characteristic
538	C₂×D₉	—	2	2	no	—
539	C₂×D₉	—	2	2	no	—
540	C₂×D₉	—	2	2	no	—
541	C₂×D₉	—	2	2	no	—
542	C₂×D₉	—	2	2	no	—
543	C₂×D₉	—	8	4	no	—
544	C₂×D₉	C₂×#41	1	4	yes	—
545	C₄×C₉	—	2	1	no	—
546	C₄×C₉	—	2	1	no	—
547	C₄×C₉	—	2	1	no	—
548	C₄×C₉	—	2	1	no	—
549	C₄×C₉	—	2	1	no	—
550	C₄×C₉	—	2	1	no	—
551	C₄×C₉	—	2	1	no	—
552	C₄×C₉	—	2	1	no	—
553	C₄×C₉	—	2	1	no	—
554	C₄×C₉	—	2	1	no	—
555	C₄×C₉	—	2	1	no	—
556	C₄×C₉	C₂×#41	1	2	yes	—
557	Dic₉	—	2	2	no	—
558	Dic₉	—	2	2	no	—
559	Dic₉	—	2	2	no	—
560	Dic₉	—	2	2	no	—
561	Dic₉	—	2	2	no	—
562	Dic₉	—	2	2	no	—
563	C₂×#41	—	9	1	no	—
564	C₂×#41	—	9	1	no	—
565	C₂²×D₄	—	9	1	no	—
566	C₄⋊Q₈	—	9	1	no	—
567	C₄⋊Q₈	—	9	1	no	—
568	#126	—	9	2	no	—
569	#126	—	9	2	no	—
570	#126	—	9	2	no	—
571	#126	—	9	2	no	—
572	#126	—	9	2	no	—
573	#126	—	9	2	no	—
574	#126	—	9	2	no	—
575	#126	—	9	2	no	—
576	#126	—	9	2	no	—
577	#126	—	9	2	no	—
578	#126	C₂×D₉	1	1	yes	characteristic
579	#126	C₂×D₉	1	1	yes	characteristic, complemented
580	#125	—	9	2	no	—
581	#125	—	9	2	no	—
582	#125	—	9	2	no	—
583	#125	—	9	1	no	—
584	#125	—	9	1	no	—
585	#125	C₂×D₉	1	1	yes	characteristic, complemented
586	#124	—	9	2	no	—
587	#124	—	9	2	no	—
588	#124	—	9	1	no	—
589	#124	—	9	1	no	—
590	#124	C₂×D₉	1	1	yes	characteristic
591	#123	—	9	2	no	—
592	#123	—	9	2	no	—
593	#123	—	9	2	no	—
594	#123	—	9	2	no	—
595	#123	—	9	2	no	—
596	#123	—	9	2	no	—
597	#123	—	9	2	no	—
598	#123	—	9	2	no	—
599	#123	C₂×D₉	1	1	yes	characteristic
600	#123	C₂×D₉	1	1	yes	characteristic, complemented
601	C₂²⋊Q₈	—	9	2	no	—
602	C₂²⋊Q₈	—	9	2	no	—
603	C₂²⋊Q₈	—	9	1	no	—
604	C₂²⋊Q₈	—	9	1	no	—
605	C₂²⋊Q₈	—	9	1	no	—
606	C₂²⋊Q₈	—	9	1	no	—
607	C₂²⋊Q₈	—	9	2	no	—
608	C₂²⋊Q₈	—	9	2	no	—
609	C₂²⋊Q₈	—	9	2	no	—
610	C₂²⋊Q₈	C₂×D₉	1	1	yes	characteristic, complemented
611	#121	—	9	2	no	—
612	#121	—	9	2	no	—
613	#121	—	9	1	no	—
614	#121	—	9	1	no	—
615	#121	—	9	2	no	—
616	#121	—	9	2	no	—
617	#121	C₂×D₉	1	1	yes	characteristic
618	#120	—	9	2	no	—
619	#120	—	9	2	no	—
620	C₄×Q₈	—	9	2	no	—
621	C₄×Q₈	—	9	1	no	—
622	C₄×Q₈	—	9	1	no	—
623	C₄×Q₈	—	9	1	no	—
624	C₄×Q₈	—	9	1	no	—
625	C₄×Q₈	C₂×D₉	1	1	yes	characteristic, complemented
626	C₄×D₄	—	9	2	no	—
627	C₄×D₄	—	9	2	no	—
628	C₄×D₄	—	9	2	no	—
629	C₄×D₄	—	9	2	no	—
630	C₄×D₄	—	9	2	no	—
631	C₄×D₄	—	9	2	no	—
632	C₄×D₄	—	9	2	no	—
633	C₄×D₄	—	9	2	no	—
634	C₄×D₄	—	9	1	no	—
635	C₄×D₄	—	9	1	no	—
636	C₄×D₄	—	9	1	no	—
637	C₄×D₄	—	9	1	no	—
638	C₄×D₄	—	9	1	no	—
639	C₄×D₄	—	9	1	no	—
640	C₄×D₄	C₂×D₉	1	1	yes	characteristic
641	C₄×D₄	C₂×D₉	1	1	yes	characteristic
642	C₄×D₄	C₂×D₉	1	1	yes	characteristic, complemented
643	#117	—	9	1	no	—
644	#117	—	9	1	no	—
645	#117	—	9	2	no	—
646	#117	—	9	2	no	—
647	#117	—	9	2	no	—
648	#117	—	9	2	no	—
649	#117	—	9	2	no	—
650	#117	C₂×D₉	1	1	yes	characteristic
651	#117	C₂×D₉	1	1	yes	characteristic, complemented
652	C₂×C₄⋊C₄	—	9	1	no	—
653	C₂×C₄⋊C₄	—	9	2	no	—
654	C₂×C₄⋊C₄	—	9	2	no	—
655	C₂×C₄⋊C₄	—	9	2	no	—
656	C₂×C₂²⋊C₄	—	9	2	no	—
657	C₂×C₂²⋊C₄	—	9	2	no	—
658	C₂×C₂²⋊C₄	—	9	2	no	—
659	C₂×C₂²⋊C₄	—	9	2	no	—
660	C₂×C₄²	—	9	2	no	—
661	C₂×C₄²	C₂×D₉	1	1	yes	characteristic, complemented
662	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
663	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
664	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
665	C₂²×D₃	—	3	2	no	—
666	C₂²×D₃	—	3	2	no	—
667	C₂²×D₃	—	6	4	no	—
668	C₂²×D₃	—	12	2	no	—
669	C₂²×D₃	—	12	2	no	—
670	C₃×Q₈	—	4	1	no	—
671	C₃×D₄	—	4	1	no	—
672	C₃×D₄	—	4	1	no	—
673	C₃×D₄	—	4	1	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	4	1	no	—
678	C₂×C₃×C₄	—	4	1	no	—
679	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
680	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
681	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
682	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
684	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
685	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
686	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
687	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
688	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
689	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
691	#67	—	6	4	no	—
692	#67	—	6	4	no	—
693	#67	—	12	2	no	—
694	#67	—	12	2	no	—
695	C₂×Dic₃	—	3	2	no	—
696	C₂×Dic₃	—	3	2	no	—
697	C₂×Dic₃	—	3	2	no	—
698	C₂×Dic₃	—	3	2	no	—
699	C₂×Dic₃	—	3	2	no	—
700	C₂×Dic₃	—	3	2	no	—
701	C₂×Dic₃	—	12	2	no	—
702	D₁₂	—	3	4	no	—
703	D₁₂	—	6	4	no	—
704	D₁₂	—	6	2	no	—
705	C₄×D₃	—	6	4	no	—
706	C₄×D₃	—	6	4	no	—
707	C₄×D₃	—	12	2	no	—
708	C₄×D₃	—	12	2	no	—
709	C₄×D₃	—	12	2	no	—
710	C₄×D₃	—	12	2	no	—
711	C₄×D₃	—	12	2	no	—
712	C₄×D₃	—	12	2	no	—
713	Dic₆	—	6	2	no	—
714	Dic₆	—	6	2	no	—
715	Dic₆	—	12	2	no	—
716	C₂×C₉	—	4	1	no	—
717	C₂×C₉	—	4	1	no	—
718	C₂×C₉	—	4	1	no	—
719	C₂×C₉	C₂²×#41	1	1	yes	characteristic
720	C₂×C₉	#585	1	1	yes	characteristic
721	C₂×C₉	#585	1	1	yes	characteristic
722	D₉	—	2	4	no	—
723	D₉	—	4	2	no	—
724	C₂⁴	—	9	2	no	—
725	#41	—	18	4	no	—
726	#41	—	18	4	no	—
727	C₂×Q₈	—	9	1	no	—
728	C₂×Q₈	—	9	1	no	—
729	C₂×Q₈	—	9	2	no	—
730	C₂×Q₈	C₂²×D₉	1	1	yes	characteristic
731	C₂×D₄	—	9	2	no	—
732	C₂×D₄	—	9	2	no	—
733	C₂×D₄	—	9	2	no	—
734	C₂×D₄	—	9	2	no	—
735	C₂×D₄	—	9	1	no	—
736	C₂×D₄	—	9	2	no	—
737	C₂×D₄	—	9	1	no	—
738	C₂×D₄	—	18	4	no	—
739	C₂×D₄	C₂²×D₉	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₉	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₉	1	1	yes	characteristic
742	C₂²×C₄	—	9	2	no	—
743	C₂²×C₄	—	9	2	no	—
744	C₂²×C₄	—	9	2	no	—
745	C₂²×C₄	—	9	2	no	—
746	C₂²×C₄	—	9	2	no	—
747	C₂²×C₄	—	9	2	no	—
748	C₂²×C₄	—	9	2	no	—
749	C₂²×C₄	—	9	2	no	—
750	C₂²×C₄	—	9	2	no	—
751	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
752	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
756	C₄⋊C₄	—	9	2	no	—
757	C₄⋊C₄	—	9	1	no	—
758	C₄⋊C₄	—	9	2	no	—
759	C₄⋊C₄	—	9	2	no	—
760	C₄⋊C₄	—	9	1	no	—
761	C₄⋊C₄	—	9	2	no	—
762	C₄⋊C₄	—	9	2	no	—
763	C₄⋊C₄	—	9	2	no	—
764	C₄⋊C₄	—	9	2	no	—
765	C₄⋊C₄	—	9	2	no	—
766	C₄⋊C₄	—	9	2	no	—
767	C₄⋊C₄	—	9	1	no	—
768	C₄⋊C₄	—	9	1	no	—
769	C₄⋊C₄	—	9	2	no	—
770	C₄⋊C₄	—	9	2	no	—
771	C₄⋊C₄	—	9	2	no	—
772	C₄⋊C₄	—	9	2	no	—
773	C₄⋊C₄	—	9	2	no	—
774	C₄⋊C₄	—	9	2	no	—
775	C₄⋊C₄	—	9	2	no	—
776	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₉	1	1	yes	characteristic
786	C₂²⋊C₄	—	9	2	no	—
787	C₂²⋊C₄	—	9	2	no	—
788	C₂²⋊C₄	—	9	2	no	—
789	C₂²⋊C₄	—	9	2	no	—
790	C₂²⋊C₄	—	9	2	no	—
791	C₂²⋊C₄	—	9	2	no	—
792	C₂²⋊C₄	—	9	2	no	—
793	C₂²⋊C₄	—	9	2	no	—
794	C₂²⋊C₄	—	9	2	no	—
795	C₂²⋊C₄	—	9	2	no	—
796	C₂²⋊C₄	—	9	2	no	—
797	C₂²⋊C₄	—	9	2	no	—
798	C₂²⋊C₄	—	9	2	no	—
799	C₂²⋊C₄	—	9	2	no	—
800	C₂²⋊C₄	—	9	2	no	—
801	C₂²⋊C₄	—	9	2	no	—
802	C₂²⋊C₄	—	9	2	no	—
803	C₂²⋊C₄	—	9	2	no	—
804	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₉	1	1	yes	characteristic
814	C₄²	—	9	2	no	—
815	C₄²	—	9	2	no	—
816	C₄²	—	9	2	no	—
817	C₄²	—	9	2	no	—
818	C₄²	—	9	2	no	—
819	C₄²	—	9	2	no	—
820	C₄²	C₂²×D₉	1	1	yes	characteristic
821	C₄²	C₂²×D₉	1	1	yes	characteristic
822	C₄²	C₂²×D₉	1	1	yes	characteristic
823	C₄²	C₂²×D₉	1	1	yes	characteristic
824	C₄²	C₂²×D₉	1	1	yes	characteristic
825	C₄²	C₂²×D₉	1	1	yes	characteristic
826	C₂²×C₃	—	2	1	no	—
827	C₂²×C₃	—	2	1	no	—
828	C₂²×C₃	—	2	1	no	—
829	C₂²×C₃	—	2	1	no	—
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	2	1	no	—
832	C₂²×C₃	—	2	1	no	—
833	C₂²×C₃	—	2	1	no	—
834	C₂²×C₃	—	2	1	no	—
835	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
836	C₂×D₃	—	3	4	no	—
837	C₂×D₃	—	6	2	no	—
838	C₂×D₃	—	6	2	no	—
839	C₂×D₃	—	6	2	no	—
840	C₂×D₃	—	6	2	no	—
841	C₂×D₃	—	6	2	no	—
842	C₂×D₃	—	24	4	no	—
843	C₃×C₄	—	2	1	no	—
844	C₃×C₄	—	2	1	no	—
845	C₃×C₄	—	2	1	no	—
846	C₃×C₄	—	2	1	no	—
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	1	no	—
849	C₃×C₄	—	2	1	no	—
850	C₃×C₄	—	2	1	no	—
851	C₃×C₄	—	2	1	no	—
852	C₃×C₄	—	2	1	no	—
853	C₃×C₄	—	2	1	no	—
854	C₃×C₄	D₃×#41	1	2	yes	—
855	Dic₃	—	6	2	no	—
856	Dic₃	—	6	2	no	—
857	Dic₃	—	6	2	no	—
858	Dic₃	—	6	2	no	—
859	Dic₃	—	6	2	no	—
860	Dic₃	—	6	2	no	—
861	C₉	#3521	1	1	yes	characteristic, complemented, Sylow
862	C₂³	—	9	2	no	—
863	C₂³	—	9	2	no	—
864	C₂³	—	18	4	no	—
865	C₂³	—	36	2	no	—
866	C₂³	—	36	2	no	—
867	C₂³	C₂³×D₉	1	1	yes	characteristic
868	C₂³	C₂³×D₉	1	1	yes	characteristic
869	C₂³	C₂³×D₉	1	1	yes	characteristic
870	Q₈	—	4	1	no	—
871	Q₈	—	18	2	no	—
872	Q₈	—	18	2	no	—
873	Q₈	—	36	2	no	—
874	D₄	—	4	1	no	—
875	D₄	—	4	1	no	—
876	D₄	—	4	1	no	—
877	D₄	—	9	4	no	—
878	D₄	—	18	4	no	—
879	D₄	—	18	4	no	—
880	D₄	—	18	4	no	—
881	D₄	—	18	2	no	—
882	D₄	—	36	2	no	—
883	D₄	—	36	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	9	2	no	—
890	C₂×C₄	—	9	2	no	—
891	C₂×C₄	—	9	2	no	—
892	C₂×C₄	—	9	2	no	—
893	C₂×C₄	—	9	2	no	—
894	C₂×C₄	—	9	2	no	—
895	C₂×C₄	—	18	4	no	—
896	C₂×C₄	—	18	4	no	—
897	C₂×C₄	—	36	2	no	—
898	C₂×C₄	—	36	2	no	—
899	C₂×C₄	—	36	2	no	—
900	C₂×C₄	—	36	2	no	—
901	C₂×C₄	—	36	2	no	—
902	C₂×C₄	—	36	2	no	—
903	C₂×C₄	—	36	2	no	—
904	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
909	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
916	C₂×C₃	—	4	1	no	—
917	C₂×C₃	—	4	1	no	—
918	C₂×C₃	—	4	1	no	—
919	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
920	C₂×C₃	#5964	1	1	yes	characteristic
921	C₂×C₃	#5964	1	1	yes	characteristic
922	D₃	—	6	4	no	—
923	D₃	—	12	2	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	9	4	no	—
934	C₂²	—	18	2	no	—
935	C₂²	—	18	2	no	—
936	C₂²	—	18	2	no	—
937	C₂²	—	18	2	no	—
938	C₂²	—	18	2	no	—
939	C₂²	—	72	4	no	—
940	C₂²	C₂⁴×D₉	1	1	yes	characteristic
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	18	2	no	—
953	C₄	—	18	2	no	—
954	C₄	—	18	2	no	—
955	C₄	—	18	2	no	—
956	C₄	—	18	2	no	—
957	C₄	—	18	2	no	—
958	C₄	#41×D₉	1	2	yes	—
959	C₃	#86170	1	1	yes	characteristic
960	C₂	—	4	1	no	—
961	C₂	—	4	1	no	—
962	C₂	—	4	1	no	—
963	C₂	—	18	4	no	—
964	C₂	—	36	2	no	—
965	C₂	C₂×#41×D₉	1	1	yes	characteristic
966	C₂	#10593139	1	1	yes	characteristic
967	C₂	#10593139	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂⁴×D₉
commutator, cosocle	C₂²×C₉	C₂⁵
Frattini, socle	C₂²×C₃	C₂⁴×D₃
Fitting	C₉×#529	C₂
hypercenter	#529	D₉
hypocenter	C₉	#3521
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₉×#529	C₂	semidirect
2. #10589808	C₂	semidirect
3. D₉×#126	C₂	semidirect
4. #10589795	C₂	semidirect
5. #10589781	C₂	semidirect
6. #10589763	C₂	semidirect
7. #10589761	C₂	semidirect
8. #10589740	C₂	semidirect
9. #10589715	C₂	semidirect
10. #10589686	C₂	semidirect
11. #10589681	C₂	semidirect
12. #10589667	C₂	semidirect
13. #10589653	C₂	semidirect
14. #10589652	C₂	semidirect
15. #10589652	C₂	semidirect
16. #10589644	C₂	semidirect
17. #10589643	C₂	semidirect
18. #10589636	C₂	semidirect
19. #10589625	C₂	semidirect
20. #10589623	C₂	semidirect
21. #10589620	C₂	semidirect
22. #10589581	C₂	semidirect
23. C₄×#3697	C₂	semidirect
29. C₉×#126	C₂²	semidirect
30. C₉×#125	C₂²	semidirect
33. C₉×#123	C₂²	semidirect
34. C₉×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₉	C₂²	semidirect
39. C₄×D₄×C₉	C₂²	semidirect
41. C₉×#117	C₂²	semidirect
42. C₂×C₄²×C₉	C₂²	semidirect
43. #63508	C₂²	semidirect
44. #63508	C₂²	semidirect
45. #63501	C₂²	semidirect
46. #63500	C₂²	semidirect
53. #63491	C₂²	semidirect
54. C₄×#611	C₂²	semidirect
55. C₄×#611	C₂²	semidirect
56. C₄×#611	C₂²	semidirect
58. #63488	C₂²	semidirect
59. C₂×C₄⋊Dic₉	C₂²	semidirect
62. #63486	C₂²	semidirect
63. #63486	C₂²	semidirect
64. #63460	C₂²	semidirect
65. #63460	C₂²	semidirect
66. #63460	C₂²	semidirect
67. #63460	C₂²	semidirect
68. #63458	C₂²	semidirect
69. #63458	C₂²	semidirect
70. #63458	C₂²	semidirect
75. #63454	C₂²	semidirect
76. #63454	C₂²	semidirect
77. C₄⋊C₄×D₉	C₂²	semidirect
78. C₄⋊C₄×D₉	C₂²	semidirect
79. C₄⋊C₄×D₉	C₂²	semidirect
80. #63451	C₂²	semidirect
81. #63451	C₂²	semidirect
82. #63451	C₂²	semidirect
83. #63449	C₂²	semidirect
84. #63447	C₂²	semidirect
87. #63445	C₂²	semidirect
88. #63445	C₂²	semidirect
89. #63445	C₂²	semidirect
90. #63445	C₂²	semidirect
91. #611⋊C₄	C₂²	semidirect
92. #611⋊C₄	C₂²	semidirect
93. #611⋊C₄	C₂²	semidirect
102. #63441	C₂²	semidirect
103. #63439	C₂²	semidirect
104. #63438	C₂²	semidirect
113. #63434	C₂²	semidirect
114. #63434	C₂²	semidirect
115. C₄²×D₉	C₂²	semidirect
116. #63432	C₂²	semidirect
117. #63432	C₂²	semidirect
118. #63431	C₂²	semidirect
119. #63431	C₂²	semidirect
120. C₄×Dic₁₈	C₂²	semidirect
121. C₄×Dic₁₈	C₂²	semidirect
122. C₄×Dic₁₈	C₂²	semidirect
123. C₄×Dic₁₈	C₂²	semidirect
421. #529	D₉	semidirect
579. #126	C₂×D₉	semidirect
585. #125	C₂×D₉	semidirect
600. #123	C₂×D₉	semidirect
610. C₂²⋊Q₈	C₂×D₉	semidirect
625. C₄×Q₈	C₂×D₉	semidirect
642. C₄×D₄	C₂×D₉	semidirect
651. #117	C₂×D₉	semidirect
661. C₂×C₄²	C₂×D₉	semidirect
861. C₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₉×#529	2
#10589808	2
D₉×#126	2
#10589795	2
#10589781	2
#10589763	2
#10589761	2
#10589740	2
#10589715	2
#10589686	2
#10589681	2
#10589667	2
#10589653	2
#10589652	2
#10589644	2
#10589643	2
#10589636	2
#10589625	2
#10589623	2
#10589620	2
#10589581	2
C₄×#3697	2
#86170	3